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SW07_Theorie_en
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{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# SW07 - Flipped Classroom \n", "\n", "*This JupyterNotebook is intended to practice the theory alongside the slides and is used as a \"practical check of the theory input\". There are no sample solutions and the file will not be corrected and does not have to be submitted.*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*** \n", "## Modules math " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.479425538604203" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import math\n", "\n", "math.sin(0.5)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.2246467991473532e-16" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "math.sin(math.pi)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "ename": "NameError", "evalue": "name 'sin' is not defined", "output_type": "error", "traceback": [ "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)", "Cell \u001b[1;32mIn[3], line 1\u001b[0m\n\u001b[1;32m----> 1\u001b[0m \u001b[43msin\u001b[49m(\u001b[38;5;241m0.5\u001b[39m)\n", "\u001b[1;31mNameError\u001b[0m: name 'sin' is not defined" ] } ], "source": [ "sin(0.5)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.0" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from math import sin, pi\n", "\n", "sin(pi/2)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3.141592653589793\n", "1.4142135623730951\n", "3.141592653589793\n", "0.479425538604203\n" ] } ], "source": [ "import math as m\n", "import numpy as np\n", "\n", "\n", "print(m.pi)\n", "print(m.sqrt(2))\n", "print(np.pi)\n", "print(np.sin(0.5))" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.449489742783178" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from math import sqrt as wurzel\n", "\n", "wurzel(6)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*** \n", "## dir() and help() " ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "['__doc__',\n", " '__loader__',\n", " '__name__',\n", " '__package__',\n", " '__spec__',\n", " 'acos',\n", " 'acosh',\n", " 'asin',\n", " 'asinh',\n", " 'atan',\n", " 'atan2',\n", " 'atanh',\n", " 'cbrt',\n", " 'ceil',\n", " 'comb',\n", " 'copysign',\n", " 'cos',\n", " 'cosh',\n", " 'degrees',\n", " 'dist',\n", " 'e',\n", " 'erf',\n", " 'erfc',\n", " 'exp',\n", " 'exp2',\n", " 'expm1',\n", " 'fabs',\n", " 'factorial',\n", " 'floor',\n", " 'fmod',\n", " 'frexp',\n", " 'fsum',\n", " 'gamma',\n", " 'gcd',\n", " 'hypot',\n", " 'inf',\n", " 'isclose',\n", " 'isfinite',\n", " 'isinf',\n", " 'isnan',\n", " 'isqrt',\n", " 'lcm',\n", " 'ldexp',\n", " 'lgamma',\n", " 'log',\n", " 'log10',\n", " 'log1p',\n", " 'log2',\n", " 'modf',\n", " 'nan',\n", " 'nextafter',\n", " 'perm',\n", " 'pi',\n", " 'pow',\n", " 'prod',\n", " 'radians',\n", " 'remainder',\n", " 'sin',\n", " 'sinh',\n", " 'sqrt',\n", " 'tan',\n", " 'tanh',\n", " 'tau',\n", " 'trunc',\n", " 'ulp']" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dir(math)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "['In',\n", " 'Out',\n", " '_',\n", " '_1',\n", " '_10',\n", " '_2',\n", " '_4',\n", " '_5',\n", " '_7',\n", " '_9',\n", " '__',\n", " '___',\n", " '__builtin__',\n", " '__builtins__',\n", " '__doc__',\n", " '__loader__',\n", " '__name__',\n", " '__package__',\n", " '__spec__',\n", " '__vsc_ipynb_file__',\n", " '_dh',\n", " '_i',\n", " '_i1',\n", " '_i10',\n", " '_i11',\n", " '_i2',\n", " '_i3',\n", " '_i4',\n", " '_i5',\n", " '_i6',\n", " '_i7',\n", " '_i8',\n", " '_i9',\n", " '_ih',\n", " '_ii',\n", " '_iii',\n", " '_oh',\n", " 'exit',\n", " 'get_ipython',\n", " 'm',\n", " 'math',\n", " 'np',\n", " 'open',\n", " 'pi',\n", " 'quit',\n", " 'sin',\n", " 'wurzel']" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dir()" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Help on package numpy:\n", "\n", "NAME\n", " numpy\n", "\n", "DESCRIPTION\n", " NumPy\n", " =====\n", " \n", " Provides\n", " 1. An array object of arbitrary homogeneous items\n", " 2. Fast mathematical operations over arrays\n", " 3. Linear Algebra, Fourier Transforms, Random Number Generation\n", " \n", " How to use the documentation\n", " ----------------------------\n", " Documentation is available in two forms: docstrings provided\n", " with the code, and a loose standing reference guide, available from\n", " `the NumPy homepage <https://numpy.org>`_.\n", " \n", " We recommend exploring the docstrings using\n", " `IPython <https://ipython.org>`_, an advanced Python shell with\n", " TAB-completion and introspection capabilities. See below for further\n", " instructions.\n", " \n", " The docstring examples assume that `numpy` has been imported as ``np``::\n", " \n", " >>> import numpy as np\n", " \n", " Code snippets are indicated by three greater-than signs::\n", " \n", " >>> x = 42\n", " >>> x = x + 1\n", " \n", " Use the built-in ``help`` function to view a function's docstring::\n", " \n", " >>> help(np.sort)\n", " ... # doctest: +SKIP\n", " \n", " For some objects, ``np.info(obj)`` may provide additional help. This is\n", " particularly true if you see the line \"Help on ufunc object:\" at the top\n", " of the help() page. Ufuncs are implemented in C, not Python, for speed.\n", " The native Python help() does not know how to view their help, but our\n", " np.info() function does.\n", " \n", " To search for documents containing a keyword, do::\n", " \n", " >>> np.lookfor('keyword')\n", " ... # doctest: +SKIP\n", " \n", " General-purpose documents like a glossary and help on the basic concepts\n", " of numpy are available under the ``doc`` sub-module::\n", " \n", " >>> from numpy import doc\n", " >>> help(doc)\n", " ... # doctest: +SKIP\n", " \n", " Available subpackages\n", " ---------------------\n", " lib\n", " Basic functions used by several sub-packages.\n", " random\n", " Core Random Tools\n", " linalg\n", " Core Linear Algebra Tools\n", " fft\n", " Core FFT routines\n", " polynomial\n", " Polynomial tools\n", " testing\n", " NumPy testing tools\n", " distutils\n", " Enhancements to distutils with support for\n", " Fortran compilers support and more.\n", " \n", " Utilities\n", " ---------\n", " test\n", " Run numpy unittests\n", " show_config\n", " Show numpy build configuration\n", " dual\n", " Overwrite certain functions with high-performance SciPy tools.\n", " Note: `numpy.dual` is deprecated. Use the functions from NumPy or Scipy\n", " directly instead of importing them from `numpy.dual`.\n", " matlib\n", " Make everything matrices.\n", " __version__\n", " NumPy version string\n", " \n", " Viewing documentation using IPython\n", " -----------------------------------\n", " \n", " Start IPython and import `numpy` usually under the alias ``np``: `import\n", " numpy as np`. Then, directly past or use the ``%cpaste`` magic to paste\n", " examples into the shell. To see which functions are available in `numpy`,\n", " type ``np.<TAB>`` (where ``<TAB>`` refers to the TAB key), or use\n", " ``np.*cos*?<ENTER>`` (where ``<ENTER>`` refers to the ENTER key) to narrow\n", " down the list. To view the docstring for a function, use\n", " ``np.cos?<ENTER>`` (to view the docstring) and ``np.cos??<ENTER>`` (to view\n", " the source code).\n", " \n", " Copies vs. in-place operation\n", " -----------------------------\n", " Most of the functions in `numpy` return a copy of the array argument\n", " (e.g., `np.sort`). In-place versions of these functions are often\n", " available as array methods, i.e. ``x = np.array([1,2,3]); x.sort()``.\n", " Exceptions to this rule are documented.\n", "\n", "PACKAGE CONTENTS\n", " __config__\n", " _distributor_init\n", " _globals\n", " _pyinstaller (package)\n", " _pytesttester\n", " _typing (package)\n", " _version\n", " array_api (package)\n", " compat (package)\n", " conftest\n", " core (package)\n", " ctypeslib\n", " distutils (package)\n", " doc (package)\n", " dual\n", " f2py (package)\n", " fft (package)\n", " lib (package)\n", " linalg (package)\n", " ma (package)\n", " matlib\n", " matrixlib (package)\n", " polynomial (package)\n", " random (package)\n", " setup\n", " testing (package)\n", " tests (package)\n", " typing (package)\n", " version\n", "\n", "SUBMODULES\n", " _mat\n", " char\n", " emath\n", " rec\n", "\n", "CLASSES\n", " builtins.DeprecationWarning(builtins.Warning)\n", " ModuleDeprecationWarning\n", " builtins.IndexError(builtins.LookupError)\n", " AxisError(builtins.ValueError, builtins.IndexError)\n", " builtins.RuntimeError(builtins.Exception)\n", " TooHardError\n", " builtins.RuntimeWarning(builtins.Warning)\n", " ComplexWarning\n", " builtins.UserWarning(builtins.Warning)\n", " RankWarning\n", " VisibleDeprecationWarning\n", " builtins.ValueError(builtins.Exception)\n", " AxisError(builtins.ValueError, builtins.IndexError)\n", " builtins.bytes(builtins.object)\n", " bytes_(builtins.bytes, character)\n", " builtins.object\n", " DataSource\n", " broadcast\n", " busdaycalendar\n", " dtype\n", " finfo\n", " flatiter\n", " format_parser\n", " generic\n", " bool_\n", " datetime64\n", " flexible\n", " character\n", " bytes_(builtins.bytes, character)\n", " str_(builtins.str, character)\n", " void\n", " record\n", " number\n", " inexact\n", " complexfloating\n", " clongdouble\n", " complex128(complexfloating, builtins.complex)\n", " complex64\n", " floating\n", " float16\n", " float32\n", " float64(floating, builtins.float)\n", " longdouble\n", " integer\n", " signedinteger\n", " int16\n", " int32\n", " int64\n", " int8\n", " intc\n", " timedelta64\n", " unsignedinteger\n", " uint16\n", " uint32\n", " uint64\n", " uint8\n", " uintc\n", " object_\n", " iinfo\n", " ndarray\n", " chararray\n", " matrix\n", " memmap\n", " recarray\n", " ndenumerate\n", " ndindex\n", " nditer\n", " poly1d\n", " ufunc\n", " vectorize\n", " builtins.str(builtins.object)\n", " str_(builtins.str, character)\n", " contextlib.ContextDecorator(builtins.object)\n", " errstate\n", " \n", " class AxisError(builtins.ValueError, builtins.IndexError)\n", " | AxisError(axis, ndim=None, msg_prefix=None)\n", " | \n", " | Axis supplied was invalid.\n", " | \n", " | This is raised whenever an ``axis`` parameter is specified that is larger\n", " | than the number of array dimensions.\n", " | For compatibility with code written against older numpy versions, which\n", " | raised a mixture of `ValueError` and `IndexError` for this situation, this\n", " | exception subclasses both to ensure that ``except ValueError`` and\n", " | ``except IndexError`` statements continue to catch `AxisError`.\n", " | \n", " | .. versionadded:: 1.13\n", " | \n", " | Parameters\n", " | ----------\n", " | axis : int or str\n", " | The out of bounds axis or a custom exception message.\n", " | If an axis is provided, then `ndim` should be specified as well.\n", " | ndim : int, optional\n", " | The number of array dimensions.\n", " | msg_prefix : str, optional\n", " | A prefix for the exception message.\n", " | \n", " | Attributes\n", " | ----------\n", " | axis : int, optional\n", " | The out of bounds axis or ``None`` if a custom exception\n", " | message was provided. This should be the axis as passed by\n", " | the user, before any normalization to resolve negative indices.\n", " | \n", " | .. versionadded:: 1.22\n", " | ndim : int, optional\n", " | The number of array dimensions or ``None`` if a custom exception\n", " | message was provided.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | \n", " | Examples\n", " | --------\n", " | >>> array_1d = np.arange(10)\n", " | >>> np.cumsum(array_1d, axis=1)\n", " | Traceback (most recent call last):\n", " | ...\n", " | numpy.AxisError: axis 1 is out of bounds for array of dimension 1\n", " | \n", " | Negative axes are preserved:\n", " | \n", " | >>> np.cumsum(array_1d, axis=-2)\n", " | Traceback (most recent call last):\n", " | ...\n", " | numpy.AxisError: axis -2 is out of bounds for array of dimension 1\n", " | \n", " | The class constructor generally takes the axis and arrays'\n", " | dimensionality as arguments:\n", " | \n", " | >>> print(np.AxisError(2, 1, msg_prefix='error'))\n", " | error: axis 2 is out of bounds for array of dimension 1\n", " | \n", " | Alternatively, a custom exception message can be passed:\n", " | \n", " | >>> print(np.AxisError('Custom error message'))\n", " | Custom error message\n", " | \n", " | Method resolution order:\n", " | AxisError\n", " | builtins.ValueError\n", " | builtins.IndexError\n", " | builtins.LookupError\n", " | builtins.Exception\n", " | builtins.BaseException\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __init__(self, axis, ndim=None, msg_prefix=None)\n", " | Initialize self. See help(type(self)) for accurate signature.\n", " | \n", " | __str__(self)\n", " | Return str(self).\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors defined here:\n", " | \n", " | axis\n", " | \n", " | ndim\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods inherited from builtins.ValueError:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from builtins.BaseException:\n", " | \n", " | __delattr__(self, name, /)\n", " | Implement delattr(self, name).\n", " | \n", " | __getattribute__(self, name, /)\n", " | Return getattr(self, name).\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __setattr__(self, name, value, /)\n", " | Implement setattr(self, name, value).\n", " | \n", " | __setstate__(...)\n", " | \n", " | add_note(...)\n", " | Exception.add_note(note) --\n", " | add a note to the exception\n", " | \n", " | with_traceback(...)\n", " | Exception.with_traceback(tb) --\n", " | set self.__traceback__ to tb and return self.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from builtins.BaseException:\n", " | \n", " | __cause__\n", " | exception cause\n", " | \n", " | __context__\n", " | exception context\n", " | \n", " | __dict__\n", " | \n", " | __suppress_context__\n", " | \n", " | __traceback__\n", " | \n", " | args\n", " \n", " class ComplexWarning(builtins.RuntimeWarning)\n", " | The warning raised when casting a complex dtype to a real dtype.\n", " | \n", " | As implemented, casting a complex number to a real discards its imaginary\n", " | part, but this behavior may not be what the user actually wants.\n", " | \n", " | Method resolution order:\n", " | ComplexWarning\n", " | builtins.RuntimeWarning\n", " | builtins.Warning\n", " | builtins.Exception\n", " | builtins.BaseException\n", " | builtins.object\n", " | \n", " | Data descriptors defined here:\n", " | \n", " | __weakref__\n", " | list of weak references to the object (if defined)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from builtins.RuntimeWarning:\n", " | \n", " | __init__(self, /, *args, **kwargs)\n", " | Initialize self. See help(type(self)) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods inherited from builtins.RuntimeWarning:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from builtins.BaseException:\n", " | \n", " | __delattr__(self, name, /)\n", " | Implement delattr(self, name).\n", " | \n", " | __getattribute__(self, name, /)\n", " | Return getattr(self, name).\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __setattr__(self, name, value, /)\n", " | Implement setattr(self, name, value).\n", " | \n", " | __setstate__(...)\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | add_note(...)\n", " | Exception.add_note(note) --\n", " | add a note to the exception\n", " | \n", " | with_traceback(...)\n", " | Exception.with_traceback(tb) --\n", " | set self.__traceback__ to tb and return self.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from builtins.BaseException:\n", " | \n", " | __cause__\n", " | exception cause\n", " | \n", " | __context__\n", " | exception context\n", " | \n", " | __dict__\n", " | \n", " | __suppress_context__\n", " | \n", " | __traceback__\n", " | \n", " | args\n", " \n", " class DataSource(builtins.object)\n", " | DataSource(destpath='.')\n", " | \n", " | DataSource(destpath='.')\n", " | \n", " | A generic data source file (file, http, ftp, ...).\n", " | \n", " | DataSources can be local files or remote files/URLs. The files may\n", " | also be compressed or uncompressed. DataSource hides some of the\n", " | low-level details of downloading the file, allowing you to simply pass\n", " | in a valid file path (or URL) and obtain a file object.\n", " | \n", " | Parameters\n", " | ----------\n", " | destpath : str or None, optional\n", " | Path to the directory where the source file gets downloaded to for\n", " | use. If `destpath` is None, a temporary directory will be created.\n", " | The default path is the current directory.\n", " | \n", " | Notes\n", " | -----\n", " | URLs require a scheme string (``http://``) to be used, without it they\n", " | will fail::\n", " | \n", " | >>> repos = np.DataSource()\n", " | >>> repos.exists('www.google.com/index.html')\n", " | False\n", " | >>> repos.exists('http://www.google.com/index.html')\n", " | True\n", " | \n", " | Temporary directories are deleted when the DataSource is deleted.\n", " | \n", " | Examples\n", " | --------\n", " | ::\n", " | \n", " | >>> ds = np.DataSource('/home/guido')\n", " | >>> urlname = 'http://www.google.com/'\n", " | >>> gfile = ds.open('http://www.google.com/')\n", " | >>> ds.abspath(urlname)\n", " | '/home/guido/www.google.com/index.html'\n", " | \n", " | >>> ds = np.DataSource(None) # use with temporary file\n", " | >>> ds.open('/home/guido/foobar.txt')\n", " | <open file '/home/guido.foobar.txt', mode 'r' at 0x91d4430>\n", " | >>> ds.abspath('/home/guido/foobar.txt')\n", " | '/tmp/.../home/guido/foobar.txt'\n", " | \n", " | Methods defined here:\n", " | \n", " | __del__(self)\n", " | \n", " | __init__(self, destpath='.')\n", " | Create a DataSource with a local path at destpath.\n", " | \n", " | abspath(self, path)\n", " | Return absolute path of file in the DataSource directory.\n", " | \n", " | If `path` is an URL, then `abspath` will return either the location\n", " | the file exists locally or the location it would exist when opened\n", " | using the `open` method.\n", " | \n", " | Parameters\n", " | ----------\n", " | path : str\n", " | Can be a local file or a remote URL.\n", " | \n", " | Returns\n", " | -------\n", " | out : str\n", " | Complete path, including the `DataSource` destination directory.\n", " | \n", " | Notes\n", " | -----\n", " | The functionality is based on `os.path.abspath`.\n", " | \n", " | exists(self, path)\n", " | Test if path exists.\n", " | \n", " | Test if `path` exists as (and in this order):\n", " | \n", " | - a local file.\n", " | - a remote URL that has been downloaded and stored locally in the\n", " | `DataSource` directory.\n", " | - a remote URL that has not been downloaded, but is valid and\n", " | accessible.\n", " | \n", " | Parameters\n", " | ----------\n", " | path : str\n", " | Can be a local file or a remote URL.\n", " | \n", " | Returns\n", " | -------\n", " | out : bool\n", " | True if `path` exists.\n", " | \n", " | Notes\n", " | -----\n", " | When `path` is an URL, `exists` will return True if it's either\n", " | stored locally in the `DataSource` directory, or is a valid remote\n", " | URL. `DataSource` does not discriminate between the two, the file\n", " | is accessible if it exists in either location.\n", " | \n", " | open(self, path, mode='r', encoding=None, newline=None)\n", " | Open and return file-like object.\n", " | \n", " | If `path` is an URL, it will be downloaded, stored in the\n", " | `DataSource` directory and opened from there.\n", " | \n", " | Parameters\n", " | ----------\n", " | path : str\n", " | Local file path or URL to open.\n", " | mode : {'r', 'w', 'a'}, optional\n", " | Mode to open `path`. Mode 'r' for reading, 'w' for writing,\n", " | 'a' to append. Available modes depend on the type of object\n", " | specified by `path`. Default is 'r'.\n", " | encoding : {None, str}, optional\n", " | Open text file with given encoding. The default encoding will be\n", " | what `io.open` uses.\n", " | newline : {None, str}, optional\n", " | Newline to use when reading text file.\n", " | \n", " | Returns\n", " | -------\n", " | out : file object\n", " | File object.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors defined here:\n", " | \n", " | __dict__\n", " | dictionary for instance variables (if defined)\n", " | \n", " | __weakref__\n", " | list of weak references to the object (if defined)\n", " \n", " class ModuleDeprecationWarning(builtins.DeprecationWarning)\n", " | Module deprecation warning.\n", " | \n", " | The nose tester turns ordinary Deprecation warnings into test failures.\n", " | That makes it hard to deprecate whole modules, because they get\n", " | imported by default. So this is a special Deprecation warning that the\n", " | nose tester will let pass without making tests fail.\n", " | \n", " | Method resolution order:\n", " | ModuleDeprecationWarning\n", " | builtins.DeprecationWarning\n", " | builtins.Warning\n", " | builtins.Exception\n", " | builtins.BaseException\n", " | builtins.object\n", " | \n", " | Data descriptors defined here:\n", " | \n", " | __weakref__\n", " | list of weak references to the object (if defined)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from builtins.DeprecationWarning:\n", " | \n", " | __init__(self, /, *args, **kwargs)\n", " | Initialize self. See help(type(self)) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods inherited from builtins.DeprecationWarning:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from builtins.BaseException:\n", " | \n", " | __delattr__(self, name, /)\n", " | Implement delattr(self, name).\n", " | \n", " | __getattribute__(self, name, /)\n", " | Return getattr(self, name).\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __setattr__(self, name, value, /)\n", " | Implement setattr(self, name, value).\n", " | \n", " | __setstate__(...)\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | add_note(...)\n", " | Exception.add_note(note) --\n", " | add a note to the exception\n", " | \n", " | with_traceback(...)\n", " | Exception.with_traceback(tb) --\n", " | set self.__traceback__ to tb and return self.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from builtins.BaseException:\n", " | \n", " | __cause__\n", " | exception cause\n", " | \n", " | __context__\n", " | exception context\n", " | \n", " | __dict__\n", " | \n", " | __suppress_context__\n", " | \n", " | __traceback__\n", " | \n", " | args\n", " \n", " class RankWarning(builtins.UserWarning)\n", " | Issued by `polyfit` when the Vandermonde matrix is rank deficient.\n", " | \n", " | For more information, a way to suppress the warning, and an example of\n", " | `RankWarning` being issued, see `polyfit`.\n", " | \n", " | Method resolution order:\n", " | RankWarning\n", " | builtins.UserWarning\n", " | builtins.Warning\n", " | builtins.Exception\n", " | builtins.BaseException\n", " | builtins.object\n", " | \n", " | Data descriptors defined here:\n", " | \n", " | __weakref__\n", " | list of weak references to the object (if defined)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from builtins.UserWarning:\n", " | \n", " | __init__(self, /, *args, **kwargs)\n", " | Initialize self. See help(type(self)) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods inherited from builtins.UserWarning:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from builtins.BaseException:\n", " | \n", " | __delattr__(self, name, /)\n", " | Implement delattr(self, name).\n", " | \n", " | __getattribute__(self, name, /)\n", " | Return getattr(self, name).\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __setattr__(self, name, value, /)\n", " | Implement setattr(self, name, value).\n", " | \n", " | __setstate__(...)\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | add_note(...)\n", " | Exception.add_note(note) --\n", " | add a note to the exception\n", " | \n", " | with_traceback(...)\n", " | Exception.with_traceback(tb) --\n", " | set self.__traceback__ to tb and return self.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from builtins.BaseException:\n", " | \n", " | __cause__\n", " | exception cause\n", " | \n", " | __context__\n", " | exception context\n", " | \n", " | __dict__\n", " | \n", " | __suppress_context__\n", " | \n", " | __traceback__\n", " | \n", " | args\n", " \n", " class TooHardError(builtins.RuntimeError)\n", " | max_work was exceeded.\n", " | \n", " | This is raised whenever the maximum number of candidate solutions \n", " | to consider specified by the ``max_work`` parameter is exceeded.\n", " | Assigning a finite number to max_work may have caused the operation \n", " | to fail.\n", " | \n", " | Method resolution order:\n", " | TooHardError\n", " | builtins.RuntimeError\n", " | builtins.Exception\n", " | builtins.BaseException\n", " | builtins.object\n", " | \n", " | Data descriptors defined here:\n", " | \n", " | __weakref__\n", " | list of weak references to the object (if defined)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from builtins.RuntimeError:\n", " | \n", " | __init__(self, /, *args, **kwargs)\n", " | Initialize self. See help(type(self)) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods inherited from builtins.RuntimeError:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from builtins.BaseException:\n", " | \n", " | __delattr__(self, name, /)\n", " | Implement delattr(self, name).\n", " | \n", " | __getattribute__(self, name, /)\n", " | Return getattr(self, name).\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __setattr__(self, name, value, /)\n", " | Implement setattr(self, name, value).\n", " | \n", " | __setstate__(...)\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | add_note(...)\n", " | Exception.add_note(note) --\n", " | add a note to the exception\n", " | \n", " | with_traceback(...)\n", " | Exception.with_traceback(tb) --\n", " | set self.__traceback__ to tb and return self.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from builtins.BaseException:\n", " | \n", " | __cause__\n", " | exception cause\n", " | \n", " | __context__\n", " | exception context\n", " | \n", " | __dict__\n", " | \n", " | __suppress_context__\n", " | \n", " | __traceback__\n", " | \n", " | args\n", " \n", " class VisibleDeprecationWarning(builtins.UserWarning)\n", " | Visible deprecation warning.\n", " | \n", " | By default, python will not show deprecation warnings, so this class\n", " | can be used when a very visible warning is helpful, for example because\n", " | the usage is most likely a user bug.\n", " | \n", " | Method resolution order:\n", " | VisibleDeprecationWarning\n", " | builtins.UserWarning\n", " | builtins.Warning\n", " | builtins.Exception\n", " | builtins.BaseException\n", " | builtins.object\n", " | \n", " | Data descriptors defined here:\n", " | \n", " | __weakref__\n", " | list of weak references to the object (if defined)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from builtins.UserWarning:\n", " | \n", " | __init__(self, /, *args, **kwargs)\n", " | Initialize self. See help(type(self)) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods inherited from builtins.UserWarning:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from builtins.BaseException:\n", " | \n", " | __delattr__(self, name, /)\n", " | Implement delattr(self, name).\n", " | \n", " | __getattribute__(self, name, /)\n", " | Return getattr(self, name).\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __setattr__(self, name, value, /)\n", " | Implement setattr(self, name, value).\n", " | \n", " | __setstate__(...)\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | add_note(...)\n", " | Exception.add_note(note) --\n", " | add a note to the exception\n", " | \n", " | with_traceback(...)\n", " | Exception.with_traceback(tb) --\n", " | set self.__traceback__ to tb and return self.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from builtins.BaseException:\n", " | \n", " | __cause__\n", " | exception cause\n", " | \n", " | __context__\n", " | exception context\n", " | \n", " | __dict__\n", " | \n", " | __suppress_context__\n", " | \n", " | __traceback__\n", " | \n", " | args\n", " \n", " class bool_(generic)\n", " | Boolean type (True or False), stored as a byte.\n", " | \n", " | .. warning::\n", " | \n", " | The :class:`bool_` type is not a subclass of the :class:`int_` type\n", " | (the :class:`bool_` is not even a number type). This is different\n", " | than Python's default implementation of :class:`bool` as a\n", " | sub-class of :class:`int`.\n", " | \n", " | :Character code: ``'?'``\n", " | :Alias: `numpy.bool8`\n", " | \n", " | Method resolution order:\n", " | bool_\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __index__(self, /)\n", " | Return self converted to an integer, if self is suitable for use as an index into a list.\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " class broadcast(builtins.object)\n", " | Produce an object that mimics broadcasting.\n", " | \n", " | Parameters\n", " | ----------\n", " | in1, in2, ... : array_like\n", " | Input parameters.\n", " | \n", " | Returns\n", " | -------\n", " | b : broadcast object\n", " | Broadcast the input parameters against one another, and\n", " | return an object that encapsulates the result.\n", " | Amongst others, it has ``shape`` and ``nd`` properties, and\n", " | may be used as an iterator.\n", " | \n", " | See Also\n", " | --------\n", " | broadcast_arrays\n", " | broadcast_to\n", " | broadcast_shapes\n", " | \n", " | Examples\n", " | --------\n", " | \n", " | Manually adding two vectors, using broadcasting:\n", " | \n", " | >>> x = np.array([[1], [2], [3]])\n", " | >>> y = np.array([4, 5, 6])\n", " | >>> b = np.broadcast(x, y)\n", " | \n", " | >>> out = np.empty(b.shape)\n", " | >>> out.flat = [u+v for (u,v) in b]\n", " | >>> out\n", " | array([[5., 6., 7.],\n", " | [6., 7., 8.],\n", " | [7., 8., 9.]])\n", " | \n", " | Compare against built-in broadcasting:\n", " | \n", " | >>> x + y\n", " | array([[5, 6, 7],\n", " | [6, 7, 8],\n", " | [7, 8, 9]])\n", " | \n", " | Methods defined here:\n", " | \n", " | __iter__(self, /)\n", " | Implement iter(self).\n", " | \n", " | __next__(self, /)\n", " | Implement next(self).\n", " | \n", " | reset(...)\n", " | reset()\n", " | \n", " | Reset the broadcasted result's iterator(s).\n", " | \n", " | Parameters\n", " | ----------\n", " | None\n", " | \n", " | Returns\n", " | -------\n", " | None\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([1, 2, 3])\n", " | >>> y = np.array([[4], [5], [6]])\n", " | >>> b = np.broadcast(x, y)\n", " | >>> b.index\n", " | 0\n", " | >>> next(b), next(b), next(b)\n", " | ((1, 4), (2, 4), (3, 4))\n", " | >>> b.index\n", " | 3\n", " | >>> b.reset()\n", " | >>> b.index\n", " | 0\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors defined here:\n", " | \n", " | index\n", " | current index in broadcasted result\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([[1], [2], [3]])\n", " | >>> y = np.array([4, 5, 6])\n", " | >>> b = np.broadcast(x, y)\n", " | >>> b.index\n", " | 0\n", " | >>> next(b), next(b), next(b)\n", " | ((1, 4), (1, 5), (1, 6))\n", " | >>> b.index\n", " | 3\n", " | \n", " | iters\n", " | tuple of iterators along ``self``'s \"components.\"\n", " | \n", " | Returns a tuple of `numpy.flatiter` objects, one for each \"component\"\n", " | of ``self``.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.flatiter\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([1, 2, 3])\n", " | >>> y = np.array([[4], [5], [6]])\n", " | >>> b = np.broadcast(x, y)\n", " | >>> row, col = b.iters\n", " | >>> next(row), next(col)\n", " | (1, 4)\n", " | \n", " | nd\n", " | Number of dimensions of broadcasted result. For code intended for NumPy\n", " | 1.12.0 and later the more consistent `ndim` is preferred.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([1, 2, 3])\n", " | >>> y = np.array([[4], [5], [6]])\n", " | >>> b = np.broadcast(x, y)\n", " | >>> b.nd\n", " | 2\n", " | \n", " | ndim\n", " | Number of dimensions of broadcasted result. Alias for `nd`.\n", " | \n", " | .. versionadded:: 1.12.0\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([1, 2, 3])\n", " | >>> y = np.array([[4], [5], [6]])\n", " | >>> b = np.broadcast(x, y)\n", " | >>> b.ndim\n", " | 2\n", " | \n", " | numiter\n", " | Number of iterators possessed by the broadcasted result.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([1, 2, 3])\n", " | >>> y = np.array([[4], [5], [6]])\n", " | >>> b = np.broadcast(x, y)\n", " | >>> b.numiter\n", " | 2\n", " | \n", " | shape\n", " | Shape of broadcasted result.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([1, 2, 3])\n", " | >>> y = np.array([[4], [5], [6]])\n", " | >>> b = np.broadcast(x, y)\n", " | >>> b.shape\n", " | (3, 3)\n", " | \n", " | size\n", " | Total size of broadcasted result.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([1, 2, 3])\n", " | >>> y = np.array([[4], [5], [6]])\n", " | >>> b = np.broadcast(x, y)\n", " | >>> b.size\n", " | 9\n", " \n", " class busdaycalendar(builtins.object)\n", " | busdaycalendar(weekmask='1111100', holidays=None)\n", " | \n", " | A business day calendar object that efficiently stores information\n", " | defining valid days for the busday family of functions.\n", " | \n", " | The default valid days are Monday through Friday (\"business days\").\n", " | A busdaycalendar object can be specified with any set of weekly\n", " | valid days, plus an optional \"holiday\" dates that always will be invalid.\n", " | \n", " | Once a busdaycalendar object is created, the weekmask and holidays\n", " | cannot be modified.\n", " | \n", " | .. versionadded:: 1.7.0\n", " | \n", " | Parameters\n", " | ----------\n", " | weekmask : str or array_like of bool, optional\n", " | A seven-element array indicating which of Monday through Sunday are\n", " | valid days. May be specified as a length-seven list or array, like\n", " | [1,1,1,1,1,0,0]; a length-seven string, like '1111100'; or a string\n", " | like \"Mon Tue Wed Thu Fri\", made up of 3-character abbreviations for\n", " | weekdays, optionally separated by white space. Valid abbreviations\n", " | are: Mon Tue Wed Thu Fri Sat Sun\n", " | holidays : array_like of datetime64[D], optional\n", " | An array of dates to consider as invalid dates, no matter which\n", " | weekday they fall upon. Holiday dates may be specified in any\n", " | order, and NaT (not-a-time) dates are ignored. This list is\n", " | saved in a normalized form that is suited for fast calculations\n", " | of valid days.\n", " | \n", " | Returns\n", " | -------\n", " | out : busdaycalendar\n", " | A business day calendar object containing the specified\n", " | weekmask and holidays values.\n", " | \n", " | See Also\n", " | --------\n", " | is_busday : Returns a boolean array indicating valid days.\n", " | busday_offset : Applies an offset counted in valid days.\n", " | busday_count : Counts how many valid days are in a half-open date range.\n", " | \n", " | Attributes\n", " | ----------\n", " | Note: once a busdaycalendar object is created, you cannot modify the\n", " | weekmask or holidays. The attributes return copies of internal data.\n", " | weekmask : (copy) seven-element array of bool\n", " | holidays : (copy) sorted array of datetime64[D]\n", " | \n", " | Examples\n", " | --------\n", " | >>> # Some important days in July\n", " | ... bdd = np.busdaycalendar(\n", " | ... holidays=['2011-07-01', '2011-07-04', '2011-07-17'])\n", " | >>> # Default is Monday to Friday weekdays\n", " | ... bdd.weekmask\n", " | array([ True, True, True, True, True, False, False])\n", " | >>> # Any holidays already on the weekend are removed\n", " | ... bdd.holidays\n", " | array(['2011-07-01', '2011-07-04'], dtype='datetime64[D]')\n", " | \n", " | Methods defined here:\n", " | \n", " | __init__(self, /, *args, **kwargs)\n", " | Initialize self. See help(type(self)) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors defined here:\n", " | \n", " | holidays\n", " | A copy of the holiday array indicating additional invalid days.\n", " | \n", " | weekmask\n", " | A copy of the seven-element boolean mask indicating valid days.\n", " \n", " byte = class int8(signedinteger)\n", " | Signed integer type, compatible with C ``char``.\n", " | \n", " | :Character code: ``'b'``\n", " | :Canonical name: `numpy.byte`\n", " | :Alias on this platform (win32 AMD64): `numpy.int8`: 8-bit signed integer (``-128`` to ``127``).\n", " | \n", " | Method resolution order:\n", " | int8\n", " | signedinteger\n", " | integer\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __index__(self, /)\n", " | Return self converted to an integer, if self is suitable for use as an index into a list.\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | bit_count(...)\n", " | int8.bit_count() -> int\n", " | \n", " | Computes the number of 1-bits in the absolute value of the input.\n", " | Analogous to the builtin `int.bit_count` or ``popcount`` in C++.\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.int8(127).bit_count()\n", " | 7\n", " | >>> np.int8(-127).bit_count()\n", " | 7\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from integer:\n", " | \n", " | __round__(...)\n", " | \n", " | is_integer(...)\n", " | integer.is_integer() -> bool\n", " | \n", " | Return ``True`` if the number is finite with integral value.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.int64(-2).is_integer()\n", " | True\n", " | >>> np.uint32(5).is_integer()\n", " | True\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from integer:\n", " | \n", " | denominator\n", " | denominator of value (1)\n", " | \n", " | numerator\n", " | numerator of value (the value itself)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " class bytes_(builtins.bytes, character)\n", " | A byte string.\n", " | \n", " | When used in arrays, this type strips trailing null bytes.\n", " | \n", " | :Character code: ``'S'``\n", " | :Alias: `numpy.string_`\n", " | \n", " | Method resolution order:\n", " | bytes_\n", " | builtins.bytes\n", " | character\n", " | flexible\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from builtins.bytes:\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __bytes__(self, /)\n", " | Convert this value to exact type bytes.\n", " | \n", " | __contains__(self, key, /)\n", " | Return key in self.\n", " | \n", " | __getattribute__(self, name, /)\n", " | Return getattr(self, name).\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __getnewargs__(...)\n", " | \n", " | __iter__(self, /)\n", " | Implement iter(self).\n", " | \n", " | __len__(self, /)\n", " | Return len(self).\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | capitalize(...)\n", " | B.capitalize() -> copy of B\n", " | \n", " | Return a copy of B with only its first character capitalized (ASCII)\n", " | and the rest lower-cased.\n", " | \n", " | center(self, width, fillchar=b' ', /)\n", " | Return a centered string of length width.\n", " | \n", " | Padding is done using the specified fill character.\n", " | \n", " | count(...)\n", " | B.count(sub[, start[, end]]) -> int\n", " | \n", " | Return the number of non-overlapping occurrences of subsection sub in\n", " | bytes B[start:end]. Optional arguments start and end are interpreted\n", " | as in slice notation.\n", " | \n", " | decode(self, /, encoding='utf-8', errors='strict')\n", " | Decode the bytes using the codec registered for encoding.\n", " | \n", " | encoding\n", " | The encoding with which to decode the bytes.\n", " | errors\n", " | The error handling scheme to use for the handling of decoding errors.\n", " | The default is 'strict' meaning that decoding errors raise a\n", " | UnicodeDecodeError. Other possible values are 'ignore' and 'replace'\n", " | as well as any other name registered with codecs.register_error that\n", " | can handle UnicodeDecodeErrors.\n", " | \n", " | endswith(...)\n", " | B.endswith(suffix[, start[, end]]) -> bool\n", " | \n", " | Return True if B ends with the specified suffix, False otherwise.\n", " | With optional start, test B beginning at that position.\n", " | With optional end, stop comparing B at that position.\n", " | suffix can also be a tuple of bytes to try.\n", " | \n", " | expandtabs(self, /, tabsize=8)\n", " | Return a copy where all tab characters are expanded using spaces.\n", " | \n", " | If tabsize is not given, a tab size of 8 characters is assumed.\n", " | \n", " | find(...)\n", " | B.find(sub[, start[, end]]) -> int\n", " | \n", " | Return the lowest index in B where subsection sub is found,\n", " | such that sub is contained within B[start,end]. Optional\n", " | arguments start and end are interpreted as in slice notation.\n", " | \n", " | Return -1 on failure.\n", " | \n", " | hex(...)\n", " | Create a string of hexadecimal numbers from a bytes object.\n", " | \n", " | sep\n", " | An optional single character or byte to separate hex bytes.\n", " | bytes_per_sep\n", " | How many bytes between separators. Positive values count from the\n", " | right, negative values count from the left.\n", " | \n", " | Example:\n", " | >>> value = b'\\xb9\\x01\\xef'\n", " | >>> value.hex()\n", " | 'b901ef'\n", " | >>> value.hex(':')\n", " | 'b9:01:ef'\n", " | >>> value.hex(':', 2)\n", " | 'b9:01ef'\n", " | >>> value.hex(':', -2)\n", " | 'b901:ef'\n", " | \n", " | index(...)\n", " | B.index(sub[, start[, end]]) -> int\n", " | \n", " | Return the lowest index in B where subsection sub is found,\n", " | such that sub is contained within B[start,end]. Optional\n", " | arguments start and end are interpreted as in slice notation.\n", " | \n", " | Raises ValueError when the subsection is not found.\n", " | \n", " | isalnum(...)\n", " | B.isalnum() -> bool\n", " | \n", " | Return True if all characters in B are alphanumeric\n", " | and there is at least one character in B, False otherwise.\n", " | \n", " | isalpha(...)\n", " | B.isalpha() -> bool\n", " | \n", " | Return True if all characters in B are alphabetic\n", " | and there is at least one character in B, False otherwise.\n", " | \n", " | isascii(...)\n", " | B.isascii() -> bool\n", " | \n", " | Return True if B is empty or all characters in B are ASCII,\n", " | False otherwise.\n", " | \n", " | isdigit(...)\n", " | B.isdigit() -> bool\n", " | \n", " | Return True if all characters in B are digits\n", " | and there is at least one character in B, False otherwise.\n", " | \n", " | islower(...)\n", " | B.islower() -> bool\n", " | \n", " | Return True if all cased characters in B are lowercase and there is\n", " | at least one cased character in B, False otherwise.\n", " | \n", " | isspace(...)\n", " | B.isspace() -> bool\n", " | \n", " | Return True if all characters in B are whitespace\n", " | and there is at least one character in B, False otherwise.\n", " | \n", " | istitle(...)\n", " | B.istitle() -> bool\n", " | \n", " | Return True if B is a titlecased string and there is at least one\n", " | character in B, i.e. uppercase characters may only follow uncased\n", " | characters and lowercase characters only cased ones. Return False\n", " | otherwise.\n", " | \n", " | isupper(...)\n", " | B.isupper() -> bool\n", " | \n", " | Return True if all cased characters in B are uppercase and there is\n", " | at least one cased character in B, False otherwise.\n", " | \n", " | join(self, iterable_of_bytes, /)\n", " | Concatenate any number of bytes objects.\n", " | \n", " | The bytes whose method is called is inserted in between each pair.\n", " | \n", " | The result is returned as a new bytes object.\n", " | \n", " | Example: b'.'.join([b'ab', b'pq', b'rs']) -> b'ab.pq.rs'.\n", " | \n", " | ljust(self, width, fillchar=b' ', /)\n", " | Return a left-justified string of length width.\n", " | \n", " | Padding is done using the specified fill character.\n", " | \n", " | lower(...)\n", " | B.lower() -> copy of B\n", " | \n", " | Return a copy of B with all ASCII characters converted to lowercase.\n", " | \n", " | lstrip(self, bytes=None, /)\n", " | Strip leading bytes contained in the argument.\n", " | \n", " | If the argument is omitted or None, strip leading ASCII whitespace.\n", " | \n", " | partition(self, sep, /)\n", " | Partition the bytes into three parts using the given separator.\n", " | \n", " | This will search for the separator sep in the bytes. If the separator is found,\n", " | returns a 3-tuple containing the part before the separator, the separator\n", " | itself, and the part after it.\n", " | \n", " | If the separator is not found, returns a 3-tuple containing the original bytes\n", " | object and two empty bytes objects.\n", " | \n", " | removeprefix(self, prefix, /)\n", " | Return a bytes object with the given prefix string removed if present.\n", " | \n", " | If the bytes starts with the prefix string, return bytes[len(prefix):].\n", " | Otherwise, return a copy of the original bytes.\n", " | \n", " | removesuffix(self, suffix, /)\n", " | Return a bytes object with the given suffix string removed if present.\n", " | \n", " | If the bytes ends with the suffix string and that suffix is not empty,\n", " | return bytes[:-len(prefix)]. Otherwise, return a copy of the original\n", " | bytes.\n", " | \n", " | replace(self, old, new, count=-1, /)\n", " | Return a copy with all occurrences of substring old replaced by new.\n", " | \n", " | count\n", " | Maximum number of occurrences to replace.\n", " | -1 (the default value) means replace all occurrences.\n", " | \n", " | If the optional argument count is given, only the first count occurrences are\n", " | replaced.\n", " | \n", " | rfind(...)\n", " | B.rfind(sub[, start[, end]]) -> int\n", " | \n", " | Return the highest index in B where subsection sub is found,\n", " | such that sub is contained within B[start,end]. Optional\n", " | arguments start and end are interpreted as in slice notation.\n", " | \n", " | Return -1 on failure.\n", " | \n", " | rindex(...)\n", " | B.rindex(sub[, start[, end]]) -> int\n", " | \n", " | Return the highest index in B where subsection sub is found,\n", " | such that sub is contained within B[start,end]. Optional\n", " | arguments start and end are interpreted as in slice notation.\n", " | \n", " | Raise ValueError when the subsection is not found.\n", " | \n", " | rjust(self, width, fillchar=b' ', /)\n", " | Return a right-justified string of length width.\n", " | \n", " | Padding is done using the specified fill character.\n", " | \n", " | rpartition(self, sep, /)\n", " | Partition the bytes into three parts using the given separator.\n", " | \n", " | This will search for the separator sep in the bytes, starting at the end. If\n", " | the separator is found, returns a 3-tuple containing the part before the\n", " | separator, the separator itself, and the part after it.\n", " | \n", " | If the separator is not found, returns a 3-tuple containing two empty bytes\n", " | objects and the original bytes object.\n", " | \n", " | rsplit(self, /, sep=None, maxsplit=-1)\n", " | Return a list of the sections in the bytes, using sep as the delimiter.\n", " | \n", " | sep\n", " | The delimiter according which to split the bytes.\n", " | None (the default value) means split on ASCII whitespace characters\n", " | (space, tab, return, newline, formfeed, vertical tab).\n", " | maxsplit\n", " | Maximum number of splits to do.\n", " | -1 (the default value) means no limit.\n", " | \n", " | Splitting is done starting at the end of the bytes and working to the front.\n", " | \n", " | rstrip(self, bytes=None, /)\n", " | Strip trailing bytes contained in the argument.\n", " | \n", " | If the argument is omitted or None, strip trailing ASCII whitespace.\n", " | \n", " | split(self, /, sep=None, maxsplit=-1)\n", " | Return a list of the sections in the bytes, using sep as the delimiter.\n", " | \n", " | sep\n", " | The delimiter according which to split the bytes.\n", " | None (the default value) means split on ASCII whitespace characters\n", " | (space, tab, return, newline, formfeed, vertical tab).\n", " | maxsplit\n", " | Maximum number of splits to do.\n", " | -1 (the default value) means no limit.\n", " | \n", " | splitlines(self, /, keepends=False)\n", " | Return a list of the lines in the bytes, breaking at line boundaries.\n", " | \n", " | Line breaks are not included in the resulting list unless keepends is given and\n", " | true.\n", " | \n", " | startswith(...)\n", " | B.startswith(prefix[, start[, end]]) -> bool\n", " | \n", " | Return True if B starts with the specified prefix, False otherwise.\n", " | With optional start, test B beginning at that position.\n", " | With optional end, stop comparing B at that position.\n", " | prefix can also be a tuple of bytes to try.\n", " | \n", " | strip(self, bytes=None, /)\n", " | Strip leading and trailing bytes contained in the argument.\n", " | \n", " | If the argument is omitted or None, strip leading and trailing ASCII whitespace.\n", " | \n", " | swapcase(...)\n", " | B.swapcase() -> copy of B\n", " | \n", " | Return a copy of B with uppercase ASCII characters converted\n", " | to lowercase ASCII and vice versa.\n", " | \n", " | title(...)\n", " | B.title() -> copy of B\n", " | \n", " | Return a titlecased version of B, i.e. ASCII words start with uppercase\n", " | characters, all remaining cased characters have lowercase.\n", " | \n", " | translate(self, table, /, delete=b'')\n", " | Return a copy with each character mapped by the given translation table.\n", " | \n", " | table\n", " | Translation table, which must be a bytes object of length 256.\n", " | \n", " | All characters occurring in the optional argument delete are removed.\n", " | The remaining characters are mapped through the given translation table.\n", " | \n", " | upper(...)\n", " | B.upper() -> copy of B\n", " | \n", " | Return a copy of B with all ASCII characters converted to uppercase.\n", " | \n", " | zfill(self, width, /)\n", " | Pad a numeric string with zeros on the left, to fill a field of the given width.\n", " | \n", " | The original string is never truncated.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods inherited from builtins.bytes:\n", " | \n", " | fromhex(string, /) from builtins.type\n", " | Create a bytes object from a string of hexadecimal numbers.\n", " | \n", " | Spaces between two numbers are accepted.\n", " | Example: bytes.fromhex('B9 01EF') -> b'\\\\xb9\\\\x01\\\\xef'.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods inherited from builtins.bytes:\n", " | \n", " | maketrans(frm, to, /)\n", " | Return a translation table useable for the bytes or bytearray translate method.\n", " | \n", " | The returned table will be one where each byte in frm is mapped to the byte at\n", " | the same position in to.\n", " | \n", " | The bytes objects frm and to must be of the same length.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " cdouble = class complex128(complexfloating, builtins.complex)\n", " | cdouble(real=0, imag=0)\n", " | \n", " | Complex number type composed of two double-precision floating-point\n", " | numbers, compatible with Python `complex`.\n", " | \n", " | :Character code: ``'D'``\n", " | :Canonical name: `numpy.cdouble`\n", " | :Alias: `numpy.cfloat`\n", " | :Alias: `numpy.complex_`\n", " | :Alias on this platform (win32 AMD64): `numpy.complex128`: Complex number type composed of 2 64-bit-precision floating-point numbers.\n", " | \n", " | Method resolution order:\n", " | complex128\n", " | complexfloating\n", " | inexact\n", " | number\n", " | generic\n", " | builtins.complex\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from complexfloating:\n", " | \n", " | __round__(...)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from builtins.complex:\n", " | \n", " | __complex__(self, /)\n", " | Convert this value to exact type complex.\n", " | \n", " | __getattribute__(self, name, /)\n", " | Return getattr(self, name).\n", " | \n", " | __getnewargs__(self, /)\n", " \n", " cfloat = class complex128(complexfloating, builtins.complex)\n", " | cfloat(real=0, imag=0)\n", " | \n", " | Complex number type composed of two double-precision floating-point\n", " | numbers, compatible with Python `complex`.\n", " | \n", " | :Character code: ``'D'``\n", " | :Canonical name: `numpy.cdouble`\n", " | :Alias: `numpy.cfloat`\n", " | :Alias: `numpy.complex_`\n", " | :Alias on this platform (win32 AMD64): `numpy.complex128`: Complex number type composed of 2 64-bit-precision floating-point numbers.\n", " | \n", " | Method resolution order:\n", " | complex128\n", " | complexfloating\n", " | inexact\n", " | number\n", " | generic\n", " | builtins.complex\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from complexfloating:\n", " | \n", " | __round__(...)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from builtins.complex:\n", " | \n", " | __complex__(self, /)\n", " | Convert this value to exact type complex.\n", " | \n", " | __getattribute__(self, name, /)\n", " | Return getattr(self, name).\n", " | \n", " | __getnewargs__(self, /)\n", " \n", " class character(flexible)\n", " | Abstract base class of all character string scalar types.\n", " | \n", " | Method resolution order:\n", " | character\n", " | flexible\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods inherited from generic:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data and other attributes inherited from generic:\n", " | \n", " | __hash__ = None\n", " \n", " class chararray(ndarray)\n", " | chararray(shape, itemsize=1, unicode=False, buffer=None, offset=0, strides=None, order='C')\n", " | \n", " | chararray(shape, itemsize=1, unicode=False, buffer=None, offset=0,\n", " | strides=None, order=None)\n", " | \n", " | Provides a convenient view on arrays of string and unicode values.\n", " | \n", " | .. note::\n", " | The `chararray` class exists for backwards compatibility with\n", " | Numarray, it is not recommended for new development. Starting from numpy\n", " | 1.4, if one needs arrays of strings, it is recommended to use arrays of\n", " | `dtype` `object_`, `string_` or `unicode_`, and use the free functions\n", " | in the `numpy.char` module for fast vectorized string operations.\n", " | \n", " | Versus a regular NumPy array of type `str` or `unicode`, this\n", " | class adds the following functionality:\n", " | \n", " | 1) values automatically have whitespace removed from the end\n", " | when indexed\n", " | \n", " | 2) comparison operators automatically remove whitespace from the\n", " | end when comparing values\n", " | \n", " | 3) vectorized string operations are provided as methods\n", " | (e.g. `.endswith`) and infix operators (e.g. ``\"+\", \"*\", \"%\"``)\n", " | \n", " | chararrays should be created using `numpy.char.array` or\n", " | `numpy.char.asarray`, rather than this constructor directly.\n", " | \n", " | This constructor creates the array, using `buffer` (with `offset`\n", " | and `strides`) if it is not ``None``. If `buffer` is ``None``, then\n", " | constructs a new array with `strides` in \"C order\", unless both\n", " | ``len(shape) >= 2`` and ``order='F'``, in which case `strides`\n", " | is in \"Fortran order\".\n", " | \n", " | Methods\n", " | -------\n", " | astype\n", " | argsort\n", " | copy\n", " | count\n", " | decode\n", " | dump\n", " | dumps\n", " | encode\n", " | endswith\n", " | expandtabs\n", " | fill\n", " | find\n", " | flatten\n", " | getfield\n", " | index\n", " | isalnum\n", " | isalpha\n", " | isdecimal\n", " | isdigit\n", " | islower\n", " | isnumeric\n", " | isspace\n", " | istitle\n", " | isupper\n", " | item\n", " | join\n", " | ljust\n", " | lower\n", " | lstrip\n", " | nonzero\n", " | put\n", " | ravel\n", " | repeat\n", " | replace\n", " | reshape\n", " | resize\n", " | rfind\n", " | rindex\n", " | rjust\n", " | rsplit\n", " | rstrip\n", " | searchsorted\n", " | setfield\n", " | setflags\n", " | sort\n", " | split\n", " | splitlines\n", " | squeeze\n", " | startswith\n", " | strip\n", " | swapaxes\n", " | swapcase\n", " | take\n", " | title\n", " | tofile\n", " | tolist\n", " | tostring\n", " | translate\n", " | transpose\n", " | upper\n", " | view\n", " | zfill\n", " | \n", " | Parameters\n", " | ----------\n", " | shape : tuple\n", " | Shape of the array.\n", " | itemsize : int, optional\n", " | Length of each array element, in number of characters. Default is 1.\n", " | unicode : bool, optional\n", " | Are the array elements of type unicode (True) or string (False).\n", " | Default is False.\n", " | buffer : object exposing the buffer interface or str, optional\n", " | Memory address of the start of the array data. Default is None,\n", " | in which case a new array is created.\n", " | offset : int, optional\n", " | Fixed stride displacement from the beginning of an axis?\n", " | Default is 0. Needs to be >=0.\n", " | strides : array_like of ints, optional\n", " | Strides for the array (see `ndarray.strides` for full description).\n", " | Default is None.\n", " | order : {'C', 'F'}, optional\n", " | The order in which the array data is stored in memory: 'C' ->\n", " | \"row major\" order (the default), 'F' -> \"column major\"\n", " | (Fortran) order.\n", " | \n", " | Examples\n", " | --------\n", " | >>> charar = np.chararray((3, 3))\n", " | >>> charar[:] = 'a'\n", " | >>> charar\n", " | chararray([[b'a', b'a', b'a'],\n", " | [b'a', b'a', b'a'],\n", " | [b'a', b'a', b'a']], dtype='|S1')\n", " | \n", " | >>> charar = np.chararray(charar.shape, itemsize=5)\n", " | >>> charar[:] = 'abc'\n", " | >>> charar\n", " | chararray([[b'abc', b'abc', b'abc'],\n", " | [b'abc', b'abc', b'abc'],\n", " | [b'abc', b'abc', b'abc']], dtype='|S5')\n", " | \n", " | Method resolution order:\n", " | chararray\n", " | ndarray\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __add__(self, other)\n", " | Return (self + other), that is string concatenation,\n", " | element-wise for a pair of array_likes of str or unicode.\n", " | \n", " | See Also\n", " | --------\n", " | add\n", " | \n", " | __array_finalize__(self, obj)\n", " | a.__array_finalize__(obj, /)\n", " | \n", " | Present so subclasses can call super. Does nothing.\n", " | \n", " | __eq__(self, other)\n", " | Return (self == other) element-wise.\n", " | \n", " | See Also\n", " | --------\n", " | equal\n", " | \n", " | __ge__(self, other)\n", " | Return (self >= other) element-wise.\n", " | \n", " | See Also\n", " | --------\n", " | greater_equal\n", " | \n", " | __getitem__(self, obj)\n", " | Return self[key].\n", " | \n", " | __gt__(self, other)\n", " | Return (self > other) element-wise.\n", " | \n", " | See Also\n", " | --------\n", " | greater\n", " | \n", " | __le__(self, other)\n", " | Return (self <= other) element-wise.\n", " | \n", " | See Also\n", " | --------\n", " | less_equal\n", " | \n", " | __lt__(self, other)\n", " | Return (self < other) element-wise.\n", " | \n", " | See Also\n", " | --------\n", " | less\n", " | \n", " | __mod__(self, i)\n", " | Return (self % i), that is pre-Python 2.6 string formatting\n", " | (interpolation), element-wise for a pair of array_likes of `string_`\n", " | or `unicode_`.\n", " | \n", " | See Also\n", " | --------\n", " | mod\n", " | \n", " | __mul__(self, i)\n", " | Return (self * i), that is string multiple concatenation,\n", " | element-wise.\n", " | \n", " | See Also\n", " | --------\n", " | multiply\n", " | \n", " | __ne__(self, other)\n", " | Return (self != other) element-wise.\n", " | \n", " | See Also\n", " | --------\n", " | not_equal\n", " | \n", " | __radd__(self, other)\n", " | Return (other + self), that is string concatenation,\n", " | element-wise for a pair of array_likes of `string_` or `unicode_`.\n", " | \n", " | See Also\n", " | --------\n", " | add\n", " | \n", " | __rmod__(self, other)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, i)\n", " | Return (self * i), that is string multiple concatenation,\n", " | element-wise.\n", " | \n", " | See Also\n", " | --------\n", " | multiply\n", " | \n", " | argsort(self, axis=-1, kind=None, order=None)\n", " | a.argsort(axis=-1, kind=None, order=None)\n", " | \n", " | Returns the indices that would sort this array.\n", " | \n", " | Refer to `numpy.argsort` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.argsort : equivalent function\n", " | \n", " | capitalize(self)\n", " | Return a copy of `self` with only the first character of each element\n", " | capitalized.\n", " | \n", " | See Also\n", " | --------\n", " | char.capitalize\n", " | \n", " | center(self, width, fillchar=' ')\n", " | Return a copy of `self` with its elements centered in a\n", " | string of length `width`.\n", " | \n", " | See Also\n", " | --------\n", " | center\n", " | \n", " | count(self, sub, start=0, end=None)\n", " | Returns an array with the number of non-overlapping occurrences of\n", " | substring `sub` in the range [`start`, `end`].\n", " | \n", " | See Also\n", " | --------\n", " | char.count\n", " | \n", " | decode(self, encoding=None, errors=None)\n", " | Calls ``bytes.decode`` element-wise.\n", " | \n", " | See Also\n", " | --------\n", " | char.decode\n", " | \n", " | encode(self, encoding=None, errors=None)\n", " | Calls `str.encode` element-wise.\n", " | \n", " | See Also\n", " | --------\n", " | char.encode\n", " | \n", " | endswith(self, suffix, start=0, end=None)\n", " | Returns a boolean array which is `True` where the string element\n", " | in `self` ends with `suffix`, otherwise `False`.\n", " | \n", " | See Also\n", " | --------\n", " | char.endswith\n", " | \n", " | expandtabs(self, tabsize=8)\n", " | Return a copy of each string element where all tab characters are\n", " | replaced by one or more spaces.\n", " | \n", " | See Also\n", " | --------\n", " | char.expandtabs\n", " | \n", " | find(self, sub, start=0, end=None)\n", " | For each element, return the lowest index in the string where\n", " | substring `sub` is found.\n", " | \n", " | See Also\n", " | --------\n", " | char.find\n", " | \n", " | index(self, sub, start=0, end=None)\n", " | Like `find`, but raises `ValueError` when the substring is not found.\n", " | \n", " | See Also\n", " | --------\n", " | char.index\n", " | \n", " | isalnum(self)\n", " | Returns true for each element if all characters in the string\n", " | are alphanumeric and there is at least one character, false\n", " | otherwise.\n", " | \n", " | See Also\n", " | --------\n", " | char.isalnum\n", " | \n", " | isalpha(self)\n", " | Returns true for each element if all characters in the string\n", " | are alphabetic and there is at least one character, false\n", " | otherwise.\n", " | \n", " | See Also\n", " | --------\n", " | char.isalpha\n", " | \n", " | isdecimal(self)\n", " | For each element in `self`, return True if there are only\n", " | decimal characters in the element.\n", " | \n", " | See Also\n", " | --------\n", " | char.isdecimal\n", " | \n", " | isdigit(self)\n", " | Returns true for each element if all characters in the string are\n", " | digits and there is at least one character, false otherwise.\n", " | \n", " | See Also\n", " | --------\n", " | char.isdigit\n", " | \n", " | islower(self)\n", " | Returns true for each element if all cased characters in the\n", " | string are lowercase and there is at least one cased character,\n", " | false otherwise.\n", " | \n", " | See Also\n", " | --------\n", " | char.islower\n", " | \n", " | isnumeric(self)\n", " | For each element in `self`, return True if there are only\n", " | numeric characters in the element.\n", " | \n", " | See Also\n", " | --------\n", " | char.isnumeric\n", " | \n", " | isspace(self)\n", " | Returns true for each element if there are only whitespace\n", " | characters in the string and there is at least one character,\n", " | false otherwise.\n", " | \n", " | See Also\n", " | --------\n", " | char.isspace\n", " | \n", " | istitle(self)\n", " | Returns true for each element if the element is a titlecased\n", " | string and there is at least one character, false otherwise.\n", " | \n", " | See Also\n", " | --------\n", " | char.istitle\n", " | \n", " | isupper(self)\n", " | Returns true for each element if all cased characters in the\n", " | string are uppercase and there is at least one character, false\n", " | otherwise.\n", " | \n", " | See Also\n", " | --------\n", " | char.isupper\n", " | \n", " | join(self, seq)\n", " | Return a string which is the concatenation of the strings in the\n", " | sequence `seq`.\n", " | \n", " | See Also\n", " | --------\n", " | char.join\n", " | \n", " | ljust(self, width, fillchar=' ')\n", " | Return an array with the elements of `self` left-justified in a\n", " | string of length `width`.\n", " | \n", " | See Also\n", " | --------\n", " | char.ljust\n", " | \n", " | lower(self)\n", " | Return an array with the elements of `self` converted to\n", " | lowercase.\n", " | \n", " | See Also\n", " | --------\n", " | char.lower\n", " | \n", " | lstrip(self, chars=None)\n", " | For each element in `self`, return a copy with the leading characters\n", " | removed.\n", " | \n", " | See Also\n", " | --------\n", " | char.lstrip\n", " | \n", " | partition(self, sep)\n", " | Partition each element in `self` around `sep`.\n", " | \n", " | See Also\n", " | --------\n", " | partition\n", " | \n", " | replace(self, old, new, count=None)\n", " | For each element in `self`, return a copy of the string with all\n", " | occurrences of substring `old` replaced by `new`.\n", " | \n", " | See Also\n", " | --------\n", " | char.replace\n", " | \n", " | rfind(self, sub, start=0, end=None)\n", " | For each element in `self`, return the highest index in the string\n", " | where substring `sub` is found, such that `sub` is contained\n", " | within [`start`, `end`].\n", " | \n", " | See Also\n", " | --------\n", " | char.rfind\n", " | \n", " | rindex(self, sub, start=0, end=None)\n", " | Like `rfind`, but raises `ValueError` when the substring `sub` is\n", " | not found.\n", " | \n", " | See Also\n", " | --------\n", " | char.rindex\n", " | \n", " | rjust(self, width, fillchar=' ')\n", " | Return an array with the elements of `self`\n", " | right-justified in a string of length `width`.\n", " | \n", " | See Also\n", " | --------\n", " | char.rjust\n", " | \n", " | rpartition(self, sep)\n", " | Partition each element in `self` around `sep`.\n", " | \n", " | See Also\n", " | --------\n", " | rpartition\n", " | \n", " | rsplit(self, sep=None, maxsplit=None)\n", " | For each element in `self`, return a list of the words in\n", " | the string, using `sep` as the delimiter string.\n", " | \n", " | See Also\n", " | --------\n", " | char.rsplit\n", " | \n", " | rstrip(self, chars=None)\n", " | For each element in `self`, return a copy with the trailing\n", " | characters removed.\n", " | \n", " | See Also\n", " | --------\n", " | char.rstrip\n", " | \n", " | split(self, sep=None, maxsplit=None)\n", " | For each element in `self`, return a list of the words in the\n", " | string, using `sep` as the delimiter string.\n", " | \n", " | See Also\n", " | --------\n", " | char.split\n", " | \n", " | splitlines(self, keepends=None)\n", " | For each element in `self`, return a list of the lines in the\n", " | element, breaking at line boundaries.\n", " | \n", " | See Also\n", " | --------\n", " | char.splitlines\n", " | \n", " | startswith(self, prefix, start=0, end=None)\n", " | Returns a boolean array which is `True` where the string element\n", " | in `self` starts with `prefix`, otherwise `False`.\n", " | \n", " | See Also\n", " | --------\n", " | char.startswith\n", " | \n", " | strip(self, chars=None)\n", " | For each element in `self`, return a copy with the leading and\n", " | trailing characters removed.\n", " | \n", " | See Also\n", " | --------\n", " | char.strip\n", " | \n", " | swapcase(self)\n", " | For each element in `self`, return a copy of the string with\n", " | uppercase characters converted to lowercase and vice versa.\n", " | \n", " | See Also\n", " | --------\n", " | char.swapcase\n", " | \n", " | title(self)\n", " | For each element in `self`, return a titlecased version of the\n", " | string: words start with uppercase characters, all remaining cased\n", " | characters are lowercase.\n", " | \n", " | See Also\n", " | --------\n", " | char.title\n", " | \n", " | translate(self, table, deletechars=None)\n", " | For each element in `self`, return a copy of the string where\n", " | all characters occurring in the optional argument\n", " | `deletechars` are removed, and the remaining characters have\n", " | been mapped through the given translation table.\n", " | \n", " | See Also\n", " | --------\n", " | char.translate\n", " | \n", " | upper(self)\n", " | Return an array with the elements of `self` converted to\n", " | uppercase.\n", " | \n", " | See Also\n", " | --------\n", " | char.upper\n", " | \n", " | zfill(self, width)\n", " | Return the numeric string left-filled with zeros in a string of\n", " | length `width`.\n", " | \n", " | See Also\n", " | --------\n", " | char.zfill\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(subtype, shape, itemsize=1, unicode=False, buffer=None, offset=0, strides=None, order='C')\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors defined here:\n", " | \n", " | __dict__\n", " | dictionary for instance variables (if defined)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data and other attributes defined here:\n", " | \n", " | __hash__ = None\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from ndarray:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | a.__array__([dtype], /) -> reference if type unchanged, copy otherwise.\n", " | \n", " | Returns either a new reference to self if dtype is not given or a new array\n", " | of provided data type if dtype is different from the current dtype of the\n", " | array.\n", " | \n", " | __array_function__(...)\n", " | \n", " | __array_prepare__(...)\n", " | a.__array_prepare__(array[, context], /)\n", " | \n", " | Returns a view of `array` with the same type as self.\n", " | \n", " | __array_ufunc__(...)\n", " | \n", " | __array_wrap__(...)\n", " | a.__array_wrap__(array[, context], /)\n", " | \n", " | Returns a view of `array` with the same type as self.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __complex__(...)\n", " | \n", " | __contains__(self, key, /)\n", " | Return key in self.\n", " | \n", " | __copy__(...)\n", " | a.__copy__()\n", " | \n", " | Used if :func:`copy.copy` is called on an array. Returns a copy of the array.\n", " | \n", " | Equivalent to ``a.copy(order='K')``.\n", " | \n", " | __deepcopy__(...)\n", " | a.__deepcopy__(memo, /) -> Deep copy of array.\n", " | \n", " | Used if :func:`copy.deepcopy` is called on an array.\n", " | \n", " | __delitem__(self, key, /)\n", " | Delete self[key].\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __dlpack__(...)\n", " | a.__dlpack__(*, stream=None)\n", " | \n", " | DLPack Protocol: Part of the Array API.\n", " | \n", " | __dlpack_device__(...)\n", " | a.__dlpack_device__()\n", " | \n", " | DLPack Protocol: Part of the Array API.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __format__(...)\n", " | Default object formatter.\n", " | \n", " | __iadd__(self, value, /)\n", " | Return self+=value.\n", " | \n", " | __iand__(self, value, /)\n", " | Return self&=value.\n", " | \n", " | __ifloordiv__(self, value, /)\n", " | Return self//=value.\n", " | \n", " | __ilshift__(self, value, /)\n", " | Return self<<=value.\n", " | \n", " | __imatmul__(self, value, /)\n", " | Return self@=value.\n", " | \n", " | __imod__(self, value, /)\n", " | Return self%=value.\n", " | \n", " | __imul__(self, value, /)\n", " | Return self*=value.\n", " | \n", " | __index__(self, /)\n", " | Return self converted to an integer, if self is suitable for use as an index into a list.\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __ior__(self, value, /)\n", " | Return self|=value.\n", " | \n", " | __ipow__(self, value, /)\n", " | Return self**=value.\n", " | \n", " | __irshift__(self, value, /)\n", " | Return self>>=value.\n", " | \n", " | __isub__(self, value, /)\n", " | Return self-=value.\n", " | \n", " | __iter__(self, /)\n", " | Implement iter(self).\n", " | \n", " | __itruediv__(self, value, /)\n", " | Return self/=value.\n", " | \n", " | __ixor__(self, value, /)\n", " | Return self^=value.\n", " | \n", " | __len__(self, /)\n", " | Return len(self).\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __matmul__(self, value, /)\n", " | Return self@value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __reduce__(...)\n", " | a.__reduce__()\n", " | \n", " | For pickling.\n", " | \n", " | __reduce_ex__(...)\n", " | Helper for pickle.\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmatmul__(self, value, /)\n", " | Return value@self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setitem__(self, key, value, /)\n", " | Set self[key] to value.\n", " | \n", " | __setstate__(...)\n", " | a.__setstate__(state, /)\n", " | \n", " | For unpickling.\n", " | \n", " | The `state` argument must be a sequence that contains the following\n", " | elements:\n", " | \n", " | Parameters\n", " | ----------\n", " | version : int\n", " | optional pickle version. If omitted defaults to 0.\n", " | shape : tuple\n", " | dtype : data-type\n", " | isFortran : bool\n", " | rawdata : string or list\n", " | a binary string with the data (or a list if 'a' is an object array)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | a.all(axis=None, out=None, keepdims=False, *, where=True)\n", " | \n", " | Returns True if all elements evaluate to True.\n", " | \n", " | Refer to `numpy.all` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.all : equivalent function\n", " | \n", " | any(...)\n", " | a.any(axis=None, out=None, keepdims=False, *, where=True)\n", " | \n", " | Returns True if any of the elements of `a` evaluate to True.\n", " | \n", " | Refer to `numpy.any` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.any : equivalent function\n", " | \n", " | argmax(...)\n", " | a.argmax(axis=None, out=None, *, keepdims=False)\n", " | \n", " | Return indices of the maximum values along the given axis.\n", " | \n", " | Refer to `numpy.argmax` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.argmax : equivalent function\n", " | \n", " | argmin(...)\n", " | a.argmin(axis=None, out=None, *, keepdims=False)\n", " | \n", " | Return indices of the minimum values along the given axis.\n", " | \n", " | Refer to `numpy.argmin` for detailed documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.argmin : equivalent function\n", " | \n", " | argpartition(...)\n", " | a.argpartition(kth, axis=-1, kind='introselect', order=None)\n", " | \n", " | Returns the indices that would partition this array.\n", " | \n", " | Refer to `numpy.argpartition` for full documentation.\n", " | \n", " | .. versionadded:: 1.8.0\n", " | \n", " | See Also\n", " | --------\n", " | numpy.argpartition : equivalent function\n", " | \n", " | astype(...)\n", " | a.astype(dtype, order='K', casting='unsafe', subok=True, copy=True)\n", " | \n", " | Copy of the array, cast to a specified type.\n", " | \n", " | Parameters\n", " | ----------\n", " | dtype : str or dtype\n", " | Typecode or data-type to which the array is cast.\n", " | order : {'C', 'F', 'A', 'K'}, optional\n", " | Controls the memory layout order of the result.\n", " | 'C' means C order, 'F' means Fortran order, 'A'\n", " | means 'F' order if all the arrays are Fortran contiguous,\n", " | 'C' order otherwise, and 'K' means as close to the\n", " | order the array elements appear in memory as possible.\n", " | Default is 'K'.\n", " | casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional\n", " | Controls what kind of data casting may occur. Defaults to 'unsafe'\n", " | for backwards compatibility.\n", " | \n", " | * 'no' means the data types should not be cast at all.\n", " | * 'equiv' means only byte-order changes are allowed.\n", " | * 'safe' means only casts which can preserve values are allowed.\n", " | * 'same_kind' means only safe casts or casts within a kind,\n", " | like float64 to float32, are allowed.\n", " | * 'unsafe' means any data conversions may be done.\n", " | subok : bool, optional\n", " | If True, then sub-classes will be passed-through (default), otherwise\n", " | the returned array will be forced to be a base-class array.\n", " | copy : bool, optional\n", " | By default, astype always returns a newly allocated array. If this\n", " | is set to false, and the `dtype`, `order`, and `subok`\n", " | requirements are satisfied, the input array is returned instead\n", " | of a copy.\n", " | \n", " | Returns\n", " | -------\n", " | arr_t : ndarray\n", " | Unless `copy` is False and the other conditions for returning the input\n", " | array are satisfied (see description for `copy` input parameter), `arr_t`\n", " | is a new array of the same shape as the input array, with dtype, order\n", " | given by `dtype`, `order`.\n", " | \n", " | Notes\n", " | -----\n", " | .. versionchanged:: 1.17.0\n", " | Casting between a simple data type and a structured one is possible only\n", " | for \"unsafe\" casting. Casting to multiple fields is allowed, but\n", " | casting from multiple fields is not.\n", " | \n", " | .. versionchanged:: 1.9.0\n", " | Casting from numeric to string types in 'safe' casting mode requires\n", " | that the string dtype length is long enough to store the max\n", " | integer/float value converted.\n", " | \n", " | Raises\n", " | ------\n", " | ComplexWarning\n", " | When casting from complex to float or int. To avoid this,\n", " | one should use ``a.real.astype(t)``.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([1, 2, 2.5])\n", " | >>> x\n", " | array([1. , 2. , 2.5])\n", " | \n", " | >>> x.astype(int)\n", " | array([1, 2, 2])\n", " | \n", " | byteswap(...)\n", " | a.byteswap(inplace=False)\n", " | \n", " | Swap the bytes of the array elements\n", " | \n", " | Toggle between low-endian and big-endian data representation by\n", " | returning a byteswapped array, optionally swapped in-place.\n", " | Arrays of byte-strings are not swapped. The real and imaginary\n", " | parts of a complex number are swapped individually.\n", " | \n", " | Parameters\n", " | ----------\n", " | inplace : bool, optional\n", " | If ``True``, swap bytes in-place, default is ``False``.\n", " | \n", " | Returns\n", " | -------\n", " | out : ndarray\n", " | The byteswapped array. If `inplace` is ``True``, this is\n", " | a view to self.\n", " | \n", " | Examples\n", " | --------\n", " | >>> A = np.array([1, 256, 8755], dtype=np.int16)\n", " | >>> list(map(hex, A))\n", " | ['0x1', '0x100', '0x2233']\n", " | >>> A.byteswap(inplace=True)\n", " | array([ 256, 1, 13090], dtype=int16)\n", " | >>> list(map(hex, A))\n", " | ['0x100', '0x1', '0x3322']\n", " | \n", " | Arrays of byte-strings are not swapped\n", " | \n", " | >>> A = np.array([b'ceg', b'fac'])\n", " | >>> A.byteswap()\n", " | array([b'ceg', b'fac'], dtype='|S3')\n", " | \n", " | ``A.newbyteorder().byteswap()`` produces an array with the same values\n", " | but different representation in memory\n", " | \n", " | >>> A = np.array([1, 2, 3])\n", " | >>> A.view(np.uint8)\n", " | array([1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0,\n", " | 0, 0], dtype=uint8)\n", " | >>> A.newbyteorder().byteswap(inplace=True)\n", " | array([1, 2, 3])\n", " | >>> A.view(np.uint8)\n", " | array([0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0,\n", " | 0, 3], dtype=uint8)\n", " | \n", " | choose(...)\n", " | a.choose(choices, out=None, mode='raise')\n", " | \n", " | Use an index array to construct a new array from a set of choices.\n", " | \n", " | Refer to `numpy.choose` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.choose : equivalent function\n", " | \n", " | clip(...)\n", " | a.clip(min=None, max=None, out=None, **kwargs)\n", " | \n", " | Return an array whose values are limited to ``[min, max]``.\n", " | One of max or min must be given.\n", " | \n", " | Refer to `numpy.clip` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.clip : equivalent function\n", " | \n", " | compress(...)\n", " | a.compress(condition, axis=None, out=None)\n", " | \n", " | Return selected slices of this array along given axis.\n", " | \n", " | Refer to `numpy.compress` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.compress : equivalent function\n", " | \n", " | conj(...)\n", " | a.conj()\n", " | \n", " | Complex-conjugate all elements.\n", " | \n", " | Refer to `numpy.conjugate` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.conjugate : equivalent function\n", " | \n", " | conjugate(...)\n", " | a.conjugate()\n", " | \n", " | Return the complex conjugate, element-wise.\n", " | \n", " | Refer to `numpy.conjugate` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.conjugate : equivalent function\n", " | \n", " | copy(...)\n", " | a.copy(order='C')\n", " | \n", " | Return a copy of the array.\n", " | \n", " | Parameters\n", " | ----------\n", " | order : {'C', 'F', 'A', 'K'}, optional\n", " | Controls the memory layout of the copy. 'C' means C-order,\n", " | 'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous,\n", " | 'C' otherwise. 'K' means match the layout of `a` as closely\n", " | as possible. (Note that this function and :func:`numpy.copy` are very\n", " | similar but have different default values for their order=\n", " | arguments, and this function always passes sub-classes through.)\n", " | \n", " | See also\n", " | --------\n", " | numpy.copy : Similar function with different default behavior\n", " | numpy.copyto\n", " | \n", " | Notes\n", " | -----\n", " | This function is the preferred method for creating an array copy. The\n", " | function :func:`numpy.copy` is similar, but it defaults to using order 'K',\n", " | and will not pass sub-classes through by default.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([[1,2,3],[4,5,6]], order='F')\n", " | \n", " | >>> y = x.copy()\n", " | \n", " | >>> x.fill(0)\n", " | \n", " | >>> x\n", " | array([[0, 0, 0],\n", " | [0, 0, 0]])\n", " | \n", " | >>> y\n", " | array([[1, 2, 3],\n", " | [4, 5, 6]])\n", " | \n", " | >>> y.flags['C_CONTIGUOUS']\n", " | True\n", " | \n", " | cumprod(...)\n", " | a.cumprod(axis=None, dtype=None, out=None)\n", " | \n", " | Return the cumulative product of the elements along the given axis.\n", " | \n", " | Refer to `numpy.cumprod` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.cumprod : equivalent function\n", " | \n", " | cumsum(...)\n", " | a.cumsum(axis=None, dtype=None, out=None)\n", " | \n", " | Return the cumulative sum of the elements along the given axis.\n", " | \n", " | Refer to `numpy.cumsum` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.cumsum : equivalent function\n", " | \n", " | diagonal(...)\n", " | a.diagonal(offset=0, axis1=0, axis2=1)\n", " | \n", " | Return specified diagonals. In NumPy 1.9 the returned array is a\n", " | read-only view instead of a copy as in previous NumPy versions. In\n", " | a future version the read-only restriction will be removed.\n", " | \n", " | Refer to :func:`numpy.diagonal` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.diagonal : equivalent function\n", " | \n", " | dot(...)\n", " | \n", " | dump(...)\n", " | a.dump(file)\n", " | \n", " | Dump a pickle of the array to the specified file.\n", " | The array can be read back with pickle.load or numpy.load.\n", " | \n", " | Parameters\n", " | ----------\n", " | file : str or Path\n", " | A string naming the dump file.\n", " | \n", " | .. versionchanged:: 1.17.0\n", " | `pathlib.Path` objects are now accepted.\n", " | \n", " | dumps(...)\n", " | a.dumps()\n", " | \n", " | Returns the pickle of the array as a string.\n", " | pickle.loads will convert the string back to an array.\n", " | \n", " | Parameters\n", " | ----------\n", " | None\n", " | \n", " | fill(...)\n", " | a.fill(value)\n", " | \n", " | Fill the array with a scalar value.\n", " | \n", " | Parameters\n", " | ----------\n", " | value : scalar\n", " | All elements of `a` will be assigned this value.\n", " | \n", " | Examples\n", " | --------\n", " | >>> a = np.array([1, 2])\n", " | >>> a.fill(0)\n", " | >>> a\n", " | array([0, 0])\n", " | >>> a = np.empty(2)\n", " | >>> a.fill(1)\n", " | >>> a\n", " | array([1., 1.])\n", " | \n", " | Fill expects a scalar value and always behaves the same as assigning\n", " | to a single array element. The following is a rare example where this\n", " | distinction is important:\n", " | \n", " | >>> a = np.array([None, None], dtype=object)\n", " | >>> a[0] = np.array(3)\n", " | >>> a\n", " | array([array(3), None], dtype=object)\n", " | >>> a.fill(np.array(3))\n", " | >>> a\n", " | array([array(3), array(3)], dtype=object)\n", " | \n", " | Where other forms of assignments will unpack the array being assigned:\n", " | \n", " | >>> a[...] = np.array(3)\n", " | >>> a\n", " | array([3, 3], dtype=object)\n", " | \n", " | flatten(...)\n", " | a.flatten(order='C')\n", " | \n", " | Return a copy of the array collapsed into one dimension.\n", " | \n", " | Parameters\n", " | ----------\n", " | order : {'C', 'F', 'A', 'K'}, optional\n", " | 'C' means to flatten in row-major (C-style) order.\n", " | 'F' means to flatten in column-major (Fortran-\n", " | style) order. 'A' means to flatten in column-major\n", " | order if `a` is Fortran *contiguous* in memory,\n", " | row-major order otherwise. 'K' means to flatten\n", " | `a` in the order the elements occur in memory.\n", " | The default is 'C'.\n", " | \n", " | Returns\n", " | -------\n", " | y : ndarray\n", " | A copy of the input array, flattened to one dimension.\n", " | \n", " | See Also\n", " | --------\n", " | ravel : Return a flattened array.\n", " | flat : A 1-D flat iterator over the array.\n", " | \n", " | Examples\n", " | --------\n", " | >>> a = np.array([[1,2], [3,4]])\n", " | >>> a.flatten()\n", " | array([1, 2, 3, 4])\n", " | >>> a.flatten('F')\n", " | array([1, 3, 2, 4])\n", " | \n", " | getfield(...)\n", " | a.getfield(dtype, offset=0)\n", " | \n", " | Returns a field of the given array as a certain type.\n", " | \n", " | A field is a view of the array data with a given data-type. The values in\n", " | the view are determined by the given type and the offset into the current\n", " | array in bytes. The offset needs to be such that the view dtype fits in the\n", " | array dtype; for example an array of dtype complex128 has 16-byte elements.\n", " | If taking a view with a 32-bit integer (4 bytes), the offset needs to be\n", " | between 0 and 12 bytes.\n", " | \n", " | Parameters\n", " | ----------\n", " | dtype : str or dtype\n", " | The data type of the view. The dtype size of the view can not be larger\n", " | than that of the array itself.\n", " | offset : int\n", " | Number of bytes to skip before beginning the element view.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.diag([1.+1.j]*2)\n", " | >>> x[1, 1] = 2 + 4.j\n", " | >>> x\n", " | array([[1.+1.j, 0.+0.j],\n", " | [0.+0.j, 2.+4.j]])\n", " | >>> x.getfield(np.float64)\n", " | array([[1., 0.],\n", " | [0., 2.]])\n", " | \n", " | By choosing an offset of 8 bytes we can select the complex part of the\n", " | array for our view:\n", " | \n", " | >>> x.getfield(np.float64, offset=8)\n", " | array([[1., 0.],\n", " | [0., 4.]])\n", " | \n", " | item(...)\n", " | a.item(*args)\n", " | \n", " | Copy an element of an array to a standard Python scalar and return it.\n", " | \n", " | Parameters\n", " | ----------\n", " | \\*args : Arguments (variable number and type)\n", " | \n", " | * none: in this case, the method only works for arrays\n", " | with one element (`a.size == 1`), which element is\n", " | copied into a standard Python scalar object and returned.\n", " | \n", " | * int_type: this argument is interpreted as a flat index into\n", " | the array, specifying which element to copy and return.\n", " | \n", " | * tuple of int_types: functions as does a single int_type argument,\n", " | except that the argument is interpreted as an nd-index into the\n", " | array.\n", " | \n", " | Returns\n", " | -------\n", " | z : Standard Python scalar object\n", " | A copy of the specified element of the array as a suitable\n", " | Python scalar\n", " | \n", " | Notes\n", " | -----\n", " | When the data type of `a` is longdouble or clongdouble, item() returns\n", " | a scalar array object because there is no available Python scalar that\n", " | would not lose information. Void arrays return a buffer object for item(),\n", " | unless fields are defined, in which case a tuple is returned.\n", " | \n", " | `item` is very similar to a[args], except, instead of an array scalar,\n", " | a standard Python scalar is returned. This can be useful for speeding up\n", " | access to elements of the array and doing arithmetic on elements of the\n", " | array using Python's optimized math.\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.random.seed(123)\n", " | >>> x = np.random.randint(9, size=(3, 3))\n", " | >>> x\n", " | array([[2, 2, 6],\n", " | [1, 3, 6],\n", " | [1, 0, 1]])\n", " | >>> x.item(3)\n", " | 1\n", " | >>> x.item(7)\n", " | 0\n", " | >>> x.item((0, 1))\n", " | 2\n", " | >>> x.item((2, 2))\n", " | 1\n", " | \n", " | itemset(...)\n", " | a.itemset(*args)\n", " | \n", " | Insert scalar into an array (scalar is cast to array's dtype, if possible)\n", " | \n", " | There must be at least 1 argument, and define the last argument\n", " | as *item*. Then, ``a.itemset(*args)`` is equivalent to but faster\n", " | than ``a[args] = item``. The item should be a scalar value and `args`\n", " | must select a single item in the array `a`.\n", " | \n", " | Parameters\n", " | ----------\n", " | \\*args : Arguments\n", " | If one argument: a scalar, only used in case `a` is of size 1.\n", " | If two arguments: the last argument is the value to be set\n", " | and must be a scalar, the first argument specifies a single array\n", " | element location. It is either an int or a tuple.\n", " | \n", " | Notes\n", " | -----\n", " | Compared to indexing syntax, `itemset` provides some speed increase\n", " | for placing a scalar into a particular location in an `ndarray`,\n", " | if you must do this. However, generally this is discouraged:\n", " | among other problems, it complicates the appearance of the code.\n", " | Also, when using `itemset` (and `item`) inside a loop, be sure\n", " | to assign the methods to a local variable to avoid the attribute\n", " | look-up at each loop iteration.\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.random.seed(123)\n", " | >>> x = np.random.randint(9, size=(3, 3))\n", " | >>> x\n", " | array([[2, 2, 6],\n", " | [1, 3, 6],\n", " | [1, 0, 1]])\n", " | >>> x.itemset(4, 0)\n", " | >>> x.itemset((2, 2), 9)\n", " | >>> x\n", " | array([[2, 2, 6],\n", " | [1, 0, 6],\n", " | [1, 0, 9]])\n", " | \n", " | max(...)\n", " | a.max(axis=None, out=None, keepdims=False, initial=<no value>, where=True)\n", " | \n", " | Return the maximum along a given axis.\n", " | \n", " | Refer to `numpy.amax` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.amax : equivalent function\n", " | \n", " | mean(...)\n", " | a.mean(axis=None, dtype=None, out=None, keepdims=False, *, where=True)\n", " | \n", " | Returns the average of the array elements along given axis.\n", " | \n", " | Refer to `numpy.mean` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.mean : equivalent function\n", " | \n", " | min(...)\n", " | a.min(axis=None, out=None, keepdims=False, initial=<no value>, where=True)\n", " | \n", " | Return the minimum along a given axis.\n", " | \n", " | Refer to `numpy.amin` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.amin : equivalent function\n", " | \n", " | newbyteorder(...)\n", " | arr.newbyteorder(new_order='S', /)\n", " | \n", " | Return the array with the same data viewed with a different byte order.\n", " | \n", " | Equivalent to::\n", " | \n", " | arr.view(arr.dtype.newbytorder(new_order))\n", " | \n", " | Changes are also made in all fields and sub-arrays of the array data\n", " | type.\n", " | \n", " | \n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : string, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | below. `new_order` codes can be any of:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order, equivalent to `sys.byteorder`\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_arr : array\n", " | New array object with the dtype reflecting given change to the\n", " | byte order.\n", " | \n", " | nonzero(...)\n", " | a.nonzero()\n", " | \n", " | Return the indices of the elements that are non-zero.\n", " | \n", " | Refer to `numpy.nonzero` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.nonzero : equivalent function\n", " | \n", " | prod(...)\n", " | a.prod(axis=None, dtype=None, out=None, keepdims=False, initial=1, where=True)\n", " | \n", " | Return the product of the array elements over the given axis\n", " | \n", " | Refer to `numpy.prod` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.prod : equivalent function\n", " | \n", " | ptp(...)\n", " | a.ptp(axis=None, out=None, keepdims=False)\n", " | \n", " | Peak to peak (maximum - minimum) value along a given axis.\n", " | \n", " | Refer to `numpy.ptp` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.ptp : equivalent function\n", " | \n", " | put(...)\n", " | a.put(indices, values, mode='raise')\n", " | \n", " | Set ``a.flat[n] = values[n]`` for all `n` in indices.\n", " | \n", " | Refer to `numpy.put` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.put : equivalent function\n", " | \n", " | ravel(...)\n", " | a.ravel([order])\n", " | \n", " | Return a flattened array.\n", " | \n", " | Refer to `numpy.ravel` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.ravel : equivalent function\n", " | \n", " | ndarray.flat : a flat iterator on the array.\n", " | \n", " | repeat(...)\n", " | a.repeat(repeats, axis=None)\n", " | \n", " | Repeat elements of an array.\n", " | \n", " | Refer to `numpy.repeat` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.repeat : equivalent function\n", " | \n", " | reshape(...)\n", " | a.reshape(shape, order='C')\n", " | \n", " | Returns an array containing the same data with a new shape.\n", " | \n", " | Refer to `numpy.reshape` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.reshape : equivalent function\n", " | \n", " | Notes\n", " | -----\n", " | Unlike the free function `numpy.reshape`, this method on `ndarray` allows\n", " | the elements of the shape parameter to be passed in as separate arguments.\n", " | For example, ``a.reshape(10, 11)`` is equivalent to\n", " | ``a.reshape((10, 11))``.\n", " | \n", " | resize(...)\n", " | a.resize(new_shape, refcheck=True)\n", " | \n", " | Change shape and size of array in-place.\n", " | \n", " | Parameters\n", " | ----------\n", " | new_shape : tuple of ints, or `n` ints\n", " | Shape of resized array.\n", " | refcheck : bool, optional\n", " | If False, reference count will not be checked. Default is True.\n", " | \n", " | Returns\n", " | -------\n", " | None\n", " | \n", " | Raises\n", " | ------\n", " | ValueError\n", " | If `a` does not own its own data or references or views to it exist,\n", " | and the data memory must be changed.\n", " | PyPy only: will always raise if the data memory must be changed, since\n", " | there is no reliable way to determine if references or views to it\n", " | exist.\n", " | \n", " | SystemError\n", " | If the `order` keyword argument is specified. This behaviour is a\n", " | bug in NumPy.\n", " | \n", " | See Also\n", " | --------\n", " | resize : Return a new array with the specified shape.\n", " | \n", " | Notes\n", " | -----\n", " | This reallocates space for the data area if necessary.\n", " | \n", " | Only contiguous arrays (data elements consecutive in memory) can be\n", " | resized.\n", " | \n", " | The purpose of the reference count check is to make sure you\n", " | do not use this array as a buffer for another Python object and then\n", " | reallocate the memory. However, reference counts can increase in\n", " | other ways so if you are sure that you have not shared the memory\n", " | for this array with another Python object, then you may safely set\n", " | `refcheck` to False.\n", " | \n", " | Examples\n", " | --------\n", " | Shrinking an array: array is flattened (in the order that the data are\n", " | stored in memory), resized, and reshaped:\n", " | \n", " | >>> a = np.array([[0, 1], [2, 3]], order='C')\n", " | >>> a.resize((2, 1))\n", " | >>> a\n", " | array([[0],\n", " | [1]])\n", " | \n", " | >>> a = np.array([[0, 1], [2, 3]], order='F')\n", " | >>> a.resize((2, 1))\n", " | >>> a\n", " | array([[0],\n", " | [2]])\n", " | \n", " | Enlarging an array: as above, but missing entries are filled with zeros:\n", " | \n", " | >>> b = np.array([[0, 1], [2, 3]])\n", " | >>> b.resize(2, 3) # new_shape parameter doesn't have to be a tuple\n", " | >>> b\n", " | array([[0, 1, 2],\n", " | [3, 0, 0]])\n", " | \n", " | Referencing an array prevents resizing...\n", " | \n", " | >>> c = a\n", " | >>> a.resize((1, 1))\n", " | Traceback (most recent call last):\n", " | ...\n", " | ValueError: cannot resize an array that references or is referenced ...\n", " | \n", " | Unless `refcheck` is False:\n", " | \n", " | >>> a.resize((1, 1), refcheck=False)\n", " | >>> a\n", " | array([[0]])\n", " | >>> c\n", " | array([[0]])\n", " | \n", " | round(...)\n", " | a.round(decimals=0, out=None)\n", " | \n", " | Return `a` with each element rounded to the given number of decimals.\n", " | \n", " | Refer to `numpy.around` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.around : equivalent function\n", " | \n", " | searchsorted(...)\n", " | a.searchsorted(v, side='left', sorter=None)\n", " | \n", " | Find indices where elements of v should be inserted in a to maintain order.\n", " | \n", " | For full documentation, see `numpy.searchsorted`\n", " | \n", " | See Also\n", " | --------\n", " | numpy.searchsorted : equivalent function\n", " | \n", " | setfield(...)\n", " | a.setfield(val, dtype, offset=0)\n", " | \n", " | Put a value into a specified place in a field defined by a data-type.\n", " | \n", " | Place `val` into `a`'s field defined by `dtype` and beginning `offset`\n", " | bytes into the field.\n", " | \n", " | Parameters\n", " | ----------\n", " | val : object\n", " | Value to be placed in field.\n", " | dtype : dtype object\n", " | Data-type of the field in which to place `val`.\n", " | offset : int, optional\n", " | The number of bytes into the field at which to place `val`.\n", " | \n", " | Returns\n", " | -------\n", " | None\n", " | \n", " | See Also\n", " | --------\n", " | getfield\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.eye(3)\n", " | >>> x.getfield(np.float64)\n", " | array([[1., 0., 0.],\n", " | [0., 1., 0.],\n", " | [0., 0., 1.]])\n", " | >>> x.setfield(3, np.int32)\n", " | >>> x.getfield(np.int32)\n", " | array([[3, 3, 3],\n", " | [3, 3, 3],\n", " | [3, 3, 3]], dtype=int32)\n", " | >>> x\n", " | array([[1.0e+000, 1.5e-323, 1.5e-323],\n", " | [1.5e-323, 1.0e+000, 1.5e-323],\n", " | [1.5e-323, 1.5e-323, 1.0e+000]])\n", " | >>> x.setfield(np.eye(3), np.int32)\n", " | >>> x\n", " | array([[1., 0., 0.],\n", " | [0., 1., 0.],\n", " | [0., 0., 1.]])\n", " | \n", " | setflags(...)\n", " | a.setflags(write=None, align=None, uic=None)\n", " | \n", " | Set array flags WRITEABLE, ALIGNED, WRITEBACKIFCOPY,\n", " | respectively.\n", " | \n", " | These Boolean-valued flags affect how numpy interprets the memory\n", " | area used by `a` (see Notes below). The ALIGNED flag can only\n", " | be set to True if the data is actually aligned according to the type.\n", " | The WRITEBACKIFCOPY and flag can never be set\n", " | to True. The flag WRITEABLE can only be set to True if the array owns its\n", " | own memory, or the ultimate owner of the memory exposes a writeable buffer\n", " | interface, or is a string. (The exception for string is made so that\n", " | unpickling can be done without copying memory.)\n", " | \n", " | Parameters\n", " | ----------\n", " | write : bool, optional\n", " | Describes whether or not `a` can be written to.\n", " | align : bool, optional\n", " | Describes whether or not `a` is aligned properly for its type.\n", " | uic : bool, optional\n", " | Describes whether or not `a` is a copy of another \"base\" array.\n", " | \n", " | Notes\n", " | -----\n", " | Array flags provide information about how the memory area used\n", " | for the array is to be interpreted. There are 7 Boolean flags\n", " | in use, only four of which can be changed by the user:\n", " | WRITEBACKIFCOPY, WRITEABLE, and ALIGNED.\n", " | \n", " | WRITEABLE (W) the data area can be written to;\n", " | \n", " | ALIGNED (A) the data and strides are aligned appropriately for the hardware\n", " | (as determined by the compiler);\n", " | \n", " | WRITEBACKIFCOPY (X) this array is a copy of some other array (referenced\n", " | by .base). When the C-API function PyArray_ResolveWritebackIfCopy is\n", " | called, the base array will be updated with the contents of this array.\n", " | \n", " | All flags can be accessed using the single (upper case) letter as well\n", " | as the full name.\n", " | \n", " | Examples\n", " | --------\n", " | >>> y = np.array([[3, 1, 7],\n", " | ... [2, 0, 0],\n", " | ... [8, 5, 9]])\n", " | >>> y\n", " | array([[3, 1, 7],\n", " | [2, 0, 0],\n", " | [8, 5, 9]])\n", " | >>> y.flags\n", " | C_CONTIGUOUS : True\n", " | F_CONTIGUOUS : False\n", " | OWNDATA : True\n", " | WRITEABLE : True\n", " | ALIGNED : True\n", " | WRITEBACKIFCOPY : False\n", " | >>> y.setflags(write=0, align=0)\n", " | >>> y.flags\n", " | C_CONTIGUOUS : True\n", " | F_CONTIGUOUS : False\n", " | OWNDATA : True\n", " | WRITEABLE : False\n", " | ALIGNED : False\n", " | WRITEBACKIFCOPY : False\n", " | >>> y.setflags(uic=1)\n", " | Traceback (most recent call last):\n", " | File \"<stdin>\", line 1, in <module>\n", " | ValueError: cannot set WRITEBACKIFCOPY flag to True\n", " | \n", " | sort(...)\n", " | a.sort(axis=-1, kind=None, order=None)\n", " | \n", " | Sort an array in-place. Refer to `numpy.sort` for full documentation.\n", " | \n", " | Parameters\n", " | ----------\n", " | axis : int, optional\n", " | Axis along which to sort. Default is -1, which means sort along the\n", " | last axis.\n", " | kind : {'quicksort', 'mergesort', 'heapsort', 'stable'}, optional\n", " | Sorting algorithm. The default is 'quicksort'. Note that both 'stable'\n", " | and 'mergesort' use timsort under the covers and, in general, the\n", " | actual implementation will vary with datatype. The 'mergesort' option\n", " | is retained for backwards compatibility.\n", " | \n", " | .. versionchanged:: 1.15.0\n", " | The 'stable' option was added.\n", " | \n", " | order : str or list of str, optional\n", " | When `a` is an array with fields defined, this argument specifies\n", " | which fields to compare first, second, etc. A single field can\n", " | be specified as a string, and not all fields need be specified,\n", " | but unspecified fields will still be used, in the order in which\n", " | they come up in the dtype, to break ties.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.sort : Return a sorted copy of an array.\n", " | numpy.argsort : Indirect sort.\n", " | numpy.lexsort : Indirect stable sort on multiple keys.\n", " | numpy.searchsorted : Find elements in sorted array.\n", " | numpy.partition: Partial sort.\n", " | \n", " | Notes\n", " | -----\n", " | See `numpy.sort` for notes on the different sorting algorithms.\n", " | \n", " | Examples\n", " | --------\n", " | >>> a = np.array([[1,4], [3,1]])\n", " | >>> a.sort(axis=1)\n", " | >>> a\n", " | array([[1, 4],\n", " | [1, 3]])\n", " | >>> a.sort(axis=0)\n", " | >>> a\n", " | array([[1, 3],\n", " | [1, 4]])\n", " | \n", " | Use the `order` keyword to specify a field to use when sorting a\n", " | structured array:\n", " | \n", " | >>> a = np.array([('a', 2), ('c', 1)], dtype=[('x', 'S1'), ('y', int)])\n", " | >>> a.sort(order='y')\n", " | >>> a\n", " | array([(b'c', 1), (b'a', 2)],\n", " | dtype=[('x', 'S1'), ('y', '<i8')])\n", " | \n", " | squeeze(...)\n", " | a.squeeze(axis=None)\n", " | \n", " | Remove axes of length one from `a`.\n", " | \n", " | Refer to `numpy.squeeze` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.squeeze : equivalent function\n", " | \n", " | std(...)\n", " | a.std(axis=None, dtype=None, out=None, ddof=0, keepdims=False, *, where=True)\n", " | \n", " | Returns the standard deviation of the array elements along given axis.\n", " | \n", " | Refer to `numpy.std` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.std : equivalent function\n", " | \n", " | sum(...)\n", " | a.sum(axis=None, dtype=None, out=None, keepdims=False, initial=0, where=True)\n", " | \n", " | Return the sum of the array elements over the given axis.\n", " | \n", " | Refer to `numpy.sum` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.sum : equivalent function\n", " | \n", " | swapaxes(...)\n", " | a.swapaxes(axis1, axis2)\n", " | \n", " | Return a view of the array with `axis1` and `axis2` interchanged.\n", " | \n", " | Refer to `numpy.swapaxes` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.swapaxes : equivalent function\n", " | \n", " | take(...)\n", " | a.take(indices, axis=None, out=None, mode='raise')\n", " | \n", " | Return an array formed from the elements of `a` at the given indices.\n", " | \n", " | Refer to `numpy.take` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.take : equivalent function\n", " | \n", " | tobytes(...)\n", " | a.tobytes(order='C')\n", " | \n", " | Construct Python bytes containing the raw data bytes in the array.\n", " | \n", " | Constructs Python bytes showing a copy of the raw contents of\n", " | data memory. The bytes object is produced in C-order by default.\n", " | This behavior is controlled by the ``order`` parameter.\n", " | \n", " | .. versionadded:: 1.9.0\n", " | \n", " | Parameters\n", " | ----------\n", " | order : {'C', 'F', 'A'}, optional\n", " | Controls the memory layout of the bytes object. 'C' means C-order,\n", " | 'F' means F-order, 'A' (short for *Any*) means 'F' if `a` is\n", " | Fortran contiguous, 'C' otherwise. Default is 'C'.\n", " | \n", " | Returns\n", " | -------\n", " | s : bytes\n", " | Python bytes exhibiting a copy of `a`'s raw data.\n", " | \n", " | See also\n", " | --------\n", " | frombuffer\n", " | Inverse of this operation, construct a 1-dimensional array from Python\n", " | bytes.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([[0, 1], [2, 3]], dtype='<u2')\n", " | >>> x.tobytes()\n", " | b'\\x00\\x00\\x01\\x00\\x02\\x00\\x03\\x00'\n", " | >>> x.tobytes('C') == x.tobytes()\n", " | True\n", " | >>> x.tobytes('F')\n", " | b'\\x00\\x00\\x02\\x00\\x01\\x00\\x03\\x00'\n", " | \n", " | tofile(...)\n", " | a.tofile(fid, sep=\"\", format=\"%s\")\n", " | \n", " | Write array to a file as text or binary (default).\n", " | \n", " | Data is always written in 'C' order, independent of the order of `a`.\n", " | The data produced by this method can be recovered using the function\n", " | fromfile().\n", " | \n", " | Parameters\n", " | ----------\n", " | fid : file or str or Path\n", " | An open file object, or a string containing a filename.\n", " | \n", " | .. versionchanged:: 1.17.0\n", " | `pathlib.Path` objects are now accepted.\n", " | \n", " | sep : str\n", " | Separator between array items for text output.\n", " | If \"\" (empty), a binary file is written, equivalent to\n", " | ``file.write(a.tobytes())``.\n", " | format : str\n", " | Format string for text file output.\n", " | Each entry in the array is formatted to text by first converting\n", " | it to the closest Python type, and then using \"format\" % item.\n", " | \n", " | Notes\n", " | -----\n", " | This is a convenience function for quick storage of array data.\n", " | Information on endianness and precision is lost, so this method is not a\n", " | good choice for files intended to archive data or transport data between\n", " | machines with different endianness. Some of these problems can be overcome\n", " | by outputting the data as text files, at the expense of speed and file\n", " | size.\n", " | \n", " | When fid is a file object, array contents are directly written to the\n", " | file, bypassing the file object's ``write`` method. As a result, tofile\n", " | cannot be used with files objects supporting compression (e.g., GzipFile)\n", " | or file-like objects that do not support ``fileno()`` (e.g., BytesIO).\n", " | \n", " | tolist(...)\n", " | a.tolist()\n", " | \n", " | Return the array as an ``a.ndim``-levels deep nested list of Python scalars.\n", " | \n", " | Return a copy of the array data as a (nested) Python list.\n", " | Data items are converted to the nearest compatible builtin Python type, via\n", " | the `~numpy.ndarray.item` function.\n", " | \n", " | If ``a.ndim`` is 0, then since the depth of the nested list is 0, it will\n", " | not be a list at all, but a simple Python scalar.\n", " | \n", " | Parameters\n", " | ----------\n", " | none\n", " | \n", " | Returns\n", " | -------\n", " | y : object, or list of object, or list of list of object, or ...\n", " | The possibly nested list of array elements.\n", " | \n", " | Notes\n", " | -----\n", " | The array may be recreated via ``a = np.array(a.tolist())``, although this\n", " | may sometimes lose precision.\n", " | \n", " | Examples\n", " | --------\n", " | For a 1D array, ``a.tolist()`` is almost the same as ``list(a)``,\n", " | except that ``tolist`` changes numpy scalars to Python scalars:\n", " | \n", " | >>> a = np.uint32([1, 2])\n", " | >>> a_list = list(a)\n", " | >>> a_list\n", " | [1, 2]\n", " | >>> type(a_list[0])\n", " | <class 'numpy.uint32'>\n", " | >>> a_tolist = a.tolist()\n", " | >>> a_tolist\n", " | [1, 2]\n", " | >>> type(a_tolist[0])\n", " | <class 'int'>\n", " | \n", " | Additionally, for a 2D array, ``tolist`` applies recursively:\n", " | \n", " | >>> a = np.array([[1, 2], [3, 4]])\n", " | >>> list(a)\n", " | [array([1, 2]), array([3, 4])]\n", " | >>> a.tolist()\n", " | [[1, 2], [3, 4]]\n", " | \n", " | The base case for this recursion is a 0D array:\n", " | \n", " | >>> a = np.array(1)\n", " | >>> list(a)\n", " | Traceback (most recent call last):\n", " | ...\n", " | TypeError: iteration over a 0-d array\n", " | >>> a.tolist()\n", " | 1\n", " | \n", " | tostring(...)\n", " | a.tostring(order='C')\n", " | \n", " | A compatibility alias for `tobytes`, with exactly the same behavior.\n", " | \n", " | Despite its name, it returns `bytes` not `str`\\ s.\n", " | \n", " | .. deprecated:: 1.19.0\n", " | \n", " | trace(...)\n", " | a.trace(offset=0, axis1=0, axis2=1, dtype=None, out=None)\n", " | \n", " | Return the sum along diagonals of the array.\n", " | \n", " | Refer to `numpy.trace` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.trace : equivalent function\n", " | \n", " | transpose(...)\n", " | a.transpose(*axes)\n", " | \n", " | Returns a view of the array with axes transposed.\n", " | \n", " | Refer to `numpy.transpose` for full documentation.\n", " | \n", " | Parameters\n", " | ----------\n", " | axes : None, tuple of ints, or `n` ints\n", " | \n", " | * None or no argument: reverses the order of the axes.\n", " | \n", " | * tuple of ints: `i` in the `j`-th place in the tuple means that the\n", " | array's `i`-th axis becomes the transposed array's `j`-th axis.\n", " | \n", " | * `n` ints: same as an n-tuple of the same ints (this form is\n", " | intended simply as a \"convenience\" alternative to the tuple form).\n", " | \n", " | Returns\n", " | -------\n", " | p : ndarray\n", " | View of the array with its axes suitably permuted.\n", " | \n", " | See Also\n", " | --------\n", " | transpose : Equivalent function.\n", " | ndarray.T : Array property returning the array transposed.\n", " | ndarray.reshape : Give a new shape to an array without changing its data.\n", " | \n", " | Examples\n", " | --------\n", " | >>> a = np.array([[1, 2], [3, 4]])\n", " | >>> a\n", " | array([[1, 2],\n", " | [3, 4]])\n", " | >>> a.transpose()\n", " | array([[1, 3],\n", " | [2, 4]])\n", " | >>> a.transpose((1, 0))\n", " | array([[1, 3],\n", " | [2, 4]])\n", " | >>> a.transpose(1, 0)\n", " | array([[1, 3],\n", " | [2, 4]])\n", " | \n", " | >>> a = np.array([1, 2, 3, 4])\n", " | >>> a\n", " | array([1, 2, 3, 4])\n", " | >>> a.transpose()\n", " | array([1, 2, 3, 4])\n", " | \n", " | var(...)\n", " | a.var(axis=None, dtype=None, out=None, ddof=0, keepdims=False, *, where=True)\n", " | \n", " | Returns the variance of the array elements, along given axis.\n", " | \n", " | Refer to `numpy.var` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.var : equivalent function\n", " | \n", " | view(...)\n", " | a.view([dtype][, type])\n", " | \n", " | New view of array with the same data.\n", " | \n", " | .. note::\n", " | Passing None for ``dtype`` is different from omitting the parameter,\n", " | since the former invokes ``dtype(None)`` which is an alias for\n", " | ``dtype('float_')``.\n", " | \n", " | Parameters\n", " | ----------\n", " | dtype : data-type or ndarray sub-class, optional\n", " | Data-type descriptor of the returned view, e.g., float32 or int16.\n", " | Omitting it results in the view having the same data-type as `a`.\n", " | This argument can also be specified as an ndarray sub-class, which\n", " | then specifies the type of the returned object (this is equivalent to\n", " | setting the ``type`` parameter).\n", " | type : Python type, optional\n", " | Type of the returned view, e.g., ndarray or matrix. Again, omission\n", " | of the parameter results in type preservation.\n", " | \n", " | Notes\n", " | -----\n", " | ``a.view()`` is used two different ways:\n", " | \n", " | ``a.view(some_dtype)`` or ``a.view(dtype=some_dtype)`` constructs a view\n", " | of the array's memory with a different data-type. This can cause a\n", " | reinterpretation of the bytes of memory.\n", " | \n", " | ``a.view(ndarray_subclass)`` or ``a.view(type=ndarray_subclass)`` just\n", " | returns an instance of `ndarray_subclass` that looks at the same array\n", " | (same shape, dtype, etc.) This does not cause a reinterpretation of the\n", " | memory.\n", " | \n", " | For ``a.view(some_dtype)``, if ``some_dtype`` has a different number of\n", " | bytes per entry than the previous dtype (for example, converting a regular\n", " | array to a structured array), then the last axis of ``a`` must be\n", " | contiguous. This axis will be resized in the result.\n", " | \n", " | .. versionchanged:: 1.23.0\n", " | Only the last axis needs to be contiguous. Previously, the entire array\n", " | had to be C-contiguous.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([(1, 2)], dtype=[('a', np.int8), ('b', np.int8)])\n", " | \n", " | Viewing array data using a different type and dtype:\n", " | \n", " | >>> y = x.view(dtype=np.int16, type=np.matrix)\n", " | >>> y\n", " | matrix([[513]], dtype=int16)\n", " | >>> print(type(y))\n", " | <class 'numpy.matrix'>\n", " | \n", " | Creating a view on a structured array so it can be used in calculations\n", " | \n", " | >>> x = np.array([(1, 2),(3,4)], dtype=[('a', np.int8), ('b', np.int8)])\n", " | >>> xv = x.view(dtype=np.int8).reshape(-1,2)\n", " | >>> xv\n", " | array([[1, 2],\n", " | [3, 4]], dtype=int8)\n", " | >>> xv.mean(0)\n", " | array([2., 3.])\n", " | \n", " | Making changes to the view changes the underlying array\n", " | \n", " | >>> xv[0,1] = 20\n", " | >>> x\n", " | array([(1, 20), (3, 4)], dtype=[('a', 'i1'), ('b', 'i1')])\n", " | \n", " | Using a view to convert an array to a recarray:\n", " | \n", " | >>> z = x.view(np.recarray)\n", " | >>> z.a\n", " | array([1, 3], dtype=int8)\n", " | \n", " | Views share data:\n", " | \n", " | >>> x[0] = (9, 10)\n", " | >>> z[0]\n", " | (9, 10)\n", " | \n", " | Views that change the dtype size (bytes per entry) should normally be\n", " | avoided on arrays defined by slices, transposes, fortran-ordering, etc.:\n", " | \n", " | >>> x = np.array([[1, 2, 3], [4, 5, 6]], dtype=np.int16)\n", " | >>> y = x[:, ::2]\n", " | >>> y\n", " | array([[1, 3],\n", " | [4, 6]], dtype=int16)\n", " | >>> y.view(dtype=[('width', np.int16), ('length', np.int16)])\n", " | Traceback (most recent call last):\n", " | ...\n", " | ValueError: To change to a dtype of a different size, the last axis must be contiguous\n", " | >>> z = y.copy()\n", " | >>> z.view(dtype=[('width', np.int16), ('length', np.int16)])\n", " | array([[(1, 3)],\n", " | [(4, 6)]], dtype=[('width', '<i2'), ('length', '<i2')])\n", " | \n", " | However, views that change dtype are totally fine for arrays with a\n", " | contiguous last axis, even if the rest of the axes are not C-contiguous:\n", " | \n", " | >>> x = np.arange(2 * 3 * 4, dtype=np.int8).reshape(2, 3, 4)\n", " | >>> x.transpose(1, 0, 2).view(np.int16)\n", " | array([[[ 256, 770],\n", " | [3340, 3854]],\n", " | <BLANKLINE>\n", " | [[1284, 1798],\n", " | [4368, 4882]],\n", " | <BLANKLINE>\n", " | [[2312, 2826],\n", " | [5396, 5910]]], dtype=int16)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods inherited from ndarray:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | a.__class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.ndarray` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.ndarray` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.ndarray[Any, np.dtype[Any]]\n", " | numpy.ndarray[typing.Any, numpy.dtype[typing.Any]]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | numpy.typing.NDArray : An ndarray alias :term:`generic <generic type>`\n", " | w.r.t. its `dtype.type <numpy.dtype.type>`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from ndarray:\n", " | \n", " | T\n", " | View of the transposed array.\n", " | \n", " | Same as ``self.transpose()``.\n", " | \n", " | Examples\n", " | --------\n", " | >>> a = np.array([[1, 2], [3, 4]])\n", " | >>> a\n", " | array([[1, 2],\n", " | [3, 4]])\n", " | >>> a.T\n", " | array([[1, 3],\n", " | [2, 4]])\n", " | \n", " | >>> a = np.array([1, 2, 3, 4])\n", " | >>> a\n", " | array([1, 2, 3, 4])\n", " | >>> a.T\n", " | array([1, 2, 3, 4])\n", " | \n", " | See Also\n", " | --------\n", " | transpose\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side.\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: C-struct side.\n", " | \n", " | base\n", " | Base object if memory is from some other object.\n", " | \n", " | Examples\n", " | --------\n", " | The base of an array that owns its memory is None:\n", " | \n", " | >>> x = np.array([1,2,3,4])\n", " | >>> x.base is None\n", " | True\n", " | \n", " | Slicing creates a view, whose memory is shared with x:\n", " | \n", " | >>> y = x[2:]\n", " | >>> y.base is x\n", " | True\n", " | \n", " | ctypes\n", " | An object to simplify the interaction of the array with the ctypes\n", " | module.\n", " | \n", " | This attribute creates an object that makes it easier to use arrays\n", " | when calling shared libraries with the ctypes module. The returned\n", " | object has, among others, data, shape, and strides attributes (see\n", " | Notes below) which themselves return ctypes objects that can be used\n", " | as arguments to a shared library.\n", " | \n", " | Parameters\n", " | ----------\n", " | None\n", " | \n", " | Returns\n", " | -------\n", " | c : Python object\n", " | Possessing attributes data, shape, strides, etc.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.ctypeslib\n", " | \n", " | Notes\n", " | -----\n", " | Below are the public attributes of this object which were documented\n", " | in \"Guide to NumPy\" (we have omitted undocumented public attributes,\n", " | as well as documented private attributes):\n", " | \n", " | .. autoattribute:: numpy.core._internal._ctypes.data\n", " | :noindex:\n", " | \n", " | .. autoattribute:: numpy.core._internal._ctypes.shape\n", " | :noindex:\n", " | \n", " | .. autoattribute:: numpy.core._internal._ctypes.strides\n", " | :noindex:\n", " | \n", " | .. automethod:: numpy.core._internal._ctypes.data_as\n", " | :noindex:\n", " | \n", " | .. automethod:: numpy.core._internal._ctypes.shape_as\n", " | :noindex:\n", " | \n", " | .. automethod:: numpy.core._internal._ctypes.strides_as\n", " | :noindex:\n", " | \n", " | If the ctypes module is not available, then the ctypes attribute\n", " | of array objects still returns something useful, but ctypes objects\n", " | are not returned and errors may be raised instead. In particular,\n", " | the object will still have the ``as_parameter`` attribute which will\n", " | return an integer equal to the data attribute.\n", " | \n", " | Examples\n", " | --------\n", " | >>> import ctypes\n", " | >>> x = np.array([[0, 1], [2, 3]], dtype=np.int32)\n", " | >>> x\n", " | array([[0, 1],\n", " | [2, 3]], dtype=int32)\n", " | >>> x.ctypes.data\n", " | 31962608 # may vary\n", " | >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32))\n", " | <__main__.LP_c_uint object at 0x7ff2fc1fc200> # may vary\n", " | >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)).contents\n", " | c_uint(0)\n", " | >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint64)).contents\n", " | c_ulong(4294967296)\n", " | >>> x.ctypes.shape\n", " | <numpy.core._internal.c_long_Array_2 object at 0x7ff2fc1fce60> # may vary\n", " | >>> x.ctypes.strides\n", " | <numpy.core._internal.c_long_Array_2 object at 0x7ff2fc1ff320> # may vary\n", " | \n", " | data\n", " | Python buffer object pointing to the start of the array's data.\n", " | \n", " | dtype\n", " | Data-type of the array's elements.\n", " | \n", " | .. warning::\n", " | \n", " | Setting ``arr.dtype`` is discouraged and may be deprecated in the\n", " | future. Setting will replace the ``dtype`` without modifying the\n", " | memory (see also `ndarray.view` and `ndarray.astype`).\n", " | \n", " | Parameters\n", " | ----------\n", " | None\n", " | \n", " | Returns\n", " | -------\n", " | d : numpy dtype object\n", " | \n", " | See Also\n", " | --------\n", " | ndarray.astype : Cast the values contained in the array to a new data-type.\n", " | ndarray.view : Create a view of the same data but a different data-type.\n", " | numpy.dtype\n", " | \n", " | Examples\n", " | --------\n", " | >>> x\n", " | array([[0, 1],\n", " | [2, 3]])\n", " | >>> x.dtype\n", " | dtype('int32')\n", " | >>> type(x.dtype)\n", " | <type 'numpy.dtype'>\n", " | \n", " | flags\n", " | Information about the memory layout of the array.\n", " | \n", " | Attributes\n", " | ----------\n", " | C_CONTIGUOUS (C)\n", " | The data is in a single, C-style contiguous segment.\n", " | F_CONTIGUOUS (F)\n", " | The data is in a single, Fortran-style contiguous segment.\n", " | OWNDATA (O)\n", " | The array owns the memory it uses or borrows it from another object.\n", " | WRITEABLE (W)\n", " | The data area can be written to. Setting this to False locks\n", " | the data, making it read-only. A view (slice, etc.) inherits WRITEABLE\n", " | from its base array at creation time, but a view of a writeable\n", " | array may be subsequently locked while the base array remains writeable.\n", " | (The opposite is not true, in that a view of a locked array may not\n", " | be made writeable. However, currently, locking a base object does not\n", " | lock any views that already reference it, so under that circumstance it\n", " | is possible to alter the contents of a locked array via a previously\n", " | created writeable view onto it.) Attempting to change a non-writeable\n", " | array raises a RuntimeError exception.\n", " | ALIGNED (A)\n", " | The data and all elements are aligned appropriately for the hardware.\n", " | WRITEBACKIFCOPY (X)\n", " | This array is a copy of some other array. The C-API function\n", " | PyArray_ResolveWritebackIfCopy must be called before deallocating\n", " | to the base array will be updated with the contents of this array.\n", " | FNC\n", " | F_CONTIGUOUS and not C_CONTIGUOUS.\n", " | FORC\n", " | F_CONTIGUOUS or C_CONTIGUOUS (one-segment test).\n", " | BEHAVED (B)\n", " | ALIGNED and WRITEABLE.\n", " | CARRAY (CA)\n", " | BEHAVED and C_CONTIGUOUS.\n", " | FARRAY (FA)\n", " | BEHAVED and F_CONTIGUOUS and not C_CONTIGUOUS.\n", " | \n", " | Notes\n", " | -----\n", " | The `flags` object can be accessed dictionary-like (as in ``a.flags['WRITEABLE']``),\n", " | or by using lowercased attribute names (as in ``a.flags.writeable``). Short flag\n", " | names are only supported in dictionary access.\n", " | \n", " | Only the WRITEBACKIFCOPY, WRITEABLE, and ALIGNED flags can be\n", " | changed by the user, via direct assignment to the attribute or dictionary\n", " | entry, or by calling `ndarray.setflags`.\n", " | \n", " | The array flags cannot be set arbitrarily:\n", " | \n", " | - WRITEBACKIFCOPY can only be set ``False``.\n", " | - ALIGNED can only be set ``True`` if the data is truly aligned.\n", " | - WRITEABLE can only be set ``True`` if the array owns its own memory\n", " | or the ultimate owner of the memory exposes a writeable buffer\n", " | interface or is a string.\n", " | \n", " | Arrays can be both C-style and Fortran-style contiguous simultaneously.\n", " | This is clear for 1-dimensional arrays, but can also be true for higher\n", " | dimensional arrays.\n", " | \n", " | Even for contiguous arrays a stride for a given dimension\n", " | ``arr.strides[dim]`` may be *arbitrary* if ``arr.shape[dim] == 1``\n", " | or the array has no elements.\n", " | It does *not* generally hold that ``self.strides[-1] == self.itemsize``\n", " | for C-style contiguous arrays or ``self.strides[0] == self.itemsize`` for\n", " | Fortran-style contiguous arrays is true.\n", " | \n", " | flat\n", " | A 1-D iterator over the array.\n", " | \n", " | This is a `numpy.flatiter` instance, which acts similarly to, but is not\n", " | a subclass of, Python's built-in iterator object.\n", " | \n", " | See Also\n", " | --------\n", " | flatten : Return a copy of the array collapsed into one dimension.\n", " | \n", " | flatiter\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.arange(1, 7).reshape(2, 3)\n", " | >>> x\n", " | array([[1, 2, 3],\n", " | [4, 5, 6]])\n", " | >>> x.flat[3]\n", " | 4\n", " | >>> x.T\n", " | array([[1, 4],\n", " | [2, 5],\n", " | [3, 6]])\n", " | >>> x.T.flat[3]\n", " | 5\n", " | >>> type(x.flat)\n", " | <class 'numpy.flatiter'>\n", " | \n", " | An assignment example:\n", " | \n", " | >>> x.flat = 3; x\n", " | array([[3, 3, 3],\n", " | [3, 3, 3]])\n", " | >>> x.flat[[1,4]] = 1; x\n", " | array([[3, 1, 3],\n", " | [3, 1, 3]])\n", " | \n", " | imag\n", " | The imaginary part of the array.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.sqrt([1+0j, 0+1j])\n", " | >>> x.imag\n", " | array([ 0. , 0.70710678])\n", " | >>> x.imag.dtype\n", " | dtype('float64')\n", " | \n", " | itemsize\n", " | Length of one array element in bytes.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([1,2,3], dtype=np.float64)\n", " | >>> x.itemsize\n", " | 8\n", " | >>> x = np.array([1,2,3], dtype=np.complex128)\n", " | >>> x.itemsize\n", " | 16\n", " | \n", " | nbytes\n", " | Total bytes consumed by the elements of the array.\n", " | \n", " | Notes\n", " | -----\n", " | Does not include memory consumed by non-element attributes of the\n", " | array object.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.zeros((3,5,2), dtype=np.complex128)\n", " | >>> x.nbytes\n", " | 480\n", " | >>> np.prod(x.shape) * x.itemsize\n", " | 480\n", " | \n", " | ndim\n", " | Number of array dimensions.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([1, 2, 3])\n", " | >>> x.ndim\n", " | 1\n", " | >>> y = np.zeros((2, 3, 4))\n", " | >>> y.ndim\n", " | 3\n", " | \n", " | real\n", " | The real part of the array.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.sqrt([1+0j, 0+1j])\n", " | >>> x.real\n", " | array([ 1. , 0.70710678])\n", " | >>> x.real.dtype\n", " | dtype('float64')\n", " | \n", " | See Also\n", " | --------\n", " | numpy.real : equivalent function\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | The shape property is usually used to get the current shape of an array,\n", " | but may also be used to reshape the array in-place by assigning a tuple of\n", " | array dimensions to it. As with `numpy.reshape`, one of the new shape\n", " | dimensions can be -1, in which case its value is inferred from the size of\n", " | the array and the remaining dimensions. Reshaping an array in-place will\n", " | fail if a copy is required.\n", " | \n", " | .. warning::\n", " | \n", " | Setting ``arr.shape`` is discouraged and may be deprecated in the\n", " | future. Using `ndarray.reshape` is the preferred approach.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([1, 2, 3, 4])\n", " | >>> x.shape\n", " | (4,)\n", " | >>> y = np.zeros((2, 3, 4))\n", " | >>> y.shape\n", " | (2, 3, 4)\n", " | >>> y.shape = (3, 8)\n", " | >>> y\n", " | array([[ 0., 0., 0., 0., 0., 0., 0., 0.],\n", " | [ 0., 0., 0., 0., 0., 0., 0., 0.],\n", " | [ 0., 0., 0., 0., 0., 0., 0., 0.]])\n", " | >>> y.shape = (3, 6)\n", " | Traceback (most recent call last):\n", " | File \"<stdin>\", line 1, in <module>\n", " | ValueError: total size of new array must be unchanged\n", " | >>> np.zeros((4,2))[::2].shape = (-1,)\n", " | Traceback (most recent call last):\n", " | File \"<stdin>\", line 1, in <module>\n", " | AttributeError: Incompatible shape for in-place modification. Use\n", " | `.reshape()` to make a copy with the desired shape.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.shape : Equivalent getter function.\n", " | numpy.reshape : Function similar to setting ``shape``.\n", " | ndarray.reshape : Method similar to setting ``shape``.\n", " | \n", " | size\n", " | Number of elements in the array.\n", " | \n", " | Equal to ``np.prod(a.shape)``, i.e., the product of the array's\n", " | dimensions.\n", " | \n", " | Notes\n", " | -----\n", " | `a.size` returns a standard arbitrary precision Python integer. This\n", " | may not be the case with other methods of obtaining the same value\n", " | (like the suggested ``np.prod(a.shape)``, which returns an instance\n", " | of ``np.int_``), and may be relevant if the value is used further in\n", " | calculations that may overflow a fixed size integer type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.zeros((3, 5, 2), dtype=np.complex128)\n", " | >>> x.size\n", " | 30\n", " | >>> np.prod(x.shape)\n", " | 30\n", " | \n", " | strides\n", " | Tuple of bytes to step in each dimension when traversing an array.\n", " | \n", " | The byte offset of element ``(i[0], i[1], ..., i[n])`` in an array `a`\n", " | is::\n", " | \n", " | offset = sum(np.array(i) * a.strides)\n", " | \n", " | A more detailed explanation of strides can be found in the\n", " | \"ndarray.rst\" file in the NumPy reference guide.\n", " | \n", " | .. warning::\n", " | \n", " | Setting ``arr.strides`` is discouraged and may be deprecated in the\n", " | future. `numpy.lib.stride_tricks.as_strided` should be preferred\n", " | to create a new view of the same data in a safer way.\n", " | \n", " | Notes\n", " | -----\n", " | Imagine an array of 32-bit integers (each 4 bytes)::\n", " | \n", " | x = np.array([[0, 1, 2, 3, 4],\n", " | [5, 6, 7, 8, 9]], dtype=np.int32)\n", " | \n", " | This array is stored in memory as 40 bytes, one after the other\n", " | (known as a contiguous block of memory). The strides of an array tell\n", " | us how many bytes we have to skip in memory to move to the next position\n", " | along a certain axis. For example, we have to skip 4 bytes (1 value) to\n", " | move to the next column, but 20 bytes (5 values) to get to the same\n", " | position in the next row. As such, the strides for the array `x` will be\n", " | ``(20, 4)``.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.lib.stride_tricks.as_strided\n", " | \n", " | Examples\n", " | --------\n", " | >>> y = np.reshape(np.arange(2*3*4), (2,3,4))\n", " | >>> y\n", " | array([[[ 0, 1, 2, 3],\n", " | [ 4, 5, 6, 7],\n", " | [ 8, 9, 10, 11]],\n", " | [[12, 13, 14, 15],\n", " | [16, 17, 18, 19],\n", " | [20, 21, 22, 23]]])\n", " | >>> y.strides\n", " | (48, 16, 4)\n", " | >>> y[1,1,1]\n", " | 17\n", " | >>> offset=sum(y.strides * np.array((1,1,1)))\n", " | >>> offset/y.itemsize\n", " | 17\n", " | \n", " | >>> x = np.reshape(np.arange(5*6*7*8), (5,6,7,8)).transpose(2,3,1,0)\n", " | >>> x.strides\n", " | (32, 4, 224, 1344)\n", " | >>> i = np.array([3,5,2,2])\n", " | >>> offset = sum(i * x.strides)\n", " | >>> x[3,5,2,2]\n", " | 813\n", " | >>> offset / x.itemsize\n", " | 813\n", " \n", " class clongdouble(complexfloating)\n", " | Complex number type composed of two extended-precision floating-point\n", " | numbers.\n", " | \n", " | :Character code: ``'G'``\n", " | :Alias: `numpy.clongfloat`\n", " | :Alias: `numpy.longcomplex`\n", " | \n", " | Method resolution order:\n", " | clongdouble\n", " | complexfloating\n", " | inexact\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __complex__(...)\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from complexfloating:\n", " | \n", " | __round__(...)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " clongfloat = class clongdouble(complexfloating)\n", " | Complex number type composed of two extended-precision floating-point\n", " | numbers.\n", " | \n", " | :Character code: ``'G'``\n", " | :Alias: `numpy.clongfloat`\n", " | :Alias: `numpy.longcomplex`\n", " | \n", " | Method resolution order:\n", " | clongdouble\n", " | complexfloating\n", " | inexact\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __complex__(...)\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from complexfloating:\n", " | \n", " | __round__(...)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " class complex128(complexfloating, builtins.complex)\n", " | complex128(real=0, imag=0)\n", " | \n", " | Complex number type composed of two double-precision floating-point\n", " | numbers, compatible with Python `complex`.\n", " | \n", " | :Character code: ``'D'``\n", " | :Canonical name: `numpy.cdouble`\n", " | :Alias: `numpy.cfloat`\n", " | :Alias: `numpy.complex_`\n", " | :Alias on this platform (win32 AMD64): `numpy.complex128`: Complex number type composed of 2 64-bit-precision floating-point numbers.\n", " | \n", " | Method resolution order:\n", " | complex128\n", " | complexfloating\n", " | inexact\n", " | number\n", " | generic\n", " | builtins.complex\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from complexfloating:\n", " | \n", " | __round__(...)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from builtins.complex:\n", " | \n", " | __complex__(self, /)\n", " | Convert this value to exact type complex.\n", " | \n", " | __getattribute__(self, name, /)\n", " | Return getattr(self, name).\n", " | \n", " | __getnewargs__(self, /)\n", " \n", " class complex64(complexfloating)\n", " | Complex number type composed of two single-precision floating-point\n", " | numbers.\n", " | \n", " | :Character code: ``'F'``\n", " | :Canonical name: `numpy.csingle`\n", " | :Alias: `numpy.singlecomplex`\n", " | :Alias on this platform (win32 AMD64): `numpy.complex64`: Complex number type composed of 2 32-bit-precision floating-point numbers.\n", " | \n", " | Method resolution order:\n", " | complex64\n", " | complexfloating\n", " | inexact\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __complex__(...)\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from complexfloating:\n", " | \n", " | __round__(...)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " complex_ = class complex128(complexfloating, builtins.complex)\n", " | complex_(real=0, imag=0)\n", " | \n", " | Complex number type composed of two double-precision floating-point\n", " | numbers, compatible with Python `complex`.\n", " | \n", " | :Character code: ``'D'``\n", " | :Canonical name: `numpy.cdouble`\n", " | :Alias: `numpy.cfloat`\n", " | :Alias: `numpy.complex_`\n", " | :Alias on this platform (win32 AMD64): `numpy.complex128`: Complex number type composed of 2 64-bit-precision floating-point numbers.\n", " | \n", " | Method resolution order:\n", " | complex128\n", " | complexfloating\n", " | inexact\n", " | number\n", " | generic\n", " | builtins.complex\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from complexfloating:\n", " | \n", " | __round__(...)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from builtins.complex:\n", " | \n", " | __complex__(self, /)\n", " | Convert this value to exact type complex.\n", " | \n", " | __getattribute__(self, name, /)\n", " | Return getattr(self, name).\n", " | \n", " | __getnewargs__(self, /)\n", " \n", " class complexfloating(inexact)\n", " | Abstract base class of all complex number scalar types that are made up of\n", " | floating-point numbers.\n", " | \n", " | Method resolution order:\n", " | complexfloating\n", " | inexact\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __round__(...)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods inherited from number:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data and other attributes inherited from generic:\n", " | \n", " | __hash__ = None\n", " \n", " csingle = class complex64(complexfloating)\n", " | Complex number type composed of two single-precision floating-point\n", " | numbers.\n", " | \n", " | :Character code: ``'F'``\n", " | :Canonical name: `numpy.csingle`\n", " | :Alias: `numpy.singlecomplex`\n", " | :Alias on this platform (win32 AMD64): `numpy.complex64`: Complex number type composed of 2 32-bit-precision floating-point numbers.\n", " | \n", " | Method resolution order:\n", " | complex64\n", " | complexfloating\n", " | inexact\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __complex__(...)\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from complexfloating:\n", " | \n", " | __round__(...)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " class datetime64(generic)\n", " | If created from a 64-bit integer, it represents an offset from\n", " | ``1970-01-01T00:00:00``.\n", " | If created from string, the string can be in ISO 8601 date\n", " | or datetime format.\n", " | \n", " | >>> np.datetime64(10, 'Y')\n", " | numpy.datetime64('1980')\n", " | >>> np.datetime64('1980', 'Y')\n", " | numpy.datetime64('1980')\n", " | >>> np.datetime64(10, 'D')\n", " | numpy.datetime64('1970-01-11')\n", " | \n", " | See :ref:`arrays.datetime` for more information.\n", " | \n", " | :Character code: ``'M'``\n", " | \n", " | Method resolution order:\n", " | datetime64\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " double = class float64(floating, builtins.float)\n", " | double(x=0, /)\n", " | \n", " | Double-precision floating-point number type, compatible with Python `float`\n", " | and C ``double``.\n", " | \n", " | :Character code: ``'d'``\n", " | :Canonical name: `numpy.double`\n", " | :Alias: `numpy.float_`\n", " | :Alias on this platform (win32 AMD64): `numpy.float64`: 64-bit precision floating-point number type: sign bit, 11 bits exponent, 52 bits mantissa.\n", " | \n", " | Method resolution order:\n", " | float64\n", " | floating\n", " | inexact\n", " | number\n", " | generic\n", " | builtins.float\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | as_integer_ratio(...)\n", " | double.as_integer_ratio() -> (int, int)\n", " | \n", " | Return a pair of integers, whose ratio is exactly equal to the original\n", " | floating point number, and with a positive denominator.\n", " | Raise `OverflowError` on infinities and a `ValueError` on NaNs.\n", " | \n", " | >>> np.double(10.0).as_integer_ratio()\n", " | (10, 1)\n", " | >>> np.double(0.0).as_integer_ratio()\n", " | (0, 1)\n", " | >>> np.double(-.25).as_integer_ratio()\n", " | (-1, 4)\n", " | \n", " | is_integer(...)\n", " | double.is_integer() -> bool\n", " | \n", " | Return ``True`` if the floating point number is finite with integral\n", " | value, and ``False`` otherwise.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.double(-2.0).is_integer()\n", " | True\n", " | >>> np.double(3.2).is_integer()\n", " | False\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from floating:\n", " | \n", " | __round__(...)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from builtins.float:\n", " | \n", " | __ceil__(self, /)\n", " | Return the ceiling as an Integral.\n", " | \n", " | __floor__(self, /)\n", " | Return the floor as an Integral.\n", " | \n", " | __getattribute__(self, name, /)\n", " | Return getattr(self, name).\n", " | \n", " | __getnewargs__(self, /)\n", " | \n", " | __trunc__(self, /)\n", " | Return the Integral closest to x between 0 and x.\n", " | \n", " | hex(self, /)\n", " | Return a hexadecimal representation of a floating-point number.\n", " | \n", " | >>> (-0.1).hex()\n", " | '-0x1.999999999999ap-4'\n", " | >>> 3.14159.hex()\n", " | '0x1.921f9f01b866ep+1'\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods inherited from builtins.float:\n", " | \n", " | __getformat__(typestr, /) from builtins.type\n", " | You probably don't want to use this function.\n", " | \n", " | typestr\n", " | Must be 'double' or 'float'.\n", " | \n", " | It exists mainly to be used in Python's test suite.\n", " | \n", " | This function returns whichever of 'unknown', 'IEEE, big-endian' or 'IEEE,\n", " | little-endian' best describes the format of floating point numbers used by the\n", " | C type named by typestr.\n", " | \n", " | fromhex(string, /) from builtins.type\n", " | Create a floating-point number from a hexadecimal string.\n", " | \n", " | >>> float.fromhex('0x1.ffffp10')\n", " | 2047.984375\n", " | >>> float.fromhex('-0x1p-1074')\n", " | -5e-324\n", " \n", " class dtype(builtins.object)\n", " | dtype(dtype, align=False, copy=False)\n", " | \n", " | Create a data type object.\n", " | \n", " | A numpy array is homogeneous, and contains elements described by a\n", " | dtype object. A dtype object can be constructed from different\n", " | combinations of fundamental numeric types.\n", " | \n", " | Parameters\n", " | ----------\n", " | dtype\n", " | Object to be converted to a data type object.\n", " | align : bool, optional\n", " | Add padding to the fields to match what a C compiler would output\n", " | for a similar C-struct. Can be ``True`` only if `obj` is a dictionary\n", " | or a comma-separated string. If a struct dtype is being created,\n", " | this also sets a sticky alignment flag ``isalignedstruct``.\n", " | copy : bool, optional\n", " | Make a new copy of the data-type object. If ``False``, the result\n", " | may just be a reference to a built-in data-type object.\n", " | \n", " | See also\n", " | --------\n", " | result_type\n", " | \n", " | Examples\n", " | --------\n", " | Using array-scalar type:\n", " | \n", " | >>> np.dtype(np.int16)\n", " | dtype('int16')\n", " | \n", " | Structured type, one field name 'f1', containing int16:\n", " | \n", " | >>> np.dtype([('f1', np.int16)])\n", " | dtype([('f1', '<i2')])\n", " | \n", " | Structured type, one field named 'f1', in itself containing a structured\n", " | type with one field:\n", " | \n", " | >>> np.dtype([('f1', [('f1', np.int16)])])\n", " | dtype([('f1', [('f1', '<i2')])])\n", " | \n", " | Structured type, two fields: the first field contains an unsigned int, the\n", " | second an int32:\n", " | \n", " | >>> np.dtype([('f1', np.uint64), ('f2', np.int32)])\n", " | dtype([('f1', '<u8'), ('f2', '<i4')])\n", " | \n", " | Using array-protocol type strings:\n", " | \n", " | >>> np.dtype([('a','f8'),('b','S10')])\n", " | dtype([('a', '<f8'), ('b', 'S10')])\n", " | \n", " | Using comma-separated field formats. The shape is (2,3):\n", " | \n", " | >>> np.dtype(\"i4, (2,3)f8\")\n", " | dtype([('f0', '<i4'), ('f1', '<f8', (2, 3))])\n", " | \n", " | Using tuples. ``int`` is a fixed type, 3 the field's shape. ``void``\n", " | is a flexible type, here of size 10:\n", " | \n", " | >>> np.dtype([('hello',(np.int64,3)),('world',np.void,10)])\n", " | dtype([('hello', '<i8', (3,)), ('world', 'V10')])\n", " | \n", " | Subdivide ``int16`` into 2 ``int8``'s, called x and y. 0 and 1 are\n", " | the offsets in bytes:\n", " | \n", " | >>> np.dtype((np.int16, {'x':(np.int8,0), 'y':(np.int8,1)}))\n", " | dtype((numpy.int16, [('x', 'i1'), ('y', 'i1')]))\n", " | \n", " | Using dictionaries. Two fields named 'gender' and 'age':\n", " | \n", " | >>> np.dtype({'names':['gender','age'], 'formats':['S1',np.uint8]})\n", " | dtype([('gender', 'S1'), ('age', 'u1')])\n", " | \n", " | Offsets in bytes, here 0 and 25:\n", " | \n", " | >>> np.dtype({'surname':('S25',0),'age':(np.uint8,25)})\n", " | dtype([('surname', 'S25'), ('age', 'u1')])\n", " | \n", " | Methods defined here:\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __len__(self, /)\n", " | Return len(self).\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new dtype with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : string, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | below. The default value ('S') results in swapping the current\n", " | byte order. `new_order` codes can be any of:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New dtype object with the given change to the byte order.\n", " | \n", " | Notes\n", " | -----\n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> import sys\n", " | >>> sys_is_le = sys.byteorder == 'little'\n", " | >>> native_code = sys_is_le and '<' or '>'\n", " | >>> swapped_code = sys_is_le and '>' or '<'\n", " | >>> native_dt = np.dtype(native_code+'i2')\n", " | >>> swapped_dt = np.dtype(swapped_code+'i2')\n", " | >>> native_dt.newbyteorder('S') == swapped_dt\n", " | True\n", " | >>> native_dt.newbyteorder() == swapped_dt\n", " | True\n", " | >>> native_dt == swapped_dt.newbyteorder('S')\n", " | True\n", " | >>> native_dt == swapped_dt.newbyteorder('=')\n", " | True\n", " | >>> native_dt == swapped_dt.newbyteorder('N')\n", " | True\n", " | >>> native_dt == native_dt.newbyteorder('|')\n", " | True\n", " | >>> np.dtype('<i2') == native_dt.newbyteorder('<')\n", " | True\n", " | >>> np.dtype('<i2') == native_dt.newbyteorder('L')\n", " | True\n", " | >>> np.dtype('>i2') == native_dt.newbyteorder('>')\n", " | True\n", " | >>> np.dtype('>i2') == native_dt.newbyteorder('B')\n", " | True\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from _DTypeMeta\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.dtype` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.dtype` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> import numpy as np\n", " | \n", " | >>> np.dtype[np.int64]\n", " | numpy.dtype[numpy.int64]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from _DTypeMeta\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors defined here:\n", " | \n", " | alignment\n", " | The required alignment (bytes) of this data-type according to the compiler.\n", " | \n", " | More information is available in the C-API section of the manual.\n", " | \n", " | Examples\n", " | --------\n", " | \n", " | >>> x = np.dtype('i4')\n", " | >>> x.alignment\n", " | 4\n", " | \n", " | >>> x = np.dtype(float)\n", " | >>> x.alignment\n", " | 8\n", " | \n", " | base\n", " | Returns dtype for the base element of the subarrays,\n", " | regardless of their dimension or shape.\n", " | \n", " | See Also\n", " | --------\n", " | dtype.subdtype\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = numpy.dtype('8f')\n", " | >>> x.base\n", " | dtype('float32')\n", " | \n", " | >>> x = numpy.dtype('i2')\n", " | >>> x.base\n", " | dtype('int16')\n", " | \n", " | byteorder\n", " | A character indicating the byte-order of this data-type object.\n", " | \n", " | One of:\n", " | \n", " | === ==============\n", " | '=' native\n", " | '<' little-endian\n", " | '>' big-endian\n", " | '|' not applicable\n", " | === ==============\n", " | \n", " | All built-in data-type objects have byteorder either '=' or '|'.\n", " | \n", " | Examples\n", " | --------\n", " | \n", " | >>> dt = np.dtype('i2')\n", " | >>> dt.byteorder\n", " | '='\n", " | >>> # endian is not relevant for 8 bit numbers\n", " | >>> np.dtype('i1').byteorder\n", " | '|'\n", " | >>> # or ASCII strings\n", " | >>> np.dtype('S2').byteorder\n", " | '|'\n", " | >>> # Even if specific code is given, and it is native\n", " | >>> # '=' is the byteorder\n", " | >>> import sys\n", " | >>> sys_is_le = sys.byteorder == 'little'\n", " | >>> native_code = sys_is_le and '<' or '>'\n", " | >>> swapped_code = sys_is_le and '>' or '<'\n", " | >>> dt = np.dtype(native_code + 'i2')\n", " | >>> dt.byteorder\n", " | '='\n", " | >>> # Swapped code shows up as itself\n", " | >>> dt = np.dtype(swapped_code + 'i2')\n", " | >>> dt.byteorder == swapped_code\n", " | True\n", " | \n", " | char\n", " | A unique character code for each of the 21 different built-in types.\n", " | \n", " | Examples\n", " | --------\n", " | \n", " | >>> x = np.dtype(float)\n", " | >>> x.char\n", " | 'd'\n", " | \n", " | descr\n", " | `__array_interface__` description of the data-type.\n", " | \n", " | The format is that required by the 'descr' key in the\n", " | `__array_interface__` attribute.\n", " | \n", " | Warning: This attribute exists specifically for `__array_interface__`,\n", " | and passing it directly to `np.dtype` will not accurately reconstruct\n", " | some dtypes (e.g., scalar and subarray dtypes).\n", " | \n", " | Examples\n", " | --------\n", " | \n", " | >>> x = np.dtype(float)\n", " | >>> x.descr\n", " | [('', '<f8')]\n", " | \n", " | >>> dt = np.dtype([('name', np.str_, 16), ('grades', np.float64, (2,))])\n", " | >>> dt.descr\n", " | [('name', '<U16'), ('grades', '<f8', (2,))]\n", " | \n", " | fields\n", " | Dictionary of named fields defined for this data type, or ``None``.\n", " | \n", " | The dictionary is indexed by keys that are the names of the fields.\n", " | Each entry in the dictionary is a tuple fully describing the field::\n", " | \n", " | (dtype, offset[, title])\n", " | \n", " | Offset is limited to C int, which is signed and usually 32 bits.\n", " | If present, the optional title can be any object (if it is a string\n", " | or unicode then it will also be a key in the fields dictionary,\n", " | otherwise it's meta-data). Notice also that the first two elements\n", " | of the tuple can be passed directly as arguments to the ``ndarray.getfield``\n", " | and ``ndarray.setfield`` methods.\n", " | \n", " | See Also\n", " | --------\n", " | ndarray.getfield, ndarray.setfield\n", " | \n", " | Examples\n", " | --------\n", " | >>> dt = np.dtype([('name', np.str_, 16), ('grades', np.float64, (2,))])\n", " | >>> print(dt.fields)\n", " | {'grades': (dtype(('float64',(2,))), 16), 'name': (dtype('|S16'), 0)}\n", " | \n", " | flags\n", " | Bit-flags describing how this data type is to be interpreted.\n", " | \n", " | Bit-masks are in `numpy.core.multiarray` as the constants\n", " | `ITEM_HASOBJECT`, `LIST_PICKLE`, `ITEM_IS_POINTER`, `NEEDS_INIT`,\n", " | `NEEDS_PYAPI`, `USE_GETITEM`, `USE_SETITEM`. A full explanation\n", " | of these flags is in C-API documentation; they are largely useful\n", " | for user-defined data-types.\n", " | \n", " | The following example demonstrates that operations on this particular\n", " | dtype requires Python C-API.\n", " | \n", " | Examples\n", " | --------\n", " | \n", " | >>> x = np.dtype([('a', np.int32, 8), ('b', np.float64, 6)])\n", " | >>> x.flags\n", " | 16\n", " | >>> np.core.multiarray.NEEDS_PYAPI\n", " | 16\n", " | \n", " | hasobject\n", " | Boolean indicating whether this dtype contains any reference-counted\n", " | objects in any fields or sub-dtypes.\n", " | \n", " | Recall that what is actually in the ndarray memory representing\n", " | the Python object is the memory address of that object (a pointer).\n", " | Special handling may be required, and this attribute is useful for\n", " | distinguishing data types that may contain arbitrary Python objects\n", " | and data-types that won't.\n", " | \n", " | isalignedstruct\n", " | Boolean indicating whether the dtype is a struct which maintains\n", " | field alignment. This flag is sticky, so when combining multiple\n", " | structs together, it is preserved and produces new dtypes which\n", " | are also aligned.\n", " | \n", " | isbuiltin\n", " | Integer indicating how this dtype relates to the built-in dtypes.\n", " | \n", " | Read-only.\n", " | \n", " | = ========================================================================\n", " | 0 if this is a structured array type, with fields\n", " | 1 if this is a dtype compiled into numpy (such as ints, floats etc)\n", " | 2 if the dtype is for a user-defined numpy type\n", " | A user-defined type uses the numpy C-API machinery to extend\n", " | numpy to handle a new array type. See\n", " | :ref:`user.user-defined-data-types` in the NumPy manual.\n", " | = ========================================================================\n", " | \n", " | Examples\n", " | --------\n", " | >>> dt = np.dtype('i2')\n", " | >>> dt.isbuiltin\n", " | 1\n", " | >>> dt = np.dtype('f8')\n", " | >>> dt.isbuiltin\n", " | 1\n", " | >>> dt = np.dtype([('field1', 'f8')])\n", " | >>> dt.isbuiltin\n", " | 0\n", " | \n", " | isnative\n", " | Boolean indicating whether the byte order of this dtype is native\n", " | to the platform.\n", " | \n", " | itemsize\n", " | The element size of this data-type object.\n", " | \n", " | For 18 of the 21 types this number is fixed by the data-type.\n", " | For the flexible data-types, this number can be anything.\n", " | \n", " | Examples\n", " | --------\n", " | \n", " | >>> arr = np.array([[1, 2], [3, 4]])\n", " | >>> arr.dtype\n", " | dtype('int64')\n", " | >>> arr.itemsize\n", " | 8\n", " | \n", " | >>> dt = np.dtype([('name', np.str_, 16), ('grades', np.float64, (2,))])\n", " | >>> dt.itemsize\n", " | 80\n", " | \n", " | kind\n", " | A character code (one of 'biufcmMOSUV') identifying the general kind of data.\n", " | \n", " | = ======================\n", " | b boolean\n", " | i signed integer\n", " | u unsigned integer\n", " | f floating-point\n", " | c complex floating-point\n", " | m timedelta\n", " | M datetime\n", " | O object\n", " | S (byte-)string\n", " | U Unicode\n", " | V void\n", " | = ======================\n", " | \n", " | Examples\n", " | --------\n", " | \n", " | >>> dt = np.dtype('i4')\n", " | >>> dt.kind\n", " | 'i'\n", " | >>> dt = np.dtype('f8')\n", " | >>> dt.kind\n", " | 'f'\n", " | >>> dt = np.dtype([('field1', 'f8')])\n", " | >>> dt.kind\n", " | 'V'\n", " | \n", " | metadata\n", " | Either ``None`` or a readonly dictionary of metadata (mappingproxy).\n", " | \n", " | The metadata field can be set using any dictionary at data-type\n", " | creation. NumPy currently has no uniform approach to propagating\n", " | metadata; although some array operations preserve it, there is no\n", " | guarantee that others will.\n", " | \n", " | .. warning::\n", " | \n", " | Although used in certain projects, this feature was long undocumented\n", " | and is not well supported. Some aspects of metadata propagation\n", " | are expected to change in the future.\n", " | \n", " | Examples\n", " | --------\n", " | \n", " | >>> dt = np.dtype(float, metadata={\"key\": \"value\"})\n", " | >>> dt.metadata[\"key\"]\n", " | 'value'\n", " | >>> arr = np.array([1, 2, 3], dtype=dt)\n", " | >>> arr.dtype.metadata\n", " | mappingproxy({'key': 'value'})\n", " | \n", " | Adding arrays with identical datatypes currently preserves the metadata:\n", " | \n", " | >>> (arr + arr).dtype.metadata\n", " | mappingproxy({'key': 'value'})\n", " | \n", " | But if the arrays have different dtype metadata, the metadata may be\n", " | dropped:\n", " | \n", " | >>> dt2 = np.dtype(float, metadata={\"key2\": \"value2\"})\n", " | >>> arr2 = np.array([3, 2, 1], dtype=dt2)\n", " | >>> (arr + arr2).dtype.metadata is None\n", " | True # The metadata field is cleared so None is returned\n", " | \n", " | name\n", " | A bit-width name for this data-type.\n", " | \n", " | Un-sized flexible data-type objects do not have this attribute.\n", " | \n", " | Examples\n", " | --------\n", " | \n", " | >>> x = np.dtype(float)\n", " | >>> x.name\n", " | 'float64'\n", " | >>> x = np.dtype([('a', np.int32, 8), ('b', np.float64, 6)])\n", " | >>> x.name\n", " | 'void640'\n", " | \n", " | names\n", " | Ordered list of field names, or ``None`` if there are no fields.\n", " | \n", " | The names are ordered according to increasing byte offset. This can be\n", " | used, for example, to walk through all of the named fields in offset order.\n", " | \n", " | Examples\n", " | --------\n", " | >>> dt = np.dtype([('name', np.str_, 16), ('grades', np.float64, (2,))])\n", " | >>> dt.names\n", " | ('name', 'grades')\n", " | \n", " | ndim\n", " | Number of dimensions of the sub-array if this data type describes a\n", " | sub-array, and ``0`` otherwise.\n", " | \n", " | .. versionadded:: 1.13.0\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.dtype(float)\n", " | >>> x.ndim\n", " | 0\n", " | \n", " | >>> x = np.dtype((float, 8))\n", " | >>> x.ndim\n", " | 1\n", " | \n", " | >>> x = np.dtype(('i4', (3, 4)))\n", " | >>> x.ndim\n", " | 2\n", " | \n", " | num\n", " | A unique number for each of the 21 different built-in types.\n", " | \n", " | These are roughly ordered from least-to-most precision.\n", " | \n", " | Examples\n", " | --------\n", " | \n", " | >>> dt = np.dtype(str)\n", " | >>> dt.num\n", " | 19\n", " | \n", " | >>> dt = np.dtype(float)\n", " | >>> dt.num\n", " | 12\n", " | \n", " | shape\n", " | Shape tuple of the sub-array if this data type describes a sub-array,\n", " | and ``()`` otherwise.\n", " | \n", " | Examples\n", " | --------\n", " | \n", " | >>> dt = np.dtype(('i4', 4))\n", " | >>> dt.shape\n", " | (4,)\n", " | \n", " | >>> dt = np.dtype(('i4', (2, 3)))\n", " | >>> dt.shape\n", " | (2, 3)\n", " | \n", " | str\n", " | The array-protocol typestring of this data-type object.\n", " | \n", " | subdtype\n", " | Tuple ``(item_dtype, shape)`` if this `dtype` describes a sub-array, and\n", " | None otherwise.\n", " | \n", " | The *shape* is the fixed shape of the sub-array described by this\n", " | data type, and *item_dtype* the data type of the array.\n", " | \n", " | If a field whose dtype object has this attribute is retrieved,\n", " | then the extra dimensions implied by *shape* are tacked on to\n", " | the end of the retrieved array.\n", " | \n", " | See Also\n", " | --------\n", " | dtype.base\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = numpy.dtype('8f')\n", " | >>> x.subdtype\n", " | (dtype('float32'), (8,))\n", " | \n", " | >>> x = numpy.dtype('i2')\n", " | >>> x.subdtype\n", " | >>>\n", " | \n", " | type\n", " \n", " class errstate(contextlib.ContextDecorator)\n", " | errstate(*, call=<numpy.core._ufunc_config._unspecified object at 0x000001E10B8B0650>, **kwargs)\n", " | \n", " | errstate(**kwargs)\n", " | \n", " | Context manager for floating-point error handling.\n", " | \n", " | Using an instance of `errstate` as a context manager allows statements in\n", " | that context to execute with a known error handling behavior. Upon entering\n", " | the context the error handling is set with `seterr` and `seterrcall`, and\n", " | upon exiting it is reset to what it was before.\n", " | \n", " | .. versionchanged:: 1.17.0\n", " | `errstate` is also usable as a function decorator, saving\n", " | a level of indentation if an entire function is wrapped.\n", " | See :py:class:`contextlib.ContextDecorator` for more information.\n", " | \n", " | Parameters\n", " | ----------\n", " | kwargs : {divide, over, under, invalid}\n", " | Keyword arguments. The valid keywords are the possible floating-point\n", " | exceptions. Each keyword should have a string value that defines the\n", " | treatment for the particular error. Possible values are\n", " | {'ignore', 'warn', 'raise', 'call', 'print', 'log'}.\n", " | \n", " | See Also\n", " | --------\n", " | seterr, geterr, seterrcall, geterrcall\n", " | \n", " | Notes\n", " | -----\n", " | For complete documentation of the types of floating-point exceptions and\n", " | treatment options, see `seterr`.\n", " | \n", " | Examples\n", " | --------\n", " | >>> olderr = np.seterr(all='ignore') # Set error handling to known state.\n", " | \n", " | >>> np.arange(3) / 0.\n", " | array([nan, inf, inf])\n", " | >>> with np.errstate(divide='warn'):\n", " | ... np.arange(3) / 0.\n", " | array([nan, inf, inf])\n", " | \n", " | >>> np.sqrt(-1)\n", " | nan\n", " | >>> with np.errstate(invalid='raise'):\n", " | ... np.sqrt(-1)\n", " | Traceback (most recent call last):\n", " | File \"<stdin>\", line 2, in <module>\n", " | FloatingPointError: invalid value encountered in sqrt\n", " | \n", " | Outside the context the error handling behavior has not changed:\n", " | \n", " | >>> np.geterr()\n", " | {'divide': 'ignore', 'over': 'ignore', 'under': 'ignore', 'invalid': 'ignore'}\n", " | \n", " | Method resolution order:\n", " | errstate\n", " | contextlib.ContextDecorator\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __enter__(self)\n", " | \n", " | __exit__(self, *exc_info)\n", " | \n", " | __init__(self, *, call=<numpy.core._ufunc_config._unspecified object at 0x000001E10B8B0650>, **kwargs)\n", " | Initialize self. See help(type(self)) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from contextlib.ContextDecorator:\n", " | \n", " | __call__(self, func)\n", " | Call self as a function.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from contextlib.ContextDecorator:\n", " | \n", " | __dict__\n", " | dictionary for instance variables (if defined)\n", " | \n", " | __weakref__\n", " | list of weak references to the object (if defined)\n", " \n", " class finfo(builtins.object)\n", " | finfo(dtype)\n", " | \n", " | finfo(dtype)\n", " | \n", " | Machine limits for floating point types.\n", " | \n", " | Attributes\n", " | ----------\n", " | bits : int\n", " | The number of bits occupied by the type.\n", " | dtype : dtype\n", " | Returns the dtype for which `finfo` returns information. For complex\n", " | input, the returned dtype is the associated ``float*`` dtype for its\n", " | real and complex components.\n", " | eps : float\n", " | The difference between 1.0 and the next smallest representable float\n", " | larger than 1.0. For example, for 64-bit binary floats in the IEEE-754\n", " | standard, ``eps = 2**-52``, approximately 2.22e-16.\n", " | epsneg : float\n", " | The difference between 1.0 and the next smallest representable float\n", " | less than 1.0. For example, for 64-bit binary floats in the IEEE-754\n", " | standard, ``epsneg = 2**-53``, approximately 1.11e-16.\n", " | iexp : int\n", " | The number of bits in the exponent portion of the floating point\n", " | representation.\n", " | machar : MachAr\n", " | The object which calculated these parameters and holds more\n", " | detailed information.\n", " | \n", " | .. deprecated:: 1.22\n", " | machep : int\n", " | The exponent that yields `eps`.\n", " | max : floating point number of the appropriate type\n", " | The largest representable number.\n", " | maxexp : int\n", " | The smallest positive power of the base (2) that causes overflow.\n", " | min : floating point number of the appropriate type\n", " | The smallest representable number, typically ``-max``.\n", " | minexp : int\n", " | The most negative power of the base (2) consistent with there\n", " | being no leading 0's in the mantissa.\n", " | negep : int\n", " | The exponent that yields `epsneg`.\n", " | nexp : int\n", " | The number of bits in the exponent including its sign and bias.\n", " | nmant : int\n", " | The number of bits in the mantissa.\n", " | precision : int\n", " | The approximate number of decimal digits to which this kind of\n", " | float is precise.\n", " | resolution : floating point number of the appropriate type\n", " | The approximate decimal resolution of this type, i.e.,\n", " | ``10**-precision``.\n", " | tiny : float\n", " | An alias for `smallest_normal`, kept for backwards compatibility.\n", " | smallest_normal : float\n", " | The smallest positive floating point number with 1 as leading bit in\n", " | the mantissa following IEEE-754 (see Notes).\n", " | smallest_subnormal : float\n", " | The smallest positive floating point number with 0 as leading bit in\n", " | the mantissa following IEEE-754.\n", " | \n", " | Parameters\n", " | ----------\n", " | dtype : float, dtype, or instance\n", " | Kind of floating point or complex floating point\n", " | data-type about which to get information.\n", " | \n", " | See Also\n", " | --------\n", " | MachAr : The implementation of the tests that produce this information.\n", " | iinfo : The equivalent for integer data types.\n", " | spacing : The distance between a value and the nearest adjacent number\n", " | nextafter : The next floating point value after x1 towards x2\n", " | \n", " | Notes\n", " | -----\n", " | For developers of NumPy: do not instantiate this at the module level.\n", " | The initial calculation of these parameters is expensive and negatively\n", " | impacts import times. These objects are cached, so calling ``finfo()``\n", " | repeatedly inside your functions is not a problem.\n", " | \n", " | Note that ``smallest_normal`` is not actually the smallest positive\n", " | representable value in a NumPy floating point type. As in the IEEE-754\n", " | standard [1]_, NumPy floating point types make use of subnormal numbers to\n", " | fill the gap between 0 and ``smallest_normal``. However, subnormal numbers\n", " | may have significantly reduced precision [2]_.\n", " | \n", " | This function can also be used for complex data types as well. If used,\n", " | the output will be the same as the corresponding real float type\n", " | (e.g. numpy.finfo(numpy.csingle) is the same as numpy.finfo(numpy.single)).\n", " | However, the output is true for the real and imaginary components.\n", " | \n", " | References\n", " | ----------\n", " | .. [1] IEEE Standard for Floating-Point Arithmetic, IEEE Std 754-2008,\n", " | pp.1-70, 2008, http://www.doi.org/10.1109/IEEESTD.2008.4610935\n", " | .. [2] Wikipedia, \"Denormal Numbers\",\n", " | https://en.wikipedia.org/wiki/Denormal_number\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.finfo(np.float64).dtype\n", " | dtype('float64')\n", " | >>> np.finfo(np.complex64).dtype\n", " | dtype('float32')\n", " | \n", " | Methods defined here:\n", " | \n", " | __repr__(self)\n", " | Return repr(self).\n", " | \n", " | __str__(self)\n", " | Return str(self).\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(cls, dtype)\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Readonly properties defined here:\n", " | \n", " | machar\n", " | The object which calculated these parameters and holds more\n", " | detailed information.\n", " | \n", " | .. deprecated:: 1.22\n", " | \n", " | smallest_normal\n", " | Return the value for the smallest normal.\n", " | \n", " | Returns\n", " | -------\n", " | smallest_normal : float\n", " | Value for the smallest normal.\n", " | \n", " | Warns\n", " | -----\n", " | UserWarning\n", " | If the calculated value for the smallest normal is requested for\n", " | double-double.\n", " | \n", " | tiny\n", " | Return the value for tiny, alias of smallest_normal.\n", " | \n", " | Returns\n", " | -------\n", " | tiny : float\n", " | Value for the smallest normal, alias of smallest_normal.\n", " | \n", " | Warns\n", " | -----\n", " | UserWarning\n", " | If the calculated value for the smallest normal is requested for\n", " | double-double.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors defined here:\n", " | \n", " | __dict__\n", " | dictionary for instance variables (if defined)\n", " | \n", " | __weakref__\n", " | list of weak references to the object (if defined)\n", " \n", " class flatiter(builtins.object)\n", " | Flat iterator object to iterate over arrays.\n", " | \n", " | A `flatiter` iterator is returned by ``x.flat`` for any array `x`.\n", " | It allows iterating over the array as if it were a 1-D array,\n", " | either in a for-loop or by calling its `next` method.\n", " | \n", " | Iteration is done in row-major, C-style order (the last\n", " | index varying the fastest). The iterator can also be indexed using\n", " | basic slicing or advanced indexing.\n", " | \n", " | See Also\n", " | --------\n", " | ndarray.flat : Return a flat iterator over an array.\n", " | ndarray.flatten : Returns a flattened copy of an array.\n", " | \n", " | Notes\n", " | -----\n", " | A `flatiter` iterator can not be constructed directly from Python code\n", " | by calling the `flatiter` constructor.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.arange(6).reshape(2, 3)\n", " | >>> fl = x.flat\n", " | >>> type(fl)\n", " | <class 'numpy.flatiter'>\n", " | >>> for item in fl:\n", " | ... print(item)\n", " | ...\n", " | 0\n", " | 1\n", " | 2\n", " | 3\n", " | 4\n", " | 5\n", " | \n", " | >>> fl[2:4]\n", " | array([2, 3])\n", " | \n", " | Methods defined here:\n", " | \n", " | __array__(...)\n", " | __array__(type=None) Get array from iterator\n", " | \n", " | __delitem__(self, key, /)\n", " | Delete self[key].\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __iter__(self, /)\n", " | Implement iter(self).\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __len__(self, /)\n", " | Return len(self).\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __next__(self, /)\n", " | Implement next(self).\n", " | \n", " | __setitem__(self, key, value, /)\n", " | Set self[key] to value.\n", " | \n", " | copy(...)\n", " | copy()\n", " | \n", " | Get a copy of the iterator as a 1-D array.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.arange(6).reshape(2, 3)\n", " | >>> x\n", " | array([[0, 1, 2],\n", " | [3, 4, 5]])\n", " | >>> fl = x.flat\n", " | >>> fl.copy()\n", " | array([0, 1, 2, 3, 4, 5])\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors defined here:\n", " | \n", " | base\n", " | A reference to the array that is iterated over.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.arange(5)\n", " | >>> fl = x.flat\n", " | >>> fl.base is x\n", " | True\n", " | \n", " | coords\n", " | An N-dimensional tuple of current coordinates.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.arange(6).reshape(2, 3)\n", " | >>> fl = x.flat\n", " | >>> fl.coords\n", " | (0, 0)\n", " | >>> next(fl)\n", " | 0\n", " | >>> fl.coords\n", " | (0, 1)\n", " | \n", " | index\n", " | Current flat index into the array.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.arange(6).reshape(2, 3)\n", " | >>> fl = x.flat\n", " | >>> fl.index\n", " | 0\n", " | >>> next(fl)\n", " | 0\n", " | >>> fl.index\n", " | 1\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data and other attributes defined here:\n", " | \n", " | __hash__ = None\n", " \n", " class flexible(generic)\n", " | Abstract base class of all scalar types without predefined length.\n", " | The actual size of these types depends on the specific `np.dtype`\n", " | instantiation.\n", " | \n", " | Method resolution order:\n", " | flexible\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods inherited from generic:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data and other attributes inherited from generic:\n", " | \n", " | __hash__ = None\n", " \n", " class float16(floating)\n", " | Half-precision floating-point number type.\n", " | \n", " | :Character code: ``'e'``\n", " | :Canonical name: `numpy.half`\n", " | :Alias on this platform (win32 AMD64): `numpy.float16`: 16-bit-precision floating-point number type: sign bit, 5 bits exponent, 10 bits mantissa.\n", " | \n", " | Method resolution order:\n", " | float16\n", " | floating\n", " | inexact\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | as_integer_ratio(...)\n", " | half.as_integer_ratio() -> (int, int)\n", " | \n", " | Return a pair of integers, whose ratio is exactly equal to the original\n", " | floating point number, and with a positive denominator.\n", " | Raise `OverflowError` on infinities and a `ValueError` on NaNs.\n", " | \n", " | >>> np.half(10.0).as_integer_ratio()\n", " | (10, 1)\n", " | >>> np.half(0.0).as_integer_ratio()\n", " | (0, 1)\n", " | >>> np.half(-.25).as_integer_ratio()\n", " | (-1, 4)\n", " | \n", " | is_integer(...)\n", " | half.is_integer() -> bool\n", " | \n", " | Return ``True`` if the floating point number is finite with integral\n", " | value, and ``False`` otherwise.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.half(-2.0).is_integer()\n", " | True\n", " | >>> np.half(3.2).is_integer()\n", " | False\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from floating:\n", " | \n", " | __round__(...)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " class float32(floating)\n", " | Single-precision floating-point number type, compatible with C ``float``.\n", " | \n", " | :Character code: ``'f'``\n", " | :Canonical name: `numpy.single`\n", " | :Alias on this platform (win32 AMD64): `numpy.float32`: 32-bit-precision floating-point number type: sign bit, 8 bits exponent, 23 bits mantissa.\n", " | \n", " | Method resolution order:\n", " | float32\n", " | floating\n", " | inexact\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | as_integer_ratio(...)\n", " | single.as_integer_ratio() -> (int, int)\n", " | \n", " | Return a pair of integers, whose ratio is exactly equal to the original\n", " | floating point number, and with a positive denominator.\n", " | Raise `OverflowError` on infinities and a `ValueError` on NaNs.\n", " | \n", " | >>> np.single(10.0).as_integer_ratio()\n", " | (10, 1)\n", " | >>> np.single(0.0).as_integer_ratio()\n", " | (0, 1)\n", " | >>> np.single(-.25).as_integer_ratio()\n", " | (-1, 4)\n", " | \n", " | is_integer(...)\n", " | single.is_integer() -> bool\n", " | \n", " | Return ``True`` if the floating point number is finite with integral\n", " | value, and ``False`` otherwise.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.single(-2.0).is_integer()\n", " | True\n", " | >>> np.single(3.2).is_integer()\n", " | False\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from floating:\n", " | \n", " | __round__(...)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " class float64(floating, builtins.float)\n", " | float64(x=0, /)\n", " | \n", " | Double-precision floating-point number type, compatible with Python `float`\n", " | and C ``double``.\n", " | \n", " | :Character code: ``'d'``\n", " | :Canonical name: `numpy.double`\n", " | :Alias: `numpy.float_`\n", " | :Alias on this platform (win32 AMD64): `numpy.float64`: 64-bit precision floating-point number type: sign bit, 11 bits exponent, 52 bits mantissa.\n", " | \n", " | Method resolution order:\n", " | float64\n", " | floating\n", " | inexact\n", " | number\n", " | generic\n", " | builtins.float\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | as_integer_ratio(...)\n", " | double.as_integer_ratio() -> (int, int)\n", " | \n", " | Return a pair of integers, whose ratio is exactly equal to the original\n", " | floating point number, and with a positive denominator.\n", " | Raise `OverflowError` on infinities and a `ValueError` on NaNs.\n", " | \n", " | >>> np.double(10.0).as_integer_ratio()\n", " | (10, 1)\n", " | >>> np.double(0.0).as_integer_ratio()\n", " | (0, 1)\n", " | >>> np.double(-.25).as_integer_ratio()\n", " | (-1, 4)\n", " | \n", " | is_integer(...)\n", " | double.is_integer() -> bool\n", " | \n", " | Return ``True`` if the floating point number is finite with integral\n", " | value, and ``False`` otherwise.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.double(-2.0).is_integer()\n", " | True\n", " | >>> np.double(3.2).is_integer()\n", " | False\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from floating:\n", " | \n", " | __round__(...)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from builtins.float:\n", " | \n", " | __ceil__(self, /)\n", " | Return the ceiling as an Integral.\n", " | \n", " | __floor__(self, /)\n", " | Return the floor as an Integral.\n", " | \n", " | __getattribute__(self, name, /)\n", " | Return getattr(self, name).\n", " | \n", " | __getnewargs__(self, /)\n", " | \n", " | __trunc__(self, /)\n", " | Return the Integral closest to x between 0 and x.\n", " | \n", " | hex(self, /)\n", " | Return a hexadecimal representation of a floating-point number.\n", " | \n", " | >>> (-0.1).hex()\n", " | '-0x1.999999999999ap-4'\n", " | >>> 3.14159.hex()\n", " | '0x1.921f9f01b866ep+1'\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods inherited from builtins.float:\n", " | \n", " | __getformat__(typestr, /) from builtins.type\n", " | You probably don't want to use this function.\n", " | \n", " | typestr\n", " | Must be 'double' or 'float'.\n", " | \n", " | It exists mainly to be used in Python's test suite.\n", " | \n", " | This function returns whichever of 'unknown', 'IEEE, big-endian' or 'IEEE,\n", " | little-endian' best describes the format of floating point numbers used by the\n", " | C type named by typestr.\n", " | \n", " | fromhex(string, /) from builtins.type\n", " | Create a floating-point number from a hexadecimal string.\n", " | \n", " | >>> float.fromhex('0x1.ffffp10')\n", " | 2047.984375\n", " | >>> float.fromhex('-0x1p-1074')\n", " | -5e-324\n", " \n", " float_ = class float64(floating, builtins.float)\n", " | float_(x=0, /)\n", " | \n", " | Double-precision floating-point number type, compatible with Python `float`\n", " | and C ``double``.\n", " | \n", " | :Character code: ``'d'``\n", " | :Canonical name: `numpy.double`\n", " | :Alias: `numpy.float_`\n", " | :Alias on this platform (win32 AMD64): `numpy.float64`: 64-bit precision floating-point number type: sign bit, 11 bits exponent, 52 bits mantissa.\n", " | \n", " | Method resolution order:\n", " | float64\n", " | floating\n", " | inexact\n", " | number\n", " | generic\n", " | builtins.float\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | as_integer_ratio(...)\n", " | double.as_integer_ratio() -> (int, int)\n", " | \n", " | Return a pair of integers, whose ratio is exactly equal to the original\n", " | floating point number, and with a positive denominator.\n", " | Raise `OverflowError` on infinities and a `ValueError` on NaNs.\n", " | \n", " | >>> np.double(10.0).as_integer_ratio()\n", " | (10, 1)\n", " | >>> np.double(0.0).as_integer_ratio()\n", " | (0, 1)\n", " | >>> np.double(-.25).as_integer_ratio()\n", " | (-1, 4)\n", " | \n", " | is_integer(...)\n", " | double.is_integer() -> bool\n", " | \n", " | Return ``True`` if the floating point number is finite with integral\n", " | value, and ``False`` otherwise.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.double(-2.0).is_integer()\n", " | True\n", " | >>> np.double(3.2).is_integer()\n", " | False\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from floating:\n", " | \n", " | __round__(...)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from builtins.float:\n", " | \n", " | __ceil__(self, /)\n", " | Return the ceiling as an Integral.\n", " | \n", " | __floor__(self, /)\n", " | Return the floor as an Integral.\n", " | \n", " | __getattribute__(self, name, /)\n", " | Return getattr(self, name).\n", " | \n", " | __getnewargs__(self, /)\n", " | \n", " | __trunc__(self, /)\n", " | Return the Integral closest to x between 0 and x.\n", " | \n", " | hex(self, /)\n", " | Return a hexadecimal representation of a floating-point number.\n", " | \n", " | >>> (-0.1).hex()\n", " | '-0x1.999999999999ap-4'\n", " | >>> 3.14159.hex()\n", " | '0x1.921f9f01b866ep+1'\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods inherited from builtins.float:\n", " | \n", " | __getformat__(typestr, /) from builtins.type\n", " | You probably don't want to use this function.\n", " | \n", " | typestr\n", " | Must be 'double' or 'float'.\n", " | \n", " | It exists mainly to be used in Python's test suite.\n", " | \n", " | This function returns whichever of 'unknown', 'IEEE, big-endian' or 'IEEE,\n", " | little-endian' best describes the format of floating point numbers used by the\n", " | C type named by typestr.\n", " | \n", " | fromhex(string, /) from builtins.type\n", " | Create a floating-point number from a hexadecimal string.\n", " | \n", " | >>> float.fromhex('0x1.ffffp10')\n", " | 2047.984375\n", " | >>> float.fromhex('-0x1p-1074')\n", " | -5e-324\n", " \n", " class floating(inexact)\n", " | Abstract base class of all floating-point scalar types.\n", " | \n", " | Method resolution order:\n", " | floating\n", " | inexact\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __round__(...)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods inherited from number:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data and other attributes inherited from generic:\n", " | \n", " | __hash__ = None\n", " \n", " class format_parser(builtins.object)\n", " | format_parser(formats, names, titles, aligned=False, byteorder=None)\n", " | \n", " | Class to convert formats, names, titles description to a dtype.\n", " | \n", " | After constructing the format_parser object, the dtype attribute is\n", " | the converted data-type:\n", " | ``dtype = format_parser(formats, names, titles).dtype``\n", " | \n", " | Attributes\n", " | ----------\n", " | dtype : dtype\n", " | The converted data-type.\n", " | \n", " | Parameters\n", " | ----------\n", " | formats : str or list of str\n", " | The format description, either specified as a string with\n", " | comma-separated format descriptions in the form ``'f8, i4, a5'``, or\n", " | a list of format description strings in the form\n", " | ``['f8', 'i4', 'a5']``.\n", " | names : str or list/tuple of str\n", " | The field names, either specified as a comma-separated string in the\n", " | form ``'col1, col2, col3'``, or as a list or tuple of strings in the\n", " | form ``['col1', 'col2', 'col3']``.\n", " | An empty list can be used, in that case default field names\n", " | ('f0', 'f1', ...) are used.\n", " | titles : sequence\n", " | Sequence of title strings. An empty list can be used to leave titles\n", " | out.\n", " | aligned : bool, optional\n", " | If True, align the fields by padding as the C-compiler would.\n", " | Default is False.\n", " | byteorder : str, optional\n", " | If specified, all the fields will be changed to the\n", " | provided byte-order. Otherwise, the default byte-order is\n", " | used. For all available string specifiers, see `dtype.newbyteorder`.\n", " | \n", " | See Also\n", " | --------\n", " | dtype, typename, sctype2char\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.format_parser(['<f8', '<i4', '<a5'], ['col1', 'col2', 'col3'],\n", " | ... ['T1', 'T2', 'T3']).dtype\n", " | dtype([(('T1', 'col1'), '<f8'), (('T2', 'col2'), '<i4'), (('T3', 'col3'), 'S5')])\n", " | \n", " | `names` and/or `titles` can be empty lists. If `titles` is an empty list,\n", " | titles will simply not appear. If `names` is empty, default field names\n", " | will be used.\n", " | \n", " | >>> np.format_parser(['f8', 'i4', 'a5'], ['col1', 'col2', 'col3'],\n", " | ... []).dtype\n", " | dtype([('col1', '<f8'), ('col2', '<i4'), ('col3', '<S5')])\n", " | >>> np.format_parser(['<f8', '<i4', '<a5'], [], []).dtype\n", " | dtype([('f0', '<f8'), ('f1', '<i4'), ('f2', 'S5')])\n", " | \n", " | Methods defined here:\n", " | \n", " | __init__(self, formats, names, titles, aligned=False, byteorder=None)\n", " | Initialize self. See help(type(self)) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors defined here:\n", " | \n", " | __dict__\n", " | dictionary for instance variables (if defined)\n", " | \n", " | __weakref__\n", " | list of weak references to the object (if defined)\n", " \n", " class generic(builtins.object)\n", " | Base class for numpy scalar types.\n", " | \n", " | Class from which most (all?) numpy scalar types are derived. For\n", " | consistency, exposes the same API as `ndarray`, despite many\n", " | consequent attributes being either \"get-only,\" or completely irrelevant.\n", " | This is the class from which it is strongly suggested users should derive\n", " | custom scalar types.\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors defined here:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data and other attributes defined here:\n", " | \n", " | __hash__ = None\n", " \n", " half = class float16(floating)\n", " | Half-precision floating-point number type.\n", " | \n", " | :Character code: ``'e'``\n", " | :Canonical name: `numpy.half`\n", " | :Alias on this platform (win32 AMD64): `numpy.float16`: 16-bit-precision floating-point number type: sign bit, 5 bits exponent, 10 bits mantissa.\n", " | \n", " | Method resolution order:\n", " | float16\n", " | floating\n", " | inexact\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | as_integer_ratio(...)\n", " | half.as_integer_ratio() -> (int, int)\n", " | \n", " | Return a pair of integers, whose ratio is exactly equal to the original\n", " | floating point number, and with a positive denominator.\n", " | Raise `OverflowError` on infinities and a `ValueError` on NaNs.\n", " | \n", " | >>> np.half(10.0).as_integer_ratio()\n", " | (10, 1)\n", " | >>> np.half(0.0).as_integer_ratio()\n", " | (0, 1)\n", " | >>> np.half(-.25).as_integer_ratio()\n", " | (-1, 4)\n", " | \n", " | is_integer(...)\n", " | half.is_integer() -> bool\n", " | \n", " | Return ``True`` if the floating point number is finite with integral\n", " | value, and ``False`` otherwise.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.half(-2.0).is_integer()\n", " | True\n", " | >>> np.half(3.2).is_integer()\n", " | False\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from floating:\n", " | \n", " | __round__(...)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " class iinfo(builtins.object)\n", " | iinfo(int_type)\n", " | \n", " | iinfo(type)\n", " | \n", " | Machine limits for integer types.\n", " | \n", " | Attributes\n", " | ----------\n", " | bits : int\n", " | The number of bits occupied by the type.\n", " | dtype : dtype\n", " | Returns the dtype for which `iinfo` returns information.\n", " | min : int\n", " | The smallest integer expressible by the type.\n", " | max : int\n", " | The largest integer expressible by the type.\n", " | \n", " | Parameters\n", " | ----------\n", " | int_type : integer type, dtype, or instance\n", " | The kind of integer data type to get information about.\n", " | \n", " | See Also\n", " | --------\n", " | finfo : The equivalent for floating point data types.\n", " | \n", " | Examples\n", " | --------\n", " | With types:\n", " | \n", " | >>> ii16 = np.iinfo(np.int16)\n", " | >>> ii16.min\n", " | -32768\n", " | >>> ii16.max\n", " | 32767\n", " | >>> ii32 = np.iinfo(np.int32)\n", " | >>> ii32.min\n", " | -2147483648\n", " | >>> ii32.max\n", " | 2147483647\n", " | \n", " | With instances:\n", " | \n", " | >>> ii32 = np.iinfo(np.int32(10))\n", " | >>> ii32.min\n", " | -2147483648\n", " | >>> ii32.max\n", " | 2147483647\n", " | \n", " | Methods defined here:\n", " | \n", " | __init__(self, int_type)\n", " | Initialize self. See help(type(self)) for accurate signature.\n", " | \n", " | __repr__(self)\n", " | Return repr(self).\n", " | \n", " | __str__(self)\n", " | String representation.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Readonly properties defined here:\n", " | \n", " | max\n", " | Maximum value of given dtype.\n", " | \n", " | min\n", " | Minimum value of given dtype.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors defined here:\n", " | \n", " | __dict__\n", " | dictionary for instance variables (if defined)\n", " | \n", " | __weakref__\n", " | list of weak references to the object (if defined)\n", " \n", " class inexact(number)\n", " | Abstract base class of all numeric scalar types with a (potentially)\n", " | inexact representation of the values in its range, such as\n", " | floating-point numbers.\n", " | \n", " | Method resolution order:\n", " | inexact\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Class methods inherited from number:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data and other attributes inherited from generic:\n", " | \n", " | __hash__ = None\n", " \n", " class int16(signedinteger)\n", " | Signed integer type, compatible with C ``short``.\n", " | \n", " | :Character code: ``'h'``\n", " | :Canonical name: `numpy.short`\n", " | :Alias on this platform (win32 AMD64): `numpy.int16`: 16-bit signed integer (``-32_768`` to ``32_767``).\n", " | \n", " | Method resolution order:\n", " | int16\n", " | signedinteger\n", " | integer\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __index__(self, /)\n", " | Return self converted to an integer, if self is suitable for use as an index into a list.\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | bit_count(...)\n", " | int16.bit_count() -> int\n", " | \n", " | Computes the number of 1-bits in the absolute value of the input.\n", " | Analogous to the builtin `int.bit_count` or ``popcount`` in C++.\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.int16(127).bit_count()\n", " | 7\n", " | >>> np.int16(-127).bit_count()\n", " | 7\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from integer:\n", " | \n", " | __round__(...)\n", " | \n", " | is_integer(...)\n", " | integer.is_integer() -> bool\n", " | \n", " | Return ``True`` if the number is finite with integral value.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.int64(-2).is_integer()\n", " | True\n", " | >>> np.uint32(5).is_integer()\n", " | True\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from integer:\n", " | \n", " | denominator\n", " | denominator of value (1)\n", " | \n", " | numerator\n", " | numerator of value (the value itself)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " class int32(signedinteger)\n", " | Signed integer type, compatible with Python `int` and C ``long``.\n", " | \n", " | :Character code: ``'l'``\n", " | :Canonical name: `numpy.int_`\n", " | :Alias on this platform (win32 AMD64): `numpy.int32`: 32-bit signed integer (``-2_147_483_648`` to ``2_147_483_647``).\n", " | \n", " | Method resolution order:\n", " | int32\n", " | signedinteger\n", " | integer\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __index__(self, /)\n", " | Return self converted to an integer, if self is suitable for use as an index into a list.\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | bit_count(...)\n", " | int32.bit_count() -> int\n", " | \n", " | Computes the number of 1-bits in the absolute value of the input.\n", " | Analogous to the builtin `int.bit_count` or ``popcount`` in C++.\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.int32(127).bit_count()\n", " | 7\n", " | >>> np.int32(-127).bit_count()\n", " | 7\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from integer:\n", " | \n", " | __round__(...)\n", " | \n", " | is_integer(...)\n", " | integer.is_integer() -> bool\n", " | \n", " | Return ``True`` if the number is finite with integral value.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.int64(-2).is_integer()\n", " | True\n", " | >>> np.uint32(5).is_integer()\n", " | True\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from integer:\n", " | \n", " | denominator\n", " | denominator of value (1)\n", " | \n", " | numerator\n", " | numerator of value (the value itself)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " class int64(signedinteger)\n", " | Signed integer type, compatible with C ``long long``.\n", " | \n", " | :Character code: ``'q'``\n", " | :Canonical name: `numpy.longlong`\n", " | :Alias on this platform (win32 AMD64): `numpy.int64`: 64-bit signed integer (``-9_223_372_036_854_775_808`` to ``9_223_372_036_854_775_807``).\n", " | :Alias on this platform (win32 AMD64): `numpy.intp`: Signed integer large enough to fit pointer, compatible with C ``intptr_t``.\n", " | \n", " | Method resolution order:\n", " | int64\n", " | signedinteger\n", " | integer\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __index__(self, /)\n", " | Return self converted to an integer, if self is suitable for use as an index into a list.\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | bit_count(...)\n", " | int64.bit_count() -> int\n", " | \n", " | Computes the number of 1-bits in the absolute value of the input.\n", " | Analogous to the builtin `int.bit_count` or ``popcount`` in C++.\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.int64(127).bit_count()\n", " | 7\n", " | >>> np.int64(-127).bit_count()\n", " | 7\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from integer:\n", " | \n", " | __round__(...)\n", " | \n", " | is_integer(...)\n", " | integer.is_integer() -> bool\n", " | \n", " | Return ``True`` if the number is finite with integral value.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.int64(-2).is_integer()\n", " | True\n", " | >>> np.uint32(5).is_integer()\n", " | True\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from integer:\n", " | \n", " | denominator\n", " | denominator of value (1)\n", " | \n", " | numerator\n", " | numerator of value (the value itself)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " class int8(signedinteger)\n", " | Signed integer type, compatible with C ``char``.\n", " | \n", " | :Character code: ``'b'``\n", " | :Canonical name: `numpy.byte`\n", " | :Alias on this platform (win32 AMD64): `numpy.int8`: 8-bit signed integer (``-128`` to ``127``).\n", " | \n", " | Method resolution order:\n", " | int8\n", " | signedinteger\n", " | integer\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __index__(self, /)\n", " | Return self converted to an integer, if self is suitable for use as an index into a list.\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | bit_count(...)\n", " | int8.bit_count() -> int\n", " | \n", " | Computes the number of 1-bits in the absolute value of the input.\n", " | Analogous to the builtin `int.bit_count` or ``popcount`` in C++.\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.int8(127).bit_count()\n", " | 7\n", " | >>> np.int8(-127).bit_count()\n", " | 7\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from integer:\n", " | \n", " | __round__(...)\n", " | \n", " | is_integer(...)\n", " | integer.is_integer() -> bool\n", " | \n", " | Return ``True`` if the number is finite with integral value.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.int64(-2).is_integer()\n", " | True\n", " | >>> np.uint32(5).is_integer()\n", " | True\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from integer:\n", " | \n", " | denominator\n", " | denominator of value (1)\n", " | \n", " | numerator\n", " | numerator of value (the value itself)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " int_ = class int32(signedinteger)\n", " | Signed integer type, compatible with Python `int` and C ``long``.\n", " | \n", " | :Character code: ``'l'``\n", " | :Canonical name: `numpy.int_`\n", " | :Alias on this platform (win32 AMD64): `numpy.int32`: 32-bit signed integer (``-2_147_483_648`` to ``2_147_483_647``).\n", " | \n", " | Method resolution order:\n", " | int32\n", " | signedinteger\n", " | integer\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __index__(self, /)\n", " | Return self converted to an integer, if self is suitable for use as an index into a list.\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | bit_count(...)\n", " | int32.bit_count() -> int\n", " | \n", " | Computes the number of 1-bits in the absolute value of the input.\n", " | Analogous to the builtin `int.bit_count` or ``popcount`` in C++.\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.int32(127).bit_count()\n", " | 7\n", " | >>> np.int32(-127).bit_count()\n", " | 7\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from integer:\n", " | \n", " | __round__(...)\n", " | \n", " | is_integer(...)\n", " | integer.is_integer() -> bool\n", " | \n", " | Return ``True`` if the number is finite with integral value.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.int64(-2).is_integer()\n", " | True\n", " | >>> np.uint32(5).is_integer()\n", " | True\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from integer:\n", " | \n", " | denominator\n", " | denominator of value (1)\n", " | \n", " | numerator\n", " | numerator of value (the value itself)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " class intc(signedinteger)\n", " | Signed integer type, compatible with C ``int``.\n", " | \n", " | :Character code: ``'i'``\n", " | \n", " | Method resolution order:\n", " | intc\n", " | signedinteger\n", " | integer\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __index__(self, /)\n", " | Return self converted to an integer, if self is suitable for use as an index into a list.\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | bit_count(...)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from integer:\n", " | \n", " | __round__(...)\n", " | \n", " | is_integer(...)\n", " | integer.is_integer() -> bool\n", " | \n", " | Return ``True`` if the number is finite with integral value.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.int64(-2).is_integer()\n", " | True\n", " | >>> np.uint32(5).is_integer()\n", " | True\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from integer:\n", " | \n", " | denominator\n", " | denominator of value (1)\n", " | \n", " | numerator\n", " | numerator of value (the value itself)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " class integer(number)\n", " | Abstract base class of all integer scalar types.\n", " | \n", " | Method resolution order:\n", " | integer\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __round__(...)\n", " | \n", " | is_integer(...)\n", " | integer.is_integer() -> bool\n", " | \n", " | Return ``True`` if the number is finite with integral value.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.int64(-2).is_integer()\n", " | True\n", " | >>> np.uint32(5).is_integer()\n", " | True\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors defined here:\n", " | \n", " | denominator\n", " | denominator of value (1)\n", " | \n", " | numerator\n", " | numerator of value (the value itself)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods inherited from number:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data and other attributes inherited from generic:\n", " | \n", " | __hash__ = None\n", " \n", " intp = class int64(signedinteger)\n", " | Signed integer type, compatible with C ``long long``.\n", " | \n", " | :Character code: ``'q'``\n", " | :Canonical name: `numpy.longlong`\n", " | :Alias on this platform (win32 AMD64): `numpy.int64`: 64-bit signed integer (``-9_223_372_036_854_775_808`` to ``9_223_372_036_854_775_807``).\n", " | :Alias on this platform (win32 AMD64): `numpy.intp`: Signed integer large enough to fit pointer, compatible with C ``intptr_t``.\n", " | \n", " | Method resolution order:\n", " | int64\n", " | signedinteger\n", " | integer\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __index__(self, /)\n", " | Return self converted to an integer, if self is suitable for use as an index into a list.\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | bit_count(...)\n", " | int64.bit_count() -> int\n", " | \n", " | Computes the number of 1-bits in the absolute value of the input.\n", " | Analogous to the builtin `int.bit_count` or ``popcount`` in C++.\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.int64(127).bit_count()\n", " | 7\n", " | >>> np.int64(-127).bit_count()\n", " | 7\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from integer:\n", " | \n", " | __round__(...)\n", " | \n", " | is_integer(...)\n", " | integer.is_integer() -> bool\n", " | \n", " | Return ``True`` if the number is finite with integral value.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.int64(-2).is_integer()\n", " | True\n", " | >>> np.uint32(5).is_integer()\n", " | True\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from integer:\n", " | \n", " | denominator\n", " | denominator of value (1)\n", " | \n", " | numerator\n", " | numerator of value (the value itself)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " longcomplex = class clongdouble(complexfloating)\n", " | Complex number type composed of two extended-precision floating-point\n", " | numbers.\n", " | \n", " | :Character code: ``'G'``\n", " | :Alias: `numpy.clongfloat`\n", " | :Alias: `numpy.longcomplex`\n", " | \n", " | Method resolution order:\n", " | clongdouble\n", " | complexfloating\n", " | inexact\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __complex__(...)\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from complexfloating:\n", " | \n", " | __round__(...)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " class longdouble(floating)\n", " | Extended-precision floating-point number type, compatible with C\n", " | ``long double`` but not necessarily with IEEE 754 quadruple-precision.\n", " | \n", " | :Character code: ``'g'``\n", " | :Alias: `numpy.longfloat`\n", " | \n", " | Method resolution order:\n", " | longdouble\n", " | floating\n", " | inexact\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | as_integer_ratio(...)\n", " | longdouble.as_integer_ratio() -> (int, int)\n", " | \n", " | Return a pair of integers, whose ratio is exactly equal to the original\n", " | floating point number, and with a positive denominator.\n", " | Raise `OverflowError` on infinities and a `ValueError` on NaNs.\n", " | \n", " | >>> np.longdouble(10.0).as_integer_ratio()\n", " | (10, 1)\n", " | >>> np.longdouble(0.0).as_integer_ratio()\n", " | (0, 1)\n", " | >>> np.longdouble(-.25).as_integer_ratio()\n", " | (-1, 4)\n", " | \n", " | is_integer(...)\n", " | longdouble.is_integer() -> bool\n", " | \n", " | Return ``True`` if the floating point number is finite with integral\n", " | value, and ``False`` otherwise.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.longdouble(-2.0).is_integer()\n", " | True\n", " | >>> np.longdouble(3.2).is_integer()\n", " | False\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from floating:\n", " | \n", " | __round__(...)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " longfloat = class longdouble(floating)\n", " | Extended-precision floating-point number type, compatible with C\n", " | ``long double`` but not necessarily with IEEE 754 quadruple-precision.\n", " | \n", " | :Character code: ``'g'``\n", " | :Alias: `numpy.longfloat`\n", " | \n", " | Method resolution order:\n", " | longdouble\n", " | floating\n", " | inexact\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | as_integer_ratio(...)\n", " | longdouble.as_integer_ratio() -> (int, int)\n", " | \n", " | Return a pair of integers, whose ratio is exactly equal to the original\n", " | floating point number, and with a positive denominator.\n", " | Raise `OverflowError` on infinities and a `ValueError` on NaNs.\n", " | \n", " | >>> np.longdouble(10.0).as_integer_ratio()\n", " | (10, 1)\n", " | >>> np.longdouble(0.0).as_integer_ratio()\n", " | (0, 1)\n", " | >>> np.longdouble(-.25).as_integer_ratio()\n", " | (-1, 4)\n", " | \n", " | is_integer(...)\n", " | longdouble.is_integer() -> bool\n", " | \n", " | Return ``True`` if the floating point number is finite with integral\n", " | value, and ``False`` otherwise.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.longdouble(-2.0).is_integer()\n", " | True\n", " | >>> np.longdouble(3.2).is_integer()\n", " | False\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from floating:\n", " | \n", " | __round__(...)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " longlong = class int64(signedinteger)\n", " | Signed integer type, compatible with C ``long long``.\n", " | \n", " | :Character code: ``'q'``\n", " | :Canonical name: `numpy.longlong`\n", " | :Alias on this platform (win32 AMD64): `numpy.int64`: 64-bit signed integer (``-9_223_372_036_854_775_808`` to ``9_223_372_036_854_775_807``).\n", " | :Alias on this platform (win32 AMD64): `numpy.intp`: Signed integer large enough to fit pointer, compatible with C ``intptr_t``.\n", " | \n", " | Method resolution order:\n", " | int64\n", " | signedinteger\n", " | integer\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __index__(self, /)\n", " | Return self converted to an integer, if self is suitable for use as an index into a list.\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | bit_count(...)\n", " | int64.bit_count() -> int\n", " | \n", " | Computes the number of 1-bits in the absolute value of the input.\n", " | Analogous to the builtin `int.bit_count` or ``popcount`` in C++.\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.int64(127).bit_count()\n", " | 7\n", " | >>> np.int64(-127).bit_count()\n", " | 7\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from integer:\n", " | \n", " | __round__(...)\n", " | \n", " | is_integer(...)\n", " | integer.is_integer() -> bool\n", " | \n", " | Return ``True`` if the number is finite with integral value.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.int64(-2).is_integer()\n", " | True\n", " | >>> np.uint32(5).is_integer()\n", " | True\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from integer:\n", " | \n", " | denominator\n", " | denominator of value (1)\n", " | \n", " | numerator\n", " | numerator of value (the value itself)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " class matrix(ndarray)\n", " | matrix(data, dtype=None, copy=True)\n", " | \n", " | matrix(data, dtype=None, copy=True)\n", " | \n", " | .. note:: It is no longer recommended to use this class, even for linear\n", " | algebra. Instead use regular arrays. The class may be removed\n", " | in the future.\n", " | \n", " | Returns a matrix from an array-like object, or from a string of data.\n", " | A matrix is a specialized 2-D array that retains its 2-D nature\n", " | through operations. It has certain special operators, such as ``*``\n", " | (matrix multiplication) and ``**`` (matrix power).\n", " | \n", " | Parameters\n", " | ----------\n", " | data : array_like or string\n", " | If `data` is a string, it is interpreted as a matrix with commas\n", " | or spaces separating columns, and semicolons separating rows.\n", " | dtype : data-type\n", " | Data-type of the output matrix.\n", " | copy : bool\n", " | If `data` is already an `ndarray`, then this flag determines\n", " | whether the data is copied (the default), or whether a view is\n", " | constructed.\n", " | \n", " | See Also\n", " | --------\n", " | array\n", " | \n", " | Examples\n", " | --------\n", " | >>> a = np.matrix('1 2; 3 4')\n", " | >>> a\n", " | matrix([[1, 2],\n", " | [3, 4]])\n", " | \n", " | >>> np.matrix([[1, 2], [3, 4]])\n", " | matrix([[1, 2],\n", " | [3, 4]])\n", " | \n", " | Method resolution order:\n", " | matrix\n", " | ndarray\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __array_finalize__(self, obj)\n", " | a.__array_finalize__(obj, /)\n", " | \n", " | Present so subclasses can call super. Does nothing.\n", " | \n", " | __getitem__(self, index)\n", " | Return self[key].\n", " | \n", " | __imul__(self, other)\n", " | Return self*=value.\n", " | \n", " | __ipow__(self, other)\n", " | Return self**=value.\n", " | \n", " | __mul__(self, other)\n", " | Return self*value.\n", " | \n", " | __pow__(self, other)\n", " | Return pow(self, value, mod).\n", " | \n", " | __rmul__(self, other)\n", " | Return value*self.\n", " | \n", " | __rpow__(self, other)\n", " | Return pow(value, self, mod).\n", " | \n", " | all(self, axis=None, out=None)\n", " | Test whether all matrix elements along a given axis evaluate to True.\n", " | \n", " | Parameters\n", " | ----------\n", " | See `numpy.all` for complete descriptions\n", " | \n", " | See Also\n", " | --------\n", " | numpy.all\n", " | \n", " | Notes\n", " | -----\n", " | This is the same as `ndarray.all`, but it returns a `matrix` object.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.matrix(np.arange(12).reshape((3,4))); x\n", " | matrix([[ 0, 1, 2, 3],\n", " | [ 4, 5, 6, 7],\n", " | [ 8, 9, 10, 11]])\n", " | >>> y = x[0]; y\n", " | matrix([[0, 1, 2, 3]])\n", " | >>> (x == y)\n", " | matrix([[ True, True, True, True],\n", " | [False, False, False, False],\n", " | [False, False, False, False]])\n", " | >>> (x == y).all()\n", " | False\n", " | >>> (x == y).all(0)\n", " | matrix([[False, False, False, False]])\n", " | >>> (x == y).all(1)\n", " | matrix([[ True],\n", " | [False],\n", " | [False]])\n", " | \n", " | any(self, axis=None, out=None)\n", " | Test whether any array element along a given axis evaluates to True.\n", " | \n", " | Refer to `numpy.any` for full documentation.\n", " | \n", " | Parameters\n", " | ----------\n", " | axis : int, optional\n", " | Axis along which logical OR is performed\n", " | out : ndarray, optional\n", " | Output to existing array instead of creating new one, must have\n", " | same shape as expected output\n", " | \n", " | Returns\n", " | -------\n", " | any : bool, ndarray\n", " | Returns a single bool if `axis` is ``None``; otherwise,\n", " | returns `ndarray`\n", " | \n", " | argmax(self, axis=None, out=None)\n", " | Indexes of the maximum values along an axis.\n", " | \n", " | Return the indexes of the first occurrences of the maximum values\n", " | along the specified axis. If axis is None, the index is for the\n", " | flattened matrix.\n", " | \n", " | Parameters\n", " | ----------\n", " | See `numpy.argmax` for complete descriptions\n", " | \n", " | See Also\n", " | --------\n", " | numpy.argmax\n", " | \n", " | Notes\n", " | -----\n", " | This is the same as `ndarray.argmax`, but returns a `matrix` object\n", " | where `ndarray.argmax` would return an `ndarray`.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.matrix(np.arange(12).reshape((3,4))); x\n", " | matrix([[ 0, 1, 2, 3],\n", " | [ 4, 5, 6, 7],\n", " | [ 8, 9, 10, 11]])\n", " | >>> x.argmax()\n", " | 11\n", " | >>> x.argmax(0)\n", " | matrix([[2, 2, 2, 2]])\n", " | >>> x.argmax(1)\n", " | matrix([[3],\n", " | [3],\n", " | [3]])\n", " | \n", " | argmin(self, axis=None, out=None)\n", " | Indexes of the minimum values along an axis.\n", " | \n", " | Return the indexes of the first occurrences of the minimum values\n", " | along the specified axis. If axis is None, the index is for the\n", " | flattened matrix.\n", " | \n", " | Parameters\n", " | ----------\n", " | See `numpy.argmin` for complete descriptions.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.argmin\n", " | \n", " | Notes\n", " | -----\n", " | This is the same as `ndarray.argmin`, but returns a `matrix` object\n", " | where `ndarray.argmin` would return an `ndarray`.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = -np.matrix(np.arange(12).reshape((3,4))); x\n", " | matrix([[ 0, -1, -2, -3],\n", " | [ -4, -5, -6, -7],\n", " | [ -8, -9, -10, -11]])\n", " | >>> x.argmin()\n", " | 11\n", " | >>> x.argmin(0)\n", " | matrix([[2, 2, 2, 2]])\n", " | >>> x.argmin(1)\n", " | matrix([[3],\n", " | [3],\n", " | [3]])\n", " | \n", " | flatten(self, order='C')\n", " | Return a flattened copy of the matrix.\n", " | \n", " | All `N` elements of the matrix are placed into a single row.\n", " | \n", " | Parameters\n", " | ----------\n", " | order : {'C', 'F', 'A', 'K'}, optional\n", " | 'C' means to flatten in row-major (C-style) order. 'F' means to\n", " | flatten in column-major (Fortran-style) order. 'A' means to\n", " | flatten in column-major order if `m` is Fortran *contiguous* in\n", " | memory, row-major order otherwise. 'K' means to flatten `m` in\n", " | the order the elements occur in memory. The default is 'C'.\n", " | \n", " | Returns\n", " | -------\n", " | y : matrix\n", " | A copy of the matrix, flattened to a `(1, N)` matrix where `N`\n", " | is the number of elements in the original matrix.\n", " | \n", " | See Also\n", " | --------\n", " | ravel : Return a flattened array.\n", " | flat : A 1-D flat iterator over the matrix.\n", " | \n", " | Examples\n", " | --------\n", " | >>> m = np.matrix([[1,2], [3,4]])\n", " | >>> m.flatten()\n", " | matrix([[1, 2, 3, 4]])\n", " | >>> m.flatten('F')\n", " | matrix([[1, 3, 2, 4]])\n", " | \n", " | getA = A(self)\n", " | Return `self` as an `ndarray` object.\n", " | \n", " | Equivalent to ``np.asarray(self)``.\n", " | \n", " | Parameters\n", " | ----------\n", " | None\n", " | \n", " | Returns\n", " | -------\n", " | ret : ndarray\n", " | `self` as an `ndarray`\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.matrix(np.arange(12).reshape((3,4))); x\n", " | matrix([[ 0, 1, 2, 3],\n", " | [ 4, 5, 6, 7],\n", " | [ 8, 9, 10, 11]])\n", " | >>> x.getA()\n", " | array([[ 0, 1, 2, 3],\n", " | [ 4, 5, 6, 7],\n", " | [ 8, 9, 10, 11]])\n", " | \n", " | getA1 = A1(self)\n", " | Return `self` as a flattened `ndarray`.\n", " | \n", " | Equivalent to ``np.asarray(x).ravel()``\n", " | \n", " | Parameters\n", " | ----------\n", " | None\n", " | \n", " | Returns\n", " | -------\n", " | ret : ndarray\n", " | `self`, 1-D, as an `ndarray`\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.matrix(np.arange(12).reshape((3,4))); x\n", " | matrix([[ 0, 1, 2, 3],\n", " | [ 4, 5, 6, 7],\n", " | [ 8, 9, 10, 11]])\n", " | >>> x.getA1()\n", " | array([ 0, 1, 2, ..., 9, 10, 11])\n", " | \n", " | getH = H(self)\n", " | Returns the (complex) conjugate transpose of `self`.\n", " | \n", " | Equivalent to ``np.transpose(self)`` if `self` is real-valued.\n", " | \n", " | Parameters\n", " | ----------\n", " | None\n", " | \n", " | Returns\n", " | -------\n", " | ret : matrix object\n", " | complex conjugate transpose of `self`\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.matrix(np.arange(12).reshape((3,4)))\n", " | >>> z = x - 1j*x; z\n", " | matrix([[ 0. +0.j, 1. -1.j, 2. -2.j, 3. -3.j],\n", " | [ 4. -4.j, 5. -5.j, 6. -6.j, 7. -7.j],\n", " | [ 8. -8.j, 9. -9.j, 10.-10.j, 11.-11.j]])\n", " | >>> z.getH()\n", " | matrix([[ 0. -0.j, 4. +4.j, 8. +8.j],\n", " | [ 1. +1.j, 5. +5.j, 9. +9.j],\n", " | [ 2. +2.j, 6. +6.j, 10.+10.j],\n", " | [ 3. +3.j, 7. +7.j, 11.+11.j]])\n", " | \n", " | getI = I(self)\n", " | Returns the (multiplicative) inverse of invertible `self`.\n", " | \n", " | Parameters\n", " | ----------\n", " | None\n", " | \n", " | Returns\n", " | -------\n", " | ret : matrix object\n", " | If `self` is non-singular, `ret` is such that ``ret * self`` ==\n", " | ``self * ret`` == ``np.matrix(np.eye(self[0,:].size))`` all return\n", " | ``True``.\n", " | \n", " | Raises\n", " | ------\n", " | numpy.linalg.LinAlgError: Singular matrix\n", " | If `self` is singular.\n", " | \n", " | See Also\n", " | --------\n", " | linalg.inv\n", " | \n", " | Examples\n", " | --------\n", " | >>> m = np.matrix('[1, 2; 3, 4]'); m\n", " | matrix([[1, 2],\n", " | [3, 4]])\n", " | >>> m.getI()\n", " | matrix([[-2. , 1. ],\n", " | [ 1.5, -0.5]])\n", " | >>> m.getI() * m\n", " | matrix([[ 1., 0.], # may vary\n", " | [ 0., 1.]])\n", " | \n", " | getT = T(self)\n", " | Returns the transpose of the matrix.\n", " | \n", " | Does *not* conjugate! For the complex conjugate transpose, use ``.H``.\n", " | \n", " | Parameters\n", " | ----------\n", " | None\n", " | \n", " | Returns\n", " | -------\n", " | ret : matrix object\n", " | The (non-conjugated) transpose of the matrix.\n", " | \n", " | See Also\n", " | --------\n", " | transpose, getH\n", " | \n", " | Examples\n", " | --------\n", " | >>> m = np.matrix('[1, 2; 3, 4]')\n", " | >>> m\n", " | matrix([[1, 2],\n", " | [3, 4]])\n", " | >>> m.getT()\n", " | matrix([[1, 3],\n", " | [2, 4]])\n", " | \n", " | max(self, axis=None, out=None)\n", " | Return the maximum value along an axis.\n", " | \n", " | Parameters\n", " | ----------\n", " | See `amax` for complete descriptions\n", " | \n", " | See Also\n", " | --------\n", " | amax, ndarray.max\n", " | \n", " | Notes\n", " | -----\n", " | This is the same as `ndarray.max`, but returns a `matrix` object\n", " | where `ndarray.max` would return an ndarray.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.matrix(np.arange(12).reshape((3,4))); x\n", " | matrix([[ 0, 1, 2, 3],\n", " | [ 4, 5, 6, 7],\n", " | [ 8, 9, 10, 11]])\n", " | >>> x.max()\n", " | 11\n", " | >>> x.max(0)\n", " | matrix([[ 8, 9, 10, 11]])\n", " | >>> x.max(1)\n", " | matrix([[ 3],\n", " | [ 7],\n", " | [11]])\n", " | \n", " | mean(self, axis=None, dtype=None, out=None)\n", " | Returns the average of the matrix elements along the given axis.\n", " | \n", " | Refer to `numpy.mean` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.mean\n", " | \n", " | Notes\n", " | -----\n", " | Same as `ndarray.mean` except that, where that returns an `ndarray`,\n", " | this returns a `matrix` object.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.matrix(np.arange(12).reshape((3, 4)))\n", " | >>> x\n", " | matrix([[ 0, 1, 2, 3],\n", " | [ 4, 5, 6, 7],\n", " | [ 8, 9, 10, 11]])\n", " | >>> x.mean()\n", " | 5.5\n", " | >>> x.mean(0)\n", " | matrix([[4., 5., 6., 7.]])\n", " | >>> x.mean(1)\n", " | matrix([[ 1.5],\n", " | [ 5.5],\n", " | [ 9.5]])\n", " | \n", " | min(self, axis=None, out=None)\n", " | Return the minimum value along an axis.\n", " | \n", " | Parameters\n", " | ----------\n", " | See `amin` for complete descriptions.\n", " | \n", " | See Also\n", " | --------\n", " | amin, ndarray.min\n", " | \n", " | Notes\n", " | -----\n", " | This is the same as `ndarray.min`, but returns a `matrix` object\n", " | where `ndarray.min` would return an ndarray.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = -np.matrix(np.arange(12).reshape((3,4))); x\n", " | matrix([[ 0, -1, -2, -3],\n", " | [ -4, -5, -6, -7],\n", " | [ -8, -9, -10, -11]])\n", " | >>> x.min()\n", " | -11\n", " | >>> x.min(0)\n", " | matrix([[ -8, -9, -10, -11]])\n", " | >>> x.min(1)\n", " | matrix([[ -3],\n", " | [ -7],\n", " | [-11]])\n", " | \n", " | prod(self, axis=None, dtype=None, out=None)\n", " | Return the product of the array elements over the given axis.\n", " | \n", " | Refer to `prod` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | prod, ndarray.prod\n", " | \n", " | Notes\n", " | -----\n", " | Same as `ndarray.prod`, except, where that returns an `ndarray`, this\n", " | returns a `matrix` object instead.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.matrix(np.arange(12).reshape((3,4))); x\n", " | matrix([[ 0, 1, 2, 3],\n", " | [ 4, 5, 6, 7],\n", " | [ 8, 9, 10, 11]])\n", " | >>> x.prod()\n", " | 0\n", " | >>> x.prod(0)\n", " | matrix([[ 0, 45, 120, 231]])\n", " | >>> x.prod(1)\n", " | matrix([[ 0],\n", " | [ 840],\n", " | [7920]])\n", " | \n", " | ptp(self, axis=None, out=None)\n", " | Peak-to-peak (maximum - minimum) value along the given axis.\n", " | \n", " | Refer to `numpy.ptp` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.ptp\n", " | \n", " | Notes\n", " | -----\n", " | Same as `ndarray.ptp`, except, where that would return an `ndarray` object,\n", " | this returns a `matrix` object.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.matrix(np.arange(12).reshape((3,4))); x\n", " | matrix([[ 0, 1, 2, 3],\n", " | [ 4, 5, 6, 7],\n", " | [ 8, 9, 10, 11]])\n", " | >>> x.ptp()\n", " | 11\n", " | >>> x.ptp(0)\n", " | matrix([[8, 8, 8, 8]])\n", " | >>> x.ptp(1)\n", " | matrix([[3],\n", " | [3],\n", " | [3]])\n", " | \n", " | ravel(self, order='C')\n", " | Return a flattened matrix.\n", " | \n", " | Refer to `numpy.ravel` for more documentation.\n", " | \n", " | Parameters\n", " | ----------\n", " | order : {'C', 'F', 'A', 'K'}, optional\n", " | The elements of `m` are read using this index order. 'C' means to\n", " | index the elements in C-like order, with the last axis index\n", " | changing fastest, back to the first axis index changing slowest.\n", " | 'F' means to index the elements in Fortran-like index order, with\n", " | the first index changing fastest, and the last index changing\n", " | slowest. Note that the 'C' and 'F' options take no account of the\n", " | memory layout of the underlying array, and only refer to the order\n", " | of axis indexing. 'A' means to read the elements in Fortran-like\n", " | index order if `m` is Fortran *contiguous* in memory, C-like order\n", " | otherwise. 'K' means to read the elements in the order they occur\n", " | in memory, except for reversing the data when strides are negative.\n", " | By default, 'C' index order is used.\n", " | \n", " | Returns\n", " | -------\n", " | ret : matrix\n", " | Return the matrix flattened to shape `(1, N)` where `N`\n", " | is the number of elements in the original matrix.\n", " | A copy is made only if necessary.\n", " | \n", " | See Also\n", " | --------\n", " | matrix.flatten : returns a similar output matrix but always a copy\n", " | matrix.flat : a flat iterator on the array.\n", " | numpy.ravel : related function which returns an ndarray\n", " | \n", " | squeeze(self, axis=None)\n", " | Return a possibly reshaped matrix.\n", " | \n", " | Refer to `numpy.squeeze` for more documentation.\n", " | \n", " | Parameters\n", " | ----------\n", " | axis : None or int or tuple of ints, optional\n", " | Selects a subset of the axes of length one in the shape.\n", " | If an axis is selected with shape entry greater than one,\n", " | an error is raised.\n", " | \n", " | Returns\n", " | -------\n", " | squeezed : matrix\n", " | The matrix, but as a (1, N) matrix if it had shape (N, 1).\n", " | \n", " | See Also\n", " | --------\n", " | numpy.squeeze : related function\n", " | \n", " | Notes\n", " | -----\n", " | If `m` has a single column then that column is returned\n", " | as the single row of a matrix. Otherwise `m` is returned.\n", " | The returned matrix is always either `m` itself or a view into `m`.\n", " | Supplying an axis keyword argument will not affect the returned matrix\n", " | but it may cause an error to be raised.\n", " | \n", " | Examples\n", " | --------\n", " | >>> c = np.matrix([[1], [2]])\n", " | >>> c\n", " | matrix([[1],\n", " | [2]])\n", " | >>> c.squeeze()\n", " | matrix([[1, 2]])\n", " | >>> r = c.T\n", " | >>> r\n", " | matrix([[1, 2]])\n", " | >>> r.squeeze()\n", " | matrix([[1, 2]])\n", " | >>> m = np.matrix([[1, 2], [3, 4]])\n", " | >>> m.squeeze()\n", " | matrix([[1, 2],\n", " | [3, 4]])\n", " | \n", " | std(self, axis=None, dtype=None, out=None, ddof=0)\n", " | Return the standard deviation of the array elements along the given axis.\n", " | \n", " | Refer to `numpy.std` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.std\n", " | \n", " | Notes\n", " | -----\n", " | This is the same as `ndarray.std`, except that where an `ndarray` would\n", " | be returned, a `matrix` object is returned instead.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.matrix(np.arange(12).reshape((3, 4)))\n", " | >>> x\n", " | matrix([[ 0, 1, 2, 3],\n", " | [ 4, 5, 6, 7],\n", " | [ 8, 9, 10, 11]])\n", " | >>> x.std()\n", " | 3.4520525295346629 # may vary\n", " | >>> x.std(0)\n", " | matrix([[ 3.26598632, 3.26598632, 3.26598632, 3.26598632]]) # may vary\n", " | >>> x.std(1)\n", " | matrix([[ 1.11803399],\n", " | [ 1.11803399],\n", " | [ 1.11803399]])\n", " | \n", " | sum(self, axis=None, dtype=None, out=None)\n", " | Returns the sum of the matrix elements, along the given axis.\n", " | \n", " | Refer to `numpy.sum` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.sum\n", " | \n", " | Notes\n", " | -----\n", " | This is the same as `ndarray.sum`, except that where an `ndarray` would\n", " | be returned, a `matrix` object is returned instead.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.matrix([[1, 2], [4, 3]])\n", " | >>> x.sum()\n", " | 10\n", " | >>> x.sum(axis=1)\n", " | matrix([[3],\n", " | [7]])\n", " | >>> x.sum(axis=1, dtype='float')\n", " | matrix([[3.],\n", " | [7.]])\n", " | >>> out = np.zeros((2, 1), dtype='float')\n", " | >>> x.sum(axis=1, dtype='float', out=np.asmatrix(out))\n", " | matrix([[3.],\n", " | [7.]])\n", " | \n", " | tolist(self)\n", " | Return the matrix as a (possibly nested) list.\n", " | \n", " | See `ndarray.tolist` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | ndarray.tolist\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.matrix(np.arange(12).reshape((3,4))); x\n", " | matrix([[ 0, 1, 2, 3],\n", " | [ 4, 5, 6, 7],\n", " | [ 8, 9, 10, 11]])\n", " | >>> x.tolist()\n", " | [[0, 1, 2, 3], [4, 5, 6, 7], [8, 9, 10, 11]]\n", " | \n", " | var(self, axis=None, dtype=None, out=None, ddof=0)\n", " | Returns the variance of the matrix elements, along the given axis.\n", " | \n", " | Refer to `numpy.var` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.var\n", " | \n", " | Notes\n", " | -----\n", " | This is the same as `ndarray.var`, except that where an `ndarray` would\n", " | be returned, a `matrix` object is returned instead.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.matrix(np.arange(12).reshape((3, 4)))\n", " | >>> x\n", " | matrix([[ 0, 1, 2, 3],\n", " | [ 4, 5, 6, 7],\n", " | [ 8, 9, 10, 11]])\n", " | >>> x.var()\n", " | 11.916666666666666\n", " | >>> x.var(0)\n", " | matrix([[ 10.66666667, 10.66666667, 10.66666667, 10.66666667]]) # may vary\n", " | >>> x.var(1)\n", " | matrix([[1.25],\n", " | [1.25],\n", " | [1.25]])\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(subtype, data, dtype=None, copy=True)\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Readonly properties defined here:\n", " | \n", " | A\n", " | Return `self` as an `ndarray` object.\n", " | \n", " | Equivalent to ``np.asarray(self)``.\n", " | \n", " | Parameters\n", " | ----------\n", " | None\n", " | \n", " | Returns\n", " | -------\n", " | ret : ndarray\n", " | `self` as an `ndarray`\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.matrix(np.arange(12).reshape((3,4))); x\n", " | matrix([[ 0, 1, 2, 3],\n", " | [ 4, 5, 6, 7],\n", " | [ 8, 9, 10, 11]])\n", " | >>> x.getA()\n", " | array([[ 0, 1, 2, 3],\n", " | [ 4, 5, 6, 7],\n", " | [ 8, 9, 10, 11]])\n", " | \n", " | A1\n", " | Return `self` as a flattened `ndarray`.\n", " | \n", " | Equivalent to ``np.asarray(x).ravel()``\n", " | \n", " | Parameters\n", " | ----------\n", " | None\n", " | \n", " | Returns\n", " | -------\n", " | ret : ndarray\n", " | `self`, 1-D, as an `ndarray`\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.matrix(np.arange(12).reshape((3,4))); x\n", " | matrix([[ 0, 1, 2, 3],\n", " | [ 4, 5, 6, 7],\n", " | [ 8, 9, 10, 11]])\n", " | >>> x.getA1()\n", " | array([ 0, 1, 2, ..., 9, 10, 11])\n", " | \n", " | H\n", " | Returns the (complex) conjugate transpose of `self`.\n", " | \n", " | Equivalent to ``np.transpose(self)`` if `self` is real-valued.\n", " | \n", " | Parameters\n", " | ----------\n", " | None\n", " | \n", " | Returns\n", " | -------\n", " | ret : matrix object\n", " | complex conjugate transpose of `self`\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.matrix(np.arange(12).reshape((3,4)))\n", " | >>> z = x - 1j*x; z\n", " | matrix([[ 0. +0.j, 1. -1.j, 2. -2.j, 3. -3.j],\n", " | [ 4. -4.j, 5. -5.j, 6. -6.j, 7. -7.j],\n", " | [ 8. -8.j, 9. -9.j, 10.-10.j, 11.-11.j]])\n", " | >>> z.getH()\n", " | matrix([[ 0. -0.j, 4. +4.j, 8. +8.j],\n", " | [ 1. +1.j, 5. +5.j, 9. +9.j],\n", " | [ 2. +2.j, 6. +6.j, 10.+10.j],\n", " | [ 3. +3.j, 7. +7.j, 11.+11.j]])\n", " | \n", " | I\n", " | Returns the (multiplicative) inverse of invertible `self`.\n", " | \n", " | Parameters\n", " | ----------\n", " | None\n", " | \n", " | Returns\n", " | -------\n", " | ret : matrix object\n", " | If `self` is non-singular, `ret` is such that ``ret * self`` ==\n", " | ``self * ret`` == ``np.matrix(np.eye(self[0,:].size))`` all return\n", " | ``True``.\n", " | \n", " | Raises\n", " | ------\n", " | numpy.linalg.LinAlgError: Singular matrix\n", " | If `self` is singular.\n", " | \n", " | See Also\n", " | --------\n", " | linalg.inv\n", " | \n", " | Examples\n", " | --------\n", " | >>> m = np.matrix('[1, 2; 3, 4]'); m\n", " | matrix([[1, 2],\n", " | [3, 4]])\n", " | >>> m.getI()\n", " | matrix([[-2. , 1. ],\n", " | [ 1.5, -0.5]])\n", " | >>> m.getI() * m\n", " | matrix([[ 1., 0.], # may vary\n", " | [ 0., 1.]])\n", " | \n", " | T\n", " | Returns the transpose of the matrix.\n", " | \n", " | Does *not* conjugate! For the complex conjugate transpose, use ``.H``.\n", " | \n", " | Parameters\n", " | ----------\n", " | None\n", " | \n", " | Returns\n", " | -------\n", " | ret : matrix object\n", " | The (non-conjugated) transpose of the matrix.\n", " | \n", " | See Also\n", " | --------\n", " | transpose, getH\n", " | \n", " | Examples\n", " | --------\n", " | >>> m = np.matrix('[1, 2; 3, 4]')\n", " | >>> m\n", " | matrix([[1, 2],\n", " | [3, 4]])\n", " | >>> m.getT()\n", " | matrix([[1, 3],\n", " | [2, 4]])\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors defined here:\n", " | \n", " | __dict__\n", " | dictionary for instance variables (if defined)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data and other attributes defined here:\n", " | \n", " | __annotations__ = {}\n", " | \n", " | __array_priority__ = 10.0\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from ndarray:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | a.__array__([dtype], /) -> reference if type unchanged, copy otherwise.\n", " | \n", " | Returns either a new reference to self if dtype is not given or a new array\n", " | of provided data type if dtype is different from the current dtype of the\n", " | array.\n", " | \n", " | __array_function__(...)\n", " | \n", " | __array_prepare__(...)\n", " | a.__array_prepare__(array[, context], /)\n", " | \n", " | Returns a view of `array` with the same type as self.\n", " | \n", " | __array_ufunc__(...)\n", " | \n", " | __array_wrap__(...)\n", " | a.__array_wrap__(array[, context], /)\n", " | \n", " | Returns a view of `array` with the same type as self.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __complex__(...)\n", " | \n", " | __contains__(self, key, /)\n", " | Return key in self.\n", " | \n", " | __copy__(...)\n", " | a.__copy__()\n", " | \n", " | Used if :func:`copy.copy` is called on an array. Returns a copy of the array.\n", " | \n", " | Equivalent to ``a.copy(order='K')``.\n", " | \n", " | __deepcopy__(...)\n", " | a.__deepcopy__(memo, /) -> Deep copy of array.\n", " | \n", " | Used if :func:`copy.deepcopy` is called on an array.\n", " | \n", " | __delitem__(self, key, /)\n", " | Delete self[key].\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __dlpack__(...)\n", " | a.__dlpack__(*, stream=None)\n", " | \n", " | DLPack Protocol: Part of the Array API.\n", " | \n", " | __dlpack_device__(...)\n", " | a.__dlpack_device__()\n", " | \n", " | DLPack Protocol: Part of the Array API.\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __format__(...)\n", " | Default object formatter.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __iadd__(self, value, /)\n", " | Return self+=value.\n", " | \n", " | __iand__(self, value, /)\n", " | Return self&=value.\n", " | \n", " | __ifloordiv__(self, value, /)\n", " | Return self//=value.\n", " | \n", " | __ilshift__(self, value, /)\n", " | Return self<<=value.\n", " | \n", " | __imatmul__(self, value, /)\n", " | Return self@=value.\n", " | \n", " | __imod__(self, value, /)\n", " | Return self%=value.\n", " | \n", " | __index__(self, /)\n", " | Return self converted to an integer, if self is suitable for use as an index into a list.\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __ior__(self, value, /)\n", " | Return self|=value.\n", " | \n", " | __irshift__(self, value, /)\n", " | Return self>>=value.\n", " | \n", " | __isub__(self, value, /)\n", " | Return self-=value.\n", " | \n", " | __iter__(self, /)\n", " | Implement iter(self).\n", " | \n", " | __itruediv__(self, value, /)\n", " | Return self/=value.\n", " | \n", " | __ixor__(self, value, /)\n", " | Return self^=value.\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __len__(self, /)\n", " | Return len(self).\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __matmul__(self, value, /)\n", " | Return self@value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __reduce__(...)\n", " | a.__reduce__()\n", " | \n", " | For pickling.\n", " | \n", " | __reduce_ex__(...)\n", " | Helper for pickle.\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmatmul__(self, value, /)\n", " | Return value@self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setitem__(self, key, value, /)\n", " | Set self[key] to value.\n", " | \n", " | __setstate__(...)\n", " | a.__setstate__(state, /)\n", " | \n", " | For unpickling.\n", " | \n", " | The `state` argument must be a sequence that contains the following\n", " | elements:\n", " | \n", " | Parameters\n", " | ----------\n", " | version : int\n", " | optional pickle version. If omitted defaults to 0.\n", " | shape : tuple\n", " | dtype : data-type\n", " | isFortran : bool\n", " | rawdata : string or list\n", " | a binary string with the data (or a list if 'a' is an object array)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | argpartition(...)\n", " | a.argpartition(kth, axis=-1, kind='introselect', order=None)\n", " | \n", " | Returns the indices that would partition this array.\n", " | \n", " | Refer to `numpy.argpartition` for full documentation.\n", " | \n", " | .. versionadded:: 1.8.0\n", " | \n", " | See Also\n", " | --------\n", " | numpy.argpartition : equivalent function\n", " | \n", " | argsort(...)\n", " | a.argsort(axis=-1, kind=None, order=None)\n", " | \n", " | Returns the indices that would sort this array.\n", " | \n", " | Refer to `numpy.argsort` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.argsort : equivalent function\n", " | \n", " | astype(...)\n", " | a.astype(dtype, order='K', casting='unsafe', subok=True, copy=True)\n", " | \n", " | Copy of the array, cast to a specified type.\n", " | \n", " | Parameters\n", " | ----------\n", " | dtype : str or dtype\n", " | Typecode or data-type to which the array is cast.\n", " | order : {'C', 'F', 'A', 'K'}, optional\n", " | Controls the memory layout order of the result.\n", " | 'C' means C order, 'F' means Fortran order, 'A'\n", " | means 'F' order if all the arrays are Fortran contiguous,\n", " | 'C' order otherwise, and 'K' means as close to the\n", " | order the array elements appear in memory as possible.\n", " | Default is 'K'.\n", " | casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional\n", " | Controls what kind of data casting may occur. Defaults to 'unsafe'\n", " | for backwards compatibility.\n", " | \n", " | * 'no' means the data types should not be cast at all.\n", " | * 'equiv' means only byte-order changes are allowed.\n", " | * 'safe' means only casts which can preserve values are allowed.\n", " | * 'same_kind' means only safe casts or casts within a kind,\n", " | like float64 to float32, are allowed.\n", " | * 'unsafe' means any data conversions may be done.\n", " | subok : bool, optional\n", " | If True, then sub-classes will be passed-through (default), otherwise\n", " | the returned array will be forced to be a base-class array.\n", " | copy : bool, optional\n", " | By default, astype always returns a newly allocated array. If this\n", " | is set to false, and the `dtype`, `order`, and `subok`\n", " | requirements are satisfied, the input array is returned instead\n", " | of a copy.\n", " | \n", " | Returns\n", " | -------\n", " | arr_t : ndarray\n", " | Unless `copy` is False and the other conditions for returning the input\n", " | array are satisfied (see description for `copy` input parameter), `arr_t`\n", " | is a new array of the same shape as the input array, with dtype, order\n", " | given by `dtype`, `order`.\n", " | \n", " | Notes\n", " | -----\n", " | .. versionchanged:: 1.17.0\n", " | Casting between a simple data type and a structured one is possible only\n", " | for \"unsafe\" casting. Casting to multiple fields is allowed, but\n", " | casting from multiple fields is not.\n", " | \n", " | .. versionchanged:: 1.9.0\n", " | Casting from numeric to string types in 'safe' casting mode requires\n", " | that the string dtype length is long enough to store the max\n", " | integer/float value converted.\n", " | \n", " | Raises\n", " | ------\n", " | ComplexWarning\n", " | When casting from complex to float or int. To avoid this,\n", " | one should use ``a.real.astype(t)``.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([1, 2, 2.5])\n", " | >>> x\n", " | array([1. , 2. , 2.5])\n", " | \n", " | >>> x.astype(int)\n", " | array([1, 2, 2])\n", " | \n", " | byteswap(...)\n", " | a.byteswap(inplace=False)\n", " | \n", " | Swap the bytes of the array elements\n", " | \n", " | Toggle between low-endian and big-endian data representation by\n", " | returning a byteswapped array, optionally swapped in-place.\n", " | Arrays of byte-strings are not swapped. The real and imaginary\n", " | parts of a complex number are swapped individually.\n", " | \n", " | Parameters\n", " | ----------\n", " | inplace : bool, optional\n", " | If ``True``, swap bytes in-place, default is ``False``.\n", " | \n", " | Returns\n", " | -------\n", " | out : ndarray\n", " | The byteswapped array. If `inplace` is ``True``, this is\n", " | a view to self.\n", " | \n", " | Examples\n", " | --------\n", " | >>> A = np.array([1, 256, 8755], dtype=np.int16)\n", " | >>> list(map(hex, A))\n", " | ['0x1', '0x100', '0x2233']\n", " | >>> A.byteswap(inplace=True)\n", " | array([ 256, 1, 13090], dtype=int16)\n", " | >>> list(map(hex, A))\n", " | ['0x100', '0x1', '0x3322']\n", " | \n", " | Arrays of byte-strings are not swapped\n", " | \n", " | >>> A = np.array([b'ceg', b'fac'])\n", " | >>> A.byteswap()\n", " | array([b'ceg', b'fac'], dtype='|S3')\n", " | \n", " | ``A.newbyteorder().byteswap()`` produces an array with the same values\n", " | but different representation in memory\n", " | \n", " | >>> A = np.array([1, 2, 3])\n", " | >>> A.view(np.uint8)\n", " | array([1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0,\n", " | 0, 0], dtype=uint8)\n", " | >>> A.newbyteorder().byteswap(inplace=True)\n", " | array([1, 2, 3])\n", " | >>> A.view(np.uint8)\n", " | array([0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0,\n", " | 0, 3], dtype=uint8)\n", " | \n", " | choose(...)\n", " | a.choose(choices, out=None, mode='raise')\n", " | \n", " | Use an index array to construct a new array from a set of choices.\n", " | \n", " | Refer to `numpy.choose` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.choose : equivalent function\n", " | \n", " | clip(...)\n", " | a.clip(min=None, max=None, out=None, **kwargs)\n", " | \n", " | Return an array whose values are limited to ``[min, max]``.\n", " | One of max or min must be given.\n", " | \n", " | Refer to `numpy.clip` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.clip : equivalent function\n", " | \n", " | compress(...)\n", " | a.compress(condition, axis=None, out=None)\n", " | \n", " | Return selected slices of this array along given axis.\n", " | \n", " | Refer to `numpy.compress` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.compress : equivalent function\n", " | \n", " | conj(...)\n", " | a.conj()\n", " | \n", " | Complex-conjugate all elements.\n", " | \n", " | Refer to `numpy.conjugate` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.conjugate : equivalent function\n", " | \n", " | conjugate(...)\n", " | a.conjugate()\n", " | \n", " | Return the complex conjugate, element-wise.\n", " | \n", " | Refer to `numpy.conjugate` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.conjugate : equivalent function\n", " | \n", " | copy(...)\n", " | a.copy(order='C')\n", " | \n", " | Return a copy of the array.\n", " | \n", " | Parameters\n", " | ----------\n", " | order : {'C', 'F', 'A', 'K'}, optional\n", " | Controls the memory layout of the copy. 'C' means C-order,\n", " | 'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous,\n", " | 'C' otherwise. 'K' means match the layout of `a` as closely\n", " | as possible. (Note that this function and :func:`numpy.copy` are very\n", " | similar but have different default values for their order=\n", " | arguments, and this function always passes sub-classes through.)\n", " | \n", " | See also\n", " | --------\n", " | numpy.copy : Similar function with different default behavior\n", " | numpy.copyto\n", " | \n", " | Notes\n", " | -----\n", " | This function is the preferred method for creating an array copy. The\n", " | function :func:`numpy.copy` is similar, but it defaults to using order 'K',\n", " | and will not pass sub-classes through by default.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([[1,2,3],[4,5,6]], order='F')\n", " | \n", " | >>> y = x.copy()\n", " | \n", " | >>> x.fill(0)\n", " | \n", " | >>> x\n", " | array([[0, 0, 0],\n", " | [0, 0, 0]])\n", " | \n", " | >>> y\n", " | array([[1, 2, 3],\n", " | [4, 5, 6]])\n", " | \n", " | >>> y.flags['C_CONTIGUOUS']\n", " | True\n", " | \n", " | cumprod(...)\n", " | a.cumprod(axis=None, dtype=None, out=None)\n", " | \n", " | Return the cumulative product of the elements along the given axis.\n", " | \n", " | Refer to `numpy.cumprod` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.cumprod : equivalent function\n", " | \n", " | cumsum(...)\n", " | a.cumsum(axis=None, dtype=None, out=None)\n", " | \n", " | Return the cumulative sum of the elements along the given axis.\n", " | \n", " | Refer to `numpy.cumsum` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.cumsum : equivalent function\n", " | \n", " | diagonal(...)\n", " | a.diagonal(offset=0, axis1=0, axis2=1)\n", " | \n", " | Return specified diagonals. In NumPy 1.9 the returned array is a\n", " | read-only view instead of a copy as in previous NumPy versions. In\n", " | a future version the read-only restriction will be removed.\n", " | \n", " | Refer to :func:`numpy.diagonal` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.diagonal : equivalent function\n", " | \n", " | dot(...)\n", " | \n", " | dump(...)\n", " | a.dump(file)\n", " | \n", " | Dump a pickle of the array to the specified file.\n", " | The array can be read back with pickle.load or numpy.load.\n", " | \n", " | Parameters\n", " | ----------\n", " | file : str or Path\n", " | A string naming the dump file.\n", " | \n", " | .. versionchanged:: 1.17.0\n", " | `pathlib.Path` objects are now accepted.\n", " | \n", " | dumps(...)\n", " | a.dumps()\n", " | \n", " | Returns the pickle of the array as a string.\n", " | pickle.loads will convert the string back to an array.\n", " | \n", " | Parameters\n", " | ----------\n", " | None\n", " | \n", " | fill(...)\n", " | a.fill(value)\n", " | \n", " | Fill the array with a scalar value.\n", " | \n", " | Parameters\n", " | ----------\n", " | value : scalar\n", " | All elements of `a` will be assigned this value.\n", " | \n", " | Examples\n", " | --------\n", " | >>> a = np.array([1, 2])\n", " | >>> a.fill(0)\n", " | >>> a\n", " | array([0, 0])\n", " | >>> a = np.empty(2)\n", " | >>> a.fill(1)\n", " | >>> a\n", " | array([1., 1.])\n", " | \n", " | Fill expects a scalar value and always behaves the same as assigning\n", " | to a single array element. The following is a rare example where this\n", " | distinction is important:\n", " | \n", " | >>> a = np.array([None, None], dtype=object)\n", " | >>> a[0] = np.array(3)\n", " | >>> a\n", " | array([array(3), None], dtype=object)\n", " | >>> a.fill(np.array(3))\n", " | >>> a\n", " | array([array(3), array(3)], dtype=object)\n", " | \n", " | Where other forms of assignments will unpack the array being assigned:\n", " | \n", " | >>> a[...] = np.array(3)\n", " | >>> a\n", " | array([3, 3], dtype=object)\n", " | \n", " | getfield(...)\n", " | a.getfield(dtype, offset=0)\n", " | \n", " | Returns a field of the given array as a certain type.\n", " | \n", " | A field is a view of the array data with a given data-type. The values in\n", " | the view are determined by the given type and the offset into the current\n", " | array in bytes. The offset needs to be such that the view dtype fits in the\n", " | array dtype; for example an array of dtype complex128 has 16-byte elements.\n", " | If taking a view with a 32-bit integer (4 bytes), the offset needs to be\n", " | between 0 and 12 bytes.\n", " | \n", " | Parameters\n", " | ----------\n", " | dtype : str or dtype\n", " | The data type of the view. The dtype size of the view can not be larger\n", " | than that of the array itself.\n", " | offset : int\n", " | Number of bytes to skip before beginning the element view.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.diag([1.+1.j]*2)\n", " | >>> x[1, 1] = 2 + 4.j\n", " | >>> x\n", " | array([[1.+1.j, 0.+0.j],\n", " | [0.+0.j, 2.+4.j]])\n", " | >>> x.getfield(np.float64)\n", " | array([[1., 0.],\n", " | [0., 2.]])\n", " | \n", " | By choosing an offset of 8 bytes we can select the complex part of the\n", " | array for our view:\n", " | \n", " | >>> x.getfield(np.float64, offset=8)\n", " | array([[1., 0.],\n", " | [0., 4.]])\n", " | \n", " | item(...)\n", " | a.item(*args)\n", " | \n", " | Copy an element of an array to a standard Python scalar and return it.\n", " | \n", " | Parameters\n", " | ----------\n", " | \\*args : Arguments (variable number and type)\n", " | \n", " | * none: in this case, the method only works for arrays\n", " | with one element (`a.size == 1`), which element is\n", " | copied into a standard Python scalar object and returned.\n", " | \n", " | * int_type: this argument is interpreted as a flat index into\n", " | the array, specifying which element to copy and return.\n", " | \n", " | * tuple of int_types: functions as does a single int_type argument,\n", " | except that the argument is interpreted as an nd-index into the\n", " | array.\n", " | \n", " | Returns\n", " | -------\n", " | z : Standard Python scalar object\n", " | A copy of the specified element of the array as a suitable\n", " | Python scalar\n", " | \n", " | Notes\n", " | -----\n", " | When the data type of `a` is longdouble or clongdouble, item() returns\n", " | a scalar array object because there is no available Python scalar that\n", " | would not lose information. Void arrays return a buffer object for item(),\n", " | unless fields are defined, in which case a tuple is returned.\n", " | \n", " | `item` is very similar to a[args], except, instead of an array scalar,\n", " | a standard Python scalar is returned. This can be useful for speeding up\n", " | access to elements of the array and doing arithmetic on elements of the\n", " | array using Python's optimized math.\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.random.seed(123)\n", " | >>> x = np.random.randint(9, size=(3, 3))\n", " | >>> x\n", " | array([[2, 2, 6],\n", " | [1, 3, 6],\n", " | [1, 0, 1]])\n", " | >>> x.item(3)\n", " | 1\n", " | >>> x.item(7)\n", " | 0\n", " | >>> x.item((0, 1))\n", " | 2\n", " | >>> x.item((2, 2))\n", " | 1\n", " | \n", " | itemset(...)\n", " | a.itemset(*args)\n", " | \n", " | Insert scalar into an array (scalar is cast to array's dtype, if possible)\n", " | \n", " | There must be at least 1 argument, and define the last argument\n", " | as *item*. Then, ``a.itemset(*args)`` is equivalent to but faster\n", " | than ``a[args] = item``. The item should be a scalar value and `args`\n", " | must select a single item in the array `a`.\n", " | \n", " | Parameters\n", " | ----------\n", " | \\*args : Arguments\n", " | If one argument: a scalar, only used in case `a` is of size 1.\n", " | If two arguments: the last argument is the value to be set\n", " | and must be a scalar, the first argument specifies a single array\n", " | element location. It is either an int or a tuple.\n", " | \n", " | Notes\n", " | -----\n", " | Compared to indexing syntax, `itemset` provides some speed increase\n", " | for placing a scalar into a particular location in an `ndarray`,\n", " | if you must do this. However, generally this is discouraged:\n", " | among other problems, it complicates the appearance of the code.\n", " | Also, when using `itemset` (and `item`) inside a loop, be sure\n", " | to assign the methods to a local variable to avoid the attribute\n", " | look-up at each loop iteration.\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.random.seed(123)\n", " | >>> x = np.random.randint(9, size=(3, 3))\n", " | >>> x\n", " | array([[2, 2, 6],\n", " | [1, 3, 6],\n", " | [1, 0, 1]])\n", " | >>> x.itemset(4, 0)\n", " | >>> x.itemset((2, 2), 9)\n", " | >>> x\n", " | array([[2, 2, 6],\n", " | [1, 0, 6],\n", " | [1, 0, 9]])\n", " | \n", " | newbyteorder(...)\n", " | arr.newbyteorder(new_order='S', /)\n", " | \n", " | Return the array with the same data viewed with a different byte order.\n", " | \n", " | Equivalent to::\n", " | \n", " | arr.view(arr.dtype.newbytorder(new_order))\n", " | \n", " | Changes are also made in all fields and sub-arrays of the array data\n", " | type.\n", " | \n", " | \n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : string, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | below. `new_order` codes can be any of:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order, equivalent to `sys.byteorder`\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_arr : array\n", " | New array object with the dtype reflecting given change to the\n", " | byte order.\n", " | \n", " | nonzero(...)\n", " | a.nonzero()\n", " | \n", " | Return the indices of the elements that are non-zero.\n", " | \n", " | Refer to `numpy.nonzero` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.nonzero : equivalent function\n", " | \n", " | partition(...)\n", " | a.partition(kth, axis=-1, kind='introselect', order=None)\n", " | \n", " | Rearranges the elements in the array in such a way that the value of the\n", " | element in kth position is in the position it would be in a sorted array.\n", " | All elements smaller than the kth element are moved before this element and\n", " | all equal or greater are moved behind it. The ordering of the elements in\n", " | the two partitions is undefined.\n", " | \n", " | .. versionadded:: 1.8.0\n", " | \n", " | Parameters\n", " | ----------\n", " | kth : int or sequence of ints\n", " | Element index to partition by. The kth element value will be in its\n", " | final sorted position and all smaller elements will be moved before it\n", " | and all equal or greater elements behind it.\n", " | The order of all elements in the partitions is undefined.\n", " | If provided with a sequence of kth it will partition all elements\n", " | indexed by kth of them into their sorted position at once.\n", " | \n", " | .. deprecated:: 1.22.0\n", " | Passing booleans as index is deprecated.\n", " | axis : int, optional\n", " | Axis along which to sort. Default is -1, which means sort along the\n", " | last axis.\n", " | kind : {'introselect'}, optional\n", " | Selection algorithm. Default is 'introselect'.\n", " | order : str or list of str, optional\n", " | When `a` is an array with fields defined, this argument specifies\n", " | which fields to compare first, second, etc. A single field can\n", " | be specified as a string, and not all fields need to be specified,\n", " | but unspecified fields will still be used, in the order in which\n", " | they come up in the dtype, to break ties.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.partition : Return a partitioned copy of an array.\n", " | argpartition : Indirect partition.\n", " | sort : Full sort.\n", " | \n", " | Notes\n", " | -----\n", " | See ``np.partition`` for notes on the different algorithms.\n", " | \n", " | Examples\n", " | --------\n", " | >>> a = np.array([3, 4, 2, 1])\n", " | >>> a.partition(3)\n", " | >>> a\n", " | array([2, 1, 3, 4])\n", " | \n", " | >>> a.partition((1, 3))\n", " | >>> a\n", " | array([1, 2, 3, 4])\n", " | \n", " | put(...)\n", " | a.put(indices, values, mode='raise')\n", " | \n", " | Set ``a.flat[n] = values[n]`` for all `n` in indices.\n", " | \n", " | Refer to `numpy.put` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.put : equivalent function\n", " | \n", " | repeat(...)\n", " | a.repeat(repeats, axis=None)\n", " | \n", " | Repeat elements of an array.\n", " | \n", " | Refer to `numpy.repeat` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.repeat : equivalent function\n", " | \n", " | reshape(...)\n", " | a.reshape(shape, order='C')\n", " | \n", " | Returns an array containing the same data with a new shape.\n", " | \n", " | Refer to `numpy.reshape` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.reshape : equivalent function\n", " | \n", " | Notes\n", " | -----\n", " | Unlike the free function `numpy.reshape`, this method on `ndarray` allows\n", " | the elements of the shape parameter to be passed in as separate arguments.\n", " | For example, ``a.reshape(10, 11)`` is equivalent to\n", " | ``a.reshape((10, 11))``.\n", " | \n", " | resize(...)\n", " | a.resize(new_shape, refcheck=True)\n", " | \n", " | Change shape and size of array in-place.\n", " | \n", " | Parameters\n", " | ----------\n", " | new_shape : tuple of ints, or `n` ints\n", " | Shape of resized array.\n", " | refcheck : bool, optional\n", " | If False, reference count will not be checked. Default is True.\n", " | \n", " | Returns\n", " | -------\n", " | None\n", " | \n", " | Raises\n", " | ------\n", " | ValueError\n", " | If `a` does not own its own data or references or views to it exist,\n", " | and the data memory must be changed.\n", " | PyPy only: will always raise if the data memory must be changed, since\n", " | there is no reliable way to determine if references or views to it\n", " | exist.\n", " | \n", " | SystemError\n", " | If the `order` keyword argument is specified. This behaviour is a\n", " | bug in NumPy.\n", " | \n", " | See Also\n", " | --------\n", " | resize : Return a new array with the specified shape.\n", " | \n", " | Notes\n", " | -----\n", " | This reallocates space for the data area if necessary.\n", " | \n", " | Only contiguous arrays (data elements consecutive in memory) can be\n", " | resized.\n", " | \n", " | The purpose of the reference count check is to make sure you\n", " | do not use this array as a buffer for another Python object and then\n", " | reallocate the memory. However, reference counts can increase in\n", " | other ways so if you are sure that you have not shared the memory\n", " | for this array with another Python object, then you may safely set\n", " | `refcheck` to False.\n", " | \n", " | Examples\n", " | --------\n", " | Shrinking an array: array is flattened (in the order that the data are\n", " | stored in memory), resized, and reshaped:\n", " | \n", " | >>> a = np.array([[0, 1], [2, 3]], order='C')\n", " | >>> a.resize((2, 1))\n", " | >>> a\n", " | array([[0],\n", " | [1]])\n", " | \n", " | >>> a = np.array([[0, 1], [2, 3]], order='F')\n", " | >>> a.resize((2, 1))\n", " | >>> a\n", " | array([[0],\n", " | [2]])\n", " | \n", " | Enlarging an array: as above, but missing entries are filled with zeros:\n", " | \n", " | >>> b = np.array([[0, 1], [2, 3]])\n", " | >>> b.resize(2, 3) # new_shape parameter doesn't have to be a tuple\n", " | >>> b\n", " | array([[0, 1, 2],\n", " | [3, 0, 0]])\n", " | \n", " | Referencing an array prevents resizing...\n", " | \n", " | >>> c = a\n", " | >>> a.resize((1, 1))\n", " | Traceback (most recent call last):\n", " | ...\n", " | ValueError: cannot resize an array that references or is referenced ...\n", " | \n", " | Unless `refcheck` is False:\n", " | \n", " | >>> a.resize((1, 1), refcheck=False)\n", " | >>> a\n", " | array([[0]])\n", " | >>> c\n", " | array([[0]])\n", " | \n", " | round(...)\n", " | a.round(decimals=0, out=None)\n", " | \n", " | Return `a` with each element rounded to the given number of decimals.\n", " | \n", " | Refer to `numpy.around` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.around : equivalent function\n", " | \n", " | searchsorted(...)\n", " | a.searchsorted(v, side='left', sorter=None)\n", " | \n", " | Find indices where elements of v should be inserted in a to maintain order.\n", " | \n", " | For full documentation, see `numpy.searchsorted`\n", " | \n", " | See Also\n", " | --------\n", " | numpy.searchsorted : equivalent function\n", " | \n", " | setfield(...)\n", " | a.setfield(val, dtype, offset=0)\n", " | \n", " | Put a value into a specified place in a field defined by a data-type.\n", " | \n", " | Place `val` into `a`'s field defined by `dtype` and beginning `offset`\n", " | bytes into the field.\n", " | \n", " | Parameters\n", " | ----------\n", " | val : object\n", " | Value to be placed in field.\n", " | dtype : dtype object\n", " | Data-type of the field in which to place `val`.\n", " | offset : int, optional\n", " | The number of bytes into the field at which to place `val`.\n", " | \n", " | Returns\n", " | -------\n", " | None\n", " | \n", " | See Also\n", " | --------\n", " | getfield\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.eye(3)\n", " | >>> x.getfield(np.float64)\n", " | array([[1., 0., 0.],\n", " | [0., 1., 0.],\n", " | [0., 0., 1.]])\n", " | >>> x.setfield(3, np.int32)\n", " | >>> x.getfield(np.int32)\n", " | array([[3, 3, 3],\n", " | [3, 3, 3],\n", " | [3, 3, 3]], dtype=int32)\n", " | >>> x\n", " | array([[1.0e+000, 1.5e-323, 1.5e-323],\n", " | [1.5e-323, 1.0e+000, 1.5e-323],\n", " | [1.5e-323, 1.5e-323, 1.0e+000]])\n", " | >>> x.setfield(np.eye(3), np.int32)\n", " | >>> x\n", " | array([[1., 0., 0.],\n", " | [0., 1., 0.],\n", " | [0., 0., 1.]])\n", " | \n", " | setflags(...)\n", " | a.setflags(write=None, align=None, uic=None)\n", " | \n", " | Set array flags WRITEABLE, ALIGNED, WRITEBACKIFCOPY,\n", " | respectively.\n", " | \n", " | These Boolean-valued flags affect how numpy interprets the memory\n", " | area used by `a` (see Notes below). The ALIGNED flag can only\n", " | be set to True if the data is actually aligned according to the type.\n", " | The WRITEBACKIFCOPY and flag can never be set\n", " | to True. The flag WRITEABLE can only be set to True if the array owns its\n", " | own memory, or the ultimate owner of the memory exposes a writeable buffer\n", " | interface, or is a string. (The exception for string is made so that\n", " | unpickling can be done without copying memory.)\n", " | \n", " | Parameters\n", " | ----------\n", " | write : bool, optional\n", " | Describes whether or not `a` can be written to.\n", " | align : bool, optional\n", " | Describes whether or not `a` is aligned properly for its type.\n", " | uic : bool, optional\n", " | Describes whether or not `a` is a copy of another \"base\" array.\n", " | \n", " | Notes\n", " | -----\n", " | Array flags provide information about how the memory area used\n", " | for the array is to be interpreted. There are 7 Boolean flags\n", " | in use, only four of which can be changed by the user:\n", " | WRITEBACKIFCOPY, WRITEABLE, and ALIGNED.\n", " | \n", " | WRITEABLE (W) the data area can be written to;\n", " | \n", " | ALIGNED (A) the data and strides are aligned appropriately for the hardware\n", " | (as determined by the compiler);\n", " | \n", " | WRITEBACKIFCOPY (X) this array is a copy of some other array (referenced\n", " | by .base). When the C-API function PyArray_ResolveWritebackIfCopy is\n", " | called, the base array will be updated with the contents of this array.\n", " | \n", " | All flags can be accessed using the single (upper case) letter as well\n", " | as the full name.\n", " | \n", " | Examples\n", " | --------\n", " | >>> y = np.array([[3, 1, 7],\n", " | ... [2, 0, 0],\n", " | ... [8, 5, 9]])\n", " | >>> y\n", " | array([[3, 1, 7],\n", " | [2, 0, 0],\n", " | [8, 5, 9]])\n", " | >>> y.flags\n", " | C_CONTIGUOUS : True\n", " | F_CONTIGUOUS : False\n", " | OWNDATA : True\n", " | WRITEABLE : True\n", " | ALIGNED : True\n", " | WRITEBACKIFCOPY : False\n", " | >>> y.setflags(write=0, align=0)\n", " | >>> y.flags\n", " | C_CONTIGUOUS : True\n", " | F_CONTIGUOUS : False\n", " | OWNDATA : True\n", " | WRITEABLE : False\n", " | ALIGNED : False\n", " | WRITEBACKIFCOPY : False\n", " | >>> y.setflags(uic=1)\n", " | Traceback (most recent call last):\n", " | File \"<stdin>\", line 1, in <module>\n", " | ValueError: cannot set WRITEBACKIFCOPY flag to True\n", " | \n", " | sort(...)\n", " | a.sort(axis=-1, kind=None, order=None)\n", " | \n", " | Sort an array in-place. Refer to `numpy.sort` for full documentation.\n", " | \n", " | Parameters\n", " | ----------\n", " | axis : int, optional\n", " | Axis along which to sort. Default is -1, which means sort along the\n", " | last axis.\n", " | kind : {'quicksort', 'mergesort', 'heapsort', 'stable'}, optional\n", " | Sorting algorithm. The default is 'quicksort'. Note that both 'stable'\n", " | and 'mergesort' use timsort under the covers and, in general, the\n", " | actual implementation will vary with datatype. The 'mergesort' option\n", " | is retained for backwards compatibility.\n", " | \n", " | .. versionchanged:: 1.15.0\n", " | The 'stable' option was added.\n", " | \n", " | order : str or list of str, optional\n", " | When `a` is an array with fields defined, this argument specifies\n", " | which fields to compare first, second, etc. A single field can\n", " | be specified as a string, and not all fields need be specified,\n", " | but unspecified fields will still be used, in the order in which\n", " | they come up in the dtype, to break ties.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.sort : Return a sorted copy of an array.\n", " | numpy.argsort : Indirect sort.\n", " | numpy.lexsort : Indirect stable sort on multiple keys.\n", " | numpy.searchsorted : Find elements in sorted array.\n", " | numpy.partition: Partial sort.\n", " | \n", " | Notes\n", " | -----\n", " | See `numpy.sort` for notes on the different sorting algorithms.\n", " | \n", " | Examples\n", " | --------\n", " | >>> a = np.array([[1,4], [3,1]])\n", " | >>> a.sort(axis=1)\n", " | >>> a\n", " | array([[1, 4],\n", " | [1, 3]])\n", " | >>> a.sort(axis=0)\n", " | >>> a\n", " | array([[1, 3],\n", " | [1, 4]])\n", " | \n", " | Use the `order` keyword to specify a field to use when sorting a\n", " | structured array:\n", " | \n", " | >>> a = np.array([('a', 2), ('c', 1)], dtype=[('x', 'S1'), ('y', int)])\n", " | >>> a.sort(order='y')\n", " | >>> a\n", " | array([(b'c', 1), (b'a', 2)],\n", " | dtype=[('x', 'S1'), ('y', '<i8')])\n", " | \n", " | swapaxes(...)\n", " | a.swapaxes(axis1, axis2)\n", " | \n", " | Return a view of the array with `axis1` and `axis2` interchanged.\n", " | \n", " | Refer to `numpy.swapaxes` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.swapaxes : equivalent function\n", " | \n", " | take(...)\n", " | a.take(indices, axis=None, out=None, mode='raise')\n", " | \n", " | Return an array formed from the elements of `a` at the given indices.\n", " | \n", " | Refer to `numpy.take` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.take : equivalent function\n", " | \n", " | tobytes(...)\n", " | a.tobytes(order='C')\n", " | \n", " | Construct Python bytes containing the raw data bytes in the array.\n", " | \n", " | Constructs Python bytes showing a copy of the raw contents of\n", " | data memory. The bytes object is produced in C-order by default.\n", " | This behavior is controlled by the ``order`` parameter.\n", " | \n", " | .. versionadded:: 1.9.0\n", " | \n", " | Parameters\n", " | ----------\n", " | order : {'C', 'F', 'A'}, optional\n", " | Controls the memory layout of the bytes object. 'C' means C-order,\n", " | 'F' means F-order, 'A' (short for *Any*) means 'F' if `a` is\n", " | Fortran contiguous, 'C' otherwise. Default is 'C'.\n", " | \n", " | Returns\n", " | -------\n", " | s : bytes\n", " | Python bytes exhibiting a copy of `a`'s raw data.\n", " | \n", " | See also\n", " | --------\n", " | frombuffer\n", " | Inverse of this operation, construct a 1-dimensional array from Python\n", " | bytes.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([[0, 1], [2, 3]], dtype='<u2')\n", " | >>> x.tobytes()\n", " | b'\\x00\\x00\\x01\\x00\\x02\\x00\\x03\\x00'\n", " | >>> x.tobytes('C') == x.tobytes()\n", " | True\n", " | >>> x.tobytes('F')\n", " | b'\\x00\\x00\\x02\\x00\\x01\\x00\\x03\\x00'\n", " | \n", " | tofile(...)\n", " | a.tofile(fid, sep=\"\", format=\"%s\")\n", " | \n", " | Write array to a file as text or binary (default).\n", " | \n", " | Data is always written in 'C' order, independent of the order of `a`.\n", " | The data produced by this method can be recovered using the function\n", " | fromfile().\n", " | \n", " | Parameters\n", " | ----------\n", " | fid : file or str or Path\n", " | An open file object, or a string containing a filename.\n", " | \n", " | .. versionchanged:: 1.17.0\n", " | `pathlib.Path` objects are now accepted.\n", " | \n", " | sep : str\n", " | Separator between array items for text output.\n", " | If \"\" (empty), a binary file is written, equivalent to\n", " | ``file.write(a.tobytes())``.\n", " | format : str\n", " | Format string for text file output.\n", " | Each entry in the array is formatted to text by first converting\n", " | it to the closest Python type, and then using \"format\" % item.\n", " | \n", " | Notes\n", " | -----\n", " | This is a convenience function for quick storage of array data.\n", " | Information on endianness and precision is lost, so this method is not a\n", " | good choice for files intended to archive data or transport data between\n", " | machines with different endianness. Some of these problems can be overcome\n", " | by outputting the data as text files, at the expense of speed and file\n", " | size.\n", " | \n", " | When fid is a file object, array contents are directly written to the\n", " | file, bypassing the file object's ``write`` method. As a result, tofile\n", " | cannot be used with files objects supporting compression (e.g., GzipFile)\n", " | or file-like objects that do not support ``fileno()`` (e.g., BytesIO).\n", " | \n", " | tostring(...)\n", " | a.tostring(order='C')\n", " | \n", " | A compatibility alias for `tobytes`, with exactly the same behavior.\n", " | \n", " | Despite its name, it returns `bytes` not `str`\\ s.\n", " | \n", " | .. deprecated:: 1.19.0\n", " | \n", " | trace(...)\n", " | a.trace(offset=0, axis1=0, axis2=1, dtype=None, out=None)\n", " | \n", " | Return the sum along diagonals of the array.\n", " | \n", " | Refer to `numpy.trace` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.trace : equivalent function\n", " | \n", " | transpose(...)\n", " | a.transpose(*axes)\n", " | \n", " | Returns a view of the array with axes transposed.\n", " | \n", " | Refer to `numpy.transpose` for full documentation.\n", " | \n", " | Parameters\n", " | ----------\n", " | axes : None, tuple of ints, or `n` ints\n", " | \n", " | * None or no argument: reverses the order of the axes.\n", " | \n", " | * tuple of ints: `i` in the `j`-th place in the tuple means that the\n", " | array's `i`-th axis becomes the transposed array's `j`-th axis.\n", " | \n", " | * `n` ints: same as an n-tuple of the same ints (this form is\n", " | intended simply as a \"convenience\" alternative to the tuple form).\n", " | \n", " | Returns\n", " | -------\n", " | p : ndarray\n", " | View of the array with its axes suitably permuted.\n", " | \n", " | See Also\n", " | --------\n", " | transpose : Equivalent function.\n", " | ndarray.T : Array property returning the array transposed.\n", " | ndarray.reshape : Give a new shape to an array without changing its data.\n", " | \n", " | Examples\n", " | --------\n", " | >>> a = np.array([[1, 2], [3, 4]])\n", " | >>> a\n", " | array([[1, 2],\n", " | [3, 4]])\n", " | >>> a.transpose()\n", " | array([[1, 3],\n", " | [2, 4]])\n", " | >>> a.transpose((1, 0))\n", " | array([[1, 3],\n", " | [2, 4]])\n", " | >>> a.transpose(1, 0)\n", " | array([[1, 3],\n", " | [2, 4]])\n", " | \n", " | >>> a = np.array([1, 2, 3, 4])\n", " | >>> a\n", " | array([1, 2, 3, 4])\n", " | >>> a.transpose()\n", " | array([1, 2, 3, 4])\n", " | \n", " | view(...)\n", " | a.view([dtype][, type])\n", " | \n", " | New view of array with the same data.\n", " | \n", " | .. note::\n", " | Passing None for ``dtype`` is different from omitting the parameter,\n", " | since the former invokes ``dtype(None)`` which is an alias for\n", " | ``dtype('float_')``.\n", " | \n", " | Parameters\n", " | ----------\n", " | dtype : data-type or ndarray sub-class, optional\n", " | Data-type descriptor of the returned view, e.g., float32 or int16.\n", " | Omitting it results in the view having the same data-type as `a`.\n", " | This argument can also be specified as an ndarray sub-class, which\n", " | then specifies the type of the returned object (this is equivalent to\n", " | setting the ``type`` parameter).\n", " | type : Python type, optional\n", " | Type of the returned view, e.g., ndarray or matrix. Again, omission\n", " | of the parameter results in type preservation.\n", " | \n", " | Notes\n", " | -----\n", " | ``a.view()`` is used two different ways:\n", " | \n", " | ``a.view(some_dtype)`` or ``a.view(dtype=some_dtype)`` constructs a view\n", " | of the array's memory with a different data-type. This can cause a\n", " | reinterpretation of the bytes of memory.\n", " | \n", " | ``a.view(ndarray_subclass)`` or ``a.view(type=ndarray_subclass)`` just\n", " | returns an instance of `ndarray_subclass` that looks at the same array\n", " | (same shape, dtype, etc.) This does not cause a reinterpretation of the\n", " | memory.\n", " | \n", " | For ``a.view(some_dtype)``, if ``some_dtype`` has a different number of\n", " | bytes per entry than the previous dtype (for example, converting a regular\n", " | array to a structured array), then the last axis of ``a`` must be\n", " | contiguous. This axis will be resized in the result.\n", " | \n", " | .. versionchanged:: 1.23.0\n", " | Only the last axis needs to be contiguous. Previously, the entire array\n", " | had to be C-contiguous.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([(1, 2)], dtype=[('a', np.int8), ('b', np.int8)])\n", " | \n", " | Viewing array data using a different type and dtype:\n", " | \n", " | >>> y = x.view(dtype=np.int16, type=np.matrix)\n", " | >>> y\n", " | matrix([[513]], dtype=int16)\n", " | >>> print(type(y))\n", " | <class 'numpy.matrix'>\n", " | \n", " | Creating a view on a structured array so it can be used in calculations\n", " | \n", " | >>> x = np.array([(1, 2),(3,4)], dtype=[('a', np.int8), ('b', np.int8)])\n", " | >>> xv = x.view(dtype=np.int8).reshape(-1,2)\n", " | >>> xv\n", " | array([[1, 2],\n", " | [3, 4]], dtype=int8)\n", " | >>> xv.mean(0)\n", " | array([2., 3.])\n", " | \n", " | Making changes to the view changes the underlying array\n", " | \n", " | >>> xv[0,1] = 20\n", " | >>> x\n", " | array([(1, 20), (3, 4)], dtype=[('a', 'i1'), ('b', 'i1')])\n", " | \n", " | Using a view to convert an array to a recarray:\n", " | \n", " | >>> z = x.view(np.recarray)\n", " | >>> z.a\n", " | array([1, 3], dtype=int8)\n", " | \n", " | Views share data:\n", " | \n", " | >>> x[0] = (9, 10)\n", " | >>> z[0]\n", " | (9, 10)\n", " | \n", " | Views that change the dtype size (bytes per entry) should normally be\n", " | avoided on arrays defined by slices, transposes, fortran-ordering, etc.:\n", " | \n", " | >>> x = np.array([[1, 2, 3], [4, 5, 6]], dtype=np.int16)\n", " | >>> y = x[:, ::2]\n", " | >>> y\n", " | array([[1, 3],\n", " | [4, 6]], dtype=int16)\n", " | >>> y.view(dtype=[('width', np.int16), ('length', np.int16)])\n", " | Traceback (most recent call last):\n", " | ...\n", " | ValueError: To change to a dtype of a different size, the last axis must be contiguous\n", " | >>> z = y.copy()\n", " | >>> z.view(dtype=[('width', np.int16), ('length', np.int16)])\n", " | array([[(1, 3)],\n", " | [(4, 6)]], dtype=[('width', '<i2'), ('length', '<i2')])\n", " | \n", " | However, views that change dtype are totally fine for arrays with a\n", " | contiguous last axis, even if the rest of the axes are not C-contiguous:\n", " | \n", " | >>> x = np.arange(2 * 3 * 4, dtype=np.int8).reshape(2, 3, 4)\n", " | >>> x.transpose(1, 0, 2).view(np.int16)\n", " | array([[[ 256, 770],\n", " | [3340, 3854]],\n", " | <BLANKLINE>\n", " | [[1284, 1798],\n", " | [4368, 4882]],\n", " | <BLANKLINE>\n", " | [[2312, 2826],\n", " | [5396, 5910]]], dtype=int16)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods inherited from ndarray:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | a.__class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.ndarray` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.ndarray` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.ndarray[Any, np.dtype[Any]]\n", " | numpy.ndarray[typing.Any, numpy.dtype[typing.Any]]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | numpy.typing.NDArray : An ndarray alias :term:`generic <generic type>`\n", " | w.r.t. its `dtype.type <numpy.dtype.type>`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from ndarray:\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side.\n", " | \n", " | __array_struct__\n", " | Array protocol: C-struct side.\n", " | \n", " | base\n", " | Base object if memory is from some other object.\n", " | \n", " | Examples\n", " | --------\n", " | The base of an array that owns its memory is None:\n", " | \n", " | >>> x = np.array([1,2,3,4])\n", " | >>> x.base is None\n", " | True\n", " | \n", " | Slicing creates a view, whose memory is shared with x:\n", " | \n", " | >>> y = x[2:]\n", " | >>> y.base is x\n", " | True\n", " | \n", " | ctypes\n", " | An object to simplify the interaction of the array with the ctypes\n", " | module.\n", " | \n", " | This attribute creates an object that makes it easier to use arrays\n", " | when calling shared libraries with the ctypes module. The returned\n", " | object has, among others, data, shape, and strides attributes (see\n", " | Notes below) which themselves return ctypes objects that can be used\n", " | as arguments to a shared library.\n", " | \n", " | Parameters\n", " | ----------\n", " | None\n", " | \n", " | Returns\n", " | -------\n", " | c : Python object\n", " | Possessing attributes data, shape, strides, etc.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.ctypeslib\n", " | \n", " | Notes\n", " | -----\n", " | Below are the public attributes of this object which were documented\n", " | in \"Guide to NumPy\" (we have omitted undocumented public attributes,\n", " | as well as documented private attributes):\n", " | \n", " | .. autoattribute:: numpy.core._internal._ctypes.data\n", " | :noindex:\n", " | \n", " | .. autoattribute:: numpy.core._internal._ctypes.shape\n", " | :noindex:\n", " | \n", " | .. autoattribute:: numpy.core._internal._ctypes.strides\n", " | :noindex:\n", " | \n", " | .. automethod:: numpy.core._internal._ctypes.data_as\n", " | :noindex:\n", " | \n", " | .. automethod:: numpy.core._internal._ctypes.shape_as\n", " | :noindex:\n", " | \n", " | .. automethod:: numpy.core._internal._ctypes.strides_as\n", " | :noindex:\n", " | \n", " | If the ctypes module is not available, then the ctypes attribute\n", " | of array objects still returns something useful, but ctypes objects\n", " | are not returned and errors may be raised instead. In particular,\n", " | the object will still have the ``as_parameter`` attribute which will\n", " | return an integer equal to the data attribute.\n", " | \n", " | Examples\n", " | --------\n", " | >>> import ctypes\n", " | >>> x = np.array([[0, 1], [2, 3]], dtype=np.int32)\n", " | >>> x\n", " | array([[0, 1],\n", " | [2, 3]], dtype=int32)\n", " | >>> x.ctypes.data\n", " | 31962608 # may vary\n", " | >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32))\n", " | <__main__.LP_c_uint object at 0x7ff2fc1fc200> # may vary\n", " | >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)).contents\n", " | c_uint(0)\n", " | >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint64)).contents\n", " | c_ulong(4294967296)\n", " | >>> x.ctypes.shape\n", " | <numpy.core._internal.c_long_Array_2 object at 0x7ff2fc1fce60> # may vary\n", " | >>> x.ctypes.strides\n", " | <numpy.core._internal.c_long_Array_2 object at 0x7ff2fc1ff320> # may vary\n", " | \n", " | data\n", " | Python buffer object pointing to the start of the array's data.\n", " | \n", " | dtype\n", " | Data-type of the array's elements.\n", " | \n", " | .. warning::\n", " | \n", " | Setting ``arr.dtype`` is discouraged and may be deprecated in the\n", " | future. Setting will replace the ``dtype`` without modifying the\n", " | memory (see also `ndarray.view` and `ndarray.astype`).\n", " | \n", " | Parameters\n", " | ----------\n", " | None\n", " | \n", " | Returns\n", " | -------\n", " | d : numpy dtype object\n", " | \n", " | See Also\n", " | --------\n", " | ndarray.astype : Cast the values contained in the array to a new data-type.\n", " | ndarray.view : Create a view of the same data but a different data-type.\n", " | numpy.dtype\n", " | \n", " | Examples\n", " | --------\n", " | >>> x\n", " | array([[0, 1],\n", " | [2, 3]])\n", " | >>> x.dtype\n", " | dtype('int32')\n", " | >>> type(x.dtype)\n", " | <type 'numpy.dtype'>\n", " | \n", " | flags\n", " | Information about the memory layout of the array.\n", " | \n", " | Attributes\n", " | ----------\n", " | C_CONTIGUOUS (C)\n", " | The data is in a single, C-style contiguous segment.\n", " | F_CONTIGUOUS (F)\n", " | The data is in a single, Fortran-style contiguous segment.\n", " | OWNDATA (O)\n", " | The array owns the memory it uses or borrows it from another object.\n", " | WRITEABLE (W)\n", " | The data area can be written to. Setting this to False locks\n", " | the data, making it read-only. A view (slice, etc.) inherits WRITEABLE\n", " | from its base array at creation time, but a view of a writeable\n", " | array may be subsequently locked while the base array remains writeable.\n", " | (The opposite is not true, in that a view of a locked array may not\n", " | be made writeable. However, currently, locking a base object does not\n", " | lock any views that already reference it, so under that circumstance it\n", " | is possible to alter the contents of a locked array via a previously\n", " | created writeable view onto it.) Attempting to change a non-writeable\n", " | array raises a RuntimeError exception.\n", " | ALIGNED (A)\n", " | The data and all elements are aligned appropriately for the hardware.\n", " | WRITEBACKIFCOPY (X)\n", " | This array is a copy of some other array. The C-API function\n", " | PyArray_ResolveWritebackIfCopy must be called before deallocating\n", " | to the base array will be updated with the contents of this array.\n", " | FNC\n", " | F_CONTIGUOUS and not C_CONTIGUOUS.\n", " | FORC\n", " | F_CONTIGUOUS or C_CONTIGUOUS (one-segment test).\n", " | BEHAVED (B)\n", " | ALIGNED and WRITEABLE.\n", " | CARRAY (CA)\n", " | BEHAVED and C_CONTIGUOUS.\n", " | FARRAY (FA)\n", " | BEHAVED and F_CONTIGUOUS and not C_CONTIGUOUS.\n", " | \n", " | Notes\n", " | -----\n", " | The `flags` object can be accessed dictionary-like (as in ``a.flags['WRITEABLE']``),\n", " | or by using lowercased attribute names (as in ``a.flags.writeable``). Short flag\n", " | names are only supported in dictionary access.\n", " | \n", " | Only the WRITEBACKIFCOPY, WRITEABLE, and ALIGNED flags can be\n", " | changed by the user, via direct assignment to the attribute or dictionary\n", " | entry, or by calling `ndarray.setflags`.\n", " | \n", " | The array flags cannot be set arbitrarily:\n", " | \n", " | - WRITEBACKIFCOPY can only be set ``False``.\n", " | - ALIGNED can only be set ``True`` if the data is truly aligned.\n", " | - WRITEABLE can only be set ``True`` if the array owns its own memory\n", " | or the ultimate owner of the memory exposes a writeable buffer\n", " | interface or is a string.\n", " | \n", " | Arrays can be both C-style and Fortran-style contiguous simultaneously.\n", " | This is clear for 1-dimensional arrays, but can also be true for higher\n", " | dimensional arrays.\n", " | \n", " | Even for contiguous arrays a stride for a given dimension\n", " | ``arr.strides[dim]`` may be *arbitrary* if ``arr.shape[dim] == 1``\n", " | or the array has no elements.\n", " | It does *not* generally hold that ``self.strides[-1] == self.itemsize``\n", " | for C-style contiguous arrays or ``self.strides[0] == self.itemsize`` for\n", " | Fortran-style contiguous arrays is true.\n", " | \n", " | flat\n", " | A 1-D iterator over the array.\n", " | \n", " | This is a `numpy.flatiter` instance, which acts similarly to, but is not\n", " | a subclass of, Python's built-in iterator object.\n", " | \n", " | See Also\n", " | --------\n", " | flatten : Return a copy of the array collapsed into one dimension.\n", " | \n", " | flatiter\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.arange(1, 7).reshape(2, 3)\n", " | >>> x\n", " | array([[1, 2, 3],\n", " | [4, 5, 6]])\n", " | >>> x.flat[3]\n", " | 4\n", " | >>> x.T\n", " | array([[1, 4],\n", " | [2, 5],\n", " | [3, 6]])\n", " | >>> x.T.flat[3]\n", " | 5\n", " | >>> type(x.flat)\n", " | <class 'numpy.flatiter'>\n", " | \n", " | An assignment example:\n", " | \n", " | >>> x.flat = 3; x\n", " | array([[3, 3, 3],\n", " | [3, 3, 3]])\n", " | >>> x.flat[[1,4]] = 1; x\n", " | array([[3, 1, 3],\n", " | [3, 1, 3]])\n", " | \n", " | imag\n", " | The imaginary part of the array.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.sqrt([1+0j, 0+1j])\n", " | >>> x.imag\n", " | array([ 0. , 0.70710678])\n", " | >>> x.imag.dtype\n", " | dtype('float64')\n", " | \n", " | itemsize\n", " | Length of one array element in bytes.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([1,2,3], dtype=np.float64)\n", " | >>> x.itemsize\n", " | 8\n", " | >>> x = np.array([1,2,3], dtype=np.complex128)\n", " | >>> x.itemsize\n", " | 16\n", " | \n", " | nbytes\n", " | Total bytes consumed by the elements of the array.\n", " | \n", " | Notes\n", " | -----\n", " | Does not include memory consumed by non-element attributes of the\n", " | array object.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.zeros((3,5,2), dtype=np.complex128)\n", " | >>> x.nbytes\n", " | 480\n", " | >>> np.prod(x.shape) * x.itemsize\n", " | 480\n", " | \n", " | ndim\n", " | Number of array dimensions.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([1, 2, 3])\n", " | >>> x.ndim\n", " | 1\n", " | >>> y = np.zeros((2, 3, 4))\n", " | >>> y.ndim\n", " | 3\n", " | \n", " | real\n", " | The real part of the array.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.sqrt([1+0j, 0+1j])\n", " | >>> x.real\n", " | array([ 1. , 0.70710678])\n", " | >>> x.real.dtype\n", " | dtype('float64')\n", " | \n", " | See Also\n", " | --------\n", " | numpy.real : equivalent function\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | The shape property is usually used to get the current shape of an array,\n", " | but may also be used to reshape the array in-place by assigning a tuple of\n", " | array dimensions to it. As with `numpy.reshape`, one of the new shape\n", " | dimensions can be -1, in which case its value is inferred from the size of\n", " | the array and the remaining dimensions. Reshaping an array in-place will\n", " | fail if a copy is required.\n", " | \n", " | .. warning::\n", " | \n", " | Setting ``arr.shape`` is discouraged and may be deprecated in the\n", " | future. Using `ndarray.reshape` is the preferred approach.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([1, 2, 3, 4])\n", " | >>> x.shape\n", " | (4,)\n", " | >>> y = np.zeros((2, 3, 4))\n", " | >>> y.shape\n", " | (2, 3, 4)\n", " | >>> y.shape = (3, 8)\n", " | >>> y\n", " | array([[ 0., 0., 0., 0., 0., 0., 0., 0.],\n", " | [ 0., 0., 0., 0., 0., 0., 0., 0.],\n", " | [ 0., 0., 0., 0., 0., 0., 0., 0.]])\n", " | >>> y.shape = (3, 6)\n", " | Traceback (most recent call last):\n", " | File \"<stdin>\", line 1, in <module>\n", " | ValueError: total size of new array must be unchanged\n", " | >>> np.zeros((4,2))[::2].shape = (-1,)\n", " | Traceback (most recent call last):\n", " | File \"<stdin>\", line 1, in <module>\n", " | AttributeError: Incompatible shape for in-place modification. Use\n", " | `.reshape()` to make a copy with the desired shape.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.shape : Equivalent getter function.\n", " | numpy.reshape : Function similar to setting ``shape``.\n", " | ndarray.reshape : Method similar to setting ``shape``.\n", " | \n", " | size\n", " | Number of elements in the array.\n", " | \n", " | Equal to ``np.prod(a.shape)``, i.e., the product of the array's\n", " | dimensions.\n", " | \n", " | Notes\n", " | -----\n", " | `a.size` returns a standard arbitrary precision Python integer. This\n", " | may not be the case with other methods of obtaining the same value\n", " | (like the suggested ``np.prod(a.shape)``, which returns an instance\n", " | of ``np.int_``), and may be relevant if the value is used further in\n", " | calculations that may overflow a fixed size integer type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.zeros((3, 5, 2), dtype=np.complex128)\n", " | >>> x.size\n", " | 30\n", " | >>> np.prod(x.shape)\n", " | 30\n", " | \n", " | strides\n", " | Tuple of bytes to step in each dimension when traversing an array.\n", " | \n", " | The byte offset of element ``(i[0], i[1], ..., i[n])`` in an array `a`\n", " | is::\n", " | \n", " | offset = sum(np.array(i) * a.strides)\n", " | \n", " | A more detailed explanation of strides can be found in the\n", " | \"ndarray.rst\" file in the NumPy reference guide.\n", " | \n", " | .. warning::\n", " | \n", " | Setting ``arr.strides`` is discouraged and may be deprecated in the\n", " | future. `numpy.lib.stride_tricks.as_strided` should be preferred\n", " | to create a new view of the same data in a safer way.\n", " | \n", " | Notes\n", " | -----\n", " | Imagine an array of 32-bit integers (each 4 bytes)::\n", " | \n", " | x = np.array([[0, 1, 2, 3, 4],\n", " | [5, 6, 7, 8, 9]], dtype=np.int32)\n", " | \n", " | This array is stored in memory as 40 bytes, one after the other\n", " | (known as a contiguous block of memory). The strides of an array tell\n", " | us how many bytes we have to skip in memory to move to the next position\n", " | along a certain axis. For example, we have to skip 4 bytes (1 value) to\n", " | move to the next column, but 20 bytes (5 values) to get to the same\n", " | position in the next row. As such, the strides for the array `x` will be\n", " | ``(20, 4)``.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.lib.stride_tricks.as_strided\n", " | \n", " | Examples\n", " | --------\n", " | >>> y = np.reshape(np.arange(2*3*4), (2,3,4))\n", " | >>> y\n", " | array([[[ 0, 1, 2, 3],\n", " | [ 4, 5, 6, 7],\n", " | [ 8, 9, 10, 11]],\n", " | [[12, 13, 14, 15],\n", " | [16, 17, 18, 19],\n", " | [20, 21, 22, 23]]])\n", " | >>> y.strides\n", " | (48, 16, 4)\n", " | >>> y[1,1,1]\n", " | 17\n", " | >>> offset=sum(y.strides * np.array((1,1,1)))\n", " | >>> offset/y.itemsize\n", " | 17\n", " | \n", " | >>> x = np.reshape(np.arange(5*6*7*8), (5,6,7,8)).transpose(2,3,1,0)\n", " | >>> x.strides\n", " | (32, 4, 224, 1344)\n", " | >>> i = np.array([3,5,2,2])\n", " | >>> offset = sum(i * x.strides)\n", " | >>> x[3,5,2,2]\n", " | 813\n", " | >>> offset / x.itemsize\n", " | 813\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data and other attributes inherited from ndarray:\n", " | \n", " | __hash__ = None\n", " \n", " class memmap(ndarray)\n", " | memmap(filename, dtype=<class 'numpy.uint8'>, mode='r+', offset=0, shape=None, order='C')\n", " | \n", " | Create a memory-map to an array stored in a *binary* file on disk.\n", " | \n", " | Memory-mapped files are used for accessing small segments of large files\n", " | on disk, without reading the entire file into memory. NumPy's\n", " | memmap's are array-like objects. This differs from Python's ``mmap``\n", " | module, which uses file-like objects.\n", " | \n", " | This subclass of ndarray has some unpleasant interactions with\n", " | some operations, because it doesn't quite fit properly as a subclass.\n", " | An alternative to using this subclass is to create the ``mmap``\n", " | object yourself, then create an ndarray with ndarray.__new__ directly,\n", " | passing the object created in its 'buffer=' parameter.\n", " | \n", " | This class may at some point be turned into a factory function\n", " | which returns a view into an mmap buffer.\n", " | \n", " | Flush the memmap instance to write the changes to the file. Currently there\n", " | is no API to close the underlying ``mmap``. It is tricky to ensure the\n", " | resource is actually closed, since it may be shared between different\n", " | memmap instances.\n", " | \n", " | \n", " | Parameters\n", " | ----------\n", " | filename : str, file-like object, or pathlib.Path instance\n", " | The file name or file object to be used as the array data buffer.\n", " | dtype : data-type, optional\n", " | The data-type used to interpret the file contents.\n", " | Default is `uint8`.\n", " | mode : {'r+', 'r', 'w+', 'c'}, optional\n", " | The file is opened in this mode:\n", " | \n", " | +------+-------------------------------------------------------------+\n", " | | 'r' | Open existing file for reading only. |\n", " | +------+-------------------------------------------------------------+\n", " | | 'r+' | Open existing file for reading and writing. |\n", " | +------+-------------------------------------------------------------+\n", " | | 'w+' | Create or overwrite existing file for reading and writing. |\n", " | +------+-------------------------------------------------------------+\n", " | | 'c' | Copy-on-write: assignments affect data in memory, but |\n", " | | | changes are not saved to disk. The file on disk is |\n", " | | | read-only. |\n", " | +------+-------------------------------------------------------------+\n", " | \n", " | Default is 'r+'.\n", " | offset : int, optional\n", " | In the file, array data starts at this offset. Since `offset` is\n", " | measured in bytes, it should normally be a multiple of the byte-size\n", " | of `dtype`. When ``mode != 'r'``, even positive offsets beyond end of\n", " | file are valid; The file will be extended to accommodate the\n", " | additional data. By default, ``memmap`` will start at the beginning of\n", " | the file, even if ``filename`` is a file pointer ``fp`` and\n", " | ``fp.tell() != 0``.\n", " | shape : tuple, optional\n", " | The desired shape of the array. If ``mode == 'r'`` and the number\n", " | of remaining bytes after `offset` is not a multiple of the byte-size\n", " | of `dtype`, you must specify `shape`. By default, the returned array\n", " | will be 1-D with the number of elements determined by file size\n", " | and data-type.\n", " | order : {'C', 'F'}, optional\n", " | Specify the order of the ndarray memory layout:\n", " | :term:`row-major`, C-style or :term:`column-major`,\n", " | Fortran-style. This only has an effect if the shape is\n", " | greater than 1-D. The default order is 'C'.\n", " | \n", " | Attributes\n", " | ----------\n", " | filename : str or pathlib.Path instance\n", " | Path to the mapped file.\n", " | offset : int\n", " | Offset position in the file.\n", " | mode : str\n", " | File mode.\n", " | \n", " | Methods\n", " | -------\n", " | flush\n", " | Flush any changes in memory to file on disk.\n", " | When you delete a memmap object, flush is called first to write\n", " | changes to disk.\n", " | \n", " | \n", " | See also\n", " | --------\n", " | lib.format.open_memmap : Create or load a memory-mapped ``.npy`` file.\n", " | \n", " | Notes\n", " | -----\n", " | The memmap object can be used anywhere an ndarray is accepted.\n", " | Given a memmap ``fp``, ``isinstance(fp, numpy.ndarray)`` returns\n", " | ``True``.\n", " | \n", " | Memory-mapped files cannot be larger than 2GB on 32-bit systems.\n", " | \n", " | When a memmap causes a file to be created or extended beyond its\n", " | current size in the filesystem, the contents of the new part are\n", " | unspecified. On systems with POSIX filesystem semantics, the extended\n", " | part will be filled with zero bytes.\n", " | \n", " | Examples\n", " | --------\n", " | >>> data = np.arange(12, dtype='float32')\n", " | >>> data.resize((3,4))\n", " | \n", " | This example uses a temporary file so that doctest doesn't write\n", " | files to your directory. You would use a 'normal' filename.\n", " | \n", " | >>> from tempfile import mkdtemp\n", " | >>> import os.path as path\n", " | >>> filename = path.join(mkdtemp(), 'newfile.dat')\n", " | \n", " | Create a memmap with dtype and shape that matches our data:\n", " | \n", " | >>> fp = np.memmap(filename, dtype='float32', mode='w+', shape=(3,4))\n", " | >>> fp\n", " | memmap([[0., 0., 0., 0.],\n", " | [0., 0., 0., 0.],\n", " | [0., 0., 0., 0.]], dtype=float32)\n", " | \n", " | Write data to memmap array:\n", " | \n", " | >>> fp[:] = data[:]\n", " | >>> fp\n", " | memmap([[ 0., 1., 2., 3.],\n", " | [ 4., 5., 6., 7.],\n", " | [ 8., 9., 10., 11.]], dtype=float32)\n", " | \n", " | >>> fp.filename == path.abspath(filename)\n", " | True\n", " | \n", " | Flushes memory changes to disk in order to read them back\n", " | \n", " | >>> fp.flush()\n", " | \n", " | Load the memmap and verify data was stored:\n", " | \n", " | >>> newfp = np.memmap(filename, dtype='float32', mode='r', shape=(3,4))\n", " | >>> newfp\n", " | memmap([[ 0., 1., 2., 3.],\n", " | [ 4., 5., 6., 7.],\n", " | [ 8., 9., 10., 11.]], dtype=float32)\n", " | \n", " | Read-only memmap:\n", " | \n", " | >>> fpr = np.memmap(filename, dtype='float32', mode='r', shape=(3,4))\n", " | >>> fpr.flags.writeable\n", " | False\n", " | \n", " | Copy-on-write memmap:\n", " | \n", " | >>> fpc = np.memmap(filename, dtype='float32', mode='c', shape=(3,4))\n", " | >>> fpc.flags.writeable\n", " | True\n", " | \n", " | It's possible to assign to copy-on-write array, but values are only\n", " | written into the memory copy of the array, and not written to disk:\n", " | \n", " | >>> fpc\n", " | memmap([[ 0., 1., 2., 3.],\n", " | [ 4., 5., 6., 7.],\n", " | [ 8., 9., 10., 11.]], dtype=float32)\n", " | >>> fpc[0,:] = 0\n", " | >>> fpc\n", " | memmap([[ 0., 0., 0., 0.],\n", " | [ 4., 5., 6., 7.],\n", " | [ 8., 9., 10., 11.]], dtype=float32)\n", " | \n", " | File on disk is unchanged:\n", " | \n", " | >>> fpr\n", " | memmap([[ 0., 1., 2., 3.],\n", " | [ 4., 5., 6., 7.],\n", " | [ 8., 9., 10., 11.]], dtype=float32)\n", " | \n", " | Offset into a memmap:\n", " | \n", " | >>> fpo = np.memmap(filename, dtype='float32', mode='r', offset=16)\n", " | >>> fpo\n", " | memmap([ 4., 5., 6., 7., 8., 9., 10., 11.], dtype=float32)\n", " | \n", " | Method resolution order:\n", " | memmap\n", " | ndarray\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __array_finalize__(self, obj)\n", " | a.__array_finalize__(obj, /)\n", " | \n", " | Present so subclasses can call super. Does nothing.\n", " | \n", " | __array_wrap__(self, arr, context=None)\n", " | a.__array_wrap__(array[, context], /)\n", " | \n", " | Returns a view of `array` with the same type as self.\n", " | \n", " | __getitem__(self, index)\n", " | Return self[key].\n", " | \n", " | flush(self)\n", " | Write any changes in the array to the file on disk.\n", " | \n", " | For further information, see `memmap`.\n", " | \n", " | Parameters\n", " | ----------\n", " | None\n", " | \n", " | See Also\n", " | --------\n", " | memmap\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(subtype, filename, dtype=<class 'numpy.uint8'>, mode='r+', offset=0, shape=None, order='C')\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors defined here:\n", " | \n", " | __dict__\n", " | dictionary for instance variables (if defined)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data and other attributes defined here:\n", " | \n", " | __array_priority__ = -100.0\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from ndarray:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | a.__array__([dtype], /) -> reference if type unchanged, copy otherwise.\n", " | \n", " | Returns either a new reference to self if dtype is not given or a new array\n", " | of provided data type if dtype is different from the current dtype of the\n", " | array.\n", " | \n", " | __array_function__(...)\n", " | \n", " | __array_prepare__(...)\n", " | a.__array_prepare__(array[, context], /)\n", " | \n", " | Returns a view of `array` with the same type as self.\n", " | \n", " | __array_ufunc__(...)\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __complex__(...)\n", " | \n", " | __contains__(self, key, /)\n", " | Return key in self.\n", " | \n", " | __copy__(...)\n", " | a.__copy__()\n", " | \n", " | Used if :func:`copy.copy` is called on an array. Returns a copy of the array.\n", " | \n", " | Equivalent to ``a.copy(order='K')``.\n", " | \n", " | __deepcopy__(...)\n", " | a.__deepcopy__(memo, /) -> Deep copy of array.\n", " | \n", " | Used if :func:`copy.deepcopy` is called on an array.\n", " | \n", " | __delitem__(self, key, /)\n", " | Delete self[key].\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __dlpack__(...)\n", " | a.__dlpack__(*, stream=None)\n", " | \n", " | DLPack Protocol: Part of the Array API.\n", " | \n", " | __dlpack_device__(...)\n", " | a.__dlpack_device__()\n", " | \n", " | DLPack Protocol: Part of the Array API.\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __format__(...)\n", " | Default object formatter.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __iadd__(self, value, /)\n", " | Return self+=value.\n", " | \n", " | __iand__(self, value, /)\n", " | Return self&=value.\n", " | \n", " | __ifloordiv__(self, value, /)\n", " | Return self//=value.\n", " | \n", " | __ilshift__(self, value, /)\n", " | Return self<<=value.\n", " | \n", " | __imatmul__(self, value, /)\n", " | Return self@=value.\n", " | \n", " | __imod__(self, value, /)\n", " | Return self%=value.\n", " | \n", " | __imul__(self, value, /)\n", " | Return self*=value.\n", " | \n", " | __index__(self, /)\n", " | Return self converted to an integer, if self is suitable for use as an index into a list.\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __ior__(self, value, /)\n", " | Return self|=value.\n", " | \n", " | __ipow__(self, value, /)\n", " | Return self**=value.\n", " | \n", " | __irshift__(self, value, /)\n", " | Return self>>=value.\n", " | \n", " | __isub__(self, value, /)\n", " | Return self-=value.\n", " | \n", " | __iter__(self, /)\n", " | Implement iter(self).\n", " | \n", " | __itruediv__(self, value, /)\n", " | Return self/=value.\n", " | \n", " | __ixor__(self, value, /)\n", " | Return self^=value.\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __len__(self, /)\n", " | Return len(self).\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __matmul__(self, value, /)\n", " | Return self@value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __reduce__(...)\n", " | a.__reduce__()\n", " | \n", " | For pickling.\n", " | \n", " | __reduce_ex__(...)\n", " | Helper for pickle.\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmatmul__(self, value, /)\n", " | Return value@self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setitem__(self, key, value, /)\n", " | Set self[key] to value.\n", " | \n", " | __setstate__(...)\n", " | a.__setstate__(state, /)\n", " | \n", " | For unpickling.\n", " | \n", " | The `state` argument must be a sequence that contains the following\n", " | elements:\n", " | \n", " | Parameters\n", " | ----------\n", " | version : int\n", " | optional pickle version. If omitted defaults to 0.\n", " | shape : tuple\n", " | dtype : data-type\n", " | isFortran : bool\n", " | rawdata : string or list\n", " | a binary string with the data (or a list if 'a' is an object array)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | a.all(axis=None, out=None, keepdims=False, *, where=True)\n", " | \n", " | Returns True if all elements evaluate to True.\n", " | \n", " | Refer to `numpy.all` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.all : equivalent function\n", " | \n", " | any(...)\n", " | a.any(axis=None, out=None, keepdims=False, *, where=True)\n", " | \n", " | Returns True if any of the elements of `a` evaluate to True.\n", " | \n", " | Refer to `numpy.any` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.any : equivalent function\n", " | \n", " | argmax(...)\n", " | a.argmax(axis=None, out=None, *, keepdims=False)\n", " | \n", " | Return indices of the maximum values along the given axis.\n", " | \n", " | Refer to `numpy.argmax` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.argmax : equivalent function\n", " | \n", " | argmin(...)\n", " | a.argmin(axis=None, out=None, *, keepdims=False)\n", " | \n", " | Return indices of the minimum values along the given axis.\n", " | \n", " | Refer to `numpy.argmin` for detailed documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.argmin : equivalent function\n", " | \n", " | argpartition(...)\n", " | a.argpartition(kth, axis=-1, kind='introselect', order=None)\n", " | \n", " | Returns the indices that would partition this array.\n", " | \n", " | Refer to `numpy.argpartition` for full documentation.\n", " | \n", " | .. versionadded:: 1.8.0\n", " | \n", " | See Also\n", " | --------\n", " | numpy.argpartition : equivalent function\n", " | \n", " | argsort(...)\n", " | a.argsort(axis=-1, kind=None, order=None)\n", " | \n", " | Returns the indices that would sort this array.\n", " | \n", " | Refer to `numpy.argsort` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.argsort : equivalent function\n", " | \n", " | astype(...)\n", " | a.astype(dtype, order='K', casting='unsafe', subok=True, copy=True)\n", " | \n", " | Copy of the array, cast to a specified type.\n", " | \n", " | Parameters\n", " | ----------\n", " | dtype : str or dtype\n", " | Typecode or data-type to which the array is cast.\n", " | order : {'C', 'F', 'A', 'K'}, optional\n", " | Controls the memory layout order of the result.\n", " | 'C' means C order, 'F' means Fortran order, 'A'\n", " | means 'F' order if all the arrays are Fortran contiguous,\n", " | 'C' order otherwise, and 'K' means as close to the\n", " | order the array elements appear in memory as possible.\n", " | Default is 'K'.\n", " | casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional\n", " | Controls what kind of data casting may occur. Defaults to 'unsafe'\n", " | for backwards compatibility.\n", " | \n", " | * 'no' means the data types should not be cast at all.\n", " | * 'equiv' means only byte-order changes are allowed.\n", " | * 'safe' means only casts which can preserve values are allowed.\n", " | * 'same_kind' means only safe casts or casts within a kind,\n", " | like float64 to float32, are allowed.\n", " | * 'unsafe' means any data conversions may be done.\n", " | subok : bool, optional\n", " | If True, then sub-classes will be passed-through (default), otherwise\n", " | the returned array will be forced to be a base-class array.\n", " | copy : bool, optional\n", " | By default, astype always returns a newly allocated array. If this\n", " | is set to false, and the `dtype`, `order`, and `subok`\n", " | requirements are satisfied, the input array is returned instead\n", " | of a copy.\n", " | \n", " | Returns\n", " | -------\n", " | arr_t : ndarray\n", " | Unless `copy` is False and the other conditions for returning the input\n", " | array are satisfied (see description for `copy` input parameter), `arr_t`\n", " | is a new array of the same shape as the input array, with dtype, order\n", " | given by `dtype`, `order`.\n", " | \n", " | Notes\n", " | -----\n", " | .. versionchanged:: 1.17.0\n", " | Casting between a simple data type and a structured one is possible only\n", " | for \"unsafe\" casting. Casting to multiple fields is allowed, but\n", " | casting from multiple fields is not.\n", " | \n", " | .. versionchanged:: 1.9.0\n", " | Casting from numeric to string types in 'safe' casting mode requires\n", " | that the string dtype length is long enough to store the max\n", " | integer/float value converted.\n", " | \n", " | Raises\n", " | ------\n", " | ComplexWarning\n", " | When casting from complex to float or int. To avoid this,\n", " | one should use ``a.real.astype(t)``.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([1, 2, 2.5])\n", " | >>> x\n", " | array([1. , 2. , 2.5])\n", " | \n", " | >>> x.astype(int)\n", " | array([1, 2, 2])\n", " | \n", " | byteswap(...)\n", " | a.byteswap(inplace=False)\n", " | \n", " | Swap the bytes of the array elements\n", " | \n", " | Toggle between low-endian and big-endian data representation by\n", " | returning a byteswapped array, optionally swapped in-place.\n", " | Arrays of byte-strings are not swapped. The real and imaginary\n", " | parts of a complex number are swapped individually.\n", " | \n", " | Parameters\n", " | ----------\n", " | inplace : bool, optional\n", " | If ``True``, swap bytes in-place, default is ``False``.\n", " | \n", " | Returns\n", " | -------\n", " | out : ndarray\n", " | The byteswapped array. If `inplace` is ``True``, this is\n", " | a view to self.\n", " | \n", " | Examples\n", " | --------\n", " | >>> A = np.array([1, 256, 8755], dtype=np.int16)\n", " | >>> list(map(hex, A))\n", " | ['0x1', '0x100', '0x2233']\n", " | >>> A.byteswap(inplace=True)\n", " | array([ 256, 1, 13090], dtype=int16)\n", " | >>> list(map(hex, A))\n", " | ['0x100', '0x1', '0x3322']\n", " | \n", " | Arrays of byte-strings are not swapped\n", " | \n", " | >>> A = np.array([b'ceg', b'fac'])\n", " | >>> A.byteswap()\n", " | array([b'ceg', b'fac'], dtype='|S3')\n", " | \n", " | ``A.newbyteorder().byteswap()`` produces an array with the same values\n", " | but different representation in memory\n", " | \n", " | >>> A = np.array([1, 2, 3])\n", " | >>> A.view(np.uint8)\n", " | array([1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0,\n", " | 0, 0], dtype=uint8)\n", " | >>> A.newbyteorder().byteswap(inplace=True)\n", " | array([1, 2, 3])\n", " | >>> A.view(np.uint8)\n", " | array([0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0,\n", " | 0, 3], dtype=uint8)\n", " | \n", " | choose(...)\n", " | a.choose(choices, out=None, mode='raise')\n", " | \n", " | Use an index array to construct a new array from a set of choices.\n", " | \n", " | Refer to `numpy.choose` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.choose : equivalent function\n", " | \n", " | clip(...)\n", " | a.clip(min=None, max=None, out=None, **kwargs)\n", " | \n", " | Return an array whose values are limited to ``[min, max]``.\n", " | One of max or min must be given.\n", " | \n", " | Refer to `numpy.clip` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.clip : equivalent function\n", " | \n", " | compress(...)\n", " | a.compress(condition, axis=None, out=None)\n", " | \n", " | Return selected slices of this array along given axis.\n", " | \n", " | Refer to `numpy.compress` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.compress : equivalent function\n", " | \n", " | conj(...)\n", " | a.conj()\n", " | \n", " | Complex-conjugate all elements.\n", " | \n", " | Refer to `numpy.conjugate` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.conjugate : equivalent function\n", " | \n", " | conjugate(...)\n", " | a.conjugate()\n", " | \n", " | Return the complex conjugate, element-wise.\n", " | \n", " | Refer to `numpy.conjugate` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.conjugate : equivalent function\n", " | \n", " | copy(...)\n", " | a.copy(order='C')\n", " | \n", " | Return a copy of the array.\n", " | \n", " | Parameters\n", " | ----------\n", " | order : {'C', 'F', 'A', 'K'}, optional\n", " | Controls the memory layout of the copy. 'C' means C-order,\n", " | 'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous,\n", " | 'C' otherwise. 'K' means match the layout of `a` as closely\n", " | as possible. (Note that this function and :func:`numpy.copy` are very\n", " | similar but have different default values for their order=\n", " | arguments, and this function always passes sub-classes through.)\n", " | \n", " | See also\n", " | --------\n", " | numpy.copy : Similar function with different default behavior\n", " | numpy.copyto\n", " | \n", " | Notes\n", " | -----\n", " | This function is the preferred method for creating an array copy. The\n", " | function :func:`numpy.copy` is similar, but it defaults to using order 'K',\n", " | and will not pass sub-classes through by default.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([[1,2,3],[4,5,6]], order='F')\n", " | \n", " | >>> y = x.copy()\n", " | \n", " | >>> x.fill(0)\n", " | \n", " | >>> x\n", " | array([[0, 0, 0],\n", " | [0, 0, 0]])\n", " | \n", " | >>> y\n", " | array([[1, 2, 3],\n", " | [4, 5, 6]])\n", " | \n", " | >>> y.flags['C_CONTIGUOUS']\n", " | True\n", " | \n", " | cumprod(...)\n", " | a.cumprod(axis=None, dtype=None, out=None)\n", " | \n", " | Return the cumulative product of the elements along the given axis.\n", " | \n", " | Refer to `numpy.cumprod` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.cumprod : equivalent function\n", " | \n", " | cumsum(...)\n", " | a.cumsum(axis=None, dtype=None, out=None)\n", " | \n", " | Return the cumulative sum of the elements along the given axis.\n", " | \n", " | Refer to `numpy.cumsum` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.cumsum : equivalent function\n", " | \n", " | diagonal(...)\n", " | a.diagonal(offset=0, axis1=0, axis2=1)\n", " | \n", " | Return specified diagonals. In NumPy 1.9 the returned array is a\n", " | read-only view instead of a copy as in previous NumPy versions. In\n", " | a future version the read-only restriction will be removed.\n", " | \n", " | Refer to :func:`numpy.diagonal` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.diagonal : equivalent function\n", " | \n", " | dot(...)\n", " | \n", " | dump(...)\n", " | a.dump(file)\n", " | \n", " | Dump a pickle of the array to the specified file.\n", " | The array can be read back with pickle.load or numpy.load.\n", " | \n", " | Parameters\n", " | ----------\n", " | file : str or Path\n", " | A string naming the dump file.\n", " | \n", " | .. versionchanged:: 1.17.0\n", " | `pathlib.Path` objects are now accepted.\n", " | \n", " | dumps(...)\n", " | a.dumps()\n", " | \n", " | Returns the pickle of the array as a string.\n", " | pickle.loads will convert the string back to an array.\n", " | \n", " | Parameters\n", " | ----------\n", " | None\n", " | \n", " | fill(...)\n", " | a.fill(value)\n", " | \n", " | Fill the array with a scalar value.\n", " | \n", " | Parameters\n", " | ----------\n", " | value : scalar\n", " | All elements of `a` will be assigned this value.\n", " | \n", " | Examples\n", " | --------\n", " | >>> a = np.array([1, 2])\n", " | >>> a.fill(0)\n", " | >>> a\n", " | array([0, 0])\n", " | >>> a = np.empty(2)\n", " | >>> a.fill(1)\n", " | >>> a\n", " | array([1., 1.])\n", " | \n", " | Fill expects a scalar value and always behaves the same as assigning\n", " | to a single array element. The following is a rare example where this\n", " | distinction is important:\n", " | \n", " | >>> a = np.array([None, None], dtype=object)\n", " | >>> a[0] = np.array(3)\n", " | >>> a\n", " | array([array(3), None], dtype=object)\n", " | >>> a.fill(np.array(3))\n", " | >>> a\n", " | array([array(3), array(3)], dtype=object)\n", " | \n", " | Where other forms of assignments will unpack the array being assigned:\n", " | \n", " | >>> a[...] = np.array(3)\n", " | >>> a\n", " | array([3, 3], dtype=object)\n", " | \n", " | flatten(...)\n", " | a.flatten(order='C')\n", " | \n", " | Return a copy of the array collapsed into one dimension.\n", " | \n", " | Parameters\n", " | ----------\n", " | order : {'C', 'F', 'A', 'K'}, optional\n", " | 'C' means to flatten in row-major (C-style) order.\n", " | 'F' means to flatten in column-major (Fortran-\n", " | style) order. 'A' means to flatten in column-major\n", " | order if `a` is Fortran *contiguous* in memory,\n", " | row-major order otherwise. 'K' means to flatten\n", " | `a` in the order the elements occur in memory.\n", " | The default is 'C'.\n", " | \n", " | Returns\n", " | -------\n", " | y : ndarray\n", " | A copy of the input array, flattened to one dimension.\n", " | \n", " | See Also\n", " | --------\n", " | ravel : Return a flattened array.\n", " | flat : A 1-D flat iterator over the array.\n", " | \n", " | Examples\n", " | --------\n", " | >>> a = np.array([[1,2], [3,4]])\n", " | >>> a.flatten()\n", " | array([1, 2, 3, 4])\n", " | >>> a.flatten('F')\n", " | array([1, 3, 2, 4])\n", " | \n", " | getfield(...)\n", " | a.getfield(dtype, offset=0)\n", " | \n", " | Returns a field of the given array as a certain type.\n", " | \n", " | A field is a view of the array data with a given data-type. The values in\n", " | the view are determined by the given type and the offset into the current\n", " | array in bytes. The offset needs to be such that the view dtype fits in the\n", " | array dtype; for example an array of dtype complex128 has 16-byte elements.\n", " | If taking a view with a 32-bit integer (4 bytes), the offset needs to be\n", " | between 0 and 12 bytes.\n", " | \n", " | Parameters\n", " | ----------\n", " | dtype : str or dtype\n", " | The data type of the view. The dtype size of the view can not be larger\n", " | than that of the array itself.\n", " | offset : int\n", " | Number of bytes to skip before beginning the element view.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.diag([1.+1.j]*2)\n", " | >>> x[1, 1] = 2 + 4.j\n", " | >>> x\n", " | array([[1.+1.j, 0.+0.j],\n", " | [0.+0.j, 2.+4.j]])\n", " | >>> x.getfield(np.float64)\n", " | array([[1., 0.],\n", " | [0., 2.]])\n", " | \n", " | By choosing an offset of 8 bytes we can select the complex part of the\n", " | array for our view:\n", " | \n", " | >>> x.getfield(np.float64, offset=8)\n", " | array([[1., 0.],\n", " | [0., 4.]])\n", " | \n", " | item(...)\n", " | a.item(*args)\n", " | \n", " | Copy an element of an array to a standard Python scalar and return it.\n", " | \n", " | Parameters\n", " | ----------\n", " | \\*args : Arguments (variable number and type)\n", " | \n", " | * none: in this case, the method only works for arrays\n", " | with one element (`a.size == 1`), which element is\n", " | copied into a standard Python scalar object and returned.\n", " | \n", " | * int_type: this argument is interpreted as a flat index into\n", " | the array, specifying which element to copy and return.\n", " | \n", " | * tuple of int_types: functions as does a single int_type argument,\n", " | except that the argument is interpreted as an nd-index into the\n", " | array.\n", " | \n", " | Returns\n", " | -------\n", " | z : Standard Python scalar object\n", " | A copy of the specified element of the array as a suitable\n", " | Python scalar\n", " | \n", " | Notes\n", " | -----\n", " | When the data type of `a` is longdouble or clongdouble, item() returns\n", " | a scalar array object because there is no available Python scalar that\n", " | would not lose information. Void arrays return a buffer object for item(),\n", " | unless fields are defined, in which case a tuple is returned.\n", " | \n", " | `item` is very similar to a[args], except, instead of an array scalar,\n", " | a standard Python scalar is returned. This can be useful for speeding up\n", " | access to elements of the array and doing arithmetic on elements of the\n", " | array using Python's optimized math.\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.random.seed(123)\n", " | >>> x = np.random.randint(9, size=(3, 3))\n", " | >>> x\n", " | array([[2, 2, 6],\n", " | [1, 3, 6],\n", " | [1, 0, 1]])\n", " | >>> x.item(3)\n", " | 1\n", " | >>> x.item(7)\n", " | 0\n", " | >>> x.item((0, 1))\n", " | 2\n", " | >>> x.item((2, 2))\n", " | 1\n", " | \n", " | itemset(...)\n", " | a.itemset(*args)\n", " | \n", " | Insert scalar into an array (scalar is cast to array's dtype, if possible)\n", " | \n", " | There must be at least 1 argument, and define the last argument\n", " | as *item*. Then, ``a.itemset(*args)`` is equivalent to but faster\n", " | than ``a[args] = item``. The item should be a scalar value and `args`\n", " | must select a single item in the array `a`.\n", " | \n", " | Parameters\n", " | ----------\n", " | \\*args : Arguments\n", " | If one argument: a scalar, only used in case `a` is of size 1.\n", " | If two arguments: the last argument is the value to be set\n", " | and must be a scalar, the first argument specifies a single array\n", " | element location. It is either an int or a tuple.\n", " | \n", " | Notes\n", " | -----\n", " | Compared to indexing syntax, `itemset` provides some speed increase\n", " | for placing a scalar into a particular location in an `ndarray`,\n", " | if you must do this. However, generally this is discouraged:\n", " | among other problems, it complicates the appearance of the code.\n", " | Also, when using `itemset` (and `item`) inside a loop, be sure\n", " | to assign the methods to a local variable to avoid the attribute\n", " | look-up at each loop iteration.\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.random.seed(123)\n", " | >>> x = np.random.randint(9, size=(3, 3))\n", " | >>> x\n", " | array([[2, 2, 6],\n", " | [1, 3, 6],\n", " | [1, 0, 1]])\n", " | >>> x.itemset(4, 0)\n", " | >>> x.itemset((2, 2), 9)\n", " | >>> x\n", " | array([[2, 2, 6],\n", " | [1, 0, 6],\n", " | [1, 0, 9]])\n", " | \n", " | max(...)\n", " | a.max(axis=None, out=None, keepdims=False, initial=<no value>, where=True)\n", " | \n", " | Return the maximum along a given axis.\n", " | \n", " | Refer to `numpy.amax` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.amax : equivalent function\n", " | \n", " | mean(...)\n", " | a.mean(axis=None, dtype=None, out=None, keepdims=False, *, where=True)\n", " | \n", " | Returns the average of the array elements along given axis.\n", " | \n", " | Refer to `numpy.mean` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.mean : equivalent function\n", " | \n", " | min(...)\n", " | a.min(axis=None, out=None, keepdims=False, initial=<no value>, where=True)\n", " | \n", " | Return the minimum along a given axis.\n", " | \n", " | Refer to `numpy.amin` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.amin : equivalent function\n", " | \n", " | newbyteorder(...)\n", " | arr.newbyteorder(new_order='S', /)\n", " | \n", " | Return the array with the same data viewed with a different byte order.\n", " | \n", " | Equivalent to::\n", " | \n", " | arr.view(arr.dtype.newbytorder(new_order))\n", " | \n", " | Changes are also made in all fields and sub-arrays of the array data\n", " | type.\n", " | \n", " | \n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : string, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | below. `new_order` codes can be any of:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order, equivalent to `sys.byteorder`\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_arr : array\n", " | New array object with the dtype reflecting given change to the\n", " | byte order.\n", " | \n", " | nonzero(...)\n", " | a.nonzero()\n", " | \n", " | Return the indices of the elements that are non-zero.\n", " | \n", " | Refer to `numpy.nonzero` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.nonzero : equivalent function\n", " | \n", " | partition(...)\n", " | a.partition(kth, axis=-1, kind='introselect', order=None)\n", " | \n", " | Rearranges the elements in the array in such a way that the value of the\n", " | element in kth position is in the position it would be in a sorted array.\n", " | All elements smaller than the kth element are moved before this element and\n", " | all equal or greater are moved behind it. The ordering of the elements in\n", " | the two partitions is undefined.\n", " | \n", " | .. versionadded:: 1.8.0\n", " | \n", " | Parameters\n", " | ----------\n", " | kth : int or sequence of ints\n", " | Element index to partition by. The kth element value will be in its\n", " | final sorted position and all smaller elements will be moved before it\n", " | and all equal or greater elements behind it.\n", " | The order of all elements in the partitions is undefined.\n", " | If provided with a sequence of kth it will partition all elements\n", " | indexed by kth of them into their sorted position at once.\n", " | \n", " | .. deprecated:: 1.22.0\n", " | Passing booleans as index is deprecated.\n", " | axis : int, optional\n", " | Axis along which to sort. Default is -1, which means sort along the\n", " | last axis.\n", " | kind : {'introselect'}, optional\n", " | Selection algorithm. Default is 'introselect'.\n", " | order : str or list of str, optional\n", " | When `a` is an array with fields defined, this argument specifies\n", " | which fields to compare first, second, etc. A single field can\n", " | be specified as a string, and not all fields need to be specified,\n", " | but unspecified fields will still be used, in the order in which\n", " | they come up in the dtype, to break ties.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.partition : Return a partitioned copy of an array.\n", " | argpartition : Indirect partition.\n", " | sort : Full sort.\n", " | \n", " | Notes\n", " | -----\n", " | See ``np.partition`` for notes on the different algorithms.\n", " | \n", " | Examples\n", " | --------\n", " | >>> a = np.array([3, 4, 2, 1])\n", " | >>> a.partition(3)\n", " | >>> a\n", " | array([2, 1, 3, 4])\n", " | \n", " | >>> a.partition((1, 3))\n", " | >>> a\n", " | array([1, 2, 3, 4])\n", " | \n", " | prod(...)\n", " | a.prod(axis=None, dtype=None, out=None, keepdims=False, initial=1, where=True)\n", " | \n", " | Return the product of the array elements over the given axis\n", " | \n", " | Refer to `numpy.prod` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.prod : equivalent function\n", " | \n", " | ptp(...)\n", " | a.ptp(axis=None, out=None, keepdims=False)\n", " | \n", " | Peak to peak (maximum - minimum) value along a given axis.\n", " | \n", " | Refer to `numpy.ptp` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.ptp : equivalent function\n", " | \n", " | put(...)\n", " | a.put(indices, values, mode='raise')\n", " | \n", " | Set ``a.flat[n] = values[n]`` for all `n` in indices.\n", " | \n", " | Refer to `numpy.put` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.put : equivalent function\n", " | \n", " | ravel(...)\n", " | a.ravel([order])\n", " | \n", " | Return a flattened array.\n", " | \n", " | Refer to `numpy.ravel` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.ravel : equivalent function\n", " | \n", " | ndarray.flat : a flat iterator on the array.\n", " | \n", " | repeat(...)\n", " | a.repeat(repeats, axis=None)\n", " | \n", " | Repeat elements of an array.\n", " | \n", " | Refer to `numpy.repeat` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.repeat : equivalent function\n", " | \n", " | reshape(...)\n", " | a.reshape(shape, order='C')\n", " | \n", " | Returns an array containing the same data with a new shape.\n", " | \n", " | Refer to `numpy.reshape` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.reshape : equivalent function\n", " | \n", " | Notes\n", " | -----\n", " | Unlike the free function `numpy.reshape`, this method on `ndarray` allows\n", " | the elements of the shape parameter to be passed in as separate arguments.\n", " | For example, ``a.reshape(10, 11)`` is equivalent to\n", " | ``a.reshape((10, 11))``.\n", " | \n", " | resize(...)\n", " | a.resize(new_shape, refcheck=True)\n", " | \n", " | Change shape and size of array in-place.\n", " | \n", " | Parameters\n", " | ----------\n", " | new_shape : tuple of ints, or `n` ints\n", " | Shape of resized array.\n", " | refcheck : bool, optional\n", " | If False, reference count will not be checked. Default is True.\n", " | \n", " | Returns\n", " | -------\n", " | None\n", " | \n", " | Raises\n", " | ------\n", " | ValueError\n", " | If `a` does not own its own data or references or views to it exist,\n", " | and the data memory must be changed.\n", " | PyPy only: will always raise if the data memory must be changed, since\n", " | there is no reliable way to determine if references or views to it\n", " | exist.\n", " | \n", " | SystemError\n", " | If the `order` keyword argument is specified. This behaviour is a\n", " | bug in NumPy.\n", " | \n", " | See Also\n", " | --------\n", " | resize : Return a new array with the specified shape.\n", " | \n", " | Notes\n", " | -----\n", " | This reallocates space for the data area if necessary.\n", " | \n", " | Only contiguous arrays (data elements consecutive in memory) can be\n", " | resized.\n", " | \n", " | The purpose of the reference count check is to make sure you\n", " | do not use this array as a buffer for another Python object and then\n", " | reallocate the memory. However, reference counts can increase in\n", " | other ways so if you are sure that you have not shared the memory\n", " | for this array with another Python object, then you may safely set\n", " | `refcheck` to False.\n", " | \n", " | Examples\n", " | --------\n", " | Shrinking an array: array is flattened (in the order that the data are\n", " | stored in memory), resized, and reshaped:\n", " | \n", " | >>> a = np.array([[0, 1], [2, 3]], order='C')\n", " | >>> a.resize((2, 1))\n", " | >>> a\n", " | array([[0],\n", " | [1]])\n", " | \n", " | >>> a = np.array([[0, 1], [2, 3]], order='F')\n", " | >>> a.resize((2, 1))\n", " | >>> a\n", " | array([[0],\n", " | [2]])\n", " | \n", " | Enlarging an array: as above, but missing entries are filled with zeros:\n", " | \n", " | >>> b = np.array([[0, 1], [2, 3]])\n", " | >>> b.resize(2, 3) # new_shape parameter doesn't have to be a tuple\n", " | >>> b\n", " | array([[0, 1, 2],\n", " | [3, 0, 0]])\n", " | \n", " | Referencing an array prevents resizing...\n", " | \n", " | >>> c = a\n", " | >>> a.resize((1, 1))\n", " | Traceback (most recent call last):\n", " | ...\n", " | ValueError: cannot resize an array that references or is referenced ...\n", " | \n", " | Unless `refcheck` is False:\n", " | \n", " | >>> a.resize((1, 1), refcheck=False)\n", " | >>> a\n", " | array([[0]])\n", " | >>> c\n", " | array([[0]])\n", " | \n", " | round(...)\n", " | a.round(decimals=0, out=None)\n", " | \n", " | Return `a` with each element rounded to the given number of decimals.\n", " | \n", " | Refer to `numpy.around` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.around : equivalent function\n", " | \n", " | searchsorted(...)\n", " | a.searchsorted(v, side='left', sorter=None)\n", " | \n", " | Find indices where elements of v should be inserted in a to maintain order.\n", " | \n", " | For full documentation, see `numpy.searchsorted`\n", " | \n", " | See Also\n", " | --------\n", " | numpy.searchsorted : equivalent function\n", " | \n", " | setfield(...)\n", " | a.setfield(val, dtype, offset=0)\n", " | \n", " | Put a value into a specified place in a field defined by a data-type.\n", " | \n", " | Place `val` into `a`'s field defined by `dtype` and beginning `offset`\n", " | bytes into the field.\n", " | \n", " | Parameters\n", " | ----------\n", " | val : object\n", " | Value to be placed in field.\n", " | dtype : dtype object\n", " | Data-type of the field in which to place `val`.\n", " | offset : int, optional\n", " | The number of bytes into the field at which to place `val`.\n", " | \n", " | Returns\n", " | -------\n", " | None\n", " | \n", " | See Also\n", " | --------\n", " | getfield\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.eye(3)\n", " | >>> x.getfield(np.float64)\n", " | array([[1., 0., 0.],\n", " | [0., 1., 0.],\n", " | [0., 0., 1.]])\n", " | >>> x.setfield(3, np.int32)\n", " | >>> x.getfield(np.int32)\n", " | array([[3, 3, 3],\n", " | [3, 3, 3],\n", " | [3, 3, 3]], dtype=int32)\n", " | >>> x\n", " | array([[1.0e+000, 1.5e-323, 1.5e-323],\n", " | [1.5e-323, 1.0e+000, 1.5e-323],\n", " | [1.5e-323, 1.5e-323, 1.0e+000]])\n", " | >>> x.setfield(np.eye(3), np.int32)\n", " | >>> x\n", " | array([[1., 0., 0.],\n", " | [0., 1., 0.],\n", " | [0., 0., 1.]])\n", " | \n", " | setflags(...)\n", " | a.setflags(write=None, align=None, uic=None)\n", " | \n", " | Set array flags WRITEABLE, ALIGNED, WRITEBACKIFCOPY,\n", " | respectively.\n", " | \n", " | These Boolean-valued flags affect how numpy interprets the memory\n", " | area used by `a` (see Notes below). The ALIGNED flag can only\n", " | be set to True if the data is actually aligned according to the type.\n", " | The WRITEBACKIFCOPY and flag can never be set\n", " | to True. The flag WRITEABLE can only be set to True if the array owns its\n", " | own memory, or the ultimate owner of the memory exposes a writeable buffer\n", " | interface, or is a string. (The exception for string is made so that\n", " | unpickling can be done without copying memory.)\n", " | \n", " | Parameters\n", " | ----------\n", " | write : bool, optional\n", " | Describes whether or not `a` can be written to.\n", " | align : bool, optional\n", " | Describes whether or not `a` is aligned properly for its type.\n", " | uic : bool, optional\n", " | Describes whether or not `a` is a copy of another \"base\" array.\n", " | \n", " | Notes\n", " | -----\n", " | Array flags provide information about how the memory area used\n", " | for the array is to be interpreted. There are 7 Boolean flags\n", " | in use, only four of which can be changed by the user:\n", " | WRITEBACKIFCOPY, WRITEABLE, and ALIGNED.\n", " | \n", " | WRITEABLE (W) the data area can be written to;\n", " | \n", " | ALIGNED (A) the data and strides are aligned appropriately for the hardware\n", " | (as determined by the compiler);\n", " | \n", " | WRITEBACKIFCOPY (X) this array is a copy of some other array (referenced\n", " | by .base). When the C-API function PyArray_ResolveWritebackIfCopy is\n", " | called, the base array will be updated with the contents of this array.\n", " | \n", " | All flags can be accessed using the single (upper case) letter as well\n", " | as the full name.\n", " | \n", " | Examples\n", " | --------\n", " | >>> y = np.array([[3, 1, 7],\n", " | ... [2, 0, 0],\n", " | ... [8, 5, 9]])\n", " | >>> y\n", " | array([[3, 1, 7],\n", " | [2, 0, 0],\n", " | [8, 5, 9]])\n", " | >>> y.flags\n", " | C_CONTIGUOUS : True\n", " | F_CONTIGUOUS : False\n", " | OWNDATA : True\n", " | WRITEABLE : True\n", " | ALIGNED : True\n", " | WRITEBACKIFCOPY : False\n", " | >>> y.setflags(write=0, align=0)\n", " | >>> y.flags\n", " | C_CONTIGUOUS : True\n", " | F_CONTIGUOUS : False\n", " | OWNDATA : True\n", " | WRITEABLE : False\n", " | ALIGNED : False\n", " | WRITEBACKIFCOPY : False\n", " | >>> y.setflags(uic=1)\n", " | Traceback (most recent call last):\n", " | File \"<stdin>\", line 1, in <module>\n", " | ValueError: cannot set WRITEBACKIFCOPY flag to True\n", " | \n", " | sort(...)\n", " | a.sort(axis=-1, kind=None, order=None)\n", " | \n", " | Sort an array in-place. Refer to `numpy.sort` for full documentation.\n", " | \n", " | Parameters\n", " | ----------\n", " | axis : int, optional\n", " | Axis along which to sort. Default is -1, which means sort along the\n", " | last axis.\n", " | kind : {'quicksort', 'mergesort', 'heapsort', 'stable'}, optional\n", " | Sorting algorithm. The default is 'quicksort'. Note that both 'stable'\n", " | and 'mergesort' use timsort under the covers and, in general, the\n", " | actual implementation will vary with datatype. The 'mergesort' option\n", " | is retained for backwards compatibility.\n", " | \n", " | .. versionchanged:: 1.15.0\n", " | The 'stable' option was added.\n", " | \n", " | order : str or list of str, optional\n", " | When `a` is an array with fields defined, this argument specifies\n", " | which fields to compare first, second, etc. A single field can\n", " | be specified as a string, and not all fields need be specified,\n", " | but unspecified fields will still be used, in the order in which\n", " | they come up in the dtype, to break ties.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.sort : Return a sorted copy of an array.\n", " | numpy.argsort : Indirect sort.\n", " | numpy.lexsort : Indirect stable sort on multiple keys.\n", " | numpy.searchsorted : Find elements in sorted array.\n", " | numpy.partition: Partial sort.\n", " | \n", " | Notes\n", " | -----\n", " | See `numpy.sort` for notes on the different sorting algorithms.\n", " | \n", " | Examples\n", " | --------\n", " | >>> a = np.array([[1,4], [3,1]])\n", " | >>> a.sort(axis=1)\n", " | >>> a\n", " | array([[1, 4],\n", " | [1, 3]])\n", " | >>> a.sort(axis=0)\n", " | >>> a\n", " | array([[1, 3],\n", " | [1, 4]])\n", " | \n", " | Use the `order` keyword to specify a field to use when sorting a\n", " | structured array:\n", " | \n", " | >>> a = np.array([('a', 2), ('c', 1)], dtype=[('x', 'S1'), ('y', int)])\n", " | >>> a.sort(order='y')\n", " | >>> a\n", " | array([(b'c', 1), (b'a', 2)],\n", " | dtype=[('x', 'S1'), ('y', '<i8')])\n", " | \n", " | squeeze(...)\n", " | a.squeeze(axis=None)\n", " | \n", " | Remove axes of length one from `a`.\n", " | \n", " | Refer to `numpy.squeeze` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.squeeze : equivalent function\n", " | \n", " | std(...)\n", " | a.std(axis=None, dtype=None, out=None, ddof=0, keepdims=False, *, where=True)\n", " | \n", " | Returns the standard deviation of the array elements along given axis.\n", " | \n", " | Refer to `numpy.std` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.std : equivalent function\n", " | \n", " | sum(...)\n", " | a.sum(axis=None, dtype=None, out=None, keepdims=False, initial=0, where=True)\n", " | \n", " | Return the sum of the array elements over the given axis.\n", " | \n", " | Refer to `numpy.sum` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.sum : equivalent function\n", " | \n", " | swapaxes(...)\n", " | a.swapaxes(axis1, axis2)\n", " | \n", " | Return a view of the array with `axis1` and `axis2` interchanged.\n", " | \n", " | Refer to `numpy.swapaxes` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.swapaxes : equivalent function\n", " | \n", " | take(...)\n", " | a.take(indices, axis=None, out=None, mode='raise')\n", " | \n", " | Return an array formed from the elements of `a` at the given indices.\n", " | \n", " | Refer to `numpy.take` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.take : equivalent function\n", " | \n", " | tobytes(...)\n", " | a.tobytes(order='C')\n", " | \n", " | Construct Python bytes containing the raw data bytes in the array.\n", " | \n", " | Constructs Python bytes showing a copy of the raw contents of\n", " | data memory. The bytes object is produced in C-order by default.\n", " | This behavior is controlled by the ``order`` parameter.\n", " | \n", " | .. versionadded:: 1.9.0\n", " | \n", " | Parameters\n", " | ----------\n", " | order : {'C', 'F', 'A'}, optional\n", " | Controls the memory layout of the bytes object. 'C' means C-order,\n", " | 'F' means F-order, 'A' (short for *Any*) means 'F' if `a` is\n", " | Fortran contiguous, 'C' otherwise. Default is 'C'.\n", " | \n", " | Returns\n", " | -------\n", " | s : bytes\n", " | Python bytes exhibiting a copy of `a`'s raw data.\n", " | \n", " | See also\n", " | --------\n", " | frombuffer\n", " | Inverse of this operation, construct a 1-dimensional array from Python\n", " | bytes.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([[0, 1], [2, 3]], dtype='<u2')\n", " | >>> x.tobytes()\n", " | b'\\x00\\x00\\x01\\x00\\x02\\x00\\x03\\x00'\n", " | >>> x.tobytes('C') == x.tobytes()\n", " | True\n", " | >>> x.tobytes('F')\n", " | b'\\x00\\x00\\x02\\x00\\x01\\x00\\x03\\x00'\n", " | \n", " | tofile(...)\n", " | a.tofile(fid, sep=\"\", format=\"%s\")\n", " | \n", " | Write array to a file as text or binary (default).\n", " | \n", " | Data is always written in 'C' order, independent of the order of `a`.\n", " | The data produced by this method can be recovered using the function\n", " | fromfile().\n", " | \n", " | Parameters\n", " | ----------\n", " | fid : file or str or Path\n", " | An open file object, or a string containing a filename.\n", " | \n", " | .. versionchanged:: 1.17.0\n", " | `pathlib.Path` objects are now accepted.\n", " | \n", " | sep : str\n", " | Separator between array items for text output.\n", " | If \"\" (empty), a binary file is written, equivalent to\n", " | ``file.write(a.tobytes())``.\n", " | format : str\n", " | Format string for text file output.\n", " | Each entry in the array is formatted to text by first converting\n", " | it to the closest Python type, and then using \"format\" % item.\n", " | \n", " | Notes\n", " | -----\n", " | This is a convenience function for quick storage of array data.\n", " | Information on endianness and precision is lost, so this method is not a\n", " | good choice for files intended to archive data or transport data between\n", " | machines with different endianness. Some of these problems can be overcome\n", " | by outputting the data as text files, at the expense of speed and file\n", " | size.\n", " | \n", " | When fid is a file object, array contents are directly written to the\n", " | file, bypassing the file object's ``write`` method. As a result, tofile\n", " | cannot be used with files objects supporting compression (e.g., GzipFile)\n", " | or file-like objects that do not support ``fileno()`` (e.g., BytesIO).\n", " | \n", " | tolist(...)\n", " | a.tolist()\n", " | \n", " | Return the array as an ``a.ndim``-levels deep nested list of Python scalars.\n", " | \n", " | Return a copy of the array data as a (nested) Python list.\n", " | Data items are converted to the nearest compatible builtin Python type, via\n", " | the `~numpy.ndarray.item` function.\n", " | \n", " | If ``a.ndim`` is 0, then since the depth of the nested list is 0, it will\n", " | not be a list at all, but a simple Python scalar.\n", " | \n", " | Parameters\n", " | ----------\n", " | none\n", " | \n", " | Returns\n", " | -------\n", " | y : object, or list of object, or list of list of object, or ...\n", " | The possibly nested list of array elements.\n", " | \n", " | Notes\n", " | -----\n", " | The array may be recreated via ``a = np.array(a.tolist())``, although this\n", " | may sometimes lose precision.\n", " | \n", " | Examples\n", " | --------\n", " | For a 1D array, ``a.tolist()`` is almost the same as ``list(a)``,\n", " | except that ``tolist`` changes numpy scalars to Python scalars:\n", " | \n", " | >>> a = np.uint32([1, 2])\n", " | >>> a_list = list(a)\n", " | >>> a_list\n", " | [1, 2]\n", " | >>> type(a_list[0])\n", " | <class 'numpy.uint32'>\n", " | >>> a_tolist = a.tolist()\n", " | >>> a_tolist\n", " | [1, 2]\n", " | >>> type(a_tolist[0])\n", " | <class 'int'>\n", " | \n", " | Additionally, for a 2D array, ``tolist`` applies recursively:\n", " | \n", " | >>> a = np.array([[1, 2], [3, 4]])\n", " | >>> list(a)\n", " | [array([1, 2]), array([3, 4])]\n", " | >>> a.tolist()\n", " | [[1, 2], [3, 4]]\n", " | \n", " | The base case for this recursion is a 0D array:\n", " | \n", " | >>> a = np.array(1)\n", " | >>> list(a)\n", " | Traceback (most recent call last):\n", " | ...\n", " | TypeError: iteration over a 0-d array\n", " | >>> a.tolist()\n", " | 1\n", " | \n", " | tostring(...)\n", " | a.tostring(order='C')\n", " | \n", " | A compatibility alias for `tobytes`, with exactly the same behavior.\n", " | \n", " | Despite its name, it returns `bytes` not `str`\\ s.\n", " | \n", " | .. deprecated:: 1.19.0\n", " | \n", " | trace(...)\n", " | a.trace(offset=0, axis1=0, axis2=1, dtype=None, out=None)\n", " | \n", " | Return the sum along diagonals of the array.\n", " | \n", " | Refer to `numpy.trace` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.trace : equivalent function\n", " | \n", " | transpose(...)\n", " | a.transpose(*axes)\n", " | \n", " | Returns a view of the array with axes transposed.\n", " | \n", " | Refer to `numpy.transpose` for full documentation.\n", " | \n", " | Parameters\n", " | ----------\n", " | axes : None, tuple of ints, or `n` ints\n", " | \n", " | * None or no argument: reverses the order of the axes.\n", " | \n", " | * tuple of ints: `i` in the `j`-th place in the tuple means that the\n", " | array's `i`-th axis becomes the transposed array's `j`-th axis.\n", " | \n", " | * `n` ints: same as an n-tuple of the same ints (this form is\n", " | intended simply as a \"convenience\" alternative to the tuple form).\n", " | \n", " | Returns\n", " | -------\n", " | p : ndarray\n", " | View of the array with its axes suitably permuted.\n", " | \n", " | See Also\n", " | --------\n", " | transpose : Equivalent function.\n", " | ndarray.T : Array property returning the array transposed.\n", " | ndarray.reshape : Give a new shape to an array without changing its data.\n", " | \n", " | Examples\n", " | --------\n", " | >>> a = np.array([[1, 2], [3, 4]])\n", " | >>> a\n", " | array([[1, 2],\n", " | [3, 4]])\n", " | >>> a.transpose()\n", " | array([[1, 3],\n", " | [2, 4]])\n", " | >>> a.transpose((1, 0))\n", " | array([[1, 3],\n", " | [2, 4]])\n", " | >>> a.transpose(1, 0)\n", " | array([[1, 3],\n", " | [2, 4]])\n", " | \n", " | >>> a = np.array([1, 2, 3, 4])\n", " | >>> a\n", " | array([1, 2, 3, 4])\n", " | >>> a.transpose()\n", " | array([1, 2, 3, 4])\n", " | \n", " | var(...)\n", " | a.var(axis=None, dtype=None, out=None, ddof=0, keepdims=False, *, where=True)\n", " | \n", " | Returns the variance of the array elements, along given axis.\n", " | \n", " | Refer to `numpy.var` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.var : equivalent function\n", " | \n", " | view(...)\n", " | a.view([dtype][, type])\n", " | \n", " | New view of array with the same data.\n", " | \n", " | .. note::\n", " | Passing None for ``dtype`` is different from omitting the parameter,\n", " | since the former invokes ``dtype(None)`` which is an alias for\n", " | ``dtype('float_')``.\n", " | \n", " | Parameters\n", " | ----------\n", " | dtype : data-type or ndarray sub-class, optional\n", " | Data-type descriptor of the returned view, e.g., float32 or int16.\n", " | Omitting it results in the view having the same data-type as `a`.\n", " | This argument can also be specified as an ndarray sub-class, which\n", " | then specifies the type of the returned object (this is equivalent to\n", " | setting the ``type`` parameter).\n", " | type : Python type, optional\n", " | Type of the returned view, e.g., ndarray or matrix. Again, omission\n", " | of the parameter results in type preservation.\n", " | \n", " | Notes\n", " | -----\n", " | ``a.view()`` is used two different ways:\n", " | \n", " | ``a.view(some_dtype)`` or ``a.view(dtype=some_dtype)`` constructs a view\n", " | of the array's memory with a different data-type. This can cause a\n", " | reinterpretation of the bytes of memory.\n", " | \n", " | ``a.view(ndarray_subclass)`` or ``a.view(type=ndarray_subclass)`` just\n", " | returns an instance of `ndarray_subclass` that looks at the same array\n", " | (same shape, dtype, etc.) This does not cause a reinterpretation of the\n", " | memory.\n", " | \n", " | For ``a.view(some_dtype)``, if ``some_dtype`` has a different number of\n", " | bytes per entry than the previous dtype (for example, converting a regular\n", " | array to a structured array), then the last axis of ``a`` must be\n", " | contiguous. This axis will be resized in the result.\n", " | \n", " | .. versionchanged:: 1.23.0\n", " | Only the last axis needs to be contiguous. Previously, the entire array\n", " | had to be C-contiguous.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([(1, 2)], dtype=[('a', np.int8), ('b', np.int8)])\n", " | \n", " | Viewing array data using a different type and dtype:\n", " | \n", " | >>> y = x.view(dtype=np.int16, type=np.matrix)\n", " | >>> y\n", " | matrix([[513]], dtype=int16)\n", " | >>> print(type(y))\n", " | <class 'numpy.matrix'>\n", " | \n", " | Creating a view on a structured array so it can be used in calculations\n", " | \n", " | >>> x = np.array([(1, 2),(3,4)], dtype=[('a', np.int8), ('b', np.int8)])\n", " | >>> xv = x.view(dtype=np.int8).reshape(-1,2)\n", " | >>> xv\n", " | array([[1, 2],\n", " | [3, 4]], dtype=int8)\n", " | >>> xv.mean(0)\n", " | array([2., 3.])\n", " | \n", " | Making changes to the view changes the underlying array\n", " | \n", " | >>> xv[0,1] = 20\n", " | >>> x\n", " | array([(1, 20), (3, 4)], dtype=[('a', 'i1'), ('b', 'i1')])\n", " | \n", " | Using a view to convert an array to a recarray:\n", " | \n", " | >>> z = x.view(np.recarray)\n", " | >>> z.a\n", " | array([1, 3], dtype=int8)\n", " | \n", " | Views share data:\n", " | \n", " | >>> x[0] = (9, 10)\n", " | >>> z[0]\n", " | (9, 10)\n", " | \n", " | Views that change the dtype size (bytes per entry) should normally be\n", " | avoided on arrays defined by slices, transposes, fortran-ordering, etc.:\n", " | \n", " | >>> x = np.array([[1, 2, 3], [4, 5, 6]], dtype=np.int16)\n", " | >>> y = x[:, ::2]\n", " | >>> y\n", " | array([[1, 3],\n", " | [4, 6]], dtype=int16)\n", " | >>> y.view(dtype=[('width', np.int16), ('length', np.int16)])\n", " | Traceback (most recent call last):\n", " | ...\n", " | ValueError: To change to a dtype of a different size, the last axis must be contiguous\n", " | >>> z = y.copy()\n", " | >>> z.view(dtype=[('width', np.int16), ('length', np.int16)])\n", " | array([[(1, 3)],\n", " | [(4, 6)]], dtype=[('width', '<i2'), ('length', '<i2')])\n", " | \n", " | However, views that change dtype are totally fine for arrays with a\n", " | contiguous last axis, even if the rest of the axes are not C-contiguous:\n", " | \n", " | >>> x = np.arange(2 * 3 * 4, dtype=np.int8).reshape(2, 3, 4)\n", " | >>> x.transpose(1, 0, 2).view(np.int16)\n", " | array([[[ 256, 770],\n", " | [3340, 3854]],\n", " | <BLANKLINE>\n", " | [[1284, 1798],\n", " | [4368, 4882]],\n", " | <BLANKLINE>\n", " | [[2312, 2826],\n", " | [5396, 5910]]], dtype=int16)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods inherited from ndarray:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | a.__class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.ndarray` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.ndarray` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.ndarray[Any, np.dtype[Any]]\n", " | numpy.ndarray[typing.Any, numpy.dtype[typing.Any]]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | numpy.typing.NDArray : An ndarray alias :term:`generic <generic type>`\n", " | w.r.t. its `dtype.type <numpy.dtype.type>`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from ndarray:\n", " | \n", " | T\n", " | View of the transposed array.\n", " | \n", " | Same as ``self.transpose()``.\n", " | \n", " | Examples\n", " | --------\n", " | >>> a = np.array([[1, 2], [3, 4]])\n", " | >>> a\n", " | array([[1, 2],\n", " | [3, 4]])\n", " | >>> a.T\n", " | array([[1, 3],\n", " | [2, 4]])\n", " | \n", " | >>> a = np.array([1, 2, 3, 4])\n", " | >>> a\n", " | array([1, 2, 3, 4])\n", " | >>> a.T\n", " | array([1, 2, 3, 4])\n", " | \n", " | See Also\n", " | --------\n", " | transpose\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side.\n", " | \n", " | __array_struct__\n", " | Array protocol: C-struct side.\n", " | \n", " | base\n", " | Base object if memory is from some other object.\n", " | \n", " | Examples\n", " | --------\n", " | The base of an array that owns its memory is None:\n", " | \n", " | >>> x = np.array([1,2,3,4])\n", " | >>> x.base is None\n", " | True\n", " | \n", " | Slicing creates a view, whose memory is shared with x:\n", " | \n", " | >>> y = x[2:]\n", " | >>> y.base is x\n", " | True\n", " | \n", " | ctypes\n", " | An object to simplify the interaction of the array with the ctypes\n", " | module.\n", " | \n", " | This attribute creates an object that makes it easier to use arrays\n", " | when calling shared libraries with the ctypes module. The returned\n", " | object has, among others, data, shape, and strides attributes (see\n", " | Notes below) which themselves return ctypes objects that can be used\n", " | as arguments to a shared library.\n", " | \n", " | Parameters\n", " | ----------\n", " | None\n", " | \n", " | Returns\n", " | -------\n", " | c : Python object\n", " | Possessing attributes data, shape, strides, etc.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.ctypeslib\n", " | \n", " | Notes\n", " | -----\n", " | Below are the public attributes of this object which were documented\n", " | in \"Guide to NumPy\" (we have omitted undocumented public attributes,\n", " | as well as documented private attributes):\n", " | \n", " | .. autoattribute:: numpy.core._internal._ctypes.data\n", " | :noindex:\n", " | \n", " | .. autoattribute:: numpy.core._internal._ctypes.shape\n", " | :noindex:\n", " | \n", " | .. autoattribute:: numpy.core._internal._ctypes.strides\n", " | :noindex:\n", " | \n", " | .. automethod:: numpy.core._internal._ctypes.data_as\n", " | :noindex:\n", " | \n", " | .. automethod:: numpy.core._internal._ctypes.shape_as\n", " | :noindex:\n", " | \n", " | .. automethod:: numpy.core._internal._ctypes.strides_as\n", " | :noindex:\n", " | \n", " | If the ctypes module is not available, then the ctypes attribute\n", " | of array objects still returns something useful, but ctypes objects\n", " | are not returned and errors may be raised instead. In particular,\n", " | the object will still have the ``as_parameter`` attribute which will\n", " | return an integer equal to the data attribute.\n", " | \n", " | Examples\n", " | --------\n", " | >>> import ctypes\n", " | >>> x = np.array([[0, 1], [2, 3]], dtype=np.int32)\n", " | >>> x\n", " | array([[0, 1],\n", " | [2, 3]], dtype=int32)\n", " | >>> x.ctypes.data\n", " | 31962608 # may vary\n", " | >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32))\n", " | <__main__.LP_c_uint object at 0x7ff2fc1fc200> # may vary\n", " | >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)).contents\n", " | c_uint(0)\n", " | >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint64)).contents\n", " | c_ulong(4294967296)\n", " | >>> x.ctypes.shape\n", " | <numpy.core._internal.c_long_Array_2 object at 0x7ff2fc1fce60> # may vary\n", " | >>> x.ctypes.strides\n", " | <numpy.core._internal.c_long_Array_2 object at 0x7ff2fc1ff320> # may vary\n", " | \n", " | data\n", " | Python buffer object pointing to the start of the array's data.\n", " | \n", " | dtype\n", " | Data-type of the array's elements.\n", " | \n", " | .. warning::\n", " | \n", " | Setting ``arr.dtype`` is discouraged and may be deprecated in the\n", " | future. Setting will replace the ``dtype`` without modifying the\n", " | memory (see also `ndarray.view` and `ndarray.astype`).\n", " | \n", " | Parameters\n", " | ----------\n", " | None\n", " | \n", " | Returns\n", " | -------\n", " | d : numpy dtype object\n", " | \n", " | See Also\n", " | --------\n", " | ndarray.astype : Cast the values contained in the array to a new data-type.\n", " | ndarray.view : Create a view of the same data but a different data-type.\n", " | numpy.dtype\n", " | \n", " | Examples\n", " | --------\n", " | >>> x\n", " | array([[0, 1],\n", " | [2, 3]])\n", " | >>> x.dtype\n", " | dtype('int32')\n", " | >>> type(x.dtype)\n", " | <type 'numpy.dtype'>\n", " | \n", " | flags\n", " | Information about the memory layout of the array.\n", " | \n", " | Attributes\n", " | ----------\n", " | C_CONTIGUOUS (C)\n", " | The data is in a single, C-style contiguous segment.\n", " | F_CONTIGUOUS (F)\n", " | The data is in a single, Fortran-style contiguous segment.\n", " | OWNDATA (O)\n", " | The array owns the memory it uses or borrows it from another object.\n", " | WRITEABLE (W)\n", " | The data area can be written to. Setting this to False locks\n", " | the data, making it read-only. A view (slice, etc.) inherits WRITEABLE\n", " | from its base array at creation time, but a view of a writeable\n", " | array may be subsequently locked while the base array remains writeable.\n", " | (The opposite is not true, in that a view of a locked array may not\n", " | be made writeable. However, currently, locking a base object does not\n", " | lock any views that already reference it, so under that circumstance it\n", " | is possible to alter the contents of a locked array via a previously\n", " | created writeable view onto it.) Attempting to change a non-writeable\n", " | array raises a RuntimeError exception.\n", " | ALIGNED (A)\n", " | The data and all elements are aligned appropriately for the hardware.\n", " | WRITEBACKIFCOPY (X)\n", " | This array is a copy of some other array. The C-API function\n", " | PyArray_ResolveWritebackIfCopy must be called before deallocating\n", " | to the base array will be updated with the contents of this array.\n", " | FNC\n", " | F_CONTIGUOUS and not C_CONTIGUOUS.\n", " | FORC\n", " | F_CONTIGUOUS or C_CONTIGUOUS (one-segment test).\n", " | BEHAVED (B)\n", " | ALIGNED and WRITEABLE.\n", " | CARRAY (CA)\n", " | BEHAVED and C_CONTIGUOUS.\n", " | FARRAY (FA)\n", " | BEHAVED and F_CONTIGUOUS and not C_CONTIGUOUS.\n", " | \n", " | Notes\n", " | -----\n", " | The `flags` object can be accessed dictionary-like (as in ``a.flags['WRITEABLE']``),\n", " | or by using lowercased attribute names (as in ``a.flags.writeable``). Short flag\n", " | names are only supported in dictionary access.\n", " | \n", " | Only the WRITEBACKIFCOPY, WRITEABLE, and ALIGNED flags can be\n", " | changed by the user, via direct assignment to the attribute or dictionary\n", " | entry, or by calling `ndarray.setflags`.\n", " | \n", " | The array flags cannot be set arbitrarily:\n", " | \n", " | - WRITEBACKIFCOPY can only be set ``False``.\n", " | - ALIGNED can only be set ``True`` if the data is truly aligned.\n", " | - WRITEABLE can only be set ``True`` if the array owns its own memory\n", " | or the ultimate owner of the memory exposes a writeable buffer\n", " | interface or is a string.\n", " | \n", " | Arrays can be both C-style and Fortran-style contiguous simultaneously.\n", " | This is clear for 1-dimensional arrays, but can also be true for higher\n", " | dimensional arrays.\n", " | \n", " | Even for contiguous arrays a stride for a given dimension\n", " | ``arr.strides[dim]`` may be *arbitrary* if ``arr.shape[dim] == 1``\n", " | or the array has no elements.\n", " | It does *not* generally hold that ``self.strides[-1] == self.itemsize``\n", " | for C-style contiguous arrays or ``self.strides[0] == self.itemsize`` for\n", " | Fortran-style contiguous arrays is true.\n", " | \n", " | flat\n", " | A 1-D iterator over the array.\n", " | \n", " | This is a `numpy.flatiter` instance, which acts similarly to, but is not\n", " | a subclass of, Python's built-in iterator object.\n", " | \n", " | See Also\n", " | --------\n", " | flatten : Return a copy of the array collapsed into one dimension.\n", " | \n", " | flatiter\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.arange(1, 7).reshape(2, 3)\n", " | >>> x\n", " | array([[1, 2, 3],\n", " | [4, 5, 6]])\n", " | >>> x.flat[3]\n", " | 4\n", " | >>> x.T\n", " | array([[1, 4],\n", " | [2, 5],\n", " | [3, 6]])\n", " | >>> x.T.flat[3]\n", " | 5\n", " | >>> type(x.flat)\n", " | <class 'numpy.flatiter'>\n", " | \n", " | An assignment example:\n", " | \n", " | >>> x.flat = 3; x\n", " | array([[3, 3, 3],\n", " | [3, 3, 3]])\n", " | >>> x.flat[[1,4]] = 1; x\n", " | array([[3, 1, 3],\n", " | [3, 1, 3]])\n", " | \n", " | imag\n", " | The imaginary part of the array.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.sqrt([1+0j, 0+1j])\n", " | >>> x.imag\n", " | array([ 0. , 0.70710678])\n", " | >>> x.imag.dtype\n", " | dtype('float64')\n", " | \n", " | itemsize\n", " | Length of one array element in bytes.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([1,2,3], dtype=np.float64)\n", " | >>> x.itemsize\n", " | 8\n", " | >>> x = np.array([1,2,3], dtype=np.complex128)\n", " | >>> x.itemsize\n", " | 16\n", " | \n", " | nbytes\n", " | Total bytes consumed by the elements of the array.\n", " | \n", " | Notes\n", " | -----\n", " | Does not include memory consumed by non-element attributes of the\n", " | array object.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.zeros((3,5,2), dtype=np.complex128)\n", " | >>> x.nbytes\n", " | 480\n", " | >>> np.prod(x.shape) * x.itemsize\n", " | 480\n", " | \n", " | ndim\n", " | Number of array dimensions.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([1, 2, 3])\n", " | >>> x.ndim\n", " | 1\n", " | >>> y = np.zeros((2, 3, 4))\n", " | >>> y.ndim\n", " | 3\n", " | \n", " | real\n", " | The real part of the array.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.sqrt([1+0j, 0+1j])\n", " | >>> x.real\n", " | array([ 1. , 0.70710678])\n", " | >>> x.real.dtype\n", " | dtype('float64')\n", " | \n", " | See Also\n", " | --------\n", " | numpy.real : equivalent function\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | The shape property is usually used to get the current shape of an array,\n", " | but may also be used to reshape the array in-place by assigning a tuple of\n", " | array dimensions to it. As with `numpy.reshape`, one of the new shape\n", " | dimensions can be -1, in which case its value is inferred from the size of\n", " | the array and the remaining dimensions. Reshaping an array in-place will\n", " | fail if a copy is required.\n", " | \n", " | .. warning::\n", " | \n", " | Setting ``arr.shape`` is discouraged and may be deprecated in the\n", " | future. Using `ndarray.reshape` is the preferred approach.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([1, 2, 3, 4])\n", " | >>> x.shape\n", " | (4,)\n", " | >>> y = np.zeros((2, 3, 4))\n", " | >>> y.shape\n", " | (2, 3, 4)\n", " | >>> y.shape = (3, 8)\n", " | >>> y\n", " | array([[ 0., 0., 0., 0., 0., 0., 0., 0.],\n", " | [ 0., 0., 0., 0., 0., 0., 0., 0.],\n", " | [ 0., 0., 0., 0., 0., 0., 0., 0.]])\n", " | >>> y.shape = (3, 6)\n", " | Traceback (most recent call last):\n", " | File \"<stdin>\", line 1, in <module>\n", " | ValueError: total size of new array must be unchanged\n", " | >>> np.zeros((4,2))[::2].shape = (-1,)\n", " | Traceback (most recent call last):\n", " | File \"<stdin>\", line 1, in <module>\n", " | AttributeError: Incompatible shape for in-place modification. Use\n", " | `.reshape()` to make a copy with the desired shape.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.shape : Equivalent getter function.\n", " | numpy.reshape : Function similar to setting ``shape``.\n", " | ndarray.reshape : Method similar to setting ``shape``.\n", " | \n", " | size\n", " | Number of elements in the array.\n", " | \n", " | Equal to ``np.prod(a.shape)``, i.e., the product of the array's\n", " | dimensions.\n", " | \n", " | Notes\n", " | -----\n", " | `a.size` returns a standard arbitrary precision Python integer. This\n", " | may not be the case with other methods of obtaining the same value\n", " | (like the suggested ``np.prod(a.shape)``, which returns an instance\n", " | of ``np.int_``), and may be relevant if the value is used further in\n", " | calculations that may overflow a fixed size integer type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.zeros((3, 5, 2), dtype=np.complex128)\n", " | >>> x.size\n", " | 30\n", " | >>> np.prod(x.shape)\n", " | 30\n", " | \n", " | strides\n", " | Tuple of bytes to step in each dimension when traversing an array.\n", " | \n", " | The byte offset of element ``(i[0], i[1], ..., i[n])`` in an array `a`\n", " | is::\n", " | \n", " | offset = sum(np.array(i) * a.strides)\n", " | \n", " | A more detailed explanation of strides can be found in the\n", " | \"ndarray.rst\" file in the NumPy reference guide.\n", " | \n", " | .. warning::\n", " | \n", " | Setting ``arr.strides`` is discouraged and may be deprecated in the\n", " | future. `numpy.lib.stride_tricks.as_strided` should be preferred\n", " | to create a new view of the same data in a safer way.\n", " | \n", " | Notes\n", " | -----\n", " | Imagine an array of 32-bit integers (each 4 bytes)::\n", " | \n", " | x = np.array([[0, 1, 2, 3, 4],\n", " | [5, 6, 7, 8, 9]], dtype=np.int32)\n", " | \n", " | This array is stored in memory as 40 bytes, one after the other\n", " | (known as a contiguous block of memory). The strides of an array tell\n", " | us how many bytes we have to skip in memory to move to the next position\n", " | along a certain axis. For example, we have to skip 4 bytes (1 value) to\n", " | move to the next column, but 20 bytes (5 values) to get to the same\n", " | position in the next row. As such, the strides for the array `x` will be\n", " | ``(20, 4)``.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.lib.stride_tricks.as_strided\n", " | \n", " | Examples\n", " | --------\n", " | >>> y = np.reshape(np.arange(2*3*4), (2,3,4))\n", " | >>> y\n", " | array([[[ 0, 1, 2, 3],\n", " | [ 4, 5, 6, 7],\n", " | [ 8, 9, 10, 11]],\n", " | [[12, 13, 14, 15],\n", " | [16, 17, 18, 19],\n", " | [20, 21, 22, 23]]])\n", " | >>> y.strides\n", " | (48, 16, 4)\n", " | >>> y[1,1,1]\n", " | 17\n", " | >>> offset=sum(y.strides * np.array((1,1,1)))\n", " | >>> offset/y.itemsize\n", " | 17\n", " | \n", " | >>> x = np.reshape(np.arange(5*6*7*8), (5,6,7,8)).transpose(2,3,1,0)\n", " | >>> x.strides\n", " | (32, 4, 224, 1344)\n", " | >>> i = np.array([3,5,2,2])\n", " | >>> offset = sum(i * x.strides)\n", " | >>> x[3,5,2,2]\n", " | 813\n", " | >>> offset / x.itemsize\n", " | 813\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data and other attributes inherited from ndarray:\n", " | \n", " | __hash__ = None\n", " \n", " class ndarray(builtins.object)\n", " | ndarray(shape, dtype=float, buffer=None, offset=0,\n", " | strides=None, order=None)\n", " | \n", " | An array object represents a multidimensional, homogeneous array\n", " | of fixed-size items. An associated data-type object describes the\n", " | format of each element in the array (its byte-order, how many bytes it\n", " | occupies in memory, whether it is an integer, a floating point number,\n", " | or something else, etc.)\n", " | \n", " | Arrays should be constructed using `array`, `zeros` or `empty` (refer\n", " | to the See Also section below). The parameters given here refer to\n", " | a low-level method (`ndarray(...)`) for instantiating an array.\n", " | \n", " | For more information, refer to the `numpy` module and examine the\n", " | methods and attributes of an array.\n", " | \n", " | Parameters\n", " | ----------\n", " | (for the __new__ method; see Notes below)\n", " | \n", " | shape : tuple of ints\n", " | Shape of created array.\n", " | dtype : data-type, optional\n", " | Any object that can be interpreted as a numpy data type.\n", " | buffer : object exposing buffer interface, optional\n", " | Used to fill the array with data.\n", " | offset : int, optional\n", " | Offset of array data in buffer.\n", " | strides : tuple of ints, optional\n", " | Strides of data in memory.\n", " | order : {'C', 'F'}, optional\n", " | Row-major (C-style) or column-major (Fortran-style) order.\n", " | \n", " | Attributes\n", " | ----------\n", " | T : ndarray\n", " | Transpose of the array.\n", " | data : buffer\n", " | The array's elements, in memory.\n", " | dtype : dtype object\n", " | Describes the format of the elements in the array.\n", " | flags : dict\n", " | Dictionary containing information related to memory use, e.g.,\n", " | 'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.\n", " | flat : numpy.flatiter object\n", " | Flattened version of the array as an iterator. The iterator\n", " | allows assignments, e.g., ``x.flat = 3`` (See `ndarray.flat` for\n", " | assignment examples; TODO).\n", " | imag : ndarray\n", " | Imaginary part of the array.\n", " | real : ndarray\n", " | Real part of the array.\n", " | size : int\n", " | Number of elements in the array.\n", " | itemsize : int\n", " | The memory use of each array element in bytes.\n", " | nbytes : int\n", " | The total number of bytes required to store the array data,\n", " | i.e., ``itemsize * size``.\n", " | ndim : int\n", " | The array's number of dimensions.\n", " | shape : tuple of ints\n", " | Shape of the array.\n", " | strides : tuple of ints\n", " | The step-size required to move from one element to the next in\n", " | memory. For example, a contiguous ``(3, 4)`` array of type\n", " | ``int16`` in C-order has strides ``(8, 2)``. This implies that\n", " | to move from element to element in memory requires jumps of 2 bytes.\n", " | To move from row-to-row, one needs to jump 8 bytes at a time\n", " | (``2 * 4``).\n", " | ctypes : ctypes object\n", " | Class containing properties of the array needed for interaction\n", " | with ctypes.\n", " | base : ndarray\n", " | If the array is a view into another array, that array is its `base`\n", " | (unless that array is also a view). The `base` array is where the\n", " | array data is actually stored.\n", " | \n", " | See Also\n", " | --------\n", " | array : Construct an array.\n", " | zeros : Create an array, each element of which is zero.\n", " | empty : Create an array, but leave its allocated memory unchanged (i.e.,\n", " | it contains \"garbage\").\n", " | dtype : Create a data-type.\n", " | numpy.typing.NDArray : An ndarray alias :term:`generic <generic type>`\n", " | w.r.t. its `dtype.type <numpy.dtype.type>`.\n", " | \n", " | Notes\n", " | -----\n", " | There are two modes of creating an array using ``__new__``:\n", " | \n", " | 1. If `buffer` is None, then only `shape`, `dtype`, and `order`\n", " | are used.\n", " | 2. If `buffer` is an object exposing the buffer interface, then\n", " | all keywords are interpreted.\n", " | \n", " | No ``__init__`` method is needed because the array is fully initialized\n", " | after the ``__new__`` method.\n", " | \n", " | Examples\n", " | --------\n", " | These examples illustrate the low-level `ndarray` constructor. Refer\n", " | to the `See Also` section above for easier ways of constructing an\n", " | ndarray.\n", " | \n", " | First mode, `buffer` is None:\n", " | \n", " | >>> np.ndarray(shape=(2,2), dtype=float, order='F')\n", " | array([[0.0e+000, 0.0e+000], # random\n", " | [ nan, 2.5e-323]])\n", " | \n", " | Second mode:\n", " | \n", " | >>> np.ndarray((2,), buffer=np.array([1,2,3]),\n", " | ... offset=np.int_().itemsize,\n", " | ... dtype=int) # offset = 1*itemsize, i.e. skip first element\n", " | array([2, 3])\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | a.__array__([dtype], /) -> reference if type unchanged, copy otherwise.\n", " | \n", " | Returns either a new reference to self if dtype is not given or a new array\n", " | of provided data type if dtype is different from the current dtype of the\n", " | array.\n", " | \n", " | __array_finalize__(...)\n", " | a.__array_finalize__(obj, /)\n", " | \n", " | Present so subclasses can call super. Does nothing.\n", " | \n", " | __array_function__(...)\n", " | \n", " | __array_prepare__(...)\n", " | a.__array_prepare__(array[, context], /)\n", " | \n", " | Returns a view of `array` with the same type as self.\n", " | \n", " | __array_ufunc__(...)\n", " | \n", " | __array_wrap__(...)\n", " | a.__array_wrap__(array[, context], /)\n", " | \n", " | Returns a view of `array` with the same type as self.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __complex__(...)\n", " | \n", " | __contains__(self, key, /)\n", " | Return key in self.\n", " | \n", " | __copy__(...)\n", " | a.__copy__()\n", " | \n", " | Used if :func:`copy.copy` is called on an array. Returns a copy of the array.\n", " | \n", " | Equivalent to ``a.copy(order='K')``.\n", " | \n", " | __deepcopy__(...)\n", " | a.__deepcopy__(memo, /) -> Deep copy of array.\n", " | \n", " | Used if :func:`copy.deepcopy` is called on an array.\n", " | \n", " | __delitem__(self, key, /)\n", " | Delete self[key].\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __dlpack__(...)\n", " | a.__dlpack__(*, stream=None)\n", " | \n", " | DLPack Protocol: Part of the Array API.\n", " | \n", " | __dlpack_device__(...)\n", " | a.__dlpack_device__()\n", " | \n", " | DLPack Protocol: Part of the Array API.\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __format__(...)\n", " | Default object formatter.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __iadd__(self, value, /)\n", " | Return self+=value.\n", " | \n", " | __iand__(self, value, /)\n", " | Return self&=value.\n", " | \n", " | __ifloordiv__(self, value, /)\n", " | Return self//=value.\n", " | \n", " | __ilshift__(self, value, /)\n", " | Return self<<=value.\n", " | \n", " | __imatmul__(self, value, /)\n", " | Return self@=value.\n", " | \n", " | __imod__(self, value, /)\n", " | Return self%=value.\n", " | \n", " | __imul__(self, value, /)\n", " | Return self*=value.\n", " | \n", " | __index__(self, /)\n", " | Return self converted to an integer, if self is suitable for use as an index into a list.\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __ior__(self, value, /)\n", " | Return self|=value.\n", " | \n", " | __ipow__(self, value, /)\n", " | Return self**=value.\n", " | \n", " | __irshift__(self, value, /)\n", " | Return self>>=value.\n", " | \n", " | __isub__(self, value, /)\n", " | Return self-=value.\n", " | \n", " | __iter__(self, /)\n", " | Implement iter(self).\n", " | \n", " | __itruediv__(self, value, /)\n", " | Return self/=value.\n", " | \n", " | __ixor__(self, value, /)\n", " | Return self^=value.\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __len__(self, /)\n", " | Return len(self).\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __matmul__(self, value, /)\n", " | Return self@value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __reduce__(...)\n", " | a.__reduce__()\n", " | \n", " | For pickling.\n", " | \n", " | __reduce_ex__(...)\n", " | Helper for pickle.\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmatmul__(self, value, /)\n", " | Return value@self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setitem__(self, key, value, /)\n", " | Set self[key] to value.\n", " | \n", " | __setstate__(...)\n", " | a.__setstate__(state, /)\n", " | \n", " | For unpickling.\n", " | \n", " | The `state` argument must be a sequence that contains the following\n", " | elements:\n", " | \n", " | Parameters\n", " | ----------\n", " | version : int\n", " | optional pickle version. If omitted defaults to 0.\n", " | shape : tuple\n", " | dtype : data-type\n", " | isFortran : bool\n", " | rawdata : string or list\n", " | a binary string with the data (or a list if 'a' is an object array)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | a.all(axis=None, out=None, keepdims=False, *, where=True)\n", " | \n", " | Returns True if all elements evaluate to True.\n", " | \n", " | Refer to `numpy.all` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.all : equivalent function\n", " | \n", " | any(...)\n", " | a.any(axis=None, out=None, keepdims=False, *, where=True)\n", " | \n", " | Returns True if any of the elements of `a` evaluate to True.\n", " | \n", " | Refer to `numpy.any` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.any : equivalent function\n", " | \n", " | argmax(...)\n", " | a.argmax(axis=None, out=None, *, keepdims=False)\n", " | \n", " | Return indices of the maximum values along the given axis.\n", " | \n", " | Refer to `numpy.argmax` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.argmax : equivalent function\n", " | \n", " | argmin(...)\n", " | a.argmin(axis=None, out=None, *, keepdims=False)\n", " | \n", " | Return indices of the minimum values along the given axis.\n", " | \n", " | Refer to `numpy.argmin` for detailed documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.argmin : equivalent function\n", " | \n", " | argpartition(...)\n", " | a.argpartition(kth, axis=-1, kind='introselect', order=None)\n", " | \n", " | Returns the indices that would partition this array.\n", " | \n", " | Refer to `numpy.argpartition` for full documentation.\n", " | \n", " | .. versionadded:: 1.8.0\n", " | \n", " | See Also\n", " | --------\n", " | numpy.argpartition : equivalent function\n", " | \n", " | argsort(...)\n", " | a.argsort(axis=-1, kind=None, order=None)\n", " | \n", " | Returns the indices that would sort this array.\n", " | \n", " | Refer to `numpy.argsort` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.argsort : equivalent function\n", " | \n", " | astype(...)\n", " | a.astype(dtype, order='K', casting='unsafe', subok=True, copy=True)\n", " | \n", " | Copy of the array, cast to a specified type.\n", " | \n", " | Parameters\n", " | ----------\n", " | dtype : str or dtype\n", " | Typecode or data-type to which the array is cast.\n", " | order : {'C', 'F', 'A', 'K'}, optional\n", " | Controls the memory layout order of the result.\n", " | 'C' means C order, 'F' means Fortran order, 'A'\n", " | means 'F' order if all the arrays are Fortran contiguous,\n", " | 'C' order otherwise, and 'K' means as close to the\n", " | order the array elements appear in memory as possible.\n", " | Default is 'K'.\n", " | casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional\n", " | Controls what kind of data casting may occur. Defaults to 'unsafe'\n", " | for backwards compatibility.\n", " | \n", " | * 'no' means the data types should not be cast at all.\n", " | * 'equiv' means only byte-order changes are allowed.\n", " | * 'safe' means only casts which can preserve values are allowed.\n", " | * 'same_kind' means only safe casts or casts within a kind,\n", " | like float64 to float32, are allowed.\n", " | * 'unsafe' means any data conversions may be done.\n", " | subok : bool, optional\n", " | If True, then sub-classes will be passed-through (default), otherwise\n", " | the returned array will be forced to be a base-class array.\n", " | copy : bool, optional\n", " | By default, astype always returns a newly allocated array. If this\n", " | is set to false, and the `dtype`, `order`, and `subok`\n", " | requirements are satisfied, the input array is returned instead\n", " | of a copy.\n", " | \n", " | Returns\n", " | -------\n", " | arr_t : ndarray\n", " | Unless `copy` is False and the other conditions for returning the input\n", " | array are satisfied (see description for `copy` input parameter), `arr_t`\n", " | is a new array of the same shape as the input array, with dtype, order\n", " | given by `dtype`, `order`.\n", " | \n", " | Notes\n", " | -----\n", " | .. versionchanged:: 1.17.0\n", " | Casting between a simple data type and a structured one is possible only\n", " | for \"unsafe\" casting. Casting to multiple fields is allowed, but\n", " | casting from multiple fields is not.\n", " | \n", " | .. versionchanged:: 1.9.0\n", " | Casting from numeric to string types in 'safe' casting mode requires\n", " | that the string dtype length is long enough to store the max\n", " | integer/float value converted.\n", " | \n", " | Raises\n", " | ------\n", " | ComplexWarning\n", " | When casting from complex to float or int. To avoid this,\n", " | one should use ``a.real.astype(t)``.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([1, 2, 2.5])\n", " | >>> x\n", " | array([1. , 2. , 2.5])\n", " | \n", " | >>> x.astype(int)\n", " | array([1, 2, 2])\n", " | \n", " | byteswap(...)\n", " | a.byteswap(inplace=False)\n", " | \n", " | Swap the bytes of the array elements\n", " | \n", " | Toggle between low-endian and big-endian data representation by\n", " | returning a byteswapped array, optionally swapped in-place.\n", " | Arrays of byte-strings are not swapped. The real and imaginary\n", " | parts of a complex number are swapped individually.\n", " | \n", " | Parameters\n", " | ----------\n", " | inplace : bool, optional\n", " | If ``True``, swap bytes in-place, default is ``False``.\n", " | \n", " | Returns\n", " | -------\n", " | out : ndarray\n", " | The byteswapped array. If `inplace` is ``True``, this is\n", " | a view to self.\n", " | \n", " | Examples\n", " | --------\n", " | >>> A = np.array([1, 256, 8755], dtype=np.int16)\n", " | >>> list(map(hex, A))\n", " | ['0x1', '0x100', '0x2233']\n", " | >>> A.byteswap(inplace=True)\n", " | array([ 256, 1, 13090], dtype=int16)\n", " | >>> list(map(hex, A))\n", " | ['0x100', '0x1', '0x3322']\n", " | \n", " | Arrays of byte-strings are not swapped\n", " | \n", " | >>> A = np.array([b'ceg', b'fac'])\n", " | >>> A.byteswap()\n", " | array([b'ceg', b'fac'], dtype='|S3')\n", " | \n", " | ``A.newbyteorder().byteswap()`` produces an array with the same values\n", " | but different representation in memory\n", " | \n", " | >>> A = np.array([1, 2, 3])\n", " | >>> A.view(np.uint8)\n", " | array([1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0,\n", " | 0, 0], dtype=uint8)\n", " | >>> A.newbyteorder().byteswap(inplace=True)\n", " | array([1, 2, 3])\n", " | >>> A.view(np.uint8)\n", " | array([0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0,\n", " | 0, 3], dtype=uint8)\n", " | \n", " | choose(...)\n", " | a.choose(choices, out=None, mode='raise')\n", " | \n", " | Use an index array to construct a new array from a set of choices.\n", " | \n", " | Refer to `numpy.choose` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.choose : equivalent function\n", " | \n", " | clip(...)\n", " | a.clip(min=None, max=None, out=None, **kwargs)\n", " | \n", " | Return an array whose values are limited to ``[min, max]``.\n", " | One of max or min must be given.\n", " | \n", " | Refer to `numpy.clip` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.clip : equivalent function\n", " | \n", " | compress(...)\n", " | a.compress(condition, axis=None, out=None)\n", " | \n", " | Return selected slices of this array along given axis.\n", " | \n", " | Refer to `numpy.compress` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.compress : equivalent function\n", " | \n", " | conj(...)\n", " | a.conj()\n", " | \n", " | Complex-conjugate all elements.\n", " | \n", " | Refer to `numpy.conjugate` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.conjugate : equivalent function\n", " | \n", " | conjugate(...)\n", " | a.conjugate()\n", " | \n", " | Return the complex conjugate, element-wise.\n", " | \n", " | Refer to `numpy.conjugate` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.conjugate : equivalent function\n", " | \n", " | copy(...)\n", " | a.copy(order='C')\n", " | \n", " | Return a copy of the array.\n", " | \n", " | Parameters\n", " | ----------\n", " | order : {'C', 'F', 'A', 'K'}, optional\n", " | Controls the memory layout of the copy. 'C' means C-order,\n", " | 'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous,\n", " | 'C' otherwise. 'K' means match the layout of `a` as closely\n", " | as possible. (Note that this function and :func:`numpy.copy` are very\n", " | similar but have different default values for their order=\n", " | arguments, and this function always passes sub-classes through.)\n", " | \n", " | See also\n", " | --------\n", " | numpy.copy : Similar function with different default behavior\n", " | numpy.copyto\n", " | \n", " | Notes\n", " | -----\n", " | This function is the preferred method for creating an array copy. The\n", " | function :func:`numpy.copy` is similar, but it defaults to using order 'K',\n", " | and will not pass sub-classes through by default.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([[1,2,3],[4,5,6]], order='F')\n", " | \n", " | >>> y = x.copy()\n", " | \n", " | >>> x.fill(0)\n", " | \n", " | >>> x\n", " | array([[0, 0, 0],\n", " | [0, 0, 0]])\n", " | \n", " | >>> y\n", " | array([[1, 2, 3],\n", " | [4, 5, 6]])\n", " | \n", " | >>> y.flags['C_CONTIGUOUS']\n", " | True\n", " | \n", " | cumprod(...)\n", " | a.cumprod(axis=None, dtype=None, out=None)\n", " | \n", " | Return the cumulative product of the elements along the given axis.\n", " | \n", " | Refer to `numpy.cumprod` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.cumprod : equivalent function\n", " | \n", " | cumsum(...)\n", " | a.cumsum(axis=None, dtype=None, out=None)\n", " | \n", " | Return the cumulative sum of the elements along the given axis.\n", " | \n", " | Refer to `numpy.cumsum` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.cumsum : equivalent function\n", " | \n", " | diagonal(...)\n", " | a.diagonal(offset=0, axis1=0, axis2=1)\n", " | \n", " | Return specified diagonals. In NumPy 1.9 the returned array is a\n", " | read-only view instead of a copy as in previous NumPy versions. In\n", " | a future version the read-only restriction will be removed.\n", " | \n", " | Refer to :func:`numpy.diagonal` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.diagonal : equivalent function\n", " | \n", " | dot(...)\n", " | \n", " | dump(...)\n", " | a.dump(file)\n", " | \n", " | Dump a pickle of the array to the specified file.\n", " | The array can be read back with pickle.load or numpy.load.\n", " | \n", " | Parameters\n", " | ----------\n", " | file : str or Path\n", " | A string naming the dump file.\n", " | \n", " | .. versionchanged:: 1.17.0\n", " | `pathlib.Path` objects are now accepted.\n", " | \n", " | dumps(...)\n", " | a.dumps()\n", " | \n", " | Returns the pickle of the array as a string.\n", " | pickle.loads will convert the string back to an array.\n", " | \n", " | Parameters\n", " | ----------\n", " | None\n", " | \n", " | fill(...)\n", " | a.fill(value)\n", " | \n", " | Fill the array with a scalar value.\n", " | \n", " | Parameters\n", " | ----------\n", " | value : scalar\n", " | All elements of `a` will be assigned this value.\n", " | \n", " | Examples\n", " | --------\n", " | >>> a = np.array([1, 2])\n", " | >>> a.fill(0)\n", " | >>> a\n", " | array([0, 0])\n", " | >>> a = np.empty(2)\n", " | >>> a.fill(1)\n", " | >>> a\n", " | array([1., 1.])\n", " | \n", " | Fill expects a scalar value and always behaves the same as assigning\n", " | to a single array element. The following is a rare example where this\n", " | distinction is important:\n", " | \n", " | >>> a = np.array([None, None], dtype=object)\n", " | >>> a[0] = np.array(3)\n", " | >>> a\n", " | array([array(3), None], dtype=object)\n", " | >>> a.fill(np.array(3))\n", " | >>> a\n", " | array([array(3), array(3)], dtype=object)\n", " | \n", " | Where other forms of assignments will unpack the array being assigned:\n", " | \n", " | >>> a[...] = np.array(3)\n", " | >>> a\n", " | array([3, 3], dtype=object)\n", " | \n", " | flatten(...)\n", " | a.flatten(order='C')\n", " | \n", " | Return a copy of the array collapsed into one dimension.\n", " | \n", " | Parameters\n", " | ----------\n", " | order : {'C', 'F', 'A', 'K'}, optional\n", " | 'C' means to flatten in row-major (C-style) order.\n", " | 'F' means to flatten in column-major (Fortran-\n", " | style) order. 'A' means to flatten in column-major\n", " | order if `a` is Fortran *contiguous* in memory,\n", " | row-major order otherwise. 'K' means to flatten\n", " | `a` in the order the elements occur in memory.\n", " | The default is 'C'.\n", " | \n", " | Returns\n", " | -------\n", " | y : ndarray\n", " | A copy of the input array, flattened to one dimension.\n", " | \n", " | See Also\n", " | --------\n", " | ravel : Return a flattened array.\n", " | flat : A 1-D flat iterator over the array.\n", " | \n", " | Examples\n", " | --------\n", " | >>> a = np.array([[1,2], [3,4]])\n", " | >>> a.flatten()\n", " | array([1, 2, 3, 4])\n", " | >>> a.flatten('F')\n", " | array([1, 3, 2, 4])\n", " | \n", " | getfield(...)\n", " | a.getfield(dtype, offset=0)\n", " | \n", " | Returns a field of the given array as a certain type.\n", " | \n", " | A field is a view of the array data with a given data-type. The values in\n", " | the view are determined by the given type and the offset into the current\n", " | array in bytes. The offset needs to be such that the view dtype fits in the\n", " | array dtype; for example an array of dtype complex128 has 16-byte elements.\n", " | If taking a view with a 32-bit integer (4 bytes), the offset needs to be\n", " | between 0 and 12 bytes.\n", " | \n", " | Parameters\n", " | ----------\n", " | dtype : str or dtype\n", " | The data type of the view. The dtype size of the view can not be larger\n", " | than that of the array itself.\n", " | offset : int\n", " | Number of bytes to skip before beginning the element view.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.diag([1.+1.j]*2)\n", " | >>> x[1, 1] = 2 + 4.j\n", " | >>> x\n", " | array([[1.+1.j, 0.+0.j],\n", " | [0.+0.j, 2.+4.j]])\n", " | >>> x.getfield(np.float64)\n", " | array([[1., 0.],\n", " | [0., 2.]])\n", " | \n", " | By choosing an offset of 8 bytes we can select the complex part of the\n", " | array for our view:\n", " | \n", " | >>> x.getfield(np.float64, offset=8)\n", " | array([[1., 0.],\n", " | [0., 4.]])\n", " | \n", " | item(...)\n", " | a.item(*args)\n", " | \n", " | Copy an element of an array to a standard Python scalar and return it.\n", " | \n", " | Parameters\n", " | ----------\n", " | \\*args : Arguments (variable number and type)\n", " | \n", " | * none: in this case, the method only works for arrays\n", " | with one element (`a.size == 1`), which element is\n", " | copied into a standard Python scalar object and returned.\n", " | \n", " | * int_type: this argument is interpreted as a flat index into\n", " | the array, specifying which element to copy and return.\n", " | \n", " | * tuple of int_types: functions as does a single int_type argument,\n", " | except that the argument is interpreted as an nd-index into the\n", " | array.\n", " | \n", " | Returns\n", " | -------\n", " | z : Standard Python scalar object\n", " | A copy of the specified element of the array as a suitable\n", " | Python scalar\n", " | \n", " | Notes\n", " | -----\n", " | When the data type of `a` is longdouble or clongdouble, item() returns\n", " | a scalar array object because there is no available Python scalar that\n", " | would not lose information. Void arrays return a buffer object for item(),\n", " | unless fields are defined, in which case a tuple is returned.\n", " | \n", " | `item` is very similar to a[args], except, instead of an array scalar,\n", " | a standard Python scalar is returned. This can be useful for speeding up\n", " | access to elements of the array and doing arithmetic on elements of the\n", " | array using Python's optimized math.\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.random.seed(123)\n", " | >>> x = np.random.randint(9, size=(3, 3))\n", " | >>> x\n", " | array([[2, 2, 6],\n", " | [1, 3, 6],\n", " | [1, 0, 1]])\n", " | >>> x.item(3)\n", " | 1\n", " | >>> x.item(7)\n", " | 0\n", " | >>> x.item((0, 1))\n", " | 2\n", " | >>> x.item((2, 2))\n", " | 1\n", " | \n", " | itemset(...)\n", " | a.itemset(*args)\n", " | \n", " | Insert scalar into an array (scalar is cast to array's dtype, if possible)\n", " | \n", " | There must be at least 1 argument, and define the last argument\n", " | as *item*. Then, ``a.itemset(*args)`` is equivalent to but faster\n", " | than ``a[args] = item``. The item should be a scalar value and `args`\n", " | must select a single item in the array `a`.\n", " | \n", " | Parameters\n", " | ----------\n", " | \\*args : Arguments\n", " | If one argument: a scalar, only used in case `a` is of size 1.\n", " | If two arguments: the last argument is the value to be set\n", " | and must be a scalar, the first argument specifies a single array\n", " | element location. It is either an int or a tuple.\n", " | \n", " | Notes\n", " | -----\n", " | Compared to indexing syntax, `itemset` provides some speed increase\n", " | for placing a scalar into a particular location in an `ndarray`,\n", " | if you must do this. However, generally this is discouraged:\n", " | among other problems, it complicates the appearance of the code.\n", " | Also, when using `itemset` (and `item`) inside a loop, be sure\n", " | to assign the methods to a local variable to avoid the attribute\n", " | look-up at each loop iteration.\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.random.seed(123)\n", " | >>> x = np.random.randint(9, size=(3, 3))\n", " | >>> x\n", " | array([[2, 2, 6],\n", " | [1, 3, 6],\n", " | [1, 0, 1]])\n", " | >>> x.itemset(4, 0)\n", " | >>> x.itemset((2, 2), 9)\n", " | >>> x\n", " | array([[2, 2, 6],\n", " | [1, 0, 6],\n", " | [1, 0, 9]])\n", " | \n", " | max(...)\n", " | a.max(axis=None, out=None, keepdims=False, initial=<no value>, where=True)\n", " | \n", " | Return the maximum along a given axis.\n", " | \n", " | Refer to `numpy.amax` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.amax : equivalent function\n", " | \n", " | mean(...)\n", " | a.mean(axis=None, dtype=None, out=None, keepdims=False, *, where=True)\n", " | \n", " | Returns the average of the array elements along given axis.\n", " | \n", " | Refer to `numpy.mean` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.mean : equivalent function\n", " | \n", " | min(...)\n", " | a.min(axis=None, out=None, keepdims=False, initial=<no value>, where=True)\n", " | \n", " | Return the minimum along a given axis.\n", " | \n", " | Refer to `numpy.amin` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.amin : equivalent function\n", " | \n", " | newbyteorder(...)\n", " | arr.newbyteorder(new_order='S', /)\n", " | \n", " | Return the array with the same data viewed with a different byte order.\n", " | \n", " | Equivalent to::\n", " | \n", " | arr.view(arr.dtype.newbytorder(new_order))\n", " | \n", " | Changes are also made in all fields and sub-arrays of the array data\n", " | type.\n", " | \n", " | \n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : string, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | below. `new_order` codes can be any of:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order, equivalent to `sys.byteorder`\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_arr : array\n", " | New array object with the dtype reflecting given change to the\n", " | byte order.\n", " | \n", " | nonzero(...)\n", " | a.nonzero()\n", " | \n", " | Return the indices of the elements that are non-zero.\n", " | \n", " | Refer to `numpy.nonzero` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.nonzero : equivalent function\n", " | \n", " | partition(...)\n", " | a.partition(kth, axis=-1, kind='introselect', order=None)\n", " | \n", " | Rearranges the elements in the array in such a way that the value of the\n", " | element in kth position is in the position it would be in a sorted array.\n", " | All elements smaller than the kth element are moved before this element and\n", " | all equal or greater are moved behind it. The ordering of the elements in\n", " | the two partitions is undefined.\n", " | \n", " | .. versionadded:: 1.8.0\n", " | \n", " | Parameters\n", " | ----------\n", " | kth : int or sequence of ints\n", " | Element index to partition by. The kth element value will be in its\n", " | final sorted position and all smaller elements will be moved before it\n", " | and all equal or greater elements behind it.\n", " | The order of all elements in the partitions is undefined.\n", " | If provided with a sequence of kth it will partition all elements\n", " | indexed by kth of them into their sorted position at once.\n", " | \n", " | .. deprecated:: 1.22.0\n", " | Passing booleans as index is deprecated.\n", " | axis : int, optional\n", " | Axis along which to sort. Default is -1, which means sort along the\n", " | last axis.\n", " | kind : {'introselect'}, optional\n", " | Selection algorithm. Default is 'introselect'.\n", " | order : str or list of str, optional\n", " | When `a` is an array with fields defined, this argument specifies\n", " | which fields to compare first, second, etc. A single field can\n", " | be specified as a string, and not all fields need to be specified,\n", " | but unspecified fields will still be used, in the order in which\n", " | they come up in the dtype, to break ties.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.partition : Return a partitioned copy of an array.\n", " | argpartition : Indirect partition.\n", " | sort : Full sort.\n", " | \n", " | Notes\n", " | -----\n", " | See ``np.partition`` for notes on the different algorithms.\n", " | \n", " | Examples\n", " | --------\n", " | >>> a = np.array([3, 4, 2, 1])\n", " | >>> a.partition(3)\n", " | >>> a\n", " | array([2, 1, 3, 4])\n", " | \n", " | >>> a.partition((1, 3))\n", " | >>> a\n", " | array([1, 2, 3, 4])\n", " | \n", " | prod(...)\n", " | a.prod(axis=None, dtype=None, out=None, keepdims=False, initial=1, where=True)\n", " | \n", " | Return the product of the array elements over the given axis\n", " | \n", " | Refer to `numpy.prod` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.prod : equivalent function\n", " | \n", " | ptp(...)\n", " | a.ptp(axis=None, out=None, keepdims=False)\n", " | \n", " | Peak to peak (maximum - minimum) value along a given axis.\n", " | \n", " | Refer to `numpy.ptp` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.ptp : equivalent function\n", " | \n", " | put(...)\n", " | a.put(indices, values, mode='raise')\n", " | \n", " | Set ``a.flat[n] = values[n]`` for all `n` in indices.\n", " | \n", " | Refer to `numpy.put` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.put : equivalent function\n", " | \n", " | ravel(...)\n", " | a.ravel([order])\n", " | \n", " | Return a flattened array.\n", " | \n", " | Refer to `numpy.ravel` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.ravel : equivalent function\n", " | \n", " | ndarray.flat : a flat iterator on the array.\n", " | \n", " | repeat(...)\n", " | a.repeat(repeats, axis=None)\n", " | \n", " | Repeat elements of an array.\n", " | \n", " | Refer to `numpy.repeat` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.repeat : equivalent function\n", " | \n", " | reshape(...)\n", " | a.reshape(shape, order='C')\n", " | \n", " | Returns an array containing the same data with a new shape.\n", " | \n", " | Refer to `numpy.reshape` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.reshape : equivalent function\n", " | \n", " | Notes\n", " | -----\n", " | Unlike the free function `numpy.reshape`, this method on `ndarray` allows\n", " | the elements of the shape parameter to be passed in as separate arguments.\n", " | For example, ``a.reshape(10, 11)`` is equivalent to\n", " | ``a.reshape((10, 11))``.\n", " | \n", " | resize(...)\n", " | a.resize(new_shape, refcheck=True)\n", " | \n", " | Change shape and size of array in-place.\n", " | \n", " | Parameters\n", " | ----------\n", " | new_shape : tuple of ints, or `n` ints\n", " | Shape of resized array.\n", " | refcheck : bool, optional\n", " | If False, reference count will not be checked. Default is True.\n", " | \n", " | Returns\n", " | -------\n", " | None\n", " | \n", " | Raises\n", " | ------\n", " | ValueError\n", " | If `a` does not own its own data or references or views to it exist,\n", " | and the data memory must be changed.\n", " | PyPy only: will always raise if the data memory must be changed, since\n", " | there is no reliable way to determine if references or views to it\n", " | exist.\n", " | \n", " | SystemError\n", " | If the `order` keyword argument is specified. This behaviour is a\n", " | bug in NumPy.\n", " | \n", " | See Also\n", " | --------\n", " | resize : Return a new array with the specified shape.\n", " | \n", " | Notes\n", " | -----\n", " | This reallocates space for the data area if necessary.\n", " | \n", " | Only contiguous arrays (data elements consecutive in memory) can be\n", " | resized.\n", " | \n", " | The purpose of the reference count check is to make sure you\n", " | do not use this array as a buffer for another Python object and then\n", " | reallocate the memory. However, reference counts can increase in\n", " | other ways so if you are sure that you have not shared the memory\n", " | for this array with another Python object, then you may safely set\n", " | `refcheck` to False.\n", " | \n", " | Examples\n", " | --------\n", " | Shrinking an array: array is flattened (in the order that the data are\n", " | stored in memory), resized, and reshaped:\n", " | \n", " | >>> a = np.array([[0, 1], [2, 3]], order='C')\n", " | >>> a.resize((2, 1))\n", " | >>> a\n", " | array([[0],\n", " | [1]])\n", " | \n", " | >>> a = np.array([[0, 1], [2, 3]], order='F')\n", " | >>> a.resize((2, 1))\n", " | >>> a\n", " | array([[0],\n", " | [2]])\n", " | \n", " | Enlarging an array: as above, but missing entries are filled with zeros:\n", " | \n", " | >>> b = np.array([[0, 1], [2, 3]])\n", " | >>> b.resize(2, 3) # new_shape parameter doesn't have to be a tuple\n", " | >>> b\n", " | array([[0, 1, 2],\n", " | [3, 0, 0]])\n", " | \n", " | Referencing an array prevents resizing...\n", " | \n", " | >>> c = a\n", " | >>> a.resize((1, 1))\n", " | Traceback (most recent call last):\n", " | ...\n", " | ValueError: cannot resize an array that references or is referenced ...\n", " | \n", " | Unless `refcheck` is False:\n", " | \n", " | >>> a.resize((1, 1), refcheck=False)\n", " | >>> a\n", " | array([[0]])\n", " | >>> c\n", " | array([[0]])\n", " | \n", " | round(...)\n", " | a.round(decimals=0, out=None)\n", " | \n", " | Return `a` with each element rounded to the given number of decimals.\n", " | \n", " | Refer to `numpy.around` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.around : equivalent function\n", " | \n", " | searchsorted(...)\n", " | a.searchsorted(v, side='left', sorter=None)\n", " | \n", " | Find indices where elements of v should be inserted in a to maintain order.\n", " | \n", " | For full documentation, see `numpy.searchsorted`\n", " | \n", " | See Also\n", " | --------\n", " | numpy.searchsorted : equivalent function\n", " | \n", " | setfield(...)\n", " | a.setfield(val, dtype, offset=0)\n", " | \n", " | Put a value into a specified place in a field defined by a data-type.\n", " | \n", " | Place `val` into `a`'s field defined by `dtype` and beginning `offset`\n", " | bytes into the field.\n", " | \n", " | Parameters\n", " | ----------\n", " | val : object\n", " | Value to be placed in field.\n", " | dtype : dtype object\n", " | Data-type of the field in which to place `val`.\n", " | offset : int, optional\n", " | The number of bytes into the field at which to place `val`.\n", " | \n", " | Returns\n", " | -------\n", " | None\n", " | \n", " | See Also\n", " | --------\n", " | getfield\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.eye(3)\n", " | >>> x.getfield(np.float64)\n", " | array([[1., 0., 0.],\n", " | [0., 1., 0.],\n", " | [0., 0., 1.]])\n", " | >>> x.setfield(3, np.int32)\n", " | >>> x.getfield(np.int32)\n", " | array([[3, 3, 3],\n", " | [3, 3, 3],\n", " | [3, 3, 3]], dtype=int32)\n", " | >>> x\n", " | array([[1.0e+000, 1.5e-323, 1.5e-323],\n", " | [1.5e-323, 1.0e+000, 1.5e-323],\n", " | [1.5e-323, 1.5e-323, 1.0e+000]])\n", " | >>> x.setfield(np.eye(3), np.int32)\n", " | >>> x\n", " | array([[1., 0., 0.],\n", " | [0., 1., 0.],\n", " | [0., 0., 1.]])\n", " | \n", " | setflags(...)\n", " | a.setflags(write=None, align=None, uic=None)\n", " | \n", " | Set array flags WRITEABLE, ALIGNED, WRITEBACKIFCOPY,\n", " | respectively.\n", " | \n", " | These Boolean-valued flags affect how numpy interprets the memory\n", " | area used by `a` (see Notes below). The ALIGNED flag can only\n", " | be set to True if the data is actually aligned according to the type.\n", " | The WRITEBACKIFCOPY and flag can never be set\n", " | to True. The flag WRITEABLE can only be set to True if the array owns its\n", " | own memory, or the ultimate owner of the memory exposes a writeable buffer\n", " | interface, or is a string. (The exception for string is made so that\n", " | unpickling can be done without copying memory.)\n", " | \n", " | Parameters\n", " | ----------\n", " | write : bool, optional\n", " | Describes whether or not `a` can be written to.\n", " | align : bool, optional\n", " | Describes whether or not `a` is aligned properly for its type.\n", " | uic : bool, optional\n", " | Describes whether or not `a` is a copy of another \"base\" array.\n", " | \n", " | Notes\n", " | -----\n", " | Array flags provide information about how the memory area used\n", " | for the array is to be interpreted. There are 7 Boolean flags\n", " | in use, only four of which can be changed by the user:\n", " | WRITEBACKIFCOPY, WRITEABLE, and ALIGNED.\n", " | \n", " | WRITEABLE (W) the data area can be written to;\n", " | \n", " | ALIGNED (A) the data and strides are aligned appropriately for the hardware\n", " | (as determined by the compiler);\n", " | \n", " | WRITEBACKIFCOPY (X) this array is a copy of some other array (referenced\n", " | by .base). When the C-API function PyArray_ResolveWritebackIfCopy is\n", " | called, the base array will be updated with the contents of this array.\n", " | \n", " | All flags can be accessed using the single (upper case) letter as well\n", " | as the full name.\n", " | \n", " | Examples\n", " | --------\n", " | >>> y = np.array([[3, 1, 7],\n", " | ... [2, 0, 0],\n", " | ... [8, 5, 9]])\n", " | >>> y\n", " | array([[3, 1, 7],\n", " | [2, 0, 0],\n", " | [8, 5, 9]])\n", " | >>> y.flags\n", " | C_CONTIGUOUS : True\n", " | F_CONTIGUOUS : False\n", " | OWNDATA : True\n", " | WRITEABLE : True\n", " | ALIGNED : True\n", " | WRITEBACKIFCOPY : False\n", " | >>> y.setflags(write=0, align=0)\n", " | >>> y.flags\n", " | C_CONTIGUOUS : True\n", " | F_CONTIGUOUS : False\n", " | OWNDATA : True\n", " | WRITEABLE : False\n", " | ALIGNED : False\n", " | WRITEBACKIFCOPY : False\n", " | >>> y.setflags(uic=1)\n", " | Traceback (most recent call last):\n", " | File \"<stdin>\", line 1, in <module>\n", " | ValueError: cannot set WRITEBACKIFCOPY flag to True\n", " | \n", " | sort(...)\n", " | a.sort(axis=-1, kind=None, order=None)\n", " | \n", " | Sort an array in-place. Refer to `numpy.sort` for full documentation.\n", " | \n", " | Parameters\n", " | ----------\n", " | axis : int, optional\n", " | Axis along which to sort. Default is -1, which means sort along the\n", " | last axis.\n", " | kind : {'quicksort', 'mergesort', 'heapsort', 'stable'}, optional\n", " | Sorting algorithm. The default is 'quicksort'. Note that both 'stable'\n", " | and 'mergesort' use timsort under the covers and, in general, the\n", " | actual implementation will vary with datatype. The 'mergesort' option\n", " | is retained for backwards compatibility.\n", " | \n", " | .. versionchanged:: 1.15.0\n", " | The 'stable' option was added.\n", " | \n", " | order : str or list of str, optional\n", " | When `a` is an array with fields defined, this argument specifies\n", " | which fields to compare first, second, etc. A single field can\n", " | be specified as a string, and not all fields need be specified,\n", " | but unspecified fields will still be used, in the order in which\n", " | they come up in the dtype, to break ties.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.sort : Return a sorted copy of an array.\n", " | numpy.argsort : Indirect sort.\n", " | numpy.lexsort : Indirect stable sort on multiple keys.\n", " | numpy.searchsorted : Find elements in sorted array.\n", " | numpy.partition: Partial sort.\n", " | \n", " | Notes\n", " | -----\n", " | See `numpy.sort` for notes on the different sorting algorithms.\n", " | \n", " | Examples\n", " | --------\n", " | >>> a = np.array([[1,4], [3,1]])\n", " | >>> a.sort(axis=1)\n", " | >>> a\n", " | array([[1, 4],\n", " | [1, 3]])\n", " | >>> a.sort(axis=0)\n", " | >>> a\n", " | array([[1, 3],\n", " | [1, 4]])\n", " | \n", " | Use the `order` keyword to specify a field to use when sorting a\n", " | structured array:\n", " | \n", " | >>> a = np.array([('a', 2), ('c', 1)], dtype=[('x', 'S1'), ('y', int)])\n", " | >>> a.sort(order='y')\n", " | >>> a\n", " | array([(b'c', 1), (b'a', 2)],\n", " | dtype=[('x', 'S1'), ('y', '<i8')])\n", " | \n", " | squeeze(...)\n", " | a.squeeze(axis=None)\n", " | \n", " | Remove axes of length one from `a`.\n", " | \n", " | Refer to `numpy.squeeze` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.squeeze : equivalent function\n", " | \n", " | std(...)\n", " | a.std(axis=None, dtype=None, out=None, ddof=0, keepdims=False, *, where=True)\n", " | \n", " | Returns the standard deviation of the array elements along given axis.\n", " | \n", " | Refer to `numpy.std` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.std : equivalent function\n", " | \n", " | sum(...)\n", " | a.sum(axis=None, dtype=None, out=None, keepdims=False, initial=0, where=True)\n", " | \n", " | Return the sum of the array elements over the given axis.\n", " | \n", " | Refer to `numpy.sum` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.sum : equivalent function\n", " | \n", " | swapaxes(...)\n", " | a.swapaxes(axis1, axis2)\n", " | \n", " | Return a view of the array with `axis1` and `axis2` interchanged.\n", " | \n", " | Refer to `numpy.swapaxes` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.swapaxes : equivalent function\n", " | \n", " | take(...)\n", " | a.take(indices, axis=None, out=None, mode='raise')\n", " | \n", " | Return an array formed from the elements of `a` at the given indices.\n", " | \n", " | Refer to `numpy.take` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.take : equivalent function\n", " | \n", " | tobytes(...)\n", " | a.tobytes(order='C')\n", " | \n", " | Construct Python bytes containing the raw data bytes in the array.\n", " | \n", " | Constructs Python bytes showing a copy of the raw contents of\n", " | data memory. The bytes object is produced in C-order by default.\n", " | This behavior is controlled by the ``order`` parameter.\n", " | \n", " | .. versionadded:: 1.9.0\n", " | \n", " | Parameters\n", " | ----------\n", " | order : {'C', 'F', 'A'}, optional\n", " | Controls the memory layout of the bytes object. 'C' means C-order,\n", " | 'F' means F-order, 'A' (short for *Any*) means 'F' if `a` is\n", " | Fortran contiguous, 'C' otherwise. Default is 'C'.\n", " | \n", " | Returns\n", " | -------\n", " | s : bytes\n", " | Python bytes exhibiting a copy of `a`'s raw data.\n", " | \n", " | See also\n", " | --------\n", " | frombuffer\n", " | Inverse of this operation, construct a 1-dimensional array from Python\n", " | bytes.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([[0, 1], [2, 3]], dtype='<u2')\n", " | >>> x.tobytes()\n", " | b'\\x00\\x00\\x01\\x00\\x02\\x00\\x03\\x00'\n", " | >>> x.tobytes('C') == x.tobytes()\n", " | True\n", " | >>> x.tobytes('F')\n", " | b'\\x00\\x00\\x02\\x00\\x01\\x00\\x03\\x00'\n", " | \n", " | tofile(...)\n", " | a.tofile(fid, sep=\"\", format=\"%s\")\n", " | \n", " | Write array to a file as text or binary (default).\n", " | \n", " | Data is always written in 'C' order, independent of the order of `a`.\n", " | The data produced by this method can be recovered using the function\n", " | fromfile().\n", " | \n", " | Parameters\n", " | ----------\n", " | fid : file or str or Path\n", " | An open file object, or a string containing a filename.\n", " | \n", " | .. versionchanged:: 1.17.0\n", " | `pathlib.Path` objects are now accepted.\n", " | \n", " | sep : str\n", " | Separator between array items for text output.\n", " | If \"\" (empty), a binary file is written, equivalent to\n", " | ``file.write(a.tobytes())``.\n", " | format : str\n", " | Format string for text file output.\n", " | Each entry in the array is formatted to text by first converting\n", " | it to the closest Python type, and then using \"format\" % item.\n", " | \n", " | Notes\n", " | -----\n", " | This is a convenience function for quick storage of array data.\n", " | Information on endianness and precision is lost, so this method is not a\n", " | good choice for files intended to archive data or transport data between\n", " | machines with different endianness. Some of these problems can be overcome\n", " | by outputting the data as text files, at the expense of speed and file\n", " | size.\n", " | \n", " | When fid is a file object, array contents are directly written to the\n", " | file, bypassing the file object's ``write`` method. As a result, tofile\n", " | cannot be used with files objects supporting compression (e.g., GzipFile)\n", " | or file-like objects that do not support ``fileno()`` (e.g., BytesIO).\n", " | \n", " | tolist(...)\n", " | a.tolist()\n", " | \n", " | Return the array as an ``a.ndim``-levels deep nested list of Python scalars.\n", " | \n", " | Return a copy of the array data as a (nested) Python list.\n", " | Data items are converted to the nearest compatible builtin Python type, via\n", " | the `~numpy.ndarray.item` function.\n", " | \n", " | If ``a.ndim`` is 0, then since the depth of the nested list is 0, it will\n", " | not be a list at all, but a simple Python scalar.\n", " | \n", " | Parameters\n", " | ----------\n", " | none\n", " | \n", " | Returns\n", " | -------\n", " | y : object, or list of object, or list of list of object, or ...\n", " | The possibly nested list of array elements.\n", " | \n", " | Notes\n", " | -----\n", " | The array may be recreated via ``a = np.array(a.tolist())``, although this\n", " | may sometimes lose precision.\n", " | \n", " | Examples\n", " | --------\n", " | For a 1D array, ``a.tolist()`` is almost the same as ``list(a)``,\n", " | except that ``tolist`` changes numpy scalars to Python scalars:\n", " | \n", " | >>> a = np.uint32([1, 2])\n", " | >>> a_list = list(a)\n", " | >>> a_list\n", " | [1, 2]\n", " | >>> type(a_list[0])\n", " | <class 'numpy.uint32'>\n", " | >>> a_tolist = a.tolist()\n", " | >>> a_tolist\n", " | [1, 2]\n", " | >>> type(a_tolist[0])\n", " | <class 'int'>\n", " | \n", " | Additionally, for a 2D array, ``tolist`` applies recursively:\n", " | \n", " | >>> a = np.array([[1, 2], [3, 4]])\n", " | >>> list(a)\n", " | [array([1, 2]), array([3, 4])]\n", " | >>> a.tolist()\n", " | [[1, 2], [3, 4]]\n", " | \n", " | The base case for this recursion is a 0D array:\n", " | \n", " | >>> a = np.array(1)\n", " | >>> list(a)\n", " | Traceback (most recent call last):\n", " | ...\n", " | TypeError: iteration over a 0-d array\n", " | >>> a.tolist()\n", " | 1\n", " | \n", " | tostring(...)\n", " | a.tostring(order='C')\n", " | \n", " | A compatibility alias for `tobytes`, with exactly the same behavior.\n", " | \n", " | Despite its name, it returns `bytes` not `str`\\ s.\n", " | \n", " | .. deprecated:: 1.19.0\n", " | \n", " | trace(...)\n", " | a.trace(offset=0, axis1=0, axis2=1, dtype=None, out=None)\n", " | \n", " | Return the sum along diagonals of the array.\n", " | \n", " | Refer to `numpy.trace` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.trace : equivalent function\n", " | \n", " | transpose(...)\n", " | a.transpose(*axes)\n", " | \n", " | Returns a view of the array with axes transposed.\n", " | \n", " | Refer to `numpy.transpose` for full documentation.\n", " | \n", " | Parameters\n", " | ----------\n", " | axes : None, tuple of ints, or `n` ints\n", " | \n", " | * None or no argument: reverses the order of the axes.\n", " | \n", " | * tuple of ints: `i` in the `j`-th place in the tuple means that the\n", " | array's `i`-th axis becomes the transposed array's `j`-th axis.\n", " | \n", " | * `n` ints: same as an n-tuple of the same ints (this form is\n", " | intended simply as a \"convenience\" alternative to the tuple form).\n", " | \n", " | Returns\n", " | -------\n", " | p : ndarray\n", " | View of the array with its axes suitably permuted.\n", " | \n", " | See Also\n", " | --------\n", " | transpose : Equivalent function.\n", " | ndarray.T : Array property returning the array transposed.\n", " | ndarray.reshape : Give a new shape to an array without changing its data.\n", " | \n", " | Examples\n", " | --------\n", " | >>> a = np.array([[1, 2], [3, 4]])\n", " | >>> a\n", " | array([[1, 2],\n", " | [3, 4]])\n", " | >>> a.transpose()\n", " | array([[1, 3],\n", " | [2, 4]])\n", " | >>> a.transpose((1, 0))\n", " | array([[1, 3],\n", " | [2, 4]])\n", " | >>> a.transpose(1, 0)\n", " | array([[1, 3],\n", " | [2, 4]])\n", " | \n", " | >>> a = np.array([1, 2, 3, 4])\n", " | >>> a\n", " | array([1, 2, 3, 4])\n", " | >>> a.transpose()\n", " | array([1, 2, 3, 4])\n", " | \n", " | var(...)\n", " | a.var(axis=None, dtype=None, out=None, ddof=0, keepdims=False, *, where=True)\n", " | \n", " | Returns the variance of the array elements, along given axis.\n", " | \n", " | Refer to `numpy.var` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.var : equivalent function\n", " | \n", " | view(...)\n", " | a.view([dtype][, type])\n", " | \n", " | New view of array with the same data.\n", " | \n", " | .. note::\n", " | Passing None for ``dtype`` is different from omitting the parameter,\n", " | since the former invokes ``dtype(None)`` which is an alias for\n", " | ``dtype('float_')``.\n", " | \n", " | Parameters\n", " | ----------\n", " | dtype : data-type or ndarray sub-class, optional\n", " | Data-type descriptor of the returned view, e.g., float32 or int16.\n", " | Omitting it results in the view having the same data-type as `a`.\n", " | This argument can also be specified as an ndarray sub-class, which\n", " | then specifies the type of the returned object (this is equivalent to\n", " | setting the ``type`` parameter).\n", " | type : Python type, optional\n", " | Type of the returned view, e.g., ndarray or matrix. Again, omission\n", " | of the parameter results in type preservation.\n", " | \n", " | Notes\n", " | -----\n", " | ``a.view()`` is used two different ways:\n", " | \n", " | ``a.view(some_dtype)`` or ``a.view(dtype=some_dtype)`` constructs a view\n", " | of the array's memory with a different data-type. This can cause a\n", " | reinterpretation of the bytes of memory.\n", " | \n", " | ``a.view(ndarray_subclass)`` or ``a.view(type=ndarray_subclass)`` just\n", " | returns an instance of `ndarray_subclass` that looks at the same array\n", " | (same shape, dtype, etc.) This does not cause a reinterpretation of the\n", " | memory.\n", " | \n", " | For ``a.view(some_dtype)``, if ``some_dtype`` has a different number of\n", " | bytes per entry than the previous dtype (for example, converting a regular\n", " | array to a structured array), then the last axis of ``a`` must be\n", " | contiguous. This axis will be resized in the result.\n", " | \n", " | .. versionchanged:: 1.23.0\n", " | Only the last axis needs to be contiguous. Previously, the entire array\n", " | had to be C-contiguous.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([(1, 2)], dtype=[('a', np.int8), ('b', np.int8)])\n", " | \n", " | Viewing array data using a different type and dtype:\n", " | \n", " | >>> y = x.view(dtype=np.int16, type=np.matrix)\n", " | >>> y\n", " | matrix([[513]], dtype=int16)\n", " | >>> print(type(y))\n", " | <class 'numpy.matrix'>\n", " | \n", " | Creating a view on a structured array so it can be used in calculations\n", " | \n", " | >>> x = np.array([(1, 2),(3,4)], dtype=[('a', np.int8), ('b', np.int8)])\n", " | >>> xv = x.view(dtype=np.int8).reshape(-1,2)\n", " | >>> xv\n", " | array([[1, 2],\n", " | [3, 4]], dtype=int8)\n", " | >>> xv.mean(0)\n", " | array([2., 3.])\n", " | \n", " | Making changes to the view changes the underlying array\n", " | \n", " | >>> xv[0,1] = 20\n", " | >>> x\n", " | array([(1, 20), (3, 4)], dtype=[('a', 'i1'), ('b', 'i1')])\n", " | \n", " | Using a view to convert an array to a recarray:\n", " | \n", " | >>> z = x.view(np.recarray)\n", " | >>> z.a\n", " | array([1, 3], dtype=int8)\n", " | \n", " | Views share data:\n", " | \n", " | >>> x[0] = (9, 10)\n", " | >>> z[0]\n", " | (9, 10)\n", " | \n", " | Views that change the dtype size (bytes per entry) should normally be\n", " | avoided on arrays defined by slices, transposes, fortran-ordering, etc.:\n", " | \n", " | >>> x = np.array([[1, 2, 3], [4, 5, 6]], dtype=np.int16)\n", " | >>> y = x[:, ::2]\n", " | >>> y\n", " | array([[1, 3],\n", " | [4, 6]], dtype=int16)\n", " | >>> y.view(dtype=[('width', np.int16), ('length', np.int16)])\n", " | Traceback (most recent call last):\n", " | ...\n", " | ValueError: To change to a dtype of a different size, the last axis must be contiguous\n", " | >>> z = y.copy()\n", " | >>> z.view(dtype=[('width', np.int16), ('length', np.int16)])\n", " | array([[(1, 3)],\n", " | [(4, 6)]], dtype=[('width', '<i2'), ('length', '<i2')])\n", " | \n", " | However, views that change dtype are totally fine for arrays with a\n", " | contiguous last axis, even if the rest of the axes are not C-contiguous:\n", " | \n", " | >>> x = np.arange(2 * 3 * 4, dtype=np.int8).reshape(2, 3, 4)\n", " | >>> x.transpose(1, 0, 2).view(np.int16)\n", " | array([[[ 256, 770],\n", " | [3340, 3854]],\n", " | <BLANKLINE>\n", " | [[1284, 1798],\n", " | [4368, 4882]],\n", " | <BLANKLINE>\n", " | [[2312, 2826],\n", " | [5396, 5910]]], dtype=int16)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | a.__class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.ndarray` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.ndarray` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.ndarray[Any, np.dtype[Any]]\n", " | numpy.ndarray[typing.Any, numpy.dtype[typing.Any]]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | numpy.typing.NDArray : An ndarray alias :term:`generic <generic type>`\n", " | w.r.t. its `dtype.type <numpy.dtype.type>`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors defined here:\n", " | \n", " | T\n", " | View of the transposed array.\n", " | \n", " | Same as ``self.transpose()``.\n", " | \n", " | Examples\n", " | --------\n", " | >>> a = np.array([[1, 2], [3, 4]])\n", " | >>> a\n", " | array([[1, 2],\n", " | [3, 4]])\n", " | >>> a.T\n", " | array([[1, 3],\n", " | [2, 4]])\n", " | \n", " | >>> a = np.array([1, 2, 3, 4])\n", " | >>> a\n", " | array([1, 2, 3, 4])\n", " | >>> a.T\n", " | array([1, 2, 3, 4])\n", " | \n", " | See Also\n", " | --------\n", " | transpose\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side.\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: C-struct side.\n", " | \n", " | base\n", " | Base object if memory is from some other object.\n", " | \n", " | Examples\n", " | --------\n", " | The base of an array that owns its memory is None:\n", " | \n", " | >>> x = np.array([1,2,3,4])\n", " | >>> x.base is None\n", " | True\n", " | \n", " | Slicing creates a view, whose memory is shared with x:\n", " | \n", " | >>> y = x[2:]\n", " | >>> y.base is x\n", " | True\n", " | \n", " | ctypes\n", " | An object to simplify the interaction of the array with the ctypes\n", " | module.\n", " | \n", " | This attribute creates an object that makes it easier to use arrays\n", " | when calling shared libraries with the ctypes module. The returned\n", " | object has, among others, data, shape, and strides attributes (see\n", " | Notes below) which themselves return ctypes objects that can be used\n", " | as arguments to a shared library.\n", " | \n", " | Parameters\n", " | ----------\n", " | None\n", " | \n", " | Returns\n", " | -------\n", " | c : Python object\n", " | Possessing attributes data, shape, strides, etc.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.ctypeslib\n", " | \n", " | Notes\n", " | -----\n", " | Below are the public attributes of this object which were documented\n", " | in \"Guide to NumPy\" (we have omitted undocumented public attributes,\n", " | as well as documented private attributes):\n", " | \n", " | .. autoattribute:: numpy.core._internal._ctypes.data\n", " | :noindex:\n", " | \n", " | .. autoattribute:: numpy.core._internal._ctypes.shape\n", " | :noindex:\n", " | \n", " | .. autoattribute:: numpy.core._internal._ctypes.strides\n", " | :noindex:\n", " | \n", " | .. automethod:: numpy.core._internal._ctypes.data_as\n", " | :noindex:\n", " | \n", " | .. automethod:: numpy.core._internal._ctypes.shape_as\n", " | :noindex:\n", " | \n", " | .. automethod:: numpy.core._internal._ctypes.strides_as\n", " | :noindex:\n", " | \n", " | If the ctypes module is not available, then the ctypes attribute\n", " | of array objects still returns something useful, but ctypes objects\n", " | are not returned and errors may be raised instead. In particular,\n", " | the object will still have the ``as_parameter`` attribute which will\n", " | return an integer equal to the data attribute.\n", " | \n", " | Examples\n", " | --------\n", " | >>> import ctypes\n", " | >>> x = np.array([[0, 1], [2, 3]], dtype=np.int32)\n", " | >>> x\n", " | array([[0, 1],\n", " | [2, 3]], dtype=int32)\n", " | >>> x.ctypes.data\n", " | 31962608 # may vary\n", " | >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32))\n", " | <__main__.LP_c_uint object at 0x7ff2fc1fc200> # may vary\n", " | >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)).contents\n", " | c_uint(0)\n", " | >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint64)).contents\n", " | c_ulong(4294967296)\n", " | >>> x.ctypes.shape\n", " | <numpy.core._internal.c_long_Array_2 object at 0x7ff2fc1fce60> # may vary\n", " | >>> x.ctypes.strides\n", " | <numpy.core._internal.c_long_Array_2 object at 0x7ff2fc1ff320> # may vary\n", " | \n", " | data\n", " | Python buffer object pointing to the start of the array's data.\n", " | \n", " | dtype\n", " | Data-type of the array's elements.\n", " | \n", " | .. warning::\n", " | \n", " | Setting ``arr.dtype`` is discouraged and may be deprecated in the\n", " | future. Setting will replace the ``dtype`` without modifying the\n", " | memory (see also `ndarray.view` and `ndarray.astype`).\n", " | \n", " | Parameters\n", " | ----------\n", " | None\n", " | \n", " | Returns\n", " | -------\n", " | d : numpy dtype object\n", " | \n", " | See Also\n", " | --------\n", " | ndarray.astype : Cast the values contained in the array to a new data-type.\n", " | ndarray.view : Create a view of the same data but a different data-type.\n", " | numpy.dtype\n", " | \n", " | Examples\n", " | --------\n", " | >>> x\n", " | array([[0, 1],\n", " | [2, 3]])\n", " | >>> x.dtype\n", " | dtype('int32')\n", " | >>> type(x.dtype)\n", " | <type 'numpy.dtype'>\n", " | \n", " | flags\n", " | Information about the memory layout of the array.\n", " | \n", " | Attributes\n", " | ----------\n", " | C_CONTIGUOUS (C)\n", " | The data is in a single, C-style contiguous segment.\n", " | F_CONTIGUOUS (F)\n", " | The data is in a single, Fortran-style contiguous segment.\n", " | OWNDATA (O)\n", " | The array owns the memory it uses or borrows it from another object.\n", " | WRITEABLE (W)\n", " | The data area can be written to. Setting this to False locks\n", " | the data, making it read-only. A view (slice, etc.) inherits WRITEABLE\n", " | from its base array at creation time, but a view of a writeable\n", " | array may be subsequently locked while the base array remains writeable.\n", " | (The opposite is not true, in that a view of a locked array may not\n", " | be made writeable. However, currently, locking a base object does not\n", " | lock any views that already reference it, so under that circumstance it\n", " | is possible to alter the contents of a locked array via a previously\n", " | created writeable view onto it.) Attempting to change a non-writeable\n", " | array raises a RuntimeError exception.\n", " | ALIGNED (A)\n", " | The data and all elements are aligned appropriately for the hardware.\n", " | WRITEBACKIFCOPY (X)\n", " | This array is a copy of some other array. The C-API function\n", " | PyArray_ResolveWritebackIfCopy must be called before deallocating\n", " | to the base array will be updated with the contents of this array.\n", " | FNC\n", " | F_CONTIGUOUS and not C_CONTIGUOUS.\n", " | FORC\n", " | F_CONTIGUOUS or C_CONTIGUOUS (one-segment test).\n", " | BEHAVED (B)\n", " | ALIGNED and WRITEABLE.\n", " | CARRAY (CA)\n", " | BEHAVED and C_CONTIGUOUS.\n", " | FARRAY (FA)\n", " | BEHAVED and F_CONTIGUOUS and not C_CONTIGUOUS.\n", " | \n", " | Notes\n", " | -----\n", " | The `flags` object can be accessed dictionary-like (as in ``a.flags['WRITEABLE']``),\n", " | or by using lowercased attribute names (as in ``a.flags.writeable``). Short flag\n", " | names are only supported in dictionary access.\n", " | \n", " | Only the WRITEBACKIFCOPY, WRITEABLE, and ALIGNED flags can be\n", " | changed by the user, via direct assignment to the attribute or dictionary\n", " | entry, or by calling `ndarray.setflags`.\n", " | \n", " | The array flags cannot be set arbitrarily:\n", " | \n", " | - WRITEBACKIFCOPY can only be set ``False``.\n", " | - ALIGNED can only be set ``True`` if the data is truly aligned.\n", " | - WRITEABLE can only be set ``True`` if the array owns its own memory\n", " | or the ultimate owner of the memory exposes a writeable buffer\n", " | interface or is a string.\n", " | \n", " | Arrays can be both C-style and Fortran-style contiguous simultaneously.\n", " | This is clear for 1-dimensional arrays, but can also be true for higher\n", " | dimensional arrays.\n", " | \n", " | Even for contiguous arrays a stride for a given dimension\n", " | ``arr.strides[dim]`` may be *arbitrary* if ``arr.shape[dim] == 1``\n", " | or the array has no elements.\n", " | It does *not* generally hold that ``self.strides[-1] == self.itemsize``\n", " | for C-style contiguous arrays or ``self.strides[0] == self.itemsize`` for\n", " | Fortran-style contiguous arrays is true.\n", " | \n", " | flat\n", " | A 1-D iterator over the array.\n", " | \n", " | This is a `numpy.flatiter` instance, which acts similarly to, but is not\n", " | a subclass of, Python's built-in iterator object.\n", " | \n", " | See Also\n", " | --------\n", " | flatten : Return a copy of the array collapsed into one dimension.\n", " | \n", " | flatiter\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.arange(1, 7).reshape(2, 3)\n", " | >>> x\n", " | array([[1, 2, 3],\n", " | [4, 5, 6]])\n", " | >>> x.flat[3]\n", " | 4\n", " | >>> x.T\n", " | array([[1, 4],\n", " | [2, 5],\n", " | [3, 6]])\n", " | >>> x.T.flat[3]\n", " | 5\n", " | >>> type(x.flat)\n", " | <class 'numpy.flatiter'>\n", " | \n", " | An assignment example:\n", " | \n", " | >>> x.flat = 3; x\n", " | array([[3, 3, 3],\n", " | [3, 3, 3]])\n", " | >>> x.flat[[1,4]] = 1; x\n", " | array([[3, 1, 3],\n", " | [3, 1, 3]])\n", " | \n", " | imag\n", " | The imaginary part of the array.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.sqrt([1+0j, 0+1j])\n", " | >>> x.imag\n", " | array([ 0. , 0.70710678])\n", " | >>> x.imag.dtype\n", " | dtype('float64')\n", " | \n", " | itemsize\n", " | Length of one array element in bytes.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([1,2,3], dtype=np.float64)\n", " | >>> x.itemsize\n", " | 8\n", " | >>> x = np.array([1,2,3], dtype=np.complex128)\n", " | >>> x.itemsize\n", " | 16\n", " | \n", " | nbytes\n", " | Total bytes consumed by the elements of the array.\n", " | \n", " | Notes\n", " | -----\n", " | Does not include memory consumed by non-element attributes of the\n", " | array object.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.zeros((3,5,2), dtype=np.complex128)\n", " | >>> x.nbytes\n", " | 480\n", " | >>> np.prod(x.shape) * x.itemsize\n", " | 480\n", " | \n", " | ndim\n", " | Number of array dimensions.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([1, 2, 3])\n", " | >>> x.ndim\n", " | 1\n", " | >>> y = np.zeros((2, 3, 4))\n", " | >>> y.ndim\n", " | 3\n", " | \n", " | real\n", " | The real part of the array.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.sqrt([1+0j, 0+1j])\n", " | >>> x.real\n", " | array([ 1. , 0.70710678])\n", " | >>> x.real.dtype\n", " | dtype('float64')\n", " | \n", " | See Also\n", " | --------\n", " | numpy.real : equivalent function\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | The shape property is usually used to get the current shape of an array,\n", " | but may also be used to reshape the array in-place by assigning a tuple of\n", " | array dimensions to it. As with `numpy.reshape`, one of the new shape\n", " | dimensions can be -1, in which case its value is inferred from the size of\n", " | the array and the remaining dimensions. Reshaping an array in-place will\n", " | fail if a copy is required.\n", " | \n", " | .. warning::\n", " | \n", " | Setting ``arr.shape`` is discouraged and may be deprecated in the\n", " | future. Using `ndarray.reshape` is the preferred approach.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([1, 2, 3, 4])\n", " | >>> x.shape\n", " | (4,)\n", " | >>> y = np.zeros((2, 3, 4))\n", " | >>> y.shape\n", " | (2, 3, 4)\n", " | >>> y.shape = (3, 8)\n", " | >>> y\n", " | array([[ 0., 0., 0., 0., 0., 0., 0., 0.],\n", " | [ 0., 0., 0., 0., 0., 0., 0., 0.],\n", " | [ 0., 0., 0., 0., 0., 0., 0., 0.]])\n", " | >>> y.shape = (3, 6)\n", " | Traceback (most recent call last):\n", " | File \"<stdin>\", line 1, in <module>\n", " | ValueError: total size of new array must be unchanged\n", " | >>> np.zeros((4,2))[::2].shape = (-1,)\n", " | Traceback (most recent call last):\n", " | File \"<stdin>\", line 1, in <module>\n", " | AttributeError: Incompatible shape for in-place modification. Use\n", " | `.reshape()` to make a copy with the desired shape.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.shape : Equivalent getter function.\n", " | numpy.reshape : Function similar to setting ``shape``.\n", " | ndarray.reshape : Method similar to setting ``shape``.\n", " | \n", " | size\n", " | Number of elements in the array.\n", " | \n", " | Equal to ``np.prod(a.shape)``, i.e., the product of the array's\n", " | dimensions.\n", " | \n", " | Notes\n", " | -----\n", " | `a.size` returns a standard arbitrary precision Python integer. This\n", " | may not be the case with other methods of obtaining the same value\n", " | (like the suggested ``np.prod(a.shape)``, which returns an instance\n", " | of ``np.int_``), and may be relevant if the value is used further in\n", " | calculations that may overflow a fixed size integer type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.zeros((3, 5, 2), dtype=np.complex128)\n", " | >>> x.size\n", " | 30\n", " | >>> np.prod(x.shape)\n", " | 30\n", " | \n", " | strides\n", " | Tuple of bytes to step in each dimension when traversing an array.\n", " | \n", " | The byte offset of element ``(i[0], i[1], ..., i[n])`` in an array `a`\n", " | is::\n", " | \n", " | offset = sum(np.array(i) * a.strides)\n", " | \n", " | A more detailed explanation of strides can be found in the\n", " | \"ndarray.rst\" file in the NumPy reference guide.\n", " | \n", " | .. warning::\n", " | \n", " | Setting ``arr.strides`` is discouraged and may be deprecated in the\n", " | future. `numpy.lib.stride_tricks.as_strided` should be preferred\n", " | to create a new view of the same data in a safer way.\n", " | \n", " | Notes\n", " | -----\n", " | Imagine an array of 32-bit integers (each 4 bytes)::\n", " | \n", " | x = np.array([[0, 1, 2, 3, 4],\n", " | [5, 6, 7, 8, 9]], dtype=np.int32)\n", " | \n", " | This array is stored in memory as 40 bytes, one after the other\n", " | (known as a contiguous block of memory). The strides of an array tell\n", " | us how many bytes we have to skip in memory to move to the next position\n", " | along a certain axis. For example, we have to skip 4 bytes (1 value) to\n", " | move to the next column, but 20 bytes (5 values) to get to the same\n", " | position in the next row. As such, the strides for the array `x` will be\n", " | ``(20, 4)``.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.lib.stride_tricks.as_strided\n", " | \n", " | Examples\n", " | --------\n", " | >>> y = np.reshape(np.arange(2*3*4), (2,3,4))\n", " | >>> y\n", " | array([[[ 0, 1, 2, 3],\n", " | [ 4, 5, 6, 7],\n", " | [ 8, 9, 10, 11]],\n", " | [[12, 13, 14, 15],\n", " | [16, 17, 18, 19],\n", " | [20, 21, 22, 23]]])\n", " | >>> y.strides\n", " | (48, 16, 4)\n", " | >>> y[1,1,1]\n", " | 17\n", " | >>> offset=sum(y.strides * np.array((1,1,1)))\n", " | >>> offset/y.itemsize\n", " | 17\n", " | \n", " | >>> x = np.reshape(np.arange(5*6*7*8), (5,6,7,8)).transpose(2,3,1,0)\n", " | >>> x.strides\n", " | (32, 4, 224, 1344)\n", " | >>> i = np.array([3,5,2,2])\n", " | >>> offset = sum(i * x.strides)\n", " | >>> x[3,5,2,2]\n", " | 813\n", " | >>> offset / x.itemsize\n", " | 813\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data and other attributes defined here:\n", " | \n", " | __hash__ = None\n", " \n", " class ndenumerate(builtins.object)\n", " | ndenumerate(arr)\n", " | \n", " | Multidimensional index iterator.\n", " | \n", " | Return an iterator yielding pairs of array coordinates and values.\n", " | \n", " | Parameters\n", " | ----------\n", " | arr : ndarray\n", " | Input array.\n", " | \n", " | See Also\n", " | --------\n", " | ndindex, flatiter\n", " | \n", " | Examples\n", " | --------\n", " | >>> a = np.array([[1, 2], [3, 4]])\n", " | >>> for index, x in np.ndenumerate(a):\n", " | ... print(index, x)\n", " | (0, 0) 1\n", " | (0, 1) 2\n", " | (1, 0) 3\n", " | (1, 1) 4\n", " | \n", " | Methods defined here:\n", " | \n", " | __init__(self, arr)\n", " | Initialize self. See help(type(self)) for accurate signature.\n", " | \n", " | __iter__(self)\n", " | \n", " | __next__(self)\n", " | Standard iterator method, returns the index tuple and array value.\n", " | \n", " | Returns\n", " | -------\n", " | coords : tuple of ints\n", " | The indices of the current iteration.\n", " | val : scalar\n", " | The array element of the current iteration.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors defined here:\n", " | \n", " | __dict__\n", " | dictionary for instance variables (if defined)\n", " | \n", " | __weakref__\n", " | list of weak references to the object (if defined)\n", " \n", " class ndindex(builtins.object)\n", " | ndindex(*shape)\n", " | \n", " | An N-dimensional iterator object to index arrays.\n", " | \n", " | Given the shape of an array, an `ndindex` instance iterates over\n", " | the N-dimensional index of the array. At each iteration a tuple\n", " | of indices is returned, the last dimension is iterated over first.\n", " | \n", " | Parameters\n", " | ----------\n", " | shape : ints, or a single tuple of ints\n", " | The size of each dimension of the array can be passed as\n", " | individual parameters or as the elements of a tuple.\n", " | \n", " | See Also\n", " | --------\n", " | ndenumerate, flatiter\n", " | \n", " | Examples\n", " | --------\n", " | Dimensions as individual arguments\n", " | \n", " | >>> for index in np.ndindex(3, 2, 1):\n", " | ... print(index)\n", " | (0, 0, 0)\n", " | (0, 1, 0)\n", " | (1, 0, 0)\n", " | (1, 1, 0)\n", " | (2, 0, 0)\n", " | (2, 1, 0)\n", " | \n", " | Same dimensions - but in a tuple ``(3, 2, 1)``\n", " | \n", " | >>> for index in np.ndindex((3, 2, 1)):\n", " | ... print(index)\n", " | (0, 0, 0)\n", " | (0, 1, 0)\n", " | (1, 0, 0)\n", " | (1, 1, 0)\n", " | (2, 0, 0)\n", " | (2, 1, 0)\n", " | \n", " | Methods defined here:\n", " | \n", " | __init__(self, *shape)\n", " | Initialize self. See help(type(self)) for accurate signature.\n", " | \n", " | __iter__(self)\n", " | \n", " | __next__(self)\n", " | Standard iterator method, updates the index and returns the index\n", " | tuple.\n", " | \n", " | Returns\n", " | -------\n", " | val : tuple of ints\n", " | Returns a tuple containing the indices of the current\n", " | iteration.\n", " | \n", " | ndincr(self)\n", " | Increment the multi-dimensional index by one.\n", " | \n", " | This method is for backward compatibility only: do not use.\n", " | \n", " | .. deprecated:: 1.20.0\n", " | This method has been advised against since numpy 1.8.0, but only\n", " | started emitting DeprecationWarning as of this version.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors defined here:\n", " | \n", " | __dict__\n", " | dictionary for instance variables (if defined)\n", " | \n", " | __weakref__\n", " | list of weak references to the object (if defined)\n", " \n", " class nditer(builtins.object)\n", " | nditer(op, flags=None, op_flags=None, op_dtypes=None, order='K', casting='safe', op_axes=None, itershape=None, buffersize=0)\n", " | \n", " | Efficient multi-dimensional iterator object to iterate over arrays.\n", " | To get started using this object, see the\n", " | :ref:`introductory guide to array iteration <arrays.nditer>`.\n", " | \n", " | Parameters\n", " | ----------\n", " | op : ndarray or sequence of array_like\n", " | The array(s) to iterate over.\n", " | \n", " | flags : sequence of str, optional\n", " | Flags to control the behavior of the iterator.\n", " | \n", " | * ``buffered`` enables buffering when required.\n", " | * ``c_index`` causes a C-order index to be tracked.\n", " | * ``f_index`` causes a Fortran-order index to be tracked.\n", " | * ``multi_index`` causes a multi-index, or a tuple of indices\n", " | with one per iteration dimension, to be tracked.\n", " | * ``common_dtype`` causes all the operands to be converted to\n", " | a common data type, with copying or buffering as necessary.\n", " | * ``copy_if_overlap`` causes the iterator to determine if read\n", " | operands have overlap with write operands, and make temporary\n", " | copies as necessary to avoid overlap. False positives (needless\n", " | copying) are possible in some cases.\n", " | * ``delay_bufalloc`` delays allocation of the buffers until\n", " | a reset() call is made. Allows ``allocate`` operands to\n", " | be initialized before their values are copied into the buffers.\n", " | * ``external_loop`` causes the ``values`` given to be\n", " | one-dimensional arrays with multiple values instead of\n", " | zero-dimensional arrays.\n", " | * ``grow_inner`` allows the ``value`` array sizes to be made\n", " | larger than the buffer size when both ``buffered`` and\n", " | ``external_loop`` is used.\n", " | * ``ranged`` allows the iterator to be restricted to a sub-range\n", " | of the iterindex values.\n", " | * ``refs_ok`` enables iteration of reference types, such as\n", " | object arrays.\n", " | * ``reduce_ok`` enables iteration of ``readwrite`` operands\n", " | which are broadcasted, also known as reduction operands.\n", " | * ``zerosize_ok`` allows `itersize` to be zero.\n", " | op_flags : list of list of str, optional\n", " | This is a list of flags for each operand. At minimum, one of\n", " | ``readonly``, ``readwrite``, or ``writeonly`` must be specified.\n", " | \n", " | * ``readonly`` indicates the operand will only be read from.\n", " | * ``readwrite`` indicates the operand will be read from and written to.\n", " | * ``writeonly`` indicates the operand will only be written to.\n", " | * ``no_broadcast`` prevents the operand from being broadcasted.\n", " | * ``contig`` forces the operand data to be contiguous.\n", " | * ``aligned`` forces the operand data to be aligned.\n", " | * ``nbo`` forces the operand data to be in native byte order.\n", " | * ``copy`` allows a temporary read-only copy if required.\n", " | * ``updateifcopy`` allows a temporary read-write copy if required.\n", " | * ``allocate`` causes the array to be allocated if it is None\n", " | in the ``op`` parameter.\n", " | * ``no_subtype`` prevents an ``allocate`` operand from using a subtype.\n", " | * ``arraymask`` indicates that this operand is the mask to use\n", " | for selecting elements when writing to operands with the\n", " | 'writemasked' flag set. The iterator does not enforce this,\n", " | but when writing from a buffer back to the array, it only\n", " | copies those elements indicated by this mask.\n", " | * ``writemasked`` indicates that only elements where the chosen\n", " | ``arraymask`` operand is True will be written to.\n", " | * ``overlap_assume_elementwise`` can be used to mark operands that are\n", " | accessed only in the iterator order, to allow less conservative\n", " | copying when ``copy_if_overlap`` is present.\n", " | op_dtypes : dtype or tuple of dtype(s), optional\n", " | The required data type(s) of the operands. If copying or buffering\n", " | is enabled, the data will be converted to/from their original types.\n", " | order : {'C', 'F', 'A', 'K'}, optional\n", " | Controls the iteration order. 'C' means C order, 'F' means\n", " | Fortran order, 'A' means 'F' order if all the arrays are Fortran\n", " | contiguous, 'C' order otherwise, and 'K' means as close to the\n", " | order the array elements appear in memory as possible. This also\n", " | affects the element memory order of ``allocate`` operands, as they\n", " | are allocated to be compatible with iteration order.\n", " | Default is 'K'.\n", " | casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional\n", " | Controls what kind of data casting may occur when making a copy\n", " | or buffering. Setting this to 'unsafe' is not recommended,\n", " | as it can adversely affect accumulations.\n", " | \n", " | * 'no' means the data types should not be cast at all.\n", " | * 'equiv' means only byte-order changes are allowed.\n", " | * 'safe' means only casts which can preserve values are allowed.\n", " | * 'same_kind' means only safe casts or casts within a kind,\n", " | like float64 to float32, are allowed.\n", " | * 'unsafe' means any data conversions may be done.\n", " | op_axes : list of list of ints, optional\n", " | If provided, is a list of ints or None for each operands.\n", " | The list of axes for an operand is a mapping from the dimensions\n", " | of the iterator to the dimensions of the operand. A value of\n", " | -1 can be placed for entries, causing that dimension to be\n", " | treated as `newaxis`.\n", " | itershape : tuple of ints, optional\n", " | The desired shape of the iterator. This allows ``allocate`` operands\n", " | with a dimension mapped by op_axes not corresponding to a dimension\n", " | of a different operand to get a value not equal to 1 for that\n", " | dimension.\n", " | buffersize : int, optional\n", " | When buffering is enabled, controls the size of the temporary\n", " | buffers. Set to 0 for the default value.\n", " | \n", " | Attributes\n", " | ----------\n", " | dtypes : tuple of dtype(s)\n", " | The data types of the values provided in `value`. This may be\n", " | different from the operand data types if buffering is enabled.\n", " | Valid only before the iterator is closed.\n", " | finished : bool\n", " | Whether the iteration over the operands is finished or not.\n", " | has_delayed_bufalloc : bool\n", " | If True, the iterator was created with the ``delay_bufalloc`` flag,\n", " | and no reset() function was called on it yet.\n", " | has_index : bool\n", " | If True, the iterator was created with either the ``c_index`` or\n", " | the ``f_index`` flag, and the property `index` can be used to\n", " | retrieve it.\n", " | has_multi_index : bool\n", " | If True, the iterator was created with the ``multi_index`` flag,\n", " | and the property `multi_index` can be used to retrieve it.\n", " | index\n", " | When the ``c_index`` or ``f_index`` flag was used, this property\n", " | provides access to the index. Raises a ValueError if accessed\n", " | and ``has_index`` is False.\n", " | iterationneedsapi : bool\n", " | Whether iteration requires access to the Python API, for example\n", " | if one of the operands is an object array.\n", " | iterindex : int\n", " | An index which matches the order of iteration.\n", " | itersize : int\n", " | Size of the iterator.\n", " | itviews\n", " | Structured view(s) of `operands` in memory, matching the reordered\n", " | and optimized iterator access pattern. Valid only before the iterator\n", " | is closed.\n", " | multi_index\n", " | When the ``multi_index`` flag was used, this property\n", " | provides access to the index. Raises a ValueError if accessed\n", " | accessed and ``has_multi_index`` is False.\n", " | ndim : int\n", " | The dimensions of the iterator.\n", " | nop : int\n", " | The number of iterator operands.\n", " | operands : tuple of operand(s)\n", " | The array(s) to be iterated over. Valid only before the iterator is\n", " | closed.\n", " | shape : tuple of ints\n", " | Shape tuple, the shape of the iterator.\n", " | value\n", " | Value of ``operands`` at current iteration. Normally, this is a\n", " | tuple of array scalars, but if the flag ``external_loop`` is used,\n", " | it is a tuple of one dimensional arrays.\n", " | \n", " | Notes\n", " | -----\n", " | `nditer` supersedes `flatiter`. The iterator implementation behind\n", " | `nditer` is also exposed by the NumPy C API.\n", " | \n", " | The Python exposure supplies two iteration interfaces, one which follows\n", " | the Python iterator protocol, and another which mirrors the C-style\n", " | do-while pattern. The native Python approach is better in most cases, but\n", " | if you need the coordinates or index of an iterator, use the C-style pattern.\n", " | \n", " | Examples\n", " | --------\n", " | Here is how we might write an ``iter_add`` function, using the\n", " | Python iterator protocol:\n", " | \n", " | >>> def iter_add_py(x, y, out=None):\n", " | ... addop = np.add\n", " | ... it = np.nditer([x, y, out], [],\n", " | ... [['readonly'], ['readonly'], ['writeonly','allocate']])\n", " | ... with it:\n", " | ... for (a, b, c) in it:\n", " | ... addop(a, b, out=c)\n", " | ... return it.operands[2]\n", " | \n", " | Here is the same function, but following the C-style pattern:\n", " | \n", " | >>> def iter_add(x, y, out=None):\n", " | ... addop = np.add\n", " | ... it = np.nditer([x, y, out], [],\n", " | ... [['readonly'], ['readonly'], ['writeonly','allocate']])\n", " | ... with it:\n", " | ... while not it.finished:\n", " | ... addop(it[0], it[1], out=it[2])\n", " | ... it.iternext()\n", " | ... return it.operands[2]\n", " | \n", " | Here is an example outer product function:\n", " | \n", " | >>> def outer_it(x, y, out=None):\n", " | ... mulop = np.multiply\n", " | ... it = np.nditer([x, y, out], ['external_loop'],\n", " | ... [['readonly'], ['readonly'], ['writeonly', 'allocate']],\n", " | ... op_axes=[list(range(x.ndim)) + [-1] * y.ndim,\n", " | ... [-1] * x.ndim + list(range(y.ndim)),\n", " | ... None])\n", " | ... with it:\n", " | ... for (a, b, c) in it:\n", " | ... mulop(a, b, out=c)\n", " | ... return it.operands[2]\n", " | \n", " | >>> a = np.arange(2)+1\n", " | >>> b = np.arange(3)+1\n", " | >>> outer_it(a,b)\n", " | array([[1, 2, 3],\n", " | [2, 4, 6]])\n", " | \n", " | Here is an example function which operates like a \"lambda\" ufunc:\n", " | \n", " | >>> def luf(lamdaexpr, *args, **kwargs):\n", " | ... '''luf(lambdaexpr, op1, ..., opn, out=None, order='K', casting='safe', buffersize=0)'''\n", " | ... nargs = len(args)\n", " | ... op = (kwargs.get('out',None),) + args\n", " | ... it = np.nditer(op, ['buffered','external_loop'],\n", " | ... [['writeonly','allocate','no_broadcast']] +\n", " | ... [['readonly','nbo','aligned']]*nargs,\n", " | ... order=kwargs.get('order','K'),\n", " | ... casting=kwargs.get('casting','safe'),\n", " | ... buffersize=kwargs.get('buffersize',0))\n", " | ... while not it.finished:\n", " | ... it[0] = lamdaexpr(*it[1:])\n", " | ... it.iternext()\n", " | ... return it.operands[0]\n", " | \n", " | >>> a = np.arange(5)\n", " | >>> b = np.ones(5)\n", " | >>> luf(lambda i,j:i*i + j/2, a, b)\n", " | array([ 0.5, 1.5, 4.5, 9.5, 16.5])\n", " | \n", " | If operand flags ``\"writeonly\"`` or ``\"readwrite\"`` are used the\n", " | operands may be views into the original data with the\n", " | `WRITEBACKIFCOPY` flag. In this case `nditer` must be used as a\n", " | context manager or the `nditer.close` method must be called before\n", " | using the result. The temporary data will be written back to the\n", " | original data when the `__exit__` function is called but not before:\n", " | \n", " | >>> a = np.arange(6, dtype='i4')[::-2]\n", " | >>> with np.nditer(a, [],\n", " | ... [['writeonly', 'updateifcopy']],\n", " | ... casting='unsafe',\n", " | ... op_dtypes=[np.dtype('f4')]) as i:\n", " | ... x = i.operands[0]\n", " | ... x[:] = [-1, -2, -3]\n", " | ... # a still unchanged here\n", " | >>> a, x\n", " | (array([-1, -2, -3], dtype=int32), array([-1., -2., -3.], dtype=float32))\n", " | \n", " | It is important to note that once the iterator is exited, dangling\n", " | references (like `x` in the example) may or may not share data with\n", " | the original data `a`. If writeback semantics were active, i.e. if\n", " | `x.base.flags.writebackifcopy` is `True`, then exiting the iterator\n", " | will sever the connection between `x` and `a`, writing to `x` will\n", " | no longer write to `a`. If writeback semantics are not active, then\n", " | `x.data` will still point at some part of `a.data`, and writing to\n", " | one will affect the other.\n", " | \n", " | Context management and the `close` method appeared in version 1.15.0.\n", " | \n", " | Methods defined here:\n", " | \n", " | __copy__(...)\n", " | \n", " | __delitem__(self, key, /)\n", " | Delete self[key].\n", " | \n", " | __enter__(...)\n", " | \n", " | __exit__(...)\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __init__(self, /, *args, **kwargs)\n", " | Initialize self. See help(type(self)) for accurate signature.\n", " | \n", " | __iter__(self, /)\n", " | Implement iter(self).\n", " | \n", " | __len__(self, /)\n", " | Return len(self).\n", " | \n", " | __next__(self, /)\n", " | Implement next(self).\n", " | \n", " | __setitem__(self, key, value, /)\n", " | Set self[key] to value.\n", " | \n", " | close(...)\n", " | close()\n", " | \n", " | Resolve all writeback semantics in writeable operands.\n", " | \n", " | .. versionadded:: 1.15.0\n", " | \n", " | See Also\n", " | --------\n", " | \n", " | :ref:`nditer-context-manager`\n", " | \n", " | copy(...)\n", " | copy()\n", " | \n", " | Get a copy of the iterator in its current state.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.arange(10)\n", " | >>> y = x + 1\n", " | >>> it = np.nditer([x, y])\n", " | >>> next(it)\n", " | (array(0), array(1))\n", " | >>> it2 = it.copy()\n", " | >>> next(it2)\n", " | (array(1), array(2))\n", " | \n", " | debug_print(...)\n", " | debug_print()\n", " | \n", " | Print the current state of the `nditer` instance and debug info to stdout.\n", " | \n", " | enable_external_loop(...)\n", " | enable_external_loop()\n", " | \n", " | When the \"external_loop\" was not used during construction, but\n", " | is desired, this modifies the iterator to behave as if the flag\n", " | was specified.\n", " | \n", " | iternext(...)\n", " | iternext()\n", " | \n", " | Check whether iterations are left, and perform a single internal iteration\n", " | without returning the result. Used in the C-style pattern do-while\n", " | pattern. For an example, see `nditer`.\n", " | \n", " | Returns\n", " | -------\n", " | iternext : bool\n", " | Whether or not there are iterations left.\n", " | \n", " | remove_axis(...)\n", " | remove_axis(i, /)\n", " | \n", " | Removes axis `i` from the iterator. Requires that the flag \"multi_index\"\n", " | be enabled.\n", " | \n", " | remove_multi_index(...)\n", " | remove_multi_index()\n", " | \n", " | When the \"multi_index\" flag was specified, this removes it, allowing\n", " | the internal iteration structure to be optimized further.\n", " | \n", " | reset(...)\n", " | reset()\n", " | \n", " | Reset the iterator to its initial state.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors defined here:\n", " | \n", " | dtypes\n", " | \n", " | finished\n", " | \n", " | has_delayed_bufalloc\n", " | \n", " | has_index\n", " | \n", " | has_multi_index\n", " | \n", " | index\n", " | \n", " | iterationneedsapi\n", " | \n", " | iterindex\n", " | \n", " | iterrange\n", " | \n", " | itersize\n", " | \n", " | itviews\n", " | \n", " | multi_index\n", " | \n", " | ndim\n", " | \n", " | nop\n", " | \n", " | operands\n", " | operands[`Slice`]\n", " | \n", " | The array(s) to be iterated over. Valid only before the iterator is closed.\n", " | \n", " | shape\n", " | \n", " | value\n", " \n", " class number(generic)\n", " | Abstract base class of all numeric scalar types.\n", " | \n", " | Method resolution order:\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data and other attributes inherited from generic:\n", " | \n", " | __hash__ = None\n", " \n", " class object_(generic)\n", " | Any Python object.\n", " | \n", " | :Character code: ``'O'``\n", " | \n", " | Method resolution order:\n", " | object_\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __call__(self, /, *args, **kwargs)\n", " | Call self as a function.\n", " | \n", " | __contains__(self, key, /)\n", " | Return key in self.\n", " | \n", " | __delattr__(self, name, /)\n", " | Implement delattr(self, name).\n", " | \n", " | __delitem__(self, key, /)\n", " | Delete self[key].\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __getattribute__(self, name, /)\n", " | Return getattr(self, name).\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __iadd__(self, value, /)\n", " | Implement self+=value.\n", " | \n", " | __imul__(self, value, /)\n", " | Implement self*=value.\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __len__(self, /)\n", " | Return len(self).\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __setattr__(self, name, value, /)\n", " | Implement setattr(self, name, value).\n", " | \n", " | __setitem__(self, key, value, /)\n", " | Set self[key] to value.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " class poly1d(builtins.object)\n", " | poly1d(c_or_r, r=False, variable=None)\n", " | \n", " | A one-dimensional polynomial class.\n", " | \n", " | .. note::\n", " | This forms part of the old polynomial API. Since version 1.4, the\n", " | new polynomial API defined in `numpy.polynomial` is preferred.\n", " | A summary of the differences can be found in the\n", " | :doc:`transition guide </reference/routines.polynomials>`.\n", " | \n", " | A convenience class, used to encapsulate \"natural\" operations on\n", " | polynomials so that said operations may take on their customary\n", " | form in code (see Examples).\n", " | \n", " | Parameters\n", " | ----------\n", " | c_or_r : array_like\n", " | The polynomial's coefficients, in decreasing powers, or if\n", " | the value of the second parameter is True, the polynomial's\n", " | roots (values where the polynomial evaluates to 0). For example,\n", " | ``poly1d([1, 2, 3])`` returns an object that represents\n", " | :math:`x^2 + 2x + 3`, whereas ``poly1d([1, 2, 3], True)`` returns\n", " | one that represents :math:`(x-1)(x-2)(x-3) = x^3 - 6x^2 + 11x -6`.\n", " | r : bool, optional\n", " | If True, `c_or_r` specifies the polynomial's roots; the default\n", " | is False.\n", " | variable : str, optional\n", " | Changes the variable used when printing `p` from `x` to `variable`\n", " | (see Examples).\n", " | \n", " | Examples\n", " | --------\n", " | Construct the polynomial :math:`x^2 + 2x + 3`:\n", " | \n", " | >>> p = np.poly1d([1, 2, 3])\n", " | >>> print(np.poly1d(p))\n", " | 2\n", " | 1 x + 2 x + 3\n", " | \n", " | Evaluate the polynomial at :math:`x = 0.5`:\n", " | \n", " | >>> p(0.5)\n", " | 4.25\n", " | \n", " | Find the roots:\n", " | \n", " | >>> p.r\n", " | array([-1.+1.41421356j, -1.-1.41421356j])\n", " | >>> p(p.r)\n", " | array([ -4.44089210e-16+0.j, -4.44089210e-16+0.j]) # may vary\n", " | \n", " | These numbers in the previous line represent (0, 0) to machine precision\n", " | \n", " | Show the coefficients:\n", " | \n", " | >>> p.c\n", " | array([1, 2, 3])\n", " | \n", " | Display the order (the leading zero-coefficients are removed):\n", " | \n", " | >>> p.order\n", " | 2\n", " | \n", " | Show the coefficient of the k-th power in the polynomial\n", " | (which is equivalent to ``p.c[-(i+1)]``):\n", " | \n", " | >>> p[1]\n", " | 2\n", " | \n", " | Polynomials can be added, subtracted, multiplied, and divided\n", " | (returns quotient and remainder):\n", " | \n", " | >>> p * p\n", " | poly1d([ 1, 4, 10, 12, 9])\n", " | \n", " | >>> (p**3 + 4) / p\n", " | (poly1d([ 1., 4., 10., 12., 9.]), poly1d([4.]))\n", " | \n", " | ``asarray(p)`` gives the coefficient array, so polynomials can be\n", " | used in all functions that accept arrays:\n", " | \n", " | >>> p**2 # square of polynomial\n", " | poly1d([ 1, 4, 10, 12, 9])\n", " | \n", " | >>> np.square(p) # square of individual coefficients\n", " | array([1, 4, 9])\n", " | \n", " | The variable used in the string representation of `p` can be modified,\n", " | using the `variable` parameter:\n", " | \n", " | >>> p = np.poly1d([1,2,3], variable='z')\n", " | >>> print(p)\n", " | 2\n", " | 1 z + 2 z + 3\n", " | \n", " | Construct a polynomial from its roots:\n", " | \n", " | >>> np.poly1d([1, 2], True)\n", " | poly1d([ 1., -3., 2.])\n", " | \n", " | This is the same polynomial as obtained by:\n", " | \n", " | >>> np.poly1d([1, -1]) * np.poly1d([1, -2])\n", " | poly1d([ 1, -3, 2])\n", " | \n", " | Methods defined here:\n", " | \n", " | __add__(self, other)\n", " | \n", " | __array__(self, t=None)\n", " | \n", " | __call__(self, val)\n", " | Call self as a function.\n", " | \n", " | __div__(self, other)\n", " | \n", " | __eq__(self, other)\n", " | Return self==value.\n", " | \n", " | __getitem__(self, val)\n", " | \n", " | __init__(self, c_or_r, r=False, variable=None)\n", " | Initialize self. See help(type(self)) for accurate signature.\n", " | \n", " | __iter__(self)\n", " | \n", " | __len__(self)\n", " | \n", " | __mul__(self, other)\n", " | \n", " | __ne__(self, other)\n", " | Return self!=value.\n", " | \n", " | __neg__(self)\n", " | \n", " | __pos__(self)\n", " | \n", " | __pow__(self, val)\n", " | \n", " | __radd__(self, other)\n", " | \n", " | __rdiv__(self, other)\n", " | \n", " | __repr__(self)\n", " | Return repr(self).\n", " | \n", " | __rmul__(self, other)\n", " | \n", " | __rsub__(self, other)\n", " | \n", " | __rtruediv__ = __rdiv__(self, other)\n", " | \n", " | __setitem__(self, key, val)\n", " | \n", " | __str__(self)\n", " | Return str(self).\n", " | \n", " | __sub__(self, other)\n", " | \n", " | __truediv__ = __div__(self, other)\n", " | \n", " | deriv(self, m=1)\n", " | Return a derivative of this polynomial.\n", " | \n", " | Refer to `polyder` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | polyder : equivalent function\n", " | \n", " | integ(self, m=1, k=0)\n", " | Return an antiderivative (indefinite integral) of this polynomial.\n", " | \n", " | Refer to `polyint` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | polyint : equivalent function\n", " | \n", " | ----------------------------------------------------------------------\n", " | Readonly properties defined here:\n", " | \n", " | o\n", " | The order or degree of the polynomial\n", " | \n", " | order\n", " | The order or degree of the polynomial\n", " | \n", " | r\n", " | The roots of the polynomial, where self(x) == 0\n", " | \n", " | roots\n", " | The roots of the polynomial, where self(x) == 0\n", " | \n", " | variable\n", " | The name of the polynomial variable\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors defined here:\n", " | \n", " | __dict__\n", " | dictionary for instance variables (if defined)\n", " | \n", " | __weakref__\n", " | list of weak references to the object (if defined)\n", " | \n", " | c\n", " | The polynomial coefficients\n", " | \n", " | coef\n", " | The polynomial coefficients\n", " | \n", " | coefficients\n", " | The polynomial coefficients\n", " | \n", " | coeffs\n", " | The polynomial coefficients\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data and other attributes defined here:\n", " | \n", " | __hash__ = None\n", " \n", " class recarray(ndarray)\n", " | recarray(shape, dtype=None, buf=None, offset=0, strides=None, formats=None, names=None, titles=None, byteorder=None, aligned=False, order='C')\n", " | \n", " | Construct an ndarray that allows field access using attributes.\n", " | \n", " | Arrays may have a data-types containing fields, analogous\n", " | to columns in a spread sheet. An example is ``[(x, int), (y, float)]``,\n", " | where each entry in the array is a pair of ``(int, float)``. Normally,\n", " | these attributes are accessed using dictionary lookups such as ``arr['x']``\n", " | and ``arr['y']``. Record arrays allow the fields to be accessed as members\n", " | of the array, using ``arr.x`` and ``arr.y``.\n", " | \n", " | Parameters\n", " | ----------\n", " | shape : tuple\n", " | Shape of output array.\n", " | dtype : data-type, optional\n", " | The desired data-type. By default, the data-type is determined\n", " | from `formats`, `names`, `titles`, `aligned` and `byteorder`.\n", " | formats : list of data-types, optional\n", " | A list containing the data-types for the different columns, e.g.\n", " | ``['i4', 'f8', 'i4']``. `formats` does *not* support the new\n", " | convention of using types directly, i.e. ``(int, float, int)``.\n", " | Note that `formats` must be a list, not a tuple.\n", " | Given that `formats` is somewhat limited, we recommend specifying\n", " | `dtype` instead.\n", " | names : tuple of str, optional\n", " | The name of each column, e.g. ``('x', 'y', 'z')``.\n", " | buf : buffer, optional\n", " | By default, a new array is created of the given shape and data-type.\n", " | If `buf` is specified and is an object exposing the buffer interface,\n", " | the array will use the memory from the existing buffer. In this case,\n", " | the `offset` and `strides` keywords are available.\n", " | \n", " | Other Parameters\n", " | ----------------\n", " | titles : tuple of str, optional\n", " | Aliases for column names. For example, if `names` were\n", " | ``('x', 'y', 'z')`` and `titles` is\n", " | ``('x_coordinate', 'y_coordinate', 'z_coordinate')``, then\n", " | ``arr['x']`` is equivalent to both ``arr.x`` and ``arr.x_coordinate``.\n", " | byteorder : {'<', '>', '='}, optional\n", " | Byte-order for all fields.\n", " | aligned : bool, optional\n", " | Align the fields in memory as the C-compiler would.\n", " | strides : tuple of ints, optional\n", " | Buffer (`buf`) is interpreted according to these strides (strides\n", " | define how many bytes each array element, row, column, etc.\n", " | occupy in memory).\n", " | offset : int, optional\n", " | Start reading buffer (`buf`) from this offset onwards.\n", " | order : {'C', 'F'}, optional\n", " | Row-major (C-style) or column-major (Fortran-style) order.\n", " | \n", " | Returns\n", " | -------\n", " | rec : recarray\n", " | Empty array of the given shape and type.\n", " | \n", " | See Also\n", " | --------\n", " | core.records.fromrecords : Construct a record array from data.\n", " | record : fundamental data-type for `recarray`.\n", " | format_parser : determine a data-type from formats, names, titles.\n", " | \n", " | Notes\n", " | -----\n", " | This constructor can be compared to ``empty``: it creates a new record\n", " | array but does not fill it with data. To create a record array from data,\n", " | use one of the following methods:\n", " | \n", " | 1. Create a standard ndarray and convert it to a record array,\n", " | using ``arr.view(np.recarray)``\n", " | 2. Use the `buf` keyword.\n", " | 3. Use `np.rec.fromrecords`.\n", " | \n", " | Examples\n", " | --------\n", " | Create an array with two fields, ``x`` and ``y``:\n", " | \n", " | >>> x = np.array([(1.0, 2), (3.0, 4)], dtype=[('x', '<f8'), ('y', '<i8')])\n", " | >>> x\n", " | array([(1., 2), (3., 4)], dtype=[('x', '<f8'), ('y', '<i8')])\n", " | \n", " | >>> x['x']\n", " | array([1., 3.])\n", " | \n", " | View the array as a record array:\n", " | \n", " | >>> x = x.view(np.recarray)\n", " | \n", " | >>> x.x\n", " | array([1., 3.])\n", " | \n", " | >>> x.y\n", " | array([2, 4])\n", " | \n", " | Create a new, empty record array:\n", " | \n", " | >>> np.recarray((2,),\n", " | ... dtype=[('x', int), ('y', float), ('z', int)]) #doctest: +SKIP\n", " | rec.array([(-1073741821, 1.2249118382103472e-301, 24547520),\n", " | (3471280, 1.2134086255804012e-316, 0)],\n", " | dtype=[('x', '<i4'), ('y', '<f8'), ('z', '<i4')])\n", " | \n", " | Method resolution order:\n", " | recarray\n", " | ndarray\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __array_finalize__(self, obj)\n", " | a.__array_finalize__(obj, /)\n", " | \n", " | Present so subclasses can call super. Does nothing.\n", " | \n", " | __getattribute__(self, attr)\n", " | Return getattr(self, name).\n", " | \n", " | __getitem__(self, indx)\n", " | Return self[key].\n", " | \n", " | __repr__(self)\n", " | Return repr(self).\n", " | \n", " | __setattr__(self, attr, val)\n", " | Implement setattr(self, name, value).\n", " | \n", " | field(self, attr, val=None)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(subtype, shape, dtype=None, buf=None, offset=0, strides=None, formats=None, names=None, titles=None, byteorder=None, aligned=False, order='C')\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors defined here:\n", " | \n", " | __dict__\n", " | dictionary for instance variables (if defined)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from ndarray:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | a.__array__([dtype], /) -> reference if type unchanged, copy otherwise.\n", " | \n", " | Returns either a new reference to self if dtype is not given or a new array\n", " | of provided data type if dtype is different from the current dtype of the\n", " | array.\n", " | \n", " | __array_function__(...)\n", " | \n", " | __array_prepare__(...)\n", " | a.__array_prepare__(array[, context], /)\n", " | \n", " | Returns a view of `array` with the same type as self.\n", " | \n", " | __array_ufunc__(...)\n", " | \n", " | __array_wrap__(...)\n", " | a.__array_wrap__(array[, context], /)\n", " | \n", " | Returns a view of `array` with the same type as self.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __complex__(...)\n", " | \n", " | __contains__(self, key, /)\n", " | Return key in self.\n", " | \n", " | __copy__(...)\n", " | a.__copy__()\n", " | \n", " | Used if :func:`copy.copy` is called on an array. Returns a copy of the array.\n", " | \n", " | Equivalent to ``a.copy(order='K')``.\n", " | \n", " | __deepcopy__(...)\n", " | a.__deepcopy__(memo, /) -> Deep copy of array.\n", " | \n", " | Used if :func:`copy.deepcopy` is called on an array.\n", " | \n", " | __delitem__(self, key, /)\n", " | Delete self[key].\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __dlpack__(...)\n", " | a.__dlpack__(*, stream=None)\n", " | \n", " | DLPack Protocol: Part of the Array API.\n", " | \n", " | __dlpack_device__(...)\n", " | a.__dlpack_device__()\n", " | \n", " | DLPack Protocol: Part of the Array API.\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __format__(...)\n", " | Default object formatter.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __iadd__(self, value, /)\n", " | Return self+=value.\n", " | \n", " | __iand__(self, value, /)\n", " | Return self&=value.\n", " | \n", " | __ifloordiv__(self, value, /)\n", " | Return self//=value.\n", " | \n", " | __ilshift__(self, value, /)\n", " | Return self<<=value.\n", " | \n", " | __imatmul__(self, value, /)\n", " | Return self@=value.\n", " | \n", " | __imod__(self, value, /)\n", " | Return self%=value.\n", " | \n", " | __imul__(self, value, /)\n", " | Return self*=value.\n", " | \n", " | __index__(self, /)\n", " | Return self converted to an integer, if self is suitable for use as an index into a list.\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __ior__(self, value, /)\n", " | Return self|=value.\n", " | \n", " | __ipow__(self, value, /)\n", " | Return self**=value.\n", " | \n", " | __irshift__(self, value, /)\n", " | Return self>>=value.\n", " | \n", " | __isub__(self, value, /)\n", " | Return self-=value.\n", " | \n", " | __iter__(self, /)\n", " | Implement iter(self).\n", " | \n", " | __itruediv__(self, value, /)\n", " | Return self/=value.\n", " | \n", " | __ixor__(self, value, /)\n", " | Return self^=value.\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __len__(self, /)\n", " | Return len(self).\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __matmul__(self, value, /)\n", " | Return self@value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __reduce__(...)\n", " | a.__reduce__()\n", " | \n", " | For pickling.\n", " | \n", " | __reduce_ex__(...)\n", " | Helper for pickle.\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmatmul__(self, value, /)\n", " | Return value@self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setitem__(self, key, value, /)\n", " | Set self[key] to value.\n", " | \n", " | __setstate__(...)\n", " | a.__setstate__(state, /)\n", " | \n", " | For unpickling.\n", " | \n", " | The `state` argument must be a sequence that contains the following\n", " | elements:\n", " | \n", " | Parameters\n", " | ----------\n", " | version : int\n", " | optional pickle version. If omitted defaults to 0.\n", " | shape : tuple\n", " | dtype : data-type\n", " | isFortran : bool\n", " | rawdata : string or list\n", " | a binary string with the data (or a list if 'a' is an object array)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | a.all(axis=None, out=None, keepdims=False, *, where=True)\n", " | \n", " | Returns True if all elements evaluate to True.\n", " | \n", " | Refer to `numpy.all` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.all : equivalent function\n", " | \n", " | any(...)\n", " | a.any(axis=None, out=None, keepdims=False, *, where=True)\n", " | \n", " | Returns True if any of the elements of `a` evaluate to True.\n", " | \n", " | Refer to `numpy.any` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.any : equivalent function\n", " | \n", " | argmax(...)\n", " | a.argmax(axis=None, out=None, *, keepdims=False)\n", " | \n", " | Return indices of the maximum values along the given axis.\n", " | \n", " | Refer to `numpy.argmax` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.argmax : equivalent function\n", " | \n", " | argmin(...)\n", " | a.argmin(axis=None, out=None, *, keepdims=False)\n", " | \n", " | Return indices of the minimum values along the given axis.\n", " | \n", " | Refer to `numpy.argmin` for detailed documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.argmin : equivalent function\n", " | \n", " | argpartition(...)\n", " | a.argpartition(kth, axis=-1, kind='introselect', order=None)\n", " | \n", " | Returns the indices that would partition this array.\n", " | \n", " | Refer to `numpy.argpartition` for full documentation.\n", " | \n", " | .. versionadded:: 1.8.0\n", " | \n", " | See Also\n", " | --------\n", " | numpy.argpartition : equivalent function\n", " | \n", " | argsort(...)\n", " | a.argsort(axis=-1, kind=None, order=None)\n", " | \n", " | Returns the indices that would sort this array.\n", " | \n", " | Refer to `numpy.argsort` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.argsort : equivalent function\n", " | \n", " | astype(...)\n", " | a.astype(dtype, order='K', casting='unsafe', subok=True, copy=True)\n", " | \n", " | Copy of the array, cast to a specified type.\n", " | \n", " | Parameters\n", " | ----------\n", " | dtype : str or dtype\n", " | Typecode or data-type to which the array is cast.\n", " | order : {'C', 'F', 'A', 'K'}, optional\n", " | Controls the memory layout order of the result.\n", " | 'C' means C order, 'F' means Fortran order, 'A'\n", " | means 'F' order if all the arrays are Fortran contiguous,\n", " | 'C' order otherwise, and 'K' means as close to the\n", " | order the array elements appear in memory as possible.\n", " | Default is 'K'.\n", " | casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional\n", " | Controls what kind of data casting may occur. Defaults to 'unsafe'\n", " | for backwards compatibility.\n", " | \n", " | * 'no' means the data types should not be cast at all.\n", " | * 'equiv' means only byte-order changes are allowed.\n", " | * 'safe' means only casts which can preserve values are allowed.\n", " | * 'same_kind' means only safe casts or casts within a kind,\n", " | like float64 to float32, are allowed.\n", " | * 'unsafe' means any data conversions may be done.\n", " | subok : bool, optional\n", " | If True, then sub-classes will be passed-through (default), otherwise\n", " | the returned array will be forced to be a base-class array.\n", " | copy : bool, optional\n", " | By default, astype always returns a newly allocated array. If this\n", " | is set to false, and the `dtype`, `order`, and `subok`\n", " | requirements are satisfied, the input array is returned instead\n", " | of a copy.\n", " | \n", " | Returns\n", " | -------\n", " | arr_t : ndarray\n", " | Unless `copy` is False and the other conditions for returning the input\n", " | array are satisfied (see description for `copy` input parameter), `arr_t`\n", " | is a new array of the same shape as the input array, with dtype, order\n", " | given by `dtype`, `order`.\n", " | \n", " | Notes\n", " | -----\n", " | .. versionchanged:: 1.17.0\n", " | Casting between a simple data type and a structured one is possible only\n", " | for \"unsafe\" casting. Casting to multiple fields is allowed, but\n", " | casting from multiple fields is not.\n", " | \n", " | .. versionchanged:: 1.9.0\n", " | Casting from numeric to string types in 'safe' casting mode requires\n", " | that the string dtype length is long enough to store the max\n", " | integer/float value converted.\n", " | \n", " | Raises\n", " | ------\n", " | ComplexWarning\n", " | When casting from complex to float or int. To avoid this,\n", " | one should use ``a.real.astype(t)``.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([1, 2, 2.5])\n", " | >>> x\n", " | array([1. , 2. , 2.5])\n", " | \n", " | >>> x.astype(int)\n", " | array([1, 2, 2])\n", " | \n", " | byteswap(...)\n", " | a.byteswap(inplace=False)\n", " | \n", " | Swap the bytes of the array elements\n", " | \n", " | Toggle between low-endian and big-endian data representation by\n", " | returning a byteswapped array, optionally swapped in-place.\n", " | Arrays of byte-strings are not swapped. The real and imaginary\n", " | parts of a complex number are swapped individually.\n", " | \n", " | Parameters\n", " | ----------\n", " | inplace : bool, optional\n", " | If ``True``, swap bytes in-place, default is ``False``.\n", " | \n", " | Returns\n", " | -------\n", " | out : ndarray\n", " | The byteswapped array. If `inplace` is ``True``, this is\n", " | a view to self.\n", " | \n", " | Examples\n", " | --------\n", " | >>> A = np.array([1, 256, 8755], dtype=np.int16)\n", " | >>> list(map(hex, A))\n", " | ['0x1', '0x100', '0x2233']\n", " | >>> A.byteswap(inplace=True)\n", " | array([ 256, 1, 13090], dtype=int16)\n", " | >>> list(map(hex, A))\n", " | ['0x100', '0x1', '0x3322']\n", " | \n", " | Arrays of byte-strings are not swapped\n", " | \n", " | >>> A = np.array([b'ceg', b'fac'])\n", " | >>> A.byteswap()\n", " | array([b'ceg', b'fac'], dtype='|S3')\n", " | \n", " | ``A.newbyteorder().byteswap()`` produces an array with the same values\n", " | but different representation in memory\n", " | \n", " | >>> A = np.array([1, 2, 3])\n", " | >>> A.view(np.uint8)\n", " | array([1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0,\n", " | 0, 0], dtype=uint8)\n", " | >>> A.newbyteorder().byteswap(inplace=True)\n", " | array([1, 2, 3])\n", " | >>> A.view(np.uint8)\n", " | array([0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0,\n", " | 0, 3], dtype=uint8)\n", " | \n", " | choose(...)\n", " | a.choose(choices, out=None, mode='raise')\n", " | \n", " | Use an index array to construct a new array from a set of choices.\n", " | \n", " | Refer to `numpy.choose` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.choose : equivalent function\n", " | \n", " | clip(...)\n", " | a.clip(min=None, max=None, out=None, **kwargs)\n", " | \n", " | Return an array whose values are limited to ``[min, max]``.\n", " | One of max or min must be given.\n", " | \n", " | Refer to `numpy.clip` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.clip : equivalent function\n", " | \n", " | compress(...)\n", " | a.compress(condition, axis=None, out=None)\n", " | \n", " | Return selected slices of this array along given axis.\n", " | \n", " | Refer to `numpy.compress` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.compress : equivalent function\n", " | \n", " | conj(...)\n", " | a.conj()\n", " | \n", " | Complex-conjugate all elements.\n", " | \n", " | Refer to `numpy.conjugate` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.conjugate : equivalent function\n", " | \n", " | conjugate(...)\n", " | a.conjugate()\n", " | \n", " | Return the complex conjugate, element-wise.\n", " | \n", " | Refer to `numpy.conjugate` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.conjugate : equivalent function\n", " | \n", " | copy(...)\n", " | a.copy(order='C')\n", " | \n", " | Return a copy of the array.\n", " | \n", " | Parameters\n", " | ----------\n", " | order : {'C', 'F', 'A', 'K'}, optional\n", " | Controls the memory layout of the copy. 'C' means C-order,\n", " | 'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous,\n", " | 'C' otherwise. 'K' means match the layout of `a` as closely\n", " | as possible. (Note that this function and :func:`numpy.copy` are very\n", " | similar but have different default values for their order=\n", " | arguments, and this function always passes sub-classes through.)\n", " | \n", " | See also\n", " | --------\n", " | numpy.copy : Similar function with different default behavior\n", " | numpy.copyto\n", " | \n", " | Notes\n", " | -----\n", " | This function is the preferred method for creating an array copy. The\n", " | function :func:`numpy.copy` is similar, but it defaults to using order 'K',\n", " | and will not pass sub-classes through by default.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([[1,2,3],[4,5,6]], order='F')\n", " | \n", " | >>> y = x.copy()\n", " | \n", " | >>> x.fill(0)\n", " | \n", " | >>> x\n", " | array([[0, 0, 0],\n", " | [0, 0, 0]])\n", " | \n", " | >>> y\n", " | array([[1, 2, 3],\n", " | [4, 5, 6]])\n", " | \n", " | >>> y.flags['C_CONTIGUOUS']\n", " | True\n", " | \n", " | cumprod(...)\n", " | a.cumprod(axis=None, dtype=None, out=None)\n", " | \n", " | Return the cumulative product of the elements along the given axis.\n", " | \n", " | Refer to `numpy.cumprod` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.cumprod : equivalent function\n", " | \n", " | cumsum(...)\n", " | a.cumsum(axis=None, dtype=None, out=None)\n", " | \n", " | Return the cumulative sum of the elements along the given axis.\n", " | \n", " | Refer to `numpy.cumsum` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.cumsum : equivalent function\n", " | \n", " | diagonal(...)\n", " | a.diagonal(offset=0, axis1=0, axis2=1)\n", " | \n", " | Return specified diagonals. In NumPy 1.9 the returned array is a\n", " | read-only view instead of a copy as in previous NumPy versions. In\n", " | a future version the read-only restriction will be removed.\n", " | \n", " | Refer to :func:`numpy.diagonal` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.diagonal : equivalent function\n", " | \n", " | dot(...)\n", " | \n", " | dump(...)\n", " | a.dump(file)\n", " | \n", " | Dump a pickle of the array to the specified file.\n", " | The array can be read back with pickle.load or numpy.load.\n", " | \n", " | Parameters\n", " | ----------\n", " | file : str or Path\n", " | A string naming the dump file.\n", " | \n", " | .. versionchanged:: 1.17.0\n", " | `pathlib.Path` objects are now accepted.\n", " | \n", " | dumps(...)\n", " | a.dumps()\n", " | \n", " | Returns the pickle of the array as a string.\n", " | pickle.loads will convert the string back to an array.\n", " | \n", " | Parameters\n", " | ----------\n", " | None\n", " | \n", " | fill(...)\n", " | a.fill(value)\n", " | \n", " | Fill the array with a scalar value.\n", " | \n", " | Parameters\n", " | ----------\n", " | value : scalar\n", " | All elements of `a` will be assigned this value.\n", " | \n", " | Examples\n", " | --------\n", " | >>> a = np.array([1, 2])\n", " | >>> a.fill(0)\n", " | >>> a\n", " | array([0, 0])\n", " | >>> a = np.empty(2)\n", " | >>> a.fill(1)\n", " | >>> a\n", " | array([1., 1.])\n", " | \n", " | Fill expects a scalar value and always behaves the same as assigning\n", " | to a single array element. The following is a rare example where this\n", " | distinction is important:\n", " | \n", " | >>> a = np.array([None, None], dtype=object)\n", " | >>> a[0] = np.array(3)\n", " | >>> a\n", " | array([array(3), None], dtype=object)\n", " | >>> a.fill(np.array(3))\n", " | >>> a\n", " | array([array(3), array(3)], dtype=object)\n", " | \n", " | Where other forms of assignments will unpack the array being assigned:\n", " | \n", " | >>> a[...] = np.array(3)\n", " | >>> a\n", " | array([3, 3], dtype=object)\n", " | \n", " | flatten(...)\n", " | a.flatten(order='C')\n", " | \n", " | Return a copy of the array collapsed into one dimension.\n", " | \n", " | Parameters\n", " | ----------\n", " | order : {'C', 'F', 'A', 'K'}, optional\n", " | 'C' means to flatten in row-major (C-style) order.\n", " | 'F' means to flatten in column-major (Fortran-\n", " | style) order. 'A' means to flatten in column-major\n", " | order if `a` is Fortran *contiguous* in memory,\n", " | row-major order otherwise. 'K' means to flatten\n", " | `a` in the order the elements occur in memory.\n", " | The default is 'C'.\n", " | \n", " | Returns\n", " | -------\n", " | y : ndarray\n", " | A copy of the input array, flattened to one dimension.\n", " | \n", " | See Also\n", " | --------\n", " | ravel : Return a flattened array.\n", " | flat : A 1-D flat iterator over the array.\n", " | \n", " | Examples\n", " | --------\n", " | >>> a = np.array([[1,2], [3,4]])\n", " | >>> a.flatten()\n", " | array([1, 2, 3, 4])\n", " | >>> a.flatten('F')\n", " | array([1, 3, 2, 4])\n", " | \n", " | getfield(...)\n", " | a.getfield(dtype, offset=0)\n", " | \n", " | Returns a field of the given array as a certain type.\n", " | \n", " | A field is a view of the array data with a given data-type. The values in\n", " | the view are determined by the given type and the offset into the current\n", " | array in bytes. The offset needs to be such that the view dtype fits in the\n", " | array dtype; for example an array of dtype complex128 has 16-byte elements.\n", " | If taking a view with a 32-bit integer (4 bytes), the offset needs to be\n", " | between 0 and 12 bytes.\n", " | \n", " | Parameters\n", " | ----------\n", " | dtype : str or dtype\n", " | The data type of the view. The dtype size of the view can not be larger\n", " | than that of the array itself.\n", " | offset : int\n", " | Number of bytes to skip before beginning the element view.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.diag([1.+1.j]*2)\n", " | >>> x[1, 1] = 2 + 4.j\n", " | >>> x\n", " | array([[1.+1.j, 0.+0.j],\n", " | [0.+0.j, 2.+4.j]])\n", " | >>> x.getfield(np.float64)\n", " | array([[1., 0.],\n", " | [0., 2.]])\n", " | \n", " | By choosing an offset of 8 bytes we can select the complex part of the\n", " | array for our view:\n", " | \n", " | >>> x.getfield(np.float64, offset=8)\n", " | array([[1., 0.],\n", " | [0., 4.]])\n", " | \n", " | item(...)\n", " | a.item(*args)\n", " | \n", " | Copy an element of an array to a standard Python scalar and return it.\n", " | \n", " | Parameters\n", " | ----------\n", " | \\*args : Arguments (variable number and type)\n", " | \n", " | * none: in this case, the method only works for arrays\n", " | with one element (`a.size == 1`), which element is\n", " | copied into a standard Python scalar object and returned.\n", " | \n", " | * int_type: this argument is interpreted as a flat index into\n", " | the array, specifying which element to copy and return.\n", " | \n", " | * tuple of int_types: functions as does a single int_type argument,\n", " | except that the argument is interpreted as an nd-index into the\n", " | array.\n", " | \n", " | Returns\n", " | -------\n", " | z : Standard Python scalar object\n", " | A copy of the specified element of the array as a suitable\n", " | Python scalar\n", " | \n", " | Notes\n", " | -----\n", " | When the data type of `a` is longdouble or clongdouble, item() returns\n", " | a scalar array object because there is no available Python scalar that\n", " | would not lose information. Void arrays return a buffer object for item(),\n", " | unless fields are defined, in which case a tuple is returned.\n", " | \n", " | `item` is very similar to a[args], except, instead of an array scalar,\n", " | a standard Python scalar is returned. This can be useful for speeding up\n", " | access to elements of the array and doing arithmetic on elements of the\n", " | array using Python's optimized math.\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.random.seed(123)\n", " | >>> x = np.random.randint(9, size=(3, 3))\n", " | >>> x\n", " | array([[2, 2, 6],\n", " | [1, 3, 6],\n", " | [1, 0, 1]])\n", " | >>> x.item(3)\n", " | 1\n", " | >>> x.item(7)\n", " | 0\n", " | >>> x.item((0, 1))\n", " | 2\n", " | >>> x.item((2, 2))\n", " | 1\n", " | \n", " | itemset(...)\n", " | a.itemset(*args)\n", " | \n", " | Insert scalar into an array (scalar is cast to array's dtype, if possible)\n", " | \n", " | There must be at least 1 argument, and define the last argument\n", " | as *item*. Then, ``a.itemset(*args)`` is equivalent to but faster\n", " | than ``a[args] = item``. The item should be a scalar value and `args`\n", " | must select a single item in the array `a`.\n", " | \n", " | Parameters\n", " | ----------\n", " | \\*args : Arguments\n", " | If one argument: a scalar, only used in case `a` is of size 1.\n", " | If two arguments: the last argument is the value to be set\n", " | and must be a scalar, the first argument specifies a single array\n", " | element location. It is either an int or a tuple.\n", " | \n", " | Notes\n", " | -----\n", " | Compared to indexing syntax, `itemset` provides some speed increase\n", " | for placing a scalar into a particular location in an `ndarray`,\n", " | if you must do this. However, generally this is discouraged:\n", " | among other problems, it complicates the appearance of the code.\n", " | Also, when using `itemset` (and `item`) inside a loop, be sure\n", " | to assign the methods to a local variable to avoid the attribute\n", " | look-up at each loop iteration.\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.random.seed(123)\n", " | >>> x = np.random.randint(9, size=(3, 3))\n", " | >>> x\n", " | array([[2, 2, 6],\n", " | [1, 3, 6],\n", " | [1, 0, 1]])\n", " | >>> x.itemset(4, 0)\n", " | >>> x.itemset((2, 2), 9)\n", " | >>> x\n", " | array([[2, 2, 6],\n", " | [1, 0, 6],\n", " | [1, 0, 9]])\n", " | \n", " | max(...)\n", " | a.max(axis=None, out=None, keepdims=False, initial=<no value>, where=True)\n", " | \n", " | Return the maximum along a given axis.\n", " | \n", " | Refer to `numpy.amax` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.amax : equivalent function\n", " | \n", " | mean(...)\n", " | a.mean(axis=None, dtype=None, out=None, keepdims=False, *, where=True)\n", " | \n", " | Returns the average of the array elements along given axis.\n", " | \n", " | Refer to `numpy.mean` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.mean : equivalent function\n", " | \n", " | min(...)\n", " | a.min(axis=None, out=None, keepdims=False, initial=<no value>, where=True)\n", " | \n", " | Return the minimum along a given axis.\n", " | \n", " | Refer to `numpy.amin` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.amin : equivalent function\n", " | \n", " | newbyteorder(...)\n", " | arr.newbyteorder(new_order='S', /)\n", " | \n", " | Return the array with the same data viewed with a different byte order.\n", " | \n", " | Equivalent to::\n", " | \n", " | arr.view(arr.dtype.newbytorder(new_order))\n", " | \n", " | Changes are also made in all fields and sub-arrays of the array data\n", " | type.\n", " | \n", " | \n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : string, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | below. `new_order` codes can be any of:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order, equivalent to `sys.byteorder`\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_arr : array\n", " | New array object with the dtype reflecting given change to the\n", " | byte order.\n", " | \n", " | nonzero(...)\n", " | a.nonzero()\n", " | \n", " | Return the indices of the elements that are non-zero.\n", " | \n", " | Refer to `numpy.nonzero` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.nonzero : equivalent function\n", " | \n", " | partition(...)\n", " | a.partition(kth, axis=-1, kind='introselect', order=None)\n", " | \n", " | Rearranges the elements in the array in such a way that the value of the\n", " | element in kth position is in the position it would be in a sorted array.\n", " | All elements smaller than the kth element are moved before this element and\n", " | all equal or greater are moved behind it. The ordering of the elements in\n", " | the two partitions is undefined.\n", " | \n", " | .. versionadded:: 1.8.0\n", " | \n", " | Parameters\n", " | ----------\n", " | kth : int or sequence of ints\n", " | Element index to partition by. The kth element value will be in its\n", " | final sorted position and all smaller elements will be moved before it\n", " | and all equal or greater elements behind it.\n", " | The order of all elements in the partitions is undefined.\n", " | If provided with a sequence of kth it will partition all elements\n", " | indexed by kth of them into their sorted position at once.\n", " | \n", " | .. deprecated:: 1.22.0\n", " | Passing booleans as index is deprecated.\n", " | axis : int, optional\n", " | Axis along which to sort. Default is -1, which means sort along the\n", " | last axis.\n", " | kind : {'introselect'}, optional\n", " | Selection algorithm. Default is 'introselect'.\n", " | order : str or list of str, optional\n", " | When `a` is an array with fields defined, this argument specifies\n", " | which fields to compare first, second, etc. A single field can\n", " | be specified as a string, and not all fields need to be specified,\n", " | but unspecified fields will still be used, in the order in which\n", " | they come up in the dtype, to break ties.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.partition : Return a partitioned copy of an array.\n", " | argpartition : Indirect partition.\n", " | sort : Full sort.\n", " | \n", " | Notes\n", " | -----\n", " | See ``np.partition`` for notes on the different algorithms.\n", " | \n", " | Examples\n", " | --------\n", " | >>> a = np.array([3, 4, 2, 1])\n", " | >>> a.partition(3)\n", " | >>> a\n", " | array([2, 1, 3, 4])\n", " | \n", " | >>> a.partition((1, 3))\n", " | >>> a\n", " | array([1, 2, 3, 4])\n", " | \n", " | prod(...)\n", " | a.prod(axis=None, dtype=None, out=None, keepdims=False, initial=1, where=True)\n", " | \n", " | Return the product of the array elements over the given axis\n", " | \n", " | Refer to `numpy.prod` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.prod : equivalent function\n", " | \n", " | ptp(...)\n", " | a.ptp(axis=None, out=None, keepdims=False)\n", " | \n", " | Peak to peak (maximum - minimum) value along a given axis.\n", " | \n", " | Refer to `numpy.ptp` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.ptp : equivalent function\n", " | \n", " | put(...)\n", " | a.put(indices, values, mode='raise')\n", " | \n", " | Set ``a.flat[n] = values[n]`` for all `n` in indices.\n", " | \n", " | Refer to `numpy.put` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.put : equivalent function\n", " | \n", " | ravel(...)\n", " | a.ravel([order])\n", " | \n", " | Return a flattened array.\n", " | \n", " | Refer to `numpy.ravel` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.ravel : equivalent function\n", " | \n", " | ndarray.flat : a flat iterator on the array.\n", " | \n", " | repeat(...)\n", " | a.repeat(repeats, axis=None)\n", " | \n", " | Repeat elements of an array.\n", " | \n", " | Refer to `numpy.repeat` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.repeat : equivalent function\n", " | \n", " | reshape(...)\n", " | a.reshape(shape, order='C')\n", " | \n", " | Returns an array containing the same data with a new shape.\n", " | \n", " | Refer to `numpy.reshape` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.reshape : equivalent function\n", " | \n", " | Notes\n", " | -----\n", " | Unlike the free function `numpy.reshape`, this method on `ndarray` allows\n", " | the elements of the shape parameter to be passed in as separate arguments.\n", " | For example, ``a.reshape(10, 11)`` is equivalent to\n", " | ``a.reshape((10, 11))``.\n", " | \n", " | resize(...)\n", " | a.resize(new_shape, refcheck=True)\n", " | \n", " | Change shape and size of array in-place.\n", " | \n", " | Parameters\n", " | ----------\n", " | new_shape : tuple of ints, or `n` ints\n", " | Shape of resized array.\n", " | refcheck : bool, optional\n", " | If False, reference count will not be checked. Default is True.\n", " | \n", " | Returns\n", " | -------\n", " | None\n", " | \n", " | Raises\n", " | ------\n", " | ValueError\n", " | If `a` does not own its own data or references or views to it exist,\n", " | and the data memory must be changed.\n", " | PyPy only: will always raise if the data memory must be changed, since\n", " | there is no reliable way to determine if references or views to it\n", " | exist.\n", " | \n", " | SystemError\n", " | If the `order` keyword argument is specified. This behaviour is a\n", " | bug in NumPy.\n", " | \n", " | See Also\n", " | --------\n", " | resize : Return a new array with the specified shape.\n", " | \n", " | Notes\n", " | -----\n", " | This reallocates space for the data area if necessary.\n", " | \n", " | Only contiguous arrays (data elements consecutive in memory) can be\n", " | resized.\n", " | \n", " | The purpose of the reference count check is to make sure you\n", " | do not use this array as a buffer for another Python object and then\n", " | reallocate the memory. However, reference counts can increase in\n", " | other ways so if you are sure that you have not shared the memory\n", " | for this array with another Python object, then you may safely set\n", " | `refcheck` to False.\n", " | \n", " | Examples\n", " | --------\n", " | Shrinking an array: array is flattened (in the order that the data are\n", " | stored in memory), resized, and reshaped:\n", " | \n", " | >>> a = np.array([[0, 1], [2, 3]], order='C')\n", " | >>> a.resize((2, 1))\n", " | >>> a\n", " | array([[0],\n", " | [1]])\n", " | \n", " | >>> a = np.array([[0, 1], [2, 3]], order='F')\n", " | >>> a.resize((2, 1))\n", " | >>> a\n", " | array([[0],\n", " | [2]])\n", " | \n", " | Enlarging an array: as above, but missing entries are filled with zeros:\n", " | \n", " | >>> b = np.array([[0, 1], [2, 3]])\n", " | >>> b.resize(2, 3) # new_shape parameter doesn't have to be a tuple\n", " | >>> b\n", " | array([[0, 1, 2],\n", " | [3, 0, 0]])\n", " | \n", " | Referencing an array prevents resizing...\n", " | \n", " | >>> c = a\n", " | >>> a.resize((1, 1))\n", " | Traceback (most recent call last):\n", " | ...\n", " | ValueError: cannot resize an array that references or is referenced ...\n", " | \n", " | Unless `refcheck` is False:\n", " | \n", " | >>> a.resize((1, 1), refcheck=False)\n", " | >>> a\n", " | array([[0]])\n", " | >>> c\n", " | array([[0]])\n", " | \n", " | round(...)\n", " | a.round(decimals=0, out=None)\n", " | \n", " | Return `a` with each element rounded to the given number of decimals.\n", " | \n", " | Refer to `numpy.around` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.around : equivalent function\n", " | \n", " | searchsorted(...)\n", " | a.searchsorted(v, side='left', sorter=None)\n", " | \n", " | Find indices where elements of v should be inserted in a to maintain order.\n", " | \n", " | For full documentation, see `numpy.searchsorted`\n", " | \n", " | See Also\n", " | --------\n", " | numpy.searchsorted : equivalent function\n", " | \n", " | setfield(...)\n", " | a.setfield(val, dtype, offset=0)\n", " | \n", " | Put a value into a specified place in a field defined by a data-type.\n", " | \n", " | Place `val` into `a`'s field defined by `dtype` and beginning `offset`\n", " | bytes into the field.\n", " | \n", " | Parameters\n", " | ----------\n", " | val : object\n", " | Value to be placed in field.\n", " | dtype : dtype object\n", " | Data-type of the field in which to place `val`.\n", " | offset : int, optional\n", " | The number of bytes into the field at which to place `val`.\n", " | \n", " | Returns\n", " | -------\n", " | None\n", " | \n", " | See Also\n", " | --------\n", " | getfield\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.eye(3)\n", " | >>> x.getfield(np.float64)\n", " | array([[1., 0., 0.],\n", " | [0., 1., 0.],\n", " | [0., 0., 1.]])\n", " | >>> x.setfield(3, np.int32)\n", " | >>> x.getfield(np.int32)\n", " | array([[3, 3, 3],\n", " | [3, 3, 3],\n", " | [3, 3, 3]], dtype=int32)\n", " | >>> x\n", " | array([[1.0e+000, 1.5e-323, 1.5e-323],\n", " | [1.5e-323, 1.0e+000, 1.5e-323],\n", " | [1.5e-323, 1.5e-323, 1.0e+000]])\n", " | >>> x.setfield(np.eye(3), np.int32)\n", " | >>> x\n", " | array([[1., 0., 0.],\n", " | [0., 1., 0.],\n", " | [0., 0., 1.]])\n", " | \n", " | setflags(...)\n", " | a.setflags(write=None, align=None, uic=None)\n", " | \n", " | Set array flags WRITEABLE, ALIGNED, WRITEBACKIFCOPY,\n", " | respectively.\n", " | \n", " | These Boolean-valued flags affect how numpy interprets the memory\n", " | area used by `a` (see Notes below). The ALIGNED flag can only\n", " | be set to True if the data is actually aligned according to the type.\n", " | The WRITEBACKIFCOPY and flag can never be set\n", " | to True. The flag WRITEABLE can only be set to True if the array owns its\n", " | own memory, or the ultimate owner of the memory exposes a writeable buffer\n", " | interface, or is a string. (The exception for string is made so that\n", " | unpickling can be done without copying memory.)\n", " | \n", " | Parameters\n", " | ----------\n", " | write : bool, optional\n", " | Describes whether or not `a` can be written to.\n", " | align : bool, optional\n", " | Describes whether or not `a` is aligned properly for its type.\n", " | uic : bool, optional\n", " | Describes whether or not `a` is a copy of another \"base\" array.\n", " | \n", " | Notes\n", " | -----\n", " | Array flags provide information about how the memory area used\n", " | for the array is to be interpreted. There are 7 Boolean flags\n", " | in use, only four of which can be changed by the user:\n", " | WRITEBACKIFCOPY, WRITEABLE, and ALIGNED.\n", " | \n", " | WRITEABLE (W) the data area can be written to;\n", " | \n", " | ALIGNED (A) the data and strides are aligned appropriately for the hardware\n", " | (as determined by the compiler);\n", " | \n", " | WRITEBACKIFCOPY (X) this array is a copy of some other array (referenced\n", " | by .base). When the C-API function PyArray_ResolveWritebackIfCopy is\n", " | called, the base array will be updated with the contents of this array.\n", " | \n", " | All flags can be accessed using the single (upper case) letter as well\n", " | as the full name.\n", " | \n", " | Examples\n", " | --------\n", " | >>> y = np.array([[3, 1, 7],\n", " | ... [2, 0, 0],\n", " | ... [8, 5, 9]])\n", " | >>> y\n", " | array([[3, 1, 7],\n", " | [2, 0, 0],\n", " | [8, 5, 9]])\n", " | >>> y.flags\n", " | C_CONTIGUOUS : True\n", " | F_CONTIGUOUS : False\n", " | OWNDATA : True\n", " | WRITEABLE : True\n", " | ALIGNED : True\n", " | WRITEBACKIFCOPY : False\n", " | >>> y.setflags(write=0, align=0)\n", " | >>> y.flags\n", " | C_CONTIGUOUS : True\n", " | F_CONTIGUOUS : False\n", " | OWNDATA : True\n", " | WRITEABLE : False\n", " | ALIGNED : False\n", " | WRITEBACKIFCOPY : False\n", " | >>> y.setflags(uic=1)\n", " | Traceback (most recent call last):\n", " | File \"<stdin>\", line 1, in <module>\n", " | ValueError: cannot set WRITEBACKIFCOPY flag to True\n", " | \n", " | sort(...)\n", " | a.sort(axis=-1, kind=None, order=None)\n", " | \n", " | Sort an array in-place. Refer to `numpy.sort` for full documentation.\n", " | \n", " | Parameters\n", " | ----------\n", " | axis : int, optional\n", " | Axis along which to sort. Default is -1, which means sort along the\n", " | last axis.\n", " | kind : {'quicksort', 'mergesort', 'heapsort', 'stable'}, optional\n", " | Sorting algorithm. The default is 'quicksort'. Note that both 'stable'\n", " | and 'mergesort' use timsort under the covers and, in general, the\n", " | actual implementation will vary with datatype. The 'mergesort' option\n", " | is retained for backwards compatibility.\n", " | \n", " | .. versionchanged:: 1.15.0\n", " | The 'stable' option was added.\n", " | \n", " | order : str or list of str, optional\n", " | When `a` is an array with fields defined, this argument specifies\n", " | which fields to compare first, second, etc. A single field can\n", " | be specified as a string, and not all fields need be specified,\n", " | but unspecified fields will still be used, in the order in which\n", " | they come up in the dtype, to break ties.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.sort : Return a sorted copy of an array.\n", " | numpy.argsort : Indirect sort.\n", " | numpy.lexsort : Indirect stable sort on multiple keys.\n", " | numpy.searchsorted : Find elements in sorted array.\n", " | numpy.partition: Partial sort.\n", " | \n", " | Notes\n", " | -----\n", " | See `numpy.sort` for notes on the different sorting algorithms.\n", " | \n", " | Examples\n", " | --------\n", " | >>> a = np.array([[1,4], [3,1]])\n", " | >>> a.sort(axis=1)\n", " | >>> a\n", " | array([[1, 4],\n", " | [1, 3]])\n", " | >>> a.sort(axis=0)\n", " | >>> a\n", " | array([[1, 3],\n", " | [1, 4]])\n", " | \n", " | Use the `order` keyword to specify a field to use when sorting a\n", " | structured array:\n", " | \n", " | >>> a = np.array([('a', 2), ('c', 1)], dtype=[('x', 'S1'), ('y', int)])\n", " | >>> a.sort(order='y')\n", " | >>> a\n", " | array([(b'c', 1), (b'a', 2)],\n", " | dtype=[('x', 'S1'), ('y', '<i8')])\n", " | \n", " | squeeze(...)\n", " | a.squeeze(axis=None)\n", " | \n", " | Remove axes of length one from `a`.\n", " | \n", " | Refer to `numpy.squeeze` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.squeeze : equivalent function\n", " | \n", " | std(...)\n", " | a.std(axis=None, dtype=None, out=None, ddof=0, keepdims=False, *, where=True)\n", " | \n", " | Returns the standard deviation of the array elements along given axis.\n", " | \n", " | Refer to `numpy.std` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.std : equivalent function\n", " | \n", " | sum(...)\n", " | a.sum(axis=None, dtype=None, out=None, keepdims=False, initial=0, where=True)\n", " | \n", " | Return the sum of the array elements over the given axis.\n", " | \n", " | Refer to `numpy.sum` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.sum : equivalent function\n", " | \n", " | swapaxes(...)\n", " | a.swapaxes(axis1, axis2)\n", " | \n", " | Return a view of the array with `axis1` and `axis2` interchanged.\n", " | \n", " | Refer to `numpy.swapaxes` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.swapaxes : equivalent function\n", " | \n", " | take(...)\n", " | a.take(indices, axis=None, out=None, mode='raise')\n", " | \n", " | Return an array formed from the elements of `a` at the given indices.\n", " | \n", " | Refer to `numpy.take` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.take : equivalent function\n", " | \n", " | tobytes(...)\n", " | a.tobytes(order='C')\n", " | \n", " | Construct Python bytes containing the raw data bytes in the array.\n", " | \n", " | Constructs Python bytes showing a copy of the raw contents of\n", " | data memory. The bytes object is produced in C-order by default.\n", " | This behavior is controlled by the ``order`` parameter.\n", " | \n", " | .. versionadded:: 1.9.0\n", " | \n", " | Parameters\n", " | ----------\n", " | order : {'C', 'F', 'A'}, optional\n", " | Controls the memory layout of the bytes object. 'C' means C-order,\n", " | 'F' means F-order, 'A' (short for *Any*) means 'F' if `a` is\n", " | Fortran contiguous, 'C' otherwise. Default is 'C'.\n", " | \n", " | Returns\n", " | -------\n", " | s : bytes\n", " | Python bytes exhibiting a copy of `a`'s raw data.\n", " | \n", " | See also\n", " | --------\n", " | frombuffer\n", " | Inverse of this operation, construct a 1-dimensional array from Python\n", " | bytes.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([[0, 1], [2, 3]], dtype='<u2')\n", " | >>> x.tobytes()\n", " | b'\\x00\\x00\\x01\\x00\\x02\\x00\\x03\\x00'\n", " | >>> x.tobytes('C') == x.tobytes()\n", " | True\n", " | >>> x.tobytes('F')\n", " | b'\\x00\\x00\\x02\\x00\\x01\\x00\\x03\\x00'\n", " | \n", " | tofile(...)\n", " | a.tofile(fid, sep=\"\", format=\"%s\")\n", " | \n", " | Write array to a file as text or binary (default).\n", " | \n", " | Data is always written in 'C' order, independent of the order of `a`.\n", " | The data produced by this method can be recovered using the function\n", " | fromfile().\n", " | \n", " | Parameters\n", " | ----------\n", " | fid : file or str or Path\n", " | An open file object, or a string containing a filename.\n", " | \n", " | .. versionchanged:: 1.17.0\n", " | `pathlib.Path` objects are now accepted.\n", " | \n", " | sep : str\n", " | Separator between array items for text output.\n", " | If \"\" (empty), a binary file is written, equivalent to\n", " | ``file.write(a.tobytes())``.\n", " | format : str\n", " | Format string for text file output.\n", " | Each entry in the array is formatted to text by first converting\n", " | it to the closest Python type, and then using \"format\" % item.\n", " | \n", " | Notes\n", " | -----\n", " | This is a convenience function for quick storage of array data.\n", " | Information on endianness and precision is lost, so this method is not a\n", " | good choice for files intended to archive data or transport data between\n", " | machines with different endianness. Some of these problems can be overcome\n", " | by outputting the data as text files, at the expense of speed and file\n", " | size.\n", " | \n", " | When fid is a file object, array contents are directly written to the\n", " | file, bypassing the file object's ``write`` method. As a result, tofile\n", " | cannot be used with files objects supporting compression (e.g., GzipFile)\n", " | or file-like objects that do not support ``fileno()`` (e.g., BytesIO).\n", " | \n", " | tolist(...)\n", " | a.tolist()\n", " | \n", " | Return the array as an ``a.ndim``-levels deep nested list of Python scalars.\n", " | \n", " | Return a copy of the array data as a (nested) Python list.\n", " | Data items are converted to the nearest compatible builtin Python type, via\n", " | the `~numpy.ndarray.item` function.\n", " | \n", " | If ``a.ndim`` is 0, then since the depth of the nested list is 0, it will\n", " | not be a list at all, but a simple Python scalar.\n", " | \n", " | Parameters\n", " | ----------\n", " | none\n", " | \n", " | Returns\n", " | -------\n", " | y : object, or list of object, or list of list of object, or ...\n", " | The possibly nested list of array elements.\n", " | \n", " | Notes\n", " | -----\n", " | The array may be recreated via ``a = np.array(a.tolist())``, although this\n", " | may sometimes lose precision.\n", " | \n", " | Examples\n", " | --------\n", " | For a 1D array, ``a.tolist()`` is almost the same as ``list(a)``,\n", " | except that ``tolist`` changes numpy scalars to Python scalars:\n", " | \n", " | >>> a = np.uint32([1, 2])\n", " | >>> a_list = list(a)\n", " | >>> a_list\n", " | [1, 2]\n", " | >>> type(a_list[0])\n", " | <class 'numpy.uint32'>\n", " | >>> a_tolist = a.tolist()\n", " | >>> a_tolist\n", " | [1, 2]\n", " | >>> type(a_tolist[0])\n", " | <class 'int'>\n", " | \n", " | Additionally, for a 2D array, ``tolist`` applies recursively:\n", " | \n", " | >>> a = np.array([[1, 2], [3, 4]])\n", " | >>> list(a)\n", " | [array([1, 2]), array([3, 4])]\n", " | >>> a.tolist()\n", " | [[1, 2], [3, 4]]\n", " | \n", " | The base case for this recursion is a 0D array:\n", " | \n", " | >>> a = np.array(1)\n", " | >>> list(a)\n", " | Traceback (most recent call last):\n", " | ...\n", " | TypeError: iteration over a 0-d array\n", " | >>> a.tolist()\n", " | 1\n", " | \n", " | tostring(...)\n", " | a.tostring(order='C')\n", " | \n", " | A compatibility alias for `tobytes`, with exactly the same behavior.\n", " | \n", " | Despite its name, it returns `bytes` not `str`\\ s.\n", " | \n", " | .. deprecated:: 1.19.0\n", " | \n", " | trace(...)\n", " | a.trace(offset=0, axis1=0, axis2=1, dtype=None, out=None)\n", " | \n", " | Return the sum along diagonals of the array.\n", " | \n", " | Refer to `numpy.trace` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.trace : equivalent function\n", " | \n", " | transpose(...)\n", " | a.transpose(*axes)\n", " | \n", " | Returns a view of the array with axes transposed.\n", " | \n", " | Refer to `numpy.transpose` for full documentation.\n", " | \n", " | Parameters\n", " | ----------\n", " | axes : None, tuple of ints, or `n` ints\n", " | \n", " | * None or no argument: reverses the order of the axes.\n", " | \n", " | * tuple of ints: `i` in the `j`-th place in the tuple means that the\n", " | array's `i`-th axis becomes the transposed array's `j`-th axis.\n", " | \n", " | * `n` ints: same as an n-tuple of the same ints (this form is\n", " | intended simply as a \"convenience\" alternative to the tuple form).\n", " | \n", " | Returns\n", " | -------\n", " | p : ndarray\n", " | View of the array with its axes suitably permuted.\n", " | \n", " | See Also\n", " | --------\n", " | transpose : Equivalent function.\n", " | ndarray.T : Array property returning the array transposed.\n", " | ndarray.reshape : Give a new shape to an array without changing its data.\n", " | \n", " | Examples\n", " | --------\n", " | >>> a = np.array([[1, 2], [3, 4]])\n", " | >>> a\n", " | array([[1, 2],\n", " | [3, 4]])\n", " | >>> a.transpose()\n", " | array([[1, 3],\n", " | [2, 4]])\n", " | >>> a.transpose((1, 0))\n", " | array([[1, 3],\n", " | [2, 4]])\n", " | >>> a.transpose(1, 0)\n", " | array([[1, 3],\n", " | [2, 4]])\n", " | \n", " | >>> a = np.array([1, 2, 3, 4])\n", " | >>> a\n", " | array([1, 2, 3, 4])\n", " | >>> a.transpose()\n", " | array([1, 2, 3, 4])\n", " | \n", " | var(...)\n", " | a.var(axis=None, dtype=None, out=None, ddof=0, keepdims=False, *, where=True)\n", " | \n", " | Returns the variance of the array elements, along given axis.\n", " | \n", " | Refer to `numpy.var` for full documentation.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.var : equivalent function\n", " | \n", " | view(...)\n", " | a.view([dtype][, type])\n", " | \n", " | New view of array with the same data.\n", " | \n", " | .. note::\n", " | Passing None for ``dtype`` is different from omitting the parameter,\n", " | since the former invokes ``dtype(None)`` which is an alias for\n", " | ``dtype('float_')``.\n", " | \n", " | Parameters\n", " | ----------\n", " | dtype : data-type or ndarray sub-class, optional\n", " | Data-type descriptor of the returned view, e.g., float32 or int16.\n", " | Omitting it results in the view having the same data-type as `a`.\n", " | This argument can also be specified as an ndarray sub-class, which\n", " | then specifies the type of the returned object (this is equivalent to\n", " | setting the ``type`` parameter).\n", " | type : Python type, optional\n", " | Type of the returned view, e.g., ndarray or matrix. Again, omission\n", " | of the parameter results in type preservation.\n", " | \n", " | Notes\n", " | -----\n", " | ``a.view()`` is used two different ways:\n", " | \n", " | ``a.view(some_dtype)`` or ``a.view(dtype=some_dtype)`` constructs a view\n", " | of the array's memory with a different data-type. This can cause a\n", " | reinterpretation of the bytes of memory.\n", " | \n", " | ``a.view(ndarray_subclass)`` or ``a.view(type=ndarray_subclass)`` just\n", " | returns an instance of `ndarray_subclass` that looks at the same array\n", " | (same shape, dtype, etc.) This does not cause a reinterpretation of the\n", " | memory.\n", " | \n", " | For ``a.view(some_dtype)``, if ``some_dtype`` has a different number of\n", " | bytes per entry than the previous dtype (for example, converting a regular\n", " | array to a structured array), then the last axis of ``a`` must be\n", " | contiguous. This axis will be resized in the result.\n", " | \n", " | .. versionchanged:: 1.23.0\n", " | Only the last axis needs to be contiguous. Previously, the entire array\n", " | had to be C-contiguous.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([(1, 2)], dtype=[('a', np.int8), ('b', np.int8)])\n", " | \n", " | Viewing array data using a different type and dtype:\n", " | \n", " | >>> y = x.view(dtype=np.int16, type=np.matrix)\n", " | >>> y\n", " | matrix([[513]], dtype=int16)\n", " | >>> print(type(y))\n", " | <class 'numpy.matrix'>\n", " | \n", " | Creating a view on a structured array so it can be used in calculations\n", " | \n", " | >>> x = np.array([(1, 2),(3,4)], dtype=[('a', np.int8), ('b', np.int8)])\n", " | >>> xv = x.view(dtype=np.int8).reshape(-1,2)\n", " | >>> xv\n", " | array([[1, 2],\n", " | [3, 4]], dtype=int8)\n", " | >>> xv.mean(0)\n", " | array([2., 3.])\n", " | \n", " | Making changes to the view changes the underlying array\n", " | \n", " | >>> xv[0,1] = 20\n", " | >>> x\n", " | array([(1, 20), (3, 4)], dtype=[('a', 'i1'), ('b', 'i1')])\n", " | \n", " | Using a view to convert an array to a recarray:\n", " | \n", " | >>> z = x.view(np.recarray)\n", " | >>> z.a\n", " | array([1, 3], dtype=int8)\n", " | \n", " | Views share data:\n", " | \n", " | >>> x[0] = (9, 10)\n", " | >>> z[0]\n", " | (9, 10)\n", " | \n", " | Views that change the dtype size (bytes per entry) should normally be\n", " | avoided on arrays defined by slices, transposes, fortran-ordering, etc.:\n", " | \n", " | >>> x = np.array([[1, 2, 3], [4, 5, 6]], dtype=np.int16)\n", " | >>> y = x[:, ::2]\n", " | >>> y\n", " | array([[1, 3],\n", " | [4, 6]], dtype=int16)\n", " | >>> y.view(dtype=[('width', np.int16), ('length', np.int16)])\n", " | Traceback (most recent call last):\n", " | ...\n", " | ValueError: To change to a dtype of a different size, the last axis must be contiguous\n", " | >>> z = y.copy()\n", " | >>> z.view(dtype=[('width', np.int16), ('length', np.int16)])\n", " | array([[(1, 3)],\n", " | [(4, 6)]], dtype=[('width', '<i2'), ('length', '<i2')])\n", " | \n", " | However, views that change dtype are totally fine for arrays with a\n", " | contiguous last axis, even if the rest of the axes are not C-contiguous:\n", " | \n", " | >>> x = np.arange(2 * 3 * 4, dtype=np.int8).reshape(2, 3, 4)\n", " | >>> x.transpose(1, 0, 2).view(np.int16)\n", " | array([[[ 256, 770],\n", " | [3340, 3854]],\n", " | <BLANKLINE>\n", " | [[1284, 1798],\n", " | [4368, 4882]],\n", " | <BLANKLINE>\n", " | [[2312, 2826],\n", " | [5396, 5910]]], dtype=int16)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods inherited from ndarray:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | a.__class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.ndarray` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.ndarray` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.ndarray[Any, np.dtype[Any]]\n", " | numpy.ndarray[typing.Any, numpy.dtype[typing.Any]]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | numpy.typing.NDArray : An ndarray alias :term:`generic <generic type>`\n", " | w.r.t. its `dtype.type <numpy.dtype.type>`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from ndarray:\n", " | \n", " | T\n", " | View of the transposed array.\n", " | \n", " | Same as ``self.transpose()``.\n", " | \n", " | Examples\n", " | --------\n", " | >>> a = np.array([[1, 2], [3, 4]])\n", " | >>> a\n", " | array([[1, 2],\n", " | [3, 4]])\n", " | >>> a.T\n", " | array([[1, 3],\n", " | [2, 4]])\n", " | \n", " | >>> a = np.array([1, 2, 3, 4])\n", " | >>> a\n", " | array([1, 2, 3, 4])\n", " | >>> a.T\n", " | array([1, 2, 3, 4])\n", " | \n", " | See Also\n", " | --------\n", " | transpose\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side.\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: C-struct side.\n", " | \n", " | base\n", " | Base object if memory is from some other object.\n", " | \n", " | Examples\n", " | --------\n", " | The base of an array that owns its memory is None:\n", " | \n", " | >>> x = np.array([1,2,3,4])\n", " | >>> x.base is None\n", " | True\n", " | \n", " | Slicing creates a view, whose memory is shared with x:\n", " | \n", " | >>> y = x[2:]\n", " | >>> y.base is x\n", " | True\n", " | \n", " | ctypes\n", " | An object to simplify the interaction of the array with the ctypes\n", " | module.\n", " | \n", " | This attribute creates an object that makes it easier to use arrays\n", " | when calling shared libraries with the ctypes module. The returned\n", " | object has, among others, data, shape, and strides attributes (see\n", " | Notes below) which themselves return ctypes objects that can be used\n", " | as arguments to a shared library.\n", " | \n", " | Parameters\n", " | ----------\n", " | None\n", " | \n", " | Returns\n", " | -------\n", " | c : Python object\n", " | Possessing attributes data, shape, strides, etc.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.ctypeslib\n", " | \n", " | Notes\n", " | -----\n", " | Below are the public attributes of this object which were documented\n", " | in \"Guide to NumPy\" (we have omitted undocumented public attributes,\n", " | as well as documented private attributes):\n", " | \n", " | .. autoattribute:: numpy.core._internal._ctypes.data\n", " | :noindex:\n", " | \n", " | .. autoattribute:: numpy.core._internal._ctypes.shape\n", " | :noindex:\n", " | \n", " | .. autoattribute:: numpy.core._internal._ctypes.strides\n", " | :noindex:\n", " | \n", " | .. automethod:: numpy.core._internal._ctypes.data_as\n", " | :noindex:\n", " | \n", " | .. automethod:: numpy.core._internal._ctypes.shape_as\n", " | :noindex:\n", " | \n", " | .. automethod:: numpy.core._internal._ctypes.strides_as\n", " | :noindex:\n", " | \n", " | If the ctypes module is not available, then the ctypes attribute\n", " | of array objects still returns something useful, but ctypes objects\n", " | are not returned and errors may be raised instead. In particular,\n", " | the object will still have the ``as_parameter`` attribute which will\n", " | return an integer equal to the data attribute.\n", " | \n", " | Examples\n", " | --------\n", " | >>> import ctypes\n", " | >>> x = np.array([[0, 1], [2, 3]], dtype=np.int32)\n", " | >>> x\n", " | array([[0, 1],\n", " | [2, 3]], dtype=int32)\n", " | >>> x.ctypes.data\n", " | 31962608 # may vary\n", " | >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32))\n", " | <__main__.LP_c_uint object at 0x7ff2fc1fc200> # may vary\n", " | >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)).contents\n", " | c_uint(0)\n", " | >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint64)).contents\n", " | c_ulong(4294967296)\n", " | >>> x.ctypes.shape\n", " | <numpy.core._internal.c_long_Array_2 object at 0x7ff2fc1fce60> # may vary\n", " | >>> x.ctypes.strides\n", " | <numpy.core._internal.c_long_Array_2 object at 0x7ff2fc1ff320> # may vary\n", " | \n", " | data\n", " | Python buffer object pointing to the start of the array's data.\n", " | \n", " | dtype\n", " | Data-type of the array's elements.\n", " | \n", " | .. warning::\n", " | \n", " | Setting ``arr.dtype`` is discouraged and may be deprecated in the\n", " | future. Setting will replace the ``dtype`` without modifying the\n", " | memory (see also `ndarray.view` and `ndarray.astype`).\n", " | \n", " | Parameters\n", " | ----------\n", " | None\n", " | \n", " | Returns\n", " | -------\n", " | d : numpy dtype object\n", " | \n", " | See Also\n", " | --------\n", " | ndarray.astype : Cast the values contained in the array to a new data-type.\n", " | ndarray.view : Create a view of the same data but a different data-type.\n", " | numpy.dtype\n", " | \n", " | Examples\n", " | --------\n", " | >>> x\n", " | array([[0, 1],\n", " | [2, 3]])\n", " | >>> x.dtype\n", " | dtype('int32')\n", " | >>> type(x.dtype)\n", " | <type 'numpy.dtype'>\n", " | \n", " | flags\n", " | Information about the memory layout of the array.\n", " | \n", " | Attributes\n", " | ----------\n", " | C_CONTIGUOUS (C)\n", " | The data is in a single, C-style contiguous segment.\n", " | F_CONTIGUOUS (F)\n", " | The data is in a single, Fortran-style contiguous segment.\n", " | OWNDATA (O)\n", " | The array owns the memory it uses or borrows it from another object.\n", " | WRITEABLE (W)\n", " | The data area can be written to. Setting this to False locks\n", " | the data, making it read-only. A view (slice, etc.) inherits WRITEABLE\n", " | from its base array at creation time, but a view of a writeable\n", " | array may be subsequently locked while the base array remains writeable.\n", " | (The opposite is not true, in that a view of a locked array may not\n", " | be made writeable. However, currently, locking a base object does not\n", " | lock any views that already reference it, so under that circumstance it\n", " | is possible to alter the contents of a locked array via a previously\n", " | created writeable view onto it.) Attempting to change a non-writeable\n", " | array raises a RuntimeError exception.\n", " | ALIGNED (A)\n", " | The data and all elements are aligned appropriately for the hardware.\n", " | WRITEBACKIFCOPY (X)\n", " | This array is a copy of some other array. The C-API function\n", " | PyArray_ResolveWritebackIfCopy must be called before deallocating\n", " | to the base array will be updated with the contents of this array.\n", " | FNC\n", " | F_CONTIGUOUS and not C_CONTIGUOUS.\n", " | FORC\n", " | F_CONTIGUOUS or C_CONTIGUOUS (one-segment test).\n", " | BEHAVED (B)\n", " | ALIGNED and WRITEABLE.\n", " | CARRAY (CA)\n", " | BEHAVED and C_CONTIGUOUS.\n", " | FARRAY (FA)\n", " | BEHAVED and F_CONTIGUOUS and not C_CONTIGUOUS.\n", " | \n", " | Notes\n", " | -----\n", " | The `flags` object can be accessed dictionary-like (as in ``a.flags['WRITEABLE']``),\n", " | or by using lowercased attribute names (as in ``a.flags.writeable``). Short flag\n", " | names are only supported in dictionary access.\n", " | \n", " | Only the WRITEBACKIFCOPY, WRITEABLE, and ALIGNED flags can be\n", " | changed by the user, via direct assignment to the attribute or dictionary\n", " | entry, or by calling `ndarray.setflags`.\n", " | \n", " | The array flags cannot be set arbitrarily:\n", " | \n", " | - WRITEBACKIFCOPY can only be set ``False``.\n", " | - ALIGNED can only be set ``True`` if the data is truly aligned.\n", " | - WRITEABLE can only be set ``True`` if the array owns its own memory\n", " | or the ultimate owner of the memory exposes a writeable buffer\n", " | interface or is a string.\n", " | \n", " | Arrays can be both C-style and Fortran-style contiguous simultaneously.\n", " | This is clear for 1-dimensional arrays, but can also be true for higher\n", " | dimensional arrays.\n", " | \n", " | Even for contiguous arrays a stride for a given dimension\n", " | ``arr.strides[dim]`` may be *arbitrary* if ``arr.shape[dim] == 1``\n", " | or the array has no elements.\n", " | It does *not* generally hold that ``self.strides[-1] == self.itemsize``\n", " | for C-style contiguous arrays or ``self.strides[0] == self.itemsize`` for\n", " | Fortran-style contiguous arrays is true.\n", " | \n", " | flat\n", " | A 1-D iterator over the array.\n", " | \n", " | This is a `numpy.flatiter` instance, which acts similarly to, but is not\n", " | a subclass of, Python's built-in iterator object.\n", " | \n", " | See Also\n", " | --------\n", " | flatten : Return a copy of the array collapsed into one dimension.\n", " | \n", " | flatiter\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.arange(1, 7).reshape(2, 3)\n", " | >>> x\n", " | array([[1, 2, 3],\n", " | [4, 5, 6]])\n", " | >>> x.flat[3]\n", " | 4\n", " | >>> x.T\n", " | array([[1, 4],\n", " | [2, 5],\n", " | [3, 6]])\n", " | >>> x.T.flat[3]\n", " | 5\n", " | >>> type(x.flat)\n", " | <class 'numpy.flatiter'>\n", " | \n", " | An assignment example:\n", " | \n", " | >>> x.flat = 3; x\n", " | array([[3, 3, 3],\n", " | [3, 3, 3]])\n", " | >>> x.flat[[1,4]] = 1; x\n", " | array([[3, 1, 3],\n", " | [3, 1, 3]])\n", " | \n", " | imag\n", " | The imaginary part of the array.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.sqrt([1+0j, 0+1j])\n", " | >>> x.imag\n", " | array([ 0. , 0.70710678])\n", " | >>> x.imag.dtype\n", " | dtype('float64')\n", " | \n", " | itemsize\n", " | Length of one array element in bytes.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([1,2,3], dtype=np.float64)\n", " | >>> x.itemsize\n", " | 8\n", " | >>> x = np.array([1,2,3], dtype=np.complex128)\n", " | >>> x.itemsize\n", " | 16\n", " | \n", " | nbytes\n", " | Total bytes consumed by the elements of the array.\n", " | \n", " | Notes\n", " | -----\n", " | Does not include memory consumed by non-element attributes of the\n", " | array object.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.zeros((3,5,2), dtype=np.complex128)\n", " | >>> x.nbytes\n", " | 480\n", " | >>> np.prod(x.shape) * x.itemsize\n", " | 480\n", " | \n", " | ndim\n", " | Number of array dimensions.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([1, 2, 3])\n", " | >>> x.ndim\n", " | 1\n", " | >>> y = np.zeros((2, 3, 4))\n", " | >>> y.ndim\n", " | 3\n", " | \n", " | real\n", " | The real part of the array.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.sqrt([1+0j, 0+1j])\n", " | >>> x.real\n", " | array([ 1. , 0.70710678])\n", " | >>> x.real.dtype\n", " | dtype('float64')\n", " | \n", " | See Also\n", " | --------\n", " | numpy.real : equivalent function\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | The shape property is usually used to get the current shape of an array,\n", " | but may also be used to reshape the array in-place by assigning a tuple of\n", " | array dimensions to it. As with `numpy.reshape`, one of the new shape\n", " | dimensions can be -1, in which case its value is inferred from the size of\n", " | the array and the remaining dimensions. Reshaping an array in-place will\n", " | fail if a copy is required.\n", " | \n", " | .. warning::\n", " | \n", " | Setting ``arr.shape`` is discouraged and may be deprecated in the\n", " | future. Using `ndarray.reshape` is the preferred approach.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.array([1, 2, 3, 4])\n", " | >>> x.shape\n", " | (4,)\n", " | >>> y = np.zeros((2, 3, 4))\n", " | >>> y.shape\n", " | (2, 3, 4)\n", " | >>> y.shape = (3, 8)\n", " | >>> y\n", " | array([[ 0., 0., 0., 0., 0., 0., 0., 0.],\n", " | [ 0., 0., 0., 0., 0., 0., 0., 0.],\n", " | [ 0., 0., 0., 0., 0., 0., 0., 0.]])\n", " | >>> y.shape = (3, 6)\n", " | Traceback (most recent call last):\n", " | File \"<stdin>\", line 1, in <module>\n", " | ValueError: total size of new array must be unchanged\n", " | >>> np.zeros((4,2))[::2].shape = (-1,)\n", " | Traceback (most recent call last):\n", " | File \"<stdin>\", line 1, in <module>\n", " | AttributeError: Incompatible shape for in-place modification. Use\n", " | `.reshape()` to make a copy with the desired shape.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.shape : Equivalent getter function.\n", " | numpy.reshape : Function similar to setting ``shape``.\n", " | ndarray.reshape : Method similar to setting ``shape``.\n", " | \n", " | size\n", " | Number of elements in the array.\n", " | \n", " | Equal to ``np.prod(a.shape)``, i.e., the product of the array's\n", " | dimensions.\n", " | \n", " | Notes\n", " | -----\n", " | `a.size` returns a standard arbitrary precision Python integer. This\n", " | may not be the case with other methods of obtaining the same value\n", " | (like the suggested ``np.prod(a.shape)``, which returns an instance\n", " | of ``np.int_``), and may be relevant if the value is used further in\n", " | calculations that may overflow a fixed size integer type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> x = np.zeros((3, 5, 2), dtype=np.complex128)\n", " | >>> x.size\n", " | 30\n", " | >>> np.prod(x.shape)\n", " | 30\n", " | \n", " | strides\n", " | Tuple of bytes to step in each dimension when traversing an array.\n", " | \n", " | The byte offset of element ``(i[0], i[1], ..., i[n])`` in an array `a`\n", " | is::\n", " | \n", " | offset = sum(np.array(i) * a.strides)\n", " | \n", " | A more detailed explanation of strides can be found in the\n", " | \"ndarray.rst\" file in the NumPy reference guide.\n", " | \n", " | .. warning::\n", " | \n", " | Setting ``arr.strides`` is discouraged and may be deprecated in the\n", " | future. `numpy.lib.stride_tricks.as_strided` should be preferred\n", " | to create a new view of the same data in a safer way.\n", " | \n", " | Notes\n", " | -----\n", " | Imagine an array of 32-bit integers (each 4 bytes)::\n", " | \n", " | x = np.array([[0, 1, 2, 3, 4],\n", " | [5, 6, 7, 8, 9]], dtype=np.int32)\n", " | \n", " | This array is stored in memory as 40 bytes, one after the other\n", " | (known as a contiguous block of memory). The strides of an array tell\n", " | us how many bytes we have to skip in memory to move to the next position\n", " | along a certain axis. For example, we have to skip 4 bytes (1 value) to\n", " | move to the next column, but 20 bytes (5 values) to get to the same\n", " | position in the next row. As such, the strides for the array `x` will be\n", " | ``(20, 4)``.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.lib.stride_tricks.as_strided\n", " | \n", " | Examples\n", " | --------\n", " | >>> y = np.reshape(np.arange(2*3*4), (2,3,4))\n", " | >>> y\n", " | array([[[ 0, 1, 2, 3],\n", " | [ 4, 5, 6, 7],\n", " | [ 8, 9, 10, 11]],\n", " | [[12, 13, 14, 15],\n", " | [16, 17, 18, 19],\n", " | [20, 21, 22, 23]]])\n", " | >>> y.strides\n", " | (48, 16, 4)\n", " | >>> y[1,1,1]\n", " | 17\n", " | >>> offset=sum(y.strides * np.array((1,1,1)))\n", " | >>> offset/y.itemsize\n", " | 17\n", " | \n", " | >>> x = np.reshape(np.arange(5*6*7*8), (5,6,7,8)).transpose(2,3,1,0)\n", " | >>> x.strides\n", " | (32, 4, 224, 1344)\n", " | >>> i = np.array([3,5,2,2])\n", " | >>> offset = sum(i * x.strides)\n", " | >>> x[3,5,2,2]\n", " | 813\n", " | >>> offset / x.itemsize\n", " | 813\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data and other attributes inherited from ndarray:\n", " | \n", " | __hash__ = None\n", " \n", " class record(void)\n", " | A data-type scalar that allows field access as attribute lookup.\n", " | \n", " | Method resolution order:\n", " | record\n", " | void\n", " | flexible\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __getattribute__(self, attr)\n", " | Return getattr(self, name).\n", " | \n", " | __getitem__(self, indx)\n", " | Return self[key].\n", " | \n", " | __repr__(self)\n", " | Return repr(self).\n", " | \n", " | __setattr__(self, attr, val)\n", " | Implement setattr(self, name, value).\n", " | \n", " | __str__(self)\n", " | Return str(self).\n", " | \n", " | pprint(self)\n", " | Pretty-print all fields.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors defined here:\n", " | \n", " | __dict__\n", " | dictionary for instance variables (if defined)\n", " | \n", " | __weakref__\n", " | list of weak references to the object (if defined)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from void:\n", " | \n", " | __delitem__(self, key, /)\n", " | Delete self[key].\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __len__(self, /)\n", " | Return len(self).\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __setitem__(self, key, value, /)\n", " | Set self[key] to value.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods inherited from void:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from void:\n", " | \n", " | base\n", " | base object\n", " | \n", " | dtype\n", " | dtype object\n", " | \n", " | flags\n", " | integer value of flags\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " short = class int16(signedinteger)\n", " | Signed integer type, compatible with C ``short``.\n", " | \n", " | :Character code: ``'h'``\n", " | :Canonical name: `numpy.short`\n", " | :Alias on this platform (win32 AMD64): `numpy.int16`: 16-bit signed integer (``-32_768`` to ``32_767``).\n", " | \n", " | Method resolution order:\n", " | int16\n", " | signedinteger\n", " | integer\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __index__(self, /)\n", " | Return self converted to an integer, if self is suitable for use as an index into a list.\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | bit_count(...)\n", " | int16.bit_count() -> int\n", " | \n", " | Computes the number of 1-bits in the absolute value of the input.\n", " | Analogous to the builtin `int.bit_count` or ``popcount`` in C++.\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.int16(127).bit_count()\n", " | 7\n", " | >>> np.int16(-127).bit_count()\n", " | 7\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from integer:\n", " | \n", " | __round__(...)\n", " | \n", " | is_integer(...)\n", " | integer.is_integer() -> bool\n", " | \n", " | Return ``True`` if the number is finite with integral value.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.int64(-2).is_integer()\n", " | True\n", " | >>> np.uint32(5).is_integer()\n", " | True\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from integer:\n", " | \n", " | denominator\n", " | denominator of value (1)\n", " | \n", " | numerator\n", " | numerator of value (the value itself)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " class signedinteger(integer)\n", " | Abstract base class of all signed integer scalar types.\n", " | \n", " | Method resolution order:\n", " | signedinteger\n", " | integer\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods inherited from integer:\n", " | \n", " | __round__(...)\n", " | \n", " | is_integer(...)\n", " | integer.is_integer() -> bool\n", " | \n", " | Return ``True`` if the number is finite with integral value.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.int64(-2).is_integer()\n", " | True\n", " | >>> np.uint32(5).is_integer()\n", " | True\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from integer:\n", " | \n", " | denominator\n", " | denominator of value (1)\n", " | \n", " | numerator\n", " | numerator of value (the value itself)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods inherited from number:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data and other attributes inherited from generic:\n", " | \n", " | __hash__ = None\n", " \n", " single = class float32(floating)\n", " | Single-precision floating-point number type, compatible with C ``float``.\n", " | \n", " | :Character code: ``'f'``\n", " | :Canonical name: `numpy.single`\n", " | :Alias on this platform (win32 AMD64): `numpy.float32`: 32-bit-precision floating-point number type: sign bit, 8 bits exponent, 23 bits mantissa.\n", " | \n", " | Method resolution order:\n", " | float32\n", " | floating\n", " | inexact\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | as_integer_ratio(...)\n", " | single.as_integer_ratio() -> (int, int)\n", " | \n", " | Return a pair of integers, whose ratio is exactly equal to the original\n", " | floating point number, and with a positive denominator.\n", " | Raise `OverflowError` on infinities and a `ValueError` on NaNs.\n", " | \n", " | >>> np.single(10.0).as_integer_ratio()\n", " | (10, 1)\n", " | >>> np.single(0.0).as_integer_ratio()\n", " | (0, 1)\n", " | >>> np.single(-.25).as_integer_ratio()\n", " | (-1, 4)\n", " | \n", " | is_integer(...)\n", " | single.is_integer() -> bool\n", " | \n", " | Return ``True`` if the floating point number is finite with integral\n", " | value, and ``False`` otherwise.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.single(-2.0).is_integer()\n", " | True\n", " | >>> np.single(3.2).is_integer()\n", " | False\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from floating:\n", " | \n", " | __round__(...)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " singlecomplex = class complex64(complexfloating)\n", " | Complex number type composed of two single-precision floating-point\n", " | numbers.\n", " | \n", " | :Character code: ``'F'``\n", " | :Canonical name: `numpy.csingle`\n", " | :Alias: `numpy.singlecomplex`\n", " | :Alias on this platform (win32 AMD64): `numpy.complex64`: Complex number type composed of 2 32-bit-precision floating-point numbers.\n", " | \n", " | Method resolution order:\n", " | complex64\n", " | complexfloating\n", " | inexact\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __complex__(...)\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from complexfloating:\n", " | \n", " | __round__(...)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " class str_(builtins.str, character)\n", " | A unicode string.\n", " | \n", " | When used in arrays, this type strips trailing null codepoints.\n", " | \n", " | Unlike the builtin `str`, this supports the :ref:`python:bufferobjects`, exposing its\n", " | contents as UCS4:\n", " | \n", " | >>> m = memoryview(np.str_(\"abc\"))\n", " | >>> m.format\n", " | '3w'\n", " | >>> m.tobytes()\n", " | b'a\\x00\\x00\\x00b\\x00\\x00\\x00c\\x00\\x00\\x00'\n", " | \n", " | :Character code: ``'U'``\n", " | :Alias: `numpy.unicode_`\n", " | \n", " | Method resolution order:\n", " | str_\n", " | builtins.str\n", " | character\n", " | flexible\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from builtins.str:\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __contains__(self, key, /)\n", " | Return key in self.\n", " | \n", " | __format__(self, format_spec, /)\n", " | Return a formatted version of the string as described by format_spec.\n", " | \n", " | __getattribute__(self, name, /)\n", " | Return getattr(self, name).\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __getnewargs__(...)\n", " | \n", " | __iter__(self, /)\n", " | Implement iter(self).\n", " | \n", " | __len__(self, /)\n", " | Return len(self).\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __sizeof__(self, /)\n", " | Return the size of the string in memory, in bytes.\n", " | \n", " | capitalize(self, /)\n", " | Return a capitalized version of the string.\n", " | \n", " | More specifically, make the first character have upper case and the rest lower\n", " | case.\n", " | \n", " | casefold(self, /)\n", " | Return a version of the string suitable for caseless comparisons.\n", " | \n", " | center(self, width, fillchar=' ', /)\n", " | Return a centered string of length width.\n", " | \n", " | Padding is done using the specified fill character (default is a space).\n", " | \n", " | count(...)\n", " | S.count(sub[, start[, end]]) -> int\n", " | \n", " | Return the number of non-overlapping occurrences of substring sub in\n", " | string S[start:end]. Optional arguments start and end are\n", " | interpreted as in slice notation.\n", " | \n", " | encode(self, /, encoding='utf-8', errors='strict')\n", " | Encode the string using the codec registered for encoding.\n", " | \n", " | encoding\n", " | The encoding in which to encode the string.\n", " | errors\n", " | The error handling scheme to use for encoding errors.\n", " | The default is 'strict' meaning that encoding errors raise a\n", " | UnicodeEncodeError. Other possible values are 'ignore', 'replace' and\n", " | 'xmlcharrefreplace' as well as any other name registered with\n", " | codecs.register_error that can handle UnicodeEncodeErrors.\n", " | \n", " | endswith(...)\n", " | S.endswith(suffix[, start[, end]]) -> bool\n", " | \n", " | Return True if S ends with the specified suffix, False otherwise.\n", " | With optional start, test S beginning at that position.\n", " | With optional end, stop comparing S at that position.\n", " | suffix can also be a tuple of strings to try.\n", " | \n", " | expandtabs(self, /, tabsize=8)\n", " | Return a copy where all tab characters are expanded using spaces.\n", " | \n", " | If tabsize is not given, a tab size of 8 characters is assumed.\n", " | \n", " | find(...)\n", " | S.find(sub[, start[, end]]) -> int\n", " | \n", " | Return the lowest index in S where substring sub is found,\n", " | such that sub is contained within S[start:end]. Optional\n", " | arguments start and end are interpreted as in slice notation.\n", " | \n", " | Return -1 on failure.\n", " | \n", " | format(...)\n", " | S.format(*args, **kwargs) -> str\n", " | \n", " | Return a formatted version of S, using substitutions from args and kwargs.\n", " | The substitutions are identified by braces ('{' and '}').\n", " | \n", " | format_map(...)\n", " | S.format_map(mapping) -> str\n", " | \n", " | Return a formatted version of S, using substitutions from mapping.\n", " | The substitutions are identified by braces ('{' and '}').\n", " | \n", " | index(...)\n", " | S.index(sub[, start[, end]]) -> int\n", " | \n", " | Return the lowest index in S where substring sub is found,\n", " | such that sub is contained within S[start:end]. Optional\n", " | arguments start and end are interpreted as in slice notation.\n", " | \n", " | Raises ValueError when the substring is not found.\n", " | \n", " | isalnum(self, /)\n", " | Return True if the string is an alpha-numeric string, False otherwise.\n", " | \n", " | A string is alpha-numeric if all characters in the string are alpha-numeric and\n", " | there is at least one character in the string.\n", " | \n", " | isalpha(self, /)\n", " | Return True if the string is an alphabetic string, False otherwise.\n", " | \n", " | A string is alphabetic if all characters in the string are alphabetic and there\n", " | is at least one character in the string.\n", " | \n", " | isascii(self, /)\n", " | Return True if all characters in the string are ASCII, False otherwise.\n", " | \n", " | ASCII characters have code points in the range U+0000-U+007F.\n", " | Empty string is ASCII too.\n", " | \n", " | isdecimal(self, /)\n", " | Return True if the string is a decimal string, False otherwise.\n", " | \n", " | A string is a decimal string if all characters in the string are decimal and\n", " | there is at least one character in the string.\n", " | \n", " | isdigit(self, /)\n", " | Return True if the string is a digit string, False otherwise.\n", " | \n", " | A string is a digit string if all characters in the string are digits and there\n", " | is at least one character in the string.\n", " | \n", " | isidentifier(self, /)\n", " | Return True if the string is a valid Python identifier, False otherwise.\n", " | \n", " | Call keyword.iskeyword(s) to test whether string s is a reserved identifier,\n", " | such as \"def\" or \"class\".\n", " | \n", " | islower(self, /)\n", " | Return True if the string is a lowercase string, False otherwise.\n", " | \n", " | A string is lowercase if all cased characters in the string are lowercase and\n", " | there is at least one cased character in the string.\n", " | \n", " | isnumeric(self, /)\n", " | Return True if the string is a numeric string, False otherwise.\n", " | \n", " | A string is numeric if all characters in the string are numeric and there is at\n", " | least one character in the string.\n", " | \n", " | isprintable(self, /)\n", " | Return True if the string is printable, False otherwise.\n", " | \n", " | A string is printable if all of its characters are considered printable in\n", " | repr() or if it is empty.\n", " | \n", " | isspace(self, /)\n", " | Return True if the string is a whitespace string, False otherwise.\n", " | \n", " | A string is whitespace if all characters in the string are whitespace and there\n", " | is at least one character in the string.\n", " | \n", " | istitle(self, /)\n", " | Return True if the string is a title-cased string, False otherwise.\n", " | \n", " | In a title-cased string, upper- and title-case characters may only\n", " | follow uncased characters and lowercase characters only cased ones.\n", " | \n", " | isupper(self, /)\n", " | Return True if the string is an uppercase string, False otherwise.\n", " | \n", " | A string is uppercase if all cased characters in the string are uppercase and\n", " | there is at least one cased character in the string.\n", " | \n", " | join(self, iterable, /)\n", " | Concatenate any number of strings.\n", " | \n", " | The string whose method is called is inserted in between each given string.\n", " | The result is returned as a new string.\n", " | \n", " | Example: '.'.join(['ab', 'pq', 'rs']) -> 'ab.pq.rs'\n", " | \n", " | ljust(self, width, fillchar=' ', /)\n", " | Return a left-justified string of length width.\n", " | \n", " | Padding is done using the specified fill character (default is a space).\n", " | \n", " | lower(self, /)\n", " | Return a copy of the string converted to lowercase.\n", " | \n", " | lstrip(self, chars=None, /)\n", " | Return a copy of the string with leading whitespace removed.\n", " | \n", " | If chars is given and not None, remove characters in chars instead.\n", " | \n", " | partition(self, sep, /)\n", " | Partition the string into three parts using the given separator.\n", " | \n", " | This will search for the separator in the string. If the separator is found,\n", " | returns a 3-tuple containing the part before the separator, the separator\n", " | itself, and the part after it.\n", " | \n", " | If the separator is not found, returns a 3-tuple containing the original string\n", " | and two empty strings.\n", " | \n", " | removeprefix(self, prefix, /)\n", " | Return a str with the given prefix string removed if present.\n", " | \n", " | If the string starts with the prefix string, return string[len(prefix):].\n", " | Otherwise, return a copy of the original string.\n", " | \n", " | removesuffix(self, suffix, /)\n", " | Return a str with the given suffix string removed if present.\n", " | \n", " | If the string ends with the suffix string and that suffix is not empty,\n", " | return string[:-len(suffix)]. Otherwise, return a copy of the original\n", " | string.\n", " | \n", " | replace(self, old, new, count=-1, /)\n", " | Return a copy with all occurrences of substring old replaced by new.\n", " | \n", " | count\n", " | Maximum number of occurrences to replace.\n", " | -1 (the default value) means replace all occurrences.\n", " | \n", " | If the optional argument count is given, only the first count occurrences are\n", " | replaced.\n", " | \n", " | rfind(...)\n", " | S.rfind(sub[, start[, end]]) -> int\n", " | \n", " | Return the highest index in S where substring sub is found,\n", " | such that sub is contained within S[start:end]. Optional\n", " | arguments start and end are interpreted as in slice notation.\n", " | \n", " | Return -1 on failure.\n", " | \n", " | rindex(...)\n", " | S.rindex(sub[, start[, end]]) -> int\n", " | \n", " | Return the highest index in S where substring sub is found,\n", " | such that sub is contained within S[start:end]. Optional\n", " | arguments start and end are interpreted as in slice notation.\n", " | \n", " | Raises ValueError when the substring is not found.\n", " | \n", " | rjust(self, width, fillchar=' ', /)\n", " | Return a right-justified string of length width.\n", " | \n", " | Padding is done using the specified fill character (default is a space).\n", " | \n", " | rpartition(self, sep, /)\n", " | Partition the string into three parts using the given separator.\n", " | \n", " | This will search for the separator in the string, starting at the end. If\n", " | the separator is found, returns a 3-tuple containing the part before the\n", " | separator, the separator itself, and the part after it.\n", " | \n", " | If the separator is not found, returns a 3-tuple containing two empty strings\n", " | and the original string.\n", " | \n", " | rsplit(self, /, sep=None, maxsplit=-1)\n", " | Return a list of the substrings in the string, using sep as the separator string.\n", " | \n", " | sep\n", " | The separator used to split the string.\n", " | \n", " | When set to None (the default value), will split on any whitespace\n", " | character (including \\\\n \\\\r \\\\t \\\\f and spaces) and will discard\n", " | empty strings from the result.\n", " | maxsplit\n", " | Maximum number of splits (starting from the left).\n", " | -1 (the default value) means no limit.\n", " | \n", " | Splitting starts at the end of the string and works to the front.\n", " | \n", " | rstrip(self, chars=None, /)\n", " | Return a copy of the string with trailing whitespace removed.\n", " | \n", " | If chars is given and not None, remove characters in chars instead.\n", " | \n", " | split(self, /, sep=None, maxsplit=-1)\n", " | Return a list of the substrings in the string, using sep as the separator string.\n", " | \n", " | sep\n", " | The separator used to split the string.\n", " | \n", " | When set to None (the default value), will split on any whitespace\n", " | character (including \\\\n \\\\r \\\\t \\\\f and spaces) and will discard\n", " | empty strings from the result.\n", " | maxsplit\n", " | Maximum number of splits (starting from the left).\n", " | -1 (the default value) means no limit.\n", " | \n", " | Note, str.split() is mainly useful for data that has been intentionally\n", " | delimited. With natural text that includes punctuation, consider using\n", " | the regular expression module.\n", " | \n", " | splitlines(self, /, keepends=False)\n", " | Return a list of the lines in the string, breaking at line boundaries.\n", " | \n", " | Line breaks are not included in the resulting list unless keepends is given and\n", " | true.\n", " | \n", " | startswith(...)\n", " | S.startswith(prefix[, start[, end]]) -> bool\n", " | \n", " | Return True if S starts with the specified prefix, False otherwise.\n", " | With optional start, test S beginning at that position.\n", " | With optional end, stop comparing S at that position.\n", " | prefix can also be a tuple of strings to try.\n", " | \n", " | strip(self, chars=None, /)\n", " | Return a copy of the string with leading and trailing whitespace removed.\n", " | \n", " | If chars is given and not None, remove characters in chars instead.\n", " | \n", " | swapcase(self, /)\n", " | Convert uppercase characters to lowercase and lowercase characters to uppercase.\n", " | \n", " | title(self, /)\n", " | Return a version of the string where each word is titlecased.\n", " | \n", " | More specifically, words start with uppercased characters and all remaining\n", " | cased characters have lower case.\n", " | \n", " | translate(self, table, /)\n", " | Replace each character in the string using the given translation table.\n", " | \n", " | table\n", " | Translation table, which must be a mapping of Unicode ordinals to\n", " | Unicode ordinals, strings, or None.\n", " | \n", " | The table must implement lookup/indexing via __getitem__, for instance a\n", " | dictionary or list. If this operation raises LookupError, the character is\n", " | left untouched. Characters mapped to None are deleted.\n", " | \n", " | upper(self, /)\n", " | Return a copy of the string converted to uppercase.\n", " | \n", " | zfill(self, width, /)\n", " | Pad a numeric string with zeros on the left, to fill a field of the given width.\n", " | \n", " | The string is never truncated.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods inherited from builtins.str:\n", " | \n", " | maketrans(...)\n", " | Return a translation table usable for str.translate().\n", " | \n", " | If there is only one argument, it must be a dictionary mapping Unicode\n", " | ordinals (integers) or characters to Unicode ordinals, strings or None.\n", " | Character keys will be then converted to ordinals.\n", " | If there are two arguments, they must be strings of equal length, and\n", " | in the resulting dictionary, each character in x will be mapped to the\n", " | character at the same position in y. If there is a third argument, it\n", " | must be a string, whose characters will be mapped to None in the result.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " string_ = class bytes_(builtins.bytes, character)\n", " | A byte string.\n", " | \n", " | When used in arrays, this type strips trailing null bytes.\n", " | \n", " | :Character code: ``'S'``\n", " | :Alias: `numpy.string_`\n", " | \n", " | Method resolution order:\n", " | bytes_\n", " | builtins.bytes\n", " | character\n", " | flexible\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from builtins.bytes:\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __bytes__(self, /)\n", " | Convert this value to exact type bytes.\n", " | \n", " | __contains__(self, key, /)\n", " | Return key in self.\n", " | \n", " | __getattribute__(self, name, /)\n", " | Return getattr(self, name).\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __getnewargs__(...)\n", " | \n", " | __iter__(self, /)\n", " | Implement iter(self).\n", " | \n", " | __len__(self, /)\n", " | Return len(self).\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | capitalize(...)\n", " | B.capitalize() -> copy of B\n", " | \n", " | Return a copy of B with only its first character capitalized (ASCII)\n", " | and the rest lower-cased.\n", " | \n", " | center(self, width, fillchar=b' ', /)\n", " | Return a centered string of length width.\n", " | \n", " | Padding is done using the specified fill character.\n", " | \n", " | count(...)\n", " | B.count(sub[, start[, end]]) -> int\n", " | \n", " | Return the number of non-overlapping occurrences of subsection sub in\n", " | bytes B[start:end]. Optional arguments start and end are interpreted\n", " | as in slice notation.\n", " | \n", " | decode(self, /, encoding='utf-8', errors='strict')\n", " | Decode the bytes using the codec registered for encoding.\n", " | \n", " | encoding\n", " | The encoding with which to decode the bytes.\n", " | errors\n", " | The error handling scheme to use for the handling of decoding errors.\n", " | The default is 'strict' meaning that decoding errors raise a\n", " | UnicodeDecodeError. Other possible values are 'ignore' and 'replace'\n", " | as well as any other name registered with codecs.register_error that\n", " | can handle UnicodeDecodeErrors.\n", " | \n", " | endswith(...)\n", " | B.endswith(suffix[, start[, end]]) -> bool\n", " | \n", " | Return True if B ends with the specified suffix, False otherwise.\n", " | With optional start, test B beginning at that position.\n", " | With optional end, stop comparing B at that position.\n", " | suffix can also be a tuple of bytes to try.\n", " | \n", " | expandtabs(self, /, tabsize=8)\n", " | Return a copy where all tab characters are expanded using spaces.\n", " | \n", " | If tabsize is not given, a tab size of 8 characters is assumed.\n", " | \n", " | find(...)\n", " | B.find(sub[, start[, end]]) -> int\n", " | \n", " | Return the lowest index in B where subsection sub is found,\n", " | such that sub is contained within B[start,end]. Optional\n", " | arguments start and end are interpreted as in slice notation.\n", " | \n", " | Return -1 on failure.\n", " | \n", " | hex(...)\n", " | Create a string of hexadecimal numbers from a bytes object.\n", " | \n", " | sep\n", " | An optional single character or byte to separate hex bytes.\n", " | bytes_per_sep\n", " | How many bytes between separators. Positive values count from the\n", " | right, negative values count from the left.\n", " | \n", " | Example:\n", " | >>> value = b'\\xb9\\x01\\xef'\n", " | >>> value.hex()\n", " | 'b901ef'\n", " | >>> value.hex(':')\n", " | 'b9:01:ef'\n", " | >>> value.hex(':', 2)\n", " | 'b9:01ef'\n", " | >>> value.hex(':', -2)\n", " | 'b901:ef'\n", " | \n", " | index(...)\n", " | B.index(sub[, start[, end]]) -> int\n", " | \n", " | Return the lowest index in B where subsection sub is found,\n", " | such that sub is contained within B[start,end]. Optional\n", " | arguments start and end are interpreted as in slice notation.\n", " | \n", " | Raises ValueError when the subsection is not found.\n", " | \n", " | isalnum(...)\n", " | B.isalnum() -> bool\n", " | \n", " | Return True if all characters in B are alphanumeric\n", " | and there is at least one character in B, False otherwise.\n", " | \n", " | isalpha(...)\n", " | B.isalpha() -> bool\n", " | \n", " | Return True if all characters in B are alphabetic\n", " | and there is at least one character in B, False otherwise.\n", " | \n", " | isascii(...)\n", " | B.isascii() -> bool\n", " | \n", " | Return True if B is empty or all characters in B are ASCII,\n", " | False otherwise.\n", " | \n", " | isdigit(...)\n", " | B.isdigit() -> bool\n", " | \n", " | Return True if all characters in B are digits\n", " | and there is at least one character in B, False otherwise.\n", " | \n", " | islower(...)\n", " | B.islower() -> bool\n", " | \n", " | Return True if all cased characters in B are lowercase and there is\n", " | at least one cased character in B, False otherwise.\n", " | \n", " | isspace(...)\n", " | B.isspace() -> bool\n", " | \n", " | Return True if all characters in B are whitespace\n", " | and there is at least one character in B, False otherwise.\n", " | \n", " | istitle(...)\n", " | B.istitle() -> bool\n", " | \n", " | Return True if B is a titlecased string and there is at least one\n", " | character in B, i.e. uppercase characters may only follow uncased\n", " | characters and lowercase characters only cased ones. Return False\n", " | otherwise.\n", " | \n", " | isupper(...)\n", " | B.isupper() -> bool\n", " | \n", " | Return True if all cased characters in B are uppercase and there is\n", " | at least one cased character in B, False otherwise.\n", " | \n", " | join(self, iterable_of_bytes, /)\n", " | Concatenate any number of bytes objects.\n", " | \n", " | The bytes whose method is called is inserted in between each pair.\n", " | \n", " | The result is returned as a new bytes object.\n", " | \n", " | Example: b'.'.join([b'ab', b'pq', b'rs']) -> b'ab.pq.rs'.\n", " | \n", " | ljust(self, width, fillchar=b' ', /)\n", " | Return a left-justified string of length width.\n", " | \n", " | Padding is done using the specified fill character.\n", " | \n", " | lower(...)\n", " | B.lower() -> copy of B\n", " | \n", " | Return a copy of B with all ASCII characters converted to lowercase.\n", " | \n", " | lstrip(self, bytes=None, /)\n", " | Strip leading bytes contained in the argument.\n", " | \n", " | If the argument is omitted or None, strip leading ASCII whitespace.\n", " | \n", " | partition(self, sep, /)\n", " | Partition the bytes into three parts using the given separator.\n", " | \n", " | This will search for the separator sep in the bytes. If the separator is found,\n", " | returns a 3-tuple containing the part before the separator, the separator\n", " | itself, and the part after it.\n", " | \n", " | If the separator is not found, returns a 3-tuple containing the original bytes\n", " | object and two empty bytes objects.\n", " | \n", " | removeprefix(self, prefix, /)\n", " | Return a bytes object with the given prefix string removed if present.\n", " | \n", " | If the bytes starts with the prefix string, return bytes[len(prefix):].\n", " | Otherwise, return a copy of the original bytes.\n", " | \n", " | removesuffix(self, suffix, /)\n", " | Return a bytes object with the given suffix string removed if present.\n", " | \n", " | If the bytes ends with the suffix string and that suffix is not empty,\n", " | return bytes[:-len(prefix)]. Otherwise, return a copy of the original\n", " | bytes.\n", " | \n", " | replace(self, old, new, count=-1, /)\n", " | Return a copy with all occurrences of substring old replaced by new.\n", " | \n", " | count\n", " | Maximum number of occurrences to replace.\n", " | -1 (the default value) means replace all occurrences.\n", " | \n", " | If the optional argument count is given, only the first count occurrences are\n", " | replaced.\n", " | \n", " | rfind(...)\n", " | B.rfind(sub[, start[, end]]) -> int\n", " | \n", " | Return the highest index in B where subsection sub is found,\n", " | such that sub is contained within B[start,end]. Optional\n", " | arguments start and end are interpreted as in slice notation.\n", " | \n", " | Return -1 on failure.\n", " | \n", " | rindex(...)\n", " | B.rindex(sub[, start[, end]]) -> int\n", " | \n", " | Return the highest index in B where subsection sub is found,\n", " | such that sub is contained within B[start,end]. Optional\n", " | arguments start and end are interpreted as in slice notation.\n", " | \n", " | Raise ValueError when the subsection is not found.\n", " | \n", " | rjust(self, width, fillchar=b' ', /)\n", " | Return a right-justified string of length width.\n", " | \n", " | Padding is done using the specified fill character.\n", " | \n", " | rpartition(self, sep, /)\n", " | Partition the bytes into three parts using the given separator.\n", " | \n", " | This will search for the separator sep in the bytes, starting at the end. If\n", " | the separator is found, returns a 3-tuple containing the part before the\n", " | separator, the separator itself, and the part after it.\n", " | \n", " | If the separator is not found, returns a 3-tuple containing two empty bytes\n", " | objects and the original bytes object.\n", " | \n", " | rsplit(self, /, sep=None, maxsplit=-1)\n", " | Return a list of the sections in the bytes, using sep as the delimiter.\n", " | \n", " | sep\n", " | The delimiter according which to split the bytes.\n", " | None (the default value) means split on ASCII whitespace characters\n", " | (space, tab, return, newline, formfeed, vertical tab).\n", " | maxsplit\n", " | Maximum number of splits to do.\n", " | -1 (the default value) means no limit.\n", " | \n", " | Splitting is done starting at the end of the bytes and working to the front.\n", " | \n", " | rstrip(self, bytes=None, /)\n", " | Strip trailing bytes contained in the argument.\n", " | \n", " | If the argument is omitted or None, strip trailing ASCII whitespace.\n", " | \n", " | split(self, /, sep=None, maxsplit=-1)\n", " | Return a list of the sections in the bytes, using sep as the delimiter.\n", " | \n", " | sep\n", " | The delimiter according which to split the bytes.\n", " | None (the default value) means split on ASCII whitespace characters\n", " | (space, tab, return, newline, formfeed, vertical tab).\n", " | maxsplit\n", " | Maximum number of splits to do.\n", " | -1 (the default value) means no limit.\n", " | \n", " | splitlines(self, /, keepends=False)\n", " | Return a list of the lines in the bytes, breaking at line boundaries.\n", " | \n", " | Line breaks are not included in the resulting list unless keepends is given and\n", " | true.\n", " | \n", " | startswith(...)\n", " | B.startswith(prefix[, start[, end]]) -> bool\n", " | \n", " | Return True if B starts with the specified prefix, False otherwise.\n", " | With optional start, test B beginning at that position.\n", " | With optional end, stop comparing B at that position.\n", " | prefix can also be a tuple of bytes to try.\n", " | \n", " | strip(self, bytes=None, /)\n", " | Strip leading and trailing bytes contained in the argument.\n", " | \n", " | If the argument is omitted or None, strip leading and trailing ASCII whitespace.\n", " | \n", " | swapcase(...)\n", " | B.swapcase() -> copy of B\n", " | \n", " | Return a copy of B with uppercase ASCII characters converted\n", " | to lowercase ASCII and vice versa.\n", " | \n", " | title(...)\n", " | B.title() -> copy of B\n", " | \n", " | Return a titlecased version of B, i.e. ASCII words start with uppercase\n", " | characters, all remaining cased characters have lowercase.\n", " | \n", " | translate(self, table, /, delete=b'')\n", " | Return a copy with each character mapped by the given translation table.\n", " | \n", " | table\n", " | Translation table, which must be a bytes object of length 256.\n", " | \n", " | All characters occurring in the optional argument delete are removed.\n", " | The remaining characters are mapped through the given translation table.\n", " | \n", " | upper(...)\n", " | B.upper() -> copy of B\n", " | \n", " | Return a copy of B with all ASCII characters converted to uppercase.\n", " | \n", " | zfill(self, width, /)\n", " | Pad a numeric string with zeros on the left, to fill a field of the given width.\n", " | \n", " | The original string is never truncated.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods inherited from builtins.bytes:\n", " | \n", " | fromhex(string, /) from builtins.type\n", " | Create a bytes object from a string of hexadecimal numbers.\n", " | \n", " | Spaces between two numbers are accepted.\n", " | Example: bytes.fromhex('B9 01EF') -> b'\\\\xb9\\\\x01\\\\xef'.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods inherited from builtins.bytes:\n", " | \n", " | maketrans(frm, to, /)\n", " | Return a translation table useable for the bytes or bytearray translate method.\n", " | \n", " | The returned table will be one where each byte in frm is mapped to the byte at\n", " | the same position in to.\n", " | \n", " | The bytes objects frm and to must be of the same length.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " class timedelta64(signedinteger)\n", " | A timedelta stored as a 64-bit integer.\n", " | \n", " | See :ref:`arrays.datetime` for more information.\n", " | \n", " | :Character code: ``'m'``\n", " | \n", " | Method resolution order:\n", " | timedelta64\n", " | signedinteger\n", " | integer\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from integer:\n", " | \n", " | __round__(...)\n", " | \n", " | is_integer(...)\n", " | integer.is_integer() -> bool\n", " | \n", " | Return ``True`` if the number is finite with integral value.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.int64(-2).is_integer()\n", " | True\n", " | >>> np.uint32(5).is_integer()\n", " | True\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from integer:\n", " | \n", " | denominator\n", " | denominator of value (1)\n", " | \n", " | numerator\n", " | numerator of value (the value itself)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " ubyte = class uint8(unsignedinteger)\n", " | Unsigned integer type, compatible with C ``unsigned char``.\n", " | \n", " | :Character code: ``'B'``\n", " | :Canonical name: `numpy.ubyte`\n", " | :Alias on this platform (win32 AMD64): `numpy.uint8`: 8-bit unsigned integer (``0`` to ``255``).\n", " | \n", " | Method resolution order:\n", " | uint8\n", " | unsignedinteger\n", " | integer\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __index__(self, /)\n", " | Return self converted to an integer, if self is suitable for use as an index into a list.\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | bit_count(...)\n", " | uint8.bit_count() -> int\n", " | \n", " | Computes the number of 1-bits in the absolute value of the input.\n", " | Analogous to the builtin `int.bit_count` or ``popcount`` in C++.\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.uint8(127).bit_count()\n", " | 7\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from integer:\n", " | \n", " | __round__(...)\n", " | \n", " | is_integer(...)\n", " | integer.is_integer() -> bool\n", " | \n", " | Return ``True`` if the number is finite with integral value.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.int64(-2).is_integer()\n", " | True\n", " | >>> np.uint32(5).is_integer()\n", " | True\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from integer:\n", " | \n", " | denominator\n", " | denominator of value (1)\n", " | \n", " | numerator\n", " | numerator of value (the value itself)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " class ufunc(builtins.object)\n", " | Functions that operate element by element on whole arrays.\n", " | \n", " | To see the documentation for a specific ufunc, use `info`. For\n", " | example, ``np.info(np.sin)``. Because ufuncs are written in C\n", " | (for speed) and linked into Python with NumPy's ufunc facility,\n", " | Python's help() function finds this page whenever help() is called\n", " | on a ufunc.\n", " | \n", " | A detailed explanation of ufuncs can be found in the docs for :ref:`ufuncs`.\n", " | \n", " | **Calling ufuncs:** ``op(*x[, out], where=True, **kwargs)``\n", " | \n", " | Apply `op` to the arguments `*x` elementwise, broadcasting the arguments.\n", " | \n", " | The broadcasting rules are:\n", " | \n", " | * Dimensions of length 1 may be prepended to either array.\n", " | * Arrays may be repeated along dimensions of length 1.\n", " | \n", " | Parameters\n", " | ----------\n", " | *x : array_like\n", " | Input arrays.\n", " | out : ndarray, None, or tuple of ndarray and None, optional\n", " | Alternate array object(s) in which to put the result; if provided, it\n", " | must have a shape that the inputs broadcast to. A tuple of arrays\n", " | (possible only as a keyword argument) must have length equal to the\n", " | number of outputs; use None for uninitialized outputs to be\n", " | allocated by the ufunc.\n", " | where : array_like, optional\n", " | This condition is broadcast over the input. At locations where the\n", " | condition is True, the `out` array will be set to the ufunc result.\n", " | Elsewhere, the `out` array will retain its original value.\n", " | Note that if an uninitialized `out` array is created via the default\n", " | ``out=None``, locations within it where the condition is False will\n", " | remain uninitialized.\n", " | **kwargs\n", " | For other keyword-only arguments, see the :ref:`ufunc docs <ufuncs.kwargs>`.\n", " | \n", " | Returns\n", " | -------\n", " | r : ndarray or tuple of ndarray\n", " | `r` will have the shape that the arrays in `x` broadcast to; if `out` is\n", " | provided, it will be returned. If not, `r` will be allocated and\n", " | may contain uninitialized values. If the function has more than one\n", " | output, then the result will be a tuple of arrays.\n", " | \n", " | Methods defined here:\n", " | \n", " | __call__(self, /, *args, **kwargs)\n", " | Call self as a function.\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | accumulate(...)\n", " | accumulate(array, axis=0, dtype=None, out=None)\n", " | \n", " | Accumulate the result of applying the operator to all elements.\n", " | \n", " | For a one-dimensional array, accumulate produces results equivalent to::\n", " | \n", " | r = np.empty(len(A))\n", " | t = op.identity # op = the ufunc being applied to A's elements\n", " | for i in range(len(A)):\n", " | t = op(t, A[i])\n", " | r[i] = t\n", " | return r\n", " | \n", " | For example, add.accumulate() is equivalent to np.cumsum().\n", " | \n", " | For a multi-dimensional array, accumulate is applied along only one\n", " | axis (axis zero by default; see Examples below) so repeated use is\n", " | necessary if one wants to accumulate over multiple axes.\n", " | \n", " | Parameters\n", " | ----------\n", " | array : array_like\n", " | The array to act on.\n", " | axis : int, optional\n", " | The axis along which to apply the accumulation; default is zero.\n", " | dtype : data-type code, optional\n", " | The data-type used to represent the intermediate results. Defaults\n", " | to the data-type of the output array if such is provided, or the\n", " | data-type of the input array if no output array is provided.\n", " | out : ndarray, None, or tuple of ndarray and None, optional\n", " | A location into which the result is stored. If not provided or None,\n", " | a freshly-allocated array is returned. For consistency with\n", " | ``ufunc.__call__``, if given as a keyword, this may be wrapped in a\n", " | 1-element tuple.\n", " | \n", " | .. versionchanged:: 1.13.0\n", " | Tuples are allowed for keyword argument.\n", " | \n", " | Returns\n", " | -------\n", " | r : ndarray\n", " | The accumulated values. If `out` was supplied, `r` is a reference to\n", " | `out`.\n", " | \n", " | Examples\n", " | --------\n", " | 1-D array examples:\n", " | \n", " | >>> np.add.accumulate([2, 3, 5])\n", " | array([ 2, 5, 10])\n", " | >>> np.multiply.accumulate([2, 3, 5])\n", " | array([ 2, 6, 30])\n", " | \n", " | 2-D array examples:\n", " | \n", " | >>> I = np.eye(2)\n", " | >>> I\n", " | array([[1., 0.],\n", " | [0., 1.]])\n", " | \n", " | Accumulate along axis 0 (rows), down columns:\n", " | \n", " | >>> np.add.accumulate(I, 0)\n", " | array([[1., 0.],\n", " | [1., 1.]])\n", " | >>> np.add.accumulate(I) # no axis specified = axis zero\n", " | array([[1., 0.],\n", " | [1., 1.]])\n", " | \n", " | Accumulate along axis 1 (columns), through rows:\n", " | \n", " | >>> np.add.accumulate(I, 1)\n", " | array([[1., 1.],\n", " | [0., 1.]])\n", " | \n", " | at(...)\n", " | at(a, indices, b=None, /)\n", " | \n", " | Performs unbuffered in place operation on operand 'a' for elements\n", " | specified by 'indices'. For addition ufunc, this method is equivalent to\n", " | ``a[indices] += b``, except that results are accumulated for elements that\n", " | are indexed more than once. For example, ``a[[0,0]] += 1`` will only\n", " | increment the first element once because of buffering, whereas\n", " | ``add.at(a, [0,0], 1)`` will increment the first element twice.\n", " | \n", " | .. versionadded:: 1.8.0\n", " | \n", " | Parameters\n", " | ----------\n", " | a : array_like\n", " | The array to perform in place operation on.\n", " | indices : array_like or tuple\n", " | Array like index object or slice object for indexing into first\n", " | operand. If first operand has multiple dimensions, indices can be a\n", " | tuple of array like index objects or slice objects.\n", " | b : array_like\n", " | Second operand for ufuncs requiring two operands. Operand must be\n", " | broadcastable over first operand after indexing or slicing.\n", " | \n", " | Examples\n", " | --------\n", " | Set items 0 and 1 to their negative values:\n", " | \n", " | >>> a = np.array([1, 2, 3, 4])\n", " | >>> np.negative.at(a, [0, 1])\n", " | >>> a\n", " | array([-1, -2, 3, 4])\n", " | \n", " | Increment items 0 and 1, and increment item 2 twice:\n", " | \n", " | >>> a = np.array([1, 2, 3, 4])\n", " | >>> np.add.at(a, [0, 1, 2, 2], 1)\n", " | >>> a\n", " | array([2, 3, 5, 4])\n", " | \n", " | Add items 0 and 1 in first array to second array,\n", " | and store results in first array:\n", " | \n", " | >>> a = np.array([1, 2, 3, 4])\n", " | >>> b = np.array([1, 2])\n", " | >>> np.add.at(a, [0, 1], b)\n", " | >>> a\n", " | array([2, 4, 3, 4])\n", " | \n", " | outer(...)\n", " | outer(A, B, /, **kwargs)\n", " | \n", " | Apply the ufunc `op` to all pairs (a, b) with a in `A` and b in `B`.\n", " | \n", " | Let ``M = A.ndim``, ``N = B.ndim``. Then the result, `C`, of\n", " | ``op.outer(A, B)`` is an array of dimension M + N such that:\n", " | \n", " | .. math:: C[i_0, ..., i_{M-1}, j_0, ..., j_{N-1}] =\n", " | op(A[i_0, ..., i_{M-1}], B[j_0, ..., j_{N-1}])\n", " | \n", " | For `A` and `B` one-dimensional, this is equivalent to::\n", " | \n", " | r = empty(len(A),len(B))\n", " | for i in range(len(A)):\n", " | for j in range(len(B)):\n", " | r[i,j] = op(A[i], B[j]) # op = ufunc in question\n", " | \n", " | Parameters\n", " | ----------\n", " | A : array_like\n", " | First array\n", " | B : array_like\n", " | Second array\n", " | kwargs : any\n", " | Arguments to pass on to the ufunc. Typically `dtype` or `out`.\n", " | See `ufunc` for a comprehensive overview of all available arguments.\n", " | \n", " | Returns\n", " | -------\n", " | r : ndarray\n", " | Output array\n", " | \n", " | See Also\n", " | --------\n", " | numpy.outer : A less powerful version of ``np.multiply.outer``\n", " | that `ravel`\\ s all inputs to 1D. This exists\n", " | primarily for compatibility with old code.\n", " | \n", " | tensordot : ``np.tensordot(a, b, axes=((), ()))`` and\n", " | ``np.multiply.outer(a, b)`` behave same for all\n", " | dimensions of a and b.\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.multiply.outer([1, 2, 3], [4, 5, 6])\n", " | array([[ 4, 5, 6],\n", " | [ 8, 10, 12],\n", " | [12, 15, 18]])\n", " | \n", " | A multi-dimensional example:\n", " | \n", " | >>> A = np.array([[1, 2, 3], [4, 5, 6]])\n", " | >>> A.shape\n", " | (2, 3)\n", " | >>> B = np.array([[1, 2, 3, 4]])\n", " | >>> B.shape\n", " | (1, 4)\n", " | >>> C = np.multiply.outer(A, B)\n", " | >>> C.shape; C\n", " | (2, 3, 1, 4)\n", " | array([[[[ 1, 2, 3, 4]],\n", " | [[ 2, 4, 6, 8]],\n", " | [[ 3, 6, 9, 12]]],\n", " | [[[ 4, 8, 12, 16]],\n", " | [[ 5, 10, 15, 20]],\n", " | [[ 6, 12, 18, 24]]]])\n", " | \n", " | reduce(...)\n", " | reduce(array, axis=0, dtype=None, out=None, keepdims=False, initial=<no value>, where=True)\n", " | \n", " | Reduces `array`'s dimension by one, by applying ufunc along one axis.\n", " | \n", " | Let :math:`array.shape = (N_0, ..., N_i, ..., N_{M-1})`. Then\n", " | :math:`ufunc.reduce(array, axis=i)[k_0, ..,k_{i-1}, k_{i+1}, .., k_{M-1}]` =\n", " | the result of iterating `j` over :math:`range(N_i)`, cumulatively applying\n", " | ufunc to each :math:`array[k_0, ..,k_{i-1}, j, k_{i+1}, .., k_{M-1}]`.\n", " | For a one-dimensional array, reduce produces results equivalent to:\n", " | ::\n", " | \n", " | r = op.identity # op = ufunc\n", " | for i in range(len(A)):\n", " | r = op(r, A[i])\n", " | return r\n", " | \n", " | For example, add.reduce() is equivalent to sum().\n", " | \n", " | Parameters\n", " | ----------\n", " | array : array_like\n", " | The array to act on.\n", " | axis : None or int or tuple of ints, optional\n", " | Axis or axes along which a reduction is performed.\n", " | The default (`axis` = 0) is perform a reduction over the first\n", " | dimension of the input array. `axis` may be negative, in\n", " | which case it counts from the last to the first axis.\n", " | \n", " | .. versionadded:: 1.7.0\n", " | \n", " | If this is None, a reduction is performed over all the axes.\n", " | If this is a tuple of ints, a reduction is performed on multiple\n", " | axes, instead of a single axis or all the axes as before.\n", " | \n", " | For operations which are either not commutative or not associative,\n", " | doing a reduction over multiple axes is not well-defined. The\n", " | ufuncs do not currently raise an exception in this case, but will\n", " | likely do so in the future.\n", " | dtype : data-type code, optional\n", " | The type used to represent the intermediate results. Defaults\n", " | to the data-type of the output array if this is provided, or\n", " | the data-type of the input array if no output array is provided.\n", " | out : ndarray, None, or tuple of ndarray and None, optional\n", " | A location into which the result is stored. If not provided or None,\n", " | a freshly-allocated array is returned. For consistency with\n", " | ``ufunc.__call__``, if given as a keyword, this may be wrapped in a\n", " | 1-element tuple.\n", " | \n", " | .. versionchanged:: 1.13.0\n", " | Tuples are allowed for keyword argument.\n", " | keepdims : bool, optional\n", " | If this is set to True, the axes which are reduced are left\n", " | in the result as dimensions with size one. With this option,\n", " | the result will broadcast correctly against the original `array`.\n", " | \n", " | .. versionadded:: 1.7.0\n", " | initial : scalar, optional\n", " | The value with which to start the reduction.\n", " | If the ufunc has no identity or the dtype is object, this defaults\n", " | to None - otherwise it defaults to ufunc.identity.\n", " | If ``None`` is given, the first element of the reduction is used,\n", " | and an error is thrown if the reduction is empty.\n", " | \n", " | .. versionadded:: 1.15.0\n", " | \n", " | where : array_like of bool, optional\n", " | A boolean array which is broadcasted to match the dimensions\n", " | of `array`, and selects elements to include in the reduction. Note\n", " | that for ufuncs like ``minimum`` that do not have an identity\n", " | defined, one has to pass in also ``initial``.\n", " | \n", " | .. versionadded:: 1.17.0\n", " | \n", " | Returns\n", " | -------\n", " | r : ndarray\n", " | The reduced array. If `out` was supplied, `r` is a reference to it.\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.multiply.reduce([2,3,5])\n", " | 30\n", " | \n", " | A multi-dimensional array example:\n", " | \n", " | >>> X = np.arange(8).reshape((2,2,2))\n", " | >>> X\n", " | array([[[0, 1],\n", " | [2, 3]],\n", " | [[4, 5],\n", " | [6, 7]]])\n", " | >>> np.add.reduce(X, 0)\n", " | array([[ 4, 6],\n", " | [ 8, 10]])\n", " | >>> np.add.reduce(X) # confirm: default axis value is 0\n", " | array([[ 4, 6],\n", " | [ 8, 10]])\n", " | >>> np.add.reduce(X, 1)\n", " | array([[ 2, 4],\n", " | [10, 12]])\n", " | >>> np.add.reduce(X, 2)\n", " | array([[ 1, 5],\n", " | [ 9, 13]])\n", " | \n", " | You can use the ``initial`` keyword argument to initialize the reduction\n", " | with a different value, and ``where`` to select specific elements to include:\n", " | \n", " | >>> np.add.reduce([10], initial=5)\n", " | 15\n", " | >>> np.add.reduce(np.ones((2, 2, 2)), axis=(0, 2), initial=10)\n", " | array([14., 14.])\n", " | >>> a = np.array([10., np.nan, 10])\n", " | >>> np.add.reduce(a, where=~np.isnan(a))\n", " | 20.0\n", " | \n", " | Allows reductions of empty arrays where they would normally fail, i.e.\n", " | for ufuncs without an identity.\n", " | \n", " | >>> np.minimum.reduce([], initial=np.inf)\n", " | inf\n", " | >>> np.minimum.reduce([[1., 2.], [3., 4.]], initial=10., where=[True, False])\n", " | array([ 1., 10.])\n", " | >>> np.minimum.reduce([])\n", " | Traceback (most recent call last):\n", " | ...\n", " | ValueError: zero-size array to reduction operation minimum which has no identity\n", " | \n", " | reduceat(...)\n", " | reduceat(array, indices, axis=0, dtype=None, out=None)\n", " | \n", " | Performs a (local) reduce with specified slices over a single axis.\n", " | \n", " | For i in ``range(len(indices))``, `reduceat` computes\n", " | ``ufunc.reduce(array[indices[i]:indices[i+1]])``, which becomes the i-th\n", " | generalized \"row\" parallel to `axis` in the final result (i.e., in a\n", " | 2-D array, for example, if `axis = 0`, it becomes the i-th row, but if\n", " | `axis = 1`, it becomes the i-th column). There are three exceptions to this:\n", " | \n", " | * when ``i = len(indices) - 1`` (so for the last index),\n", " | ``indices[i+1] = array.shape[axis]``.\n", " | * if ``indices[i] >= indices[i + 1]``, the i-th generalized \"row\" is\n", " | simply ``array[indices[i]]``.\n", " | * if ``indices[i] >= len(array)`` or ``indices[i] < 0``, an error is raised.\n", " | \n", " | The shape of the output depends on the size of `indices`, and may be\n", " | larger than `array` (this happens if ``len(indices) > array.shape[axis]``).\n", " | \n", " | Parameters\n", " | ----------\n", " | array : array_like\n", " | The array to act on.\n", " | indices : array_like\n", " | Paired indices, comma separated (not colon), specifying slices to\n", " | reduce.\n", " | axis : int, optional\n", " | The axis along which to apply the reduceat.\n", " | dtype : data-type code, optional\n", " | The type used to represent the intermediate results. Defaults\n", " | to the data type of the output array if this is provided, or\n", " | the data type of the input array if no output array is provided.\n", " | out : ndarray, None, or tuple of ndarray and None, optional\n", " | A location into which the result is stored. If not provided or None,\n", " | a freshly-allocated array is returned. For consistency with\n", " | ``ufunc.__call__``, if given as a keyword, this may be wrapped in a\n", " | 1-element tuple.\n", " | \n", " | .. versionchanged:: 1.13.0\n", " | Tuples are allowed for keyword argument.\n", " | \n", " | Returns\n", " | -------\n", " | r : ndarray\n", " | The reduced values. If `out` was supplied, `r` is a reference to\n", " | `out`.\n", " | \n", " | Notes\n", " | -----\n", " | A descriptive example:\n", " | \n", " | If `array` is 1-D, the function `ufunc.accumulate(array)` is the same as\n", " | ``ufunc.reduceat(array, indices)[::2]`` where `indices` is\n", " | ``range(len(array) - 1)`` with a zero placed\n", " | in every other element:\n", " | ``indices = zeros(2 * len(array) - 1)``,\n", " | ``indices[1::2] = range(1, len(array))``.\n", " | \n", " | Don't be fooled by this attribute's name: `reduceat(array)` is not\n", " | necessarily smaller than `array`.\n", " | \n", " | Examples\n", " | --------\n", " | To take the running sum of four successive values:\n", " | \n", " | >>> np.add.reduceat(np.arange(8),[0,4, 1,5, 2,6, 3,7])[::2]\n", " | array([ 6, 10, 14, 18])\n", " | \n", " | A 2-D example:\n", " | \n", " | >>> x = np.linspace(0, 15, 16).reshape(4,4)\n", " | >>> x\n", " | array([[ 0., 1., 2., 3.],\n", " | [ 4., 5., 6., 7.],\n", " | [ 8., 9., 10., 11.],\n", " | [12., 13., 14., 15.]])\n", " | \n", " | ::\n", " | \n", " | # reduce such that the result has the following five rows:\n", " | # [row1 + row2 + row3]\n", " | # [row4]\n", " | # [row2]\n", " | # [row3]\n", " | # [row1 + row2 + row3 + row4]\n", " | \n", " | >>> np.add.reduceat(x, [0, 3, 1, 2, 0])\n", " | array([[12., 15., 18., 21.],\n", " | [12., 13., 14., 15.],\n", " | [ 4., 5., 6., 7.],\n", " | [ 8., 9., 10., 11.],\n", " | [24., 28., 32., 36.]])\n", " | \n", " | ::\n", " | \n", " | # reduce such that result has the following two columns:\n", " | # [col1 * col2 * col3, col4]\n", " | \n", " | >>> np.multiply.reduceat(x, [0, 3], 1)\n", " | array([[ 0., 3.],\n", " | [ 120., 7.],\n", " | [ 720., 11.],\n", " | [2184., 15.]])\n", " | \n", " | resolve_dtypes(...)\n", " | resolve_dtypes(dtypes, *, signature=None, casting=None, reduction=False)\n", " | \n", " | Find the dtypes NumPy will use for the operation. Both input and\n", " | output dtypes are returned and may differ from those provided.\n", " | \n", " | .. note::\n", " | \n", " | This function always applies NEP 50 rules since it is not provided\n", " | any actual values. The Python types ``int``, ``float``, and\n", " | ``complex`` thus behave weak and should be passed for \"untyped\"\n", " | Python input.\n", " | \n", " | Parameters\n", " | ----------\n", " | dtypes : tuple of dtypes, None, or literal int, float, complex\n", " | The input dtypes for each operand. Output operands can be\n", " | None, indicating that the dtype must be found.\n", " | signature : tuple of DTypes or None, optional\n", " | If given, enforces exact DType (classes) of the specific operand.\n", " | The ufunc ``dtype`` argument is equivalent to passing a tuple with\n", " | only output dtypes set.\n", " | casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional\n", " | The casting mode when casting is necessary. This is identical to\n", " | the ufunc call casting modes.\n", " | reduction : boolean\n", " | If given, the resolution assumes a reduce operation is happening\n", " | which slightly changes the promotion and type resolution rules.\n", " | `dtypes` is usually something like ``(None, np.dtype(\"i2\"), None)``\n", " | for reductions (first input is also the output).\n", " | \n", " | .. note::\n", " | \n", " | The default casting mode is \"same_kind\", however, as of\n", " | NumPy 1.24, NumPy uses \"unsafe\" for reductions.\n", " | \n", " | Returns\n", " | -------\n", " | dtypes : tuple of dtypes\n", " | The dtypes which NumPy would use for the calculation. Note that\n", " | dtypes may not match the passed in ones (casting is necessary).\n", " | \n", " | See Also\n", " | --------\n", " | numpy.ufunc._resolve_dtypes_and_context :\n", " | Similar function to this, but returns additional information which\n", " | give access to the core C functionality of NumPy.\n", " | \n", " | Examples\n", " | --------\n", " | This API requires passing dtypes, define them for convenience:\n", " | \n", " | >>> int32 = np.dtype(\"int32\")\n", " | >>> float32 = np.dtype(\"float32\")\n", " | \n", " | The typical ufunc call does not pass an output dtype. `np.add` has two\n", " | inputs and one output, so leave the output as ``None`` (not provided):\n", " | \n", " | >>> np.add.resolve_dtypes((int32, float32, None))\n", " | (dtype('float64'), dtype('float64'), dtype('float64'))\n", " | \n", " | The loop found uses \"float64\" for all operands (including the output), the\n", " | first input would be cast.\n", " | \n", " | ``resolve_dtypes`` supports \"weak\" handling for Python scalars by passing\n", " | ``int``, ``float``, or ``complex``:\n", " | \n", " | >>> np.add.resolve_dtypes((float32, float, None))\n", " | (dtype('float32'), dtype('float32'), dtype('float32'))\n", " | \n", " | Where the Python ``float`` behaves samilar to a Python value ``0.0``\n", " | in a ufunc call. (See :ref:`NEP 50 <NEP50>` for details.)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors defined here:\n", " | \n", " | identity\n", " | The identity value.\n", " | \n", " | Data attribute containing the identity element for the ufunc, if it has one.\n", " | If it does not, the attribute value is None.\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.add.identity\n", " | 0\n", " | >>> np.multiply.identity\n", " | 1\n", " | >>> np.power.identity\n", " | 1\n", " | >>> print(np.exp.identity)\n", " | None\n", " | \n", " | nargs\n", " | The number of arguments.\n", " | \n", " | Data attribute containing the number of arguments the ufunc takes, including\n", " | optional ones.\n", " | \n", " | Notes\n", " | -----\n", " | Typically this value will be one more than what you might expect because all\n", " | ufuncs take the optional \"out\" argument.\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.add.nargs\n", " | 3\n", " | >>> np.multiply.nargs\n", " | 3\n", " | >>> np.power.nargs\n", " | 3\n", " | >>> np.exp.nargs\n", " | 2\n", " | \n", " | nin\n", " | The number of inputs.\n", " | \n", " | Data attribute containing the number of arguments the ufunc treats as input.\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.add.nin\n", " | 2\n", " | >>> np.multiply.nin\n", " | 2\n", " | >>> np.power.nin\n", " | 2\n", " | >>> np.exp.nin\n", " | 1\n", " | \n", " | nout\n", " | The number of outputs.\n", " | \n", " | Data attribute containing the number of arguments the ufunc treats as output.\n", " | \n", " | Notes\n", " | -----\n", " | Since all ufuncs can take output arguments, this will always be (at least) 1.\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.add.nout\n", " | 1\n", " | >>> np.multiply.nout\n", " | 1\n", " | >>> np.power.nout\n", " | 1\n", " | >>> np.exp.nout\n", " | 1\n", " | \n", " | ntypes\n", " | The number of types.\n", " | \n", " | The number of numerical NumPy types - of which there are 18 total - on which\n", " | the ufunc can operate.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.ufunc.types\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.add.ntypes\n", " | 18\n", " | >>> np.multiply.ntypes\n", " | 18\n", " | >>> np.power.ntypes\n", " | 17\n", " | >>> np.exp.ntypes\n", " | 7\n", " | >>> np.remainder.ntypes\n", " | 14\n", " | \n", " | signature\n", " | Definition of the core elements a generalized ufunc operates on.\n", " | \n", " | The signature determines how the dimensions of each input/output array\n", " | are split into core and loop dimensions:\n", " | \n", " | 1. Each dimension in the signature is matched to a dimension of the\n", " | corresponding passed-in array, starting from the end of the shape tuple.\n", " | 2. Core dimensions assigned to the same label in the signature must have\n", " | exactly matching sizes, no broadcasting is performed.\n", " | 3. The core dimensions are removed from all inputs and the remaining\n", " | dimensions are broadcast together, defining the loop dimensions.\n", " | \n", " | Notes\n", " | -----\n", " | Generalized ufuncs are used internally in many linalg functions, and in\n", " | the testing suite; the examples below are taken from these.\n", " | For ufuncs that operate on scalars, the signature is None, which is\n", " | equivalent to '()' for every argument.\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.core.umath_tests.matrix_multiply.signature\n", " | '(m,n),(n,p)->(m,p)'\n", " | >>> np.linalg._umath_linalg.det.signature\n", " | '(m,m)->()'\n", " | >>> np.add.signature is None\n", " | True # equivalent to '(),()->()'\n", " | \n", " | types\n", " | Returns a list with types grouped input->output.\n", " | \n", " | Data attribute listing the data-type \"Domain-Range\" groupings the ufunc can\n", " | deliver. The data-types are given using the character codes.\n", " | \n", " | See Also\n", " | --------\n", " | numpy.ufunc.ntypes\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.add.types\n", " | ['??->?', 'bb->b', 'BB->B', 'hh->h', 'HH->H', 'ii->i', 'II->I', 'll->l',\n", " | 'LL->L', 'qq->q', 'QQ->Q', 'ff->f', 'dd->d', 'gg->g', 'FF->F', 'DD->D',\n", " | 'GG->G', 'OO->O']\n", " | \n", " | >>> np.multiply.types\n", " | ['??->?', 'bb->b', 'BB->B', 'hh->h', 'HH->H', 'ii->i', 'II->I', 'll->l',\n", " | 'LL->L', 'qq->q', 'QQ->Q', 'ff->f', 'dd->d', 'gg->g', 'FF->F', 'DD->D',\n", " | 'GG->G', 'OO->O']\n", " | \n", " | >>> np.power.types\n", " | ['bb->b', 'BB->B', 'hh->h', 'HH->H', 'ii->i', 'II->I', 'll->l', 'LL->L',\n", " | 'qq->q', 'QQ->Q', 'ff->f', 'dd->d', 'gg->g', 'FF->F', 'DD->D', 'GG->G',\n", " | 'OO->O']\n", " | \n", " | >>> np.exp.types\n", " | ['f->f', 'd->d', 'g->g', 'F->F', 'D->D', 'G->G', 'O->O']\n", " | \n", " | >>> np.remainder.types\n", " | ['bb->b', 'BB->B', 'hh->h', 'HH->H', 'ii->i', 'II->I', 'll->l', 'LL->L',\n", " | 'qq->q', 'QQ->Q', 'ff->f', 'dd->d', 'gg->g', 'OO->O']\n", " \n", " uint = class uint32(unsignedinteger)\n", " | Unsigned integer type, compatible with C ``unsigned long``.\n", " | \n", " | :Character code: ``'L'``\n", " | :Canonical name: `numpy.uint`\n", " | :Alias on this platform (win32 AMD64): `numpy.uint32`: 32-bit unsigned integer (``0`` to ``4_294_967_295``).\n", " | \n", " | Method resolution order:\n", " | uint32\n", " | unsignedinteger\n", " | integer\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __index__(self, /)\n", " | Return self converted to an integer, if self is suitable for use as an index into a list.\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | bit_count(...)\n", " | uint32.bit_count() -> int\n", " | \n", " | Computes the number of 1-bits in the absolute value of the input.\n", " | Analogous to the builtin `int.bit_count` or ``popcount`` in C++.\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.uint32(127).bit_count()\n", " | 7\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from integer:\n", " | \n", " | __round__(...)\n", " | \n", " | is_integer(...)\n", " | integer.is_integer() -> bool\n", " | \n", " | Return ``True`` if the number is finite with integral value.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.int64(-2).is_integer()\n", " | True\n", " | >>> np.uint32(5).is_integer()\n", " | True\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from integer:\n", " | \n", " | denominator\n", " | denominator of value (1)\n", " | \n", " | numerator\n", " | numerator of value (the value itself)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " class uint16(unsignedinteger)\n", " | Unsigned integer type, compatible with C ``unsigned short``.\n", " | \n", " | :Character code: ``'H'``\n", " | :Canonical name: `numpy.ushort`\n", " | :Alias on this platform (win32 AMD64): `numpy.uint16`: 16-bit unsigned integer (``0`` to ``65_535``).\n", " | \n", " | Method resolution order:\n", " | uint16\n", " | unsignedinteger\n", " | integer\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __index__(self, /)\n", " | Return self converted to an integer, if self is suitable for use as an index into a list.\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | bit_count(...)\n", " | uint16.bit_count() -> int\n", " | \n", " | Computes the number of 1-bits in the absolute value of the input.\n", " | Analogous to the builtin `int.bit_count` or ``popcount`` in C++.\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.uint16(127).bit_count()\n", " | 7\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from integer:\n", " | \n", " | __round__(...)\n", " | \n", " | is_integer(...)\n", " | integer.is_integer() -> bool\n", " | \n", " | Return ``True`` if the number is finite with integral value.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.int64(-2).is_integer()\n", " | True\n", " | >>> np.uint32(5).is_integer()\n", " | True\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from integer:\n", " | \n", " | denominator\n", " | denominator of value (1)\n", " | \n", " | numerator\n", " | numerator of value (the value itself)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " class uint32(unsignedinteger)\n", " | Unsigned integer type, compatible with C ``unsigned long``.\n", " | \n", " | :Character code: ``'L'``\n", " | :Canonical name: `numpy.uint`\n", " | :Alias on this platform (win32 AMD64): `numpy.uint32`: 32-bit unsigned integer (``0`` to ``4_294_967_295``).\n", " | \n", " | Method resolution order:\n", " | uint32\n", " | unsignedinteger\n", " | integer\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __index__(self, /)\n", " | Return self converted to an integer, if self is suitable for use as an index into a list.\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | bit_count(...)\n", " | uint32.bit_count() -> int\n", " | \n", " | Computes the number of 1-bits in the absolute value of the input.\n", " | Analogous to the builtin `int.bit_count` or ``popcount`` in C++.\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.uint32(127).bit_count()\n", " | 7\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from integer:\n", " | \n", " | __round__(...)\n", " | \n", " | is_integer(...)\n", " | integer.is_integer() -> bool\n", " | \n", " | Return ``True`` if the number is finite with integral value.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.int64(-2).is_integer()\n", " | True\n", " | >>> np.uint32(5).is_integer()\n", " | True\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from integer:\n", " | \n", " | denominator\n", " | denominator of value (1)\n", " | \n", " | numerator\n", " | numerator of value (the value itself)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " class uint64(unsignedinteger)\n", " | Signed integer type, compatible with C ``unsigned long long``.\n", " | \n", " | :Character code: ``'Q'``\n", " | :Canonical name: `numpy.ulonglong`\n", " | :Alias on this platform (win32 AMD64): `numpy.uint64`: 64-bit unsigned integer (``0`` to ``18_446_744_073_709_551_615``).\n", " | :Alias on this platform (win32 AMD64): `numpy.uintp`: Unsigned integer large enough to fit pointer, compatible with C ``uintptr_t``.\n", " | \n", " | Method resolution order:\n", " | uint64\n", " | unsignedinteger\n", " | integer\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __index__(self, /)\n", " | Return self converted to an integer, if self is suitable for use as an index into a list.\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | bit_count(...)\n", " | uint64.bit_count() -> int\n", " | \n", " | Computes the number of 1-bits in the absolute value of the input.\n", " | Analogous to the builtin `int.bit_count` or ``popcount`` in C++.\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.uint64(127).bit_count()\n", " | 7\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from integer:\n", " | \n", " | __round__(...)\n", " | \n", " | is_integer(...)\n", " | integer.is_integer() -> bool\n", " | \n", " | Return ``True`` if the number is finite with integral value.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.int64(-2).is_integer()\n", " | True\n", " | >>> np.uint32(5).is_integer()\n", " | True\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from integer:\n", " | \n", " | denominator\n", " | denominator of value (1)\n", " | \n", " | numerator\n", " | numerator of value (the value itself)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " class uint8(unsignedinteger)\n", " | Unsigned integer type, compatible with C ``unsigned char``.\n", " | \n", " | :Character code: ``'B'``\n", " | :Canonical name: `numpy.ubyte`\n", " | :Alias on this platform (win32 AMD64): `numpy.uint8`: 8-bit unsigned integer (``0`` to ``255``).\n", " | \n", " | Method resolution order:\n", " | uint8\n", " | unsignedinteger\n", " | integer\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __index__(self, /)\n", " | Return self converted to an integer, if self is suitable for use as an index into a list.\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | bit_count(...)\n", " | uint8.bit_count() -> int\n", " | \n", " | Computes the number of 1-bits in the absolute value of the input.\n", " | Analogous to the builtin `int.bit_count` or ``popcount`` in C++.\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.uint8(127).bit_count()\n", " | 7\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from integer:\n", " | \n", " | __round__(...)\n", " | \n", " | is_integer(...)\n", " | integer.is_integer() -> bool\n", " | \n", " | Return ``True`` if the number is finite with integral value.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.int64(-2).is_integer()\n", " | True\n", " | >>> np.uint32(5).is_integer()\n", " | True\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from integer:\n", " | \n", " | denominator\n", " | denominator of value (1)\n", " | \n", " | numerator\n", " | numerator of value (the value itself)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " class uintc(unsignedinteger)\n", " | Unsigned integer type, compatible with C ``unsigned int``.\n", " | \n", " | :Character code: ``'I'``\n", " | \n", " | Method resolution order:\n", " | uintc\n", " | unsignedinteger\n", " | integer\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __index__(self, /)\n", " | Return self converted to an integer, if self is suitable for use as an index into a list.\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | bit_count(...)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from integer:\n", " | \n", " | __round__(...)\n", " | \n", " | is_integer(...)\n", " | integer.is_integer() -> bool\n", " | \n", " | Return ``True`` if the number is finite with integral value.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.int64(-2).is_integer()\n", " | True\n", " | >>> np.uint32(5).is_integer()\n", " | True\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from integer:\n", " | \n", " | denominator\n", " | denominator of value (1)\n", " | \n", " | numerator\n", " | numerator of value (the value itself)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " uintp = class uint64(unsignedinteger)\n", " | Signed integer type, compatible with C ``unsigned long long``.\n", " | \n", " | :Character code: ``'Q'``\n", " | :Canonical name: `numpy.ulonglong`\n", " | :Alias on this platform (win32 AMD64): `numpy.uint64`: 64-bit unsigned integer (``0`` to ``18_446_744_073_709_551_615``).\n", " | :Alias on this platform (win32 AMD64): `numpy.uintp`: Unsigned integer large enough to fit pointer, compatible with C ``uintptr_t``.\n", " | \n", " | Method resolution order:\n", " | uint64\n", " | unsignedinteger\n", " | integer\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __index__(self, /)\n", " | Return self converted to an integer, if self is suitable for use as an index into a list.\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | bit_count(...)\n", " | uint64.bit_count() -> int\n", " | \n", " | Computes the number of 1-bits in the absolute value of the input.\n", " | Analogous to the builtin `int.bit_count` or ``popcount`` in C++.\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.uint64(127).bit_count()\n", " | 7\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from integer:\n", " | \n", " | __round__(...)\n", " | \n", " | is_integer(...)\n", " | integer.is_integer() -> bool\n", " | \n", " | Return ``True`` if the number is finite with integral value.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.int64(-2).is_integer()\n", " | True\n", " | >>> np.uint32(5).is_integer()\n", " | True\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from integer:\n", " | \n", " | denominator\n", " | denominator of value (1)\n", " | \n", " | numerator\n", " | numerator of value (the value itself)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " ulonglong = class uint64(unsignedinteger)\n", " | Signed integer type, compatible with C ``unsigned long long``.\n", " | \n", " | :Character code: ``'Q'``\n", " | :Canonical name: `numpy.ulonglong`\n", " | :Alias on this platform (win32 AMD64): `numpy.uint64`: 64-bit unsigned integer (``0`` to ``18_446_744_073_709_551_615``).\n", " | :Alias on this platform (win32 AMD64): `numpy.uintp`: Unsigned integer large enough to fit pointer, compatible with C ``uintptr_t``.\n", " | \n", " | Method resolution order:\n", " | uint64\n", " | unsignedinteger\n", " | integer\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __index__(self, /)\n", " | Return self converted to an integer, if self is suitable for use as an index into a list.\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | bit_count(...)\n", " | uint64.bit_count() -> int\n", " | \n", " | Computes the number of 1-bits in the absolute value of the input.\n", " | Analogous to the builtin `int.bit_count` or ``popcount`` in C++.\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.uint64(127).bit_count()\n", " | 7\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from integer:\n", " | \n", " | __round__(...)\n", " | \n", " | is_integer(...)\n", " | integer.is_integer() -> bool\n", " | \n", " | Return ``True`` if the number is finite with integral value.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.int64(-2).is_integer()\n", " | True\n", " | >>> np.uint32(5).is_integer()\n", " | True\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from integer:\n", " | \n", " | denominator\n", " | denominator of value (1)\n", " | \n", " | numerator\n", " | numerator of value (the value itself)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " unicode_ = class str_(builtins.str, character)\n", " | A unicode string.\n", " | \n", " | When used in arrays, this type strips trailing null codepoints.\n", " | \n", " | Unlike the builtin `str`, this supports the :ref:`python:bufferobjects`, exposing its\n", " | contents as UCS4:\n", " | \n", " | >>> m = memoryview(np.str_(\"abc\"))\n", " | >>> m.format\n", " | '3w'\n", " | >>> m.tobytes()\n", " | b'a\\x00\\x00\\x00b\\x00\\x00\\x00c\\x00\\x00\\x00'\n", " | \n", " | :Character code: ``'U'``\n", " | :Alias: `numpy.unicode_`\n", " | \n", " | Method resolution order:\n", " | str_\n", " | builtins.str\n", " | character\n", " | flexible\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from builtins.str:\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __contains__(self, key, /)\n", " | Return key in self.\n", " | \n", " | __format__(self, format_spec, /)\n", " | Return a formatted version of the string as described by format_spec.\n", " | \n", " | __getattribute__(self, name, /)\n", " | Return getattr(self, name).\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __getnewargs__(...)\n", " | \n", " | __iter__(self, /)\n", " | Implement iter(self).\n", " | \n", " | __len__(self, /)\n", " | Return len(self).\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __sizeof__(self, /)\n", " | Return the size of the string in memory, in bytes.\n", " | \n", " | capitalize(self, /)\n", " | Return a capitalized version of the string.\n", " | \n", " | More specifically, make the first character have upper case and the rest lower\n", " | case.\n", " | \n", " | casefold(self, /)\n", " | Return a version of the string suitable for caseless comparisons.\n", " | \n", " | center(self, width, fillchar=' ', /)\n", " | Return a centered string of length width.\n", " | \n", " | Padding is done using the specified fill character (default is a space).\n", " | \n", " | count(...)\n", " | S.count(sub[, start[, end]]) -> int\n", " | \n", " | Return the number of non-overlapping occurrences of substring sub in\n", " | string S[start:end]. Optional arguments start and end are\n", " | interpreted as in slice notation.\n", " | \n", " | encode(self, /, encoding='utf-8', errors='strict')\n", " | Encode the string using the codec registered for encoding.\n", " | \n", " | encoding\n", " | The encoding in which to encode the string.\n", " | errors\n", " | The error handling scheme to use for encoding errors.\n", " | The default is 'strict' meaning that encoding errors raise a\n", " | UnicodeEncodeError. Other possible values are 'ignore', 'replace' and\n", " | 'xmlcharrefreplace' as well as any other name registered with\n", " | codecs.register_error that can handle UnicodeEncodeErrors.\n", " | \n", " | endswith(...)\n", " | S.endswith(suffix[, start[, end]]) -> bool\n", " | \n", " | Return True if S ends with the specified suffix, False otherwise.\n", " | With optional start, test S beginning at that position.\n", " | With optional end, stop comparing S at that position.\n", " | suffix can also be a tuple of strings to try.\n", " | \n", " | expandtabs(self, /, tabsize=8)\n", " | Return a copy where all tab characters are expanded using spaces.\n", " | \n", " | If tabsize is not given, a tab size of 8 characters is assumed.\n", " | \n", " | find(...)\n", " | S.find(sub[, start[, end]]) -> int\n", " | \n", " | Return the lowest index in S where substring sub is found,\n", " | such that sub is contained within S[start:end]. Optional\n", " | arguments start and end are interpreted as in slice notation.\n", " | \n", " | Return -1 on failure.\n", " | \n", " | format(...)\n", " | S.format(*args, **kwargs) -> str\n", " | \n", " | Return a formatted version of S, using substitutions from args and kwargs.\n", " | The substitutions are identified by braces ('{' and '}').\n", " | \n", " | format_map(...)\n", " | S.format_map(mapping) -> str\n", " | \n", " | Return a formatted version of S, using substitutions from mapping.\n", " | The substitutions are identified by braces ('{' and '}').\n", " | \n", " | index(...)\n", " | S.index(sub[, start[, end]]) -> int\n", " | \n", " | Return the lowest index in S where substring sub is found,\n", " | such that sub is contained within S[start:end]. Optional\n", " | arguments start and end are interpreted as in slice notation.\n", " | \n", " | Raises ValueError when the substring is not found.\n", " | \n", " | isalnum(self, /)\n", " | Return True if the string is an alpha-numeric string, False otherwise.\n", " | \n", " | A string is alpha-numeric if all characters in the string are alpha-numeric and\n", " | there is at least one character in the string.\n", " | \n", " | isalpha(self, /)\n", " | Return True if the string is an alphabetic string, False otherwise.\n", " | \n", " | A string is alphabetic if all characters in the string are alphabetic and there\n", " | is at least one character in the string.\n", " | \n", " | isascii(self, /)\n", " | Return True if all characters in the string are ASCII, False otherwise.\n", " | \n", " | ASCII characters have code points in the range U+0000-U+007F.\n", " | Empty string is ASCII too.\n", " | \n", " | isdecimal(self, /)\n", " | Return True if the string is a decimal string, False otherwise.\n", " | \n", " | A string is a decimal string if all characters in the string are decimal and\n", " | there is at least one character in the string.\n", " | \n", " | isdigit(self, /)\n", " | Return True if the string is a digit string, False otherwise.\n", " | \n", " | A string is a digit string if all characters in the string are digits and there\n", " | is at least one character in the string.\n", " | \n", " | isidentifier(self, /)\n", " | Return True if the string is a valid Python identifier, False otherwise.\n", " | \n", " | Call keyword.iskeyword(s) to test whether string s is a reserved identifier,\n", " | such as \"def\" or \"class\".\n", " | \n", " | islower(self, /)\n", " | Return True if the string is a lowercase string, False otherwise.\n", " | \n", " | A string is lowercase if all cased characters in the string are lowercase and\n", " | there is at least one cased character in the string.\n", " | \n", " | isnumeric(self, /)\n", " | Return True if the string is a numeric string, False otherwise.\n", " | \n", " | A string is numeric if all characters in the string are numeric and there is at\n", " | least one character in the string.\n", " | \n", " | isprintable(self, /)\n", " | Return True if the string is printable, False otherwise.\n", " | \n", " | A string is printable if all of its characters are considered printable in\n", " | repr() or if it is empty.\n", " | \n", " | isspace(self, /)\n", " | Return True if the string is a whitespace string, False otherwise.\n", " | \n", " | A string is whitespace if all characters in the string are whitespace and there\n", " | is at least one character in the string.\n", " | \n", " | istitle(self, /)\n", " | Return True if the string is a title-cased string, False otherwise.\n", " | \n", " | In a title-cased string, upper- and title-case characters may only\n", " | follow uncased characters and lowercase characters only cased ones.\n", " | \n", " | isupper(self, /)\n", " | Return True if the string is an uppercase string, False otherwise.\n", " | \n", " | A string is uppercase if all cased characters in the string are uppercase and\n", " | there is at least one cased character in the string.\n", " | \n", " | join(self, iterable, /)\n", " | Concatenate any number of strings.\n", " | \n", " | The string whose method is called is inserted in between each given string.\n", " | The result is returned as a new string.\n", " | \n", " | Example: '.'.join(['ab', 'pq', 'rs']) -> 'ab.pq.rs'\n", " | \n", " | ljust(self, width, fillchar=' ', /)\n", " | Return a left-justified string of length width.\n", " | \n", " | Padding is done using the specified fill character (default is a space).\n", " | \n", " | lower(self, /)\n", " | Return a copy of the string converted to lowercase.\n", " | \n", " | lstrip(self, chars=None, /)\n", " | Return a copy of the string with leading whitespace removed.\n", " | \n", " | If chars is given and not None, remove characters in chars instead.\n", " | \n", " | partition(self, sep, /)\n", " | Partition the string into three parts using the given separator.\n", " | \n", " | This will search for the separator in the string. If the separator is found,\n", " | returns a 3-tuple containing the part before the separator, the separator\n", " | itself, and the part after it.\n", " | \n", " | If the separator is not found, returns a 3-tuple containing the original string\n", " | and two empty strings.\n", " | \n", " | removeprefix(self, prefix, /)\n", " | Return a str with the given prefix string removed if present.\n", " | \n", " | If the string starts with the prefix string, return string[len(prefix):].\n", " | Otherwise, return a copy of the original string.\n", " | \n", " | removesuffix(self, suffix, /)\n", " | Return a str with the given suffix string removed if present.\n", " | \n", " | If the string ends with the suffix string and that suffix is not empty,\n", " | return string[:-len(suffix)]. Otherwise, return a copy of the original\n", " | string.\n", " | \n", " | replace(self, old, new, count=-1, /)\n", " | Return a copy with all occurrences of substring old replaced by new.\n", " | \n", " | count\n", " | Maximum number of occurrences to replace.\n", " | -1 (the default value) means replace all occurrences.\n", " | \n", " | If the optional argument count is given, only the first count occurrences are\n", " | replaced.\n", " | \n", " | rfind(...)\n", " | S.rfind(sub[, start[, end]]) -> int\n", " | \n", " | Return the highest index in S where substring sub is found,\n", " | such that sub is contained within S[start:end]. Optional\n", " | arguments start and end are interpreted as in slice notation.\n", " | \n", " | Return -1 on failure.\n", " | \n", " | rindex(...)\n", " | S.rindex(sub[, start[, end]]) -> int\n", " | \n", " | Return the highest index in S where substring sub is found,\n", " | such that sub is contained within S[start:end]. Optional\n", " | arguments start and end are interpreted as in slice notation.\n", " | \n", " | Raises ValueError when the substring is not found.\n", " | \n", " | rjust(self, width, fillchar=' ', /)\n", " | Return a right-justified string of length width.\n", " | \n", " | Padding is done using the specified fill character (default is a space).\n", " | \n", " | rpartition(self, sep, /)\n", " | Partition the string into three parts using the given separator.\n", " | \n", " | This will search for the separator in the string, starting at the end. If\n", " | the separator is found, returns a 3-tuple containing the part before the\n", " | separator, the separator itself, and the part after it.\n", " | \n", " | If the separator is not found, returns a 3-tuple containing two empty strings\n", " | and the original string.\n", " | \n", " | rsplit(self, /, sep=None, maxsplit=-1)\n", " | Return a list of the substrings in the string, using sep as the separator string.\n", " | \n", " | sep\n", " | The separator used to split the string.\n", " | \n", " | When set to None (the default value), will split on any whitespace\n", " | character (including \\\\n \\\\r \\\\t \\\\f and spaces) and will discard\n", " | empty strings from the result.\n", " | maxsplit\n", " | Maximum number of splits (starting from the left).\n", " | -1 (the default value) means no limit.\n", " | \n", " | Splitting starts at the end of the string and works to the front.\n", " | \n", " | rstrip(self, chars=None, /)\n", " | Return a copy of the string with trailing whitespace removed.\n", " | \n", " | If chars is given and not None, remove characters in chars instead.\n", " | \n", " | split(self, /, sep=None, maxsplit=-1)\n", " | Return a list of the substrings in the string, using sep as the separator string.\n", " | \n", " | sep\n", " | The separator used to split the string.\n", " | \n", " | When set to None (the default value), will split on any whitespace\n", " | character (including \\\\n \\\\r \\\\t \\\\f and spaces) and will discard\n", " | empty strings from the result.\n", " | maxsplit\n", " | Maximum number of splits (starting from the left).\n", " | -1 (the default value) means no limit.\n", " | \n", " | Note, str.split() is mainly useful for data that has been intentionally\n", " | delimited. With natural text that includes punctuation, consider using\n", " | the regular expression module.\n", " | \n", " | splitlines(self, /, keepends=False)\n", " | Return a list of the lines in the string, breaking at line boundaries.\n", " | \n", " | Line breaks are not included in the resulting list unless keepends is given and\n", " | true.\n", " | \n", " | startswith(...)\n", " | S.startswith(prefix[, start[, end]]) -> bool\n", " | \n", " | Return True if S starts with the specified prefix, False otherwise.\n", " | With optional start, test S beginning at that position.\n", " | With optional end, stop comparing S at that position.\n", " | prefix can also be a tuple of strings to try.\n", " | \n", " | strip(self, chars=None, /)\n", " | Return a copy of the string with leading and trailing whitespace removed.\n", " | \n", " | If chars is given and not None, remove characters in chars instead.\n", " | \n", " | swapcase(self, /)\n", " | Convert uppercase characters to lowercase and lowercase characters to uppercase.\n", " | \n", " | title(self, /)\n", " | Return a version of the string where each word is titlecased.\n", " | \n", " | More specifically, words start with uppercased characters and all remaining\n", " | cased characters have lower case.\n", " | \n", " | translate(self, table, /)\n", " | Replace each character in the string using the given translation table.\n", " | \n", " | table\n", " | Translation table, which must be a mapping of Unicode ordinals to\n", " | Unicode ordinals, strings, or None.\n", " | \n", " | The table must implement lookup/indexing via __getitem__, for instance a\n", " | dictionary or list. If this operation raises LookupError, the character is\n", " | left untouched. Characters mapped to None are deleted.\n", " | \n", " | upper(self, /)\n", " | Return a copy of the string converted to uppercase.\n", " | \n", " | zfill(self, width, /)\n", " | Pad a numeric string with zeros on the left, to fill a field of the given width.\n", " | \n", " | The string is never truncated.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods inherited from builtins.str:\n", " | \n", " | maketrans(...)\n", " | Return a translation table usable for str.translate().\n", " | \n", " | If there is only one argument, it must be a dictionary mapping Unicode\n", " | ordinals (integers) or characters to Unicode ordinals, strings or None.\n", " | Character keys will be then converted to ordinals.\n", " | If there are two arguments, they must be strings of equal length, and\n", " | in the resulting dictionary, each character in x will be mapped to the\n", " | character at the same position in y. If there is a third argument, it\n", " | must be a string, whose characters will be mapped to None in the result.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " class unsignedinteger(integer)\n", " | Abstract base class of all unsigned integer scalar types.\n", " | \n", " | Method resolution order:\n", " | unsignedinteger\n", " | integer\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods inherited from integer:\n", " | \n", " | __round__(...)\n", " | \n", " | is_integer(...)\n", " | integer.is_integer() -> bool\n", " | \n", " | Return ``True`` if the number is finite with integral value.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.int64(-2).is_integer()\n", " | True\n", " | >>> np.uint32(5).is_integer()\n", " | True\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from integer:\n", " | \n", " | denominator\n", " | denominator of value (1)\n", " | \n", " | numerator\n", " | numerator of value (the value itself)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods inherited from number:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data and other attributes inherited from generic:\n", " | \n", " | __hash__ = None\n", " \n", " ushort = class uint16(unsignedinteger)\n", " | Unsigned integer type, compatible with C ``unsigned short``.\n", " | \n", " | :Character code: ``'H'``\n", " | :Canonical name: `numpy.ushort`\n", " | :Alias on this platform (win32 AMD64): `numpy.uint16`: 16-bit unsigned integer (``0`` to ``65_535``).\n", " | \n", " | Method resolution order:\n", " | uint16\n", " | unsignedinteger\n", " | integer\n", " | number\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __index__(self, /)\n", " | Return self converted to an integer, if self is suitable for use as an index into a list.\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | bit_count(...)\n", " | uint16.bit_count() -> int\n", " | \n", " | Computes the number of 1-bits in the absolute value of the input.\n", " | Analogous to the builtin `int.bit_count` or ``popcount`` in C++.\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.uint16(127).bit_count()\n", " | 7\n", " | \n", " | ----------------------------------------------------------------------\n", " | Class methods defined here:\n", " | \n", " | __class_getitem__(...) from builtins.type\n", " | __class_getitem__(item, /)\n", " | \n", " | Return a parametrized wrapper around the `~numpy.number` type.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Returns\n", " | -------\n", " | alias : types.GenericAlias\n", " | A parametrized `~numpy.number` type.\n", " | \n", " | Examples\n", " | --------\n", " | >>> from typing import Any\n", " | >>> import numpy as np\n", " | \n", " | >>> np.signedinteger[Any]\n", " | numpy.signedinteger[typing.Any]\n", " | \n", " | Notes\n", " | -----\n", " | This method is only available for python 3.9 and later.\n", " | \n", " | See Also\n", " | --------\n", " | :pep:`585` : Type hinting generics in standard collections.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from integer:\n", " | \n", " | __round__(...)\n", " | \n", " | is_integer(...)\n", " | integer.is_integer() -> bool\n", " | \n", " | Return ``True`` if the number is finite with integral value.\n", " | \n", " | .. versionadded:: 1.22\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.int64(-2).is_integer()\n", " | True\n", " | >>> np.uint32(5).is_integer()\n", " | True\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from integer:\n", " | \n", " | denominator\n", " | denominator of value (1)\n", " | \n", " | numerator\n", " | numerator of value (the value itself)\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | base\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.base`.\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | dtype\n", " | Get array data-descriptor.\n", " | \n", " | flags\n", " | The integer value of flags.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", " \n", " class vectorize(builtins.object)\n", " | vectorize(pyfunc, otypes=None, doc=None, excluded=None, cache=False, signature=None)\n", " | \n", " | vectorize(pyfunc, otypes=None, doc=None, excluded=None, cache=False,\n", " | signature=None)\n", " | \n", " | Generalized function class.\n", " | \n", " | Define a vectorized function which takes a nested sequence of objects or\n", " | numpy arrays as inputs and returns a single numpy array or a tuple of numpy\n", " | arrays. The vectorized function evaluates `pyfunc` over successive tuples\n", " | of the input arrays like the python map function, except it uses the\n", " | broadcasting rules of numpy.\n", " | \n", " | The data type of the output of `vectorized` is determined by calling\n", " | the function with the first element of the input. This can be avoided\n", " | by specifying the `otypes` argument.\n", " | \n", " | Parameters\n", " | ----------\n", " | pyfunc : callable\n", " | A python function or method.\n", " | otypes : str or list of dtypes, optional\n", " | The output data type. It must be specified as either a string of\n", " | typecode characters or a list of data type specifiers. There should\n", " | be one data type specifier for each output.\n", " | doc : str, optional\n", " | The docstring for the function. If None, the docstring will be the\n", " | ``pyfunc.__doc__``.\n", " | excluded : set, optional\n", " | Set of strings or integers representing the positional or keyword\n", " | arguments for which the function will not be vectorized. These will be\n", " | passed directly to `pyfunc` unmodified.\n", " | \n", " | .. versionadded:: 1.7.0\n", " | \n", " | cache : bool, optional\n", " | If `True`, then cache the first function call that determines the number\n", " | of outputs if `otypes` is not provided.\n", " | \n", " | .. versionadded:: 1.7.0\n", " | \n", " | signature : string, optional\n", " | Generalized universal function signature, e.g., ``(m,n),(n)->(m)`` for\n", " | vectorized matrix-vector multiplication. If provided, ``pyfunc`` will\n", " | be called with (and expected to return) arrays with shapes given by the\n", " | size of corresponding core dimensions. By default, ``pyfunc`` is\n", " | assumed to take scalars as input and output.\n", " | \n", " | .. versionadded:: 1.12.0\n", " | \n", " | Returns\n", " | -------\n", " | vectorized : callable\n", " | Vectorized function.\n", " | \n", " | See Also\n", " | --------\n", " | frompyfunc : Takes an arbitrary Python function and returns a ufunc\n", " | \n", " | Notes\n", " | -----\n", " | The `vectorize` function is provided primarily for convenience, not for\n", " | performance. The implementation is essentially a for loop.\n", " | \n", " | If `otypes` is not specified, then a call to the function with the\n", " | first argument will be used to determine the number of outputs. The\n", " | results of this call will be cached if `cache` is `True` to prevent\n", " | calling the function twice. However, to implement the cache, the\n", " | original function must be wrapped which will slow down subsequent\n", " | calls, so only do this if your function is expensive.\n", " | \n", " | The new keyword argument interface and `excluded` argument support\n", " | further degrades performance.\n", " | \n", " | References\n", " | ----------\n", " | .. [1] :doc:`/reference/c-api/generalized-ufuncs`\n", " | \n", " | Examples\n", " | --------\n", " | >>> def myfunc(a, b):\n", " | ... \"Return a-b if a>b, otherwise return a+b\"\n", " | ... if a > b:\n", " | ... return a - b\n", " | ... else:\n", " | ... return a + b\n", " | \n", " | >>> vfunc = np.vectorize(myfunc)\n", " | >>> vfunc([1, 2, 3, 4], 2)\n", " | array([3, 4, 1, 2])\n", " | \n", " | The docstring is taken from the input function to `vectorize` unless it\n", " | is specified:\n", " | \n", " | >>> vfunc.__doc__\n", " | 'Return a-b if a>b, otherwise return a+b'\n", " | >>> vfunc = np.vectorize(myfunc, doc='Vectorized `myfunc`')\n", " | >>> vfunc.__doc__\n", " | 'Vectorized `myfunc`'\n", " | \n", " | The output type is determined by evaluating the first element of the input,\n", " | unless it is specified:\n", " | \n", " | >>> out = vfunc([1, 2, 3, 4], 2)\n", " | >>> type(out[0])\n", " | <class 'numpy.int64'>\n", " | >>> vfunc = np.vectorize(myfunc, otypes=[float])\n", " | >>> out = vfunc([1, 2, 3, 4], 2)\n", " | >>> type(out[0])\n", " | <class 'numpy.float64'>\n", " | \n", " | The `excluded` argument can be used to prevent vectorizing over certain\n", " | arguments. This can be useful for array-like arguments of a fixed length\n", " | such as the coefficients for a polynomial as in `polyval`:\n", " | \n", " | >>> def mypolyval(p, x):\n", " | ... _p = list(p)\n", " | ... res = _p.pop(0)\n", " | ... while _p:\n", " | ... res = res*x + _p.pop(0)\n", " | ... return res\n", " | >>> vpolyval = np.vectorize(mypolyval, excluded=['p'])\n", " | >>> vpolyval(p=[1, 2, 3], x=[0, 1])\n", " | array([3, 6])\n", " | \n", " | Positional arguments may also be excluded by specifying their position:\n", " | \n", " | >>> vpolyval.excluded.add(0)\n", " | >>> vpolyval([1, 2, 3], x=[0, 1])\n", " | array([3, 6])\n", " | \n", " | The `signature` argument allows for vectorizing functions that act on\n", " | non-scalar arrays of fixed length. For example, you can use it for a\n", " | vectorized calculation of Pearson correlation coefficient and its p-value:\n", " | \n", " | >>> import scipy.stats\n", " | >>> pearsonr = np.vectorize(scipy.stats.pearsonr,\n", " | ... signature='(n),(n)->(),()')\n", " | >>> pearsonr([[0, 1, 2, 3]], [[1, 2, 3, 4], [4, 3, 2, 1]])\n", " | (array([ 1., -1.]), array([ 0., 0.]))\n", " | \n", " | Or for a vectorized convolution:\n", " | \n", " | >>> convolve = np.vectorize(np.convolve, signature='(n),(m)->(k)')\n", " | >>> convolve(np.eye(4), [1, 2, 1])\n", " | array([[1., 2., 1., 0., 0., 0.],\n", " | [0., 1., 2., 1., 0., 0.],\n", " | [0., 0., 1., 2., 1., 0.],\n", " | [0., 0., 0., 1., 2., 1.]])\n", " | \n", " | Methods defined here:\n", " | \n", " | __call__(self, *args, **kwargs)\n", " | Return arrays with the results of `pyfunc` broadcast (vectorized) over\n", " | `args` and `kwargs` not in `excluded`.\n", " | \n", " | __init__(self, pyfunc, otypes=None, doc=None, excluded=None, cache=False, signature=None)\n", " | Initialize self. See help(type(self)) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors defined here:\n", " | \n", " | __dict__\n", " | dictionary for instance variables (if defined)\n", " | \n", " | __weakref__\n", " | list of weak references to the object (if defined)\n", " \n", " class void(flexible)\n", " | np.void(length_or_data, /, dtype=None)\n", " | \n", " | Create a new structured or unstructured void scalar.\n", " | \n", " | Parameters\n", " | ----------\n", " | length_or_data : int, array-like, bytes-like, object\n", " | One of multiple meanings (see notes). The length or\n", " | bytes data of an unstructured void. Or alternatively,\n", " | the data to be stored in the new scalar when `dtype`\n", " | is provided.\n", " | This can be an array-like, in which case an array may\n", " | be returned.\n", " | dtype : dtype, optional\n", " | If provided the dtype of the new scalar. This dtype must\n", " | be \"void\" dtype (i.e. a structured or unstructured void,\n", " | see also :ref:`defining-structured-types`).\n", " | \n", " | ..versionadded:: 1.24\n", " | \n", " | Notes\n", " | -----\n", " | For historical reasons and because void scalars can represent both\n", " | arbitrary byte data and structured dtypes, the void constructor\n", " | has three calling conventions:\n", " | \n", " | 1. ``np.void(5)`` creates a ``dtype=\"V5\"`` scalar filled with five\n", " | ``\\0`` bytes. The 5 can be a Python or NumPy integer.\n", " | 2. ``np.void(b\"bytes-like\")`` creates a void scalar from the byte string.\n", " | The dtype itemsize will match the byte string length, here ``\"V10\"``.\n", " | 3. When a ``dtype=`` is passed the call is rougly the same as an\n", " | array creation. However, a void scalar rather than array is returned.\n", " | \n", " | Please see the examples which show all three different conventions.\n", " | \n", " | Examples\n", " | --------\n", " | >>> np.void(5)\n", " | void(b'\\x00\\x00\\x00\\x00\\x00')\n", " | >>> np.void(b'abcd')\n", " | void(b'\\x61\\x62\\x63\\x64')\n", " | >>> np.void((5, 3.2, \"eggs\"), dtype=\"i,d,S5\")\n", " | (5, 3.2, b'eggs') # looks like a tuple, but is `np.void`\n", " | >>> np.void(3, dtype=[('x', np.int8), ('y', np.int8)])\n", " | (3, 3) # looks like a tuple, but is `np.void`\n", " | \n", " | :Character code: ``'V'``\n", " | \n", " | Method resolution order:\n", " | void\n", " | flexible\n", " | generic\n", " | builtins.object\n", " | \n", " | Methods defined here:\n", " | \n", " | __delitem__(self, key, /)\n", " | Delete self[key].\n", " | \n", " | __eq__(self, value, /)\n", " | Return self==value.\n", " | \n", " | __ge__(self, value, /)\n", " | Return self>=value.\n", " | \n", " | __getitem__(self, key, /)\n", " | Return self[key].\n", " | \n", " | __gt__(self, value, /)\n", " | Return self>value.\n", " | \n", " | __hash__(self, /)\n", " | Return hash(self).\n", " | \n", " | __le__(self, value, /)\n", " | Return self<=value.\n", " | \n", " | __len__(self, /)\n", " | Return len(self).\n", " | \n", " | __lt__(self, value, /)\n", " | Return self<value.\n", " | \n", " | __ne__(self, value, /)\n", " | Return self!=value.\n", " | \n", " | __repr__(self, /)\n", " | Return repr(self).\n", " | \n", " | __setitem__(self, key, value, /)\n", " | Set self[key] to value.\n", " | \n", " | __str__(self, /)\n", " | Return str(self).\n", " | \n", " | getfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.getfield`.\n", " | \n", " | setfield(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setfield`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Static methods defined here:\n", " | \n", " | __new__(*args, **kwargs) from builtins.type\n", " | Create and return a new object. See help(type) for accurate signature.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors defined here:\n", " | \n", " | base\n", " | base object\n", " | \n", " | dtype\n", " | dtype object\n", " | \n", " | flags\n", " | integer value of flags\n", " | \n", " | ----------------------------------------------------------------------\n", " | Methods inherited from generic:\n", " | \n", " | __abs__(self, /)\n", " | abs(self)\n", " | \n", " | __add__(self, value, /)\n", " | Return self+value.\n", " | \n", " | __and__(self, value, /)\n", " | Return self&value.\n", " | \n", " | __array__(...)\n", " | sc.__array__(dtype) return 0-dim array from scalar with specified dtype\n", " | \n", " | __array_wrap__(...)\n", " | sc.__array_wrap__(obj) return scalar from array\n", " | \n", " | __bool__(self, /)\n", " | True if self else False\n", " | \n", " | __copy__(...)\n", " | \n", " | __deepcopy__(...)\n", " | \n", " | __divmod__(self, value, /)\n", " | Return divmod(self, value).\n", " | \n", " | __float__(self, /)\n", " | float(self)\n", " | \n", " | __floordiv__(self, value, /)\n", " | Return self//value.\n", " | \n", " | __format__(...)\n", " | NumPy array scalar formatter\n", " | \n", " | __int__(self, /)\n", " | int(self)\n", " | \n", " | __invert__(self, /)\n", " | ~self\n", " | \n", " | __lshift__(self, value, /)\n", " | Return self<<value.\n", " | \n", " | __mod__(self, value, /)\n", " | Return self%value.\n", " | \n", " | __mul__(self, value, /)\n", " | Return self*value.\n", " | \n", " | __neg__(self, /)\n", " | -self\n", " | \n", " | __or__(self, value, /)\n", " | Return self|value.\n", " | \n", " | __pos__(self, /)\n", " | +self\n", " | \n", " | __pow__(self, value, mod=None, /)\n", " | Return pow(self, value, mod).\n", " | \n", " | __radd__(self, value, /)\n", " | Return value+self.\n", " | \n", " | __rand__(self, value, /)\n", " | Return value&self.\n", " | \n", " | __rdivmod__(self, value, /)\n", " | Return divmod(value, self).\n", " | \n", " | __reduce__(...)\n", " | Helper for pickle.\n", " | \n", " | __rfloordiv__(self, value, /)\n", " | Return value//self.\n", " | \n", " | __rlshift__(self, value, /)\n", " | Return value<<self.\n", " | \n", " | __rmod__(self, value, /)\n", " | Return value%self.\n", " | \n", " | __rmul__(self, value, /)\n", " | Return value*self.\n", " | \n", " | __ror__(self, value, /)\n", " | Return value|self.\n", " | \n", " | __rpow__(self, value, mod=None, /)\n", " | Return pow(value, self, mod).\n", " | \n", " | __rrshift__(self, value, /)\n", " | Return value>>self.\n", " | \n", " | __rshift__(self, value, /)\n", " | Return self>>value.\n", " | \n", " | __rsub__(self, value, /)\n", " | Return value-self.\n", " | \n", " | __rtruediv__(self, value, /)\n", " | Return value/self.\n", " | \n", " | __rxor__(self, value, /)\n", " | Return value^self.\n", " | \n", " | __setstate__(...)\n", " | \n", " | __sizeof__(...)\n", " | Size of object in memory, in bytes.\n", " | \n", " | __sub__(self, value, /)\n", " | Return self-value.\n", " | \n", " | __truediv__(self, value, /)\n", " | Return self/value.\n", " | \n", " | __xor__(self, value, /)\n", " | Return self^value.\n", " | \n", " | all(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.all`.\n", " | \n", " | any(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.any`.\n", " | \n", " | argmax(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmax`.\n", " | \n", " | argmin(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argmin`.\n", " | \n", " | argsort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.argsort`.\n", " | \n", " | astype(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.astype`.\n", " | \n", " | byteswap(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.byteswap`.\n", " | \n", " | choose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.choose`.\n", " | \n", " | clip(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.clip`.\n", " | \n", " | compress(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.compress`.\n", " | \n", " | conj(...)\n", " | \n", " | conjugate(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.conjugate`.\n", " | \n", " | copy(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.copy`.\n", " | \n", " | cumprod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumprod`.\n", " | \n", " | cumsum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.cumsum`.\n", " | \n", " | diagonal(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.diagonal`.\n", " | \n", " | dump(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dump`.\n", " | \n", " | dumps(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.dumps`.\n", " | \n", " | fill(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.fill`.\n", " | \n", " | flatten(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.flatten`.\n", " | \n", " | item(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.item`.\n", " | \n", " | itemset(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.itemset`.\n", " | \n", " | max(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.max`.\n", " | \n", " | mean(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.mean`.\n", " | \n", " | min(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.min`.\n", " | \n", " | newbyteorder(...)\n", " | newbyteorder(new_order='S', /)\n", " | \n", " | Return a new `dtype` with a different byte order.\n", " | \n", " | Changes are also made in all fields and sub-arrays of the data type.\n", " | \n", " | The `new_order` code can be any from the following:\n", " | \n", " | * 'S' - swap dtype from current to opposite endian\n", " | * {'<', 'little'} - little endian\n", " | * {'>', 'big'} - big endian\n", " | * {'=', 'native'} - native order\n", " | * {'|', 'I'} - ignore (no change to byte order)\n", " | \n", " | Parameters\n", " | ----------\n", " | new_order : str, optional\n", " | Byte order to force; a value from the byte order specifications\n", " | above. The default value ('S') results in swapping the current\n", " | byte order.\n", " | \n", " | \n", " | Returns\n", " | -------\n", " | new_dtype : dtype\n", " | New `dtype` object with the given change to the byte order.\n", " | \n", " | nonzero(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.nonzero`.\n", " | \n", " | prod(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.prod`.\n", " | \n", " | ptp(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ptp`.\n", " | \n", " | put(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.put`.\n", " | \n", " | ravel(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.ravel`.\n", " | \n", " | repeat(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.repeat`.\n", " | \n", " | reshape(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.reshape`.\n", " | \n", " | resize(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.resize`.\n", " | \n", " | round(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.round`.\n", " | \n", " | searchsorted(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.searchsorted`.\n", " | \n", " | setflags(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.setflags`.\n", " | \n", " | sort(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sort`.\n", " | \n", " | squeeze(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.squeeze`.\n", " | \n", " | std(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.std`.\n", " | \n", " | sum(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.sum`.\n", " | \n", " | swapaxes(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.swapaxes`.\n", " | \n", " | take(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.take`.\n", " | \n", " | tobytes(...)\n", " | \n", " | tofile(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tofile`.\n", " | \n", " | tolist(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tolist`.\n", " | \n", " | tostring(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.tostring`.\n", " | \n", " | trace(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.trace`.\n", " | \n", " | transpose(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.transpose`.\n", " | \n", " | var(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.var`.\n", " | \n", " | view(...)\n", " | Scalar method identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.view`.\n", " | \n", " | ----------------------------------------------------------------------\n", " | Data descriptors inherited from generic:\n", " | \n", " | T\n", " | Scalar attribute identical to the corresponding array attribute.\n", " | \n", " | Please see `ndarray.T`.\n", " | \n", " | __array_interface__\n", " | Array protocol: Python side\n", " | \n", " | __array_priority__\n", " | Array priority.\n", " | \n", " | __array_struct__\n", " | Array protocol: struct\n", " | \n", " | data\n", " | Pointer to start of data.\n", " | \n", " | flat\n", " | A 1-D view of the scalar.\n", " | \n", " | imag\n", " | The imaginary part of the scalar.\n", " | \n", " | itemsize\n", " | The length of one element in bytes.\n", " | \n", " | nbytes\n", " | The length of the scalar in bytes.\n", " | \n", " | ndim\n", " | The number of array dimensions.\n", " | \n", " | real\n", " | The real part of the scalar.\n", " | \n", " | shape\n", " | Tuple of array dimensions.\n", " | \n", " | size\n", " | The number of elements in the gentype.\n", " | \n", " | strides\n", " | Tuple of bytes steps in each dimension.\n", "\n", "FUNCTIONS\n", " __dir__()\n", " \n", " __getattr__(attr)\n", " \n", " _add_newdoc_ufunc(...)\n", " add_ufunc_docstring(ufunc, new_docstring)\n", " \n", " Replace the docstring for a ufunc with new_docstring.\n", " This method will only work if the current docstring for\n", " the ufunc is NULL. (At the C level, i.e. when ufunc->doc is NULL.)\n", " \n", " Parameters\n", " ----------\n", " ufunc : numpy.ufunc\n", " A ufunc whose current doc is NULL.\n", " new_docstring : string\n", " The new docstring for the ufunc.\n", " \n", " Notes\n", " -----\n", " This method allocates memory for new_docstring on\n", " the heap. Technically this creates a mempory leak, since this\n", " memory will not be reclaimed until the end of the program\n", " even if the ufunc itself is removed. However this will only\n", " be a problem if the user is repeatedly creating ufuncs with\n", " no documentation, adding documentation via add_newdoc_ufunc,\n", " and then throwing away the ufunc.\n", " \n", " _get_promotion_state(...)\n", " Get the current NEP 50 promotion state.\n", " \n", " _no_nep50_warning()\n", " Context manager to disable NEP 50 warnings. This context manager is\n", " only relevant if the NEP 50 warnings are enabled globally (which is not\n", " thread/context safe).\n", " \n", " This warning context manager itself is fully safe, however.\n", " \n", " _set_promotion_state(...)\n", " Set the NEP 50 promotion state. This is not thread-safe.\n", " The optional warnings can be safely silenced using the \n", " `np._no_nep50_warning()` context manager.\n", " \n", " add_docstring(...)\n", " add_docstring(obj, docstring)\n", " \n", " Add a docstring to a built-in obj if possible.\n", " If the obj already has a docstring raise a RuntimeError\n", " If this routine does not know how to add a docstring to the object\n", " raise a TypeError\n", " \n", " add_newdoc(place, obj, doc, warn_on_python=True)\n", " Add documentation to an existing object, typically one defined in C\n", " \n", " The purpose is to allow easier editing of the docstrings without requiring\n", " a re-compile. This exists primarily for internal use within numpy itself.\n", " \n", " Parameters\n", " ----------\n", " place : str\n", " The absolute name of the module to import from\n", " obj : str\n", " The name of the object to add documentation to, typically a class or\n", " function name\n", " doc : {str, Tuple[str, str], List[Tuple[str, str]]}\n", " If a string, the documentation to apply to `obj`\n", " \n", " If a tuple, then the first element is interpreted as an attribute of\n", " `obj` and the second as the docstring to apply - ``(method, docstring)``\n", " \n", " If a list, then each element of the list should be a tuple of length\n", " two - ``[(method1, docstring1), (method2, docstring2), ...]``\n", " warn_on_python : bool\n", " If True, the default, emit `UserWarning` if this is used to attach\n", " documentation to a pure-python object.\n", " \n", " Notes\n", " -----\n", " This routine never raises an error if the docstring can't be written, but\n", " will raise an error if the object being documented does not exist.\n", " \n", " This routine cannot modify read-only docstrings, as appear\n", " in new-style classes or built-in functions. Because this\n", " routine never raises an error the caller must check manually\n", " that the docstrings were changed.\n", " \n", " Since this function grabs the ``char *`` from a c-level str object and puts\n", " it into the ``tp_doc`` slot of the type of `obj`, it violates a number of\n", " C-API best-practices, by:\n", " \n", " - modifying a `PyTypeObject` after calling `PyType_Ready`\n", " - calling `Py_INCREF` on the str and losing the reference, so the str\n", " will never be released\n", " \n", " If possible it should be avoided.\n", " \n", " add_newdoc_ufunc = _add_newdoc_ufunc(...)\n", " add_ufunc_docstring(ufunc, new_docstring)\n", " \n", " Replace the docstring for a ufunc with new_docstring.\n", " This method will only work if the current docstring for\n", " the ufunc is NULL. (At the C level, i.e. when ufunc->doc is NULL.)\n", " \n", " Parameters\n", " ----------\n", " ufunc : numpy.ufunc\n", " A ufunc whose current doc is NULL.\n", " new_docstring : string\n", " The new docstring for the ufunc.\n", " \n", " Notes\n", " -----\n", " This method allocates memory for new_docstring on\n", " the heap. Technically this creates a mempory leak, since this\n", " memory will not be reclaimed until the end of the program\n", " even if the ufunc itself is removed. However this will only\n", " be a problem if the user is repeatedly creating ufuncs with\n", " no documentation, adding documentation via add_newdoc_ufunc,\n", " and then throwing away the ufunc.\n", " \n", " all(a, axis=None, out=None, keepdims=<no value>, *, where=<no value>)\n", " Test whether all array elements along a given axis evaluate to True.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input array or object that can be converted to an array.\n", " axis : None or int or tuple of ints, optional\n", " Axis or axes along which a logical AND reduction is performed.\n", " The default (``axis=None``) is to perform a logical AND over all\n", " the dimensions of the input array. `axis` may be negative, in\n", " which case it counts from the last to the first axis.\n", " \n", " .. versionadded:: 1.7.0\n", " \n", " If this is a tuple of ints, a reduction is performed on multiple\n", " axes, instead of a single axis or all the axes as before.\n", " out : ndarray, optional\n", " Alternate output array in which to place the result.\n", " It must have the same shape as the expected output and its\n", " type is preserved (e.g., if ``dtype(out)`` is float, the result\n", " will consist of 0.0's and 1.0's). See :ref:`ufuncs-output-type` for more\n", " details.\n", " \n", " keepdims : bool, optional\n", " If this is set to True, the axes which are reduced are left\n", " in the result as dimensions with size one. With this option,\n", " the result will broadcast correctly against the input array.\n", " \n", " If the default value is passed, then `keepdims` will not be\n", " passed through to the `all` method of sub-classes of\n", " `ndarray`, however any non-default value will be. If the\n", " sub-class' method does not implement `keepdims` any\n", " exceptions will be raised.\n", " \n", " where : array_like of bool, optional\n", " Elements to include in checking for all `True` values.\n", " See `~numpy.ufunc.reduce` for details.\n", " \n", " .. versionadded:: 1.20.0\n", " \n", " Returns\n", " -------\n", " all : ndarray, bool\n", " A new boolean or array is returned unless `out` is specified,\n", " in which case a reference to `out` is returned.\n", " \n", " See Also\n", " --------\n", " ndarray.all : equivalent method\n", " \n", " any : Test whether any element along a given axis evaluates to True.\n", " \n", " Notes\n", " -----\n", " Not a Number (NaN), positive infinity and negative infinity\n", " evaluate to `True` because these are not equal to zero.\n", " \n", " Examples\n", " --------\n", " >>> np.all([[True,False],[True,True]])\n", " False\n", " \n", " >>> np.all([[True,False],[True,True]], axis=0)\n", " array([ True, False])\n", " \n", " >>> np.all([-1, 4, 5])\n", " True\n", " \n", " >>> np.all([1.0, np.nan])\n", " True\n", " \n", " >>> np.all([[True, True], [False, True]], where=[[True], [False]])\n", " True\n", " \n", " >>> o=np.array(False)\n", " >>> z=np.all([-1, 4, 5], out=o)\n", " >>> id(z), id(o), z\n", " (28293632, 28293632, array(True)) # may vary\n", " \n", " allclose(a, b, rtol=1e-05, atol=1e-08, equal_nan=False)\n", " Returns True if two arrays are element-wise equal within a tolerance.\n", " \n", " The tolerance values are positive, typically very small numbers. The\n", " relative difference (`rtol` * abs(`b`)) and the absolute difference\n", " `atol` are added together to compare against the absolute difference\n", " between `a` and `b`.\n", " \n", " NaNs are treated as equal if they are in the same place and if\n", " ``equal_nan=True``. Infs are treated as equal if they are in the same\n", " place and of the same sign in both arrays.\n", " \n", " Parameters\n", " ----------\n", " a, b : array_like\n", " Input arrays to compare.\n", " rtol : float\n", " The relative tolerance parameter (see Notes).\n", " atol : float\n", " The absolute tolerance parameter (see Notes).\n", " equal_nan : bool\n", " Whether to compare NaN's as equal. If True, NaN's in `a` will be\n", " considered equal to NaN's in `b` in the output array.\n", " \n", " .. versionadded:: 1.10.0\n", " \n", " Returns\n", " -------\n", " allclose : bool\n", " Returns True if the two arrays are equal within the given\n", " tolerance; False otherwise.\n", " \n", " See Also\n", " --------\n", " isclose, all, any, equal\n", " \n", " Notes\n", " -----\n", " If the following equation is element-wise True, then allclose returns\n", " True.\n", " \n", " absolute(`a` - `b`) <= (`atol` + `rtol` * absolute(`b`))\n", " \n", " The above equation is not symmetric in `a` and `b`, so that\n", " ``allclose(a, b)`` might be different from ``allclose(b, a)`` in\n", " some rare cases.\n", " \n", " The comparison of `a` and `b` uses standard broadcasting, which\n", " means that `a` and `b` need not have the same shape in order for\n", " ``allclose(a, b)`` to evaluate to True. The same is true for\n", " `equal` but not `array_equal`.\n", " \n", " `allclose` is not defined for non-numeric data types.\n", " `bool` is considered a numeric data-type for this purpose.\n", " \n", " Examples\n", " --------\n", " >>> np.allclose([1e10,1e-7], [1.00001e10,1e-8])\n", " False\n", " >>> np.allclose([1e10,1e-8], [1.00001e10,1e-9])\n", " True\n", " >>> np.allclose([1e10,1e-8], [1.0001e10,1e-9])\n", " False\n", " >>> np.allclose([1.0, np.nan], [1.0, np.nan])\n", " False\n", " >>> np.allclose([1.0, np.nan], [1.0, np.nan], equal_nan=True)\n", " True\n", " \n", " alltrue(*args, **kwargs)\n", " Check if all elements of input array are true.\n", " \n", " See Also\n", " --------\n", " numpy.all : Equivalent function; see for details.\n", " \n", " amax(a, axis=None, out=None, keepdims=<no value>, initial=<no value>, where=<no value>)\n", " Return the maximum of an array or maximum along an axis.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input data.\n", " axis : None or int or tuple of ints, optional\n", " Axis or axes along which to operate. By default, flattened input is\n", " used.\n", " \n", " .. versionadded:: 1.7.0\n", " \n", " If this is a tuple of ints, the maximum is selected over multiple axes,\n", " instead of a single axis or all the axes as before.\n", " out : ndarray, optional\n", " Alternative output array in which to place the result. Must\n", " be of the same shape and buffer length as the expected output.\n", " See :ref:`ufuncs-output-type` for more details.\n", " \n", " keepdims : bool, optional\n", " If this is set to True, the axes which are reduced are left\n", " in the result as dimensions with size one. With this option,\n", " the result will broadcast correctly against the input array.\n", " \n", " If the default value is passed, then `keepdims` will not be\n", " passed through to the `amax` method of sub-classes of\n", " `ndarray`, however any non-default value will be. If the\n", " sub-class' method does not implement `keepdims` any\n", " exceptions will be raised.\n", " \n", " initial : scalar, optional\n", " The minimum value of an output element. Must be present to allow\n", " computation on empty slice. See `~numpy.ufunc.reduce` for details.\n", " \n", " .. versionadded:: 1.15.0\n", " \n", " where : array_like of bool, optional\n", " Elements to compare for the maximum. See `~numpy.ufunc.reduce`\n", " for details.\n", " \n", " .. versionadded:: 1.17.0\n", " \n", " Returns\n", " -------\n", " amax : ndarray or scalar\n", " Maximum of `a`. If `axis` is None, the result is a scalar value.\n", " If `axis` is an int, the result is an array of dimension\n", " ``a.ndim - 1``. If `axis` is a tuple, the result is an array of \n", " dimension ``a.ndim - len(axis)``.\n", " \n", " See Also\n", " --------\n", " amin :\n", " The minimum value of an array along a given axis, propagating any NaNs.\n", " nanmax :\n", " The maximum value of an array along a given axis, ignoring any NaNs.\n", " maximum :\n", " Element-wise maximum of two arrays, propagating any NaNs.\n", " fmax :\n", " Element-wise maximum of two arrays, ignoring any NaNs.\n", " argmax :\n", " Return the indices of the maximum values.\n", " \n", " nanmin, minimum, fmin\n", " \n", " Notes\n", " -----\n", " NaN values are propagated, that is if at least one item is NaN, the\n", " corresponding max value will be NaN as well. To ignore NaN values\n", " (MATLAB behavior), please use nanmax.\n", " \n", " Don't use `amax` for element-wise comparison of 2 arrays; when\n", " ``a.shape[0]`` is 2, ``maximum(a[0], a[1])`` is faster than\n", " ``amax(a, axis=0)``.\n", " \n", " Examples\n", " --------\n", " >>> a = np.arange(4).reshape((2,2))\n", " >>> a\n", " array([[0, 1],\n", " [2, 3]])\n", " >>> np.amax(a) # Maximum of the flattened array\n", " 3\n", " >>> np.amax(a, axis=0) # Maxima along the first axis\n", " array([2, 3])\n", " >>> np.amax(a, axis=1) # Maxima along the second axis\n", " array([1, 3])\n", " >>> np.amax(a, where=[False, True], initial=-1, axis=0)\n", " array([-1, 3])\n", " >>> b = np.arange(5, dtype=float)\n", " >>> b[2] = np.NaN\n", " >>> np.amax(b)\n", " nan\n", " >>> np.amax(b, where=~np.isnan(b), initial=-1)\n", " 4.0\n", " >>> np.nanmax(b)\n", " 4.0\n", " \n", " You can use an initial value to compute the maximum of an empty slice, or\n", " to initialize it to a different value:\n", " \n", " >>> np.amax([[-50], [10]], axis=-1, initial=0)\n", " array([ 0, 10])\n", " \n", " Notice that the initial value is used as one of the elements for which the\n", " maximum is determined, unlike for the default argument Python's max\n", " function, which is only used for empty iterables.\n", " \n", " >>> np.amax([5], initial=6)\n", " 6\n", " >>> max([5], default=6)\n", " 5\n", " \n", " amin(a, axis=None, out=None, keepdims=<no value>, initial=<no value>, where=<no value>)\n", " Return the minimum of an array or minimum along an axis.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input data.\n", " axis : None or int or tuple of ints, optional\n", " Axis or axes along which to operate. By default, flattened input is\n", " used.\n", " \n", " .. versionadded:: 1.7.0\n", " \n", " If this is a tuple of ints, the minimum is selected over multiple axes,\n", " instead of a single axis or all the axes as before.\n", " out : ndarray, optional\n", " Alternative output array in which to place the result. Must\n", " be of the same shape and buffer length as the expected output.\n", " See :ref:`ufuncs-output-type` for more details.\n", " \n", " keepdims : bool, optional\n", " If this is set to True, the axes which are reduced are left\n", " in the result as dimensions with size one. With this option,\n", " the result will broadcast correctly against the input array.\n", " \n", " If the default value is passed, then `keepdims` will not be\n", " passed through to the `amin` method of sub-classes of\n", " `ndarray`, however any non-default value will be. If the\n", " sub-class' method does not implement `keepdims` any\n", " exceptions will be raised.\n", " \n", " initial : scalar, optional\n", " The maximum value of an output element. Must be present to allow\n", " computation on empty slice. See `~numpy.ufunc.reduce` for details.\n", " \n", " .. versionadded:: 1.15.0\n", " \n", " where : array_like of bool, optional\n", " Elements to compare for the minimum. See `~numpy.ufunc.reduce`\n", " for details.\n", " \n", " .. versionadded:: 1.17.0\n", " \n", " Returns\n", " -------\n", " amin : ndarray or scalar\n", " Minimum of `a`. If `axis` is None, the result is a scalar value.\n", " If `axis` is an int, the result is an array of dimension\n", " ``a.ndim - 1``. If `axis` is a tuple, the result is an array of \n", " dimension ``a.ndim - len(axis)``.\n", " \n", " See Also\n", " --------\n", " amax :\n", " The maximum value of an array along a given axis, propagating any NaNs.\n", " nanmin :\n", " The minimum value of an array along a given axis, ignoring any NaNs.\n", " minimum :\n", " Element-wise minimum of two arrays, propagating any NaNs.\n", " fmin :\n", " Element-wise minimum of two arrays, ignoring any NaNs.\n", " argmin :\n", " Return the indices of the minimum values.\n", " \n", " nanmax, maximum, fmax\n", " \n", " Notes\n", " -----\n", " NaN values are propagated, that is if at least one item is NaN, the\n", " corresponding min value will be NaN as well. To ignore NaN values\n", " (MATLAB behavior), please use nanmin.\n", " \n", " Don't use `amin` for element-wise comparison of 2 arrays; when\n", " ``a.shape[0]`` is 2, ``minimum(a[0], a[1])`` is faster than\n", " ``amin(a, axis=0)``.\n", " \n", " Examples\n", " --------\n", " >>> a = np.arange(4).reshape((2,2))\n", " >>> a\n", " array([[0, 1],\n", " [2, 3]])\n", " >>> np.amin(a) # Minimum of the flattened array\n", " 0\n", " >>> np.amin(a, axis=0) # Minima along the first axis\n", " array([0, 1])\n", " >>> np.amin(a, axis=1) # Minima along the second axis\n", " array([0, 2])\n", " >>> np.amin(a, where=[False, True], initial=10, axis=0)\n", " array([10, 1])\n", " \n", " >>> b = np.arange(5, dtype=float)\n", " >>> b[2] = np.NaN\n", " >>> np.amin(b)\n", " nan\n", " >>> np.amin(b, where=~np.isnan(b), initial=10)\n", " 0.0\n", " >>> np.nanmin(b)\n", " 0.0\n", " \n", " >>> np.amin([[-50], [10]], axis=-1, initial=0)\n", " array([-50, 0])\n", " \n", " Notice that the initial value is used as one of the elements for which the\n", " minimum is determined, unlike for the default argument Python's max\n", " function, which is only used for empty iterables.\n", " \n", " Notice that this isn't the same as Python's ``default`` argument.\n", " \n", " >>> np.amin([6], initial=5)\n", " 5\n", " >>> min([6], default=5)\n", " 6\n", " \n", " angle(z, deg=False)\n", " Return the angle of the complex argument.\n", " \n", " Parameters\n", " ----------\n", " z : array_like\n", " A complex number or sequence of complex numbers.\n", " deg : bool, optional\n", " Return angle in degrees if True, radians if False (default).\n", " \n", " Returns\n", " -------\n", " angle : ndarray or scalar\n", " The counterclockwise angle from the positive real axis on the complex\n", " plane in the range ``(-pi, pi]``, with dtype as numpy.float64.\n", " \n", " .. versionchanged:: 1.16.0\n", " This function works on subclasses of ndarray like `ma.array`.\n", " \n", " See Also\n", " --------\n", " arctan2\n", " absolute\n", " \n", " Notes\n", " -----\n", " Although the angle of the complex number 0 is undefined, ``numpy.angle(0)``\n", " returns the value 0.\n", " \n", " Examples\n", " --------\n", " >>> np.angle([1.0, 1.0j, 1+1j]) # in radians\n", " array([ 0. , 1.57079633, 0.78539816]) # may vary\n", " >>> np.angle(1+1j, deg=True) # in degrees\n", " 45.0\n", " \n", " any(a, axis=None, out=None, keepdims=<no value>, *, where=<no value>)\n", " Test whether any array element along a given axis evaluates to True.\n", " \n", " Returns single boolean if `axis` is ``None``\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input array or object that can be converted to an array.\n", " axis : None or int or tuple of ints, optional\n", " Axis or axes along which a logical OR reduction is performed.\n", " The default (``axis=None``) is to perform a logical OR over all\n", " the dimensions of the input array. `axis` may be negative, in\n", " which case it counts from the last to the first axis.\n", " \n", " .. versionadded:: 1.7.0\n", " \n", " If this is a tuple of ints, a reduction is performed on multiple\n", " axes, instead of a single axis or all the axes as before.\n", " out : ndarray, optional\n", " Alternate output array in which to place the result. It must have\n", " the same shape as the expected output and its type is preserved\n", " (e.g., if it is of type float, then it will remain so, returning\n", " 1.0 for True and 0.0 for False, regardless of the type of `a`).\n", " See :ref:`ufuncs-output-type` for more details.\n", " \n", " keepdims : bool, optional\n", " If this is set to True, the axes which are reduced are left\n", " in the result as dimensions with size one. With this option,\n", " the result will broadcast correctly against the input array.\n", " \n", " If the default value is passed, then `keepdims` will not be\n", " passed through to the `any` method of sub-classes of\n", " `ndarray`, however any non-default value will be. If the\n", " sub-class' method does not implement `keepdims` any\n", " exceptions will be raised.\n", " \n", " where : array_like of bool, optional\n", " Elements to include in checking for any `True` values.\n", " See `~numpy.ufunc.reduce` for details.\n", " \n", " .. versionadded:: 1.20.0\n", " \n", " Returns\n", " -------\n", " any : bool or ndarray\n", " A new boolean or `ndarray` is returned unless `out` is specified,\n", " in which case a reference to `out` is returned.\n", " \n", " See Also\n", " --------\n", " ndarray.any : equivalent method\n", " \n", " all : Test whether all elements along a given axis evaluate to True.\n", " \n", " Notes\n", " -----\n", " Not a Number (NaN), positive infinity and negative infinity evaluate\n", " to `True` because these are not equal to zero.\n", " \n", " Examples\n", " --------\n", " >>> np.any([[True, False], [True, True]])\n", " True\n", " \n", " >>> np.any([[True, False], [False, False]], axis=0)\n", " array([ True, False])\n", " \n", " >>> np.any([-1, 0, 5])\n", " True\n", " \n", " >>> np.any(np.nan)\n", " True\n", " \n", " >>> np.any([[True, False], [False, False]], where=[[False], [True]])\n", " False\n", " \n", " >>> o=np.array(False)\n", " >>> z=np.any([-1, 4, 5], out=o)\n", " >>> z, o\n", " (array(True), array(True))\n", " >>> # Check now that z is a reference to o\n", " >>> z is o\n", " True\n", " >>> id(z), id(o) # identity of z and o # doctest: +SKIP\n", " (191614240, 191614240)\n", " \n", " append(arr, values, axis=None)\n", " Append values to the end of an array.\n", " \n", " Parameters\n", " ----------\n", " arr : array_like\n", " Values are appended to a copy of this array.\n", " values : array_like\n", " These values are appended to a copy of `arr`. It must be of the\n", " correct shape (the same shape as `arr`, excluding `axis`). If\n", " `axis` is not specified, `values` can be any shape and will be\n", " flattened before use.\n", " axis : int, optional\n", " The axis along which `values` are appended. If `axis` is not\n", " given, both `arr` and `values` are flattened before use.\n", " \n", " Returns\n", " -------\n", " append : ndarray\n", " A copy of `arr` with `values` appended to `axis`. Note that\n", " `append` does not occur in-place: a new array is allocated and\n", " filled. If `axis` is None, `out` is a flattened array.\n", " \n", " See Also\n", " --------\n", " insert : Insert elements into an array.\n", " delete : Delete elements from an array.\n", " \n", " Examples\n", " --------\n", " >>> np.append([1, 2, 3], [[4, 5, 6], [7, 8, 9]])\n", " array([1, 2, 3, ..., 7, 8, 9])\n", " \n", " When `axis` is specified, `values` must have the correct shape.\n", " \n", " >>> np.append([[1, 2, 3], [4, 5, 6]], [[7, 8, 9]], axis=0)\n", " array([[1, 2, 3],\n", " [4, 5, 6],\n", " [7, 8, 9]])\n", " >>> np.append([[1, 2, 3], [4, 5, 6]], [7, 8, 9], axis=0)\n", " Traceback (most recent call last):\n", " ...\n", " ValueError: all the input arrays must have same number of dimensions, but\n", " the array at index 0 has 2 dimension(s) and the array at index 1 has 1\n", " dimension(s)\n", " \n", " apply_along_axis(func1d, axis, arr, *args, **kwargs)\n", " Apply a function to 1-D slices along the given axis.\n", " \n", " Execute `func1d(a, *args, **kwargs)` where `func1d` operates on 1-D arrays\n", " and `a` is a 1-D slice of `arr` along `axis`.\n", " \n", " This is equivalent to (but faster than) the following use of `ndindex` and\n", " `s_`, which sets each of ``ii``, ``jj``, and ``kk`` to a tuple of indices::\n", " \n", " Ni, Nk = a.shape[:axis], a.shape[axis+1:]\n", " for ii in ndindex(Ni):\n", " for kk in ndindex(Nk):\n", " f = func1d(arr[ii + s_[:,] + kk])\n", " Nj = f.shape\n", " for jj in ndindex(Nj):\n", " out[ii + jj + kk] = f[jj]\n", " \n", " Equivalently, eliminating the inner loop, this can be expressed as::\n", " \n", " Ni, Nk = a.shape[:axis], a.shape[axis+1:]\n", " for ii in ndindex(Ni):\n", " for kk in ndindex(Nk):\n", " out[ii + s_[...,] + kk] = func1d(arr[ii + s_[:,] + kk])\n", " \n", " Parameters\n", " ----------\n", " func1d : function (M,) -> (Nj...)\n", " This function should accept 1-D arrays. It is applied to 1-D\n", " slices of `arr` along the specified axis.\n", " axis : integer\n", " Axis along which `arr` is sliced.\n", " arr : ndarray (Ni..., M, Nk...)\n", " Input array.\n", " args : any\n", " Additional arguments to `func1d`.\n", " kwargs : any\n", " Additional named arguments to `func1d`.\n", " \n", " .. versionadded:: 1.9.0\n", " \n", " \n", " Returns\n", " -------\n", " out : ndarray (Ni..., Nj..., Nk...)\n", " The output array. The shape of `out` is identical to the shape of\n", " `arr`, except along the `axis` dimension. This axis is removed, and\n", " replaced with new dimensions equal to the shape of the return value\n", " of `func1d`. So if `func1d` returns a scalar `out` will have one\n", " fewer dimensions than `arr`.\n", " \n", " See Also\n", " --------\n", " apply_over_axes : Apply a function repeatedly over multiple axes.\n", " \n", " Examples\n", " --------\n", " >>> def my_func(a):\n", " ... \"\"\"Average first and last element of a 1-D array\"\"\"\n", " ... return (a[0] + a[-1]) * 0.5\n", " >>> b = np.array([[1,2,3], [4,5,6], [7,8,9]])\n", " >>> np.apply_along_axis(my_func, 0, b)\n", " array([4., 5., 6.])\n", " >>> np.apply_along_axis(my_func, 1, b)\n", " array([2., 5., 8.])\n", " \n", " For a function that returns a 1D array, the number of dimensions in\n", " `outarr` is the same as `arr`.\n", " \n", " >>> b = np.array([[8,1,7], [4,3,9], [5,2,6]])\n", " >>> np.apply_along_axis(sorted, 1, b)\n", " array([[1, 7, 8],\n", " [3, 4, 9],\n", " [2, 5, 6]])\n", " \n", " For a function that returns a higher dimensional array, those dimensions\n", " are inserted in place of the `axis` dimension.\n", " \n", " >>> b = np.array([[1,2,3], [4,5,6], [7,8,9]])\n", " >>> np.apply_along_axis(np.diag, -1, b)\n", " array([[[1, 0, 0],\n", " [0, 2, 0],\n", " [0, 0, 3]],\n", " [[4, 0, 0],\n", " [0, 5, 0],\n", " [0, 0, 6]],\n", " [[7, 0, 0],\n", " [0, 8, 0],\n", " [0, 0, 9]]])\n", " \n", " apply_over_axes(func, a, axes)\n", " Apply a function repeatedly over multiple axes.\n", " \n", " `func` is called as `res = func(a, axis)`, where `axis` is the first\n", " element of `axes`. The result `res` of the function call must have\n", " either the same dimensions as `a` or one less dimension. If `res`\n", " has one less dimension than `a`, a dimension is inserted before\n", " `axis`. The call to `func` is then repeated for each axis in `axes`,\n", " with `res` as the first argument.\n", " \n", " Parameters\n", " ----------\n", " func : function\n", " This function must take two arguments, `func(a, axis)`.\n", " a : array_like\n", " Input array.\n", " axes : array_like\n", " Axes over which `func` is applied; the elements must be integers.\n", " \n", " Returns\n", " -------\n", " apply_over_axis : ndarray\n", " The output array. The number of dimensions is the same as `a`,\n", " but the shape can be different. This depends on whether `func`\n", " changes the shape of its output with respect to its input.\n", " \n", " See Also\n", " --------\n", " apply_along_axis :\n", " Apply a function to 1-D slices of an array along the given axis.\n", " \n", " Notes\n", " -----\n", " This function is equivalent to tuple axis arguments to reorderable ufuncs\n", " with keepdims=True. Tuple axis arguments to ufuncs have been available since\n", " version 1.7.0.\n", " \n", " Examples\n", " --------\n", " >>> a = np.arange(24).reshape(2,3,4)\n", " >>> a\n", " array([[[ 0, 1, 2, 3],\n", " [ 4, 5, 6, 7],\n", " [ 8, 9, 10, 11]],\n", " [[12, 13, 14, 15],\n", " [16, 17, 18, 19],\n", " [20, 21, 22, 23]]])\n", " \n", " Sum over axes 0 and 2. The result has same number of dimensions\n", " as the original array:\n", " \n", " >>> np.apply_over_axes(np.sum, a, [0,2])\n", " array([[[ 60],\n", " [ 92],\n", " [124]]])\n", " \n", " Tuple axis arguments to ufuncs are equivalent:\n", " \n", " >>> np.sum(a, axis=(0,2), keepdims=True)\n", " array([[[ 60],\n", " [ 92],\n", " [124]]])\n", " \n", " arange(...)\n", " arange([start,] stop[, step,], dtype=None, *, like=None)\n", " \n", " Return evenly spaced values within a given interval.\n", " \n", " ``arange`` can be called with a varying number of positional arguments:\n", " \n", " * ``arange(stop)``: Values are generated within the half-open interval\n", " ``[0, stop)`` (in other words, the interval including `start` but\n", " excluding `stop`).\n", " * ``arange(start, stop)``: Values are generated within the half-open\n", " interval ``[start, stop)``.\n", " * ``arange(start, stop, step)`` Values are generated within the half-open\n", " interval ``[start, stop)``, with spacing between values given by\n", " ``step``.\n", " \n", " For integer arguments the function is roughly equivalent to the Python\n", " built-in :py:class:`range`, but returns an ndarray rather than a ``range``\n", " instance.\n", " \n", " When using a non-integer step, such as 0.1, it is often better to use\n", " `numpy.linspace`.\n", " \n", " See the Warning sections below for more information.\n", " \n", " Parameters\n", " ----------\n", " start : integer or real, optional\n", " Start of interval. The interval includes this value. The default\n", " start value is 0.\n", " stop : integer or real\n", " End of interval. The interval does not include this value, except\n", " in some cases where `step` is not an integer and floating point\n", " round-off affects the length of `out`.\n", " step : integer or real, optional\n", " Spacing between values. For any output `out`, this is the distance\n", " between two adjacent values, ``out[i+1] - out[i]``. The default\n", " step size is 1. If `step` is specified as a position argument,\n", " `start` must also be given.\n", " dtype : dtype, optional\n", " The type of the output array. If `dtype` is not given, infer the data\n", " type from the other input arguments.\n", " like : array_like, optional\n", " Reference object to allow the creation of arrays which are not\n", " NumPy arrays. If an array-like passed in as ``like`` supports\n", " the ``__array_function__`` protocol, the result will be defined\n", " by it. In this case, it ensures the creation of an array object\n", " compatible with that passed in via this argument.\n", " \n", " .. versionadded:: 1.20.0\n", " \n", " Returns\n", " -------\n", " arange : ndarray\n", " Array of evenly spaced values.\n", " \n", " For floating point arguments, the length of the result is\n", " ``ceil((stop - start)/step)``. Because of floating point overflow,\n", " this rule may result in the last element of `out` being greater\n", " than `stop`.\n", " \n", " Warnings\n", " --------\n", " The length of the output might not be numerically stable.\n", " \n", " Another stability issue is due to the internal implementation of\n", " `numpy.arange`.\n", " The actual step value used to populate the array is\n", " ``dtype(start + step) - dtype(start)`` and not `step`. Precision loss\n", " can occur here, due to casting or due to using floating points when\n", " `start` is much larger than `step`. This can lead to unexpected\n", " behaviour. For example::\n", " \n", " >>> np.arange(0, 5, 0.5, dtype=int)\n", " array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])\n", " >>> np.arange(-3, 3, 0.5, dtype=int)\n", " array([-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8])\n", " \n", " In such cases, the use of `numpy.linspace` should be preferred.\n", " \n", " The built-in :py:class:`range` generates :std:doc:`Python built-in integers\n", " that have arbitrary size <python:c-api/long>`, while `numpy.arange`\n", " produces `numpy.int32` or `numpy.int64` numbers. This may result in\n", " incorrect results for large integer values::\n", " \n", " >>> power = 40\n", " >>> modulo = 10000\n", " >>> x1 = [(n ** power) % modulo for n in range(8)]\n", " >>> x2 = [(n ** power) % modulo for n in np.arange(8)]\n", " >>> print(x1)\n", " [0, 1, 7776, 8801, 6176, 625, 6576, 4001] # correct\n", " >>> print(x2)\n", " [0, 1, 7776, 7185, 0, 5969, 4816, 3361] # incorrect\n", " \n", " See Also\n", " --------\n", " numpy.linspace : Evenly spaced numbers with careful handling of endpoints.\n", " numpy.ogrid: Arrays of evenly spaced numbers in N-dimensions.\n", " numpy.mgrid: Grid-shaped arrays of evenly spaced numbers in N-dimensions.\n", " :ref:`how-to-partition`\n", " \n", " Examples\n", " --------\n", " >>> np.arange(3)\n", " array([0, 1, 2])\n", " >>> np.arange(3.0)\n", " array([ 0., 1., 2.])\n", " >>> np.arange(3,7)\n", " array([3, 4, 5, 6])\n", " >>> np.arange(3,7,2)\n", " array([3, 5])\n", " \n", " argmax(a, axis=None, out=None, *, keepdims=<no value>)\n", " Returns the indices of the maximum values along an axis.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input array.\n", " axis : int, optional\n", " By default, the index is into the flattened array, otherwise\n", " along the specified axis.\n", " out : array, optional\n", " If provided, the result will be inserted into this array. It should\n", " be of the appropriate shape and dtype.\n", " keepdims : bool, optional\n", " If this is set to True, the axes which are reduced are left\n", " in the result as dimensions with size one. With this option,\n", " the result will broadcast correctly against the array.\n", " \n", " .. versionadded:: 1.22.0\n", " \n", " Returns\n", " -------\n", " index_array : ndarray of ints\n", " Array of indices into the array. It has the same shape as `a.shape`\n", " with the dimension along `axis` removed. If `keepdims` is set to True,\n", " then the size of `axis` will be 1 with the resulting array having same\n", " shape as `a.shape`.\n", " \n", " See Also\n", " --------\n", " ndarray.argmax, argmin\n", " amax : The maximum value along a given axis.\n", " unravel_index : Convert a flat index into an index tuple.\n", " take_along_axis : Apply ``np.expand_dims(index_array, axis)``\n", " from argmax to an array as if by calling max.\n", " \n", " Notes\n", " -----\n", " In case of multiple occurrences of the maximum values, the indices\n", " corresponding to the first occurrence are returned.\n", " \n", " Examples\n", " --------\n", " >>> a = np.arange(6).reshape(2,3) + 10\n", " >>> a\n", " array([[10, 11, 12],\n", " [13, 14, 15]])\n", " >>> np.argmax(a)\n", " 5\n", " >>> np.argmax(a, axis=0)\n", " array([1, 1, 1])\n", " >>> np.argmax(a, axis=1)\n", " array([2, 2])\n", " \n", " Indexes of the maximal elements of a N-dimensional array:\n", " \n", " >>> ind = np.unravel_index(np.argmax(a, axis=None), a.shape)\n", " >>> ind\n", " (1, 2)\n", " >>> a[ind]\n", " 15\n", " \n", " >>> b = np.arange(6)\n", " >>> b[1] = 5\n", " >>> b\n", " array([0, 5, 2, 3, 4, 5])\n", " >>> np.argmax(b) # Only the first occurrence is returned.\n", " 1\n", " \n", " >>> x = np.array([[4,2,3], [1,0,3]])\n", " >>> index_array = np.argmax(x, axis=-1)\n", " >>> # Same as np.amax(x, axis=-1, keepdims=True)\n", " >>> np.take_along_axis(x, np.expand_dims(index_array, axis=-1), axis=-1)\n", " array([[4],\n", " [3]])\n", " >>> # Same as np.amax(x, axis=-1)\n", " >>> np.take_along_axis(x, np.expand_dims(index_array, axis=-1), axis=-1).squeeze(axis=-1)\n", " array([4, 3])\n", " \n", " Setting `keepdims` to `True`,\n", " \n", " >>> x = np.arange(24).reshape((2, 3, 4))\n", " >>> res = np.argmax(x, axis=1, keepdims=True)\n", " >>> res.shape\n", " (2, 1, 4)\n", " \n", " argmin(a, axis=None, out=None, *, keepdims=<no value>)\n", " Returns the indices of the minimum values along an axis.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input array.\n", " axis : int, optional\n", " By default, the index is into the flattened array, otherwise\n", " along the specified axis.\n", " out : array, optional\n", " If provided, the result will be inserted into this array. It should\n", " be of the appropriate shape and dtype.\n", " keepdims : bool, optional\n", " If this is set to True, the axes which are reduced are left\n", " in the result as dimensions with size one. With this option,\n", " the result will broadcast correctly against the array.\n", " \n", " .. versionadded:: 1.22.0\n", " \n", " Returns\n", " -------\n", " index_array : ndarray of ints\n", " Array of indices into the array. It has the same shape as `a.shape`\n", " with the dimension along `axis` removed. If `keepdims` is set to True,\n", " then the size of `axis` will be 1 with the resulting array having same\n", " shape as `a.shape`.\n", " \n", " See Also\n", " --------\n", " ndarray.argmin, argmax\n", " amin : The minimum value along a given axis.\n", " unravel_index : Convert a flat index into an index tuple.\n", " take_along_axis : Apply ``np.expand_dims(index_array, axis)``\n", " from argmin to an array as if by calling min.\n", " \n", " Notes\n", " -----\n", " In case of multiple occurrences of the minimum values, the indices\n", " corresponding to the first occurrence are returned.\n", " \n", " Examples\n", " --------\n", " >>> a = np.arange(6).reshape(2,3) + 10\n", " >>> a\n", " array([[10, 11, 12],\n", " [13, 14, 15]])\n", " >>> np.argmin(a)\n", " 0\n", " >>> np.argmin(a, axis=0)\n", " array([0, 0, 0])\n", " >>> np.argmin(a, axis=1)\n", " array([0, 0])\n", " \n", " Indices of the minimum elements of a N-dimensional array:\n", " \n", " >>> ind = np.unravel_index(np.argmin(a, axis=None), a.shape)\n", " >>> ind\n", " (0, 0)\n", " >>> a[ind]\n", " 10\n", " \n", " >>> b = np.arange(6) + 10\n", " >>> b[4] = 10\n", " >>> b\n", " array([10, 11, 12, 13, 10, 15])\n", " >>> np.argmin(b) # Only the first occurrence is returned.\n", " 0\n", " \n", " >>> x = np.array([[4,2,3], [1,0,3]])\n", " >>> index_array = np.argmin(x, axis=-1)\n", " >>> # Same as np.amin(x, axis=-1, keepdims=True)\n", " >>> np.take_along_axis(x, np.expand_dims(index_array, axis=-1), axis=-1)\n", " array([[2],\n", " [0]])\n", " >>> # Same as np.amax(x, axis=-1)\n", " >>> np.take_along_axis(x, np.expand_dims(index_array, axis=-1), axis=-1).squeeze(axis=-1)\n", " array([2, 0])\n", " \n", " Setting `keepdims` to `True`,\n", " \n", " >>> x = np.arange(24).reshape((2, 3, 4))\n", " >>> res = np.argmin(x, axis=1, keepdims=True)\n", " >>> res.shape\n", " (2, 1, 4)\n", " \n", " argpartition(a, kth, axis=-1, kind='introselect', order=None)\n", " Perform an indirect partition along the given axis using the\n", " algorithm specified by the `kind` keyword. It returns an array of\n", " indices of the same shape as `a` that index data along the given\n", " axis in partitioned order.\n", " \n", " .. versionadded:: 1.8.0\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Array to sort.\n", " kth : int or sequence of ints\n", " Element index to partition by. The k-th element will be in its\n", " final sorted position and all smaller elements will be moved\n", " before it and all larger elements behind it. The order of all\n", " elements in the partitions is undefined. If provided with a\n", " sequence of k-th it will partition all of them into their sorted\n", " position at once.\n", " \n", " .. deprecated:: 1.22.0\n", " Passing booleans as index is deprecated.\n", " axis : int or None, optional\n", " Axis along which to sort. The default is -1 (the last axis). If\n", " None, the flattened array is used.\n", " kind : {'introselect'}, optional\n", " Selection algorithm. Default is 'introselect'\n", " order : str or list of str, optional\n", " When `a` is an array with fields defined, this argument\n", " specifies which fields to compare first, second, etc. A single\n", " field can be specified as a string, and not all fields need be\n", " specified, but unspecified fields will still be used, in the\n", " order in which they come up in the dtype, to break ties.\n", " \n", " Returns\n", " -------\n", " index_array : ndarray, int\n", " Array of indices that partition `a` along the specified axis.\n", " If `a` is one-dimensional, ``a[index_array]`` yields a partitioned `a`.\n", " More generally, ``np.take_along_axis(a, index_array, axis=axis)``\n", " always yields the partitioned `a`, irrespective of dimensionality.\n", " \n", " See Also\n", " --------\n", " partition : Describes partition algorithms used.\n", " ndarray.partition : Inplace partition.\n", " argsort : Full indirect sort.\n", " take_along_axis : Apply ``index_array`` from argpartition\n", " to an array as if by calling partition.\n", " \n", " Notes\n", " -----\n", " See `partition` for notes on the different selection algorithms.\n", " \n", " Examples\n", " --------\n", " One dimensional array:\n", " \n", " >>> x = np.array([3, 4, 2, 1])\n", " >>> x[np.argpartition(x, 3)]\n", " array([2, 1, 3, 4])\n", " >>> x[np.argpartition(x, (1, 3))]\n", " array([1, 2, 3, 4])\n", " \n", " >>> x = [3, 4, 2, 1]\n", " >>> np.array(x)[np.argpartition(x, 3)]\n", " array([2, 1, 3, 4])\n", " \n", " Multi-dimensional array:\n", " \n", " >>> x = np.array([[3, 4, 2], [1, 3, 1]])\n", " >>> index_array = np.argpartition(x, kth=1, axis=-1)\n", " >>> np.take_along_axis(x, index_array, axis=-1) # same as np.partition(x, kth=1)\n", " array([[2, 3, 4],\n", " [1, 1, 3]])\n", " \n", " argsort(a, axis=-1, kind=None, order=None)\n", " Returns the indices that would sort an array.\n", " \n", " Perform an indirect sort along the given axis using the algorithm specified\n", " by the `kind` keyword. It returns an array of indices of the same shape as\n", " `a` that index data along the given axis in sorted order.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Array to sort.\n", " axis : int or None, optional\n", " Axis along which to sort. The default is -1 (the last axis). If None,\n", " the flattened array is used.\n", " kind : {'quicksort', 'mergesort', 'heapsort', 'stable'}, optional\n", " Sorting algorithm. The default is 'quicksort'. Note that both 'stable'\n", " and 'mergesort' use timsort under the covers and, in general, the\n", " actual implementation will vary with data type. The 'mergesort' option\n", " is retained for backwards compatibility.\n", " \n", " .. versionchanged:: 1.15.0.\n", " The 'stable' option was added.\n", " order : str or list of str, optional\n", " When `a` is an array with fields defined, this argument specifies\n", " which fields to compare first, second, etc. A single field can\n", " be specified as a string, and not all fields need be specified,\n", " but unspecified fields will still be used, in the order in which\n", " they come up in the dtype, to break ties.\n", " \n", " Returns\n", " -------\n", " index_array : ndarray, int\n", " Array of indices that sort `a` along the specified `axis`.\n", " If `a` is one-dimensional, ``a[index_array]`` yields a sorted `a`.\n", " More generally, ``np.take_along_axis(a, index_array, axis=axis)``\n", " always yields the sorted `a`, irrespective of dimensionality.\n", " \n", " See Also\n", " --------\n", " sort : Describes sorting algorithms used.\n", " lexsort : Indirect stable sort with multiple keys.\n", " ndarray.sort : Inplace sort.\n", " argpartition : Indirect partial sort.\n", " take_along_axis : Apply ``index_array`` from argsort\n", " to an array as if by calling sort.\n", " \n", " Notes\n", " -----\n", " See `sort` for notes on the different sorting algorithms.\n", " \n", " As of NumPy 1.4.0 `argsort` works with real/complex arrays containing\n", " nan values. The enhanced sort order is documented in `sort`.\n", " \n", " Examples\n", " --------\n", " One dimensional array:\n", " \n", " >>> x = np.array([3, 1, 2])\n", " >>> np.argsort(x)\n", " array([1, 2, 0])\n", " \n", " Two-dimensional array:\n", " \n", " >>> x = np.array([[0, 3], [2, 2]])\n", " >>> x\n", " array([[0, 3],\n", " [2, 2]])\n", " \n", " >>> ind = np.argsort(x, axis=0) # sorts along first axis (down)\n", " >>> ind\n", " array([[0, 1],\n", " [1, 0]])\n", " >>> np.take_along_axis(x, ind, axis=0) # same as np.sort(x, axis=0)\n", " array([[0, 2],\n", " [2, 3]])\n", " \n", " >>> ind = np.argsort(x, axis=1) # sorts along last axis (across)\n", " >>> ind\n", " array([[0, 1],\n", " [0, 1]])\n", " >>> np.take_along_axis(x, ind, axis=1) # same as np.sort(x, axis=1)\n", " array([[0, 3],\n", " [2, 2]])\n", " \n", " Indices of the sorted elements of a N-dimensional array:\n", " \n", " >>> ind = np.unravel_index(np.argsort(x, axis=None), x.shape)\n", " >>> ind\n", " (array([0, 1, 1, 0]), array([0, 0, 1, 1]))\n", " >>> x[ind] # same as np.sort(x, axis=None)\n", " array([0, 2, 2, 3])\n", " \n", " Sorting with keys:\n", " \n", " >>> x = np.array([(1, 0), (0, 1)], dtype=[('x', '<i4'), ('y', '<i4')])\n", " >>> x\n", " array([(1, 0), (0, 1)],\n", " dtype=[('x', '<i4'), ('y', '<i4')])\n", " \n", " >>> np.argsort(x, order=('x','y'))\n", " array([1, 0])\n", " \n", " >>> np.argsort(x, order=('y','x'))\n", " array([0, 1])\n", " \n", " argwhere(a)\n", " Find the indices of array elements that are non-zero, grouped by element.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input data.\n", " \n", " Returns\n", " -------\n", " index_array : (N, a.ndim) ndarray\n", " Indices of elements that are non-zero. Indices are grouped by element.\n", " This array will have shape ``(N, a.ndim)`` where ``N`` is the number of\n", " non-zero items.\n", " \n", " See Also\n", " --------\n", " where, nonzero\n", " \n", " Notes\n", " -----\n", " ``np.argwhere(a)`` is almost the same as ``np.transpose(np.nonzero(a))``,\n", " but produces a result of the correct shape for a 0D array.\n", " \n", " The output of ``argwhere`` is not suitable for indexing arrays.\n", " For this purpose use ``nonzero(a)`` instead.\n", " \n", " Examples\n", " --------\n", " >>> x = np.arange(6).reshape(2,3)\n", " >>> x\n", " array([[0, 1, 2],\n", " [3, 4, 5]])\n", " >>> np.argwhere(x>1)\n", " array([[0, 2],\n", " [1, 0],\n", " [1, 1],\n", " [1, 2]])\n", " \n", " around(a, decimals=0, out=None)\n", " Evenly round to the given number of decimals.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input data.\n", " decimals : int, optional\n", " Number of decimal places to round to (default: 0). If\n", " decimals is negative, it specifies the number of positions to\n", " the left of the decimal point.\n", " out : ndarray, optional\n", " Alternative output array in which to place the result. It must have\n", " the same shape as the expected output, but the type of the output\n", " values will be cast if necessary. See :ref:`ufuncs-output-type` for more\n", " details.\n", " \n", " Returns\n", " -------\n", " rounded_array : ndarray\n", " An array of the same type as `a`, containing the rounded values.\n", " Unless `out` was specified, a new array is created. A reference to\n", " the result is returned.\n", " \n", " The real and imaginary parts of complex numbers are rounded\n", " separately. The result of rounding a float is a float.\n", " \n", " See Also\n", " --------\n", " ndarray.round : equivalent method\n", " ceil, fix, floor, rint, trunc\n", " \n", " \n", " Notes\n", " -----\n", " `~numpy.round` is often used as an alias for `~numpy.around`.\n", " \n", " For values exactly halfway between rounded decimal values, NumPy\n", " rounds to the nearest even value. Thus 1.5 and 2.5 round to 2.0,\n", " -0.5 and 0.5 round to 0.0, etc.\n", " \n", " ``np.around`` uses a fast but sometimes inexact algorithm to round\n", " floating-point datatypes. For positive `decimals` it is equivalent to\n", " ``np.true_divide(np.rint(a * 10**decimals), 10**decimals)``, which has\n", " error due to the inexact representation of decimal fractions in the IEEE\n", " floating point standard [1]_ and errors introduced when scaling by powers\n", " of ten. For instance, note the extra \"1\" in the following:\n", " \n", " >>> np.round(56294995342131.5, 3)\n", " 56294995342131.51\n", " \n", " If your goal is to print such values with a fixed number of decimals, it is\n", " preferable to use numpy's float printing routines to limit the number of\n", " printed decimals:\n", " \n", " >>> np.format_float_positional(56294995342131.5, precision=3)\n", " '56294995342131.5'\n", " \n", " The float printing routines use an accurate but much more computationally\n", " demanding algorithm to compute the number of digits after the decimal\n", " point.\n", " \n", " Alternatively, Python's builtin `round` function uses a more accurate\n", " but slower algorithm for 64-bit floating point values:\n", " \n", " >>> round(56294995342131.5, 3)\n", " 56294995342131.5\n", " >>> np.round(16.055, 2), round(16.055, 2) # equals 16.0549999999999997\n", " (16.06, 16.05)\n", " \n", " \n", " References\n", " ----------\n", " .. [1] \"Lecture Notes on the Status of IEEE 754\", William Kahan,\n", " https://people.eecs.berkeley.edu/~wkahan/ieee754status/IEEE754.PDF\n", " \n", " Examples\n", " --------\n", " >>> np.around([0.37, 1.64])\n", " array([0., 2.])\n", " >>> np.around([0.37, 1.64], decimals=1)\n", " array([0.4, 1.6])\n", " >>> np.around([.5, 1.5, 2.5, 3.5, 4.5]) # rounds to nearest even value\n", " array([0., 2., 2., 4., 4.])\n", " >>> np.around([1,2,3,11], decimals=1) # ndarray of ints is returned\n", " array([ 1, 2, 3, 11])\n", " >>> np.around([1,2,3,11], decimals=-1)\n", " array([ 0, 0, 0, 10])\n", " \n", " array(...)\n", " array(object, dtype=None, *, copy=True, order='K', subok=False, ndmin=0,\n", " like=None)\n", " \n", " Create an array.\n", " \n", " Parameters\n", " ----------\n", " object : array_like\n", " An array, any object exposing the array interface, an object whose\n", " __array__ method returns an array, or any (nested) sequence.\n", " If object is a scalar, a 0-dimensional array containing object is\n", " returned.\n", " dtype : data-type, optional\n", " The desired data-type for the array. If not given, then the type will\n", " be determined as the minimum type required to hold the objects in the\n", " sequence.\n", " copy : bool, optional\n", " If true (default), then the object is copied. Otherwise, a copy will\n", " only be made if __array__ returns a copy, if obj is a nested sequence,\n", " or if a copy is needed to satisfy any of the other requirements\n", " (`dtype`, `order`, etc.).\n", " order : {'K', 'A', 'C', 'F'}, optional\n", " Specify the memory layout of the array. If object is not an array, the\n", " newly created array will be in C order (row major) unless 'F' is\n", " specified, in which case it will be in Fortran order (column major).\n", " If object is an array the following holds.\n", " \n", " ===== ========= ===================================================\n", " order no copy copy=True\n", " ===== ========= ===================================================\n", " 'K' unchanged F & C order preserved, otherwise most similar order\n", " 'A' unchanged F order if input is F and not C, otherwise C order\n", " 'C' C order C order\n", " 'F' F order F order\n", " ===== ========= ===================================================\n", " \n", " When ``copy=False`` and a copy is made for other reasons, the result is\n", " the same as if ``copy=True``, with some exceptions for 'A', see the\n", " Notes section. The default order is 'K'.\n", " subok : bool, optional\n", " If True, then sub-classes will be passed-through, otherwise\n", " the returned array will be forced to be a base-class array (default).\n", " ndmin : int, optional\n", " Specifies the minimum number of dimensions that the resulting\n", " array should have. Ones will be prepended to the shape as\n", " needed to meet this requirement.\n", " like : array_like, optional\n", " Reference object to allow the creation of arrays which are not\n", " NumPy arrays. If an array-like passed in as ``like`` supports\n", " the ``__array_function__`` protocol, the result will be defined\n", " by it. In this case, it ensures the creation of an array object\n", " compatible with that passed in via this argument.\n", " \n", " .. versionadded:: 1.20.0\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " An array object satisfying the specified requirements.\n", " \n", " See Also\n", " --------\n", " empty_like : Return an empty array with shape and type of input.\n", " ones_like : Return an array of ones with shape and type of input.\n", " zeros_like : Return an array of zeros with shape and type of input.\n", " full_like : Return a new array with shape of input filled with value.\n", " empty : Return a new uninitialized array.\n", " ones : Return a new array setting values to one.\n", " zeros : Return a new array setting values to zero.\n", " full : Return a new array of given shape filled with value.\n", " \n", " \n", " Notes\n", " -----\n", " When order is 'A' and `object` is an array in neither 'C' nor 'F' order,\n", " and a copy is forced by a change in dtype, then the order of the result is\n", " not necessarily 'C' as expected. This is likely a bug.\n", " \n", " Examples\n", " --------\n", " >>> np.array([1, 2, 3])\n", " array([1, 2, 3])\n", " \n", " Upcasting:\n", " \n", " >>> np.array([1, 2, 3.0])\n", " array([ 1., 2., 3.])\n", " \n", " More than one dimension:\n", " \n", " >>> np.array([[1, 2], [3, 4]])\n", " array([[1, 2],\n", " [3, 4]])\n", " \n", " Minimum dimensions 2:\n", " \n", " >>> np.array([1, 2, 3], ndmin=2)\n", " array([[1, 2, 3]])\n", " \n", " Type provided:\n", " \n", " >>> np.array([1, 2, 3], dtype=complex)\n", " array([ 1.+0.j, 2.+0.j, 3.+0.j])\n", " \n", " Data-type consisting of more than one element:\n", " \n", " >>> x = np.array([(1,2),(3,4)],dtype=[('a','<i4'),('b','<i4')])\n", " >>> x['a']\n", " array([1, 3])\n", " \n", " Creating an array from sub-classes:\n", " \n", " >>> np.array(np.mat('1 2; 3 4'))\n", " array([[1, 2],\n", " [3, 4]])\n", " \n", " >>> np.array(np.mat('1 2; 3 4'), subok=True)\n", " matrix([[1, 2],\n", " [3, 4]])\n", " \n", " array2string(a, max_line_width=None, precision=None, suppress_small=None, separator=' ', prefix='', style=<no value>, formatter=None, threshold=None, edgeitems=None, sign=None, floatmode=None, suffix='', *, legacy=None)\n", " Return a string representation of an array.\n", " \n", " Parameters\n", " ----------\n", " a : ndarray\n", " Input array.\n", " max_line_width : int, optional\n", " Inserts newlines if text is longer than `max_line_width`.\n", " Defaults to ``numpy.get_printoptions()['linewidth']``.\n", " precision : int or None, optional\n", " Floating point precision.\n", " Defaults to ``numpy.get_printoptions()['precision']``.\n", " suppress_small : bool, optional\n", " Represent numbers \"very close\" to zero as zero; default is False.\n", " Very close is defined by precision: if the precision is 8, e.g.,\n", " numbers smaller (in absolute value) than 5e-9 are represented as\n", " zero.\n", " Defaults to ``numpy.get_printoptions()['suppress']``.\n", " separator : str, optional\n", " Inserted between elements.\n", " prefix : str, optional\n", " suffix : str, optional\n", " The length of the prefix and suffix strings are used to respectively\n", " align and wrap the output. An array is typically printed as::\n", " \n", " prefix + array2string(a) + suffix\n", " \n", " The output is left-padded by the length of the prefix string, and\n", " wrapping is forced at the column ``max_line_width - len(suffix)``.\n", " It should be noted that the content of prefix and suffix strings are\n", " not included in the output.\n", " style : _NoValue, optional\n", " Has no effect, do not use.\n", " \n", " .. deprecated:: 1.14.0\n", " formatter : dict of callables, optional\n", " If not None, the keys should indicate the type(s) that the respective\n", " formatting function applies to. Callables should return a string.\n", " Types that are not specified (by their corresponding keys) are handled\n", " by the default formatters. Individual types for which a formatter\n", " can be set are:\n", " \n", " - 'bool'\n", " - 'int'\n", " - 'timedelta' : a `numpy.timedelta64`\n", " - 'datetime' : a `numpy.datetime64`\n", " - 'float'\n", " - 'longfloat' : 128-bit floats\n", " - 'complexfloat'\n", " - 'longcomplexfloat' : composed of two 128-bit floats\n", " - 'void' : type `numpy.void`\n", " - 'numpystr' : types `numpy.string_` and `numpy.unicode_`\n", " \n", " Other keys that can be used to set a group of types at once are:\n", " \n", " - 'all' : sets all types\n", " - 'int_kind' : sets 'int'\n", " - 'float_kind' : sets 'float' and 'longfloat'\n", " - 'complex_kind' : sets 'complexfloat' and 'longcomplexfloat'\n", " - 'str_kind' : sets 'numpystr'\n", " threshold : int, optional\n", " Total number of array elements which trigger summarization\n", " rather than full repr.\n", " Defaults to ``numpy.get_printoptions()['threshold']``.\n", " edgeitems : int, optional\n", " Number of array items in summary at beginning and end of\n", " each dimension.\n", " Defaults to ``numpy.get_printoptions()['edgeitems']``.\n", " sign : string, either '-', '+', or ' ', optional\n", " Controls printing of the sign of floating-point types. If '+', always\n", " print the sign of positive values. If ' ', always prints a space\n", " (whitespace character) in the sign position of positive values. If\n", " '-', omit the sign character of positive values.\n", " Defaults to ``numpy.get_printoptions()['sign']``.\n", " floatmode : str, optional\n", " Controls the interpretation of the `precision` option for\n", " floating-point types.\n", " Defaults to ``numpy.get_printoptions()['floatmode']``.\n", " Can take the following values:\n", " \n", " - 'fixed': Always print exactly `precision` fractional digits,\n", " even if this would print more or fewer digits than\n", " necessary to specify the value uniquely.\n", " - 'unique': Print the minimum number of fractional digits necessary\n", " to represent each value uniquely. Different elements may\n", " have a different number of digits. The value of the\n", " `precision` option is ignored.\n", " - 'maxprec': Print at most `precision` fractional digits, but if\n", " an element can be uniquely represented with fewer digits\n", " only print it with that many.\n", " - 'maxprec_equal': Print at most `precision` fractional digits,\n", " but if every element in the array can be uniquely\n", " represented with an equal number of fewer digits, use that\n", " many digits for all elements.\n", " legacy : string or `False`, optional\n", " If set to the string `'1.13'` enables 1.13 legacy printing mode. This\n", " approximates numpy 1.13 print output by including a space in the sign\n", " position of floats and different behavior for 0d arrays. If set to\n", " `False`, disables legacy mode. Unrecognized strings will be ignored\n", " with a warning for forward compatibility.\n", " \n", " .. versionadded:: 1.14.0\n", " \n", " Returns\n", " -------\n", " array_str : str\n", " String representation of the array.\n", " \n", " Raises\n", " ------\n", " TypeError\n", " if a callable in `formatter` does not return a string.\n", " \n", " See Also\n", " --------\n", " array_str, array_repr, set_printoptions, get_printoptions\n", " \n", " Notes\n", " -----\n", " If a formatter is specified for a certain type, the `precision` keyword is\n", " ignored for that type.\n", " \n", " This is a very flexible function; `array_repr` and `array_str` are using\n", " `array2string` internally so keywords with the same name should work\n", " identically in all three functions.\n", " \n", " Examples\n", " --------\n", " >>> x = np.array([1e-16,1,2,3])\n", " >>> np.array2string(x, precision=2, separator=',',\n", " ... suppress_small=True)\n", " '[0.,1.,2.,3.]'\n", " \n", " >>> x = np.arange(3.)\n", " >>> np.array2string(x, formatter={'float_kind':lambda x: \"%.2f\" % x})\n", " '[0.00 1.00 2.00]'\n", " \n", " >>> x = np.arange(3)\n", " >>> np.array2string(x, formatter={'int':lambda x: hex(x)})\n", " '[0x0 0x1 0x2]'\n", " \n", " array_equal(a1, a2, equal_nan=False)\n", " True if two arrays have the same shape and elements, False otherwise.\n", " \n", " Parameters\n", " ----------\n", " a1, a2 : array_like\n", " Input arrays.\n", " equal_nan : bool\n", " Whether to compare NaN's as equal. If the dtype of a1 and a2 is\n", " complex, values will be considered equal if either the real or the\n", " imaginary component of a given value is ``nan``.\n", " \n", " .. versionadded:: 1.19.0\n", " \n", " Returns\n", " -------\n", " b : bool\n", " Returns True if the arrays are equal.\n", " \n", " See Also\n", " --------\n", " allclose: Returns True if two arrays are element-wise equal within a\n", " tolerance.\n", " array_equiv: Returns True if input arrays are shape consistent and all\n", " elements equal.\n", " \n", " Examples\n", " --------\n", " >>> np.array_equal([1, 2], [1, 2])\n", " True\n", " >>> np.array_equal(np.array([1, 2]), np.array([1, 2]))\n", " True\n", " >>> np.array_equal([1, 2], [1, 2, 3])\n", " False\n", " >>> np.array_equal([1, 2], [1, 4])\n", " False\n", " >>> a = np.array([1, np.nan])\n", " >>> np.array_equal(a, a)\n", " False\n", " >>> np.array_equal(a, a, equal_nan=True)\n", " True\n", " \n", " When ``equal_nan`` is True, complex values with nan components are\n", " considered equal if either the real *or* the imaginary components are nan.\n", " \n", " >>> a = np.array([1 + 1j])\n", " >>> b = a.copy()\n", " >>> a.real = np.nan\n", " >>> b.imag = np.nan\n", " >>> np.array_equal(a, b, equal_nan=True)\n", " True\n", " \n", " array_equiv(a1, a2)\n", " Returns True if input arrays are shape consistent and all elements equal.\n", " \n", " Shape consistent means they are either the same shape, or one input array\n", " can be broadcasted to create the same shape as the other one.\n", " \n", " Parameters\n", " ----------\n", " a1, a2 : array_like\n", " Input arrays.\n", " \n", " Returns\n", " -------\n", " out : bool\n", " True if equivalent, False otherwise.\n", " \n", " Examples\n", " --------\n", " >>> np.array_equiv([1, 2], [1, 2])\n", " True\n", " >>> np.array_equiv([1, 2], [1, 3])\n", " False\n", " \n", " Showing the shape equivalence:\n", " \n", " >>> np.array_equiv([1, 2], [[1, 2], [1, 2]])\n", " True\n", " >>> np.array_equiv([1, 2], [[1, 2, 1, 2], [1, 2, 1, 2]])\n", " False\n", " \n", " >>> np.array_equiv([1, 2], [[1, 2], [1, 3]])\n", " False\n", " \n", " array_repr(arr, max_line_width=None, precision=None, suppress_small=None)\n", " Return the string representation of an array.\n", " \n", " Parameters\n", " ----------\n", " arr : ndarray\n", " Input array.\n", " max_line_width : int, optional\n", " Inserts newlines if text is longer than `max_line_width`.\n", " Defaults to ``numpy.get_printoptions()['linewidth']``.\n", " precision : int, optional\n", " Floating point precision.\n", " Defaults to ``numpy.get_printoptions()['precision']``.\n", " suppress_small : bool, optional\n", " Represent numbers \"very close\" to zero as zero; default is False.\n", " Very close is defined by precision: if the precision is 8, e.g.,\n", " numbers smaller (in absolute value) than 5e-9 are represented as\n", " zero.\n", " Defaults to ``numpy.get_printoptions()['suppress']``.\n", " \n", " Returns\n", " -------\n", " string : str\n", " The string representation of an array.\n", " \n", " See Also\n", " --------\n", " array_str, array2string, set_printoptions\n", " \n", " Examples\n", " --------\n", " >>> np.array_repr(np.array([1,2]))\n", " 'array([1, 2])'\n", " >>> np.array_repr(np.ma.array([0.]))\n", " 'MaskedArray([0.])'\n", " >>> np.array_repr(np.array([], np.int32))\n", " 'array([], dtype=int32)'\n", " \n", " >>> x = np.array([1e-6, 4e-7, 2, 3])\n", " >>> np.array_repr(x, precision=6, suppress_small=True)\n", " 'array([0.000001, 0. , 2. , 3. ])'\n", " \n", " array_split(ary, indices_or_sections, axis=0)\n", " Split an array into multiple sub-arrays.\n", " \n", " Please refer to the ``split`` documentation. The only difference\n", " between these functions is that ``array_split`` allows\n", " `indices_or_sections` to be an integer that does *not* equally\n", " divide the axis. For an array of length l that should be split\n", " into n sections, it returns l % n sub-arrays of size l//n + 1\n", " and the rest of size l//n.\n", " \n", " See Also\n", " --------\n", " split : Split array into multiple sub-arrays of equal size.\n", " \n", " Examples\n", " --------\n", " >>> x = np.arange(8.0)\n", " >>> np.array_split(x, 3)\n", " [array([0., 1., 2.]), array([3., 4., 5.]), array([6., 7.])]\n", " \n", " >>> x = np.arange(9)\n", " >>> np.array_split(x, 4)\n", " [array([0, 1, 2]), array([3, 4]), array([5, 6]), array([7, 8])]\n", " \n", " array_str(a, max_line_width=None, precision=None, suppress_small=None)\n", " Return a string representation of the data in an array.\n", " \n", " The data in the array is returned as a single string. This function is\n", " similar to `array_repr`, the difference being that `array_repr` also\n", " returns information on the kind of array and its data type.\n", " \n", " Parameters\n", " ----------\n", " a : ndarray\n", " Input array.\n", " max_line_width : int, optional\n", " Inserts newlines if text is longer than `max_line_width`.\n", " Defaults to ``numpy.get_printoptions()['linewidth']``.\n", " precision : int, optional\n", " Floating point precision.\n", " Defaults to ``numpy.get_printoptions()['precision']``.\n", " suppress_small : bool, optional\n", " Represent numbers \"very close\" to zero as zero; default is False.\n", " Very close is defined by precision: if the precision is 8, e.g.,\n", " numbers smaller (in absolute value) than 5e-9 are represented as\n", " zero.\n", " Defaults to ``numpy.get_printoptions()['suppress']``.\n", " \n", " See Also\n", " --------\n", " array2string, array_repr, set_printoptions\n", " \n", " Examples\n", " --------\n", " >>> np.array_str(np.arange(3))\n", " '[0 1 2]'\n", " \n", " asanyarray(...)\n", " asanyarray(a, dtype=None, order=None, *, like=None)\n", " \n", " Convert the input to an ndarray, but pass ndarray subclasses through.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input data, in any form that can be converted to an array. This\n", " includes scalars, lists, lists of tuples, tuples, tuples of tuples,\n", " tuples of lists, and ndarrays.\n", " dtype : data-type, optional\n", " By default, the data-type is inferred from the input data.\n", " order : {'C', 'F', 'A', 'K'}, optional\n", " Memory layout. 'A' and 'K' depend on the order of input array a.\n", " 'C' row-major (C-style),\n", " 'F' column-major (Fortran-style) memory representation.\n", " 'A' (any) means 'F' if `a` is Fortran contiguous, 'C' otherwise\n", " 'K' (keep) preserve input order\n", " Defaults to 'C'.\n", " like : array_like, optional\n", " Reference object to allow the creation of arrays which are not\n", " NumPy arrays. If an array-like passed in as ``like`` supports\n", " the ``__array_function__`` protocol, the result will be defined\n", " by it. In this case, it ensures the creation of an array object\n", " compatible with that passed in via this argument.\n", " \n", " .. versionadded:: 1.20.0\n", " \n", " Returns\n", " -------\n", " out : ndarray or an ndarray subclass\n", " Array interpretation of `a`. If `a` is an ndarray or a subclass\n", " of ndarray, it is returned as-is and no copy is performed.\n", " \n", " See Also\n", " --------\n", " asarray : Similar function which always returns ndarrays.\n", " ascontiguousarray : Convert input to a contiguous array.\n", " asfarray : Convert input to a floating point ndarray.\n", " asfortranarray : Convert input to an ndarray with column-major\n", " memory order.\n", " asarray_chkfinite : Similar function which checks input for NaNs and\n", " Infs.\n", " fromiter : Create an array from an iterator.\n", " fromfunction : Construct an array by executing a function on grid\n", " positions.\n", " \n", " Examples\n", " --------\n", " Convert a list into an array:\n", " \n", " >>> a = [1, 2]\n", " >>> np.asanyarray(a)\n", " array([1, 2])\n", " \n", " Instances of `ndarray` subclasses are passed through as-is:\n", " \n", " >>> a = np.array([(1.0, 2), (3.0, 4)], dtype='f4,i4').view(np.recarray)\n", " >>> np.asanyarray(a) is a\n", " True\n", " \n", " asarray(...)\n", " asarray(a, dtype=None, order=None, *, like=None)\n", " \n", " Convert the input to an array.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input data, in any form that can be converted to an array. This\n", " includes lists, lists of tuples, tuples, tuples of tuples, tuples\n", " of lists and ndarrays.\n", " dtype : data-type, optional\n", " By default, the data-type is inferred from the input data.\n", " order : {'C', 'F', 'A', 'K'}, optional\n", " Memory layout. 'A' and 'K' depend on the order of input array a.\n", " 'C' row-major (C-style),\n", " 'F' column-major (Fortran-style) memory representation.\n", " 'A' (any) means 'F' if `a` is Fortran contiguous, 'C' otherwise\n", " 'K' (keep) preserve input order\n", " Defaults to 'K'.\n", " like : array_like, optional\n", " Reference object to allow the creation of arrays which are not\n", " NumPy arrays. If an array-like passed in as ``like`` supports\n", " the ``__array_function__`` protocol, the result will be defined\n", " by it. In this case, it ensures the creation of an array object\n", " compatible with that passed in via this argument.\n", " \n", " .. versionadded:: 1.20.0\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " Array interpretation of `a`. No copy is performed if the input\n", " is already an ndarray with matching dtype and order. If `a` is a\n", " subclass of ndarray, a base class ndarray is returned.\n", " \n", " See Also\n", " --------\n", " asanyarray : Similar function which passes through subclasses.\n", " ascontiguousarray : Convert input to a contiguous array.\n", " asfarray : Convert input to a floating point ndarray.\n", " asfortranarray : Convert input to an ndarray with column-major\n", " memory order.\n", " asarray_chkfinite : Similar function which checks input for NaNs and Infs.\n", " fromiter : Create an array from an iterator.\n", " fromfunction : Construct an array by executing a function on grid\n", " positions.\n", " \n", " Examples\n", " --------\n", " Convert a list into an array:\n", " \n", " >>> a = [1, 2]\n", " >>> np.asarray(a)\n", " array([1, 2])\n", " \n", " Existing arrays are not copied:\n", " \n", " >>> a = np.array([1, 2])\n", " >>> np.asarray(a) is a\n", " True\n", " \n", " If `dtype` is set, array is copied only if dtype does not match:\n", " \n", " >>> a = np.array([1, 2], dtype=np.float32)\n", " >>> np.asarray(a, dtype=np.float32) is a\n", " True\n", " >>> np.asarray(a, dtype=np.float64) is a\n", " False\n", " \n", " Contrary to `asanyarray`, ndarray subclasses are not passed through:\n", " \n", " >>> issubclass(np.recarray, np.ndarray)\n", " True\n", " >>> a = np.array([(1.0, 2), (3.0, 4)], dtype='f4,i4').view(np.recarray)\n", " >>> np.asarray(a) is a\n", " False\n", " >>> np.asanyarray(a) is a\n", " True\n", " \n", " asarray_chkfinite(a, dtype=None, order=None)\n", " Convert the input to an array, checking for NaNs or Infs.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input data, in any form that can be converted to an array. This\n", " includes lists, lists of tuples, tuples, tuples of tuples, tuples\n", " of lists and ndarrays. Success requires no NaNs or Infs.\n", " dtype : data-type, optional\n", " By default, the data-type is inferred from the input data.\n", " order : {'C', 'F', 'A', 'K'}, optional\n", " Memory layout. 'A' and 'K' depend on the order of input array a.\n", " 'C' row-major (C-style),\n", " 'F' column-major (Fortran-style) memory representation.\n", " 'A' (any) means 'F' if `a` is Fortran contiguous, 'C' otherwise\n", " 'K' (keep) preserve input order\n", " Defaults to 'C'.\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " Array interpretation of `a`. No copy is performed if the input\n", " is already an ndarray. If `a` is a subclass of ndarray, a base\n", " class ndarray is returned.\n", " \n", " Raises\n", " ------\n", " ValueError\n", " Raises ValueError if `a` contains NaN (Not a Number) or Inf (Infinity).\n", " \n", " See Also\n", " --------\n", " asarray : Create and array.\n", " asanyarray : Similar function which passes through subclasses.\n", " ascontiguousarray : Convert input to a contiguous array.\n", " asfarray : Convert input to a floating point ndarray.\n", " asfortranarray : Convert input to an ndarray with column-major\n", " memory order.\n", " fromiter : Create an array from an iterator.\n", " fromfunction : Construct an array by executing a function on grid\n", " positions.\n", " \n", " Examples\n", " --------\n", " Convert a list into an array. If all elements are finite\n", " ``asarray_chkfinite`` is identical to ``asarray``.\n", " \n", " >>> a = [1, 2]\n", " >>> np.asarray_chkfinite(a, dtype=float)\n", " array([1., 2.])\n", " \n", " Raises ValueError if array_like contains Nans or Infs.\n", " \n", " >>> a = [1, 2, np.inf]\n", " >>> try:\n", " ... np.asarray_chkfinite(a)\n", " ... except ValueError:\n", " ... print('ValueError')\n", " ...\n", " ValueError\n", " \n", " ascontiguousarray(...)\n", " ascontiguousarray(a, dtype=None, *, like=None)\n", " \n", " Return a contiguous array (ndim >= 1) in memory (C order).\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input array.\n", " dtype : str or dtype object, optional\n", " Data-type of returned array.\n", " like : array_like, optional\n", " Reference object to allow the creation of arrays which are not\n", " NumPy arrays. If an array-like passed in as ``like`` supports\n", " the ``__array_function__`` protocol, the result will be defined\n", " by it. In this case, it ensures the creation of an array object\n", " compatible with that passed in via this argument.\n", " \n", " .. versionadded:: 1.20.0\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " Contiguous array of same shape and content as `a`, with type `dtype`\n", " if specified.\n", " \n", " See Also\n", " --------\n", " asfortranarray : Convert input to an ndarray with column-major\n", " memory order.\n", " require : Return an ndarray that satisfies requirements.\n", " ndarray.flags : Information about the memory layout of the array.\n", " \n", " Examples\n", " --------\n", " Starting with a Fortran-contiguous array:\n", " \n", " >>> x = np.ones((2, 3), order='F')\n", " >>> x.flags['F_CONTIGUOUS']\n", " True\n", " \n", " Calling ``ascontiguousarray`` makes a C-contiguous copy:\n", " \n", " >>> y = np.ascontiguousarray(x)\n", " >>> y.flags['C_CONTIGUOUS']\n", " True\n", " >>> np.may_share_memory(x, y)\n", " False\n", " \n", " Now, starting with a C-contiguous array:\n", " \n", " >>> x = np.ones((2, 3), order='C')\n", " >>> x.flags['C_CONTIGUOUS']\n", " True\n", " \n", " Then, calling ``ascontiguousarray`` returns the same object:\n", " \n", " >>> y = np.ascontiguousarray(x)\n", " >>> x is y\n", " True\n", " \n", " Note: This function returns an array with at least one-dimension (1-d)\n", " so it will not preserve 0-d arrays.\n", " \n", " asfarray(a, dtype=<class 'numpy.float64'>)\n", " Return an array converted to a float type.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " The input array.\n", " dtype : str or dtype object, optional\n", " Float type code to coerce input array `a`. If `dtype` is one of the\n", " 'int' dtypes, it is replaced with float64.\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " The input `a` as a float ndarray.\n", " \n", " Examples\n", " --------\n", " >>> np.asfarray([2, 3])\n", " array([2., 3.])\n", " >>> np.asfarray([2, 3], dtype='float')\n", " array([2., 3.])\n", " >>> np.asfarray([2, 3], dtype='int8')\n", " array([2., 3.])\n", " \n", " asfortranarray(...)\n", " asfortranarray(a, dtype=None, *, like=None)\n", " \n", " Return an array (ndim >= 1) laid out in Fortran order in memory.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input array.\n", " dtype : str or dtype object, optional\n", " By default, the data-type is inferred from the input data.\n", " like : array_like, optional\n", " Reference object to allow the creation of arrays which are not\n", " NumPy arrays. If an array-like passed in as ``like`` supports\n", " the ``__array_function__`` protocol, the result will be defined\n", " by it. In this case, it ensures the creation of an array object\n", " compatible with that passed in via this argument.\n", " \n", " .. versionadded:: 1.20.0\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " The input `a` in Fortran, or column-major, order.\n", " \n", " See Also\n", " --------\n", " ascontiguousarray : Convert input to a contiguous (C order) array.\n", " asanyarray : Convert input to an ndarray with either row or\n", " column-major memory order.\n", " require : Return an ndarray that satisfies requirements.\n", " ndarray.flags : Information about the memory layout of the array.\n", " \n", " Examples\n", " --------\n", " Starting with a C-contiguous array:\n", " \n", " >>> x = np.ones((2, 3), order='C')\n", " >>> x.flags['C_CONTIGUOUS']\n", " True\n", " \n", " Calling ``asfortranarray`` makes a Fortran-contiguous copy:\n", " \n", " >>> y = np.asfortranarray(x)\n", " >>> y.flags['F_CONTIGUOUS']\n", " True\n", " >>> np.may_share_memory(x, y)\n", " False\n", " \n", " Now, starting with a Fortran-contiguous array:\n", " \n", " >>> x = np.ones((2, 3), order='F')\n", " >>> x.flags['F_CONTIGUOUS']\n", " True\n", " \n", " Then, calling ``asfortranarray`` returns the same object:\n", " \n", " >>> y = np.asfortranarray(x)\n", " >>> x is y\n", " True\n", " \n", " Note: This function returns an array with at least one-dimension (1-d)\n", " so it will not preserve 0-d arrays.\n", " \n", " asmatrix(data, dtype=None)\n", " Interpret the input as a matrix.\n", " \n", " Unlike `matrix`, `asmatrix` does not make a copy if the input is already\n", " a matrix or an ndarray. Equivalent to ``matrix(data, copy=False)``.\n", " \n", " Parameters\n", " ----------\n", " data : array_like\n", " Input data.\n", " dtype : data-type\n", " Data-type of the output matrix.\n", " \n", " Returns\n", " -------\n", " mat : matrix\n", " `data` interpreted as a matrix.\n", " \n", " Examples\n", " --------\n", " >>> x = np.array([[1, 2], [3, 4]])\n", " \n", " >>> m = np.asmatrix(x)\n", " \n", " >>> x[0,0] = 5\n", " \n", " >>> m\n", " matrix([[5, 2],\n", " [3, 4]])\n", " \n", " atleast_1d(*arys)\n", " Convert inputs to arrays with at least one dimension.\n", " \n", " Scalar inputs are converted to 1-dimensional arrays, whilst\n", " higher-dimensional inputs are preserved.\n", " \n", " Parameters\n", " ----------\n", " arys1, arys2, ... : array_like\n", " One or more input arrays.\n", " \n", " Returns\n", " -------\n", " ret : ndarray\n", " An array, or list of arrays, each with ``a.ndim >= 1``.\n", " Copies are made only if necessary.\n", " \n", " See Also\n", " --------\n", " atleast_2d, atleast_3d\n", " \n", " Examples\n", " --------\n", " >>> np.atleast_1d(1.0)\n", " array([1.])\n", " \n", " >>> x = np.arange(9.0).reshape(3,3)\n", " >>> np.atleast_1d(x)\n", " array([[0., 1., 2.],\n", " [3., 4., 5.],\n", " [6., 7., 8.]])\n", " >>> np.atleast_1d(x) is x\n", " True\n", " \n", " >>> np.atleast_1d(1, [3, 4])\n", " [array([1]), array([3, 4])]\n", " \n", " atleast_2d(*arys)\n", " View inputs as arrays with at least two dimensions.\n", " \n", " Parameters\n", " ----------\n", " arys1, arys2, ... : array_like\n", " One or more array-like sequences. Non-array inputs are converted\n", " to arrays. Arrays that already have two or more dimensions are\n", " preserved.\n", " \n", " Returns\n", " -------\n", " res, res2, ... : ndarray\n", " An array, or list of arrays, each with ``a.ndim >= 2``.\n", " Copies are avoided where possible, and views with two or more\n", " dimensions are returned.\n", " \n", " See Also\n", " --------\n", " atleast_1d, atleast_3d\n", " \n", " Examples\n", " --------\n", " >>> np.atleast_2d(3.0)\n", " array([[3.]])\n", " \n", " >>> x = np.arange(3.0)\n", " >>> np.atleast_2d(x)\n", " array([[0., 1., 2.]])\n", " >>> np.atleast_2d(x).base is x\n", " True\n", " \n", " >>> np.atleast_2d(1, [1, 2], [[1, 2]])\n", " [array([[1]]), array([[1, 2]]), array([[1, 2]])]\n", " \n", " atleast_3d(*arys)\n", " View inputs as arrays with at least three dimensions.\n", " \n", " Parameters\n", " ----------\n", " arys1, arys2, ... : array_like\n", " One or more array-like sequences. Non-array inputs are converted to\n", " arrays. Arrays that already have three or more dimensions are\n", " preserved.\n", " \n", " Returns\n", " -------\n", " res1, res2, ... : ndarray\n", " An array, or list of arrays, each with ``a.ndim >= 3``. Copies are\n", " avoided where possible, and views with three or more dimensions are\n", " returned. For example, a 1-D array of shape ``(N,)`` becomes a view\n", " of shape ``(1, N, 1)``, and a 2-D array of shape ``(M, N)`` becomes a\n", " view of shape ``(M, N, 1)``.\n", " \n", " See Also\n", " --------\n", " atleast_1d, atleast_2d\n", " \n", " Examples\n", " --------\n", " >>> np.atleast_3d(3.0)\n", " array([[[3.]]])\n", " \n", " >>> x = np.arange(3.0)\n", " >>> np.atleast_3d(x).shape\n", " (1, 3, 1)\n", " \n", " >>> x = np.arange(12.0).reshape(4,3)\n", " >>> np.atleast_3d(x).shape\n", " (4, 3, 1)\n", " >>> np.atleast_3d(x).base is x.base # x is a reshape, so not base itself\n", " True\n", " \n", " >>> for arr in np.atleast_3d([1, 2], [[1, 2]], [[[1, 2]]]):\n", " ... print(arr, arr.shape) # doctest: +SKIP\n", " ...\n", " [[[1]\n", " [2]]] (1, 2, 1)\n", " [[[1]\n", " [2]]] (1, 2, 1)\n", " [[[1 2]]] (1, 1, 2)\n", " \n", " average(a, axis=None, weights=None, returned=False, *, keepdims=<no value>)\n", " Compute the weighted average along the specified axis.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Array containing data to be averaged. If `a` is not an array, a\n", " conversion is attempted.\n", " axis : None or int or tuple of ints, optional\n", " Axis or axes along which to average `a`. The default,\n", " axis=None, will average over all of the elements of the input array.\n", " If axis is negative it counts from the last to the first axis.\n", " \n", " .. versionadded:: 1.7.0\n", " \n", " If axis is a tuple of ints, averaging is performed on all of the axes\n", " specified in the tuple instead of a single axis or all the axes as\n", " before.\n", " weights : array_like, optional\n", " An array of weights associated with the values in `a`. Each value in\n", " `a` contributes to the average according to its associated weight.\n", " The weights array can either be 1-D (in which case its length must be\n", " the size of `a` along the given axis) or of the same shape as `a`.\n", " If `weights=None`, then all data in `a` are assumed to have a\n", " weight equal to one. The 1-D calculation is::\n", " \n", " avg = sum(a * weights) / sum(weights)\n", " \n", " The only constraint on `weights` is that `sum(weights)` must not be 0.\n", " returned : bool, optional\n", " Default is `False`. If `True`, the tuple (`average`, `sum_of_weights`)\n", " is returned, otherwise only the average is returned.\n", " If `weights=None`, `sum_of_weights` is equivalent to the number of\n", " elements over which the average is taken.\n", " keepdims : bool, optional\n", " If this is set to True, the axes which are reduced are left\n", " in the result as dimensions with size one. With this option,\n", " the result will broadcast correctly against the original `a`.\n", " *Note:* `keepdims` will not work with instances of `numpy.matrix`\n", " or other classes whose methods do not support `keepdims`.\n", " \n", " .. versionadded:: 1.23.0\n", " \n", " Returns\n", " -------\n", " retval, [sum_of_weights] : array_type or double\n", " Return the average along the specified axis. When `returned` is `True`,\n", " return a tuple with the average as the first element and the sum\n", " of the weights as the second element. `sum_of_weights` is of the\n", " same type as `retval`. The result dtype follows a genereal pattern.\n", " If `weights` is None, the result dtype will be that of `a` , or ``float64``\n", " if `a` is integral. Otherwise, if `weights` is not None and `a` is non-\n", " integral, the result type will be the type of lowest precision capable of\n", " representing values of both `a` and `weights`. If `a` happens to be\n", " integral, the previous rules still applies but the result dtype will\n", " at least be ``float64``.\n", " \n", " Raises\n", " ------\n", " ZeroDivisionError\n", " When all weights along axis are zero. See `numpy.ma.average` for a\n", " version robust to this type of error.\n", " TypeError\n", " When the length of 1D `weights` is not the same as the shape of `a`\n", " along axis.\n", " \n", " See Also\n", " --------\n", " mean\n", " \n", " ma.average : average for masked arrays -- useful if your data contains\n", " \"missing\" values\n", " numpy.result_type : Returns the type that results from applying the\n", " numpy type promotion rules to the arguments.\n", " \n", " Examples\n", " --------\n", " >>> data = np.arange(1, 5)\n", " >>> data\n", " array([1, 2, 3, 4])\n", " >>> np.average(data)\n", " 2.5\n", " >>> np.average(np.arange(1, 11), weights=np.arange(10, 0, -1))\n", " 4.0\n", " \n", " >>> data = np.arange(6).reshape((3, 2))\n", " >>> data\n", " array([[0, 1],\n", " [2, 3],\n", " [4, 5]])\n", " >>> np.average(data, axis=1, weights=[1./4, 3./4])\n", " array([0.75, 2.75, 4.75])\n", " >>> np.average(data, weights=[1./4, 3./4])\n", " Traceback (most recent call last):\n", " ...\n", " TypeError: Axis must be specified when shapes of a and weights differ.\n", " \n", " >>> a = np.ones(5, dtype=np.float128)\n", " >>> w = np.ones(5, dtype=np.complex64)\n", " >>> avg = np.average(a, weights=w)\n", " >>> print(avg.dtype)\n", " complex256\n", " \n", " With ``keepdims=True``, the following result has shape (3, 1).\n", " \n", " >>> np.average(data, axis=1, keepdims=True)\n", " array([[0.5],\n", " [2.5],\n", " [4.5]])\n", " \n", " bartlett(M)\n", " Return the Bartlett window.\n", " \n", " The Bartlett window is very similar to a triangular window, except\n", " that the end points are at zero. It is often used in signal\n", " processing for tapering a signal, without generating too much\n", " ripple in the frequency domain.\n", " \n", " Parameters\n", " ----------\n", " M : int\n", " Number of points in the output window. If zero or less, an\n", " empty array is returned.\n", " \n", " Returns\n", " -------\n", " out : array\n", " The triangular window, with the maximum value normalized to one\n", " (the value one appears only if the number of samples is odd), with\n", " the first and last samples equal to zero.\n", " \n", " See Also\n", " --------\n", " blackman, hamming, hanning, kaiser\n", " \n", " Notes\n", " -----\n", " The Bartlett window is defined as\n", " \n", " .. math:: w(n) = \\frac{2}{M-1} \\left(\n", " \\frac{M-1}{2} - \\left|n - \\frac{M-1}{2}\\right|\n", " \\right)\n", " \n", " Most references to the Bartlett window come from the signal processing\n", " literature, where it is used as one of many windowing functions for\n", " smoothing values. Note that convolution with this window produces linear\n", " interpolation. It is also known as an apodization (which means \"removing\n", " the foot\", i.e. smoothing discontinuities at the beginning and end of the\n", " sampled signal) or tapering function. The Fourier transform of the\n", " Bartlett window is the product of two sinc functions. Note the excellent\n", " discussion in Kanasewich [2]_.\n", " \n", " References\n", " ----------\n", " .. [1] M.S. Bartlett, \"Periodogram Analysis and Continuous Spectra\",\n", " Biometrika 37, 1-16, 1950.\n", " .. [2] E.R. Kanasewich, \"Time Sequence Analysis in Geophysics\",\n", " The University of Alberta Press, 1975, pp. 109-110.\n", " .. [3] A.V. Oppenheim and R.W. Schafer, \"Discrete-Time Signal\n", " Processing\", Prentice-Hall, 1999, pp. 468-471.\n", " .. [4] Wikipedia, \"Window function\",\n", " https://en.wikipedia.org/wiki/Window_function\n", " .. [5] W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling,\n", " \"Numerical Recipes\", Cambridge University Press, 1986, page 429.\n", " \n", " Examples\n", " --------\n", " >>> import matplotlib.pyplot as plt\n", " >>> np.bartlett(12)\n", " array([ 0. , 0.18181818, 0.36363636, 0.54545455, 0.72727273, # may vary\n", " 0.90909091, 0.90909091, 0.72727273, 0.54545455, 0.36363636,\n", " 0.18181818, 0. ])\n", " \n", " Plot the window and its frequency response (requires SciPy and matplotlib):\n", " \n", " >>> from numpy.fft import fft, fftshift\n", " >>> window = np.bartlett(51)\n", " >>> plt.plot(window)\n", " [<matplotlib.lines.Line2D object at 0x...>]\n", " >>> plt.title(\"Bartlett window\")\n", " Text(0.5, 1.0, 'Bartlett window')\n", " >>> plt.ylabel(\"Amplitude\")\n", " Text(0, 0.5, 'Amplitude')\n", " >>> plt.xlabel(\"Sample\")\n", " Text(0.5, 0, 'Sample')\n", " >>> plt.show()\n", " \n", " >>> plt.figure()\n", " <Figure size 640x480 with 0 Axes>\n", " >>> A = fft(window, 2048) / 25.5\n", " >>> mag = np.abs(fftshift(A))\n", " >>> freq = np.linspace(-0.5, 0.5, len(A))\n", " >>> with np.errstate(divide='ignore', invalid='ignore'):\n", " ... response = 20 * np.log10(mag)\n", " ...\n", " >>> response = np.clip(response, -100, 100)\n", " >>> plt.plot(freq, response)\n", " [<matplotlib.lines.Line2D object at 0x...>]\n", " >>> plt.title(\"Frequency response of Bartlett window\")\n", " Text(0.5, 1.0, 'Frequency response of Bartlett window')\n", " >>> plt.ylabel(\"Magnitude [dB]\")\n", " Text(0, 0.5, 'Magnitude [dB]')\n", " >>> plt.xlabel(\"Normalized frequency [cycles per sample]\")\n", " Text(0.5, 0, 'Normalized frequency [cycles per sample]')\n", " >>> _ = plt.axis('tight')\n", " >>> plt.show()\n", " \n", " base_repr(number, base=2, padding=0)\n", " Return a string representation of a number in the given base system.\n", " \n", " Parameters\n", " ----------\n", " number : int\n", " The value to convert. Positive and negative values are handled.\n", " base : int, optional\n", " Convert `number` to the `base` number system. The valid range is 2-36,\n", " the default value is 2.\n", " padding : int, optional\n", " Number of zeros padded on the left. Default is 0 (no padding).\n", " \n", " Returns\n", " -------\n", " out : str\n", " String representation of `number` in `base` system.\n", " \n", " See Also\n", " --------\n", " binary_repr : Faster version of `base_repr` for base 2.\n", " \n", " Examples\n", " --------\n", " >>> np.base_repr(5)\n", " '101'\n", " >>> np.base_repr(6, 5)\n", " '11'\n", " >>> np.base_repr(7, base=5, padding=3)\n", " '00012'\n", " \n", " >>> np.base_repr(10, base=16)\n", " 'A'\n", " >>> np.base_repr(32, base=16)\n", " '20'\n", " \n", " binary_repr(num, width=None)\n", " Return the binary representation of the input number as a string.\n", " \n", " For negative numbers, if width is not given, a minus sign is added to the\n", " front. If width is given, the two's complement of the number is\n", " returned, with respect to that width.\n", " \n", " In a two's-complement system negative numbers are represented by the two's\n", " complement of the absolute value. This is the most common method of\n", " representing signed integers on computers [1]_. A N-bit two's-complement\n", " system can represent every integer in the range\n", " :math:`-2^{N-1}` to :math:`+2^{N-1}-1`.\n", " \n", " Parameters\n", " ----------\n", " num : int\n", " Only an integer decimal number can be used.\n", " width : int, optional\n", " The length of the returned string if `num` is positive, or the length\n", " of the two's complement if `num` is negative, provided that `width` is\n", " at least a sufficient number of bits for `num` to be represented in the\n", " designated form.\n", " \n", " If the `width` value is insufficient, it will be ignored, and `num` will\n", " be returned in binary (`num` > 0) or two's complement (`num` < 0) form\n", " with its width equal to the minimum number of bits needed to represent\n", " the number in the designated form. This behavior is deprecated and will\n", " later raise an error.\n", " \n", " .. deprecated:: 1.12.0\n", " \n", " Returns\n", " -------\n", " bin : str\n", " Binary representation of `num` or two's complement of `num`.\n", " \n", " See Also\n", " --------\n", " base_repr: Return a string representation of a number in the given base\n", " system.\n", " bin: Python's built-in binary representation generator of an integer.\n", " \n", " Notes\n", " -----\n", " `binary_repr` is equivalent to using `base_repr` with base 2, but about 25x\n", " faster.\n", " \n", " References\n", " ----------\n", " .. [1] Wikipedia, \"Two's complement\",\n", " https://en.wikipedia.org/wiki/Two's_complement\n", " \n", " Examples\n", " --------\n", " >>> np.binary_repr(3)\n", " '11'\n", " >>> np.binary_repr(-3)\n", " '-11'\n", " >>> np.binary_repr(3, width=4)\n", " '0011'\n", " \n", " The two's complement is returned when the input number is negative and\n", " width is specified:\n", " \n", " >>> np.binary_repr(-3, width=3)\n", " '101'\n", " >>> np.binary_repr(-3, width=5)\n", " '11101'\n", " \n", " bincount(...)\n", " bincount(x, /, weights=None, minlength=0)\n", " \n", " Count number of occurrences of each value in array of non-negative ints.\n", " \n", " The number of bins (of size 1) is one larger than the largest value in\n", " `x`. If `minlength` is specified, there will be at least this number\n", " of bins in the output array (though it will be longer if necessary,\n", " depending on the contents of `x`).\n", " Each bin gives the number of occurrences of its index value in `x`.\n", " If `weights` is specified the input array is weighted by it, i.e. if a\n", " value ``n`` is found at position ``i``, ``out[n] += weight[i]`` instead\n", " of ``out[n] += 1``.\n", " \n", " Parameters\n", " ----------\n", " x : array_like, 1 dimension, nonnegative ints\n", " Input array.\n", " weights : array_like, optional\n", " Weights, array of the same shape as `x`.\n", " minlength : int, optional\n", " A minimum number of bins for the output array.\n", " \n", " .. versionadded:: 1.6.0\n", " \n", " Returns\n", " -------\n", " out : ndarray of ints\n", " The result of binning the input array.\n", " The length of `out` is equal to ``np.amax(x)+1``.\n", " \n", " Raises\n", " ------\n", " ValueError\n", " If the input is not 1-dimensional, or contains elements with negative\n", " values, or if `minlength` is negative.\n", " TypeError\n", " If the type of the input is float or complex.\n", " \n", " See Also\n", " --------\n", " histogram, digitize, unique\n", " \n", " Examples\n", " --------\n", " >>> np.bincount(np.arange(5))\n", " array([1, 1, 1, 1, 1])\n", " >>> np.bincount(np.array([0, 1, 1, 3, 2, 1, 7]))\n", " array([1, 3, 1, 1, 0, 0, 0, 1])\n", " \n", " >>> x = np.array([0, 1, 1, 3, 2, 1, 7, 23])\n", " >>> np.bincount(x).size == np.amax(x)+1\n", " True\n", " \n", " The input array needs to be of integer dtype, otherwise a\n", " TypeError is raised:\n", " \n", " >>> np.bincount(np.arange(5, dtype=float))\n", " Traceback (most recent call last):\n", " ...\n", " TypeError: Cannot cast array data from dtype('float64') to dtype('int64')\n", " according to the rule 'safe'\n", " \n", " A possible use of ``bincount`` is to perform sums over\n", " variable-size chunks of an array, using the ``weights`` keyword.\n", " \n", " >>> w = np.array([0.3, 0.5, 0.2, 0.7, 1., -0.6]) # weights\n", " >>> x = np.array([0, 1, 1, 2, 2, 2])\n", " >>> np.bincount(x, weights=w)\n", " array([ 0.3, 0.7, 1.1])\n", " \n", " blackman(M)\n", " Return the Blackman window.\n", " \n", " The Blackman window is a taper formed by using the first three\n", " terms of a summation of cosines. It was designed to have close to the\n", " minimal leakage possible. It is close to optimal, only slightly worse\n", " than a Kaiser window.\n", " \n", " Parameters\n", " ----------\n", " M : int\n", " Number of points in the output window. If zero or less, an empty\n", " array is returned.\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " The window, with the maximum value normalized to one (the value one\n", " appears only if the number of samples is odd).\n", " \n", " See Also\n", " --------\n", " bartlett, hamming, hanning, kaiser\n", " \n", " Notes\n", " -----\n", " The Blackman window is defined as\n", " \n", " .. math:: w(n) = 0.42 - 0.5 \\cos(2\\pi n/M) + 0.08 \\cos(4\\pi n/M)\n", " \n", " Most references to the Blackman window come from the signal processing\n", " literature, where it is used as one of many windowing functions for\n", " smoothing values. It is also known as an apodization (which means\n", " \"removing the foot\", i.e. smoothing discontinuities at the beginning\n", " and end of the sampled signal) or tapering function. It is known as a\n", " \"near optimal\" tapering function, almost as good (by some measures)\n", " as the kaiser window.\n", " \n", " References\n", " ----------\n", " Blackman, R.B. and Tukey, J.W., (1958) The measurement of power spectra,\n", " Dover Publications, New York.\n", " \n", " Oppenheim, A.V., and R.W. Schafer. Discrete-Time Signal Processing.\n", " Upper Saddle River, NJ: Prentice-Hall, 1999, pp. 468-471.\n", " \n", " Examples\n", " --------\n", " >>> import matplotlib.pyplot as plt\n", " >>> np.blackman(12)\n", " array([-1.38777878e-17, 3.26064346e-02, 1.59903635e-01, # may vary\n", " 4.14397981e-01, 7.36045180e-01, 9.67046769e-01,\n", " 9.67046769e-01, 7.36045180e-01, 4.14397981e-01,\n", " 1.59903635e-01, 3.26064346e-02, -1.38777878e-17])\n", " \n", " Plot the window and the frequency response:\n", " \n", " >>> from numpy.fft import fft, fftshift\n", " >>> window = np.blackman(51)\n", " >>> plt.plot(window)\n", " [<matplotlib.lines.Line2D object at 0x...>]\n", " >>> plt.title(\"Blackman window\")\n", " Text(0.5, 1.0, 'Blackman window')\n", " >>> plt.ylabel(\"Amplitude\")\n", " Text(0, 0.5, 'Amplitude')\n", " >>> plt.xlabel(\"Sample\")\n", " Text(0.5, 0, 'Sample')\n", " >>> plt.show()\n", " \n", " >>> plt.figure()\n", " <Figure size 640x480 with 0 Axes>\n", " >>> A = fft(window, 2048) / 25.5\n", " >>> mag = np.abs(fftshift(A))\n", " >>> freq = np.linspace(-0.5, 0.5, len(A))\n", " >>> with np.errstate(divide='ignore', invalid='ignore'):\n", " ... response = 20 * np.log10(mag)\n", " ...\n", " >>> response = np.clip(response, -100, 100)\n", " >>> plt.plot(freq, response)\n", " [<matplotlib.lines.Line2D object at 0x...>]\n", " >>> plt.title(\"Frequency response of Blackman window\")\n", " Text(0.5, 1.0, 'Frequency response of Blackman window')\n", " >>> plt.ylabel(\"Magnitude [dB]\")\n", " Text(0, 0.5, 'Magnitude [dB]')\n", " >>> plt.xlabel(\"Normalized frequency [cycles per sample]\")\n", " Text(0.5, 0, 'Normalized frequency [cycles per sample]')\n", " >>> _ = plt.axis('tight')\n", " >>> plt.show()\n", " \n", " block(arrays)\n", " Assemble an nd-array from nested lists of blocks.\n", " \n", " Blocks in the innermost lists are concatenated (see `concatenate`) along\n", " the last dimension (-1), then these are concatenated along the\n", " second-last dimension (-2), and so on until the outermost list is reached.\n", " \n", " Blocks can be of any dimension, but will not be broadcasted using the normal\n", " rules. Instead, leading axes of size 1 are inserted, to make ``block.ndim``\n", " the same for all blocks. This is primarily useful for working with scalars,\n", " and means that code like ``np.block([v, 1])`` is valid, where\n", " ``v.ndim == 1``.\n", " \n", " When the nested list is two levels deep, this allows block matrices to be\n", " constructed from their components.\n", " \n", " .. versionadded:: 1.13.0\n", " \n", " Parameters\n", " ----------\n", " arrays : nested list of array_like or scalars (but not tuples)\n", " If passed a single ndarray or scalar (a nested list of depth 0), this\n", " is returned unmodified (and not copied).\n", " \n", " Elements shapes must match along the appropriate axes (without\n", " broadcasting), but leading 1s will be prepended to the shape as\n", " necessary to make the dimensions match.\n", " \n", " Returns\n", " -------\n", " block_array : ndarray\n", " The array assembled from the given blocks.\n", " \n", " The dimensionality of the output is equal to the greatest of:\n", " * the dimensionality of all the inputs\n", " * the depth to which the input list is nested\n", " \n", " Raises\n", " ------\n", " ValueError\n", " * If list depths are mismatched - for instance, ``[[a, b], c]`` is\n", " illegal, and should be spelt ``[[a, b], [c]]``\n", " * If lists are empty - for instance, ``[[a, b], []]``\n", " \n", " See Also\n", " --------\n", " concatenate : Join a sequence of arrays along an existing axis.\n", " stack : Join a sequence of arrays along a new axis.\n", " vstack : Stack arrays in sequence vertically (row wise).\n", " hstack : Stack arrays in sequence horizontally (column wise).\n", " dstack : Stack arrays in sequence depth wise (along third axis).\n", " column_stack : Stack 1-D arrays as columns into a 2-D array.\n", " vsplit : Split an array into multiple sub-arrays vertically (row-wise).\n", " \n", " Notes\n", " -----\n", " \n", " When called with only scalars, ``np.block`` is equivalent to an ndarray\n", " call. So ``np.block([[1, 2], [3, 4]])`` is equivalent to\n", " ``np.array([[1, 2], [3, 4]])``.\n", " \n", " This function does not enforce that the blocks lie on a fixed grid.\n", " ``np.block([[a, b], [c, d]])`` is not restricted to arrays of the form::\n", " \n", " AAAbb\n", " AAAbb\n", " cccDD\n", " \n", " But is also allowed to produce, for some ``a, b, c, d``::\n", " \n", " AAAbb\n", " AAAbb\n", " cDDDD\n", " \n", " Since concatenation happens along the last axis first, `block` is _not_\n", " capable of producing the following directly::\n", " \n", " AAAbb\n", " cccbb\n", " cccDD\n", " \n", " Matlab's \"square bracket stacking\", ``[A, B, ...; p, q, ...]``, is\n", " equivalent to ``np.block([[A, B, ...], [p, q, ...]])``.\n", " \n", " Examples\n", " --------\n", " The most common use of this function is to build a block matrix\n", " \n", " >>> A = np.eye(2) * 2\n", " >>> B = np.eye(3) * 3\n", " >>> np.block([\n", " ... [A, np.zeros((2, 3))],\n", " ... [np.ones((3, 2)), B ]\n", " ... ])\n", " array([[2., 0., 0., 0., 0.],\n", " [0., 2., 0., 0., 0.],\n", " [1., 1., 3., 0., 0.],\n", " [1., 1., 0., 3., 0.],\n", " [1., 1., 0., 0., 3.]])\n", " \n", " With a list of depth 1, `block` can be used as `hstack`\n", " \n", " >>> np.block([1, 2, 3]) # hstack([1, 2, 3])\n", " array([1, 2, 3])\n", " \n", " >>> a = np.array([1, 2, 3])\n", " >>> b = np.array([4, 5, 6])\n", " >>> np.block([a, b, 10]) # hstack([a, b, 10])\n", " array([ 1, 2, 3, 4, 5, 6, 10])\n", " \n", " >>> A = np.ones((2, 2), int)\n", " >>> B = 2 * A\n", " >>> np.block([A, B]) # hstack([A, B])\n", " array([[1, 1, 2, 2],\n", " [1, 1, 2, 2]])\n", " \n", " With a list of depth 2, `block` can be used in place of `vstack`:\n", " \n", " >>> a = np.array([1, 2, 3])\n", " >>> b = np.array([4, 5, 6])\n", " >>> np.block([[a], [b]]) # vstack([a, b])\n", " array([[1, 2, 3],\n", " [4, 5, 6]])\n", " \n", " >>> A = np.ones((2, 2), int)\n", " >>> B = 2 * A\n", " >>> np.block([[A], [B]]) # vstack([A, B])\n", " array([[1, 1],\n", " [1, 1],\n", " [2, 2],\n", " [2, 2]])\n", " \n", " It can also be used in places of `atleast_1d` and `atleast_2d`\n", " \n", " >>> a = np.array(0)\n", " >>> b = np.array([1])\n", " >>> np.block([a]) # atleast_1d(a)\n", " array([0])\n", " >>> np.block([b]) # atleast_1d(b)\n", " array([1])\n", " \n", " >>> np.block([[a]]) # atleast_2d(a)\n", " array([[0]])\n", " >>> np.block([[b]]) # atleast_2d(b)\n", " array([[1]])\n", " \n", " bmat(obj, ldict=None, gdict=None)\n", " Build a matrix object from a string, nested sequence, or array.\n", " \n", " Parameters\n", " ----------\n", " obj : str or array_like\n", " Input data. If a string, variables in the current scope may be\n", " referenced by name.\n", " ldict : dict, optional\n", " A dictionary that replaces local operands in current frame.\n", " Ignored if `obj` is not a string or `gdict` is None.\n", " gdict : dict, optional\n", " A dictionary that replaces global operands in current frame.\n", " Ignored if `obj` is not a string.\n", " \n", " Returns\n", " -------\n", " out : matrix\n", " Returns a matrix object, which is a specialized 2-D array.\n", " \n", " See Also\n", " --------\n", " block :\n", " A generalization of this function for N-d arrays, that returns normal\n", " ndarrays.\n", " \n", " Examples\n", " --------\n", " >>> A = np.mat('1 1; 1 1')\n", " >>> B = np.mat('2 2; 2 2')\n", " >>> C = np.mat('3 4; 5 6')\n", " >>> D = np.mat('7 8; 9 0')\n", " \n", " All the following expressions construct the same block matrix:\n", " \n", " >>> np.bmat([[A, B], [C, D]])\n", " matrix([[1, 1, 2, 2],\n", " [1, 1, 2, 2],\n", " [3, 4, 7, 8],\n", " [5, 6, 9, 0]])\n", " >>> np.bmat(np.r_[np.c_[A, B], np.c_[C, D]])\n", " matrix([[1, 1, 2, 2],\n", " [1, 1, 2, 2],\n", " [3, 4, 7, 8],\n", " [5, 6, 9, 0]])\n", " >>> np.bmat('A,B; C,D')\n", " matrix([[1, 1, 2, 2],\n", " [1, 1, 2, 2],\n", " [3, 4, 7, 8],\n", " [5, 6, 9, 0]])\n", " \n", " broadcast_arrays(*args, subok=False)\n", " Broadcast any number of arrays against each other.\n", " \n", " Parameters\n", " ----------\n", " `*args` : array_likes\n", " The arrays to broadcast.\n", " \n", " subok : bool, optional\n", " If True, then sub-classes will be passed-through, otherwise\n", " the returned arrays will be forced to be a base-class array (default).\n", " \n", " Returns\n", " -------\n", " broadcasted : list of arrays\n", " These arrays are views on the original arrays. They are typically\n", " not contiguous. Furthermore, more than one element of a\n", " broadcasted array may refer to a single memory location. If you need\n", " to write to the arrays, make copies first. While you can set the\n", " ``writable`` flag True, writing to a single output value may end up\n", " changing more than one location in the output array.\n", " \n", " .. deprecated:: 1.17\n", " The output is currently marked so that if written to, a deprecation\n", " warning will be emitted. A future version will set the\n", " ``writable`` flag False so writing to it will raise an error.\n", " \n", " See Also\n", " --------\n", " broadcast\n", " broadcast_to\n", " broadcast_shapes\n", " \n", " Examples\n", " --------\n", " >>> x = np.array([[1,2,3]])\n", " >>> y = np.array([[4],[5]])\n", " >>> np.broadcast_arrays(x, y)\n", " [array([[1, 2, 3],\n", " [1, 2, 3]]), array([[4, 4, 4],\n", " [5, 5, 5]])]\n", " \n", " Here is a useful idiom for getting contiguous copies instead of\n", " non-contiguous views.\n", " \n", " >>> [np.array(a) for a in np.broadcast_arrays(x, y)]\n", " [array([[1, 2, 3],\n", " [1, 2, 3]]), array([[4, 4, 4],\n", " [5, 5, 5]])]\n", " \n", " broadcast_shapes(*args)\n", " Broadcast the input shapes into a single shape.\n", " \n", " :ref:`Learn more about broadcasting here <basics.broadcasting>`.\n", " \n", " .. versionadded:: 1.20.0\n", " \n", " Parameters\n", " ----------\n", " `*args` : tuples of ints, or ints\n", " The shapes to be broadcast against each other.\n", " \n", " Returns\n", " -------\n", " tuple\n", " Broadcasted shape.\n", " \n", " Raises\n", " ------\n", " ValueError\n", " If the shapes are not compatible and cannot be broadcast according\n", " to NumPy's broadcasting rules.\n", " \n", " See Also\n", " --------\n", " broadcast\n", " broadcast_arrays\n", " broadcast_to\n", " \n", " Examples\n", " --------\n", " >>> np.broadcast_shapes((1, 2), (3, 1), (3, 2))\n", " (3, 2)\n", " \n", " >>> np.broadcast_shapes((6, 7), (5, 6, 1), (7,), (5, 1, 7))\n", " (5, 6, 7)\n", " \n", " broadcast_to(array, shape, subok=False)\n", " Broadcast an array to a new shape.\n", " \n", " Parameters\n", " ----------\n", " array : array_like\n", " The array to broadcast.\n", " shape : tuple or int\n", " The shape of the desired array. A single integer ``i`` is interpreted\n", " as ``(i,)``.\n", " subok : bool, optional\n", " If True, then sub-classes will be passed-through, otherwise\n", " the returned array will be forced to be a base-class array (default).\n", " \n", " Returns\n", " -------\n", " broadcast : array\n", " A readonly view on the original array with the given shape. It is\n", " typically not contiguous. Furthermore, more than one element of a\n", " broadcasted array may refer to a single memory location.\n", " \n", " Raises\n", " ------\n", " ValueError\n", " If the array is not compatible with the new shape according to NumPy's\n", " broadcasting rules.\n", " \n", " See Also\n", " --------\n", " broadcast\n", " broadcast_arrays\n", " broadcast_shapes\n", " \n", " Notes\n", " -----\n", " .. versionadded:: 1.10.0\n", " \n", " Examples\n", " --------\n", " >>> x = np.array([1, 2, 3])\n", " >>> np.broadcast_to(x, (3, 3))\n", " array([[1, 2, 3],\n", " [1, 2, 3],\n", " [1, 2, 3]])\n", " \n", " busday_count(...)\n", " busday_count(begindates, enddates, weekmask='1111100', holidays=[], busdaycal=None, out=None)\n", " \n", " Counts the number of valid days between `begindates` and\n", " `enddates`, not including the day of `enddates`.\n", " \n", " If ``enddates`` specifies a date value that is earlier than the\n", " corresponding ``begindates`` date value, the count will be negative.\n", " \n", " .. versionadded:: 1.7.0\n", " \n", " Parameters\n", " ----------\n", " begindates : array_like of datetime64[D]\n", " The array of the first dates for counting.\n", " enddates : array_like of datetime64[D]\n", " The array of the end dates for counting, which are excluded\n", " from the count themselves.\n", " weekmask : str or array_like of bool, optional\n", " A seven-element array indicating which of Monday through Sunday are\n", " valid days. May be specified as a length-seven list or array, like\n", " [1,1,1,1,1,0,0]; a length-seven string, like '1111100'; or a string\n", " like \"Mon Tue Wed Thu Fri\", made up of 3-character abbreviations for\n", " weekdays, optionally separated by white space. Valid abbreviations\n", " are: Mon Tue Wed Thu Fri Sat Sun\n", " holidays : array_like of datetime64[D], optional\n", " An array of dates to consider as invalid dates. They may be\n", " specified in any order, and NaT (not-a-time) dates are ignored.\n", " This list is saved in a normalized form that is suited for\n", " fast calculations of valid days.\n", " busdaycal : busdaycalendar, optional\n", " A `busdaycalendar` object which specifies the valid days. If this\n", " parameter is provided, neither weekmask nor holidays may be\n", " provided.\n", " out : array of int, optional\n", " If provided, this array is filled with the result.\n", " \n", " Returns\n", " -------\n", " out : array of int\n", " An array with a shape from broadcasting ``begindates`` and ``enddates``\n", " together, containing the number of valid days between\n", " the begin and end dates.\n", " \n", " See Also\n", " --------\n", " busdaycalendar : An object that specifies a custom set of valid days.\n", " is_busday : Returns a boolean array indicating valid days.\n", " busday_offset : Applies an offset counted in valid days.\n", " \n", " Examples\n", " --------\n", " >>> # Number of weekdays in January 2011\n", " ... np.busday_count('2011-01', '2011-02')\n", " 21\n", " >>> # Number of weekdays in 2011\n", " >>> np.busday_count('2011', '2012')\n", " 260\n", " >>> # Number of Saturdays in 2011\n", " ... np.busday_count('2011', '2012', weekmask='Sat')\n", " 53\n", " \n", " busday_offset(...)\n", " busday_offset(dates, offsets, roll='raise', weekmask='1111100', holidays=None, busdaycal=None, out=None)\n", " \n", " First adjusts the date to fall on a valid day according to\n", " the ``roll`` rule, then applies offsets to the given dates\n", " counted in valid days.\n", " \n", " .. versionadded:: 1.7.0\n", " \n", " Parameters\n", " ----------\n", " dates : array_like of datetime64[D]\n", " The array of dates to process.\n", " offsets : array_like of int\n", " The array of offsets, which is broadcast with ``dates``.\n", " roll : {'raise', 'nat', 'forward', 'following', 'backward', 'preceding', 'modifiedfollowing', 'modifiedpreceding'}, optional\n", " How to treat dates that do not fall on a valid day. The default\n", " is 'raise'.\n", " \n", " * 'raise' means to raise an exception for an invalid day.\n", " * 'nat' means to return a NaT (not-a-time) for an invalid day.\n", " * 'forward' and 'following' mean to take the first valid day\n", " later in time.\n", " * 'backward' and 'preceding' mean to take the first valid day\n", " earlier in time.\n", " * 'modifiedfollowing' means to take the first valid day\n", " later in time unless it is across a Month boundary, in which\n", " case to take the first valid day earlier in time.\n", " * 'modifiedpreceding' means to take the first valid day\n", " earlier in time unless it is across a Month boundary, in which\n", " case to take the first valid day later in time.\n", " weekmask : str or array_like of bool, optional\n", " A seven-element array indicating which of Monday through Sunday are\n", " valid days. May be specified as a length-seven list or array, like\n", " [1,1,1,1,1,0,0]; a length-seven string, like '1111100'; or a string\n", " like \"Mon Tue Wed Thu Fri\", made up of 3-character abbreviations for\n", " weekdays, optionally separated by white space. Valid abbreviations\n", " are: Mon Tue Wed Thu Fri Sat Sun\n", " holidays : array_like of datetime64[D], optional\n", " An array of dates to consider as invalid dates. They may be\n", " specified in any order, and NaT (not-a-time) dates are ignored.\n", " This list is saved in a normalized form that is suited for\n", " fast calculations of valid days.\n", " busdaycal : busdaycalendar, optional\n", " A `busdaycalendar` object which specifies the valid days. If this\n", " parameter is provided, neither weekmask nor holidays may be\n", " provided.\n", " out : array of datetime64[D], optional\n", " If provided, this array is filled with the result.\n", " \n", " Returns\n", " -------\n", " out : array of datetime64[D]\n", " An array with a shape from broadcasting ``dates`` and ``offsets``\n", " together, containing the dates with offsets applied.\n", " \n", " See Also\n", " --------\n", " busdaycalendar : An object that specifies a custom set of valid days.\n", " is_busday : Returns a boolean array indicating valid days.\n", " busday_count : Counts how many valid days are in a half-open date range.\n", " \n", " Examples\n", " --------\n", " >>> # First business day in October 2011 (not accounting for holidays)\n", " ... np.busday_offset('2011-10', 0, roll='forward')\n", " numpy.datetime64('2011-10-03')\n", " >>> # Last business day in February 2012 (not accounting for holidays)\n", " ... np.busday_offset('2012-03', -1, roll='forward')\n", " numpy.datetime64('2012-02-29')\n", " >>> # Third Wednesday in January 2011\n", " ... np.busday_offset('2011-01', 2, roll='forward', weekmask='Wed')\n", " numpy.datetime64('2011-01-19')\n", " >>> # 2012 Mother's Day in Canada and the U.S.\n", " ... np.busday_offset('2012-05', 1, roll='forward', weekmask='Sun')\n", " numpy.datetime64('2012-05-13')\n", " \n", " >>> # First business day on or after a date\n", " ... np.busday_offset('2011-03-20', 0, roll='forward')\n", " numpy.datetime64('2011-03-21')\n", " >>> np.busday_offset('2011-03-22', 0, roll='forward')\n", " numpy.datetime64('2011-03-22')\n", " >>> # First business day after a date\n", " ... np.busday_offset('2011-03-20', 1, roll='backward')\n", " numpy.datetime64('2011-03-21')\n", " >>> np.busday_offset('2011-03-22', 1, roll='backward')\n", " numpy.datetime64('2011-03-23')\n", " \n", " byte_bounds(a)\n", " Returns pointers to the end-points of an array.\n", " \n", " Parameters\n", " ----------\n", " a : ndarray\n", " Input array. It must conform to the Python-side of the array\n", " interface.\n", " \n", " Returns\n", " -------\n", " (low, high) : tuple of 2 integers\n", " The first integer is the first byte of the array, the second\n", " integer is just past the last byte of the array. If `a` is not\n", " contiguous it will not use every byte between the (`low`, `high`)\n", " values.\n", " \n", " Examples\n", " --------\n", " >>> I = np.eye(2, dtype='f'); I.dtype\n", " dtype('float32')\n", " >>> low, high = np.byte_bounds(I)\n", " >>> high - low == I.size*I.itemsize\n", " True\n", " >>> I = np.eye(2); I.dtype\n", " dtype('float64')\n", " >>> low, high = np.byte_bounds(I)\n", " >>> high - low == I.size*I.itemsize\n", " True\n", " \n", " can_cast(...)\n", " can_cast(from_, to, casting='safe')\n", " \n", " Returns True if cast between data types can occur according to the\n", " casting rule. If from is a scalar or array scalar, also returns\n", " True if the scalar value can be cast without overflow or truncation\n", " to an integer.\n", " \n", " Parameters\n", " ----------\n", " from_ : dtype, dtype specifier, scalar, or array\n", " Data type, scalar, or array to cast from.\n", " to : dtype or dtype specifier\n", " Data type to cast to.\n", " casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional\n", " Controls what kind of data casting may occur.\n", " \n", " * 'no' means the data types should not be cast at all.\n", " * 'equiv' means only byte-order changes are allowed.\n", " * 'safe' means only casts which can preserve values are allowed.\n", " * 'same_kind' means only safe casts or casts within a kind,\n", " like float64 to float32, are allowed.\n", " * 'unsafe' means any data conversions may be done.\n", " \n", " Returns\n", " -------\n", " out : bool\n", " True if cast can occur according to the casting rule.\n", " \n", " Notes\n", " -----\n", " .. versionchanged:: 1.17.0\n", " Casting between a simple data type and a structured one is possible only\n", " for \"unsafe\" casting. Casting to multiple fields is allowed, but\n", " casting from multiple fields is not.\n", " \n", " .. versionchanged:: 1.9.0\n", " Casting from numeric to string types in 'safe' casting mode requires\n", " that the string dtype length is long enough to store the maximum\n", " integer/float value converted.\n", " \n", " See also\n", " --------\n", " dtype, result_type\n", " \n", " Examples\n", " --------\n", " Basic examples\n", " \n", " >>> np.can_cast(np.int32, np.int64)\n", " True\n", " >>> np.can_cast(np.float64, complex)\n", " True\n", " >>> np.can_cast(complex, float)\n", " False\n", " \n", " >>> np.can_cast('i8', 'f8')\n", " True\n", " >>> np.can_cast('i8', 'f4')\n", " False\n", " >>> np.can_cast('i4', 'S4')\n", " False\n", " \n", " Casting scalars\n", " \n", " >>> np.can_cast(100, 'i1')\n", " True\n", " >>> np.can_cast(150, 'i1')\n", " False\n", " >>> np.can_cast(150, 'u1')\n", " True\n", " \n", " >>> np.can_cast(3.5e100, np.float32)\n", " False\n", " >>> np.can_cast(1000.0, np.float32)\n", " True\n", " \n", " Array scalar checks the value, array does not\n", " \n", " >>> np.can_cast(np.array(1000.0), np.float32)\n", " True\n", " >>> np.can_cast(np.array([1000.0]), np.float32)\n", " False\n", " \n", " Using the casting rules\n", " \n", " >>> np.can_cast('i8', 'i8', 'no')\n", " True\n", " >>> np.can_cast('<i8', '>i8', 'no')\n", " False\n", " \n", " >>> np.can_cast('<i8', '>i8', 'equiv')\n", " True\n", " >>> np.can_cast('<i4', '>i8', 'equiv')\n", " False\n", " \n", " >>> np.can_cast('<i4', '>i8', 'safe')\n", " True\n", " >>> np.can_cast('<i8', '>i4', 'safe')\n", " False\n", " \n", " >>> np.can_cast('<i8', '>i4', 'same_kind')\n", " True\n", " >>> np.can_cast('<i8', '>u4', 'same_kind')\n", " False\n", " \n", " >>> np.can_cast('<i8', '>u4', 'unsafe')\n", " True\n", " \n", " choose(a, choices, out=None, mode='raise')\n", " Construct an array from an index array and a list of arrays to choose from.\n", " \n", " First of all, if confused or uncertain, definitely look at the Examples -\n", " in its full generality, this function is less simple than it might\n", " seem from the following code description (below ndi =\n", " `numpy.lib.index_tricks`):\n", " \n", " ``np.choose(a,c) == np.array([c[a[I]][I] for I in ndi.ndindex(a.shape)])``.\n", " \n", " But this omits some subtleties. Here is a fully general summary:\n", " \n", " Given an \"index\" array (`a`) of integers and a sequence of ``n`` arrays\n", " (`choices`), `a` and each choice array are first broadcast, as necessary,\n", " to arrays of a common shape; calling these *Ba* and *Bchoices[i], i =\n", " 0,...,n-1* we have that, necessarily, ``Ba.shape == Bchoices[i].shape``\n", " for each ``i``. Then, a new array with shape ``Ba.shape`` is created as\n", " follows:\n", " \n", " * if ``mode='raise'`` (the default), then, first of all, each element of\n", " ``a`` (and thus ``Ba``) must be in the range ``[0, n-1]``; now, suppose\n", " that ``i`` (in that range) is the value at the ``(j0, j1, ..., jm)``\n", " position in ``Ba`` - then the value at the same position in the new array\n", " is the value in ``Bchoices[i]`` at that same position;\n", " \n", " * if ``mode='wrap'``, values in `a` (and thus `Ba`) may be any (signed)\n", " integer; modular arithmetic is used to map integers outside the range\n", " `[0, n-1]` back into that range; and then the new array is constructed\n", " as above;\n", " \n", " * if ``mode='clip'``, values in `a` (and thus ``Ba``) may be any (signed)\n", " integer; negative integers are mapped to 0; values greater than ``n-1``\n", " are mapped to ``n-1``; and then the new array is constructed as above.\n", " \n", " Parameters\n", " ----------\n", " a : int array\n", " This array must contain integers in ``[0, n-1]``, where ``n`` is the\n", " number of choices, unless ``mode=wrap`` or ``mode=clip``, in which\n", " cases any integers are permissible.\n", " choices : sequence of arrays\n", " Choice arrays. `a` and all of the choices must be broadcastable to the\n", " same shape. If `choices` is itself an array (not recommended), then\n", " its outermost dimension (i.e., the one corresponding to\n", " ``choices.shape[0]``) is taken as defining the \"sequence\".\n", " out : array, optional\n", " If provided, the result will be inserted into this array. It should\n", " be of the appropriate shape and dtype. Note that `out` is always\n", " buffered if ``mode='raise'``; use other modes for better performance.\n", " mode : {'raise' (default), 'wrap', 'clip'}, optional\n", " Specifies how indices outside ``[0, n-1]`` will be treated:\n", " \n", " * 'raise' : an exception is raised\n", " * 'wrap' : value becomes value mod ``n``\n", " * 'clip' : values < 0 are mapped to 0, values > n-1 are mapped to n-1\n", " \n", " Returns\n", " -------\n", " merged_array : array\n", " The merged result.\n", " \n", " Raises\n", " ------\n", " ValueError: shape mismatch\n", " If `a` and each choice array are not all broadcastable to the same\n", " shape.\n", " \n", " See Also\n", " --------\n", " ndarray.choose : equivalent method\n", " numpy.take_along_axis : Preferable if `choices` is an array\n", " \n", " Notes\n", " -----\n", " To reduce the chance of misinterpretation, even though the following\n", " \"abuse\" is nominally supported, `choices` should neither be, nor be\n", " thought of as, a single array, i.e., the outermost sequence-like container\n", " should be either a list or a tuple.\n", " \n", " Examples\n", " --------\n", " \n", " >>> choices = [[0, 1, 2, 3], [10, 11, 12, 13],\n", " ... [20, 21, 22, 23], [30, 31, 32, 33]]\n", " >>> np.choose([2, 3, 1, 0], choices\n", " ... # the first element of the result will be the first element of the\n", " ... # third (2+1) \"array\" in choices, namely, 20; the second element\n", " ... # will be the second element of the fourth (3+1) choice array, i.e.,\n", " ... # 31, etc.\n", " ... )\n", " array([20, 31, 12, 3])\n", " >>> np.choose([2, 4, 1, 0], choices, mode='clip') # 4 goes to 3 (4-1)\n", " array([20, 31, 12, 3])\n", " >>> # because there are 4 choice arrays\n", " >>> np.choose([2, 4, 1, 0], choices, mode='wrap') # 4 goes to (4 mod 4)\n", " array([20, 1, 12, 3])\n", " >>> # i.e., 0\n", " \n", " A couple examples illustrating how choose broadcasts:\n", " \n", " >>> a = [[1, 0, 1], [0, 1, 0], [1, 0, 1]]\n", " >>> choices = [-10, 10]\n", " >>> np.choose(a, choices)\n", " array([[ 10, -10, 10],\n", " [-10, 10, -10],\n", " [ 10, -10, 10]])\n", " \n", " >>> # With thanks to Anne Archibald\n", " >>> a = np.array([0, 1]).reshape((2,1,1))\n", " >>> c1 = np.array([1, 2, 3]).reshape((1,3,1))\n", " >>> c2 = np.array([-1, -2, -3, -4, -5]).reshape((1,1,5))\n", " >>> np.choose(a, (c1, c2)) # result is 2x3x5, res[0,:,:]=c1, res[1,:,:]=c2\n", " array([[[ 1, 1, 1, 1, 1],\n", " [ 2, 2, 2, 2, 2],\n", " [ 3, 3, 3, 3, 3]],\n", " [[-1, -2, -3, -4, -5],\n", " [-1, -2, -3, -4, -5],\n", " [-1, -2, -3, -4, -5]]])\n", " \n", " clip(a, a_min, a_max, out=None, **kwargs)\n", " Clip (limit) the values in an array.\n", " \n", " Given an interval, values outside the interval are clipped to\n", " the interval edges. For example, if an interval of ``[0, 1]``\n", " is specified, values smaller than 0 become 0, and values larger\n", " than 1 become 1.\n", " \n", " Equivalent to but faster than ``np.minimum(a_max, np.maximum(a, a_min))``.\n", " \n", " No check is performed to ensure ``a_min < a_max``.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Array containing elements to clip.\n", " a_min, a_max : array_like or None\n", " Minimum and maximum value. If ``None``, clipping is not performed on\n", " the corresponding edge. Only one of `a_min` and `a_max` may be\n", " ``None``. Both are broadcast against `a`.\n", " out : ndarray, optional\n", " The results will be placed in this array. It may be the input\n", " array for in-place clipping. `out` must be of the right shape\n", " to hold the output. Its type is preserved.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " .. versionadded:: 1.17.0\n", " \n", " Returns\n", " -------\n", " clipped_array : ndarray\n", " An array with the elements of `a`, but where values\n", " < `a_min` are replaced with `a_min`, and those > `a_max`\n", " with `a_max`.\n", " \n", " See Also\n", " --------\n", " :ref:`ufuncs-output-type`\n", " \n", " Notes\n", " -----\n", " When `a_min` is greater than `a_max`, `clip` returns an\n", " array in which all values are equal to `a_max`,\n", " as shown in the second example.\n", " \n", " Examples\n", " --------\n", " >>> a = np.arange(10)\n", " >>> a\n", " array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])\n", " >>> np.clip(a, 1, 8)\n", " array([1, 1, 2, 3, 4, 5, 6, 7, 8, 8])\n", " >>> np.clip(a, 8, 1)\n", " array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1])\n", " >>> np.clip(a, 3, 6, out=a)\n", " array([3, 3, 3, 3, 4, 5, 6, 6, 6, 6])\n", " >>> a\n", " array([3, 3, 3, 3, 4, 5, 6, 6, 6, 6])\n", " >>> a = np.arange(10)\n", " >>> a\n", " array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])\n", " >>> np.clip(a, [3, 4, 1, 1, 1, 4, 4, 4, 4, 4], 8)\n", " array([3, 4, 2, 3, 4, 5, 6, 7, 8, 8])\n", " \n", " column_stack(tup)\n", " Stack 1-D arrays as columns into a 2-D array.\n", " \n", " Take a sequence of 1-D arrays and stack them as columns\n", " to make a single 2-D array. 2-D arrays are stacked as-is,\n", " just like with `hstack`. 1-D arrays are turned into 2-D columns\n", " first.\n", " \n", " Parameters\n", " ----------\n", " tup : sequence of 1-D or 2-D arrays.\n", " Arrays to stack. All of them must have the same first dimension.\n", " \n", " Returns\n", " -------\n", " stacked : 2-D array\n", " The array formed by stacking the given arrays.\n", " \n", " See Also\n", " --------\n", " stack, hstack, vstack, concatenate\n", " \n", " Examples\n", " --------\n", " >>> a = np.array((1,2,3))\n", " >>> b = np.array((2,3,4))\n", " >>> np.column_stack((a,b))\n", " array([[1, 2],\n", " [2, 3],\n", " [3, 4]])\n", " \n", " common_type(*arrays)\n", " Return a scalar type which is common to the input arrays.\n", " \n", " The return type will always be an inexact (i.e. floating point) scalar\n", " type, even if all the arrays are integer arrays. If one of the inputs is\n", " an integer array, the minimum precision type that is returned is a\n", " 64-bit floating point dtype.\n", " \n", " All input arrays except int64 and uint64 can be safely cast to the\n", " returned dtype without loss of information.\n", " \n", " Parameters\n", " ----------\n", " array1, array2, ... : ndarrays\n", " Input arrays.\n", " \n", " Returns\n", " -------\n", " out : data type code\n", " Data type code.\n", " \n", " See Also\n", " --------\n", " dtype, mintypecode\n", " \n", " Examples\n", " --------\n", " >>> np.common_type(np.arange(2, dtype=np.float32))\n", " <class 'numpy.float32'>\n", " >>> np.common_type(np.arange(2, dtype=np.float32), np.arange(2))\n", " <class 'numpy.float64'>\n", " >>> np.common_type(np.arange(4), np.array([45, 6.j]), np.array([45.0]))\n", " <class 'numpy.complex128'>\n", " \n", " compare_chararrays(...)\n", " compare_chararrays(a1, a2, cmp, rstrip)\n", " \n", " Performs element-wise comparison of two string arrays using the\n", " comparison operator specified by `cmp_op`.\n", " \n", " Parameters\n", " ----------\n", " a1, a2 : array_like\n", " Arrays to be compared.\n", " cmp : {\"<\", \"<=\", \"==\", \">=\", \">\", \"!=\"}\n", " Type of comparison.\n", " rstrip : Boolean\n", " If True, the spaces at the end of Strings are removed before the comparison.\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " The output array of type Boolean with the same shape as a and b.\n", " \n", " Raises\n", " ------\n", " ValueError\n", " If `cmp_op` is not valid.\n", " TypeError\n", " If at least one of `a` or `b` is a non-string array\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([\"a\", \"b\", \"cde\"])\n", " >>> b = np.array([\"a\", \"a\", \"dec\"])\n", " >>> np.compare_chararrays(a, b, \">\", True)\n", " array([False, True, False])\n", " \n", " compress(condition, a, axis=None, out=None)\n", " Return selected slices of an array along given axis.\n", " \n", " When working along a given axis, a slice along that axis is returned in\n", " `output` for each index where `condition` evaluates to True. When\n", " working on a 1-D array, `compress` is equivalent to `extract`.\n", " \n", " Parameters\n", " ----------\n", " condition : 1-D array of bools\n", " Array that selects which entries to return. If len(condition)\n", " is less than the size of `a` along the given axis, then output is\n", " truncated to the length of the condition array.\n", " a : array_like\n", " Array from which to extract a part.\n", " axis : int, optional\n", " Axis along which to take slices. If None (default), work on the\n", " flattened array.\n", " out : ndarray, optional\n", " Output array. Its type is preserved and it must be of the right\n", " shape to hold the output.\n", " \n", " Returns\n", " -------\n", " compressed_array : ndarray\n", " A copy of `a` without the slices along axis for which `condition`\n", " is false.\n", " \n", " See Also\n", " --------\n", " take, choose, diag, diagonal, select\n", " ndarray.compress : Equivalent method in ndarray\n", " extract : Equivalent method when working on 1-D arrays\n", " :ref:`ufuncs-output-type`\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([[1, 2], [3, 4], [5, 6]])\n", " >>> a\n", " array([[1, 2],\n", " [3, 4],\n", " [5, 6]])\n", " >>> np.compress([0, 1], a, axis=0)\n", " array([[3, 4]])\n", " >>> np.compress([False, True, True], a, axis=0)\n", " array([[3, 4],\n", " [5, 6]])\n", " >>> np.compress([False, True], a, axis=1)\n", " array([[2],\n", " [4],\n", " [6]])\n", " \n", " Working on the flattened array does not return slices along an axis but\n", " selects elements.\n", " \n", " >>> np.compress([False, True], a)\n", " array([2])\n", " \n", " concatenate(...)\n", " concatenate((a1, a2, ...), axis=0, out=None, dtype=None, casting=\"same_kind\")\n", " \n", " Join a sequence of arrays along an existing axis.\n", " \n", " Parameters\n", " ----------\n", " a1, a2, ... : sequence of array_like\n", " The arrays must have the same shape, except in the dimension\n", " corresponding to `axis` (the first, by default).\n", " axis : int, optional\n", " The axis along which the arrays will be joined. If axis is None,\n", " arrays are flattened before use. Default is 0.\n", " out : ndarray, optional\n", " If provided, the destination to place the result. The shape must be\n", " correct, matching that of what concatenate would have returned if no\n", " out argument were specified.\n", " dtype : str or dtype\n", " If provided, the destination array will have this dtype. Cannot be\n", " provided together with `out`.\n", " \n", " .. versionadded:: 1.20.0\n", " \n", " casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional\n", " Controls what kind of data casting may occur. Defaults to 'same_kind'.\n", " \n", " .. versionadded:: 1.20.0\n", " \n", " Returns\n", " -------\n", " res : ndarray\n", " The concatenated array.\n", " \n", " See Also\n", " --------\n", " ma.concatenate : Concatenate function that preserves input masks.\n", " array_split : Split an array into multiple sub-arrays of equal or\n", " near-equal size.\n", " split : Split array into a list of multiple sub-arrays of equal size.\n", " hsplit : Split array into multiple sub-arrays horizontally (column wise).\n", " vsplit : Split array into multiple sub-arrays vertically (row wise).\n", " dsplit : Split array into multiple sub-arrays along the 3rd axis (depth).\n", " stack : Stack a sequence of arrays along a new axis.\n", " block : Assemble arrays from blocks.\n", " hstack : Stack arrays in sequence horizontally (column wise).\n", " vstack : Stack arrays in sequence vertically (row wise).\n", " dstack : Stack arrays in sequence depth wise (along third dimension).\n", " column_stack : Stack 1-D arrays as columns into a 2-D array.\n", " \n", " Notes\n", " -----\n", " When one or more of the arrays to be concatenated is a MaskedArray,\n", " this function will return a MaskedArray object instead of an ndarray,\n", " but the input masks are *not* preserved. In cases where a MaskedArray\n", " is expected as input, use the ma.concatenate function from the masked\n", " array module instead.\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([[1, 2], [3, 4]])\n", " >>> b = np.array([[5, 6]])\n", " >>> np.concatenate((a, b), axis=0)\n", " array([[1, 2],\n", " [3, 4],\n", " [5, 6]])\n", " >>> np.concatenate((a, b.T), axis=1)\n", " array([[1, 2, 5],\n", " [3, 4, 6]])\n", " >>> np.concatenate((a, b), axis=None)\n", " array([1, 2, 3, 4, 5, 6])\n", " \n", " This function will not preserve masking of MaskedArray inputs.\n", " \n", " >>> a = np.ma.arange(3)\n", " >>> a[1] = np.ma.masked\n", " >>> b = np.arange(2, 5)\n", " >>> a\n", " masked_array(data=[0, --, 2],\n", " mask=[False, True, False],\n", " fill_value=999999)\n", " >>> b\n", " array([2, 3, 4])\n", " >>> np.concatenate([a, b])\n", " masked_array(data=[0, 1, 2, 2, 3, 4],\n", " mask=False,\n", " fill_value=999999)\n", " >>> np.ma.concatenate([a, b])\n", " masked_array(data=[0, --, 2, 2, 3, 4],\n", " mask=[False, True, False, False, False, False],\n", " fill_value=999999)\n", " \n", " convolve(a, v, mode='full')\n", " Returns the discrete, linear convolution of two one-dimensional sequences.\n", " \n", " The convolution operator is often seen in signal processing, where it\n", " models the effect of a linear time-invariant system on a signal [1]_. In\n", " probability theory, the sum of two independent random variables is\n", " distributed according to the convolution of their individual\n", " distributions.\n", " \n", " If `v` is longer than `a`, the arrays are swapped before computation.\n", " \n", " Parameters\n", " ----------\n", " a : (N,) array_like\n", " First one-dimensional input array.\n", " v : (M,) array_like\n", " Second one-dimensional input array.\n", " mode : {'full', 'valid', 'same'}, optional\n", " 'full':\n", " By default, mode is 'full'. This returns the convolution\n", " at each point of overlap, with an output shape of (N+M-1,). At\n", " the end-points of the convolution, the signals do not overlap\n", " completely, and boundary effects may be seen.\n", " \n", " 'same':\n", " Mode 'same' returns output of length ``max(M, N)``. Boundary\n", " effects are still visible.\n", " \n", " 'valid':\n", " Mode 'valid' returns output of length\n", " ``max(M, N) - min(M, N) + 1``. The convolution product is only given\n", " for points where the signals overlap completely. Values outside\n", " the signal boundary have no effect.\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " Discrete, linear convolution of `a` and `v`.\n", " \n", " See Also\n", " --------\n", " scipy.signal.fftconvolve : Convolve two arrays using the Fast Fourier\n", " Transform.\n", " scipy.linalg.toeplitz : Used to construct the convolution operator.\n", " polymul : Polynomial multiplication. Same output as convolve, but also\n", " accepts poly1d objects as input.\n", " \n", " Notes\n", " -----\n", " The discrete convolution operation is defined as\n", " \n", " .. math:: (a * v)_n = \\sum_{m = -\\infty}^{\\infty} a_m v_{n - m}\n", " \n", " It can be shown that a convolution :math:`x(t) * y(t)` in time/space\n", " is equivalent to the multiplication :math:`X(f) Y(f)` in the Fourier\n", " domain, after appropriate padding (padding is necessary to prevent\n", " circular convolution). Since multiplication is more efficient (faster)\n", " than convolution, the function `scipy.signal.fftconvolve` exploits the\n", " FFT to calculate the convolution of large data-sets.\n", " \n", " References\n", " ----------\n", " .. [1] Wikipedia, \"Convolution\",\n", " https://en.wikipedia.org/wiki/Convolution\n", " \n", " Examples\n", " --------\n", " Note how the convolution operator flips the second array\n", " before \"sliding\" the two across one another:\n", " \n", " >>> np.convolve([1, 2, 3], [0, 1, 0.5])\n", " array([0. , 1. , 2.5, 4. , 1.5])\n", " \n", " Only return the middle values of the convolution.\n", " Contains boundary effects, where zeros are taken\n", " into account:\n", " \n", " >>> np.convolve([1,2,3],[0,1,0.5], 'same')\n", " array([1. , 2.5, 4. ])\n", " \n", " The two arrays are of the same length, so there\n", " is only one position where they completely overlap:\n", " \n", " >>> np.convolve([1,2,3],[0,1,0.5], 'valid')\n", " array([2.5])\n", " \n", " copy(a, order='K', subok=False)\n", " Return an array copy of the given object.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input data.\n", " order : {'C', 'F', 'A', 'K'}, optional\n", " Controls the memory layout of the copy. 'C' means C-order,\n", " 'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous,\n", " 'C' otherwise. 'K' means match the layout of `a` as closely\n", " as possible. (Note that this function and :meth:`ndarray.copy` are very\n", " similar, but have different default values for their order=\n", " arguments.)\n", " subok : bool, optional\n", " If True, then sub-classes will be passed-through, otherwise the\n", " returned array will be forced to be a base-class array (defaults to False).\n", " \n", " .. versionadded:: 1.19.0\n", " \n", " Returns\n", " -------\n", " arr : ndarray\n", " Array interpretation of `a`.\n", " \n", " See Also\n", " --------\n", " ndarray.copy : Preferred method for creating an array copy\n", " \n", " Notes\n", " -----\n", " This is equivalent to:\n", " \n", " >>> np.array(a, copy=True) #doctest: +SKIP\n", " \n", " Examples\n", " --------\n", " Create an array x, with a reference y and a copy z:\n", " \n", " >>> x = np.array([1, 2, 3])\n", " >>> y = x\n", " >>> z = np.copy(x)\n", " \n", " Note that, when we modify x, y changes, but not z:\n", " \n", " >>> x[0] = 10\n", " >>> x[0] == y[0]\n", " True\n", " >>> x[0] == z[0]\n", " False\n", " \n", " Note that, np.copy clears previously set WRITEABLE=False flag.\n", " \n", " >>> a = np.array([1, 2, 3])\n", " >>> a.flags[\"WRITEABLE\"] = False\n", " >>> b = np.copy(a)\n", " >>> b.flags[\"WRITEABLE\"]\n", " True\n", " >>> b[0] = 3\n", " >>> b\n", " array([3, 2, 3])\n", " \n", " Note that np.copy is a shallow copy and will not copy object\n", " elements within arrays. This is mainly important for arrays\n", " containing Python objects. The new array will contain the\n", " same object which may lead to surprises if that object can\n", " be modified (is mutable):\n", " \n", " >>> a = np.array([1, 'm', [2, 3, 4]], dtype=object)\n", " >>> b = np.copy(a)\n", " >>> b[2][0] = 10\n", " >>> a\n", " array([1, 'm', list([10, 3, 4])], dtype=object)\n", " \n", " To ensure all elements within an ``object`` array are copied,\n", " use `copy.deepcopy`:\n", " \n", " >>> import copy\n", " >>> a = np.array([1, 'm', [2, 3, 4]], dtype=object)\n", " >>> c = copy.deepcopy(a)\n", " >>> c[2][0] = 10\n", " >>> c\n", " array([1, 'm', list([10, 3, 4])], dtype=object)\n", " >>> a\n", " array([1, 'm', list([2, 3, 4])], dtype=object)\n", " \n", " copyto(...)\n", " copyto(dst, src, casting='same_kind', where=True)\n", " \n", " Copies values from one array to another, broadcasting as necessary.\n", " \n", " Raises a TypeError if the `casting` rule is violated, and if\n", " `where` is provided, it selects which elements to copy.\n", " \n", " .. versionadded:: 1.7.0\n", " \n", " Parameters\n", " ----------\n", " dst : ndarray\n", " The array into which values are copied.\n", " src : array_like\n", " The array from which values are copied.\n", " casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional\n", " Controls what kind of data casting may occur when copying.\n", " \n", " * 'no' means the data types should not be cast at all.\n", " * 'equiv' means only byte-order changes are allowed.\n", " * 'safe' means only casts which can preserve values are allowed.\n", " * 'same_kind' means only safe casts or casts within a kind,\n", " like float64 to float32, are allowed.\n", " * 'unsafe' means any data conversions may be done.\n", " where : array_like of bool, optional\n", " A boolean array which is broadcasted to match the dimensions\n", " of `dst`, and selects elements to copy from `src` to `dst`\n", " wherever it contains the value True.\n", " \n", " Examples\n", " --------\n", " >>> A = np.array([4, 5, 6])\n", " >>> B = [1, 2, 3]\n", " >>> np.copyto(A, B)\n", " >>> A\n", " array([1, 2, 3])\n", " \n", " >>> A = np.array([[1, 2, 3], [4, 5, 6]])\n", " >>> B = [[4, 5, 6], [7, 8, 9]]\n", " >>> np.copyto(A, B)\n", " >>> A\n", " array([[4, 5, 6],\n", " [7, 8, 9]])\n", " \n", " corrcoef(x, y=None, rowvar=True, bias=<no value>, ddof=<no value>, *, dtype=None)\n", " Return Pearson product-moment correlation coefficients.\n", " \n", " Please refer to the documentation for `cov` for more detail. The\n", " relationship between the correlation coefficient matrix, `R`, and the\n", " covariance matrix, `C`, is\n", " \n", " .. math:: R_{ij} = \\frac{ C_{ij} } { \\sqrt{ C_{ii} C_{jj} } }\n", " \n", " The values of `R` are between -1 and 1, inclusive.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " A 1-D or 2-D array containing multiple variables and observations.\n", " Each row of `x` represents a variable, and each column a single\n", " observation of all those variables. Also see `rowvar` below.\n", " y : array_like, optional\n", " An additional set of variables and observations. `y` has the same\n", " shape as `x`.\n", " rowvar : bool, optional\n", " If `rowvar` is True (default), then each row represents a\n", " variable, with observations in the columns. Otherwise, the relationship\n", " is transposed: each column represents a variable, while the rows\n", " contain observations.\n", " bias : _NoValue, optional\n", " Has no effect, do not use.\n", " \n", " .. deprecated:: 1.10.0\n", " ddof : _NoValue, optional\n", " Has no effect, do not use.\n", " \n", " .. deprecated:: 1.10.0\n", " dtype : data-type, optional\n", " Data-type of the result. By default, the return data-type will have\n", " at least `numpy.float64` precision.\n", " \n", " .. versionadded:: 1.20\n", " \n", " Returns\n", " -------\n", " R : ndarray\n", " The correlation coefficient matrix of the variables.\n", " \n", " See Also\n", " --------\n", " cov : Covariance matrix\n", " \n", " Notes\n", " -----\n", " Due to floating point rounding the resulting array may not be Hermitian,\n", " the diagonal elements may not be 1, and the elements may not satisfy the\n", " inequality abs(a) <= 1. The real and imaginary parts are clipped to the\n", " interval [-1, 1] in an attempt to improve on that situation but is not\n", " much help in the complex case.\n", " \n", " This function accepts but discards arguments `bias` and `ddof`. This is\n", " for backwards compatibility with previous versions of this function. These\n", " arguments had no effect on the return values of the function and can be\n", " safely ignored in this and previous versions of numpy.\n", " \n", " Examples\n", " --------\n", " In this example we generate two random arrays, ``xarr`` and ``yarr``, and\n", " compute the row-wise and column-wise Pearson correlation coefficients,\n", " ``R``. Since ``rowvar`` is true by default, we first find the row-wise\n", " Pearson correlation coefficients between the variables of ``xarr``.\n", " \n", " >>> import numpy as np\n", " >>> rng = np.random.default_rng(seed=42)\n", " >>> xarr = rng.random((3, 3))\n", " >>> xarr\n", " array([[0.77395605, 0.43887844, 0.85859792],\n", " [0.69736803, 0.09417735, 0.97562235],\n", " [0.7611397 , 0.78606431, 0.12811363]])\n", " >>> R1 = np.corrcoef(xarr)\n", " >>> R1\n", " array([[ 1. , 0.99256089, -0.68080986],\n", " [ 0.99256089, 1. , -0.76492172],\n", " [-0.68080986, -0.76492172, 1. ]])\n", " \n", " If we add another set of variables and observations ``yarr``, we can\n", " compute the row-wise Pearson correlation coefficients between the\n", " variables in ``xarr`` and ``yarr``.\n", " \n", " >>> yarr = rng.random((3, 3))\n", " >>> yarr\n", " array([[0.45038594, 0.37079802, 0.92676499],\n", " [0.64386512, 0.82276161, 0.4434142 ],\n", " [0.22723872, 0.55458479, 0.06381726]])\n", " >>> R2 = np.corrcoef(xarr, yarr)\n", " >>> R2\n", " array([[ 1. , 0.99256089, -0.68080986, 0.75008178, -0.934284 ,\n", " -0.99004057],\n", " [ 0.99256089, 1. , -0.76492172, 0.82502011, -0.97074098,\n", " -0.99981569],\n", " [-0.68080986, -0.76492172, 1. , -0.99507202, 0.89721355,\n", " 0.77714685],\n", " [ 0.75008178, 0.82502011, -0.99507202, 1. , -0.93657855,\n", " -0.83571711],\n", " [-0.934284 , -0.97074098, 0.89721355, -0.93657855, 1. ,\n", " 0.97517215],\n", " [-0.99004057, -0.99981569, 0.77714685, -0.83571711, 0.97517215,\n", " 1. ]])\n", " \n", " Finally if we use the option ``rowvar=False``, the columns are now\n", " being treated as the variables and we will find the column-wise Pearson\n", " correlation coefficients between variables in ``xarr`` and ``yarr``.\n", " \n", " >>> R3 = np.corrcoef(xarr, yarr, rowvar=False)\n", " >>> R3\n", " array([[ 1. , 0.77598074, -0.47458546, -0.75078643, -0.9665554 ,\n", " 0.22423734],\n", " [ 0.77598074, 1. , -0.92346708, -0.99923895, -0.58826587,\n", " -0.44069024],\n", " [-0.47458546, -0.92346708, 1. , 0.93773029, 0.23297648,\n", " 0.75137473],\n", " [-0.75078643, -0.99923895, 0.93773029, 1. , 0.55627469,\n", " 0.47536961],\n", " [-0.9665554 , -0.58826587, 0.23297648, 0.55627469, 1. ,\n", " -0.46666491],\n", " [ 0.22423734, -0.44069024, 0.75137473, 0.47536961, -0.46666491,\n", " 1. ]])\n", " \n", " correlate(a, v, mode='valid')\n", " Cross-correlation of two 1-dimensional sequences.\n", " \n", " This function computes the correlation as generally defined in signal\n", " processing texts:\n", " \n", " .. math:: c_k = \\sum_n a_{n+k} \\cdot \\overline{v}_n\n", " \n", " with a and v sequences being zero-padded where necessary and\n", " :math:`\\overline x` denoting complex conjugation.\n", " \n", " Parameters\n", " ----------\n", " a, v : array_like\n", " Input sequences.\n", " mode : {'valid', 'same', 'full'}, optional\n", " Refer to the `convolve` docstring. Note that the default\n", " is 'valid', unlike `convolve`, which uses 'full'.\n", " old_behavior : bool\n", " `old_behavior` was removed in NumPy 1.10. If you need the old\n", " behavior, use `multiarray.correlate`.\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " Discrete cross-correlation of `a` and `v`.\n", " \n", " See Also\n", " --------\n", " convolve : Discrete, linear convolution of two one-dimensional sequences.\n", " multiarray.correlate : Old, no conjugate, version of correlate.\n", " scipy.signal.correlate : uses FFT which has superior performance on large arrays. \n", " \n", " Notes\n", " -----\n", " The definition of correlation above is not unique and sometimes correlation\n", " may be defined differently. Another common definition is:\n", " \n", " .. math:: c'_k = \\sum_n a_{n} \\cdot \\overline{v_{n+k}}\n", " \n", " which is related to :math:`c_k` by :math:`c'_k = c_{-k}`.\n", " \n", " `numpy.correlate` may perform slowly in large arrays (i.e. n = 1e5) because it does\n", " not use the FFT to compute the convolution; in that case, `scipy.signal.correlate` might\n", " be preferable.\n", " \n", " \n", " Examples\n", " --------\n", " >>> np.correlate([1, 2, 3], [0, 1, 0.5])\n", " array([3.5])\n", " >>> np.correlate([1, 2, 3], [0, 1, 0.5], \"same\")\n", " array([2. , 3.5, 3. ])\n", " >>> np.correlate([1, 2, 3], [0, 1, 0.5], \"full\")\n", " array([0.5, 2. , 3.5, 3. , 0. ])\n", " \n", " Using complex sequences:\n", " \n", " >>> np.correlate([1+1j, 2, 3-1j], [0, 1, 0.5j], 'full')\n", " array([ 0.5-0.5j, 1.0+0.j , 1.5-1.5j, 3.0-1.j , 0.0+0.j ])\n", " \n", " Note that you get the time reversed, complex conjugated result\n", " (:math:`\\overline{c_{-k}}`) when the two input sequences a and v change \n", " places:\n", " \n", " >>> np.correlate([0, 1, 0.5j], [1+1j, 2, 3-1j], 'full')\n", " array([ 0.0+0.j , 3.0+1.j , 1.5+1.5j, 1.0+0.j , 0.5+0.5j])\n", " \n", " count_nonzero(a, axis=None, *, keepdims=False)\n", " Counts the number of non-zero values in the array ``a``.\n", " \n", " The word \"non-zero\" is in reference to the Python 2.x\n", " built-in method ``__nonzero__()`` (renamed ``__bool__()``\n", " in Python 3.x) of Python objects that tests an object's\n", " \"truthfulness\". For example, any number is considered\n", " truthful if it is nonzero, whereas any string is considered\n", " truthful if it is not the empty string. Thus, this function\n", " (recursively) counts how many elements in ``a`` (and in\n", " sub-arrays thereof) have their ``__nonzero__()`` or ``__bool__()``\n", " method evaluated to ``True``.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " The array for which to count non-zeros.\n", " axis : int or tuple, optional\n", " Axis or tuple of axes along which to count non-zeros.\n", " Default is None, meaning that non-zeros will be counted\n", " along a flattened version of ``a``.\n", " \n", " .. versionadded:: 1.12.0\n", " \n", " keepdims : bool, optional\n", " If this is set to True, the axes that are counted are left\n", " in the result as dimensions with size one. With this option,\n", " the result will broadcast correctly against the input array.\n", " \n", " .. versionadded:: 1.19.0\n", " \n", " Returns\n", " -------\n", " count : int or array of int\n", " Number of non-zero values in the array along a given axis.\n", " Otherwise, the total number of non-zero values in the array\n", " is returned.\n", " \n", " See Also\n", " --------\n", " nonzero : Return the coordinates of all the non-zero values.\n", " \n", " Examples\n", " --------\n", " >>> np.count_nonzero(np.eye(4))\n", " 4\n", " >>> a = np.array([[0, 1, 7, 0],\n", " ... [3, 0, 2, 19]])\n", " >>> np.count_nonzero(a)\n", " 5\n", " >>> np.count_nonzero(a, axis=0)\n", " array([1, 1, 2, 1])\n", " >>> np.count_nonzero(a, axis=1)\n", " array([2, 3])\n", " >>> np.count_nonzero(a, axis=1, keepdims=True)\n", " array([[2],\n", " [3]])\n", " \n", " cov(m, y=None, rowvar=True, bias=False, ddof=None, fweights=None, aweights=None, *, dtype=None)\n", " Estimate a covariance matrix, given data and weights.\n", " \n", " Covariance indicates the level to which two variables vary together.\n", " If we examine N-dimensional samples, :math:`X = [x_1, x_2, ... x_N]^T`,\n", " then the covariance matrix element :math:`C_{ij}` is the covariance of\n", " :math:`x_i` and :math:`x_j`. The element :math:`C_{ii}` is the variance\n", " of :math:`x_i`.\n", " \n", " See the notes for an outline of the algorithm.\n", " \n", " Parameters\n", " ----------\n", " m : array_like\n", " A 1-D or 2-D array containing multiple variables and observations.\n", " Each row of `m` represents a variable, and each column a single\n", " observation of all those variables. Also see `rowvar` below.\n", " y : array_like, optional\n", " An additional set of variables and observations. `y` has the same form\n", " as that of `m`.\n", " rowvar : bool, optional\n", " If `rowvar` is True (default), then each row represents a\n", " variable, with observations in the columns. Otherwise, the relationship\n", " is transposed: each column represents a variable, while the rows\n", " contain observations.\n", " bias : bool, optional\n", " Default normalization (False) is by ``(N - 1)``, where ``N`` is the\n", " number of observations given (unbiased estimate). If `bias` is True,\n", " then normalization is by ``N``. These values can be overridden by using\n", " the keyword ``ddof`` in numpy versions >= 1.5.\n", " ddof : int, optional\n", " If not ``None`` the default value implied by `bias` is overridden.\n", " Note that ``ddof=1`` will return the unbiased estimate, even if both\n", " `fweights` and `aweights` are specified, and ``ddof=0`` will return\n", " the simple average. See the notes for the details. The default value\n", " is ``None``.\n", " \n", " .. versionadded:: 1.5\n", " fweights : array_like, int, optional\n", " 1-D array of integer frequency weights; the number of times each\n", " observation vector should be repeated.\n", " \n", " .. versionadded:: 1.10\n", " aweights : array_like, optional\n", " 1-D array of observation vector weights. These relative weights are\n", " typically large for observations considered \"important\" and smaller for\n", " observations considered less \"important\". If ``ddof=0`` the array of\n", " weights can be used to assign probabilities to observation vectors.\n", " \n", " .. versionadded:: 1.10\n", " dtype : data-type, optional\n", " Data-type of the result. By default, the return data-type will have\n", " at least `numpy.float64` precision.\n", " \n", " .. versionadded:: 1.20\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " The covariance matrix of the variables.\n", " \n", " See Also\n", " --------\n", " corrcoef : Normalized covariance matrix\n", " \n", " Notes\n", " -----\n", " Assume that the observations are in the columns of the observation\n", " array `m` and let ``f = fweights`` and ``a = aweights`` for brevity. The\n", " steps to compute the weighted covariance are as follows::\n", " \n", " >>> m = np.arange(10, dtype=np.float64)\n", " >>> f = np.arange(10) * 2\n", " >>> a = np.arange(10) ** 2.\n", " >>> ddof = 1\n", " >>> w = f * a\n", " >>> v1 = np.sum(w)\n", " >>> v2 = np.sum(w * a)\n", " >>> m -= np.sum(m * w, axis=None, keepdims=True) / v1\n", " >>> cov = np.dot(m * w, m.T) * v1 / (v1**2 - ddof * v2)\n", " \n", " Note that when ``a == 1``, the normalization factor\n", " ``v1 / (v1**2 - ddof * v2)`` goes over to ``1 / (np.sum(f) - ddof)``\n", " as it should.\n", " \n", " Examples\n", " --------\n", " Consider two variables, :math:`x_0` and :math:`x_1`, which\n", " correlate perfectly, but in opposite directions:\n", " \n", " >>> x = np.array([[0, 2], [1, 1], [2, 0]]).T\n", " >>> x\n", " array([[0, 1, 2],\n", " [2, 1, 0]])\n", " \n", " Note how :math:`x_0` increases while :math:`x_1` decreases. The covariance\n", " matrix shows this clearly:\n", " \n", " >>> np.cov(x)\n", " array([[ 1., -1.],\n", " [-1., 1.]])\n", " \n", " Note that element :math:`C_{0,1}`, which shows the correlation between\n", " :math:`x_0` and :math:`x_1`, is negative.\n", " \n", " Further, note how `x` and `y` are combined:\n", " \n", " >>> x = [-2.1, -1, 4.3]\n", " >>> y = [3, 1.1, 0.12]\n", " >>> X = np.stack((x, y), axis=0)\n", " >>> np.cov(X)\n", " array([[11.71 , -4.286 ], # may vary\n", " [-4.286 , 2.144133]])\n", " >>> np.cov(x, y)\n", " array([[11.71 , -4.286 ], # may vary\n", " [-4.286 , 2.144133]])\n", " >>> np.cov(x)\n", " array(11.71)\n", " \n", " cross(a, b, axisa=-1, axisb=-1, axisc=-1, axis=None)\n", " Return the cross product of two (arrays of) vectors.\n", " \n", " The cross product of `a` and `b` in :math:`R^3` is a vector perpendicular\n", " to both `a` and `b`. If `a` and `b` are arrays of vectors, the vectors\n", " are defined by the last axis of `a` and `b` by default, and these axes\n", " can have dimensions 2 or 3. Where the dimension of either `a` or `b` is\n", " 2, the third component of the input vector is assumed to be zero and the\n", " cross product calculated accordingly. In cases where both input vectors\n", " have dimension 2, the z-component of the cross product is returned.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Components of the first vector(s).\n", " b : array_like\n", " Components of the second vector(s).\n", " axisa : int, optional\n", " Axis of `a` that defines the vector(s). By default, the last axis.\n", " axisb : int, optional\n", " Axis of `b` that defines the vector(s). By default, the last axis.\n", " axisc : int, optional\n", " Axis of `c` containing the cross product vector(s). Ignored if\n", " both input vectors have dimension 2, as the return is scalar.\n", " By default, the last axis.\n", " axis : int, optional\n", " If defined, the axis of `a`, `b` and `c` that defines the vector(s)\n", " and cross product(s). Overrides `axisa`, `axisb` and `axisc`.\n", " \n", " Returns\n", " -------\n", " c : ndarray\n", " Vector cross product(s).\n", " \n", " Raises\n", " ------\n", " ValueError\n", " When the dimension of the vector(s) in `a` and/or `b` does not\n", " equal 2 or 3.\n", " \n", " See Also\n", " --------\n", " inner : Inner product\n", " outer : Outer product.\n", " ix_ : Construct index arrays.\n", " \n", " Notes\n", " -----\n", " .. versionadded:: 1.9.0\n", " \n", " Supports full broadcasting of the inputs.\n", " \n", " Examples\n", " --------\n", " Vector cross-product.\n", " \n", " >>> x = [1, 2, 3]\n", " >>> y = [4, 5, 6]\n", " >>> np.cross(x, y)\n", " array([-3, 6, -3])\n", " \n", " One vector with dimension 2.\n", " \n", " >>> x = [1, 2]\n", " >>> y = [4, 5, 6]\n", " >>> np.cross(x, y)\n", " array([12, -6, -3])\n", " \n", " Equivalently:\n", " \n", " >>> x = [1, 2, 0]\n", " >>> y = [4, 5, 6]\n", " >>> np.cross(x, y)\n", " array([12, -6, -3])\n", " \n", " Both vectors with dimension 2.\n", " \n", " >>> x = [1,2]\n", " >>> y = [4,5]\n", " >>> np.cross(x, y)\n", " array(-3)\n", " \n", " Multiple vector cross-products. Note that the direction of the cross\n", " product vector is defined by the *right-hand rule*.\n", " \n", " >>> x = np.array([[1,2,3], [4,5,6]])\n", " >>> y = np.array([[4,5,6], [1,2,3]])\n", " >>> np.cross(x, y)\n", " array([[-3, 6, -3],\n", " [ 3, -6, 3]])\n", " \n", " The orientation of `c` can be changed using the `axisc` keyword.\n", " \n", " >>> np.cross(x, y, axisc=0)\n", " array([[-3, 3],\n", " [ 6, -6],\n", " [-3, 3]])\n", " \n", " Change the vector definition of `x` and `y` using `axisa` and `axisb`.\n", " \n", " >>> x = np.array([[1,2,3], [4,5,6], [7, 8, 9]])\n", " >>> y = np.array([[7, 8, 9], [4,5,6], [1,2,3]])\n", " >>> np.cross(x, y)\n", " array([[ -6, 12, -6],\n", " [ 0, 0, 0],\n", " [ 6, -12, 6]])\n", " >>> np.cross(x, y, axisa=0, axisb=0)\n", " array([[-24, 48, -24],\n", " [-30, 60, -30],\n", " [-36, 72, -36]])\n", " \n", " cumprod(a, axis=None, dtype=None, out=None)\n", " Return the cumulative product of elements along a given axis.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input array.\n", " axis : int, optional\n", " Axis along which the cumulative product is computed. By default\n", " the input is flattened.\n", " dtype : dtype, optional\n", " Type of the returned array, as well as of the accumulator in which\n", " the elements are multiplied. If *dtype* is not specified, it\n", " defaults to the dtype of `a`, unless `a` has an integer dtype with\n", " a precision less than that of the default platform integer. In\n", " that case, the default platform integer is used instead.\n", " out : ndarray, optional\n", " Alternative output array in which to place the result. It must\n", " have the same shape and buffer length as the expected output\n", " but the type of the resulting values will be cast if necessary.\n", " \n", " Returns\n", " -------\n", " cumprod : ndarray\n", " A new array holding the result is returned unless `out` is\n", " specified, in which case a reference to out is returned.\n", " \n", " See Also\n", " --------\n", " :ref:`ufuncs-output-type`\n", " \n", " Notes\n", " -----\n", " Arithmetic is modular when using integer types, and no error is\n", " raised on overflow.\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([1,2,3])\n", " >>> np.cumprod(a) # intermediate results 1, 1*2\n", " ... # total product 1*2*3 = 6\n", " array([1, 2, 6])\n", " >>> a = np.array([[1, 2, 3], [4, 5, 6]])\n", " >>> np.cumprod(a, dtype=float) # specify type of output\n", " array([ 1., 2., 6., 24., 120., 720.])\n", " \n", " The cumulative product for each column (i.e., over the rows) of `a`:\n", " \n", " >>> np.cumprod(a, axis=0)\n", " array([[ 1, 2, 3],\n", " [ 4, 10, 18]])\n", " \n", " The cumulative product for each row (i.e. over the columns) of `a`:\n", " \n", " >>> np.cumprod(a,axis=1)\n", " array([[ 1, 2, 6],\n", " [ 4, 20, 120]])\n", " \n", " cumproduct(*args, **kwargs)\n", " Return the cumulative product over the given axis.\n", " \n", " See Also\n", " --------\n", " cumprod : equivalent function; see for details.\n", " \n", " cumsum(a, axis=None, dtype=None, out=None)\n", " Return the cumulative sum of the elements along a given axis.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input array.\n", " axis : int, optional\n", " Axis along which the cumulative sum is computed. The default\n", " (None) is to compute the cumsum over the flattened array.\n", " dtype : dtype, optional\n", " Type of the returned array and of the accumulator in which the\n", " elements are summed. If `dtype` is not specified, it defaults\n", " to the dtype of `a`, unless `a` has an integer dtype with a\n", " precision less than that of the default platform integer. In\n", " that case, the default platform integer is used.\n", " out : ndarray, optional\n", " Alternative output array in which to place the result. It must\n", " have the same shape and buffer length as the expected output\n", " but the type will be cast if necessary. See :ref:`ufuncs-output-type` for\n", " more details.\n", " \n", " Returns\n", " -------\n", " cumsum_along_axis : ndarray.\n", " A new array holding the result is returned unless `out` is\n", " specified, in which case a reference to `out` is returned. The\n", " result has the same size as `a`, and the same shape as `a` if\n", " `axis` is not None or `a` is a 1-d array.\n", " \n", " See Also\n", " --------\n", " sum : Sum array elements.\n", " trapz : Integration of array values using the composite trapezoidal rule.\n", " diff : Calculate the n-th discrete difference along given axis.\n", " \n", " Notes\n", " -----\n", " Arithmetic is modular when using integer types, and no error is\n", " raised on overflow.\n", " \n", " ``cumsum(a)[-1]`` may not be equal to ``sum(a)`` for floating-point\n", " values since ``sum`` may use a pairwise summation routine, reducing\n", " the roundoff-error. See `sum` for more information.\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([[1,2,3], [4,5,6]])\n", " >>> a\n", " array([[1, 2, 3],\n", " [4, 5, 6]])\n", " >>> np.cumsum(a)\n", " array([ 1, 3, 6, 10, 15, 21])\n", " >>> np.cumsum(a, dtype=float) # specifies type of output value(s)\n", " array([ 1., 3., 6., 10., 15., 21.])\n", " \n", " >>> np.cumsum(a,axis=0) # sum over rows for each of the 3 columns\n", " array([[1, 2, 3],\n", " [5, 7, 9]])\n", " >>> np.cumsum(a,axis=1) # sum over columns for each of the 2 rows\n", " array([[ 1, 3, 6],\n", " [ 4, 9, 15]])\n", " \n", " ``cumsum(b)[-1]`` may not be equal to ``sum(b)``\n", " \n", " >>> b = np.array([1, 2e-9, 3e-9] * 1000000)\n", " >>> b.cumsum()[-1]\n", " 1000000.0050045159\n", " >>> b.sum()\n", " 1000000.0050000029\n", " \n", " datetime_as_string(...)\n", " datetime_as_string(arr, unit=None, timezone='naive', casting='same_kind')\n", " \n", " Convert an array of datetimes into an array of strings.\n", " \n", " Parameters\n", " ----------\n", " arr : array_like of datetime64\n", " The array of UTC timestamps to format.\n", " unit : str\n", " One of None, 'auto', or a :ref:`datetime unit <arrays.dtypes.dateunits>`.\n", " timezone : {'naive', 'UTC', 'local'} or tzinfo\n", " Timezone information to use when displaying the datetime. If 'UTC', end\n", " with a Z to indicate UTC time. If 'local', convert to the local timezone\n", " first, and suffix with a +-#### timezone offset. If a tzinfo object,\n", " then do as with 'local', but use the specified timezone.\n", " casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}\n", " Casting to allow when changing between datetime units.\n", " \n", " Returns\n", " -------\n", " str_arr : ndarray\n", " An array of strings the same shape as `arr`.\n", " \n", " Examples\n", " --------\n", " >>> import pytz\n", " >>> d = np.arange('2002-10-27T04:30', 4*60, 60, dtype='M8[m]')\n", " >>> d\n", " array(['2002-10-27T04:30', '2002-10-27T05:30', '2002-10-27T06:30',\n", " '2002-10-27T07:30'], dtype='datetime64[m]')\n", " \n", " Setting the timezone to UTC shows the same information, but with a Z suffix\n", " \n", " >>> np.datetime_as_string(d, timezone='UTC')\n", " array(['2002-10-27T04:30Z', '2002-10-27T05:30Z', '2002-10-27T06:30Z',\n", " '2002-10-27T07:30Z'], dtype='<U35')\n", " \n", " Note that we picked datetimes that cross a DST boundary. Passing in a\n", " ``pytz`` timezone object will print the appropriate offset\n", " \n", " >>> np.datetime_as_string(d, timezone=pytz.timezone('US/Eastern'))\n", " array(['2002-10-27T00:30-0400', '2002-10-27T01:30-0400',\n", " '2002-10-27T01:30-0500', '2002-10-27T02:30-0500'], dtype='<U39')\n", " \n", " Passing in a unit will change the precision\n", " \n", " >>> np.datetime_as_string(d, unit='h')\n", " array(['2002-10-27T04', '2002-10-27T05', '2002-10-27T06', '2002-10-27T07'],\n", " dtype='<U32')\n", " >>> np.datetime_as_string(d, unit='s')\n", " array(['2002-10-27T04:30:00', '2002-10-27T05:30:00', '2002-10-27T06:30:00',\n", " '2002-10-27T07:30:00'], dtype='<U38')\n", " \n", " 'casting' can be used to specify whether precision can be changed\n", " \n", " >>> np.datetime_as_string(d, unit='h', casting='safe')\n", " Traceback (most recent call last):\n", " ...\n", " TypeError: Cannot create a datetime string as units 'h' from a NumPy\n", " datetime with units 'm' according to the rule 'safe'\n", " \n", " datetime_data(...)\n", " datetime_data(dtype, /)\n", " \n", " Get information about the step size of a date or time type.\n", " \n", " The returned tuple can be passed as the second argument of `numpy.datetime64` and\n", " `numpy.timedelta64`.\n", " \n", " Parameters\n", " ----------\n", " dtype : dtype\n", " The dtype object, which must be a `datetime64` or `timedelta64` type.\n", " \n", " Returns\n", " -------\n", " unit : str\n", " The :ref:`datetime unit <arrays.dtypes.dateunits>` on which this dtype\n", " is based.\n", " count : int\n", " The number of base units in a step.\n", " \n", " Examples\n", " --------\n", " >>> dt_25s = np.dtype('timedelta64[25s]')\n", " >>> np.datetime_data(dt_25s)\n", " ('s', 25)\n", " >>> np.array(10, dt_25s).astype('timedelta64[s]')\n", " array(250, dtype='timedelta64[s]')\n", " \n", " The result can be used to construct a datetime that uses the same units\n", " as a timedelta\n", " \n", " >>> np.datetime64('2010', np.datetime_data(dt_25s))\n", " numpy.datetime64('2010-01-01T00:00:00','25s')\n", " \n", " delete(arr, obj, axis=None)\n", " Return a new array with sub-arrays along an axis deleted. For a one\n", " dimensional array, this returns those entries not returned by\n", " `arr[obj]`.\n", " \n", " Parameters\n", " ----------\n", " arr : array_like\n", " Input array.\n", " obj : slice, int or array of ints\n", " Indicate indices of sub-arrays to remove along the specified axis.\n", " \n", " .. versionchanged:: 1.19.0\n", " Boolean indices are now treated as a mask of elements to remove,\n", " rather than being cast to the integers 0 and 1.\n", " \n", " axis : int, optional\n", " The axis along which to delete the subarray defined by `obj`.\n", " If `axis` is None, `obj` is applied to the flattened array.\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " A copy of `arr` with the elements specified by `obj` removed. Note\n", " that `delete` does not occur in-place. If `axis` is None, `out` is\n", " a flattened array.\n", " \n", " See Also\n", " --------\n", " insert : Insert elements into an array.\n", " append : Append elements at the end of an array.\n", " \n", " Notes\n", " -----\n", " Often it is preferable to use a boolean mask. For example:\n", " \n", " >>> arr = np.arange(12) + 1\n", " >>> mask = np.ones(len(arr), dtype=bool)\n", " >>> mask[[0,2,4]] = False\n", " >>> result = arr[mask,...]\n", " \n", " Is equivalent to ``np.delete(arr, [0,2,4], axis=0)``, but allows further\n", " use of `mask`.\n", " \n", " Examples\n", " --------\n", " >>> arr = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]])\n", " >>> arr\n", " array([[ 1, 2, 3, 4],\n", " [ 5, 6, 7, 8],\n", " [ 9, 10, 11, 12]])\n", " >>> np.delete(arr, 1, 0)\n", " array([[ 1, 2, 3, 4],\n", " [ 9, 10, 11, 12]])\n", " \n", " >>> np.delete(arr, np.s_[::2], 1)\n", " array([[ 2, 4],\n", " [ 6, 8],\n", " [10, 12]])\n", " >>> np.delete(arr, [1,3,5], None)\n", " array([ 1, 3, 5, 7, 8, 9, 10, 11, 12])\n", " \n", " deprecate(*args, **kwargs)\n", " Issues a DeprecationWarning, adds warning to `old_name`'s\n", " docstring, rebinds ``old_name.__name__`` and returns the new\n", " function object.\n", " \n", " This function may also be used as a decorator.\n", " \n", " Parameters\n", " ----------\n", " func : function\n", " The function to be deprecated.\n", " old_name : str, optional\n", " The name of the function to be deprecated. Default is None, in\n", " which case the name of `func` is used.\n", " new_name : str, optional\n", " The new name for the function. Default is None, in which case the\n", " deprecation message is that `old_name` is deprecated. If given, the\n", " deprecation message is that `old_name` is deprecated and `new_name`\n", " should be used instead.\n", " message : str, optional\n", " Additional explanation of the deprecation. Displayed in the\n", " docstring after the warning.\n", " \n", " Returns\n", " -------\n", " old_func : function\n", " The deprecated function.\n", " \n", " Examples\n", " --------\n", " Note that ``olduint`` returns a value after printing Deprecation\n", " Warning:\n", " \n", " >>> olduint = np.deprecate(np.uint)\n", " DeprecationWarning: `uint64` is deprecated! # may vary\n", " >>> olduint(6)\n", " 6\n", " \n", " deprecate_with_doc(msg)\n", " Deprecates a function and includes the deprecation in its docstring.\n", " \n", " This function is used as a decorator. It returns an object that can be\n", " used to issue a DeprecationWarning, by passing the to-be decorated\n", " function as argument, this adds warning to the to-be decorated function's\n", " docstring and returns the new function object.\n", " \n", " See Also\n", " --------\n", " deprecate : Decorate a function such that it issues a `DeprecationWarning`\n", " \n", " Parameters\n", " ----------\n", " msg : str\n", " Additional explanation of the deprecation. Displayed in the\n", " docstring after the warning.\n", " \n", " Returns\n", " -------\n", " obj : object\n", " \n", " diag(v, k=0)\n", " Extract a diagonal or construct a diagonal array.\n", " \n", " See the more detailed documentation for ``numpy.diagonal`` if you use this\n", " function to extract a diagonal and wish to write to the resulting array;\n", " whether it returns a copy or a view depends on what version of numpy you\n", " are using.\n", " \n", " Parameters\n", " ----------\n", " v : array_like\n", " If `v` is a 2-D array, return a copy of its `k`-th diagonal.\n", " If `v` is a 1-D array, return a 2-D array with `v` on the `k`-th\n", " diagonal.\n", " k : int, optional\n", " Diagonal in question. The default is 0. Use `k>0` for diagonals\n", " above the main diagonal, and `k<0` for diagonals below the main\n", " diagonal.\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " The extracted diagonal or constructed diagonal array.\n", " \n", " See Also\n", " --------\n", " diagonal : Return specified diagonals.\n", " diagflat : Create a 2-D array with the flattened input as a diagonal.\n", " trace : Sum along diagonals.\n", " triu : Upper triangle of an array.\n", " tril : Lower triangle of an array.\n", " \n", " Examples\n", " --------\n", " >>> x = np.arange(9).reshape((3,3))\n", " >>> x\n", " array([[0, 1, 2],\n", " [3, 4, 5],\n", " [6, 7, 8]])\n", " \n", " >>> np.diag(x)\n", " array([0, 4, 8])\n", " >>> np.diag(x, k=1)\n", " array([1, 5])\n", " >>> np.diag(x, k=-1)\n", " array([3, 7])\n", " \n", " >>> np.diag(np.diag(x))\n", " array([[0, 0, 0],\n", " [0, 4, 0],\n", " [0, 0, 8]])\n", " \n", " diag_indices(n, ndim=2)\n", " Return the indices to access the main diagonal of an array.\n", " \n", " This returns a tuple of indices that can be used to access the main\n", " diagonal of an array `a` with ``a.ndim >= 2`` dimensions and shape\n", " (n, n, ..., n). For ``a.ndim = 2`` this is the usual diagonal, for\n", " ``a.ndim > 2`` this is the set of indices to access ``a[i, i, ..., i]``\n", " for ``i = [0..n-1]``.\n", " \n", " Parameters\n", " ----------\n", " n : int\n", " The size, along each dimension, of the arrays for which the returned\n", " indices can be used.\n", " \n", " ndim : int, optional\n", " The number of dimensions.\n", " \n", " See Also\n", " --------\n", " diag_indices_from\n", " \n", " Notes\n", " -----\n", " .. versionadded:: 1.4.0\n", " \n", " Examples\n", " --------\n", " Create a set of indices to access the diagonal of a (4, 4) array:\n", " \n", " >>> di = np.diag_indices(4)\n", " >>> di\n", " (array([0, 1, 2, 3]), array([0, 1, 2, 3]))\n", " >>> a = np.arange(16).reshape(4, 4)\n", " >>> a\n", " array([[ 0, 1, 2, 3],\n", " [ 4, 5, 6, 7],\n", " [ 8, 9, 10, 11],\n", " [12, 13, 14, 15]])\n", " >>> a[di] = 100\n", " >>> a\n", " array([[100, 1, 2, 3],\n", " [ 4, 100, 6, 7],\n", " [ 8, 9, 100, 11],\n", " [ 12, 13, 14, 100]])\n", " \n", " Now, we create indices to manipulate a 3-D array:\n", " \n", " >>> d3 = np.diag_indices(2, 3)\n", " >>> d3\n", " (array([0, 1]), array([0, 1]), array([0, 1]))\n", " \n", " And use it to set the diagonal of an array of zeros to 1:\n", " \n", " >>> a = np.zeros((2, 2, 2), dtype=int)\n", " >>> a[d3] = 1\n", " >>> a\n", " array([[[1, 0],\n", " [0, 0]],\n", " [[0, 0],\n", " [0, 1]]])\n", " \n", " diag_indices_from(arr)\n", " Return the indices to access the main diagonal of an n-dimensional array.\n", " \n", " See `diag_indices` for full details.\n", " \n", " Parameters\n", " ----------\n", " arr : array, at least 2-D\n", " \n", " See Also\n", " --------\n", " diag_indices\n", " \n", " Notes\n", " -----\n", " .. versionadded:: 1.4.0\n", " \n", " diagflat(v, k=0)\n", " Create a two-dimensional array with the flattened input as a diagonal.\n", " \n", " Parameters\n", " ----------\n", " v : array_like\n", " Input data, which is flattened and set as the `k`-th\n", " diagonal of the output.\n", " k : int, optional\n", " Diagonal to set; 0, the default, corresponds to the \"main\" diagonal,\n", " a positive (negative) `k` giving the number of the diagonal above\n", " (below) the main.\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " The 2-D output array.\n", " \n", " See Also\n", " --------\n", " diag : MATLAB work-alike for 1-D and 2-D arrays.\n", " diagonal : Return specified diagonals.\n", " trace : Sum along diagonals.\n", " \n", " Examples\n", " --------\n", " >>> np.diagflat([[1,2], [3,4]])\n", " array([[1, 0, 0, 0],\n", " [0, 2, 0, 0],\n", " [0, 0, 3, 0],\n", " [0, 0, 0, 4]])\n", " \n", " >>> np.diagflat([1,2], 1)\n", " array([[0, 1, 0],\n", " [0, 0, 2],\n", " [0, 0, 0]])\n", " \n", " diagonal(a, offset=0, axis1=0, axis2=1)\n", " Return specified diagonals.\n", " \n", " If `a` is 2-D, returns the diagonal of `a` with the given offset,\n", " i.e., the collection of elements of the form ``a[i, i+offset]``. If\n", " `a` has more than two dimensions, then the axes specified by `axis1`\n", " and `axis2` are used to determine the 2-D sub-array whose diagonal is\n", " returned. The shape of the resulting array can be determined by\n", " removing `axis1` and `axis2` and appending an index to the right equal\n", " to the size of the resulting diagonals.\n", " \n", " In versions of NumPy prior to 1.7, this function always returned a new,\n", " independent array containing a copy of the values in the diagonal.\n", " \n", " In NumPy 1.7 and 1.8, it continues to return a copy of the diagonal,\n", " but depending on this fact is deprecated. Writing to the resulting\n", " array continues to work as it used to, but a FutureWarning is issued.\n", " \n", " Starting in NumPy 1.9 it returns a read-only view on the original array.\n", " Attempting to write to the resulting array will produce an error.\n", " \n", " In some future release, it will return a read/write view and writing to\n", " the returned array will alter your original array. The returned array\n", " will have the same type as the input array.\n", " \n", " If you don't write to the array returned by this function, then you can\n", " just ignore all of the above.\n", " \n", " If you depend on the current behavior, then we suggest copying the\n", " returned array explicitly, i.e., use ``np.diagonal(a).copy()`` instead\n", " of just ``np.diagonal(a)``. This will work with both past and future\n", " versions of NumPy.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Array from which the diagonals are taken.\n", " offset : int, optional\n", " Offset of the diagonal from the main diagonal. Can be positive or\n", " negative. Defaults to main diagonal (0).\n", " axis1 : int, optional\n", " Axis to be used as the first axis of the 2-D sub-arrays from which\n", " the diagonals should be taken. Defaults to first axis (0).\n", " axis2 : int, optional\n", " Axis to be used as the second axis of the 2-D sub-arrays from\n", " which the diagonals should be taken. Defaults to second axis (1).\n", " \n", " Returns\n", " -------\n", " array_of_diagonals : ndarray\n", " If `a` is 2-D, then a 1-D array containing the diagonal and of the\n", " same type as `a` is returned unless `a` is a `matrix`, in which case\n", " a 1-D array rather than a (2-D) `matrix` is returned in order to\n", " maintain backward compatibility.\n", " \n", " If ``a.ndim > 2``, then the dimensions specified by `axis1` and `axis2`\n", " are removed, and a new axis inserted at the end corresponding to the\n", " diagonal.\n", " \n", " Raises\n", " ------\n", " ValueError\n", " If the dimension of `a` is less than 2.\n", " \n", " See Also\n", " --------\n", " diag : MATLAB work-a-like for 1-D and 2-D arrays.\n", " diagflat : Create diagonal arrays.\n", " trace : Sum along diagonals.\n", " \n", " Examples\n", " --------\n", " >>> a = np.arange(4).reshape(2,2)\n", " >>> a\n", " array([[0, 1],\n", " [2, 3]])\n", " >>> a.diagonal()\n", " array([0, 3])\n", " >>> a.diagonal(1)\n", " array([1])\n", " \n", " A 3-D example:\n", " \n", " >>> a = np.arange(8).reshape(2,2,2); a\n", " array([[[0, 1],\n", " [2, 3]],\n", " [[4, 5],\n", " [6, 7]]])\n", " >>> a.diagonal(0, # Main diagonals of two arrays created by skipping\n", " ... 0, # across the outer(left)-most axis last and\n", " ... 1) # the \"middle\" (row) axis first.\n", " array([[0, 6],\n", " [1, 7]])\n", " \n", " The sub-arrays whose main diagonals we just obtained; note that each\n", " corresponds to fixing the right-most (column) axis, and that the\n", " diagonals are \"packed\" in rows.\n", " \n", " >>> a[:,:,0] # main diagonal is [0 6]\n", " array([[0, 2],\n", " [4, 6]])\n", " >>> a[:,:,1] # main diagonal is [1 7]\n", " array([[1, 3],\n", " [5, 7]])\n", " \n", " The anti-diagonal can be obtained by reversing the order of elements\n", " using either `numpy.flipud` or `numpy.fliplr`.\n", " \n", " >>> a = np.arange(9).reshape(3, 3)\n", " >>> a\n", " array([[0, 1, 2],\n", " [3, 4, 5],\n", " [6, 7, 8]])\n", " >>> np.fliplr(a).diagonal() # Horizontal flip\n", " array([2, 4, 6])\n", " >>> np.flipud(a).diagonal() # Vertical flip\n", " array([6, 4, 2])\n", " \n", " Note that the order in which the diagonal is retrieved varies depending\n", " on the flip function.\n", " \n", " diff(a, n=1, axis=-1, prepend=<no value>, append=<no value>)\n", " Calculate the n-th discrete difference along the given axis.\n", " \n", " The first difference is given by ``out[i] = a[i+1] - a[i]`` along\n", " the given axis, higher differences are calculated by using `diff`\n", " recursively.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input array\n", " n : int, optional\n", " The number of times values are differenced. If zero, the input\n", " is returned as-is.\n", " axis : int, optional\n", " The axis along which the difference is taken, default is the\n", " last axis.\n", " prepend, append : array_like, optional\n", " Values to prepend or append to `a` along axis prior to\n", " performing the difference. Scalar values are expanded to\n", " arrays with length 1 in the direction of axis and the shape\n", " of the input array in along all other axes. Otherwise the\n", " dimension and shape must match `a` except along axis.\n", " \n", " .. versionadded:: 1.16.0\n", " \n", " Returns\n", " -------\n", " diff : ndarray\n", " The n-th differences. The shape of the output is the same as `a`\n", " except along `axis` where the dimension is smaller by `n`. The\n", " type of the output is the same as the type of the difference\n", " between any two elements of `a`. This is the same as the type of\n", " `a` in most cases. A notable exception is `datetime64`, which\n", " results in a `timedelta64` output array.\n", " \n", " See Also\n", " --------\n", " gradient, ediff1d, cumsum\n", " \n", " Notes\n", " -----\n", " Type is preserved for boolean arrays, so the result will contain\n", " `False` when consecutive elements are the same and `True` when they\n", " differ.\n", " \n", " For unsigned integer arrays, the results will also be unsigned. This\n", " should not be surprising, as the result is consistent with\n", " calculating the difference directly:\n", " \n", " >>> u8_arr = np.array([1, 0], dtype=np.uint8)\n", " >>> np.diff(u8_arr)\n", " array([255], dtype=uint8)\n", " >>> u8_arr[1,...] - u8_arr[0,...]\n", " 255\n", " \n", " If this is not desirable, then the array should be cast to a larger\n", " integer type first:\n", " \n", " >>> i16_arr = u8_arr.astype(np.int16)\n", " >>> np.diff(i16_arr)\n", " array([-1], dtype=int16)\n", " \n", " Examples\n", " --------\n", " >>> x = np.array([1, 2, 4, 7, 0])\n", " >>> np.diff(x)\n", " array([ 1, 2, 3, -7])\n", " >>> np.diff(x, n=2)\n", " array([ 1, 1, -10])\n", " \n", " >>> x = np.array([[1, 3, 6, 10], [0, 5, 6, 8]])\n", " >>> np.diff(x)\n", " array([[2, 3, 4],\n", " [5, 1, 2]])\n", " >>> np.diff(x, axis=0)\n", " array([[-1, 2, 0, -2]])\n", " \n", " >>> x = np.arange('1066-10-13', '1066-10-16', dtype=np.datetime64)\n", " >>> np.diff(x)\n", " array([1, 1], dtype='timedelta64[D]')\n", " \n", " digitize(x, bins, right=False)\n", " Return the indices of the bins to which each value in input array belongs.\n", " \n", " ========= ============= ============================\n", " `right` order of bins returned index `i` satisfies\n", " ========= ============= ============================\n", " ``False`` increasing ``bins[i-1] <= x < bins[i]``\n", " ``True`` increasing ``bins[i-1] < x <= bins[i]``\n", " ``False`` decreasing ``bins[i-1] > x >= bins[i]``\n", " ``True`` decreasing ``bins[i-1] >= x > bins[i]``\n", " ========= ============= ============================\n", " \n", " If values in `x` are beyond the bounds of `bins`, 0 or ``len(bins)`` is\n", " returned as appropriate.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Input array to be binned. Prior to NumPy 1.10.0, this array had to\n", " be 1-dimensional, but can now have any shape.\n", " bins : array_like\n", " Array of bins. It has to be 1-dimensional and monotonic.\n", " right : bool, optional\n", " Indicating whether the intervals include the right or the left bin\n", " edge. Default behavior is (right==False) indicating that the interval\n", " does not include the right edge. The left bin end is open in this\n", " case, i.e., bins[i-1] <= x < bins[i] is the default behavior for\n", " monotonically increasing bins.\n", " \n", " Returns\n", " -------\n", " indices : ndarray of ints\n", " Output array of indices, of same shape as `x`.\n", " \n", " Raises\n", " ------\n", " ValueError\n", " If `bins` is not monotonic.\n", " TypeError\n", " If the type of the input is complex.\n", " \n", " See Also\n", " --------\n", " bincount, histogram, unique, searchsorted\n", " \n", " Notes\n", " -----\n", " If values in `x` are such that they fall outside the bin range,\n", " attempting to index `bins` with the indices that `digitize` returns\n", " will result in an IndexError.\n", " \n", " .. versionadded:: 1.10.0\n", " \n", " `np.digitize` is implemented in terms of `np.searchsorted`. This means\n", " that a binary search is used to bin the values, which scales much better\n", " for larger number of bins than the previous linear search. It also removes\n", " the requirement for the input array to be 1-dimensional.\n", " \n", " For monotonically _increasing_ `bins`, the following are equivalent::\n", " \n", " np.digitize(x, bins, right=True)\n", " np.searchsorted(bins, x, side='left')\n", " \n", " Note that as the order of the arguments are reversed, the side must be too.\n", " The `searchsorted` call is marginally faster, as it does not do any\n", " monotonicity checks. Perhaps more importantly, it supports all dtypes.\n", " \n", " Examples\n", " --------\n", " >>> x = np.array([0.2, 6.4, 3.0, 1.6])\n", " >>> bins = np.array([0.0, 1.0, 2.5, 4.0, 10.0])\n", " >>> inds = np.digitize(x, bins)\n", " >>> inds\n", " array([1, 4, 3, 2])\n", " >>> for n in range(x.size):\n", " ... print(bins[inds[n]-1], \"<=\", x[n], \"<\", bins[inds[n]])\n", " ...\n", " 0.0 <= 0.2 < 1.0\n", " 4.0 <= 6.4 < 10.0\n", " 2.5 <= 3.0 < 4.0\n", " 1.0 <= 1.6 < 2.5\n", " \n", " >>> x = np.array([1.2, 10.0, 12.4, 15.5, 20.])\n", " >>> bins = np.array([0, 5, 10, 15, 20])\n", " >>> np.digitize(x,bins,right=True)\n", " array([1, 2, 3, 4, 4])\n", " >>> np.digitize(x,bins,right=False)\n", " array([1, 3, 3, 4, 5])\n", " \n", " disp(mesg, device=None, linefeed=True)\n", " Display a message on a device.\n", " \n", " Parameters\n", " ----------\n", " mesg : str\n", " Message to display.\n", " device : object\n", " Device to write message. If None, defaults to ``sys.stdout`` which is\n", " very similar to ``print``. `device` needs to have ``write()`` and\n", " ``flush()`` methods.\n", " linefeed : bool, optional\n", " Option whether to print a line feed or not. Defaults to True.\n", " \n", " Raises\n", " ------\n", " AttributeError\n", " If `device` does not have a ``write()`` or ``flush()`` method.\n", " \n", " Examples\n", " --------\n", " Besides ``sys.stdout``, a file-like object can also be used as it has\n", " both required methods:\n", " \n", " >>> from io import StringIO\n", " >>> buf = StringIO()\n", " >>> np.disp(u'\"Display\" in a file', device=buf)\n", " >>> buf.getvalue()\n", " '\"Display\" in a file\\n'\n", " \n", " dot(...)\n", " dot(a, b, out=None)\n", " \n", " Dot product of two arrays. Specifically,\n", " \n", " - If both `a` and `b` are 1-D arrays, it is inner product of vectors\n", " (without complex conjugation).\n", " \n", " - If both `a` and `b` are 2-D arrays, it is matrix multiplication,\n", " but using :func:`matmul` or ``a @ b`` is preferred.\n", " \n", " - If either `a` or `b` is 0-D (scalar), it is equivalent to\n", " :func:`multiply` and using ``numpy.multiply(a, b)`` or ``a * b`` is\n", " preferred.\n", " \n", " - If `a` is an N-D array and `b` is a 1-D array, it is a sum product over\n", " the last axis of `a` and `b`.\n", " \n", " - If `a` is an N-D array and `b` is an M-D array (where ``M>=2``), it is a\n", " sum product over the last axis of `a` and the second-to-last axis of\n", " `b`::\n", " \n", " dot(a, b)[i,j,k,m] = sum(a[i,j,:] * b[k,:,m])\n", " \n", " It uses an optimized BLAS library when possible (see `numpy.linalg`).\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " First argument.\n", " b : array_like\n", " Second argument.\n", " out : ndarray, optional\n", " Output argument. This must have the exact kind that would be returned\n", " if it was not used. In particular, it must have the right type, must be\n", " C-contiguous, and its dtype must be the dtype that would be returned\n", " for `dot(a,b)`. This is a performance feature. Therefore, if these\n", " conditions are not met, an exception is raised, instead of attempting\n", " to be flexible.\n", " \n", " Returns\n", " -------\n", " output : ndarray\n", " Returns the dot product of `a` and `b`. If `a` and `b` are both\n", " scalars or both 1-D arrays then a scalar is returned; otherwise\n", " an array is returned.\n", " If `out` is given, then it is returned.\n", " \n", " Raises\n", " ------\n", " ValueError\n", " If the last dimension of `a` is not the same size as\n", " the second-to-last dimension of `b`.\n", " \n", " See Also\n", " --------\n", " vdot : Complex-conjugating dot product.\n", " tensordot : Sum products over arbitrary axes.\n", " einsum : Einstein summation convention.\n", " matmul : '@' operator as method with out parameter.\n", " linalg.multi_dot : Chained dot product.\n", " \n", " Examples\n", " --------\n", " >>> np.dot(3, 4)\n", " 12\n", " \n", " Neither argument is complex-conjugated:\n", " \n", " >>> np.dot([2j, 3j], [2j, 3j])\n", " (-13+0j)\n", " \n", " For 2-D arrays it is the matrix product:\n", " \n", " >>> a = [[1, 0], [0, 1]]\n", " >>> b = [[4, 1], [2, 2]]\n", " >>> np.dot(a, b)\n", " array([[4, 1],\n", " [2, 2]])\n", " \n", " >>> a = np.arange(3*4*5*6).reshape((3,4,5,6))\n", " >>> b = np.arange(3*4*5*6)[::-1].reshape((5,4,6,3))\n", " >>> np.dot(a, b)[2,3,2,1,2,2]\n", " 499128\n", " >>> sum(a[2,3,2,:] * b[1,2,:,2])\n", " 499128\n", " \n", " dsplit(ary, indices_or_sections)\n", " Split array into multiple sub-arrays along the 3rd axis (depth).\n", " \n", " Please refer to the `split` documentation. `dsplit` is equivalent\n", " to `split` with ``axis=2``, the array is always split along the third\n", " axis provided the array dimension is greater than or equal to 3.\n", " \n", " See Also\n", " --------\n", " split : Split an array into multiple sub-arrays of equal size.\n", " \n", " Examples\n", " --------\n", " >>> x = np.arange(16.0).reshape(2, 2, 4)\n", " >>> x\n", " array([[[ 0., 1., 2., 3.],\n", " [ 4., 5., 6., 7.]],\n", " [[ 8., 9., 10., 11.],\n", " [12., 13., 14., 15.]]])\n", " >>> np.dsplit(x, 2)\n", " [array([[[ 0., 1.],\n", " [ 4., 5.]],\n", " [[ 8., 9.],\n", " [12., 13.]]]), array([[[ 2., 3.],\n", " [ 6., 7.]],\n", " [[10., 11.],\n", " [14., 15.]]])]\n", " >>> np.dsplit(x, np.array([3, 6]))\n", " [array([[[ 0., 1., 2.],\n", " [ 4., 5., 6.]],\n", " [[ 8., 9., 10.],\n", " [12., 13., 14.]]]),\n", " array([[[ 3.],\n", " [ 7.]],\n", " [[11.],\n", " [15.]]]),\n", " array([], shape=(2, 2, 0), dtype=float64)]\n", " \n", " dstack(tup)\n", " Stack arrays in sequence depth wise (along third axis).\n", " \n", " This is equivalent to concatenation along the third axis after 2-D arrays\n", " of shape `(M,N)` have been reshaped to `(M,N,1)` and 1-D arrays of shape\n", " `(N,)` have been reshaped to `(1,N,1)`. Rebuilds arrays divided by\n", " `dsplit`.\n", " \n", " This function makes most sense for arrays with up to 3 dimensions. For\n", " instance, for pixel-data with a height (first axis), width (second axis),\n", " and r/g/b channels (third axis). The functions `concatenate`, `stack` and\n", " `block` provide more general stacking and concatenation operations.\n", " \n", " Parameters\n", " ----------\n", " tup : sequence of arrays\n", " The arrays must have the same shape along all but the third axis.\n", " 1-D or 2-D arrays must have the same shape.\n", " \n", " Returns\n", " -------\n", " stacked : ndarray\n", " The array formed by stacking the given arrays, will be at least 3-D.\n", " \n", " See Also\n", " --------\n", " concatenate : Join a sequence of arrays along an existing axis.\n", " stack : Join a sequence of arrays along a new axis.\n", " block : Assemble an nd-array from nested lists of blocks.\n", " vstack : Stack arrays in sequence vertically (row wise).\n", " hstack : Stack arrays in sequence horizontally (column wise).\n", " column_stack : Stack 1-D arrays as columns into a 2-D array.\n", " dsplit : Split array along third axis.\n", " \n", " Examples\n", " --------\n", " >>> a = np.array((1,2,3))\n", " >>> b = np.array((2,3,4))\n", " >>> np.dstack((a,b))\n", " array([[[1, 2],\n", " [2, 3],\n", " [3, 4]]])\n", " \n", " >>> a = np.array([[1],[2],[3]])\n", " >>> b = np.array([[2],[3],[4]])\n", " >>> np.dstack((a,b))\n", " array([[[1, 2]],\n", " [[2, 3]],\n", " [[3, 4]]])\n", " \n", " ediff1d(ary, to_end=None, to_begin=None)\n", " The differences between consecutive elements of an array.\n", " \n", " Parameters\n", " ----------\n", " ary : array_like\n", " If necessary, will be flattened before the differences are taken.\n", " to_end : array_like, optional\n", " Number(s) to append at the end of the returned differences.\n", " to_begin : array_like, optional\n", " Number(s) to prepend at the beginning of the returned differences.\n", " \n", " Returns\n", " -------\n", " ediff1d : ndarray\n", " The differences. Loosely, this is ``ary.flat[1:] - ary.flat[:-1]``.\n", " \n", " See Also\n", " --------\n", " diff, gradient\n", " \n", " Notes\n", " -----\n", " When applied to masked arrays, this function drops the mask information\n", " if the `to_begin` and/or `to_end` parameters are used.\n", " \n", " Examples\n", " --------\n", " >>> x = np.array([1, 2, 4, 7, 0])\n", " >>> np.ediff1d(x)\n", " array([ 1, 2, 3, -7])\n", " \n", " >>> np.ediff1d(x, to_begin=-99, to_end=np.array([88, 99]))\n", " array([-99, 1, 2, ..., -7, 88, 99])\n", " \n", " The returned array is always 1D.\n", " \n", " >>> y = [[1, 2, 4], [1, 6, 24]]\n", " >>> np.ediff1d(y)\n", " array([ 1, 2, -3, 5, 18])\n", " \n", " einsum(*operands, out=None, optimize=False, **kwargs)\n", " einsum(subscripts, *operands, out=None, dtype=None, order='K',\n", " casting='safe', optimize=False)\n", " \n", " Evaluates the Einstein summation convention on the operands.\n", " \n", " Using the Einstein summation convention, many common multi-dimensional,\n", " linear algebraic array operations can be represented in a simple fashion.\n", " In *implicit* mode `einsum` computes these values.\n", " \n", " In *explicit* mode, `einsum` provides further flexibility to compute\n", " other array operations that might not be considered classical Einstein\n", " summation operations, by disabling, or forcing summation over specified\n", " subscript labels.\n", " \n", " See the notes and examples for clarification.\n", " \n", " Parameters\n", " ----------\n", " subscripts : str\n", " Specifies the subscripts for summation as comma separated list of\n", " subscript labels. An implicit (classical Einstein summation)\n", " calculation is performed unless the explicit indicator '->' is\n", " included as well as subscript labels of the precise output form.\n", " operands : list of array_like\n", " These are the arrays for the operation.\n", " out : ndarray, optional\n", " If provided, the calculation is done into this array.\n", " dtype : {data-type, None}, optional\n", " If provided, forces the calculation to use the data type specified.\n", " Note that you may have to also give a more liberal `casting`\n", " parameter to allow the conversions. Default is None.\n", " order : {'C', 'F', 'A', 'K'}, optional\n", " Controls the memory layout of the output. 'C' means it should\n", " be C contiguous. 'F' means it should be Fortran contiguous,\n", " 'A' means it should be 'F' if the inputs are all 'F', 'C' otherwise.\n", " 'K' means it should be as close to the layout as the inputs as\n", " is possible, including arbitrarily permuted axes.\n", " Default is 'K'.\n", " casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional\n", " Controls what kind of data casting may occur. Setting this to\n", " 'unsafe' is not recommended, as it can adversely affect accumulations.\n", " \n", " * 'no' means the data types should not be cast at all.\n", " * 'equiv' means only byte-order changes are allowed.\n", " * 'safe' means only casts which can preserve values are allowed.\n", " * 'same_kind' means only safe casts or casts within a kind,\n", " like float64 to float32, are allowed.\n", " * 'unsafe' means any data conversions may be done.\n", " \n", " Default is 'safe'.\n", " optimize : {False, True, 'greedy', 'optimal'}, optional\n", " Controls if intermediate optimization should occur. No optimization\n", " will occur if False and True will default to the 'greedy' algorithm.\n", " Also accepts an explicit contraction list from the ``np.einsum_path``\n", " function. See ``np.einsum_path`` for more details. Defaults to False.\n", " \n", " Returns\n", " -------\n", " output : ndarray\n", " The calculation based on the Einstein summation convention.\n", " \n", " See Also\n", " --------\n", " einsum_path, dot, inner, outer, tensordot, linalg.multi_dot\n", " einops :\n", " similar verbose interface is provided by\n", " `einops <https://github.com/arogozhnikov/einops>`_ package to cover\n", " additional operations: transpose, reshape/flatten, repeat/tile,\n", " squeeze/unsqueeze and reductions.\n", " opt_einsum :\n", " `opt_einsum <https://optimized-einsum.readthedocs.io/en/stable/>`_\n", " optimizes contraction order for einsum-like expressions\n", " in backend-agnostic manner.\n", " \n", " Notes\n", " -----\n", " .. versionadded:: 1.6.0\n", " \n", " The Einstein summation convention can be used to compute\n", " many multi-dimensional, linear algebraic array operations. `einsum`\n", " provides a succinct way of representing these.\n", " \n", " A non-exhaustive list of these operations,\n", " which can be computed by `einsum`, is shown below along with examples:\n", " \n", " * Trace of an array, :py:func:`numpy.trace`.\n", " * Return a diagonal, :py:func:`numpy.diag`.\n", " * Array axis summations, :py:func:`numpy.sum`.\n", " * Transpositions and permutations, :py:func:`numpy.transpose`.\n", " * Matrix multiplication and dot product, :py:func:`numpy.matmul` :py:func:`numpy.dot`.\n", " * Vector inner and outer products, :py:func:`numpy.inner` :py:func:`numpy.outer`.\n", " * Broadcasting, element-wise and scalar multiplication, :py:func:`numpy.multiply`.\n", " * Tensor contractions, :py:func:`numpy.tensordot`.\n", " * Chained array operations, in efficient calculation order, :py:func:`numpy.einsum_path`.\n", " \n", " The subscripts string is a comma-separated list of subscript labels,\n", " where each label refers to a dimension of the corresponding operand.\n", " Whenever a label is repeated it is summed, so ``np.einsum('i,i', a, b)``\n", " is equivalent to :py:func:`np.inner(a,b) <numpy.inner>`. If a label\n", " appears only once, it is not summed, so ``np.einsum('i', a)`` produces a\n", " view of ``a`` with no changes. A further example ``np.einsum('ij,jk', a, b)``\n", " describes traditional matrix multiplication and is equivalent to\n", " :py:func:`np.matmul(a,b) <numpy.matmul>`. Repeated subscript labels in one\n", " operand take the diagonal. For example, ``np.einsum('ii', a)`` is equivalent\n", " to :py:func:`np.trace(a) <numpy.trace>`.\n", " \n", " In *implicit mode*, the chosen subscripts are important\n", " since the axes of the output are reordered alphabetically. This\n", " means that ``np.einsum('ij', a)`` doesn't affect a 2D array, while\n", " ``np.einsum('ji', a)`` takes its transpose. Additionally,\n", " ``np.einsum('ij,jk', a, b)`` returns a matrix multiplication, while,\n", " ``np.einsum('ij,jh', a, b)`` returns the transpose of the\n", " multiplication since subscript 'h' precedes subscript 'i'.\n", " \n", " In *explicit mode* the output can be directly controlled by\n", " specifying output subscript labels. This requires the\n", " identifier '->' as well as the list of output subscript labels.\n", " This feature increases the flexibility of the function since\n", " summing can be disabled or forced when required. The call\n", " ``np.einsum('i->', a)`` is like :py:func:`np.sum(a, axis=-1) <numpy.sum>`,\n", " and ``np.einsum('ii->i', a)`` is like :py:func:`np.diag(a) <numpy.diag>`.\n", " The difference is that `einsum` does not allow broadcasting by default.\n", " Additionally ``np.einsum('ij,jh->ih', a, b)`` directly specifies the\n", " order of the output subscript labels and therefore returns matrix\n", " multiplication, unlike the example above in implicit mode.\n", " \n", " To enable and control broadcasting, use an ellipsis. Default\n", " NumPy-style broadcasting is done by adding an ellipsis\n", " to the left of each term, like ``np.einsum('...ii->...i', a)``.\n", " To take the trace along the first and last axes,\n", " you can do ``np.einsum('i...i', a)``, or to do a matrix-matrix\n", " product with the left-most indices instead of rightmost, one can do\n", " ``np.einsum('ij...,jk...->ik...', a, b)``.\n", " \n", " When there is only one operand, no axes are summed, and no output\n", " parameter is provided, a view into the operand is returned instead\n", " of a new array. Thus, taking the diagonal as ``np.einsum('ii->i', a)``\n", " produces a view (changed in version 1.10.0).\n", " \n", " `einsum` also provides an alternative way to provide the subscripts\n", " and operands as ``einsum(op0, sublist0, op1, sublist1, ..., [sublistout])``.\n", " If the output shape is not provided in this format `einsum` will be\n", " calculated in implicit mode, otherwise it will be performed explicitly.\n", " The examples below have corresponding `einsum` calls with the two\n", " parameter methods.\n", " \n", " .. versionadded:: 1.10.0\n", " \n", " Views returned from einsum are now writeable whenever the input array\n", " is writeable. For example, ``np.einsum('ijk...->kji...', a)`` will now\n", " have the same effect as :py:func:`np.swapaxes(a, 0, 2) <numpy.swapaxes>`\n", " and ``np.einsum('ii->i', a)`` will return a writeable view of the diagonal\n", " of a 2D array.\n", " \n", " .. versionadded:: 1.12.0\n", " \n", " Added the ``optimize`` argument which will optimize the contraction order\n", " of an einsum expression. For a contraction with three or more operands this\n", " can greatly increase the computational efficiency at the cost of a larger\n", " memory footprint during computation.\n", " \n", " Typically a 'greedy' algorithm is applied which empirical tests have shown\n", " returns the optimal path in the majority of cases. In some cases 'optimal'\n", " will return the superlative path through a more expensive, exhaustive search.\n", " For iterative calculations it may be advisable to calculate the optimal path\n", " once and reuse that path by supplying it as an argument. An example is given\n", " below.\n", " \n", " See :py:func:`numpy.einsum_path` for more details.\n", " \n", " Examples\n", " --------\n", " >>> a = np.arange(25).reshape(5,5)\n", " >>> b = np.arange(5)\n", " >>> c = np.arange(6).reshape(2,3)\n", " \n", " Trace of a matrix:\n", " \n", " >>> np.einsum('ii', a)\n", " 60\n", " >>> np.einsum(a, [0,0])\n", " 60\n", " >>> np.trace(a)\n", " 60\n", " \n", " Extract the diagonal (requires explicit form):\n", " \n", " >>> np.einsum('ii->i', a)\n", " array([ 0, 6, 12, 18, 24])\n", " >>> np.einsum(a, [0,0], [0])\n", " array([ 0, 6, 12, 18, 24])\n", " >>> np.diag(a)\n", " array([ 0, 6, 12, 18, 24])\n", " \n", " Sum over an axis (requires explicit form):\n", " \n", " >>> np.einsum('ij->i', a)\n", " array([ 10, 35, 60, 85, 110])\n", " >>> np.einsum(a, [0,1], [0])\n", " array([ 10, 35, 60, 85, 110])\n", " >>> np.sum(a, axis=1)\n", " array([ 10, 35, 60, 85, 110])\n", " \n", " For higher dimensional arrays summing a single axis can be done with ellipsis:\n", " \n", " >>> np.einsum('...j->...', a)\n", " array([ 10, 35, 60, 85, 110])\n", " >>> np.einsum(a, [Ellipsis,1], [Ellipsis])\n", " array([ 10, 35, 60, 85, 110])\n", " \n", " Compute a matrix transpose, or reorder any number of axes:\n", " \n", " >>> np.einsum('ji', c)\n", " array([[0, 3],\n", " [1, 4],\n", " [2, 5]])\n", " >>> np.einsum('ij->ji', c)\n", " array([[0, 3],\n", " [1, 4],\n", " [2, 5]])\n", " >>> np.einsum(c, [1,0])\n", " array([[0, 3],\n", " [1, 4],\n", " [2, 5]])\n", " >>> np.transpose(c)\n", " array([[0, 3],\n", " [1, 4],\n", " [2, 5]])\n", " \n", " Vector inner products:\n", " \n", " >>> np.einsum('i,i', b, b)\n", " 30\n", " >>> np.einsum(b, [0], b, [0])\n", " 30\n", " >>> np.inner(b,b)\n", " 30\n", " \n", " Matrix vector multiplication:\n", " \n", " >>> np.einsum('ij,j', a, b)\n", " array([ 30, 80, 130, 180, 230])\n", " >>> np.einsum(a, [0,1], b, [1])\n", " array([ 30, 80, 130, 180, 230])\n", " >>> np.dot(a, b)\n", " array([ 30, 80, 130, 180, 230])\n", " >>> np.einsum('...j,j', a, b)\n", " array([ 30, 80, 130, 180, 230])\n", " \n", " Broadcasting and scalar multiplication:\n", " \n", " >>> np.einsum('..., ...', 3, c)\n", " array([[ 0, 3, 6],\n", " [ 9, 12, 15]])\n", " >>> np.einsum(',ij', 3, c)\n", " array([[ 0, 3, 6],\n", " [ 9, 12, 15]])\n", " >>> np.einsum(3, [Ellipsis], c, [Ellipsis])\n", " array([[ 0, 3, 6],\n", " [ 9, 12, 15]])\n", " >>> np.multiply(3, c)\n", " array([[ 0, 3, 6],\n", " [ 9, 12, 15]])\n", " \n", " Vector outer product:\n", " \n", " >>> np.einsum('i,j', np.arange(2)+1, b)\n", " array([[0, 1, 2, 3, 4],\n", " [0, 2, 4, 6, 8]])\n", " >>> np.einsum(np.arange(2)+1, [0], b, [1])\n", " array([[0, 1, 2, 3, 4],\n", " [0, 2, 4, 6, 8]])\n", " >>> np.outer(np.arange(2)+1, b)\n", " array([[0, 1, 2, 3, 4],\n", " [0, 2, 4, 6, 8]])\n", " \n", " Tensor contraction:\n", " \n", " >>> a = np.arange(60.).reshape(3,4,5)\n", " >>> b = np.arange(24.).reshape(4,3,2)\n", " >>> np.einsum('ijk,jil->kl', a, b)\n", " array([[4400., 4730.],\n", " [4532., 4874.],\n", " [4664., 5018.],\n", " [4796., 5162.],\n", " [4928., 5306.]])\n", " >>> np.einsum(a, [0,1,2], b, [1,0,3], [2,3])\n", " array([[4400., 4730.],\n", " [4532., 4874.],\n", " [4664., 5018.],\n", " [4796., 5162.],\n", " [4928., 5306.]])\n", " >>> np.tensordot(a,b, axes=([1,0],[0,1]))\n", " array([[4400., 4730.],\n", " [4532., 4874.],\n", " [4664., 5018.],\n", " [4796., 5162.],\n", " [4928., 5306.]])\n", " \n", " Writeable returned arrays (since version 1.10.0):\n", " \n", " >>> a = np.zeros((3, 3))\n", " >>> np.einsum('ii->i', a)[:] = 1\n", " >>> a\n", " array([[1., 0., 0.],\n", " [0., 1., 0.],\n", " [0., 0., 1.]])\n", " \n", " Example of ellipsis use:\n", " \n", " >>> a = np.arange(6).reshape((3,2))\n", " >>> b = np.arange(12).reshape((4,3))\n", " >>> np.einsum('ki,jk->ij', a, b)\n", " array([[10, 28, 46, 64],\n", " [13, 40, 67, 94]])\n", " >>> np.einsum('ki,...k->i...', a, b)\n", " array([[10, 28, 46, 64],\n", " [13, 40, 67, 94]])\n", " >>> np.einsum('k...,jk', a, b)\n", " array([[10, 28, 46, 64],\n", " [13, 40, 67, 94]])\n", " \n", " Chained array operations. For more complicated contractions, speed ups\n", " might be achieved by repeatedly computing a 'greedy' path or pre-computing the\n", " 'optimal' path and repeatedly applying it, using an\n", " `einsum_path` insertion (since version 1.12.0). Performance improvements can be\n", " particularly significant with larger arrays:\n", " \n", " >>> a = np.ones(64).reshape(2,4,8)\n", " \n", " Basic `einsum`: ~1520ms (benchmarked on 3.1GHz Intel i5.)\n", " \n", " >>> for iteration in range(500):\n", " ... _ = np.einsum('ijk,ilm,njm,nlk,abc->',a,a,a,a,a)\n", " \n", " Sub-optimal `einsum` (due to repeated path calculation time): ~330ms\n", " \n", " >>> for iteration in range(500):\n", " ... _ = np.einsum('ijk,ilm,njm,nlk,abc->',a,a,a,a,a, optimize='optimal')\n", " \n", " Greedy `einsum` (faster optimal path approximation): ~160ms\n", " \n", " >>> for iteration in range(500):\n", " ... _ = np.einsum('ijk,ilm,njm,nlk,abc->',a,a,a,a,a, optimize='greedy')\n", " \n", " Optimal `einsum` (best usage pattern in some use cases): ~110ms\n", " \n", " >>> path = np.einsum_path('ijk,ilm,njm,nlk,abc->',a,a,a,a,a, optimize='optimal')[0]\n", " >>> for iteration in range(500):\n", " ... _ = np.einsum('ijk,ilm,njm,nlk,abc->',a,a,a,a,a, optimize=path)\n", " \n", " einsum_path(*operands, optimize='greedy', einsum_call=False)\n", " einsum_path(subscripts, *operands, optimize='greedy')\n", " \n", " Evaluates the lowest cost contraction order for an einsum expression by\n", " considering the creation of intermediate arrays.\n", " \n", " Parameters\n", " ----------\n", " subscripts : str\n", " Specifies the subscripts for summation.\n", " *operands : list of array_like\n", " These are the arrays for the operation.\n", " optimize : {bool, list, tuple, 'greedy', 'optimal'}\n", " Choose the type of path. If a tuple is provided, the second argument is\n", " assumed to be the maximum intermediate size created. If only a single\n", " argument is provided the largest input or output array size is used\n", " as a maximum intermediate size.\n", " \n", " * if a list is given that starts with ``einsum_path``, uses this as the\n", " contraction path\n", " * if False no optimization is taken\n", " * if True defaults to the 'greedy' algorithm\n", " * 'optimal' An algorithm that combinatorially explores all possible\n", " ways of contracting the listed tensors and choosest the least costly\n", " path. Scales exponentially with the number of terms in the\n", " contraction.\n", " * 'greedy' An algorithm that chooses the best pair contraction\n", " at each step. Effectively, this algorithm searches the largest inner,\n", " Hadamard, and then outer products at each step. Scales cubically with\n", " the number of terms in the contraction. Equivalent to the 'optimal'\n", " path for most contractions.\n", " \n", " Default is 'greedy'.\n", " \n", " Returns\n", " -------\n", " path : list of tuples\n", " A list representation of the einsum path.\n", " string_repr : str\n", " A printable representation of the einsum path.\n", " \n", " Notes\n", " -----\n", " The resulting path indicates which terms of the input contraction should be\n", " contracted first, the result of this contraction is then appended to the\n", " end of the contraction list. This list can then be iterated over until all\n", " intermediate contractions are complete.\n", " \n", " See Also\n", " --------\n", " einsum, linalg.multi_dot\n", " \n", " Examples\n", " --------\n", " \n", " We can begin with a chain dot example. In this case, it is optimal to\n", " contract the ``b`` and ``c`` tensors first as represented by the first\n", " element of the path ``(1, 2)``. The resulting tensor is added to the end\n", " of the contraction and the remaining contraction ``(0, 1)`` is then\n", " completed.\n", " \n", " >>> np.random.seed(123)\n", " >>> a = np.random.rand(2, 2)\n", " >>> b = np.random.rand(2, 5)\n", " >>> c = np.random.rand(5, 2)\n", " >>> path_info = np.einsum_path('ij,jk,kl->il', a, b, c, optimize='greedy')\n", " >>> print(path_info[0])\n", " ['einsum_path', (1, 2), (0, 1)]\n", " >>> print(path_info[1])\n", " Complete contraction: ij,jk,kl->il # may vary\n", " Naive scaling: 4\n", " Optimized scaling: 3\n", " Naive FLOP count: 1.600e+02\n", " Optimized FLOP count: 5.600e+01\n", " Theoretical speedup: 2.857\n", " Largest intermediate: 4.000e+00 elements\n", " -------------------------------------------------------------------------\n", " scaling current remaining\n", " -------------------------------------------------------------------------\n", " 3 kl,jk->jl ij,jl->il\n", " 3 jl,ij->il il->il\n", " \n", " \n", " A more complex index transformation example.\n", " \n", " >>> I = np.random.rand(10, 10, 10, 10)\n", " >>> C = np.random.rand(10, 10)\n", " >>> path_info = np.einsum_path('ea,fb,abcd,gc,hd->efgh', C, C, I, C, C,\n", " ... optimize='greedy')\n", " \n", " >>> print(path_info[0])\n", " ['einsum_path', (0, 2), (0, 3), (0, 2), (0, 1)]\n", " >>> print(path_info[1]) \n", " Complete contraction: ea,fb,abcd,gc,hd->efgh # may vary\n", " Naive scaling: 8\n", " Optimized scaling: 5\n", " Naive FLOP count: 8.000e+08\n", " Optimized FLOP count: 8.000e+05\n", " Theoretical speedup: 1000.000\n", " Largest intermediate: 1.000e+04 elements\n", " --------------------------------------------------------------------------\n", " scaling current remaining\n", " --------------------------------------------------------------------------\n", " 5 abcd,ea->bcde fb,gc,hd,bcde->efgh\n", " 5 bcde,fb->cdef gc,hd,cdef->efgh\n", " 5 cdef,gc->defg hd,defg->efgh\n", " 5 defg,hd->efgh efgh->efgh\n", " \n", " empty(...)\n", " empty(shape, dtype=float, order='C', *, like=None)\n", " \n", " Return a new array of given shape and type, without initializing entries.\n", " \n", " Parameters\n", " ----------\n", " shape : int or tuple of int\n", " Shape of the empty array, e.g., ``(2, 3)`` or ``2``.\n", " dtype : data-type, optional\n", " Desired output data-type for the array, e.g, `numpy.int8`. Default is\n", " `numpy.float64`.\n", " order : {'C', 'F'}, optional, default: 'C'\n", " Whether to store multi-dimensional data in row-major\n", " (C-style) or column-major (Fortran-style) order in\n", " memory.\n", " like : array_like, optional\n", " Reference object to allow the creation of arrays which are not\n", " NumPy arrays. If an array-like passed in as ``like`` supports\n", " the ``__array_function__`` protocol, the result will be defined\n", " by it. In this case, it ensures the creation of an array object\n", " compatible with that passed in via this argument.\n", " \n", " .. versionadded:: 1.20.0\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " Array of uninitialized (arbitrary) data of the given shape, dtype, and\n", " order. Object arrays will be initialized to None.\n", " \n", " See Also\n", " --------\n", " empty_like : Return an empty array with shape and type of input.\n", " ones : Return a new array setting values to one.\n", " zeros : Return a new array setting values to zero.\n", " full : Return a new array of given shape filled with value.\n", " \n", " \n", " Notes\n", " -----\n", " `empty`, unlike `zeros`, does not set the array values to zero,\n", " and may therefore be marginally faster. On the other hand, it requires\n", " the user to manually set all the values in the array, and should be\n", " used with caution.\n", " \n", " Examples\n", " --------\n", " >>> np.empty([2, 2])\n", " array([[ -9.74499359e+001, 6.69583040e-309],\n", " [ 2.13182611e-314, 3.06959433e-309]]) #uninitialized\n", " \n", " >>> np.empty([2, 2], dtype=int)\n", " array([[-1073741821, -1067949133],\n", " [ 496041986, 19249760]]) #uninitialized\n", " \n", " empty_like(...)\n", " empty_like(prototype, dtype=None, order='K', subok=True, shape=None)\n", " \n", " Return a new array with the same shape and type as a given array.\n", " \n", " Parameters\n", " ----------\n", " prototype : array_like\n", " The shape and data-type of `prototype` define these same attributes\n", " of the returned array.\n", " dtype : data-type, optional\n", " Overrides the data type of the result.\n", " \n", " .. versionadded:: 1.6.0\n", " order : {'C', 'F', 'A', or 'K'}, optional\n", " Overrides the memory layout of the result. 'C' means C-order,\n", " 'F' means F-order, 'A' means 'F' if `prototype` is Fortran\n", " contiguous, 'C' otherwise. 'K' means match the layout of `prototype`\n", " as closely as possible.\n", " \n", " .. versionadded:: 1.6.0\n", " subok : bool, optional.\n", " If True, then the newly created array will use the sub-class\n", " type of `prototype`, otherwise it will be a base-class array. Defaults\n", " to True.\n", " shape : int or sequence of ints, optional.\n", " Overrides the shape of the result. If order='K' and the number of\n", " dimensions is unchanged, will try to keep order, otherwise,\n", " order='C' is implied.\n", " \n", " .. versionadded:: 1.17.0\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " Array of uninitialized (arbitrary) data with the same\n", " shape and type as `prototype`.\n", " \n", " See Also\n", " --------\n", " ones_like : Return an array of ones with shape and type of input.\n", " zeros_like : Return an array of zeros with shape and type of input.\n", " full_like : Return a new array with shape of input filled with value.\n", " empty : Return a new uninitialized array.\n", " \n", " Notes\n", " -----\n", " This function does *not* initialize the returned array; to do that use\n", " `zeros_like` or `ones_like` instead. It may be marginally faster than\n", " the functions that do set the array values.\n", " \n", " Examples\n", " --------\n", " >>> a = ([1,2,3], [4,5,6]) # a is array-like\n", " >>> np.empty_like(a)\n", " array([[-1073741821, -1073741821, 3], # uninitialized\n", " [ 0, 0, -1073741821]])\n", " >>> a = np.array([[1., 2., 3.],[4.,5.,6.]])\n", " >>> np.empty_like(a)\n", " array([[ -2.00000715e+000, 1.48219694e-323, -2.00000572e+000], # uninitialized\n", " [ 4.38791518e-305, -2.00000715e+000, 4.17269252e-309]])\n", " \n", " expand_dims(a, axis)\n", " Expand the shape of an array.\n", " \n", " Insert a new axis that will appear at the `axis` position in the expanded\n", " array shape.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input array.\n", " axis : int or tuple of ints\n", " Position in the expanded axes where the new axis (or axes) is placed.\n", " \n", " .. deprecated:: 1.13.0\n", " Passing an axis where ``axis > a.ndim`` will be treated as\n", " ``axis == a.ndim``, and passing ``axis < -a.ndim - 1`` will\n", " be treated as ``axis == 0``. This behavior is deprecated.\n", " \n", " .. versionchanged:: 1.18.0\n", " A tuple of axes is now supported. Out of range axes as\n", " described above are now forbidden and raise an `AxisError`.\n", " \n", " Returns\n", " -------\n", " result : ndarray\n", " View of `a` with the number of dimensions increased.\n", " \n", " See Also\n", " --------\n", " squeeze : The inverse operation, removing singleton dimensions\n", " reshape : Insert, remove, and combine dimensions, and resize existing ones\n", " doc.indexing, atleast_1d, atleast_2d, atleast_3d\n", " \n", " Examples\n", " --------\n", " >>> x = np.array([1, 2])\n", " >>> x.shape\n", " (2,)\n", " \n", " The following is equivalent to ``x[np.newaxis, :]`` or ``x[np.newaxis]``:\n", " \n", " >>> y = np.expand_dims(x, axis=0)\n", " >>> y\n", " array([[1, 2]])\n", " >>> y.shape\n", " (1, 2)\n", " \n", " The following is equivalent to ``x[:, np.newaxis]``:\n", " \n", " >>> y = np.expand_dims(x, axis=1)\n", " >>> y\n", " array([[1],\n", " [2]])\n", " >>> y.shape\n", " (2, 1)\n", " \n", " ``axis`` may also be a tuple:\n", " \n", " >>> y = np.expand_dims(x, axis=(0, 1))\n", " >>> y\n", " array([[[1, 2]]])\n", " \n", " >>> y = np.expand_dims(x, axis=(2, 0))\n", " >>> y\n", " array([[[1],\n", " [2]]])\n", " \n", " Note that some examples may use ``None`` instead of ``np.newaxis``. These\n", " are the same objects:\n", " \n", " >>> np.newaxis is None\n", " True\n", " \n", " extract(condition, arr)\n", " Return the elements of an array that satisfy some condition.\n", " \n", " This is equivalent to ``np.compress(ravel(condition), ravel(arr))``. If\n", " `condition` is boolean ``np.extract`` is equivalent to ``arr[condition]``.\n", " \n", " Note that `place` does the exact opposite of `extract`.\n", " \n", " Parameters\n", " ----------\n", " condition : array_like\n", " An array whose nonzero or True entries indicate the elements of `arr`\n", " to extract.\n", " arr : array_like\n", " Input array of the same size as `condition`.\n", " \n", " Returns\n", " -------\n", " extract : ndarray\n", " Rank 1 array of values from `arr` where `condition` is True.\n", " \n", " See Also\n", " --------\n", " take, put, copyto, compress, place\n", " \n", " Examples\n", " --------\n", " >>> arr = np.arange(12).reshape((3, 4))\n", " >>> arr\n", " array([[ 0, 1, 2, 3],\n", " [ 4, 5, 6, 7],\n", " [ 8, 9, 10, 11]])\n", " >>> condition = np.mod(arr, 3)==0\n", " >>> condition\n", " array([[ True, False, False, True],\n", " [False, False, True, False],\n", " [False, True, False, False]])\n", " >>> np.extract(condition, arr)\n", " array([0, 3, 6, 9])\n", " \n", " \n", " If `condition` is boolean:\n", " \n", " >>> arr[condition]\n", " array([0, 3, 6, 9])\n", " \n", " eye(N, M=None, k=0, dtype=<class 'float'>, order='C', *, like=None)\n", " Return a 2-D array with ones on the diagonal and zeros elsewhere.\n", " \n", " Parameters\n", " ----------\n", " N : int\n", " Number of rows in the output.\n", " M : int, optional\n", " Number of columns in the output. If None, defaults to `N`.\n", " k : int, optional\n", " Index of the diagonal: 0 (the default) refers to the main diagonal,\n", " a positive value refers to an upper diagonal, and a negative value\n", " to a lower diagonal.\n", " dtype : data-type, optional\n", " Data-type of the returned array.\n", " order : {'C', 'F'}, optional\n", " Whether the output should be stored in row-major (C-style) or\n", " column-major (Fortran-style) order in memory.\n", " \n", " .. versionadded:: 1.14.0\n", " like : array_like, optional\n", " Reference object to allow the creation of arrays which are not\n", " NumPy arrays. If an array-like passed in as ``like`` supports\n", " the ``__array_function__`` protocol, the result will be defined\n", " by it. In this case, it ensures the creation of an array object\n", " compatible with that passed in via this argument.\n", " \n", " .. versionadded:: 1.20.0\n", " \n", " Returns\n", " -------\n", " I : ndarray of shape (N,M)\n", " An array where all elements are equal to zero, except for the `k`-th\n", " diagonal, whose values are equal to one.\n", " \n", " See Also\n", " --------\n", " identity : (almost) equivalent function\n", " diag : diagonal 2-D array from a 1-D array specified by the user.\n", " \n", " Examples\n", " --------\n", " >>> np.eye(2, dtype=int)\n", " array([[1, 0],\n", " [0, 1]])\n", " >>> np.eye(3, k=1)\n", " array([[0., 1., 0.],\n", " [0., 0., 1.],\n", " [0., 0., 0.]])\n", " \n", " fastCopyAndTranspose(...)\n", " fastCopyAndTranspose(a)\n", " \n", " .. deprecated:: 1.24\n", " \n", " fastCopyAndTranspose is deprecated and will be removed. Use the copy and\n", " transpose methods instead, e.g. ``arr.T.copy()``\n", " \n", " fill_diagonal(a, val, wrap=False)\n", " Fill the main diagonal of the given array of any dimensionality.\n", " \n", " For an array `a` with ``a.ndim >= 2``, the diagonal is the list of\n", " locations with indices ``a[i, ..., i]`` all identical. This function\n", " modifies the input array in-place, it does not return a value.\n", " \n", " Parameters\n", " ----------\n", " a : array, at least 2-D.\n", " Array whose diagonal is to be filled, it gets modified in-place.\n", " \n", " val : scalar or array_like\n", " Value(s) to write on the diagonal. If `val` is scalar, the value is\n", " written along the diagonal. If array-like, the flattened `val` is\n", " written along the diagonal, repeating if necessary to fill all\n", " diagonal entries.\n", " \n", " wrap : bool\n", " For tall matrices in NumPy version up to 1.6.2, the\n", " diagonal \"wrapped\" after N columns. You can have this behavior\n", " with this option. This affects only tall matrices.\n", " \n", " See also\n", " --------\n", " diag_indices, diag_indices_from\n", " \n", " Notes\n", " -----\n", " .. versionadded:: 1.4.0\n", " \n", " This functionality can be obtained via `diag_indices`, but internally\n", " this version uses a much faster implementation that never constructs the\n", " indices and uses simple slicing.\n", " \n", " Examples\n", " --------\n", " >>> a = np.zeros((3, 3), int)\n", " >>> np.fill_diagonal(a, 5)\n", " >>> a\n", " array([[5, 0, 0],\n", " [0, 5, 0],\n", " [0, 0, 5]])\n", " \n", " The same function can operate on a 4-D array:\n", " \n", " >>> a = np.zeros((3, 3, 3, 3), int)\n", " >>> np.fill_diagonal(a, 4)\n", " \n", " We only show a few blocks for clarity:\n", " \n", " >>> a[0, 0]\n", " array([[4, 0, 0],\n", " [0, 0, 0],\n", " [0, 0, 0]])\n", " >>> a[1, 1]\n", " array([[0, 0, 0],\n", " [0, 4, 0],\n", " [0, 0, 0]])\n", " >>> a[2, 2]\n", " array([[0, 0, 0],\n", " [0, 0, 0],\n", " [0, 0, 4]])\n", " \n", " The wrap option affects only tall matrices:\n", " \n", " >>> # tall matrices no wrap\n", " >>> a = np.zeros((5, 3), int)\n", " >>> np.fill_diagonal(a, 4)\n", " >>> a\n", " array([[4, 0, 0],\n", " [0, 4, 0],\n", " [0, 0, 4],\n", " [0, 0, 0],\n", " [0, 0, 0]])\n", " \n", " >>> # tall matrices wrap\n", " >>> a = np.zeros((5, 3), int)\n", " >>> np.fill_diagonal(a, 4, wrap=True)\n", " >>> a\n", " array([[4, 0, 0],\n", " [0, 4, 0],\n", " [0, 0, 4],\n", " [0, 0, 0],\n", " [4, 0, 0]])\n", " \n", " >>> # wide matrices\n", " >>> a = np.zeros((3, 5), int)\n", " >>> np.fill_diagonal(a, 4, wrap=True)\n", " >>> a\n", " array([[4, 0, 0, 0, 0],\n", " [0, 4, 0, 0, 0],\n", " [0, 0, 4, 0, 0]])\n", " \n", " The anti-diagonal can be filled by reversing the order of elements\n", " using either `numpy.flipud` or `numpy.fliplr`.\n", " \n", " >>> a = np.zeros((3, 3), int);\n", " >>> np.fill_diagonal(np.fliplr(a), [1,2,3]) # Horizontal flip\n", " >>> a\n", " array([[0, 0, 1],\n", " [0, 2, 0],\n", " [3, 0, 0]])\n", " >>> np.fill_diagonal(np.flipud(a), [1,2,3]) # Vertical flip\n", " >>> a\n", " array([[0, 0, 3],\n", " [0, 2, 0],\n", " [1, 0, 0]])\n", " \n", " Note that the order in which the diagonal is filled varies depending\n", " on the flip function.\n", " \n", " find_common_type(array_types, scalar_types)\n", " Determine common type following standard coercion rules.\n", " \n", " Parameters\n", " ----------\n", " array_types : sequence\n", " A list of dtypes or dtype convertible objects representing arrays.\n", " scalar_types : sequence\n", " A list of dtypes or dtype convertible objects representing scalars.\n", " \n", " Returns\n", " -------\n", " datatype : dtype\n", " The common data type, which is the maximum of `array_types` ignoring\n", " `scalar_types`, unless the maximum of `scalar_types` is of a\n", " different kind (`dtype.kind`). If the kind is not understood, then\n", " None is returned.\n", " \n", " See Also\n", " --------\n", " dtype, common_type, can_cast, mintypecode\n", " \n", " Examples\n", " --------\n", " >>> np.find_common_type([], [np.int64, np.float32, complex])\n", " dtype('complex128')\n", " >>> np.find_common_type([np.int64, np.float32], [])\n", " dtype('float64')\n", " \n", " The standard casting rules ensure that a scalar cannot up-cast an\n", " array unless the scalar is of a fundamentally different kind of data\n", " (i.e. under a different hierarchy in the data type hierarchy) then\n", " the array:\n", " \n", " >>> np.find_common_type([np.float32], [np.int64, np.float64])\n", " dtype('float32')\n", " \n", " Complex is of a different type, so it up-casts the float in the\n", " `array_types` argument:\n", " \n", " >>> np.find_common_type([np.float32], [complex])\n", " dtype('complex128')\n", " \n", " Type specifier strings are convertible to dtypes and can therefore\n", " be used instead of dtypes:\n", " \n", " >>> np.find_common_type(['f4', 'f4', 'i4'], ['c8'])\n", " dtype('complex128')\n", " \n", " fix(x, out=None)\n", " Round to nearest integer towards zero.\n", " \n", " Round an array of floats element-wise to nearest integer towards zero.\n", " The rounded values are returned as floats.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " An array of floats to be rounded\n", " out : ndarray, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the input broadcasts to. If not provided or None, a\n", " freshly-allocated array is returned.\n", " \n", " Returns\n", " -------\n", " out : ndarray of floats\n", " A float array with the same dimensions as the input.\n", " If second argument is not supplied then a float array is returned\n", " with the rounded values.\n", " \n", " If a second argument is supplied the result is stored there.\n", " The return value `out` is then a reference to that array.\n", " \n", " See Also\n", " --------\n", " rint, trunc, floor, ceil\n", " around : Round to given number of decimals\n", " \n", " Examples\n", " --------\n", " >>> np.fix(3.14)\n", " 3.0\n", " >>> np.fix(3)\n", " 3.0\n", " >>> np.fix([2.1, 2.9, -2.1, -2.9])\n", " array([ 2., 2., -2., -2.])\n", " \n", " flatnonzero(a)\n", " Return indices that are non-zero in the flattened version of a.\n", " \n", " This is equivalent to ``np.nonzero(np.ravel(a))[0]``.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input data.\n", " \n", " Returns\n", " -------\n", " res : ndarray\n", " Output array, containing the indices of the elements of ``a.ravel()``\n", " that are non-zero.\n", " \n", " See Also\n", " --------\n", " nonzero : Return the indices of the non-zero elements of the input array.\n", " ravel : Return a 1-D array containing the elements of the input array.\n", " \n", " Examples\n", " --------\n", " >>> x = np.arange(-2, 3)\n", " >>> x\n", " array([-2, -1, 0, 1, 2])\n", " >>> np.flatnonzero(x)\n", " array([0, 1, 3, 4])\n", " \n", " Use the indices of the non-zero elements as an index array to extract\n", " these elements:\n", " \n", " >>> x.ravel()[np.flatnonzero(x)]\n", " array([-2, -1, 1, 2])\n", " \n", " flip(m, axis=None)\n", " Reverse the order of elements in an array along the given axis.\n", " \n", " The shape of the array is preserved, but the elements are reordered.\n", " \n", " .. versionadded:: 1.12.0\n", " \n", " Parameters\n", " ----------\n", " m : array_like\n", " Input array.\n", " axis : None or int or tuple of ints, optional\n", " Axis or axes along which to flip over. The default,\n", " axis=None, will flip over all of the axes of the input array.\n", " If axis is negative it counts from the last to the first axis.\n", " \n", " If axis is a tuple of ints, flipping is performed on all of the axes\n", " specified in the tuple.\n", " \n", " .. versionchanged:: 1.15.0\n", " None and tuples of axes are supported\n", " \n", " Returns\n", " -------\n", " out : array_like\n", " A view of `m` with the entries of axis reversed. Since a view is\n", " returned, this operation is done in constant time.\n", " \n", " See Also\n", " --------\n", " flipud : Flip an array vertically (axis=0).\n", " fliplr : Flip an array horizontally (axis=1).\n", " \n", " Notes\n", " -----\n", " flip(m, 0) is equivalent to flipud(m).\n", " \n", " flip(m, 1) is equivalent to fliplr(m).\n", " \n", " flip(m, n) corresponds to ``m[...,::-1,...]`` with ``::-1`` at position n.\n", " \n", " flip(m) corresponds to ``m[::-1,::-1,...,::-1]`` with ``::-1`` at all\n", " positions.\n", " \n", " flip(m, (0, 1)) corresponds to ``m[::-1,::-1,...]`` with ``::-1`` at\n", " position 0 and position 1.\n", " \n", " Examples\n", " --------\n", " >>> A = np.arange(8).reshape((2,2,2))\n", " >>> A\n", " array([[[0, 1],\n", " [2, 3]],\n", " [[4, 5],\n", " [6, 7]]])\n", " >>> np.flip(A, 0)\n", " array([[[4, 5],\n", " [6, 7]],\n", " [[0, 1],\n", " [2, 3]]])\n", " >>> np.flip(A, 1)\n", " array([[[2, 3],\n", " [0, 1]],\n", " [[6, 7],\n", " [4, 5]]])\n", " >>> np.flip(A)\n", " array([[[7, 6],\n", " [5, 4]],\n", " [[3, 2],\n", " [1, 0]]])\n", " >>> np.flip(A, (0, 2))\n", " array([[[5, 4],\n", " [7, 6]],\n", " [[1, 0],\n", " [3, 2]]])\n", " >>> A = np.random.randn(3,4,5)\n", " >>> np.all(np.flip(A,2) == A[:,:,::-1,...])\n", " True\n", " \n", " fliplr(m)\n", " Reverse the order of elements along axis 1 (left/right).\n", " \n", " For a 2-D array, this flips the entries in each row in the left/right\n", " direction. Columns are preserved, but appear in a different order than\n", " before.\n", " \n", " Parameters\n", " ----------\n", " m : array_like\n", " Input array, must be at least 2-D.\n", " \n", " Returns\n", " -------\n", " f : ndarray\n", " A view of `m` with the columns reversed. Since a view\n", " is returned, this operation is :math:`\\mathcal O(1)`.\n", " \n", " See Also\n", " --------\n", " flipud : Flip array in the up/down direction.\n", " flip : Flip array in one or more dimensions.\n", " rot90 : Rotate array counterclockwise.\n", " \n", " Notes\n", " -----\n", " Equivalent to ``m[:,::-1]`` or ``np.flip(m, axis=1)``.\n", " Requires the array to be at least 2-D.\n", " \n", " Examples\n", " --------\n", " >>> A = np.diag([1.,2.,3.])\n", " >>> A\n", " array([[1., 0., 0.],\n", " [0., 2., 0.],\n", " [0., 0., 3.]])\n", " >>> np.fliplr(A)\n", " array([[0., 0., 1.],\n", " [0., 2., 0.],\n", " [3., 0., 0.]])\n", " \n", " >>> A = np.random.randn(2,3,5)\n", " >>> np.all(np.fliplr(A) == A[:,::-1,...])\n", " True\n", " \n", " flipud(m)\n", " Reverse the order of elements along axis 0 (up/down).\n", " \n", " For a 2-D array, this flips the entries in each column in the up/down\n", " direction. Rows are preserved, but appear in a different order than before.\n", " \n", " Parameters\n", " ----------\n", " m : array_like\n", " Input array.\n", " \n", " Returns\n", " -------\n", " out : array_like\n", " A view of `m` with the rows reversed. Since a view is\n", " returned, this operation is :math:`\\mathcal O(1)`.\n", " \n", " See Also\n", " --------\n", " fliplr : Flip array in the left/right direction.\n", " flip : Flip array in one or more dimensions.\n", " rot90 : Rotate array counterclockwise.\n", " \n", " Notes\n", " -----\n", " Equivalent to ``m[::-1, ...]`` or ``np.flip(m, axis=0)``.\n", " Requires the array to be at least 1-D.\n", " \n", " Examples\n", " --------\n", " >>> A = np.diag([1.0, 2, 3])\n", " >>> A\n", " array([[1., 0., 0.],\n", " [0., 2., 0.],\n", " [0., 0., 3.]])\n", " >>> np.flipud(A)\n", " array([[0., 0., 3.],\n", " [0., 2., 0.],\n", " [1., 0., 0.]])\n", " \n", " >>> A = np.random.randn(2,3,5)\n", " >>> np.all(np.flipud(A) == A[::-1,...])\n", " True\n", " \n", " >>> np.flipud([1,2])\n", " array([2, 1])\n", " \n", " format_float_positional(x, precision=None, unique=True, fractional=True, trim='k', sign=False, pad_left=None, pad_right=None, min_digits=None)\n", " Format a floating-point scalar as a decimal string in positional notation.\n", " \n", " Provides control over rounding, trimming and padding. Uses and assumes\n", " IEEE unbiased rounding. Uses the \"Dragon4\" algorithm.\n", " \n", " Parameters\n", " ----------\n", " x : python float or numpy floating scalar\n", " Value to format.\n", " precision : non-negative integer or None, optional\n", " Maximum number of digits to print. May be None if `unique` is\n", " `True`, but must be an integer if unique is `False`.\n", " unique : boolean, optional\n", " If `True`, use a digit-generation strategy which gives the shortest\n", " representation which uniquely identifies the floating-point number from\n", " other values of the same type, by judicious rounding. If `precision`\n", " is given fewer digits than necessary can be printed, or if `min_digits`\n", " is given more can be printed, in which cases the last digit is rounded\n", " with unbiased rounding.\n", " If `False`, digits are generated as if printing an infinite-precision\n", " value and stopping after `precision` digits, rounding the remaining\n", " value with unbiased rounding\n", " fractional : boolean, optional\n", " If `True`, the cutoffs of `precision` and `min_digits` refer to the\n", " total number of digits after the decimal point, including leading\n", " zeros.\n", " If `False`, `precision` and `min_digits` refer to the total number of\n", " significant digits, before or after the decimal point, ignoring leading\n", " zeros.\n", " trim : one of 'k', '.', '0', '-', optional\n", " Controls post-processing trimming of trailing digits, as follows:\n", " \n", " * 'k' : keep trailing zeros, keep decimal point (no trimming)\n", " * '.' : trim all trailing zeros, leave decimal point\n", " * '0' : trim all but the zero before the decimal point. Insert the\n", " zero if it is missing.\n", " * '-' : trim trailing zeros and any trailing decimal point\n", " sign : boolean, optional\n", " Whether to show the sign for positive values.\n", " pad_left : non-negative integer, optional\n", " Pad the left side of the string with whitespace until at least that\n", " many characters are to the left of the decimal point.\n", " pad_right : non-negative integer, optional\n", " Pad the right side of the string with whitespace until at least that\n", " many characters are to the right of the decimal point.\n", " min_digits : non-negative integer or None, optional\n", " Minimum number of digits to print. Only has an effect if `unique=True`\n", " in which case additional digits past those necessary to uniquely\n", " identify the value may be printed, rounding the last additional digit.\n", " \n", " -- versionadded:: 1.21.0\n", " \n", " Returns\n", " -------\n", " rep : string\n", " The string representation of the floating point value\n", " \n", " See Also\n", " --------\n", " format_float_scientific\n", " \n", " Examples\n", " --------\n", " >>> np.format_float_positional(np.float32(np.pi))\n", " '3.1415927'\n", " >>> np.format_float_positional(np.float16(np.pi))\n", " '3.14'\n", " >>> np.format_float_positional(np.float16(0.3))\n", " '0.3'\n", " >>> np.format_float_positional(np.float16(0.3), unique=False, precision=10)\n", " '0.3000488281'\n", " \n", " format_float_scientific(x, precision=None, unique=True, trim='k', sign=False, pad_left=None, exp_digits=None, min_digits=None)\n", " Format a floating-point scalar as a decimal string in scientific notation.\n", " \n", " Provides control over rounding, trimming and padding. Uses and assumes\n", " IEEE unbiased rounding. Uses the \"Dragon4\" algorithm.\n", " \n", " Parameters\n", " ----------\n", " x : python float or numpy floating scalar\n", " Value to format.\n", " precision : non-negative integer or None, optional\n", " Maximum number of digits to print. May be None if `unique` is\n", " `True`, but must be an integer if unique is `False`.\n", " unique : boolean, optional\n", " If `True`, use a digit-generation strategy which gives the shortest\n", " representation which uniquely identifies the floating-point number from\n", " other values of the same type, by judicious rounding. If `precision`\n", " is given fewer digits than necessary can be printed. If `min_digits`\n", " is given more can be printed, in which cases the last digit is rounded\n", " with unbiased rounding.\n", " If `False`, digits are generated as if printing an infinite-precision\n", " value and stopping after `precision` digits, rounding the remaining\n", " value with unbiased rounding\n", " trim : one of 'k', '.', '0', '-', optional\n", " Controls post-processing trimming of trailing digits, as follows:\n", " \n", " * 'k' : keep trailing zeros, keep decimal point (no trimming)\n", " * '.' : trim all trailing zeros, leave decimal point\n", " * '0' : trim all but the zero before the decimal point. Insert the\n", " zero if it is missing.\n", " * '-' : trim trailing zeros and any trailing decimal point\n", " sign : boolean, optional\n", " Whether to show the sign for positive values.\n", " pad_left : non-negative integer, optional\n", " Pad the left side of the string with whitespace until at least that\n", " many characters are to the left of the decimal point.\n", " exp_digits : non-negative integer, optional\n", " Pad the exponent with zeros until it contains at least this many digits.\n", " If omitted, the exponent will be at least 2 digits.\n", " min_digits : non-negative integer or None, optional\n", " Minimum number of digits to print. This only has an effect for\n", " `unique=True`. In that case more digits than necessary to uniquely\n", " identify the value may be printed and rounded unbiased.\n", " \n", " -- versionadded:: 1.21.0\n", " \n", " Returns\n", " -------\n", " rep : string\n", " The string representation of the floating point value\n", " \n", " See Also\n", " --------\n", " format_float_positional\n", " \n", " Examples\n", " --------\n", " >>> np.format_float_scientific(np.float32(np.pi))\n", " '3.1415927e+00'\n", " >>> s = np.float32(1.23e24)\n", " >>> np.format_float_scientific(s, unique=False, precision=15)\n", " '1.230000071797338e+24'\n", " >>> np.format_float_scientific(s, exp_digits=4)\n", " '1.23e+0024'\n", " \n", " from_dlpack(...)\n", " from_dlpack(x, /)\n", " \n", " Create a NumPy array from an object implementing the ``__dlpack__``\n", " protocol. Generally, the returned NumPy array is a read-only view\n", " of the input object. See [1]_ and [2]_ for more details.\n", " \n", " Parameters\n", " ----------\n", " x : object\n", " A Python object that implements the ``__dlpack__`` and\n", " ``__dlpack_device__`` methods.\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " \n", " References\n", " ----------\n", " .. [1] Array API documentation,\n", " https://data-apis.org/array-api/latest/design_topics/data_interchange.html#syntax-for-data-interchange-with-dlpack\n", " \n", " .. [2] Python specification for DLPack,\n", " https://dmlc.github.io/dlpack/latest/python_spec.html\n", " \n", " Examples\n", " --------\n", " >>> import torch\n", " >>> x = torch.arange(10)\n", " >>> # create a view of the torch tensor \"x\" in NumPy\n", " >>> y = np.from_dlpack(x)\n", " \n", " frombuffer(...)\n", " frombuffer(buffer, dtype=float, count=-1, offset=0, *, like=None)\n", " \n", " Interpret a buffer as a 1-dimensional array.\n", " \n", " Parameters\n", " ----------\n", " buffer : buffer_like\n", " An object that exposes the buffer interface.\n", " dtype : data-type, optional\n", " Data-type of the returned array; default: float.\n", " count : int, optional\n", " Number of items to read. ``-1`` means all data in the buffer.\n", " offset : int, optional\n", " Start reading the buffer from this offset (in bytes); default: 0.\n", " like : array_like, optional\n", " Reference object to allow the creation of arrays which are not\n", " NumPy arrays. If an array-like passed in as ``like`` supports\n", " the ``__array_function__`` protocol, the result will be defined\n", " by it. In this case, it ensures the creation of an array object\n", " compatible with that passed in via this argument.\n", " \n", " .. versionadded:: 1.20.0\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " \n", " See also\n", " --------\n", " ndarray.tobytes\n", " Inverse of this operation, construct Python bytes from the raw data\n", " bytes in the array.\n", " \n", " Notes\n", " -----\n", " If the buffer has data that is not in machine byte-order, this should\n", " be specified as part of the data-type, e.g.::\n", " \n", " >>> dt = np.dtype(int)\n", " >>> dt = dt.newbyteorder('>')\n", " >>> np.frombuffer(buf, dtype=dt) # doctest: +SKIP\n", " \n", " The data of the resulting array will not be byteswapped, but will be\n", " interpreted correctly.\n", " \n", " This function creates a view into the original object. This should be safe\n", " in general, but it may make sense to copy the result when the original\n", " object is mutable or untrusted.\n", " \n", " Examples\n", " --------\n", " >>> s = b'hello world'\n", " >>> np.frombuffer(s, dtype='S1', count=5, offset=6)\n", " array([b'w', b'o', b'r', b'l', b'd'], dtype='|S1')\n", " \n", " >>> np.frombuffer(b'\\x01\\x02', dtype=np.uint8)\n", " array([1, 2], dtype=uint8)\n", " >>> np.frombuffer(b'\\x01\\x02\\x03\\x04\\x05', dtype=np.uint8, count=3)\n", " array([1, 2, 3], dtype=uint8)\n", " \n", " fromfile(...)\n", " fromfile(file, dtype=float, count=-1, sep='', offset=0, *, like=None)\n", " \n", " Construct an array from data in a text or binary file.\n", " \n", " A highly efficient way of reading binary data with a known data-type,\n", " as well as parsing simply formatted text files. Data written using the\n", " `tofile` method can be read using this function.\n", " \n", " Parameters\n", " ----------\n", " file : file or str or Path\n", " Open file object or filename.\n", " \n", " .. versionchanged:: 1.17.0\n", " `pathlib.Path` objects are now accepted.\n", " \n", " dtype : data-type\n", " Data type of the returned array.\n", " For binary files, it is used to determine the size and byte-order\n", " of the items in the file.\n", " Most builtin numeric types are supported and extension types may be supported.\n", " \n", " .. versionadded:: 1.18.0\n", " Complex dtypes.\n", " \n", " count : int\n", " Number of items to read. ``-1`` means all items (i.e., the complete\n", " file).\n", " sep : str\n", " Separator between items if file is a text file.\n", " Empty (\"\") separator means the file should be treated as binary.\n", " Spaces (\" \") in the separator match zero or more whitespace characters.\n", " A separator consisting only of spaces must match at least one\n", " whitespace.\n", " offset : int\n", " The offset (in bytes) from the file's current position. Defaults to 0.\n", " Only permitted for binary files.\n", " \n", " .. versionadded:: 1.17.0\n", " like : array_like, optional\n", " Reference object to allow the creation of arrays which are not\n", " NumPy arrays. If an array-like passed in as ``like`` supports\n", " the ``__array_function__`` protocol, the result will be defined\n", " by it. In this case, it ensures the creation of an array object\n", " compatible with that passed in via this argument.\n", " \n", " .. versionadded:: 1.20.0\n", " \n", " See also\n", " --------\n", " load, save\n", " ndarray.tofile\n", " loadtxt : More flexible way of loading data from a text file.\n", " \n", " Notes\n", " -----\n", " Do not rely on the combination of `tofile` and `fromfile` for\n", " data storage, as the binary files generated are not platform\n", " independent. In particular, no byte-order or data-type information is\n", " saved. Data can be stored in the platform independent ``.npy`` format\n", " using `save` and `load` instead.\n", " \n", " Examples\n", " --------\n", " Construct an ndarray:\n", " \n", " >>> dt = np.dtype([('time', [('min', np.int64), ('sec', np.int64)]),\n", " ... ('temp', float)])\n", " >>> x = np.zeros((1,), dtype=dt)\n", " >>> x['time']['min'] = 10; x['temp'] = 98.25\n", " >>> x\n", " array([((10, 0), 98.25)],\n", " dtype=[('time', [('min', '<i8'), ('sec', '<i8')]), ('temp', '<f8')])\n", " \n", " Save the raw data to disk:\n", " \n", " >>> import tempfile\n", " >>> fname = tempfile.mkstemp()[1]\n", " >>> x.tofile(fname)\n", " \n", " Read the raw data from disk:\n", " \n", " >>> np.fromfile(fname, dtype=dt)\n", " array([((10, 0), 98.25)],\n", " dtype=[('time', [('min', '<i8'), ('sec', '<i8')]), ('temp', '<f8')])\n", " \n", " The recommended way to store and load data:\n", " \n", " >>> np.save(fname, x)\n", " >>> np.load(fname + '.npy')\n", " array([((10, 0), 98.25)],\n", " dtype=[('time', [('min', '<i8'), ('sec', '<i8')]), ('temp', '<f8')])\n", " \n", " fromfunction(function, shape, *, dtype=<class 'float'>, like=None, **kwargs)\n", " Construct an array by executing a function over each coordinate.\n", " \n", " The resulting array therefore has a value ``fn(x, y, z)`` at\n", " coordinate ``(x, y, z)``.\n", " \n", " Parameters\n", " ----------\n", " function : callable\n", " The function is called with N parameters, where N is the rank of\n", " `shape`. Each parameter represents the coordinates of the array\n", " varying along a specific axis. For example, if `shape`\n", " were ``(2, 2)``, then the parameters would be\n", " ``array([[0, 0], [1, 1]])`` and ``array([[0, 1], [0, 1]])``\n", " shape : (N,) tuple of ints\n", " Shape of the output array, which also determines the shape of\n", " the coordinate arrays passed to `function`.\n", " dtype : data-type, optional\n", " Data-type of the coordinate arrays passed to `function`.\n", " By default, `dtype` is float.\n", " like : array_like, optional\n", " Reference object to allow the creation of arrays which are not\n", " NumPy arrays. If an array-like passed in as ``like`` supports\n", " the ``__array_function__`` protocol, the result will be defined\n", " by it. In this case, it ensures the creation of an array object\n", " compatible with that passed in via this argument.\n", " \n", " .. versionadded:: 1.20.0\n", " \n", " Returns\n", " -------\n", " fromfunction : any\n", " The result of the call to `function` is passed back directly.\n", " Therefore the shape of `fromfunction` is completely determined by\n", " `function`. If `function` returns a scalar value, the shape of\n", " `fromfunction` would not match the `shape` parameter.\n", " \n", " See Also\n", " --------\n", " indices, meshgrid\n", " \n", " Notes\n", " -----\n", " Keywords other than `dtype` and `like` are passed to `function`.\n", " \n", " Examples\n", " --------\n", " >>> np.fromfunction(lambda i, j: i, (2, 2), dtype=float)\n", " array([[0., 0.],\n", " [1., 1.]])\n", " \n", " >>> np.fromfunction(lambda i, j: j, (2, 2), dtype=float) \n", " array([[0., 1.],\n", " [0., 1.]])\n", " \n", " >>> np.fromfunction(lambda i, j: i == j, (3, 3), dtype=int)\n", " array([[ True, False, False],\n", " [False, True, False],\n", " [False, False, True]])\n", " \n", " >>> np.fromfunction(lambda i, j: i + j, (3, 3), dtype=int)\n", " array([[0, 1, 2],\n", " [1, 2, 3],\n", " [2, 3, 4]])\n", " \n", " fromiter(...)\n", " fromiter(iter, dtype, count=-1, *, like=None)\n", " \n", " Create a new 1-dimensional array from an iterable object.\n", " \n", " Parameters\n", " ----------\n", " iter : iterable object\n", " An iterable object providing data for the array.\n", " dtype : data-type\n", " The data-type of the returned array.\n", " \n", " .. versionchanged:: 1.23\n", " Object and subarray dtypes are now supported (note that the final\n", " result is not 1-D for a subarray dtype).\n", " \n", " count : int, optional\n", " The number of items to read from *iterable*. The default is -1,\n", " which means all data is read.\n", " like : array_like, optional\n", " Reference object to allow the creation of arrays which are not\n", " NumPy arrays. If an array-like passed in as ``like`` supports\n", " the ``__array_function__`` protocol, the result will be defined\n", " by it. In this case, it ensures the creation of an array object\n", " compatible with that passed in via this argument.\n", " \n", " .. versionadded:: 1.20.0\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " The output array.\n", " \n", " Notes\n", " -----\n", " Specify `count` to improve performance. It allows ``fromiter`` to\n", " pre-allocate the output array, instead of resizing it on demand.\n", " \n", " Examples\n", " --------\n", " >>> iterable = (x*x for x in range(5))\n", " >>> np.fromiter(iterable, float)\n", " array([ 0., 1., 4., 9., 16.])\n", " \n", " A carefully constructed subarray dtype will lead to higher dimensional\n", " results:\n", " \n", " >>> iterable = ((x+1, x+2) for x in range(5))\n", " >>> np.fromiter(iterable, dtype=np.dtype((int, 2)))\n", " array([[1, 2],\n", " [2, 3],\n", " [3, 4],\n", " [4, 5],\n", " [5, 6]])\n", " \n", " frompyfunc(...)\n", " frompyfunc(func, /, nin, nout, *[, identity])\n", " \n", " Takes an arbitrary Python function and returns a NumPy ufunc.\n", " \n", " Can be used, for example, to add broadcasting to a built-in Python\n", " function (see Examples section).\n", " \n", " Parameters\n", " ----------\n", " func : Python function object\n", " An arbitrary Python function.\n", " nin : int\n", " The number of input arguments.\n", " nout : int\n", " The number of objects returned by `func`.\n", " identity : object, optional\n", " The value to use for the `~numpy.ufunc.identity` attribute of the resulting\n", " object. If specified, this is equivalent to setting the underlying\n", " C ``identity`` field to ``PyUFunc_IdentityValue``.\n", " If omitted, the identity is set to ``PyUFunc_None``. Note that this is\n", " _not_ equivalent to setting the identity to ``None``, which implies the\n", " operation is reorderable.\n", " \n", " Returns\n", " -------\n", " out : ufunc\n", " Returns a NumPy universal function (``ufunc``) object.\n", " \n", " See Also\n", " --------\n", " vectorize : Evaluates pyfunc over input arrays using broadcasting rules of numpy.\n", " \n", " Notes\n", " -----\n", " The returned ufunc always returns PyObject arrays.\n", " \n", " Examples\n", " --------\n", " Use frompyfunc to add broadcasting to the Python function ``oct``:\n", " \n", " >>> oct_array = np.frompyfunc(oct, 1, 1)\n", " >>> oct_array(np.array((10, 30, 100)))\n", " array(['0o12', '0o36', '0o144'], dtype=object)\n", " >>> np.array((oct(10), oct(30), oct(100))) # for comparison\n", " array(['0o12', '0o36', '0o144'], dtype='<U5')\n", " \n", " fromregex(file, regexp, dtype, encoding=None)\n", " Construct an array from a text file, using regular expression parsing.\n", " \n", " The returned array is always a structured array, and is constructed from\n", " all matches of the regular expression in the file. Groups in the regular\n", " expression are converted to fields of the structured array.\n", " \n", " Parameters\n", " ----------\n", " file : path or file\n", " Filename or file object to read.\n", " \n", " .. versionchanged:: 1.22.0\n", " Now accepts `os.PathLike` implementations.\n", " regexp : str or regexp\n", " Regular expression used to parse the file.\n", " Groups in the regular expression correspond to fields in the dtype.\n", " dtype : dtype or list of dtypes\n", " Dtype for the structured array; must be a structured datatype.\n", " encoding : str, optional\n", " Encoding used to decode the inputfile. Does not apply to input streams.\n", " \n", " .. versionadded:: 1.14.0\n", " \n", " Returns\n", " -------\n", " output : ndarray\n", " The output array, containing the part of the content of `file` that\n", " was matched by `regexp`. `output` is always a structured array.\n", " \n", " Raises\n", " ------\n", " TypeError\n", " When `dtype` is not a valid dtype for a structured array.\n", " \n", " See Also\n", " --------\n", " fromstring, loadtxt\n", " \n", " Notes\n", " -----\n", " Dtypes for structured arrays can be specified in several forms, but all\n", " forms specify at least the data type and field name. For details see\n", " `basics.rec`.\n", " \n", " Examples\n", " --------\n", " >>> from io import StringIO\n", " >>> text = StringIO(\"1312 foo\\n1534 bar\\n444 qux\")\n", " \n", " >>> regexp = r\"(\\d+)\\s+(...)\" # match [digits, whitespace, anything]\n", " >>> output = np.fromregex(text, regexp,\n", " ... [('num', np.int64), ('key', 'S3')])\n", " >>> output\n", " array([(1312, b'foo'), (1534, b'bar'), ( 444, b'qux')],\n", " dtype=[('num', '<i8'), ('key', 'S3')])\n", " >>> output['num']\n", " array([1312, 1534, 444])\n", " \n", " fromstring(...)\n", " fromstring(string, dtype=float, count=-1, *, sep, like=None)\n", " \n", " A new 1-D array initialized from text data in a string.\n", " \n", " Parameters\n", " ----------\n", " string : str\n", " A string containing the data.\n", " dtype : data-type, optional\n", " The data type of the array; default: float. For binary input data,\n", " the data must be in exactly this format. Most builtin numeric types are\n", " supported and extension types may be supported.\n", " \n", " .. versionadded:: 1.18.0\n", " Complex dtypes.\n", " \n", " count : int, optional\n", " Read this number of `dtype` elements from the data. If this is\n", " negative (the default), the count will be determined from the\n", " length of the data.\n", " sep : str, optional\n", " The string separating numbers in the data; extra whitespace between\n", " elements is also ignored.\n", " \n", " .. deprecated:: 1.14\n", " Passing ``sep=''``, the default, is deprecated since it will\n", " trigger the deprecated binary mode of this function. This mode\n", " interprets `string` as binary bytes, rather than ASCII text with\n", " decimal numbers, an operation which is better spelt\n", " ``frombuffer(string, dtype, count)``. If `string` contains unicode\n", " text, the binary mode of `fromstring` will first encode it into\n", " bytes using utf-8, which will not produce sane results.\n", " \n", " like : array_like, optional\n", " Reference object to allow the creation of arrays which are not\n", " NumPy arrays. If an array-like passed in as ``like`` supports\n", " the ``__array_function__`` protocol, the result will be defined\n", " by it. In this case, it ensures the creation of an array object\n", " compatible with that passed in via this argument.\n", " \n", " .. versionadded:: 1.20.0\n", " \n", " Returns\n", " -------\n", " arr : ndarray\n", " The constructed array.\n", " \n", " Raises\n", " ------\n", " ValueError\n", " If the string is not the correct size to satisfy the requested\n", " `dtype` and `count`.\n", " \n", " See Also\n", " --------\n", " frombuffer, fromfile, fromiter\n", " \n", " Examples\n", " --------\n", " >>> np.fromstring('1 2', dtype=int, sep=' ')\n", " array([1, 2])\n", " >>> np.fromstring('1, 2', dtype=int, sep=',')\n", " array([1, 2])\n", " \n", " full(shape, fill_value, dtype=None, order='C', *, like=None)\n", " Return a new array of given shape and type, filled with `fill_value`.\n", " \n", " Parameters\n", " ----------\n", " shape : int or sequence of ints\n", " Shape of the new array, e.g., ``(2, 3)`` or ``2``.\n", " fill_value : scalar or array_like\n", " Fill value.\n", " dtype : data-type, optional\n", " The desired data-type for the array The default, None, means\n", " ``np.array(fill_value).dtype``.\n", " order : {'C', 'F'}, optional\n", " Whether to store multidimensional data in C- or Fortran-contiguous\n", " (row- or column-wise) order in memory.\n", " like : array_like, optional\n", " Reference object to allow the creation of arrays which are not\n", " NumPy arrays. If an array-like passed in as ``like`` supports\n", " the ``__array_function__`` protocol, the result will be defined\n", " by it. In this case, it ensures the creation of an array object\n", " compatible with that passed in via this argument.\n", " \n", " .. versionadded:: 1.20.0\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " Array of `fill_value` with the given shape, dtype, and order.\n", " \n", " See Also\n", " --------\n", " full_like : Return a new array with shape of input filled with value.\n", " empty : Return a new uninitialized array.\n", " ones : Return a new array setting values to one.\n", " zeros : Return a new array setting values to zero.\n", " \n", " Examples\n", " --------\n", " >>> np.full((2, 2), np.inf)\n", " array([[inf, inf],\n", " [inf, inf]])\n", " >>> np.full((2, 2), 10)\n", " array([[10, 10],\n", " [10, 10]])\n", " \n", " >>> np.full((2, 2), [1, 2])\n", " array([[1, 2],\n", " [1, 2]])\n", " \n", " full_like(a, fill_value, dtype=None, order='K', subok=True, shape=None)\n", " Return a full array with the same shape and type as a given array.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " The shape and data-type of `a` define these same attributes of\n", " the returned array.\n", " fill_value : array_like\n", " Fill value.\n", " dtype : data-type, optional\n", " Overrides the data type of the result.\n", " order : {'C', 'F', 'A', or 'K'}, optional\n", " Overrides the memory layout of the result. 'C' means C-order,\n", " 'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous,\n", " 'C' otherwise. 'K' means match the layout of `a` as closely\n", " as possible.\n", " subok : bool, optional.\n", " If True, then the newly created array will use the sub-class\n", " type of `a`, otherwise it will be a base-class array. Defaults\n", " to True.\n", " shape : int or sequence of ints, optional.\n", " Overrides the shape of the result. If order='K' and the number of\n", " dimensions is unchanged, will try to keep order, otherwise,\n", " order='C' is implied.\n", " \n", " .. versionadded:: 1.17.0\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " Array of `fill_value` with the same shape and type as `a`.\n", " \n", " See Also\n", " --------\n", " empty_like : Return an empty array with shape and type of input.\n", " ones_like : Return an array of ones with shape and type of input.\n", " zeros_like : Return an array of zeros with shape and type of input.\n", " full : Return a new array of given shape filled with value.\n", " \n", " Examples\n", " --------\n", " >>> x = np.arange(6, dtype=int)\n", " >>> np.full_like(x, 1)\n", " array([1, 1, 1, 1, 1, 1])\n", " >>> np.full_like(x, 0.1)\n", " array([0, 0, 0, 0, 0, 0])\n", " >>> np.full_like(x, 0.1, dtype=np.double)\n", " array([0.1, 0.1, 0.1, 0.1, 0.1, 0.1])\n", " >>> np.full_like(x, np.nan, dtype=np.double)\n", " array([nan, nan, nan, nan, nan, nan])\n", " \n", " >>> y = np.arange(6, dtype=np.double)\n", " >>> np.full_like(y, 0.1)\n", " array([0.1, 0.1, 0.1, 0.1, 0.1, 0.1])\n", " \n", " >>> y = np.zeros([2, 2, 3], dtype=int)\n", " >>> np.full_like(y, [0, 0, 255])\n", " array([[[ 0, 0, 255],\n", " [ 0, 0, 255]],\n", " [[ 0, 0, 255],\n", " [ 0, 0, 255]]])\n", " \n", " genfromtxt(fname, dtype=<class 'float'>, comments='#', delimiter=None, skip_header=0, skip_footer=0, converters=None, missing_values=None, filling_values=None, usecols=None, names=None, excludelist=None, deletechars=\" !#$%&'()*+,-./:;<=>?@[\\\\]^{|}~\", replace_space='_', autostrip=False, case_sensitive=True, defaultfmt='f%i', unpack=None, usemask=False, loose=True, invalid_raise=True, max_rows=None, encoding='bytes', *, ndmin=0, like=None)\n", " Load data from a text file, with missing values handled as specified.\n", " \n", " Each line past the first `skip_header` lines is split at the `delimiter`\n", " character, and characters following the `comments` character are discarded.\n", " \n", " Parameters\n", " ----------\n", " fname : file, str, pathlib.Path, list of str, generator\n", " File, filename, list, or generator to read. If the filename\n", " extension is ``.gz`` or ``.bz2``, the file is first decompressed. Note\n", " that generators must return bytes or strings. The strings\n", " in a list or produced by a generator are treated as lines.\n", " dtype : dtype, optional\n", " Data type of the resulting array.\n", " If None, the dtypes will be determined by the contents of each\n", " column, individually.\n", " comments : str, optional\n", " The character used to indicate the start of a comment.\n", " All the characters occurring on a line after a comment are discarded.\n", " delimiter : str, int, or sequence, optional\n", " The string used to separate values. By default, any consecutive\n", " whitespaces act as delimiter. An integer or sequence of integers\n", " can also be provided as width(s) of each field.\n", " skiprows : int, optional\n", " `skiprows` was removed in numpy 1.10. Please use `skip_header` instead.\n", " skip_header : int, optional\n", " The number of lines to skip at the beginning of the file.\n", " skip_footer : int, optional\n", " The number of lines to skip at the end of the file.\n", " converters : variable, optional\n", " The set of functions that convert the data of a column to a value.\n", " The converters can also be used to provide a default value\n", " for missing data: ``converters = {3: lambda s: float(s or 0)}``.\n", " missing : variable, optional\n", " `missing` was removed in numpy 1.10. Please use `missing_values`\n", " instead.\n", " missing_values : variable, optional\n", " The set of strings corresponding to missing data.\n", " filling_values : variable, optional\n", " The set of values to be used as default when the data are missing.\n", " usecols : sequence, optional\n", " Which columns to read, with 0 being the first. For example,\n", " ``usecols = (1, 4, 5)`` will extract the 2nd, 5th and 6th columns.\n", " names : {None, True, str, sequence}, optional\n", " If `names` is True, the field names are read from the first line after\n", " the first `skip_header` lines. This line can optionally be preceded\n", " by a comment delimiter. If `names` is a sequence or a single-string of\n", " comma-separated names, the names will be used to define the field names\n", " in a structured dtype. If `names` is None, the names of the dtype\n", " fields will be used, if any.\n", " excludelist : sequence, optional\n", " A list of names to exclude. This list is appended to the default list\n", " ['return','file','print']. Excluded names are appended with an\n", " underscore: for example, `file` would become `file_`.\n", " deletechars : str, optional\n", " A string combining invalid characters that must be deleted from the\n", " names.\n", " defaultfmt : str, optional\n", " A format used to define default field names, such as \"f%i\" or \"f_%02i\".\n", " autostrip : bool, optional\n", " Whether to automatically strip white spaces from the variables.\n", " replace_space : char, optional\n", " Character(s) used in replacement of white spaces in the variable\n", " names. By default, use a '_'.\n", " case_sensitive : {True, False, 'upper', 'lower'}, optional\n", " If True, field names are case sensitive.\n", " If False or 'upper', field names are converted to upper case.\n", " If 'lower', field names are converted to lower case.\n", " unpack : bool, optional\n", " If True, the returned array is transposed, so that arguments may be\n", " unpacked using ``x, y, z = genfromtxt(...)``. When used with a\n", " structured data-type, arrays are returned for each field.\n", " Default is False.\n", " usemask : bool, optional\n", " If True, return a masked array.\n", " If False, return a regular array.\n", " loose : bool, optional\n", " If True, do not raise errors for invalid values.\n", " invalid_raise : bool, optional\n", " If True, an exception is raised if an inconsistency is detected in the\n", " number of columns.\n", " If False, a warning is emitted and the offending lines are skipped.\n", " max_rows : int, optional\n", " The maximum number of rows to read. Must not be used with skip_footer\n", " at the same time. If given, the value must be at least 1. Default is\n", " to read the entire file.\n", " \n", " .. versionadded:: 1.10.0\n", " encoding : str, optional\n", " Encoding used to decode the inputfile. Does not apply when `fname` is\n", " a file object. The special value 'bytes' enables backward compatibility\n", " workarounds that ensure that you receive byte arrays when possible\n", " and passes latin1 encoded strings to converters. Override this value to\n", " receive unicode arrays and pass strings as input to converters. If set\n", " to None the system default is used. The default value is 'bytes'.\n", " \n", " .. versionadded:: 1.14.0\n", " ndmin : int, optional\n", " Same parameter as `loadtxt`\n", " \n", " .. versionadded:: 1.23.0\n", " like : array_like, optional\n", " Reference object to allow the creation of arrays which are not\n", " NumPy arrays. If an array-like passed in as ``like`` supports\n", " the ``__array_function__`` protocol, the result will be defined\n", " by it. In this case, it ensures the creation of an array object\n", " compatible with that passed in via this argument.\n", " \n", " .. versionadded:: 1.20.0\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " Data read from the text file. If `usemask` is True, this is a\n", " masked array.\n", " \n", " See Also\n", " --------\n", " numpy.loadtxt : equivalent function when no data is missing.\n", " \n", " Notes\n", " -----\n", " * When spaces are used as delimiters, or when no delimiter has been given\n", " as input, there should not be any missing data between two fields.\n", " * When the variables are named (either by a flexible dtype or with `names`),\n", " there must not be any header in the file (else a ValueError\n", " exception is raised).\n", " * Individual values are not stripped of spaces by default.\n", " When using a custom converter, make sure the function does remove spaces.\n", " \n", " References\n", " ----------\n", " .. [1] NumPy User Guide, section `I/O with NumPy\n", " <https://docs.scipy.org/doc/numpy/user/basics.io.genfromtxt.html>`_.\n", " \n", " Examples\n", " --------\n", " >>> from io import StringIO\n", " >>> import numpy as np\n", " \n", " Comma delimited file with mixed dtype\n", " \n", " >>> s = StringIO(u\"1,1.3,abcde\")\n", " >>> data = np.genfromtxt(s, dtype=[('myint','i8'),('myfloat','f8'),\n", " ... ('mystring','S5')], delimiter=\",\")\n", " >>> data\n", " array((1, 1.3, b'abcde'),\n", " dtype=[('myint', '<i8'), ('myfloat', '<f8'), ('mystring', 'S5')])\n", " \n", " Using dtype = None\n", " \n", " >>> _ = s.seek(0) # needed for StringIO example only\n", " >>> data = np.genfromtxt(s, dtype=None,\n", " ... names = ['myint','myfloat','mystring'], delimiter=\",\")\n", " >>> data\n", " array((1, 1.3, b'abcde'),\n", " dtype=[('myint', '<i8'), ('myfloat', '<f8'), ('mystring', 'S5')])\n", " \n", " Specifying dtype and names\n", " \n", " >>> _ = s.seek(0)\n", " >>> data = np.genfromtxt(s, dtype=\"i8,f8,S5\",\n", " ... names=['myint','myfloat','mystring'], delimiter=\",\")\n", " >>> data\n", " array((1, 1.3, b'abcde'),\n", " dtype=[('myint', '<i8'), ('myfloat', '<f8'), ('mystring', 'S5')])\n", " \n", " An example with fixed-width columns\n", " \n", " >>> s = StringIO(u\"11.3abcde\")\n", " >>> data = np.genfromtxt(s, dtype=None, names=['intvar','fltvar','strvar'],\n", " ... delimiter=[1,3,5])\n", " >>> data\n", " array((1, 1.3, b'abcde'),\n", " dtype=[('intvar', '<i8'), ('fltvar', '<f8'), ('strvar', 'S5')])\n", " \n", " An example to show comments\n", " \n", " >>> f = StringIO('''\n", " ... text,# of chars\n", " ... hello world,11\n", " ... numpy,5''')\n", " >>> np.genfromtxt(f, dtype='S12,S12', delimiter=',')\n", " array([(b'text', b''), (b'hello world', b'11'), (b'numpy', b'5')],\n", " dtype=[('f0', 'S12'), ('f1', 'S12')])\n", " \n", " geomspace(start, stop, num=50, endpoint=True, dtype=None, axis=0)\n", " Return numbers spaced evenly on a log scale (a geometric progression).\n", " \n", " This is similar to `logspace`, but with endpoints specified directly.\n", " Each output sample is a constant multiple of the previous.\n", " \n", " .. versionchanged:: 1.16.0\n", " Non-scalar `start` and `stop` are now supported.\n", " \n", " Parameters\n", " ----------\n", " start : array_like\n", " The starting value of the sequence.\n", " stop : array_like\n", " The final value of the sequence, unless `endpoint` is False.\n", " In that case, ``num + 1`` values are spaced over the\n", " interval in log-space, of which all but the last (a sequence of\n", " length `num`) are returned.\n", " num : integer, optional\n", " Number of samples to generate. Default is 50.\n", " endpoint : boolean, optional\n", " If true, `stop` is the last sample. Otherwise, it is not included.\n", " Default is True.\n", " dtype : dtype\n", " The type of the output array. If `dtype` is not given, the data type\n", " is inferred from `start` and `stop`. The inferred dtype will never be\n", " an integer; `float` is chosen even if the arguments would produce an\n", " array of integers.\n", " axis : int, optional\n", " The axis in the result to store the samples. Relevant only if start\n", " or stop are array-like. By default (0), the samples will be along a\n", " new axis inserted at the beginning. Use -1 to get an axis at the end.\n", " \n", " .. versionadded:: 1.16.0\n", " \n", " Returns\n", " -------\n", " samples : ndarray\n", " `num` samples, equally spaced on a log scale.\n", " \n", " See Also\n", " --------\n", " logspace : Similar to geomspace, but with endpoints specified using log\n", " and base.\n", " linspace : Similar to geomspace, but with arithmetic instead of geometric\n", " progression.\n", " arange : Similar to linspace, with the step size specified instead of the\n", " number of samples.\n", " :ref:`how-to-partition`\n", " \n", " Notes\n", " -----\n", " If the inputs or dtype are complex, the output will follow a logarithmic\n", " spiral in the complex plane. (There are an infinite number of spirals\n", " passing through two points; the output will follow the shortest such path.)\n", " \n", " Examples\n", " --------\n", " >>> np.geomspace(1, 1000, num=4)\n", " array([ 1., 10., 100., 1000.])\n", " >>> np.geomspace(1, 1000, num=3, endpoint=False)\n", " array([ 1., 10., 100.])\n", " >>> np.geomspace(1, 1000, num=4, endpoint=False)\n", " array([ 1. , 5.62341325, 31.6227766 , 177.827941 ])\n", " >>> np.geomspace(1, 256, num=9)\n", " array([ 1., 2., 4., 8., 16., 32., 64., 128., 256.])\n", " \n", " Note that the above may not produce exact integers:\n", " \n", " >>> np.geomspace(1, 256, num=9, dtype=int)\n", " array([ 1, 2, 4, 7, 16, 32, 63, 127, 256])\n", " >>> np.around(np.geomspace(1, 256, num=9)).astype(int)\n", " array([ 1, 2, 4, 8, 16, 32, 64, 128, 256])\n", " \n", " Negative, decreasing, and complex inputs are allowed:\n", " \n", " >>> np.geomspace(1000, 1, num=4)\n", " array([1000., 100., 10., 1.])\n", " >>> np.geomspace(-1000, -1, num=4)\n", " array([-1000., -100., -10., -1.])\n", " >>> np.geomspace(1j, 1000j, num=4) # Straight line\n", " array([0. +1.j, 0. +10.j, 0. +100.j, 0.+1000.j])\n", " >>> np.geomspace(-1+0j, 1+0j, num=5) # Circle\n", " array([-1.00000000e+00+1.22464680e-16j, -7.07106781e-01+7.07106781e-01j,\n", " 6.12323400e-17+1.00000000e+00j, 7.07106781e-01+7.07106781e-01j,\n", " 1.00000000e+00+0.00000000e+00j])\n", " \n", " Graphical illustration of `endpoint` parameter:\n", " \n", " >>> import matplotlib.pyplot as plt\n", " >>> N = 10\n", " >>> y = np.zeros(N)\n", " >>> plt.semilogx(np.geomspace(1, 1000, N, endpoint=True), y + 1, 'o')\n", " [<matplotlib.lines.Line2D object at 0x...>]\n", " >>> plt.semilogx(np.geomspace(1, 1000, N, endpoint=False), y + 2, 'o')\n", " [<matplotlib.lines.Line2D object at 0x...>]\n", " >>> plt.axis([0.5, 2000, 0, 3])\n", " [0.5, 2000, 0, 3]\n", " >>> plt.grid(True, color='0.7', linestyle='-', which='both', axis='both')\n", " >>> plt.show()\n", " \n", " get_array_wrap(*args)\n", " Find the wrapper for the array with the highest priority.\n", " \n", " In case of ties, leftmost wins. If no wrapper is found, return None\n", " \n", " get_include()\n", " Return the directory that contains the NumPy \\*.h header files.\n", " \n", " Extension modules that need to compile against NumPy should use this\n", " function to locate the appropriate include directory.\n", " \n", " Notes\n", " -----\n", " When using ``distutils``, for example in ``setup.py``::\n", " \n", " import numpy as np\n", " ...\n", " Extension('extension_name', ...\n", " include_dirs=[np.get_include()])\n", " ...\n", " \n", " get_printoptions()\n", " Return the current print options.\n", " \n", " Returns\n", " -------\n", " print_opts : dict\n", " Dictionary of current print options with keys\n", " \n", " - precision : int\n", " - threshold : int\n", " - edgeitems : int\n", " - linewidth : int\n", " - suppress : bool\n", " - nanstr : str\n", " - infstr : str\n", " - formatter : dict of callables\n", " - sign : str\n", " \n", " For a full description of these options, see `set_printoptions`.\n", " \n", " See Also\n", " --------\n", " set_printoptions, printoptions, set_string_function\n", " \n", " getbufsize()\n", " Return the size of the buffer used in ufuncs.\n", " \n", " Returns\n", " -------\n", " getbufsize : int\n", " Size of ufunc buffer in bytes.\n", " \n", " geterr()\n", " Get the current way of handling floating-point errors.\n", " \n", " Returns\n", " -------\n", " res : dict\n", " A dictionary with keys \"divide\", \"over\", \"under\", and \"invalid\",\n", " whose values are from the strings \"ignore\", \"print\", \"log\", \"warn\",\n", " \"raise\", and \"call\". The keys represent possible floating-point\n", " exceptions, and the values define how these exceptions are handled.\n", " \n", " See Also\n", " --------\n", " geterrcall, seterr, seterrcall\n", " \n", " Notes\n", " -----\n", " For complete documentation of the types of floating-point exceptions and\n", " treatment options, see `seterr`.\n", " \n", " Examples\n", " --------\n", " >>> np.geterr()\n", " {'divide': 'warn', 'over': 'warn', 'under': 'ignore', 'invalid': 'warn'}\n", " >>> np.arange(3.) / np.arange(3.)\n", " array([nan, 1., 1.])\n", " \n", " >>> oldsettings = np.seterr(all='warn', over='raise')\n", " >>> np.geterr()\n", " {'divide': 'warn', 'over': 'raise', 'under': 'warn', 'invalid': 'warn'}\n", " >>> np.arange(3.) / np.arange(3.)\n", " array([nan, 1., 1.])\n", " \n", " geterrcall()\n", " Return the current callback function used on floating-point errors.\n", " \n", " When the error handling for a floating-point error (one of \"divide\",\n", " \"over\", \"under\", or \"invalid\") is set to 'call' or 'log', the function\n", " that is called or the log instance that is written to is returned by\n", " `geterrcall`. This function or log instance has been set with\n", " `seterrcall`.\n", " \n", " Returns\n", " -------\n", " errobj : callable, log instance or None\n", " The current error handler. If no handler was set through `seterrcall`,\n", " ``None`` is returned.\n", " \n", " See Also\n", " --------\n", " seterrcall, seterr, geterr\n", " \n", " Notes\n", " -----\n", " For complete documentation of the types of floating-point exceptions and\n", " treatment options, see `seterr`.\n", " \n", " Examples\n", " --------\n", " >>> np.geterrcall() # we did not yet set a handler, returns None\n", " \n", " >>> oldsettings = np.seterr(all='call')\n", " >>> def err_handler(type, flag):\n", " ... print(\"Floating point error (%s), with flag %s\" % (type, flag))\n", " >>> oldhandler = np.seterrcall(err_handler)\n", " >>> np.array([1, 2, 3]) / 0.0\n", " Floating point error (divide by zero), with flag 1\n", " array([inf, inf, inf])\n", " \n", " >>> cur_handler = np.geterrcall()\n", " >>> cur_handler is err_handler\n", " True\n", " \n", " geterrobj(...)\n", " geterrobj()\n", " \n", " Return the current object that defines floating-point error handling.\n", " \n", " The error object contains all information that defines the error handling\n", " behavior in NumPy. `geterrobj` is used internally by the other\n", " functions that get and set error handling behavior (`geterr`, `seterr`,\n", " `geterrcall`, `seterrcall`).\n", " \n", " Returns\n", " -------\n", " errobj : list\n", " The error object, a list containing three elements:\n", " [internal numpy buffer size, error mask, error callback function].\n", " \n", " The error mask is a single integer that holds the treatment information\n", " on all four floating point errors. The information for each error type\n", " is contained in three bits of the integer. If we print it in base 8, we\n", " can see what treatment is set for \"invalid\", \"under\", \"over\", and\n", " \"divide\" (in that order). The printed string can be interpreted with\n", " \n", " * 0 : 'ignore'\n", " * 1 : 'warn'\n", " * 2 : 'raise'\n", " * 3 : 'call'\n", " * 4 : 'print'\n", " * 5 : 'log'\n", " \n", " See Also\n", " --------\n", " seterrobj, seterr, geterr, seterrcall, geterrcall\n", " getbufsize, setbufsize\n", " \n", " Notes\n", " -----\n", " For complete documentation of the types of floating-point exceptions and\n", " treatment options, see `seterr`.\n", " \n", " Examples\n", " --------\n", " >>> np.geterrobj() # first get the defaults\n", " [8192, 521, None]\n", " \n", " >>> def err_handler(type, flag):\n", " ... print(\"Floating point error (%s), with flag %s\" % (type, flag))\n", " ...\n", " >>> old_bufsize = np.setbufsize(20000)\n", " >>> old_err = np.seterr(divide='raise')\n", " >>> old_handler = np.seterrcall(err_handler)\n", " >>> np.geterrobj()\n", " [8192, 521, <function err_handler at 0x91dcaac>]\n", " \n", " >>> old_err = np.seterr(all='ignore')\n", " >>> np.base_repr(np.geterrobj()[1], 8)\n", " '0'\n", " >>> old_err = np.seterr(divide='warn', over='log', under='call',\n", " ... invalid='print')\n", " >>> np.base_repr(np.geterrobj()[1], 8)\n", " '4351'\n", " \n", " gradient(f, *varargs, axis=None, edge_order=1)\n", " Return the gradient of an N-dimensional array.\n", " \n", " The gradient is computed using second order accurate central differences\n", " in the interior points and either first or second order accurate one-sides\n", " (forward or backwards) differences at the boundaries.\n", " The returned gradient hence has the same shape as the input array.\n", " \n", " Parameters\n", " ----------\n", " f : array_like\n", " An N-dimensional array containing samples of a scalar function.\n", " varargs : list of scalar or array, optional\n", " Spacing between f values. Default unitary spacing for all dimensions.\n", " Spacing can be specified using:\n", " \n", " 1. single scalar to specify a sample distance for all dimensions.\n", " 2. N scalars to specify a constant sample distance for each dimension.\n", " i.e. `dx`, `dy`, `dz`, ...\n", " 3. N arrays to specify the coordinates of the values along each\n", " dimension of F. The length of the array must match the size of\n", " the corresponding dimension\n", " 4. Any combination of N scalars/arrays with the meaning of 2. and 3.\n", " \n", " If `axis` is given, the number of varargs must equal the number of axes.\n", " Default: 1.\n", " \n", " edge_order : {1, 2}, optional\n", " Gradient is calculated using N-th order accurate differences\n", " at the boundaries. Default: 1.\n", " \n", " .. versionadded:: 1.9.1\n", " \n", " axis : None or int or tuple of ints, optional\n", " Gradient is calculated only along the given axis or axes\n", " The default (axis = None) is to calculate the gradient for all the axes\n", " of the input array. axis may be negative, in which case it counts from\n", " the last to the first axis.\n", " \n", " .. versionadded:: 1.11.0\n", " \n", " Returns\n", " -------\n", " gradient : ndarray or list of ndarray\n", " A list of ndarrays (or a single ndarray if there is only one dimension)\n", " corresponding to the derivatives of f with respect to each dimension.\n", " Each derivative has the same shape as f.\n", " \n", " Examples\n", " --------\n", " >>> f = np.array([1, 2, 4, 7, 11, 16], dtype=float)\n", " >>> np.gradient(f)\n", " array([1. , 1.5, 2.5, 3.5, 4.5, 5. ])\n", " >>> np.gradient(f, 2)\n", " array([0.5 , 0.75, 1.25, 1.75, 2.25, 2.5 ])\n", " \n", " Spacing can be also specified with an array that represents the coordinates\n", " of the values F along the dimensions.\n", " For instance a uniform spacing:\n", " \n", " >>> x = np.arange(f.size)\n", " >>> np.gradient(f, x)\n", " array([1. , 1.5, 2.5, 3.5, 4.5, 5. ])\n", " \n", " Or a non uniform one:\n", " \n", " >>> x = np.array([0., 1., 1.5, 3.5, 4., 6.], dtype=float)\n", " >>> np.gradient(f, x)\n", " array([1. , 3. , 3.5, 6.7, 6.9, 2.5])\n", " \n", " For two dimensional arrays, the return will be two arrays ordered by\n", " axis. In this example the first array stands for the gradient in\n", " rows and the second one in columns direction:\n", " \n", " >>> np.gradient(np.array([[1, 2, 6], [3, 4, 5]], dtype=float))\n", " [array([[ 2., 2., -1.],\n", " [ 2., 2., -1.]]), array([[1. , 2.5, 4. ],\n", " [1. , 1. , 1. ]])]\n", " \n", " In this example the spacing is also specified:\n", " uniform for axis=0 and non uniform for axis=1\n", " \n", " >>> dx = 2.\n", " >>> y = [1., 1.5, 3.5]\n", " >>> np.gradient(np.array([[1, 2, 6], [3, 4, 5]], dtype=float), dx, y)\n", " [array([[ 1. , 1. , -0.5],\n", " [ 1. , 1. , -0.5]]), array([[2. , 2. , 2. ],\n", " [2. , 1.7, 0.5]])]\n", " \n", " It is possible to specify how boundaries are treated using `edge_order`\n", " \n", " >>> x = np.array([0, 1, 2, 3, 4])\n", " >>> f = x**2\n", " >>> np.gradient(f, edge_order=1)\n", " array([1., 2., 4., 6., 7.])\n", " >>> np.gradient(f, edge_order=2)\n", " array([0., 2., 4., 6., 8.])\n", " \n", " The `axis` keyword can be used to specify a subset of axes of which the\n", " gradient is calculated\n", " \n", " >>> np.gradient(np.array([[1, 2, 6], [3, 4, 5]], dtype=float), axis=0)\n", " array([[ 2., 2., -1.],\n", " [ 2., 2., -1.]])\n", " \n", " Notes\n", " -----\n", " Assuming that :math:`f\\in C^{3}` (i.e., :math:`f` has at least 3 continuous\n", " derivatives) and let :math:`h_{*}` be a non-homogeneous stepsize, we\n", " minimize the \"consistency error\" :math:`\\eta_{i}` between the true gradient\n", " and its estimate from a linear combination of the neighboring grid-points:\n", " \n", " .. math::\n", " \n", " \\eta_{i} = f_{i}^{\\left(1\\right)} -\n", " \\left[ \\alpha f\\left(x_{i}\\right) +\n", " \\beta f\\left(x_{i} + h_{d}\\right) +\n", " \\gamma f\\left(x_{i}-h_{s}\\right)\n", " \\right]\n", " \n", " By substituting :math:`f(x_{i} + h_{d})` and :math:`f(x_{i} - h_{s})`\n", " with their Taylor series expansion, this translates into solving\n", " the following the linear system:\n", " \n", " .. math::\n", " \n", " \\left\\{\n", " \\begin{array}{r}\n", " \\alpha+\\beta+\\gamma=0 \\\\\n", " \\beta h_{d}-\\gamma h_{s}=1 \\\\\n", " \\beta h_{d}^{2}+\\gamma h_{s}^{2}=0\n", " \\end{array}\n", " \\right.\n", " \n", " The resulting approximation of :math:`f_{i}^{(1)}` is the following:\n", " \n", " .. math::\n", " \n", " \\hat f_{i}^{(1)} =\n", " \\frac{\n", " h_{s}^{2}f\\left(x_{i} + h_{d}\\right)\n", " + \\left(h_{d}^{2} - h_{s}^{2}\\right)f\\left(x_{i}\\right)\n", " - h_{d}^{2}f\\left(x_{i}-h_{s}\\right)}\n", " { h_{s}h_{d}\\left(h_{d} + h_{s}\\right)}\n", " + \\mathcal{O}\\left(\\frac{h_{d}h_{s}^{2}\n", " + h_{s}h_{d}^{2}}{h_{d}\n", " + h_{s}}\\right)\n", " \n", " It is worth noting that if :math:`h_{s}=h_{d}`\n", " (i.e., data are evenly spaced)\n", " we find the standard second order approximation:\n", " \n", " .. math::\n", " \n", " \\hat f_{i}^{(1)}=\n", " \\frac{f\\left(x_{i+1}\\right) - f\\left(x_{i-1}\\right)}{2h}\n", " + \\mathcal{O}\\left(h^{2}\\right)\n", " \n", " With a similar procedure the forward/backward approximations used for\n", " boundaries can be derived.\n", " \n", " References\n", " ----------\n", " .. [1] Quarteroni A., Sacco R., Saleri F. (2007) Numerical Mathematics\n", " (Texts in Applied Mathematics). New York: Springer.\n", " .. [2] Durran D. R. (1999) Numerical Methods for Wave Equations\n", " in Geophysical Fluid Dynamics. New York: Springer.\n", " .. [3] Fornberg B. (1988) Generation of Finite Difference Formulas on\n", " Arbitrarily Spaced Grids,\n", " Mathematics of Computation 51, no. 184 : 699-706.\n", " `PDF <http://www.ams.org/journals/mcom/1988-51-184/\n", " S0025-5718-1988-0935077-0/S0025-5718-1988-0935077-0.pdf>`_.\n", " \n", " hamming(M)\n", " Return the Hamming window.\n", " \n", " The Hamming window is a taper formed by using a weighted cosine.\n", " \n", " Parameters\n", " ----------\n", " M : int\n", " Number of points in the output window. If zero or less, an\n", " empty array is returned.\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " The window, with the maximum value normalized to one (the value\n", " one appears only if the number of samples is odd).\n", " \n", " See Also\n", " --------\n", " bartlett, blackman, hanning, kaiser\n", " \n", " Notes\n", " -----\n", " The Hamming window is defined as\n", " \n", " .. math:: w(n) = 0.54 - 0.46\\cos\\left(\\frac{2\\pi{n}}{M-1}\\right)\n", " \\qquad 0 \\leq n \\leq M-1\n", " \n", " The Hamming was named for R. W. Hamming, an associate of J. W. Tukey\n", " and is described in Blackman and Tukey. It was recommended for\n", " smoothing the truncated autocovariance function in the time domain.\n", " Most references to the Hamming window come from the signal processing\n", " literature, where it is used as one of many windowing functions for\n", " smoothing values. It is also known as an apodization (which means\n", " \"removing the foot\", i.e. smoothing discontinuities at the beginning\n", " and end of the sampled signal) or tapering function.\n", " \n", " References\n", " ----------\n", " .. [1] Blackman, R.B. and Tukey, J.W., (1958) The measurement of power\n", " spectra, Dover Publications, New York.\n", " .. [2] E.R. Kanasewich, \"Time Sequence Analysis in Geophysics\", The\n", " University of Alberta Press, 1975, pp. 109-110.\n", " .. [3] Wikipedia, \"Window function\",\n", " https://en.wikipedia.org/wiki/Window_function\n", " .. [4] W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling,\n", " \"Numerical Recipes\", Cambridge University Press, 1986, page 425.\n", " \n", " Examples\n", " --------\n", " >>> np.hamming(12)\n", " array([ 0.08 , 0.15302337, 0.34890909, 0.60546483, 0.84123594, # may vary\n", " 0.98136677, 0.98136677, 0.84123594, 0.60546483, 0.34890909,\n", " 0.15302337, 0.08 ])\n", " \n", " Plot the window and the frequency response:\n", " \n", " >>> import matplotlib.pyplot as plt\n", " >>> from numpy.fft import fft, fftshift\n", " >>> window = np.hamming(51)\n", " >>> plt.plot(window)\n", " [<matplotlib.lines.Line2D object at 0x...>]\n", " >>> plt.title(\"Hamming window\")\n", " Text(0.5, 1.0, 'Hamming window')\n", " >>> plt.ylabel(\"Amplitude\")\n", " Text(0, 0.5, 'Amplitude')\n", " >>> plt.xlabel(\"Sample\")\n", " Text(0.5, 0, 'Sample')\n", " >>> plt.show()\n", " \n", " >>> plt.figure()\n", " <Figure size 640x480 with 0 Axes>\n", " >>> A = fft(window, 2048) / 25.5\n", " >>> mag = np.abs(fftshift(A))\n", " >>> freq = np.linspace(-0.5, 0.5, len(A))\n", " >>> response = 20 * np.log10(mag)\n", " >>> response = np.clip(response, -100, 100)\n", " >>> plt.plot(freq, response)\n", " [<matplotlib.lines.Line2D object at 0x...>]\n", " >>> plt.title(\"Frequency response of Hamming window\")\n", " Text(0.5, 1.0, 'Frequency response of Hamming window')\n", " >>> plt.ylabel(\"Magnitude [dB]\")\n", " Text(0, 0.5, 'Magnitude [dB]')\n", " >>> plt.xlabel(\"Normalized frequency [cycles per sample]\")\n", " Text(0.5, 0, 'Normalized frequency [cycles per sample]')\n", " >>> plt.axis('tight')\n", " ...\n", " >>> plt.show()\n", " \n", " hanning(M)\n", " Return the Hanning window.\n", " \n", " The Hanning window is a taper formed by using a weighted cosine.\n", " \n", " Parameters\n", " ----------\n", " M : int\n", " Number of points in the output window. If zero or less, an\n", " empty array is returned.\n", " \n", " Returns\n", " -------\n", " out : ndarray, shape(M,)\n", " The window, with the maximum value normalized to one (the value\n", " one appears only if `M` is odd).\n", " \n", " See Also\n", " --------\n", " bartlett, blackman, hamming, kaiser\n", " \n", " Notes\n", " -----\n", " The Hanning window is defined as\n", " \n", " .. math:: w(n) = 0.5 - 0.5\\cos\\left(\\frac{2\\pi{n}}{M-1}\\right)\n", " \\qquad 0 \\leq n \\leq M-1\n", " \n", " The Hanning was named for Julius von Hann, an Austrian meteorologist.\n", " It is also known as the Cosine Bell. Some authors prefer that it be\n", " called a Hann window, to help avoid confusion with the very similar\n", " Hamming window.\n", " \n", " Most references to the Hanning window come from the signal processing\n", " literature, where it is used as one of many windowing functions for\n", " smoothing values. It is also known as an apodization (which means\n", " \"removing the foot\", i.e. smoothing discontinuities at the beginning\n", " and end of the sampled signal) or tapering function.\n", " \n", " References\n", " ----------\n", " .. [1] Blackman, R.B. and Tukey, J.W., (1958) The measurement of power\n", " spectra, Dover Publications, New York.\n", " .. [2] E.R. Kanasewich, \"Time Sequence Analysis in Geophysics\",\n", " The University of Alberta Press, 1975, pp. 106-108.\n", " .. [3] Wikipedia, \"Window function\",\n", " https://en.wikipedia.org/wiki/Window_function\n", " .. [4] W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling,\n", " \"Numerical Recipes\", Cambridge University Press, 1986, page 425.\n", " \n", " Examples\n", " --------\n", " >>> np.hanning(12)\n", " array([0. , 0.07937323, 0.29229249, 0.57115742, 0.82743037,\n", " 0.97974649, 0.97974649, 0.82743037, 0.57115742, 0.29229249,\n", " 0.07937323, 0. ])\n", " \n", " Plot the window and its frequency response:\n", " \n", " >>> import matplotlib.pyplot as plt\n", " >>> from numpy.fft import fft, fftshift\n", " >>> window = np.hanning(51)\n", " >>> plt.plot(window)\n", " [<matplotlib.lines.Line2D object at 0x...>]\n", " >>> plt.title(\"Hann window\")\n", " Text(0.5, 1.0, 'Hann window')\n", " >>> plt.ylabel(\"Amplitude\")\n", " Text(0, 0.5, 'Amplitude')\n", " >>> plt.xlabel(\"Sample\")\n", " Text(0.5, 0, 'Sample')\n", " >>> plt.show()\n", " \n", " >>> plt.figure()\n", " <Figure size 640x480 with 0 Axes>\n", " >>> A = fft(window, 2048) / 25.5\n", " >>> mag = np.abs(fftshift(A))\n", " >>> freq = np.linspace(-0.5, 0.5, len(A))\n", " >>> with np.errstate(divide='ignore', invalid='ignore'):\n", " ... response = 20 * np.log10(mag)\n", " ...\n", " >>> response = np.clip(response, -100, 100)\n", " >>> plt.plot(freq, response)\n", " [<matplotlib.lines.Line2D object at 0x...>]\n", " >>> plt.title(\"Frequency response of the Hann window\")\n", " Text(0.5, 1.0, 'Frequency response of the Hann window')\n", " >>> plt.ylabel(\"Magnitude [dB]\")\n", " Text(0, 0.5, 'Magnitude [dB]')\n", " >>> plt.xlabel(\"Normalized frequency [cycles per sample]\")\n", " Text(0.5, 0, 'Normalized frequency [cycles per sample]')\n", " >>> plt.axis('tight')\n", " ...\n", " >>> plt.show()\n", " \n", " histogram(a, bins=10, range=None, density=None, weights=None)\n", " Compute the histogram of a dataset.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input data. The histogram is computed over the flattened array.\n", " bins : int or sequence of scalars or str, optional\n", " If `bins` is an int, it defines the number of equal-width\n", " bins in the given range (10, by default). If `bins` is a\n", " sequence, it defines a monotonically increasing array of bin edges,\n", " including the rightmost edge, allowing for non-uniform bin widths.\n", " \n", " .. versionadded:: 1.11.0\n", " \n", " If `bins` is a string, it defines the method used to calculate the\n", " optimal bin width, as defined by `histogram_bin_edges`.\n", " \n", " range : (float, float), optional\n", " The lower and upper range of the bins. If not provided, range\n", " is simply ``(a.min(), a.max())``. Values outside the range are\n", " ignored. The first element of the range must be less than or\n", " equal to the second. `range` affects the automatic bin\n", " computation as well. While bin width is computed to be optimal\n", " based on the actual data within `range`, the bin count will fill\n", " the entire range including portions containing no data.\n", " weights : array_like, optional\n", " An array of weights, of the same shape as `a`. Each value in\n", " `a` only contributes its associated weight towards the bin count\n", " (instead of 1). If `density` is True, the weights are\n", " normalized, so that the integral of the density over the range\n", " remains 1.\n", " density : bool, optional\n", " If ``False``, the result will contain the number of samples in\n", " each bin. If ``True``, the result is the value of the\n", " probability *density* function at the bin, normalized such that\n", " the *integral* over the range is 1. Note that the sum of the\n", " histogram values will not be equal to 1 unless bins of unity\n", " width are chosen; it is not a probability *mass* function.\n", " \n", " Returns\n", " -------\n", " hist : array\n", " The values of the histogram. See `density` and `weights` for a\n", " description of the possible semantics.\n", " bin_edges : array of dtype float\n", " Return the bin edges ``(length(hist)+1)``.\n", " \n", " \n", " See Also\n", " --------\n", " histogramdd, bincount, searchsorted, digitize, histogram_bin_edges\n", " \n", " Notes\n", " -----\n", " All but the last (righthand-most) bin is half-open. In other words,\n", " if `bins` is::\n", " \n", " [1, 2, 3, 4]\n", " \n", " then the first bin is ``[1, 2)`` (including 1, but excluding 2) and\n", " the second ``[2, 3)``. The last bin, however, is ``[3, 4]``, which\n", " *includes* 4.\n", " \n", " \n", " Examples\n", " --------\n", " >>> np.histogram([1, 2, 1], bins=[0, 1, 2, 3])\n", " (array([0, 2, 1]), array([0, 1, 2, 3]))\n", " >>> np.histogram(np.arange(4), bins=np.arange(5), density=True)\n", " (array([0.25, 0.25, 0.25, 0.25]), array([0, 1, 2, 3, 4]))\n", " >>> np.histogram([[1, 2, 1], [1, 0, 1]], bins=[0,1,2,3])\n", " (array([1, 4, 1]), array([0, 1, 2, 3]))\n", " \n", " >>> a = np.arange(5)\n", " >>> hist, bin_edges = np.histogram(a, density=True)\n", " >>> hist\n", " array([0.5, 0. , 0.5, 0. , 0. , 0.5, 0. , 0.5, 0. , 0.5])\n", " >>> hist.sum()\n", " 2.4999999999999996\n", " >>> np.sum(hist * np.diff(bin_edges))\n", " 1.0\n", " \n", " .. versionadded:: 1.11.0\n", " \n", " Automated Bin Selection Methods example, using 2 peak random data\n", " with 2000 points:\n", " \n", " >>> import matplotlib.pyplot as plt\n", " >>> rng = np.random.RandomState(10) # deterministic random data\n", " >>> a = np.hstack((rng.normal(size=1000),\n", " ... rng.normal(loc=5, scale=2, size=1000)))\n", " >>> _ = plt.hist(a, bins='auto') # arguments are passed to np.histogram\n", " >>> plt.title(\"Histogram with 'auto' bins\")\n", " Text(0.5, 1.0, \"Histogram with 'auto' bins\")\n", " >>> plt.show()\n", " \n", " histogram2d(x, y, bins=10, range=None, density=None, weights=None)\n", " Compute the bi-dimensional histogram of two data samples.\n", " \n", " Parameters\n", " ----------\n", " x : array_like, shape (N,)\n", " An array containing the x coordinates of the points to be\n", " histogrammed.\n", " y : array_like, shape (N,)\n", " An array containing the y coordinates of the points to be\n", " histogrammed.\n", " bins : int or array_like or [int, int] or [array, array], optional\n", " The bin specification:\n", " \n", " * If int, the number of bins for the two dimensions (nx=ny=bins).\n", " * If array_like, the bin edges for the two dimensions\n", " (x_edges=y_edges=bins).\n", " * If [int, int], the number of bins in each dimension\n", " (nx, ny = bins).\n", " * If [array, array], the bin edges in each dimension\n", " (x_edges, y_edges = bins).\n", " * A combination [int, array] or [array, int], where int\n", " is the number of bins and array is the bin edges.\n", " \n", " range : array_like, shape(2,2), optional\n", " The leftmost and rightmost edges of the bins along each dimension\n", " (if not specified explicitly in the `bins` parameters):\n", " ``[[xmin, xmax], [ymin, ymax]]``. All values outside of this range\n", " will be considered outliers and not tallied in the histogram.\n", " density : bool, optional\n", " If False, the default, returns the number of samples in each bin.\n", " If True, returns the probability *density* function at the bin,\n", " ``bin_count / sample_count / bin_area``.\n", " weights : array_like, shape(N,), optional\n", " An array of values ``w_i`` weighing each sample ``(x_i, y_i)``.\n", " Weights are normalized to 1 if `density` is True. If `density` is\n", " False, the values of the returned histogram are equal to the sum of\n", " the weights belonging to the samples falling into each bin.\n", " \n", " Returns\n", " -------\n", " H : ndarray, shape(nx, ny)\n", " The bi-dimensional histogram of samples `x` and `y`. Values in `x`\n", " are histogrammed along the first dimension and values in `y` are\n", " histogrammed along the second dimension.\n", " xedges : ndarray, shape(nx+1,)\n", " The bin edges along the first dimension.\n", " yedges : ndarray, shape(ny+1,)\n", " The bin edges along the second dimension.\n", " \n", " See Also\n", " --------\n", " histogram : 1D histogram\n", " histogramdd : Multidimensional histogram\n", " \n", " Notes\n", " -----\n", " When `density` is True, then the returned histogram is the sample\n", " density, defined such that the sum over bins of the product\n", " ``bin_value * bin_area`` is 1.\n", " \n", " Please note that the histogram does not follow the Cartesian convention\n", " where `x` values are on the abscissa and `y` values on the ordinate\n", " axis. Rather, `x` is histogrammed along the first dimension of the\n", " array (vertical), and `y` along the second dimension of the array\n", " (horizontal). This ensures compatibility with `histogramdd`.\n", " \n", " Examples\n", " --------\n", " >>> from matplotlib.image import NonUniformImage\n", " >>> import matplotlib.pyplot as plt\n", " \n", " Construct a 2-D histogram with variable bin width. First define the bin\n", " edges:\n", " \n", " >>> xedges = [0, 1, 3, 5]\n", " >>> yedges = [0, 2, 3, 4, 6]\n", " \n", " Next we create a histogram H with random bin content:\n", " \n", " >>> x = np.random.normal(2, 1, 100)\n", " >>> y = np.random.normal(1, 1, 100)\n", " >>> H, xedges, yedges = np.histogram2d(x, y, bins=(xedges, yedges))\n", " >>> # Histogram does not follow Cartesian convention (see Notes),\n", " >>> # therefore transpose H for visualization purposes.\n", " >>> H = H.T\n", " \n", " :func:`imshow <matplotlib.pyplot.imshow>` can only display square bins:\n", " \n", " >>> fig = plt.figure(figsize=(7, 3))\n", " >>> ax = fig.add_subplot(131, title='imshow: square bins')\n", " >>> plt.imshow(H, interpolation='nearest', origin='lower',\n", " ... extent=[xedges[0], xedges[-1], yedges[0], yedges[-1]])\n", " <matplotlib.image.AxesImage object at 0x...>\n", " \n", " :func:`pcolormesh <matplotlib.pyplot.pcolormesh>` can display actual edges:\n", " \n", " >>> ax = fig.add_subplot(132, title='pcolormesh: actual edges',\n", " ... aspect='equal')\n", " >>> X, Y = np.meshgrid(xedges, yedges)\n", " >>> ax.pcolormesh(X, Y, H)\n", " <matplotlib.collections.QuadMesh object at 0x...>\n", " \n", " :class:`NonUniformImage <matplotlib.image.NonUniformImage>` can be used to\n", " display actual bin edges with interpolation:\n", " \n", " >>> ax = fig.add_subplot(133, title='NonUniformImage: interpolated',\n", " ... aspect='equal', xlim=xedges[[0, -1]], ylim=yedges[[0, -1]])\n", " >>> im = NonUniformImage(ax, interpolation='bilinear')\n", " >>> xcenters = (xedges[:-1] + xedges[1:]) / 2\n", " >>> ycenters = (yedges[:-1] + yedges[1:]) / 2\n", " >>> im.set_data(xcenters, ycenters, H)\n", " >>> ax.add_image(im)\n", " >>> plt.show()\n", " \n", " It is also possible to construct a 2-D histogram without specifying bin\n", " edges:\n", " \n", " >>> # Generate non-symmetric test data\n", " >>> n = 10000\n", " >>> x = np.linspace(1, 100, n)\n", " >>> y = 2*np.log(x) + np.random.rand(n) - 0.5\n", " >>> # Compute 2d histogram. Note the order of x/y and xedges/yedges\n", " >>> H, yedges, xedges = np.histogram2d(y, x, bins=20)\n", " \n", " Now we can plot the histogram using\n", " :func:`pcolormesh <matplotlib.pyplot.pcolormesh>`, and a\n", " :func:`hexbin <matplotlib.pyplot.hexbin>` for comparison.\n", " \n", " >>> # Plot histogram using pcolormesh\n", " >>> fig, (ax1, ax2) = plt.subplots(ncols=2, sharey=True)\n", " >>> ax1.pcolormesh(xedges, yedges, H, cmap='rainbow')\n", " >>> ax1.plot(x, 2*np.log(x), 'k-')\n", " >>> ax1.set_xlim(x.min(), x.max())\n", " >>> ax1.set_ylim(y.min(), y.max())\n", " >>> ax1.set_xlabel('x')\n", " >>> ax1.set_ylabel('y')\n", " >>> ax1.set_title('histogram2d')\n", " >>> ax1.grid()\n", " \n", " >>> # Create hexbin plot for comparison\n", " >>> ax2.hexbin(x, y, gridsize=20, cmap='rainbow')\n", " >>> ax2.plot(x, 2*np.log(x), 'k-')\n", " >>> ax2.set_title('hexbin')\n", " >>> ax2.set_xlim(x.min(), x.max())\n", " >>> ax2.set_xlabel('x')\n", " >>> ax2.grid()\n", " \n", " >>> plt.show()\n", " \n", " histogram_bin_edges(a, bins=10, range=None, weights=None)\n", " Function to calculate only the edges of the bins used by the `histogram`\n", " function.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input data. The histogram is computed over the flattened array.\n", " bins : int or sequence of scalars or str, optional\n", " If `bins` is an int, it defines the number of equal-width\n", " bins in the given range (10, by default). If `bins` is a\n", " sequence, it defines the bin edges, including the rightmost\n", " edge, allowing for non-uniform bin widths.\n", " \n", " If `bins` is a string from the list below, `histogram_bin_edges` will use\n", " the method chosen to calculate the optimal bin width and\n", " consequently the number of bins (see `Notes` for more detail on\n", " the estimators) from the data that falls within the requested\n", " range. While the bin width will be optimal for the actual data\n", " in the range, the number of bins will be computed to fill the\n", " entire range, including the empty portions. For visualisation,\n", " using the 'auto' option is suggested. Weighted data is not\n", " supported for automated bin size selection.\n", " \n", " 'auto'\n", " Maximum of the 'sturges' and 'fd' estimators. Provides good\n", " all around performance.\n", " \n", " 'fd' (Freedman Diaconis Estimator)\n", " Robust (resilient to outliers) estimator that takes into\n", " account data variability and data size.\n", " \n", " 'doane'\n", " An improved version of Sturges' estimator that works better\n", " with non-normal datasets.\n", " \n", " 'scott'\n", " Less robust estimator that takes into account data variability\n", " and data size.\n", " \n", " 'stone'\n", " Estimator based on leave-one-out cross-validation estimate of\n", " the integrated squared error. Can be regarded as a generalization\n", " of Scott's rule.\n", " \n", " 'rice'\n", " Estimator does not take variability into account, only data\n", " size. Commonly overestimates number of bins required.\n", " \n", " 'sturges'\n", " R's default method, only accounts for data size. Only\n", " optimal for gaussian data and underestimates number of bins\n", " for large non-gaussian datasets.\n", " \n", " 'sqrt'\n", " Square root (of data size) estimator, used by Excel and\n", " other programs for its speed and simplicity.\n", " \n", " range : (float, float), optional\n", " The lower and upper range of the bins. If not provided, range\n", " is simply ``(a.min(), a.max())``. Values outside the range are\n", " ignored. The first element of the range must be less than or\n", " equal to the second. `range` affects the automatic bin\n", " computation as well. While bin width is computed to be optimal\n", " based on the actual data within `range`, the bin count will fill\n", " the entire range including portions containing no data.\n", " \n", " weights : array_like, optional\n", " An array of weights, of the same shape as `a`. Each value in\n", " `a` only contributes its associated weight towards the bin count\n", " (instead of 1). This is currently not used by any of the bin estimators,\n", " but may be in the future.\n", " \n", " Returns\n", " -------\n", " bin_edges : array of dtype float\n", " The edges to pass into `histogram`\n", " \n", " See Also\n", " --------\n", " histogram\n", " \n", " Notes\n", " -----\n", " The methods to estimate the optimal number of bins are well founded\n", " in literature, and are inspired by the choices R provides for\n", " histogram visualisation. Note that having the number of bins\n", " proportional to :math:`n^{1/3}` is asymptotically optimal, which is\n", " why it appears in most estimators. These are simply plug-in methods\n", " that give good starting points for number of bins. In the equations\n", " below, :math:`h` is the binwidth and :math:`n_h` is the number of\n", " bins. All estimators that compute bin counts are recast to bin width\n", " using the `ptp` of the data. The final bin count is obtained from\n", " ``np.round(np.ceil(range / h))``. The final bin width is often less\n", " than what is returned by the estimators below.\n", " \n", " 'auto' (maximum of the 'sturges' and 'fd' estimators)\n", " A compromise to get a good value. For small datasets the Sturges\n", " value will usually be chosen, while larger datasets will usually\n", " default to FD. Avoids the overly conservative behaviour of FD\n", " and Sturges for small and large datasets respectively.\n", " Switchover point is usually :math:`a.size \\approx 1000`.\n", " \n", " 'fd' (Freedman Diaconis Estimator)\n", " .. math:: h = 2 \\frac{IQR}{n^{1/3}}\n", " \n", " The binwidth is proportional to the interquartile range (IQR)\n", " and inversely proportional to cube root of a.size. Can be too\n", " conservative for small datasets, but is quite good for large\n", " datasets. The IQR is very robust to outliers.\n", " \n", " 'scott'\n", " .. math:: h = \\sigma \\sqrt[3]{\\frac{24 \\sqrt{\\pi}}{n}}\n", " \n", " The binwidth is proportional to the standard deviation of the\n", " data and inversely proportional to cube root of ``x.size``. Can\n", " be too conservative for small datasets, but is quite good for\n", " large datasets. The standard deviation is not very robust to\n", " outliers. Values are very similar to the Freedman-Diaconis\n", " estimator in the absence of outliers.\n", " \n", " 'rice'\n", " .. math:: n_h = 2n^{1/3}\n", " \n", " The number of bins is only proportional to cube root of\n", " ``a.size``. It tends to overestimate the number of bins and it\n", " does not take into account data variability.\n", " \n", " 'sturges'\n", " .. math:: n_h = \\log _{2}(n) + 1\n", " \n", " The number of bins is the base 2 log of ``a.size``. This\n", " estimator assumes normality of data and is too conservative for\n", " larger, non-normal datasets. This is the default method in R's\n", " ``hist`` method.\n", " \n", " 'doane'\n", " .. math:: n_h = 1 + \\log_{2}(n) +\n", " \\log_{2}\\left(1 + \\frac{|g_1|}{\\sigma_{g_1}}\\right)\n", " \n", " g_1 = mean\\left[\\left(\\frac{x - \\mu}{\\sigma}\\right)^3\\right]\n", " \n", " \\sigma_{g_1} = \\sqrt{\\frac{6(n - 2)}{(n + 1)(n + 3)}}\n", " \n", " An improved version of Sturges' formula that produces better\n", " estimates for non-normal datasets. This estimator attempts to\n", " account for the skew of the data.\n", " \n", " 'sqrt'\n", " .. math:: n_h = \\sqrt n\n", " \n", " The simplest and fastest estimator. Only takes into account the\n", " data size.\n", " \n", " Examples\n", " --------\n", " >>> arr = np.array([0, 0, 0, 1, 2, 3, 3, 4, 5])\n", " >>> np.histogram_bin_edges(arr, bins='auto', range=(0, 1))\n", " array([0. , 0.25, 0.5 , 0.75, 1. ])\n", " >>> np.histogram_bin_edges(arr, bins=2)\n", " array([0. , 2.5, 5. ])\n", " \n", " For consistency with histogram, an array of pre-computed bins is\n", " passed through unmodified:\n", " \n", " >>> np.histogram_bin_edges(arr, [1, 2])\n", " array([1, 2])\n", " \n", " This function allows one set of bins to be computed, and reused across\n", " multiple histograms:\n", " \n", " >>> shared_bins = np.histogram_bin_edges(arr, bins='auto')\n", " >>> shared_bins\n", " array([0., 1., 2., 3., 4., 5.])\n", " \n", " >>> group_id = np.array([0, 1, 1, 0, 1, 1, 0, 1, 1])\n", " >>> hist_0, _ = np.histogram(arr[group_id == 0], bins=shared_bins)\n", " >>> hist_1, _ = np.histogram(arr[group_id == 1], bins=shared_bins)\n", " \n", " >>> hist_0; hist_1\n", " array([1, 1, 0, 1, 0])\n", " array([2, 0, 1, 1, 2])\n", " \n", " Which gives more easily comparable results than using separate bins for\n", " each histogram:\n", " \n", " >>> hist_0, bins_0 = np.histogram(arr[group_id == 0], bins='auto')\n", " >>> hist_1, bins_1 = np.histogram(arr[group_id == 1], bins='auto')\n", " >>> hist_0; hist_1\n", " array([1, 1, 1])\n", " array([2, 1, 1, 2])\n", " >>> bins_0; bins_1\n", " array([0., 1., 2., 3.])\n", " array([0. , 1.25, 2.5 , 3.75, 5. ])\n", " \n", " histogramdd(sample, bins=10, range=None, density=None, weights=None)\n", " Compute the multidimensional histogram of some data.\n", " \n", " Parameters\n", " ----------\n", " sample : (N, D) array, or (N, D) array_like\n", " The data to be histogrammed.\n", " \n", " Note the unusual interpretation of sample when an array_like:\n", " \n", " * When an array, each row is a coordinate in a D-dimensional space -\n", " such as ``histogramdd(np.array([p1, p2, p3]))``.\n", " * When an array_like, each element is the list of values for single\n", " coordinate - such as ``histogramdd((X, Y, Z))``.\n", " \n", " The first form should be preferred.\n", " \n", " bins : sequence or int, optional\n", " The bin specification:\n", " \n", " * A sequence of arrays describing the monotonically increasing bin\n", " edges along each dimension.\n", " * The number of bins for each dimension (nx, ny, ... =bins)\n", " * The number of bins for all dimensions (nx=ny=...=bins).\n", " \n", " range : sequence, optional\n", " A sequence of length D, each an optional (lower, upper) tuple giving\n", " the outer bin edges to be used if the edges are not given explicitly in\n", " `bins`.\n", " An entry of None in the sequence results in the minimum and maximum\n", " values being used for the corresponding dimension.\n", " The default, None, is equivalent to passing a tuple of D None values.\n", " density : bool, optional\n", " If False, the default, returns the number of samples in each bin.\n", " If True, returns the probability *density* function at the bin,\n", " ``bin_count / sample_count / bin_volume``.\n", " weights : (N,) array_like, optional\n", " An array of values `w_i` weighing each sample `(x_i, y_i, z_i, ...)`.\n", " Weights are normalized to 1 if density is True. If density is False,\n", " the values of the returned histogram are equal to the sum of the\n", " weights belonging to the samples falling into each bin.\n", " \n", " Returns\n", " -------\n", " H : ndarray\n", " The multidimensional histogram of sample x. See density and weights\n", " for the different possible semantics.\n", " edges : list\n", " A list of D arrays describing the bin edges for each dimension.\n", " \n", " See Also\n", " --------\n", " histogram: 1-D histogram\n", " histogram2d: 2-D histogram\n", " \n", " Examples\n", " --------\n", " >>> r = np.random.randn(100,3)\n", " >>> H, edges = np.histogramdd(r, bins = (5, 8, 4))\n", " >>> H.shape, edges[0].size, edges[1].size, edges[2].size\n", " ((5, 8, 4), 6, 9, 5)\n", " \n", " hsplit(ary, indices_or_sections)\n", " Split an array into multiple sub-arrays horizontally (column-wise).\n", " \n", " Please refer to the `split` documentation. `hsplit` is equivalent\n", " to `split` with ``axis=1``, the array is always split along the second\n", " axis except for 1-D arrays, where it is split at ``axis=0``.\n", " \n", " See Also\n", " --------\n", " split : Split an array into multiple sub-arrays of equal size.\n", " \n", " Examples\n", " --------\n", " >>> x = np.arange(16.0).reshape(4, 4)\n", " >>> x\n", " array([[ 0., 1., 2., 3.],\n", " [ 4., 5., 6., 7.],\n", " [ 8., 9., 10., 11.],\n", " [12., 13., 14., 15.]])\n", " >>> np.hsplit(x, 2)\n", " [array([[ 0., 1.],\n", " [ 4., 5.],\n", " [ 8., 9.],\n", " [12., 13.]]),\n", " array([[ 2., 3.],\n", " [ 6., 7.],\n", " [10., 11.],\n", " [14., 15.]])]\n", " >>> np.hsplit(x, np.array([3, 6]))\n", " [array([[ 0., 1., 2.],\n", " [ 4., 5., 6.],\n", " [ 8., 9., 10.],\n", " [12., 13., 14.]]),\n", " array([[ 3.],\n", " [ 7.],\n", " [11.],\n", " [15.]]),\n", " array([], shape=(4, 0), dtype=float64)]\n", " \n", " With a higher dimensional array the split is still along the second axis.\n", " \n", " >>> x = np.arange(8.0).reshape(2, 2, 2)\n", " >>> x\n", " array([[[0., 1.],\n", " [2., 3.]],\n", " [[4., 5.],\n", " [6., 7.]]])\n", " >>> np.hsplit(x, 2)\n", " [array([[[0., 1.]],\n", " [[4., 5.]]]),\n", " array([[[2., 3.]],\n", " [[6., 7.]]])]\n", " \n", " With a 1-D array, the split is along axis 0.\n", " \n", " >>> x = np.array([0, 1, 2, 3, 4, 5])\n", " >>> np.hsplit(x, 2)\n", " [array([0, 1, 2]), array([3, 4, 5])]\n", " \n", " hstack(tup, *, dtype=None, casting='same_kind')\n", " Stack arrays in sequence horizontally (column wise).\n", " \n", " This is equivalent to concatenation along the second axis, except for 1-D\n", " arrays where it concatenates along the first axis. Rebuilds arrays divided\n", " by `hsplit`.\n", " \n", " This function makes most sense for arrays with up to 3 dimensions. For\n", " instance, for pixel-data with a height (first axis), width (second axis),\n", " and r/g/b channels (third axis). The functions `concatenate`, `stack` and\n", " `block` provide more general stacking and concatenation operations.\n", " \n", " Parameters\n", " ----------\n", " tup : sequence of ndarrays\n", " The arrays must have the same shape along all but the second axis,\n", " except 1-D arrays which can be any length.\n", " \n", " dtype : str or dtype\n", " If provided, the destination array will have this dtype. Cannot be\n", " provided together with `out`.\n", " \n", " .. versionadded:: 1.24\n", " \n", " casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional\n", " Controls what kind of data casting may occur. Defaults to 'same_kind'.\n", " \n", " .. versionadded:: 1.24\n", " \n", " Returns\n", " -------\n", " stacked : ndarray\n", " The array formed by stacking the given arrays.\n", " \n", " See Also\n", " --------\n", " concatenate : Join a sequence of arrays along an existing axis.\n", " stack : Join a sequence of arrays along a new axis.\n", " block : Assemble an nd-array from nested lists of blocks.\n", " vstack : Stack arrays in sequence vertically (row wise).\n", " dstack : Stack arrays in sequence depth wise (along third axis).\n", " column_stack : Stack 1-D arrays as columns into a 2-D array.\n", " hsplit : Split an array into multiple sub-arrays horizontally (column-wise).\n", " \n", " Examples\n", " --------\n", " >>> a = np.array((1,2,3))\n", " >>> b = np.array((4,5,6))\n", " >>> np.hstack((a,b))\n", " array([1, 2, 3, 4, 5, 6])\n", " >>> a = np.array([[1],[2],[3]])\n", " >>> b = np.array([[4],[5],[6]])\n", " >>> np.hstack((a,b))\n", " array([[1, 4],\n", " [2, 5],\n", " [3, 6]])\n", " \n", " i0(x)\n", " Modified Bessel function of the first kind, order 0.\n", " \n", " Usually denoted :math:`I_0`.\n", " \n", " Parameters\n", " ----------\n", " x : array_like of float\n", " Argument of the Bessel function.\n", " \n", " Returns\n", " -------\n", " out : ndarray, shape = x.shape, dtype = float\n", " The modified Bessel function evaluated at each of the elements of `x`.\n", " \n", " See Also\n", " --------\n", " scipy.special.i0, scipy.special.iv, scipy.special.ive\n", " \n", " Notes\n", " -----\n", " The scipy implementation is recommended over this function: it is a\n", " proper ufunc written in C, and more than an order of magnitude faster.\n", " \n", " We use the algorithm published by Clenshaw [1]_ and referenced by\n", " Abramowitz and Stegun [2]_, for which the function domain is\n", " partitioned into the two intervals [0,8] and (8,inf), and Chebyshev\n", " polynomial expansions are employed in each interval. Relative error on\n", " the domain [0,30] using IEEE arithmetic is documented [3]_ as having a\n", " peak of 5.8e-16 with an rms of 1.4e-16 (n = 30000).\n", " \n", " References\n", " ----------\n", " .. [1] C. W. Clenshaw, \"Chebyshev series for mathematical functions\", in\n", " *National Physical Laboratory Mathematical Tables*, vol. 5, London:\n", " Her Majesty's Stationery Office, 1962.\n", " .. [2] M. Abramowitz and I. A. Stegun, *Handbook of Mathematical\n", " Functions*, 10th printing, New York: Dover, 1964, pp. 379.\n", " https://personal.math.ubc.ca/~cbm/aands/page_379.htm\n", " .. [3] https://metacpan.org/pod/distribution/Math-Cephes/lib/Math/Cephes.pod#i0:-Modified-Bessel-function-of-order-zero\n", " \n", " Examples\n", " --------\n", " >>> np.i0(0.)\n", " array(1.0)\n", " >>> np.i0([0, 1, 2, 3])\n", " array([1. , 1.26606588, 2.2795853 , 4.88079259])\n", " \n", " identity(n, dtype=None, *, like=None)\n", " Return the identity array.\n", " \n", " The identity array is a square array with ones on\n", " the main diagonal.\n", " \n", " Parameters\n", " ----------\n", " n : int\n", " Number of rows (and columns) in `n` x `n` output.\n", " dtype : data-type, optional\n", " Data-type of the output. Defaults to ``float``.\n", " like : array_like, optional\n", " Reference object to allow the creation of arrays which are not\n", " NumPy arrays. If an array-like passed in as ``like`` supports\n", " the ``__array_function__`` protocol, the result will be defined\n", " by it. In this case, it ensures the creation of an array object\n", " compatible with that passed in via this argument.\n", " \n", " .. versionadded:: 1.20.0\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " `n` x `n` array with its main diagonal set to one,\n", " and all other elements 0.\n", " \n", " Examples\n", " --------\n", " >>> np.identity(3)\n", " array([[1., 0., 0.],\n", " [0., 1., 0.],\n", " [0., 0., 1.]])\n", " \n", " imag(val)\n", " Return the imaginary part of the complex argument.\n", " \n", " Parameters\n", " ----------\n", " val : array_like\n", " Input array.\n", " \n", " Returns\n", " -------\n", " out : ndarray or scalar\n", " The imaginary component of the complex argument. If `val` is real,\n", " the type of `val` is used for the output. If `val` has complex\n", " elements, the returned type is float.\n", " \n", " See Also\n", " --------\n", " real, angle, real_if_close\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([1+2j, 3+4j, 5+6j])\n", " >>> a.imag\n", " array([2., 4., 6.])\n", " >>> a.imag = np.array([8, 10, 12])\n", " >>> a\n", " array([1. +8.j, 3.+10.j, 5.+12.j])\n", " >>> np.imag(1 + 1j)\n", " 1.0\n", " \n", " in1d(ar1, ar2, assume_unique=False, invert=False, *, kind=None)\n", " Test whether each element of a 1-D array is also present in a second array.\n", " \n", " Returns a boolean array the same length as `ar1` that is True\n", " where an element of `ar1` is in `ar2` and False otherwise.\n", " \n", " We recommend using :func:`isin` instead of `in1d` for new code.\n", " \n", " Parameters\n", " ----------\n", " ar1 : (M,) array_like\n", " Input array.\n", " ar2 : array_like\n", " The values against which to test each value of `ar1`.\n", " assume_unique : bool, optional\n", " If True, the input arrays are both assumed to be unique, which\n", " can speed up the calculation. Default is False.\n", " invert : bool, optional\n", " If True, the values in the returned array are inverted (that is,\n", " False where an element of `ar1` is in `ar2` and True otherwise).\n", " Default is False. ``np.in1d(a, b, invert=True)`` is equivalent\n", " to (but is faster than) ``np.invert(in1d(a, b))``.\n", " kind : {None, 'sort', 'table'}, optional\n", " The algorithm to use. This will not affect the final result,\n", " but will affect the speed and memory use. The default, None,\n", " will select automatically based on memory considerations.\n", " \n", " * If 'sort', will use a mergesort-based approach. This will have\n", " a memory usage of roughly 6 times the sum of the sizes of\n", " `ar1` and `ar2`, not accounting for size of dtypes.\n", " * If 'table', will use a lookup table approach similar\n", " to a counting sort. This is only available for boolean and\n", " integer arrays. This will have a memory usage of the\n", " size of `ar1` plus the max-min value of `ar2`. `assume_unique`\n", " has no effect when the 'table' option is used.\n", " * If None, will automatically choose 'table' if\n", " the required memory allocation is less than or equal to\n", " 6 times the sum of the sizes of `ar1` and `ar2`,\n", " otherwise will use 'sort'. This is done to not use\n", " a large amount of memory by default, even though\n", " 'table' may be faster in most cases. If 'table' is chosen,\n", " `assume_unique` will have no effect.\n", " \n", " .. versionadded:: 1.8.0\n", " \n", " Returns\n", " -------\n", " in1d : (M,) ndarray, bool\n", " The values `ar1[in1d]` are in `ar2`.\n", " \n", " See Also\n", " --------\n", " isin : Version of this function that preserves the\n", " shape of ar1.\n", " numpy.lib.arraysetops : Module with a number of other functions for\n", " performing set operations on arrays.\n", " \n", " Notes\n", " -----\n", " `in1d` can be considered as an element-wise function version of the\n", " python keyword `in`, for 1-D sequences. ``in1d(a, b)`` is roughly\n", " equivalent to ``np.array([item in b for item in a])``.\n", " However, this idea fails if `ar2` is a set, or similar (non-sequence)\n", " container: As ``ar2`` is converted to an array, in those cases\n", " ``asarray(ar2)`` is an object array rather than the expected array of\n", " contained values.\n", " \n", " Using ``kind='table'`` tends to be faster than `kind='sort'` if the\n", " following relationship is true:\n", " ``log10(len(ar2)) > (log10(max(ar2)-min(ar2)) - 2.27) / 0.927``,\n", " but may use greater memory. The default value for `kind` will\n", " be automatically selected based only on memory usage, so one may\n", " manually set ``kind='table'`` if memory constraints can be relaxed.\n", " \n", " .. versionadded:: 1.4.0\n", " \n", " Examples\n", " --------\n", " >>> test = np.array([0, 1, 2, 5, 0])\n", " >>> states = [0, 2]\n", " >>> mask = np.in1d(test, states)\n", " >>> mask\n", " array([ True, False, True, False, True])\n", " >>> test[mask]\n", " array([0, 2, 0])\n", " >>> mask = np.in1d(test, states, invert=True)\n", " >>> mask\n", " array([False, True, False, True, False])\n", " >>> test[mask]\n", " array([1, 5])\n", " \n", " indices(dimensions, dtype=<class 'int'>, sparse=False)\n", " Return an array representing the indices of a grid.\n", " \n", " Compute an array where the subarrays contain index values 0, 1, ...\n", " varying only along the corresponding axis.\n", " \n", " Parameters\n", " ----------\n", " dimensions : sequence of ints\n", " The shape of the grid.\n", " dtype : dtype, optional\n", " Data type of the result.\n", " sparse : boolean, optional\n", " Return a sparse representation of the grid instead of a dense\n", " representation. Default is False.\n", " \n", " .. versionadded:: 1.17\n", " \n", " Returns\n", " -------\n", " grid : one ndarray or tuple of ndarrays\n", " If sparse is False:\n", " Returns one array of grid indices,\n", " ``grid.shape = (len(dimensions),) + tuple(dimensions)``.\n", " If sparse is True:\n", " Returns a tuple of arrays, with\n", " ``grid[i].shape = (1, ..., 1, dimensions[i], 1, ..., 1)`` with\n", " dimensions[i] in the ith place\n", " \n", " See Also\n", " --------\n", " mgrid, ogrid, meshgrid\n", " \n", " Notes\n", " -----\n", " The output shape in the dense case is obtained by prepending the number\n", " of dimensions in front of the tuple of dimensions, i.e. if `dimensions`\n", " is a tuple ``(r0, ..., rN-1)`` of length ``N``, the output shape is\n", " ``(N, r0, ..., rN-1)``.\n", " \n", " The subarrays ``grid[k]`` contains the N-D array of indices along the\n", " ``k-th`` axis. Explicitly::\n", " \n", " grid[k, i0, i1, ..., iN-1] = ik\n", " \n", " Examples\n", " --------\n", " >>> grid = np.indices((2, 3))\n", " >>> grid.shape\n", " (2, 2, 3)\n", " >>> grid[0] # row indices\n", " array([[0, 0, 0],\n", " [1, 1, 1]])\n", " >>> grid[1] # column indices\n", " array([[0, 1, 2],\n", " [0, 1, 2]])\n", " \n", " The indices can be used as an index into an array.\n", " \n", " >>> x = np.arange(20).reshape(5, 4)\n", " >>> row, col = np.indices((2, 3))\n", " >>> x[row, col]\n", " array([[0, 1, 2],\n", " [4, 5, 6]])\n", " \n", " Note that it would be more straightforward in the above example to\n", " extract the required elements directly with ``x[:2, :3]``.\n", " \n", " If sparse is set to true, the grid will be returned in a sparse\n", " representation.\n", " \n", " >>> i, j = np.indices((2, 3), sparse=True)\n", " >>> i.shape\n", " (2, 1)\n", " >>> j.shape\n", " (1, 3)\n", " >>> i # row indices\n", " array([[0],\n", " [1]])\n", " >>> j # column indices\n", " array([[0, 1, 2]])\n", " \n", " info(object=None, maxwidth=76, output=None, toplevel='numpy')\n", " Get help information for a function, class, or module.\n", " \n", " Parameters\n", " ----------\n", " object : object or str, optional\n", " Input object or name to get information about. If `object` is a\n", " numpy object, its docstring is given. If it is a string, available\n", " modules are searched for matching objects. If None, information\n", " about `info` itself is returned.\n", " maxwidth : int, optional\n", " Printing width.\n", " output : file like object, optional\n", " File like object that the output is written to, default is\n", " ``None``, in which case ``sys.stdout`` will be used.\n", " The object has to be opened in 'w' or 'a' mode.\n", " toplevel : str, optional\n", " Start search at this level.\n", " \n", " See Also\n", " --------\n", " source, lookfor\n", " \n", " Notes\n", " -----\n", " When used interactively with an object, ``np.info(obj)`` is equivalent\n", " to ``help(obj)`` on the Python prompt or ``obj?`` on the IPython\n", " prompt.\n", " \n", " Examples\n", " --------\n", " >>> np.info(np.polyval) # doctest: +SKIP\n", " polyval(p, x)\n", " Evaluate the polynomial p at x.\n", " ...\n", " \n", " When using a string for `object` it is possible to get multiple results.\n", " \n", " >>> np.info('fft') # doctest: +SKIP\n", " *** Found in numpy ***\n", " Core FFT routines\n", " ...\n", " *** Found in numpy.fft ***\n", " fft(a, n=None, axis=-1)\n", " ...\n", " *** Repeat reference found in numpy.fft.fftpack ***\n", " *** Total of 3 references found. ***\n", " \n", " inner(...)\n", " inner(a, b, /)\n", " \n", " Inner product of two arrays.\n", " \n", " Ordinary inner product of vectors for 1-D arrays (without complex\n", " conjugation), in higher dimensions a sum product over the last axes.\n", " \n", " Parameters\n", " ----------\n", " a, b : array_like\n", " If `a` and `b` are nonscalar, their last dimensions must match.\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " If `a` and `b` are both\n", " scalars or both 1-D arrays then a scalar is returned; otherwise\n", " an array is returned.\n", " ``out.shape = (*a.shape[:-1], *b.shape[:-1])``\n", " \n", " Raises\n", " ------\n", " ValueError\n", " If both `a` and `b` are nonscalar and their last dimensions have\n", " different sizes.\n", " \n", " See Also\n", " --------\n", " tensordot : Sum products over arbitrary axes.\n", " dot : Generalised matrix product, using second last dimension of `b`.\n", " einsum : Einstein summation convention.\n", " \n", " Notes\n", " -----\n", " For vectors (1-D arrays) it computes the ordinary inner-product::\n", " \n", " np.inner(a, b) = sum(a[:]*b[:])\n", " \n", " More generally, if ``ndim(a) = r > 0`` and ``ndim(b) = s > 0``::\n", " \n", " np.inner(a, b) = np.tensordot(a, b, axes=(-1,-1))\n", " \n", " or explicitly::\n", " \n", " np.inner(a, b)[i0,...,ir-2,j0,...,js-2]\n", " = sum(a[i0,...,ir-2,:]*b[j0,...,js-2,:])\n", " \n", " In addition `a` or `b` may be scalars, in which case::\n", " \n", " np.inner(a,b) = a*b\n", " \n", " Examples\n", " --------\n", " Ordinary inner product for vectors:\n", " \n", " >>> a = np.array([1,2,3])\n", " >>> b = np.array([0,1,0])\n", " >>> np.inner(a, b)\n", " 2\n", " \n", " Some multidimensional examples:\n", " \n", " >>> a = np.arange(24).reshape((2,3,4))\n", " >>> b = np.arange(4)\n", " >>> c = np.inner(a, b)\n", " >>> c.shape\n", " (2, 3)\n", " >>> c\n", " array([[ 14, 38, 62],\n", " [ 86, 110, 134]])\n", " \n", " >>> a = np.arange(2).reshape((1,1,2))\n", " >>> b = np.arange(6).reshape((3,2))\n", " >>> c = np.inner(a, b)\n", " >>> c.shape\n", " (1, 1, 3)\n", " >>> c\n", " array([[[1, 3, 5]]])\n", " \n", " An example where `b` is a scalar:\n", " \n", " >>> np.inner(np.eye(2), 7)\n", " array([[7., 0.],\n", " [0., 7.]])\n", " \n", " insert(arr, obj, values, axis=None)\n", " Insert values along the given axis before the given indices.\n", " \n", " Parameters\n", " ----------\n", " arr : array_like\n", " Input array.\n", " obj : int, slice or sequence of ints\n", " Object that defines the index or indices before which `values` is\n", " inserted.\n", " \n", " .. versionadded:: 1.8.0\n", " \n", " Support for multiple insertions when `obj` is a single scalar or a\n", " sequence with one element (similar to calling insert multiple\n", " times).\n", " values : array_like\n", " Values to insert into `arr`. If the type of `values` is different\n", " from that of `arr`, `values` is converted to the type of `arr`.\n", " `values` should be shaped so that ``arr[...,obj,...] = values``\n", " is legal.\n", " axis : int, optional\n", " Axis along which to insert `values`. If `axis` is None then `arr`\n", " is flattened first.\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " A copy of `arr` with `values` inserted. Note that `insert`\n", " does not occur in-place: a new array is returned. If\n", " `axis` is None, `out` is a flattened array.\n", " \n", " See Also\n", " --------\n", " append : Append elements at the end of an array.\n", " concatenate : Join a sequence of arrays along an existing axis.\n", " delete : Delete elements from an array.\n", " \n", " Notes\n", " -----\n", " Note that for higher dimensional inserts ``obj=0`` behaves very different\n", " from ``obj=[0]`` just like ``arr[:,0,:] = values`` is different from\n", " ``arr[:,[0],:] = values``.\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([[1, 1], [2, 2], [3, 3]])\n", " >>> a\n", " array([[1, 1],\n", " [2, 2],\n", " [3, 3]])\n", " >>> np.insert(a, 1, 5)\n", " array([1, 5, 1, ..., 2, 3, 3])\n", " >>> np.insert(a, 1, 5, axis=1)\n", " array([[1, 5, 1],\n", " [2, 5, 2],\n", " [3, 5, 3]])\n", " \n", " Difference between sequence and scalars:\n", " \n", " >>> np.insert(a, [1], [[1],[2],[3]], axis=1)\n", " array([[1, 1, 1],\n", " [2, 2, 2],\n", " [3, 3, 3]])\n", " >>> np.array_equal(np.insert(a, 1, [1, 2, 3], axis=1),\n", " ... np.insert(a, [1], [[1],[2],[3]], axis=1))\n", " True\n", " \n", " >>> b = a.flatten()\n", " >>> b\n", " array([1, 1, 2, 2, 3, 3])\n", " >>> np.insert(b, [2, 2], [5, 6])\n", " array([1, 1, 5, ..., 2, 3, 3])\n", " \n", " >>> np.insert(b, slice(2, 4), [5, 6])\n", " array([1, 1, 5, ..., 2, 3, 3])\n", " \n", " >>> np.insert(b, [2, 2], [7.13, False]) # type casting\n", " array([1, 1, 7, ..., 2, 3, 3])\n", " \n", " >>> x = np.arange(8).reshape(2, 4)\n", " >>> idx = (1, 3)\n", " >>> np.insert(x, idx, 999, axis=1)\n", " array([[ 0, 999, 1, 2, 999, 3],\n", " [ 4, 999, 5, 6, 999, 7]])\n", " \n", " interp(x, xp, fp, left=None, right=None, period=None)\n", " One-dimensional linear interpolation for monotonically increasing sample points.\n", " \n", " Returns the one-dimensional piecewise linear interpolant to a function\n", " with given discrete data points (`xp`, `fp`), evaluated at `x`.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " The x-coordinates at which to evaluate the interpolated values.\n", " \n", " xp : 1-D sequence of floats\n", " The x-coordinates of the data points, must be increasing if argument\n", " `period` is not specified. Otherwise, `xp` is internally sorted after\n", " normalizing the periodic boundaries with ``xp = xp % period``.\n", " \n", " fp : 1-D sequence of float or complex\n", " The y-coordinates of the data points, same length as `xp`.\n", " \n", " left : optional float or complex corresponding to fp\n", " Value to return for `x < xp[0]`, default is `fp[0]`.\n", " \n", " right : optional float or complex corresponding to fp\n", " Value to return for `x > xp[-1]`, default is `fp[-1]`.\n", " \n", " period : None or float, optional\n", " A period for the x-coordinates. This parameter allows the proper\n", " interpolation of angular x-coordinates. Parameters `left` and `right`\n", " are ignored if `period` is specified.\n", " \n", " .. versionadded:: 1.10.0\n", " \n", " Returns\n", " -------\n", " y : float or complex (corresponding to fp) or ndarray\n", " The interpolated values, same shape as `x`.\n", " \n", " Raises\n", " ------\n", " ValueError\n", " If `xp` and `fp` have different length\n", " If `xp` or `fp` are not 1-D sequences\n", " If `period == 0`\n", " \n", " See Also\n", " --------\n", " scipy.interpolate\n", " \n", " Warnings\n", " --------\n", " The x-coordinate sequence is expected to be increasing, but this is not\n", " explicitly enforced. However, if the sequence `xp` is non-increasing,\n", " interpolation results are meaningless.\n", " \n", " Note that, since NaN is unsortable, `xp` also cannot contain NaNs.\n", " \n", " A simple check for `xp` being strictly increasing is::\n", " \n", " np.all(np.diff(xp) > 0)\n", " \n", " Examples\n", " --------\n", " >>> xp = [1, 2, 3]\n", " >>> fp = [3, 2, 0]\n", " >>> np.interp(2.5, xp, fp)\n", " 1.0\n", " >>> np.interp([0, 1, 1.5, 2.72, 3.14], xp, fp)\n", " array([3. , 3. , 2.5 , 0.56, 0. ])\n", " >>> UNDEF = -99.0\n", " >>> np.interp(3.14, xp, fp, right=UNDEF)\n", " -99.0\n", " \n", " Plot an interpolant to the sine function:\n", " \n", " >>> x = np.linspace(0, 2*np.pi, 10)\n", " >>> y = np.sin(x)\n", " >>> xvals = np.linspace(0, 2*np.pi, 50)\n", " >>> yinterp = np.interp(xvals, x, y)\n", " >>> import matplotlib.pyplot as plt\n", " >>> plt.plot(x, y, 'o')\n", " [<matplotlib.lines.Line2D object at 0x...>]\n", " >>> plt.plot(xvals, yinterp, '-x')\n", " [<matplotlib.lines.Line2D object at 0x...>]\n", " >>> plt.show()\n", " \n", " Interpolation with periodic x-coordinates:\n", " \n", " >>> x = [-180, -170, -185, 185, -10, -5, 0, 365]\n", " >>> xp = [190, -190, 350, -350]\n", " >>> fp = [5, 10, 3, 4]\n", " >>> np.interp(x, xp, fp, period=360)\n", " array([7.5 , 5. , 8.75, 6.25, 3. , 3.25, 3.5 , 3.75])\n", " \n", " Complex interpolation:\n", " \n", " >>> x = [1.5, 4.0]\n", " >>> xp = [2,3,5]\n", " >>> fp = [1.0j, 0, 2+3j]\n", " >>> np.interp(x, xp, fp)\n", " array([0.+1.j , 1.+1.5j])\n", " \n", " intersect1d(ar1, ar2, assume_unique=False, return_indices=False)\n", " Find the intersection of two arrays.\n", " \n", " Return the sorted, unique values that are in both of the input arrays.\n", " \n", " Parameters\n", " ----------\n", " ar1, ar2 : array_like\n", " Input arrays. Will be flattened if not already 1D.\n", " assume_unique : bool\n", " If True, the input arrays are both assumed to be unique, which\n", " can speed up the calculation. If True but ``ar1`` or ``ar2`` are not\n", " unique, incorrect results and out-of-bounds indices could result.\n", " Default is False.\n", " return_indices : bool\n", " If True, the indices which correspond to the intersection of the two\n", " arrays are returned. The first instance of a value is used if there are\n", " multiple. Default is False.\n", " \n", " .. versionadded:: 1.15.0\n", " \n", " Returns\n", " -------\n", " intersect1d : ndarray\n", " Sorted 1D array of common and unique elements.\n", " comm1 : ndarray\n", " The indices of the first occurrences of the common values in `ar1`.\n", " Only provided if `return_indices` is True.\n", " comm2 : ndarray\n", " The indices of the first occurrences of the common values in `ar2`.\n", " Only provided if `return_indices` is True.\n", " \n", " \n", " See Also\n", " --------\n", " numpy.lib.arraysetops : Module with a number of other functions for\n", " performing set operations on arrays.\n", " \n", " Examples\n", " --------\n", " >>> np.intersect1d([1, 3, 4, 3], [3, 1, 2, 1])\n", " array([1, 3])\n", " \n", " To intersect more than two arrays, use functools.reduce:\n", " \n", " >>> from functools import reduce\n", " >>> reduce(np.intersect1d, ([1, 3, 4, 3], [3, 1, 2, 1], [6, 3, 4, 2]))\n", " array([3])\n", " \n", " To return the indices of the values common to the input arrays\n", " along with the intersected values:\n", " \n", " >>> x = np.array([1, 1, 2, 3, 4])\n", " >>> y = np.array([2, 1, 4, 6])\n", " >>> xy, x_ind, y_ind = np.intersect1d(x, y, return_indices=True)\n", " >>> x_ind, y_ind\n", " (array([0, 2, 4]), array([1, 0, 2]))\n", " >>> xy, x[x_ind], y[y_ind]\n", " (array([1, 2, 4]), array([1, 2, 4]), array([1, 2, 4]))\n", " \n", " is_busday(...)\n", " is_busday(dates, weekmask='1111100', holidays=None, busdaycal=None, out=None)\n", " \n", " Calculates which of the given dates are valid days, and which are not.\n", " \n", " .. versionadded:: 1.7.0\n", " \n", " Parameters\n", " ----------\n", " dates : array_like of datetime64[D]\n", " The array of dates to process.\n", " weekmask : str or array_like of bool, optional\n", " A seven-element array indicating which of Monday through Sunday are\n", " valid days. May be specified as a length-seven list or array, like\n", " [1,1,1,1,1,0,0]; a length-seven string, like '1111100'; or a string\n", " like \"Mon Tue Wed Thu Fri\", made up of 3-character abbreviations for\n", " weekdays, optionally separated by white space. Valid abbreviations\n", " are: Mon Tue Wed Thu Fri Sat Sun\n", " holidays : array_like of datetime64[D], optional\n", " An array of dates to consider as invalid dates. They may be\n", " specified in any order, and NaT (not-a-time) dates are ignored.\n", " This list is saved in a normalized form that is suited for\n", " fast calculations of valid days.\n", " busdaycal : busdaycalendar, optional\n", " A `busdaycalendar` object which specifies the valid days. If this\n", " parameter is provided, neither weekmask nor holidays may be\n", " provided.\n", " out : array of bool, optional\n", " If provided, this array is filled with the result.\n", " \n", " Returns\n", " -------\n", " out : array of bool\n", " An array with the same shape as ``dates``, containing True for\n", " each valid day, and False for each invalid day.\n", " \n", " See Also\n", " --------\n", " busdaycalendar : An object that specifies a custom set of valid days.\n", " busday_offset : Applies an offset counted in valid days.\n", " busday_count : Counts how many valid days are in a half-open date range.\n", " \n", " Examples\n", " --------\n", " >>> # The weekdays are Friday, Saturday, and Monday\n", " ... np.is_busday(['2011-07-01', '2011-07-02', '2011-07-18'],\n", " ... holidays=['2011-07-01', '2011-07-04', '2011-07-17'])\n", " array([False, False, True])\n", " \n", " isclose(a, b, rtol=1e-05, atol=1e-08, equal_nan=False)\n", " Returns a boolean array where two arrays are element-wise equal within a\n", " tolerance.\n", " \n", " The tolerance values are positive, typically very small numbers. The\n", " relative difference (`rtol` * abs(`b`)) and the absolute difference\n", " `atol` are added together to compare against the absolute difference\n", " between `a` and `b`.\n", " \n", " .. warning:: The default `atol` is not appropriate for comparing numbers\n", " that are much smaller than one (see Notes).\n", " \n", " Parameters\n", " ----------\n", " a, b : array_like\n", " Input arrays to compare.\n", " rtol : float\n", " The relative tolerance parameter (see Notes).\n", " atol : float\n", " The absolute tolerance parameter (see Notes).\n", " equal_nan : bool\n", " Whether to compare NaN's as equal. If True, NaN's in `a` will be\n", " considered equal to NaN's in `b` in the output array.\n", " \n", " Returns\n", " -------\n", " y : array_like\n", " Returns a boolean array of where `a` and `b` are equal within the\n", " given tolerance. If both `a` and `b` are scalars, returns a single\n", " boolean value.\n", " \n", " See Also\n", " --------\n", " allclose\n", " math.isclose\n", " \n", " Notes\n", " -----\n", " .. versionadded:: 1.7.0\n", " \n", " For finite values, isclose uses the following equation to test whether\n", " two floating point values are equivalent.\n", " \n", " absolute(`a` - `b`) <= (`atol` + `rtol` * absolute(`b`))\n", " \n", " Unlike the built-in `math.isclose`, the above equation is not symmetric\n", " in `a` and `b` -- it assumes `b` is the reference value -- so that\n", " `isclose(a, b)` might be different from `isclose(b, a)`. Furthermore,\n", " the default value of atol is not zero, and is used to determine what\n", " small values should be considered close to zero. The default value is\n", " appropriate for expected values of order unity: if the expected values\n", " are significantly smaller than one, it can result in false positives.\n", " `atol` should be carefully selected for the use case at hand. A zero value\n", " for `atol` will result in `False` if either `a` or `b` is zero.\n", " \n", " `isclose` is not defined for non-numeric data types.\n", " `bool` is considered a numeric data-type for this purpose.\n", " \n", " Examples\n", " --------\n", " >>> np.isclose([1e10,1e-7], [1.00001e10,1e-8])\n", " array([ True, False])\n", " >>> np.isclose([1e10,1e-8], [1.00001e10,1e-9])\n", " array([ True, True])\n", " >>> np.isclose([1e10,1e-8], [1.0001e10,1e-9])\n", " array([False, True])\n", " >>> np.isclose([1.0, np.nan], [1.0, np.nan])\n", " array([ True, False])\n", " >>> np.isclose([1.0, np.nan], [1.0, np.nan], equal_nan=True)\n", " array([ True, True])\n", " >>> np.isclose([1e-8, 1e-7], [0.0, 0.0])\n", " array([ True, False])\n", " >>> np.isclose([1e-100, 1e-7], [0.0, 0.0], atol=0.0)\n", " array([False, False])\n", " >>> np.isclose([1e-10, 1e-10], [1e-20, 0.0])\n", " array([ True, True])\n", " >>> np.isclose([1e-10, 1e-10], [1e-20, 0.999999e-10], atol=0.0)\n", " array([False, True])\n", " \n", " iscomplex(x)\n", " Returns a bool array, where True if input element is complex.\n", " \n", " What is tested is whether the input has a non-zero imaginary part, not if\n", " the input type is complex.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Input array.\n", " \n", " Returns\n", " -------\n", " out : ndarray of bools\n", " Output array.\n", " \n", " See Also\n", " --------\n", " isreal\n", " iscomplexobj : Return True if x is a complex type or an array of complex\n", " numbers.\n", " \n", " Examples\n", " --------\n", " >>> np.iscomplex([1+1j, 1+0j, 4.5, 3, 2, 2j])\n", " array([ True, False, False, False, False, True])\n", " \n", " iscomplexobj(x)\n", " Check for a complex type or an array of complex numbers.\n", " \n", " The type of the input is checked, not the value. Even if the input\n", " has an imaginary part equal to zero, `iscomplexobj` evaluates to True.\n", " \n", " Parameters\n", " ----------\n", " x : any\n", " The input can be of any type and shape.\n", " \n", " Returns\n", " -------\n", " iscomplexobj : bool\n", " The return value, True if `x` is of a complex type or has at least\n", " one complex element.\n", " \n", " See Also\n", " --------\n", " isrealobj, iscomplex\n", " \n", " Examples\n", " --------\n", " >>> np.iscomplexobj(1)\n", " False\n", " >>> np.iscomplexobj(1+0j)\n", " True\n", " >>> np.iscomplexobj([3, 1+0j, True])\n", " True\n", " \n", " isfortran(a)\n", " Check if the array is Fortran contiguous but *not* C contiguous.\n", " \n", " This function is obsolete and, because of changes due to relaxed stride\n", " checking, its return value for the same array may differ for versions\n", " of NumPy >= 1.10.0 and previous versions. If you only want to check if an\n", " array is Fortran contiguous use ``a.flags.f_contiguous`` instead.\n", " \n", " Parameters\n", " ----------\n", " a : ndarray\n", " Input array.\n", " \n", " Returns\n", " -------\n", " isfortran : bool\n", " Returns True if the array is Fortran contiguous but *not* C contiguous.\n", " \n", " \n", " Examples\n", " --------\n", " \n", " np.array allows to specify whether the array is written in C-contiguous\n", " order (last index varies the fastest), or FORTRAN-contiguous order in\n", " memory (first index varies the fastest).\n", " \n", " >>> a = np.array([[1, 2, 3], [4, 5, 6]], order='C')\n", " >>> a\n", " array([[1, 2, 3],\n", " [4, 5, 6]])\n", " >>> np.isfortran(a)\n", " False\n", " \n", " >>> b = np.array([[1, 2, 3], [4, 5, 6]], order='F')\n", " >>> b\n", " array([[1, 2, 3],\n", " [4, 5, 6]])\n", " >>> np.isfortran(b)\n", " True\n", " \n", " \n", " The transpose of a C-ordered array is a FORTRAN-ordered array.\n", " \n", " >>> a = np.array([[1, 2, 3], [4, 5, 6]], order='C')\n", " >>> a\n", " array([[1, 2, 3],\n", " [4, 5, 6]])\n", " >>> np.isfortran(a)\n", " False\n", " >>> b = a.T\n", " >>> b\n", " array([[1, 4],\n", " [2, 5],\n", " [3, 6]])\n", " >>> np.isfortran(b)\n", " True\n", " \n", " C-ordered arrays evaluate as False even if they are also FORTRAN-ordered.\n", " \n", " >>> np.isfortran(np.array([1, 2], order='F'))\n", " False\n", " \n", " isin(element, test_elements, assume_unique=False, invert=False, *, kind=None)\n", " Calculates ``element in test_elements``, broadcasting over `element` only.\n", " Returns a boolean array of the same shape as `element` that is True\n", " where an element of `element` is in `test_elements` and False otherwise.\n", " \n", " Parameters\n", " ----------\n", " element : array_like\n", " Input array.\n", " test_elements : array_like\n", " The values against which to test each value of `element`.\n", " This argument is flattened if it is an array or array_like.\n", " See notes for behavior with non-array-like parameters.\n", " assume_unique : bool, optional\n", " If True, the input arrays are both assumed to be unique, which\n", " can speed up the calculation. Default is False.\n", " invert : bool, optional\n", " If True, the values in the returned array are inverted, as if\n", " calculating `element not in test_elements`. Default is False.\n", " ``np.isin(a, b, invert=True)`` is equivalent to (but faster\n", " than) ``np.invert(np.isin(a, b))``.\n", " kind : {None, 'sort', 'table'}, optional\n", " The algorithm to use. This will not affect the final result,\n", " but will affect the speed and memory use. The default, None,\n", " will select automatically based on memory considerations.\n", " \n", " * If 'sort', will use a mergesort-based approach. This will have\n", " a memory usage of roughly 6 times the sum of the sizes of\n", " `ar1` and `ar2`, not accounting for size of dtypes.\n", " * If 'table', will use a lookup table approach similar\n", " to a counting sort. This is only available for boolean and\n", " integer arrays. This will have a memory usage of the\n", " size of `ar1` plus the max-min value of `ar2`. `assume_unique`\n", " has no effect when the 'table' option is used.\n", " * If None, will automatically choose 'table' if\n", " the required memory allocation is less than or equal to\n", " 6 times the sum of the sizes of `ar1` and `ar2`,\n", " otherwise will use 'sort'. This is done to not use\n", " a large amount of memory by default, even though\n", " 'table' may be faster in most cases. If 'table' is chosen,\n", " `assume_unique` will have no effect.\n", " \n", " \n", " Returns\n", " -------\n", " isin : ndarray, bool\n", " Has the same shape as `element`. The values `element[isin]`\n", " are in `test_elements`.\n", " \n", " See Also\n", " --------\n", " in1d : Flattened version of this function.\n", " numpy.lib.arraysetops : Module with a number of other functions for\n", " performing set operations on arrays.\n", " \n", " Notes\n", " -----\n", " \n", " `isin` is an element-wise function version of the python keyword `in`.\n", " ``isin(a, b)`` is roughly equivalent to\n", " ``np.array([item in b for item in a])`` if `a` and `b` are 1-D sequences.\n", " \n", " `element` and `test_elements` are converted to arrays if they are not\n", " already. If `test_elements` is a set (or other non-sequence collection)\n", " it will be converted to an object array with one element, rather than an\n", " array of the values contained in `test_elements`. This is a consequence\n", " of the `array` constructor's way of handling non-sequence collections.\n", " Converting the set to a list usually gives the desired behavior.\n", " \n", " Using ``kind='table'`` tends to be faster than `kind='sort'` if the\n", " following relationship is true:\n", " ``log10(len(ar2)) > (log10(max(ar2)-min(ar2)) - 2.27) / 0.927``,\n", " but may use greater memory. The default value for `kind` will\n", " be automatically selected based only on memory usage, so one may\n", " manually set ``kind='table'`` if memory constraints can be relaxed.\n", " \n", " .. versionadded:: 1.13.0\n", " \n", " Examples\n", " --------\n", " >>> element = 2*np.arange(4).reshape((2, 2))\n", " >>> element\n", " array([[0, 2],\n", " [4, 6]])\n", " >>> test_elements = [1, 2, 4, 8]\n", " >>> mask = np.isin(element, test_elements)\n", " >>> mask\n", " array([[False, True],\n", " [ True, False]])\n", " >>> element[mask]\n", " array([2, 4])\n", " \n", " The indices of the matched values can be obtained with `nonzero`:\n", " \n", " >>> np.nonzero(mask)\n", " (array([0, 1]), array([1, 0]))\n", " \n", " The test can also be inverted:\n", " \n", " >>> mask = np.isin(element, test_elements, invert=True)\n", " >>> mask\n", " array([[ True, False],\n", " [False, True]])\n", " >>> element[mask]\n", " array([0, 6])\n", " \n", " Because of how `array` handles sets, the following does not\n", " work as expected:\n", " \n", " >>> test_set = {1, 2, 4, 8}\n", " >>> np.isin(element, test_set)\n", " array([[False, False],\n", " [False, False]])\n", " \n", " Casting the set to a list gives the expected result:\n", " \n", " >>> np.isin(element, list(test_set))\n", " array([[False, True],\n", " [ True, False]])\n", " \n", " isneginf(x, out=None)\n", " Test element-wise for negative infinity, return result as bool array.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " The input array.\n", " out : array_like, optional\n", " A location into which the result is stored. If provided, it must have a\n", " shape that the input broadcasts to. If not provided or None, a\n", " freshly-allocated boolean array is returned.\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " A boolean array with the same dimensions as the input.\n", " If second argument is not supplied then a numpy boolean array is\n", " returned with values True where the corresponding element of the\n", " input is negative infinity and values False where the element of\n", " the input is not negative infinity.\n", " \n", " If a second argument is supplied the result is stored there. If the\n", " type of that array is a numeric type the result is represented as\n", " zeros and ones, if the type is boolean then as False and True. The\n", " return value `out` is then a reference to that array.\n", " \n", " See Also\n", " --------\n", " isinf, isposinf, isnan, isfinite\n", " \n", " Notes\n", " -----\n", " NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic\n", " (IEEE 754).\n", " \n", " Errors result if the second argument is also supplied when x is a scalar\n", " input, if first and second arguments have different shapes, or if the\n", " first argument has complex values.\n", " \n", " Examples\n", " --------\n", " >>> np.isneginf(np.NINF)\n", " True\n", " >>> np.isneginf(np.inf)\n", " False\n", " >>> np.isneginf(np.PINF)\n", " False\n", " >>> np.isneginf([-np.inf, 0., np.inf])\n", " array([ True, False, False])\n", " \n", " >>> x = np.array([-np.inf, 0., np.inf])\n", " >>> y = np.array([2, 2, 2])\n", " >>> np.isneginf(x, y)\n", " array([1, 0, 0])\n", " >>> y\n", " array([1, 0, 0])\n", " \n", " isposinf(x, out=None)\n", " Test element-wise for positive infinity, return result as bool array.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " The input array.\n", " out : array_like, optional\n", " A location into which the result is stored. If provided, it must have a\n", " shape that the input broadcasts to. If not provided or None, a\n", " freshly-allocated boolean array is returned.\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " A boolean array with the same dimensions as the input.\n", " If second argument is not supplied then a boolean array is returned\n", " with values True where the corresponding element of the input is\n", " positive infinity and values False where the element of the input is\n", " not positive infinity.\n", " \n", " If a second argument is supplied the result is stored there. If the\n", " type of that array is a numeric type the result is represented as zeros\n", " and ones, if the type is boolean then as False and True.\n", " The return value `out` is then a reference to that array.\n", " \n", " See Also\n", " --------\n", " isinf, isneginf, isfinite, isnan\n", " \n", " Notes\n", " -----\n", " NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic\n", " (IEEE 754).\n", " \n", " Errors result if the second argument is also supplied when x is a scalar\n", " input, if first and second arguments have different shapes, or if the\n", " first argument has complex values\n", " \n", " Examples\n", " --------\n", " >>> np.isposinf(np.PINF)\n", " True\n", " >>> np.isposinf(np.inf)\n", " True\n", " >>> np.isposinf(np.NINF)\n", " False\n", " >>> np.isposinf([-np.inf, 0., np.inf])\n", " array([False, False, True])\n", " \n", " >>> x = np.array([-np.inf, 0., np.inf])\n", " >>> y = np.array([2, 2, 2])\n", " >>> np.isposinf(x, y)\n", " array([0, 0, 1])\n", " >>> y\n", " array([0, 0, 1])\n", " \n", " isreal(x)\n", " Returns a bool array, where True if input element is real.\n", " \n", " If element has complex type with zero complex part, the return value\n", " for that element is True.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Input array.\n", " \n", " Returns\n", " -------\n", " out : ndarray, bool\n", " Boolean array of same shape as `x`.\n", " \n", " Notes\n", " -----\n", " `isreal` may behave unexpectedly for string or object arrays (see examples)\n", " \n", " See Also\n", " --------\n", " iscomplex\n", " isrealobj : Return True if x is not a complex type.\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([1+1j, 1+0j, 4.5, 3, 2, 2j], dtype=complex)\n", " >>> np.isreal(a)\n", " array([False, True, True, True, True, False])\n", " \n", " The function does not work on string arrays.\n", " \n", " >>> a = np.array([2j, \"a\"], dtype=\"U\")\n", " >>> np.isreal(a) # Warns about non-elementwise comparison\n", " False\n", " \n", " Returns True for all elements in input array of ``dtype=object`` even if\n", " any of the elements is complex.\n", " \n", " >>> a = np.array([1, \"2\", 3+4j], dtype=object)\n", " >>> np.isreal(a)\n", " array([ True, True, True])\n", " \n", " isreal should not be used with object arrays\n", " \n", " >>> a = np.array([1+2j, 2+1j], dtype=object)\n", " >>> np.isreal(a)\n", " array([ True, True])\n", " \n", " isrealobj(x)\n", " Return True if x is a not complex type or an array of complex numbers.\n", " \n", " The type of the input is checked, not the value. So even if the input\n", " has an imaginary part equal to zero, `isrealobj` evaluates to False\n", " if the data type is complex.\n", " \n", " Parameters\n", " ----------\n", " x : any\n", " The input can be of any type and shape.\n", " \n", " Returns\n", " -------\n", " y : bool\n", " The return value, False if `x` is of a complex type.\n", " \n", " See Also\n", " --------\n", " iscomplexobj, isreal\n", " \n", " Notes\n", " -----\n", " The function is only meant for arrays with numerical values but it\n", " accepts all other objects. Since it assumes array input, the return\n", " value of other objects may be True.\n", " \n", " >>> np.isrealobj('A string')\n", " True\n", " >>> np.isrealobj(False)\n", " True\n", " >>> np.isrealobj(None)\n", " True\n", " \n", " Examples\n", " --------\n", " >>> np.isrealobj(1)\n", " True\n", " >>> np.isrealobj(1+0j)\n", " False\n", " >>> np.isrealobj([3, 1+0j, True])\n", " False\n", " \n", " isscalar(element)\n", " Returns True if the type of `element` is a scalar type.\n", " \n", " Parameters\n", " ----------\n", " element : any\n", " Input argument, can be of any type and shape.\n", " \n", " Returns\n", " -------\n", " val : bool\n", " True if `element` is a scalar type, False if it is not.\n", " \n", " See Also\n", " --------\n", " ndim : Get the number of dimensions of an array\n", " \n", " Notes\n", " -----\n", " If you need a stricter way to identify a *numerical* scalar, use\n", " ``isinstance(x, numbers.Number)``, as that returns ``False`` for most\n", " non-numerical elements such as strings.\n", " \n", " In most cases ``np.ndim(x) == 0`` should be used instead of this function,\n", " as that will also return true for 0d arrays. This is how numpy overloads\n", " functions in the style of the ``dx`` arguments to `gradient` and the ``bins``\n", " argument to `histogram`. Some key differences:\n", " \n", " +--------------------------------------+---------------+-------------------+\n", " | x |``isscalar(x)``|``np.ndim(x) == 0``|\n", " +======================================+===============+===================+\n", " | PEP 3141 numeric objects (including | ``True`` | ``True`` |\n", " | builtins) | | |\n", " +--------------------------------------+---------------+-------------------+\n", " | builtin string and buffer objects | ``True`` | ``True`` |\n", " +--------------------------------------+---------------+-------------------+\n", " | other builtin objects, like | ``False`` | ``True`` |\n", " | `pathlib.Path`, `Exception`, | | |\n", " | the result of `re.compile` | | |\n", " +--------------------------------------+---------------+-------------------+\n", " | third-party objects like | ``False`` | ``True`` |\n", " | `matplotlib.figure.Figure` | | |\n", " +--------------------------------------+---------------+-------------------+\n", " | zero-dimensional numpy arrays | ``False`` | ``True`` |\n", " +--------------------------------------+---------------+-------------------+\n", " | other numpy arrays | ``False`` | ``False`` |\n", " +--------------------------------------+---------------+-------------------+\n", " | `list`, `tuple`, and other sequence | ``False`` | ``False`` |\n", " | objects | | |\n", " +--------------------------------------+---------------+-------------------+\n", " \n", " Examples\n", " --------\n", " >>> np.isscalar(3.1)\n", " True\n", " >>> np.isscalar(np.array(3.1))\n", " False\n", " >>> np.isscalar([3.1])\n", " False\n", " >>> np.isscalar(False)\n", " True\n", " >>> np.isscalar('numpy')\n", " True\n", " \n", " NumPy supports PEP 3141 numbers:\n", " \n", " >>> from fractions import Fraction\n", " >>> np.isscalar(Fraction(5, 17))\n", " True\n", " >>> from numbers import Number\n", " >>> np.isscalar(Number())\n", " True\n", " \n", " issctype(rep)\n", " Determines whether the given object represents a scalar data-type.\n", " \n", " Parameters\n", " ----------\n", " rep : any\n", " If `rep` is an instance of a scalar dtype, True is returned. If not,\n", " False is returned.\n", " \n", " Returns\n", " -------\n", " out : bool\n", " Boolean result of check whether `rep` is a scalar dtype.\n", " \n", " See Also\n", " --------\n", " issubsctype, issubdtype, obj2sctype, sctype2char\n", " \n", " Examples\n", " --------\n", " >>> np.issctype(np.int32)\n", " True\n", " >>> np.issctype(list)\n", " False\n", " >>> np.issctype(1.1)\n", " False\n", " \n", " Strings are also a scalar type:\n", " \n", " >>> np.issctype(np.dtype('str'))\n", " True\n", " \n", " issubclass_(arg1, arg2)\n", " Determine if a class is a subclass of a second class.\n", " \n", " `issubclass_` is equivalent to the Python built-in ``issubclass``,\n", " except that it returns False instead of raising a TypeError if one\n", " of the arguments is not a class.\n", " \n", " Parameters\n", " ----------\n", " arg1 : class\n", " Input class. True is returned if `arg1` is a subclass of `arg2`.\n", " arg2 : class or tuple of classes.\n", " Input class. If a tuple of classes, True is returned if `arg1` is a\n", " subclass of any of the tuple elements.\n", " \n", " Returns\n", " -------\n", " out : bool\n", " Whether `arg1` is a subclass of `arg2` or not.\n", " \n", " See Also\n", " --------\n", " issubsctype, issubdtype, issctype\n", " \n", " Examples\n", " --------\n", " >>> np.issubclass_(np.int32, int)\n", " False\n", " >>> np.issubclass_(np.int32, float)\n", " False\n", " >>> np.issubclass_(np.float64, float)\n", " True\n", " \n", " issubdtype(arg1, arg2)\n", " Returns True if first argument is a typecode lower/equal in type hierarchy.\n", " \n", " This is like the builtin :func:`issubclass`, but for `dtype`\\ s.\n", " \n", " Parameters\n", " ----------\n", " arg1, arg2 : dtype_like\n", " `dtype` or object coercible to one\n", " \n", " Returns\n", " -------\n", " out : bool\n", " \n", " See Also\n", " --------\n", " :ref:`arrays.scalars` : Overview of the numpy type hierarchy.\n", " issubsctype, issubclass_\n", " \n", " Examples\n", " --------\n", " `issubdtype` can be used to check the type of arrays:\n", " \n", " >>> ints = np.array([1, 2, 3], dtype=np.int32)\n", " >>> np.issubdtype(ints.dtype, np.integer)\n", " True\n", " >>> np.issubdtype(ints.dtype, np.floating)\n", " False\n", " \n", " >>> floats = np.array([1, 2, 3], dtype=np.float32)\n", " >>> np.issubdtype(floats.dtype, np.integer)\n", " False\n", " >>> np.issubdtype(floats.dtype, np.floating)\n", " True\n", " \n", " Similar types of different sizes are not subdtypes of each other:\n", " \n", " >>> np.issubdtype(np.float64, np.float32)\n", " False\n", " >>> np.issubdtype(np.float32, np.float64)\n", " False\n", " \n", " but both are subtypes of `floating`:\n", " \n", " >>> np.issubdtype(np.float64, np.floating)\n", " True\n", " >>> np.issubdtype(np.float32, np.floating)\n", " True\n", " \n", " For convenience, dtype-like objects are allowed too:\n", " \n", " >>> np.issubdtype('S1', np.string_)\n", " True\n", " >>> np.issubdtype('i4', np.signedinteger)\n", " True\n", " \n", " issubsctype(arg1, arg2)\n", " Determine if the first argument is a subclass of the second argument.\n", " \n", " Parameters\n", " ----------\n", " arg1, arg2 : dtype or dtype specifier\n", " Data-types.\n", " \n", " Returns\n", " -------\n", " out : bool\n", " The result.\n", " \n", " See Also\n", " --------\n", " issctype, issubdtype, obj2sctype\n", " \n", " Examples\n", " --------\n", " >>> np.issubsctype('S8', str)\n", " False\n", " >>> np.issubsctype(np.array([1]), int)\n", " True\n", " >>> np.issubsctype(np.array([1]), float)\n", " False\n", " \n", " iterable(y)\n", " Check whether or not an object can be iterated over.\n", " \n", " Parameters\n", " ----------\n", " y : object\n", " Input object.\n", " \n", " Returns\n", " -------\n", " b : bool\n", " Return ``True`` if the object has an iterator method or is a\n", " sequence and ``False`` otherwise.\n", " \n", " \n", " Examples\n", " --------\n", " >>> np.iterable([1, 2, 3])\n", " True\n", " >>> np.iterable(2)\n", " False\n", " \n", " Notes\n", " -----\n", " In most cases, the results of ``np.iterable(obj)`` are consistent with\n", " ``isinstance(obj, collections.abc.Iterable)``. One notable exception is\n", " the treatment of 0-dimensional arrays::\n", " \n", " >>> from collections.abc import Iterable\n", " >>> a = np.array(1.0) # 0-dimensional numpy array\n", " >>> isinstance(a, Iterable)\n", " True\n", " >>> np.iterable(a)\n", " False\n", " \n", " ix_(*args)\n", " Construct an open mesh from multiple sequences.\n", " \n", " This function takes N 1-D sequences and returns N outputs with N\n", " dimensions each, such that the shape is 1 in all but one dimension\n", " and the dimension with the non-unit shape value cycles through all\n", " N dimensions.\n", " \n", " Using `ix_` one can quickly construct index arrays that will index\n", " the cross product. ``a[np.ix_([1,3],[2,5])]`` returns the array\n", " ``[[a[1,2] a[1,5]], [a[3,2] a[3,5]]]``.\n", " \n", " Parameters\n", " ----------\n", " args : 1-D sequences\n", " Each sequence should be of integer or boolean type.\n", " Boolean sequences will be interpreted as boolean masks for the\n", " corresponding dimension (equivalent to passing in\n", " ``np.nonzero(boolean_sequence)``).\n", " \n", " Returns\n", " -------\n", " out : tuple of ndarrays\n", " N arrays with N dimensions each, with N the number of input\n", " sequences. Together these arrays form an open mesh.\n", " \n", " See Also\n", " --------\n", " ogrid, mgrid, meshgrid\n", " \n", " Examples\n", " --------\n", " >>> a = np.arange(10).reshape(2, 5)\n", " >>> a\n", " array([[0, 1, 2, 3, 4],\n", " [5, 6, 7, 8, 9]])\n", " >>> ixgrid = np.ix_([0, 1], [2, 4])\n", " >>> ixgrid\n", " (array([[0],\n", " [1]]), array([[2, 4]]))\n", " >>> ixgrid[0].shape, ixgrid[1].shape\n", " ((2, 1), (1, 2))\n", " >>> a[ixgrid]\n", " array([[2, 4],\n", " [7, 9]])\n", " \n", " >>> ixgrid = np.ix_([True, True], [2, 4])\n", " >>> a[ixgrid]\n", " array([[2, 4],\n", " [7, 9]])\n", " >>> ixgrid = np.ix_([True, True], [False, False, True, False, True])\n", " >>> a[ixgrid]\n", " array([[2, 4],\n", " [7, 9]])\n", " \n", " kaiser(M, beta)\n", " Return the Kaiser window.\n", " \n", " The Kaiser window is a taper formed by using a Bessel function.\n", " \n", " Parameters\n", " ----------\n", " M : int\n", " Number of points in the output window. If zero or less, an\n", " empty array is returned.\n", " beta : float\n", " Shape parameter for window.\n", " \n", " Returns\n", " -------\n", " out : array\n", " The window, with the maximum value normalized to one (the value\n", " one appears only if the number of samples is odd).\n", " \n", " See Also\n", " --------\n", " bartlett, blackman, hamming, hanning\n", " \n", " Notes\n", " -----\n", " The Kaiser window is defined as\n", " \n", " .. math:: w(n) = I_0\\left( \\beta \\sqrt{1-\\frac{4n^2}{(M-1)^2}}\n", " \\right)/I_0(\\beta)\n", " \n", " with\n", " \n", " .. math:: \\quad -\\frac{M-1}{2} \\leq n \\leq \\frac{M-1}{2},\n", " \n", " where :math:`I_0` is the modified zeroth-order Bessel function.\n", " \n", " The Kaiser was named for Jim Kaiser, who discovered a simple\n", " approximation to the DPSS window based on Bessel functions. The Kaiser\n", " window is a very good approximation to the Digital Prolate Spheroidal\n", " Sequence, or Slepian window, which is the transform which maximizes the\n", " energy in the main lobe of the window relative to total energy.\n", " \n", " The Kaiser can approximate many other windows by varying the beta\n", " parameter.\n", " \n", " ==== =======================\n", " beta Window shape\n", " ==== =======================\n", " 0 Rectangular\n", " 5 Similar to a Hamming\n", " 6 Similar to a Hanning\n", " 8.6 Similar to a Blackman\n", " ==== =======================\n", " \n", " A beta value of 14 is probably a good starting point. Note that as beta\n", " gets large, the window narrows, and so the number of samples needs to be\n", " large enough to sample the increasingly narrow spike, otherwise NaNs will\n", " get returned.\n", " \n", " Most references to the Kaiser window come from the signal processing\n", " literature, where it is used as one of many windowing functions for\n", " smoothing values. It is also known as an apodization (which means\n", " \"removing the foot\", i.e. smoothing discontinuities at the beginning\n", " and end of the sampled signal) or tapering function.\n", " \n", " References\n", " ----------\n", " .. [1] J. F. Kaiser, \"Digital Filters\" - Ch 7 in \"Systems analysis by\n", " digital computer\", Editors: F.F. Kuo and J.F. Kaiser, p 218-285.\n", " John Wiley and Sons, New York, (1966).\n", " .. [2] E.R. Kanasewich, \"Time Sequence Analysis in Geophysics\", The\n", " University of Alberta Press, 1975, pp. 177-178.\n", " .. [3] Wikipedia, \"Window function\",\n", " https://en.wikipedia.org/wiki/Window_function\n", " \n", " Examples\n", " --------\n", " >>> import matplotlib.pyplot as plt\n", " >>> np.kaiser(12, 14)\n", " array([7.72686684e-06, 3.46009194e-03, 4.65200189e-02, # may vary\n", " 2.29737120e-01, 5.99885316e-01, 9.45674898e-01,\n", " 9.45674898e-01, 5.99885316e-01, 2.29737120e-01,\n", " 4.65200189e-02, 3.46009194e-03, 7.72686684e-06])\n", " \n", " \n", " Plot the window and the frequency response:\n", " \n", " >>> from numpy.fft import fft, fftshift\n", " >>> window = np.kaiser(51, 14)\n", " >>> plt.plot(window)\n", " [<matplotlib.lines.Line2D object at 0x...>]\n", " >>> plt.title(\"Kaiser window\")\n", " Text(0.5, 1.0, 'Kaiser window')\n", " >>> plt.ylabel(\"Amplitude\")\n", " Text(0, 0.5, 'Amplitude')\n", " >>> plt.xlabel(\"Sample\")\n", " Text(0.5, 0, 'Sample')\n", " >>> plt.show()\n", " \n", " >>> plt.figure()\n", " <Figure size 640x480 with 0 Axes>\n", " >>> A = fft(window, 2048) / 25.5\n", " >>> mag = np.abs(fftshift(A))\n", " >>> freq = np.linspace(-0.5, 0.5, len(A))\n", " >>> response = 20 * np.log10(mag)\n", " >>> response = np.clip(response, -100, 100)\n", " >>> plt.plot(freq, response)\n", " [<matplotlib.lines.Line2D object at 0x...>]\n", " >>> plt.title(\"Frequency response of Kaiser window\")\n", " Text(0.5, 1.0, 'Frequency response of Kaiser window')\n", " >>> plt.ylabel(\"Magnitude [dB]\")\n", " Text(0, 0.5, 'Magnitude [dB]')\n", " >>> plt.xlabel(\"Normalized frequency [cycles per sample]\")\n", " Text(0.5, 0, 'Normalized frequency [cycles per sample]')\n", " >>> plt.axis('tight')\n", " (-0.5, 0.5, -100.0, ...) # may vary\n", " >>> plt.show()\n", " \n", " kron(a, b)\n", " Kronecker product of two arrays.\n", " \n", " Computes the Kronecker product, a composite array made of blocks of the\n", " second array scaled by the first.\n", " \n", " Parameters\n", " ----------\n", " a, b : array_like\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " \n", " See Also\n", " --------\n", " outer : The outer product\n", " \n", " Notes\n", " -----\n", " The function assumes that the number of dimensions of `a` and `b`\n", " are the same, if necessary prepending the smallest with ones.\n", " If ``a.shape = (r0,r1,..,rN)`` and ``b.shape = (s0,s1,...,sN)``,\n", " the Kronecker product has shape ``(r0*s0, r1*s1, ..., rN*SN)``.\n", " The elements are products of elements from `a` and `b`, organized\n", " explicitly by::\n", " \n", " kron(a,b)[k0,k1,...,kN] = a[i0,i1,...,iN] * b[j0,j1,...,jN]\n", " \n", " where::\n", " \n", " kt = it * st + jt, t = 0,...,N\n", " \n", " In the common 2-D case (N=1), the block structure can be visualized::\n", " \n", " [[ a[0,0]*b, a[0,1]*b, ... , a[0,-1]*b ],\n", " [ ... ... ],\n", " [ a[-1,0]*b, a[-1,1]*b, ... , a[-1,-1]*b ]]\n", " \n", " \n", " Examples\n", " --------\n", " >>> np.kron([1,10,100], [5,6,7])\n", " array([ 5, 6, 7, ..., 500, 600, 700])\n", " >>> np.kron([5,6,7], [1,10,100])\n", " array([ 5, 50, 500, ..., 7, 70, 700])\n", " \n", " >>> np.kron(np.eye(2), np.ones((2,2)))\n", " array([[1., 1., 0., 0.],\n", " [1., 1., 0., 0.],\n", " [0., 0., 1., 1.],\n", " [0., 0., 1., 1.]])\n", " \n", " >>> a = np.arange(100).reshape((2,5,2,5))\n", " >>> b = np.arange(24).reshape((2,3,4))\n", " >>> c = np.kron(a,b)\n", " >>> c.shape\n", " (2, 10, 6, 20)\n", " >>> I = (1,3,0,2)\n", " >>> J = (0,2,1)\n", " >>> J1 = (0,) + J # extend to ndim=4\n", " >>> S1 = (1,) + b.shape\n", " >>> K = tuple(np.array(I) * np.array(S1) + np.array(J1))\n", " >>> c[K] == a[I]*b[J]\n", " True\n", " \n", " lexsort(...)\n", " lexsort(keys, axis=-1)\n", " \n", " Perform an indirect stable sort using a sequence of keys.\n", " \n", " Given multiple sorting keys, which can be interpreted as columns in a\n", " spreadsheet, lexsort returns an array of integer indices that describes\n", " the sort order by multiple columns. The last key in the sequence is used\n", " for the primary sort order, the second-to-last key for the secondary sort\n", " order, and so on. The keys argument must be a sequence of objects that\n", " can be converted to arrays of the same shape. If a 2D array is provided\n", " for the keys argument, its rows are interpreted as the sorting keys and\n", " sorting is according to the last row, second last row etc.\n", " \n", " Parameters\n", " ----------\n", " keys : (k, N) array or tuple containing k (N,)-shaped sequences\n", " The `k` different \"columns\" to be sorted. The last column (or row if\n", " `keys` is a 2D array) is the primary sort key.\n", " axis : int, optional\n", " Axis to be indirectly sorted. By default, sort over the last axis.\n", " \n", " Returns\n", " -------\n", " indices : (N,) ndarray of ints\n", " Array of indices that sort the keys along the specified axis.\n", " \n", " See Also\n", " --------\n", " argsort : Indirect sort.\n", " ndarray.sort : In-place sort.\n", " sort : Return a sorted copy of an array.\n", " \n", " Examples\n", " --------\n", " Sort names: first by surname, then by name.\n", " \n", " >>> surnames = ('Hertz', 'Galilei', 'Hertz')\n", " >>> first_names = ('Heinrich', 'Galileo', 'Gustav')\n", " >>> ind = np.lexsort((first_names, surnames))\n", " >>> ind\n", " array([1, 2, 0])\n", " \n", " >>> [surnames[i] + \", \" + first_names[i] for i in ind]\n", " ['Galilei, Galileo', 'Hertz, Gustav', 'Hertz, Heinrich']\n", " \n", " Sort two columns of numbers:\n", " \n", " >>> a = [1,5,1,4,3,4,4] # First column\n", " >>> b = [9,4,0,4,0,2,1] # Second column\n", " >>> ind = np.lexsort((b,a)) # Sort by a, then by b\n", " >>> ind\n", " array([2, 0, 4, 6, 5, 3, 1])\n", " \n", " >>> [(a[i],b[i]) for i in ind]\n", " [(1, 0), (1, 9), (3, 0), (4, 1), (4, 2), (4, 4), (5, 4)]\n", " \n", " Note that sorting is first according to the elements of ``a``.\n", " Secondary sorting is according to the elements of ``b``.\n", " \n", " A normal ``argsort`` would have yielded:\n", " \n", " >>> [(a[i],b[i]) for i in np.argsort(a)]\n", " [(1, 9), (1, 0), (3, 0), (4, 4), (4, 2), (4, 1), (5, 4)]\n", " \n", " Structured arrays are sorted lexically by ``argsort``:\n", " \n", " >>> x = np.array([(1,9), (5,4), (1,0), (4,4), (3,0), (4,2), (4,1)],\n", " ... dtype=np.dtype([('x', int), ('y', int)]))\n", " \n", " >>> np.argsort(x) # or np.argsort(x, order=('x', 'y'))\n", " array([2, 0, 4, 6, 5, 3, 1])\n", " \n", " linspace(start, stop, num=50, endpoint=True, retstep=False, dtype=None, axis=0)\n", " Return evenly spaced numbers over a specified interval.\n", " \n", " Returns `num` evenly spaced samples, calculated over the\n", " interval [`start`, `stop`].\n", " \n", " The endpoint of the interval can optionally be excluded.\n", " \n", " .. versionchanged:: 1.16.0\n", " Non-scalar `start` and `stop` are now supported.\n", " \n", " .. versionchanged:: 1.20.0\n", " Values are rounded towards ``-inf`` instead of ``0`` when an\n", " integer ``dtype`` is specified. The old behavior can\n", " still be obtained with ``np.linspace(start, stop, num).astype(int)``\n", " \n", " Parameters\n", " ----------\n", " start : array_like\n", " The starting value of the sequence.\n", " stop : array_like\n", " The end value of the sequence, unless `endpoint` is set to False.\n", " In that case, the sequence consists of all but the last of ``num + 1``\n", " evenly spaced samples, so that `stop` is excluded. Note that the step\n", " size changes when `endpoint` is False.\n", " num : int, optional\n", " Number of samples to generate. Default is 50. Must be non-negative.\n", " endpoint : bool, optional\n", " If True, `stop` is the last sample. Otherwise, it is not included.\n", " Default is True.\n", " retstep : bool, optional\n", " If True, return (`samples`, `step`), where `step` is the spacing\n", " between samples.\n", " dtype : dtype, optional\n", " The type of the output array. If `dtype` is not given, the data type\n", " is inferred from `start` and `stop`. The inferred dtype will never be\n", " an integer; `float` is chosen even if the arguments would produce an\n", " array of integers.\n", " \n", " .. versionadded:: 1.9.0\n", " \n", " axis : int, optional\n", " The axis in the result to store the samples. Relevant only if start\n", " or stop are array-like. By default (0), the samples will be along a\n", " new axis inserted at the beginning. Use -1 to get an axis at the end.\n", " \n", " .. versionadded:: 1.16.0\n", " \n", " Returns\n", " -------\n", " samples : ndarray\n", " There are `num` equally spaced samples in the closed interval\n", " ``[start, stop]`` or the half-open interval ``[start, stop)``\n", " (depending on whether `endpoint` is True or False).\n", " step : float, optional\n", " Only returned if `retstep` is True\n", " \n", " Size of spacing between samples.\n", " \n", " \n", " See Also\n", " --------\n", " arange : Similar to `linspace`, but uses a step size (instead of the\n", " number of samples).\n", " geomspace : Similar to `linspace`, but with numbers spaced evenly on a log\n", " scale (a geometric progression).\n", " logspace : Similar to `geomspace`, but with the end points specified as\n", " logarithms.\n", " :ref:`how-to-partition`\n", " \n", " Examples\n", " --------\n", " >>> np.linspace(2.0, 3.0, num=5)\n", " array([2. , 2.25, 2.5 , 2.75, 3. ])\n", " >>> np.linspace(2.0, 3.0, num=5, endpoint=False)\n", " array([2. , 2.2, 2.4, 2.6, 2.8])\n", " >>> np.linspace(2.0, 3.0, num=5, retstep=True)\n", " (array([2. , 2.25, 2.5 , 2.75, 3. ]), 0.25)\n", " \n", " Graphical illustration:\n", " \n", " >>> import matplotlib.pyplot as plt\n", " >>> N = 8\n", " >>> y = np.zeros(N)\n", " >>> x1 = np.linspace(0, 10, N, endpoint=True)\n", " >>> x2 = np.linspace(0, 10, N, endpoint=False)\n", " >>> plt.plot(x1, y, 'o')\n", " [<matplotlib.lines.Line2D object at 0x...>]\n", " >>> plt.plot(x2, y + 0.5, 'o')\n", " [<matplotlib.lines.Line2D object at 0x...>]\n", " >>> plt.ylim([-0.5, 1])\n", " (-0.5, 1)\n", " >>> plt.show()\n", " \n", " load(file, mmap_mode=None, allow_pickle=False, fix_imports=True, encoding='ASCII', *, max_header_size=10000)\n", " Load arrays or pickled objects from ``.npy``, ``.npz`` or pickled files.\n", " \n", " .. warning:: Loading files that contain object arrays uses the ``pickle``\n", " module, which is not secure against erroneous or maliciously\n", " constructed data. Consider passing ``allow_pickle=False`` to\n", " load data that is known not to contain object arrays for the\n", " safer handling of untrusted sources.\n", " \n", " Parameters\n", " ----------\n", " file : file-like object, string, or pathlib.Path\n", " The file to read. File-like objects must support the\n", " ``seek()`` and ``read()`` methods and must always\n", " be opened in binary mode. Pickled files require that the\n", " file-like object support the ``readline()`` method as well.\n", " mmap_mode : {None, 'r+', 'r', 'w+', 'c'}, optional\n", " If not None, then memory-map the file, using the given mode (see\n", " `numpy.memmap` for a detailed description of the modes). A\n", " memory-mapped array is kept on disk. However, it can be accessed\n", " and sliced like any ndarray. Memory mapping is especially useful\n", " for accessing small fragments of large files without reading the\n", " entire file into memory.\n", " allow_pickle : bool, optional\n", " Allow loading pickled object arrays stored in npy files. Reasons for\n", " disallowing pickles include security, as loading pickled data can\n", " execute arbitrary code. If pickles are disallowed, loading object\n", " arrays will fail. Default: False\n", " \n", " .. versionchanged:: 1.16.3\n", " Made default False in response to CVE-2019-6446.\n", " \n", " fix_imports : bool, optional\n", " Only useful when loading Python 2 generated pickled files on Python 3,\n", " which includes npy/npz files containing object arrays. If `fix_imports`\n", " is True, pickle will try to map the old Python 2 names to the new names\n", " used in Python 3.\n", " encoding : str, optional\n", " What encoding to use when reading Python 2 strings. Only useful when\n", " loading Python 2 generated pickled files in Python 3, which includes\n", " npy/npz files containing object arrays. Values other than 'latin1',\n", " 'ASCII', and 'bytes' are not allowed, as they can corrupt numerical\n", " data. Default: 'ASCII'\n", " max_header_size : int, optional\n", " Maximum allowed size of the header. Large headers may not be safe\n", " to load securely and thus require explicitly passing a larger value.\n", " See :py:meth:`ast.literal_eval()` for details.\n", " This option is ignored when `allow_pickle` is passed. In that case\n", " the file is by definition trusted and the limit is unnecessary.\n", " \n", " Returns\n", " -------\n", " result : array, tuple, dict, etc.\n", " Data stored in the file. For ``.npz`` files, the returned instance\n", " of NpzFile class must be closed to avoid leaking file descriptors.\n", " \n", " Raises\n", " ------\n", " OSError\n", " If the input file does not exist or cannot be read.\n", " UnpicklingError\n", " If ``allow_pickle=True``, but the file cannot be loaded as a pickle.\n", " ValueError\n", " The file contains an object array, but ``allow_pickle=False`` given.\n", " \n", " See Also\n", " --------\n", " save, savez, savez_compressed, loadtxt\n", " memmap : Create a memory-map to an array stored in a file on disk.\n", " lib.format.open_memmap : Create or load a memory-mapped ``.npy`` file.\n", " \n", " Notes\n", " -----\n", " - If the file contains pickle data, then whatever object is stored\n", " in the pickle is returned.\n", " - If the file is a ``.npy`` file, then a single array is returned.\n", " - If the file is a ``.npz`` file, then a dictionary-like object is\n", " returned, containing ``{filename: array}`` key-value pairs, one for\n", " each file in the archive.\n", " - If the file is a ``.npz`` file, the returned value supports the\n", " context manager protocol in a similar fashion to the open function::\n", " \n", " with load('foo.npz') as data:\n", " a = data['a']\n", " \n", " The underlying file descriptor is closed when exiting the 'with'\n", " block.\n", " \n", " Examples\n", " --------\n", " Store data to disk, and load it again:\n", " \n", " >>> np.save('/tmp/123', np.array([[1, 2, 3], [4, 5, 6]]))\n", " >>> np.load('/tmp/123.npy')\n", " array([[1, 2, 3],\n", " [4, 5, 6]])\n", " \n", " Store compressed data to disk, and load it again:\n", " \n", " >>> a=np.array([[1, 2, 3], [4, 5, 6]])\n", " >>> b=np.array([1, 2])\n", " >>> np.savez('/tmp/123.npz', a=a, b=b)\n", " >>> data = np.load('/tmp/123.npz')\n", " >>> data['a']\n", " array([[1, 2, 3],\n", " [4, 5, 6]])\n", " >>> data['b']\n", " array([1, 2])\n", " >>> data.close()\n", " \n", " Mem-map the stored array, and then access the second row\n", " directly from disk:\n", " \n", " >>> X = np.load('/tmp/123.npy', mmap_mode='r')\n", " >>> X[1, :]\n", " memmap([4, 5, 6])\n", " \n", " loadtxt(fname, dtype=<class 'float'>, comments='#', delimiter=None, converters=None, skiprows=0, usecols=None, unpack=False, ndmin=0, encoding='bytes', max_rows=None, *, quotechar=None, like=None)\n", " Load data from a text file.\n", " \n", " Parameters\n", " ----------\n", " fname : file, str, pathlib.Path, list of str, generator\n", " File, filename, list, or generator to read. If the filename\n", " extension is ``.gz`` or ``.bz2``, the file is first decompressed. Note\n", " that generators must return bytes or strings. The strings\n", " in a list or produced by a generator are treated as lines.\n", " dtype : data-type, optional\n", " Data-type of the resulting array; default: float. If this is a\n", " structured data-type, the resulting array will be 1-dimensional, and\n", " each row will be interpreted as an element of the array. In this\n", " case, the number of columns used must match the number of fields in\n", " the data-type.\n", " comments : str or sequence of str or None, optional\n", " The characters or list of characters used to indicate the start of a\n", " comment. None implies no comments. For backwards compatibility, byte\n", " strings will be decoded as 'latin1'. The default is '#'.\n", " delimiter : str, optional\n", " The character used to separate the values. For backwards compatibility,\n", " byte strings will be decoded as 'latin1'. The default is whitespace.\n", " \n", " .. versionchanged:: 1.23.0\n", " Only single character delimiters are supported. Newline characters\n", " cannot be used as the delimiter.\n", " \n", " converters : dict or callable, optional\n", " Converter functions to customize value parsing. If `converters` is\n", " callable, the function is applied to all columns, else it must be a\n", " dict that maps column number to a parser function.\n", " See examples for further details.\n", " Default: None.\n", " \n", " .. versionchanged:: 1.23.0\n", " The ability to pass a single callable to be applied to all columns\n", " was added.\n", " \n", " skiprows : int, optional\n", " Skip the first `skiprows` lines, including comments; default: 0.\n", " usecols : int or sequence, optional\n", " Which columns to read, with 0 being the first. For example,\n", " ``usecols = (1,4,5)`` will extract the 2nd, 5th and 6th columns.\n", " The default, None, results in all columns being read.\n", " \n", " .. versionchanged:: 1.11.0\n", " When a single column has to be read it is possible to use\n", " an integer instead of a tuple. E.g ``usecols = 3`` reads the\n", " fourth column the same way as ``usecols = (3,)`` would.\n", " unpack : bool, optional\n", " If True, the returned array is transposed, so that arguments may be\n", " unpacked using ``x, y, z = loadtxt(...)``. When used with a\n", " structured data-type, arrays are returned for each field.\n", " Default is False.\n", " ndmin : int, optional\n", " The returned array will have at least `ndmin` dimensions.\n", " Otherwise mono-dimensional axes will be squeezed.\n", " Legal values: 0 (default), 1 or 2.\n", " \n", " .. versionadded:: 1.6.0\n", " encoding : str, optional\n", " Encoding used to decode the inputfile. Does not apply to input streams.\n", " The special value 'bytes' enables backward compatibility workarounds\n", " that ensures you receive byte arrays as results if possible and passes\n", " 'latin1' encoded strings to converters. Override this value to receive\n", " unicode arrays and pass strings as input to converters. If set to None\n", " the system default is used. The default value is 'bytes'.\n", " \n", " .. versionadded:: 1.14.0\n", " max_rows : int, optional\n", " Read `max_rows` rows of content after `skiprows` lines. The default is\n", " to read all the rows. Note that empty rows containing no data such as\n", " empty lines and comment lines are not counted towards `max_rows`,\n", " while such lines are counted in `skiprows`.\n", " \n", " .. versionadded:: 1.16.0\n", " \n", " .. versionchanged:: 1.23.0\n", " Lines containing no data, including comment lines (e.g., lines \n", " starting with '#' or as specified via `comments`) are not counted \n", " towards `max_rows`.\n", " quotechar : unicode character or None, optional\n", " The character used to denote the start and end of a quoted item.\n", " Occurrences of the delimiter or comment characters are ignored within\n", " a quoted item. The default value is ``quotechar=None``, which means\n", " quoting support is disabled.\n", " \n", " If two consecutive instances of `quotechar` are found within a quoted\n", " field, the first is treated as an escape character. See examples.\n", " \n", " .. versionadded:: 1.23.0\n", " like : array_like, optional\n", " Reference object to allow the creation of arrays which are not\n", " NumPy arrays. If an array-like passed in as ``like`` supports\n", " the ``__array_function__`` protocol, the result will be defined\n", " by it. In this case, it ensures the creation of an array object\n", " compatible with that passed in via this argument.\n", " \n", " .. versionadded:: 1.20.0\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " Data read from the text file.\n", " \n", " See Also\n", " --------\n", " load, fromstring, fromregex\n", " genfromtxt : Load data with missing values handled as specified.\n", " scipy.io.loadmat : reads MATLAB data files\n", " \n", " Notes\n", " -----\n", " This function aims to be a fast reader for simply formatted files. The\n", " `genfromtxt` function provides more sophisticated handling of, e.g.,\n", " lines with missing values.\n", " \n", " Each row in the input text file must have the same number of values to be\n", " able to read all values. If all rows do not have same number of values, a\n", " subset of up to n columns (where n is the least number of values present\n", " in all rows) can be read by specifying the columns via `usecols`.\n", " \n", " .. versionadded:: 1.10.0\n", " \n", " The strings produced by the Python float.hex method can be used as\n", " input for floats.\n", " \n", " Examples\n", " --------\n", " >>> from io import StringIO # StringIO behaves like a file object\n", " >>> c = StringIO(\"0 1\\n2 3\")\n", " >>> np.loadtxt(c)\n", " array([[0., 1.],\n", " [2., 3.]])\n", " \n", " >>> d = StringIO(\"M 21 72\\nF 35 58\")\n", " >>> np.loadtxt(d, dtype={'names': ('gender', 'age', 'weight'),\n", " ... 'formats': ('S1', 'i4', 'f4')})\n", " array([(b'M', 21, 72.), (b'F', 35, 58.)],\n", " dtype=[('gender', 'S1'), ('age', '<i4'), ('weight', '<f4')])\n", " \n", " >>> c = StringIO(\"1,0,2\\n3,0,4\")\n", " >>> x, y = np.loadtxt(c, delimiter=',', usecols=(0, 2), unpack=True)\n", " >>> x\n", " array([1., 3.])\n", " >>> y\n", " array([2., 4.])\n", " \n", " The `converters` argument is used to specify functions to preprocess the\n", " text prior to parsing. `converters` can be a dictionary that maps\n", " preprocessing functions to each column:\n", " \n", " >>> s = StringIO(\"1.618, 2.296\\n3.141, 4.669\\n\")\n", " >>> conv = {\n", " ... 0: lambda x: np.floor(float(x)), # conversion fn for column 0\n", " ... 1: lambda x: np.ceil(float(x)), # conversion fn for column 1\n", " ... }\n", " >>> np.loadtxt(s, delimiter=\",\", converters=conv)\n", " array([[1., 3.],\n", " [3., 5.]])\n", " \n", " `converters` can be a callable instead of a dictionary, in which case it\n", " is applied to all columns:\n", " \n", " >>> s = StringIO(\"0xDE 0xAD\\n0xC0 0xDE\")\n", " >>> import functools\n", " >>> conv = functools.partial(int, base=16)\n", " >>> np.loadtxt(s, converters=conv)\n", " array([[222., 173.],\n", " [192., 222.]])\n", " \n", " This example shows how `converters` can be used to convert a field\n", " with a trailing minus sign into a negative number.\n", " \n", " >>> s = StringIO('10.01 31.25-\\n19.22 64.31\\n17.57- 63.94')\n", " >>> def conv(fld):\n", " ... return -float(fld[:-1]) if fld.endswith(b'-') else float(fld)\n", " ...\n", " >>> np.loadtxt(s, converters=conv)\n", " array([[ 10.01, -31.25],\n", " [ 19.22, 64.31],\n", " [-17.57, 63.94]])\n", " \n", " Using a callable as the converter can be particularly useful for handling\n", " values with different formatting, e.g. floats with underscores:\n", " \n", " >>> s = StringIO(\"1 2.7 100_000\")\n", " >>> np.loadtxt(s, converters=float)\n", " array([1.e+00, 2.7e+00, 1.e+05])\n", " \n", " This idea can be extended to automatically handle values specified in\n", " many different formats:\n", " \n", " >>> def conv(val):\n", " ... try:\n", " ... return float(val)\n", " ... except ValueError:\n", " ... return float.fromhex(val)\n", " >>> s = StringIO(\"1, 2.5, 3_000, 0b4, 0x1.4000000000000p+2\")\n", " >>> np.loadtxt(s, delimiter=\",\", converters=conv, encoding=None)\n", " array([1.0e+00, 2.5e+00, 3.0e+03, 1.8e+02, 5.0e+00])\n", " \n", " Note that with the default ``encoding=\"bytes\"``, the inputs to the\n", " converter function are latin-1 encoded byte strings. To deactivate the\n", " implicit encoding prior to conversion, use ``encoding=None``\n", " \n", " >>> s = StringIO('10.01 31.25-\\n19.22 64.31\\n17.57- 63.94')\n", " >>> conv = lambda x: -float(x[:-1]) if x.endswith('-') else float(x)\n", " >>> np.loadtxt(s, converters=conv, encoding=None)\n", " array([[ 10.01, -31.25],\n", " [ 19.22, 64.31],\n", " [-17.57, 63.94]])\n", " \n", " Support for quoted fields is enabled with the `quotechar` parameter.\n", " Comment and delimiter characters are ignored when they appear within a\n", " quoted item delineated by `quotechar`:\n", " \n", " >>> s = StringIO('\"alpha, #42\", 10.0\\n\"beta, #64\", 2.0\\n')\n", " >>> dtype = np.dtype([(\"label\", \"U12\"), (\"value\", float)])\n", " >>> np.loadtxt(s, dtype=dtype, delimiter=\",\", quotechar='\"')\n", " array([('alpha, #42', 10.), ('beta, #64', 2.)],\n", " dtype=[('label', '<U12'), ('value', '<f8')])\n", " \n", " Quoted fields can be separated by multiple whitespace characters:\n", " \n", " >>> s = StringIO('\"alpha, #42\" 10.0\\n\"beta, #64\" 2.0\\n')\n", " >>> dtype = np.dtype([(\"label\", \"U12\"), (\"value\", float)])\n", " >>> np.loadtxt(s, dtype=dtype, delimiter=None, quotechar='\"')\n", " array([('alpha, #42', 10.), ('beta, #64', 2.)],\n", " dtype=[('label', '<U12'), ('value', '<f8')])\n", " \n", " Two consecutive quote characters within a quoted field are treated as a\n", " single escaped character:\n", " \n", " >>> s = StringIO('\"Hello, my name is \"\"Monty\"\"!\"')\n", " >>> np.loadtxt(s, dtype=\"U\", delimiter=\",\", quotechar='\"')\n", " array('Hello, my name is \"Monty\"!', dtype='<U26')\n", " \n", " Read subset of columns when all rows do not contain equal number of values:\n", " \n", " >>> d = StringIO(\"1 2\\n2 4\\n3 9 12\\n4 16 20\")\n", " >>> np.loadtxt(d, usecols=(0, 1))\n", " array([[ 1., 2.],\n", " [ 2., 4.],\n", " [ 3., 9.],\n", " [ 4., 16.]])\n", " \n", " logspace(start, stop, num=50, endpoint=True, base=10.0, dtype=None, axis=0)\n", " Return numbers spaced evenly on a log scale.\n", " \n", " In linear space, the sequence starts at ``base ** start``\n", " (`base` to the power of `start`) and ends with ``base ** stop``\n", " (see `endpoint` below).\n", " \n", " .. versionchanged:: 1.16.0\n", " Non-scalar `start` and `stop` are now supported.\n", " \n", " Parameters\n", " ----------\n", " start : array_like\n", " ``base ** start`` is the starting value of the sequence.\n", " stop : array_like\n", " ``base ** stop`` is the final value of the sequence, unless `endpoint`\n", " is False. In that case, ``num + 1`` values are spaced over the\n", " interval in log-space, of which all but the last (a sequence of\n", " length `num`) are returned.\n", " num : integer, optional\n", " Number of samples to generate. Default is 50.\n", " endpoint : boolean, optional\n", " If true, `stop` is the last sample. Otherwise, it is not included.\n", " Default is True.\n", " base : array_like, optional\n", " The base of the log space. The step size between the elements in\n", " ``ln(samples) / ln(base)`` (or ``log_base(samples)``) is uniform.\n", " Default is 10.0.\n", " dtype : dtype\n", " The type of the output array. If `dtype` is not given, the data type\n", " is inferred from `start` and `stop`. The inferred type will never be\n", " an integer; `float` is chosen even if the arguments would produce an\n", " array of integers.\n", " axis : int, optional\n", " The axis in the result to store the samples. Relevant only if start\n", " or stop are array-like. By default (0), the samples will be along a\n", " new axis inserted at the beginning. Use -1 to get an axis at the end.\n", " \n", " .. versionadded:: 1.16.0\n", " \n", " \n", " Returns\n", " -------\n", " samples : ndarray\n", " `num` samples, equally spaced on a log scale.\n", " \n", " See Also\n", " --------\n", " arange : Similar to linspace, with the step size specified instead of the\n", " number of samples. Note that, when used with a float endpoint, the\n", " endpoint may or may not be included.\n", " linspace : Similar to logspace, but with the samples uniformly distributed\n", " in linear space, instead of log space.\n", " geomspace : Similar to logspace, but with endpoints specified directly.\n", " :ref:`how-to-partition`\n", " \n", " Notes\n", " -----\n", " Logspace is equivalent to the code\n", " \n", " >>> y = np.linspace(start, stop, num=num, endpoint=endpoint)\n", " ... # doctest: +SKIP\n", " >>> power(base, y).astype(dtype)\n", " ... # doctest: +SKIP\n", " \n", " Examples\n", " --------\n", " >>> np.logspace(2.0, 3.0, num=4)\n", " array([ 100. , 215.443469 , 464.15888336, 1000. ])\n", " >>> np.logspace(2.0, 3.0, num=4, endpoint=False)\n", " array([100. , 177.827941 , 316.22776602, 562.34132519])\n", " >>> np.logspace(2.0, 3.0, num=4, base=2.0)\n", " array([4. , 5.0396842 , 6.34960421, 8. ])\n", " \n", " Graphical illustration:\n", " \n", " >>> import matplotlib.pyplot as plt\n", " >>> N = 10\n", " >>> x1 = np.logspace(0.1, 1, N, endpoint=True)\n", " >>> x2 = np.logspace(0.1, 1, N, endpoint=False)\n", " >>> y = np.zeros(N)\n", " >>> plt.plot(x1, y, 'o')\n", " [<matplotlib.lines.Line2D object at 0x...>]\n", " >>> plt.plot(x2, y + 0.5, 'o')\n", " [<matplotlib.lines.Line2D object at 0x...>]\n", " >>> plt.ylim([-0.5, 1])\n", " (-0.5, 1)\n", " >>> plt.show()\n", " \n", " lookfor(what, module=None, import_modules=True, regenerate=False, output=None)\n", " Do a keyword search on docstrings.\n", " \n", " A list of objects that matched the search is displayed,\n", " sorted by relevance. All given keywords need to be found in the\n", " docstring for it to be returned as a result, but the order does\n", " not matter.\n", " \n", " Parameters\n", " ----------\n", " what : str\n", " String containing words to look for.\n", " module : str or list, optional\n", " Name of module(s) whose docstrings to go through.\n", " import_modules : bool, optional\n", " Whether to import sub-modules in packages. Default is True.\n", " regenerate : bool, optional\n", " Whether to re-generate the docstring cache. Default is False.\n", " output : file-like, optional\n", " File-like object to write the output to. If omitted, use a pager.\n", " \n", " See Also\n", " --------\n", " source, info\n", " \n", " Notes\n", " -----\n", " Relevance is determined only roughly, by checking if the keywords occur\n", " in the function name, at the start of a docstring, etc.\n", " \n", " Examples\n", " --------\n", " >>> np.lookfor('binary representation') # doctest: +SKIP\n", " Search results for 'binary representation'\n", " ------------------------------------------\n", " numpy.binary_repr\n", " Return the binary representation of the input number as a string.\n", " numpy.core.setup_common.long_double_representation\n", " Given a binary dump as given by GNU od -b, look for long double\n", " numpy.base_repr\n", " Return a string representation of a number in the given base system.\n", " ...\n", " \n", " mask_indices(n, mask_func, k=0)\n", " Return the indices to access (n, n) arrays, given a masking function.\n", " \n", " Assume `mask_func` is a function that, for a square array a of size\n", " ``(n, n)`` with a possible offset argument `k`, when called as\n", " ``mask_func(a, k)`` returns a new array with zeros in certain locations\n", " (functions like `triu` or `tril` do precisely this). Then this function\n", " returns the indices where the non-zero values would be located.\n", " \n", " Parameters\n", " ----------\n", " n : int\n", " The returned indices will be valid to access arrays of shape (n, n).\n", " mask_func : callable\n", " A function whose call signature is similar to that of `triu`, `tril`.\n", " That is, ``mask_func(x, k)`` returns a boolean array, shaped like `x`.\n", " `k` is an optional argument to the function.\n", " k : scalar\n", " An optional argument which is passed through to `mask_func`. Functions\n", " like `triu`, `tril` take a second argument that is interpreted as an\n", " offset.\n", " \n", " Returns\n", " -------\n", " indices : tuple of arrays.\n", " The `n` arrays of indices corresponding to the locations where\n", " ``mask_func(np.ones((n, n)), k)`` is True.\n", " \n", " See Also\n", " --------\n", " triu, tril, triu_indices, tril_indices\n", " \n", " Notes\n", " -----\n", " .. versionadded:: 1.4.0\n", " \n", " Examples\n", " --------\n", " These are the indices that would allow you to access the upper triangular\n", " part of any 3x3 array:\n", " \n", " >>> iu = np.mask_indices(3, np.triu)\n", " \n", " For example, if `a` is a 3x3 array:\n", " \n", " >>> a = np.arange(9).reshape(3, 3)\n", " >>> a\n", " array([[0, 1, 2],\n", " [3, 4, 5],\n", " [6, 7, 8]])\n", " >>> a[iu]\n", " array([0, 1, 2, 4, 5, 8])\n", " \n", " An offset can be passed also to the masking function. This gets us the\n", " indices starting on the first diagonal right of the main one:\n", " \n", " >>> iu1 = np.mask_indices(3, np.triu, 1)\n", " \n", " with which we now extract only three elements:\n", " \n", " >>> a[iu1]\n", " array([1, 2, 5])\n", " \n", " mat = asmatrix(data, dtype=None)\n", " Interpret the input as a matrix.\n", " \n", " Unlike `matrix`, `asmatrix` does not make a copy if the input is already\n", " a matrix or an ndarray. Equivalent to ``matrix(data, copy=False)``.\n", " \n", " Parameters\n", " ----------\n", " data : array_like\n", " Input data.\n", " dtype : data-type\n", " Data-type of the output matrix.\n", " \n", " Returns\n", " -------\n", " mat : matrix\n", " `data` interpreted as a matrix.\n", " \n", " Examples\n", " --------\n", " >>> x = np.array([[1, 2], [3, 4]])\n", " \n", " >>> m = np.asmatrix(x)\n", " \n", " >>> x[0,0] = 5\n", " \n", " >>> m\n", " matrix([[5, 2],\n", " [3, 4]])\n", " \n", " maximum_sctype(t)\n", " Return the scalar type of highest precision of the same kind as the input.\n", " \n", " Parameters\n", " ----------\n", " t : dtype or dtype specifier\n", " The input data type. This can be a `dtype` object or an object that\n", " is convertible to a `dtype`.\n", " \n", " Returns\n", " -------\n", " out : dtype\n", " The highest precision data type of the same kind (`dtype.kind`) as `t`.\n", " \n", " See Also\n", " --------\n", " obj2sctype, mintypecode, sctype2char\n", " dtype\n", " \n", " Examples\n", " --------\n", " >>> np.maximum_sctype(int)\n", " <class 'numpy.int64'>\n", " >>> np.maximum_sctype(np.uint8)\n", " <class 'numpy.uint64'>\n", " >>> np.maximum_sctype(complex)\n", " <class 'numpy.complex256'> # may vary\n", " \n", " >>> np.maximum_sctype(str)\n", " <class 'numpy.str_'>\n", " \n", " >>> np.maximum_sctype('i2')\n", " <class 'numpy.int64'>\n", " >>> np.maximum_sctype('f4')\n", " <class 'numpy.float128'> # may vary\n", " \n", " may_share_memory(...)\n", " may_share_memory(a, b, /, max_work=None)\n", " \n", " Determine if two arrays might share memory\n", " \n", " A return of True does not necessarily mean that the two arrays\n", " share any element. It just means that they *might*.\n", " \n", " Only the memory bounds of a and b are checked by default.\n", " \n", " Parameters\n", " ----------\n", " a, b : ndarray\n", " Input arrays\n", " max_work : int, optional\n", " Effort to spend on solving the overlap problem. See\n", " `shares_memory` for details. Default for ``may_share_memory``\n", " is to do a bounds check.\n", " \n", " Returns\n", " -------\n", " out : bool\n", " \n", " See Also\n", " --------\n", " shares_memory\n", " \n", " Examples\n", " --------\n", " >>> np.may_share_memory(np.array([1,2]), np.array([5,8,9]))\n", " False\n", " >>> x = np.zeros([3, 4])\n", " >>> np.may_share_memory(x[:,0], x[:,1])\n", " True\n", " \n", " mean(a, axis=None, dtype=None, out=None, keepdims=<no value>, *, where=<no value>)\n", " Compute the arithmetic mean along the specified axis.\n", " \n", " Returns the average of the array elements. The average is taken over\n", " the flattened array by default, otherwise over the specified axis.\n", " `float64` intermediate and return values are used for integer inputs.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Array containing numbers whose mean is desired. If `a` is not an\n", " array, a conversion is attempted.\n", " axis : None or int or tuple of ints, optional\n", " Axis or axes along which the means are computed. The default is to\n", " compute the mean of the flattened array.\n", " \n", " .. versionadded:: 1.7.0\n", " \n", " If this is a tuple of ints, a mean is performed over multiple axes,\n", " instead of a single axis or all the axes as before.\n", " dtype : data-type, optional\n", " Type to use in computing the mean. For integer inputs, the default\n", " is `float64`; for floating point inputs, it is the same as the\n", " input dtype.\n", " out : ndarray, optional\n", " Alternate output array in which to place the result. The default\n", " is ``None``; if provided, it must have the same shape as the\n", " expected output, but the type will be cast if necessary.\n", " See :ref:`ufuncs-output-type` for more details.\n", " \n", " keepdims : bool, optional\n", " If this is set to True, the axes which are reduced are left\n", " in the result as dimensions with size one. With this option,\n", " the result will broadcast correctly against the input array.\n", " \n", " If the default value is passed, then `keepdims` will not be\n", " passed through to the `mean` method of sub-classes of\n", " `ndarray`, however any non-default value will be. If the\n", " sub-class' method does not implement `keepdims` any\n", " exceptions will be raised.\n", " \n", " where : array_like of bool, optional\n", " Elements to include in the mean. See `~numpy.ufunc.reduce` for details.\n", " \n", " .. versionadded:: 1.20.0\n", " \n", " Returns\n", " -------\n", " m : ndarray, see dtype parameter above\n", " If `out=None`, returns a new array containing the mean values,\n", " otherwise a reference to the output array is returned.\n", " \n", " See Also\n", " --------\n", " average : Weighted average\n", " std, var, nanmean, nanstd, nanvar\n", " \n", " Notes\n", " -----\n", " The arithmetic mean is the sum of the elements along the axis divided\n", " by the number of elements.\n", " \n", " Note that for floating-point input, the mean is computed using the\n", " same precision the input has. Depending on the input data, this can\n", " cause the results to be inaccurate, especially for `float32` (see\n", " example below). Specifying a higher-precision accumulator using the\n", " `dtype` keyword can alleviate this issue.\n", " \n", " By default, `float16` results are computed using `float32` intermediates\n", " for extra precision.\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([[1, 2], [3, 4]])\n", " >>> np.mean(a)\n", " 2.5\n", " >>> np.mean(a, axis=0)\n", " array([2., 3.])\n", " >>> np.mean(a, axis=1)\n", " array([1.5, 3.5])\n", " \n", " In single precision, `mean` can be inaccurate:\n", " \n", " >>> a = np.zeros((2, 512*512), dtype=np.float32)\n", " >>> a[0, :] = 1.0\n", " >>> a[1, :] = 0.1\n", " >>> np.mean(a)\n", " 0.54999924\n", " \n", " Computing the mean in float64 is more accurate:\n", " \n", " >>> np.mean(a, dtype=np.float64)\n", " 0.55000000074505806 # may vary\n", " \n", " Specifying a where argument:\n", " \n", " >>> a = np.array([[5, 9, 13], [14, 10, 12], [11, 15, 19]])\n", " >>> np.mean(a)\n", " 12.0\n", " >>> np.mean(a, where=[[True], [False], [False]])\n", " 9.0\n", " \n", " median(a, axis=None, out=None, overwrite_input=False, keepdims=False)\n", " Compute the median along the specified axis.\n", " \n", " Returns the median of the array elements.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input array or object that can be converted to an array.\n", " axis : {int, sequence of int, None}, optional\n", " Axis or axes along which the medians are computed. The default\n", " is to compute the median along a flattened version of the array.\n", " A sequence of axes is supported since version 1.9.0.\n", " out : ndarray, optional\n", " Alternative output array in which to place the result. It must\n", " have the same shape and buffer length as the expected output,\n", " but the type (of the output) will be cast if necessary.\n", " overwrite_input : bool, optional\n", " If True, then allow use of memory of input array `a` for\n", " calculations. The input array will be modified by the call to\n", " `median`. This will save memory when you do not need to preserve\n", " the contents of the input array. Treat the input as undefined,\n", " but it will probably be fully or partially sorted. Default is\n", " False. If `overwrite_input` is ``True`` and `a` is not already an\n", " `ndarray`, an error will be raised.\n", " keepdims : bool, optional\n", " If this is set to True, the axes which are reduced are left\n", " in the result as dimensions with size one. With this option,\n", " the result will broadcast correctly against the original `arr`.\n", " \n", " .. versionadded:: 1.9.0\n", " \n", " Returns\n", " -------\n", " median : ndarray\n", " A new array holding the result. If the input contains integers\n", " or floats smaller than ``float64``, then the output data-type is\n", " ``np.float64``. Otherwise, the data-type of the output is the\n", " same as that of the input. If `out` is specified, that array is\n", " returned instead.\n", " \n", " See Also\n", " --------\n", " mean, percentile\n", " \n", " Notes\n", " -----\n", " Given a vector ``V`` of length ``N``, the median of ``V`` is the\n", " middle value of a sorted copy of ``V``, ``V_sorted`` - i\n", " e., ``V_sorted[(N-1)/2]``, when ``N`` is odd, and the average of the\n", " two middle values of ``V_sorted`` when ``N`` is even.\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([[10, 7, 4], [3, 2, 1]])\n", " >>> a\n", " array([[10, 7, 4],\n", " [ 3, 2, 1]])\n", " >>> np.median(a)\n", " 3.5\n", " >>> np.median(a, axis=0)\n", " array([6.5, 4.5, 2.5])\n", " >>> np.median(a, axis=1)\n", " array([7., 2.])\n", " >>> m = np.median(a, axis=0)\n", " >>> out = np.zeros_like(m)\n", " >>> np.median(a, axis=0, out=m)\n", " array([6.5, 4.5, 2.5])\n", " >>> m\n", " array([6.5, 4.5, 2.5])\n", " >>> b = a.copy()\n", " >>> np.median(b, axis=1, overwrite_input=True)\n", " array([7., 2.])\n", " >>> assert not np.all(a==b)\n", " >>> b = a.copy()\n", " >>> np.median(b, axis=None, overwrite_input=True)\n", " 3.5\n", " >>> assert not np.all(a==b)\n", " \n", " meshgrid(*xi, copy=True, sparse=False, indexing='xy')\n", " Return coordinate matrices from coordinate vectors.\n", " \n", " Make N-D coordinate arrays for vectorized evaluations of\n", " N-D scalar/vector fields over N-D grids, given\n", " one-dimensional coordinate arrays x1, x2,..., xn.\n", " \n", " .. versionchanged:: 1.9\n", " 1-D and 0-D cases are allowed.\n", " \n", " Parameters\n", " ----------\n", " x1, x2,..., xn : array_like\n", " 1-D arrays representing the coordinates of a grid.\n", " indexing : {'xy', 'ij'}, optional\n", " Cartesian ('xy', default) or matrix ('ij') indexing of output.\n", " See Notes for more details.\n", " \n", " .. versionadded:: 1.7.0\n", " sparse : bool, optional\n", " If True the shape of the returned coordinate array for dimension *i*\n", " is reduced from ``(N1, ..., Ni, ... Nn)`` to\n", " ``(1, ..., 1, Ni, 1, ..., 1)``. These sparse coordinate grids are\n", " intended to be use with :ref:`basics.broadcasting`. When all\n", " coordinates are used in an expression, broadcasting still leads to a\n", " fully-dimensonal result array.\n", " \n", " Default is False.\n", " \n", " .. versionadded:: 1.7.0\n", " copy : bool, optional\n", " If False, a view into the original arrays are returned in order to\n", " conserve memory. Default is True. Please note that\n", " ``sparse=False, copy=False`` will likely return non-contiguous\n", " arrays. Furthermore, more than one element of a broadcast array\n", " may refer to a single memory location. If you need to write to the\n", " arrays, make copies first.\n", " \n", " .. versionadded:: 1.7.0\n", " \n", " Returns\n", " -------\n", " X1, X2,..., XN : ndarray\n", " For vectors `x1`, `x2`,..., `xn` with lengths ``Ni=len(xi)``,\n", " returns ``(N1, N2, N3,..., Nn)`` shaped arrays if indexing='ij'\n", " or ``(N2, N1, N3,..., Nn)`` shaped arrays if indexing='xy'\n", " with the elements of `xi` repeated to fill the matrix along\n", " the first dimension for `x1`, the second for `x2` and so on.\n", " \n", " Notes\n", " -----\n", " This function supports both indexing conventions through the indexing\n", " keyword argument. Giving the string 'ij' returns a meshgrid with\n", " matrix indexing, while 'xy' returns a meshgrid with Cartesian indexing.\n", " In the 2-D case with inputs of length M and N, the outputs are of shape\n", " (N, M) for 'xy' indexing and (M, N) for 'ij' indexing. In the 3-D case\n", " with inputs of length M, N and P, outputs are of shape (N, M, P) for\n", " 'xy' indexing and (M, N, P) for 'ij' indexing. The difference is\n", " illustrated by the following code snippet::\n", " \n", " xv, yv = np.meshgrid(x, y, indexing='ij')\n", " for i in range(nx):\n", " for j in range(ny):\n", " # treat xv[i,j], yv[i,j]\n", " \n", " xv, yv = np.meshgrid(x, y, indexing='xy')\n", " for i in range(nx):\n", " for j in range(ny):\n", " # treat xv[j,i], yv[j,i]\n", " \n", " In the 1-D and 0-D case, the indexing and sparse keywords have no effect.\n", " \n", " See Also\n", " --------\n", " mgrid : Construct a multi-dimensional \"meshgrid\" using indexing notation.\n", " ogrid : Construct an open multi-dimensional \"meshgrid\" using indexing\n", " notation.\n", " how-to-index\n", " \n", " Examples\n", " --------\n", " >>> nx, ny = (3, 2)\n", " >>> x = np.linspace(0, 1, nx)\n", " >>> y = np.linspace(0, 1, ny)\n", " >>> xv, yv = np.meshgrid(x, y)\n", " >>> xv\n", " array([[0. , 0.5, 1. ],\n", " [0. , 0.5, 1. ]])\n", " >>> yv\n", " array([[0., 0., 0.],\n", " [1., 1., 1.]])\n", " \n", " The result of `meshgrid` is a coordinate grid:\n", " \n", " >>> import matplotlib.pyplot as plt\n", " >>> plt.plot(xv, yv, marker='o', color='k', linestyle='none')\n", " >>> plt.show()\n", " \n", " You can create sparse output arrays to save memory and computation time.\n", " \n", " >>> xv, yv = np.meshgrid(x, y, sparse=True)\n", " >>> xv\n", " array([[0. , 0.5, 1. ]])\n", " >>> yv\n", " array([[0.],\n", " [1.]])\n", " \n", " `meshgrid` is very useful to evaluate functions on a grid. If the\n", " function depends on all coordinates, both dense and sparse outputs can be\n", " used.\n", " \n", " >>> x = np.linspace(-5, 5, 101)\n", " >>> y = np.linspace(-5, 5, 101)\n", " >>> # full coordinate arrays\n", " >>> xx, yy = np.meshgrid(x, y)\n", " >>> zz = np.sqrt(xx**2 + yy**2)\n", " >>> xx.shape, yy.shape, zz.shape\n", " ((101, 101), (101, 101), (101, 101))\n", " >>> # sparse coordinate arrays\n", " >>> xs, ys = np.meshgrid(x, y, sparse=True)\n", " >>> zs = np.sqrt(xs**2 + ys**2)\n", " >>> xs.shape, ys.shape, zs.shape\n", " ((1, 101), (101, 1), (101, 101))\n", " >>> np.array_equal(zz, zs)\n", " True\n", " \n", " >>> h = plt.contourf(x, y, zs)\n", " >>> plt.axis('scaled')\n", " >>> plt.colorbar()\n", " >>> plt.show()\n", " \n", " min_scalar_type(...)\n", " min_scalar_type(a, /)\n", " \n", " For scalar ``a``, returns the data type with the smallest size\n", " and smallest scalar kind which can hold its value. For non-scalar\n", " array ``a``, returns the vector's dtype unmodified.\n", " \n", " Floating point values are not demoted to integers,\n", " and complex values are not demoted to floats.\n", " \n", " Parameters\n", " ----------\n", " a : scalar or array_like\n", " The value whose minimal data type is to be found.\n", " \n", " Returns\n", " -------\n", " out : dtype\n", " The minimal data type.\n", " \n", " Notes\n", " -----\n", " .. versionadded:: 1.6.0\n", " \n", " See Also\n", " --------\n", " result_type, promote_types, dtype, can_cast\n", " \n", " Examples\n", " --------\n", " >>> np.min_scalar_type(10)\n", " dtype('uint8')\n", " \n", " >>> np.min_scalar_type(-260)\n", " dtype('int16')\n", " \n", " >>> np.min_scalar_type(3.1)\n", " dtype('float16')\n", " \n", " >>> np.min_scalar_type(1e50)\n", " dtype('float64')\n", " \n", " >>> np.min_scalar_type(np.arange(4,dtype='f8'))\n", " dtype('float64')\n", " \n", " mintypecode(typechars, typeset='GDFgdf', default='d')\n", " Return the character for the minimum-size type to which given types can\n", " be safely cast.\n", " \n", " The returned type character must represent the smallest size dtype such\n", " that an array of the returned type can handle the data from an array of\n", " all types in `typechars` (or if `typechars` is an array, then its\n", " dtype.char).\n", " \n", " Parameters\n", " ----------\n", " typechars : list of str or array_like\n", " If a list of strings, each string should represent a dtype.\n", " If array_like, the character representation of the array dtype is used.\n", " typeset : str or list of str, optional\n", " The set of characters that the returned character is chosen from.\n", " The default set is 'GDFgdf'.\n", " default : str, optional\n", " The default character, this is returned if none of the characters in\n", " `typechars` matches a character in `typeset`.\n", " \n", " Returns\n", " -------\n", " typechar : str\n", " The character representing the minimum-size type that was found.\n", " \n", " See Also\n", " --------\n", " dtype, sctype2char, maximum_sctype\n", " \n", " Examples\n", " --------\n", " >>> np.mintypecode(['d', 'f', 'S'])\n", " 'd'\n", " >>> x = np.array([1.1, 2-3.j])\n", " >>> np.mintypecode(x)\n", " 'D'\n", " \n", " >>> np.mintypecode('abceh', default='G')\n", " 'G'\n", " \n", " moveaxis(a, source, destination)\n", " Move axes of an array to new positions.\n", " \n", " Other axes remain in their original order.\n", " \n", " .. versionadded:: 1.11.0\n", " \n", " Parameters\n", " ----------\n", " a : np.ndarray\n", " The array whose axes should be reordered.\n", " source : int or sequence of int\n", " Original positions of the axes to move. These must be unique.\n", " destination : int or sequence of int\n", " Destination positions for each of the original axes. These must also be\n", " unique.\n", " \n", " Returns\n", " -------\n", " result : np.ndarray\n", " Array with moved axes. This array is a view of the input array.\n", " \n", " See Also\n", " --------\n", " transpose : Permute the dimensions of an array.\n", " swapaxes : Interchange two axes of an array.\n", " \n", " Examples\n", " --------\n", " >>> x = np.zeros((3, 4, 5))\n", " >>> np.moveaxis(x, 0, -1).shape\n", " (4, 5, 3)\n", " >>> np.moveaxis(x, -1, 0).shape\n", " (5, 3, 4)\n", " \n", " These all achieve the same result:\n", " \n", " >>> np.transpose(x).shape\n", " (5, 4, 3)\n", " >>> np.swapaxes(x, 0, -1).shape\n", " (5, 4, 3)\n", " >>> np.moveaxis(x, [0, 1], [-1, -2]).shape\n", " (5, 4, 3)\n", " >>> np.moveaxis(x, [0, 1, 2], [-1, -2, -3]).shape\n", " (5, 4, 3)\n", " \n", " msort(a)\n", " Return a copy of an array sorted along the first axis.\n", " \n", " .. deprecated:: 1.24\n", " \n", " msort is deprecated, use ``np.sort(a, axis=0)`` instead.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Array to be sorted.\n", " \n", " Returns\n", " -------\n", " sorted_array : ndarray\n", " Array of the same type and shape as `a`.\n", " \n", " See Also\n", " --------\n", " sort\n", " \n", " Notes\n", " -----\n", " ``np.msort(a)`` is equivalent to ``np.sort(a, axis=0)``.\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([[1, 4], [3, 1]])\n", " >>> np.msort(a) # sort along the first axis\n", " array([[1, 1],\n", " [3, 4]])\n", " \n", " nan_to_num(x, copy=True, nan=0.0, posinf=None, neginf=None)\n", " Replace NaN with zero and infinity with large finite numbers (default\n", " behaviour) or with the numbers defined by the user using the `nan`,\n", " `posinf` and/or `neginf` keywords.\n", " \n", " If `x` is inexact, NaN is replaced by zero or by the user defined value in\n", " `nan` keyword, infinity is replaced by the largest finite floating point\n", " values representable by ``x.dtype`` or by the user defined value in\n", " `posinf` keyword and -infinity is replaced by the most negative finite\n", " floating point values representable by ``x.dtype`` or by the user defined\n", " value in `neginf` keyword.\n", " \n", " For complex dtypes, the above is applied to each of the real and\n", " imaginary components of `x` separately.\n", " \n", " If `x` is not inexact, then no replacements are made.\n", " \n", " Parameters\n", " ----------\n", " x : scalar or array_like\n", " Input data.\n", " copy : bool, optional\n", " Whether to create a copy of `x` (True) or to replace values\n", " in-place (False). The in-place operation only occurs if\n", " casting to an array does not require a copy.\n", " Default is True.\n", " \n", " .. versionadded:: 1.13\n", " nan : int, float, optional\n", " Value to be used to fill NaN values. If no value is passed\n", " then NaN values will be replaced with 0.0.\n", " \n", " .. versionadded:: 1.17\n", " posinf : int, float, optional\n", " Value to be used to fill positive infinity values. If no value is\n", " passed then positive infinity values will be replaced with a very\n", " large number.\n", " \n", " .. versionadded:: 1.17\n", " neginf : int, float, optional\n", " Value to be used to fill negative infinity values. If no value is\n", " passed then negative infinity values will be replaced with a very\n", " small (or negative) number.\n", " \n", " .. versionadded:: 1.17\n", " \n", " \n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " `x`, with the non-finite values replaced. If `copy` is False, this may\n", " be `x` itself.\n", " \n", " See Also\n", " --------\n", " isinf : Shows which elements are positive or negative infinity.\n", " isneginf : Shows which elements are negative infinity.\n", " isposinf : Shows which elements are positive infinity.\n", " isnan : Shows which elements are Not a Number (NaN).\n", " isfinite : Shows which elements are finite (not NaN, not infinity)\n", " \n", " Notes\n", " -----\n", " NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic\n", " (IEEE 754). This means that Not a Number is not equivalent to infinity.\n", " \n", " Examples\n", " --------\n", " >>> np.nan_to_num(np.inf)\n", " 1.7976931348623157e+308\n", " >>> np.nan_to_num(-np.inf)\n", " -1.7976931348623157e+308\n", " >>> np.nan_to_num(np.nan)\n", " 0.0\n", " >>> x = np.array([np.inf, -np.inf, np.nan, -128, 128])\n", " >>> np.nan_to_num(x)\n", " array([ 1.79769313e+308, -1.79769313e+308, 0.00000000e+000, # may vary\n", " -1.28000000e+002, 1.28000000e+002])\n", " >>> np.nan_to_num(x, nan=-9999, posinf=33333333, neginf=33333333)\n", " array([ 3.3333333e+07, 3.3333333e+07, -9.9990000e+03,\n", " -1.2800000e+02, 1.2800000e+02])\n", " >>> y = np.array([complex(np.inf, np.nan), np.nan, complex(np.nan, np.inf)])\n", " array([ 1.79769313e+308, -1.79769313e+308, 0.00000000e+000, # may vary\n", " -1.28000000e+002, 1.28000000e+002])\n", " >>> np.nan_to_num(y)\n", " array([ 1.79769313e+308 +0.00000000e+000j, # may vary\n", " 0.00000000e+000 +0.00000000e+000j,\n", " 0.00000000e+000 +1.79769313e+308j])\n", " >>> np.nan_to_num(y, nan=111111, posinf=222222)\n", " array([222222.+111111.j, 111111. +0.j, 111111.+222222.j])\n", " \n", " nanargmax(a, axis=None, out=None, *, keepdims=<no value>)\n", " Return the indices of the maximum values in the specified axis ignoring\n", " NaNs. For all-NaN slices ``ValueError`` is raised. Warning: the\n", " results cannot be trusted if a slice contains only NaNs and -Infs.\n", " \n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input data.\n", " axis : int, optional\n", " Axis along which to operate. By default flattened input is used.\n", " out : array, optional\n", " If provided, the result will be inserted into this array. It should\n", " be of the appropriate shape and dtype.\n", " \n", " .. versionadded:: 1.22.0\n", " keepdims : bool, optional\n", " If this is set to True, the axes which are reduced are left\n", " in the result as dimensions with size one. With this option,\n", " the result will broadcast correctly against the array.\n", " \n", " .. versionadded:: 1.22.0\n", " \n", " Returns\n", " -------\n", " index_array : ndarray\n", " An array of indices or a single index value.\n", " \n", " See Also\n", " --------\n", " argmax, nanargmin\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([[np.nan, 4], [2, 3]])\n", " >>> np.argmax(a)\n", " 0\n", " >>> np.nanargmax(a)\n", " 1\n", " >>> np.nanargmax(a, axis=0)\n", " array([1, 0])\n", " >>> np.nanargmax(a, axis=1)\n", " array([1, 1])\n", " \n", " nanargmin(a, axis=None, out=None, *, keepdims=<no value>)\n", " Return the indices of the minimum values in the specified axis ignoring\n", " NaNs. For all-NaN slices ``ValueError`` is raised. Warning: the results\n", " cannot be trusted if a slice contains only NaNs and Infs.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input data.\n", " axis : int, optional\n", " Axis along which to operate. By default flattened input is used.\n", " out : array, optional\n", " If provided, the result will be inserted into this array. It should\n", " be of the appropriate shape and dtype.\n", " \n", " .. versionadded:: 1.22.0\n", " keepdims : bool, optional\n", " If this is set to True, the axes which are reduced are left\n", " in the result as dimensions with size one. With this option,\n", " the result will broadcast correctly against the array.\n", " \n", " .. versionadded:: 1.22.0\n", " \n", " Returns\n", " -------\n", " index_array : ndarray\n", " An array of indices or a single index value.\n", " \n", " See Also\n", " --------\n", " argmin, nanargmax\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([[np.nan, 4], [2, 3]])\n", " >>> np.argmin(a)\n", " 0\n", " >>> np.nanargmin(a)\n", " 2\n", " >>> np.nanargmin(a, axis=0)\n", " array([1, 1])\n", " >>> np.nanargmin(a, axis=1)\n", " array([1, 0])\n", " \n", " nancumprod(a, axis=None, dtype=None, out=None)\n", " Return the cumulative product of array elements over a given axis treating Not a\n", " Numbers (NaNs) as one. The cumulative product does not change when NaNs are\n", " encountered and leading NaNs are replaced by ones.\n", " \n", " Ones are returned for slices that are all-NaN or empty.\n", " \n", " .. versionadded:: 1.12.0\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input array.\n", " axis : int, optional\n", " Axis along which the cumulative product is computed. By default\n", " the input is flattened.\n", " dtype : dtype, optional\n", " Type of the returned array, as well as of the accumulator in which\n", " the elements are multiplied. If *dtype* is not specified, it\n", " defaults to the dtype of `a`, unless `a` has an integer dtype with\n", " a precision less than that of the default platform integer. In\n", " that case, the default platform integer is used instead.\n", " out : ndarray, optional\n", " Alternative output array in which to place the result. It must\n", " have the same shape and buffer length as the expected output\n", " but the type of the resulting values will be cast if necessary.\n", " \n", " Returns\n", " -------\n", " nancumprod : ndarray\n", " A new array holding the result is returned unless `out` is\n", " specified, in which case it is returned.\n", " \n", " See Also\n", " --------\n", " numpy.cumprod : Cumulative product across array propagating NaNs.\n", " isnan : Show which elements are NaN.\n", " \n", " Examples\n", " --------\n", " >>> np.nancumprod(1)\n", " array([1])\n", " >>> np.nancumprod([1])\n", " array([1])\n", " >>> np.nancumprod([1, np.nan])\n", " array([1., 1.])\n", " >>> a = np.array([[1, 2], [3, np.nan]])\n", " >>> np.nancumprod(a)\n", " array([1., 2., 6., 6.])\n", " >>> np.nancumprod(a, axis=0)\n", " array([[1., 2.],\n", " [3., 2.]])\n", " >>> np.nancumprod(a, axis=1)\n", " array([[1., 2.],\n", " [3., 3.]])\n", " \n", " nancumsum(a, axis=None, dtype=None, out=None)\n", " Return the cumulative sum of array elements over a given axis treating Not a\n", " Numbers (NaNs) as zero. The cumulative sum does not change when NaNs are\n", " encountered and leading NaNs are replaced by zeros.\n", " \n", " Zeros are returned for slices that are all-NaN or empty.\n", " \n", " .. versionadded:: 1.12.0\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input array.\n", " axis : int, optional\n", " Axis along which the cumulative sum is computed. The default\n", " (None) is to compute the cumsum over the flattened array.\n", " dtype : dtype, optional\n", " Type of the returned array and of the accumulator in which the\n", " elements are summed. If `dtype` is not specified, it defaults\n", " to the dtype of `a`, unless `a` has an integer dtype with a\n", " precision less than that of the default platform integer. In\n", " that case, the default platform integer is used.\n", " out : ndarray, optional\n", " Alternative output array in which to place the result. It must\n", " have the same shape and buffer length as the expected output\n", " but the type will be cast if necessary. See :ref:`ufuncs-output-type` for\n", " more details.\n", " \n", " Returns\n", " -------\n", " nancumsum : ndarray.\n", " A new array holding the result is returned unless `out` is\n", " specified, in which it is returned. The result has the same\n", " size as `a`, and the same shape as `a` if `axis` is not None\n", " or `a` is a 1-d array.\n", " \n", " See Also\n", " --------\n", " numpy.cumsum : Cumulative sum across array propagating NaNs.\n", " isnan : Show which elements are NaN.\n", " \n", " Examples\n", " --------\n", " >>> np.nancumsum(1)\n", " array([1])\n", " >>> np.nancumsum([1])\n", " array([1])\n", " >>> np.nancumsum([1, np.nan])\n", " array([1., 1.])\n", " >>> a = np.array([[1, 2], [3, np.nan]])\n", " >>> np.nancumsum(a)\n", " array([1., 3., 6., 6.])\n", " >>> np.nancumsum(a, axis=0)\n", " array([[1., 2.],\n", " [4., 2.]])\n", " >>> np.nancumsum(a, axis=1)\n", " array([[1., 3.],\n", " [3., 3.]])\n", " \n", " nanmax(a, axis=None, out=None, keepdims=<no value>, initial=<no value>, where=<no value>)\n", " Return the maximum of an array or maximum along an axis, ignoring any\n", " NaNs. When all-NaN slices are encountered a ``RuntimeWarning`` is\n", " raised and NaN is returned for that slice.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Array containing numbers whose maximum is desired. If `a` is not an\n", " array, a conversion is attempted.\n", " axis : {int, tuple of int, None}, optional\n", " Axis or axes along which the maximum is computed. The default is to compute\n", " the maximum of the flattened array.\n", " out : ndarray, optional\n", " Alternate output array in which to place the result. The default\n", " is ``None``; if provided, it must have the same shape as the\n", " expected output, but the type will be cast if necessary. See\n", " :ref:`ufuncs-output-type` for more details.\n", " \n", " .. versionadded:: 1.8.0\n", " keepdims : bool, optional\n", " If this is set to True, the axes which are reduced are left\n", " in the result as dimensions with size one. With this option,\n", " the result will broadcast correctly against the original `a`.\n", " \n", " If the value is anything but the default, then\n", " `keepdims` will be passed through to the `max` method\n", " of sub-classes of `ndarray`. If the sub-classes methods\n", " does not implement `keepdims` any exceptions will be raised.\n", " \n", " .. versionadded:: 1.8.0\n", " initial : scalar, optional\n", " The minimum value of an output element. Must be present to allow\n", " computation on empty slice. See `~numpy.ufunc.reduce` for details.\n", " \n", " .. versionadded:: 1.22.0\n", " where : array_like of bool, optional\n", " Elements to compare for the maximum. See `~numpy.ufunc.reduce`\n", " for details.\n", " \n", " .. versionadded:: 1.22.0\n", " \n", " Returns\n", " -------\n", " nanmax : ndarray\n", " An array with the same shape as `a`, with the specified axis removed.\n", " If `a` is a 0-d array, or if axis is None, an ndarray scalar is\n", " returned. The same dtype as `a` is returned.\n", " \n", " See Also\n", " --------\n", " nanmin :\n", " The minimum value of an array along a given axis, ignoring any NaNs.\n", " amax :\n", " The maximum value of an array along a given axis, propagating any NaNs.\n", " fmax :\n", " Element-wise maximum of two arrays, ignoring any NaNs.\n", " maximum :\n", " Element-wise maximum of two arrays, propagating any NaNs.\n", " isnan :\n", " Shows which elements are Not a Number (NaN).\n", " isfinite:\n", " Shows which elements are neither NaN nor infinity.\n", " \n", " amin, fmin, minimum\n", " \n", " Notes\n", " -----\n", " NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic\n", " (IEEE 754). This means that Not a Number is not equivalent to infinity.\n", " Positive infinity is treated as a very large number and negative\n", " infinity is treated as a very small (i.e. negative) number.\n", " \n", " If the input has a integer type the function is equivalent to np.max.\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([[1, 2], [3, np.nan]])\n", " >>> np.nanmax(a)\n", " 3.0\n", " >>> np.nanmax(a, axis=0)\n", " array([3., 2.])\n", " >>> np.nanmax(a, axis=1)\n", " array([2., 3.])\n", " \n", " When positive infinity and negative infinity are present:\n", " \n", " >>> np.nanmax([1, 2, np.nan, np.NINF])\n", " 2.0\n", " >>> np.nanmax([1, 2, np.nan, np.inf])\n", " inf\n", " \n", " nanmean(a, axis=None, dtype=None, out=None, keepdims=<no value>, *, where=<no value>)\n", " Compute the arithmetic mean along the specified axis, ignoring NaNs.\n", " \n", " Returns the average of the array elements. The average is taken over\n", " the flattened array by default, otherwise over the specified axis.\n", " `float64` intermediate and return values are used for integer inputs.\n", " \n", " For all-NaN slices, NaN is returned and a `RuntimeWarning` is raised.\n", " \n", " .. versionadded:: 1.8.0\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Array containing numbers whose mean is desired. If `a` is not an\n", " array, a conversion is attempted.\n", " axis : {int, tuple of int, None}, optional\n", " Axis or axes along which the means are computed. The default is to compute\n", " the mean of the flattened array.\n", " dtype : data-type, optional\n", " Type to use in computing the mean. For integer inputs, the default\n", " is `float64`; for inexact inputs, it is the same as the input\n", " dtype.\n", " out : ndarray, optional\n", " Alternate output array in which to place the result. The default\n", " is ``None``; if provided, it must have the same shape as the\n", " expected output, but the type will be cast if necessary. See\n", " :ref:`ufuncs-output-type` for more details.\n", " keepdims : bool, optional\n", " If this is set to True, the axes which are reduced are left\n", " in the result as dimensions with size one. With this option,\n", " the result will broadcast correctly against the original `a`.\n", " \n", " If the value is anything but the default, then\n", " `keepdims` will be passed through to the `mean` or `sum` methods\n", " of sub-classes of `ndarray`. If the sub-classes methods\n", " does not implement `keepdims` any exceptions will be raised.\n", " where : array_like of bool, optional\n", " Elements to include in the mean. See `~numpy.ufunc.reduce` for details.\n", " \n", " .. versionadded:: 1.22.0\n", " \n", " Returns\n", " -------\n", " m : ndarray, see dtype parameter above\n", " If `out=None`, returns a new array containing the mean values,\n", " otherwise a reference to the output array is returned. Nan is\n", " returned for slices that contain only NaNs.\n", " \n", " See Also\n", " --------\n", " average : Weighted average\n", " mean : Arithmetic mean taken while not ignoring NaNs\n", " var, nanvar\n", " \n", " Notes\n", " -----\n", " The arithmetic mean is the sum of the non-NaN elements along the axis\n", " divided by the number of non-NaN elements.\n", " \n", " Note that for floating-point input, the mean is computed using the same\n", " precision the input has. Depending on the input data, this can cause\n", " the results to be inaccurate, especially for `float32`. Specifying a\n", " higher-precision accumulator using the `dtype` keyword can alleviate\n", " this issue.\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([[1, np.nan], [3, 4]])\n", " >>> np.nanmean(a)\n", " 2.6666666666666665\n", " >>> np.nanmean(a, axis=0)\n", " array([2., 4.])\n", " >>> np.nanmean(a, axis=1)\n", " array([1., 3.5]) # may vary\n", " \n", " nanmedian(a, axis=None, out=None, overwrite_input=False, keepdims=<no value>)\n", " Compute the median along the specified axis, while ignoring NaNs.\n", " \n", " Returns the median of the array elements.\n", " \n", " .. versionadded:: 1.9.0\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input array or object that can be converted to an array.\n", " axis : {int, sequence of int, None}, optional\n", " Axis or axes along which the medians are computed. The default\n", " is to compute the median along a flattened version of the array.\n", " A sequence of axes is supported since version 1.9.0.\n", " out : ndarray, optional\n", " Alternative output array in which to place the result. It must\n", " have the same shape and buffer length as the expected output,\n", " but the type (of the output) will be cast if necessary.\n", " overwrite_input : bool, optional\n", " If True, then allow use of memory of input array `a` for\n", " calculations. The input array will be modified by the call to\n", " `median`. This will save memory when you do not need to preserve\n", " the contents of the input array. Treat the input as undefined,\n", " but it will probably be fully or partially sorted. Default is\n", " False. If `overwrite_input` is ``True`` and `a` is not already an\n", " `ndarray`, an error will be raised.\n", " keepdims : bool, optional\n", " If this is set to True, the axes which are reduced are left\n", " in the result as dimensions with size one. With this option,\n", " the result will broadcast correctly against the original `a`.\n", " \n", " If this is anything but the default value it will be passed\n", " through (in the special case of an empty array) to the\n", " `mean` function of the underlying array. If the array is\n", " a sub-class and `mean` does not have the kwarg `keepdims` this\n", " will raise a RuntimeError.\n", " \n", " Returns\n", " -------\n", " median : ndarray\n", " A new array holding the result. If the input contains integers\n", " or floats smaller than ``float64``, then the output data-type is\n", " ``np.float64``. Otherwise, the data-type of the output is the\n", " same as that of the input. If `out` is specified, that array is\n", " returned instead.\n", " \n", " See Also\n", " --------\n", " mean, median, percentile\n", " \n", " Notes\n", " -----\n", " Given a vector ``V`` of length ``N``, the median of ``V`` is the\n", " middle value of a sorted copy of ``V``, ``V_sorted`` - i.e.,\n", " ``V_sorted[(N-1)/2]``, when ``N`` is odd and the average of the two\n", " middle values of ``V_sorted`` when ``N`` is even.\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([[10.0, 7, 4], [3, 2, 1]])\n", " >>> a[0, 1] = np.nan\n", " >>> a\n", " array([[10., nan, 4.],\n", " [ 3., 2., 1.]])\n", " >>> np.median(a)\n", " nan\n", " >>> np.nanmedian(a)\n", " 3.0\n", " >>> np.nanmedian(a, axis=0)\n", " array([6.5, 2. , 2.5])\n", " >>> np.median(a, axis=1)\n", " array([nan, 2.])\n", " >>> b = a.copy()\n", " >>> np.nanmedian(b, axis=1, overwrite_input=True)\n", " array([7., 2.])\n", " >>> assert not np.all(a==b)\n", " >>> b = a.copy()\n", " >>> np.nanmedian(b, axis=None, overwrite_input=True)\n", " 3.0\n", " >>> assert not np.all(a==b)\n", " \n", " nanmin(a, axis=None, out=None, keepdims=<no value>, initial=<no value>, where=<no value>)\n", " Return minimum of an array or minimum along an axis, ignoring any NaNs.\n", " When all-NaN slices are encountered a ``RuntimeWarning`` is raised and\n", " Nan is returned for that slice.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Array containing numbers whose minimum is desired. If `a` is not an\n", " array, a conversion is attempted.\n", " axis : {int, tuple of int, None}, optional\n", " Axis or axes along which the minimum is computed. The default is to compute\n", " the minimum of the flattened array.\n", " out : ndarray, optional\n", " Alternate output array in which to place the result. The default\n", " is ``None``; if provided, it must have the same shape as the\n", " expected output, but the type will be cast if necessary. See\n", " :ref:`ufuncs-output-type` for more details.\n", " \n", " .. versionadded:: 1.8.0\n", " keepdims : bool, optional\n", " If this is set to True, the axes which are reduced are left\n", " in the result as dimensions with size one. With this option,\n", " the result will broadcast correctly against the original `a`.\n", " \n", " If the value is anything but the default, then\n", " `keepdims` will be passed through to the `min` method\n", " of sub-classes of `ndarray`. If the sub-classes methods\n", " does not implement `keepdims` any exceptions will be raised.\n", " \n", " .. versionadded:: 1.8.0\n", " initial : scalar, optional\n", " The maximum value of an output element. Must be present to allow\n", " computation on empty slice. See `~numpy.ufunc.reduce` for details.\n", " \n", " .. versionadded:: 1.22.0\n", " where : array_like of bool, optional\n", " Elements to compare for the minimum. See `~numpy.ufunc.reduce`\n", " for details.\n", " \n", " .. versionadded:: 1.22.0\n", " \n", " Returns\n", " -------\n", " nanmin : ndarray\n", " An array with the same shape as `a`, with the specified axis\n", " removed. If `a` is a 0-d array, or if axis is None, an ndarray\n", " scalar is returned. The same dtype as `a` is returned.\n", " \n", " See Also\n", " --------\n", " nanmax :\n", " The maximum value of an array along a given axis, ignoring any NaNs.\n", " amin :\n", " The minimum value of an array along a given axis, propagating any NaNs.\n", " fmin :\n", " Element-wise minimum of two arrays, ignoring any NaNs.\n", " minimum :\n", " Element-wise minimum of two arrays, propagating any NaNs.\n", " isnan :\n", " Shows which elements are Not a Number (NaN).\n", " isfinite:\n", " Shows which elements are neither NaN nor infinity.\n", " \n", " amax, fmax, maximum\n", " \n", " Notes\n", " -----\n", " NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic\n", " (IEEE 754). This means that Not a Number is not equivalent to infinity.\n", " Positive infinity is treated as a very large number and negative\n", " infinity is treated as a very small (i.e. negative) number.\n", " \n", " If the input has a integer type the function is equivalent to np.min.\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([[1, 2], [3, np.nan]])\n", " >>> np.nanmin(a)\n", " 1.0\n", " >>> np.nanmin(a, axis=0)\n", " array([1., 2.])\n", " >>> np.nanmin(a, axis=1)\n", " array([1., 3.])\n", " \n", " When positive infinity and negative infinity are present:\n", " \n", " >>> np.nanmin([1, 2, np.nan, np.inf])\n", " 1.0\n", " >>> np.nanmin([1, 2, np.nan, np.NINF])\n", " -inf\n", " \n", " nanpercentile(a, q, axis=None, out=None, overwrite_input=False, method='linear', keepdims=<no value>, *, interpolation=None)\n", " Compute the qth percentile of the data along the specified axis,\n", " while ignoring nan values.\n", " \n", " Returns the qth percentile(s) of the array elements.\n", " \n", " .. versionadded:: 1.9.0\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input array or object that can be converted to an array, containing\n", " nan values to be ignored.\n", " q : array_like of float\n", " Percentile or sequence of percentiles to compute, which must be\n", " between 0 and 100 inclusive.\n", " axis : {int, tuple of int, None}, optional\n", " Axis or axes along which the percentiles are computed. The default\n", " is to compute the percentile(s) along a flattened version of the\n", " array.\n", " out : ndarray, optional\n", " Alternative output array in which to place the result. It must have\n", " the same shape and buffer length as the expected output, but the\n", " type (of the output) will be cast if necessary.\n", " overwrite_input : bool, optional\n", " If True, then allow the input array `a` to be modified by\n", " intermediate calculations, to save memory. In this case, the\n", " contents of the input `a` after this function completes is\n", " undefined.\n", " method : str, optional\n", " This parameter specifies the method to use for estimating the\n", " percentile. There are many different methods, some unique to NumPy.\n", " See the notes for explanation. The options sorted by their R type\n", " as summarized in the H&F paper [1]_ are:\n", " \n", " 1. 'inverted_cdf'\n", " 2. 'averaged_inverted_cdf'\n", " 3. 'closest_observation'\n", " 4. 'interpolated_inverted_cdf'\n", " 5. 'hazen'\n", " 6. 'weibull'\n", " 7. 'linear' (default)\n", " 8. 'median_unbiased'\n", " 9. 'normal_unbiased'\n", " \n", " The first three methods are discontinuous. NumPy further defines the\n", " following discontinuous variations of the default 'linear' (7.) option:\n", " \n", " * 'lower'\n", " * 'higher',\n", " * 'midpoint'\n", " * 'nearest'\n", " \n", " .. versionchanged:: 1.22.0\n", " This argument was previously called \"interpolation\" and only\n", " offered the \"linear\" default and last four options.\n", " \n", " keepdims : bool, optional\n", " If this is set to True, the axes which are reduced are left in\n", " the result as dimensions with size one. With this option, the\n", " result will broadcast correctly against the original array `a`.\n", " \n", " If this is anything but the default value it will be passed\n", " through (in the special case of an empty array) to the\n", " `mean` function of the underlying array. If the array is\n", " a sub-class and `mean` does not have the kwarg `keepdims` this\n", " will raise a RuntimeError.\n", " \n", " interpolation : str, optional\n", " Deprecated name for the method keyword argument.\n", " \n", " .. deprecated:: 1.22.0\n", " \n", " Returns\n", " -------\n", " percentile : scalar or ndarray\n", " If `q` is a single percentile and `axis=None`, then the result\n", " is a scalar. If multiple percentiles are given, first axis of\n", " the result corresponds to the percentiles. The other axes are\n", " the axes that remain after the reduction of `a`. If the input\n", " contains integers or floats smaller than ``float64``, the output\n", " data-type is ``float64``. Otherwise, the output data-type is the\n", " same as that of the input. If `out` is specified, that array is\n", " returned instead.\n", " \n", " See Also\n", " --------\n", " nanmean\n", " nanmedian : equivalent to ``nanpercentile(..., 50)``\n", " percentile, median, mean\n", " nanquantile : equivalent to nanpercentile, except q in range [0, 1].\n", " \n", " Notes\n", " -----\n", " For more information please see `numpy.percentile`\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([[10., 7., 4.], [3., 2., 1.]])\n", " >>> a[0][1] = np.nan\n", " >>> a\n", " array([[10., nan, 4.],\n", " [ 3., 2., 1.]])\n", " >>> np.percentile(a, 50)\n", " nan\n", " >>> np.nanpercentile(a, 50)\n", " 3.0\n", " >>> np.nanpercentile(a, 50, axis=0)\n", " array([6.5, 2. , 2.5])\n", " >>> np.nanpercentile(a, 50, axis=1, keepdims=True)\n", " array([[7.],\n", " [2.]])\n", " >>> m = np.nanpercentile(a, 50, axis=0)\n", " >>> out = np.zeros_like(m)\n", " >>> np.nanpercentile(a, 50, axis=0, out=out)\n", " array([6.5, 2. , 2.5])\n", " >>> m\n", " array([6.5, 2. , 2.5])\n", " \n", " >>> b = a.copy()\n", " >>> np.nanpercentile(b, 50, axis=1, overwrite_input=True)\n", " array([7., 2.])\n", " >>> assert not np.all(a==b)\n", " \n", " References\n", " ----------\n", " .. [1] R. J. Hyndman and Y. Fan,\n", " \"Sample quantiles in statistical packages,\"\n", " The American Statistician, 50(4), pp. 361-365, 1996\n", " \n", " nanprod(a, axis=None, dtype=None, out=None, keepdims=<no value>, initial=<no value>, where=<no value>)\n", " Return the product of array elements over a given axis treating Not a\n", " Numbers (NaNs) as ones.\n", " \n", " One is returned for slices that are all-NaN or empty.\n", " \n", " .. versionadded:: 1.10.0\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Array containing numbers whose product is desired. If `a` is not an\n", " array, a conversion is attempted.\n", " axis : {int, tuple of int, None}, optional\n", " Axis or axes along which the product is computed. The default is to compute\n", " the product of the flattened array.\n", " dtype : data-type, optional\n", " The type of the returned array and of the accumulator in which the\n", " elements are summed. By default, the dtype of `a` is used. An\n", " exception is when `a` has an integer type with less precision than\n", " the platform (u)intp. In that case, the default will be either\n", " (u)int32 or (u)int64 depending on whether the platform is 32 or 64\n", " bits. For inexact inputs, dtype must be inexact.\n", " out : ndarray, optional\n", " Alternate output array in which to place the result. The default\n", " is ``None``. If provided, it must have the same shape as the\n", " expected output, but the type will be cast if necessary. See\n", " :ref:`ufuncs-output-type` for more details. The casting of NaN to integer\n", " can yield unexpected results.\n", " keepdims : bool, optional\n", " If True, the axes which are reduced are left in the result as\n", " dimensions with size one. With this option, the result will\n", " broadcast correctly against the original `arr`.\n", " initial : scalar, optional\n", " The starting value for this product. See `~numpy.ufunc.reduce`\n", " for details.\n", " \n", " .. versionadded:: 1.22.0\n", " where : array_like of bool, optional\n", " Elements to include in the product. See `~numpy.ufunc.reduce`\n", " for details.\n", " \n", " .. versionadded:: 1.22.0\n", " \n", " Returns\n", " -------\n", " nanprod : ndarray\n", " A new array holding the result is returned unless `out` is\n", " specified, in which case it is returned.\n", " \n", " See Also\n", " --------\n", " numpy.prod : Product across array propagating NaNs.\n", " isnan : Show which elements are NaN.\n", " \n", " Examples\n", " --------\n", " >>> np.nanprod(1)\n", " 1\n", " >>> np.nanprod([1])\n", " 1\n", " >>> np.nanprod([1, np.nan])\n", " 1.0\n", " >>> a = np.array([[1, 2], [3, np.nan]])\n", " >>> np.nanprod(a)\n", " 6.0\n", " >>> np.nanprod(a, axis=0)\n", " array([3., 2.])\n", " \n", " nanquantile(a, q, axis=None, out=None, overwrite_input=False, method='linear', keepdims=<no value>, *, interpolation=None)\n", " Compute the qth quantile of the data along the specified axis,\n", " while ignoring nan values.\n", " Returns the qth quantile(s) of the array elements.\n", " \n", " .. versionadded:: 1.15.0\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input array or object that can be converted to an array, containing\n", " nan values to be ignored\n", " q : array_like of float\n", " Quantile or sequence of quantiles to compute, which must be between\n", " 0 and 1 inclusive.\n", " axis : {int, tuple of int, None}, optional\n", " Axis or axes along which the quantiles are computed. The\n", " default is to compute the quantile(s) along a flattened\n", " version of the array.\n", " out : ndarray, optional\n", " Alternative output array in which to place the result. It must\n", " have the same shape and buffer length as the expected output,\n", " but the type (of the output) will be cast if necessary.\n", " overwrite_input : bool, optional\n", " If True, then allow the input array `a` to be modified by intermediate\n", " calculations, to save memory. In this case, the contents of the input\n", " `a` after this function completes is undefined.\n", " method : str, optional\n", " This parameter specifies the method to use for estimating the\n", " quantile. There are many different methods, some unique to NumPy.\n", " See the notes for explanation. The options sorted by their R type\n", " as summarized in the H&F paper [1]_ are:\n", " \n", " 1. 'inverted_cdf'\n", " 2. 'averaged_inverted_cdf'\n", " 3. 'closest_observation'\n", " 4. 'interpolated_inverted_cdf'\n", " 5. 'hazen'\n", " 6. 'weibull'\n", " 7. 'linear' (default)\n", " 8. 'median_unbiased'\n", " 9. 'normal_unbiased'\n", " \n", " The first three methods are discontinuous. NumPy further defines the\n", " following discontinuous variations of the default 'linear' (7.) option:\n", " \n", " * 'lower'\n", " * 'higher',\n", " * 'midpoint'\n", " * 'nearest'\n", " \n", " .. versionchanged:: 1.22.0\n", " This argument was previously called \"interpolation\" and only\n", " offered the \"linear\" default and last four options.\n", " \n", " keepdims : bool, optional\n", " If this is set to True, the axes which are reduced are left in\n", " the result as dimensions with size one. With this option, the\n", " result will broadcast correctly against the original array `a`.\n", " \n", " If this is anything but the default value it will be passed\n", " through (in the special case of an empty array) to the\n", " `mean` function of the underlying array. If the array is\n", " a sub-class and `mean` does not have the kwarg `keepdims` this\n", " will raise a RuntimeError.\n", " \n", " interpolation : str, optional\n", " Deprecated name for the method keyword argument.\n", " \n", " .. deprecated:: 1.22.0\n", " \n", " Returns\n", " -------\n", " quantile : scalar or ndarray\n", " If `q` is a single percentile and `axis=None`, then the result\n", " is a scalar. If multiple quantiles are given, first axis of\n", " the result corresponds to the quantiles. The other axes are\n", " the axes that remain after the reduction of `a`. If the input\n", " contains integers or floats smaller than ``float64``, the output\n", " data-type is ``float64``. Otherwise, the output data-type is the\n", " same as that of the input. If `out` is specified, that array is\n", " returned instead.\n", " \n", " See Also\n", " --------\n", " quantile\n", " nanmean, nanmedian\n", " nanmedian : equivalent to ``nanquantile(..., 0.5)``\n", " nanpercentile : same as nanquantile, but with q in the range [0, 100].\n", " \n", " Notes\n", " -----\n", " For more information please see `numpy.quantile`\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([[10., 7., 4.], [3., 2., 1.]])\n", " >>> a[0][1] = np.nan\n", " >>> a\n", " array([[10., nan, 4.],\n", " [ 3., 2., 1.]])\n", " >>> np.quantile(a, 0.5)\n", " nan\n", " >>> np.nanquantile(a, 0.5)\n", " 3.0\n", " >>> np.nanquantile(a, 0.5, axis=0)\n", " array([6.5, 2. , 2.5])\n", " >>> np.nanquantile(a, 0.5, axis=1, keepdims=True)\n", " array([[7.],\n", " [2.]])\n", " >>> m = np.nanquantile(a, 0.5, axis=0)\n", " >>> out = np.zeros_like(m)\n", " >>> np.nanquantile(a, 0.5, axis=0, out=out)\n", " array([6.5, 2. , 2.5])\n", " >>> m\n", " array([6.5, 2. , 2.5])\n", " >>> b = a.copy()\n", " >>> np.nanquantile(b, 0.5, axis=1, overwrite_input=True)\n", " array([7., 2.])\n", " >>> assert not np.all(a==b)\n", " \n", " References\n", " ----------\n", " .. [1] R. J. Hyndman and Y. Fan,\n", " \"Sample quantiles in statistical packages,\"\n", " The American Statistician, 50(4), pp. 361-365, 1996\n", " \n", " nanstd(a, axis=None, dtype=None, out=None, ddof=0, keepdims=<no value>, *, where=<no value>)\n", " Compute the standard deviation along the specified axis, while\n", " ignoring NaNs.\n", " \n", " Returns the standard deviation, a measure of the spread of a\n", " distribution, of the non-NaN array elements. The standard deviation is\n", " computed for the flattened array by default, otherwise over the\n", " specified axis.\n", " \n", " For all-NaN slices or slices with zero degrees of freedom, NaN is\n", " returned and a `RuntimeWarning` is raised.\n", " \n", " .. versionadded:: 1.8.0\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Calculate the standard deviation of the non-NaN values.\n", " axis : {int, tuple of int, None}, optional\n", " Axis or axes along which the standard deviation is computed. The default is\n", " to compute the standard deviation of the flattened array.\n", " dtype : dtype, optional\n", " Type to use in computing the standard deviation. For arrays of\n", " integer type the default is float64, for arrays of float types it\n", " is the same as the array type.\n", " out : ndarray, optional\n", " Alternative output array in which to place the result. It must have\n", " the same shape as the expected output but the type (of the\n", " calculated values) will be cast if necessary.\n", " ddof : int, optional\n", " Means Delta Degrees of Freedom. The divisor used in calculations\n", " is ``N - ddof``, where ``N`` represents the number of non-NaN\n", " elements. By default `ddof` is zero.\n", " \n", " keepdims : bool, optional\n", " If this is set to True, the axes which are reduced are left\n", " in the result as dimensions with size one. With this option,\n", " the result will broadcast correctly against the original `a`.\n", " \n", " If this value is anything but the default it is passed through\n", " as-is to the relevant functions of the sub-classes. If these\n", " functions do not have a `keepdims` kwarg, a RuntimeError will\n", " be raised.\n", " where : array_like of bool, optional\n", " Elements to include in the standard deviation.\n", " See `~numpy.ufunc.reduce` for details.\n", " \n", " .. versionadded:: 1.22.0\n", " \n", " Returns\n", " -------\n", " standard_deviation : ndarray, see dtype parameter above.\n", " If `out` is None, return a new array containing the standard\n", " deviation, otherwise return a reference to the output array. If\n", " ddof is >= the number of non-NaN elements in a slice or the slice\n", " contains only NaNs, then the result for that slice is NaN.\n", " \n", " See Also\n", " --------\n", " var, mean, std\n", " nanvar, nanmean\n", " :ref:`ufuncs-output-type`\n", " \n", " Notes\n", " -----\n", " The standard deviation is the square root of the average of the squared\n", " deviations from the mean: ``std = sqrt(mean(abs(x - x.mean())**2))``.\n", " \n", " The average squared deviation is normally calculated as\n", " ``x.sum() / N``, where ``N = len(x)``. If, however, `ddof` is\n", " specified, the divisor ``N - ddof`` is used instead. In standard\n", " statistical practice, ``ddof=1`` provides an unbiased estimator of the\n", " variance of the infinite population. ``ddof=0`` provides a maximum\n", " likelihood estimate of the variance for normally distributed variables.\n", " The standard deviation computed in this function is the square root of\n", " the estimated variance, so even with ``ddof=1``, it will not be an\n", " unbiased estimate of the standard deviation per se.\n", " \n", " Note that, for complex numbers, `std` takes the absolute value before\n", " squaring, so that the result is always real and nonnegative.\n", " \n", " For floating-point input, the *std* is computed using the same\n", " precision the input has. Depending on the input data, this can cause\n", " the results to be inaccurate, especially for float32 (see example\n", " below). Specifying a higher-accuracy accumulator using the `dtype`\n", " keyword can alleviate this issue.\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([[1, np.nan], [3, 4]])\n", " >>> np.nanstd(a)\n", " 1.247219128924647\n", " >>> np.nanstd(a, axis=0)\n", " array([1., 0.])\n", " >>> np.nanstd(a, axis=1)\n", " array([0., 0.5]) # may vary\n", " \n", " nansum(a, axis=None, dtype=None, out=None, keepdims=<no value>, initial=<no value>, where=<no value>)\n", " Return the sum of array elements over a given axis treating Not a\n", " Numbers (NaNs) as zero.\n", " \n", " In NumPy versions <= 1.9.0 Nan is returned for slices that are all-NaN or\n", " empty. In later versions zero is returned.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Array containing numbers whose sum is desired. If `a` is not an\n", " array, a conversion is attempted.\n", " axis : {int, tuple of int, None}, optional\n", " Axis or axes along which the sum is computed. The default is to compute the\n", " sum of the flattened array.\n", " dtype : data-type, optional\n", " The type of the returned array and of the accumulator in which the\n", " elements are summed. By default, the dtype of `a` is used. An\n", " exception is when `a` has an integer type with less precision than\n", " the platform (u)intp. In that case, the default will be either\n", " (u)int32 or (u)int64 depending on whether the platform is 32 or 64\n", " bits. For inexact inputs, dtype must be inexact.\n", " \n", " .. versionadded:: 1.8.0\n", " out : ndarray, optional\n", " Alternate output array in which to place the result. The default\n", " is ``None``. If provided, it must have the same shape as the\n", " expected output, but the type will be cast if necessary. See\n", " :ref:`ufuncs-output-type` for more details. The casting of NaN to integer\n", " can yield unexpected results.\n", " \n", " .. versionadded:: 1.8.0\n", " keepdims : bool, optional\n", " If this is set to True, the axes which are reduced are left\n", " in the result as dimensions with size one. With this option,\n", " the result will broadcast correctly against the original `a`.\n", " \n", " \n", " If the value is anything but the default, then\n", " `keepdims` will be passed through to the `mean` or `sum` methods\n", " of sub-classes of `ndarray`. If the sub-classes methods\n", " does not implement `keepdims` any exceptions will be raised.\n", " \n", " .. versionadded:: 1.8.0\n", " initial : scalar, optional\n", " Starting value for the sum. See `~numpy.ufunc.reduce` for details.\n", " \n", " .. versionadded:: 1.22.0\n", " where : array_like of bool, optional\n", " Elements to include in the sum. See `~numpy.ufunc.reduce` for details.\n", " \n", " .. versionadded:: 1.22.0\n", " \n", " Returns\n", " -------\n", " nansum : ndarray.\n", " A new array holding the result is returned unless `out` is\n", " specified, in which it is returned. The result has the same\n", " size as `a`, and the same shape as `a` if `axis` is not None\n", " or `a` is a 1-d array.\n", " \n", " See Also\n", " --------\n", " numpy.sum : Sum across array propagating NaNs.\n", " isnan : Show which elements are NaN.\n", " isfinite : Show which elements are not NaN or +/-inf.\n", " \n", " Notes\n", " -----\n", " If both positive and negative infinity are present, the sum will be Not\n", " A Number (NaN).\n", " \n", " Examples\n", " --------\n", " >>> np.nansum(1)\n", " 1\n", " >>> np.nansum([1])\n", " 1\n", " >>> np.nansum([1, np.nan])\n", " 1.0\n", " >>> a = np.array([[1, 1], [1, np.nan]])\n", " >>> np.nansum(a)\n", " 3.0\n", " >>> np.nansum(a, axis=0)\n", " array([2., 1.])\n", " >>> np.nansum([1, np.nan, np.inf])\n", " inf\n", " >>> np.nansum([1, np.nan, np.NINF])\n", " -inf\n", " >>> from numpy.testing import suppress_warnings\n", " >>> with suppress_warnings() as sup:\n", " ... sup.filter(RuntimeWarning)\n", " ... np.nansum([1, np.nan, np.inf, -np.inf]) # both +/- infinity present\n", " nan\n", " \n", " nanvar(a, axis=None, dtype=None, out=None, ddof=0, keepdims=<no value>, *, where=<no value>)\n", " Compute the variance along the specified axis, while ignoring NaNs.\n", " \n", " Returns the variance of the array elements, a measure of the spread of\n", " a distribution. The variance is computed for the flattened array by\n", " default, otherwise over the specified axis.\n", " \n", " For all-NaN slices or slices with zero degrees of freedom, NaN is\n", " returned and a `RuntimeWarning` is raised.\n", " \n", " .. versionadded:: 1.8.0\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Array containing numbers whose variance is desired. If `a` is not an\n", " array, a conversion is attempted.\n", " axis : {int, tuple of int, None}, optional\n", " Axis or axes along which the variance is computed. The default is to compute\n", " the variance of the flattened array.\n", " dtype : data-type, optional\n", " Type to use in computing the variance. For arrays of integer type\n", " the default is `float64`; for arrays of float types it is the same as\n", " the array type.\n", " out : ndarray, optional\n", " Alternate output array in which to place the result. It must have\n", " the same shape as the expected output, but the type is cast if\n", " necessary.\n", " ddof : int, optional\n", " \"Delta Degrees of Freedom\": the divisor used in the calculation is\n", " ``N - ddof``, where ``N`` represents the number of non-NaN\n", " elements. By default `ddof` is zero.\n", " keepdims : bool, optional\n", " If this is set to True, the axes which are reduced are left\n", " in the result as dimensions with size one. With this option,\n", " the result will broadcast correctly against the original `a`.\n", " where : array_like of bool, optional\n", " Elements to include in the variance. See `~numpy.ufunc.reduce` for\n", " details.\n", " \n", " .. versionadded:: 1.22.0\n", " \n", " Returns\n", " -------\n", " variance : ndarray, see dtype parameter above\n", " If `out` is None, return a new array containing the variance,\n", " otherwise return a reference to the output array. If ddof is >= the\n", " number of non-NaN elements in a slice or the slice contains only\n", " NaNs, then the result for that slice is NaN.\n", " \n", " See Also\n", " --------\n", " std : Standard deviation\n", " mean : Average\n", " var : Variance while not ignoring NaNs\n", " nanstd, nanmean\n", " :ref:`ufuncs-output-type`\n", " \n", " Notes\n", " -----\n", " The variance is the average of the squared deviations from the mean,\n", " i.e., ``var = mean(abs(x - x.mean())**2)``.\n", " \n", " The mean is normally calculated as ``x.sum() / N``, where ``N = len(x)``.\n", " If, however, `ddof` is specified, the divisor ``N - ddof`` is used\n", " instead. In standard statistical practice, ``ddof=1`` provides an\n", " unbiased estimator of the variance of a hypothetical infinite\n", " population. ``ddof=0`` provides a maximum likelihood estimate of the\n", " variance for normally distributed variables.\n", " \n", " Note that for complex numbers, the absolute value is taken before\n", " squaring, so that the result is always real and nonnegative.\n", " \n", " For floating-point input, the variance is computed using the same\n", " precision the input has. Depending on the input data, this can cause\n", " the results to be inaccurate, especially for `float32` (see example\n", " below). Specifying a higher-accuracy accumulator using the ``dtype``\n", " keyword can alleviate this issue.\n", " \n", " For this function to work on sub-classes of ndarray, they must define\n", " `sum` with the kwarg `keepdims`\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([[1, np.nan], [3, 4]])\n", " >>> np.nanvar(a)\n", " 1.5555555555555554\n", " >>> np.nanvar(a, axis=0)\n", " array([1., 0.])\n", " >>> np.nanvar(a, axis=1)\n", " array([0., 0.25]) # may vary\n", " \n", " ndim(a)\n", " Return the number of dimensions of an array.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input array. If it is not already an ndarray, a conversion is\n", " attempted.\n", " \n", " Returns\n", " -------\n", " number_of_dimensions : int\n", " The number of dimensions in `a`. Scalars are zero-dimensional.\n", " \n", " See Also\n", " --------\n", " ndarray.ndim : equivalent method\n", " shape : dimensions of array\n", " ndarray.shape : dimensions of array\n", " \n", " Examples\n", " --------\n", " >>> np.ndim([[1,2,3],[4,5,6]])\n", " 2\n", " >>> np.ndim(np.array([[1,2,3],[4,5,6]]))\n", " 2\n", " >>> np.ndim(1)\n", " 0\n", " \n", " nested_iters(...)\n", " nested_iters(op, axes, flags=None, op_flags=None, op_dtypes=None, order=\"K\", casting=\"safe\", buffersize=0)\n", " \n", " Create nditers for use in nested loops\n", " \n", " Create a tuple of `nditer` objects which iterate in nested loops over\n", " different axes of the op argument. The first iterator is used in the\n", " outermost loop, the last in the innermost loop. Advancing one will change\n", " the subsequent iterators to point at its new element.\n", " \n", " Parameters\n", " ----------\n", " op : ndarray or sequence of array_like\n", " The array(s) to iterate over.\n", " \n", " axes : list of list of int\n", " Each item is used as an \"op_axes\" argument to an nditer\n", " \n", " flags, op_flags, op_dtypes, order, casting, buffersize (optional)\n", " See `nditer` parameters of the same name\n", " \n", " Returns\n", " -------\n", " iters : tuple of nditer\n", " An nditer for each item in `axes`, outermost first\n", " \n", " See Also\n", " --------\n", " nditer\n", " \n", " Examples\n", " --------\n", " \n", " Basic usage. Note how y is the \"flattened\" version of\n", " [a[:, 0, :], a[:, 1, 0], a[:, 2, :]] since we specified\n", " the first iter's axes as [1]\n", " \n", " >>> a = np.arange(12).reshape(2, 3, 2)\n", " >>> i, j = np.nested_iters(a, [[1], [0, 2]], flags=[\"multi_index\"])\n", " >>> for x in i:\n", " ... print(i.multi_index)\n", " ... for y in j:\n", " ... print('', j.multi_index, y)\n", " (0,)\n", " (0, 0) 0\n", " (0, 1) 1\n", " (1, 0) 6\n", " (1, 1) 7\n", " (1,)\n", " (0, 0) 2\n", " (0, 1) 3\n", " (1, 0) 8\n", " (1, 1) 9\n", " (2,)\n", " (0, 0) 4\n", " (0, 1) 5\n", " (1, 0) 10\n", " (1, 1) 11\n", " \n", " nonzero(a)\n", " Return the indices of the elements that are non-zero.\n", " \n", " Returns a tuple of arrays, one for each dimension of `a`,\n", " containing the indices of the non-zero elements in that\n", " dimension. The values in `a` are always tested and returned in\n", " row-major, C-style order.\n", " \n", " To group the indices by element, rather than dimension, use `argwhere`,\n", " which returns a row for each non-zero element.\n", " \n", " .. note::\n", " \n", " When called on a zero-d array or scalar, ``nonzero(a)`` is treated\n", " as ``nonzero(atleast_1d(a))``.\n", " \n", " .. deprecated:: 1.17.0\n", " \n", " Use `atleast_1d` explicitly if this behavior is deliberate.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input array.\n", " \n", " Returns\n", " -------\n", " tuple_of_arrays : tuple\n", " Indices of elements that are non-zero.\n", " \n", " See Also\n", " --------\n", " flatnonzero :\n", " Return indices that are non-zero in the flattened version of the input\n", " array.\n", " ndarray.nonzero :\n", " Equivalent ndarray method.\n", " count_nonzero :\n", " Counts the number of non-zero elements in the input array.\n", " \n", " Notes\n", " -----\n", " While the nonzero values can be obtained with ``a[nonzero(a)]``, it is\n", " recommended to use ``x[x.astype(bool)]`` or ``x[x != 0]`` instead, which\n", " will correctly handle 0-d arrays.\n", " \n", " Examples\n", " --------\n", " >>> x = np.array([[3, 0, 0], [0, 4, 0], [5, 6, 0]])\n", " >>> x\n", " array([[3, 0, 0],\n", " [0, 4, 0],\n", " [5, 6, 0]])\n", " >>> np.nonzero(x)\n", " (array([0, 1, 2, 2]), array([0, 1, 0, 1]))\n", " \n", " >>> x[np.nonzero(x)]\n", " array([3, 4, 5, 6])\n", " >>> np.transpose(np.nonzero(x))\n", " array([[0, 0],\n", " [1, 1],\n", " [2, 0],\n", " [2, 1]])\n", " \n", " A common use for ``nonzero`` is to find the indices of an array, where\n", " a condition is True. Given an array `a`, the condition `a` > 3 is a\n", " boolean array and since False is interpreted as 0, np.nonzero(a > 3)\n", " yields the indices of the `a` where the condition is true.\n", " \n", " >>> a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])\n", " >>> a > 3\n", " array([[False, False, False],\n", " [ True, True, True],\n", " [ True, True, True]])\n", " >>> np.nonzero(a > 3)\n", " (array([1, 1, 1, 2, 2, 2]), array([0, 1, 2, 0, 1, 2]))\n", " \n", " Using this result to index `a` is equivalent to using the mask directly:\n", " \n", " >>> a[np.nonzero(a > 3)]\n", " array([4, 5, 6, 7, 8, 9])\n", " >>> a[a > 3] # prefer this spelling\n", " array([4, 5, 6, 7, 8, 9])\n", " \n", " ``nonzero`` can also be called as a method of the array.\n", " \n", " >>> (a > 3).nonzero()\n", " (array([1, 1, 1, 2, 2, 2]), array([0, 1, 2, 0, 1, 2]))\n", " \n", " obj2sctype(rep, default=None)\n", " Return the scalar dtype or NumPy equivalent of Python type of an object.\n", " \n", " Parameters\n", " ----------\n", " rep : any\n", " The object of which the type is returned.\n", " default : any, optional\n", " If given, this is returned for objects whose types can not be\n", " determined. If not given, None is returned for those objects.\n", " \n", " Returns\n", " -------\n", " dtype : dtype or Python type\n", " The data type of `rep`.\n", " \n", " See Also\n", " --------\n", " sctype2char, issctype, issubsctype, issubdtype, maximum_sctype\n", " \n", " Examples\n", " --------\n", " >>> np.obj2sctype(np.int32)\n", " <class 'numpy.int32'>\n", " >>> np.obj2sctype(np.array([1., 2.]))\n", " <class 'numpy.float64'>\n", " >>> np.obj2sctype(np.array([1.j]))\n", " <class 'numpy.complex128'>\n", " \n", " >>> np.obj2sctype(dict)\n", " <class 'numpy.object_'>\n", " >>> np.obj2sctype('string')\n", " \n", " >>> np.obj2sctype(1, default=list)\n", " <class 'list'>\n", " \n", " ones(shape, dtype=None, order='C', *, like=None)\n", " Return a new array of given shape and type, filled with ones.\n", " \n", " Parameters\n", " ----------\n", " shape : int or sequence of ints\n", " Shape of the new array, e.g., ``(2, 3)`` or ``2``.\n", " dtype : data-type, optional\n", " The desired data-type for the array, e.g., `numpy.int8`. Default is\n", " `numpy.float64`.\n", " order : {'C', 'F'}, optional, default: C\n", " Whether to store multi-dimensional data in row-major\n", " (C-style) or column-major (Fortran-style) order in\n", " memory.\n", " like : array_like, optional\n", " Reference object to allow the creation of arrays which are not\n", " NumPy arrays. If an array-like passed in as ``like`` supports\n", " the ``__array_function__`` protocol, the result will be defined\n", " by it. In this case, it ensures the creation of an array object\n", " compatible with that passed in via this argument.\n", " \n", " .. versionadded:: 1.20.0\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " Array of ones with the given shape, dtype, and order.\n", " \n", " See Also\n", " --------\n", " ones_like : Return an array of ones with shape and type of input.\n", " empty : Return a new uninitialized array.\n", " zeros : Return a new array setting values to zero.\n", " full : Return a new array of given shape filled with value.\n", " \n", " \n", " Examples\n", " --------\n", " >>> np.ones(5)\n", " array([1., 1., 1., 1., 1.])\n", " \n", " >>> np.ones((5,), dtype=int)\n", " array([1, 1, 1, 1, 1])\n", " \n", " >>> np.ones((2, 1))\n", " array([[1.],\n", " [1.]])\n", " \n", " >>> s = (2,2)\n", " >>> np.ones(s)\n", " array([[1., 1.],\n", " [1., 1.]])\n", " \n", " ones_like(a, dtype=None, order='K', subok=True, shape=None)\n", " Return an array of ones with the same shape and type as a given array.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " The shape and data-type of `a` define these same attributes of\n", " the returned array.\n", " dtype : data-type, optional\n", " Overrides the data type of the result.\n", " \n", " .. versionadded:: 1.6.0\n", " order : {'C', 'F', 'A', or 'K'}, optional\n", " Overrides the memory layout of the result. 'C' means C-order,\n", " 'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous,\n", " 'C' otherwise. 'K' means match the layout of `a` as closely\n", " as possible.\n", " \n", " .. versionadded:: 1.6.0\n", " subok : bool, optional.\n", " If True, then the newly created array will use the sub-class\n", " type of `a`, otherwise it will be a base-class array. Defaults\n", " to True.\n", " shape : int or sequence of ints, optional.\n", " Overrides the shape of the result. If order='K' and the number of\n", " dimensions is unchanged, will try to keep order, otherwise,\n", " order='C' is implied.\n", " \n", " .. versionadded:: 1.17.0\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " Array of ones with the same shape and type as `a`.\n", " \n", " See Also\n", " --------\n", " empty_like : Return an empty array with shape and type of input.\n", " zeros_like : Return an array of zeros with shape and type of input.\n", " full_like : Return a new array with shape of input filled with value.\n", " ones : Return a new array setting values to one.\n", " \n", " Examples\n", " --------\n", " >>> x = np.arange(6)\n", " >>> x = x.reshape((2, 3))\n", " >>> x\n", " array([[0, 1, 2],\n", " [3, 4, 5]])\n", " >>> np.ones_like(x)\n", " array([[1, 1, 1],\n", " [1, 1, 1]])\n", " \n", " >>> y = np.arange(3, dtype=float)\n", " >>> y\n", " array([0., 1., 2.])\n", " >>> np.ones_like(y)\n", " array([1., 1., 1.])\n", " \n", " outer(a, b, out=None)\n", " Compute the outer product of two vectors.\n", " \n", " Given two vectors, ``a = [a0, a1, ..., aM]`` and\n", " ``b = [b0, b1, ..., bN]``,\n", " the outer product [1]_ is::\n", " \n", " [[a0*b0 a0*b1 ... a0*bN ]\n", " [a1*b0 .\n", " [ ... .\n", " [aM*b0 aM*bN ]]\n", " \n", " Parameters\n", " ----------\n", " a : (M,) array_like\n", " First input vector. Input is flattened if\n", " not already 1-dimensional.\n", " b : (N,) array_like\n", " Second input vector. Input is flattened if\n", " not already 1-dimensional.\n", " out : (M, N) ndarray, optional\n", " A location where the result is stored\n", " \n", " .. versionadded:: 1.9.0\n", " \n", " Returns\n", " -------\n", " out : (M, N) ndarray\n", " ``out[i, j] = a[i] * b[j]``\n", " \n", " See also\n", " --------\n", " inner\n", " einsum : ``einsum('i,j->ij', a.ravel(), b.ravel())`` is the equivalent.\n", " ufunc.outer : A generalization to dimensions other than 1D and other\n", " operations. ``np.multiply.outer(a.ravel(), b.ravel())``\n", " is the equivalent.\n", " tensordot : ``np.tensordot(a.ravel(), b.ravel(), axes=((), ()))``\n", " is the equivalent.\n", " \n", " References\n", " ----------\n", " .. [1] : G. H. Golub and C. F. Van Loan, *Matrix Computations*, 3rd\n", " ed., Baltimore, MD, Johns Hopkins University Press, 1996,\n", " pg. 8.\n", " \n", " Examples\n", " --------\n", " Make a (*very* coarse) grid for computing a Mandelbrot set:\n", " \n", " >>> rl = np.outer(np.ones((5,)), np.linspace(-2, 2, 5))\n", " >>> rl\n", " array([[-2., -1., 0., 1., 2.],\n", " [-2., -1., 0., 1., 2.],\n", " [-2., -1., 0., 1., 2.],\n", " [-2., -1., 0., 1., 2.],\n", " [-2., -1., 0., 1., 2.]])\n", " >>> im = np.outer(1j*np.linspace(2, -2, 5), np.ones((5,)))\n", " >>> im\n", " array([[0.+2.j, 0.+2.j, 0.+2.j, 0.+2.j, 0.+2.j],\n", " [0.+1.j, 0.+1.j, 0.+1.j, 0.+1.j, 0.+1.j],\n", " [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n", " [0.-1.j, 0.-1.j, 0.-1.j, 0.-1.j, 0.-1.j],\n", " [0.-2.j, 0.-2.j, 0.-2.j, 0.-2.j, 0.-2.j]])\n", " >>> grid = rl + im\n", " >>> grid\n", " array([[-2.+2.j, -1.+2.j, 0.+2.j, 1.+2.j, 2.+2.j],\n", " [-2.+1.j, -1.+1.j, 0.+1.j, 1.+1.j, 2.+1.j],\n", " [-2.+0.j, -1.+0.j, 0.+0.j, 1.+0.j, 2.+0.j],\n", " [-2.-1.j, -1.-1.j, 0.-1.j, 1.-1.j, 2.-1.j],\n", " [-2.-2.j, -1.-2.j, 0.-2.j, 1.-2.j, 2.-2.j]])\n", " \n", " An example using a \"vector\" of letters:\n", " \n", " >>> x = np.array(['a', 'b', 'c'], dtype=object)\n", " >>> np.outer(x, [1, 2, 3])\n", " array([['a', 'aa', 'aaa'],\n", " ['b', 'bb', 'bbb'],\n", " ['c', 'cc', 'ccc']], dtype=object)\n", " \n", " packbits(...)\n", " packbits(a, /, axis=None, bitorder='big')\n", " \n", " Packs the elements of a binary-valued array into bits in a uint8 array.\n", " \n", " The result is padded to full bytes by inserting zero bits at the end.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " An array of integers or booleans whose elements should be packed to\n", " bits.\n", " axis : int, optional\n", " The dimension over which bit-packing is done.\n", " ``None`` implies packing the flattened array.\n", " bitorder : {'big', 'little'}, optional\n", " The order of the input bits. 'big' will mimic bin(val),\n", " ``[0, 0, 0, 0, 0, 0, 1, 1] => 3 = 0b00000011``, 'little' will\n", " reverse the order so ``[1, 1, 0, 0, 0, 0, 0, 0] => 3``.\n", " Defaults to 'big'.\n", " \n", " .. versionadded:: 1.17.0\n", " \n", " Returns\n", " -------\n", " packed : ndarray\n", " Array of type uint8 whose elements represent bits corresponding to the\n", " logical (0 or nonzero) value of the input elements. The shape of\n", " `packed` has the same number of dimensions as the input (unless `axis`\n", " is None, in which case the output is 1-D).\n", " \n", " See Also\n", " --------\n", " unpackbits: Unpacks elements of a uint8 array into a binary-valued output\n", " array.\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([[[1,0,1],\n", " ... [0,1,0]],\n", " ... [[1,1,0],\n", " ... [0,0,1]]])\n", " >>> b = np.packbits(a, axis=-1)\n", " >>> b\n", " array([[[160],\n", " [ 64]],\n", " [[192],\n", " [ 32]]], dtype=uint8)\n", " \n", " Note that in binary 160 = 1010 0000, 64 = 0100 0000, 192 = 1100 0000,\n", " and 32 = 0010 0000.\n", " \n", " pad(array, pad_width, mode='constant', **kwargs)\n", " Pad an array.\n", " \n", " Parameters\n", " ----------\n", " array : array_like of rank N\n", " The array to pad.\n", " pad_width : {sequence, array_like, int}\n", " Number of values padded to the edges of each axis.\n", " ``((before_1, after_1), ... (before_N, after_N))`` unique pad widths\n", " for each axis.\n", " ``(before, after)`` or ``((before, after),)`` yields same before\n", " and after pad for each axis.\n", " ``(pad,)`` or ``int`` is a shortcut for before = after = pad width\n", " for all axes.\n", " mode : str or function, optional\n", " One of the following string values or a user supplied function.\n", " \n", " 'constant' (default)\n", " Pads with a constant value.\n", " 'edge'\n", " Pads with the edge values of array.\n", " 'linear_ramp'\n", " Pads with the linear ramp between end_value and the\n", " array edge value.\n", " 'maximum'\n", " Pads with the maximum value of all or part of the\n", " vector along each axis.\n", " 'mean'\n", " Pads with the mean value of all or part of the\n", " vector along each axis.\n", " 'median'\n", " Pads with the median value of all or part of the\n", " vector along each axis.\n", " 'minimum'\n", " Pads with the minimum value of all or part of the\n", " vector along each axis.\n", " 'reflect'\n", " Pads with the reflection of the vector mirrored on\n", " the first and last values of the vector along each\n", " axis.\n", " 'symmetric'\n", " Pads with the reflection of the vector mirrored\n", " along the edge of the array.\n", " 'wrap'\n", " Pads with the wrap of the vector along the axis.\n", " The first values are used to pad the end and the\n", " end values are used to pad the beginning.\n", " 'empty'\n", " Pads with undefined values.\n", " \n", " .. versionadded:: 1.17\n", " \n", " <function>\n", " Padding function, see Notes.\n", " stat_length : sequence or int, optional\n", " Used in 'maximum', 'mean', 'median', and 'minimum'. Number of\n", " values at edge of each axis used to calculate the statistic value.\n", " \n", " ``((before_1, after_1), ... (before_N, after_N))`` unique statistic\n", " lengths for each axis.\n", " \n", " ``(before, after)`` or ``((before, after),)`` yields same before\n", " and after statistic lengths for each axis.\n", " \n", " ``(stat_length,)`` or ``int`` is a shortcut for\n", " ``before = after = statistic`` length for all axes.\n", " \n", " Default is ``None``, to use the entire axis.\n", " constant_values : sequence or scalar, optional\n", " Used in 'constant'. The values to set the padded values for each\n", " axis.\n", " \n", " ``((before_1, after_1), ... (before_N, after_N))`` unique pad constants\n", " for each axis.\n", " \n", " ``(before, after)`` or ``((before, after),)`` yields same before\n", " and after constants for each axis.\n", " \n", " ``(constant,)`` or ``constant`` is a shortcut for\n", " ``before = after = constant`` for all axes.\n", " \n", " Default is 0.\n", " end_values : sequence or scalar, optional\n", " Used in 'linear_ramp'. The values used for the ending value of the\n", " linear_ramp and that will form the edge of the padded array.\n", " \n", " ``((before_1, after_1), ... (before_N, after_N))`` unique end values\n", " for each axis.\n", " \n", " ``(before, after)`` or ``((before, after),)`` yields same before\n", " and after end values for each axis.\n", " \n", " ``(constant,)`` or ``constant`` is a shortcut for\n", " ``before = after = constant`` for all axes.\n", " \n", " Default is 0.\n", " reflect_type : {'even', 'odd'}, optional\n", " Used in 'reflect', and 'symmetric'. The 'even' style is the\n", " default with an unaltered reflection around the edge value. For\n", " the 'odd' style, the extended part of the array is created by\n", " subtracting the reflected values from two times the edge value.\n", " \n", " Returns\n", " -------\n", " pad : ndarray\n", " Padded array of rank equal to `array` with shape increased\n", " according to `pad_width`.\n", " \n", " Notes\n", " -----\n", " .. versionadded:: 1.7.0\n", " \n", " For an array with rank greater than 1, some of the padding of later\n", " axes is calculated from padding of previous axes. This is easiest to\n", " think about with a rank 2 array where the corners of the padded array\n", " are calculated by using padded values from the first axis.\n", " \n", " The padding function, if used, should modify a rank 1 array in-place. It\n", " has the following signature::\n", " \n", " padding_func(vector, iaxis_pad_width, iaxis, kwargs)\n", " \n", " where\n", " \n", " vector : ndarray\n", " A rank 1 array already padded with zeros. Padded values are\n", " vector[:iaxis_pad_width[0]] and vector[-iaxis_pad_width[1]:].\n", " iaxis_pad_width : tuple\n", " A 2-tuple of ints, iaxis_pad_width[0] represents the number of\n", " values padded at the beginning of vector where\n", " iaxis_pad_width[1] represents the number of values padded at\n", " the end of vector.\n", " iaxis : int\n", " The axis currently being calculated.\n", " kwargs : dict\n", " Any keyword arguments the function requires.\n", " \n", " Examples\n", " --------\n", " >>> a = [1, 2, 3, 4, 5]\n", " >>> np.pad(a, (2, 3), 'constant', constant_values=(4, 6))\n", " array([4, 4, 1, ..., 6, 6, 6])\n", " \n", " >>> np.pad(a, (2, 3), 'edge')\n", " array([1, 1, 1, ..., 5, 5, 5])\n", " \n", " >>> np.pad(a, (2, 3), 'linear_ramp', end_values=(5, -4))\n", " array([ 5, 3, 1, 2, 3, 4, 5, 2, -1, -4])\n", " \n", " >>> np.pad(a, (2,), 'maximum')\n", " array([5, 5, 1, 2, 3, 4, 5, 5, 5])\n", " \n", " >>> np.pad(a, (2,), 'mean')\n", " array([3, 3, 1, 2, 3, 4, 5, 3, 3])\n", " \n", " >>> np.pad(a, (2,), 'median')\n", " array([3, 3, 1, 2, 3, 4, 5, 3, 3])\n", " \n", " >>> a = [[1, 2], [3, 4]]\n", " >>> np.pad(a, ((3, 2), (2, 3)), 'minimum')\n", " array([[1, 1, 1, 2, 1, 1, 1],\n", " [1, 1, 1, 2, 1, 1, 1],\n", " [1, 1, 1, 2, 1, 1, 1],\n", " [1, 1, 1, 2, 1, 1, 1],\n", " [3, 3, 3, 4, 3, 3, 3],\n", " [1, 1, 1, 2, 1, 1, 1],\n", " [1, 1, 1, 2, 1, 1, 1]])\n", " \n", " >>> a = [1, 2, 3, 4, 5]\n", " >>> np.pad(a, (2, 3), 'reflect')\n", " array([3, 2, 1, 2, 3, 4, 5, 4, 3, 2])\n", " \n", " >>> np.pad(a, (2, 3), 'reflect', reflect_type='odd')\n", " array([-1, 0, 1, 2, 3, 4, 5, 6, 7, 8])\n", " \n", " >>> np.pad(a, (2, 3), 'symmetric')\n", " array([2, 1, 1, 2, 3, 4, 5, 5, 4, 3])\n", " \n", " >>> np.pad(a, (2, 3), 'symmetric', reflect_type='odd')\n", " array([0, 1, 1, 2, 3, 4, 5, 5, 6, 7])\n", " \n", " >>> np.pad(a, (2, 3), 'wrap')\n", " array([4, 5, 1, 2, 3, 4, 5, 1, 2, 3])\n", " \n", " >>> def pad_with(vector, pad_width, iaxis, kwargs):\n", " ... pad_value = kwargs.get('padder', 10)\n", " ... vector[:pad_width[0]] = pad_value\n", " ... vector[-pad_width[1]:] = pad_value\n", " >>> a = np.arange(6)\n", " >>> a = a.reshape((2, 3))\n", " >>> np.pad(a, 2, pad_with)\n", " array([[10, 10, 10, 10, 10, 10, 10],\n", " [10, 10, 10, 10, 10, 10, 10],\n", " [10, 10, 0, 1, 2, 10, 10],\n", " [10, 10, 3, 4, 5, 10, 10],\n", " [10, 10, 10, 10, 10, 10, 10],\n", " [10, 10, 10, 10, 10, 10, 10]])\n", " >>> np.pad(a, 2, pad_with, padder=100)\n", " array([[100, 100, 100, 100, 100, 100, 100],\n", " [100, 100, 100, 100, 100, 100, 100],\n", " [100, 100, 0, 1, 2, 100, 100],\n", " [100, 100, 3, 4, 5, 100, 100],\n", " [100, 100, 100, 100, 100, 100, 100],\n", " [100, 100, 100, 100, 100, 100, 100]])\n", " \n", " partition(a, kth, axis=-1, kind='introselect', order=None)\n", " Return a partitioned copy of an array.\n", " \n", " Creates a copy of the array with its elements rearranged in such a\n", " way that the value of the element in k-th position is in the position\n", " the value would be in a sorted array. In the partitioned array, all\n", " elements before the k-th element are less than or equal to that\n", " element, and all the elements after the k-th element are greater than\n", " or equal to that element. The ordering of the elements in the two\n", " partitions is undefined.\n", " \n", " .. versionadded:: 1.8.0\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Array to be sorted.\n", " kth : int or sequence of ints\n", " Element index to partition by. The k-th value of the element\n", " will be in its final sorted position and all smaller elements\n", " will be moved before it and all equal or greater elements behind\n", " it. The order of all elements in the partitions is undefined. If\n", " provided with a sequence of k-th it will partition all elements\n", " indexed by k-th of them into their sorted position at once.\n", " \n", " .. deprecated:: 1.22.0\n", " Passing booleans as index is deprecated.\n", " axis : int or None, optional\n", " Axis along which to sort. If None, the array is flattened before\n", " sorting. The default is -1, which sorts along the last axis.\n", " kind : {'introselect'}, optional\n", " Selection algorithm. Default is 'introselect'.\n", " order : str or list of str, optional\n", " When `a` is an array with fields defined, this argument\n", " specifies which fields to compare first, second, etc. A single\n", " field can be specified as a string. Not all fields need be\n", " specified, but unspecified fields will still be used, in the\n", " order in which they come up in the dtype, to break ties.\n", " \n", " Returns\n", " -------\n", " partitioned_array : ndarray\n", " Array of the same type and shape as `a`.\n", " \n", " See Also\n", " --------\n", " ndarray.partition : Method to sort an array in-place.\n", " argpartition : Indirect partition.\n", " sort : Full sorting\n", " \n", " Notes\n", " -----\n", " The various selection algorithms are characterized by their average\n", " speed, worst case performance, work space size, and whether they are\n", " stable. A stable sort keeps items with the same key in the same\n", " relative order. The available algorithms have the following\n", " properties:\n", " \n", " ================= ======= ============= ============ =======\n", " kind speed worst case work space stable\n", " ================= ======= ============= ============ =======\n", " 'introselect' 1 O(n) 0 no\n", " ================= ======= ============= ============ =======\n", " \n", " All the partition algorithms make temporary copies of the data when\n", " partitioning along any but the last axis. Consequently,\n", " partitioning along the last axis is faster and uses less space than\n", " partitioning along any other axis.\n", " \n", " The sort order for complex numbers is lexicographic. If both the\n", " real and imaginary parts are non-nan then the order is determined by\n", " the real parts except when they are equal, in which case the order\n", " is determined by the imaginary parts.\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([7, 1, 7, 7, 1, 5, 7, 2, 3, 2, 6, 2, 3, 0])\n", " >>> p = np.partition(a, 4)\n", " >>> p\n", " array([0, 1, 2, 1, 2, 5, 2, 3, 3, 6, 7, 7, 7, 7])\n", " \n", " ``p[4]`` is 2; all elements in ``p[:4]`` are less than or equal\n", " to ``p[4]``, and all elements in ``p[5:]`` are greater than or\n", " equal to ``p[4]``. The partition is::\n", " \n", " [0, 1, 2, 1], [2], [5, 2, 3, 3, 6, 7, 7, 7, 7]\n", " \n", " The next example shows the use of multiple values passed to `kth`.\n", " \n", " >>> p2 = np.partition(a, (4, 8))\n", " >>> p2\n", " array([0, 1, 2, 1, 2, 3, 3, 2, 5, 6, 7, 7, 7, 7])\n", " \n", " ``p2[4]`` is 2 and ``p2[8]`` is 5. All elements in ``p2[:4]``\n", " are less than or equal to ``p2[4]``, all elements in ``p2[5:8]``\n", " are greater than or equal to ``p2[4]`` and less than or equal to\n", " ``p2[8]``, and all elements in ``p2[9:]`` are greater than or\n", " equal to ``p2[8]``. The partition is::\n", " \n", " [0, 1, 2, 1], [2], [3, 3, 2], [5], [6, 7, 7, 7, 7]\n", " \n", " percentile(a, q, axis=None, out=None, overwrite_input=False, method='linear', keepdims=False, *, interpolation=None)\n", " Compute the q-th percentile of the data along the specified axis.\n", " \n", " Returns the q-th percentile(s) of the array elements.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input array or object that can be converted to an array.\n", " q : array_like of float\n", " Percentile or sequence of percentiles to compute, which must be between\n", " 0 and 100 inclusive.\n", " axis : {int, tuple of int, None}, optional\n", " Axis or axes along which the percentiles are computed. The\n", " default is to compute the percentile(s) along a flattened\n", " version of the array.\n", " \n", " .. versionchanged:: 1.9.0\n", " A tuple of axes is supported\n", " out : ndarray, optional\n", " Alternative output array in which to place the result. It must\n", " have the same shape and buffer length as the expected output,\n", " but the type (of the output) will be cast if necessary.\n", " overwrite_input : bool, optional\n", " If True, then allow the input array `a` to be modified by intermediate\n", " calculations, to save memory. In this case, the contents of the input\n", " `a` after this function completes is undefined.\n", " method : str, optional\n", " This parameter specifies the method to use for estimating the\n", " percentile. There are many different methods, some unique to NumPy.\n", " See the notes for explanation. The options sorted by their R type\n", " as summarized in the H&F paper [1]_ are:\n", " \n", " 1. 'inverted_cdf'\n", " 2. 'averaged_inverted_cdf'\n", " 3. 'closest_observation'\n", " 4. 'interpolated_inverted_cdf'\n", " 5. 'hazen'\n", " 6. 'weibull'\n", " 7. 'linear' (default)\n", " 8. 'median_unbiased'\n", " 9. 'normal_unbiased'\n", " \n", " The first three methods are discontinuous. NumPy further defines the\n", " following discontinuous variations of the default 'linear' (7.) option:\n", " \n", " * 'lower'\n", " * 'higher',\n", " * 'midpoint'\n", " * 'nearest'\n", " \n", " .. versionchanged:: 1.22.0\n", " This argument was previously called \"interpolation\" and only\n", " offered the \"linear\" default and last four options.\n", " \n", " keepdims : bool, optional\n", " If this is set to True, the axes which are reduced are left in\n", " the result as dimensions with size one. With this option, the\n", " result will broadcast correctly against the original array `a`.\n", " \n", " .. versionadded:: 1.9.0\n", " \n", " interpolation : str, optional\n", " Deprecated name for the method keyword argument.\n", " \n", " .. deprecated:: 1.22.0\n", " \n", " Returns\n", " -------\n", " percentile : scalar or ndarray\n", " If `q` is a single percentile and `axis=None`, then the result\n", " is a scalar. If multiple percentiles are given, first axis of\n", " the result corresponds to the percentiles. The other axes are\n", " the axes that remain after the reduction of `a`. If the input\n", " contains integers or floats smaller than ``float64``, the output\n", " data-type is ``float64``. Otherwise, the output data-type is the\n", " same as that of the input. If `out` is specified, that array is\n", " returned instead.\n", " \n", " See Also\n", " --------\n", " mean\n", " median : equivalent to ``percentile(..., 50)``\n", " nanpercentile\n", " quantile : equivalent to percentile, except q in the range [0, 1].\n", " \n", " Notes\n", " -----\n", " Given a vector ``V`` of length ``n``, the q-th percentile of ``V`` is\n", " the value ``q/100`` of the way from the minimum to the maximum in a\n", " sorted copy of ``V``. The values and distances of the two nearest\n", " neighbors as well as the `method` parameter will determine the\n", " percentile if the normalized ranking does not match the location of\n", " ``q`` exactly. This function is the same as the median if ``q=50``, the\n", " same as the minimum if ``q=0`` and the same as the maximum if\n", " ``q=100``.\n", " \n", " The optional `method` parameter specifies the method to use when the\n", " desired percentile lies between two indexes ``i`` and ``j = i + 1``.\n", " In that case, we first determine ``i + g``, a virtual index that lies\n", " between ``i`` and ``j``, where ``i`` is the floor and ``g`` is the\n", " fractional part of the index. The final result is, then, an interpolation\n", " of ``a[i]`` and ``a[j]`` based on ``g``. During the computation of ``g``,\n", " ``i`` and ``j`` are modified using correction constants ``alpha`` and\n", " ``beta`` whose choices depend on the ``method`` used. Finally, note that\n", " since Python uses 0-based indexing, the code subtracts another 1 from the\n", " index internally.\n", " \n", " The following formula determines the virtual index ``i + g``, the location \n", " of the percentile in the sorted sample:\n", " \n", " .. math::\n", " i + g = (q / 100) * ( n - alpha - beta + 1 ) + alpha\n", " \n", " The different methods then work as follows\n", " \n", " inverted_cdf:\n", " method 1 of H&F [1]_.\n", " This method gives discontinuous results:\n", " \n", " * if g > 0 ; then take j\n", " * if g = 0 ; then take i\n", " \n", " averaged_inverted_cdf:\n", " method 2 of H&F [1]_.\n", " This method give discontinuous results:\n", " \n", " * if g > 0 ; then take j\n", " * if g = 0 ; then average between bounds\n", " \n", " closest_observation:\n", " method 3 of H&F [1]_.\n", " This method give discontinuous results:\n", " \n", " * if g > 0 ; then take j\n", " * if g = 0 and index is odd ; then take j\n", " * if g = 0 and index is even ; then take i\n", " \n", " interpolated_inverted_cdf:\n", " method 4 of H&F [1]_.\n", " This method give continuous results using:\n", " \n", " * alpha = 0\n", " * beta = 1\n", " \n", " hazen:\n", " method 5 of H&F [1]_.\n", " This method give continuous results using:\n", " \n", " * alpha = 1/2\n", " * beta = 1/2\n", " \n", " weibull:\n", " method 6 of H&F [1]_.\n", " This method give continuous results using:\n", " \n", " * alpha = 0\n", " * beta = 0\n", " \n", " linear:\n", " method 7 of H&F [1]_.\n", " This method give continuous results using:\n", " \n", " * alpha = 1\n", " * beta = 1\n", " \n", " median_unbiased:\n", " method 8 of H&F [1]_.\n", " This method is probably the best method if the sample\n", " distribution function is unknown (see reference).\n", " This method give continuous results using:\n", " \n", " * alpha = 1/3\n", " * beta = 1/3\n", " \n", " normal_unbiased:\n", " method 9 of H&F [1]_.\n", " This method is probably the best method if the sample\n", " distribution function is known to be normal.\n", " This method give continuous results using:\n", " \n", " * alpha = 3/8\n", " * beta = 3/8\n", " \n", " lower:\n", " NumPy method kept for backwards compatibility.\n", " Takes ``i`` as the interpolation point.\n", " \n", " higher:\n", " NumPy method kept for backwards compatibility.\n", " Takes ``j`` as the interpolation point.\n", " \n", " nearest:\n", " NumPy method kept for backwards compatibility.\n", " Takes ``i`` or ``j``, whichever is nearest.\n", " \n", " midpoint:\n", " NumPy method kept for backwards compatibility.\n", " Uses ``(i + j) / 2``.\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([[10, 7, 4], [3, 2, 1]])\n", " >>> a\n", " array([[10, 7, 4],\n", " [ 3, 2, 1]])\n", " >>> np.percentile(a, 50)\n", " 3.5\n", " >>> np.percentile(a, 50, axis=0)\n", " array([6.5, 4.5, 2.5])\n", " >>> np.percentile(a, 50, axis=1)\n", " array([7., 2.])\n", " >>> np.percentile(a, 50, axis=1, keepdims=True)\n", " array([[7.],\n", " [2.]])\n", " \n", " >>> m = np.percentile(a, 50, axis=0)\n", " >>> out = np.zeros_like(m)\n", " >>> np.percentile(a, 50, axis=0, out=out)\n", " array([6.5, 4.5, 2.5])\n", " >>> m\n", " array([6.5, 4.5, 2.5])\n", " \n", " >>> b = a.copy()\n", " >>> np.percentile(b, 50, axis=1, overwrite_input=True)\n", " array([7., 2.])\n", " >>> assert not np.all(a == b)\n", " \n", " The different methods can be visualized graphically:\n", " \n", " .. plot::\n", " \n", " import matplotlib.pyplot as plt\n", " \n", " a = np.arange(4)\n", " p = np.linspace(0, 100, 6001)\n", " ax = plt.gca()\n", " lines = [\n", " ('linear', '-', 'C0'),\n", " ('inverted_cdf', ':', 'C1'),\n", " # Almost the same as `inverted_cdf`:\n", " ('averaged_inverted_cdf', '-.', 'C1'),\n", " ('closest_observation', ':', 'C2'),\n", " ('interpolated_inverted_cdf', '--', 'C1'),\n", " ('hazen', '--', 'C3'),\n", " ('weibull', '-.', 'C4'),\n", " ('median_unbiased', '--', 'C5'),\n", " ('normal_unbiased', '-.', 'C6'),\n", " ]\n", " for method, style, color in lines:\n", " ax.plot(\n", " p, np.percentile(a, p, method=method),\n", " label=method, linestyle=style, color=color)\n", " ax.set(\n", " title='Percentiles for different methods and data: ' + str(a),\n", " xlabel='Percentile',\n", " ylabel='Estimated percentile value',\n", " yticks=a)\n", " ax.legend()\n", " plt.show()\n", " \n", " References\n", " ----------\n", " .. [1] R. J. Hyndman and Y. Fan,\n", " \"Sample quantiles in statistical packages,\"\n", " The American Statistician, 50(4), pp. 361-365, 1996\n", " \n", " piecewise(x, condlist, funclist, *args, **kw)\n", " Evaluate a piecewise-defined function.\n", " \n", " Given a set of conditions and corresponding functions, evaluate each\n", " function on the input data wherever its condition is true.\n", " \n", " Parameters\n", " ----------\n", " x : ndarray or scalar\n", " The input domain.\n", " condlist : list of bool arrays or bool scalars\n", " Each boolean array corresponds to a function in `funclist`. Wherever\n", " `condlist[i]` is True, `funclist[i](x)` is used as the output value.\n", " \n", " Each boolean array in `condlist` selects a piece of `x`,\n", " and should therefore be of the same shape as `x`.\n", " \n", " The length of `condlist` must correspond to that of `funclist`.\n", " If one extra function is given, i.e. if\n", " ``len(funclist) == len(condlist) + 1``, then that extra function\n", " is the default value, used wherever all conditions are false.\n", " funclist : list of callables, f(x,*args,**kw), or scalars\n", " Each function is evaluated over `x` wherever its corresponding\n", " condition is True. It should take a 1d array as input and give an 1d\n", " array or a scalar value as output. If, instead of a callable,\n", " a scalar is provided then a constant function (``lambda x: scalar``) is\n", " assumed.\n", " args : tuple, optional\n", " Any further arguments given to `piecewise` are passed to the functions\n", " upon execution, i.e., if called ``piecewise(..., ..., 1, 'a')``, then\n", " each function is called as ``f(x, 1, 'a')``.\n", " kw : dict, optional\n", " Keyword arguments used in calling `piecewise` are passed to the\n", " functions upon execution, i.e., if called\n", " ``piecewise(..., ..., alpha=1)``, then each function is called as\n", " ``f(x, alpha=1)``.\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " The output is the same shape and type as x and is found by\n", " calling the functions in `funclist` on the appropriate portions of `x`,\n", " as defined by the boolean arrays in `condlist`. Portions not covered\n", " by any condition have a default value of 0.\n", " \n", " \n", " See Also\n", " --------\n", " choose, select, where\n", " \n", " Notes\n", " -----\n", " This is similar to choose or select, except that functions are\n", " evaluated on elements of `x` that satisfy the corresponding condition from\n", " `condlist`.\n", " \n", " The result is::\n", " \n", " |--\n", " |funclist[0](x[condlist[0]])\n", " out = |funclist[1](x[condlist[1]])\n", " |...\n", " |funclist[n2](x[condlist[n2]])\n", " |--\n", " \n", " Examples\n", " --------\n", " Define the sigma function, which is -1 for ``x < 0`` and +1 for ``x >= 0``.\n", " \n", " >>> x = np.linspace(-2.5, 2.5, 6)\n", " >>> np.piecewise(x, [x < 0, x >= 0], [-1, 1])\n", " array([-1., -1., -1., 1., 1., 1.])\n", " \n", " Define the absolute value, which is ``-x`` for ``x <0`` and ``x`` for\n", " ``x >= 0``.\n", " \n", " >>> np.piecewise(x, [x < 0, x >= 0], [lambda x: -x, lambda x: x])\n", " array([2.5, 1.5, 0.5, 0.5, 1.5, 2.5])\n", " \n", " Apply the same function to a scalar value.\n", " \n", " >>> y = -2\n", " >>> np.piecewise(y, [y < 0, y >= 0], [lambda x: -x, lambda x: x])\n", " array(2)\n", " \n", " place(arr, mask, vals)\n", " Change elements of an array based on conditional and input values.\n", " \n", " Similar to ``np.copyto(arr, vals, where=mask)``, the difference is that\n", " `place` uses the first N elements of `vals`, where N is the number of\n", " True values in `mask`, while `copyto` uses the elements where `mask`\n", " is True.\n", " \n", " Note that `extract` does the exact opposite of `place`.\n", " \n", " Parameters\n", " ----------\n", " arr : ndarray\n", " Array to put data into.\n", " mask : array_like\n", " Boolean mask array. Must have the same size as `a`.\n", " vals : 1-D sequence\n", " Values to put into `a`. Only the first N elements are used, where\n", " N is the number of True values in `mask`. If `vals` is smaller\n", " than N, it will be repeated, and if elements of `a` are to be masked,\n", " this sequence must be non-empty.\n", " \n", " See Also\n", " --------\n", " copyto, put, take, extract\n", " \n", " Examples\n", " --------\n", " >>> arr = np.arange(6).reshape(2, 3)\n", " >>> np.place(arr, arr>2, [44, 55])\n", " >>> arr\n", " array([[ 0, 1, 2],\n", " [44, 55, 44]])\n", " \n", " poly(seq_of_zeros)\n", " Find the coefficients of a polynomial with the given sequence of roots.\n", " \n", " .. note::\n", " This forms part of the old polynomial API. Since version 1.4, the\n", " new polynomial API defined in `numpy.polynomial` is preferred.\n", " A summary of the differences can be found in the\n", " :doc:`transition guide </reference/routines.polynomials>`.\n", " \n", " Returns the coefficients of the polynomial whose leading coefficient\n", " is one for the given sequence of zeros (multiple roots must be included\n", " in the sequence as many times as their multiplicity; see Examples).\n", " A square matrix (or array, which will be treated as a matrix) can also\n", " be given, in which case the coefficients of the characteristic polynomial\n", " of the matrix are returned.\n", " \n", " Parameters\n", " ----------\n", " seq_of_zeros : array_like, shape (N,) or (N, N)\n", " A sequence of polynomial roots, or a square array or matrix object.\n", " \n", " Returns\n", " -------\n", " c : ndarray\n", " 1D array of polynomial coefficients from highest to lowest degree:\n", " \n", " ``c[0] * x**(N) + c[1] * x**(N-1) + ... + c[N-1] * x + c[N]``\n", " where c[0] always equals 1.\n", " \n", " Raises\n", " ------\n", " ValueError\n", " If input is the wrong shape (the input must be a 1-D or square\n", " 2-D array).\n", " \n", " See Also\n", " --------\n", " polyval : Compute polynomial values.\n", " roots : Return the roots of a polynomial.\n", " polyfit : Least squares polynomial fit.\n", " poly1d : A one-dimensional polynomial class.\n", " \n", " Notes\n", " -----\n", " Specifying the roots of a polynomial still leaves one degree of\n", " freedom, typically represented by an undetermined leading\n", " coefficient. [1]_ In the case of this function, that coefficient -\n", " the first one in the returned array - is always taken as one. (If\n", " for some reason you have one other point, the only automatic way\n", " presently to leverage that information is to use ``polyfit``.)\n", " \n", " The characteristic polynomial, :math:`p_a(t)`, of an `n`-by-`n`\n", " matrix **A** is given by\n", " \n", " :math:`p_a(t) = \\mathrm{det}(t\\, \\mathbf{I} - \\mathbf{A})`,\n", " \n", " where **I** is the `n`-by-`n` identity matrix. [2]_\n", " \n", " References\n", " ----------\n", " .. [1] M. Sullivan and M. Sullivan, III, \"Algebra and Trignometry,\n", " Enhanced With Graphing Utilities,\" Prentice-Hall, pg. 318, 1996.\n", " \n", " .. [2] G. Strang, \"Linear Algebra and Its Applications, 2nd Edition,\"\n", " Academic Press, pg. 182, 1980.\n", " \n", " Examples\n", " --------\n", " Given a sequence of a polynomial's zeros:\n", " \n", " >>> np.poly((0, 0, 0)) # Multiple root example\n", " array([1., 0., 0., 0.])\n", " \n", " The line above represents z**3 + 0*z**2 + 0*z + 0.\n", " \n", " >>> np.poly((-1./2, 0, 1./2))\n", " array([ 1. , 0. , -0.25, 0. ])\n", " \n", " The line above represents z**3 - z/4\n", " \n", " >>> np.poly((np.random.random(1)[0], 0, np.random.random(1)[0]))\n", " array([ 1. , -0.77086955, 0.08618131, 0. ]) # random\n", " \n", " Given a square array object:\n", " \n", " >>> P = np.array([[0, 1./3], [-1./2, 0]])\n", " >>> np.poly(P)\n", " array([1. , 0. , 0.16666667])\n", " \n", " Note how in all cases the leading coefficient is always 1.\n", " \n", " polyadd(a1, a2)\n", " Find the sum of two polynomials.\n", " \n", " .. note::\n", " This forms part of the old polynomial API. Since version 1.4, the\n", " new polynomial API defined in `numpy.polynomial` is preferred.\n", " A summary of the differences can be found in the\n", " :doc:`transition guide </reference/routines.polynomials>`.\n", " \n", " Returns the polynomial resulting from the sum of two input polynomials.\n", " Each input must be either a poly1d object or a 1D sequence of polynomial\n", " coefficients, from highest to lowest degree.\n", " \n", " Parameters\n", " ----------\n", " a1, a2 : array_like or poly1d object\n", " Input polynomials.\n", " \n", " Returns\n", " -------\n", " out : ndarray or poly1d object\n", " The sum of the inputs. If either input is a poly1d object, then the\n", " output is also a poly1d object. Otherwise, it is a 1D array of\n", " polynomial coefficients from highest to lowest degree.\n", " \n", " See Also\n", " --------\n", " poly1d : A one-dimensional polynomial class.\n", " poly, polyadd, polyder, polydiv, polyfit, polyint, polysub, polyval\n", " \n", " Examples\n", " --------\n", " >>> np.polyadd([1, 2], [9, 5, 4])\n", " array([9, 6, 6])\n", " \n", " Using poly1d objects:\n", " \n", " >>> p1 = np.poly1d([1, 2])\n", " >>> p2 = np.poly1d([9, 5, 4])\n", " >>> print(p1)\n", " 1 x + 2\n", " >>> print(p2)\n", " 2\n", " 9 x + 5 x + 4\n", " >>> print(np.polyadd(p1, p2))\n", " 2\n", " 9 x + 6 x + 6\n", " \n", " polyder(p, m=1)\n", " Return the derivative of the specified order of a polynomial.\n", " \n", " .. note::\n", " This forms part of the old polynomial API. Since version 1.4, the\n", " new polynomial API defined in `numpy.polynomial` is preferred.\n", " A summary of the differences can be found in the\n", " :doc:`transition guide </reference/routines.polynomials>`.\n", " \n", " Parameters\n", " ----------\n", " p : poly1d or sequence\n", " Polynomial to differentiate.\n", " A sequence is interpreted as polynomial coefficients, see `poly1d`.\n", " m : int, optional\n", " Order of differentiation (default: 1)\n", " \n", " Returns\n", " -------\n", " der : poly1d\n", " A new polynomial representing the derivative.\n", " \n", " See Also\n", " --------\n", " polyint : Anti-derivative of a polynomial.\n", " poly1d : Class for one-dimensional polynomials.\n", " \n", " Examples\n", " --------\n", " The derivative of the polynomial :math:`x^3 + x^2 + x^1 + 1` is:\n", " \n", " >>> p = np.poly1d([1,1,1,1])\n", " >>> p2 = np.polyder(p)\n", " >>> p2\n", " poly1d([3, 2, 1])\n", " \n", " which evaluates to:\n", " \n", " >>> p2(2.)\n", " 17.0\n", " \n", " We can verify this, approximating the derivative with\n", " ``(f(x + h) - f(x))/h``:\n", " \n", " >>> (p(2. + 0.001) - p(2.)) / 0.001\n", " 17.007000999997857\n", " \n", " The fourth-order derivative of a 3rd-order polynomial is zero:\n", " \n", " >>> np.polyder(p, 2)\n", " poly1d([6, 2])\n", " >>> np.polyder(p, 3)\n", " poly1d([6])\n", " >>> np.polyder(p, 4)\n", " poly1d([0])\n", " \n", " polydiv(u, v)\n", " Returns the quotient and remainder of polynomial division.\n", " \n", " .. note::\n", " This forms part of the old polynomial API. Since version 1.4, the\n", " new polynomial API defined in `numpy.polynomial` is preferred.\n", " A summary of the differences can be found in the\n", " :doc:`transition guide </reference/routines.polynomials>`.\n", " \n", " The input arrays are the coefficients (including any coefficients\n", " equal to zero) of the \"numerator\" (dividend) and \"denominator\"\n", " (divisor) polynomials, respectively.\n", " \n", " Parameters\n", " ----------\n", " u : array_like or poly1d\n", " Dividend polynomial's coefficients.\n", " \n", " v : array_like or poly1d\n", " Divisor polynomial's coefficients.\n", " \n", " Returns\n", " -------\n", " q : ndarray\n", " Coefficients, including those equal to zero, of the quotient.\n", " r : ndarray\n", " Coefficients, including those equal to zero, of the remainder.\n", " \n", " See Also\n", " --------\n", " poly, polyadd, polyder, polydiv, polyfit, polyint, polymul, polysub\n", " polyval\n", " \n", " Notes\n", " -----\n", " Both `u` and `v` must be 0-d or 1-d (ndim = 0 or 1), but `u.ndim` need\n", " not equal `v.ndim`. In other words, all four possible combinations -\n", " ``u.ndim = v.ndim = 0``, ``u.ndim = v.ndim = 1``,\n", " ``u.ndim = 1, v.ndim = 0``, and ``u.ndim = 0, v.ndim = 1`` - work.\n", " \n", " Examples\n", " --------\n", " .. math:: \\frac{3x^2 + 5x + 2}{2x + 1} = 1.5x + 1.75, remainder 0.25\n", " \n", " >>> x = np.array([3.0, 5.0, 2.0])\n", " >>> y = np.array([2.0, 1.0])\n", " >>> np.polydiv(x, y)\n", " (array([1.5 , 1.75]), array([0.25]))\n", " \n", " polyfit(x, y, deg, rcond=None, full=False, w=None, cov=False)\n", " Least squares polynomial fit.\n", " \n", " .. note::\n", " This forms part of the old polynomial API. Since version 1.4, the\n", " new polynomial API defined in `numpy.polynomial` is preferred.\n", " A summary of the differences can be found in the\n", " :doc:`transition guide </reference/routines.polynomials>`.\n", " \n", " Fit a polynomial ``p(x) = p[0] * x**deg + ... + p[deg]`` of degree `deg`\n", " to points `(x, y)`. Returns a vector of coefficients `p` that minimises\n", " the squared error in the order `deg`, `deg-1`, ... `0`.\n", " \n", " The `Polynomial.fit <numpy.polynomial.polynomial.Polynomial.fit>` class\n", " method is recommended for new code as it is more stable numerically. See\n", " the documentation of the method for more information.\n", " \n", " Parameters\n", " ----------\n", " x : array_like, shape (M,)\n", " x-coordinates of the M sample points ``(x[i], y[i])``.\n", " y : array_like, shape (M,) or (M, K)\n", " y-coordinates of the sample points. Several data sets of sample\n", " points sharing the same x-coordinates can be fitted at once by\n", " passing in a 2D-array that contains one dataset per column.\n", " deg : int\n", " Degree of the fitting polynomial\n", " rcond : float, optional\n", " Relative condition number of the fit. Singular values smaller than\n", " this relative to the largest singular value will be ignored. The\n", " default value is len(x)*eps, where eps is the relative precision of\n", " the float type, about 2e-16 in most cases.\n", " full : bool, optional\n", " Switch determining nature of return value. When it is False (the\n", " default) just the coefficients are returned, when True diagnostic\n", " information from the singular value decomposition is also returned.\n", " w : array_like, shape (M,), optional\n", " Weights. If not None, the weight ``w[i]`` applies to the unsquared\n", " residual ``y[i] - y_hat[i]`` at ``x[i]``. Ideally the weights are\n", " chosen so that the errors of the products ``w[i]*y[i]`` all have the\n", " same variance. When using inverse-variance weighting, use\n", " ``w[i] = 1/sigma(y[i])``. The default value is None.\n", " cov : bool or str, optional\n", " If given and not `False`, return not just the estimate but also its\n", " covariance matrix. By default, the covariance are scaled by\n", " chi2/dof, where dof = M - (deg + 1), i.e., the weights are presumed\n", " to be unreliable except in a relative sense and everything is scaled\n", " such that the reduced chi2 is unity. This scaling is omitted if\n", " ``cov='unscaled'``, as is relevant for the case that the weights are\n", " w = 1/sigma, with sigma known to be a reliable estimate of the\n", " uncertainty.\n", " \n", " Returns\n", " -------\n", " p : ndarray, shape (deg + 1,) or (deg + 1, K)\n", " Polynomial coefficients, highest power first. If `y` was 2-D, the\n", " coefficients for `k`-th data set are in ``p[:,k]``.\n", " \n", " residuals, rank, singular_values, rcond\n", " These values are only returned if ``full == True``\n", " \n", " - residuals -- sum of squared residuals of the least squares fit\n", " - rank -- the effective rank of the scaled Vandermonde\n", " coefficient matrix\n", " - singular_values -- singular values of the scaled Vandermonde\n", " coefficient matrix\n", " - rcond -- value of `rcond`.\n", " \n", " For more details, see `numpy.linalg.lstsq`.\n", " \n", " V : ndarray, shape (M,M) or (M,M,K)\n", " Present only if ``full == False`` and ``cov == True``. The covariance\n", " matrix of the polynomial coefficient estimates. The diagonal of\n", " this matrix are the variance estimates for each coefficient. If y\n", " is a 2-D array, then the covariance matrix for the `k`-th data set\n", " are in ``V[:,:,k]``\n", " \n", " \n", " Warns\n", " -----\n", " RankWarning\n", " The rank of the coefficient matrix in the least-squares fit is\n", " deficient. The warning is only raised if ``full == False``.\n", " \n", " The warnings can be turned off by\n", " \n", " >>> import warnings\n", " >>> warnings.simplefilter('ignore', np.RankWarning)\n", " \n", " See Also\n", " --------\n", " polyval : Compute polynomial values.\n", " linalg.lstsq : Computes a least-squares fit.\n", " scipy.interpolate.UnivariateSpline : Computes spline fits.\n", " \n", " Notes\n", " -----\n", " The solution minimizes the squared error\n", " \n", " .. math::\n", " E = \\sum_{j=0}^k |p(x_j) - y_j|^2\n", " \n", " in the equations::\n", " \n", " x[0]**n * p[0] + ... + x[0] * p[n-1] + p[n] = y[0]\n", " x[1]**n * p[0] + ... + x[1] * p[n-1] + p[n] = y[1]\n", " ...\n", " x[k]**n * p[0] + ... + x[k] * p[n-1] + p[n] = y[k]\n", " \n", " The coefficient matrix of the coefficients `p` is a Vandermonde matrix.\n", " \n", " `polyfit` issues a `RankWarning` when the least-squares fit is badly\n", " conditioned. This implies that the best fit is not well-defined due\n", " to numerical error. The results may be improved by lowering the polynomial\n", " degree or by replacing `x` by `x` - `x`.mean(). The `rcond` parameter\n", " can also be set to a value smaller than its default, but the resulting\n", " fit may be spurious: including contributions from the small singular\n", " values can add numerical noise to the result.\n", " \n", " Note that fitting polynomial coefficients is inherently badly conditioned\n", " when the degree of the polynomial is large or the interval of sample points\n", " is badly centered. The quality of the fit should always be checked in these\n", " cases. When polynomial fits are not satisfactory, splines may be a good\n", " alternative.\n", " \n", " References\n", " ----------\n", " .. [1] Wikipedia, \"Curve fitting\",\n", " https://en.wikipedia.org/wiki/Curve_fitting\n", " .. [2] Wikipedia, \"Polynomial interpolation\",\n", " https://en.wikipedia.org/wiki/Polynomial_interpolation\n", " \n", " Examples\n", " --------\n", " >>> import warnings\n", " >>> x = np.array([0.0, 1.0, 2.0, 3.0, 4.0, 5.0])\n", " >>> y = np.array([0.0, 0.8, 0.9, 0.1, -0.8, -1.0])\n", " >>> z = np.polyfit(x, y, 3)\n", " >>> z\n", " array([ 0.08703704, -0.81349206, 1.69312169, -0.03968254]) # may vary\n", " \n", " It is convenient to use `poly1d` objects for dealing with polynomials:\n", " \n", " >>> p = np.poly1d(z)\n", " >>> p(0.5)\n", " 0.6143849206349179 # may vary\n", " >>> p(3.5)\n", " -0.34732142857143039 # may vary\n", " >>> p(10)\n", " 22.579365079365115 # may vary\n", " \n", " High-order polynomials may oscillate wildly:\n", " \n", " >>> with warnings.catch_warnings():\n", " ... warnings.simplefilter('ignore', np.RankWarning)\n", " ... p30 = np.poly1d(np.polyfit(x, y, 30))\n", " ...\n", " >>> p30(4)\n", " -0.80000000000000204 # may vary\n", " >>> p30(5)\n", " -0.99999999999999445 # may vary\n", " >>> p30(4.5)\n", " -0.10547061179440398 # may vary\n", " \n", " Illustration:\n", " \n", " >>> import matplotlib.pyplot as plt\n", " >>> xp = np.linspace(-2, 6, 100)\n", " >>> _ = plt.plot(x, y, '.', xp, p(xp), '-', xp, p30(xp), '--')\n", " >>> plt.ylim(-2,2)\n", " (-2, 2)\n", " >>> plt.show()\n", " \n", " polyint(p, m=1, k=None)\n", " Return an antiderivative (indefinite integral) of a polynomial.\n", " \n", " .. note::\n", " This forms part of the old polynomial API. Since version 1.4, the\n", " new polynomial API defined in `numpy.polynomial` is preferred.\n", " A summary of the differences can be found in the\n", " :doc:`transition guide </reference/routines.polynomials>`.\n", " \n", " The returned order `m` antiderivative `P` of polynomial `p` satisfies\n", " :math:`\\frac{d^m}{dx^m}P(x) = p(x)` and is defined up to `m - 1`\n", " integration constants `k`. The constants determine the low-order\n", " polynomial part\n", " \n", " .. math:: \\frac{k_{m-1}}{0!} x^0 + \\ldots + \\frac{k_0}{(m-1)!}x^{m-1}\n", " \n", " of `P` so that :math:`P^{(j)}(0) = k_{m-j-1}`.\n", " \n", " Parameters\n", " ----------\n", " p : array_like or poly1d\n", " Polynomial to integrate.\n", " A sequence is interpreted as polynomial coefficients, see `poly1d`.\n", " m : int, optional\n", " Order of the antiderivative. (Default: 1)\n", " k : list of `m` scalars or scalar, optional\n", " Integration constants. They are given in the order of integration:\n", " those corresponding to highest-order terms come first.\n", " \n", " If ``None`` (default), all constants are assumed to be zero.\n", " If `m = 1`, a single scalar can be given instead of a list.\n", " \n", " See Also\n", " --------\n", " polyder : derivative of a polynomial\n", " poly1d.integ : equivalent method\n", " \n", " Examples\n", " --------\n", " The defining property of the antiderivative:\n", " \n", " >>> p = np.poly1d([1,1,1])\n", " >>> P = np.polyint(p)\n", " >>> P\n", " poly1d([ 0.33333333, 0.5 , 1. , 0. ]) # may vary\n", " >>> np.polyder(P) == p\n", " True\n", " \n", " The integration constants default to zero, but can be specified:\n", " \n", " >>> P = np.polyint(p, 3)\n", " >>> P(0)\n", " 0.0\n", " >>> np.polyder(P)(0)\n", " 0.0\n", " >>> np.polyder(P, 2)(0)\n", " 0.0\n", " >>> P = np.polyint(p, 3, k=[6,5,3])\n", " >>> P\n", " poly1d([ 0.01666667, 0.04166667, 0.16666667, 3. , 5. , 3. ]) # may vary\n", " \n", " Note that 3 = 6 / 2!, and that the constants are given in the order of\n", " integrations. Constant of the highest-order polynomial term comes first:\n", " \n", " >>> np.polyder(P, 2)(0)\n", " 6.0\n", " >>> np.polyder(P, 1)(0)\n", " 5.0\n", " >>> P(0)\n", " 3.0\n", " \n", " polymul(a1, a2)\n", " Find the product of two polynomials.\n", " \n", " .. note::\n", " This forms part of the old polynomial API. Since version 1.4, the\n", " new polynomial API defined in `numpy.polynomial` is preferred.\n", " A summary of the differences can be found in the\n", " :doc:`transition guide </reference/routines.polynomials>`.\n", " \n", " Finds the polynomial resulting from the multiplication of the two input\n", " polynomials. Each input must be either a poly1d object or a 1D sequence\n", " of polynomial coefficients, from highest to lowest degree.\n", " \n", " Parameters\n", " ----------\n", " a1, a2 : array_like or poly1d object\n", " Input polynomials.\n", " \n", " Returns\n", " -------\n", " out : ndarray or poly1d object\n", " The polynomial resulting from the multiplication of the inputs. If\n", " either inputs is a poly1d object, then the output is also a poly1d\n", " object. Otherwise, it is a 1D array of polynomial coefficients from\n", " highest to lowest degree.\n", " \n", " See Also\n", " --------\n", " poly1d : A one-dimensional polynomial class.\n", " poly, polyadd, polyder, polydiv, polyfit, polyint, polysub, polyval\n", " convolve : Array convolution. Same output as polymul, but has parameter\n", " for overlap mode.\n", " \n", " Examples\n", " --------\n", " >>> np.polymul([1, 2, 3], [9, 5, 1])\n", " array([ 9, 23, 38, 17, 3])\n", " \n", " Using poly1d objects:\n", " \n", " >>> p1 = np.poly1d([1, 2, 3])\n", " >>> p2 = np.poly1d([9, 5, 1])\n", " >>> print(p1)\n", " 2\n", " 1 x + 2 x + 3\n", " >>> print(p2)\n", " 2\n", " 9 x + 5 x + 1\n", " >>> print(np.polymul(p1, p2))\n", " 4 3 2\n", " 9 x + 23 x + 38 x + 17 x + 3\n", " \n", " polysub(a1, a2)\n", " Difference (subtraction) of two polynomials.\n", " \n", " .. note::\n", " This forms part of the old polynomial API. Since version 1.4, the\n", " new polynomial API defined in `numpy.polynomial` is preferred.\n", " A summary of the differences can be found in the\n", " :doc:`transition guide </reference/routines.polynomials>`.\n", " \n", " Given two polynomials `a1` and `a2`, returns ``a1 - a2``.\n", " `a1` and `a2` can be either array_like sequences of the polynomials'\n", " coefficients (including coefficients equal to zero), or `poly1d` objects.\n", " \n", " Parameters\n", " ----------\n", " a1, a2 : array_like or poly1d\n", " Minuend and subtrahend polynomials, respectively.\n", " \n", " Returns\n", " -------\n", " out : ndarray or poly1d\n", " Array or `poly1d` object of the difference polynomial's coefficients.\n", " \n", " See Also\n", " --------\n", " polyval, polydiv, polymul, polyadd\n", " \n", " Examples\n", " --------\n", " .. math:: (2 x^2 + 10 x - 2) - (3 x^2 + 10 x -4) = (-x^2 + 2)\n", " \n", " >>> np.polysub([2, 10, -2], [3, 10, -4])\n", " array([-1, 0, 2])\n", " \n", " polyval(p, x)\n", " Evaluate a polynomial at specific values.\n", " \n", " .. note::\n", " This forms part of the old polynomial API. Since version 1.4, the\n", " new polynomial API defined in `numpy.polynomial` is preferred.\n", " A summary of the differences can be found in the\n", " :doc:`transition guide </reference/routines.polynomials>`.\n", " \n", " If `p` is of length N, this function returns the value:\n", " \n", " ``p[0]*x**(N-1) + p[1]*x**(N-2) + ... + p[N-2]*x + p[N-1]``\n", " \n", " If `x` is a sequence, then ``p(x)`` is returned for each element of ``x``.\n", " If `x` is another polynomial then the composite polynomial ``p(x(t))``\n", " is returned.\n", " \n", " Parameters\n", " ----------\n", " p : array_like or poly1d object\n", " 1D array of polynomial coefficients (including coefficients equal\n", " to zero) from highest degree to the constant term, or an\n", " instance of poly1d.\n", " x : array_like or poly1d object\n", " A number, an array of numbers, or an instance of poly1d, at\n", " which to evaluate `p`.\n", " \n", " Returns\n", " -------\n", " values : ndarray or poly1d\n", " If `x` is a poly1d instance, the result is the composition of the two\n", " polynomials, i.e., `x` is \"substituted\" in `p` and the simplified\n", " result is returned. In addition, the type of `x` - array_like or\n", " poly1d - governs the type of the output: `x` array_like => `values`\n", " array_like, `x` a poly1d object => `values` is also.\n", " \n", " See Also\n", " --------\n", " poly1d: A polynomial class.\n", " \n", " Notes\n", " -----\n", " Horner's scheme [1]_ is used to evaluate the polynomial. Even so,\n", " for polynomials of high degree the values may be inaccurate due to\n", " rounding errors. Use carefully.\n", " \n", " If `x` is a subtype of `ndarray` the return value will be of the same type.\n", " \n", " References\n", " ----------\n", " .. [1] I. N. Bronshtein, K. A. Semendyayev, and K. A. Hirsch (Eng.\n", " trans. Ed.), *Handbook of Mathematics*, New York, Van Nostrand\n", " Reinhold Co., 1985, pg. 720.\n", " \n", " Examples\n", " --------\n", " >>> np.polyval([3,0,1], 5) # 3 * 5**2 + 0 * 5**1 + 1\n", " 76\n", " >>> np.polyval([3,0,1], np.poly1d(5))\n", " poly1d([76])\n", " >>> np.polyval(np.poly1d([3,0,1]), 5)\n", " 76\n", " >>> np.polyval(np.poly1d([3,0,1]), np.poly1d(5))\n", " poly1d([76])\n", " \n", " printoptions(*args, **kwargs)\n", " Context manager for setting print options.\n", " \n", " Set print options for the scope of the `with` block, and restore the old\n", " options at the end. See `set_printoptions` for the full description of\n", " available options.\n", " \n", " Examples\n", " --------\n", " \n", " >>> from numpy.testing import assert_equal\n", " >>> with np.printoptions(precision=2):\n", " ... np.array([2.0]) / 3\n", " array([0.67])\n", " \n", " The `as`-clause of the `with`-statement gives the current print options:\n", " \n", " >>> with np.printoptions(precision=2) as opts:\n", " ... assert_equal(opts, np.get_printoptions())\n", " \n", " See Also\n", " --------\n", " set_printoptions, get_printoptions\n", " \n", " prod(a, axis=None, dtype=None, out=None, keepdims=<no value>, initial=<no value>, where=<no value>)\n", " Return the product of array elements over a given axis.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input data.\n", " axis : None or int or tuple of ints, optional\n", " Axis or axes along which a product is performed. The default,\n", " axis=None, will calculate the product of all the elements in the\n", " input array. If axis is negative it counts from the last to the\n", " first axis.\n", " \n", " .. versionadded:: 1.7.0\n", " \n", " If axis is a tuple of ints, a product is performed on all of the\n", " axes specified in the tuple instead of a single axis or all the\n", " axes as before.\n", " dtype : dtype, optional\n", " The type of the returned array, as well as of the accumulator in\n", " which the elements are multiplied. The dtype of `a` is used by\n", " default unless `a` has an integer dtype of less precision than the\n", " default platform integer. In that case, if `a` is signed then the\n", " platform integer is used while if `a` is unsigned then an unsigned\n", " integer of the same precision as the platform integer is used.\n", " out : ndarray, optional\n", " Alternative output array in which to place the result. It must have\n", " the same shape as the expected output, but the type of the output\n", " values will be cast if necessary.\n", " keepdims : bool, optional\n", " If this is set to True, the axes which are reduced are left in the\n", " result as dimensions with size one. With this option, the result\n", " will broadcast correctly against the input array.\n", " \n", " If the default value is passed, then `keepdims` will not be\n", " passed through to the `prod` method of sub-classes of\n", " `ndarray`, however any non-default value will be. If the\n", " sub-class' method does not implement `keepdims` any\n", " exceptions will be raised.\n", " initial : scalar, optional\n", " The starting value for this product. See `~numpy.ufunc.reduce` for details.\n", " \n", " .. versionadded:: 1.15.0\n", " \n", " where : array_like of bool, optional\n", " Elements to include in the product. See `~numpy.ufunc.reduce` for details.\n", " \n", " .. versionadded:: 1.17.0\n", " \n", " Returns\n", " -------\n", " product_along_axis : ndarray, see `dtype` parameter above.\n", " An array shaped as `a` but with the specified axis removed.\n", " Returns a reference to `out` if specified.\n", " \n", " See Also\n", " --------\n", " ndarray.prod : equivalent method\n", " :ref:`ufuncs-output-type`\n", " \n", " Notes\n", " -----\n", " Arithmetic is modular when using integer types, and no error is\n", " raised on overflow. That means that, on a 32-bit platform:\n", " \n", " >>> x = np.array([536870910, 536870910, 536870910, 536870910])\n", " >>> np.prod(x)\n", " 16 # may vary\n", " \n", " The product of an empty array is the neutral element 1:\n", " \n", " >>> np.prod([])\n", " 1.0\n", " \n", " Examples\n", " --------\n", " By default, calculate the product of all elements:\n", " \n", " >>> np.prod([1.,2.])\n", " 2.0\n", " \n", " Even when the input array is two-dimensional:\n", " \n", " >>> a = np.array([[1., 2.], [3., 4.]])\n", " >>> np.prod(a)\n", " 24.0\n", " \n", " But we can also specify the axis over which to multiply:\n", " \n", " >>> np.prod(a, axis=1)\n", " array([ 2., 12.])\n", " >>> np.prod(a, axis=0)\n", " array([3., 8.])\n", " \n", " Or select specific elements to include:\n", " \n", " >>> np.prod([1., np.nan, 3.], where=[True, False, True])\n", " 3.0\n", " \n", " If the type of `x` is unsigned, then the output type is\n", " the unsigned platform integer:\n", " \n", " >>> x = np.array([1, 2, 3], dtype=np.uint8)\n", " >>> np.prod(x).dtype == np.uint\n", " True\n", " \n", " If `x` is of a signed integer type, then the output type\n", " is the default platform integer:\n", " \n", " >>> x = np.array([1, 2, 3], dtype=np.int8)\n", " >>> np.prod(x).dtype == int\n", " True\n", " \n", " You can also start the product with a value other than one:\n", " \n", " >>> np.prod([1, 2], initial=5)\n", " 10\n", " \n", " product(*args, **kwargs)\n", " Return the product of array elements over a given axis.\n", " \n", " See Also\n", " --------\n", " prod : equivalent function; see for details.\n", " \n", " promote_types(...)\n", " promote_types(type1, type2)\n", " \n", " Returns the data type with the smallest size and smallest scalar\n", " kind to which both ``type1`` and ``type2`` may be safely cast.\n", " The returned data type is always considered \"canonical\", this mainly\n", " means that the promoted dtype will always be in native byte order.\n", " \n", " This function is symmetric, but rarely associative.\n", " \n", " Parameters\n", " ----------\n", " type1 : dtype or dtype specifier\n", " First data type.\n", " type2 : dtype or dtype specifier\n", " Second data type.\n", " \n", " Returns\n", " -------\n", " out : dtype\n", " The promoted data type.\n", " \n", " Notes\n", " -----\n", " Please see `numpy.result_type` for additional information about promotion.\n", " \n", " .. versionadded:: 1.6.0\n", " \n", " Starting in NumPy 1.9, promote_types function now returns a valid string\n", " length when given an integer or float dtype as one argument and a string\n", " dtype as another argument. Previously it always returned the input string\n", " dtype, even if it wasn't long enough to store the max integer/float value\n", " converted to a string.\n", " \n", " .. versionchanged:: 1.23.0\n", " \n", " NumPy now supports promotion for more structured dtypes. It will now\n", " remove unnecessary padding from a structure dtype and promote included\n", " fields individually.\n", " \n", " See Also\n", " --------\n", " result_type, dtype, can_cast\n", " \n", " Examples\n", " --------\n", " >>> np.promote_types('f4', 'f8')\n", " dtype('float64')\n", " \n", " >>> np.promote_types('i8', 'f4')\n", " dtype('float64')\n", " \n", " >>> np.promote_types('>i8', '<c8')\n", " dtype('complex128')\n", " \n", " >>> np.promote_types('i4', 'S8')\n", " dtype('S11')\n", " \n", " An example of a non-associative case:\n", " \n", " >>> p = np.promote_types\n", " >>> p('S', p('i1', 'u1'))\n", " dtype('S6')\n", " >>> p(p('S', 'i1'), 'u1')\n", " dtype('S4')\n", " \n", " ptp(a, axis=None, out=None, keepdims=<no value>)\n", " Range of values (maximum - minimum) along an axis.\n", " \n", " The name of the function comes from the acronym for 'peak to peak'.\n", " \n", " .. warning::\n", " `ptp` preserves the data type of the array. This means the\n", " return value for an input of signed integers with n bits\n", " (e.g. `np.int8`, `np.int16`, etc) is also a signed integer\n", " with n bits. In that case, peak-to-peak values greater than\n", " ``2**(n-1)-1`` will be returned as negative values. An example\n", " with a work-around is shown below.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input values.\n", " axis : None or int or tuple of ints, optional\n", " Axis along which to find the peaks. By default, flatten the\n", " array. `axis` may be negative, in\n", " which case it counts from the last to the first axis.\n", " \n", " .. versionadded:: 1.15.0\n", " \n", " If this is a tuple of ints, a reduction is performed on multiple\n", " axes, instead of a single axis or all the axes as before.\n", " out : array_like\n", " Alternative output array in which to place the result. It must\n", " have the same shape and buffer length as the expected output,\n", " but the type of the output values will be cast if necessary.\n", " \n", " keepdims : bool, optional\n", " If this is set to True, the axes which are reduced are left\n", " in the result as dimensions with size one. With this option,\n", " the result will broadcast correctly against the input array.\n", " \n", " If the default value is passed, then `keepdims` will not be\n", " passed through to the `ptp` method of sub-classes of\n", " `ndarray`, however any non-default value will be. If the\n", " sub-class' method does not implement `keepdims` any\n", " exceptions will be raised.\n", " \n", " Returns\n", " -------\n", " ptp : ndarray or scalar\n", " The range of a given array - `scalar` if array is one-dimensional\n", " or a new array holding the result along the given axis\n", " \n", " Examples\n", " --------\n", " >>> x = np.array([[4, 9, 2, 10],\n", " ... [6, 9, 7, 12]])\n", " \n", " >>> np.ptp(x, axis=1)\n", " array([8, 6])\n", " \n", " >>> np.ptp(x, axis=0)\n", " array([2, 0, 5, 2])\n", " \n", " >>> np.ptp(x)\n", " 10\n", " \n", " This example shows that a negative value can be returned when\n", " the input is an array of signed integers.\n", " \n", " >>> y = np.array([[1, 127],\n", " ... [0, 127],\n", " ... [-1, 127],\n", " ... [-2, 127]], dtype=np.int8)\n", " >>> np.ptp(y, axis=1)\n", " array([ 126, 127, -128, -127], dtype=int8)\n", " \n", " A work-around is to use the `view()` method to view the result as\n", " unsigned integers with the same bit width:\n", " \n", " >>> np.ptp(y, axis=1).view(np.uint8)\n", " array([126, 127, 128, 129], dtype=uint8)\n", " \n", " put(a, ind, v, mode='raise')\n", " Replaces specified elements of an array with given values.\n", " \n", " The indexing works on the flattened target array. `put` is roughly\n", " equivalent to:\n", " \n", " ::\n", " \n", " a.flat[ind] = v\n", " \n", " Parameters\n", " ----------\n", " a : ndarray\n", " Target array.\n", " ind : array_like\n", " Target indices, interpreted as integers.\n", " v : array_like\n", " Values to place in `a` at target indices. If `v` is shorter than\n", " `ind` it will be repeated as necessary.\n", " mode : {'raise', 'wrap', 'clip'}, optional\n", " Specifies how out-of-bounds indices will behave.\n", " \n", " * 'raise' -- raise an error (default)\n", " * 'wrap' -- wrap around\n", " * 'clip' -- clip to the range\n", " \n", " 'clip' mode means that all indices that are too large are replaced\n", " by the index that addresses the last element along that axis. Note\n", " that this disables indexing with negative numbers. In 'raise' mode,\n", " if an exception occurs the target array may still be modified.\n", " \n", " See Also\n", " --------\n", " putmask, place\n", " put_along_axis : Put elements by matching the array and the index arrays\n", " \n", " Examples\n", " --------\n", " >>> a = np.arange(5)\n", " >>> np.put(a, [0, 2], [-44, -55])\n", " >>> a\n", " array([-44, 1, -55, 3, 4])\n", " \n", " >>> a = np.arange(5)\n", " >>> np.put(a, 22, -5, mode='clip')\n", " >>> a\n", " array([ 0, 1, 2, 3, -5])\n", " \n", " put_along_axis(arr, indices, values, axis)\n", " Put values into the destination array by matching 1d index and data slices.\n", " \n", " This iterates over matching 1d slices oriented along the specified axis in\n", " the index and data arrays, and uses the former to place values into the\n", " latter. These slices can be different lengths.\n", " \n", " Functions returning an index along an axis, like `argsort` and\n", " `argpartition`, produce suitable indices for this function.\n", " \n", " .. versionadded:: 1.15.0\n", " \n", " Parameters\n", " ----------\n", " arr : ndarray (Ni..., M, Nk...)\n", " Destination array.\n", " indices : ndarray (Ni..., J, Nk...)\n", " Indices to change along each 1d slice of `arr`. This must match the\n", " dimension of arr, but dimensions in Ni and Nj may be 1 to broadcast\n", " against `arr`.\n", " values : array_like (Ni..., J, Nk...)\n", " values to insert at those indices. Its shape and dimension are\n", " broadcast to match that of `indices`.\n", " axis : int\n", " The axis to take 1d slices along. If axis is None, the destination\n", " array is treated as if a flattened 1d view had been created of it.\n", " \n", " Notes\n", " -----\n", " This is equivalent to (but faster than) the following use of `ndindex` and\n", " `s_`, which sets each of ``ii`` and ``kk`` to a tuple of indices::\n", " \n", " Ni, M, Nk = a.shape[:axis], a.shape[axis], a.shape[axis+1:]\n", " J = indices.shape[axis] # Need not equal M\n", " \n", " for ii in ndindex(Ni):\n", " for kk in ndindex(Nk):\n", " a_1d = a [ii + s_[:,] + kk]\n", " indices_1d = indices[ii + s_[:,] + kk]\n", " values_1d = values [ii + s_[:,] + kk]\n", " for j in range(J):\n", " a_1d[indices_1d[j]] = values_1d[j]\n", " \n", " Equivalently, eliminating the inner loop, the last two lines would be::\n", " \n", " a_1d[indices_1d] = values_1d\n", " \n", " See Also\n", " --------\n", " take_along_axis :\n", " Take values from the input array by matching 1d index and data slices\n", " \n", " Examples\n", " --------\n", " \n", " For this sample array\n", " \n", " >>> a = np.array([[10, 30, 20], [60, 40, 50]])\n", " \n", " We can replace the maximum values with:\n", " \n", " >>> ai = np.expand_dims(np.argmax(a, axis=1), axis=1)\n", " >>> ai\n", " array([[1],\n", " [0]])\n", " >>> np.put_along_axis(a, ai, 99, axis=1)\n", " >>> a\n", " array([[10, 99, 20],\n", " [99, 40, 50]])\n", " \n", " putmask(...)\n", " putmask(a, mask, values)\n", " \n", " Changes elements of an array based on conditional and input values.\n", " \n", " Sets ``a.flat[n] = values[n]`` for each n where ``mask.flat[n]==True``.\n", " \n", " If `values` is not the same size as `a` and `mask` then it will repeat.\n", " This gives behavior different from ``a[mask] = values``.\n", " \n", " Parameters\n", " ----------\n", " a : ndarray\n", " Target array.\n", " mask : array_like\n", " Boolean mask array. It has to be the same shape as `a`.\n", " values : array_like\n", " Values to put into `a` where `mask` is True. If `values` is smaller\n", " than `a` it will be repeated.\n", " \n", " See Also\n", " --------\n", " place, put, take, copyto\n", " \n", " Examples\n", " --------\n", " >>> x = np.arange(6).reshape(2, 3)\n", " >>> np.putmask(x, x>2, x**2)\n", " >>> x\n", " array([[ 0, 1, 2],\n", " [ 9, 16, 25]])\n", " \n", " If `values` is smaller than `a` it is repeated:\n", " \n", " >>> x = np.arange(5)\n", " >>> np.putmask(x, x>1, [-33, -44])\n", " >>> x\n", " array([ 0, 1, -33, -44, -33])\n", " \n", " quantile(a, q, axis=None, out=None, overwrite_input=False, method='linear', keepdims=False, *, interpolation=None)\n", " Compute the q-th quantile of the data along the specified axis.\n", " \n", " .. versionadded:: 1.15.0\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input array or object that can be converted to an array.\n", " q : array_like of float\n", " Quantile or sequence of quantiles to compute, which must be between\n", " 0 and 1 inclusive.\n", " axis : {int, tuple of int, None}, optional\n", " Axis or axes along which the quantiles are computed. The default is\n", " to compute the quantile(s) along a flattened version of the array.\n", " out : ndarray, optional\n", " Alternative output array in which to place the result. It must have\n", " the same shape and buffer length as the expected output, but the\n", " type (of the output) will be cast if necessary.\n", " overwrite_input : bool, optional\n", " If True, then allow the input array `a` to be modified by\n", " intermediate calculations, to save memory. In this case, the\n", " contents of the input `a` after this function completes is\n", " undefined.\n", " method : str, optional\n", " This parameter specifies the method to use for estimating the\n", " quantile. There are many different methods, some unique to NumPy.\n", " See the notes for explanation. The options sorted by their R type\n", " as summarized in the H&F paper [1]_ are:\n", " \n", " 1. 'inverted_cdf'\n", " 2. 'averaged_inverted_cdf'\n", " 3. 'closest_observation'\n", " 4. 'interpolated_inverted_cdf'\n", " 5. 'hazen'\n", " 6. 'weibull'\n", " 7. 'linear' (default)\n", " 8. 'median_unbiased'\n", " 9. 'normal_unbiased'\n", " \n", " The first three methods are discontinuous. NumPy further defines the\n", " following discontinuous variations of the default 'linear' (7.) option:\n", " \n", " * 'lower'\n", " * 'higher',\n", " * 'midpoint'\n", " * 'nearest'\n", " \n", " .. versionchanged:: 1.22.0\n", " This argument was previously called \"interpolation\" and only\n", " offered the \"linear\" default and last four options.\n", " \n", " keepdims : bool, optional\n", " If this is set to True, the axes which are reduced are left in\n", " the result as dimensions with size one. With this option, the\n", " result will broadcast correctly against the original array `a`.\n", " \n", " interpolation : str, optional\n", " Deprecated name for the method keyword argument.\n", " \n", " .. deprecated:: 1.22.0\n", " \n", " Returns\n", " -------\n", " quantile : scalar or ndarray\n", " If `q` is a single quantile and `axis=None`, then the result\n", " is a scalar. If multiple quantiles are given, first axis of\n", " the result corresponds to the quantiles. The other axes are\n", " the axes that remain after the reduction of `a`. If the input\n", " contains integers or floats smaller than ``float64``, the output\n", " data-type is ``float64``. Otherwise, the output data-type is the\n", " same as that of the input. If `out` is specified, that array is\n", " returned instead.\n", " \n", " See Also\n", " --------\n", " mean\n", " percentile : equivalent to quantile, but with q in the range [0, 100].\n", " median : equivalent to ``quantile(..., 0.5)``\n", " nanquantile\n", " \n", " Notes\n", " -----\n", " Given a vector ``V`` of length ``n``, the q-th quantile of ``V`` is\n", " the value ``q`` of the way from the minimum to the maximum in a\n", " sorted copy of ``V``. The values and distances of the two nearest\n", " neighbors as well as the `method` parameter will determine the\n", " quantile if the normalized ranking does not match the location of\n", " ``q`` exactly. This function is the same as the median if ``q=0.5``, the\n", " same as the minimum if ``q=0.0`` and the same as the maximum if\n", " ``q=1.0``.\n", " \n", " The optional `method` parameter specifies the method to use when the\n", " desired quantile lies between two indexes ``i`` and ``j = i + 1``.\n", " In that case, we first determine ``i + g``, a virtual index that lies\n", " between ``i`` and ``j``, where ``i`` is the floor and ``g`` is the\n", " fractional part of the index. The final result is, then, an interpolation\n", " of ``a[i]`` and ``a[j]`` based on ``g``. During the computation of ``g``,\n", " ``i`` and ``j`` are modified using correction constants ``alpha`` and\n", " ``beta`` whose choices depend on the ``method`` used. Finally, note that\n", " since Python uses 0-based indexing, the code subtracts another 1 from the\n", " index internally.\n", " \n", " The following formula determines the virtual index ``i + g``, the location \n", " of the quantile in the sorted sample:\n", " \n", " .. math::\n", " i + g = q * ( n - alpha - beta + 1 ) + alpha\n", " \n", " The different methods then work as follows\n", " \n", " inverted_cdf:\n", " method 1 of H&F [1]_.\n", " This method gives discontinuous results:\n", " \n", " * if g > 0 ; then take j\n", " * if g = 0 ; then take i\n", " \n", " averaged_inverted_cdf:\n", " method 2 of H&F [1]_.\n", " This method gives discontinuous results:\n", " \n", " * if g > 0 ; then take j\n", " * if g = 0 ; then average between bounds\n", " \n", " closest_observation:\n", " method 3 of H&F [1]_.\n", " This method gives discontinuous results:\n", " \n", " * if g > 0 ; then take j\n", " * if g = 0 and index is odd ; then take j\n", " * if g = 0 and index is even ; then take i\n", " \n", " interpolated_inverted_cdf:\n", " method 4 of H&F [1]_.\n", " This method gives continuous results using:\n", " \n", " * alpha = 0\n", " * beta = 1\n", " \n", " hazen:\n", " method 5 of H&F [1]_.\n", " This method gives continuous results using:\n", " \n", " * alpha = 1/2\n", " * beta = 1/2\n", " \n", " weibull:\n", " method 6 of H&F [1]_.\n", " This method gives continuous results using:\n", " \n", " * alpha = 0\n", " * beta = 0\n", " \n", " linear:\n", " method 7 of H&F [1]_.\n", " This method gives continuous results using:\n", " \n", " * alpha = 1\n", " * beta = 1\n", " \n", " median_unbiased:\n", " method 8 of H&F [1]_.\n", " This method is probably the best method if the sample\n", " distribution function is unknown (see reference).\n", " This method gives continuous results using:\n", " \n", " * alpha = 1/3\n", " * beta = 1/3\n", " \n", " normal_unbiased:\n", " method 9 of H&F [1]_.\n", " This method is probably the best method if the sample\n", " distribution function is known to be normal.\n", " This method gives continuous results using:\n", " \n", " * alpha = 3/8\n", " * beta = 3/8\n", " \n", " lower:\n", " NumPy method kept for backwards compatibility.\n", " Takes ``i`` as the interpolation point.\n", " \n", " higher:\n", " NumPy method kept for backwards compatibility.\n", " Takes ``j`` as the interpolation point.\n", " \n", " nearest:\n", " NumPy method kept for backwards compatibility.\n", " Takes ``i`` or ``j``, whichever is nearest.\n", " \n", " midpoint:\n", " NumPy method kept for backwards compatibility.\n", " Uses ``(i + j) / 2``.\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([[10, 7, 4], [3, 2, 1]])\n", " >>> a\n", " array([[10, 7, 4],\n", " [ 3, 2, 1]])\n", " >>> np.quantile(a, 0.5)\n", " 3.5\n", " >>> np.quantile(a, 0.5, axis=0)\n", " array([6.5, 4.5, 2.5])\n", " >>> np.quantile(a, 0.5, axis=1)\n", " array([7., 2.])\n", " >>> np.quantile(a, 0.5, axis=1, keepdims=True)\n", " array([[7.],\n", " [2.]])\n", " >>> m = np.quantile(a, 0.5, axis=0)\n", " >>> out = np.zeros_like(m)\n", " >>> np.quantile(a, 0.5, axis=0, out=out)\n", " array([6.5, 4.5, 2.5])\n", " >>> m\n", " array([6.5, 4.5, 2.5])\n", " >>> b = a.copy()\n", " >>> np.quantile(b, 0.5, axis=1, overwrite_input=True)\n", " array([7., 2.])\n", " >>> assert not np.all(a == b)\n", " \n", " See also `numpy.percentile` for a visualization of most methods.\n", " \n", " References\n", " ----------\n", " .. [1] R. J. Hyndman and Y. Fan,\n", " \"Sample quantiles in statistical packages,\"\n", " The American Statistician, 50(4), pp. 361-365, 1996\n", " \n", " ravel(a, order='C')\n", " Return a contiguous flattened array.\n", " \n", " A 1-D array, containing the elements of the input, is returned. A copy is\n", " made only if needed.\n", " \n", " As of NumPy 1.10, the returned array will have the same type as the input\n", " array. (for example, a masked array will be returned for a masked array\n", " input)\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input array. The elements in `a` are read in the order specified by\n", " `order`, and packed as a 1-D array.\n", " order : {'C','F', 'A', 'K'}, optional\n", " \n", " The elements of `a` are read using this index order. 'C' means\n", " to index the elements in row-major, C-style order,\n", " with the last axis index changing fastest, back to the first\n", " axis index changing slowest. 'F' means to index the elements\n", " in column-major, Fortran-style order, with the\n", " first index changing fastest, and the last index changing\n", " slowest. Note that the 'C' and 'F' options take no account of\n", " the memory layout of the underlying array, and only refer to\n", " the order of axis indexing. 'A' means to read the elements in\n", " Fortran-like index order if `a` is Fortran *contiguous* in\n", " memory, C-like order otherwise. 'K' means to read the\n", " elements in the order they occur in memory, except for\n", " reversing the data when strides are negative. By default, 'C'\n", " index order is used.\n", " \n", " Returns\n", " -------\n", " y : array_like\n", " y is an array of the same subtype as `a`, with shape ``(a.size,)``.\n", " Note that matrices are special cased for backward compatibility, if `a`\n", " is a matrix, then y is a 1-D ndarray.\n", " \n", " See Also\n", " --------\n", " ndarray.flat : 1-D iterator over an array.\n", " ndarray.flatten : 1-D array copy of the elements of an array\n", " in row-major order.\n", " ndarray.reshape : Change the shape of an array without changing its data.\n", " \n", " Notes\n", " -----\n", " In row-major, C-style order, in two dimensions, the row index\n", " varies the slowest, and the column index the quickest. This can\n", " be generalized to multiple dimensions, where row-major order\n", " implies that the index along the first axis varies slowest, and\n", " the index along the last quickest. The opposite holds for\n", " column-major, Fortran-style index ordering.\n", " \n", " When a view is desired in as many cases as possible, ``arr.reshape(-1)``\n", " may be preferable.\n", " \n", " Examples\n", " --------\n", " It is equivalent to ``reshape(-1, order=order)``.\n", " \n", " >>> x = np.array([[1, 2, 3], [4, 5, 6]])\n", " >>> np.ravel(x)\n", " array([1, 2, 3, 4, 5, 6])\n", " \n", " >>> x.reshape(-1)\n", " array([1, 2, 3, 4, 5, 6])\n", " \n", " >>> np.ravel(x, order='F')\n", " array([1, 4, 2, 5, 3, 6])\n", " \n", " When ``order`` is 'A', it will preserve the array's 'C' or 'F' ordering:\n", " \n", " >>> np.ravel(x.T)\n", " array([1, 4, 2, 5, 3, 6])\n", " >>> np.ravel(x.T, order='A')\n", " array([1, 2, 3, 4, 5, 6])\n", " \n", " When ``order`` is 'K', it will preserve orderings that are neither 'C'\n", " nor 'F', but won't reverse axes:\n", " \n", " >>> a = np.arange(3)[::-1]; a\n", " array([2, 1, 0])\n", " >>> a.ravel(order='C')\n", " array([2, 1, 0])\n", " >>> a.ravel(order='K')\n", " array([2, 1, 0])\n", " \n", " >>> a = np.arange(12).reshape(2,3,2).swapaxes(1,2); a\n", " array([[[ 0, 2, 4],\n", " [ 1, 3, 5]],\n", " [[ 6, 8, 10],\n", " [ 7, 9, 11]]])\n", " >>> a.ravel(order='C')\n", " array([ 0, 2, 4, 1, 3, 5, 6, 8, 10, 7, 9, 11])\n", " >>> a.ravel(order='K')\n", " array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11])\n", " \n", " ravel_multi_index(...)\n", " ravel_multi_index(multi_index, dims, mode='raise', order='C')\n", " \n", " Converts a tuple of index arrays into an array of flat\n", " indices, applying boundary modes to the multi-index.\n", " \n", " Parameters\n", " ----------\n", " multi_index : tuple of array_like\n", " A tuple of integer arrays, one array for each dimension.\n", " dims : tuple of ints\n", " The shape of array into which the indices from ``multi_index`` apply.\n", " mode : {'raise', 'wrap', 'clip'}, optional\n", " Specifies how out-of-bounds indices are handled. Can specify\n", " either one mode or a tuple of modes, one mode per index.\n", " \n", " * 'raise' -- raise an error (default)\n", " * 'wrap' -- wrap around\n", " * 'clip' -- clip to the range\n", " \n", " In 'clip' mode, a negative index which would normally\n", " wrap will clip to 0 instead.\n", " order : {'C', 'F'}, optional\n", " Determines whether the multi-index should be viewed as\n", " indexing in row-major (C-style) or column-major\n", " (Fortran-style) order.\n", " \n", " Returns\n", " -------\n", " raveled_indices : ndarray\n", " An array of indices into the flattened version of an array\n", " of dimensions ``dims``.\n", " \n", " See Also\n", " --------\n", " unravel_index\n", " \n", " Notes\n", " -----\n", " .. versionadded:: 1.6.0\n", " \n", " Examples\n", " --------\n", " >>> arr = np.array([[3,6,6],[4,5,1]])\n", " >>> np.ravel_multi_index(arr, (7,6))\n", " array([22, 41, 37])\n", " >>> np.ravel_multi_index(arr, (7,6), order='F')\n", " array([31, 41, 13])\n", " >>> np.ravel_multi_index(arr, (4,6), mode='clip')\n", " array([22, 23, 19])\n", " >>> np.ravel_multi_index(arr, (4,4), mode=('clip','wrap'))\n", " array([12, 13, 13])\n", " \n", " >>> np.ravel_multi_index((3,1,4,1), (6,7,8,9))\n", " 1621\n", " \n", " real(val)\n", " Return the real part of the complex argument.\n", " \n", " Parameters\n", " ----------\n", " val : array_like\n", " Input array.\n", " \n", " Returns\n", " -------\n", " out : ndarray or scalar\n", " The real component of the complex argument. If `val` is real, the type\n", " of `val` is used for the output. If `val` has complex elements, the\n", " returned type is float.\n", " \n", " See Also\n", " --------\n", " real_if_close, imag, angle\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([1+2j, 3+4j, 5+6j])\n", " >>> a.real\n", " array([1., 3., 5.])\n", " >>> a.real = 9\n", " >>> a\n", " array([9.+2.j, 9.+4.j, 9.+6.j])\n", " >>> a.real = np.array([9, 8, 7])\n", " >>> a\n", " array([9.+2.j, 8.+4.j, 7.+6.j])\n", " >>> np.real(1 + 1j)\n", " 1.0\n", " \n", " real_if_close(a, tol=100)\n", " If input is complex with all imaginary parts close to zero, return\n", " real parts.\n", " \n", " \"Close to zero\" is defined as `tol` * (machine epsilon of the type for\n", " `a`).\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input array.\n", " tol : float\n", " Tolerance in machine epsilons for the complex part of the elements\n", " in the array.\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " If `a` is real, the type of `a` is used for the output. If `a`\n", " has complex elements, the returned type is float.\n", " \n", " See Also\n", " --------\n", " real, imag, angle\n", " \n", " Notes\n", " -----\n", " Machine epsilon varies from machine to machine and between data types\n", " but Python floats on most platforms have a machine epsilon equal to\n", " 2.2204460492503131e-16. You can use 'np.finfo(float).eps' to print\n", " out the machine epsilon for floats.\n", " \n", " Examples\n", " --------\n", " >>> np.finfo(float).eps\n", " 2.2204460492503131e-16 # may vary\n", " \n", " >>> np.real_if_close([2.1 + 4e-14j, 5.2 + 3e-15j], tol=1000)\n", " array([2.1, 5.2])\n", " >>> np.real_if_close([2.1 + 4e-13j, 5.2 + 3e-15j], tol=1000)\n", " array([2.1+4.e-13j, 5.2 + 3e-15j])\n", " \n", " recfromcsv(fname, **kwargs)\n", " Load ASCII data stored in a comma-separated file.\n", " \n", " The returned array is a record array (if ``usemask=False``, see\n", " `recarray`) or a masked record array (if ``usemask=True``,\n", " see `ma.mrecords.MaskedRecords`).\n", " \n", " Parameters\n", " ----------\n", " fname, kwargs : For a description of input parameters, see `genfromtxt`.\n", " \n", " See Also\n", " --------\n", " numpy.genfromtxt : generic function to load ASCII data.\n", " \n", " Notes\n", " -----\n", " By default, `dtype` is None, which means that the data-type of the output\n", " array will be determined from the data.\n", " \n", " recfromtxt(fname, **kwargs)\n", " Load ASCII data from a file and return it in a record array.\n", " \n", " If ``usemask=False`` a standard `recarray` is returned,\n", " if ``usemask=True`` a MaskedRecords array is returned.\n", " \n", " Parameters\n", " ----------\n", " fname, kwargs : For a description of input parameters, see `genfromtxt`.\n", " \n", " See Also\n", " --------\n", " numpy.genfromtxt : generic function\n", " \n", " Notes\n", " -----\n", " By default, `dtype` is None, which means that the data-type of the output\n", " array will be determined from the data.\n", " \n", " repeat(a, repeats, axis=None)\n", " Repeat elements of an array.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input array.\n", " repeats : int or array of ints\n", " The number of repetitions for each element. `repeats` is broadcasted\n", " to fit the shape of the given axis.\n", " axis : int, optional\n", " The axis along which to repeat values. By default, use the\n", " flattened input array, and return a flat output array.\n", " \n", " Returns\n", " -------\n", " repeated_array : ndarray\n", " Output array which has the same shape as `a`, except along\n", " the given axis.\n", " \n", " See Also\n", " --------\n", " tile : Tile an array.\n", " unique : Find the unique elements of an array.\n", " \n", " Examples\n", " --------\n", " >>> np.repeat(3, 4)\n", " array([3, 3, 3, 3])\n", " >>> x = np.array([[1,2],[3,4]])\n", " >>> np.repeat(x, 2)\n", " array([1, 1, 2, 2, 3, 3, 4, 4])\n", " >>> np.repeat(x, 3, axis=1)\n", " array([[1, 1, 1, 2, 2, 2],\n", " [3, 3, 3, 4, 4, 4]])\n", " >>> np.repeat(x, [1, 2], axis=0)\n", " array([[1, 2],\n", " [3, 4],\n", " [3, 4]])\n", " \n", " require(a, dtype=None, requirements=None, *, like=None)\n", " Return an ndarray of the provided type that satisfies requirements.\n", " \n", " This function is useful to be sure that an array with the correct flags\n", " is returned for passing to compiled code (perhaps through ctypes).\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " The object to be converted to a type-and-requirement-satisfying array.\n", " dtype : data-type\n", " The required data-type. If None preserve the current dtype. If your\n", " application requires the data to be in native byteorder, include\n", " a byteorder specification as a part of the dtype specification.\n", " requirements : str or sequence of str\n", " The requirements list can be any of the following\n", " \n", " * 'F_CONTIGUOUS' ('F') - ensure a Fortran-contiguous array\n", " * 'C_CONTIGUOUS' ('C') - ensure a C-contiguous array\n", " * 'ALIGNED' ('A') - ensure a data-type aligned array\n", " * 'WRITEABLE' ('W') - ensure a writable array\n", " * 'OWNDATA' ('O') - ensure an array that owns its own data\n", " * 'ENSUREARRAY', ('E') - ensure a base array, instead of a subclass\n", " like : array_like, optional\n", " Reference object to allow the creation of arrays which are not\n", " NumPy arrays. If an array-like passed in as ``like`` supports\n", " the ``__array_function__`` protocol, the result will be defined\n", " by it. In this case, it ensures the creation of an array object\n", " compatible with that passed in via this argument.\n", " \n", " .. versionadded:: 1.20.0\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " Array with specified requirements and type if given.\n", " \n", " See Also\n", " --------\n", " asarray : Convert input to an ndarray.\n", " asanyarray : Convert to an ndarray, but pass through ndarray subclasses.\n", " ascontiguousarray : Convert input to a contiguous array.\n", " asfortranarray : Convert input to an ndarray with column-major\n", " memory order.\n", " ndarray.flags : Information about the memory layout of the array.\n", " \n", " Notes\n", " -----\n", " The returned array will be guaranteed to have the listed requirements\n", " by making a copy if needed.\n", " \n", " Examples\n", " --------\n", " >>> x = np.arange(6).reshape(2,3)\n", " >>> x.flags\n", " C_CONTIGUOUS : True\n", " F_CONTIGUOUS : False\n", " OWNDATA : False\n", " WRITEABLE : True\n", " ALIGNED : True\n", " WRITEBACKIFCOPY : False\n", " \n", " >>> y = np.require(x, dtype=np.float32, requirements=['A', 'O', 'W', 'F'])\n", " >>> y.flags\n", " C_CONTIGUOUS : False\n", " F_CONTIGUOUS : True\n", " OWNDATA : True\n", " WRITEABLE : True\n", " ALIGNED : True\n", " WRITEBACKIFCOPY : False\n", " \n", " reshape(a, newshape, order='C')\n", " Gives a new shape to an array without changing its data.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Array to be reshaped.\n", " newshape : int or tuple of ints\n", " The new shape should be compatible with the original shape. If\n", " an integer, then the result will be a 1-D array of that length.\n", " One shape dimension can be -1. In this case, the value is\n", " inferred from the length of the array and remaining dimensions.\n", " order : {'C', 'F', 'A'}, optional\n", " Read the elements of `a` using this index order, and place the\n", " elements into the reshaped array using this index order. 'C'\n", " means to read / write the elements using C-like index order,\n", " with the last axis index changing fastest, back to the first\n", " axis index changing slowest. 'F' means to read / write the\n", " elements using Fortran-like index order, with the first index\n", " changing fastest, and the last index changing slowest. Note that\n", " the 'C' and 'F' options take no account of the memory layout of\n", " the underlying array, and only refer to the order of indexing.\n", " 'A' means to read / write the elements in Fortran-like index\n", " order if `a` is Fortran *contiguous* in memory, C-like order\n", " otherwise.\n", " \n", " Returns\n", " -------\n", " reshaped_array : ndarray\n", " This will be a new view object if possible; otherwise, it will\n", " be a copy. Note there is no guarantee of the *memory layout* (C- or\n", " Fortran- contiguous) of the returned array.\n", " \n", " See Also\n", " --------\n", " ndarray.reshape : Equivalent method.\n", " \n", " Notes\n", " -----\n", " It is not always possible to change the shape of an array without\n", " copying the data. If you want an error to be raised when the data is copied,\n", " you should assign the new shape to the shape attribute of the array::\n", " \n", " >>> a = np.zeros((10, 2))\n", " \n", " # A transpose makes the array non-contiguous\n", " >>> b = a.T\n", " \n", " # Taking a view makes it possible to modify the shape without modifying\n", " # the initial object.\n", " >>> c = b.view()\n", " >>> c.shape = (20)\n", " Traceback (most recent call last):\n", " ...\n", " AttributeError: Incompatible shape for in-place modification. Use\n", " `.reshape()` to make a copy with the desired shape.\n", " \n", " The `order` keyword gives the index ordering both for *fetching* the values\n", " from `a`, and then *placing* the values into the output array.\n", " For example, let's say you have an array:\n", " \n", " >>> a = np.arange(6).reshape((3, 2))\n", " >>> a\n", " array([[0, 1],\n", " [2, 3],\n", " [4, 5]])\n", " \n", " You can think of reshaping as first raveling the array (using the given\n", " index order), then inserting the elements from the raveled array into the\n", " new array using the same kind of index ordering as was used for the\n", " raveling.\n", " \n", " >>> np.reshape(a, (2, 3)) # C-like index ordering\n", " array([[0, 1, 2],\n", " [3, 4, 5]])\n", " >>> np.reshape(np.ravel(a), (2, 3)) # equivalent to C ravel then C reshape\n", " array([[0, 1, 2],\n", " [3, 4, 5]])\n", " >>> np.reshape(a, (2, 3), order='F') # Fortran-like index ordering\n", " array([[0, 4, 3],\n", " [2, 1, 5]])\n", " >>> np.reshape(np.ravel(a, order='F'), (2, 3), order='F')\n", " array([[0, 4, 3],\n", " [2, 1, 5]])\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([[1,2,3], [4,5,6]])\n", " >>> np.reshape(a, 6)\n", " array([1, 2, 3, 4, 5, 6])\n", " >>> np.reshape(a, 6, order='F')\n", " array([1, 4, 2, 5, 3, 6])\n", " \n", " >>> np.reshape(a, (3,-1)) # the unspecified value is inferred to be 2\n", " array([[1, 2],\n", " [3, 4],\n", " [5, 6]])\n", " \n", " resize(a, new_shape)\n", " Return a new array with the specified shape.\n", " \n", " If the new array is larger than the original array, then the new\n", " array is filled with repeated copies of `a`. Note that this behavior\n", " is different from a.resize(new_shape) which fills with zeros instead\n", " of repeated copies of `a`.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Array to be resized.\n", " \n", " new_shape : int or tuple of int\n", " Shape of resized array.\n", " \n", " Returns\n", " -------\n", " reshaped_array : ndarray\n", " The new array is formed from the data in the old array, repeated\n", " if necessary to fill out the required number of elements. The\n", " data are repeated iterating over the array in C-order.\n", " \n", " See Also\n", " --------\n", " numpy.reshape : Reshape an array without changing the total size.\n", " numpy.pad : Enlarge and pad an array.\n", " numpy.repeat : Repeat elements of an array.\n", " ndarray.resize : resize an array in-place.\n", " \n", " Notes\n", " -----\n", " When the total size of the array does not change `~numpy.reshape` should\n", " be used. In most other cases either indexing (to reduce the size)\n", " or padding (to increase the size) may be a more appropriate solution.\n", " \n", " Warning: This functionality does **not** consider axes separately,\n", " i.e. it does not apply interpolation/extrapolation.\n", " It fills the return array with the required number of elements, iterating\n", " over `a` in C-order, disregarding axes (and cycling back from the start if\n", " the new shape is larger). This functionality is therefore not suitable to\n", " resize images, or data where each axis represents a separate and distinct\n", " entity.\n", " \n", " Examples\n", " --------\n", " >>> a=np.array([[0,1],[2,3]])\n", " >>> np.resize(a,(2,3))\n", " array([[0, 1, 2],\n", " [3, 0, 1]])\n", " >>> np.resize(a,(1,4))\n", " array([[0, 1, 2, 3]])\n", " >>> np.resize(a,(2,4))\n", " array([[0, 1, 2, 3],\n", " [0, 1, 2, 3]])\n", " \n", " result_type(...)\n", " result_type(*arrays_and_dtypes)\n", " \n", " Returns the type that results from applying the NumPy\n", " type promotion rules to the arguments.\n", " \n", " Type promotion in NumPy works similarly to the rules in languages\n", " like C++, with some slight differences. When both scalars and\n", " arrays are used, the array's type takes precedence and the actual value\n", " of the scalar is taken into account.\n", " \n", " For example, calculating 3*a, where a is an array of 32-bit floats,\n", " intuitively should result in a 32-bit float output. If the 3 is a\n", " 32-bit integer, the NumPy rules indicate it can't convert losslessly\n", " into a 32-bit float, so a 64-bit float should be the result type.\n", " By examining the value of the constant, '3', we see that it fits in\n", " an 8-bit integer, which can be cast losslessly into the 32-bit float.\n", " \n", " Parameters\n", " ----------\n", " arrays_and_dtypes : list of arrays and dtypes\n", " The operands of some operation whose result type is needed.\n", " \n", " Returns\n", " -------\n", " out : dtype\n", " The result type.\n", " \n", " See also\n", " --------\n", " dtype, promote_types, min_scalar_type, can_cast\n", " \n", " Notes\n", " -----\n", " .. versionadded:: 1.6.0\n", " \n", " The specific algorithm used is as follows.\n", " \n", " Categories are determined by first checking which of boolean,\n", " integer (int/uint), or floating point (float/complex) the maximum\n", " kind of all the arrays and the scalars are.\n", " \n", " If there are only scalars or the maximum category of the scalars\n", " is higher than the maximum category of the arrays,\n", " the data types are combined with :func:`promote_types`\n", " to produce the return value.\n", " \n", " Otherwise, `min_scalar_type` is called on each array, and\n", " the resulting data types are all combined with :func:`promote_types`\n", " to produce the return value.\n", " \n", " The set of int values is not a subset of the uint values for types\n", " with the same number of bits, something not reflected in\n", " :func:`min_scalar_type`, but handled as a special case in `result_type`.\n", " \n", " Examples\n", " --------\n", " >>> np.result_type(3, np.arange(7, dtype='i1'))\n", " dtype('int8')\n", " \n", " >>> np.result_type('i4', 'c8')\n", " dtype('complex128')\n", " \n", " >>> np.result_type(3.0, -2)\n", " dtype('float64')\n", " \n", " roll(a, shift, axis=None)\n", " Roll array elements along a given axis.\n", " \n", " Elements that roll beyond the last position are re-introduced at\n", " the first.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input array.\n", " shift : int or tuple of ints\n", " The number of places by which elements are shifted. If a tuple,\n", " then `axis` must be a tuple of the same size, and each of the\n", " given axes is shifted by the corresponding number. If an int\n", " while `axis` is a tuple of ints, then the same value is used for\n", " all given axes.\n", " axis : int or tuple of ints, optional\n", " Axis or axes along which elements are shifted. By default, the\n", " array is flattened before shifting, after which the original\n", " shape is restored.\n", " \n", " Returns\n", " -------\n", " res : ndarray\n", " Output array, with the same shape as `a`.\n", " \n", " See Also\n", " --------\n", " rollaxis : Roll the specified axis backwards, until it lies in a\n", " given position.\n", " \n", " Notes\n", " -----\n", " .. versionadded:: 1.12.0\n", " \n", " Supports rolling over multiple dimensions simultaneously.\n", " \n", " Examples\n", " --------\n", " >>> x = np.arange(10)\n", " >>> np.roll(x, 2)\n", " array([8, 9, 0, 1, 2, 3, 4, 5, 6, 7])\n", " >>> np.roll(x, -2)\n", " array([2, 3, 4, 5, 6, 7, 8, 9, 0, 1])\n", " \n", " >>> x2 = np.reshape(x, (2, 5))\n", " >>> x2\n", " array([[0, 1, 2, 3, 4],\n", " [5, 6, 7, 8, 9]])\n", " >>> np.roll(x2, 1)\n", " array([[9, 0, 1, 2, 3],\n", " [4, 5, 6, 7, 8]])\n", " >>> np.roll(x2, -1)\n", " array([[1, 2, 3, 4, 5],\n", " [6, 7, 8, 9, 0]])\n", " >>> np.roll(x2, 1, axis=0)\n", " array([[5, 6, 7, 8, 9],\n", " [0, 1, 2, 3, 4]])\n", " >>> np.roll(x2, -1, axis=0)\n", " array([[5, 6, 7, 8, 9],\n", " [0, 1, 2, 3, 4]])\n", " >>> np.roll(x2, 1, axis=1)\n", " array([[4, 0, 1, 2, 3],\n", " [9, 5, 6, 7, 8]])\n", " >>> np.roll(x2, -1, axis=1)\n", " array([[1, 2, 3, 4, 0],\n", " [6, 7, 8, 9, 5]])\n", " >>> np.roll(x2, (1, 1), axis=(1, 0))\n", " array([[9, 5, 6, 7, 8],\n", " [4, 0, 1, 2, 3]])\n", " >>> np.roll(x2, (2, 1), axis=(1, 0))\n", " array([[8, 9, 5, 6, 7],\n", " [3, 4, 0, 1, 2]])\n", " \n", " rollaxis(a, axis, start=0)\n", " Roll the specified axis backwards, until it lies in a given position.\n", " \n", " This function continues to be supported for backward compatibility, but you\n", " should prefer `moveaxis`. The `moveaxis` function was added in NumPy\n", " 1.11.\n", " \n", " Parameters\n", " ----------\n", " a : ndarray\n", " Input array.\n", " axis : int\n", " The axis to be rolled. The positions of the other axes do not\n", " change relative to one another.\n", " start : int, optional\n", " When ``start <= axis``, the axis is rolled back until it lies in\n", " this position. When ``start > axis``, the axis is rolled until it\n", " lies before this position. The default, 0, results in a \"complete\"\n", " roll. The following table describes how negative values of ``start``\n", " are interpreted:\n", " \n", " .. table::\n", " :align: left\n", " \n", " +-------------------+----------------------+\n", " | ``start`` | Normalized ``start`` |\n", " +===================+======================+\n", " | ``-(arr.ndim+1)`` | raise ``AxisError`` |\n", " +-------------------+----------------------+\n", " | ``-arr.ndim`` | 0 |\n", " +-------------------+----------------------+\n", " | |vdots| | |vdots| |\n", " +-------------------+----------------------+\n", " | ``-1`` | ``arr.ndim-1`` |\n", " +-------------------+----------------------+\n", " | ``0`` | ``0`` |\n", " +-------------------+----------------------+\n", " | |vdots| | |vdots| |\n", " +-------------------+----------------------+\n", " | ``arr.ndim`` | ``arr.ndim`` |\n", " +-------------------+----------------------+\n", " | ``arr.ndim + 1`` | raise ``AxisError`` |\n", " +-------------------+----------------------+\n", " \n", " .. |vdots| unicode:: U+22EE .. Vertical Ellipsis\n", " \n", " Returns\n", " -------\n", " res : ndarray\n", " For NumPy >= 1.10.0 a view of `a` is always returned. For earlier\n", " NumPy versions a view of `a` is returned only if the order of the\n", " axes is changed, otherwise the input array is returned.\n", " \n", " See Also\n", " --------\n", " moveaxis : Move array axes to new positions.\n", " roll : Roll the elements of an array by a number of positions along a\n", " given axis.\n", " \n", " Examples\n", " --------\n", " >>> a = np.ones((3,4,5,6))\n", " >>> np.rollaxis(a, 3, 1).shape\n", " (3, 6, 4, 5)\n", " >>> np.rollaxis(a, 2).shape\n", " (5, 3, 4, 6)\n", " >>> np.rollaxis(a, 1, 4).shape\n", " (3, 5, 6, 4)\n", " \n", " roots(p)\n", " Return the roots of a polynomial with coefficients given in p.\n", " \n", " .. note::\n", " This forms part of the old polynomial API. Since version 1.4, the\n", " new polynomial API defined in `numpy.polynomial` is preferred.\n", " A summary of the differences can be found in the\n", " :doc:`transition guide </reference/routines.polynomials>`.\n", " \n", " The values in the rank-1 array `p` are coefficients of a polynomial.\n", " If the length of `p` is n+1 then the polynomial is described by::\n", " \n", " p[0] * x**n + p[1] * x**(n-1) + ... + p[n-1]*x + p[n]\n", " \n", " Parameters\n", " ----------\n", " p : array_like\n", " Rank-1 array of polynomial coefficients.\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " An array containing the roots of the polynomial.\n", " \n", " Raises\n", " ------\n", " ValueError\n", " When `p` cannot be converted to a rank-1 array.\n", " \n", " See also\n", " --------\n", " poly : Find the coefficients of a polynomial with a given sequence\n", " of roots.\n", " polyval : Compute polynomial values.\n", " polyfit : Least squares polynomial fit.\n", " poly1d : A one-dimensional polynomial class.\n", " \n", " Notes\n", " -----\n", " The algorithm relies on computing the eigenvalues of the\n", " companion matrix [1]_.\n", " \n", " References\n", " ----------\n", " .. [1] R. A. Horn & C. R. Johnson, *Matrix Analysis*. Cambridge, UK:\n", " Cambridge University Press, 1999, pp. 146-7.\n", " \n", " Examples\n", " --------\n", " >>> coeff = [3.2, 2, 1]\n", " >>> np.roots(coeff)\n", " array([-0.3125+0.46351241j, -0.3125-0.46351241j])\n", " \n", " rot90(m, k=1, axes=(0, 1))\n", " Rotate an array by 90 degrees in the plane specified by axes.\n", " \n", " Rotation direction is from the first towards the second axis.\n", " \n", " Parameters\n", " ----------\n", " m : array_like\n", " Array of two or more dimensions.\n", " k : integer\n", " Number of times the array is rotated by 90 degrees.\n", " axes : (2,) array_like\n", " The array is rotated in the plane defined by the axes.\n", " Axes must be different.\n", " \n", " .. versionadded:: 1.12.0\n", " \n", " Returns\n", " -------\n", " y : ndarray\n", " A rotated view of `m`.\n", " \n", " See Also\n", " --------\n", " flip : Reverse the order of elements in an array along the given axis.\n", " fliplr : Flip an array horizontally.\n", " flipud : Flip an array vertically.\n", " \n", " Notes\n", " -----\n", " ``rot90(m, k=1, axes=(1,0))`` is the reverse of\n", " ``rot90(m, k=1, axes=(0,1))``\n", " \n", " ``rot90(m, k=1, axes=(1,0))`` is equivalent to\n", " ``rot90(m, k=-1, axes=(0,1))``\n", " \n", " Examples\n", " --------\n", " >>> m = np.array([[1,2],[3,4]], int)\n", " >>> m\n", " array([[1, 2],\n", " [3, 4]])\n", " >>> np.rot90(m)\n", " array([[2, 4],\n", " [1, 3]])\n", " >>> np.rot90(m, 2)\n", " array([[4, 3],\n", " [2, 1]])\n", " >>> m = np.arange(8).reshape((2,2,2))\n", " >>> np.rot90(m, 1, (1,2))\n", " array([[[1, 3],\n", " [0, 2]],\n", " [[5, 7],\n", " [4, 6]]])\n", " \n", " round_(a, decimals=0, out=None)\n", " Round an array to the given number of decimals.\n", " \n", " See Also\n", " --------\n", " around : equivalent function; see for details.\n", " \n", " row_stack = vstack(tup, *, dtype=None, casting='same_kind')\n", " Stack arrays in sequence vertically (row wise).\n", " \n", " This is equivalent to concatenation along the first axis after 1-D arrays\n", " of shape `(N,)` have been reshaped to `(1,N)`. Rebuilds arrays divided by\n", " `vsplit`.\n", " \n", " This function makes most sense for arrays with up to 3 dimensions. For\n", " instance, for pixel-data with a height (first axis), width (second axis),\n", " and r/g/b channels (third axis). The functions `concatenate`, `stack` and\n", " `block` provide more general stacking and concatenation operations.\n", " \n", " ``np.row_stack`` is an alias for `vstack`. They are the same function.\n", " \n", " Parameters\n", " ----------\n", " tup : sequence of ndarrays\n", " The arrays must have the same shape along all but the first axis.\n", " 1-D arrays must have the same length.\n", " \n", " dtype : str or dtype\n", " If provided, the destination array will have this dtype. Cannot be\n", " provided together with `out`.\n", " \n", " .. versionadded:: 1.24\n", " \n", " casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional\n", " Controls what kind of data casting may occur. Defaults to 'same_kind'.\n", " \n", " .. versionadded:: 1.24\n", " \n", " Returns\n", " -------\n", " stacked : ndarray\n", " The array formed by stacking the given arrays, will be at least 2-D.\n", " \n", " See Also\n", " --------\n", " concatenate : Join a sequence of arrays along an existing axis.\n", " stack : Join a sequence of arrays along a new axis.\n", " block : Assemble an nd-array from nested lists of blocks.\n", " hstack : Stack arrays in sequence horizontally (column wise).\n", " dstack : Stack arrays in sequence depth wise (along third axis).\n", " column_stack : Stack 1-D arrays as columns into a 2-D array.\n", " vsplit : Split an array into multiple sub-arrays vertically (row-wise).\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([1, 2, 3])\n", " >>> b = np.array([4, 5, 6])\n", " >>> np.vstack((a,b))\n", " array([[1, 2, 3],\n", " [4, 5, 6]])\n", " \n", " >>> a = np.array([[1], [2], [3]])\n", " >>> b = np.array([[4], [5], [6]])\n", " >>> np.vstack((a,b))\n", " array([[1],\n", " [2],\n", " [3],\n", " [4],\n", " [5],\n", " [6]])\n", " \n", " safe_eval(source)\n", " Protected string evaluation.\n", " \n", " Evaluate a string containing a Python literal expression without\n", " allowing the execution of arbitrary non-literal code.\n", " \n", " .. warning::\n", " \n", " This function is identical to :py:meth:`ast.literal_eval` and\n", " has the same security implications. It may not always be safe\n", " to evaluate large input strings.\n", " \n", " Parameters\n", " ----------\n", " source : str\n", " The string to evaluate.\n", " \n", " Returns\n", " -------\n", " obj : object\n", " The result of evaluating `source`.\n", " \n", " Raises\n", " ------\n", " SyntaxError\n", " If the code has invalid Python syntax, or if it contains\n", " non-literal code.\n", " \n", " Examples\n", " --------\n", " >>> np.safe_eval('1')\n", " 1\n", " >>> np.safe_eval('[1, 2, 3]')\n", " [1, 2, 3]\n", " >>> np.safe_eval('{\"foo\": (\"bar\", 10.0)}')\n", " {'foo': ('bar', 10.0)}\n", " \n", " >>> np.safe_eval('import os')\n", " Traceback (most recent call last):\n", " ...\n", " SyntaxError: invalid syntax\n", " \n", " >>> np.safe_eval('open(\"/home/user/.ssh/id_dsa\").read()')\n", " Traceback (most recent call last):\n", " ...\n", " ValueError: malformed node or string: <_ast.Call object at 0x...>\n", " \n", " save(file, arr, allow_pickle=True, fix_imports=True)\n", " Save an array to a binary file in NumPy ``.npy`` format.\n", " \n", " Parameters\n", " ----------\n", " file : file, str, or pathlib.Path\n", " File or filename to which the data is saved. If file is a file-object,\n", " then the filename is unchanged. If file is a string or Path, a ``.npy``\n", " extension will be appended to the filename if it does not already\n", " have one.\n", " arr : array_like\n", " Array data to be saved.\n", " allow_pickle : bool, optional\n", " Allow saving object arrays using Python pickles. Reasons for disallowing\n", " pickles include security (loading pickled data can execute arbitrary\n", " code) and portability (pickled objects may not be loadable on different\n", " Python installations, for example if the stored objects require libraries\n", " that are not available, and not all pickled data is compatible between\n", " Python 2 and Python 3).\n", " Default: True\n", " fix_imports : bool, optional\n", " Only useful in forcing objects in object arrays on Python 3 to be\n", " pickled in a Python 2 compatible way. If `fix_imports` is True, pickle\n", " will try to map the new Python 3 names to the old module names used in\n", " Python 2, so that the pickle data stream is readable with Python 2.\n", " \n", " See Also\n", " --------\n", " savez : Save several arrays into a ``.npz`` archive\n", " savetxt, load\n", " \n", " Notes\n", " -----\n", " For a description of the ``.npy`` format, see :py:mod:`numpy.lib.format`.\n", " \n", " Any data saved to the file is appended to the end of the file.\n", " \n", " Examples\n", " --------\n", " >>> from tempfile import TemporaryFile\n", " >>> outfile = TemporaryFile()\n", " \n", " >>> x = np.arange(10)\n", " >>> np.save(outfile, x)\n", " \n", " >>> _ = outfile.seek(0) # Only needed here to simulate closing & reopening file\n", " >>> np.load(outfile)\n", " array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])\n", " \n", " \n", " >>> with open('test.npy', 'wb') as f:\n", " ... np.save(f, np.array([1, 2]))\n", " ... np.save(f, np.array([1, 3]))\n", " >>> with open('test.npy', 'rb') as f:\n", " ... a = np.load(f)\n", " ... b = np.load(f)\n", " >>> print(a, b)\n", " # [1 2] [1 3]\n", " \n", " savetxt(fname, X, fmt='%.18e', delimiter=' ', newline='\\n', header='', footer='', comments='# ', encoding=None)\n", " Save an array to a text file.\n", " \n", " Parameters\n", " ----------\n", " fname : filename or file handle\n", " If the filename ends in ``.gz``, the file is automatically saved in\n", " compressed gzip format. `loadtxt` understands gzipped files\n", " transparently.\n", " X : 1D or 2D array_like\n", " Data to be saved to a text file.\n", " fmt : str or sequence of strs, optional\n", " A single format (%10.5f), a sequence of formats, or a\n", " multi-format string, e.g. 'Iteration %d -- %10.5f', in which\n", " case `delimiter` is ignored. For complex `X`, the legal options\n", " for `fmt` are:\n", " \n", " * a single specifier, `fmt='%.4e'`, resulting in numbers formatted\n", " like `' (%s+%sj)' % (fmt, fmt)`\n", " * a full string specifying every real and imaginary part, e.g.\n", " `' %.4e %+.4ej %.4e %+.4ej %.4e %+.4ej'` for 3 columns\n", " * a list of specifiers, one per column - in this case, the real\n", " and imaginary part must have separate specifiers,\n", " e.g. `['%.3e + %.3ej', '(%.15e%+.15ej)']` for 2 columns\n", " delimiter : str, optional\n", " String or character separating columns.\n", " newline : str, optional\n", " String or character separating lines.\n", " \n", " .. versionadded:: 1.5.0\n", " header : str, optional\n", " String that will be written at the beginning of the file.\n", " \n", " .. versionadded:: 1.7.0\n", " footer : str, optional\n", " String that will be written at the end of the file.\n", " \n", " .. versionadded:: 1.7.0\n", " comments : str, optional\n", " String that will be prepended to the ``header`` and ``footer`` strings,\n", " to mark them as comments. Default: '# ', as expected by e.g.\n", " ``numpy.loadtxt``.\n", " \n", " .. versionadded:: 1.7.0\n", " encoding : {None, str}, optional\n", " Encoding used to encode the outputfile. Does not apply to output\n", " streams. If the encoding is something other than 'bytes' or 'latin1'\n", " you will not be able to load the file in NumPy versions < 1.14. Default\n", " is 'latin1'.\n", " \n", " .. versionadded:: 1.14.0\n", " \n", " \n", " See Also\n", " --------\n", " save : Save an array to a binary file in NumPy ``.npy`` format\n", " savez : Save several arrays into an uncompressed ``.npz`` archive\n", " savez_compressed : Save several arrays into a compressed ``.npz`` archive\n", " \n", " Notes\n", " -----\n", " Further explanation of the `fmt` parameter\n", " (``%[flag]width[.precision]specifier``):\n", " \n", " flags:\n", " ``-`` : left justify\n", " \n", " ``+`` : Forces to precede result with + or -.\n", " \n", " ``0`` : Left pad the number with zeros instead of space (see width).\n", " \n", " width:\n", " Minimum number of characters to be printed. The value is not truncated\n", " if it has more characters.\n", " \n", " precision:\n", " - For integer specifiers (eg. ``d,i,o,x``), the minimum number of\n", " digits.\n", " - For ``e, E`` and ``f`` specifiers, the number of digits to print\n", " after the decimal point.\n", " - For ``g`` and ``G``, the maximum number of significant digits.\n", " - For ``s``, the maximum number of characters.\n", " \n", " specifiers:\n", " ``c`` : character\n", " \n", " ``d`` or ``i`` : signed decimal integer\n", " \n", " ``e`` or ``E`` : scientific notation with ``e`` or ``E``.\n", " \n", " ``f`` : decimal floating point\n", " \n", " ``g,G`` : use the shorter of ``e,E`` or ``f``\n", " \n", " ``o`` : signed octal\n", " \n", " ``s`` : string of characters\n", " \n", " ``u`` : unsigned decimal integer\n", " \n", " ``x,X`` : unsigned hexadecimal integer\n", " \n", " This explanation of ``fmt`` is not complete, for an exhaustive\n", " specification see [1]_.\n", " \n", " References\n", " ----------\n", " .. [1] `Format Specification Mini-Language\n", " <https://docs.python.org/library/string.html#format-specification-mini-language>`_,\n", " Python Documentation.\n", " \n", " Examples\n", " --------\n", " >>> x = y = z = np.arange(0.0,5.0,1.0)\n", " >>> np.savetxt('test.out', x, delimiter=',') # X is an array\n", " >>> np.savetxt('test.out', (x,y,z)) # x,y,z equal sized 1D arrays\n", " >>> np.savetxt('test.out', x, fmt='%1.4e') # use exponential notation\n", " \n", " savez(file, *args, **kwds)\n", " Save several arrays into a single file in uncompressed ``.npz`` format.\n", " \n", " Provide arrays as keyword arguments to store them under the\n", " corresponding name in the output file: ``savez(fn, x=x, y=y)``.\n", " \n", " If arrays are specified as positional arguments, i.e., ``savez(fn,\n", " x, y)``, their names will be `arr_0`, `arr_1`, etc.\n", " \n", " Parameters\n", " ----------\n", " file : str or file\n", " Either the filename (string) or an open file (file-like object)\n", " where the data will be saved. If file is a string or a Path, the\n", " ``.npz`` extension will be appended to the filename if it is not\n", " already there.\n", " args : Arguments, optional\n", " Arrays to save to the file. Please use keyword arguments (see\n", " `kwds` below) to assign names to arrays. Arrays specified as\n", " args will be named \"arr_0\", \"arr_1\", and so on.\n", " kwds : Keyword arguments, optional\n", " Arrays to save to the file. Each array will be saved to the\n", " output file with its corresponding keyword name.\n", " \n", " Returns\n", " -------\n", " None\n", " \n", " See Also\n", " --------\n", " save : Save a single array to a binary file in NumPy format.\n", " savetxt : Save an array to a file as plain text.\n", " savez_compressed : Save several arrays into a compressed ``.npz`` archive\n", " \n", " Notes\n", " -----\n", " The ``.npz`` file format is a zipped archive of files named after the\n", " variables they contain. The archive is not compressed and each file\n", " in the archive contains one variable in ``.npy`` format. For a\n", " description of the ``.npy`` format, see :py:mod:`numpy.lib.format`.\n", " \n", " When opening the saved ``.npz`` file with `load` a `NpzFile` object is\n", " returned. This is a dictionary-like object which can be queried for\n", " its list of arrays (with the ``.files`` attribute), and for the arrays\n", " themselves.\n", " \n", " Keys passed in `kwds` are used as filenames inside the ZIP archive.\n", " Therefore, keys should be valid filenames; e.g., avoid keys that begin with\n", " ``/`` or contain ``.``.\n", " \n", " When naming variables with keyword arguments, it is not possible to name a\n", " variable ``file``, as this would cause the ``file`` argument to be defined\n", " twice in the call to ``savez``.\n", " \n", " Examples\n", " --------\n", " >>> from tempfile import TemporaryFile\n", " >>> outfile = TemporaryFile()\n", " >>> x = np.arange(10)\n", " >>> y = np.sin(x)\n", " \n", " Using `savez` with \\*args, the arrays are saved with default names.\n", " \n", " >>> np.savez(outfile, x, y)\n", " >>> _ = outfile.seek(0) # Only needed here to simulate closing & reopening file\n", " >>> npzfile = np.load(outfile)\n", " >>> npzfile.files\n", " ['arr_0', 'arr_1']\n", " >>> npzfile['arr_0']\n", " array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])\n", " \n", " Using `savez` with \\**kwds, the arrays are saved with the keyword names.\n", " \n", " >>> outfile = TemporaryFile()\n", " >>> np.savez(outfile, x=x, y=y)\n", " >>> _ = outfile.seek(0)\n", " >>> npzfile = np.load(outfile)\n", " >>> sorted(npzfile.files)\n", " ['x', 'y']\n", " >>> npzfile['x']\n", " array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])\n", " \n", " savez_compressed(file, *args, **kwds)\n", " Save several arrays into a single file in compressed ``.npz`` format.\n", " \n", " Provide arrays as keyword arguments to store them under the\n", " corresponding name in the output file: ``savez(fn, x=x, y=y)``.\n", " \n", " If arrays are specified as positional arguments, i.e., ``savez(fn,\n", " x, y)``, their names will be `arr_0`, `arr_1`, etc.\n", " \n", " Parameters\n", " ----------\n", " file : str or file\n", " Either the filename (string) or an open file (file-like object)\n", " where the data will be saved. If file is a string or a Path, the\n", " ``.npz`` extension will be appended to the filename if it is not\n", " already there.\n", " args : Arguments, optional\n", " Arrays to save to the file. Please use keyword arguments (see\n", " `kwds` below) to assign names to arrays. Arrays specified as\n", " args will be named \"arr_0\", \"arr_1\", and so on.\n", " kwds : Keyword arguments, optional\n", " Arrays to save to the file. Each array will be saved to the\n", " output file with its corresponding keyword name.\n", " \n", " Returns\n", " -------\n", " None\n", " \n", " See Also\n", " --------\n", " numpy.save : Save a single array to a binary file in NumPy format.\n", " numpy.savetxt : Save an array to a file as plain text.\n", " numpy.savez : Save several arrays into an uncompressed ``.npz`` file format\n", " numpy.load : Load the files created by savez_compressed.\n", " \n", " Notes\n", " -----\n", " The ``.npz`` file format is a zipped archive of files named after the\n", " variables they contain. The archive is compressed with\n", " ``zipfile.ZIP_DEFLATED`` and each file in the archive contains one variable\n", " in ``.npy`` format. For a description of the ``.npy`` format, see\n", " :py:mod:`numpy.lib.format`.\n", " \n", " \n", " When opening the saved ``.npz`` file with `load` a `NpzFile` object is\n", " returned. This is a dictionary-like object which can be queried for\n", " its list of arrays (with the ``.files`` attribute), and for the arrays\n", " themselves.\n", " \n", " Examples\n", " --------\n", " >>> test_array = np.random.rand(3, 2)\n", " >>> test_vector = np.random.rand(4)\n", " >>> np.savez_compressed('/tmp/123', a=test_array, b=test_vector)\n", " >>> loaded = np.load('/tmp/123.npz')\n", " >>> print(np.array_equal(test_array, loaded['a']))\n", " True\n", " >>> print(np.array_equal(test_vector, loaded['b']))\n", " True\n", " \n", " sctype2char(sctype)\n", " Return the string representation of a scalar dtype.\n", " \n", " Parameters\n", " ----------\n", " sctype : scalar dtype or object\n", " If a scalar dtype, the corresponding string character is\n", " returned. If an object, `sctype2char` tries to infer its scalar type\n", " and then return the corresponding string character.\n", " \n", " Returns\n", " -------\n", " typechar : str\n", " The string character corresponding to the scalar type.\n", " \n", " Raises\n", " ------\n", " ValueError\n", " If `sctype` is an object for which the type can not be inferred.\n", " \n", " See Also\n", " --------\n", " obj2sctype, issctype, issubsctype, mintypecode\n", " \n", " Examples\n", " --------\n", " >>> for sctype in [np.int32, np.double, np.complex_, np.string_, np.ndarray]:\n", " ... print(np.sctype2char(sctype))\n", " l # may vary\n", " d\n", " D\n", " S\n", " O\n", " \n", " >>> x = np.array([1., 2-1.j])\n", " >>> np.sctype2char(x)\n", " 'D'\n", " >>> np.sctype2char(list)\n", " 'O'\n", " \n", " searchsorted(a, v, side='left', sorter=None)\n", " Find indices where elements should be inserted to maintain order.\n", " \n", " Find the indices into a sorted array `a` such that, if the\n", " corresponding elements in `v` were inserted before the indices, the\n", " order of `a` would be preserved.\n", " \n", " Assuming that `a` is sorted:\n", " \n", " ====== ============================\n", " `side` returned index `i` satisfies\n", " ====== ============================\n", " left ``a[i-1] < v <= a[i]``\n", " right ``a[i-1] <= v < a[i]``\n", " ====== ============================\n", " \n", " Parameters\n", " ----------\n", " a : 1-D array_like\n", " Input array. If `sorter` is None, then it must be sorted in\n", " ascending order, otherwise `sorter` must be an array of indices\n", " that sort it.\n", " v : array_like\n", " Values to insert into `a`.\n", " side : {'left', 'right'}, optional\n", " If 'left', the index of the first suitable location found is given.\n", " If 'right', return the last such index. If there is no suitable\n", " index, return either 0 or N (where N is the length of `a`).\n", " sorter : 1-D array_like, optional\n", " Optional array of integer indices that sort array a into ascending\n", " order. They are typically the result of argsort.\n", " \n", " .. versionadded:: 1.7.0\n", " \n", " Returns\n", " -------\n", " indices : int or array of ints\n", " Array of insertion points with the same shape as `v`,\n", " or an integer if `v` is a scalar.\n", " \n", " See Also\n", " --------\n", " sort : Return a sorted copy of an array.\n", " histogram : Produce histogram from 1-D data.\n", " \n", " Notes\n", " -----\n", " Binary search is used to find the required insertion points.\n", " \n", " As of NumPy 1.4.0 `searchsorted` works with real/complex arrays containing\n", " `nan` values. The enhanced sort order is documented in `sort`.\n", " \n", " This function uses the same algorithm as the builtin python `bisect.bisect_left`\n", " (``side='left'``) and `bisect.bisect_right` (``side='right'``) functions,\n", " which is also vectorized in the `v` argument.\n", " \n", " Examples\n", " --------\n", " >>> np.searchsorted([1,2,3,4,5], 3)\n", " 2\n", " >>> np.searchsorted([1,2,3,4,5], 3, side='right')\n", " 3\n", " >>> np.searchsorted([1,2,3,4,5], [-10, 10, 2, 3])\n", " array([0, 5, 1, 2])\n", " \n", " select(condlist, choicelist, default=0)\n", " Return an array drawn from elements in choicelist, depending on conditions.\n", " \n", " Parameters\n", " ----------\n", " condlist : list of bool ndarrays\n", " The list of conditions which determine from which array in `choicelist`\n", " the output elements are taken. When multiple conditions are satisfied,\n", " the first one encountered in `condlist` is used.\n", " choicelist : list of ndarrays\n", " The list of arrays from which the output elements are taken. It has\n", " to be of the same length as `condlist`.\n", " default : scalar, optional\n", " The element inserted in `output` when all conditions evaluate to False.\n", " \n", " Returns\n", " -------\n", " output : ndarray\n", " The output at position m is the m-th element of the array in\n", " `choicelist` where the m-th element of the corresponding array in\n", " `condlist` is True.\n", " \n", " See Also\n", " --------\n", " where : Return elements from one of two arrays depending on condition.\n", " take, choose, compress, diag, diagonal\n", " \n", " Examples\n", " --------\n", " >>> x = np.arange(6)\n", " >>> condlist = [x<3, x>3]\n", " >>> choicelist = [x, x**2]\n", " >>> np.select(condlist, choicelist, 42)\n", " array([ 0, 1, 2, 42, 16, 25])\n", " \n", " >>> condlist = [x<=4, x>3]\n", " >>> choicelist = [x, x**2]\n", " >>> np.select(condlist, choicelist, 55)\n", " array([ 0, 1, 2, 3, 4, 25])\n", " \n", " set_numeric_ops(...)\n", " set_numeric_ops(op1=func1, op2=func2, ...)\n", " \n", " Set numerical operators for array objects.\n", " \n", " .. deprecated:: 1.16\n", " \n", " For the general case, use :c:func:`PyUFunc_ReplaceLoopBySignature`.\n", " For ndarray subclasses, define the ``__array_ufunc__`` method and\n", " override the relevant ufunc.\n", " \n", " Parameters\n", " ----------\n", " op1, op2, ... : callable\n", " Each ``op = func`` pair describes an operator to be replaced.\n", " For example, ``add = lambda x, y: np.add(x, y) % 5`` would replace\n", " addition by modulus 5 addition.\n", " \n", " Returns\n", " -------\n", " saved_ops : list of callables\n", " A list of all operators, stored before making replacements.\n", " \n", " Notes\n", " -----\n", " .. warning::\n", " Use with care! Incorrect usage may lead to memory errors.\n", " \n", " A function replacing an operator cannot make use of that operator.\n", " For example, when replacing add, you may not use ``+``. Instead,\n", " directly call ufuncs.\n", " \n", " Examples\n", " --------\n", " >>> def add_mod5(x, y):\n", " ... return np.add(x, y) % 5\n", " ...\n", " >>> old_funcs = np.set_numeric_ops(add=add_mod5)\n", " \n", " >>> x = np.arange(12).reshape((3, 4))\n", " >>> x + x\n", " array([[0, 2, 4, 1],\n", " [3, 0, 2, 4],\n", " [1, 3, 0, 2]])\n", " \n", " >>> ignore = np.set_numeric_ops(**old_funcs) # restore operators\n", " \n", " set_printoptions(precision=None, threshold=None, edgeitems=None, linewidth=None, suppress=None, nanstr=None, infstr=None, formatter=None, sign=None, floatmode=None, *, legacy=None)\n", " Set printing options.\n", " \n", " These options determine the way floating point numbers, arrays and\n", " other NumPy objects are displayed.\n", " \n", " Parameters\n", " ----------\n", " precision : int or None, optional\n", " Number of digits of precision for floating point output (default 8).\n", " May be None if `floatmode` is not `fixed`, to print as many digits as\n", " necessary to uniquely specify the value.\n", " threshold : int, optional\n", " Total number of array elements which trigger summarization\n", " rather than full repr (default 1000).\n", " To always use the full repr without summarization, pass `sys.maxsize`.\n", " edgeitems : int, optional\n", " Number of array items in summary at beginning and end of\n", " each dimension (default 3).\n", " linewidth : int, optional\n", " The number of characters per line for the purpose of inserting\n", " line breaks (default 75).\n", " suppress : bool, optional\n", " If True, always print floating point numbers using fixed point\n", " notation, in which case numbers equal to zero in the current precision\n", " will print as zero. If False, then scientific notation is used when\n", " absolute value of the smallest number is < 1e-4 or the ratio of the\n", " maximum absolute value to the minimum is > 1e3. The default is False.\n", " nanstr : str, optional\n", " String representation of floating point not-a-number (default nan).\n", " infstr : str, optional\n", " String representation of floating point infinity (default inf).\n", " sign : string, either '-', '+', or ' ', optional\n", " Controls printing of the sign of floating-point types. If '+', always\n", " print the sign of positive values. If ' ', always prints a space\n", " (whitespace character) in the sign position of positive values. If\n", " '-', omit the sign character of positive values. (default '-')\n", " formatter : dict of callables, optional\n", " If not None, the keys should indicate the type(s) that the respective\n", " formatting function applies to. Callables should return a string.\n", " Types that are not specified (by their corresponding keys) are handled\n", " by the default formatters. Individual types for which a formatter\n", " can be set are:\n", " \n", " - 'bool'\n", " - 'int'\n", " - 'timedelta' : a `numpy.timedelta64`\n", " - 'datetime' : a `numpy.datetime64`\n", " - 'float'\n", " - 'longfloat' : 128-bit floats\n", " - 'complexfloat'\n", " - 'longcomplexfloat' : composed of two 128-bit floats\n", " - 'numpystr' : types `numpy.string_` and `numpy.unicode_`\n", " - 'object' : `np.object_` arrays\n", " \n", " Other keys that can be used to set a group of types at once are:\n", " \n", " - 'all' : sets all types\n", " - 'int_kind' : sets 'int'\n", " - 'float_kind' : sets 'float' and 'longfloat'\n", " - 'complex_kind' : sets 'complexfloat' and 'longcomplexfloat'\n", " - 'str_kind' : sets 'numpystr'\n", " floatmode : str, optional\n", " Controls the interpretation of the `precision` option for\n", " floating-point types. Can take the following values\n", " (default maxprec_equal):\n", " \n", " * 'fixed': Always print exactly `precision` fractional digits,\n", " even if this would print more or fewer digits than\n", " necessary to specify the value uniquely.\n", " * 'unique': Print the minimum number of fractional digits necessary\n", " to represent each value uniquely. Different elements may\n", " have a different number of digits. The value of the\n", " `precision` option is ignored.\n", " * 'maxprec': Print at most `precision` fractional digits, but if\n", " an element can be uniquely represented with fewer digits\n", " only print it with that many.\n", " * 'maxprec_equal': Print at most `precision` fractional digits,\n", " but if every element in the array can be uniquely\n", " represented with an equal number of fewer digits, use that\n", " many digits for all elements.\n", " legacy : string or `False`, optional\n", " If set to the string `'1.13'` enables 1.13 legacy printing mode. This\n", " approximates numpy 1.13 print output by including a space in the sign\n", " position of floats and different behavior for 0d arrays. This also\n", " enables 1.21 legacy printing mode (described below).\n", " \n", " If set to the string `'1.21'` enables 1.21 legacy printing mode. This\n", " approximates numpy 1.21 print output of complex structured dtypes\n", " by not inserting spaces after commas that separate fields and after\n", " colons.\n", " \n", " If set to `False`, disables legacy mode.\n", " \n", " Unrecognized strings will be ignored with a warning for forward\n", " compatibility.\n", " \n", " .. versionadded:: 1.14.0\n", " .. versionchanged:: 1.22.0\n", " \n", " See Also\n", " --------\n", " get_printoptions, printoptions, set_string_function, array2string\n", " \n", " Notes\n", " -----\n", " `formatter` is always reset with a call to `set_printoptions`.\n", " \n", " Use `printoptions` as a context manager to set the values temporarily.\n", " \n", " Examples\n", " --------\n", " Floating point precision can be set:\n", " \n", " >>> np.set_printoptions(precision=4)\n", " >>> np.array([1.123456789])\n", " [1.1235]\n", " \n", " Long arrays can be summarised:\n", " \n", " >>> np.set_printoptions(threshold=5)\n", " >>> np.arange(10)\n", " array([0, 1, 2, ..., 7, 8, 9])\n", " \n", " Small results can be suppressed:\n", " \n", " >>> eps = np.finfo(float).eps\n", " >>> x = np.arange(4.)\n", " >>> x**2 - (x + eps)**2\n", " array([-4.9304e-32, -4.4409e-16, 0.0000e+00, 0.0000e+00])\n", " >>> np.set_printoptions(suppress=True)\n", " >>> x**2 - (x + eps)**2\n", " array([-0., -0., 0., 0.])\n", " \n", " A custom formatter can be used to display array elements as desired:\n", " \n", " >>> np.set_printoptions(formatter={'all':lambda x: 'int: '+str(-x)})\n", " >>> x = np.arange(3)\n", " >>> x\n", " array([int: 0, int: -1, int: -2])\n", " >>> np.set_printoptions() # formatter gets reset\n", " >>> x\n", " array([0, 1, 2])\n", " \n", " To put back the default options, you can use:\n", " \n", " >>> np.set_printoptions(edgeitems=3, infstr='inf',\n", " ... linewidth=75, nanstr='nan', precision=8,\n", " ... suppress=False, threshold=1000, formatter=None)\n", " \n", " Also to temporarily override options, use `printoptions` as a context manager:\n", " \n", " >>> with np.printoptions(precision=2, suppress=True, threshold=5):\n", " ... np.linspace(0, 10, 10)\n", " array([ 0. , 1.11, 2.22, ..., 7.78, 8.89, 10. ])\n", " \n", " set_string_function(f, repr=True)\n", " Set a Python function to be used when pretty printing arrays.\n", " \n", " Parameters\n", " ----------\n", " f : function or None\n", " Function to be used to pretty print arrays. The function should expect\n", " a single array argument and return a string of the representation of\n", " the array. If None, the function is reset to the default NumPy function\n", " to print arrays.\n", " repr : bool, optional\n", " If True (default), the function for pretty printing (``__repr__``)\n", " is set, if False the function that returns the default string\n", " representation (``__str__``) is set.\n", " \n", " See Also\n", " --------\n", " set_printoptions, get_printoptions\n", " \n", " Examples\n", " --------\n", " >>> def pprint(arr):\n", " ... return 'HA! - What are you going to do now?'\n", " ...\n", " >>> np.set_string_function(pprint)\n", " >>> a = np.arange(10)\n", " >>> a\n", " HA! - What are you going to do now?\n", " >>> _ = a\n", " >>> # [0 1 2 3 4 5 6 7 8 9]\n", " \n", " We can reset the function to the default:\n", " \n", " >>> np.set_string_function(None)\n", " >>> a\n", " array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])\n", " \n", " `repr` affects either pretty printing or normal string representation.\n", " Note that ``__repr__`` is still affected by setting ``__str__``\n", " because the width of each array element in the returned string becomes\n", " equal to the length of the result of ``__str__()``.\n", " \n", " >>> x = np.arange(4)\n", " >>> np.set_string_function(lambda x:'random', repr=False)\n", " >>> x.__str__()\n", " 'random'\n", " >>> x.__repr__()\n", " 'array([0, 1, 2, 3])'\n", " \n", " setbufsize(size)\n", " Set the size of the buffer used in ufuncs.\n", " \n", " Parameters\n", " ----------\n", " size : int\n", " Size of buffer.\n", " \n", " setdiff1d(ar1, ar2, assume_unique=False)\n", " Find the set difference of two arrays.\n", " \n", " Return the unique values in `ar1` that are not in `ar2`.\n", " \n", " Parameters\n", " ----------\n", " ar1 : array_like\n", " Input array.\n", " ar2 : array_like\n", " Input comparison array.\n", " assume_unique : bool\n", " If True, the input arrays are both assumed to be unique, which\n", " can speed up the calculation. Default is False.\n", " \n", " Returns\n", " -------\n", " setdiff1d : ndarray\n", " 1D array of values in `ar1` that are not in `ar2`. The result\n", " is sorted when `assume_unique=False`, but otherwise only sorted\n", " if the input is sorted.\n", " \n", " See Also\n", " --------\n", " numpy.lib.arraysetops : Module with a number of other functions for\n", " performing set operations on arrays.\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([1, 2, 3, 2, 4, 1])\n", " >>> b = np.array([3, 4, 5, 6])\n", " >>> np.setdiff1d(a, b)\n", " array([1, 2])\n", " \n", " seterr(all=None, divide=None, over=None, under=None, invalid=None)\n", " Set how floating-point errors are handled.\n", " \n", " Note that operations on integer scalar types (such as `int16`) are\n", " handled like floating point, and are affected by these settings.\n", " \n", " Parameters\n", " ----------\n", " all : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional\n", " Set treatment for all types of floating-point errors at once:\n", " \n", " - ignore: Take no action when the exception occurs.\n", " - warn: Print a `RuntimeWarning` (via the Python `warnings` module).\n", " - raise: Raise a `FloatingPointError`.\n", " - call: Call a function specified using the `seterrcall` function.\n", " - print: Print a warning directly to ``stdout``.\n", " - log: Record error in a Log object specified by `seterrcall`.\n", " \n", " The default is not to change the current behavior.\n", " divide : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional\n", " Treatment for division by zero.\n", " over : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional\n", " Treatment for floating-point overflow.\n", " under : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional\n", " Treatment for floating-point underflow.\n", " invalid : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional\n", " Treatment for invalid floating-point operation.\n", " \n", " Returns\n", " -------\n", " old_settings : dict\n", " Dictionary containing the old settings.\n", " \n", " See also\n", " --------\n", " seterrcall : Set a callback function for the 'call' mode.\n", " geterr, geterrcall, errstate\n", " \n", " Notes\n", " -----\n", " The floating-point exceptions are defined in the IEEE 754 standard [1]_:\n", " \n", " - Division by zero: infinite result obtained from finite numbers.\n", " - Overflow: result too large to be expressed.\n", " - Underflow: result so close to zero that some precision\n", " was lost.\n", " - Invalid operation: result is not an expressible number, typically\n", " indicates that a NaN was produced.\n", " \n", " .. [1] https://en.wikipedia.org/wiki/IEEE_754\n", " \n", " Examples\n", " --------\n", " >>> old_settings = np.seterr(all='ignore') #seterr to known value\n", " >>> np.seterr(over='raise')\n", " {'divide': 'ignore', 'over': 'ignore', 'under': 'ignore', 'invalid': 'ignore'}\n", " >>> np.seterr(**old_settings) # reset to default\n", " {'divide': 'ignore', 'over': 'raise', 'under': 'ignore', 'invalid': 'ignore'}\n", " \n", " >>> np.int16(32000) * np.int16(3)\n", " 30464\n", " >>> old_settings = np.seterr(all='warn', over='raise')\n", " >>> np.int16(32000) * np.int16(3)\n", " Traceback (most recent call last):\n", " File \"<stdin>\", line 1, in <module>\n", " FloatingPointError: overflow encountered in scalar multiply\n", " \n", " >>> old_settings = np.seterr(all='print')\n", " >>> np.geterr()\n", " {'divide': 'print', 'over': 'print', 'under': 'print', 'invalid': 'print'}\n", " >>> np.int16(32000) * np.int16(3)\n", " 30464\n", " \n", " seterrcall(func)\n", " Set the floating-point error callback function or log object.\n", " \n", " There are two ways to capture floating-point error messages. The first\n", " is to set the error-handler to 'call', using `seterr`. Then, set\n", " the function to call using this function.\n", " \n", " The second is to set the error-handler to 'log', using `seterr`.\n", " Floating-point errors then trigger a call to the 'write' method of\n", " the provided object.\n", " \n", " Parameters\n", " ----------\n", " func : callable f(err, flag) or object with write method\n", " Function to call upon floating-point errors ('call'-mode) or\n", " object whose 'write' method is used to log such message ('log'-mode).\n", " \n", " The call function takes two arguments. The first is a string describing\n", " the type of error (such as \"divide by zero\", \"overflow\", \"underflow\",\n", " or \"invalid value\"), and the second is the status flag. The flag is a\n", " byte, whose four least-significant bits indicate the type of error, one\n", " of \"divide\", \"over\", \"under\", \"invalid\"::\n", " \n", " [0 0 0 0 divide over under invalid]\n", " \n", " In other words, ``flags = divide + 2*over + 4*under + 8*invalid``.\n", " \n", " If an object is provided, its write method should take one argument,\n", " a string.\n", " \n", " Returns\n", " -------\n", " h : callable, log instance or None\n", " The old error handler.\n", " \n", " See Also\n", " --------\n", " seterr, geterr, geterrcall\n", " \n", " Examples\n", " --------\n", " Callback upon error:\n", " \n", " >>> def err_handler(type, flag):\n", " ... print(\"Floating point error (%s), with flag %s\" % (type, flag))\n", " ...\n", " \n", " >>> saved_handler = np.seterrcall(err_handler)\n", " >>> save_err = np.seterr(all='call')\n", " \n", " >>> np.array([1, 2, 3]) / 0.0\n", " Floating point error (divide by zero), with flag 1\n", " array([inf, inf, inf])\n", " \n", " >>> np.seterrcall(saved_handler)\n", " <function err_handler at 0x...>\n", " >>> np.seterr(**save_err)\n", " {'divide': 'call', 'over': 'call', 'under': 'call', 'invalid': 'call'}\n", " \n", " Log error message:\n", " \n", " >>> class Log:\n", " ... def write(self, msg):\n", " ... print(\"LOG: %s\" % msg)\n", " ...\n", " \n", " >>> log = Log()\n", " >>> saved_handler = np.seterrcall(log)\n", " >>> save_err = np.seterr(all='log')\n", " \n", " >>> np.array([1, 2, 3]) / 0.0\n", " LOG: Warning: divide by zero encountered in divide\n", " array([inf, inf, inf])\n", " \n", " >>> np.seterrcall(saved_handler)\n", " <numpy.core.numeric.Log object at 0x...>\n", " >>> np.seterr(**save_err)\n", " {'divide': 'log', 'over': 'log', 'under': 'log', 'invalid': 'log'}\n", " \n", " seterrobj(...)\n", " seterrobj(errobj, /)\n", " \n", " Set the object that defines floating-point error handling.\n", " \n", " The error object contains all information that defines the error handling\n", " behavior in NumPy. `seterrobj` is used internally by the other\n", " functions that set error handling behavior (`seterr`, `seterrcall`).\n", " \n", " Parameters\n", " ----------\n", " errobj : list\n", " The error object, a list containing three elements:\n", " [internal numpy buffer size, error mask, error callback function].\n", " \n", " The error mask is a single integer that holds the treatment information\n", " on all four floating point errors. The information for each error type\n", " is contained in three bits of the integer. If we print it in base 8, we\n", " can see what treatment is set for \"invalid\", \"under\", \"over\", and\n", " \"divide\" (in that order). The printed string can be interpreted with\n", " \n", " * 0 : 'ignore'\n", " * 1 : 'warn'\n", " * 2 : 'raise'\n", " * 3 : 'call'\n", " * 4 : 'print'\n", " * 5 : 'log'\n", " \n", " See Also\n", " --------\n", " geterrobj, seterr, geterr, seterrcall, geterrcall\n", " getbufsize, setbufsize\n", " \n", " Notes\n", " -----\n", " For complete documentation of the types of floating-point exceptions and\n", " treatment options, see `seterr`.\n", " \n", " Examples\n", " --------\n", " >>> old_errobj = np.geterrobj() # first get the defaults\n", " >>> old_errobj\n", " [8192, 521, None]\n", " \n", " >>> def err_handler(type, flag):\n", " ... print(\"Floating point error (%s), with flag %s\" % (type, flag))\n", " ...\n", " >>> new_errobj = [20000, 12, err_handler]\n", " >>> np.seterrobj(new_errobj)\n", " >>> np.base_repr(12, 8) # int for divide=4 ('print') and over=1 ('warn')\n", " '14'\n", " >>> np.geterr()\n", " {'over': 'warn', 'divide': 'print', 'invalid': 'ignore', 'under': 'ignore'}\n", " >>> np.geterrcall() is err_handler\n", " True\n", " \n", " setxor1d(ar1, ar2, assume_unique=False)\n", " Find the set exclusive-or of two arrays.\n", " \n", " Return the sorted, unique values that are in only one (not both) of the\n", " input arrays.\n", " \n", " Parameters\n", " ----------\n", " ar1, ar2 : array_like\n", " Input arrays.\n", " assume_unique : bool\n", " If True, the input arrays are both assumed to be unique, which\n", " can speed up the calculation. Default is False.\n", " \n", " Returns\n", " -------\n", " setxor1d : ndarray\n", " Sorted 1D array of unique values that are in only one of the input\n", " arrays.\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([1, 2, 3, 2, 4])\n", " >>> b = np.array([2, 3, 5, 7, 5])\n", " >>> np.setxor1d(a,b)\n", " array([1, 4, 5, 7])\n", " \n", " shape(a)\n", " Return the shape of an array.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input array.\n", " \n", " Returns\n", " -------\n", " shape : tuple of ints\n", " The elements of the shape tuple give the lengths of the\n", " corresponding array dimensions.\n", " \n", " See Also\n", " --------\n", " len : ``len(a)`` is equivalent to ``np.shape(a)[0]`` for N-D arrays with\n", " ``N>=1``.\n", " ndarray.shape : Equivalent array method.\n", " \n", " Examples\n", " --------\n", " >>> np.shape(np.eye(3))\n", " (3, 3)\n", " >>> np.shape([[1, 3]])\n", " (1, 2)\n", " >>> np.shape([0])\n", " (1,)\n", " >>> np.shape(0)\n", " ()\n", " \n", " >>> a = np.array([(1, 2), (3, 4), (5, 6)],\n", " ... dtype=[('x', 'i4'), ('y', 'i4')])\n", " >>> np.shape(a)\n", " (3,)\n", " >>> a.shape\n", " (3,)\n", " \n", " shares_memory(...)\n", " shares_memory(a, b, /, max_work=None)\n", " \n", " Determine if two arrays share memory.\n", " \n", " .. warning::\n", " \n", " This function can be exponentially slow for some inputs, unless\n", " `max_work` is set to a finite number or ``MAY_SHARE_BOUNDS``.\n", " If in doubt, use `numpy.may_share_memory` instead.\n", " \n", " Parameters\n", " ----------\n", " a, b : ndarray\n", " Input arrays\n", " max_work : int, optional\n", " Effort to spend on solving the overlap problem (maximum number\n", " of candidate solutions to consider). The following special\n", " values are recognized:\n", " \n", " max_work=MAY_SHARE_EXACT (default)\n", " The problem is solved exactly. In this case, the function returns\n", " True only if there is an element shared between the arrays. Finding\n", " the exact solution may take extremely long in some cases.\n", " max_work=MAY_SHARE_BOUNDS\n", " Only the memory bounds of a and b are checked.\n", " \n", " Raises\n", " ------\n", " numpy.TooHardError\n", " Exceeded max_work.\n", " \n", " Returns\n", " -------\n", " out : bool\n", " \n", " See Also\n", " --------\n", " may_share_memory\n", " \n", " Examples\n", " --------\n", " >>> x = np.array([1, 2, 3, 4])\n", " >>> np.shares_memory(x, np.array([5, 6, 7]))\n", " False\n", " >>> np.shares_memory(x[::2], x)\n", " True\n", " >>> np.shares_memory(x[::2], x[1::2])\n", " False\n", " \n", " Checking whether two arrays share memory is NP-complete, and\n", " runtime may increase exponentially in the number of\n", " dimensions. Hence, `max_work` should generally be set to a finite\n", " number, as it is possible to construct examples that take\n", " extremely long to run:\n", " \n", " >>> from numpy.lib.stride_tricks import as_strided\n", " >>> x = np.zeros([192163377], dtype=np.int8)\n", " >>> x1 = as_strided(x, strides=(36674, 61119, 85569), shape=(1049, 1049, 1049))\n", " >>> x2 = as_strided(x[64023025:], strides=(12223, 12224, 1), shape=(1049, 1049, 1))\n", " >>> np.shares_memory(x1, x2, max_work=1000)\n", " Traceback (most recent call last):\n", " ...\n", " numpy.TooHardError: Exceeded max_work\n", " \n", " Running ``np.shares_memory(x1, x2)`` without `max_work` set takes\n", " around 1 minute for this case. It is possible to find problems\n", " that take still significantly longer.\n", " \n", " show_config = show()\n", " Show libraries in the system on which NumPy was built.\n", " \n", " Print information about various resources (libraries, library\n", " directories, include directories, etc.) in the system on which\n", " NumPy was built.\n", " \n", " See Also\n", " --------\n", " get_include : Returns the directory containing NumPy C\n", " header files.\n", " \n", " Notes\n", " -----\n", " 1. Classes specifying the information to be printed are defined\n", " in the `numpy.distutils.system_info` module.\n", " \n", " Information may include:\n", " \n", " * ``language``: language used to write the libraries (mostly\n", " C or f77)\n", " * ``libraries``: names of libraries found in the system\n", " * ``library_dirs``: directories containing the libraries\n", " * ``include_dirs``: directories containing library header files\n", " * ``src_dirs``: directories containing library source files\n", " * ``define_macros``: preprocessor macros used by\n", " ``distutils.setup``\n", " * ``baseline``: minimum CPU features required\n", " * ``found``: dispatched features supported in the system\n", " * ``not found``: dispatched features that are not supported\n", " in the system\n", " \n", " 2. NumPy BLAS/LAPACK Installation Notes\n", " \n", " Installing a numpy wheel (``pip install numpy`` or force it\n", " via ``pip install numpy --only-binary :numpy: numpy``) includes\n", " an OpenBLAS implementation of the BLAS and LAPACK linear algebra\n", " APIs. In this case, ``library_dirs`` reports the original build\n", " time configuration as compiled with gcc/gfortran; at run time\n", " the OpenBLAS library is in\n", " ``site-packages/numpy.libs/`` (linux), or\n", " ``site-packages/numpy/.dylibs/`` (macOS), or\n", " ``site-packages/numpy/.libs/`` (windows).\n", " \n", " Installing numpy from source\n", " (``pip install numpy --no-binary numpy``) searches for BLAS and\n", " LAPACK dynamic link libraries at build time as influenced by\n", " environment variables NPY_BLAS_LIBS, NPY_CBLAS_LIBS, and\n", " NPY_LAPACK_LIBS; or NPY_BLAS_ORDER and NPY_LAPACK_ORDER;\n", " or the optional file ``~/.numpy-site.cfg``.\n", " NumPy remembers those locations and expects to load the same\n", " libraries at run-time.\n", " In NumPy 1.21+ on macOS, 'accelerate' (Apple's Accelerate BLAS\n", " library) is in the default build-time search order after\n", " 'openblas'.\n", " \n", " Examples\n", " --------\n", " >>> import numpy as np\n", " >>> np.show_config()\n", " blas_opt_info:\n", " language = c\n", " define_macros = [('HAVE_CBLAS', None)]\n", " libraries = ['openblas', 'openblas']\n", " library_dirs = ['/usr/local/lib']\n", " \n", " show_runtime()\n", " Print information about various resources in the system\n", " including available intrinsic support and BLAS/LAPACK library\n", " in use\n", " \n", " See Also\n", " --------\n", " show_config : Show libraries in the system on which NumPy was built.\n", " \n", " Notes\n", " -----\n", " 1. Information is derived with the help of `threadpoolctl <https://pypi.org/project/threadpoolctl/>`_\n", " library.\n", " 2. SIMD related information is derived from ``__cpu_features__``,\n", " ``__cpu_baseline__`` and ``__cpu_dispatch__``\n", " \n", " Examples\n", " --------\n", " >>> import numpy as np\n", " >>> np.show_runtime()\n", " [{'simd_extensions': {'baseline': ['SSE', 'SSE2', 'SSE3'],\n", " 'found': ['SSSE3',\n", " 'SSE41',\n", " 'POPCNT',\n", " 'SSE42',\n", " 'AVX',\n", " 'F16C',\n", " 'FMA3',\n", " 'AVX2'],\n", " 'not_found': ['AVX512F',\n", " 'AVX512CD',\n", " 'AVX512_KNL',\n", " 'AVX512_KNM',\n", " 'AVX512_SKX',\n", " 'AVX512_CLX',\n", " 'AVX512_CNL',\n", " 'AVX512_ICL']}},\n", " {'architecture': 'Zen',\n", " 'filepath': '/usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.20.so',\n", " 'internal_api': 'openblas',\n", " 'num_threads': 12,\n", " 'prefix': 'libopenblas',\n", " 'threading_layer': 'pthreads',\n", " 'user_api': 'blas',\n", " 'version': '0.3.20'}]\n", " \n", " sinc(x)\n", " Return the normalized sinc function.\n", " \n", " The sinc function is equal to :math:`\\sin(\\pi x)/(\\pi x)` for any argument\n", " :math:`x\\ne 0`. ``sinc(0)`` takes the limit value 1, making ``sinc`` not\n", " only everywhere continuous but also infinitely differentiable.\n", " \n", " .. note::\n", " \n", " Note the normalization factor of ``pi`` used in the definition.\n", " This is the most commonly used definition in signal processing.\n", " Use ``sinc(x / np.pi)`` to obtain the unnormalized sinc function\n", " :math:`\\sin(x)/x` that is more common in mathematics.\n", " \n", " Parameters\n", " ----------\n", " x : ndarray\n", " Array (possibly multi-dimensional) of values for which to calculate\n", " ``sinc(x)``.\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " ``sinc(x)``, which has the same shape as the input.\n", " \n", " Notes\n", " -----\n", " The name sinc is short for \"sine cardinal\" or \"sinus cardinalis\".\n", " \n", " The sinc function is used in various signal processing applications,\n", " including in anti-aliasing, in the construction of a Lanczos resampling\n", " filter, and in interpolation.\n", " \n", " For bandlimited interpolation of discrete-time signals, the ideal\n", " interpolation kernel is proportional to the sinc function.\n", " \n", " References\n", " ----------\n", " .. [1] Weisstein, Eric W. \"Sinc Function.\" From MathWorld--A Wolfram Web\n", " Resource. http://mathworld.wolfram.com/SincFunction.html\n", " .. [2] Wikipedia, \"Sinc function\",\n", " https://en.wikipedia.org/wiki/Sinc_function\n", " \n", " Examples\n", " --------\n", " >>> import matplotlib.pyplot as plt\n", " >>> x = np.linspace(-4, 4, 41)\n", " >>> np.sinc(x)\n", " array([-3.89804309e-17, -4.92362781e-02, -8.40918587e-02, # may vary\n", " -8.90384387e-02, -5.84680802e-02, 3.89804309e-17,\n", " 6.68206631e-02, 1.16434881e-01, 1.26137788e-01,\n", " 8.50444803e-02, -3.89804309e-17, -1.03943254e-01,\n", " -1.89206682e-01, -2.16236208e-01, -1.55914881e-01,\n", " 3.89804309e-17, 2.33872321e-01, 5.04551152e-01,\n", " 7.56826729e-01, 9.35489284e-01, 1.00000000e+00,\n", " 9.35489284e-01, 7.56826729e-01, 5.04551152e-01,\n", " 2.33872321e-01, 3.89804309e-17, -1.55914881e-01,\n", " -2.16236208e-01, -1.89206682e-01, -1.03943254e-01,\n", " -3.89804309e-17, 8.50444803e-02, 1.26137788e-01,\n", " 1.16434881e-01, 6.68206631e-02, 3.89804309e-17,\n", " -5.84680802e-02, -8.90384387e-02, -8.40918587e-02,\n", " -4.92362781e-02, -3.89804309e-17])\n", " \n", " >>> plt.plot(x, np.sinc(x))\n", " [<matplotlib.lines.Line2D object at 0x...>]\n", " >>> plt.title(\"Sinc Function\")\n", " Text(0.5, 1.0, 'Sinc Function')\n", " >>> plt.ylabel(\"Amplitude\")\n", " Text(0, 0.5, 'Amplitude')\n", " >>> plt.xlabel(\"X\")\n", " Text(0.5, 0, 'X')\n", " >>> plt.show()\n", " \n", " size(a, axis=None)\n", " Return the number of elements along a given axis.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input data.\n", " axis : int, optional\n", " Axis along which the elements are counted. By default, give\n", " the total number of elements.\n", " \n", " Returns\n", " -------\n", " element_count : int\n", " Number of elements along the specified axis.\n", " \n", " See Also\n", " --------\n", " shape : dimensions of array\n", " ndarray.shape : dimensions of array\n", " ndarray.size : number of elements in array\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([[1,2,3],[4,5,6]])\n", " >>> np.size(a)\n", " 6\n", " >>> np.size(a,1)\n", " 3\n", " >>> np.size(a,0)\n", " 2\n", " \n", " sometrue(*args, **kwargs)\n", " Check whether some values are true.\n", " \n", " Refer to `any` for full documentation.\n", " \n", " See Also\n", " --------\n", " any : equivalent function; see for details.\n", " \n", " sort(a, axis=-1, kind=None, order=None)\n", " Return a sorted copy of an array.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Array to be sorted.\n", " axis : int or None, optional\n", " Axis along which to sort. If None, the array is flattened before\n", " sorting. The default is -1, which sorts along the last axis.\n", " kind : {'quicksort', 'mergesort', 'heapsort', 'stable'}, optional\n", " Sorting algorithm. The default is 'quicksort'. Note that both 'stable'\n", " and 'mergesort' use timsort or radix sort under the covers and, in general,\n", " the actual implementation will vary with data type. The 'mergesort' option\n", " is retained for backwards compatibility.\n", " \n", " .. versionchanged:: 1.15.0.\n", " The 'stable' option was added.\n", " \n", " order : str or list of str, optional\n", " When `a` is an array with fields defined, this argument specifies\n", " which fields to compare first, second, etc. A single field can\n", " be specified as a string, and not all fields need be specified,\n", " but unspecified fields will still be used, in the order in which\n", " they come up in the dtype, to break ties.\n", " \n", " Returns\n", " -------\n", " sorted_array : ndarray\n", " Array of the same type and shape as `a`.\n", " \n", " See Also\n", " --------\n", " ndarray.sort : Method to sort an array in-place.\n", " argsort : Indirect sort.\n", " lexsort : Indirect stable sort on multiple keys.\n", " searchsorted : Find elements in a sorted array.\n", " partition : Partial sort.\n", " \n", " Notes\n", " -----\n", " The various sorting algorithms are characterized by their average speed,\n", " worst case performance, work space size, and whether they are stable. A\n", " stable sort keeps items with the same key in the same relative\n", " order. The four algorithms implemented in NumPy have the following\n", " properties:\n", " \n", " =========== ======= ============= ============ ========\n", " kind speed worst case work space stable\n", " =========== ======= ============= ============ ========\n", " 'quicksort' 1 O(n^2) 0 no\n", " 'heapsort' 3 O(n*log(n)) 0 no\n", " 'mergesort' 2 O(n*log(n)) ~n/2 yes\n", " 'timsort' 2 O(n*log(n)) ~n/2 yes\n", " =========== ======= ============= ============ ========\n", " \n", " .. note:: The datatype determines which of 'mergesort' or 'timsort'\n", " is actually used, even if 'mergesort' is specified. User selection\n", " at a finer scale is not currently available.\n", " \n", " All the sort algorithms make temporary copies of the data when\n", " sorting along any but the last axis. Consequently, sorting along\n", " the last axis is faster and uses less space than sorting along\n", " any other axis.\n", " \n", " The sort order for complex numbers is lexicographic. If both the real\n", " and imaginary parts are non-nan then the order is determined by the\n", " real parts except when they are equal, in which case the order is\n", " determined by the imaginary parts.\n", " \n", " Previous to numpy 1.4.0 sorting real and complex arrays containing nan\n", " values led to undefined behaviour. In numpy versions >= 1.4.0 nan\n", " values are sorted to the end. The extended sort order is:\n", " \n", " * Real: [R, nan]\n", " * Complex: [R + Rj, R + nanj, nan + Rj, nan + nanj]\n", " \n", " where R is a non-nan real value. Complex values with the same nan\n", " placements are sorted according to the non-nan part if it exists.\n", " Non-nan values are sorted as before.\n", " \n", " .. versionadded:: 1.12.0\n", " \n", " quicksort has been changed to `introsort <https://en.wikipedia.org/wiki/Introsort>`_.\n", " When sorting does not make enough progress it switches to\n", " `heapsort <https://en.wikipedia.org/wiki/Heapsort>`_.\n", " This implementation makes quicksort O(n*log(n)) in the worst case.\n", " \n", " 'stable' automatically chooses the best stable sorting algorithm\n", " for the data type being sorted.\n", " It, along with 'mergesort' is currently mapped to\n", " `timsort <https://en.wikipedia.org/wiki/Timsort>`_\n", " or `radix sort <https://en.wikipedia.org/wiki/Radix_sort>`_\n", " depending on the data type.\n", " API forward compatibility currently limits the\n", " ability to select the implementation and it is hardwired for the different\n", " data types.\n", " \n", " .. versionadded:: 1.17.0\n", " \n", " Timsort is added for better performance on already or nearly\n", " sorted data. On random data timsort is almost identical to\n", " mergesort. It is now used for stable sort while quicksort is still the\n", " default sort if none is chosen. For timsort details, refer to\n", " `CPython listsort.txt <https://github.com/python/cpython/blob/3.7/Objects/listsort.txt>`_.\n", " 'mergesort' and 'stable' are mapped to radix sort for integer data types. Radix sort is an\n", " O(n) sort instead of O(n log n).\n", " \n", " .. versionchanged:: 1.18.0\n", " \n", " NaT now sorts to the end of arrays for consistency with NaN.\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([[1,4],[3,1]])\n", " >>> np.sort(a) # sort along the last axis\n", " array([[1, 4],\n", " [1, 3]])\n", " >>> np.sort(a, axis=None) # sort the flattened array\n", " array([1, 1, 3, 4])\n", " >>> np.sort(a, axis=0) # sort along the first axis\n", " array([[1, 1],\n", " [3, 4]])\n", " \n", " Use the `order` keyword to specify a field to use when sorting a\n", " structured array:\n", " \n", " >>> dtype = [('name', 'S10'), ('height', float), ('age', int)]\n", " >>> values = [('Arthur', 1.8, 41), ('Lancelot', 1.9, 38),\n", " ... ('Galahad', 1.7, 38)]\n", " >>> a = np.array(values, dtype=dtype) # create a structured array\n", " >>> np.sort(a, order='height') # doctest: +SKIP\n", " array([('Galahad', 1.7, 38), ('Arthur', 1.8, 41),\n", " ('Lancelot', 1.8999999999999999, 38)],\n", " dtype=[('name', '|S10'), ('height', '<f8'), ('age', '<i4')])\n", " \n", " Sort by age, then height if ages are equal:\n", " \n", " >>> np.sort(a, order=['age', 'height']) # doctest: +SKIP\n", " array([('Galahad', 1.7, 38), ('Lancelot', 1.8999999999999999, 38),\n", " ('Arthur', 1.8, 41)],\n", " dtype=[('name', '|S10'), ('height', '<f8'), ('age', '<i4')])\n", " \n", " sort_complex(a)\n", " Sort a complex array using the real part first, then the imaginary part.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input array\n", " \n", " Returns\n", " -------\n", " out : complex ndarray\n", " Always returns a sorted complex array.\n", " \n", " Examples\n", " --------\n", " >>> np.sort_complex([5, 3, 6, 2, 1])\n", " array([1.+0.j, 2.+0.j, 3.+0.j, 5.+0.j, 6.+0.j])\n", " \n", " >>> np.sort_complex([1 + 2j, 2 - 1j, 3 - 2j, 3 - 3j, 3 + 5j])\n", " array([1.+2.j, 2.-1.j, 3.-3.j, 3.-2.j, 3.+5.j])\n", " \n", " source(object, output=<ipykernel.iostream.OutStream object at 0x000001E10B030B50>)\n", " Print or write to a file the source code for a NumPy object.\n", " \n", " The source code is only returned for objects written in Python. Many\n", " functions and classes are defined in C and will therefore not return\n", " useful information.\n", " \n", " Parameters\n", " ----------\n", " object : numpy object\n", " Input object. This can be any object (function, class, module,\n", " ...).\n", " output : file object, optional\n", " If `output` not supplied then source code is printed to screen\n", " (sys.stdout). File object must be created with either write 'w' or\n", " append 'a' modes.\n", " \n", " See Also\n", " --------\n", " lookfor, info\n", " \n", " Examples\n", " --------\n", " >>> np.source(np.interp) #doctest: +SKIP\n", " In file: /usr/lib/python2.6/dist-packages/numpy/lib/function_base.py\n", " def interp(x, xp, fp, left=None, right=None):\n", " \"\"\".... (full docstring printed)\"\"\"\n", " if isinstance(x, (float, int, number)):\n", " return compiled_interp([x], xp, fp, left, right).item()\n", " else:\n", " return compiled_interp(x, xp, fp, left, right)\n", " \n", " The source code is only returned for objects written in Python.\n", " \n", " >>> np.source(np.array) #doctest: +SKIP\n", " Not available for this object.\n", " \n", " split(ary, indices_or_sections, axis=0)\n", " Split an array into multiple sub-arrays as views into `ary`.\n", " \n", " Parameters\n", " ----------\n", " ary : ndarray\n", " Array to be divided into sub-arrays.\n", " indices_or_sections : int or 1-D array\n", " If `indices_or_sections` is an integer, N, the array will be divided\n", " into N equal arrays along `axis`. If such a split is not possible,\n", " an error is raised.\n", " \n", " If `indices_or_sections` is a 1-D array of sorted integers, the entries\n", " indicate where along `axis` the array is split. For example,\n", " ``[2, 3]`` would, for ``axis=0``, result in\n", " \n", " - ary[:2]\n", " - ary[2:3]\n", " - ary[3:]\n", " \n", " If an index exceeds the dimension of the array along `axis`,\n", " an empty sub-array is returned correspondingly.\n", " axis : int, optional\n", " The axis along which to split, default is 0.\n", " \n", " Returns\n", " -------\n", " sub-arrays : list of ndarrays\n", " A list of sub-arrays as views into `ary`.\n", " \n", " Raises\n", " ------\n", " ValueError\n", " If `indices_or_sections` is given as an integer, but\n", " a split does not result in equal division.\n", " \n", " See Also\n", " --------\n", " array_split : Split an array into multiple sub-arrays of equal or\n", " near-equal size. Does not raise an exception if\n", " an equal division cannot be made.\n", " hsplit : Split array into multiple sub-arrays horizontally (column-wise).\n", " vsplit : Split array into multiple sub-arrays vertically (row wise).\n", " dsplit : Split array into multiple sub-arrays along the 3rd axis (depth).\n", " concatenate : Join a sequence of arrays along an existing axis.\n", " stack : Join a sequence of arrays along a new axis.\n", " hstack : Stack arrays in sequence horizontally (column wise).\n", " vstack : Stack arrays in sequence vertically (row wise).\n", " dstack : Stack arrays in sequence depth wise (along third dimension).\n", " \n", " Examples\n", " --------\n", " >>> x = np.arange(9.0)\n", " >>> np.split(x, 3)\n", " [array([0., 1., 2.]), array([3., 4., 5.]), array([6., 7., 8.])]\n", " \n", " >>> x = np.arange(8.0)\n", " >>> np.split(x, [3, 5, 6, 10])\n", " [array([0., 1., 2.]),\n", " array([3., 4.]),\n", " array([5.]),\n", " array([6., 7.]),\n", " array([], dtype=float64)]\n", " \n", " squeeze(a, axis=None)\n", " Remove axes of length one from `a`.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input data.\n", " axis : None or int or tuple of ints, optional\n", " .. versionadded:: 1.7.0\n", " \n", " Selects a subset of the entries of length one in the\n", " shape. If an axis is selected with shape entry greater than\n", " one, an error is raised.\n", " \n", " Returns\n", " -------\n", " squeezed : ndarray\n", " The input array, but with all or a subset of the\n", " dimensions of length 1 removed. This is always `a` itself\n", " or a view into `a`. Note that if all axes are squeezed,\n", " the result is a 0d array and not a scalar.\n", " \n", " Raises\n", " ------\n", " ValueError\n", " If `axis` is not None, and an axis being squeezed is not of length 1\n", " \n", " See Also\n", " --------\n", " expand_dims : The inverse operation, adding entries of length one\n", " reshape : Insert, remove, and combine dimensions, and resize existing ones\n", " \n", " Examples\n", " --------\n", " >>> x = np.array([[[0], [1], [2]]])\n", " >>> x.shape\n", " (1, 3, 1)\n", " >>> np.squeeze(x).shape\n", " (3,)\n", " >>> np.squeeze(x, axis=0).shape\n", " (3, 1)\n", " >>> np.squeeze(x, axis=1).shape\n", " Traceback (most recent call last):\n", " ...\n", " ValueError: cannot select an axis to squeeze out which has size not equal to one\n", " >>> np.squeeze(x, axis=2).shape\n", " (1, 3)\n", " >>> x = np.array([[1234]])\n", " >>> x.shape\n", " (1, 1)\n", " >>> np.squeeze(x)\n", " array(1234) # 0d array\n", " >>> np.squeeze(x).shape\n", " ()\n", " >>> np.squeeze(x)[()]\n", " 1234\n", " \n", " stack(arrays, axis=0, out=None, *, dtype=None, casting='same_kind')\n", " Join a sequence of arrays along a new axis.\n", " \n", " The ``axis`` parameter specifies the index of the new axis in the\n", " dimensions of the result. For example, if ``axis=0`` it will be the first\n", " dimension and if ``axis=-1`` it will be the last dimension.\n", " \n", " .. versionadded:: 1.10.0\n", " \n", " Parameters\n", " ----------\n", " arrays : sequence of array_like\n", " Each array must have the same shape.\n", " \n", " axis : int, optional\n", " The axis in the result array along which the input arrays are stacked.\n", " \n", " out : ndarray, optional\n", " If provided, the destination to place the result. The shape must be\n", " correct, matching that of what stack would have returned if no\n", " out argument were specified.\n", " \n", " dtype : str or dtype\n", " If provided, the destination array will have this dtype. Cannot be\n", " provided together with `out`.\n", " \n", " .. versionadded:: 1.24\n", " \n", " casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional\n", " Controls what kind of data casting may occur. Defaults to 'same_kind'.\n", " \n", " .. versionadded:: 1.24\n", " \n", " \n", " Returns\n", " -------\n", " stacked : ndarray\n", " The stacked array has one more dimension than the input arrays.\n", " \n", " See Also\n", " --------\n", " concatenate : Join a sequence of arrays along an existing axis.\n", " block : Assemble an nd-array from nested lists of blocks.\n", " split : Split array into a list of multiple sub-arrays of equal size.\n", " \n", " Examples\n", " --------\n", " >>> arrays = [np.random.randn(3, 4) for _ in range(10)]\n", " >>> np.stack(arrays, axis=0).shape\n", " (10, 3, 4)\n", " \n", " >>> np.stack(arrays, axis=1).shape\n", " (3, 10, 4)\n", " \n", " >>> np.stack(arrays, axis=2).shape\n", " (3, 4, 10)\n", " \n", " >>> a = np.array([1, 2, 3])\n", " >>> b = np.array([4, 5, 6])\n", " >>> np.stack((a, b))\n", " array([[1, 2, 3],\n", " [4, 5, 6]])\n", " \n", " >>> np.stack((a, b), axis=-1)\n", " array([[1, 4],\n", " [2, 5],\n", " [3, 6]])\n", " \n", " std(a, axis=None, dtype=None, out=None, ddof=0, keepdims=<no value>, *, where=<no value>)\n", " Compute the standard deviation along the specified axis.\n", " \n", " Returns the standard deviation, a measure of the spread of a distribution,\n", " of the array elements. The standard deviation is computed for the\n", " flattened array by default, otherwise over the specified axis.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Calculate the standard deviation of these values.\n", " axis : None or int or tuple of ints, optional\n", " Axis or axes along which the standard deviation is computed. The\n", " default is to compute the standard deviation of the flattened array.\n", " \n", " .. versionadded:: 1.7.0\n", " \n", " If this is a tuple of ints, a standard deviation is performed over\n", " multiple axes, instead of a single axis or all the axes as before.\n", " dtype : dtype, optional\n", " Type to use in computing the standard deviation. For arrays of\n", " integer type the default is float64, for arrays of float types it is\n", " the same as the array type.\n", " out : ndarray, optional\n", " Alternative output array in which to place the result. It must have\n", " the same shape as the expected output but the type (of the calculated\n", " values) will be cast if necessary.\n", " ddof : int, optional\n", " Means Delta Degrees of Freedom. The divisor used in calculations\n", " is ``N - ddof``, where ``N`` represents the number of elements.\n", " By default `ddof` is zero.\n", " keepdims : bool, optional\n", " If this is set to True, the axes which are reduced are left\n", " in the result as dimensions with size one. With this option,\n", " the result will broadcast correctly against the input array.\n", " \n", " If the default value is passed, then `keepdims` will not be\n", " passed through to the `std` method of sub-classes of\n", " `ndarray`, however any non-default value will be. If the\n", " sub-class' method does not implement `keepdims` any\n", " exceptions will be raised.\n", " \n", " where : array_like of bool, optional\n", " Elements to include in the standard deviation.\n", " See `~numpy.ufunc.reduce` for details.\n", " \n", " .. versionadded:: 1.20.0\n", " \n", " Returns\n", " -------\n", " standard_deviation : ndarray, see dtype parameter above.\n", " If `out` is None, return a new array containing the standard deviation,\n", " otherwise return a reference to the output array.\n", " \n", " See Also\n", " --------\n", " var, mean, nanmean, nanstd, nanvar\n", " :ref:`ufuncs-output-type`\n", " \n", " Notes\n", " -----\n", " The standard deviation is the square root of the average of the squared\n", " deviations from the mean, i.e., ``std = sqrt(mean(x))``, where\n", " ``x = abs(a - a.mean())**2``.\n", " \n", " The average squared deviation is typically calculated as ``x.sum() / N``,\n", " where ``N = len(x)``. If, however, `ddof` is specified, the divisor\n", " ``N - ddof`` is used instead. In standard statistical practice, ``ddof=1``\n", " provides an unbiased estimator of the variance of the infinite population.\n", " ``ddof=0`` provides a maximum likelihood estimate of the variance for\n", " normally distributed variables. The standard deviation computed in this\n", " function is the square root of the estimated variance, so even with\n", " ``ddof=1``, it will not be an unbiased estimate of the standard deviation\n", " per se.\n", " \n", " Note that, for complex numbers, `std` takes the absolute\n", " value before squaring, so that the result is always real and nonnegative.\n", " \n", " For floating-point input, the *std* is computed using the same\n", " precision the input has. Depending on the input data, this can cause\n", " the results to be inaccurate, especially for float32 (see example below).\n", " Specifying a higher-accuracy accumulator using the `dtype` keyword can\n", " alleviate this issue.\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([[1, 2], [3, 4]])\n", " >>> np.std(a)\n", " 1.1180339887498949 # may vary\n", " >>> np.std(a, axis=0)\n", " array([1., 1.])\n", " >>> np.std(a, axis=1)\n", " array([0.5, 0.5])\n", " \n", " In single precision, std() can be inaccurate:\n", " \n", " >>> a = np.zeros((2, 512*512), dtype=np.float32)\n", " >>> a[0, :] = 1.0\n", " >>> a[1, :] = 0.1\n", " >>> np.std(a)\n", " 0.45000005\n", " \n", " Computing the standard deviation in float64 is more accurate:\n", " \n", " >>> np.std(a, dtype=np.float64)\n", " 0.44999999925494177 # may vary\n", " \n", " Specifying a where argument:\n", " \n", " >>> a = np.array([[14, 8, 11, 10], [7, 9, 10, 11], [10, 15, 5, 10]])\n", " >>> np.std(a)\n", " 2.614064523559687 # may vary\n", " >>> np.std(a, where=[[True], [True], [False]])\n", " 2.0\n", " \n", " sum(a, axis=None, dtype=None, out=None, keepdims=<no value>, initial=<no value>, where=<no value>)\n", " Sum of array elements over a given axis.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Elements to sum.\n", " axis : None or int or tuple of ints, optional\n", " Axis or axes along which a sum is performed. The default,\n", " axis=None, will sum all of the elements of the input array. If\n", " axis is negative it counts from the last to the first axis.\n", " \n", " .. versionadded:: 1.7.0\n", " \n", " If axis is a tuple of ints, a sum is performed on all of the axes\n", " specified in the tuple instead of a single axis or all the axes as\n", " before.\n", " dtype : dtype, optional\n", " The type of the returned array and of the accumulator in which the\n", " elements are summed. The dtype of `a` is used by default unless `a`\n", " has an integer dtype of less precision than the default platform\n", " integer. In that case, if `a` is signed then the platform integer\n", " is used while if `a` is unsigned then an unsigned integer of the\n", " same precision as the platform integer is used.\n", " out : ndarray, optional\n", " Alternative output array in which to place the result. It must have\n", " the same shape as the expected output, but the type of the output\n", " values will be cast if necessary.\n", " keepdims : bool, optional\n", " If this is set to True, the axes which are reduced are left\n", " in the result as dimensions with size one. With this option,\n", " the result will broadcast correctly against the input array.\n", " \n", " If the default value is passed, then `keepdims` will not be\n", " passed through to the `sum` method of sub-classes of\n", " `ndarray`, however any non-default value will be. If the\n", " sub-class' method does not implement `keepdims` any\n", " exceptions will be raised.\n", " initial : scalar, optional\n", " Starting value for the sum. See `~numpy.ufunc.reduce` for details.\n", " \n", " .. versionadded:: 1.15.0\n", " \n", " where : array_like of bool, optional\n", " Elements to include in the sum. See `~numpy.ufunc.reduce` for details.\n", " \n", " .. versionadded:: 1.17.0\n", " \n", " Returns\n", " -------\n", " sum_along_axis : ndarray\n", " An array with the same shape as `a`, with the specified\n", " axis removed. If `a` is a 0-d array, or if `axis` is None, a scalar\n", " is returned. If an output array is specified, a reference to\n", " `out` is returned.\n", " \n", " See Also\n", " --------\n", " ndarray.sum : Equivalent method.\n", " \n", " add.reduce : Equivalent functionality of `add`.\n", " \n", " cumsum : Cumulative sum of array elements.\n", " \n", " trapz : Integration of array values using the composite trapezoidal rule.\n", " \n", " mean, average\n", " \n", " Notes\n", " -----\n", " Arithmetic is modular when using integer types, and no error is\n", " raised on overflow.\n", " \n", " The sum of an empty array is the neutral element 0:\n", " \n", " >>> np.sum([])\n", " 0.0\n", " \n", " For floating point numbers the numerical precision of sum (and\n", " ``np.add.reduce``) is in general limited by directly adding each number\n", " individually to the result causing rounding errors in every step.\n", " However, often numpy will use a numerically better approach (partial\n", " pairwise summation) leading to improved precision in many use-cases.\n", " This improved precision is always provided when no ``axis`` is given.\n", " When ``axis`` is given, it will depend on which axis is summed.\n", " Technically, to provide the best speed possible, the improved precision\n", " is only used when the summation is along the fast axis in memory.\n", " Note that the exact precision may vary depending on other parameters.\n", " In contrast to NumPy, Python's ``math.fsum`` function uses a slower but\n", " more precise approach to summation.\n", " Especially when summing a large number of lower precision floating point\n", " numbers, such as ``float32``, numerical errors can become significant.\n", " In such cases it can be advisable to use `dtype=\"float64\"` to use a higher\n", " precision for the output.\n", " \n", " Examples\n", " --------\n", " >>> np.sum([0.5, 1.5])\n", " 2.0\n", " >>> np.sum([0.5, 0.7, 0.2, 1.5], dtype=np.int32)\n", " 1\n", " >>> np.sum([[0, 1], [0, 5]])\n", " 6\n", " >>> np.sum([[0, 1], [0, 5]], axis=0)\n", " array([0, 6])\n", " >>> np.sum([[0, 1], [0, 5]], axis=1)\n", " array([1, 5])\n", " >>> np.sum([[0, 1], [np.nan, 5]], where=[False, True], axis=1)\n", " array([1., 5.])\n", " \n", " If the accumulator is too small, overflow occurs:\n", " \n", " >>> np.ones(128, dtype=np.int8).sum(dtype=np.int8)\n", " -128\n", " \n", " You can also start the sum with a value other than zero:\n", " \n", " >>> np.sum([10], initial=5)\n", " 15\n", " \n", " swapaxes(a, axis1, axis2)\n", " Interchange two axes of an array.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input array.\n", " axis1 : int\n", " First axis.\n", " axis2 : int\n", " Second axis.\n", " \n", " Returns\n", " -------\n", " a_swapped : ndarray\n", " For NumPy >= 1.10.0, if `a` is an ndarray, then a view of `a` is\n", " returned; otherwise a new array is created. For earlier NumPy\n", " versions a view of `a` is returned only if the order of the\n", " axes is changed, otherwise the input array is returned.\n", " \n", " Examples\n", " --------\n", " >>> x = np.array([[1,2,3]])\n", " >>> np.swapaxes(x,0,1)\n", " array([[1],\n", " [2],\n", " [3]])\n", " \n", " >>> x = np.array([[[0,1],[2,3]],[[4,5],[6,7]]])\n", " >>> x\n", " array([[[0, 1],\n", " [2, 3]],\n", " [[4, 5],\n", " [6, 7]]])\n", " \n", " >>> np.swapaxes(x,0,2)\n", " array([[[0, 4],\n", " [2, 6]],\n", " [[1, 5],\n", " [3, 7]]])\n", " \n", " take(a, indices, axis=None, out=None, mode='raise')\n", " Take elements from an array along an axis.\n", " \n", " When axis is not None, this function does the same thing as \"fancy\"\n", " indexing (indexing arrays using arrays); however, it can be easier to use\n", " if you need elements along a given axis. A call such as\n", " ``np.take(arr, indices, axis=3)`` is equivalent to\n", " ``arr[:,:,:,indices,...]``.\n", " \n", " Explained without fancy indexing, this is equivalent to the following use\n", " of `ndindex`, which sets each of ``ii``, ``jj``, and ``kk`` to a tuple of\n", " indices::\n", " \n", " Ni, Nk = a.shape[:axis], a.shape[axis+1:]\n", " Nj = indices.shape\n", " for ii in ndindex(Ni):\n", " for jj in ndindex(Nj):\n", " for kk in ndindex(Nk):\n", " out[ii + jj + kk] = a[ii + (indices[jj],) + kk]\n", " \n", " Parameters\n", " ----------\n", " a : array_like (Ni..., M, Nk...)\n", " The source array.\n", " indices : array_like (Nj...)\n", " The indices of the values to extract.\n", " \n", " .. versionadded:: 1.8.0\n", " \n", " Also allow scalars for indices.\n", " axis : int, optional\n", " The axis over which to select values. By default, the flattened\n", " input array is used.\n", " out : ndarray, optional (Ni..., Nj..., Nk...)\n", " If provided, the result will be placed in this array. It should\n", " be of the appropriate shape and dtype. Note that `out` is always\n", " buffered if `mode='raise'`; use other modes for better performance.\n", " mode : {'raise', 'wrap', 'clip'}, optional\n", " Specifies how out-of-bounds indices will behave.\n", " \n", " * 'raise' -- raise an error (default)\n", " * 'wrap' -- wrap around\n", " * 'clip' -- clip to the range\n", " \n", " 'clip' mode means that all indices that are too large are replaced\n", " by the index that addresses the last element along that axis. Note\n", " that this disables indexing with negative numbers.\n", " \n", " Returns\n", " -------\n", " out : ndarray (Ni..., Nj..., Nk...)\n", " The returned array has the same type as `a`.\n", " \n", " See Also\n", " --------\n", " compress : Take elements using a boolean mask\n", " ndarray.take : equivalent method\n", " take_along_axis : Take elements by matching the array and the index arrays\n", " \n", " Notes\n", " -----\n", " \n", " By eliminating the inner loop in the description above, and using `s_` to\n", " build simple slice objects, `take` can be expressed in terms of applying\n", " fancy indexing to each 1-d slice::\n", " \n", " Ni, Nk = a.shape[:axis], a.shape[axis+1:]\n", " for ii in ndindex(Ni):\n", " for kk in ndindex(Nj):\n", " out[ii + s_[...,] + kk] = a[ii + s_[:,] + kk][indices]\n", " \n", " For this reason, it is equivalent to (but faster than) the following use\n", " of `apply_along_axis`::\n", " \n", " out = np.apply_along_axis(lambda a_1d: a_1d[indices], axis, a)\n", " \n", " Examples\n", " --------\n", " >>> a = [4, 3, 5, 7, 6, 8]\n", " >>> indices = [0, 1, 4]\n", " >>> np.take(a, indices)\n", " array([4, 3, 6])\n", " \n", " In this example if `a` is an ndarray, \"fancy\" indexing can be used.\n", " \n", " >>> a = np.array(a)\n", " >>> a[indices]\n", " array([4, 3, 6])\n", " \n", " If `indices` is not one dimensional, the output also has these dimensions.\n", " \n", " >>> np.take(a, [[0, 1], [2, 3]])\n", " array([[4, 3],\n", " [5, 7]])\n", " \n", " take_along_axis(arr, indices, axis)\n", " Take values from the input array by matching 1d index and data slices.\n", " \n", " This iterates over matching 1d slices oriented along the specified axis in\n", " the index and data arrays, and uses the former to look up values in the\n", " latter. These slices can be different lengths.\n", " \n", " Functions returning an index along an axis, like `argsort` and\n", " `argpartition`, produce suitable indices for this function.\n", " \n", " .. versionadded:: 1.15.0\n", " \n", " Parameters\n", " ----------\n", " arr : ndarray (Ni..., M, Nk...)\n", " Source array\n", " indices : ndarray (Ni..., J, Nk...)\n", " Indices to take along each 1d slice of `arr`. This must match the\n", " dimension of arr, but dimensions Ni and Nj only need to broadcast\n", " against `arr`.\n", " axis : int\n", " The axis to take 1d slices along. If axis is None, the input array is\n", " treated as if it had first been flattened to 1d, for consistency with\n", " `sort` and `argsort`.\n", " \n", " Returns\n", " -------\n", " out: ndarray (Ni..., J, Nk...)\n", " The indexed result.\n", " \n", " Notes\n", " -----\n", " This is equivalent to (but faster than) the following use of `ndindex` and\n", " `s_`, which sets each of ``ii`` and ``kk`` to a tuple of indices::\n", " \n", " Ni, M, Nk = a.shape[:axis], a.shape[axis], a.shape[axis+1:]\n", " J = indices.shape[axis] # Need not equal M\n", " out = np.empty(Ni + (J,) + Nk)\n", " \n", " for ii in ndindex(Ni):\n", " for kk in ndindex(Nk):\n", " a_1d = a [ii + s_[:,] + kk]\n", " indices_1d = indices[ii + s_[:,] + kk]\n", " out_1d = out [ii + s_[:,] + kk]\n", " for j in range(J):\n", " out_1d[j] = a_1d[indices_1d[j]]\n", " \n", " Equivalently, eliminating the inner loop, the last two lines would be::\n", " \n", " out_1d[:] = a_1d[indices_1d]\n", " \n", " See Also\n", " --------\n", " take : Take along an axis, using the same indices for every 1d slice\n", " put_along_axis :\n", " Put values into the destination array by matching 1d index and data slices\n", " \n", " Examples\n", " --------\n", " \n", " For this sample array\n", " \n", " >>> a = np.array([[10, 30, 20], [60, 40, 50]])\n", " \n", " We can sort either by using sort directly, or argsort and this function\n", " \n", " >>> np.sort(a, axis=1)\n", " array([[10, 20, 30],\n", " [40, 50, 60]])\n", " >>> ai = np.argsort(a, axis=1); ai\n", " array([[0, 2, 1],\n", " [1, 2, 0]])\n", " >>> np.take_along_axis(a, ai, axis=1)\n", " array([[10, 20, 30],\n", " [40, 50, 60]])\n", " \n", " The same works for max and min, if you expand the dimensions:\n", " \n", " >>> np.expand_dims(np.max(a, axis=1), axis=1)\n", " array([[30],\n", " [60]])\n", " >>> ai = np.expand_dims(np.argmax(a, axis=1), axis=1)\n", " >>> ai\n", " array([[1],\n", " [0]])\n", " >>> np.take_along_axis(a, ai, axis=1)\n", " array([[30],\n", " [60]])\n", " \n", " If we want to get the max and min at the same time, we can stack the\n", " indices first\n", " \n", " >>> ai_min = np.expand_dims(np.argmin(a, axis=1), axis=1)\n", " >>> ai_max = np.expand_dims(np.argmax(a, axis=1), axis=1)\n", " >>> ai = np.concatenate([ai_min, ai_max], axis=1)\n", " >>> ai\n", " array([[0, 1],\n", " [1, 0]])\n", " >>> np.take_along_axis(a, ai, axis=1)\n", " array([[10, 30],\n", " [40, 60]])\n", " \n", " tensordot(a, b, axes=2)\n", " Compute tensor dot product along specified axes.\n", " \n", " Given two tensors, `a` and `b`, and an array_like object containing\n", " two array_like objects, ``(a_axes, b_axes)``, sum the products of\n", " `a`'s and `b`'s elements (components) over the axes specified by\n", " ``a_axes`` and ``b_axes``. The third argument can be a single non-negative\n", " integer_like scalar, ``N``; if it is such, then the last ``N`` dimensions\n", " of `a` and the first ``N`` dimensions of `b` are summed over.\n", " \n", " Parameters\n", " ----------\n", " a, b : array_like\n", " Tensors to \"dot\".\n", " \n", " axes : int or (2,) array_like\n", " * integer_like\n", " If an int N, sum over the last N axes of `a` and the first N axes\n", " of `b` in order. The sizes of the corresponding axes must match.\n", " * (2,) array_like\n", " Or, a list of axes to be summed over, first sequence applying to `a`,\n", " second to `b`. Both elements array_like must be of the same length.\n", " \n", " Returns\n", " -------\n", " output : ndarray\n", " The tensor dot product of the input.\n", " \n", " See Also\n", " --------\n", " dot, einsum\n", " \n", " Notes\n", " -----\n", " Three common use cases are:\n", " * ``axes = 0`` : tensor product :math:`a\\otimes b`\n", " * ``axes = 1`` : tensor dot product :math:`a\\cdot b`\n", " * ``axes = 2`` : (default) tensor double contraction :math:`a:b`\n", " \n", " When `axes` is integer_like, the sequence for evaluation will be: first\n", " the -Nth axis in `a` and 0th axis in `b`, and the -1th axis in `a` and\n", " Nth axis in `b` last.\n", " \n", " When there is more than one axis to sum over - and they are not the last\n", " (first) axes of `a` (`b`) - the argument `axes` should consist of\n", " two sequences of the same length, with the first axis to sum over given\n", " first in both sequences, the second axis second, and so forth.\n", " \n", " The shape of the result consists of the non-contracted axes of the\n", " first tensor, followed by the non-contracted axes of the second.\n", " \n", " Examples\n", " --------\n", " A \"traditional\" example:\n", " \n", " >>> a = np.arange(60.).reshape(3,4,5)\n", " >>> b = np.arange(24.).reshape(4,3,2)\n", " >>> c = np.tensordot(a,b, axes=([1,0],[0,1]))\n", " >>> c.shape\n", " (5, 2)\n", " >>> c\n", " array([[4400., 4730.],\n", " [4532., 4874.],\n", " [4664., 5018.],\n", " [4796., 5162.],\n", " [4928., 5306.]])\n", " >>> # A slower but equivalent way of computing the same...\n", " >>> d = np.zeros((5,2))\n", " >>> for i in range(5):\n", " ... for j in range(2):\n", " ... for k in range(3):\n", " ... for n in range(4):\n", " ... d[i,j] += a[k,n,i] * b[n,k,j]\n", " >>> c == d\n", " array([[ True, True],\n", " [ True, True],\n", " [ True, True],\n", " [ True, True],\n", " [ True, True]])\n", " \n", " An extended example taking advantage of the overloading of + and \\*:\n", " \n", " >>> a = np.array(range(1, 9))\n", " >>> a.shape = (2, 2, 2)\n", " >>> A = np.array(('a', 'b', 'c', 'd'), dtype=object)\n", " >>> A.shape = (2, 2)\n", " >>> a; A\n", " array([[[1, 2],\n", " [3, 4]],\n", " [[5, 6],\n", " [7, 8]]])\n", " array([['a', 'b'],\n", " ['c', 'd']], dtype=object)\n", " \n", " >>> np.tensordot(a, A) # third argument default is 2 for double-contraction\n", " array(['abbcccdddd', 'aaaaabbbbbbcccccccdddddddd'], dtype=object)\n", " \n", " >>> np.tensordot(a, A, 1)\n", " array([[['acc', 'bdd'],\n", " ['aaacccc', 'bbbdddd']],\n", " [['aaaaacccccc', 'bbbbbdddddd'],\n", " ['aaaaaaacccccccc', 'bbbbbbbdddddddd']]], dtype=object)\n", " \n", " >>> np.tensordot(a, A, 0) # tensor product (result too long to incl.)\n", " array([[[[['a', 'b'],\n", " ['c', 'd']],\n", " ...\n", " \n", " >>> np.tensordot(a, A, (0, 1))\n", " array([[['abbbbb', 'cddddd'],\n", " ['aabbbbbb', 'ccdddddd']],\n", " [['aaabbbbbbb', 'cccddddddd'],\n", " ['aaaabbbbbbbb', 'ccccdddddddd']]], dtype=object)\n", " \n", " >>> np.tensordot(a, A, (2, 1))\n", " array([[['abb', 'cdd'],\n", " ['aaabbbb', 'cccdddd']],\n", " [['aaaaabbbbbb', 'cccccdddddd'],\n", " ['aaaaaaabbbbbbbb', 'cccccccdddddddd']]], dtype=object)\n", " \n", " >>> np.tensordot(a, A, ((0, 1), (0, 1)))\n", " array(['abbbcccccddddddd', 'aabbbbccccccdddddddd'], dtype=object)\n", " \n", " >>> np.tensordot(a, A, ((2, 1), (1, 0)))\n", " array(['acccbbdddd', 'aaaaacccccccbbbbbbdddddddd'], dtype=object)\n", " \n", " tile(A, reps)\n", " Construct an array by repeating A the number of times given by reps.\n", " \n", " If `reps` has length ``d``, the result will have dimension of\n", " ``max(d, A.ndim)``.\n", " \n", " If ``A.ndim < d``, `A` is promoted to be d-dimensional by prepending new\n", " axes. So a shape (3,) array is promoted to (1, 3) for 2-D replication,\n", " or shape (1, 1, 3) for 3-D replication. If this is not the desired\n", " behavior, promote `A` to d-dimensions manually before calling this\n", " function.\n", " \n", " If ``A.ndim > d``, `reps` is promoted to `A`.ndim by pre-pending 1's to it.\n", " Thus for an `A` of shape (2, 3, 4, 5), a `reps` of (2, 2) is treated as\n", " (1, 1, 2, 2).\n", " \n", " Note : Although tile may be used for broadcasting, it is strongly\n", " recommended to use numpy's broadcasting operations and functions.\n", " \n", " Parameters\n", " ----------\n", " A : array_like\n", " The input array.\n", " reps : array_like\n", " The number of repetitions of `A` along each axis.\n", " \n", " Returns\n", " -------\n", " c : ndarray\n", " The tiled output array.\n", " \n", " See Also\n", " --------\n", " repeat : Repeat elements of an array.\n", " broadcast_to : Broadcast an array to a new shape\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([0, 1, 2])\n", " >>> np.tile(a, 2)\n", " array([0, 1, 2, 0, 1, 2])\n", " >>> np.tile(a, (2, 2))\n", " array([[0, 1, 2, 0, 1, 2],\n", " [0, 1, 2, 0, 1, 2]])\n", " >>> np.tile(a, (2, 1, 2))\n", " array([[[0, 1, 2, 0, 1, 2]],\n", " [[0, 1, 2, 0, 1, 2]]])\n", " \n", " >>> b = np.array([[1, 2], [3, 4]])\n", " >>> np.tile(b, 2)\n", " array([[1, 2, 1, 2],\n", " [3, 4, 3, 4]])\n", " >>> np.tile(b, (2, 1))\n", " array([[1, 2],\n", " [3, 4],\n", " [1, 2],\n", " [3, 4]])\n", " \n", " >>> c = np.array([1,2,3,4])\n", " >>> np.tile(c,(4,1))\n", " array([[1, 2, 3, 4],\n", " [1, 2, 3, 4],\n", " [1, 2, 3, 4],\n", " [1, 2, 3, 4]])\n", " \n", " trace(a, offset=0, axis1=0, axis2=1, dtype=None, out=None)\n", " Return the sum along diagonals of the array.\n", " \n", " If `a` is 2-D, the sum along its diagonal with the given offset\n", " is returned, i.e., the sum of elements ``a[i,i+offset]`` for all i.\n", " \n", " If `a` has more than two dimensions, then the axes specified by axis1 and\n", " axis2 are used to determine the 2-D sub-arrays whose traces are returned.\n", " The shape of the resulting array is the same as that of `a` with `axis1`\n", " and `axis2` removed.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input array, from which the diagonals are taken.\n", " offset : int, optional\n", " Offset of the diagonal from the main diagonal. Can be both positive\n", " and negative. Defaults to 0.\n", " axis1, axis2 : int, optional\n", " Axes to be used as the first and second axis of the 2-D sub-arrays\n", " from which the diagonals should be taken. Defaults are the first two\n", " axes of `a`.\n", " dtype : dtype, optional\n", " Determines the data-type of the returned array and of the accumulator\n", " where the elements are summed. If dtype has the value None and `a` is\n", " of integer type of precision less than the default integer\n", " precision, then the default integer precision is used. Otherwise,\n", " the precision is the same as that of `a`.\n", " out : ndarray, optional\n", " Array into which the output is placed. Its type is preserved and\n", " it must be of the right shape to hold the output.\n", " \n", " Returns\n", " -------\n", " sum_along_diagonals : ndarray\n", " If `a` is 2-D, the sum along the diagonal is returned. If `a` has\n", " larger dimensions, then an array of sums along diagonals is returned.\n", " \n", " See Also\n", " --------\n", " diag, diagonal, diagflat\n", " \n", " Examples\n", " --------\n", " >>> np.trace(np.eye(3))\n", " 3.0\n", " >>> a = np.arange(8).reshape((2,2,2))\n", " >>> np.trace(a)\n", " array([6, 8])\n", " \n", " >>> a = np.arange(24).reshape((2,2,2,3))\n", " >>> np.trace(a).shape\n", " (2, 3)\n", " \n", " transpose(a, axes=None)\n", " Returns an array with axes transposed.\n", " \n", " For a 1-D array, this returns an unchanged view of the original array, as a\n", " transposed vector is simply the same vector.\n", " To convert a 1-D array into a 2-D column vector, an additional dimension\n", " must be added, e.g., ``np.atleast2d(a).T`` achieves this, as does\n", " ``a[:, np.newaxis]``.\n", " For a 2-D array, this is the standard matrix transpose.\n", " For an n-D array, if axes are given, their order indicates how the\n", " axes are permuted (see Examples). If axes are not provided, then\n", " ``transpose(a).shape == a.shape[::-1]``.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Input array.\n", " axes : tuple or list of ints, optional\n", " If specified, it must be a tuple or list which contains a permutation\n", " of [0,1,...,N-1] where N is the number of axes of `a`. The `i`'th axis\n", " of the returned array will correspond to the axis numbered ``axes[i]``\n", " of the input. If not specified, defaults to ``range(a.ndim)[::-1]``,\n", " which reverses the order of the axes.\n", " \n", " Returns\n", " -------\n", " p : ndarray\n", " `a` with its axes permuted. A view is returned whenever possible.\n", " \n", " See Also\n", " --------\n", " ndarray.transpose : Equivalent method.\n", " moveaxis : Move axes of an array to new positions.\n", " argsort : Return the indices that would sort an array.\n", " \n", " Notes\n", " -----\n", " Use ``transpose(a, argsort(axes))`` to invert the transposition of tensors\n", " when using the `axes` keyword argument.\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([[1, 2], [3, 4]])\n", " >>> a\n", " array([[1, 2],\n", " [3, 4]])\n", " >>> np.transpose(a)\n", " array([[1, 3],\n", " [2, 4]])\n", " \n", " >>> a = np.array([1, 2, 3, 4])\n", " >>> a\n", " array([1, 2, 3, 4])\n", " >>> np.transpose(a)\n", " array([1, 2, 3, 4])\n", " \n", " >>> a = np.ones((1, 2, 3))\n", " >>> np.transpose(a, (1, 0, 2)).shape\n", " (2, 1, 3)\n", " \n", " >>> a = np.ones((2, 3, 4, 5))\n", " >>> np.transpose(a).shape\n", " (5, 4, 3, 2)\n", " \n", " trapz(y, x=None, dx=1.0, axis=-1)\n", " Integrate along the given axis using the composite trapezoidal rule.\n", " \n", " If `x` is provided, the integration happens in sequence along its\n", " elements - they are not sorted.\n", " \n", " Integrate `y` (`x`) along each 1d slice on the given axis, compute\n", " :math:`\\int y(x) dx`.\n", " When `x` is specified, this integrates along the parametric curve,\n", " computing :math:`\\int_t y(t) dt =\n", " \\int_t y(t) \\left.\\frac{dx}{dt}\\right|_{x=x(t)} dt`.\n", " \n", " Parameters\n", " ----------\n", " y : array_like\n", " Input array to integrate.\n", " x : array_like, optional\n", " The sample points corresponding to the `y` values. If `x` is None,\n", " the sample points are assumed to be evenly spaced `dx` apart. The\n", " default is None.\n", " dx : scalar, optional\n", " The spacing between sample points when `x` is None. The default is 1.\n", " axis : int, optional\n", " The axis along which to integrate.\n", " \n", " Returns\n", " -------\n", " trapz : float or ndarray\n", " Definite integral of `y` = n-dimensional array as approximated along\n", " a single axis by the trapezoidal rule. If `y` is a 1-dimensional array,\n", " then the result is a float. If `n` is greater than 1, then the result\n", " is an `n`-1 dimensional array.\n", " \n", " See Also\n", " --------\n", " sum, cumsum\n", " \n", " Notes\n", " -----\n", " Image [2]_ illustrates trapezoidal rule -- y-axis locations of points\n", " will be taken from `y` array, by default x-axis distances between\n", " points will be 1.0, alternatively they can be provided with `x` array\n", " or with `dx` scalar. Return value will be equal to combined area under\n", " the red lines.\n", " \n", " \n", " References\n", " ----------\n", " .. [1] Wikipedia page: https://en.wikipedia.org/wiki/Trapezoidal_rule\n", " \n", " .. [2] Illustration image:\n", " https://en.wikipedia.org/wiki/File:Composite_trapezoidal_rule_illustration.png\n", " \n", " Examples\n", " --------\n", " >>> np.trapz([1,2,3])\n", " 4.0\n", " >>> np.trapz([1,2,3], x=[4,6,8])\n", " 8.0\n", " >>> np.trapz([1,2,3], dx=2)\n", " 8.0\n", " \n", " Using a decreasing `x` corresponds to integrating in reverse:\n", " \n", " >>> np.trapz([1,2,3], x=[8,6,4])\n", " -8.0\n", " \n", " More generally `x` is used to integrate along a parametric curve.\n", " This finds the area of a circle, noting we repeat the sample which closes\n", " the curve:\n", " \n", " >>> theta = np.linspace(0, 2 * np.pi, num=1000, endpoint=True)\n", " >>> np.trapz(np.cos(theta), x=np.sin(theta))\n", " 3.141571941375841\n", " \n", " >>> a = np.arange(6).reshape(2, 3)\n", " >>> a\n", " array([[0, 1, 2],\n", " [3, 4, 5]])\n", " >>> np.trapz(a, axis=0)\n", " array([1.5, 2.5, 3.5])\n", " >>> np.trapz(a, axis=1)\n", " array([2., 8.])\n", " \n", " tri(N, M=None, k=0, dtype=<class 'float'>, *, like=None)\n", " An array with ones at and below the given diagonal and zeros elsewhere.\n", " \n", " Parameters\n", " ----------\n", " N : int\n", " Number of rows in the array.\n", " M : int, optional\n", " Number of columns in the array.\n", " By default, `M` is taken equal to `N`.\n", " k : int, optional\n", " The sub-diagonal at and below which the array is filled.\n", " `k` = 0 is the main diagonal, while `k` < 0 is below it,\n", " and `k` > 0 is above. The default is 0.\n", " dtype : dtype, optional\n", " Data type of the returned array. The default is float.\n", " like : array_like, optional\n", " Reference object to allow the creation of arrays which are not\n", " NumPy arrays. If an array-like passed in as ``like`` supports\n", " the ``__array_function__`` protocol, the result will be defined\n", " by it. In this case, it ensures the creation of an array object\n", " compatible with that passed in via this argument.\n", " \n", " .. versionadded:: 1.20.0\n", " \n", " Returns\n", " -------\n", " tri : ndarray of shape (N, M)\n", " Array with its lower triangle filled with ones and zero elsewhere;\n", " in other words ``T[i,j] == 1`` for ``j <= i + k``, 0 otherwise.\n", " \n", " Examples\n", " --------\n", " >>> np.tri(3, 5, 2, dtype=int)\n", " array([[1, 1, 1, 0, 0],\n", " [1, 1, 1, 1, 0],\n", " [1, 1, 1, 1, 1]])\n", " \n", " >>> np.tri(3, 5, -1)\n", " array([[0., 0., 0., 0., 0.],\n", " [1., 0., 0., 0., 0.],\n", " [1., 1., 0., 0., 0.]])\n", " \n", " tril(m, k=0)\n", " Lower triangle of an array.\n", " \n", " Return a copy of an array with elements above the `k`-th diagonal zeroed.\n", " For arrays with ``ndim`` exceeding 2, `tril` will apply to the final two\n", " axes.\n", " \n", " Parameters\n", " ----------\n", " m : array_like, shape (..., M, N)\n", " Input array.\n", " k : int, optional\n", " Diagonal above which to zero elements. `k = 0` (the default) is the\n", " main diagonal, `k < 0` is below it and `k > 0` is above.\n", " \n", " Returns\n", " -------\n", " tril : ndarray, shape (..., M, N)\n", " Lower triangle of `m`, of same shape and data-type as `m`.\n", " \n", " See Also\n", " --------\n", " triu : same thing, only for the upper triangle\n", " \n", " Examples\n", " --------\n", " >>> np.tril([[1,2,3],[4,5,6],[7,8,9],[10,11,12]], -1)\n", " array([[ 0, 0, 0],\n", " [ 4, 0, 0],\n", " [ 7, 8, 0],\n", " [10, 11, 12]])\n", " \n", " >>> np.tril(np.arange(3*4*5).reshape(3, 4, 5))\n", " array([[[ 0, 0, 0, 0, 0],\n", " [ 5, 6, 0, 0, 0],\n", " [10, 11, 12, 0, 0],\n", " [15, 16, 17, 18, 0]],\n", " [[20, 0, 0, 0, 0],\n", " [25, 26, 0, 0, 0],\n", " [30, 31, 32, 0, 0],\n", " [35, 36, 37, 38, 0]],\n", " [[40, 0, 0, 0, 0],\n", " [45, 46, 0, 0, 0],\n", " [50, 51, 52, 0, 0],\n", " [55, 56, 57, 58, 0]]])\n", " \n", " tril_indices(n, k=0, m=None)\n", " Return the indices for the lower-triangle of an (n, m) array.\n", " \n", " Parameters\n", " ----------\n", " n : int\n", " The row dimension of the arrays for which the returned\n", " indices will be valid.\n", " k : int, optional\n", " Diagonal offset (see `tril` for details).\n", " m : int, optional\n", " .. versionadded:: 1.9.0\n", " \n", " The column dimension of the arrays for which the returned\n", " arrays will be valid.\n", " By default `m` is taken equal to `n`.\n", " \n", " \n", " Returns\n", " -------\n", " inds : tuple of arrays\n", " The indices for the triangle. The returned tuple contains two arrays,\n", " each with the indices along one dimension of the array.\n", " \n", " See also\n", " --------\n", " triu_indices : similar function, for upper-triangular.\n", " mask_indices : generic function accepting an arbitrary mask function.\n", " tril, triu\n", " \n", " Notes\n", " -----\n", " .. versionadded:: 1.4.0\n", " \n", " Examples\n", " --------\n", " Compute two different sets of indices to access 4x4 arrays, one for the\n", " lower triangular part starting at the main diagonal, and one starting two\n", " diagonals further right:\n", " \n", " >>> il1 = np.tril_indices(4)\n", " >>> il2 = np.tril_indices(4, 2)\n", " \n", " Here is how they can be used with a sample array:\n", " \n", " >>> a = np.arange(16).reshape(4, 4)\n", " >>> a\n", " array([[ 0, 1, 2, 3],\n", " [ 4, 5, 6, 7],\n", " [ 8, 9, 10, 11],\n", " [12, 13, 14, 15]])\n", " \n", " Both for indexing:\n", " \n", " >>> a[il1]\n", " array([ 0, 4, 5, ..., 13, 14, 15])\n", " \n", " And for assigning values:\n", " \n", " >>> a[il1] = -1\n", " >>> a\n", " array([[-1, 1, 2, 3],\n", " [-1, -1, 6, 7],\n", " [-1, -1, -1, 11],\n", " [-1, -1, -1, -1]])\n", " \n", " These cover almost the whole array (two diagonals right of the main one):\n", " \n", " >>> a[il2] = -10\n", " >>> a\n", " array([[-10, -10, -10, 3],\n", " [-10, -10, -10, -10],\n", " [-10, -10, -10, -10],\n", " [-10, -10, -10, -10]])\n", " \n", " tril_indices_from(arr, k=0)\n", " Return the indices for the lower-triangle of arr.\n", " \n", " See `tril_indices` for full details.\n", " \n", " Parameters\n", " ----------\n", " arr : array_like\n", " The indices will be valid for square arrays whose dimensions are\n", " the same as arr.\n", " k : int, optional\n", " Diagonal offset (see `tril` for details).\n", " \n", " See Also\n", " --------\n", " tril_indices, tril\n", " \n", " Notes\n", " -----\n", " .. versionadded:: 1.4.0\n", " \n", " trim_zeros(filt, trim='fb')\n", " Trim the leading and/or trailing zeros from a 1-D array or sequence.\n", " \n", " Parameters\n", " ----------\n", " filt : 1-D array or sequence\n", " Input array.\n", " trim : str, optional\n", " A string with 'f' representing trim from front and 'b' to trim from\n", " back. Default is 'fb', trim zeros from both front and back of the\n", " array.\n", " \n", " Returns\n", " -------\n", " trimmed : 1-D array or sequence\n", " The result of trimming the input. The input data type is preserved.\n", " \n", " Examples\n", " --------\n", " >>> a = np.array((0, 0, 0, 1, 2, 3, 0, 2, 1, 0))\n", " >>> np.trim_zeros(a)\n", " array([1, 2, 3, 0, 2, 1])\n", " \n", " >>> np.trim_zeros(a, 'b')\n", " array([0, 0, 0, ..., 0, 2, 1])\n", " \n", " The input data type is preserved, list/tuple in means list/tuple out.\n", " \n", " >>> np.trim_zeros([0, 1, 2, 0])\n", " [1, 2]\n", " \n", " triu(m, k=0)\n", " Upper triangle of an array.\n", " \n", " Return a copy of an array with the elements below the `k`-th diagonal\n", " zeroed. For arrays with ``ndim`` exceeding 2, `triu` will apply to the\n", " final two axes.\n", " \n", " Please refer to the documentation for `tril` for further details.\n", " \n", " See Also\n", " --------\n", " tril : lower triangle of an array\n", " \n", " Examples\n", " --------\n", " >>> np.triu([[1,2,3],[4,5,6],[7,8,9],[10,11,12]], -1)\n", " array([[ 1, 2, 3],\n", " [ 4, 5, 6],\n", " [ 0, 8, 9],\n", " [ 0, 0, 12]])\n", " \n", " >>> np.triu(np.arange(3*4*5).reshape(3, 4, 5))\n", " array([[[ 0, 1, 2, 3, 4],\n", " [ 0, 6, 7, 8, 9],\n", " [ 0, 0, 12, 13, 14],\n", " [ 0, 0, 0, 18, 19]],\n", " [[20, 21, 22, 23, 24],\n", " [ 0, 26, 27, 28, 29],\n", " [ 0, 0, 32, 33, 34],\n", " [ 0, 0, 0, 38, 39]],\n", " [[40, 41, 42, 43, 44],\n", " [ 0, 46, 47, 48, 49],\n", " [ 0, 0, 52, 53, 54],\n", " [ 0, 0, 0, 58, 59]]])\n", " \n", " triu_indices(n, k=0, m=None)\n", " Return the indices for the upper-triangle of an (n, m) array.\n", " \n", " Parameters\n", " ----------\n", " n : int\n", " The size of the arrays for which the returned indices will\n", " be valid.\n", " k : int, optional\n", " Diagonal offset (see `triu` for details).\n", " m : int, optional\n", " .. versionadded:: 1.9.0\n", " \n", " The column dimension of the arrays for which the returned\n", " arrays will be valid.\n", " By default `m` is taken equal to `n`.\n", " \n", " \n", " Returns\n", " -------\n", " inds : tuple, shape(2) of ndarrays, shape(`n`)\n", " The indices for the triangle. The returned tuple contains two arrays,\n", " each with the indices along one dimension of the array. Can be used\n", " to slice a ndarray of shape(`n`, `n`).\n", " \n", " See also\n", " --------\n", " tril_indices : similar function, for lower-triangular.\n", " mask_indices : generic function accepting an arbitrary mask function.\n", " triu, tril\n", " \n", " Notes\n", " -----\n", " .. versionadded:: 1.4.0\n", " \n", " Examples\n", " --------\n", " Compute two different sets of indices to access 4x4 arrays, one for the\n", " upper triangular part starting at the main diagonal, and one starting two\n", " diagonals further right:\n", " \n", " >>> iu1 = np.triu_indices(4)\n", " >>> iu2 = np.triu_indices(4, 2)\n", " \n", " Here is how they can be used with a sample array:\n", " \n", " >>> a = np.arange(16).reshape(4, 4)\n", " >>> a\n", " array([[ 0, 1, 2, 3],\n", " [ 4, 5, 6, 7],\n", " [ 8, 9, 10, 11],\n", " [12, 13, 14, 15]])\n", " \n", " Both for indexing:\n", " \n", " >>> a[iu1]\n", " array([ 0, 1, 2, ..., 10, 11, 15])\n", " \n", " And for assigning values:\n", " \n", " >>> a[iu1] = -1\n", " >>> a\n", " array([[-1, -1, -1, -1],\n", " [ 4, -1, -1, -1],\n", " [ 8, 9, -1, -1],\n", " [12, 13, 14, -1]])\n", " \n", " These cover only a small part of the whole array (two diagonals right\n", " of the main one):\n", " \n", " >>> a[iu2] = -10\n", " >>> a\n", " array([[ -1, -1, -10, -10],\n", " [ 4, -1, -1, -10],\n", " [ 8, 9, -1, -1],\n", " [ 12, 13, 14, -1]])\n", " \n", " triu_indices_from(arr, k=0)\n", " Return the indices for the upper-triangle of arr.\n", " \n", " See `triu_indices` for full details.\n", " \n", " Parameters\n", " ----------\n", " arr : ndarray, shape(N, N)\n", " The indices will be valid for square arrays.\n", " k : int, optional\n", " Diagonal offset (see `triu` for details).\n", " \n", " Returns\n", " -------\n", " triu_indices_from : tuple, shape(2) of ndarray, shape(N)\n", " Indices for the upper-triangle of `arr`.\n", " \n", " See Also\n", " --------\n", " triu_indices, triu\n", " \n", " Notes\n", " -----\n", " .. versionadded:: 1.4.0\n", " \n", " typename(char)\n", " Return a description for the given data type code.\n", " \n", " Parameters\n", " ----------\n", " char : str\n", " Data type code.\n", " \n", " Returns\n", " -------\n", " out : str\n", " Description of the input data type code.\n", " \n", " See Also\n", " --------\n", " dtype, typecodes\n", " \n", " Examples\n", " --------\n", " >>> typechars = ['S1', '?', 'B', 'D', 'G', 'F', 'I', 'H', 'L', 'O', 'Q',\n", " ... 'S', 'U', 'V', 'b', 'd', 'g', 'f', 'i', 'h', 'l', 'q']\n", " >>> for typechar in typechars:\n", " ... print(typechar, ' : ', np.typename(typechar))\n", " ...\n", " S1 : character\n", " ? : bool\n", " B : unsigned char\n", " D : complex double precision\n", " G : complex long double precision\n", " F : complex single precision\n", " I : unsigned integer\n", " H : unsigned short\n", " L : unsigned long integer\n", " O : object\n", " Q : unsigned long long integer\n", " S : string\n", " U : unicode\n", " V : void\n", " b : signed char\n", " d : double precision\n", " g : long precision\n", " f : single precision\n", " i : integer\n", " h : short\n", " l : long integer\n", " q : long long integer\n", " \n", " union1d(ar1, ar2)\n", " Find the union of two arrays.\n", " \n", " Return the unique, sorted array of values that are in either of the two\n", " input arrays.\n", " \n", " Parameters\n", " ----------\n", " ar1, ar2 : array_like\n", " Input arrays. They are flattened if they are not already 1D.\n", " \n", " Returns\n", " -------\n", " union1d : ndarray\n", " Unique, sorted union of the input arrays.\n", " \n", " See Also\n", " --------\n", " numpy.lib.arraysetops : Module with a number of other functions for\n", " performing set operations on arrays.\n", " \n", " Examples\n", " --------\n", " >>> np.union1d([-1, 0, 1], [-2, 0, 2])\n", " array([-2, -1, 0, 1, 2])\n", " \n", " To find the union of more than two arrays, use functools.reduce:\n", " \n", " >>> from functools import reduce\n", " >>> reduce(np.union1d, ([1, 3, 4, 3], [3, 1, 2, 1], [6, 3, 4, 2]))\n", " array([1, 2, 3, 4, 6])\n", " \n", " unique(ar, return_index=False, return_inverse=False, return_counts=False, axis=None, *, equal_nan=True)\n", " Find the unique elements of an array.\n", " \n", " Returns the sorted unique elements of an array. There are three optional\n", " outputs in addition to the unique elements:\n", " \n", " * the indices of the input array that give the unique values\n", " * the indices of the unique array that reconstruct the input array\n", " * the number of times each unique value comes up in the input array\n", " \n", " Parameters\n", " ----------\n", " ar : array_like\n", " Input array. Unless `axis` is specified, this will be flattened if it\n", " is not already 1-D.\n", " return_index : bool, optional\n", " If True, also return the indices of `ar` (along the specified axis,\n", " if provided, or in the flattened array) that result in the unique array.\n", " return_inverse : bool, optional\n", " If True, also return the indices of the unique array (for the specified\n", " axis, if provided) that can be used to reconstruct `ar`.\n", " return_counts : bool, optional\n", " If True, also return the number of times each unique item appears\n", " in `ar`.\n", " axis : int or None, optional\n", " The axis to operate on. If None, `ar` will be flattened. If an integer,\n", " the subarrays indexed by the given axis will be flattened and treated\n", " as the elements of a 1-D array with the dimension of the given axis,\n", " see the notes for more details. Object arrays or structured arrays\n", " that contain objects are not supported if the `axis` kwarg is used. The\n", " default is None.\n", " \n", " .. versionadded:: 1.13.0\n", " \n", " equal_nan : bool, optional\n", " If True, collapses multiple NaN values in the return array into one.\n", " \n", " .. versionadded:: 1.24\n", " \n", " Returns\n", " -------\n", " unique : ndarray\n", " The sorted unique values.\n", " unique_indices : ndarray, optional\n", " The indices of the first occurrences of the unique values in the\n", " original array. Only provided if `return_index` is True.\n", " unique_inverse : ndarray, optional\n", " The indices to reconstruct the original array from the\n", " unique array. Only provided if `return_inverse` is True.\n", " unique_counts : ndarray, optional\n", " The number of times each of the unique values comes up in the\n", " original array. Only provided if `return_counts` is True.\n", " \n", " .. versionadded:: 1.9.0\n", " \n", " See Also\n", " --------\n", " numpy.lib.arraysetops : Module with a number of other functions for\n", " performing set operations on arrays.\n", " repeat : Repeat elements of an array.\n", " \n", " Notes\n", " -----\n", " When an axis is specified the subarrays indexed by the axis are sorted.\n", " This is done by making the specified axis the first dimension of the array\n", " (move the axis to the first dimension to keep the order of the other axes)\n", " and then flattening the subarrays in C order. The flattened subarrays are\n", " then viewed as a structured type with each element given a label, with the\n", " effect that we end up with a 1-D array of structured types that can be\n", " treated in the same way as any other 1-D array. The result is that the\n", " flattened subarrays are sorted in lexicographic order starting with the\n", " first element.\n", " \n", " .. versionchanged: NumPy 1.21\n", " If nan values are in the input array, a single nan is put\n", " to the end of the sorted unique values.\n", " \n", " Also for complex arrays all NaN values are considered equivalent\n", " (no matter whether the NaN is in the real or imaginary part).\n", " As the representant for the returned array the smallest one in the\n", " lexicographical order is chosen - see np.sort for how the lexicographical\n", " order is defined for complex arrays.\n", " \n", " Examples\n", " --------\n", " >>> np.unique([1, 1, 2, 2, 3, 3])\n", " array([1, 2, 3])\n", " >>> a = np.array([[1, 1], [2, 3]])\n", " >>> np.unique(a)\n", " array([1, 2, 3])\n", " \n", " Return the unique rows of a 2D array\n", " \n", " >>> a = np.array([[1, 0, 0], [1, 0, 0], [2, 3, 4]])\n", " >>> np.unique(a, axis=0)\n", " array([[1, 0, 0], [2, 3, 4]])\n", " \n", " Return the indices of the original array that give the unique values:\n", " \n", " >>> a = np.array(['a', 'b', 'b', 'c', 'a'])\n", " >>> u, indices = np.unique(a, return_index=True)\n", " >>> u\n", " array(['a', 'b', 'c'], dtype='<U1')\n", " >>> indices\n", " array([0, 1, 3])\n", " >>> a[indices]\n", " array(['a', 'b', 'c'], dtype='<U1')\n", " \n", " Reconstruct the input array from the unique values and inverse:\n", " \n", " >>> a = np.array([1, 2, 6, 4, 2, 3, 2])\n", " >>> u, indices = np.unique(a, return_inverse=True)\n", " >>> u\n", " array([1, 2, 3, 4, 6])\n", " >>> indices\n", " array([0, 1, 4, 3, 1, 2, 1])\n", " >>> u[indices]\n", " array([1, 2, 6, 4, 2, 3, 2])\n", " \n", " Reconstruct the input values from the unique values and counts:\n", " \n", " >>> a = np.array([1, 2, 6, 4, 2, 3, 2])\n", " >>> values, counts = np.unique(a, return_counts=True)\n", " >>> values\n", " array([1, 2, 3, 4, 6])\n", " >>> counts\n", " array([1, 3, 1, 1, 1])\n", " >>> np.repeat(values, counts)\n", " array([1, 2, 2, 2, 3, 4, 6]) # original order not preserved\n", " \n", " unpackbits(...)\n", " unpackbits(a, /, axis=None, count=None, bitorder='big')\n", " \n", " Unpacks elements of a uint8 array into a binary-valued output array.\n", " \n", " Each element of `a` represents a bit-field that should be unpacked\n", " into a binary-valued output array. The shape of the output array is\n", " either 1-D (if `axis` is ``None``) or the same shape as the input\n", " array with unpacking done along the axis specified.\n", " \n", " Parameters\n", " ----------\n", " a : ndarray, uint8 type\n", " Input array.\n", " axis : int, optional\n", " The dimension over which bit-unpacking is done.\n", " ``None`` implies unpacking the flattened array.\n", " count : int or None, optional\n", " The number of elements to unpack along `axis`, provided as a way\n", " of undoing the effect of packing a size that is not a multiple\n", " of eight. A non-negative number means to only unpack `count`\n", " bits. A negative number means to trim off that many bits from\n", " the end. ``None`` means to unpack the entire array (the\n", " default). Counts larger than the available number of bits will\n", " add zero padding to the output. Negative counts must not\n", " exceed the available number of bits.\n", " \n", " .. versionadded:: 1.17.0\n", " \n", " bitorder : {'big', 'little'}, optional\n", " The order of the returned bits. 'big' will mimic bin(val),\n", " ``3 = 0b00000011 => [0, 0, 0, 0, 0, 0, 1, 1]``, 'little' will reverse\n", " the order to ``[1, 1, 0, 0, 0, 0, 0, 0]``.\n", " Defaults to 'big'.\n", " \n", " .. versionadded:: 1.17.0\n", " \n", " Returns\n", " -------\n", " unpacked : ndarray, uint8 type\n", " The elements are binary-valued (0 or 1).\n", " \n", " See Also\n", " --------\n", " packbits : Packs the elements of a binary-valued array into bits in\n", " a uint8 array.\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([[2], [7], [23]], dtype=np.uint8)\n", " >>> a\n", " array([[ 2],\n", " [ 7],\n", " [23]], dtype=uint8)\n", " >>> b = np.unpackbits(a, axis=1)\n", " >>> b\n", " array([[0, 0, 0, 0, 0, 0, 1, 0],\n", " [0, 0, 0, 0, 0, 1, 1, 1],\n", " [0, 0, 0, 1, 0, 1, 1, 1]], dtype=uint8)\n", " >>> c = np.unpackbits(a, axis=1, count=-3)\n", " >>> c\n", " array([[0, 0, 0, 0, 0],\n", " [0, 0, 0, 0, 0],\n", " [0, 0, 0, 1, 0]], dtype=uint8)\n", " \n", " >>> p = np.packbits(b, axis=0)\n", " >>> np.unpackbits(p, axis=0)\n", " array([[0, 0, 0, 0, 0, 0, 1, 0],\n", " [0, 0, 0, 0, 0, 1, 1, 1],\n", " [0, 0, 0, 1, 0, 1, 1, 1],\n", " [0, 0, 0, 0, 0, 0, 0, 0],\n", " [0, 0, 0, 0, 0, 0, 0, 0],\n", " [0, 0, 0, 0, 0, 0, 0, 0],\n", " [0, 0, 0, 0, 0, 0, 0, 0],\n", " [0, 0, 0, 0, 0, 0, 0, 0]], dtype=uint8)\n", " >>> np.array_equal(b, np.unpackbits(p, axis=0, count=b.shape[0]))\n", " True\n", " \n", " unravel_index(...)\n", " unravel_index(indices, shape, order='C')\n", " \n", " Converts a flat index or array of flat indices into a tuple\n", " of coordinate arrays.\n", " \n", " Parameters\n", " ----------\n", " indices : array_like\n", " An integer array whose elements are indices into the flattened\n", " version of an array of dimensions ``shape``. Before version 1.6.0,\n", " this function accepted just one index value.\n", " shape : tuple of ints\n", " The shape of the array to use for unraveling ``indices``.\n", " \n", " .. versionchanged:: 1.16.0\n", " Renamed from ``dims`` to ``shape``.\n", " \n", " order : {'C', 'F'}, optional\n", " Determines whether the indices should be viewed as indexing in\n", " row-major (C-style) or column-major (Fortran-style) order.\n", " \n", " .. versionadded:: 1.6.0\n", " \n", " Returns\n", " -------\n", " unraveled_coords : tuple of ndarray\n", " Each array in the tuple has the same shape as the ``indices``\n", " array.\n", " \n", " See Also\n", " --------\n", " ravel_multi_index\n", " \n", " Examples\n", " --------\n", " >>> np.unravel_index([22, 41, 37], (7,6))\n", " (array([3, 6, 6]), array([4, 5, 1]))\n", " >>> np.unravel_index([31, 41, 13], (7,6), order='F')\n", " (array([3, 6, 6]), array([4, 5, 1]))\n", " \n", " >>> np.unravel_index(1621, (6,7,8,9))\n", " (3, 1, 4, 1)\n", " \n", " unwrap(p, discont=None, axis=-1, *, period=6.283185307179586)\n", " Unwrap by taking the complement of large deltas with respect to the period.\n", " \n", " This unwraps a signal `p` by changing elements which have an absolute\n", " difference from their predecessor of more than ``max(discont, period/2)``\n", " to their `period`-complementary values.\n", " \n", " For the default case where `period` is :math:`2\\pi` and `discont` is\n", " :math:`\\pi`, this unwraps a radian phase `p` such that adjacent differences\n", " are never greater than :math:`\\pi` by adding :math:`2k\\pi` for some\n", " integer :math:`k`.\n", " \n", " Parameters\n", " ----------\n", " p : array_like\n", " Input array.\n", " discont : float, optional\n", " Maximum discontinuity between values, default is ``period/2``.\n", " Values below ``period/2`` are treated as if they were ``period/2``.\n", " To have an effect different from the default, `discont` should be\n", " larger than ``period/2``.\n", " axis : int, optional\n", " Axis along which unwrap will operate, default is the last axis.\n", " period : float, optional\n", " Size of the range over which the input wraps. By default, it is\n", " ``2 pi``.\n", " \n", " .. versionadded:: 1.21.0\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " Output array.\n", " \n", " See Also\n", " --------\n", " rad2deg, deg2rad\n", " \n", " Notes\n", " -----\n", " If the discontinuity in `p` is smaller than ``period/2``,\n", " but larger than `discont`, no unwrapping is done because taking\n", " the complement would only make the discontinuity larger.\n", " \n", " Examples\n", " --------\n", " >>> phase = np.linspace(0, np.pi, num=5)\n", " >>> phase[3:] += np.pi\n", " >>> phase\n", " array([ 0. , 0.78539816, 1.57079633, 5.49778714, 6.28318531]) # may vary\n", " >>> np.unwrap(phase)\n", " array([ 0. , 0.78539816, 1.57079633, -0.78539816, 0. ]) # may vary\n", " >>> np.unwrap([0, 1, 2, -1, 0], period=4)\n", " array([0, 1, 2, 3, 4])\n", " >>> np.unwrap([ 1, 2, 3, 4, 5, 6, 1, 2, 3], period=6)\n", " array([1, 2, 3, 4, 5, 6, 7, 8, 9])\n", " >>> np.unwrap([2, 3, 4, 5, 2, 3, 4, 5], period=4)\n", " array([2, 3, 4, 5, 6, 7, 8, 9])\n", " >>> phase_deg = np.mod(np.linspace(0 ,720, 19), 360) - 180\n", " >>> np.unwrap(phase_deg, period=360)\n", " array([-180., -140., -100., -60., -20., 20., 60., 100., 140.,\n", " 180., 220., 260., 300., 340., 380., 420., 460., 500.,\n", " 540.])\n", " \n", " vander(x, N=None, increasing=False)\n", " Generate a Vandermonde matrix.\n", " \n", " The columns of the output matrix are powers of the input vector. The\n", " order of the powers is determined by the `increasing` boolean argument.\n", " Specifically, when `increasing` is False, the `i`-th output column is\n", " the input vector raised element-wise to the power of ``N - i - 1``. Such\n", " a matrix with a geometric progression in each row is named for Alexandre-\n", " Theophile Vandermonde.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " 1-D input array.\n", " N : int, optional\n", " Number of columns in the output. If `N` is not specified, a square\n", " array is returned (``N = len(x)``).\n", " increasing : bool, optional\n", " Order of the powers of the columns. If True, the powers increase\n", " from left to right, if False (the default) they are reversed.\n", " \n", " .. versionadded:: 1.9.0\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " Vandermonde matrix. If `increasing` is False, the first column is\n", " ``x^(N-1)``, the second ``x^(N-2)`` and so forth. If `increasing` is\n", " True, the columns are ``x^0, x^1, ..., x^(N-1)``.\n", " \n", " See Also\n", " --------\n", " polynomial.polynomial.polyvander\n", " \n", " Examples\n", " --------\n", " >>> x = np.array([1, 2, 3, 5])\n", " >>> N = 3\n", " >>> np.vander(x, N)\n", " array([[ 1, 1, 1],\n", " [ 4, 2, 1],\n", " [ 9, 3, 1],\n", " [25, 5, 1]])\n", " \n", " >>> np.column_stack([x**(N-1-i) for i in range(N)])\n", " array([[ 1, 1, 1],\n", " [ 4, 2, 1],\n", " [ 9, 3, 1],\n", " [25, 5, 1]])\n", " \n", " >>> x = np.array([1, 2, 3, 5])\n", " >>> np.vander(x)\n", " array([[ 1, 1, 1, 1],\n", " [ 8, 4, 2, 1],\n", " [ 27, 9, 3, 1],\n", " [125, 25, 5, 1]])\n", " >>> np.vander(x, increasing=True)\n", " array([[ 1, 1, 1, 1],\n", " [ 1, 2, 4, 8],\n", " [ 1, 3, 9, 27],\n", " [ 1, 5, 25, 125]])\n", " \n", " The determinant of a square Vandermonde matrix is the product\n", " of the differences between the values of the input vector:\n", " \n", " >>> np.linalg.det(np.vander(x))\n", " 48.000000000000043 # may vary\n", " >>> (5-3)*(5-2)*(5-1)*(3-2)*(3-1)*(2-1)\n", " 48\n", " \n", " var(a, axis=None, dtype=None, out=None, ddof=0, keepdims=<no value>, *, where=<no value>)\n", " Compute the variance along the specified axis.\n", " \n", " Returns the variance of the array elements, a measure of the spread of a\n", " distribution. The variance is computed for the flattened array by\n", " default, otherwise over the specified axis.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " Array containing numbers whose variance is desired. If `a` is not an\n", " array, a conversion is attempted.\n", " axis : None or int or tuple of ints, optional\n", " Axis or axes along which the variance is computed. The default is to\n", " compute the variance of the flattened array.\n", " \n", " .. versionadded:: 1.7.0\n", " \n", " If this is a tuple of ints, a variance is performed over multiple axes,\n", " instead of a single axis or all the axes as before.\n", " dtype : data-type, optional\n", " Type to use in computing the variance. For arrays of integer type\n", " the default is `float64`; for arrays of float types it is the same as\n", " the array type.\n", " out : ndarray, optional\n", " Alternate output array in which to place the result. It must have\n", " the same shape as the expected output, but the type is cast if\n", " necessary.\n", " ddof : int, optional\n", " \"Delta Degrees of Freedom\": the divisor used in the calculation is\n", " ``N - ddof``, where ``N`` represents the number of elements. By\n", " default `ddof` is zero.\n", " keepdims : bool, optional\n", " If this is set to True, the axes which are reduced are left\n", " in the result as dimensions with size one. With this option,\n", " the result will broadcast correctly against the input array.\n", " \n", " If the default value is passed, then `keepdims` will not be\n", " passed through to the `var` method of sub-classes of\n", " `ndarray`, however any non-default value will be. If the\n", " sub-class' method does not implement `keepdims` any\n", " exceptions will be raised.\n", " \n", " where : array_like of bool, optional\n", " Elements to include in the variance. See `~numpy.ufunc.reduce` for\n", " details.\n", " \n", " .. versionadded:: 1.20.0\n", " \n", " Returns\n", " -------\n", " variance : ndarray, see dtype parameter above\n", " If ``out=None``, returns a new array containing the variance;\n", " otherwise, a reference to the output array is returned.\n", " \n", " See Also\n", " --------\n", " std, mean, nanmean, nanstd, nanvar\n", " :ref:`ufuncs-output-type`\n", " \n", " Notes\n", " -----\n", " The variance is the average of the squared deviations from the mean,\n", " i.e., ``var = mean(x)``, where ``x = abs(a - a.mean())**2``.\n", " \n", " The mean is typically calculated as ``x.sum() / N``, where ``N = len(x)``.\n", " If, however, `ddof` is specified, the divisor ``N - ddof`` is used\n", " instead. In standard statistical practice, ``ddof=1`` provides an\n", " unbiased estimator of the variance of a hypothetical infinite population.\n", " ``ddof=0`` provides a maximum likelihood estimate of the variance for\n", " normally distributed variables.\n", " \n", " Note that for complex numbers, the absolute value is taken before\n", " squaring, so that the result is always real and nonnegative.\n", " \n", " For floating-point input, the variance is computed using the same\n", " precision the input has. Depending on the input data, this can cause\n", " the results to be inaccurate, especially for `float32` (see example\n", " below). Specifying a higher-accuracy accumulator using the ``dtype``\n", " keyword can alleviate this issue.\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([[1, 2], [3, 4]])\n", " >>> np.var(a)\n", " 1.25\n", " >>> np.var(a, axis=0)\n", " array([1., 1.])\n", " >>> np.var(a, axis=1)\n", " array([0.25, 0.25])\n", " \n", " In single precision, var() can be inaccurate:\n", " \n", " >>> a = np.zeros((2, 512*512), dtype=np.float32)\n", " >>> a[0, :] = 1.0\n", " >>> a[1, :] = 0.1\n", " >>> np.var(a)\n", " 0.20250003\n", " \n", " Computing the variance in float64 is more accurate:\n", " \n", " >>> np.var(a, dtype=np.float64)\n", " 0.20249999932944759 # may vary\n", " >>> ((1-0.55)**2 + (0.1-0.55)**2)/2\n", " 0.2025\n", " \n", " Specifying a where argument:\n", " \n", " >>> a = np.array([[14, 8, 11, 10], [7, 9, 10, 11], [10, 15, 5, 10]])\n", " >>> np.var(a)\n", " 6.833333333333333 # may vary\n", " >>> np.var(a, where=[[True], [True], [False]])\n", " 4.0\n", " \n", " vdot(...)\n", " vdot(a, b, /)\n", " \n", " Return the dot product of two vectors.\n", " \n", " The vdot(`a`, `b`) function handles complex numbers differently than\n", " dot(`a`, `b`). If the first argument is complex the complex conjugate\n", " of the first argument is used for the calculation of the dot product.\n", " \n", " Note that `vdot` handles multidimensional arrays differently than `dot`:\n", " it does *not* perform a matrix product, but flattens input arguments\n", " to 1-D vectors first. Consequently, it should only be used for vectors.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " If `a` is complex the complex conjugate is taken before calculation\n", " of the dot product.\n", " b : array_like\n", " Second argument to the dot product.\n", " \n", " Returns\n", " -------\n", " output : ndarray\n", " Dot product of `a` and `b`. Can be an int, float, or\n", " complex depending on the types of `a` and `b`.\n", " \n", " See Also\n", " --------\n", " dot : Return the dot product without using the complex conjugate of the\n", " first argument.\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([1+2j,3+4j])\n", " >>> b = np.array([5+6j,7+8j])\n", " >>> np.vdot(a, b)\n", " (70-8j)\n", " >>> np.vdot(b, a)\n", " (70+8j)\n", " \n", " Note that higher-dimensional arrays are flattened!\n", " \n", " >>> a = np.array([[1, 4], [5, 6]])\n", " >>> b = np.array([[4, 1], [2, 2]])\n", " >>> np.vdot(a, b)\n", " 30\n", " >>> np.vdot(b, a)\n", " 30\n", " >>> 1*4 + 4*1 + 5*2 + 6*2\n", " 30\n", " \n", " vsplit(ary, indices_or_sections)\n", " Split an array into multiple sub-arrays vertically (row-wise).\n", " \n", " Please refer to the ``split`` documentation. ``vsplit`` is equivalent\n", " to ``split`` with `axis=0` (default), the array is always split along the\n", " first axis regardless of the array dimension.\n", " \n", " See Also\n", " --------\n", " split : Split an array into multiple sub-arrays of equal size.\n", " \n", " Examples\n", " --------\n", " >>> x = np.arange(16.0).reshape(4, 4)\n", " >>> x\n", " array([[ 0., 1., 2., 3.],\n", " [ 4., 5., 6., 7.],\n", " [ 8., 9., 10., 11.],\n", " [12., 13., 14., 15.]])\n", " >>> np.vsplit(x, 2)\n", " [array([[0., 1., 2., 3.],\n", " [4., 5., 6., 7.]]), array([[ 8., 9., 10., 11.],\n", " [12., 13., 14., 15.]])]\n", " >>> np.vsplit(x, np.array([3, 6]))\n", " [array([[ 0., 1., 2., 3.],\n", " [ 4., 5., 6., 7.],\n", " [ 8., 9., 10., 11.]]), array([[12., 13., 14., 15.]]), array([], shape=(0, 4), dtype=float64)]\n", " \n", " With a higher dimensional array the split is still along the first axis.\n", " \n", " >>> x = np.arange(8.0).reshape(2, 2, 2)\n", " >>> x\n", " array([[[0., 1.],\n", " [2., 3.]],\n", " [[4., 5.],\n", " [6., 7.]]])\n", " >>> np.vsplit(x, 2)\n", " [array([[[0., 1.],\n", " [2., 3.]]]), array([[[4., 5.],\n", " [6., 7.]]])]\n", " \n", " vstack(tup, *, dtype=None, casting='same_kind')\n", " Stack arrays in sequence vertically (row wise).\n", " \n", " This is equivalent to concatenation along the first axis after 1-D arrays\n", " of shape `(N,)` have been reshaped to `(1,N)`. Rebuilds arrays divided by\n", " `vsplit`.\n", " \n", " This function makes most sense for arrays with up to 3 dimensions. For\n", " instance, for pixel-data with a height (first axis), width (second axis),\n", " and r/g/b channels (third axis). The functions `concatenate`, `stack` and\n", " `block` provide more general stacking and concatenation operations.\n", " \n", " ``np.row_stack`` is an alias for `vstack`. They are the same function.\n", " \n", " Parameters\n", " ----------\n", " tup : sequence of ndarrays\n", " The arrays must have the same shape along all but the first axis.\n", " 1-D arrays must have the same length.\n", " \n", " dtype : str or dtype\n", " If provided, the destination array will have this dtype. Cannot be\n", " provided together with `out`.\n", " \n", " .. versionadded:: 1.24\n", " \n", " casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional\n", " Controls what kind of data casting may occur. Defaults to 'same_kind'.\n", " \n", " .. versionadded:: 1.24\n", " \n", " Returns\n", " -------\n", " stacked : ndarray\n", " The array formed by stacking the given arrays, will be at least 2-D.\n", " \n", " See Also\n", " --------\n", " concatenate : Join a sequence of arrays along an existing axis.\n", " stack : Join a sequence of arrays along a new axis.\n", " block : Assemble an nd-array from nested lists of blocks.\n", " hstack : Stack arrays in sequence horizontally (column wise).\n", " dstack : Stack arrays in sequence depth wise (along third axis).\n", " column_stack : Stack 1-D arrays as columns into a 2-D array.\n", " vsplit : Split an array into multiple sub-arrays vertically (row-wise).\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([1, 2, 3])\n", " >>> b = np.array([4, 5, 6])\n", " >>> np.vstack((a,b))\n", " array([[1, 2, 3],\n", " [4, 5, 6]])\n", " \n", " >>> a = np.array([[1], [2], [3]])\n", " >>> b = np.array([[4], [5], [6]])\n", " >>> np.vstack((a,b))\n", " array([[1],\n", " [2],\n", " [3],\n", " [4],\n", " [5],\n", " [6]])\n", " \n", " where(...)\n", " where(condition, [x, y], /)\n", " \n", " Return elements chosen from `x` or `y` depending on `condition`.\n", " \n", " .. note::\n", " When only `condition` is provided, this function is a shorthand for\n", " ``np.asarray(condition).nonzero()``. Using `nonzero` directly should be\n", " preferred, as it behaves correctly for subclasses. The rest of this\n", " documentation covers only the case where all three arguments are\n", " provided.\n", " \n", " Parameters\n", " ----------\n", " condition : array_like, bool\n", " Where True, yield `x`, otherwise yield `y`.\n", " x, y : array_like\n", " Values from which to choose. `x`, `y` and `condition` need to be\n", " broadcastable to some shape.\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " An array with elements from `x` where `condition` is True, and elements\n", " from `y` elsewhere.\n", " \n", " See Also\n", " --------\n", " choose\n", " nonzero : The function that is called when x and y are omitted\n", " \n", " Notes\n", " -----\n", " If all the arrays are 1-D, `where` is equivalent to::\n", " \n", " [xv if c else yv\n", " for c, xv, yv in zip(condition, x, y)]\n", " \n", " Examples\n", " --------\n", " >>> a = np.arange(10)\n", " >>> a\n", " array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])\n", " >>> np.where(a < 5, a, 10*a)\n", " array([ 0, 1, 2, 3, 4, 50, 60, 70, 80, 90])\n", " \n", " This can be used on multidimensional arrays too:\n", " \n", " >>> np.where([[True, False], [True, True]],\n", " ... [[1, 2], [3, 4]],\n", " ... [[9, 8], [7, 6]])\n", " array([[1, 8],\n", " [3, 4]])\n", " \n", " The shapes of x, y, and the condition are broadcast together:\n", " \n", " >>> x, y = np.ogrid[:3, :4]\n", " >>> np.where(x < y, x, 10 + y) # both x and 10+y are broadcast\n", " array([[10, 0, 0, 0],\n", " [10, 11, 1, 1],\n", " [10, 11, 12, 2]])\n", " \n", " >>> a = np.array([[0, 1, 2],\n", " ... [0, 2, 4],\n", " ... [0, 3, 6]])\n", " >>> np.where(a < 4, a, -1) # -1 is broadcast\n", " array([[ 0, 1, 2],\n", " [ 0, 2, -1],\n", " [ 0, 3, -1]])\n", " \n", " who(vardict=None)\n", " Print the NumPy arrays in the given dictionary.\n", " \n", " If there is no dictionary passed in or `vardict` is None then returns\n", " NumPy arrays in the globals() dictionary (all NumPy arrays in the\n", " namespace).\n", " \n", " Parameters\n", " ----------\n", " vardict : dict, optional\n", " A dictionary possibly containing ndarrays. Default is globals().\n", " \n", " Returns\n", " -------\n", " out : None\n", " Returns 'None'.\n", " \n", " Notes\n", " -----\n", " Prints out the name, shape, bytes and type of all of the ndarrays\n", " present in `vardict`.\n", " \n", " Examples\n", " --------\n", " >>> a = np.arange(10)\n", " >>> b = np.ones(20)\n", " >>> np.who()\n", " Name Shape Bytes Type\n", " ===========================================================\n", " a 10 80 int64\n", " b 20 160 float64\n", " Upper bound on total bytes = 240\n", " \n", " >>> d = {'x': np.arange(2.0), 'y': np.arange(3.0), 'txt': 'Some str',\n", " ... 'idx':5}\n", " >>> np.who(d)\n", " Name Shape Bytes Type\n", " ===========================================================\n", " x 2 16 float64\n", " y 3 24 float64\n", " Upper bound on total bytes = 40\n", " \n", " zeros(...)\n", " zeros(shape, dtype=float, order='C', *, like=None)\n", " \n", " Return a new array of given shape and type, filled with zeros.\n", " \n", " Parameters\n", " ----------\n", " shape : int or tuple of ints\n", " Shape of the new array, e.g., ``(2, 3)`` or ``2``.\n", " dtype : data-type, optional\n", " The desired data-type for the array, e.g., `numpy.int8`. Default is\n", " `numpy.float64`.\n", " order : {'C', 'F'}, optional, default: 'C'\n", " Whether to store multi-dimensional data in row-major\n", " (C-style) or column-major (Fortran-style) order in\n", " memory.\n", " like : array_like, optional\n", " Reference object to allow the creation of arrays which are not\n", " NumPy arrays. If an array-like passed in as ``like`` supports\n", " the ``__array_function__`` protocol, the result will be defined\n", " by it. In this case, it ensures the creation of an array object\n", " compatible with that passed in via this argument.\n", " \n", " .. versionadded:: 1.20.0\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " Array of zeros with the given shape, dtype, and order.\n", " \n", " See Also\n", " --------\n", " zeros_like : Return an array of zeros with shape and type of input.\n", " empty : Return a new uninitialized array.\n", " ones : Return a new array setting values to one.\n", " full : Return a new array of given shape filled with value.\n", " \n", " Examples\n", " --------\n", " >>> np.zeros(5)\n", " array([ 0., 0., 0., 0., 0.])\n", " \n", " >>> np.zeros((5,), dtype=int)\n", " array([0, 0, 0, 0, 0])\n", " \n", " >>> np.zeros((2, 1))\n", " array([[ 0.],\n", " [ 0.]])\n", " \n", " >>> s = (2,2)\n", " >>> np.zeros(s)\n", " array([[ 0., 0.],\n", " [ 0., 0.]])\n", " \n", " >>> np.zeros((2,), dtype=[('x', 'i4'), ('y', 'i4')]) # custom dtype\n", " array([(0, 0), (0, 0)],\n", " dtype=[('x', '<i4'), ('y', '<i4')])\n", " \n", " zeros_like(a, dtype=None, order='K', subok=True, shape=None)\n", " Return an array of zeros with the same shape and type as a given array.\n", " \n", " Parameters\n", " ----------\n", " a : array_like\n", " The shape and data-type of `a` define these same attributes of\n", " the returned array.\n", " dtype : data-type, optional\n", " Overrides the data type of the result.\n", " \n", " .. versionadded:: 1.6.0\n", " order : {'C', 'F', 'A', or 'K'}, optional\n", " Overrides the memory layout of the result. 'C' means C-order,\n", " 'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous,\n", " 'C' otherwise. 'K' means match the layout of `a` as closely\n", " as possible.\n", " \n", " .. versionadded:: 1.6.0\n", " subok : bool, optional.\n", " If True, then the newly created array will use the sub-class\n", " type of `a`, otherwise it will be a base-class array. Defaults\n", " to True.\n", " shape : int or sequence of ints, optional.\n", " Overrides the shape of the result. If order='K' and the number of\n", " dimensions is unchanged, will try to keep order, otherwise,\n", " order='C' is implied.\n", " \n", " .. versionadded:: 1.17.0\n", " \n", " Returns\n", " -------\n", " out : ndarray\n", " Array of zeros with the same shape and type as `a`.\n", " \n", " See Also\n", " --------\n", " empty_like : Return an empty array with shape and type of input.\n", " ones_like : Return an array of ones with shape and type of input.\n", " full_like : Return a new array with shape of input filled with value.\n", " zeros : Return a new array setting values to zero.\n", " \n", " Examples\n", " --------\n", " >>> x = np.arange(6)\n", " >>> x = x.reshape((2, 3))\n", " >>> x\n", " array([[0, 1, 2],\n", " [3, 4, 5]])\n", " >>> np.zeros_like(x)\n", " array([[0, 0, 0],\n", " [0, 0, 0]])\n", " \n", " >>> y = np.arange(3, dtype=float)\n", " >>> y\n", " array([0., 1., 2.])\n", " >>> np.zeros_like(y)\n", " array([0., 0., 0.])\n", "\n", "DATA\n", " ALLOW_THREADS = 1\n", " BUFSIZE = 8192\n", " CLIP = 0\n", " ERR_CALL = 3\n", " ERR_DEFAULT = 521\n", " ERR_IGNORE = 0\n", " ERR_LOG = 5\n", " ERR_PRINT = 4\n", " ERR_RAISE = 2\n", " ERR_WARN = 1\n", " FLOATING_POINT_SUPPORT = 1\n", " FPE_DIVIDEBYZERO = 1\n", " FPE_INVALID = 8\n", " FPE_OVERFLOW = 2\n", " FPE_UNDERFLOW = 4\n", " False_ = False\n", " Inf = inf\n", " Infinity = inf\n", " MAXDIMS = 32\n", " MAY_SHARE_BOUNDS = 0\n", " MAY_SHARE_EXACT = -1\n", " NAN = nan\n", " NINF = -inf\n", " NZERO = -0.0\n", " NaN = nan\n", " PINF = inf\n", " PZERO = 0.0\n", " RAISE = 2\n", " SHIFT_DIVIDEBYZERO = 0\n", " SHIFT_INVALID = 9\n", " SHIFT_OVERFLOW = 3\n", " SHIFT_UNDERFLOW = 6\n", " ScalarType = (<class 'int'>, <class 'float'>, <class 'complex'>, <clas...\n", " True_ = True\n", " UFUNC_BUFSIZE_DEFAULT = 8192\n", " UFUNC_PYVALS_NAME = 'UFUNC_PYVALS'\n", " WRAP = 1\n", " _UFUNC_API = <capsule object NULL>\n", " __NUMPY_SETUP__ = False\n", " __all__ = ['ModuleDeprecationWarning', 'VisibleDeprecationWarning', '_...\n", " __deprecated_attrs__ = {'bool8': (<class 'numpy.bool_'>, '`np.bool8` i...\n", " __expired_functions__ = {'fv': 'In accordance with NEP 32, the functio...\n", " __former_attrs__ = {'bool': \"module 'numpy' has no attribute 'bool'.\\n...\n", " __future_scalars__ = {'bool', 'bytes', 'long', 'object', 'str', 'ulong...\n", " __git_version__ = '14bb214bca49b167abc375fa873466a811e62102'\n", " __mkl_version__ = '2023.0.1'\n", " absolute = <ufunc 'absolute'>\n", " absolute(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Calculate the absolute value element-wise.\n", " \n", " ``np.abs`` is a shorthand for this function.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Input array.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " absolute : ndarray\n", " An ndarray containing the absolute value of\n", " each element in `x`. For complex input, ``a + ib``, the\n", " absolute value is :math:`\\sqrt{ a^2 + b^2 }`.\n", " This is a scalar if `x` is a scalar.\n", " \n", " Examples\n", " --------\n", " >>> x = np.array([-1.2, 1.2])\n", " >>> np.absolute(x)\n", " array([ 1.2, 1.2])\n", " >>> np.absolute(1.2 + 1j)\n", " 1.5620499351813308\n", " \n", " Plot the function over ``[-10, 10]``:\n", " \n", " >>> import matplotlib.pyplot as plt\n", " \n", " >>> x = np.linspace(start=-10, stop=10, num=101)\n", " >>> plt.plot(x, np.absolute(x))\n", " >>> plt.show()\n", " \n", " Plot the function over the complex plane:\n", " \n", " >>> xx = x + 1j * x[:, np.newaxis]\n", " >>> plt.imshow(np.abs(xx), extent=[-10, 10, -10, 10], cmap='gray')\n", " >>> plt.show()\n", " \n", " The `abs` function can be used as a shorthand for ``np.absolute`` on\n", " ndarrays.\n", " \n", " >>> x = np.array([-1.2, 1.2])\n", " >>> abs(x)\n", " array([1.2, 1.2])\n", " \n", " add = <ufunc 'add'>\n", " add(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Add arguments element-wise.\n", " \n", " Parameters\n", " ----------\n", " x1, x2 : array_like\n", " The arrays to be added.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " add : ndarray or scalar\n", " The sum of `x1` and `x2`, element-wise.\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " Notes\n", " -----\n", " Equivalent to `x1` + `x2` in terms of array broadcasting.\n", " \n", " Examples\n", " --------\n", " >>> np.add(1.0, 4.0)\n", " 5.0\n", " >>> x1 = np.arange(9.0).reshape((3, 3))\n", " >>> x2 = np.arange(3.0)\n", " >>> np.add(x1, x2)\n", " array([[ 0., 2., 4.],\n", " [ 3., 5., 7.],\n", " [ 6., 8., 10.]])\n", " \n", " The ``+`` operator can be used as a shorthand for ``np.add`` on ndarrays.\n", " \n", " >>> x1 = np.arange(9.0).reshape((3, 3))\n", " >>> x2 = np.arange(3.0)\n", " >>> x1 + x2\n", " array([[ 0., 2., 4.],\n", " [ 3., 5., 7.],\n", " [ 6., 8., 10.]])\n", " \n", " arccos = <ufunc 'arccos'>\n", " arccos(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Trigonometric inverse cosine, element-wise.\n", " \n", " The inverse of `cos` so that, if ``y = cos(x)``, then ``x = arccos(y)``.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " `x`-coordinate on the unit circle.\n", " For real arguments, the domain is [-1, 1].\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " angle : ndarray\n", " The angle of the ray intersecting the unit circle at the given\n", " `x`-coordinate in radians [0, pi].\n", " This is a scalar if `x` is a scalar.\n", " \n", " See Also\n", " --------\n", " cos, arctan, arcsin, emath.arccos\n", " \n", " Notes\n", " -----\n", " `arccos` is a multivalued function: for each `x` there are infinitely\n", " many numbers `z` such that ``cos(z) = x``. The convention is to return\n", " the angle `z` whose real part lies in `[0, pi]`.\n", " \n", " For real-valued input data types, `arccos` always returns real output.\n", " For each value that cannot be expressed as a real number or infinity,\n", " it yields ``nan`` and sets the `invalid` floating point error flag.\n", " \n", " For complex-valued input, `arccos` is a complex analytic function that\n", " has branch cuts ``[-inf, -1]`` and `[1, inf]` and is continuous from\n", " above on the former and from below on the latter.\n", " \n", " The inverse `cos` is also known as `acos` or cos^-1.\n", " \n", " References\n", " ----------\n", " M. Abramowitz and I.A. Stegun, \"Handbook of Mathematical Functions\",\n", " 10th printing, 1964, pp. 79.\n", " https://personal.math.ubc.ca/~cbm/aands/page_79.htm\n", " \n", " Examples\n", " --------\n", " We expect the arccos of 1 to be 0, and of -1 to be pi:\n", " \n", " >>> np.arccos([1, -1])\n", " array([ 0. , 3.14159265])\n", " \n", " Plot arccos:\n", " \n", " >>> import matplotlib.pyplot as plt\n", " >>> x = np.linspace(-1, 1, num=100)\n", " >>> plt.plot(x, np.arccos(x))\n", " >>> plt.axis('tight')\n", " >>> plt.show()\n", " \n", " arccosh = <ufunc 'arccosh'>\n", " arccosh(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Inverse hyperbolic cosine, element-wise.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Input array.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " arccosh : ndarray\n", " Array of the same shape as `x`.\n", " This is a scalar if `x` is a scalar.\n", " \n", " See Also\n", " --------\n", " \n", " cosh, arcsinh, sinh, arctanh, tanh\n", " \n", " Notes\n", " -----\n", " `arccosh` is a multivalued function: for each `x` there are infinitely\n", " many numbers `z` such that `cosh(z) = x`. The convention is to return the\n", " `z` whose imaginary part lies in ``[-pi, pi]`` and the real part in\n", " ``[0, inf]``.\n", " \n", " For real-valued input data types, `arccosh` always returns real output.\n", " For each value that cannot be expressed as a real number or infinity, it\n", " yields ``nan`` and sets the `invalid` floating point error flag.\n", " \n", " For complex-valued input, `arccosh` is a complex analytical function that\n", " has a branch cut `[-inf, 1]` and is continuous from above on it.\n", " \n", " References\n", " ----------\n", " .. [1] M. Abramowitz and I.A. Stegun, \"Handbook of Mathematical Functions\",\n", " 10th printing, 1964, pp. 86.\n", " https://personal.math.ubc.ca/~cbm/aands/page_86.htm\n", " .. [2] Wikipedia, \"Inverse hyperbolic function\",\n", " https://en.wikipedia.org/wiki/Arccosh\n", " \n", " Examples\n", " --------\n", " >>> np.arccosh([np.e, 10.0])\n", " array([ 1.65745445, 2.99322285])\n", " >>> np.arccosh(1)\n", " 0.0\n", " \n", " arcsin = <ufunc 'arcsin'>\n", " arcsin(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Inverse sine, element-wise.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " `y`-coordinate on the unit circle.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " angle : ndarray\n", " The inverse sine of each element in `x`, in radians and in the\n", " closed interval ``[-pi/2, pi/2]``.\n", " This is a scalar if `x` is a scalar.\n", " \n", " See Also\n", " --------\n", " sin, cos, arccos, tan, arctan, arctan2, emath.arcsin\n", " \n", " Notes\n", " -----\n", " `arcsin` is a multivalued function: for each `x` there are infinitely\n", " many numbers `z` such that :math:`sin(z) = x`. The convention is to\n", " return the angle `z` whose real part lies in [-pi/2, pi/2].\n", " \n", " For real-valued input data types, *arcsin* always returns real output.\n", " For each value that cannot be expressed as a real number or infinity,\n", " it yields ``nan`` and sets the `invalid` floating point error flag.\n", " \n", " For complex-valued input, `arcsin` is a complex analytic function that\n", " has, by convention, the branch cuts [-inf, -1] and [1, inf] and is\n", " continuous from above on the former and from below on the latter.\n", " \n", " The inverse sine is also known as `asin` or sin^{-1}.\n", " \n", " References\n", " ----------\n", " Abramowitz, M. and Stegun, I. A., *Handbook of Mathematical Functions*,\n", " 10th printing, New York: Dover, 1964, pp. 79ff.\n", " https://personal.math.ubc.ca/~cbm/aands/page_79.htm\n", " \n", " Examples\n", " --------\n", " >>> np.arcsin(1) # pi/2\n", " 1.5707963267948966\n", " >>> np.arcsin(-1) # -pi/2\n", " -1.5707963267948966\n", " >>> np.arcsin(0)\n", " 0.0\n", " \n", " arcsinh = <ufunc 'arcsinh'>\n", " arcsinh(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Inverse hyperbolic sine element-wise.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Input array.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " out : ndarray or scalar\n", " Array of the same shape as `x`.\n", " This is a scalar if `x` is a scalar.\n", " \n", " Notes\n", " -----\n", " `arcsinh` is a multivalued function: for each `x` there are infinitely\n", " many numbers `z` such that `sinh(z) = x`. The convention is to return the\n", " `z` whose imaginary part lies in `[-pi/2, pi/2]`.\n", " \n", " For real-valued input data types, `arcsinh` always returns real output.\n", " For each value that cannot be expressed as a real number or infinity, it\n", " returns ``nan`` and sets the `invalid` floating point error flag.\n", " \n", " For complex-valued input, `arccos` is a complex analytical function that\n", " has branch cuts `[1j, infj]` and `[-1j, -infj]` and is continuous from\n", " the right on the former and from the left on the latter.\n", " \n", " The inverse hyperbolic sine is also known as `asinh` or ``sinh^-1``.\n", " \n", " References\n", " ----------\n", " .. [1] M. Abramowitz and I.A. Stegun, \"Handbook of Mathematical Functions\",\n", " 10th printing, 1964, pp. 86.\n", " https://personal.math.ubc.ca/~cbm/aands/page_86.htm\n", " .. [2] Wikipedia, \"Inverse hyperbolic function\",\n", " https://en.wikipedia.org/wiki/Arcsinh\n", " \n", " Examples\n", " --------\n", " >>> np.arcsinh(np.array([np.e, 10.0]))\n", " array([ 1.72538256, 2.99822295])\n", " \n", " arctan = <ufunc 'arctan'>\n", " arctan(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Trigonometric inverse tangent, element-wise.\n", " \n", " The inverse of tan, so that if ``y = tan(x)`` then ``x = arctan(y)``.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " out : ndarray or scalar\n", " Out has the same shape as `x`. Its real part is in\n", " ``[-pi/2, pi/2]`` (``arctan(+/-inf)`` returns ``+/-pi/2``).\n", " This is a scalar if `x` is a scalar.\n", " \n", " See Also\n", " --------\n", " arctan2 : The \"four quadrant\" arctan of the angle formed by (`x`, `y`)\n", " and the positive `x`-axis.\n", " angle : Argument of complex values.\n", " \n", " Notes\n", " -----\n", " `arctan` is a multi-valued function: for each `x` there are infinitely\n", " many numbers `z` such that tan(`z`) = `x`. The convention is to return\n", " the angle `z` whose real part lies in [-pi/2, pi/2].\n", " \n", " For real-valued input data types, `arctan` always returns real output.\n", " For each value that cannot be expressed as a real number or infinity,\n", " it yields ``nan`` and sets the `invalid` floating point error flag.\n", " \n", " For complex-valued input, `arctan` is a complex analytic function that\n", " has [``1j, infj``] and [``-1j, -infj``] as branch cuts, and is continuous\n", " from the left on the former and from the right on the latter.\n", " \n", " The inverse tangent is also known as `atan` or tan^{-1}.\n", " \n", " References\n", " ----------\n", " Abramowitz, M. and Stegun, I. A., *Handbook of Mathematical Functions*,\n", " 10th printing, New York: Dover, 1964, pp. 79.\n", " https://personal.math.ubc.ca/~cbm/aands/page_79.htm\n", " \n", " Examples\n", " --------\n", " We expect the arctan of 0 to be 0, and of 1 to be pi/4:\n", " \n", " >>> np.arctan([0, 1])\n", " array([ 0. , 0.78539816])\n", " \n", " >>> np.pi/4\n", " 0.78539816339744828\n", " \n", " Plot arctan:\n", " \n", " >>> import matplotlib.pyplot as plt\n", " >>> x = np.linspace(-10, 10)\n", " >>> plt.plot(x, np.arctan(x))\n", " >>> plt.axis('tight')\n", " >>> plt.show()\n", " \n", " arctan2 = <ufunc 'arctan2'>\n", " arctan2(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Element-wise arc tangent of ``x1/x2`` choosing the quadrant correctly.\n", " \n", " The quadrant (i.e., branch) is chosen so that ``arctan2(x1, x2)`` is\n", " the signed angle in radians between the ray ending at the origin and\n", " passing through the point (1,0), and the ray ending at the origin and\n", " passing through the point (`x2`, `x1`). (Note the role reversal: the\n", " \"`y`-coordinate\" is the first function parameter, the \"`x`-coordinate\"\n", " is the second.) By IEEE convention, this function is defined for\n", " `x2` = +/-0 and for either or both of `x1` and `x2` = +/-inf (see\n", " Notes for specific values).\n", " \n", " This function is not defined for complex-valued arguments; for the\n", " so-called argument of complex values, use `angle`.\n", " \n", " Parameters\n", " ----------\n", " x1 : array_like, real-valued\n", " `y`-coordinates.\n", " x2 : array_like, real-valued\n", " `x`-coordinates.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " angle : ndarray\n", " Array of angles in radians, in the range ``[-pi, pi]``.\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " See Also\n", " --------\n", " arctan, tan, angle\n", " \n", " Notes\n", " -----\n", " *arctan2* is identical to the `atan2` function of the underlying\n", " C library. The following special values are defined in the C\n", " standard: [1]_\n", " \n", " ====== ====== ================\n", " `x1` `x2` `arctan2(x1,x2)`\n", " ====== ====== ================\n", " +/- 0 +0 +/- 0\n", " +/- 0 -0 +/- pi\n", " > 0 +/-inf +0 / +pi\n", " < 0 +/-inf -0 / -pi\n", " +/-inf +inf +/- (pi/4)\n", " +/-inf -inf +/- (3*pi/4)\n", " ====== ====== ================\n", " \n", " Note that +0 and -0 are distinct floating point numbers, as are +inf\n", " and -inf.\n", " \n", " References\n", " ----------\n", " .. [1] ISO/IEC standard 9899:1999, \"Programming language C.\"\n", " \n", " Examples\n", " --------\n", " Consider four points in different quadrants:\n", " \n", " >>> x = np.array([-1, +1, +1, -1])\n", " >>> y = np.array([-1, -1, +1, +1])\n", " >>> np.arctan2(y, x) * 180 / np.pi\n", " array([-135., -45., 45., 135.])\n", " \n", " Note the order of the parameters. `arctan2` is defined also when `x2` = 0\n", " and at several other special points, obtaining values in\n", " the range ``[-pi, pi]``:\n", " \n", " >>> np.arctan2([1., -1.], [0., 0.])\n", " array([ 1.57079633, -1.57079633])\n", " >>> np.arctan2([0., 0., np.inf], [+0., -0., np.inf])\n", " array([0. , 3.14159265, 0.78539816])\n", " \n", " arctanh = <ufunc 'arctanh'>\n", " arctanh(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Inverse hyperbolic tangent element-wise.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Input array.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " out : ndarray or scalar\n", " Array of the same shape as `x`.\n", " This is a scalar if `x` is a scalar.\n", " \n", " See Also\n", " --------\n", " emath.arctanh\n", " \n", " Notes\n", " -----\n", " `arctanh` is a multivalued function: for each `x` there are infinitely\n", " many numbers `z` such that ``tanh(z) = x``. The convention is to return\n", " the `z` whose imaginary part lies in `[-pi/2, pi/2]`.\n", " \n", " For real-valued input data types, `arctanh` always returns real output.\n", " For each value that cannot be expressed as a real number or infinity,\n", " it yields ``nan`` and sets the `invalid` floating point error flag.\n", " \n", " For complex-valued input, `arctanh` is a complex analytical function\n", " that has branch cuts `[-1, -inf]` and `[1, inf]` and is continuous from\n", " above on the former and from below on the latter.\n", " \n", " The inverse hyperbolic tangent is also known as `atanh` or ``tanh^-1``.\n", " \n", " References\n", " ----------\n", " .. [1] M. Abramowitz and I.A. Stegun, \"Handbook of Mathematical Functions\",\n", " 10th printing, 1964, pp. 86.\n", " https://personal.math.ubc.ca/~cbm/aands/page_86.htm\n", " .. [2] Wikipedia, \"Inverse hyperbolic function\",\n", " https://en.wikipedia.org/wiki/Arctanh\n", " \n", " Examples\n", " --------\n", " >>> np.arctanh([0, -0.5])\n", " array([ 0. , -0.54930614])\n", " \n", " bitwise_and = <ufunc 'bitwise_and'>\n", " bitwise_and(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Compute the bit-wise AND of two arrays element-wise.\n", " \n", " Computes the bit-wise AND of the underlying binary representation of\n", " the integers in the input arrays. This ufunc implements the C/Python\n", " operator ``&``.\n", " \n", " Parameters\n", " ----------\n", " x1, x2 : array_like\n", " Only integer and boolean types are handled.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " out : ndarray or scalar\n", " Result.\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " See Also\n", " --------\n", " logical_and\n", " bitwise_or\n", " bitwise_xor\n", " binary_repr :\n", " Return the binary representation of the input number as a string.\n", " \n", " Examples\n", " --------\n", " The number 13 is represented by ``00001101``. Likewise, 17 is\n", " represented by ``00010001``. The bit-wise AND of 13 and 17 is\n", " therefore ``000000001``, or 1:\n", " \n", " >>> np.bitwise_and(13, 17)\n", " 1\n", " \n", " >>> np.bitwise_and(14, 13)\n", " 12\n", " >>> np.binary_repr(12)\n", " '1100'\n", " >>> np.bitwise_and([14,3], 13)\n", " array([12, 1])\n", " \n", " >>> np.bitwise_and([11,7], [4,25])\n", " array([0, 1])\n", " >>> np.bitwise_and(np.array([2,5,255]), np.array([3,14,16]))\n", " array([ 2, 4, 16])\n", " >>> np.bitwise_and([True, True], [False, True])\n", " array([False, True])\n", " \n", " The ``&`` operator can be used as a shorthand for ``np.bitwise_and`` on\n", " ndarrays.\n", " \n", " >>> x1 = np.array([2, 5, 255])\n", " >>> x2 = np.array([3, 14, 16])\n", " >>> x1 & x2\n", " array([ 2, 4, 16])\n", " \n", " bitwise_not = <ufunc 'invert'>\n", " invert(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Compute bit-wise inversion, or bit-wise NOT, element-wise.\n", " \n", " Computes the bit-wise NOT of the underlying binary representation of\n", " the integers in the input arrays. This ufunc implements the C/Python\n", " operator ``~``.\n", " \n", " For signed integer inputs, the two's complement is returned. In a\n", " two's-complement system negative numbers are represented by the two's\n", " complement of the absolute value. This is the most common method of\n", " representing signed integers on computers [1]_. A N-bit\n", " two's-complement system can represent every integer in the range\n", " :math:`-2^{N-1}` to :math:`+2^{N-1}-1`.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Only integer and boolean types are handled.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " out : ndarray or scalar\n", " Result.\n", " This is a scalar if `x` is a scalar.\n", " \n", " See Also\n", " --------\n", " bitwise_and, bitwise_or, bitwise_xor\n", " logical_not\n", " binary_repr :\n", " Return the binary representation of the input number as a string.\n", " \n", " Notes\n", " -----\n", " `bitwise_not` is an alias for `invert`:\n", " \n", " >>> np.bitwise_not is np.invert\n", " True\n", " \n", " References\n", " ----------\n", " .. [1] Wikipedia, \"Two's complement\",\n", " https://en.wikipedia.org/wiki/Two's_complement\n", " \n", " Examples\n", " --------\n", " We've seen that 13 is represented by ``00001101``.\n", " The invert or bit-wise NOT of 13 is then:\n", " \n", " >>> x = np.invert(np.array(13, dtype=np.uint8))\n", " >>> x\n", " 242\n", " >>> np.binary_repr(x, width=8)\n", " '11110010'\n", " \n", " The result depends on the bit-width:\n", " \n", " >>> x = np.invert(np.array(13, dtype=np.uint16))\n", " >>> x\n", " 65522\n", " >>> np.binary_repr(x, width=16)\n", " '1111111111110010'\n", " \n", " When using signed integer types the result is the two's complement of\n", " the result for the unsigned type:\n", " \n", " >>> np.invert(np.array([13], dtype=np.int8))\n", " array([-14], dtype=int8)\n", " >>> np.binary_repr(-14, width=8)\n", " '11110010'\n", " \n", " Booleans are accepted as well:\n", " \n", " >>> np.invert(np.array([True, False]))\n", " array([False, True])\n", " \n", " The ``~`` operator can be used as a shorthand for ``np.invert`` on\n", " ndarrays.\n", " \n", " >>> x1 = np.array([True, False])\n", " >>> ~x1\n", " array([False, True])\n", " \n", " bitwise_or = <ufunc 'bitwise_or'>\n", " bitwise_or(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Compute the bit-wise OR of two arrays element-wise.\n", " \n", " Computes the bit-wise OR of the underlying binary representation of\n", " the integers in the input arrays. This ufunc implements the C/Python\n", " operator ``|``.\n", " \n", " Parameters\n", " ----------\n", " x1, x2 : array_like\n", " Only integer and boolean types are handled.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " out : ndarray or scalar\n", " Result.\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " See Also\n", " --------\n", " logical_or\n", " bitwise_and\n", " bitwise_xor\n", " binary_repr :\n", " Return the binary representation of the input number as a string.\n", " \n", " Examples\n", " --------\n", " The number 13 has the binary representation ``00001101``. Likewise,\n", " 16 is represented by ``00010000``. The bit-wise OR of 13 and 16 is\n", " then ``000111011``, or 29:\n", " \n", " >>> np.bitwise_or(13, 16)\n", " 29\n", " >>> np.binary_repr(29)\n", " '11101'\n", " \n", " >>> np.bitwise_or(32, 2)\n", " 34\n", " >>> np.bitwise_or([33, 4], 1)\n", " array([33, 5])\n", " >>> np.bitwise_or([33, 4], [1, 2])\n", " array([33, 6])\n", " \n", " >>> np.bitwise_or(np.array([2, 5, 255]), np.array([4, 4, 4]))\n", " array([ 6, 5, 255])\n", " >>> np.array([2, 5, 255]) | np.array([4, 4, 4])\n", " array([ 6, 5, 255])\n", " >>> np.bitwise_or(np.array([2, 5, 255, 2147483647], dtype=np.int32),\n", " ... np.array([4, 4, 4, 2147483647], dtype=np.int32))\n", " array([ 6, 5, 255, 2147483647])\n", " >>> np.bitwise_or([True, True], [False, True])\n", " array([ True, True])\n", " \n", " The ``|`` operator can be used as a shorthand for ``np.bitwise_or`` on\n", " ndarrays.\n", " \n", " >>> x1 = np.array([2, 5, 255])\n", " >>> x2 = np.array([4, 4, 4])\n", " >>> x1 | x2\n", " array([ 6, 5, 255])\n", " \n", " bitwise_xor = <ufunc 'bitwise_xor'>\n", " bitwise_xor(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Compute the bit-wise XOR of two arrays element-wise.\n", " \n", " Computes the bit-wise XOR of the underlying binary representation of\n", " the integers in the input arrays. This ufunc implements the C/Python\n", " operator ``^``.\n", " \n", " Parameters\n", " ----------\n", " x1, x2 : array_like\n", " Only integer and boolean types are handled.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " out : ndarray or scalar\n", " Result.\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " See Also\n", " --------\n", " logical_xor\n", " bitwise_and\n", " bitwise_or\n", " binary_repr :\n", " Return the binary representation of the input number as a string.\n", " \n", " Examples\n", " --------\n", " The number 13 is represented by ``00001101``. Likewise, 17 is\n", " represented by ``00010001``. The bit-wise XOR of 13 and 17 is\n", " therefore ``00011100``, or 28:\n", " \n", " >>> np.bitwise_xor(13, 17)\n", " 28\n", " >>> np.binary_repr(28)\n", " '11100'\n", " \n", " >>> np.bitwise_xor(31, 5)\n", " 26\n", " >>> np.bitwise_xor([31,3], 5)\n", " array([26, 6])\n", " \n", " >>> np.bitwise_xor([31,3], [5,6])\n", " array([26, 5])\n", " >>> np.bitwise_xor([True, True], [False, True])\n", " array([ True, False])\n", " \n", " The ``^`` operator can be used as a shorthand for ``np.bitwise_xor`` on\n", " ndarrays.\n", " \n", " >>> x1 = np.array([True, True])\n", " >>> x2 = np.array([False, True])\n", " >>> x1 ^ x2\n", " array([ True, False])\n", " \n", " c_ = <numpy.lib.index_tricks.CClass object>\n", " cast = {<class 'numpy.uintc'>: <function <lambda> at 0x...128'>: <func...\n", " cbrt = <ufunc 'cbrt'>\n", " cbrt(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Return the cube-root of an array, element-wise.\n", " \n", " .. versionadded:: 1.10.0\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " The values whose cube-roots are required.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray\n", " An array of the same shape as `x`, containing the cube\n", " cube-root of each element in `x`.\n", " If `out` was provided, `y` is a reference to it.\n", " This is a scalar if `x` is a scalar.\n", " \n", " \n", " Examples\n", " --------\n", " >>> np.cbrt([1,8,27])\n", " array([ 1., 2., 3.])\n", " \n", " ceil = <ufunc 'ceil'>\n", " ceil(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Return the ceiling of the input, element-wise.\n", " \n", " The ceil of the scalar `x` is the smallest integer `i`, such that\n", " ``i >= x``. It is often denoted as :math:`\\lceil x \\rceil`.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Input data.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray or scalar\n", " The ceiling of each element in `x`, with `float` dtype.\n", " This is a scalar if `x` is a scalar.\n", " \n", " See Also\n", " --------\n", " floor, trunc, rint, fix\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([-1.7, -1.5, -0.2, 0.2, 1.5, 1.7, 2.0])\n", " >>> np.ceil(a)\n", " array([-1., -1., -0., 1., 2., 2., 2.])\n", " \n", " conj = <ufunc 'conjugate'>\n", " conjugate(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Return the complex conjugate, element-wise.\n", " \n", " The complex conjugate of a complex number is obtained by changing the\n", " sign of its imaginary part.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Input value.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray\n", " The complex conjugate of `x`, with same dtype as `y`.\n", " This is a scalar if `x` is a scalar.\n", " \n", " Notes\n", " -----\n", " `conj` is an alias for `conjugate`:\n", " \n", " >>> np.conj is np.conjugate\n", " True\n", " \n", " Examples\n", " --------\n", " >>> np.conjugate(1+2j)\n", " (1-2j)\n", " \n", " >>> x = np.eye(2) + 1j * np.eye(2)\n", " >>> np.conjugate(x)\n", " array([[ 1.-1.j, 0.-0.j],\n", " [ 0.-0.j, 1.-1.j]])\n", " \n", " conjugate = <ufunc 'conjugate'>\n", " conjugate(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Return the complex conjugate, element-wise.\n", " \n", " The complex conjugate of a complex number is obtained by changing the\n", " sign of its imaginary part.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Input value.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray\n", " The complex conjugate of `x`, with same dtype as `y`.\n", " This is a scalar if `x` is a scalar.\n", " \n", " Notes\n", " -----\n", " `conj` is an alias for `conjugate`:\n", " \n", " >>> np.conj is np.conjugate\n", " True\n", " \n", " Examples\n", " --------\n", " >>> np.conjugate(1+2j)\n", " (1-2j)\n", " \n", " >>> x = np.eye(2) + 1j * np.eye(2)\n", " >>> np.conjugate(x)\n", " array([[ 1.-1.j, 0.-0.j],\n", " [ 0.-0.j, 1.-1.j]])\n", " \n", " copysign = <ufunc 'copysign'>\n", " copysign(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Change the sign of x1 to that of x2, element-wise.\n", " \n", " If `x2` is a scalar, its sign will be copied to all elements of `x1`.\n", " \n", " Parameters\n", " ----------\n", " x1 : array_like\n", " Values to change the sign of.\n", " x2 : array_like\n", " The sign of `x2` is copied to `x1`.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " out : ndarray or scalar\n", " The values of `x1` with the sign of `x2`.\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " Examples\n", " --------\n", " >>> np.copysign(1.3, -1)\n", " -1.3\n", " >>> 1/np.copysign(0, 1)\n", " inf\n", " >>> 1/np.copysign(0, -1)\n", " -inf\n", " \n", " >>> np.copysign([-1, 0, 1], -1.1)\n", " array([-1., -0., -1.])\n", " >>> np.copysign([-1, 0, 1], np.arange(3)-1)\n", " array([-1., 0., 1.])\n", " \n", " cos = <ufunc 'cos'>\n", " cos(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Cosine element-wise.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Input array in radians.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray\n", " The corresponding cosine values.\n", " This is a scalar if `x` is a scalar.\n", " \n", " Notes\n", " -----\n", " If `out` is provided, the function writes the result into it,\n", " and returns a reference to `out`. (See Examples)\n", " \n", " References\n", " ----------\n", " M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions.\n", " New York, NY: Dover, 1972.\n", " \n", " Examples\n", " --------\n", " >>> np.cos(np.array([0, np.pi/2, np.pi]))\n", " array([ 1.00000000e+00, 6.12303177e-17, -1.00000000e+00])\n", " >>>\n", " >>> # Example of providing the optional output parameter\n", " >>> out1 = np.array([0], dtype='d')\n", " >>> out2 = np.cos([0.1], out1)\n", " >>> out2 is out1\n", " True\n", " >>>\n", " >>> # Example of ValueError due to provision of shape mis-matched `out`\n", " >>> np.cos(np.zeros((3,3)),np.zeros((2,2)))\n", " Traceback (most recent call last):\n", " File \"<stdin>\", line 1, in <module>\n", " ValueError: operands could not be broadcast together with shapes (3,3) (2,2)\n", " \n", " cosh = <ufunc 'cosh'>\n", " cosh(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Hyperbolic cosine, element-wise.\n", " \n", " Equivalent to ``1/2 * (np.exp(x) + np.exp(-x))`` and ``np.cos(1j*x)``.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Input array.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " out : ndarray or scalar\n", " Output array of same shape as `x`.\n", " This is a scalar if `x` is a scalar.\n", " \n", " Examples\n", " --------\n", " >>> np.cosh(0)\n", " 1.0\n", " \n", " The hyperbolic cosine describes the shape of a hanging cable:\n", " \n", " >>> import matplotlib.pyplot as plt\n", " >>> x = np.linspace(-4, 4, 1000)\n", " >>> plt.plot(x, np.cosh(x))\n", " >>> plt.show()\n", " \n", " deg2rad = <ufunc 'deg2rad'>\n", " deg2rad(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Convert angles from degrees to radians.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Angles in degrees.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray\n", " The corresponding angle in radians.\n", " This is a scalar if `x` is a scalar.\n", " \n", " See Also\n", " --------\n", " rad2deg : Convert angles from radians to degrees.\n", " unwrap : Remove large jumps in angle by wrapping.\n", " \n", " Notes\n", " -----\n", " .. versionadded:: 1.3.0\n", " \n", " ``deg2rad(x)`` is ``x * pi / 180``.\n", " \n", " Examples\n", " --------\n", " >>> np.deg2rad(180)\n", " 3.1415926535897931\n", " \n", " degrees = <ufunc 'degrees'>\n", " degrees(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Convert angles from radians to degrees.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Input array in radians.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray of floats\n", " The corresponding degree values; if `out` was supplied this is a\n", " reference to it.\n", " This is a scalar if `x` is a scalar.\n", " \n", " See Also\n", " --------\n", " rad2deg : equivalent function\n", " \n", " Examples\n", " --------\n", " Convert a radian array to degrees\n", " \n", " >>> rad = np.arange(12.)*np.pi/6\n", " >>> np.degrees(rad)\n", " array([ 0., 30., 60., 90., 120., 150., 180., 210., 240.,\n", " 270., 300., 330.])\n", " \n", " >>> out = np.zeros((rad.shape))\n", " >>> r = np.degrees(rad, out)\n", " >>> np.all(r == out)\n", " True\n", " \n", " divide = <ufunc 'divide'>\n", " divide(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Divide arguments element-wise.\n", " \n", " Parameters\n", " ----------\n", " x1 : array_like\n", " Dividend array.\n", " x2 : array_like\n", " Divisor array.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray or scalar\n", " The quotient ``x1/x2``, element-wise.\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " See Also\n", " --------\n", " seterr : Set whether to raise or warn on overflow, underflow and\n", " division by zero.\n", " \n", " Notes\n", " -----\n", " Equivalent to ``x1`` / ``x2`` in terms of array-broadcasting.\n", " \n", " The ``true_divide(x1, x2)`` function is an alias for\n", " ``divide(x1, x2)``.\n", " \n", " Examples\n", " --------\n", " >>> np.divide(2.0, 4.0)\n", " 0.5\n", " >>> x1 = np.arange(9.0).reshape((3, 3))\n", " >>> x2 = np.arange(3.0)\n", " >>> np.divide(x1, x2)\n", " array([[nan, 1. , 1. ],\n", " [inf, 4. , 2.5],\n", " [inf, 7. , 4. ]])\n", " \n", " The ``/`` operator can be used as a shorthand for ``np.divide`` on\n", " ndarrays.\n", " \n", " >>> x1 = np.arange(9.0).reshape((3, 3))\n", " >>> x2 = 2 * np.ones(3)\n", " >>> x1 / x2\n", " array([[0. , 0.5, 1. ],\n", " [1.5, 2. , 2.5],\n", " [3. , 3.5, 4. ]])\n", " \n", " divmod = <ufunc 'divmod'>\n", " divmod(x1, x2[, out1, out2], / [, out=(None, None)], *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Return element-wise quotient and remainder simultaneously.\n", " \n", " .. versionadded:: 1.13.0\n", " \n", " ``np.divmod(x, y)`` is equivalent to ``(x // y, x % y)``, but faster\n", " because it avoids redundant work. It is used to implement the Python\n", " built-in function ``divmod`` on NumPy arrays.\n", " \n", " Parameters\n", " ----------\n", " x1 : array_like\n", " Dividend array.\n", " x2 : array_like\n", " Divisor array.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " out1 : ndarray\n", " Element-wise quotient resulting from floor division.\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " out2 : ndarray\n", " Element-wise remainder from floor division.\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " See Also\n", " --------\n", " floor_divide : Equivalent to Python's ``//`` operator.\n", " remainder : Equivalent to Python's ``%`` operator.\n", " modf : Equivalent to ``divmod(x, 1)`` for positive ``x`` with the return\n", " values switched.\n", " \n", " Examples\n", " --------\n", " >>> np.divmod(np.arange(5), 3)\n", " (array([0, 0, 0, 1, 1]), array([0, 1, 2, 0, 1]))\n", " \n", " The `divmod` function can be used as a shorthand for ``np.divmod`` on\n", " ndarrays.\n", " \n", " >>> x = np.arange(5)\n", " >>> divmod(x, 3)\n", " (array([0, 0, 0, 1, 1]), array([0, 1, 2, 0, 1]))\n", " \n", " e = 2.718281828459045\n", " equal = <ufunc 'equal'>\n", " equal(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Return (x1 == x2) element-wise.\n", " \n", " Parameters\n", " ----------\n", " x1, x2 : array_like\n", " Input arrays.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " out : ndarray or scalar\n", " Output array, element-wise comparison of `x1` and `x2`.\n", " Typically of type bool, unless ``dtype=object`` is passed.\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " See Also\n", " --------\n", " not_equal, greater_equal, less_equal, greater, less\n", " \n", " Examples\n", " --------\n", " >>> np.equal([0, 1, 3], np.arange(3))\n", " array([ True, True, False])\n", " \n", " What is compared are values, not types. So an int (1) and an array of\n", " length one can evaluate as True:\n", " \n", " >>> np.equal(1, np.ones(1))\n", " array([ True])\n", " \n", " The ``==`` operator can be used as a shorthand for ``np.equal`` on\n", " ndarrays.\n", " \n", " >>> a = np.array([2, 4, 6])\n", " >>> b = np.array([2, 4, 2])\n", " >>> a == b\n", " array([ True, True, False])\n", " \n", " euler_gamma = 0.5772156649015329\n", " exp = <ufunc 'exp'>\n", " exp(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Calculate the exponential of all elements in the input array.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Input values.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " out : ndarray or scalar\n", " Output array, element-wise exponential of `x`.\n", " This is a scalar if `x` is a scalar.\n", " \n", " See Also\n", " --------\n", " expm1 : Calculate ``exp(x) - 1`` for all elements in the array.\n", " exp2 : Calculate ``2**x`` for all elements in the array.\n", " \n", " Notes\n", " -----\n", " The irrational number ``e`` is also known as Euler's number. It is\n", " approximately 2.718281, and is the base of the natural logarithm,\n", " ``ln`` (this means that, if :math:`x = \\ln y = \\log_e y`,\n", " then :math:`e^x = y`. For real input, ``exp(x)`` is always positive.\n", " \n", " For complex arguments, ``x = a + ib``, we can write\n", " :math:`e^x = e^a e^{ib}`. The first term, :math:`e^a`, is already\n", " known (it is the real argument, described above). The second term,\n", " :math:`e^{ib}`, is :math:`\\cos b + i \\sin b`, a function with\n", " magnitude 1 and a periodic phase.\n", " \n", " References\n", " ----------\n", " .. [1] Wikipedia, \"Exponential function\",\n", " https://en.wikipedia.org/wiki/Exponential_function\n", " .. [2] M. Abramovitz and I. A. Stegun, \"Handbook of Mathematical Functions\n", " with Formulas, Graphs, and Mathematical Tables,\" Dover, 1964, p. 69,\n", " https://personal.math.ubc.ca/~cbm/aands/page_69.htm\n", " \n", " Examples\n", " --------\n", " Plot the magnitude and phase of ``exp(x)`` in the complex plane:\n", " \n", " >>> import matplotlib.pyplot as plt\n", " \n", " >>> x = np.linspace(-2*np.pi, 2*np.pi, 100)\n", " >>> xx = x + 1j * x[:, np.newaxis] # a + ib over complex plane\n", " >>> out = np.exp(xx)\n", " \n", " >>> plt.subplot(121)\n", " >>> plt.imshow(np.abs(out),\n", " ... extent=[-2*np.pi, 2*np.pi, -2*np.pi, 2*np.pi], cmap='gray')\n", " >>> plt.title('Magnitude of exp(x)')\n", " \n", " >>> plt.subplot(122)\n", " >>> plt.imshow(np.angle(out),\n", " ... extent=[-2*np.pi, 2*np.pi, -2*np.pi, 2*np.pi], cmap='hsv')\n", " >>> plt.title('Phase (angle) of exp(x)')\n", " >>> plt.show()\n", " \n", " exp2 = <ufunc 'exp2'>\n", " exp2(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Calculate `2**p` for all `p` in the input array.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Input values.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " out : ndarray or scalar\n", " Element-wise 2 to the power `x`.\n", " This is a scalar if `x` is a scalar.\n", " \n", " See Also\n", " --------\n", " power\n", " \n", " Notes\n", " -----\n", " .. versionadded:: 1.3.0\n", " \n", " \n", " \n", " Examples\n", " --------\n", " >>> np.exp2([2, 3])\n", " array([ 4., 8.])\n", " \n", " expm1 = <ufunc 'expm1'>\n", " expm1(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Calculate ``exp(x) - 1`` for all elements in the array.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Input values.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " out : ndarray or scalar\n", " Element-wise exponential minus one: ``out = exp(x) - 1``.\n", " This is a scalar if `x` is a scalar.\n", " \n", " See Also\n", " --------\n", " log1p : ``log(1 + x)``, the inverse of expm1.\n", " \n", " \n", " Notes\n", " -----\n", " This function provides greater precision than ``exp(x) - 1``\n", " for small values of ``x``.\n", " \n", " Examples\n", " --------\n", " The true value of ``exp(1e-10) - 1`` is ``1.00000000005e-10`` to\n", " about 32 significant digits. This example shows the superiority of\n", " expm1 in this case.\n", " \n", " >>> np.expm1(1e-10)\n", " 1.00000000005e-10\n", " >>> np.exp(1e-10) - 1\n", " 1.000000082740371e-10\n", " \n", " fabs = <ufunc 'fabs'>\n", " fabs(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Compute the absolute values element-wise.\n", " \n", " This function returns the absolute values (positive magnitude) of the\n", " data in `x`. Complex values are not handled, use `absolute` to find the\n", " absolute values of complex data.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " The array of numbers for which the absolute values are required. If\n", " `x` is a scalar, the result `y` will also be a scalar.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray or scalar\n", " The absolute values of `x`, the returned values are always floats.\n", " This is a scalar if `x` is a scalar.\n", " \n", " See Also\n", " --------\n", " absolute : Absolute values including `complex` types.\n", " \n", " Examples\n", " --------\n", " >>> np.fabs(-1)\n", " 1.0\n", " >>> np.fabs([-1.2, 1.2])\n", " array([ 1.2, 1.2])\n", " \n", " float_power = <ufunc 'float_power'>\n", " float_power(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " First array elements raised to powers from second array, element-wise.\n", " \n", " Raise each base in `x1` to the positionally-corresponding power in `x2`.\n", " `x1` and `x2` must be broadcastable to the same shape. This differs from\n", " the power function in that integers, float16, and float32 are promoted to\n", " floats with a minimum precision of float64 so that the result is always\n", " inexact. The intent is that the function will return a usable result for\n", " negative powers and seldom overflow for positive powers.\n", " \n", " Negative values raised to a non-integral value will return ``nan``.\n", " To get complex results, cast the input to complex, or specify the\n", " ``dtype`` to be ``complex`` (see the example below).\n", " \n", " .. versionadded:: 1.12.0\n", " \n", " Parameters\n", " ----------\n", " x1 : array_like\n", " The bases.\n", " x2 : array_like\n", " The exponents.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray\n", " The bases in `x1` raised to the exponents in `x2`.\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " See Also\n", " --------\n", " power : power function that preserves type\n", " \n", " Examples\n", " --------\n", " Cube each element in a list.\n", " \n", " >>> x1 = range(6)\n", " >>> x1\n", " [0, 1, 2, 3, 4, 5]\n", " >>> np.float_power(x1, 3)\n", " array([ 0., 1., 8., 27., 64., 125.])\n", " \n", " Raise the bases to different exponents.\n", " \n", " >>> x2 = [1.0, 2.0, 3.0, 3.0, 2.0, 1.0]\n", " >>> np.float_power(x1, x2)\n", " array([ 0., 1., 8., 27., 16., 5.])\n", " \n", " The effect of broadcasting.\n", " \n", " >>> x2 = np.array([[1, 2, 3, 3, 2, 1], [1, 2, 3, 3, 2, 1]])\n", " >>> x2\n", " array([[1, 2, 3, 3, 2, 1],\n", " [1, 2, 3, 3, 2, 1]])\n", " >>> np.float_power(x1, x2)\n", " array([[ 0., 1., 8., 27., 16., 5.],\n", " [ 0., 1., 8., 27., 16., 5.]])\n", " \n", " Negative values raised to a non-integral value will result in ``nan``\n", " (and a warning will be generated).\n", " \n", " >>> x3 = np.array([-1, -4])\n", " >>> with np.errstate(invalid='ignore'):\n", " ... p = np.float_power(x3, 1.5)\n", " ...\n", " >>> p\n", " array([nan, nan])\n", " \n", " To get complex results, give the argument ``dtype=complex``.\n", " \n", " >>> np.float_power(x3, 1.5, dtype=complex)\n", " array([-1.83697020e-16-1.j, -1.46957616e-15-8.j])\n", " \n", " floor = <ufunc 'floor'>\n", " floor(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Return the floor of the input, element-wise.\n", " \n", " The floor of the scalar `x` is the largest integer `i`, such that\n", " `i <= x`. It is often denoted as :math:`\\lfloor x \\rfloor`.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Input data.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray or scalar\n", " The floor of each element in `x`.\n", " This is a scalar if `x` is a scalar.\n", " \n", " See Also\n", " --------\n", " ceil, trunc, rint, fix\n", " \n", " Notes\n", " -----\n", " Some spreadsheet programs calculate the \"floor-towards-zero\", where\n", " ``floor(-2.5) == -2``. NumPy instead uses the definition of\n", " `floor` where `floor(-2.5) == -3`. The \"floor-towards-zero\"\n", " function is called ``fix`` in NumPy.\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([-1.7, -1.5, -0.2, 0.2, 1.5, 1.7, 2.0])\n", " >>> np.floor(a)\n", " array([-2., -2., -1., 0., 1., 1., 2.])\n", " \n", " floor_divide = <ufunc 'floor_divide'>\n", " floor_divide(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Return the largest integer smaller or equal to the division of the inputs.\n", " It is equivalent to the Python ``//`` operator and pairs with the\n", " Python ``%`` (`remainder`), function so that ``a = a % b + b * (a // b)``\n", " up to roundoff.\n", " \n", " Parameters\n", " ----------\n", " x1 : array_like\n", " Numerator.\n", " x2 : array_like\n", " Denominator.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray\n", " y = floor(`x1`/`x2`)\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " See Also\n", " --------\n", " remainder : Remainder complementary to floor_divide.\n", " divmod : Simultaneous floor division and remainder.\n", " divide : Standard division.\n", " floor : Round a number to the nearest integer toward minus infinity.\n", " ceil : Round a number to the nearest integer toward infinity.\n", " \n", " Examples\n", " --------\n", " >>> np.floor_divide(7,3)\n", " 2\n", " >>> np.floor_divide([1., 2., 3., 4.], 2.5)\n", " array([ 0., 0., 1., 1.])\n", " \n", " The ``//`` operator can be used as a shorthand for ``np.floor_divide``\n", " on ndarrays.\n", " \n", " >>> x1 = np.array([1., 2., 3., 4.])\n", " >>> x1 // 2.5\n", " array([0., 0., 1., 1.])\n", " \n", " fmax = <ufunc 'fmax'>\n", " fmax(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Element-wise maximum of array elements.\n", " \n", " Compare two arrays and returns a new array containing the element-wise\n", " maxima. If one of the elements being compared is a NaN, then the\n", " non-nan element is returned. If both elements are NaNs then the first\n", " is returned. The latter distinction is important for complex NaNs,\n", " which are defined as at least one of the real or imaginary parts being\n", " a NaN. The net effect is that NaNs are ignored when possible.\n", " \n", " Parameters\n", " ----------\n", " x1, x2 : array_like\n", " The arrays holding the elements to be compared.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray or scalar\n", " The maximum of `x1` and `x2`, element-wise.\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " See Also\n", " --------\n", " fmin :\n", " Element-wise minimum of two arrays, ignores NaNs.\n", " maximum :\n", " Element-wise maximum of two arrays, propagates NaNs.\n", " amax :\n", " The maximum value of an array along a given axis, propagates NaNs.\n", " nanmax :\n", " The maximum value of an array along a given axis, ignores NaNs.\n", " \n", " minimum, amin, nanmin\n", " \n", " Notes\n", " -----\n", " .. versionadded:: 1.3.0\n", " \n", " The fmax is equivalent to ``np.where(x1 >= x2, x1, x2)`` when neither\n", " x1 nor x2 are NaNs, but it is faster and does proper broadcasting.\n", " \n", " Examples\n", " --------\n", " >>> np.fmax([2, 3, 4], [1, 5, 2])\n", " array([ 2., 5., 4.])\n", " \n", " >>> np.fmax(np.eye(2), [0.5, 2])\n", " array([[ 1. , 2. ],\n", " [ 0.5, 2. ]])\n", " \n", " >>> np.fmax([np.nan, 0, np.nan],[0, np.nan, np.nan])\n", " array([ 0., 0., nan])\n", " \n", " fmin = <ufunc 'fmin'>\n", " fmin(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Element-wise minimum of array elements.\n", " \n", " Compare two arrays and returns a new array containing the element-wise\n", " minima. If one of the elements being compared is a NaN, then the\n", " non-nan element is returned. If both elements are NaNs then the first\n", " is returned. The latter distinction is important for complex NaNs,\n", " which are defined as at least one of the real or imaginary parts being\n", " a NaN. The net effect is that NaNs are ignored when possible.\n", " \n", " Parameters\n", " ----------\n", " x1, x2 : array_like\n", " The arrays holding the elements to be compared.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray or scalar\n", " The minimum of `x1` and `x2`, element-wise.\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " See Also\n", " --------\n", " fmax :\n", " Element-wise maximum of two arrays, ignores NaNs.\n", " minimum :\n", " Element-wise minimum of two arrays, propagates NaNs.\n", " amin :\n", " The minimum value of an array along a given axis, propagates NaNs.\n", " nanmin :\n", " The minimum value of an array along a given axis, ignores NaNs.\n", " \n", " maximum, amax, nanmax\n", " \n", " Notes\n", " -----\n", " .. versionadded:: 1.3.0\n", " \n", " The fmin is equivalent to ``np.where(x1 <= x2, x1, x2)`` when neither\n", " x1 nor x2 are NaNs, but it is faster and does proper broadcasting.\n", " \n", " Examples\n", " --------\n", " >>> np.fmin([2, 3, 4], [1, 5, 2])\n", " array([1, 3, 2])\n", " \n", " >>> np.fmin(np.eye(2), [0.5, 2])\n", " array([[ 0.5, 0. ],\n", " [ 0. , 1. ]])\n", " \n", " >>> np.fmin([np.nan, 0, np.nan],[0, np.nan, np.nan])\n", " array([ 0., 0., nan])\n", " \n", " fmod = <ufunc 'fmod'>\n", " fmod(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Returns the element-wise remainder of division.\n", " \n", " This is the NumPy implementation of the C library function fmod, the\n", " remainder has the same sign as the dividend `x1`. It is equivalent to\n", " the Matlab(TM) ``rem`` function and should not be confused with the\n", " Python modulus operator ``x1 % x2``.\n", " \n", " Parameters\n", " ----------\n", " x1 : array_like\n", " Dividend.\n", " x2 : array_like\n", " Divisor.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : array_like\n", " The remainder of the division of `x1` by `x2`.\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " See Also\n", " --------\n", " remainder : Equivalent to the Python ``%`` operator.\n", " divide\n", " \n", " Notes\n", " -----\n", " The result of the modulo operation for negative dividend and divisors\n", " is bound by conventions. For `fmod`, the sign of result is the sign of\n", " the dividend, while for `remainder` the sign of the result is the sign\n", " of the divisor. The `fmod` function is equivalent to the Matlab(TM)\n", " ``rem`` function.\n", " \n", " Examples\n", " --------\n", " >>> np.fmod([-3, -2, -1, 1, 2, 3], 2)\n", " array([-1, 0, -1, 1, 0, 1])\n", " >>> np.remainder([-3, -2, -1, 1, 2, 3], 2)\n", " array([1, 0, 1, 1, 0, 1])\n", " \n", " >>> np.fmod([5, 3], [2, 2.])\n", " array([ 1., 1.])\n", " >>> a = np.arange(-3, 3).reshape(3, 2)\n", " >>> a\n", " array([[-3, -2],\n", " [-1, 0],\n", " [ 1, 2]])\n", " >>> np.fmod(a, [2,2])\n", " array([[-1, 0],\n", " [-1, 0],\n", " [ 1, 0]])\n", " \n", " frexp = <ufunc 'frexp'>\n", " frexp(x[, out1, out2], / [, out=(None, None)], *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Decompose the elements of x into mantissa and twos exponent.\n", " \n", " Returns (`mantissa`, `exponent`), where ``x = mantissa * 2**exponent``.\n", " The mantissa lies in the open interval(-1, 1), while the twos\n", " exponent is a signed integer.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Array of numbers to be decomposed.\n", " out1 : ndarray, optional\n", " Output array for the mantissa. Must have the same shape as `x`.\n", " out2 : ndarray, optional\n", " Output array for the exponent. Must have the same shape as `x`.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " mantissa : ndarray\n", " Floating values between -1 and 1.\n", " This is a scalar if `x` is a scalar.\n", " exponent : ndarray\n", " Integer exponents of 2.\n", " This is a scalar if `x` is a scalar.\n", " \n", " See Also\n", " --------\n", " ldexp : Compute ``y = x1 * 2**x2``, the inverse of `frexp`.\n", " \n", " Notes\n", " -----\n", " Complex dtypes are not supported, they will raise a TypeError.\n", " \n", " Examples\n", " --------\n", " >>> x = np.arange(9)\n", " >>> y1, y2 = np.frexp(x)\n", " >>> y1\n", " array([ 0. , 0.5 , 0.5 , 0.75 , 0.5 , 0.625, 0.75 , 0.875,\n", " 0.5 ])\n", " >>> y2\n", " array([0, 1, 2, 2, 3, 3, 3, 3, 4])\n", " >>> y1 * 2**y2\n", " array([ 0., 1., 2., 3., 4., 5., 6., 7., 8.])\n", " \n", " gcd = <ufunc 'gcd'>\n", " gcd(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Returns the greatest common divisor of ``|x1|`` and ``|x2|``\n", " \n", " Parameters\n", " ----------\n", " x1, x2 : array_like, int\n", " Arrays of values.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " \n", " Returns\n", " -------\n", " y : ndarray or scalar\n", " The greatest common divisor of the absolute value of the inputs\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " See Also\n", " --------\n", " lcm : The lowest common multiple\n", " \n", " Examples\n", " --------\n", " >>> np.gcd(12, 20)\n", " 4\n", " >>> np.gcd.reduce([15, 25, 35])\n", " 5\n", " >>> np.gcd(np.arange(6), 20)\n", " array([20, 1, 2, 1, 4, 5])\n", " \n", " greater = <ufunc 'greater'>\n", " greater(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Return the truth value of (x1 > x2) element-wise.\n", " \n", " Parameters\n", " ----------\n", " x1, x2 : array_like\n", " Input arrays.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " out : ndarray or scalar\n", " Output array, element-wise comparison of `x1` and `x2`.\n", " Typically of type bool, unless ``dtype=object`` is passed.\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " \n", " See Also\n", " --------\n", " greater_equal, less, less_equal, equal, not_equal\n", " \n", " Examples\n", " --------\n", " >>> np.greater([4,2],[2,2])\n", " array([ True, False])\n", " \n", " The ``>`` operator can be used as a shorthand for ``np.greater`` on\n", " ndarrays.\n", " \n", " >>> a = np.array([4, 2])\n", " >>> b = np.array([2, 2])\n", " >>> a > b\n", " array([ True, False])\n", " \n", " greater_equal = <ufunc 'greater_equal'>\n", " greater_equal(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Return the truth value of (x1 >= x2) element-wise.\n", " \n", " Parameters\n", " ----------\n", " x1, x2 : array_like\n", " Input arrays.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " out : bool or ndarray of bool\n", " Output array, element-wise comparison of `x1` and `x2`.\n", " Typically of type bool, unless ``dtype=object`` is passed.\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " See Also\n", " --------\n", " greater, less, less_equal, equal, not_equal\n", " \n", " Examples\n", " --------\n", " >>> np.greater_equal([4, 2, 1], [2, 2, 2])\n", " array([ True, True, False])\n", " \n", " The ``>=`` operator can be used as a shorthand for ``np.greater_equal``\n", " on ndarrays.\n", " \n", " >>> a = np.array([4, 2, 1])\n", " >>> b = np.array([2, 2, 2])\n", " >>> a >= b\n", " array([ True, True, False])\n", " \n", " heaviside = <ufunc 'heaviside'>\n", " heaviside(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Compute the Heaviside step function.\n", " \n", " The Heaviside step function is defined as::\n", " \n", " 0 if x1 < 0\n", " heaviside(x1, x2) = x2 if x1 == 0\n", " 1 if x1 > 0\n", " \n", " where `x2` is often taken to be 0.5, but 0 and 1 are also sometimes used.\n", " \n", " Parameters\n", " ----------\n", " x1 : array_like\n", " Input values.\n", " x2 : array_like\n", " The value of the function when x1 is 0.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " out : ndarray or scalar\n", " The output array, element-wise Heaviside step function of `x1`.\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " Notes\n", " -----\n", " .. versionadded:: 1.13.0\n", " \n", " References\n", " ----------\n", " .. Wikipedia, \"Heaviside step function\",\n", " https://en.wikipedia.org/wiki/Heaviside_step_function\n", " \n", " Examples\n", " --------\n", " >>> np.heaviside([-1.5, 0, 2.0], 0.5)\n", " array([ 0. , 0.5, 1. ])\n", " >>> np.heaviside([-1.5, 0, 2.0], 1)\n", " array([ 0., 1., 1.])\n", " \n", " hypot = <ufunc 'hypot'>\n", " hypot(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Given the \"legs\" of a right triangle, return its hypotenuse.\n", " \n", " Equivalent to ``sqrt(x1**2 + x2**2)``, element-wise. If `x1` or\n", " `x2` is scalar_like (i.e., unambiguously cast-able to a scalar type),\n", " it is broadcast for use with each element of the other argument.\n", " (See Examples)\n", " \n", " Parameters\n", " ----------\n", " x1, x2 : array_like\n", " Leg of the triangle(s).\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " z : ndarray\n", " The hypotenuse of the triangle(s).\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " Examples\n", " --------\n", " >>> np.hypot(3*np.ones((3, 3)), 4*np.ones((3, 3)))\n", " array([[ 5., 5., 5.],\n", " [ 5., 5., 5.],\n", " [ 5., 5., 5.]])\n", " \n", " Example showing broadcast of scalar_like argument:\n", " \n", " >>> np.hypot(3*np.ones((3, 3)), [4])\n", " array([[ 5., 5., 5.],\n", " [ 5., 5., 5.],\n", " [ 5., 5., 5.]])\n", " \n", " index_exp = <numpy.lib.index_tricks.IndexExpression object>\n", " inf = inf\n", " infty = inf\n", " invert = <ufunc 'invert'>\n", " invert(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Compute bit-wise inversion, or bit-wise NOT, element-wise.\n", " \n", " Computes the bit-wise NOT of the underlying binary representation of\n", " the integers in the input arrays. This ufunc implements the C/Python\n", " operator ``~``.\n", " \n", " For signed integer inputs, the two's complement is returned. In a\n", " two's-complement system negative numbers are represented by the two's\n", " complement of the absolute value. This is the most common method of\n", " representing signed integers on computers [1]_. A N-bit\n", " two's-complement system can represent every integer in the range\n", " :math:`-2^{N-1}` to :math:`+2^{N-1}-1`.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Only integer and boolean types are handled.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " out : ndarray or scalar\n", " Result.\n", " This is a scalar if `x` is a scalar.\n", " \n", " See Also\n", " --------\n", " bitwise_and, bitwise_or, bitwise_xor\n", " logical_not\n", " binary_repr :\n", " Return the binary representation of the input number as a string.\n", " \n", " Notes\n", " -----\n", " `bitwise_not` is an alias for `invert`:\n", " \n", " >>> np.bitwise_not is np.invert\n", " True\n", " \n", " References\n", " ----------\n", " .. [1] Wikipedia, \"Two's complement\",\n", " https://en.wikipedia.org/wiki/Two's_complement\n", " \n", " Examples\n", " --------\n", " We've seen that 13 is represented by ``00001101``.\n", " The invert or bit-wise NOT of 13 is then:\n", " \n", " >>> x = np.invert(np.array(13, dtype=np.uint8))\n", " >>> x\n", " 242\n", " >>> np.binary_repr(x, width=8)\n", " '11110010'\n", " \n", " The result depends on the bit-width:\n", " \n", " >>> x = np.invert(np.array(13, dtype=np.uint16))\n", " >>> x\n", " 65522\n", " >>> np.binary_repr(x, width=16)\n", " '1111111111110010'\n", " \n", " When using signed integer types the result is the two's complement of\n", " the result for the unsigned type:\n", " \n", " >>> np.invert(np.array([13], dtype=np.int8))\n", " array([-14], dtype=int8)\n", " >>> np.binary_repr(-14, width=8)\n", " '11110010'\n", " \n", " Booleans are accepted as well:\n", " \n", " >>> np.invert(np.array([True, False]))\n", " array([False, True])\n", " \n", " The ``~`` operator can be used as a shorthand for ``np.invert`` on\n", " ndarrays.\n", " \n", " >>> x1 = np.array([True, False])\n", " >>> ~x1\n", " array([False, True])\n", " \n", " isfinite = <ufunc 'isfinite'>\n", " isfinite(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Test element-wise for finiteness (not infinity and not Not a Number).\n", " \n", " The result is returned as a boolean array.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Input values.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray, bool\n", " True where ``x`` is not positive infinity, negative infinity,\n", " or NaN; false otherwise.\n", " This is a scalar if `x` is a scalar.\n", " \n", " See Also\n", " --------\n", " isinf, isneginf, isposinf, isnan\n", " \n", " Notes\n", " -----\n", " Not a Number, positive infinity and negative infinity are considered\n", " to be non-finite.\n", " \n", " NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic\n", " (IEEE 754). This means that Not a Number is not equivalent to infinity.\n", " Also that positive infinity is not equivalent to negative infinity. But\n", " infinity is equivalent to positive infinity. Errors result if the\n", " second argument is also supplied when `x` is a scalar input, or if\n", " first and second arguments have different shapes.\n", " \n", " Examples\n", " --------\n", " >>> np.isfinite(1)\n", " True\n", " >>> np.isfinite(0)\n", " True\n", " >>> np.isfinite(np.nan)\n", " False\n", " >>> np.isfinite(np.inf)\n", " False\n", " >>> np.isfinite(np.NINF)\n", " False\n", " >>> np.isfinite([np.log(-1.),1.,np.log(0)])\n", " array([False, True, False])\n", " \n", " >>> x = np.array([-np.inf, 0., np.inf])\n", " >>> y = np.array([2, 2, 2])\n", " >>> np.isfinite(x, y)\n", " array([0, 1, 0])\n", " >>> y\n", " array([0, 1, 0])\n", " \n", " isinf = <ufunc 'isinf'>\n", " isinf(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Test element-wise for positive or negative infinity.\n", " \n", " Returns a boolean array of the same shape as `x`, True where ``x ==\n", " +/-inf``, otherwise False.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Input values\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : bool (scalar) or boolean ndarray\n", " True where ``x`` is positive or negative infinity, false otherwise.\n", " This is a scalar if `x` is a scalar.\n", " \n", " See Also\n", " --------\n", " isneginf, isposinf, isnan, isfinite\n", " \n", " Notes\n", " -----\n", " NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic\n", " (IEEE 754).\n", " \n", " Errors result if the second argument is supplied when the first\n", " argument is a scalar, or if the first and second arguments have\n", " different shapes.\n", " \n", " Examples\n", " --------\n", " >>> np.isinf(np.inf)\n", " True\n", " >>> np.isinf(np.nan)\n", " False\n", " >>> np.isinf(np.NINF)\n", " True\n", " >>> np.isinf([np.inf, -np.inf, 1.0, np.nan])\n", " array([ True, True, False, False])\n", " \n", " >>> x = np.array([-np.inf, 0., np.inf])\n", " >>> y = np.array([2, 2, 2])\n", " >>> np.isinf(x, y)\n", " array([1, 0, 1])\n", " >>> y\n", " array([1, 0, 1])\n", " \n", " isnan = <ufunc 'isnan'>\n", " isnan(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Test element-wise for NaN and return result as a boolean array.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Input array.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray or bool\n", " True where ``x`` is NaN, false otherwise.\n", " This is a scalar if `x` is a scalar.\n", " \n", " See Also\n", " --------\n", " isinf, isneginf, isposinf, isfinite, isnat\n", " \n", " Notes\n", " -----\n", " NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic\n", " (IEEE 754). This means that Not a Number is not equivalent to infinity.\n", " \n", " Examples\n", " --------\n", " >>> np.isnan(np.nan)\n", " True\n", " >>> np.isnan(np.inf)\n", " False\n", " >>> np.isnan([np.log(-1.),1.,np.log(0)])\n", " array([ True, False, False])\n", " \n", " isnat = <ufunc 'isnat'>\n", " isnat(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Test element-wise for NaT (not a time) and return result as a boolean array.\n", " \n", " .. versionadded:: 1.13.0\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Input array with datetime or timedelta data type.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray or bool\n", " True where ``x`` is NaT, false otherwise.\n", " This is a scalar if `x` is a scalar.\n", " \n", " See Also\n", " --------\n", " isnan, isinf, isneginf, isposinf, isfinite\n", " \n", " Examples\n", " --------\n", " >>> np.isnat(np.datetime64(\"NaT\"))\n", " True\n", " >>> np.isnat(np.datetime64(\"2016-01-01\"))\n", " False\n", " >>> np.isnat(np.array([\"NaT\", \"2016-01-01\"], dtype=\"datetime64[ns]\"))\n", " array([ True, False])\n", " \n", " lcm = <ufunc 'lcm'>\n", " lcm(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Returns the lowest common multiple of ``|x1|`` and ``|x2|``\n", " \n", " Parameters\n", " ----------\n", " x1, x2 : array_like, int\n", " Arrays of values.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " \n", " Returns\n", " -------\n", " y : ndarray or scalar\n", " The lowest common multiple of the absolute value of the inputs\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " See Also\n", " --------\n", " gcd : The greatest common divisor\n", " \n", " Examples\n", " --------\n", " >>> np.lcm(12, 20)\n", " 60\n", " >>> np.lcm.reduce([3, 12, 20])\n", " 60\n", " >>> np.lcm.reduce([40, 12, 20])\n", " 120\n", " >>> np.lcm(np.arange(6), 20)\n", " array([ 0, 20, 20, 60, 20, 20])\n", " \n", " ldexp = <ufunc 'ldexp'>\n", " ldexp(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Returns x1 * 2**x2, element-wise.\n", " \n", " The mantissas `x1` and twos exponents `x2` are used to construct\n", " floating point numbers ``x1 * 2**x2``.\n", " \n", " Parameters\n", " ----------\n", " x1 : array_like\n", " Array of multipliers.\n", " x2 : array_like, int\n", " Array of twos exponents.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray or scalar\n", " The result of ``x1 * 2**x2``.\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " See Also\n", " --------\n", " frexp : Return (y1, y2) from ``x = y1 * 2**y2``, inverse to `ldexp`.\n", " \n", " Notes\n", " -----\n", " Complex dtypes are not supported, they will raise a TypeError.\n", " \n", " `ldexp` is useful as the inverse of `frexp`, if used by itself it is\n", " more clear to simply use the expression ``x1 * 2**x2``.\n", " \n", " Examples\n", " --------\n", " >>> np.ldexp(5, np.arange(4))\n", " array([ 5., 10., 20., 40.], dtype=float16)\n", " \n", " >>> x = np.arange(6)\n", " >>> np.ldexp(*np.frexp(x))\n", " array([ 0., 1., 2., 3., 4., 5.])\n", " \n", " left_shift = <ufunc 'left_shift'>\n", " left_shift(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Shift the bits of an integer to the left.\n", " \n", " Bits are shifted to the left by appending `x2` 0s at the right of `x1`.\n", " Since the internal representation of numbers is in binary format, this\n", " operation is equivalent to multiplying `x1` by ``2**x2``.\n", " \n", " Parameters\n", " ----------\n", " x1 : array_like of integer type\n", " Input values.\n", " x2 : array_like of integer type\n", " Number of zeros to append to `x1`. Has to be non-negative.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " out : array of integer type\n", " Return `x1` with bits shifted `x2` times to the left.\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " See Also\n", " --------\n", " right_shift : Shift the bits of an integer to the right.\n", " binary_repr : Return the binary representation of the input number\n", " as a string.\n", " \n", " Examples\n", " --------\n", " >>> np.binary_repr(5)\n", " '101'\n", " >>> np.left_shift(5, 2)\n", " 20\n", " >>> np.binary_repr(20)\n", " '10100'\n", " \n", " >>> np.left_shift(5, [1,2,3])\n", " array([10, 20, 40])\n", " \n", " Note that the dtype of the second argument may change the dtype of the\n", " result and can lead to unexpected results in some cases (see\n", " :ref:`Casting Rules <ufuncs.casting>`):\n", " \n", " >>> a = np.left_shift(np.uint8(255), 1) # Expect 254\n", " >>> print(a, type(a)) # Unexpected result due to upcasting\n", " 510 <class 'numpy.int64'>\n", " >>> b = np.left_shift(np.uint8(255), np.uint8(1))\n", " >>> print(b, type(b))\n", " 254 <class 'numpy.uint8'>\n", " \n", " The ``<<`` operator can be used as a shorthand for ``np.left_shift`` on\n", " ndarrays.\n", " \n", " >>> x1 = 5\n", " >>> x2 = np.array([1, 2, 3])\n", " >>> x1 << x2\n", " array([10, 20, 40])\n", " \n", " less = <ufunc 'less'>\n", " less(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Return the truth value of (x1 < x2) element-wise.\n", " \n", " Parameters\n", " ----------\n", " x1, x2 : array_like\n", " Input arrays.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " out : ndarray or scalar\n", " Output array, element-wise comparison of `x1` and `x2`.\n", " Typically of type bool, unless ``dtype=object`` is passed.\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " See Also\n", " --------\n", " greater, less_equal, greater_equal, equal, not_equal\n", " \n", " Examples\n", " --------\n", " >>> np.less([1, 2], [2, 2])\n", " array([ True, False])\n", " \n", " The ``<`` operator can be used as a shorthand for ``np.less`` on ndarrays.\n", " \n", " >>> a = np.array([1, 2])\n", " >>> b = np.array([2, 2])\n", " >>> a < b\n", " array([ True, False])\n", " \n", " less_equal = <ufunc 'less_equal'>\n", " less_equal(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Return the truth value of (x1 <= x2) element-wise.\n", " \n", " Parameters\n", " ----------\n", " x1, x2 : array_like\n", " Input arrays.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " out : ndarray or scalar\n", " Output array, element-wise comparison of `x1` and `x2`.\n", " Typically of type bool, unless ``dtype=object`` is passed.\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " See Also\n", " --------\n", " greater, less, greater_equal, equal, not_equal\n", " \n", " Examples\n", " --------\n", " >>> np.less_equal([4, 2, 1], [2, 2, 2])\n", " array([False, True, True])\n", " \n", " The ``<=`` operator can be used as a shorthand for ``np.less_equal`` on\n", " ndarrays.\n", " \n", " >>> a = np.array([4, 2, 1])\n", " >>> b = np.array([2, 2, 2])\n", " >>> a <= b\n", " array([False, True, True])\n", " \n", " little_endian = True\n", " log = <ufunc 'log'>\n", " log(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Natural logarithm, element-wise.\n", " \n", " The natural logarithm `log` is the inverse of the exponential function,\n", " so that `log(exp(x)) = x`. The natural logarithm is logarithm in base\n", " `e`.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Input value.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray\n", " The natural logarithm of `x`, element-wise.\n", " This is a scalar if `x` is a scalar.\n", " \n", " See Also\n", " --------\n", " log10, log2, log1p, emath.log\n", " \n", " Notes\n", " -----\n", " Logarithm is a multivalued function: for each `x` there is an infinite\n", " number of `z` such that `exp(z) = x`. The convention is to return the\n", " `z` whose imaginary part lies in `(-pi, pi]`.\n", " \n", " For real-valued input data types, `log` always returns real output. For\n", " each value that cannot be expressed as a real number or infinity, it\n", " yields ``nan`` and sets the `invalid` floating point error flag.\n", " \n", " For complex-valued input, `log` is a complex analytical function that\n", " has a branch cut `[-inf, 0]` and is continuous from above on it. `log`\n", " handles the floating-point negative zero as an infinitesimal negative\n", " number, conforming to the C99 standard.\n", " \n", " In the cases where the input has a negative real part and a very small\n", " negative complex part (approaching 0), the result is so close to `-pi`\n", " that it evaluates to exactly `-pi`.\n", " \n", " References\n", " ----------\n", " .. [1] M. Abramowitz and I.A. Stegun, \"Handbook of Mathematical Functions\",\n", " 10th printing, 1964, pp. 67.\n", " https://personal.math.ubc.ca/~cbm/aands/page_67.htm\n", " .. [2] Wikipedia, \"Logarithm\". https://en.wikipedia.org/wiki/Logarithm\n", " \n", " Examples\n", " --------\n", " >>> np.log([1, np.e, np.e**2, 0])\n", " array([ 0., 1., 2., -Inf])\n", " \n", " log10 = <ufunc 'log10'>\n", " log10(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Return the base 10 logarithm of the input array, element-wise.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Input values.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray\n", " The logarithm to the base 10 of `x`, element-wise. NaNs are\n", " returned where x is negative.\n", " This is a scalar if `x` is a scalar.\n", " \n", " See Also\n", " --------\n", " emath.log10\n", " \n", " Notes\n", " -----\n", " Logarithm is a multivalued function: for each `x` there is an infinite\n", " number of `z` such that `10**z = x`. The convention is to return the\n", " `z` whose imaginary part lies in `(-pi, pi]`.\n", " \n", " For real-valued input data types, `log10` always returns real output.\n", " For each value that cannot be expressed as a real number or infinity,\n", " it yields ``nan`` and sets the `invalid` floating point error flag.\n", " \n", " For complex-valued input, `log10` is a complex analytical function that\n", " has a branch cut `[-inf, 0]` and is continuous from above on it.\n", " `log10` handles the floating-point negative zero as an infinitesimal\n", " negative number, conforming to the C99 standard.\n", " \n", " In the cases where the input has a negative real part and a very small\n", " negative complex part (approaching 0), the result is so close to `-pi`\n", " that it evaluates to exactly `-pi`.\n", " \n", " References\n", " ----------\n", " .. [1] M. Abramowitz and I.A. Stegun, \"Handbook of Mathematical Functions\",\n", " 10th printing, 1964, pp. 67.\n", " https://personal.math.ubc.ca/~cbm/aands/page_67.htm\n", " .. [2] Wikipedia, \"Logarithm\". https://en.wikipedia.org/wiki/Logarithm\n", " \n", " Examples\n", " --------\n", " >>> np.log10([1e-15, -3.])\n", " array([-15., nan])\n", " \n", " log1p = <ufunc 'log1p'>\n", " log1p(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Return the natural logarithm of one plus the input array, element-wise.\n", " \n", " Calculates ``log(1 + x)``.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Input values.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray\n", " Natural logarithm of `1 + x`, element-wise.\n", " This is a scalar if `x` is a scalar.\n", " \n", " See Also\n", " --------\n", " expm1 : ``exp(x) - 1``, the inverse of `log1p`.\n", " \n", " Notes\n", " -----\n", " For real-valued input, `log1p` is accurate also for `x` so small\n", " that `1 + x == 1` in floating-point accuracy.\n", " \n", " Logarithm is a multivalued function: for each `x` there is an infinite\n", " number of `z` such that `exp(z) = 1 + x`. The convention is to return\n", " the `z` whose imaginary part lies in `[-pi, pi]`.\n", " \n", " For real-valued input data types, `log1p` always returns real output.\n", " For each value that cannot be expressed as a real number or infinity,\n", " it yields ``nan`` and sets the `invalid` floating point error flag.\n", " \n", " For complex-valued input, `log1p` is a complex analytical function that\n", " has a branch cut `[-inf, -1]` and is continuous from above on it.\n", " `log1p` handles the floating-point negative zero as an infinitesimal\n", " negative number, conforming to the C99 standard.\n", " \n", " References\n", " ----------\n", " .. [1] M. Abramowitz and I.A. Stegun, \"Handbook of Mathematical Functions\",\n", " 10th printing, 1964, pp. 67.\n", " https://personal.math.ubc.ca/~cbm/aands/page_67.htm\n", " .. [2] Wikipedia, \"Logarithm\". https://en.wikipedia.org/wiki/Logarithm\n", " \n", " Examples\n", " --------\n", " >>> np.log1p(1e-99)\n", " 1e-99\n", " >>> np.log(1 + 1e-99)\n", " 0.0\n", " \n", " log2 = <ufunc 'log2'>\n", " log2(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Base-2 logarithm of `x`.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Input values.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray\n", " Base-2 logarithm of `x`.\n", " This is a scalar if `x` is a scalar.\n", " \n", " See Also\n", " --------\n", " log, log10, log1p, emath.log2\n", " \n", " Notes\n", " -----\n", " .. versionadded:: 1.3.0\n", " \n", " Logarithm is a multivalued function: for each `x` there is an infinite\n", " number of `z` such that `2**z = x`. The convention is to return the `z`\n", " whose imaginary part lies in `(-pi, pi]`.\n", " \n", " For real-valued input data types, `log2` always returns real output.\n", " For each value that cannot be expressed as a real number or infinity,\n", " it yields ``nan`` and sets the `invalid` floating point error flag.\n", " \n", " For complex-valued input, `log2` is a complex analytical function that\n", " has a branch cut `[-inf, 0]` and is continuous from above on it. `log2`\n", " handles the floating-point negative zero as an infinitesimal negative\n", " number, conforming to the C99 standard.\n", " \n", " In the cases where the input has a negative real part and a very small\n", " negative complex part (approaching 0), the result is so close to `-pi`\n", " that it evaluates to exactly `-pi`.\n", " \n", " Examples\n", " --------\n", " >>> x = np.array([0, 1, 2, 2**4])\n", " >>> np.log2(x)\n", " array([-Inf, 0., 1., 4.])\n", " \n", " >>> xi = np.array([0+1.j, 1, 2+0.j, 4.j])\n", " >>> np.log2(xi)\n", " array([ 0.+2.26618007j, 0.+0.j , 1.+0.j , 2.+2.26618007j])\n", " \n", " logaddexp = <ufunc 'logaddexp'>\n", " logaddexp(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Logarithm of the sum of exponentiations of the inputs.\n", " \n", " Calculates ``log(exp(x1) + exp(x2))``. This function is useful in\n", " statistics where the calculated probabilities of events may be so small\n", " as to exceed the range of normal floating point numbers. In such cases\n", " the logarithm of the calculated probability is stored. This function\n", " allows adding probabilities stored in such a fashion.\n", " \n", " Parameters\n", " ----------\n", " x1, x2 : array_like\n", " Input values.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " result : ndarray\n", " Logarithm of ``exp(x1) + exp(x2)``.\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " See Also\n", " --------\n", " logaddexp2: Logarithm of the sum of exponentiations of inputs in base 2.\n", " \n", " Notes\n", " -----\n", " .. versionadded:: 1.3.0\n", " \n", " Examples\n", " --------\n", " >>> prob1 = np.log(1e-50)\n", " >>> prob2 = np.log(2.5e-50)\n", " >>> prob12 = np.logaddexp(prob1, prob2)\n", " >>> prob12\n", " -113.87649168120691\n", " >>> np.exp(prob12)\n", " 3.5000000000000057e-50\n", " \n", " logaddexp2 = <ufunc 'logaddexp2'>\n", " logaddexp2(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Logarithm of the sum of exponentiations of the inputs in base-2.\n", " \n", " Calculates ``log2(2**x1 + 2**x2)``. This function is useful in machine\n", " learning when the calculated probabilities of events may be so small as\n", " to exceed the range of normal floating point numbers. In such cases\n", " the base-2 logarithm of the calculated probability can be used instead.\n", " This function allows adding probabilities stored in such a fashion.\n", " \n", " Parameters\n", " ----------\n", " x1, x2 : array_like\n", " Input values.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " result : ndarray\n", " Base-2 logarithm of ``2**x1 + 2**x2``.\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " See Also\n", " --------\n", " logaddexp: Logarithm of the sum of exponentiations of the inputs.\n", " \n", " Notes\n", " -----\n", " .. versionadded:: 1.3.0\n", " \n", " Examples\n", " --------\n", " >>> prob1 = np.log2(1e-50)\n", " >>> prob2 = np.log2(2.5e-50)\n", " >>> prob12 = np.logaddexp2(prob1, prob2)\n", " >>> prob1, prob2, prob12\n", " (-166.09640474436813, -164.77447664948076, -164.28904982231052)\n", " >>> 2**prob12\n", " 3.4999999999999914e-50\n", " \n", " logical_and = <ufunc 'logical_and'>\n", " logical_and(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Compute the truth value of x1 AND x2 element-wise.\n", " \n", " Parameters\n", " ----------\n", " x1, x2 : array_like\n", " Input arrays.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray or bool\n", " Boolean result of the logical AND operation applied to the elements\n", " of `x1` and `x2`; the shape is determined by broadcasting.\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " See Also\n", " --------\n", " logical_or, logical_not, logical_xor\n", " bitwise_and\n", " \n", " Examples\n", " --------\n", " >>> np.logical_and(True, False)\n", " False\n", " >>> np.logical_and([True, False], [False, False])\n", " array([False, False])\n", " \n", " >>> x = np.arange(5)\n", " >>> np.logical_and(x>1, x<4)\n", " array([False, False, True, True, False])\n", " \n", " \n", " The ``&`` operator can be used as a shorthand for ``np.logical_and`` on\n", " boolean ndarrays.\n", " \n", " >>> a = np.array([True, False])\n", " >>> b = np.array([False, False])\n", " >>> a & b\n", " array([False, False])\n", " \n", " logical_not = <ufunc 'logical_not'>\n", " logical_not(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Compute the truth value of NOT x element-wise.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Logical NOT is applied to the elements of `x`.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : bool or ndarray of bool\n", " Boolean result with the same shape as `x` of the NOT operation\n", " on elements of `x`.\n", " This is a scalar if `x` is a scalar.\n", " \n", " See Also\n", " --------\n", " logical_and, logical_or, logical_xor\n", " \n", " Examples\n", " --------\n", " >>> np.logical_not(3)\n", " False\n", " >>> np.logical_not([True, False, 0, 1])\n", " array([False, True, True, False])\n", " \n", " >>> x = np.arange(5)\n", " >>> np.logical_not(x<3)\n", " array([False, False, False, True, True])\n", " \n", " logical_or = <ufunc 'logical_or'>\n", " logical_or(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Compute the truth value of x1 OR x2 element-wise.\n", " \n", " Parameters\n", " ----------\n", " x1, x2 : array_like\n", " Logical OR is applied to the elements of `x1` and `x2`.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray or bool\n", " Boolean result of the logical OR operation applied to the elements\n", " of `x1` and `x2`; the shape is determined by broadcasting.\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " See Also\n", " --------\n", " logical_and, logical_not, logical_xor\n", " bitwise_or\n", " \n", " Examples\n", " --------\n", " >>> np.logical_or(True, False)\n", " True\n", " >>> np.logical_or([True, False], [False, False])\n", " array([ True, False])\n", " \n", " >>> x = np.arange(5)\n", " >>> np.logical_or(x < 1, x > 3)\n", " array([ True, False, False, False, True])\n", " \n", " The ``|`` operator can be used as a shorthand for ``np.logical_or`` on\n", " boolean ndarrays.\n", " \n", " >>> a = np.array([True, False])\n", " >>> b = np.array([False, False])\n", " >>> a | b\n", " array([ True, False])\n", " \n", " logical_xor = <ufunc 'logical_xor'>\n", " logical_xor(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Compute the truth value of x1 XOR x2, element-wise.\n", " \n", " Parameters\n", " ----------\n", " x1, x2 : array_like\n", " Logical XOR is applied to the elements of `x1` and `x2`.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : bool or ndarray of bool\n", " Boolean result of the logical XOR operation applied to the elements\n", " of `x1` and `x2`; the shape is determined by broadcasting.\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " See Also\n", " --------\n", " logical_and, logical_or, logical_not, bitwise_xor\n", " \n", " Examples\n", " --------\n", " >>> np.logical_xor(True, False)\n", " True\n", " >>> np.logical_xor([True, True, False, False], [True, False, True, False])\n", " array([False, True, True, False])\n", " \n", " >>> x = np.arange(5)\n", " >>> np.logical_xor(x < 1, x > 3)\n", " array([ True, False, False, False, True])\n", " \n", " Simple example showing support of broadcasting\n", " \n", " >>> np.logical_xor(0, np.eye(2))\n", " array([[ True, False],\n", " [False, True]])\n", " \n", " matmul = <ufunc 'matmul'>\n", " matmul(x1, x2, /, out=None, *, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj, axes, axis])\n", " \n", " Matrix product of two arrays.\n", " \n", " Parameters\n", " ----------\n", " x1, x2 : array_like\n", " Input arrays, scalars not allowed.\n", " out : ndarray, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that matches the signature `(n,k),(k,m)->(n,m)`. If not\n", " provided or None, a freshly-allocated array is returned.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " .. versionadded:: 1.16\n", " Now handles ufunc kwargs\n", " \n", " Returns\n", " -------\n", " y : ndarray\n", " The matrix product of the inputs.\n", " This is a scalar only when both x1, x2 are 1-d vectors.\n", " \n", " Raises\n", " ------\n", " ValueError\n", " If the last dimension of `x1` is not the same size as\n", " the second-to-last dimension of `x2`.\n", " \n", " If a scalar value is passed in.\n", " \n", " See Also\n", " --------\n", " vdot : Complex-conjugating dot product.\n", " tensordot : Sum products over arbitrary axes.\n", " einsum : Einstein summation convention.\n", " dot : alternative matrix product with different broadcasting rules.\n", " \n", " Notes\n", " -----\n", " \n", " The behavior depends on the arguments in the following way.\n", " \n", " - If both arguments are 2-D they are multiplied like conventional\n", " matrices.\n", " - If either argument is N-D, N > 2, it is treated as a stack of\n", " matrices residing in the last two indexes and broadcast accordingly.\n", " - If the first argument is 1-D, it is promoted to a matrix by\n", " prepending a 1 to its dimensions. After matrix multiplication\n", " the prepended 1 is removed.\n", " - If the second argument is 1-D, it is promoted to a matrix by\n", " appending a 1 to its dimensions. After matrix multiplication\n", " the appended 1 is removed.\n", " \n", " ``matmul`` differs from ``dot`` in two important ways:\n", " \n", " - Multiplication by scalars is not allowed, use ``*`` instead.\n", " - Stacks of matrices are broadcast together as if the matrices\n", " were elements, respecting the signature ``(n,k),(k,m)->(n,m)``:\n", " \n", " >>> a = np.ones([9, 5, 7, 4])\n", " >>> c = np.ones([9, 5, 4, 3])\n", " >>> np.dot(a, c).shape\n", " (9, 5, 7, 9, 5, 3)\n", " >>> np.matmul(a, c).shape\n", " (9, 5, 7, 3)\n", " >>> # n is 7, k is 4, m is 3\n", " \n", " The matmul function implements the semantics of the ``@`` operator\n", " introduced in Python 3.5 following :pep:`465`.\n", " \n", " It uses an optimized BLAS library when possible (see `numpy.linalg`).\n", " \n", " Examples\n", " --------\n", " For 2-D arrays it is the matrix product:\n", " \n", " >>> a = np.array([[1, 0],\n", " ... [0, 1]])\n", " >>> b = np.array([[4, 1],\n", " ... [2, 2]])\n", " >>> np.matmul(a, b)\n", " array([[4, 1],\n", " [2, 2]])\n", " \n", " For 2-D mixed with 1-D, the result is the usual.\n", " \n", " >>> a = np.array([[1, 0],\n", " ... [0, 1]])\n", " >>> b = np.array([1, 2])\n", " >>> np.matmul(a, b)\n", " array([1, 2])\n", " >>> np.matmul(b, a)\n", " array([1, 2])\n", " \n", " \n", " Broadcasting is conventional for stacks of arrays\n", " \n", " >>> a = np.arange(2 * 2 * 4).reshape((2, 2, 4))\n", " >>> b = np.arange(2 * 2 * 4).reshape((2, 4, 2))\n", " >>> np.matmul(a,b).shape\n", " (2, 2, 2)\n", " >>> np.matmul(a, b)[0, 1, 1]\n", " 98\n", " >>> sum(a[0, 1, :] * b[0 , :, 1])\n", " 98\n", " \n", " Vector, vector returns the scalar inner product, but neither argument\n", " is complex-conjugated:\n", " \n", " >>> np.matmul([2j, 3j], [2j, 3j])\n", " (-13+0j)\n", " \n", " Scalar multiplication raises an error.\n", " \n", " >>> np.matmul([1,2], 3)\n", " Traceback (most recent call last):\n", " ...\n", " ValueError: matmul: Input operand 1 does not have enough dimensions ...\n", " \n", " The ``@`` operator can be used as a shorthand for ``np.matmul`` on\n", " ndarrays.\n", " \n", " >>> x1 = np.array([2j, 3j])\n", " >>> x2 = np.array([2j, 3j])\n", " >>> x1 @ x2\n", " (-13+0j)\n", " \n", " .. versionadded:: 1.10.0\n", " \n", " maximum = <ufunc 'maximum'>\n", " maximum(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Element-wise maximum of array elements.\n", " \n", " Compare two arrays and returns a new array containing the element-wise\n", " maxima. If one of the elements being compared is a NaN, then that\n", " element is returned. If both elements are NaNs then the first is\n", " returned. The latter distinction is important for complex NaNs, which\n", " are defined as at least one of the real or imaginary parts being a NaN.\n", " The net effect is that NaNs are propagated.\n", " \n", " Parameters\n", " ----------\n", " x1, x2 : array_like\n", " The arrays holding the elements to be compared.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray or scalar\n", " The maximum of `x1` and `x2`, element-wise.\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " See Also\n", " --------\n", " minimum :\n", " Element-wise minimum of two arrays, propagates NaNs.\n", " fmax :\n", " Element-wise maximum of two arrays, ignores NaNs.\n", " amax :\n", " The maximum value of an array along a given axis, propagates NaNs.\n", " nanmax :\n", " The maximum value of an array along a given axis, ignores NaNs.\n", " \n", " fmin, amin, nanmin\n", " \n", " Notes\n", " -----\n", " The maximum is equivalent to ``np.where(x1 >= x2, x1, x2)`` when\n", " neither x1 nor x2 are nans, but it is faster and does proper\n", " broadcasting.\n", " \n", " Examples\n", " --------\n", " >>> np.maximum([2, 3, 4], [1, 5, 2])\n", " array([2, 5, 4])\n", " \n", " >>> np.maximum(np.eye(2), [0.5, 2]) # broadcasting\n", " array([[ 1. , 2. ],\n", " [ 0.5, 2. ]])\n", " \n", " >>> np.maximum([np.nan, 0, np.nan], [0, np.nan, np.nan])\n", " array([nan, nan, nan])\n", " >>> np.maximum(np.Inf, 1)\n", " inf\n", " \n", " mgrid = <numpy.lib.index_tricks.MGridClass object>\n", " minimum = <ufunc 'minimum'>\n", " minimum(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Element-wise minimum of array elements.\n", " \n", " Compare two arrays and returns a new array containing the element-wise\n", " minima. If one of the elements being compared is a NaN, then that\n", " element is returned. If both elements are NaNs then the first is\n", " returned. The latter distinction is important for complex NaNs, which\n", " are defined as at least one of the real or imaginary parts being a NaN.\n", " The net effect is that NaNs are propagated.\n", " \n", " Parameters\n", " ----------\n", " x1, x2 : array_like\n", " The arrays holding the elements to be compared.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray or scalar\n", " The minimum of `x1` and `x2`, element-wise.\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " See Also\n", " --------\n", " maximum :\n", " Element-wise maximum of two arrays, propagates NaNs.\n", " fmin :\n", " Element-wise minimum of two arrays, ignores NaNs.\n", " amin :\n", " The minimum value of an array along a given axis, propagates NaNs.\n", " nanmin :\n", " The minimum value of an array along a given axis, ignores NaNs.\n", " \n", " fmax, amax, nanmax\n", " \n", " Notes\n", " -----\n", " The minimum is equivalent to ``np.where(x1 <= x2, x1, x2)`` when\n", " neither x1 nor x2 are NaNs, but it is faster and does proper\n", " broadcasting.\n", " \n", " Examples\n", " --------\n", " >>> np.minimum([2, 3, 4], [1, 5, 2])\n", " array([1, 3, 2])\n", " \n", " >>> np.minimum(np.eye(2), [0.5, 2]) # broadcasting\n", " array([[ 0.5, 0. ],\n", " [ 0. , 1. ]])\n", " \n", " >>> np.minimum([np.nan, 0, np.nan],[0, np.nan, np.nan])\n", " array([nan, nan, nan])\n", " >>> np.minimum(-np.Inf, 1)\n", " -inf\n", " \n", " mod = <ufunc 'remainder'>\n", " remainder(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Returns the element-wise remainder of division.\n", " \n", " Computes the remainder complementary to the `floor_divide` function. It is\n", " equivalent to the Python modulus operator``x1 % x2`` and has the same sign\n", " as the divisor `x2`. The MATLAB function equivalent to ``np.remainder``\n", " is ``mod``.\n", " \n", " .. warning::\n", " \n", " This should not be confused with:\n", " \n", " * Python 3.7's `math.remainder` and C's ``remainder``, which\n", " computes the IEEE remainder, which are the complement to\n", " ``round(x1 / x2)``.\n", " * The MATLAB ``rem`` function and or the C ``%`` operator which is the\n", " complement to ``int(x1 / x2)``.\n", " \n", " Parameters\n", " ----------\n", " x1 : array_like\n", " Dividend array.\n", " x2 : array_like\n", " Divisor array.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray\n", " The element-wise remainder of the quotient ``floor_divide(x1, x2)``.\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " See Also\n", " --------\n", " floor_divide : Equivalent of Python ``//`` operator.\n", " divmod : Simultaneous floor division and remainder.\n", " fmod : Equivalent of the MATLAB ``rem`` function.\n", " divide, floor\n", " \n", " Notes\n", " -----\n", " Returns 0 when `x2` is 0 and both `x1` and `x2` are (arrays of)\n", " integers.\n", " ``mod`` is an alias of ``remainder``.\n", " \n", " Examples\n", " --------\n", " >>> np.remainder([4, 7], [2, 3])\n", " array([0, 1])\n", " >>> np.remainder(np.arange(7), 5)\n", " array([0, 1, 2, 3, 4, 0, 1])\n", " \n", " The ``%`` operator can be used as a shorthand for ``np.remainder`` on\n", " ndarrays.\n", " \n", " >>> x1 = np.arange(7)\n", " >>> x1 % 5\n", " array([0, 1, 2, 3, 4, 0, 1])\n", " \n", " modf = <ufunc 'modf'>\n", " modf(x[, out1, out2], / [, out=(None, None)], *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Return the fractional and integral parts of an array, element-wise.\n", " \n", " The fractional and integral parts are negative if the given number is\n", " negative.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Input array.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y1 : ndarray\n", " Fractional part of `x`.\n", " This is a scalar if `x` is a scalar.\n", " y2 : ndarray\n", " Integral part of `x`.\n", " This is a scalar if `x` is a scalar.\n", " \n", " Notes\n", " -----\n", " For integer input the return values are floats.\n", " \n", " See Also\n", " --------\n", " divmod : ``divmod(x, 1)`` is equivalent to ``modf`` with the return values\n", " switched, except it always has a positive remainder.\n", " \n", " Examples\n", " --------\n", " >>> np.modf([0, 3.5])\n", " (array([ 0. , 0.5]), array([ 0., 3.]))\n", " >>> np.modf(-0.5)\n", " (-0.5, -0)\n", " \n", " multiply = <ufunc 'multiply'>\n", " multiply(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Multiply arguments element-wise.\n", " \n", " Parameters\n", " ----------\n", " x1, x2 : array_like\n", " Input arrays to be multiplied.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray\n", " The product of `x1` and `x2`, element-wise.\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " Notes\n", " -----\n", " Equivalent to `x1` * `x2` in terms of array broadcasting.\n", " \n", " Examples\n", " --------\n", " >>> np.multiply(2.0, 4.0)\n", " 8.0\n", " \n", " >>> x1 = np.arange(9.0).reshape((3, 3))\n", " >>> x2 = np.arange(3.0)\n", " >>> np.multiply(x1, x2)\n", " array([[ 0., 1., 4.],\n", " [ 0., 4., 10.],\n", " [ 0., 7., 16.]])\n", " \n", " The ``*`` operator can be used as a shorthand for ``np.multiply`` on\n", " ndarrays.\n", " \n", " >>> x1 = np.arange(9.0).reshape((3, 3))\n", " >>> x2 = np.arange(3.0)\n", " >>> x1 * x2\n", " array([[ 0., 1., 4.],\n", " [ 0., 4., 10.],\n", " [ 0., 7., 16.]])\n", " \n", " nan = nan\n", " nbytes = {<class 'numpy.bool_'>: 1, <class 'numpy.int8'>:....datetime6...\n", " negative = <ufunc 'negative'>\n", " negative(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Numerical negative, element-wise.\n", " \n", " Parameters\n", " ----------\n", " x : array_like or scalar\n", " Input array.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray or scalar\n", " Returned array or scalar: `y = -x`.\n", " This is a scalar if `x` is a scalar.\n", " \n", " Examples\n", " --------\n", " >>> np.negative([1.,-1.])\n", " array([-1., 1.])\n", " \n", " The unary ``-`` operator can be used as a shorthand for ``np.negative`` on\n", " ndarrays.\n", " \n", " >>> x1 = np.array(([1., -1.]))\n", " >>> -x1\n", " array([-1., 1.])\n", " \n", " newaxis = None\n", " nextafter = <ufunc 'nextafter'>\n", " nextafter(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Return the next floating-point value after x1 towards x2, element-wise.\n", " \n", " Parameters\n", " ----------\n", " x1 : array_like\n", " Values to find the next representable value of.\n", " x2 : array_like\n", " The direction where to look for the next representable value of `x1`.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " out : ndarray or scalar\n", " The next representable values of `x1` in the direction of `x2`.\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " Examples\n", " --------\n", " >>> eps = np.finfo(np.float64).eps\n", " >>> np.nextafter(1, 2) == eps + 1\n", " True\n", " >>> np.nextafter([1, 2], [2, 1]) == [eps + 1, 2 - eps]\n", " array([ True, True])\n", " \n", " not_equal = <ufunc 'not_equal'>\n", " not_equal(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Return (x1 != x2) element-wise.\n", " \n", " Parameters\n", " ----------\n", " x1, x2 : array_like\n", " Input arrays.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " out : ndarray or scalar\n", " Output array, element-wise comparison of `x1` and `x2`.\n", " Typically of type bool, unless ``dtype=object`` is passed.\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " See Also\n", " --------\n", " equal, greater, greater_equal, less, less_equal\n", " \n", " Examples\n", " --------\n", " >>> np.not_equal([1.,2.], [1., 3.])\n", " array([False, True])\n", " >>> np.not_equal([1, 2], [[1, 3],[1, 4]])\n", " array([[False, True],\n", " [False, True]])\n", " \n", " The ``!=`` operator can be used as a shorthand for ``np.not_equal`` on\n", " ndarrays.\n", " \n", " >>> a = np.array([1., 2.])\n", " >>> b = np.array([1., 3.])\n", " >>> a != b\n", " array([False, True])\n", " \n", " ogrid = <numpy.lib.index_tricks.OGridClass object>\n", " pi = 3.141592653589793\n", " positive = <ufunc 'positive'>\n", " positive(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Numerical positive, element-wise.\n", " \n", " .. versionadded:: 1.13.0\n", " \n", " Parameters\n", " ----------\n", " x : array_like or scalar\n", " Input array.\n", " \n", " Returns\n", " -------\n", " y : ndarray or scalar\n", " Returned array or scalar: `y = +x`.\n", " This is a scalar if `x` is a scalar.\n", " \n", " Notes\n", " -----\n", " Equivalent to `x.copy()`, but only defined for types that support\n", " arithmetic.\n", " \n", " Examples\n", " --------\n", " \n", " >>> x1 = np.array(([1., -1.]))\n", " >>> np.positive(x1)\n", " array([ 1., -1.])\n", " \n", " The unary ``+`` operator can be used as a shorthand for ``np.positive`` on\n", " ndarrays.\n", " \n", " >>> x1 = np.array(([1., -1.]))\n", " >>> +x1\n", " array([ 1., -1.])\n", " \n", " power = <ufunc 'power'>\n", " power(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " First array elements raised to powers from second array, element-wise.\n", " \n", " Raise each base in `x1` to the positionally-corresponding power in\n", " `x2`. `x1` and `x2` must be broadcastable to the same shape.\n", " \n", " An integer type raised to a negative integer power will raise a\n", " ``ValueError``.\n", " \n", " Negative values raised to a non-integral value will return ``nan``.\n", " To get complex results, cast the input to complex, or specify the\n", " ``dtype`` to be ``complex`` (see the example below).\n", " \n", " Parameters\n", " ----------\n", " x1 : array_like\n", " The bases.\n", " x2 : array_like\n", " The exponents.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray\n", " The bases in `x1` raised to the exponents in `x2`.\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " See Also\n", " --------\n", " float_power : power function that promotes integers to float\n", " \n", " Examples\n", " --------\n", " Cube each element in an array.\n", " \n", " >>> x1 = np.arange(6)\n", " >>> x1\n", " [0, 1, 2, 3, 4, 5]\n", " >>> np.power(x1, 3)\n", " array([ 0, 1, 8, 27, 64, 125])\n", " \n", " Raise the bases to different exponents.\n", " \n", " >>> x2 = [1.0, 2.0, 3.0, 3.0, 2.0, 1.0]\n", " >>> np.power(x1, x2)\n", " array([ 0., 1., 8., 27., 16., 5.])\n", " \n", " The effect of broadcasting.\n", " \n", " >>> x2 = np.array([[1, 2, 3, 3, 2, 1], [1, 2, 3, 3, 2, 1]])\n", " >>> x2\n", " array([[1, 2, 3, 3, 2, 1],\n", " [1, 2, 3, 3, 2, 1]])\n", " >>> np.power(x1, x2)\n", " array([[ 0, 1, 8, 27, 16, 5],\n", " [ 0, 1, 8, 27, 16, 5]])\n", " \n", " The ``**`` operator can be used as a shorthand for ``np.power`` on\n", " ndarrays.\n", " \n", " >>> x2 = np.array([1, 2, 3, 3, 2, 1])\n", " >>> x1 = np.arange(6)\n", " >>> x1 ** x2\n", " array([ 0, 1, 8, 27, 16, 5])\n", " \n", " Negative values raised to a non-integral value will result in ``nan``\n", " (and a warning will be generated).\n", " \n", " >>> x3 = np.array([-1.0, -4.0])\n", " >>> with np.errstate(invalid='ignore'):\n", " ... p = np.power(x3, 1.5)\n", " ...\n", " >>> p\n", " array([nan, nan])\n", " \n", " To get complex results, give the argument ``dtype=complex``.\n", " \n", " >>> np.power(x3, 1.5, dtype=complex)\n", " array([-1.83697020e-16-1.j, -1.46957616e-15-8.j])\n", " \n", " r_ = <numpy.lib.index_tricks.RClass object>\n", " rad2deg = <ufunc 'rad2deg'>\n", " rad2deg(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Convert angles from radians to degrees.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Angle in radians.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray\n", " The corresponding angle in degrees.\n", " This is a scalar if `x` is a scalar.\n", " \n", " See Also\n", " --------\n", " deg2rad : Convert angles from degrees to radians.\n", " unwrap : Remove large jumps in angle by wrapping.\n", " \n", " Notes\n", " -----\n", " .. versionadded:: 1.3.0\n", " \n", " rad2deg(x) is ``180 * x / pi``.\n", " \n", " Examples\n", " --------\n", " >>> np.rad2deg(np.pi/2)\n", " 90.0\n", " \n", " radians = <ufunc 'radians'>\n", " radians(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Convert angles from degrees to radians.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Input array in degrees.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray\n", " The corresponding radian values.\n", " This is a scalar if `x` is a scalar.\n", " \n", " See Also\n", " --------\n", " deg2rad : equivalent function\n", " \n", " Examples\n", " --------\n", " Convert a degree array to radians\n", " \n", " >>> deg = np.arange(12.) * 30.\n", " >>> np.radians(deg)\n", " array([ 0. , 0.52359878, 1.04719755, 1.57079633, 2.0943951 ,\n", " 2.61799388, 3.14159265, 3.66519143, 4.1887902 , 4.71238898,\n", " 5.23598776, 5.75958653])\n", " \n", " >>> out = np.zeros((deg.shape))\n", " >>> ret = np.radians(deg, out)\n", " >>> ret is out\n", " True\n", " \n", " reciprocal = <ufunc 'reciprocal'>\n", " reciprocal(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Return the reciprocal of the argument, element-wise.\n", " \n", " Calculates ``1/x``.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Input array.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray\n", " Return array.\n", " This is a scalar if `x` is a scalar.\n", " \n", " Notes\n", " -----\n", " .. note::\n", " This function is not designed to work with integers.\n", " \n", " For integer arguments with absolute value larger than 1 the result is\n", " always zero because of the way Python handles integer division. For\n", " integer zero the result is an overflow.\n", " \n", " Examples\n", " --------\n", " >>> np.reciprocal(2.)\n", " 0.5\n", " >>> np.reciprocal([1, 2., 3.33])\n", " array([ 1. , 0.5 , 0.3003003])\n", " \n", " remainder = <ufunc 'remainder'>\n", " remainder(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Returns the element-wise remainder of division.\n", " \n", " Computes the remainder complementary to the `floor_divide` function. It is\n", " equivalent to the Python modulus operator``x1 % x2`` and has the same sign\n", " as the divisor `x2`. The MATLAB function equivalent to ``np.remainder``\n", " is ``mod``.\n", " \n", " .. warning::\n", " \n", " This should not be confused with:\n", " \n", " * Python 3.7's `math.remainder` and C's ``remainder``, which\n", " computes the IEEE remainder, which are the complement to\n", " ``round(x1 / x2)``.\n", " * The MATLAB ``rem`` function and or the C ``%`` operator which is the\n", " complement to ``int(x1 / x2)``.\n", " \n", " Parameters\n", " ----------\n", " x1 : array_like\n", " Dividend array.\n", " x2 : array_like\n", " Divisor array.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray\n", " The element-wise remainder of the quotient ``floor_divide(x1, x2)``.\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " See Also\n", " --------\n", " floor_divide : Equivalent of Python ``//`` operator.\n", " divmod : Simultaneous floor division and remainder.\n", " fmod : Equivalent of the MATLAB ``rem`` function.\n", " divide, floor\n", " \n", " Notes\n", " -----\n", " Returns 0 when `x2` is 0 and both `x1` and `x2` are (arrays of)\n", " integers.\n", " ``mod`` is an alias of ``remainder``.\n", " \n", " Examples\n", " --------\n", " >>> np.remainder([4, 7], [2, 3])\n", " array([0, 1])\n", " >>> np.remainder(np.arange(7), 5)\n", " array([0, 1, 2, 3, 4, 0, 1])\n", " \n", " The ``%`` operator can be used as a shorthand for ``np.remainder`` on\n", " ndarrays.\n", " \n", " >>> x1 = np.arange(7)\n", " >>> x1 % 5\n", " array([0, 1, 2, 3, 4, 0, 1])\n", " \n", " right_shift = <ufunc 'right_shift'>\n", " right_shift(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Shift the bits of an integer to the right.\n", " \n", " Bits are shifted to the right `x2`. Because the internal\n", " representation of numbers is in binary format, this operation is\n", " equivalent to dividing `x1` by ``2**x2``.\n", " \n", " Parameters\n", " ----------\n", " x1 : array_like, int\n", " Input values.\n", " x2 : array_like, int\n", " Number of bits to remove at the right of `x1`.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " out : ndarray, int\n", " Return `x1` with bits shifted `x2` times to the right.\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " See Also\n", " --------\n", " left_shift : Shift the bits of an integer to the left.\n", " binary_repr : Return the binary representation of the input number\n", " as a string.\n", " \n", " Examples\n", " --------\n", " >>> np.binary_repr(10)\n", " '1010'\n", " >>> np.right_shift(10, 1)\n", " 5\n", " >>> np.binary_repr(5)\n", " '101'\n", " \n", " >>> np.right_shift(10, [1,2,3])\n", " array([5, 2, 1])\n", " \n", " The ``>>`` operator can be used as a shorthand for ``np.right_shift`` on\n", " ndarrays.\n", " \n", " >>> x1 = 10\n", " >>> x2 = np.array([1,2,3])\n", " >>> x1 >> x2\n", " array([5, 2, 1])\n", " \n", " rint = <ufunc 'rint'>\n", " rint(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Round elements of the array to the nearest integer.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Input array.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " out : ndarray or scalar\n", " Output array is same shape and type as `x`.\n", " This is a scalar if `x` is a scalar.\n", " \n", " See Also\n", " --------\n", " fix, ceil, floor, trunc\n", " \n", " Notes\n", " -----\n", " For values exactly halfway between rounded decimal values, NumPy\n", " rounds to the nearest even value. Thus 1.5 and 2.5 round to 2.0,\n", " -0.5 and 0.5 round to 0.0, etc.\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([-1.7, -1.5, -0.2, 0.2, 1.5, 1.7, 2.0])\n", " >>> np.rint(a)\n", " array([-2., -2., -0., 0., 2., 2., 2.])\n", " \n", " s_ = <numpy.lib.index_tricks.IndexExpression object>\n", " sctypeDict = {'?': <class 'numpy.bool_'>, 0: <class 'numpy.bool_'>, 'b...\n", " sctypes = {'complex': [<class 'numpy.complex64'>, <class 'numpy.comple...\n", " sign = <ufunc 'sign'>\n", " sign(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Returns an element-wise indication of the sign of a number.\n", " \n", " The `sign` function returns ``-1 if x < 0, 0 if x==0, 1 if x > 0``. nan\n", " is returned for nan inputs.\n", " \n", " For complex inputs, the `sign` function returns\n", " ``sign(x.real) + 0j if x.real != 0 else sign(x.imag) + 0j``.\n", " \n", " complex(nan, 0) is returned for complex nan inputs.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Input values.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray\n", " The sign of `x`.\n", " This is a scalar if `x` is a scalar.\n", " \n", " Notes\n", " -----\n", " There is more than one definition of sign in common use for complex\n", " numbers. The definition used here is equivalent to :math:`x/\\sqrt{x*x}`\n", " which is different from a common alternative, :math:`x/|x|`.\n", " \n", " Examples\n", " --------\n", " >>> np.sign([-5., 4.5])\n", " array([-1., 1.])\n", " >>> np.sign(0)\n", " 0\n", " >>> np.sign(5-2j)\n", " (1+0j)\n", " \n", " signbit = <ufunc 'signbit'>\n", " signbit(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Returns element-wise True where signbit is set (less than zero).\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " The input value(s).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " result : ndarray of bool\n", " Output array, or reference to `out` if that was supplied.\n", " This is a scalar if `x` is a scalar.\n", " \n", " Examples\n", " --------\n", " >>> np.signbit(-1.2)\n", " True\n", " >>> np.signbit(np.array([1, -2.3, 2.1]))\n", " array([False, True, False])\n", " \n", " sin = <ufunc 'sin'>\n", " sin(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Trigonometric sine, element-wise.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Angle, in radians (:math:`2 \\pi` rad equals 360 degrees).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : array_like\n", " The sine of each element of x.\n", " This is a scalar if `x` is a scalar.\n", " \n", " See Also\n", " --------\n", " arcsin, sinh, cos\n", " \n", " Notes\n", " -----\n", " The sine is one of the fundamental functions of trigonometry (the\n", " mathematical study of triangles). Consider a circle of radius 1\n", " centered on the origin. A ray comes in from the :math:`+x` axis, makes\n", " an angle at the origin (measured counter-clockwise from that axis), and\n", " departs from the origin. The :math:`y` coordinate of the outgoing\n", " ray's intersection with the unit circle is the sine of that angle. It\n", " ranges from -1 for :math:`x=3\\pi / 2` to +1 for :math:`\\pi / 2.` The\n", " function has zeroes where the angle is a multiple of :math:`\\pi`.\n", " Sines of angles between :math:`\\pi` and :math:`2\\pi` are negative.\n", " The numerous properties of the sine and related functions are included\n", " in any standard trigonometry text.\n", " \n", " Examples\n", " --------\n", " Print sine of one angle:\n", " \n", " >>> np.sin(np.pi/2.)\n", " 1.0\n", " \n", " Print sines of an array of angles given in degrees:\n", " \n", " >>> np.sin(np.array((0., 30., 45., 60., 90.)) * np.pi / 180. )\n", " array([ 0. , 0.5 , 0.70710678, 0.8660254 , 1. ])\n", " \n", " Plot the sine function:\n", " \n", " >>> import matplotlib.pylab as plt\n", " >>> x = np.linspace(-np.pi, np.pi, 201)\n", " >>> plt.plot(x, np.sin(x))\n", " >>> plt.xlabel('Angle [rad]')\n", " >>> plt.ylabel('sin(x)')\n", " >>> plt.axis('tight')\n", " >>> plt.show()\n", " \n", " sinh = <ufunc 'sinh'>\n", " sinh(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Hyperbolic sine, element-wise.\n", " \n", " Equivalent to ``1/2 * (np.exp(x) - np.exp(-x))`` or\n", " ``-1j * np.sin(1j*x)``.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Input array.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray\n", " The corresponding hyperbolic sine values.\n", " This is a scalar if `x` is a scalar.\n", " \n", " Notes\n", " -----\n", " If `out` is provided, the function writes the result into it,\n", " and returns a reference to `out`. (See Examples)\n", " \n", " References\n", " ----------\n", " M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions.\n", " New York, NY: Dover, 1972, pg. 83.\n", " \n", " Examples\n", " --------\n", " >>> np.sinh(0)\n", " 0.0\n", " >>> np.sinh(np.pi*1j/2)\n", " 1j\n", " >>> np.sinh(np.pi*1j) # (exact value is 0)\n", " 1.2246063538223773e-016j\n", " >>> # Discrepancy due to vagaries of floating point arithmetic.\n", " \n", " >>> # Example of providing the optional output parameter\n", " >>> out1 = np.array([0], dtype='d')\n", " >>> out2 = np.sinh([0.1], out1)\n", " >>> out2 is out1\n", " True\n", " \n", " >>> # Example of ValueError due to provision of shape mis-matched `out`\n", " >>> np.sinh(np.zeros((3,3)),np.zeros((2,2)))\n", " Traceback (most recent call last):\n", " File \"<stdin>\", line 1, in <module>\n", " ValueError: operands could not be broadcast together with shapes (3,3) (2,2)\n", " \n", " spacing = <ufunc 'spacing'>\n", " spacing(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Return the distance between x and the nearest adjacent number.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Values to find the spacing of.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " out : ndarray or scalar\n", " The spacing of values of `x`.\n", " This is a scalar if `x` is a scalar.\n", " \n", " Notes\n", " -----\n", " It can be considered as a generalization of EPS:\n", " ``spacing(np.float64(1)) == np.finfo(np.float64).eps``, and there\n", " should not be any representable number between ``x + spacing(x)`` and\n", " x for any finite x.\n", " \n", " Spacing of +- inf and NaN is NaN.\n", " \n", " Examples\n", " --------\n", " >>> np.spacing(1) == np.finfo(np.float64).eps\n", " True\n", " \n", " sqrt = <ufunc 'sqrt'>\n", " sqrt(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Return the non-negative square-root of an array, element-wise.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " The values whose square-roots are required.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray\n", " An array of the same shape as `x`, containing the positive\n", " square-root of each element in `x`. If any element in `x` is\n", " complex, a complex array is returned (and the square-roots of\n", " negative reals are calculated). If all of the elements in `x`\n", " are real, so is `y`, with negative elements returning ``nan``.\n", " If `out` was provided, `y` is a reference to it.\n", " This is a scalar if `x` is a scalar.\n", " \n", " See Also\n", " --------\n", " emath.sqrt\n", " A version which returns complex numbers when given negative reals.\n", " Note: 0.0 and -0.0 are handled differently for complex inputs.\n", " \n", " Notes\n", " -----\n", " *sqrt* has--consistent with common convention--as its branch cut the\n", " real \"interval\" [`-inf`, 0), and is continuous from above on it.\n", " A branch cut is a curve in the complex plane across which a given\n", " complex function fails to be continuous.\n", " \n", " Examples\n", " --------\n", " >>> np.sqrt([1,4,9])\n", " array([ 1., 2., 3.])\n", " \n", " >>> np.sqrt([4, -1, -3+4J])\n", " array([ 2.+0.j, 0.+1.j, 1.+2.j])\n", " \n", " >>> np.sqrt([4, -1, np.inf])\n", " array([ 2., nan, inf])\n", " \n", " square = <ufunc 'square'>\n", " square(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Return the element-wise square of the input.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Input data.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " out : ndarray or scalar\n", " Element-wise `x*x`, of the same shape and dtype as `x`.\n", " This is a scalar if `x` is a scalar.\n", " \n", " See Also\n", " --------\n", " numpy.linalg.matrix_power\n", " sqrt\n", " power\n", " \n", " Examples\n", " --------\n", " >>> np.square([-1j, 1])\n", " array([-1.-0.j, 1.+0.j])\n", " \n", " subtract = <ufunc 'subtract'>\n", " subtract(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Subtract arguments, element-wise.\n", " \n", " Parameters\n", " ----------\n", " x1, x2 : array_like\n", " The arrays to be subtracted from each other.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray\n", " The difference of `x1` and `x2`, element-wise.\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " Notes\n", " -----\n", " Equivalent to ``x1 - x2`` in terms of array broadcasting.\n", " \n", " Examples\n", " --------\n", " >>> np.subtract(1.0, 4.0)\n", " -3.0\n", " \n", " >>> x1 = np.arange(9.0).reshape((3, 3))\n", " >>> x2 = np.arange(3.0)\n", " >>> np.subtract(x1, x2)\n", " array([[ 0., 0., 0.],\n", " [ 3., 3., 3.],\n", " [ 6., 6., 6.]])\n", " \n", " The ``-`` operator can be used as a shorthand for ``np.subtract`` on\n", " ndarrays.\n", " \n", " >>> x1 = np.arange(9.0).reshape((3, 3))\n", " >>> x2 = np.arange(3.0)\n", " >>> x1 - x2\n", " array([[0., 0., 0.],\n", " [3., 3., 3.],\n", " [6., 6., 6.]])\n", " \n", " tan = <ufunc 'tan'>\n", " tan(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Compute tangent element-wise.\n", " \n", " Equivalent to ``np.sin(x)/np.cos(x)`` element-wise.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Input array.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray\n", " The corresponding tangent values.\n", " This is a scalar if `x` is a scalar.\n", " \n", " Notes\n", " -----\n", " If `out` is provided, the function writes the result into it,\n", " and returns a reference to `out`. (See Examples)\n", " \n", " References\n", " ----------\n", " M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions.\n", " New York, NY: Dover, 1972.\n", " \n", " Examples\n", " --------\n", " >>> from math import pi\n", " >>> np.tan(np.array([-pi,pi/2,pi]))\n", " array([ 1.22460635e-16, 1.63317787e+16, -1.22460635e-16])\n", " >>>\n", " >>> # Example of providing the optional output parameter illustrating\n", " >>> # that what is returned is a reference to said parameter\n", " >>> out1 = np.array([0], dtype='d')\n", " >>> out2 = np.cos([0.1], out1)\n", " >>> out2 is out1\n", " True\n", " >>>\n", " >>> # Example of ValueError due to provision of shape mis-matched `out`\n", " >>> np.cos(np.zeros((3,3)),np.zeros((2,2)))\n", " Traceback (most recent call last):\n", " File \"<stdin>\", line 1, in <module>\n", " ValueError: operands could not be broadcast together with shapes (3,3) (2,2)\n", " \n", " tanh = <ufunc 'tanh'>\n", " tanh(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Compute hyperbolic tangent element-wise.\n", " \n", " Equivalent to ``np.sinh(x)/np.cosh(x)`` or ``-1j * np.tan(1j*x)``.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Input array.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray\n", " The corresponding hyperbolic tangent values.\n", " This is a scalar if `x` is a scalar.\n", " \n", " Notes\n", " -----\n", " If `out` is provided, the function writes the result into it,\n", " and returns a reference to `out`. (See Examples)\n", " \n", " References\n", " ----------\n", " .. [1] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions.\n", " New York, NY: Dover, 1972, pg. 83.\n", " https://personal.math.ubc.ca/~cbm/aands/page_83.htm\n", " \n", " .. [2] Wikipedia, \"Hyperbolic function\",\n", " https://en.wikipedia.org/wiki/Hyperbolic_function\n", " \n", " Examples\n", " --------\n", " >>> np.tanh((0, np.pi*1j, np.pi*1j/2))\n", " array([ 0. +0.00000000e+00j, 0. -1.22460635e-16j, 0. +1.63317787e+16j])\n", " \n", " >>> # Example of providing the optional output parameter illustrating\n", " >>> # that what is returned is a reference to said parameter\n", " >>> out1 = np.array([0], dtype='d')\n", " >>> out2 = np.tanh([0.1], out1)\n", " >>> out2 is out1\n", " True\n", " \n", " >>> # Example of ValueError due to provision of shape mis-matched `out`\n", " >>> np.tanh(np.zeros((3,3)),np.zeros((2,2)))\n", " Traceback (most recent call last):\n", " File \"<stdin>\", line 1, in <module>\n", " ValueError: operands could not be broadcast together with shapes (3,3) (2,2)\n", " \n", " tracemalloc_domain = 389047\n", " true_divide = <ufunc 'divide'>\n", " divide(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Divide arguments element-wise.\n", " \n", " Parameters\n", " ----------\n", " x1 : array_like\n", " Dividend array.\n", " x2 : array_like\n", " Divisor array.\n", " If ``x1.shape != x2.shape``, they must be broadcastable to a common\n", " shape (which becomes the shape of the output).\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray or scalar\n", " The quotient ``x1/x2``, element-wise.\n", " This is a scalar if both `x1` and `x2` are scalars.\n", " \n", " See Also\n", " --------\n", " seterr : Set whether to raise or warn on overflow, underflow and\n", " division by zero.\n", " \n", " Notes\n", " -----\n", " Equivalent to ``x1`` / ``x2`` in terms of array-broadcasting.\n", " \n", " The ``true_divide(x1, x2)`` function is an alias for\n", " ``divide(x1, x2)``.\n", " \n", " Examples\n", " --------\n", " >>> np.divide(2.0, 4.0)\n", " 0.5\n", " >>> x1 = np.arange(9.0).reshape((3, 3))\n", " >>> x2 = np.arange(3.0)\n", " >>> np.divide(x1, x2)\n", " array([[nan, 1. , 1. ],\n", " [inf, 4. , 2.5],\n", " [inf, 7. , 4. ]])\n", " \n", " The ``/`` operator can be used as a shorthand for ``np.divide`` on\n", " ndarrays.\n", " \n", " >>> x1 = np.arange(9.0).reshape((3, 3))\n", " >>> x2 = 2 * np.ones(3)\n", " >>> x1 / x2\n", " array([[0. , 0.5, 1. ],\n", " [1.5, 2. , 2.5],\n", " [3. , 3.5, 4. ]])\n", " \n", " trunc = <ufunc 'trunc'>\n", " trunc(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])\n", " \n", " Return the truncated value of the input, element-wise.\n", " \n", " The truncated value of the scalar `x` is the nearest integer `i` which\n", " is closer to zero than `x` is. In short, the fractional part of the\n", " signed number `x` is discarded.\n", " \n", " Parameters\n", " ----------\n", " x : array_like\n", " Input data.\n", " out : ndarray, None, or tuple of ndarray and None, optional\n", " A location into which the result is stored. If provided, it must have\n", " a shape that the inputs broadcast to. If not provided or None,\n", " a freshly-allocated array is returned. A tuple (possible only as a\n", " keyword argument) must have length equal to the number of outputs.\n", " where : array_like, optional\n", " This condition is broadcast over the input. At locations where the\n", " condition is True, the `out` array will be set to the ufunc result.\n", " Elsewhere, the `out` array will retain its original value.\n", " Note that if an uninitialized `out` array is created via the default\n", " ``out=None``, locations within it where the condition is False will\n", " remain uninitialized.\n", " **kwargs\n", " For other keyword-only arguments, see the\n", " :ref:`ufunc docs <ufuncs.kwargs>`.\n", " \n", " Returns\n", " -------\n", " y : ndarray or scalar\n", " The truncated value of each element in `x`.\n", " This is a scalar if `x` is a scalar.\n", " \n", " See Also\n", " --------\n", " ceil, floor, rint, fix\n", " \n", " Notes\n", " -----\n", " .. versionadded:: 1.3.0\n", " \n", " Examples\n", " --------\n", " >>> a = np.array([-1.7, -1.5, -0.2, 0.2, 1.5, 1.7, 2.0])\n", " >>> np.trunc(a)\n", " array([-1., -1., -0., 0., 1., 1., 2.])\n", " \n", " typecodes = {'All': '?bhilqpBHILQPefdgFDGSUVOMm', 'AllFloat': 'efdgFDG...\n", "\n", "VERSION\n", " 1.24.3\n", "\n", "FILE\n", " c:\\users\\marti\\anaconda3\\lib\\site-packages\\numpy\\__init__.py\n", "\n", "\n" ] } ], "source": [ "import numpy\n", "help(numpy)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*** \n", "## Name conflicts " ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "ename": "ModuleNotFoundError", "evalue": "No module named 'hslu'", "output_type": "error", "traceback": [ "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[1;31mModuleNotFoundError\u001b[0m Traceback (most recent call last)", "Cell \u001b[1;32mIn[16], line 1\u001b[0m\n\u001b[1;32m----> 1\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mhslu\u001b[39;00m\n", "\u001b[1;31mModuleNotFoundError\u001b[0m: No module named 'hslu'" ] } ], "source": [ "import hslu" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'Falsch gedacht!'" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zahl = 4\n", "str(4)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "def str(irgendwas): \n", " # overwrite the str()-function in this Python File\n", " return \"wrong guess!\" \n" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'Falsch gedacht!'" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# str() built-in function is now overwritten\n", "zahl = 4\n", "str(4)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "ename": "NameError", "evalue": "name 'str' is not defined", "output_type": "error", "traceback": [ "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)", "Cell \u001b[1;32mIn[23], line 2\u001b[0m\n\u001b[0;32m 1\u001b[0m \u001b[38;5;66;03m# erases the str function definition again and built-in is now available again\u001b[39;00m\n\u001b[1;32m----> 2\u001b[0m \u001b[38;5;28;01mdel\u001b[39;00m \u001b[38;5;28;43mstr\u001b[39;49m\n", "\u001b[1;31mNameError\u001b[0m: name 'str' is not defined" ] } ], "source": [ "# erases the str function definition again and built-in is now available again\n", "del str" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'1'" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "str(1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*** \n", "## Activation task at the end " ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "78.53981633974483\n" ] } ], "source": [ "from math import pi\n", "\n", "def circle_area(radius:float=5) -> float:\n", " return pi*radius**2\n", "\n", "print(circle_area())" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "9\n", "3\n", "10\n", "7\n", "3\n", "1\n", "4\n", "8\n", "10\n", "4\n", "10\n", "4\n", "6\n", "9\n", "7\n" ] } ], "source": [ "from random import randrange\n", "\n", "for i in range(1, 16):\n", " print(randrange(1, 11))" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "number of loops: 8\n" ] } ], "source": [ "from random import randrange\n", "\n", "i = 1\n", "rand_numb = randrange(1, 11)\n", "\n", "while rand_numb != 10:\n", " rand_numb = randrange(1, 11)\n", " i += 1\n", "print(f\"number of loops: {i}\")" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.7" } }, "nbformat": 4, "nbformat_minor": 4 }
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