# numpy - pydoc - phpman Help on package numpy: ## NAME numpy ## DESCRIPTION NumPy ===== Provides 1. An array object of arbitrary homogeneous items 2. Fast mathematical operations over arrays 3. Linear Algebra, Fourier Transforms, Random Number Generation How to use the documentation ---------------------------- Documentation is available in two forms: docstrings provided with the code, and a loose standing reference guide, available from `the NumPy homepage <>`_. We recommend exploring the docstrings using `IPython <>`_, an advanced Python shell with TAB-completion and introspection capabilities. See below for further instructions. The docstring examples assume that `numpy` has been imported as `np`:: >>> import numpy as np Code snippets are indicated by three greater-than signs:: >>> x = 42 >>> x = x + 1 Use the built-in ``help`` function to view a function's docstring:: >>> help(np.sort) ... # doctest: +SKIP For some objects, ``np.info(obj)`` may provide additional help. This is particularly true if you see the line "Help on ufunc object:" at the top of the help() page. Ufuncs are implemented in C, not Python, for speed. The native Python help() does not know how to view their help, but our np.info() function does. To search for documents containing a keyword, do:: >>> np.lookfor('keyword') ... # doctest: +SKIP General-purpose documents like a glossary and help on the basic concepts of numpy are available under the ``doc`` sub-module:: >>> from numpy import doc >>> help(doc) ... # doctest: +SKIP Available subpackages --------------------- doc Topical documentation on broadcasting, indexing, etc. lib Basic functions used by several sub-packages. random Core Random Tools linalg Core Linear Algebra Tools fft Core FFT routines polynomial Polynomial tools testing NumPy testing tools f2py Fortran to Python Interface Generator. distutils Enhancements to distutils with support for Fortran compilers support and more. Utilities --------- test Run numpy unittests show_config Show numpy build configuration dual Overwrite certain functions with high-performance SciPy tools. Note: `numpy.dual` is deprecated. Use the functions from NumPy or Scipy directly instead of importing them from `numpy.dual`. matlib Make everything matrices. __version__ NumPy version string Viewing documentation using IPython ----------------------------------- Start IPython with the NumPy profile (``ipython -p numpy``), which will import `numpy` under the alias `np`. Then, use the ``cpaste`` command to paste examples into the shell. To see which functions are available in `numpy`, type ``np.`` (where ```` refers to the TAB key), or use ``np.*cos*?`` (where ```` refers to the ENTER key) to narrow down the list. To view the docstring for a function, use ``np.cos?`` (to view the docstring) and ``np.cos??`` (to view the source code). Copies vs. in-place operation ----------------------------- Most of the functions in `numpy` return a copy of the array argument (e.g., `np.sort`). In-place versions of these functions are often available as array methods, i.e. ``x = np.array([1,2,3]); x.sort()``. Exceptions to this rule are documented. ## PACKAGE CONTENTS __config__ _distributor_init _globals _pytesttester _version compat (package) conftest core (package) ctypeslib distutils (package) doc (package) dual f2py (package) fft (package) lib (package) linalg (package) ma (package) matlib matrixlib (package) polynomial (package) random (package) setup testing (package) tests (package) typing (package) version ## SUBMODULES _mat char emath rec ## CLASSES builtins.DeprecationWarning(builtins.Warning) ModuleDeprecationWarning builtins.IndexError(builtins.LookupError) AxisError(builtins.ValueError, builtins.IndexError) builtins.RuntimeError(builtins.Exception) TooHardError builtins.RuntimeWarning(builtins.Warning) ComplexWarning builtins.UserWarning(builtins.Warning) RankWarning VisibleDeprecationWarning builtins.ValueError(builtins.Exception) AxisError(builtins.ValueError, builtins.IndexError) builtins.bytes(builtins.object) bytes_(builtins.bytes, character) builtins.object DataSource MachAr broadcast busdaycalendar dtype finfo flatiter format_parser generic bool_ datetime64 flexible character bytes_(builtins.bytes, character) str_(builtins.str, character) void record number inexact complexfloating complex128(complexfloating, builtins.complex) complex256 complex64 floating float128 float16 float32 float64(floating, builtins.float) integer signedinteger int16 int32 int64 int8 longlong timedelta64 unsignedinteger uint16 uint32 uint64 uint8 ulonglong object_ iinfo ndarray chararray matrix memmap recarray ndenumerate ndindex nditer poly1d ufunc vectorize builtins.str(builtins.object) str_(builtins.str, character) contextlib.ContextDecorator(builtins.object) errstate ### class AxisError | AxisError(axis, ndim=None, msg_prefix=None) | | Axis supplied was invalid. | | Method resolution order: | AxisError | builtins.ValueError | builtins.IndexError | builtins.LookupError | builtins.Exception | builtins.BaseException | builtins.object | | Methods defined here: | | __init__(self, axis, ndim=None, msg_prefix=None) | Initialize self. See help(type(self)) for accurate signature. | | ---------------------------------------------------------------------- | Data descriptors defined here: | | __weakref__ | list of weak references to the object (if defined) | | ---------------------------------------------------------------------- | Static methods inherited from builtins.ValueError: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from builtins.BaseException: | | __delattr__(self, name, /) | Implement delattr(self, name). | | __getattribute__(self, name, /) | Return getattr(self, name). | | __reduce__(...) | Helper for pickle. | | __repr__(self, /) | Return repr(self). | | __setattr__(self, name, value, /) | Implement setattr(self, name, value). | | __setstate__(...) | | __str__(self, /) | Return str(self). | | with_traceback(...) | Exception.with_traceback(tb) -- | set self.__traceback__ to tb and return self. | | ---------------------------------------------------------------------- | Data descriptors inherited from builtins.BaseException: | | __cause__ | exception cause | | __context__ | exception context | | __dict__ | | __suppress_context__ | | __traceback__ | | args ### class ComplexWarning | The warning raised when casting a complex dtype to a real dtype. | | As implemented, casting a complex number to a real discards its imaginary | part, but this behavior may not be what the user actually wants. | | Method resolution order: | ComplexWarning | builtins.RuntimeWarning | builtins.Warning | builtins.Exception | builtins.BaseException | builtins.object | | Data descriptors defined here: | | __weakref__ | list of weak references to the object (if defined) | | ---------------------------------------------------------------------- | Methods inherited from builtins.RuntimeWarning: | | __init__(self, /, *args, **kwargs) | Initialize self. See help(type(self)) for accurate signature. | | ---------------------------------------------------------------------- | Static methods inherited from builtins.RuntimeWarning: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from builtins.BaseException: | | __delattr__(self, name, /) | Implement delattr(self, name). | | __getattribute__(self, name, /) | Return getattr(self, name). | | __reduce__(...) | Helper for pickle. | | __repr__(self, /) | Return repr(self). | | __setattr__(self, name, value, /) | Implement setattr(self, name, value). | | __setstate__(...) | | __str__(self, /) | Return str(self). | | with_traceback(...) | Exception.with_traceback(tb) -- | set self.__traceback__ to tb and return self. | | ---------------------------------------------------------------------- | Data descriptors inherited from builtins.BaseException: | | __cause__ | exception cause | | __context__ | exception context | | __dict__ | | __suppress_context__ | | __traceback__ | | args ### class DataSource | DataSource(destpath='.') | | DataSource(destpath='.') | | A generic data source file (file, http, ftp, ...). | | DataSources can be local files or remote files/URLs. The files may | also be compressed or uncompressed. DataSource hides some of the | low-level details of downloading the file, allowing you to simply pass | in a valid file path (or URL) and obtain a file object. | | Parameters | ---------- | destpath : str or None, optional | Path to the directory where the source file gets downloaded to for | use. If `destpath` is None, a temporary directory will be created. | The default path is the current directory. | | Notes | ----- | URLs require a scheme string (``http://``) to be used, without it they | will fail:: | | >>> repos = np.DataSource() | >>> repos.exists('www.google.com/index.html') | False | >>> repos.exists('') | True | | Temporary directories are deleted when the DataSource is deleted. | | Examples | -------- | :: | | >>> ds = np.DataSource('/home/guido') | >>> urlname = '' | >>> gfile = ds.open('') | >>> ds.abspath(urlname) | '/home/guido/www.google.com/index.html' | | >>> ds = np.DataSource(None) # use with temporary file | >>> ds.open('/home/guido/foobar.txt') | | >>> ds.abspath('/home/guido/foobar.txt') | '/tmp/.../home/guido/foobar.txt' | | Methods defined here: | | __del__(self) | | __init__(self, destpath='.') | Create a DataSource with a local path at destpath. | | abspath(self, path) | Return absolute path of file in the DataSource directory. | | If `path` is an URL, then `abspath` will return either the location | the file exists locally or the location it would exist when opened | using the `open` method. | | Parameters | ---------- | path : str | Can be a local file or a remote URL. | | Returns | ------- | out : str | Complete path, including the `DataSource` destination directory. | | Notes | ----- | The functionality is based on `os.path.abspath`. | | exists(self, path) | Test if path exists. | | Test if `path` exists as (and in this order): | | - a local file. | - a remote URL that has been downloaded and stored locally in the | `DataSource` directory. | - a remote URL that has not been downloaded, but is valid and | accessible. | | Parameters | ---------- | path : str | Can be a local file or a remote URL. | | Returns | ------- | out : bool | True if `path` exists. | | Notes | ----- | When `path` is an URL, `exists` will return True if it's either | stored locally in the `DataSource` directory, or is a valid remote | URL. `DataSource` does not discriminate between the two, the file | is accessible if it exists in either location. | | open(self, path, mode='r', encoding=None, newline=None) | Open and return file-like object. | | If `path` is an URL, it will be downloaded, stored in the | `DataSource` directory and opened from there. | | Parameters | ---------- | path : str | Local file path or URL to open. | mode : {'r', 'w', 'a'}, optional | Mode to open `path`. Mode 'r' for reading, 'w' for writing, | 'a' to append. Available modes depend on the type of object | specified by `path`. Default is 'r'. | encoding : {None, str}, optional | Open text file with given encoding. The default encoding will be | what `io.open` uses. | newline : {None, str}, optional | Newline to use when reading text file. | | Returns | ------- | out : file object | File object. | | ---------------------------------------------------------------------- | Data descriptors defined here: | | __dict__ | dictionary for instance variables (if defined) | | __weakref__ | list of weak references to the object (if defined) ### class MachAr | MachAr(float_conv=, int_conv=, float_to_float=, float_to_str= at 0x7fc238803130>, title='Python floating point number') | | Diagnosing machine parameters. | | Attributes | ---------- | ibeta : int | Radix in which numbers are represented. | it : int | Number of base-`ibeta` digits in the floating point mantissa M. | machep : int | Exponent of the smallest (most negative) power of `ibeta` that, | added to 1.0, gives something different from 1.0 | eps : float | Floating-point number ``beta**machep`` (floating point precision) | negep : int | Exponent of the smallest power of `ibeta` that, subtracted | from 1.0, gives something different from 1.0. | epsneg : float | Floating-point number ``beta**negep``. | iexp : int | Number of bits in the exponent (including its sign and bias). | minexp : int | Smallest (most negative) power of `ibeta` consistent with there | being no leading zeros in the mantissa. | xmin : float | Floating-point number ``beta**minexp`` (the smallest [in | magnitude] positive floating point number with full precision). | maxexp : int | Smallest (positive) power of `ibeta` that causes overflow. | xmax : float | ``(1-epsneg) * beta**maxexp`` (the largest [in magnitude] | usable floating value). | irnd : int | In ``[range(6)](https://www.chedong.com/phpMan.php/man/range/6/markdown)``, information on what kind of rounding is done | in addition, and on how underflow is handled. | ngrd : int | Number of 'guard digits' used when truncating the product | of two mantissas to fit the representation. | epsilon : float | Same as `eps`. | tiny : float | Same as `xmin`. | huge : float | Same as `xmax`. | precision : float | ``- int(-log10(eps))`` | resolution : float | ``- 10**(-precision)`` | | Parameters | ---------- | float_conv : function, optional | Function that converts an integer or integer array to a float | or float array. Default is `float`. | int_conv : function, optional | Function that converts a float or float array to an integer or | integer array. Default is `int`. | float_to_float : function, optional | Function that converts a float array to float. Default is `float`. | Note that this does not seem to do anything useful in the current | implementation. | float_to_str : function, optional | Function that converts a single float to a string. Default is | ``lambda v:'%24.16e' %v``. | title : str, optional | Title that is printed in the string representation of `MachAr`. | | See Also | -------- | finfo : Machine limits for floating point types. | iinfo : Machine limits for integer types. | | References | ---------- | .. [1] Press, Teukolsky, Vetterling and Flannery, | "Numerical Recipes in C++," 2nd ed, | Cambridge University Press, 2002, p. 31. | | Methods defined here: | | __init__(self, float_conv=, int_conv=, float_to_float=, float_to_str= at 0x7fc238803130>, title='Python floating point number') | float_conv - convert integer to float (array) | int_conv - convert float (array) to integer | float_to_float - convert float array to float | float_to_str - convert array float to str | title - description of used floating point numbers | | __str__(self) | Return str(self). | | ---------------------------------------------------------------------- | Data descriptors defined here: | | __dict__ | dictionary for instance variables (if defined) | | __weakref__ | list of weak references to the object (if defined) ### class ModuleDeprecationWarning | Module deprecation warning. | | The nose tester turns ordinary Deprecation warnings into test failures. | That makes it hard to deprecate whole modules, because they get | imported by default. So this is a special Deprecation warning that the | nose tester will let pass without making tests fail. | | Method resolution order: | ModuleDeprecationWarning | builtins.DeprecationWarning | builtins.Warning | builtins.Exception | builtins.BaseException | builtins.object | | Data descriptors defined here: | | __weakref__ | list of weak references to the object (if defined) | | ---------------------------------------------------------------------- | Methods inherited from builtins.DeprecationWarning: | | __init__(self, /, *args, **kwargs) | Initialize self. See help(type(self)) for accurate signature. | | ---------------------------------------------------------------------- | Static methods inherited from builtins.DeprecationWarning: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from builtins.BaseException: | | __delattr__(self, name, /) | Implement delattr(self, name). | | __getattribute__(self, name, /) | Return getattr(self, name). | | __reduce__(...) | Helper for pickle. | | __repr__(self, /) | Return repr(self). | | __setattr__(self, name, value, /) | Implement setattr(self, name, value). | | __setstate__(...) | | __str__(self, /) | Return str(self). | | with_traceback(...) | Exception.with_traceback(tb) -- | set self.__traceback__ to tb and return self. | | ---------------------------------------------------------------------- | Data descriptors inherited from builtins.BaseException: | | __cause__ | exception cause | | __context__ | exception context | | __dict__ | | __suppress_context__ | | __traceback__ | | args ### class RankWarning | Issued by `polyfit` when the Vandermonde matrix is rank deficient. | | For more information, a way to suppress the warning, and an example of | `RankWarning` being issued, see `polyfit`. | | Method resolution order: | RankWarning | builtins.UserWarning | builtins.Warning | builtins.Exception | builtins.BaseException | builtins.object | | Data descriptors defined here: | | __weakref__ | list of weak references to the object (if defined) | | ---------------------------------------------------------------------- | Methods inherited from builtins.UserWarning: | | __init__(self, /, *args, **kwargs) | Initialize self. See help(type(self)) for accurate signature. | | ---------------------------------------------------------------------- | Static methods inherited from builtins.UserWarning: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from builtins.BaseException: | | __delattr__(self, name, /) | Implement delattr(self, name). | | __getattribute__(self, name, /) | Return getattr(self, name). | | __reduce__(...) | Helper for pickle. | | __repr__(self, /) | Return repr(self). | | __setattr__(self, name, value, /) | Implement setattr(self, name, value). | | __setstate__(...) | | __str__(self, /) | Return str(self). | | with_traceback(...) | Exception.with_traceback(tb) -- | set self.__traceback__ to tb and return self. | | ---------------------------------------------------------------------- | Data descriptors inherited from builtins.BaseException: | | __cause__ | exception cause | | __context__ | exception context | | __dict__ | | __suppress_context__ | | __traceback__ | | args ### class TooHardError | Method resolution order: | TooHardError | builtins.RuntimeError | builtins.Exception | builtins.BaseException | builtins.object | | Data descriptors defined here: | | __weakref__ | list of weak references to the object (if defined) | | ---------------------------------------------------------------------- | Methods inherited from builtins.RuntimeError: | | __init__(self, /, *args, **kwargs) | Initialize self. See help(type(self)) for accurate signature. | | ---------------------------------------------------------------------- | Static methods inherited from builtins.RuntimeError: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from builtins.BaseException: | | __delattr__(self, name, /) | Implement delattr(self, name). | | __getattribute__(self, name, /) | Return getattr(self, name). | | __reduce__(...) | Helper for pickle. | | __repr__(self, /) | Return repr(self). | | __setattr__(self, name, value, /) | Implement setattr(self, name, value). | | __setstate__(...) | | __str__(self, /) | Return str(self). | | with_traceback(...) | Exception.with_traceback(tb) -- | set self.__traceback__ to tb and return self. | | ---------------------------------------------------------------------- | Data descriptors inherited from builtins.BaseException: | | __cause__ | exception cause | | __context__ | exception context | | __dict__ | | __suppress_context__ | | __traceback__ | | args ### class VisibleDeprecationWarning | Visible deprecation warning. | | By default, python will not show deprecation warnings, so this class | can be used when a very visible warning is helpful, for example because | the usage is most likely a user bug. | | Method resolution order: | VisibleDeprecationWarning | builtins.UserWarning | builtins.Warning | builtins.Exception | builtins.BaseException | builtins.object | | Data descriptors defined here: | | __weakref__ | list of weak references to the object (if defined) | | ---------------------------------------------------------------------- | Methods inherited from builtins.UserWarning: | | __init__(self, /, *args, **kwargs) | Initialize self. See help(type(self)) for accurate signature. | | ---------------------------------------------------------------------- | Static methods inherited from builtins.UserWarning: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from builtins.BaseException: | | __delattr__(self, name, /) | Implement delattr(self, name). | | __getattribute__(self, name, /) | Return getattr(self, name). | | __reduce__(...) | Helper for pickle. | | __repr__(self, /) | Return repr(self). | | __setattr__(self, name, value, /) | Implement setattr(self, name, value). | | __setstate__(...) | | __str__(self, /) | Return str(self). | | with_traceback(...) | Exception.with_traceback(tb) -- | set self.__traceback__ to tb and return self. | | ---------------------------------------------------------------------- | Data descriptors inherited from builtins.BaseException: | | __cause__ | exception cause | | __context__ | exception context | | __dict__ | | __suppress_context__ | | __traceback__ | | args bool8 = class bool_(generic) | Boolean type (True or False), stored as a byte. | | .. warning:: | | The :class:`bool_` type is not a subclass of the :class:`int_` type | (the :class:`bool_` is not even a number type). This is different | than Python's default implementation of :class:`bool` as a | sub-class of :class:`int`. | | :Character code: ``'?'`` | :Alias: `numpy.bool8` | | Method resolution order: | bool_ | generic | builtins.object | | Methods defined here: | | __and__(self, value, /) | Return self&value. | | __bool__(self, /) | True if self else False | | __eq__(self, value, /) | Return self==value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __index__(self, /) | Return self converted to an integer, if self is suitable for use as an index into a list. | | __le__(self, value, /) | Return self<=value. | | __lt__(self, value, /) | Return self>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. ### class bool_ | Boolean type (True or False), stored as a byte. | | .. warning:: | | The :class:`bool_` type is not a subclass of the :class:`int_` type | (the :class:`bool_` is not even a number type). This is different | than Python's default implementation of :class:`bool` as a | sub-class of :class:`int`. | | :Character code: ``'?'`` | :Alias: `numpy.bool8` | | Method resolution order: | bool_ | generic | builtins.object | | Methods defined here: | | __and__(self, value, /) | Return self&value. | | __bool__(self, /) | True if self else False | | __eq__(self, value, /) | Return self==value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __index__(self, /) | Return self converted to an integer, if self is suitable for use as an index into a list. | | __le__(self, value, /) | Return self<=value. | | __lt__(self, value, /) | Return self>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. ### class broadcast | Produce an object that mimics broadcasting. | | Parameters | ---------- | in1, in2, ... : array_like | Input parameters. | | Returns | ------- | b : broadcast object | Broadcast the input parameters against one another, and | return an object that encapsulates the result. | Amongst others, it has ``shape`` and ``nd`` properties, and | may be used as an iterator. | | See Also | -------- | broadcast_arrays | broadcast_to | broadcast_shapes | | Examples | -------- | | Manually adding two vectors, using broadcasting: | | >>> x = np.array([[1], [2], [3]]) | >>> y = np.array([4, 5, 6]) | >>> b = np.broadcast(x, y) | | >>> out = np.empty(b.shape) | >>> out.flat = [u+v for (u,v) in b] | >>> out | array([[5., 6., 7.], | [6., 7., 8.], | [7., 8., 9.]]) | | Compare against built-in broadcasting: | | >>> x + y | array([[5, 6, 7], | [6, 7, 8], | [7, 8, 9]]) | | Methods defined here: | | __iter__(self, /) | Implement iter(self). | | __next__(self, /) | Implement next(self). | | reset(...) | reset() | | Reset the broadcasted result's iterator(s). | | Parameters | ---------- | None | | Returns | ------- | None | | Examples | -------- | >>> x = np.array([1, 2, 3]) | >>> y = np.array([[4], [5], [6]]) | >>> b = np.broadcast(x, y) | >>> b.index | 0 | >>> next(b), next(b), next(b) | ((1, 4), (2, 4), (3, 4)) | >>> b.index | 3 | >>> b.reset() | >>> b.index | 0 | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Data descriptors defined here: | | index | current index in broadcasted result | | Examples | -------- | >>> x = np.array([[1], [2], [3]]) | >>> y = np.array([4, 5, 6]) | >>> b = np.broadcast(x, y) | >>> b.index | 0 | >>> next(b), next(b), next(b) | ((1, 4), (1, 5), (1, 6)) | >>> b.index | 3 | | iters | tuple of iterators along ``self``'s "components." | | Returns a tuple of `numpy.flatiter` objects, one for each "component" | of ``self``. | | See Also | -------- | numpy.flatiter | | Examples | -------- | >>> x = np.array([1, 2, 3]) | >>> y = np.array([[4], [5], [6]]) | >>> b = np.broadcast(x, y) | >>> row, col = b.iters | >>> next(row), next(col) | (1, 4) | | nd | Number of dimensions of broadcasted result. For code intended for NumPy | 1.12.0 and later the more consistent `ndim` is preferred. | | Examples | -------- | >>> x = np.array([1, 2, 3]) | >>> y = np.array([[4], [5], [6]]) | >>> b = np.broadcast(x, y) | >>> b.nd | 2 | | ndim | Number of dimensions of broadcasted result. Alias for `nd`. | | .. versionadded:: 1.12.0 | | Examples | -------- | >>> x = np.array([1, 2, 3]) | >>> y = np.array([[4], [5], [6]]) | >>> b = np.broadcast(x, y) | >>> b.ndim | 2 | | numiter | Number of iterators possessed by the broadcasted result. | | Examples | -------- | >>> x = np.array([1, 2, 3]) | >>> y = np.array([[4], [5], [6]]) | >>> b = np.broadcast(x, y) | >>> b.numiter | 2 | | shape | Shape of broadcasted result. | | Examples | -------- | >>> x = np.array([1, 2, 3]) | >>> y = np.array([[4], [5], [6]]) | >>> b = np.broadcast(x, y) | >>> b.shape | (3, 3) | | size | Total size of broadcasted result. | | Examples | -------- | >>> x = np.array([1, 2, 3]) | >>> y = np.array([[4], [5], [6]]) | >>> b = np.broadcast(x, y) | >>> b.size | 9 ### class busdaycalendar | busdaycalendar(weekmask='1111100', holidays=None) | | A business day calendar object that efficiently stores information | defining valid days for the busday family of functions. | | The default valid days are Monday through Friday ("business days"). | A busdaycalendar object can be specified with any set of weekly | valid days, plus an optional "holiday" dates that always will be invalid. | | Once a busdaycalendar object is created, the weekmask and holidays | cannot be modified. | | .. versionadded:: 1.7.0 | | Parameters | ---------- | weekmask : str or array_like of bool, optional | A seven-element array indicating which of Monday through Sunday are | valid days. May be specified as a length-seven list or array, like | [1,1,1,1,1,0,0]; a length-seven string, like '1111100'; or a string | like "Mon Tue Wed Thu Fri", made up of 3-character abbreviations for | weekdays, optionally separated by white space. Valid abbreviations | are: Mon Tue Wed Thu Fri Sat Sun | holidays : array_like of datetime64[D], optional | An array of dates to consider as invalid dates, no matter which | weekday they fall upon. Holiday dates may be specified in any | order, and NaT (not-a-time) dates are ignored. This list is | saved in a normalized form that is suited for fast calculations | of valid days. | | Returns | ------- | out : busdaycalendar | A business day calendar object containing the specified | weekmask and holidays values. | | See Also | -------- | is_busday : Returns a boolean array indicating valid days. | busday_offset : Applies an offset counted in valid days. | busday_count : Counts how many valid days are in a half-open date range. | | Attributes | ---------- | Note: once a busdaycalendar object is created, you cannot modify the | weekmask or holidays. The attributes return copies of internal data. | weekmask : (copy) seven-element array of bool | holidays : (copy) sorted array of datetime64[D] | | Examples | -------- | >>> # Some important days in July | ... bdd = np.busdaycalendar( | ... holidays=['2011-07-01', '2011-07-04', '2011-07-17']) | >>> # Default is Monday to Friday weekdays | ... bdd.weekmask | array([ True, True, True, True, True, False, False]) | >>> # Any holidays already on the weekend are removed | ... bdd.holidays | array(['2011-07-01', '2011-07-04'], dtype='datetime64[D]') | | Methods defined here: | | __init__(self, /, *args, **kwargs) | Initialize self. See help(type(self)) for accurate signature. | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Data descriptors defined here: | | holidays | A copy of the holiday array indicating additional invalid days. | | weekmask | A copy of the seven-element boolean mask indicating valid days. byte = class int8(signedinteger) | Signed integer type, compatible with C ``char``. | | :Character code: ``'b'`` | :Canonical name: `numpy.byte` | :Alias on this platform (Linux x86_64): `numpy.int8`: 8-bit signed integer (``-128`` to ``127``). | | Method resolution order: | int8 | signedinteger | integer | number | generic | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __and__(self, value, /) | Return self&value. | | __bool__(self, /) | True if self else False | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __index__(self, /) | Return self converted to an integer, if self is suitable for use as an index into a list. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __le__(self, value, /) | Return self<=value. | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __str__(self, /) | Return str(self). | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from integer: | | __round__(...) | | ---------------------------------------------------------------------- | Data descriptors inherited from integer: | | denominator | denominator of value (1) | | numerator | numerator of value (the value itself) | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __copy__(...) | | __deepcopy__(...) | | __format__(...) | NumPy array scalar formatter | | __getitem__(self, key, /) | Return self[key]. | | __reduce__(...) | Helper for pickle. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. bytes0 = class bytes_(builtins.bytes, character) | A byte string. | | When used in arrays, this type strips trailing null bytes. | | :Character code: ``'S'`` | :Alias: `numpy.string_` | | Method resolution order: | bytes_ | builtins.bytes | character | flexible | generic | builtins.object | | Methods defined here: | | __eq__(self, value, /) | Return self==value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __le__(self, value, /) | Return self<=value. | | __lt__(self, value, /) | Return self copy of B | | Return a copy of B with only its first character capitalized (ASCII) | and the rest lower-cased. | | center(self, width, fillchar=b' ', /) | Return a centered string of length width. | | Padding is done using the specified fill character. | | count(...) | B.count(sub[, start[, end]]) -> int | | Return the number of non-overlapping occurrences of subsection sub in | bytes B[start:end]. Optional arguments start and end are interpreted | as in slice notation. | | decode(self, /, encoding='utf-8', errors='strict') | Decode the bytes using the codec registered for encoding. | | encoding | The encoding with which to decode the bytes. | errors | The error handling scheme to use for the handling of decoding errors. | The default is 'strict' meaning that decoding errors raise a | UnicodeDecodeError. Other possible values are 'ignore' and 'replace' | as well as any other name registered with codecs.register_error that | can handle UnicodeDecodeErrors. | | endswith(...) | B.endswith(suffix[, start[, end]]) -> bool | | Return True if B ends with the specified suffix, False otherwise. | With optional start, test B beginning at that position. | With optional end, stop comparing B at that position. | suffix can also be a tuple of bytes to try. | | expandtabs(self, /, tabsize=8) | Return a copy where all tab characters are expanded using spaces. | | If tabsize is not given, a tab size of 8 characters is assumed. | | find(...) | B.find(sub[, start[, end]]) -> int | | Return the lowest index in B where subsection sub is found, | such that sub is contained within B[start,end]. Optional | arguments start and end are interpreted as in slice notation. | | Return -1 on failure. | | hex(...) | Create a string of hexadecimal numbers from a bytes object. | | sep | An optional single character or byte to separate hex bytes. | bytes_per_sep | How many bytes between separators. Positive values count from the | right, negative values count from the left. | | Example: | >>> value = b'\xb9\x01\xef' | >>> value.hex() | 'b901ef' | >>> value.hex(':') | 'b9:01:ef' | >>> value.hex(':', 2) | 'b9:01ef' | >>> value.hex(':', -2) | 'b901:ef' | | index(...) | B.index(sub[, start[, end]]) -> int | | Return the lowest index in B where subsection sub is found, | such that sub is contained within B[start,end]. Optional | arguments start and end are interpreted as in slice notation. | | Raises ValueError when the subsection is not found. | | isalnum(...) | B.isalnum() -> bool | | Return True if all characters in B are alphanumeric | and there is at least one character in B, False otherwise. | | isalpha(...) | B.isalpha() -> bool | | Return True if all characters in B are alphabetic | and there is at least one character in B, False otherwise. | | isascii(...) | B.isascii() -> bool | | Return True if B is empty or all characters in B are ASCII, | False otherwise. | | isdigit(...) | B.isdigit() -> bool | | Return True if all characters in B are digits | and there is at least one character in B, False otherwise. | | islower(...) | B.islower() -> bool | | Return True if all cased characters in B are lowercase and there is | at least one cased character in B, False otherwise. | | isspace(...) | B.isspace() -> bool | | Return True if all characters in B are whitespace | and there is at least one character in B, False otherwise. | | istitle(...) | B.istitle() -> bool | | Return True if B is a titlecased string and there is at least one | character in B, i.e. uppercase characters may only follow uncased | characters and lowercase characters only cased ones. Return False | otherwise. | | isupper(...) | B.isupper() -> bool | | Return True if all cased characters in B are uppercase and there is | at least one cased character in B, False otherwise. | | join(self, iterable_of_bytes, /) | Concatenate any number of bytes objects. | | The bytes whose method is called is inserted in between each pair. | | The result is returned as a new bytes object. | | Example: b'.'.join([b'ab', b'pq', b'rs']) -> b'ab.pq.rs'. | | ljust(self, width, fillchar=b' ', /) | Return a left-justified string of length width. | | Padding is done using the specified fill character. | | lower(...) | B.lower() -> copy of B | | Return a copy of B with all ASCII characters converted to lowercase. | | lstrip(self, bytes=None, /) | Strip leading bytes contained in the argument. | | If the argument is omitted or None, strip leading ASCII whitespace. | | partition(self, sep, /) | Partition the bytes into three parts using the given separator. | | This will search for the separator sep in the bytes. If the separator is found, | returns a 3-tuple containing the part before the separator, the separator | itself, and the part after it. | | If the separator is not found, returns a 3-tuple containing the original bytes | object and two empty bytes objects. | | removeprefix(self, prefix, /) | Return a bytes object with the given prefix string removed if present. | | If the bytes starts with the prefix string, return bytes[len(prefix):]. | Otherwise, return a copy of the original bytes. | | removesuffix(self, suffix, /) | Return a bytes object with the given suffix string removed if present. | | If the bytes ends with the suffix string and that suffix is not empty, | return bytes[:-len(prefix)]. Otherwise, return a copy of the original | bytes. | | replace(self, old, new, count=-1, /) | Return a copy with all occurrences of substring old replaced by new. | | count | Maximum number of occurrences to replace. | -1 (the default value) means replace all occurrences. | | If the optional argument count is given, only the first count occurrences are | replaced. | | rfind(...) | B.rfind(sub[, start[, end]]) -> int | | Return the highest index in B where subsection sub is found, | such that sub is contained within B[start,end]. Optional | arguments start and end are interpreted as in slice notation. | | Return -1 on failure. | | rindex(...) | B.rindex(sub[, start[, end]]) -> int | | Return the highest index in B where subsection sub is found, | such that sub is contained within B[start,end]. Optional | arguments start and end are interpreted as in slice notation. | | Raise ValueError when the subsection is not found. | | rjust(self, width, fillchar=b' ', /) | Return a right-justified string of length width. | | Padding is done using the specified fill character. | | rpartition(self, sep, /) | Partition the bytes into three parts using the given separator. | | This will search for the separator sep in the bytes, starting at the end. If | the separator is found, returns a 3-tuple containing the part before the | separator, the separator itself, and the part after it. | | If the separator is not found, returns a 3-tuple containing two empty bytes | objects and the original bytes object. | | rsplit(self, /, sep=None, maxsplit=-1) | Return a list of the sections in the bytes, using sep as the delimiter. | | sep | The delimiter according which to split the bytes. | None (the default value) means split on ASCII whitespace characters | (space, tab, return, newline, formfeed, vertical tab). | maxsplit | Maximum number of splits to do. | -1 (the default value) means no limit. | | Splitting is done starting at the end of the bytes and working to the front. | | rstrip(self, bytes=None, /) | Strip trailing bytes contained in the argument. | | If the argument is omitted or None, strip trailing ASCII whitespace. | | split(self, /, sep=None, maxsplit=-1) | Return a list of the sections in the bytes, using sep as the delimiter. | | sep | The delimiter according which to split the bytes. | None (the default value) means split on ASCII whitespace characters | (space, tab, return, newline, formfeed, vertical tab). | maxsplit | Maximum number of splits to do. | -1 (the default value) means no limit. | | splitlines(self, /, keepends=False) | Return a list of the lines in the bytes, breaking at line boundaries. | | Line breaks are not included in the resulting list unless keepends is given and | true. | | startswith(...) | B.startswith(prefix[, start[, end]]) -> bool | | Return True if B starts with the specified prefix, False otherwise. | With optional start, test B beginning at that position. | With optional end, stop comparing B at that position. | prefix can also be a tuple of bytes to try. | | strip(self, bytes=None, /) | Strip leading and trailing bytes contained in the argument. | | If the argument is omitted or None, strip leading and trailing ASCII whitespace. | | swapcase(...) | B.swapcase() -> copy of B | | Return a copy of B with uppercase ASCII characters converted | to lowercase ASCII and vice versa. | | title(...) | B.title() -> copy of B | | Return a titlecased version of B, i.e. ASCII words start with uppercase | characters, all remaining cased characters have lowercase. | | translate(self, table, /, delete=b'') | Return a copy with each character mapped by the given translation table. | | table | Translation table, which must be a bytes object of length 256. | | All characters occurring in the optional argument delete are removed. | The remaining characters are mapped through the given translation table. | | upper(...) | B.upper() -> copy of B | | Return a copy of B with all ASCII characters converted to uppercase. | | zfill(self, width, /) | Pad a numeric string with zeros on the left, to fill a field of the given width. | | The original string is never truncated. | | ---------------------------------------------------------------------- | Class methods inherited from builtins.bytes: | | fromhex(string, /) from builtins.type | Create a bytes object from a string of hexadecimal numbers. | | Spaces between two numbers are accepted. | Example: bytes.fromhex('B9 01EF') -> b'\\xb9\\x01\\xef'. | | ---------------------------------------------------------------------- | Static methods inherited from builtins.bytes: | | maketrans(frm, to, /) | Return a translation table useable for the bytes or bytearray translate method. | | The returned table will be one where each byte in frm is mapped to the byte at | the same position in to. | | The bytes objects frm and to must be of the same length. | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __abs__(self, /) | abs(self) | | __and__(self, value, /) | Return self&value. | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __bool__(self, /) | True if self else False | | __copy__(...) | | __deepcopy__(...) | | __divmod__(self, value, /) | Return divmod(self, value). | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __format__(...) | NumPy array scalar formatter | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. ### class bytes_ | A byte string. | | When used in arrays, this type strips trailing null bytes. | | :Character code: ``'S'`` | :Alias: `numpy.string_` | | Method resolution order: | bytes_ | builtins.bytes | character | flexible | generic | builtins.object | | Methods defined here: | | __eq__(self, value, /) | Return self==value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __le__(self, value, /) | Return self<=value. | | __lt__(self, value, /) | Return self copy of B | | Return a copy of B with only its first character capitalized (ASCII) | and the rest lower-cased. | | center(self, width, fillchar=b' ', /) | Return a centered string of length width. | | Padding is done using the specified fill character. | | count(...) | B.count(sub[, start[, end]]) -> int | | Return the number of non-overlapping occurrences of subsection sub in | bytes B[start:end]. Optional arguments start and end are interpreted | as in slice notation. | | decode(self, /, encoding='utf-8', errors='strict') | Decode the bytes using the codec registered for encoding. | | encoding | The encoding with which to decode the bytes. | errors | The error handling scheme to use for the handling of decoding errors. | The default is 'strict' meaning that decoding errors raise a | UnicodeDecodeError. Other possible values are 'ignore' and 'replace' | as well as any other name registered with codecs.register_error that | can handle UnicodeDecodeErrors. | | endswith(...) | B.endswith(suffix[, start[, end]]) -> bool | | Return True if B ends with the specified suffix, False otherwise. | With optional start, test B beginning at that position. | With optional end, stop comparing B at that position. | suffix can also be a tuple of bytes to try. | | expandtabs(self, /, tabsize=8) | Return a copy where all tab characters are expanded using spaces. | | If tabsize is not given, a tab size of 8 characters is assumed. | | find(...) | B.find(sub[, start[, end]]) -> int | | Return the lowest index in B where subsection sub is found, | such that sub is contained within B[start,end]. Optional | arguments start and end are interpreted as in slice notation. | | Return -1 on failure. | | hex(...) | Create a string of hexadecimal numbers from a bytes object. | | sep | An optional single character or byte to separate hex bytes. | bytes_per_sep | How many bytes between separators. Positive values count from the | right, negative values count from the left. | | Example: | >>> value = b'\xb9\x01\xef' | >>> value.hex() | 'b901ef' | >>> value.hex(':') | 'b9:01:ef' | >>> value.hex(':', 2) | 'b9:01ef' | >>> value.hex(':', -2) | 'b901:ef' | | index(...) | B.index(sub[, start[, end]]) -> int | | Return the lowest index in B where subsection sub is found, | such that sub is contained within B[start,end]. Optional | arguments start and end are interpreted as in slice notation. | | Raises ValueError when the subsection is not found. | | isalnum(...) | B.isalnum() -> bool | | Return True if all characters in B are alphanumeric | and there is at least one character in B, False otherwise. | | isalpha(...) | B.isalpha() -> bool | | Return True if all characters in B are alphabetic | and there is at least one character in B, False otherwise. | | isascii(...) | B.isascii() -> bool | | Return True if B is empty or all characters in B are ASCII, | False otherwise. | | isdigit(...) | B.isdigit() -> bool | | Return True if all characters in B are digits | and there is at least one character in B, False otherwise. | | islower(...) | B.islower() -> bool | | Return True if all cased characters in B are lowercase and there is | at least one cased character in B, False otherwise. | | isspace(...) | B.isspace() -> bool | | Return True if all characters in B are whitespace | and there is at least one character in B, False otherwise. | | istitle(...) | B.istitle() -> bool | | Return True if B is a titlecased string and there is at least one | character in B, i.e. uppercase characters may only follow uncased | characters and lowercase characters only cased ones. Return False | otherwise. | | isupper(...) | B.isupper() -> bool | | Return True if all cased characters in B are uppercase and there is | at least one cased character in B, False otherwise. | | join(self, iterable_of_bytes, /) | Concatenate any number of bytes objects. | | The bytes whose method is called is inserted in between each pair. | | The result is returned as a new bytes object. | | Example: b'.'.join([b'ab', b'pq', b'rs']) -> b'ab.pq.rs'. | | ljust(self, width, fillchar=b' ', /) | Return a left-justified string of length width. | | Padding is done using the specified fill character. | | lower(...) | B.lower() -> copy of B | | Return a copy of B with all ASCII characters converted to lowercase. | | lstrip(self, bytes=None, /) | Strip leading bytes contained in the argument. | | If the argument is omitted or None, strip leading ASCII whitespace. | | partition(self, sep, /) | Partition the bytes into three parts using the given separator. | | This will search for the separator sep in the bytes. If the separator is found, | returns a 3-tuple containing the part before the separator, the separator | itself, and the part after it. | | If the separator is not found, returns a 3-tuple containing the original bytes | object and two empty bytes objects. | | removeprefix(self, prefix, /) | Return a bytes object with the given prefix string removed if present. | | If the bytes starts with the prefix string, return bytes[len(prefix):]. | Otherwise, return a copy of the original bytes. | | removesuffix(self, suffix, /) | Return a bytes object with the given suffix string removed if present. | | If the bytes ends with the suffix string and that suffix is not empty, | return bytes[:-len(prefix)]. Otherwise, return a copy of the original | bytes. | | replace(self, old, new, count=-1, /) | Return a copy with all occurrences of substring old replaced by new. | | count | Maximum number of occurrences to replace. | -1 (the default value) means replace all occurrences. | | If the optional argument count is given, only the first count occurrences are | replaced. | | rfind(...) | B.rfind(sub[, start[, end]]) -> int | | Return the highest index in B where subsection sub is found, | such that sub is contained within B[start,end]. Optional | arguments start and end are interpreted as in slice notation. | | Return -1 on failure. | | rindex(...) | B.rindex(sub[, start[, end]]) -> int | | Return the highest index in B where subsection sub is found, | such that sub is contained within B[start,end]. Optional | arguments start and end are interpreted as in slice notation. | | Raise ValueError when the subsection is not found. | | rjust(self, width, fillchar=b' ', /) | Return a right-justified string of length width. | | Padding is done using the specified fill character. | | rpartition(self, sep, /) | Partition the bytes into three parts using the given separator. | | This will search for the separator sep in the bytes, starting at the end. If | the separator is found, returns a 3-tuple containing the part before the | separator, the separator itself, and the part after it. | | If the separator is not found, returns a 3-tuple containing two empty bytes | objects and the original bytes object. | | rsplit(self, /, sep=None, maxsplit=-1) | Return a list of the sections in the bytes, using sep as the delimiter. | | sep | The delimiter according which to split the bytes. | None (the default value) means split on ASCII whitespace characters | (space, tab, return, newline, formfeed, vertical tab). | maxsplit | Maximum number of splits to do. | -1 (the default value) means no limit. | | Splitting is done starting at the end of the bytes and working to the front. | | rstrip(self, bytes=None, /) | Strip trailing bytes contained in the argument. | | If the argument is omitted or None, strip trailing ASCII whitespace. | | split(self, /, sep=None, maxsplit=-1) | Return a list of the sections in the bytes, using sep as the delimiter. | | sep | The delimiter according which to split the bytes. | None (the default value) means split on ASCII whitespace characters | (space, tab, return, newline, formfeed, vertical tab). | maxsplit | Maximum number of splits to do. | -1 (the default value) means no limit. | | splitlines(self, /, keepends=False) | Return a list of the lines in the bytes, breaking at line boundaries. | | Line breaks are not included in the resulting list unless keepends is given and | true. | | startswith(...) | B.startswith(prefix[, start[, end]]) -> bool | | Return True if B starts with the specified prefix, False otherwise. | With optional start, test B beginning at that position. | With optional end, stop comparing B at that position. | prefix can also be a tuple of bytes to try. | | strip(self, bytes=None, /) | Strip leading and trailing bytes contained in the argument. | | If the argument is omitted or None, strip leading and trailing ASCII whitespace. | | swapcase(...) | B.swapcase() -> copy of B | | Return a copy of B with uppercase ASCII characters converted | to lowercase ASCII and vice versa. | | title(...) | B.title() -> copy of B | | Return a titlecased version of B, i.e. ASCII words start with uppercase | characters, all remaining cased characters have lowercase. | | translate(self, table, /, delete=b'') | Return a copy with each character mapped by the given translation table. | | table | Translation table, which must be a bytes object of length 256. | | All characters occurring in the optional argument delete are removed. | The remaining characters are mapped through the given translation table. | | upper(...) | B.upper() -> copy of B | | Return a copy of B with all ASCII characters converted to uppercase. | | zfill(self, width, /) | Pad a numeric string with zeros on the left, to fill a field of the given width. | | The original string is never truncated. | | ---------------------------------------------------------------------- | Class methods inherited from builtins.bytes: | | fromhex(string, /) from builtins.type | Create a bytes object from a string of hexadecimal numbers. | | Spaces between two numbers are accepted. | Example: bytes.fromhex('B9 01EF') -> b'\\xb9\\x01\\xef'. | | ---------------------------------------------------------------------- | Static methods inherited from builtins.bytes: | | maketrans(frm, to, /) | Return a translation table useable for the bytes or bytearray translate method. | | The returned table will be one where each byte in frm is mapped to the byte at | the same position in to. | | The bytes objects frm and to must be of the same length. | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __abs__(self, /) | abs(self) | | __and__(self, value, /) | Return self&value. | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __bool__(self, /) | True if self else False | | __copy__(...) | | __deepcopy__(...) | | __divmod__(self, value, /) | Return divmod(self, value). | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __format__(...) | NumPy array scalar formatter | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. cdouble = class complex128(complexfloating, builtins.complex) | cdouble(real=0, imag=0) | | Complex number type composed of two double-precision floating-point | numbers, compatible with Python `complex`. | | :Character code: ``'D'`` | :Canonical name: `numpy.cdouble` | :Alias: `numpy.cfloat` | :Alias: `numpy.complex_` | :Alias on this platform (Linux x86_64): `numpy.complex128`: Complex number type composed of 2 64-bit-precision floating-point numbers. | | Method resolution order: | complex128 | complexfloating | inexact | number | generic | builtins.complex | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __bool__(self, /) | True if self else False | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __int__(self, /) | int(self) | | __le__(self, value, /) | Return self<=value. | | __lt__(self, value, /) | Return self>self. | | __rshift__(self, value, /) | Return self>>value. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. | | ---------------------------------------------------------------------- | Methods inherited from builtins.complex: | | __getattribute__(self, name, /) | Return getattr(self, name). | | __getnewargs__(self, /) cfloat = class complex128(complexfloating, builtins.complex) | cfloat(real=0, imag=0) | | Complex number type composed of two double-precision floating-point | numbers, compatible with Python `complex`. | | :Character code: ``'D'`` | :Canonical name: `numpy.cdouble` | :Alias: `numpy.cfloat` | :Alias: `numpy.complex_` | :Alias on this platform (Linux x86_64): `numpy.complex128`: Complex number type composed of 2 64-bit-precision floating-point numbers. | | Method resolution order: | complex128 | complexfloating | inexact | number | generic | builtins.complex | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __bool__(self, /) | True if self else False | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __int__(self, /) | int(self) | | __le__(self, value, /) | Return self<=value. | | __lt__(self, value, /) | Return self>self. | | __rshift__(self, value, /) | Return self>>value. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. | | ---------------------------------------------------------------------- | Methods inherited from builtins.complex: | | __getattribute__(self, name, /) | Return getattr(self, name). | | __getnewargs__(self, /) ### class character | Abstract base class of all character string scalar types. | | Method resolution order: | character | flexible | generic | builtins.object | | Methods inherited from generic: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __and__(self, value, /) | Return self&value. | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __bool__(self, /) | True if self else False | | __copy__(...) | | __deepcopy__(...) | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __format__(...) | NumPy array scalar formatter | | __ge__(self, value, /) | Return self>=value. | | __getitem__(self, key, /) | Return self[key]. | | __gt__(self, value, /) | Return self>value. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __le__(self, value, /) | Return self<=value. | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. | | ---------------------------------------------------------------------- | Data and other attributes inherited from generic: | | __hash__ = None ### class chararray | chararray(shape, itemsize=1, unicode=False, buffer=None, offset=0, strides=None, order='C') | | chararray(shape, itemsize=1, unicode=False, buffer=None, offset=0, | strides=None, order=None) | | Provides a convenient view on arrays of string and unicode values. | | .. note:: | The `chararray` class exists for backwards compatibility with | Numarray, it is not recommended for new development. Starting from numpy | 1.4, if one needs arrays of strings, it is recommended to use arrays of | `dtype` `object_`, `string_` or `unicode_`, and use the free functions | in the `numpy.char` module for fast vectorized string operations. | | Versus a regular NumPy array of type `str` or `unicode`, this | class adds the following functionality: | | 1) values automatically have whitespace removed from the end | when indexed | | 2) comparison operators automatically remove whitespace from the | end when comparing values | | 3) vectorized string operations are provided as methods | (e.g. `.endswith`) and infix operators (e.g. ``"+", "*", "%"``) | | chararrays should be created using `numpy.char.array` or | `numpy.char.asarray`, rather than this constructor directly. | | This constructor creates the array, using `buffer` (with `offset` | and `strides`) if it is not ``None``. If `buffer` is ``None``, then | constructs a new array with `strides` in "C order", unless both | ``len(shape) >= 2`` and ``order='F'``, in which case `strides` | is in "Fortran order". | | Methods | ------- | astype | argsort | copy | count | decode | dump | dumps | encode | endswith | expandtabs | fill | find | flatten | getfield | index | isalnum | isalpha | isdecimal | isdigit | islower | isnumeric | isspace | istitle | isupper | item | join | ljust | lower | lstrip | nonzero | put | ravel | repeat | replace | reshape | resize | rfind | rindex | rjust | rsplit | rstrip | searchsorted | setfield | setflags | sort | split | splitlines | squeeze | startswith | strip | swapaxes | swapcase | take | title | tofile | tolist | tostring | translate | transpose | upper | view | zfill | | Parameters | ---------- | shape : tuple | Shape of the array. | itemsize : int, optional | Length of each array element, in number of characters. Default is 1. | unicode : bool, optional | Are the array elements of type unicode (True) or string (False). | Default is False. | buffer : object exposing the buffer interface or str, optional | Memory address of the start of the array data. Default is None, | in which case a new array is created. | offset : int, optional | Fixed stride displacement from the beginning of an axis? | Default is 0. Needs to be >=0. | strides : array_like of ints, optional | Strides for the array (see `ndarray.strides` for full description). | Default is None. | order : {'C', 'F'}, optional | The order in which the array data is stored in memory: 'C' -> | "row major" order (the default), 'F' -> "column major" | (Fortran) order. | | Examples | -------- | >>> charar = np.chararray((3, 3)) | >>> charar[:] = 'a' | >>> charar | chararray([[b'a', b'a', b'a'], | [b'a', b'a', b'a'], | [b'a', b'a', b'a']], dtype='|S1') | | >>> charar = np.chararray(charar.shape, itemsize=5) | >>> charar[:] = 'abc' | >>> charar | chararray([[b'abc', b'abc', b'abc'], | [b'abc', b'abc', b'abc'], | [b'abc', b'abc', b'abc']], dtype='|S5') | | Method resolution order: | chararray | ndarray | builtins.object | | Methods defined here: | | __add__(self, other) | Return (self + other), that is string concatenation, | element-wise for a pair of array_likes of str or unicode. | | See Also | -------- | add | | __array_finalize__(self, obj) | None. | | __eq__(self, other) | Return (self == other) element-wise. | | See Also | -------- | equal | | __ge__(self, other) | Return (self >= other) element-wise. | | See Also | -------- | greater_equal | | __getitem__(self, obj) | Return self[key]. | | __gt__(self, other) | Return (self > other) element-wise. | | See Also | -------- | greater | | __le__(self, other) | Return (self <= other) element-wise. | | See Also | -------- | less_equal | | __lt__(self, other) | Return (self < other) element-wise. | | See Also | -------- | less | | __mod__(self, i) | Return (self % i), that is pre-Python 2.6 string formatting | (interpolation), element-wise for a pair of array_likes of `string_` | or `unicode_`. | | See Also | -------- | mod | | __mul__(self, i) | Return (self * i), that is string multiple concatenation, | element-wise. | | See Also | -------- | multiply | | __ne__(self, other) | Return (self != other) element-wise. | | See Also | -------- | not_equal | | __radd__(self, other) | Return (other + self), that is string concatenation, | element-wise for a pair of array_likes of `string_` or `unicode_`. | | See Also | -------- | add | | __rmod__(self, other) | Return value%self. | | __rmul__(self, i) | Return (self * i), that is string multiple concatenation, | element-wise. | | See Also | -------- | multiply | | argsort(self, axis=-1, kind=None, order=None) | a.argsort(axis=-1, kind=None, order=None) | | Returns the indices that would sort this array. | | Refer to `numpy.argsort` for full documentation. | | See Also | -------- | numpy.argsort : equivalent function | | capitalize(self) | Return a copy of `self` with only the first character of each element | capitalized. | | See Also | -------- | char.capitalize | | center(self, width, fillchar=' ') | Return a copy of `self` with its elements centered in a | string of length `width`. | | See Also | -------- | center | | count(self, sub, start=0, end=None) | Returns an array with the number of non-overlapping occurrences of | substring `sub` in the range [`start`, `end`]. | | See Also | -------- | char.count | | decode(self, encoding=None, errors=None) | Calls `str.decode` element-wise. | | See Also | -------- | char.decode | | encode(self, encoding=None, errors=None) | Calls `str.encode` element-wise. | | See Also | -------- | char.encode | | endswith(self, suffix, start=0, end=None) | Returns a boolean array which is `True` where the string element | in `self` ends with `suffix`, otherwise `False`. | | See Also | -------- | char.endswith | | expandtabs(self, tabsize=8) | Return a copy of each string element where all tab characters are | replaced by one or more spaces. | | See Also | -------- | char.expandtabs | | find(self, sub, start=0, end=None) | For each element, return the lowest index in the string where | substring `sub` is found. | | See Also | -------- | char.find | | index(self, sub, start=0, end=None) | Like `find`, but raises `ValueError` when the substring is not found. | | See Also | -------- | char.index | | isalnum(self) | Returns true for each element if all characters in the string | are alphanumeric and there is at least one character, false | otherwise. | | See Also | -------- | char.isalnum | | isalpha(self) | Returns true for each element if all characters in the string | are alphabetic and there is at least one character, false | otherwise. | | See Also | -------- | char.isalpha | | isdecimal(self) | For each element in `self`, return True if there are only | decimal characters in the element. | | See Also | -------- | char.isdecimal | | isdigit(self) | Returns true for each element if all characters in the string are | digits and there is at least one character, false otherwise. | | See Also | -------- | char.isdigit | | islower(self) | Returns true for each element if all cased characters in the | string are lowercase and there is at least one cased character, | false otherwise. | | See Also | -------- | char.islower | | isnumeric(self) | For each element in `self`, return True if there are only | numeric characters in the element. | | See Also | -------- | char.isnumeric | | isspace(self) | Returns true for each element if there are only whitespace | characters in the string and there is at least one character, | false otherwise. | | See Also | -------- | char.isspace | | istitle(self) | Returns true for each element if the element is a titlecased | string and there is at least one character, false otherwise. | | See Also | -------- | char.istitle | | isupper(self) | Returns true for each element if all cased characters in the | string are uppercase and there is at least one character, false | otherwise. | | See Also | -------- | char.isupper | | join(self, seq) | Return a string which is the concatenation of the strings in the | sequence `seq`. | | See Also | -------- | char.join | | ljust(self, width, fillchar=' ') | Return an array with the elements of `self` left-justified in a | string of length `width`. | | See Also | -------- | char.ljust | | lower(self) | Return an array with the elements of `self` converted to | lowercase. | | See Also | -------- | char.lower | | lstrip(self, chars=None) | For each element in `self`, return a copy with the leading characters | removed. | | See Also | -------- | char.lstrip | | partition(self, sep) | Partition each element in `self` around `sep`. | | See Also | -------- | partition | | replace(self, old, new, count=None) | For each element in `self`, return a copy of the string with all | occurrences of substring `old` replaced by `new`. | | See Also | -------- | char.replace | | rfind(self, sub, start=0, end=None) | For each element in `self`, return the highest index in the string | where substring `sub` is found, such that `sub` is contained | within [`start`, `end`]. | | See Also | -------- | char.rfind | | rindex(self, sub, start=0, end=None) | Like `rfind`, but raises `ValueError` when the substring `sub` is | not found. | | See Also | -------- | char.rindex | | rjust(self, width, fillchar=' ') | Return an array with the elements of `self` | right-justified in a string of length `width`. | | See Also | -------- | char.rjust | | rpartition(self, sep) | Partition each element in `self` around `sep`. | | See Also | -------- | rpartition | | rsplit(self, sep=None, maxsplit=None) | For each element in `self`, return a list of the words in | the string, using `sep` as the delimiter string. | | See Also | -------- | char.rsplit | | rstrip(self, chars=None) | For each element in `self`, return a copy with the trailing | characters removed. | | See Also | -------- | char.rstrip | | split(self, sep=None, maxsplit=None) | For each element in `self`, return a list of the words in the | string, using `sep` as the delimiter string. | | See Also | -------- | char.split | | splitlines(self, keepends=None) | For each element in `self`, return a list of the lines in the | element, breaking at line boundaries. | | See Also | -------- | char.splitlines | | startswith(self, prefix, start=0, end=None) | Returns a boolean array which is `True` where the string element | in `self` starts with `prefix`, otherwise `False`. | | See Also | -------- | char.startswith | | strip(self, chars=None) | For each element in `self`, return a copy with the leading and | trailing characters removed. | | See Also | -------- | char.strip | | swapcase(self) | For each element in `self`, return a copy of the string with | uppercase characters converted to lowercase and vice versa. | | See Also | -------- | char.swapcase | | title(self) | For each element in `self`, return a titlecased version of the | string: words start with uppercase characters, all remaining cased | characters are lowercase. | | See Also | -------- | char.title | | translate(self, table, deletechars=None) | For each element in `self`, return a copy of the string where | all characters occurring in the optional argument | `deletechars` are removed, and the remaining characters have | been mapped through the given translation table. | | See Also | -------- | char.translate | | upper(self) | Return an array with the elements of `self` converted to | uppercase. | | See Also | -------- | char.upper | | zfill(self, width) | Return the numeric string left-filled with zeros in a string of | length `width`. | | See Also | -------- | char.zfill | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(subtype, shape, itemsize=1, unicode=False, buffer=None, offset=0, strides=None, order='C') | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Data descriptors defined here: | | __dict__ | dictionary for instance variables (if defined) | | ---------------------------------------------------------------------- | Data and other attributes defined here: | | __hash__ = None | | ---------------------------------------------------------------------- | Methods inherited from ndarray: | | __abs__(self, /) | abs(self) | | __and__(self, value, /) | Return self&value. | | __array__(...) | a.__array__([dtype], /) -> reference if type unchanged, copy otherwise. | | Returns either a new reference to self if dtype is not given or a new array | of provided data type if dtype is different from the current dtype of the | array. | | __array_function__(...) | | __array_prepare__(...) | a.__array_prepare__(obj) -> Object of same type as ndarray object obj. | | __array_ufunc__(...) | | __array_wrap__(...) | a.__array_wrap__(obj) -> Object of same type as ndarray object a. | | __bool__(self, /) | True if self else False | | __complex__(...) | | __contains__(self, key, /) | Return key in self. | | __copy__(...) | a.__copy__() | | Used if :func:`copy.copy` is called on an array. Returns a copy of the array. | | Equivalent to ``a.copy(order='K')``. | | __deepcopy__(...) | a.__deepcopy__(memo, /) -> Deep copy of array. | | Used if :func:`copy.deepcopy` is called on an array. | | __delitem__(self, key, /) | Delete self[key]. | | __divmod__(self, value, /) | Return divmod(self, value). | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __format__(...) | Default object formatter. | | __iadd__(self, value, /) | Return self+=value. | | __iand__(self, value, /) | Return self&=value. | | __ifloordiv__(self, value, /) | Return self//=value. | | __ilshift__(self, value, /) | Return self<<=value. | | __imatmul__(self, value, /) | Return self@=value. | | __imod__(self, value, /) | Return self%=value. | | __imul__(self, value, /) | Return self*=value. | | __index__(self, /) | Return self converted to an integer, if self is suitable for use as an index into a list. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __ior__(self, value, /) | Return self|=value. | | __ipow__(self, value, /) | Return self**=value. | | __irshift__(self, value, /) | Return self>>=value. | | __isub__(self, value, /) | Return self-=value. | | __iter__(self, /) | Implement iter(self). | | __itruediv__(self, value, /) | Return self/=value. | | __ixor__(self, value, /) | Return self^=value. | | __len__(self, /) | Return len(self). | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __setitem__(self, key, value, /) | Set self[key] to value. | | __setstate__(...) | a.__setstate__(state, /) | | For unpickling. | | The `state` argument must be a sequence that contains the following | elements: | | Parameters | ---------- | version : int | optional pickle version. If omitted defaults to 0. | shape : tuple | dtype : data-type | isFortran : bool | rawdata : string or list | a binary string with the data (or a list if 'a' is an object array) | | __sizeof__(...) | Size of object in memory, in bytes. | | __str__(self, /) | Return str(self). | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | all(...) | a.all(axis=None, out=None, keepdims=False, *, where=True) | | Returns True if all elements evaluate to True. | | Refer to `numpy.all` for full documentation. | | See Also | -------- | numpy.all : equivalent function | | any(...) | a.any(axis=None, out=None, keepdims=False, *, where=True) | | Returns True if any of the elements of `a` evaluate to True. | | Refer to `numpy.any` for full documentation. | | See Also | -------- | numpy.any : equivalent function | | argmax(...) | a.argmax(axis=None, out=None) | | Return indices of the maximum values along the given axis. | | Refer to `numpy.argmax` for full documentation. | | See Also | -------- | numpy.argmax : equivalent function | | argmin(...) | a.argmin(axis=None, out=None) | | Return indices of the minimum values along the given axis. | | Refer to `numpy.argmin` for detailed documentation. | | See Also | -------- | numpy.argmin : equivalent function | | argpartition(...) | a.argpartition(kth, axis=-1, kind='introselect', order=None) | | Returns the indices that would partition this array. | | Refer to `numpy.argpartition` for full documentation. | | .. versionadded:: 1.8.0 | | See Also | -------- | numpy.argpartition : equivalent function | | astype(...) | a.astype(dtype, order='K', casting='unsafe', subok=True, copy=True) | | Copy of the array, cast to a specified type. | | Parameters | ---------- | dtype : str or dtype | Typecode or data-type to which the array is cast. | order : {'C', 'F', 'A', 'K'}, optional | Controls the memory layout order of the result. | 'C' means C order, 'F' means Fortran order, 'A' | means 'F' order if all the arrays are Fortran contiguous, | 'C' order otherwise, and 'K' means as close to the | order the array elements appear in memory as possible. | Default is 'K'. | casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional | Controls what kind of data casting may occur. Defaults to 'unsafe' | for backwards compatibility. | | * 'no' means the data types should not be cast at all. | * 'equiv' means only byte-order changes are allowed. | * 'safe' means only casts which can preserve values are allowed. | * 'same_kind' means only safe casts or casts within a kind, | like float64 to float32, are allowed. | * 'unsafe' means any data conversions may be done. | subok : bool, optional | If True, then sub-classes will be passed-through (default), otherwise | the returned array will be forced to be a base-class array. | copy : bool, optional | By default, astype always returns a newly allocated array. If this | is set to false, and the `dtype`, `order`, and `subok` | requirements are satisfied, the input array is returned instead | of a copy. | | Returns | ------- | arr_t : ndarray | Unless `copy` is False and the other conditions for returning the input | array are satisfied (see description for `copy` input parameter), `arr_t` | is a new array of the same shape as the input array, with dtype, order | given by `dtype`, `order`. | | Notes | ----- | .. versionchanged:: 1.17.0 | Casting between a simple data type and a structured one is possible only | for "unsafe" casting. Casting to multiple fields is allowed, but | casting from multiple fields is not. | | .. versionchanged:: 1.9.0 | Casting from numeric to string types in 'safe' casting mode requires | that the string dtype length is long enough to store the max | integer/float value converted. | | Raises | ------ | ComplexWarning | When casting from complex to float or int. To avoid this, | one should use ``a.real.astype(t)``. | | Examples | -------- | >>> x = np.array([1, 2, 2.5]) | >>> x | array([1. , 2. , 2.5]) | | >>> x.astype(int) | array([1, 2, 2]) | | byteswap(...) | a.byteswap(inplace=False) | | Swap the bytes of the array elements | | Toggle between low-endian and big-endian data representation by | returning a byteswapped array, optionally swapped in-place. | Arrays of byte-strings are not swapped. The real and imaginary | parts of a complex number are swapped individually. | | Parameters | ---------- | inplace : bool, optional | If ``True``, swap bytes in-place, default is ``False``. | | Returns | ------- | out : ndarray | The byteswapped array. If `inplace` is ``True``, this is | a view to self. | | Examples | -------- | >>> A = np.array([1, 256, 8755], dtype=np.int16) | >>> list(map(hex, A)) | ['0x1', '0x100', '0x2233'] | >>> A.byteswap(inplace=True) | array([ 256, 1, 13090], dtype=int16) | >>> list(map(hex, A)) | ['0x100', '0x1', '0x3322'] | | Arrays of byte-strings are not swapped | | >>> A = np.array([b'ceg', b'fac']) | >>> A.byteswap() | array([b'ceg', b'fac'], dtype='|S3') | | ``A.newbyteorder().byteswap()`` produces an array with the same values | but different representation in memory | | >>> A = np.array([1, 2, 3]) | >>> A.view(np.uint8) | array([1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, | 0, 0], dtype=uint8) | >>> A.newbyteorder().byteswap(inplace=True) | array([1, 2, 3]) | >>> A.view(np.uint8) | array([0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, | 0, 3], dtype=uint8) | | choose(...) | a.choose(choices, out=None, mode='raise') | | Use an index array to construct a new array from a set of choices. | | Refer to `numpy.choose` for full documentation. | | See Also | -------- | numpy.choose : equivalent function | | clip(...) | a.clip(min=None, max=None, out=None, **kwargs) | | Return an array whose values are limited to ``[min, max]``. | One of max or min must be given. | | Refer to `numpy.clip` for full documentation. | | See Also | -------- | numpy.clip : equivalent function | | compress(...) | a.compress(condition, axis=None, out=None) | | Return selected slices of this array along given axis. | | Refer to `numpy.compress` for full documentation. | | See Also | -------- | numpy.compress : equivalent function | | conj(...) | a.conj() | | Complex-conjugate all elements. | | Refer to `numpy.conjugate` for full documentation. | | See Also | -------- | numpy.conjugate : equivalent function | | conjugate(...) | a.conjugate() | | Return the complex conjugate, element-wise. | | Refer to `numpy.conjugate` for full documentation. | | See Also | -------- | numpy.conjugate : equivalent function | | copy(...) | a.copy(order='C') | | Return a copy of the array. | | Parameters | ---------- | order : {'C', 'F', 'A', 'K'}, optional | Controls the memory layout of the copy. 'C' means C-order, | 'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous, | 'C' otherwise. 'K' means match the layout of `a` as closely | as possible. (Note that this function and :func:`numpy.copy` are very | similar but have different default values for their order= | arguments, and this function always passes sub-classes through.) | | See also | -------- | numpy.copy : Similar function with different default behavior | numpy.copyto | | Notes | ----- | This function is the preferred method for creating an array copy. The | function :func:`numpy.copy` is similar, but it defaults to using order 'K', | and will not pass sub-classes through by default. | | Examples | -------- | >>> x = np.array([[1,2,3],[4,5,6]], order='F') | | >>> y = x.copy() | | >>> [x.fill(0)](https://www.chedong.com/phpMan.php/man/x.fill/0/markdown) | | >>> x | array([[0, 0, 0], | [0, 0, 0]]) | | >>> y | array([[1, 2, 3], | [4, 5, 6]]) | | >>> y.flags['C_CONTIGUOUS'] | True | | cumprod(...) | a.cumprod(axis=None, dtype=None, out=None) | | Return the cumulative product of the elements along the given axis. | | Refer to `numpy.cumprod` for full documentation. | | See Also | -------- | numpy.cumprod : equivalent function | | cumsum(...) | a.cumsum(axis=None, dtype=None, out=None) | | Return the cumulative sum of the elements along the given axis. | | Refer to `numpy.cumsum` for full documentation. | | See Also | -------- | numpy.cumsum : equivalent function | | diagonal(...) | a.diagonal(offset=0, axis1=0, axis2=1) | | Return specified diagonals. In NumPy 1.9 the returned array is a | read-only view instead of a copy as in previous NumPy versions. In | a future version the read-only restriction will be removed. | | Refer to :func:`numpy.diagonal` for full documentation. | | See Also | -------- | numpy.diagonal : equivalent function | | dot(...) | a.dot(b, out=None) | | Dot product of two arrays. | | Refer to `numpy.dot` for full documentation. | | See Also | -------- | numpy.dot : equivalent function | | Examples | -------- | >>> a = [np.eye(2)](https://www.chedong.com/phpMan.php/man/np.eye/2/markdown) | >>> b = np.ones((2, 2)) * 2 | >>> a.dot(b) | array([[2., 2.], | [2., 2.]]) | | This array method can be conveniently chained: | | >>> a.dot(b).dot(b) | array([[8., 8.], | [8., 8.]]) | | dump(...) | a.dump(file) | | Dump a pickle of the array to the specified file. | The array can be read back with pickle.load or numpy.load. | | Parameters | ---------- | file : str or Path | A string naming the dump file. | | .. versionchanged:: 1.17.0 | `pathlib.Path` objects are now accepted. | | dumps(...) | a.dumps() | | Returns the pickle of the array as a string. | pickle.loads or numpy.loads will convert the string back to an array. | | Parameters | ---------- | None | | fill(...) | a.fill(value) | | Fill the array with a scalar value. | | Parameters | ---------- | value : scalar | All elements of `a` will be assigned this value. | | Examples | -------- | >>> a = np.array([1, 2]) | >>> [a.fill(0)](https://www.chedong.com/phpMan.php/man/a.fill/0/markdown) | >>> a | array([0, 0]) | >>> a = [np.empty(2)](https://www.chedong.com/phpMan.php/man/np.empty/2/markdown) | >>> [a.fill(1)](https://www.chedong.com/phpMan.php/man/a.fill/1/markdown) | >>> a | array([1., 1.]) | | flatten(...) | a.flatten(order='C') | | Return a copy of the array collapsed into one dimension. | | Parameters | ---------- | order : {'C', 'F', 'A', 'K'}, optional | 'C' means to flatten in row-major (C-style) order. | 'F' means to flatten in column-major (Fortran- | style) order. 'A' means to flatten in column-major | order if `a` is Fortran *contiguous* in memory, | row-major order otherwise. 'K' means to flatten | `a` in the order the elements occur in memory. | The default is 'C'. | | Returns | ------- | y : ndarray | A copy of the input array, flattened to one dimension. | | See Also | -------- | ravel : Return a flattened array. | flat : A 1-D flat iterator over the array. | | Examples | -------- | >>> a = np.array([[1,2], [3,4]]) | >>> a.flatten() | array([1, 2, 3, 4]) | >>> a.flatten('F') | array([1, 3, 2, 4]) | | getfield(...) | a.getfield(dtype, offset=0) | | Returns a field of the given array as a certain type. | | A field is a view of the array data with a given data-type. The values in | the view are determined by the given type and the offset into the current | array in bytes. The offset needs to be such that the view dtype fits in the | array dtype; for example an array of dtype complex128 has 16-byte elements. | If taking a view with a 32-bit integer (4 bytes), the offset needs to be | between 0 and 12 bytes. | | Parameters | ---------- | dtype : str or dtype | The data type of the view. The dtype size of the view can not be larger | than that of the array itself. | offset : int | Number of bytes to skip before beginning the element view. | | Examples | -------- | >>> x = np.diag([1.+1.j]*2) | >>> x[1, 1] = 2 + 4.j | >>> x | array([[1.+1.j, 0.+0.j], | [0.+0.j, 2.+4.j]]) | >>> x.getfield(np.float64) | array([[1., 0.], | [0., 2.]]) | | By choosing an offset of 8 bytes we can select the complex part of the | array for our view: | | >>> x.getfield(np.float64, offset=8) | array([[1., 0.], | [0., 4.]]) | | item(...) | a.item(*args) | | Copy an element of an array to a standard Python scalar and return it. | | Parameters | ---------- | \*args : Arguments (variable number and type) | | * none: in this case, the method only works for arrays | with one element (`a.size == 1`), which element is | copied into a standard Python scalar object and returned. | | * int_type: this argument is interpreted as a flat index into | the array, specifying which element to copy and return. | | * tuple of int_types: functions as does a single int_type argument, | except that the argument is interpreted as an nd-index into the | array. | | Returns | ------- | z : Standard Python scalar object | A copy of the specified element of the array as a suitable | Python scalar | | Notes | ----- | When the data type of `a` is longdouble or clongdouble, item() returns | a scalar array object because there is no available Python scalar that | would not lose information. Void arrays return a buffer object for item(), | unless fields are defined, in which case a tuple is returned. | | `item` is very similar to a[args], except, instead of an array scalar, | a standard Python scalar is returned. This can be useful for speeding up | access to elements of the array and doing arithmetic on elements of the | array using Python's optimized math. | | Examples | -------- | >>> [np.random.seed(123)](https://www.chedong.com/phpMan.php/man/np.random.seed/123/markdown) | >>> x = np.random.randint(9, size=(3, 3)) | >>> x | array([[2, 2, 6], | [1, 3, 6], | [1, 0, 1]]) | >>> [x.item(3)](https://www.chedong.com/phpMan.php/man/x.item/3/markdown) | 1 | >>> [x.item(7)](https://www.chedong.com/phpMan.php/man/x.item/7/markdown) | 0 | >>> x.item((0, 1)) | 2 | >>> x.item((2, 2)) | 1 | | itemset(...) | a.itemset(*args) | | Insert scalar into an array (scalar is cast to array's dtype, if possible) | | There must be at least 1 argument, and define the last argument | as *item*. Then, ``a.itemset(*args)`` is equivalent to but faster | than ``a[args] = item``. The item should be a scalar value and `args` | must select a single item in the array `a`. | | Parameters | ---------- | \*args : Arguments | If one argument: a scalar, only used in case `a` is of size 1. | If two arguments: the last argument is the value to be set | and must be a scalar, the first argument specifies a single array | element location. It is either an int or a tuple. | | Notes | ----- | Compared to indexing syntax, `itemset` provides some speed increase | for placing a scalar into a particular location in an `ndarray`, | if you must do this. However, generally this is discouraged: | among other problems, it complicates the appearance of the code. | Also, when using `itemset` (and `item`) inside a loop, be sure | to assign the methods to a local variable to avoid the attribute | look-up at each loop iteration. | | Examples | -------- | >>> [np.random.seed(123)](https://www.chedong.com/phpMan.php/man/np.random.seed/123/markdown) | >>> x = np.random.randint(9, size=(3, 3)) | >>> x | array([[2, 2, 6], | [1, 3, 6], | [1, 0, 1]]) | >>> x.itemset(4, 0) | >>> x.itemset((2, 2), 9) | >>> x | array([[2, 2, 6], | [1, 0, 6], | [1, 0, 9]]) | | max(...) | a.max(axis=None, out=None, keepdims=False, initial=, where=True) | | Return the maximum along a given axis. | | Refer to `numpy.amax` for full documentation. | | See Also | -------- | numpy.amax : equivalent function | | mean(...) | a.mean(axis=None, dtype=None, out=None, keepdims=False, *, where=True) | | Returns the average of the array elements along given axis. | | Refer to `numpy.mean` for full documentation. | | See Also | -------- | numpy.mean : equivalent function | | min(...) | a.min(axis=None, out=None, keepdims=False, initial=, where=True) | | Return the minimum along a given axis. | | Refer to `numpy.amin` for full documentation. | | See Also | -------- | numpy.amin : equivalent function | | newbyteorder(...) | arr.newbyteorder(new_order='S', /) | | Return the array with the same data viewed with a different byte order. | | Equivalent to:: | | arr.view([arr.dtype.newbytorder(new_order)](https://www.chedong.com/phpMan.php/man/arr.dtype.newbytorder/neworder/markdown)) | | Changes are also made in all fields and sub-arrays of the array data | type. | | | | Parameters | ---------- | new_order : string, optional | Byte order to force; a value from the byte order specifications | below. `new_order` codes can be any of: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order, equivalent to `sys.byteorder` | * {'|', 'I'} - ignore (no change to byte order) | | The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_arr : array | New array object with the dtype reflecting given change to the | byte order. | | nonzero(...) | a.nonzero() | | Return the indices of the elements that are non-zero. | | Refer to `numpy.nonzero` for full documentation. | | See Also | -------- | numpy.nonzero : equivalent function | | prod(...) | a.prod(axis=None, dtype=None, out=None, keepdims=False, initial=1, where=True) | | Return the product of the array elements over the given axis | | Refer to `numpy.prod` for full documentation. | | See Also | -------- | numpy.prod : equivalent function | | ptp(...) | a.ptp(axis=None, out=None, keepdims=False) | | Peak to peak (maximum - minimum) value along a given axis. | | Refer to `numpy.ptp` for full documentation. | | See Also | -------- | numpy.ptp : equivalent function | | put(...) | a.put(indices, values, mode='raise') | | Set ``a.flat[n] = values[n]`` for all `n` in indices. | | Refer to `numpy.put` for full documentation. | | See Also | -------- | numpy.put : equivalent function | | ravel(...) | a.ravel([order]) | | Return a flattened array. | | Refer to `numpy.ravel` for full documentation. | | See Also | -------- | numpy.ravel : equivalent function | | ndarray.flat : a flat iterator on the array. | | repeat(...) | a.repeat(repeats, axis=None) | | Repeat elements of an array. | | Refer to `numpy.repeat` for full documentation. | | See Also | -------- | numpy.repeat : equivalent function | | reshape(...) | a.reshape(shape, order='C') | | Returns an array containing the same data with a new shape. | | Refer to `numpy.reshape` for full documentation. | | See Also | -------- | numpy.reshape : equivalent function | | Notes | ----- | Unlike the free function `numpy.reshape`, this method on `ndarray` allows | the elements of the shape parameter to be passed in as separate arguments. | For example, ``a.reshape(10, 11)`` is equivalent to | ``a.reshape((10, 11))``. | | resize(...) | a.resize(new_shape, refcheck=True) | | Change shape and size of array in-place. | | Parameters | ---------- | new_shape : tuple of ints, or `n` ints | Shape of resized array. | refcheck : bool, optional | If False, reference count will not be checked. Default is True. | | Returns | ------- | None | | Raises | ------ | ValueError | If `a` does not own its own data or references or views to it exist, | and the data memory must be changed. | PyPy only: will always raise if the data memory must be changed, since | there is no reliable way to determine if references or views to it | exist. | | SystemError | If the `order` keyword argument is specified. This behaviour is a | bug in NumPy. | | See Also | -------- | resize : Return a new array with the specified shape. | | Notes | ----- | This reallocates space for the data area if necessary. | | Only contiguous arrays (data elements consecutive in memory) can be | resized. | | The purpose of the reference count check is to make sure you | do not use this array as a buffer for another Python object and then | reallocate the memory. However, reference counts can increase in | other ways so if you are sure that you have not shared the memory | for this array with another Python object, then you may safely set | `refcheck` to False. | | Examples | -------- | Shrinking an array: array is flattened (in the order that the data are | stored in memory), resized, and reshaped: | | >>> a = np.array([[0, 1], [2, 3]], order='C') | >>> a.resize((2, 1)) | >>> a | array([[0], | [1]]) | | >>> a = np.array([[0, 1], [2, 3]], order='F') | >>> a.resize((2, 1)) | >>> a | array([[0], | [2]]) | | Enlarging an array: as above, but missing entries are filled with zeros: | | >>> b = np.array([[0, 1], [2, 3]]) | >>> b.resize(2, 3) # new_shape parameter doesn't have to be a tuple | >>> b | array([[0, 1, 2], | [3, 0, 0]]) | | Referencing an array prevents resizing... | | >>> c = a | >>> a.resize((1, 1)) | Traceback (most recent call last): | ... | ValueError: cannot resize an array that references or is referenced ... | | Unless `refcheck` is False: | | >>> a.resize((1, 1), refcheck=False) | >>> a | array([[0]]) | >>> c | array([[0]]) | | round(...) | a.round(decimals=0, out=None) | | Return `a` with each element rounded to the given number of decimals. | | Refer to `numpy.around` for full documentation. | | See Also | -------- | numpy.around : equivalent function | | searchsorted(...) | a.searchsorted(v, side='left', sorter=None) | | Find indices where elements of v should be inserted in a to maintain order. | | For full documentation, see `numpy.searchsorted` | | See Also | -------- | numpy.searchsorted : equivalent function | | setfield(...) | a.setfield(val, dtype, offset=0) | | Put a value into a specified place in a field defined by a data-type. | | Place `val` into `a`'s field defined by `dtype` and beginning `offset` | bytes into the field. | | Parameters | ---------- | val : object | Value to be placed in field. | dtype : dtype object | Data-type of the field in which to place `val`. | offset : int, optional | The number of bytes into the field at which to place `val`. | | Returns | ------- | None | | See Also | -------- | getfield | | Examples | -------- | >>> x = [np.eye(3)](https://www.chedong.com/phpMan.php/man/np.eye/3/markdown) | >>> x.getfield(np.float64) | array([[1., 0., 0.], | [0., 1., 0.], | [0., 0., 1.]]) | >>> x.setfield(3, np.int32) | >>> x.getfield(np.int32) | array([[3, 3, 3], | [3, 3, 3], | [3, 3, 3]], dtype=int32) | >>> x | array([[1.0e+000, 1.5e-323, 1.5e-323], | [1.5e-323, 1.0e+000, 1.5e-323], | [1.5e-323, 1.5e-323, 1.0e+000]]) | >>> x.setfield([np.eye(3)](https://www.chedong.com/phpMan.php/man/np.eye/3/markdown), np.int32) | >>> x | array([[1., 0., 0.], | [0., 1., 0.], | [0., 0., 1.]]) | | setflags(...) | a.setflags(write=None, align=None, uic=None) | | Set array flags WRITEABLE, ALIGNED, (WRITEBACKIFCOPY and UPDATEIFCOPY), | respectively. | | These Boolean-valued flags affect how numpy interprets the memory | area used by `a` (see Notes below). The ALIGNED flag can only | be set to True if the data is actually aligned according to the type. | The WRITEBACKIFCOPY and (deprecated) UPDATEIFCOPY flags can never be set | to True. The flag WRITEABLE can only be set to True if the array owns its | own memory, or the ultimate owner of the memory exposes a writeable buffer | interface, or is a string. (The exception for string is made so that | unpickling can be done without copying memory.) | | Parameters | ---------- | write : bool, optional | Describes whether or not `a` can be written to. | align : bool, optional | Describes whether or not `a` is aligned properly for its type. | uic : bool, optional | Describes whether or not `a` is a copy of another "base" array. | | Notes | ----- | Array flags provide information about how the memory area used | for the array is to be interpreted. There are 7 Boolean flags | in use, only four of which can be changed by the user: | WRITEBACKIFCOPY, UPDATEIFCOPY, WRITEABLE, and ALIGNED. | | WRITEABLE (W) the data area can be written to; | | ALIGNED (A) the data and strides are aligned appropriately for the hardware | (as determined by the compiler); | | UPDATEIFCOPY (U) (deprecated), replaced by WRITEBACKIFCOPY; | | WRITEBACKIFCOPY (X) this array is a copy of some other array (referenced | by .base). When the C-API function PyArray_ResolveWritebackIfCopy is | called, the base array will be updated with the contents of this array. | | All flags can be accessed using the single (upper case) letter as well | as the full name. | | Examples | -------- | >>> y = np.array([[3, 1, 7], | ... [2, 0, 0], | ... [8, 5, 9]]) | >>> y | array([[3, 1, 7], | [2, 0, 0], | [8, 5, 9]]) | >>> y.flags | C_CONTIGUOUS : True | F_CONTIGUOUS : False | OWNDATA : True | WRITEABLE : True | ALIGNED : True | WRITEBACKIFCOPY : False | UPDATEIFCOPY : False | >>> y.setflags(write=0, align=0) | >>> y.flags | C_CONTIGUOUS : True | F_CONTIGUOUS : False | OWNDATA : True | WRITEABLE : False | ALIGNED : False | WRITEBACKIFCOPY : False | UPDATEIFCOPY : False | >>> y.setflags(uic=1) | Traceback (most recent call last): | File "", line 1, in | ValueError: cannot set WRITEBACKIFCOPY flag to True | | sort(...) | a.sort(axis=-1, kind=None, order=None) | | Sort an array in-place. Refer to `numpy.sort` for full documentation. | | Parameters | ---------- | axis : int, optional | Axis along which to sort. Default is -1, which means sort along the | last axis. | kind : {'quicksort', 'mergesort', 'heapsort', 'stable'}, optional | Sorting algorithm. The default is 'quicksort'. Note that both 'stable' | and 'mergesort' use timsort under the covers and, in general, the | actual implementation will vary with datatype. The 'mergesort' option | is retained for backwards compatibility. | | .. versionchanged:: 1.15.0 | The 'stable' option was added. | | order : str or list of str, optional | When `a` is an array with fields defined, this argument specifies | which fields to compare first, second, etc. A single field can | be specified as a string, and not all fields need be specified, | but unspecified fields will still be used, in the order in which | they come up in the dtype, to break ties. | | See Also | -------- | numpy.sort : Return a sorted copy of an array. | numpy.argsort : Indirect sort. | numpy.lexsort : Indirect stable sort on multiple keys. | numpy.searchsorted : Find elements in sorted array. | numpy.partition: Partial sort. | | Notes | ----- | See `numpy.sort` for notes on the different sorting algorithms. | | Examples | -------- | >>> a = np.array([[1,4], [3,1]]) | >>> a.sort(axis=1) | >>> a | array([[1, 4], | [1, 3]]) | >>> a.sort(axis=0) | >>> a | array([[1, 3], | [1, 4]]) | | Use the `order` keyword to specify a field to use when sorting a | structured array: | | >>> a = np.array([('a', 2), ('c', 1)], dtype=[('x', 'S1'), ('y', int)]) | >>> a.sort(order='y') | >>> a | array([(b'c', 1), (b'a', 2)], | dtype=[('x', 'S1'), ('y', '>> x = np.array([[0, 1], [2, 3]], dtype='>> x.tobytes() | b'\x00\x00\x01\x00\x02\x00\x03\x00' | >>> x.tobytes('C') == x.tobytes() | True | >>> x.tobytes('F') | b'\x00\x00\x02\x00\x01\x00\x03\x00' | | tofile(...) | a.tofile(fid, sep="", format="%s") | | Write array to a file as text or binary (default). | | Data is always written in 'C' order, independent of the order of `a`. | The data produced by this method can be recovered using the function | fromfile(). | | Parameters | ---------- | fid : file or str or Path | An open file object, or a string containing a filename. | | .. versionchanged:: 1.17.0 | `pathlib.Path` objects are now accepted. | | sep : str | Separator between array items for text output. | If "" (empty), a binary file is written, equivalent to | ``file.write(a.tobytes())``. | format : str | Format string for text file output. | Each entry in the array is formatted to text by first converting | it to the closest Python type, and then using "format" % item. | | Notes | ----- | This is a convenience function for quick storage of array data. | Information on endianness and precision is lost, so this method is not a | good choice for files intended to archive data or transport data between | machines with different endianness. Some of these problems can be overcome | by outputting the data as text files, at the expense of speed and file | size. | | When fid is a file object, array contents are directly written to the | file, bypassing the file object's ``write`` method. As a result, tofile | cannot be used with files objects supporting compression (e.g., GzipFile) | or file-like objects that do not support ``fileno()`` (e.g., BytesIO). | | tolist(...) | a.tolist() | | Return the array as an ``a.ndim``-levels deep nested list of Python scalars. | | Return a copy of the array data as a (nested) Python list. | Data items are converted to the nearest compatible builtin Python type, via | the `~numpy.ndarray.item` function. | | If ``a.ndim`` is 0, then since the depth of the nested list is 0, it will | not be a list at all, but a simple Python scalar. | | Parameters | ---------- | none | | Returns | ------- | y : object, or list of object, or list of list of object, or ... | The possibly nested list of array elements. | | Notes | ----- | The array may be recreated via ``a = np.array(a.tolist())``, although this | may sometimes lose precision. | | Examples | -------- | For a 1D array, ``a.tolist()`` is almost the same as ``list(a)``, | except that ``tolist`` changes numpy scalars to Python scalars: | | >>> a = np.uint32([1, 2]) | >>> a_list = list(a) | >>> a_list | [1, 2] | >>> type(a_list[0]) | | >>> a_tolist = a.tolist() | >>> a_tolist | [1, 2] | >>> type(a_tolist[0]) | | | Additionally, for a 2D array, ``tolist`` applies recursively: | | >>> a = np.array([[1, 2], [3, 4]]) | >>> list(a) | [array([1, 2]), array([3, 4])] | >>> a.tolist() | [[1, 2], [3, 4]] | | The base case for this recursion is a 0D array: | | >>> a = [np.array(1)](https://www.chedong.com/phpMan.php/man/np.array/1/markdown) | >>> list(a) | Traceback (most recent call last): | ... | TypeError: iteration over a 0-d array | >>> a.tolist() | 1 | | tostring(...) | a.tostring(order='C') | | A compatibility alias for `tobytes`, with exactly the same behavior. | | Despite its name, it returns `bytes` not `str`\ s. | | .. deprecated:: 1.19.0 | | trace(...) | a.trace(offset=0, axis1=0, axis2=1, dtype=None, out=None) | | Return the sum along diagonals of the array. | | Refer to `numpy.trace` for full documentation. | | See Also | -------- | numpy.trace : equivalent function | | transpose(...) | a.transpose(*axes) | | Returns a view of the array with axes transposed. | | For a 1-D array this has no effect, as a transposed vector is simply the | same vector. To convert a 1-D array into a 2D column vector, an additional | dimension must be added. `np.atleast2d(a).T` achieves this, as does | `a[:, np.newaxis]`. | For a 2-D array, this is a standard matrix transpose. | For an n-D array, if axes are given, their order indicates how the | axes are permuted (see Examples). If axes are not provided and | ``a.shape = (i[0], i[1], ... i[n-2], i[n-1])``, then | ``a.transpose().shape = (i[n-1], i[n-2], ... i[1], i[0])``. | | Parameters | ---------- | axes : None, tuple of ints, or `n` ints | | * None or no argument: reverses the order of the axes. | | * tuple of ints: `i` in the `j`-th place in the tuple means `a`'s | `i`-th axis becomes `a.transpose()`'s `j`-th axis. | | * `n` ints: same as an n-tuple of the same ints (this form is | intended simply as a "convenience" alternative to the tuple form) | | Returns | ------- | out : ndarray | View of `a`, with axes suitably permuted. | | See Also | -------- | transpose : Equivalent function | ndarray.T : Array property returning the array transposed. | ndarray.reshape : Give a new shape to an array without changing its data. | | Examples | -------- | >>> a = np.array([[1, 2], [3, 4]]) | >>> a | array([[1, 2], | [3, 4]]) | >>> a.transpose() | array([[1, 3], | [2, 4]]) | >>> a.transpose((1, 0)) | array([[1, 3], | [2, 4]]) | >>> a.transpose(1, 0) | array([[1, 3], | [2, 4]]) | | var(...) | a.var(axis=None, dtype=None, out=None, ddof=0, keepdims=False, *, where=True) | | Returns the variance of the array elements, along given axis. | | Refer to `numpy.var` for full documentation. | | See Also | -------- | numpy.var : equivalent function | | view(...) | a.view([dtype][, type]) | | New view of array with the same data. | | .. note:: | Passing None for ``dtype`` is different from omitting the parameter, | since the former invokes ``dtype(None)`` which is an alias for | ``dtype('float_')``. | | Parameters | ---------- | dtype : data-type or ndarray sub-class, optional | Data-type descriptor of the returned view, e.g., float32 or int16. | Omitting it results in the view having the same data-type as `a`. | This argument can also be specified as an ndarray sub-class, which | then specifies the type of the returned object (this is equivalent to | setting the ``type`` parameter). | type : Python type, optional | Type of the returned view, e.g., ndarray or matrix. Again, omission | of the parameter results in type preservation. | | Notes | ----- | ``a.view()`` is used two different ways: | | ``a.view(some_dtype)`` or ``a.view(dtype=some_dtype)`` constructs a view | of the array's memory with a different data-type. This can cause a | reinterpretation of the bytes of memory. | | ``[a.view(ndarray_subclass)](https://www.chedong.com/phpMan.php/man/a.view/ndarraysubclass/markdown)`` or ``a.view(type=ndarray_subclass)`` just | returns an instance of `ndarray_subclass` that looks at the same array | (same shape, dtype, etc.) This does not cause a reinterpretation of the | memory. | | For ``a.view(some_dtype)``, if ``some_dtype`` has a different number of | bytes per entry than the previous dtype (for example, converting a | regular array to a structured array), then the behavior of the view | cannot be predicted just from the superficial appearance of ``a`` (shown | by ``print(a)``). It also depends on exactly how ``a`` is stored in | memory. Therefore if ``a`` is C-ordered versus fortran-ordered, versus | defined as a slice or transpose, etc., the view may give different | results. | | | Examples | -------- | >>> x = np.array([(1, 2)], dtype=[('a', np.int8), ('b', np.int8)]) | | Viewing array data using a different type and dtype: | | >>> y = x.view(dtype=np.int16, type=np.matrix) | >>> y | matrix([[513]], dtype=int16) | >>> print(type(y)) | | | Creating a view on a structured array so it can be used in calculations | | >>> x = np.array([(1, 2),(3,4)], dtype=[('a', np.int8), ('b', np.int8)]) | >>> xv = x.view(dtype=np.int8).reshape(-1,2) | >>> xv | array([[1, 2], | [3, 4]], dtype=int8) | >>> [xv.mean(0)](https://www.chedong.com/phpMan.php/man/xv.mean/0/markdown) | array([2., 3.]) | | Making changes to the view changes the underlying array | | >>> xv[0,1] = 20 | >>> x | array([(1, 20), (3, 4)], dtype=[('a', 'i1'), ('b', 'i1')]) | | Using a view to convert an array to a recarray: | | >>> z = x.view(np.recarray) | >>> z.a | array([1, 3], dtype=int8) | | Views share data: | | >>> x[0] = (9, 10) | >>> z[0] | (9, 10) | | Views that change the dtype size (bytes per entry) should normally be | avoided on arrays defined by slices, transposes, fortran-ordering, etc.: | | >>> x = np.array([[1,2,3],[4,5,6]], dtype=np.int16) | >>> y = x[:, 0:2] | >>> y | array([[1, 2], | [4, 5]], dtype=int16) | >>> y.view(dtype=[('width', np.int16), ('length', np.int16)]) | Traceback (most recent call last): | ... | ValueError: To change to a dtype of a different size, the array must be C-contiguous | >>> z = y.copy() | >>> z.view(dtype=[('width', np.int16), ('length', np.int16)]) | array([[(1, 2)], | [(4, 5)]], dtype=[('width', '>> x = np.array([[1.,2.],[3.,4.]]) | >>> x | array([[ 1., 2.], | [ 3., 4.]]) | >>> x.T | array([[ 1., 3.], | [ 2., 4.]]) | >>> x = np.array([1.,2.,3.,4.]) | >>> x | array([ 1., 2., 3., 4.]) | >>> x.T | array([ 1., 2., 3., 4.]) | | See Also | -------- | transpose | | __array_interface__ | Array protocol: Python side. | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: C-struct side. | | base | Base object if memory is from some other object. | | Examples | -------- | The base of an array that owns its memory is None: | | >>> x = np.array([1,2,3,4]) | >>> x.base is None | True | | Slicing creates a view, whose memory is shared with x: | | >>> y = x[2:] | >>> y.base is x | True | | ctypes | An object to simplify the interaction of the array with the ctypes | module. | | This attribute creates an object that makes it easier to use arrays | when calling shared libraries with the ctypes module. The returned | object has, among others, data, shape, and strides attributes (see | Notes below) which themselves return ctypes objects that can be used | as arguments to a shared library. | | Parameters | ---------- | None | | Returns | ------- | c : Python object | Possessing attributes data, shape, strides, etc. | | See Also | -------- | numpy.ctypeslib | | Notes | ----- | Below are the public attributes of this object which were documented | in "Guide to NumPy" (we have omitted undocumented public attributes, | as well as documented private attributes): | | .. autoattribute:: numpy.core._internal._ctypes.data | :noindex: | | .. autoattribute:: numpy.core._internal._ctypes.shape | :noindex: | | .. autoattribute:: numpy.core._internal._ctypes.strides | :noindex: | | .. automethod:: numpy.core._internal._ctypes.data_as | :noindex: | | .. automethod:: numpy.core._internal._ctypes.shape_as | :noindex: | | .. automethod:: numpy.core._internal._ctypes.strides_as | :noindex: | | If the ctypes module is not available, then the ctypes attribute | of array objects still returns something useful, but ctypes objects | are not returned and errors may be raised instead. In particular, | the object will still have the ``as_parameter`` attribute which will | return an integer equal to the data attribute. | | Examples | -------- | >>> import ctypes | >>> x = np.array([[0, 1], [2, 3]], dtype=np.int32) | >>> x | array([[0, 1], | [2, 3]], dtype=int32) | >>> x.ctypes.data | 31962608 # may vary | >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)) | <__main__.LP_c_uint object at 0x7ff2fc1fc200> # may vary | >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)).contents | [c_uint(0)](https://www.chedong.com/phpMan.php/man/cuint/0/markdown) | >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint64)).contents | [c_ulong(4294967296)](https://www.chedong.com/phpMan.php/man/culong/4294967296/markdown) | >>> x.ctypes.shape | # may vary | >>> x.ctypes.strides | # may vary | | data | Python buffer object pointing to the start of the array's data. | | dtype | Data-type of the array's elements. | | Parameters | ---------- | None | | Returns | ------- | d : numpy dtype object | | See Also | -------- | numpy.dtype | | Examples | -------- | >>> x | array([[0, 1], | [2, 3]]) | >>> x.dtype | dtype('int32') | >>> type(x.dtype) | | | flags | Information about the memory layout of the array. | | Attributes | ---------- | C_CONTIGUOUS (C) | The data is in a single, C-style contiguous segment. | F_CONTIGUOUS (F) | The data is in a single, Fortran-style contiguous segment. | OWNDATA (O) | The array owns the memory it uses or borrows it from another object. | WRITEABLE (W) | The data area can be written to. Setting this to False locks | the data, making it read-only. A view (slice, etc.) inherits WRITEABLE | from its base array at creation time, but a view of a writeable | array may be subsequently locked while the base array remains writeable. | (The opposite is not true, in that a view of a locked array may not | be made writeable. However, currently, locking a base object does not | lock any views that already reference it, so under that circumstance it | is possible to alter the contents of a locked array via a previously | created writeable view onto it.) Attempting to change a non-writeable | array raises a RuntimeError exception. | ALIGNED (A) | The data and all elements are aligned appropriately for the hardware. | WRITEBACKIFCOPY (X) | This array is a copy of some other array. The C-API function | PyArray_ResolveWritebackIfCopy must be called before deallocating | to the base array will be updated with the contents of this array. | UPDATEIFCOPY (U) | (Deprecated, use WRITEBACKIFCOPY) This array is a copy of some other array. | When this array is | deallocated, the base array will be updated with the contents of | this array. | FNC | F_CONTIGUOUS and not C_CONTIGUOUS. | FORC | F_CONTIGUOUS or C_CONTIGUOUS (one-segment test). | BEHAVED (B) | ALIGNED and WRITEABLE. | CARRAY (CA) | BEHAVED and C_CONTIGUOUS. | FARRAY (FA) | BEHAVED and F_CONTIGUOUS and not C_CONTIGUOUS. | | Notes | ----- | The `flags` object can be accessed dictionary-like (as in ``a.flags['WRITEABLE']``), | or by using lowercased attribute names (as in ``a.flags.writeable``). Short flag | names are only supported in dictionary access. | | Only the WRITEBACKIFCOPY, UPDATEIFCOPY, WRITEABLE, and ALIGNED flags can be | changed by the user, via direct assignment to the attribute or dictionary | entry, or by calling `ndarray.setflags`. | | The array flags cannot be set arbitrarily: | | - UPDATEIFCOPY can only be set ``False``. | - WRITEBACKIFCOPY can only be set ``False``. | - ALIGNED can only be set ``True`` if the data is truly aligned. | - WRITEABLE can only be set ``True`` if the array owns its own memory | or the ultimate owner of the memory exposes a writeable buffer | interface or is a string. | | Arrays can be both C-style and Fortran-style contiguous simultaneously. | This is clear for 1-dimensional arrays, but can also be true for higher | dimensional arrays. | | Even for contiguous arrays a stride for a given dimension | ``arr.strides[dim]`` may be *arbitrary* if ``arr.shape[dim] == 1`` | or the array has no elements. | It does *not* generally hold that ``self.strides[-1] == self.itemsize`` | for C-style contiguous arrays or ``self.strides[0] == self.itemsize`` for | Fortran-style contiguous arrays is true. | | flat | A 1-D iterator over the array. | | This is a `numpy.flatiter` instance, which acts similarly to, but is not | a subclass of, Python's built-in iterator object. | | See Also | -------- | flatten : Return a copy of the array collapsed into one dimension. | | flatiter | | Examples | -------- | >>> x = np.arange(1, 7).reshape(2, 3) | >>> x | array([[1, 2, 3], | [4, 5, 6]]) | >>> x.flat[3] | 4 | >>> x.T | array([[1, 4], | [2, 5], | [3, 6]]) | >>> x.T.flat[3] | 5 | >>> type(x.flat) | | | An assignment example: | | >>> x.flat = 3; x | array([[3, 3, 3], | [3, 3, 3]]) | >>> x.flat[[1,4]] = 1; x | array([[3, 1, 3], | [3, 1, 3]]) | | imag | The imaginary part of the array. | | Examples | -------- | >>> x = np.sqrt([1+0j, 0+1j]) | >>> x.imag | array([ 0. , 0.70710678]) | >>> x.imag.dtype | dtype('float64') | | itemsize | Length of one array element in bytes. | | Examples | -------- | >>> x = np.array([1,2,3], dtype=np.float64) | >>> x.itemsize | 8 | >>> x = np.array([1,2,3], dtype=np.complex128) | >>> x.itemsize | 16 | | nbytes | Total bytes consumed by the elements of the array. | | Notes | ----- | Does not include memory consumed by non-element attributes of the | array object. | | Examples | -------- | >>> x = np.zeros((3,5,2), dtype=np.complex128) | >>> x.nbytes | 480 | >>> np.prod(x.shape) * x.itemsize | 480 | | ndim | Number of array dimensions. | | Examples | -------- | >>> x = np.array([1, 2, 3]) | >>> x.ndim | 1 | >>> y = np.zeros((2, 3, 4)) | >>> y.ndim | 3 | | real | The real part of the array. | | Examples | -------- | >>> x = np.sqrt([1+0j, 0+1j]) | >>> x.real | array([ 1. , 0.70710678]) | >>> x.real.dtype | dtype('float64') | | See Also | -------- | numpy.real : equivalent function | | shape | Tuple of array dimensions. | | The shape property is usually used to get the current shape of an array, | but may also be used to reshape the array in-place by assigning a tuple of | array dimensions to it. As with `numpy.reshape`, one of the new shape | dimensions can be -1, in which case its value is inferred from the size of | the array and the remaining dimensions. Reshaping an array in-place will | fail if a copy is required. | | Examples | -------- | >>> x = np.array([1, 2, 3, 4]) | >>> x.shape | (4,) | >>> y = np.zeros((2, 3, 4)) | >>> y.shape | (2, 3, 4) | >>> y.shape = (3, 8) | >>> y | array([[ 0., 0., 0., 0., 0., 0., 0., 0.], | [ 0., 0., 0., 0., 0., 0., 0., 0.], | [ 0., 0., 0., 0., 0., 0., 0., 0.]]) | >>> y.shape = (3, 6) | Traceback (most recent call last): | File "", line 1, in | ValueError: total size of new array must be unchanged | >>> np.zeros((4,2))[::2].shape = (-1,) | Traceback (most recent call last): | File "", line 1, in | AttributeError: Incompatible shape for in-place modification. Use | `.reshape()` to make a copy with the desired shape. | | See Also | -------- | numpy.reshape : similar function | ndarray.reshape : similar method | | size | Number of elements in the array. | | Equal to ``np.prod(a.shape)``, i.e., the product of the array's | dimensions. | | Notes | ----- | `a.size` returns a standard arbitrary precision Python integer. This | may not be the case with other methods of obtaining the same value | (like the suggested ``np.prod(a.shape)``, which returns an instance | of ``np.int_``), and may be relevant if the value is used further in | calculations that may overflow a fixed size integer type. | | Examples | -------- | >>> x = np.zeros((3, 5, 2), dtype=np.complex128) | >>> x.size | 30 | >>> np.prod(x.shape) | 30 | | strides | Tuple of bytes to step in each dimension when traversing an array. | | The byte offset of element ``(i[0], i[1], ..., i[n])`` in an array `a` | is:: | | offset = sum(np.array(i) * a.strides) | | A more detailed explanation of strides can be found in the | "ndarray.rst" file in the NumPy reference guide. | | Notes | ----- | Imagine an array of 32-bit integers (each 4 bytes):: | | x = np.array([[0, 1, 2, 3, 4], | [5, 6, 7, 8, 9]], dtype=np.int32) | | This array is stored in memory as 40 bytes, one after the other | (known as a contiguous block of memory). The strides of an array tell | us how many bytes we have to skip in memory to move to the next position | along a certain axis. For example, we have to skip 4 bytes (1 value) to | move to the next column, but 20 bytes (5 values) to get to the same | position in the next row. As such, the strides for the array `x` will be | ``(20, 4)``. | | See Also | -------- | numpy.lib.stride_tricks.as_strided | | Examples | -------- | >>> y = np.reshape(np.arange(2*3*4), (2,3,4)) | >>> y | array([[[ 0, 1, 2, 3], | [ 4, 5, 6, 7], | [ 8, 9, 10, 11]], | [[12, 13, 14, 15], | [16, 17, 18, 19], | [20, 21, 22, 23]]]) | >>> y.strides | (48, 16, 4) | >>> y[1,1,1] | 17 | >>> offset=sum(y.strides * np.array((1,1,1))) | >>> offset/y.itemsize | 17 | | >>> x = np.reshape(np.arange(5*6*7*8), (5,6,7,8)).transpose(2,3,1,0) | >>> x.strides | (32, 4, 224, 1344) | >>> i = np.array([3,5,2,2]) | >>> offset = sum(i * x.strides) | >>> x[3,5,2,2] | 813 | >>> offset / x.itemsize | 813 clongdouble = class complex256(complexfloating) | Complex number type composed of two extended-precision floating-point | numbers. | | :Character code: ``'G'`` | :Canonical name: `numpy.clongdouble` | :Alias: `numpy.clongfloat` | :Alias: `numpy.longcomplex` | :Alias on this platform (Linux x86_64): `numpy.complex256`: Complex number type composed of 2 128-bit extended-precision floating-point numbers. | | Method resolution order: | complex256 | complexfloating | inexact | number | generic | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __bool__(self, /) | True if self else False | | __complex__(...) | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __int__(self, /) | int(self) | | __le__(self, value, /) | Return self<=value. | | __lt__(self, value, /) | Return self>self. | | __rshift__(self, value, /) | Return self>>value. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. clongfloat = class complex256(complexfloating) | Complex number type composed of two extended-precision floating-point | numbers. | | :Character code: ``'G'`` | :Canonical name: `numpy.clongdouble` | :Alias: `numpy.clongfloat` | :Alias: `numpy.longcomplex` | :Alias on this platform (Linux x86_64): `numpy.complex256`: Complex number type composed of 2 128-bit extended-precision floating-point numbers. | | Method resolution order: | complex256 | complexfloating | inexact | number | generic | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __bool__(self, /) | True if self else False | | __complex__(...) | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __int__(self, /) | int(self) | | __le__(self, value, /) | Return self<=value. | | __lt__(self, value, /) | Return self>self. | | __rshift__(self, value, /) | Return self>>value. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. ### class complex128 | complex128(real=0, imag=0) | | Complex number type composed of two double-precision floating-point | numbers, compatible with Python `complex`. | | :Character code: ``'D'`` | :Canonical name: `numpy.cdouble` | :Alias: `numpy.cfloat` | :Alias: `numpy.complex_` | :Alias on this platform (Linux x86_64): `numpy.complex128`: Complex number type composed of 2 64-bit-precision floating-point numbers. | | Method resolution order: | complex128 | complexfloating | inexact | number | generic | builtins.complex | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __bool__(self, /) | True if self else False | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __int__(self, /) | int(self) | | __le__(self, value, /) | Return self<=value. | | __lt__(self, value, /) | Return self>self. | | __rshift__(self, value, /) | Return self>>value. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. | | ---------------------------------------------------------------------- | Methods inherited from builtins.complex: | | __getattribute__(self, name, /) | Return getattr(self, name). | | __getnewargs__(self, /) ### class complex256 | Complex number type composed of two extended-precision floating-point | numbers. | | :Character code: ``'G'`` | :Canonical name: `numpy.clongdouble` | :Alias: `numpy.clongfloat` | :Alias: `numpy.longcomplex` | :Alias on this platform (Linux x86_64): `numpy.complex256`: Complex number type composed of 2 128-bit extended-precision floating-point numbers. | | Method resolution order: | complex256 | complexfloating | inexact | number | generic | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __bool__(self, /) | True if self else False | | __complex__(...) | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __int__(self, /) | int(self) | | __le__(self, value, /) | Return self<=value. | | __lt__(self, value, /) | Return self>self. | | __rshift__(self, value, /) | Return self>>value. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. ### class complex64 | Complex number type composed of two single-precision floating-point | numbers. | | :Character code: ``'F'`` | :Canonical name: `numpy.csingle` | :Alias: `numpy.singlecomplex` | :Alias on this platform (Linux x86_64): `numpy.complex64`: Complex number type composed of 2 32-bit-precision floating-point numbers. | | Method resolution order: | complex64 | complexfloating | inexact | number | generic | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __bool__(self, /) | True if self else False | | __complex__(...) | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __int__(self, /) | int(self) | | __le__(self, value, /) | Return self<=value. | | __lt__(self, value, /) | Return self>self. | | __rshift__(self, value, /) | Return self>>value. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. complex_ = class complex128(complexfloating, builtins.complex) | complex_(real=0, imag=0) | | Complex number type composed of two double-precision floating-point | numbers, compatible with Python `complex`. | | :Character code: ``'D'`` | :Canonical name: `numpy.cdouble` | :Alias: `numpy.cfloat` | :Alias: `numpy.complex_` | :Alias on this platform (Linux x86_64): `numpy.complex128`: Complex number type composed of 2 64-bit-precision floating-point numbers. | | Method resolution order: | complex128 | complexfloating | inexact | number | generic | builtins.complex | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __bool__(self, /) | True if self else False | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __int__(self, /) | int(self) | | __le__(self, value, /) | Return self<=value. | | __lt__(self, value, /) | Return self>self. | | __rshift__(self, value, /) | Return self>>value. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. | | ---------------------------------------------------------------------- | Methods inherited from builtins.complex: | | __getattribute__(self, name, /) | Return getattr(self, name). | | __getnewargs__(self, /) ### class complexfloating | Abstract base class of all complex number scalar types that are made up of | floating-point numbers. | | Method resolution order: | complexfloating | inexact | number | generic | builtins.object | | Methods defined here: | | __round__(...) | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __and__(self, value, /) | Return self&value. | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __bool__(self, /) | True if self else False | | __copy__(...) | | __deepcopy__(...) | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __format__(...) | NumPy array scalar formatter | | __ge__(self, value, /) | Return self>=value. | | __getitem__(self, key, /) | Return self[key]. | | __gt__(self, value, /) | Return self>value. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __le__(self, value, /) | Return self<=value. | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. | | ---------------------------------------------------------------------- | Data and other attributes inherited from generic: | | __hash__ = None csingle = class complex64(complexfloating) | Complex number type composed of two single-precision floating-point | numbers. | | :Character code: ``'F'`` | :Canonical name: `numpy.csingle` | :Alias: `numpy.singlecomplex` | :Alias on this platform (Linux x86_64): `numpy.complex64`: Complex number type composed of 2 32-bit-precision floating-point numbers. | | Method resolution order: | complex64 | complexfloating | inexact | number | generic | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __bool__(self, /) | True if self else False | | __complex__(...) | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __int__(self, /) | int(self) | | __le__(self, value, /) | Return self<=value. | | __lt__(self, value, /) | Return self>self. | | __rshift__(self, value, /) | Return self>>value. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. ### class datetime64 | If created from a 64-bit integer, it represents an offset from | ``1970-01-01T00:00:00``. | If created from string, the string can be in ISO 8601 date | or datetime format. | | >>> np.datetime64(10, 'Y') | numpy.datetime64('1980') | >>> np.datetime64('1980', 'Y') | numpy.datetime64('1980') | >>> np.datetime64(10, 'D') | numpy.datetime64('1970-01-11') | | See :ref:`arrays.datetime` for more information. | | :Character code: ``'M'`` | | Method resolution order: | datetime64 | generic | builtins.object | | Methods defined here: | | __eq__(self, value, /) | Return self==value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __le__(self, value, /) | Return self<=value. | | __lt__(self, value, /) | Return self>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. double = class float64(floating, builtins.float) | double(x=0, /) | | Double-precision floating-point number type, compatible with Python `float` | and C ``double``. | | :Character code: ``'d'`` | :Canonical name: `numpy.double` | :Alias: `numpy.float_` | :Alias on this platform (Linux x86_64): `numpy.float64`: 64-bit precision floating-point number type: sign bit, 11 bits exponent, 52 bits mantissa. | | Method resolution order: | float64 | floating | inexact | number | generic | builtins.float | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __bool__(self, /) | True if self else False | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __int__(self, /) | int(self) | | __le__(self, value, /) | Return self<=value. | | __lt__(self, value, /) | Return self (int, int) | | Return a pair of integers, whose ratio is exactly equal to the original | floating point number, and with a positive denominator. | Raise `OverflowError` on infinities and a `ValueError` on NaNs. | | >>> np.double(10.0).as_integer_ratio() | (10, 1) | >>> np.double(0.0).as_integer_ratio() | (0, 1) | >>> np.double(-.25).as_integer_ratio() | (-1, 4) | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from floating: | | __round__(...) | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __and__(self, value, /) | Return self&value. | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __copy__(...) | | __deepcopy__(...) | | __format__(...) | NumPy array scalar formatter | | __getitem__(self, key, /) | Return self[key]. | | __invert__(self, /) | ~self | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. | | ---------------------------------------------------------------------- | Methods inherited from builtins.float: | | __ceil__(self, /) | Return the ceiling as an Integral. | | __floor__(self, /) | Return the floor as an Integral. | | __getattribute__(self, name, /) | Return getattr(self, name). | | __getnewargs__(self, /) | | __trunc__(self, /) | Return the Integral closest to x between 0 and x. | | hex(self, /) | Return a hexadecimal representation of a floating-point number. | | >>> (-0.1).hex() | '-0x1.999999999999ap-4' | >>> 3.14159.hex() | '0x1.921f9f01b866ep+1' | | is_integer(self, /) | Return True if the float is an integer. | | ---------------------------------------------------------------------- | Class methods inherited from builtins.float: | | __getformat__(typestr, /) from builtins.type | You probably don't want to use this function. | | typestr | Must be 'double' or 'float'. | | It exists mainly to be used in Python's test suite. | | This function returns whichever of 'unknown', 'IEEE, big-endian' or 'IEEE, | little-endian' best describes the format of floating point numbers used by the | C type named by typestr. | | __setformat__(typestr, fmt, /) from builtins.type | You probably don't want to use this function. | | typestr | Must be 'double' or 'float'. | fmt | Must be one of 'unknown', 'IEEE, big-endian' or 'IEEE, little-endian', | and in addition can only be one of the latter two if it appears to | match the underlying C reality. | | It exists mainly to be used in Python's test suite. | | Override the automatic determination of C-level floating point type. | This affects how floats are converted to and from binary strings. | | fromhex(string, /) from builtins.type | Create a floating-point number from a hexadecimal string. | | >>> float.fromhex('0x1.ffffp10') | 2047.984375 | >>> float.fromhex('-0x1p-1074') | -5e-324 ### class dtype | dtype(dtype, align=False, copy=False) | | Create a data type object. | | A numpy array is homogeneous, and contains elements described by a | dtype object. A dtype object can be constructed from different | combinations of fundamental numeric types. | | Parameters | ---------- | dtype | Object to be converted to a data type object. | align : bool, optional | Add padding to the fields to match what a C compiler would output | for a similar C-struct. Can be ``True`` only if `obj` is a dictionary | or a comma-separated string. If a struct dtype is being created, | this also sets a sticky alignment flag ``isalignedstruct``. | copy : bool, optional | Make a new copy of the data-type object. If ``False``, the result | may just be a reference to a built-in data-type object. | | See also | -------- | result_type | | Examples | -------- | Using array-scalar type: | | >>> np.dtype(np.int16) | dtype('int16') | | Structured type, one field name 'f1', containing int16: | | >>> np.dtype([('f1', np.int16)]) | dtype([('f1', '>> np.dtype([('f1', [('f1', np.int16)])]) | dtype([('f1', [('f1', '>> np.dtype([('f1', np.uint64), ('f2', np.int32)]) | dtype([('f1', '>> np.dtype([('a','f8'),('b','S10')]) | dtype([('a', '>> np.dtype("i4, (2,3)f8") | dtype([('f0', '>> np.dtype([('hello',(np.int64,3)),('world',np.void,10)]) | dtype([('hello', '>> np.dtype((np.int16, {'x':(np.int8,0), 'y':(np.int8,1)})) | dtype((numpy.int16, [('x', 'i1'), ('y', 'i1')])) | | Using dictionaries. Two fields named 'gender' and 'age': | | >>> np.dtype({'names':['gender','age'], 'formats':['S1',np.uint8]}) | dtype([('gender', 'S1'), ('age', 'u1')]) | | Offsets in bytes, here 0 and 25: | | >>> np.dtype({'surname':('S25',0),'age':(np.uint8,25)}) | dtype([('surname', 'S25'), ('age', 'u1')]) | | Methods defined here: | | __bool__(self, /) | True if self else False | | __eq__(self, value, /) | Return self==value. | | __ge__(self, value, /) | Return self>=value. | | __getitem__(self, key, /) | Return self[key]. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __le__(self, value, /) | Return self<=value. | | __len__(self, /) | Return len(self). | | __lt__(self, value, /) | Return self', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Returns | ------- | new_dtype : dtype | New dtype object with the given change to the byte order. | | Notes | ----- | Changes are also made in all fields and sub-arrays of the data type. | | Examples | -------- | >>> import sys | >>> sys_is_le = sys.byteorder == 'little' | >>> native_code = sys_is_le and '<' or '>' | >>> swapped_code = sys_is_le and '>' or '<' | >>> native_dt = np.dtype(native_code+'i2') | >>> swapped_dt = np.dtype(swapped_code+'i2') | >>> native_dt.newbyteorder('S') == swapped_dt | True | >>> native_dt.newbyteorder() == swapped_dt | True | >>> native_dt == swapped_dt.newbyteorder('S') | True | >>> native_dt == swapped_dt.newbyteorder('=') | True | >>> native_dt == swapped_dt.newbyteorder('N') | True | >>> native_dt == native_dt.newbyteorder('|') | True | >>> np.dtype('>> np.dtype('>> np.dtype('>i2') == native_dt.newbyteorder('>') | True | >>> np.dtype('>i2') == native_dt.newbyteorder('B') | True | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(*args, **kwargs) from _DTypeMeta | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Data descriptors defined here: | | alignment | The required alignment (bytes) of this data-type according to the compiler. | | More information is available in the C-API section of the manual. | | Examples | -------- | | >>> x = np.dtype('i4') | >>> x.alignment | 4 | | >>> x = np.dtype(float) | >>> x.alignment | 8 | | base | Returns dtype for the base element of the subarrays, | regardless of their dimension or shape. | | See Also | -------- | dtype.subdtype | | Examples | -------- | >>> x = numpy.dtype('8f') | >>> x.base | dtype('float32') | | >>> x = numpy.dtype('i2') | >>> x.base | dtype('int16') | | byteorder | A character indicating the byte-order of this data-type object. | | One of: | | === ============== | '=' native | '<' little-endian | '>' big-endian | '|' not applicable | === ============== | | All built-in data-type objects have byteorder either '=' or '|'. | | Examples | -------- | | >>> dt = np.dtype('i2') | >>> dt.byteorder | '=' | >>> # endian is not relevant for 8 bit numbers | >>> np.dtype('i1').byteorder | '|' | >>> # or ASCII strings | >>> np.dtype('S2').byteorder | '|' | >>> # Even if specific code is given, and it is native | >>> # '=' is the byteorder | >>> import sys | >>> sys_is_le = sys.byteorder == 'little' | >>> native_code = sys_is_le and '<' or '>' | >>> swapped_code = sys_is_le and '>' or '<' | >>> dt = np.dtype(native_code + 'i2') | >>> dt.byteorder | '=' | >>> # Swapped code shows up as itself | >>> dt = np.dtype(swapped_code + 'i2') | >>> dt.byteorder == swapped_code | True | | char | A unique character code for each of the 21 different built-in types. | | Examples | -------- | | >>> x = np.dtype(float) | >>> x.char | 'd' | | descr | `__array_interface__` description of the data-type. | | The format is that required by the 'descr' key in the | `__array_interface__` attribute. | | Warning: This attribute exists specifically for `__array_interface__`, | and passing it directly to `np.dtype` will not accurately reconstruct | some dtypes (e.g., scalar and subarray dtypes). | | Examples | -------- | | >>> x = np.dtype(float) | >>> x.descr | [('', '>> dt = np.dtype([('name', np.str_, 16), ('grades', np.float64, (2,))]) | >>> dt.descr | [('name', '>> dt = np.dtype([('name', np.str_, 16), ('grades', np.float64, (2,))]) | >>> print(dt.fields) | {'grades': (dtype(('float64',(2,))), 16), 'name': (dtype('|S16'), 0)} | | flags | Bit-flags describing how this data type is to be interpreted. | | Bit-masks are in `numpy.core.multiarray` as the constants | `ITEM_HASOBJECT`, `LIST_PICKLE`, `ITEM_IS_POINTER`, `NEEDS_INIT`, | `NEEDS_PYAPI`, `USE_GETITEM`, `USE_SETITEM`. A full explanation | of these flags is in C-API documentation; they are largely useful | for user-defined data-types. | | The following example demonstrates that operations on this particular | dtype requires Python C-API. | | Examples | -------- | | >>> x = np.dtype([('a', np.int32, 8), ('b', np.float64, 6)]) | >>> x.flags | 16 | >>> np.core.multiarray.NEEDS_PYAPI | 16 | | hasobject | Boolean indicating whether this dtype contains any reference-counted | objects in any fields or sub-dtypes. | | Recall that what is actually in the ndarray memory representing | the Python object is the memory address of that object (a pointer). | Special handling may be required, and this attribute is useful for | distinguishing data types that may contain arbitrary Python objects | and data-types that won't. | | isalignedstruct | Boolean indicating whether the dtype is a struct which maintains | field alignment. This flag is sticky, so when combining multiple | structs together, it is preserved and produces new dtypes which | are also aligned. | | isbuiltin | Integer indicating how this dtype relates to the built-in dtypes. | | Read-only. | | = ======================================================================== | 0 if this is a structured array type, with fields | 1 if this is a dtype compiled into numpy (such as ints, floats etc) | 2 if the dtype is for a user-defined numpy type | A user-defined type uses the numpy C-API machinery to extend | numpy to handle a new array type. See | :ref:`user.user-defined-data-types` in the NumPy manual. | = ======================================================================== | | Examples | -------- | >>> dt = np.dtype('i2') | >>> dt.isbuiltin | 1 | >>> dt = np.dtype('f8') | >>> dt.isbuiltin | 1 | >>> dt = np.dtype([('field1', 'f8')]) | >>> dt.isbuiltin | 0 | | isnative | Boolean indicating whether the byte order of this dtype is native | to the platform. | | itemsize | The element size of this data-type object. | | For 18 of the 21 types this number is fixed by the data-type. | For the flexible data-types, this number can be anything. | | Examples | -------- | | >>> arr = np.array([[1, 2], [3, 4]]) | >>> arr.dtype | dtype('int64') | >>> arr.itemsize | 8 | | >>> dt = np.dtype([('name', np.str_, 16), ('grades', np.float64, (2,))]) | >>> dt.itemsize | 80 | | kind | A character code (one of 'biufcmMOSUV') identifying the general kind of data. | | = ====================== | b boolean | i signed integer | u unsigned integer | f floating-point | c complex floating-point | m timedelta | M datetime | O object | S (byte-)string | U Unicode | V void | = ====================== | | Examples | -------- | | >>> dt = np.dtype('i4') | >>> dt.kind | 'i' | >>> dt = np.dtype('f8') | >>> dt.kind | 'f' | >>> dt = np.dtype([('field1', 'f8')]) | >>> dt.kind | 'V' | | metadata | Either ``None`` or a readonly dictionary of metadata (mappingproxy). | | The metadata field can be set using any dictionary at data-type | creation. NumPy currently has no uniform approach to propagating | metadata; although some array operations preserve it, there is no | guarantee that others will. | | .. warning:: | | Although used in certain projects, this feature was long undocumented | and is not well supported. Some aspects of metadata propagation | are expected to change in the future. | | Examples | -------- | | >>> dt = np.dtype(float, metadata={"key": "value"}) | >>> dt.metadata["key"] | 'value' | >>> arr = np.array([1, 2, 3], dtype=dt) | >>> arr.dtype.metadata | mappingproxy({'key': 'value'}) | | Adding arrays with identical datatypes currently preserves the metadata: | | >>> (arr + arr).dtype.metadata | mappingproxy({'key': 'value'}) | | But if the arrays have different dtype metadata, the metadata may be | dropped: | | >>> dt2 = np.dtype(float, metadata={"key2": "value2"}) | >>> arr2 = np.array([3, 2, 1], dtype=dt2) | >>> (arr + arr2).dtype.metadata is None | True # The metadata field is cleared so None is returned | | name | A bit-width name for this data-type. | | Un-sized flexible data-type objects do not have this attribute. | | Examples | -------- | | >>> x = np.dtype(float) | >>> x.name | 'float64' | >>> x = np.dtype([('a', np.int32, 8), ('b', np.float64, 6)]) | >>> x.name | 'void640' | | names | Ordered list of field names, or ``None`` if there are no fields. | | The names are ordered according to increasing byte offset. This can be | used, for example, to walk through all of the named fields in offset order. | | Examples | -------- | >>> dt = np.dtype([('name', np.str_, 16), ('grades', np.float64, (2,))]) | >>> dt.names | ('name', 'grades') | | ndim | Number of dimensions of the sub-array if this data type describes a | sub-array, and ``0`` otherwise. | | .. versionadded:: 1.13.0 | | Examples | -------- | >>> x = np.dtype(float) | >>> x.ndim | 0 | | >>> x = np.dtype((float, 8)) | >>> x.ndim | 1 | | >>> x = np.dtype(('i4', (3, 4))) | >>> x.ndim | 2 | | num | A unique number for each of the 21 different built-in types. | | These are roughly ordered from least-to-most precision. | | Examples | -------- | | >>> dt = np.dtype(str) | >>> dt.num | 19 | | >>> dt = np.dtype(float) | >>> dt.num | 12 | | shape | Shape tuple of the sub-array if this data type describes a sub-array, | and ``()`` otherwise. | | Examples | -------- | | >>> dt = np.dtype(('i4', 4)) | >>> dt.shape | (4,) | | >>> dt = np.dtype(('i4', (2, 3))) | >>> dt.shape | (2, 3) | | str | The array-protocol typestring of this data-type object. | | subdtype | Tuple ``(item_dtype, shape)`` if this `dtype` describes a sub-array, and | None otherwise. | | The *shape* is the fixed shape of the sub-array described by this | data type, and *item_dtype* the data type of the array. | | If a field whose dtype object has this attribute is retrieved, | then the extra dimensions implied by *shape* are tacked on to | the end of the retrieved array. | | See Also | -------- | dtype.base | | Examples | -------- | >>> x = numpy.dtype('8f') | >>> x.subdtype | (dtype('float32'), (8,)) | | >>> x = numpy.dtype('i2') | >>> x.subdtype | >>> | | type ### class errstate | errstate(*, call=, **kwargs) | | errstate(**kwargs) | | Context manager for floating-point error handling. | | Using an instance of `errstate` as a context manager allows statements in | that context to execute with a known error handling behavior. Upon entering | the context the error handling is set with `seterr` and `seterrcall`, and | upon exiting it is reset to what it was before. | | .. versionchanged:: 1.17.0 | `errstate` is also usable as a function decorator, saving | a level of indentation if an entire function is wrapped. | See :py:class:`contextlib.ContextDecorator` for more information. | | Parameters | ---------- | kwargs : {divide, over, under, invalid} | Keyword arguments. The valid keywords are the possible floating-point | exceptions. Each keyword should have a string value that defines the | treatment for the particular error. Possible values are | {'ignore', 'warn', 'raise', 'call', 'print', 'log'}. | | See Also | -------- | seterr, geterr, seterrcall, geterrcall | | Notes | ----- | For complete documentation of the types of floating-point exceptions and | treatment options, see `seterr`. | | Examples | -------- | >>> olderr = np.seterr(all='ignore') # Set error handling to known state. | | >>> [np.arange(3)](https://www.chedong.com/phpMan.php/man/np.arange/3/markdown) / 0. | array([nan, inf, inf]) | >>> with np.errstate(divide='warn'): | ... [np.arange(3)](https://www.chedong.com/phpMan.php/man/np.arange/3/markdown) / 0. | array([nan, inf, inf]) | | >>> np.sqrt(-1) | nan | >>> with np.errstate(invalid='raise'): | ... np.sqrt(-1) | Traceback (most recent call last): | File "", line 2, in | FloatingPointError: invalid value encountered in sqrt | | Outside the context the error handling behavior has not changed: | | >>> np.geterr() | {'divide': 'ignore', 'over': 'ignore', 'under': 'ignore', 'invalid': 'ignore'} | | Method resolution order: | errstate | contextlib.ContextDecorator | builtins.object | | Methods defined here: | | __enter__(self) | | __exit__(self, *exc_info) | | __init__(self, *, call=, **kwargs) | Initialize self. See help(type(self)) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from contextlib.ContextDecorator: | | __call__(self, func) | Call self as a function. | | ---------------------------------------------------------------------- | Data descriptors inherited from contextlib.ContextDecorator: | | __dict__ | dictionary for instance variables (if defined) | | __weakref__ | list of weak references to the object (if defined) ### class finfo | finfo(dtype) | | finfo(dtype) | | Machine limits for floating point types. | | Attributes | ---------- | bits : int | The number of bits occupied by the type. | eps : float | The difference between 1.0 and the next smallest representable float | larger than 1.0. For example, for 64-bit binary floats in the IEEE-754 | standard, ``eps = 2**-52``, approximately 2.22e-16. | epsneg : float | The difference between 1.0 and the next smallest representable float | less than 1.0. For example, for 64-bit binary floats in the IEEE-754 | standard, ``epsneg = 2**-53``, approximately 1.11e-16. | iexp : int | The number of bits in the exponent portion of the floating point | representation. | machar : MachAr | The object which calculated these parameters and holds more | detailed information. | machep : int | The exponent that yields `eps`. | max : floating point number of the appropriate type | The largest representable number. | maxexp : int | The smallest positive power of the base (2) that causes overflow. | min : floating point number of the appropriate type | The smallest representable number, typically ``-max``. | minexp : int | The most negative power of the base (2) consistent with there | being no leading 0's in the mantissa. | negep : int | The exponent that yields `epsneg`. | nexp : int | The number of bits in the exponent including its sign and bias. | nmant : int | The number of bits in the mantissa. | precision : int | The approximate number of decimal digits to which this kind of | float is precise. | resolution : floating point number of the appropriate type | The approximate decimal resolution of this type, i.e., | ``10**-precision``. | tiny : float | The smallest positive floating point number with full precision | (see Notes). | | Parameters | ---------- | dtype : float, dtype, or instance | Kind of floating point data-type about which to get information. | | See Also | -------- | MachAr : The implementation of the tests that produce this information. | iinfo : The equivalent for integer data types. | spacing : The distance between a value and the nearest adjacent number | nextafter : The next floating point value after x1 towards x2 | | Notes | ----- | For developers of NumPy: do not instantiate this at the module level. | The initial calculation of these parameters is expensive and negatively | impacts import times. These objects are cached, so calling ``finfo()`` | repeatedly inside your functions is not a problem. | | Note that ``tiny`` is not actually the smallest positive representable | value in a NumPy floating point type. As in the IEEE-754 standard [1]_, | NumPy floating point types make use of subnormal numbers to fill the | gap between 0 and ``tiny``. However, subnormal numbers may have | significantly reduced precision [2]_. | | References | ---------- | .. [1] IEEE Standard for Floating-Point Arithmetic, IEEE Std 754-2008, | pp.1-70, 2008, | .. [2] Wikipedia, "Denormal Numbers", | | | Methods defined here: | | __repr__(self) | Return repr(self). | | __str__(self) | Return str(self). | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(cls, dtype) | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Data descriptors defined here: | | __dict__ | dictionary for instance variables (if defined) | | __weakref__ | list of weak references to the object (if defined) ### class flatiter | Flat iterator object to iterate over arrays. | | A `flatiter` iterator is returned by ``x.flat`` for any array `x`. | It allows iterating over the array as if it were a 1-D array, | either in a for-loop or by calling its `next` method. | | Iteration is done in row-major, C-style order (the last | index varying the fastest). The iterator can also be indexed using | basic slicing or advanced indexing. | | See Also | -------- | ndarray.flat : Return a flat iterator over an array. | ndarray.flatten : Returns a flattened copy of an array. | | Notes | ----- | A `flatiter` iterator can not be constructed directly from Python code | by calling the `flatiter` constructor. | | Examples | -------- | >>> x = [np.arange(6)](https://www.chedong.com/phpMan.php/man/np.arange/6/markdown).reshape(2, 3) | >>> fl = x.flat | >>> type(fl) | | >>> for item in fl: | ... print(item) | ... | 0 | 1 | 2 | 3 | 4 | 5 | | >>> fl[2:4] | array([2, 3]) | | Methods defined here: | | __array__(...) | __array__(type=None) Get array from iterator | | __delitem__(self, key, /) | Delete self[key]. | | __eq__(self, value, /) | Return self==value. | | __ge__(self, value, /) | Return self>=value. | | __getitem__(self, key, /) | Return self[key]. | | __gt__(self, value, /) | Return self>value. | | __iter__(self, /) | Implement iter(self). | | __le__(self, value, /) | Return self<=value. | | __len__(self, /) | Return len(self). | | __lt__(self, value, /) | Return self>> x = [np.arange(6)](https://www.chedong.com/phpMan.php/man/np.arange/6/markdown).reshape(2, 3) | >>> x | array([[0, 1, 2], | [3, 4, 5]]) | >>> fl = x.flat | >>> fl.copy() | array([0, 1, 2, 3, 4, 5]) | | ---------------------------------------------------------------------- | Data descriptors defined here: | | base | A reference to the array that is iterated over. | | Examples | -------- | >>> x = [np.arange(5)](https://www.chedong.com/phpMan.php/man/np.arange/5/markdown) | >>> fl = x.flat | >>> fl.base is x | True | | coords | An N-dimensional tuple of current coordinates. | | Examples | -------- | >>> x = [np.arange(6)](https://www.chedong.com/phpMan.php/man/np.arange/6/markdown).reshape(2, 3) | >>> fl = x.flat | >>> fl.coords | (0, 0) | >>> next(fl) | 0 | >>> fl.coords | (0, 1) | | index | Current flat index into the array. | | Examples | -------- | >>> x = [np.arange(6)](https://www.chedong.com/phpMan.php/man/np.arange/6/markdown).reshape(2, 3) | >>> fl = x.flat | >>> fl.index | 0 | >>> next(fl) | 0 | >>> fl.index | 1 | | ---------------------------------------------------------------------- | Data and other attributes defined here: | | __hash__ = None ### class flexible | Abstract base class of all scalar types without predefined length. | The actual size of these types depends on the specific `np.dtype` | instantiation. | | Method resolution order: | flexible | generic | builtins.object | | Methods inherited from generic: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __and__(self, value, /) | Return self&value. | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __bool__(self, /) | True if self else False | | __copy__(...) | | __deepcopy__(...) | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __format__(...) | NumPy array scalar formatter | | __ge__(self, value, /) | Return self>=value. | | __getitem__(self, key, /) | Return self[key]. | | __gt__(self, value, /) | Return self>value. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __le__(self, value, /) | Return self<=value. | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. | | ---------------------------------------------------------------------- | Data and other attributes inherited from generic: | | __hash__ = None ### class float128 | Extended-precision floating-point number type, compatible with C | ``long double`` but not necessarily with IEEE 754 quadruple-precision. | | :Character code: ``'g'`` | :Canonical name: `numpy.longdouble` | :Alias: `numpy.longfloat` | :Alias on this platform (Linux x86_64): `numpy.float128`: 128-bit extended-precision floating-point number type. | | Method resolution order: | float128 | floating | inexact | number | generic | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __bool__(self, /) | True if self else False | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __int__(self, /) | int(self) | | __le__(self, value, /) | Return self<=value. | | __lt__(self, value, /) | Return self (int, int) | | Return a pair of integers, whose ratio is exactly equal to the original | floating point number, and with a positive denominator. | Raise `OverflowError` on infinities and a `ValueError` on NaNs. | | >>> np.longdouble(10.0).as_integer_ratio() | (10, 1) | >>> np.longdouble(0.0).as_integer_ratio() | (0, 1) | >>> np.longdouble(-.25).as_integer_ratio() | (-1, 4) | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from floating: | | __round__(...) | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __and__(self, value, /) | Return self&value. | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __copy__(...) | | __deepcopy__(...) | | __format__(...) | NumPy array scalar formatter | | __getitem__(self, key, /) | Return self[key]. | | __invert__(self, /) | ~self | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. ### class float16 | Half-precision floating-point number type. | | :Character code: ``'e'`` | :Canonical name: `numpy.half` | :Alias on this platform (Linux x86_64): `numpy.float16`: 16-bit-precision floating-point number type: sign bit, 5 bits exponent, 10 bits mantissa. | | Method resolution order: | float16 | floating | inexact | number | generic | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __bool__(self, /) | True if self else False | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __int__(self, /) | int(self) | | __le__(self, value, /) | Return self<=value. | | __lt__(self, value, /) | Return self (int, int) | | Return a pair of integers, whose ratio is exactly equal to the original | floating point number, and with a positive denominator. | Raise `OverflowError` on infinities and a `ValueError` on NaNs. | | >>> np.half(10.0).as_integer_ratio() | (10, 1) | >>> np.half(0.0).as_integer_ratio() | (0, 1) | >>> np.half(-.25).as_integer_ratio() | (-1, 4) | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from floating: | | __round__(...) | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __and__(self, value, /) | Return self&value. | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __copy__(...) | | __deepcopy__(...) | | __format__(...) | NumPy array scalar formatter | | __getitem__(self, key, /) | Return self[key]. | | __invert__(self, /) | ~self | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. ### class float32 | Single-precision floating-point number type, compatible with C ``float``. | | :Character code: ``'f'`` | :Canonical name: `numpy.single` | :Alias on this platform (Linux x86_64): `numpy.float32`: 32-bit-precision floating-point number type: sign bit, 8 bits exponent, 23 bits mantissa. | | Method resolution order: | float32 | floating | inexact | number | generic | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __bool__(self, /) | True if self else False | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __int__(self, /) | int(self) | | __le__(self, value, /) | Return self<=value. | | __lt__(self, value, /) | Return self (int, int) | | Return a pair of integers, whose ratio is exactly equal to the original | floating point number, and with a positive denominator. | Raise `OverflowError` on infinities and a `ValueError` on NaNs. | | >>> np.single(10.0).as_integer_ratio() | (10, 1) | >>> np.single(0.0).as_integer_ratio() | (0, 1) | >>> np.single(-.25).as_integer_ratio() | (-1, 4) | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from floating: | | __round__(...) | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __and__(self, value, /) | Return self&value. | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __copy__(...) | | __deepcopy__(...) | | __format__(...) | NumPy array scalar formatter | | __getitem__(self, key, /) | Return self[key]. | | __invert__(self, /) | ~self | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. ### class float64 | float64(x=0, /) | | Double-precision floating-point number type, compatible with Python `float` | and C ``double``. | | :Character code: ``'d'`` | :Canonical name: `numpy.double` | :Alias: `numpy.float_` | :Alias on this platform (Linux x86_64): `numpy.float64`: 64-bit precision floating-point number type: sign bit, 11 bits exponent, 52 bits mantissa. | | Method resolution order: | float64 | floating | inexact | number | generic | builtins.float | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __bool__(self, /) | True if self else False | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __int__(self, /) | int(self) | | __le__(self, value, /) | Return self<=value. | | __lt__(self, value, /) | Return self (int, int) | | Return a pair of integers, whose ratio is exactly equal to the original | floating point number, and with a positive denominator. | Raise `OverflowError` on infinities and a `ValueError` on NaNs. | | >>> np.double(10.0).as_integer_ratio() | (10, 1) | >>> np.double(0.0).as_integer_ratio() | (0, 1) | >>> np.double(-.25).as_integer_ratio() | (-1, 4) | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from floating: | | __round__(...) | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __and__(self, value, /) | Return self&value. | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __copy__(...) | | __deepcopy__(...) | | __format__(...) | NumPy array scalar formatter | | __getitem__(self, key, /) | Return self[key]. | | __invert__(self, /) | ~self | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. | | ---------------------------------------------------------------------- | Methods inherited from builtins.float: | | __ceil__(self, /) | Return the ceiling as an Integral. | | __floor__(self, /) | Return the floor as an Integral. | | __getattribute__(self, name, /) | Return getattr(self, name). | | __getnewargs__(self, /) | | __trunc__(self, /) | Return the Integral closest to x between 0 and x. | | hex(self, /) | Return a hexadecimal representation of a floating-point number. | | >>> (-0.1).hex() | '-0x1.999999999999ap-4' | >>> 3.14159.hex() | '0x1.921f9f01b866ep+1' | | is_integer(self, /) | Return True if the float is an integer. | | ---------------------------------------------------------------------- | Class methods inherited from builtins.float: | | __getformat__(typestr, /) from builtins.type | You probably don't want to use this function. | | typestr | Must be 'double' or 'float'. | | It exists mainly to be used in Python's test suite. | | This function returns whichever of 'unknown', 'IEEE, big-endian' or 'IEEE, | little-endian' best describes the format of floating point numbers used by the | C type named by typestr. | | __setformat__(typestr, fmt, /) from builtins.type | You probably don't want to use this function. | | typestr | Must be 'double' or 'float'. | fmt | Must be one of 'unknown', 'IEEE, big-endian' or 'IEEE, little-endian', | and in addition can only be one of the latter two if it appears to | match the underlying C reality. | | It exists mainly to be used in Python's test suite. | | Override the automatic determination of C-level floating point type. | This affects how floats are converted to and from binary strings. | | fromhex(string, /) from builtins.type | Create a floating-point number from a hexadecimal string. | | >>> float.fromhex('0x1.ffffp10') | 2047.984375 | >>> float.fromhex('-0x1p-1074') | -5e-324 float_ = class float64(floating, builtins.float) | float_(x=0, /) | | Double-precision floating-point number type, compatible with Python `float` | and C ``double``. | | :Character code: ``'d'`` | :Canonical name: `numpy.double` | :Alias: `numpy.float_` | :Alias on this platform (Linux x86_64): `numpy.float64`: 64-bit precision floating-point number type: sign bit, 11 bits exponent, 52 bits mantissa. | | Method resolution order: | float64 | floating | inexact | number | generic | builtins.float | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __bool__(self, /) | True if self else False | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __int__(self, /) | int(self) | | __le__(self, value, /) | Return self<=value. | | __lt__(self, value, /) | Return self (int, int) | | Return a pair of integers, whose ratio is exactly equal to the original | floating point number, and with a positive denominator. | Raise `OverflowError` on infinities and a `ValueError` on NaNs. | | >>> np.double(10.0).as_integer_ratio() | (10, 1) | >>> np.double(0.0).as_integer_ratio() | (0, 1) | >>> np.double(-.25).as_integer_ratio() | (-1, 4) | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from floating: | | __round__(...) | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __and__(self, value, /) | Return self&value. | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __copy__(...) | | __deepcopy__(...) | | __format__(...) | NumPy array scalar formatter | | __getitem__(self, key, /) | Return self[key]. | | __invert__(self, /) | ~self | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. | | ---------------------------------------------------------------------- | Methods inherited from builtins.float: | | __ceil__(self, /) | Return the ceiling as an Integral. | | __floor__(self, /) | Return the floor as an Integral. | | __getattribute__(self, name, /) | Return getattr(self, name). | | __getnewargs__(self, /) | | __trunc__(self, /) | Return the Integral closest to x between 0 and x. | | hex(self, /) | Return a hexadecimal representation of a floating-point number. | | >>> (-0.1).hex() | '-0x1.999999999999ap-4' | >>> 3.14159.hex() | '0x1.921f9f01b866ep+1' | | is_integer(self, /) | Return True if the float is an integer. | | ---------------------------------------------------------------------- | Class methods inherited from builtins.float: | | __getformat__(typestr, /) from builtins.type | You probably don't want to use this function. | | typestr | Must be 'double' or 'float'. | | It exists mainly to be used in Python's test suite. | | This function returns whichever of 'unknown', 'IEEE, big-endian' or 'IEEE, | little-endian' best describes the format of floating point numbers used by the | C type named by typestr. | | __setformat__(typestr, fmt, /) from builtins.type | You probably don't want to use this function. | | typestr | Must be 'double' or 'float'. | fmt | Must be one of 'unknown', 'IEEE, big-endian' or 'IEEE, little-endian', | and in addition can only be one of the latter two if it appears to | match the underlying C reality. | | It exists mainly to be used in Python's test suite. | | Override the automatic determination of C-level floating point type. | This affects how floats are converted to and from binary strings. | | fromhex(string, /) from builtins.type | Create a floating-point number from a hexadecimal string. | | >>> float.fromhex('0x1.ffffp10') | 2047.984375 | >>> float.fromhex('-0x1p-1074') | -5e-324 ### class floating | Abstract base class of all floating-point scalar types. | | Method resolution order: | floating | inexact | number | generic | builtins.object | | Methods defined here: | | __round__(...) | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __and__(self, value, /) | Return self&value. | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __bool__(self, /) | True if self else False | | __copy__(...) | | __deepcopy__(...) | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __format__(...) | NumPy array scalar formatter | | __ge__(self, value, /) | Return self>=value. | | __getitem__(self, key, /) | Return self[key]. | | __gt__(self, value, /) | Return self>value. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __le__(self, value, /) | Return self<=value. | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. | | ---------------------------------------------------------------------- | Data and other attributes inherited from generic: | | __hash__ = None ### class format_parser | format_parser(formats, names, titles, aligned=False, byteorder=None) | | Class to convert formats, names, titles description to a dtype. | | After constructing the format_parser object, the dtype attribute is | the converted data-type: | ``dtype = format_parser(formats, names, titles).dtype`` | | Attributes | ---------- | dtype : dtype | The converted data-type. | | Parameters | ---------- | formats : str or list of str | The format description, either specified as a string with | comma-separated format descriptions in the form ``'f8, i4, a5'``, or | a list of format description strings in the form | ``['f8', 'i4', 'a5']``. | names : str or list/tuple of str | The field names, either specified as a comma-separated string in the | form ``'col1, col2, col3'``, or as a list or tuple of strings in the | form ``['col1', 'col2', 'col3']``. | An empty list can be used, in that case default field names | ('f0', 'f1', ...) are used. | titles : sequence | Sequence of title strings. An empty list can be used to leave titles | out. | aligned : bool, optional | If True, align the fields by padding as the C-compiler would. | Default is False. | byteorder : str, optional | If specified, all the fields will be changed to the | provided byte-order. Otherwise, the default byte-order is | used. For all available string specifiers, see `dtype.newbyteorder`. | | See Also | -------- | dtype, typename, sctype2char | | Examples | -------- | >>> np.format_parser(['>> np.format_parser(['f8', 'i4', 'a5'], ['col1', 'col2', 'col3'], | ... []).dtype | dtype([('col1', '>> np.format_parser(['=value. | | __getitem__(self, key, /) | Return self[key]. | | __gt__(self, value, /) | Return self>value. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __le__(self, value, /) | Return self<=value. | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors defined here: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. | | ---------------------------------------------------------------------- | Data and other attributes defined here: | | __hash__ = None half = class float16(floating) | Half-precision floating-point number type. | | :Character code: ``'e'`` | :Canonical name: `numpy.half` | :Alias on this platform (Linux x86_64): `numpy.float16`: 16-bit-precision floating-point number type: sign bit, 5 bits exponent, 10 bits mantissa. | | Method resolution order: | float16 | floating | inexact | number | generic | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __bool__(self, /) | True if self else False | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __int__(self, /) | int(self) | | __le__(self, value, /) | Return self<=value. | | __lt__(self, value, /) | Return self (int, int) | | Return a pair of integers, whose ratio is exactly equal to the original | floating point number, and with a positive denominator. | Raise `OverflowError` on infinities and a `ValueError` on NaNs. | | >>> np.half(10.0).as_integer_ratio() | (10, 1) | >>> np.half(0.0).as_integer_ratio() | (0, 1) | >>> np.half(-.25).as_integer_ratio() | (-1, 4) | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from floating: | | __round__(...) | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __and__(self, value, /) | Return self&value. | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __copy__(...) | | __deepcopy__(...) | | __format__(...) | NumPy array scalar formatter | | __getitem__(self, key, /) | Return self[key]. | | __invert__(self, /) | ~self | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. ### class iinfo | iinfo(int_type) | | iinfo(type) | | Machine limits for integer types. | | Attributes | ---------- | bits : int | The number of bits occupied by the type. | min : int | The smallest integer expressible by the type. | max : int | The largest integer expressible by the type. | | Parameters | ---------- | int_type : integer type, dtype, or instance | The kind of integer data type to get information about. | | See Also | -------- | finfo : The equivalent for floating point data types. | | Examples | -------- | With types: | | >>> ii16 = np.iinfo(np.int16) | >>> ii16.min | -32768 | >>> ii16.max | 32767 | >>> ii32 = np.iinfo(np.int32) | >>> ii32.min | -2147483648 | >>> ii32.max | 2147483647 | | With instances: | | >>> ii32 = np.iinfo([np.int32(10)](https://www.chedong.com/phpMan.php/man/np.int32/10/markdown)) | >>> ii32.min | -2147483648 | >>> ii32.max | 2147483647 | | Methods defined here: | | __init__(self, int_type) | Initialize self. See help(type(self)) for accurate signature. | | __repr__(self) | Return repr(self). | | __str__(self) | String representation. | | ---------------------------------------------------------------------- | Readonly properties defined here: | | max | Maximum value of given dtype. | | min | Minimum value of given dtype. | | ---------------------------------------------------------------------- | Data descriptors defined here: | | __dict__ | dictionary for instance variables (if defined) | | __weakref__ | list of weak references to the object (if defined) ### class inexact | Abstract base class of all numeric scalar types with a (potentially) | inexact representation of the values in its range, such as | floating-point numbers. | | Method resolution order: | inexact | number | generic | builtins.object | | Methods inherited from generic: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __and__(self, value, /) | Return self&value. | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __bool__(self, /) | True if self else False | | __copy__(...) | | __deepcopy__(...) | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __format__(...) | NumPy array scalar formatter | | __ge__(self, value, /) | Return self>=value. | | __getitem__(self, key, /) | Return self[key]. | | __gt__(self, value, /) | Return self>value. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __le__(self, value, /) | Return self<=value. | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. | | ---------------------------------------------------------------------- | Data and other attributes inherited from generic: | | __hash__ = None int0 = class int64(signedinteger) | Signed integer type, compatible with Python `int` and C ``long``. | | :Character code: ``'l'`` | :Canonical name: `numpy.int_` | :Alias on this platform (Linux x86_64): `numpy.int64`: 64-bit signed integer (``-9_223_372_036_854_775_808`` to ``9_223_372_036_854_775_807``). | :Alias on this platform (Linux x86_64): `numpy.intp`: Signed integer large enough to fit pointer, compatible with C ``intptr_t``. | | Method resolution order: | int64 | signedinteger | integer | number | generic | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __and__(self, value, /) | Return self&value. | | __bool__(self, /) | True if self else False | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __index__(self, /) | Return self converted to an integer, if self is suitable for use as an index into a list. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __le__(self, value, /) | Return self<=value. | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __str__(self, /) | Return str(self). | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from integer: | | __round__(...) | | ---------------------------------------------------------------------- | Data descriptors inherited from integer: | | denominator | denominator of value (1) | | numerator | numerator of value (the value itself) | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __copy__(...) | | __deepcopy__(...) | | __format__(...) | NumPy array scalar formatter | | __getitem__(self, key, /) | Return self[key]. | | __reduce__(...) | Helper for pickle. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. ### class int16 | Signed integer type, compatible with C ``short``. | | :Character code: ``'h'`` | :Canonical name: `numpy.short` | :Alias on this platform (Linux x86_64): `numpy.int16`: 16-bit signed integer (``-32_768`` to ``32_767``). | | Method resolution order: | int16 | signedinteger | integer | number | generic | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __and__(self, value, /) | Return self&value. | | __bool__(self, /) | True if self else False | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __index__(self, /) | Return self converted to an integer, if self is suitable for use as an index into a list. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __le__(self, value, /) | Return self<=value. | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __str__(self, /) | Return str(self). | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from integer: | | __round__(...) | | ---------------------------------------------------------------------- | Data descriptors inherited from integer: | | denominator | denominator of value (1) | | numerator | numerator of value (the value itself) | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __copy__(...) | | __deepcopy__(...) | | __format__(...) | NumPy array scalar formatter | | __getitem__(self, key, /) | Return self[key]. | | __reduce__(...) | Helper for pickle. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. ### class int32 | Signed integer type, compatible with C ``int``. | | :Character code: ``'i'`` | :Canonical name: `numpy.intc` | :Alias on this platform (Linux x86_64): `numpy.int32`: 32-bit signed integer (``-2_147_483_648`` to ``2_147_483_647``). | | Method resolution order: | int32 | signedinteger | integer | number | generic | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __and__(self, value, /) | Return self&value. | | __bool__(self, /) | True if self else False | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __index__(self, /) | Return self converted to an integer, if self is suitable for use as an index into a list. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __le__(self, value, /) | Return self<=value. | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __str__(self, /) | Return str(self). | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from integer: | | __round__(...) | | ---------------------------------------------------------------------- | Data descriptors inherited from integer: | | denominator | denominator of value (1) | | numerator | numerator of value (the value itself) | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __copy__(...) | | __deepcopy__(...) | | __format__(...) | NumPy array scalar formatter | | __getitem__(self, key, /) | Return self[key]. | | __reduce__(...) | Helper for pickle. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. ### class int64 | Signed integer type, compatible with Python `int` and C ``long``. | | :Character code: ``'l'`` | :Canonical name: `numpy.int_` | :Alias on this platform (Linux x86_64): `numpy.int64`: 64-bit signed integer (``-9_223_372_036_854_775_808`` to ``9_223_372_036_854_775_807``). | :Alias on this platform (Linux x86_64): `numpy.intp`: Signed integer large enough to fit pointer, compatible with C ``intptr_t``. | | Method resolution order: | int64 | signedinteger | integer | number | generic | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __and__(self, value, /) | Return self&value. | | __bool__(self, /) | True if self else False | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __index__(self, /) | Return self converted to an integer, if self is suitable for use as an index into a list. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __le__(self, value, /) | Return self<=value. | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __str__(self, /) | Return str(self). | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from integer: | | __round__(...) | | ---------------------------------------------------------------------- | Data descriptors inherited from integer: | | denominator | denominator of value (1) | | numerator | numerator of value (the value itself) | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __copy__(...) | | __deepcopy__(...) | | __format__(...) | NumPy array scalar formatter | | __getitem__(self, key, /) | Return self[key]. | | __reduce__(...) | Helper for pickle. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. ### class int8 | Signed integer type, compatible with C ``char``. | | :Character code: ``'b'`` | :Canonical name: `numpy.byte` | :Alias on this platform (Linux x86_64): `numpy.int8`: 8-bit signed integer (``-128`` to ``127``). | | Method resolution order: | int8 | signedinteger | integer | number | generic | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __and__(self, value, /) | Return self&value. | | __bool__(self, /) | True if self else False | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __index__(self, /) | Return self converted to an integer, if self is suitable for use as an index into a list. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __le__(self, value, /) | Return self<=value. | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __str__(self, /) | Return str(self). | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from integer: | | __round__(...) | | ---------------------------------------------------------------------- | Data descriptors inherited from integer: | | denominator | denominator of value (1) | | numerator | numerator of value (the value itself) | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __copy__(...) | | __deepcopy__(...) | | __format__(...) | NumPy array scalar formatter | | __getitem__(self, key, /) | Return self[key]. | | __reduce__(...) | Helper for pickle. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. int_ = class int64(signedinteger) | Signed integer type, compatible with Python `int` and C ``long``. | | :Character code: ``'l'`` | :Canonical name: `numpy.int_` | :Alias on this platform (Linux x86_64): `numpy.int64`: 64-bit signed integer (``-9_223_372_036_854_775_808`` to ``9_223_372_036_854_775_807``). | :Alias on this platform (Linux x86_64): `numpy.intp`: Signed integer large enough to fit pointer, compatible with C ``intptr_t``. | | Method resolution order: | int64 | signedinteger | integer | number | generic | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __and__(self, value, /) | Return self&value. | | __bool__(self, /) | True if self else False | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __index__(self, /) | Return self converted to an integer, if self is suitable for use as an index into a list. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __le__(self, value, /) | Return self<=value. | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __str__(self, /) | Return str(self). | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from integer: | | __round__(...) | | ---------------------------------------------------------------------- | Data descriptors inherited from integer: | | denominator | denominator of value (1) | | numerator | numerator of value (the value itself) | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __copy__(...) | | __deepcopy__(...) | | __format__(...) | NumPy array scalar formatter | | __getitem__(self, key, /) | Return self[key]. | | __reduce__(...) | Helper for pickle. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. intc = class int32(signedinteger) | Signed integer type, compatible with C ``int``. | | :Character code: ``'i'`` | :Canonical name: `numpy.intc` | :Alias on this platform (Linux x86_64): `numpy.int32`: 32-bit signed integer (``-2_147_483_648`` to ``2_147_483_647``). | | Method resolution order: | int32 | signedinteger | integer | number | generic | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __and__(self, value, /) | Return self&value. | | __bool__(self, /) | True if self else False | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __index__(self, /) | Return self converted to an integer, if self is suitable for use as an index into a list. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __le__(self, value, /) | Return self<=value. | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __str__(self, /) | Return str(self). | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from integer: | | __round__(...) | | ---------------------------------------------------------------------- | Data descriptors inherited from integer: | | denominator | denominator of value (1) | | numerator | numerator of value (the value itself) | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __copy__(...) | | __deepcopy__(...) | | __format__(...) | NumPy array scalar formatter | | __getitem__(self, key, /) | Return self[key]. | | __reduce__(...) | Helper for pickle. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. ### class integer | Abstract base class of all integer scalar types. | | Method resolution order: | integer | number | generic | builtins.object | | Methods defined here: | | __round__(...) | | ---------------------------------------------------------------------- | Data descriptors defined here: | | denominator | denominator of value (1) | | numerator | numerator of value (the value itself) | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __and__(self, value, /) | Return self&value. | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __bool__(self, /) | True if self else False | | __copy__(...) | | __deepcopy__(...) | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __format__(...) | NumPy array scalar formatter | | __ge__(self, value, /) | Return self>=value. | | __getitem__(self, key, /) | Return self[key]. | | __gt__(self, value, /) | Return self>value. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __le__(self, value, /) | Return self<=value. | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. | | ---------------------------------------------------------------------- | Data and other attributes inherited from generic: | | __hash__ = None intp = class int64(signedinteger) | Signed integer type, compatible with Python `int` and C ``long``. | | :Character code: ``'l'`` | :Canonical name: `numpy.int_` | :Alias on this platform (Linux x86_64): `numpy.int64`: 64-bit signed integer (``-9_223_372_036_854_775_808`` to ``9_223_372_036_854_775_807``). | :Alias on this platform (Linux x86_64): `numpy.intp`: Signed integer large enough to fit pointer, compatible with C ``intptr_t``. | | Method resolution order: | int64 | signedinteger | integer | number | generic | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __and__(self, value, /) | Return self&value. | | __bool__(self, /) | True if self else False | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __index__(self, /) | Return self converted to an integer, if self is suitable for use as an index into a list. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __le__(self, value, /) | Return self<=value. | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __str__(self, /) | Return str(self). | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from integer: | | __round__(...) | | ---------------------------------------------------------------------- | Data descriptors inherited from integer: | | denominator | denominator of value (1) | | numerator | numerator of value (the value itself) | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __copy__(...) | | __deepcopy__(...) | | __format__(...) | NumPy array scalar formatter | | __getitem__(self, key, /) | Return self[key]. | | __reduce__(...) | Helper for pickle. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. longcomplex = class complex256(complexfloating) | Complex number type composed of two extended-precision floating-point | numbers. | | :Character code: ``'G'`` | :Canonical name: `numpy.clongdouble` | :Alias: `numpy.clongfloat` | :Alias: `numpy.longcomplex` | :Alias on this platform (Linux x86_64): `numpy.complex256`: Complex number type composed of 2 128-bit extended-precision floating-point numbers. | | Method resolution order: | complex256 | complexfloating | inexact | number | generic | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __bool__(self, /) | True if self else False | | __complex__(...) | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __int__(self, /) | int(self) | | __le__(self, value, /) | Return self<=value. | | __lt__(self, value, /) | Return self>self. | | __rshift__(self, value, /) | Return self>>value. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. longdouble = class float128(floating) | Extended-precision floating-point number type, compatible with C | ``long double`` but not necessarily with IEEE 754 quadruple-precision. | | :Character code: ``'g'`` | :Canonical name: `numpy.longdouble` | :Alias: `numpy.longfloat` | :Alias on this platform (Linux x86_64): `numpy.float128`: 128-bit extended-precision floating-point number type. | | Method resolution order: | float128 | floating | inexact | number | generic | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __bool__(self, /) | True if self else False | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __int__(self, /) | int(self) | | __le__(self, value, /) | Return self<=value. | | __lt__(self, value, /) | Return self (int, int) | | Return a pair of integers, whose ratio is exactly equal to the original | floating point number, and with a positive denominator. | Raise `OverflowError` on infinities and a `ValueError` on NaNs. | | >>> np.longdouble(10.0).as_integer_ratio() | (10, 1) | >>> np.longdouble(0.0).as_integer_ratio() | (0, 1) | >>> np.longdouble(-.25).as_integer_ratio() | (-1, 4) | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from floating: | | __round__(...) | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __and__(self, value, /) | Return self&value. | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __copy__(...) | | __deepcopy__(...) | | __format__(...) | NumPy array scalar formatter | | __getitem__(self, key, /) | Return self[key]. | | __invert__(self, /) | ~self | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. longfloat = class float128(floating) | Extended-precision floating-point number type, compatible with C | ``long double`` but not necessarily with IEEE 754 quadruple-precision. | | :Character code: ``'g'`` | :Canonical name: `numpy.longdouble` | :Alias: `numpy.longfloat` | :Alias on this platform (Linux x86_64): `numpy.float128`: 128-bit extended-precision floating-point number type. | | Method resolution order: | float128 | floating | inexact | number | generic | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __bool__(self, /) | True if self else False | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __int__(self, /) | int(self) | | __le__(self, value, /) | Return self<=value. | | __lt__(self, value, /) | Return self (int, int) | | Return a pair of integers, whose ratio is exactly equal to the original | floating point number, and with a positive denominator. | Raise `OverflowError` on infinities and a `ValueError` on NaNs. | | >>> np.longdouble(10.0).as_integer_ratio() | (10, 1) | >>> np.longdouble(0.0).as_integer_ratio() | (0, 1) | >>> np.longdouble(-.25).as_integer_ratio() | (-1, 4) | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from floating: | | __round__(...) | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __and__(self, value, /) | Return self&value. | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __copy__(...) | | __deepcopy__(...) | | __format__(...) | NumPy array scalar formatter | | __getitem__(self, key, /) | Return self[key]. | | __invert__(self, /) | ~self | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. ### class longlong | Signed integer type, compatible with C ``long long``. | | :Character code: ``'q'`` | | Method resolution order: | longlong | signedinteger | integer | number | generic | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __and__(self, value, /) | Return self&value. | | __bool__(self, /) | True if self else False | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __index__(self, /) | Return self converted to an integer, if self is suitable for use as an index into a list. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __le__(self, value, /) | Return self<=value. | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __str__(self, /) | Return str(self). | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from integer: | | __round__(...) | | ---------------------------------------------------------------------- | Data descriptors inherited from integer: | | denominator | denominator of value (1) | | numerator | numerator of value (the value itself) | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __copy__(...) | | __deepcopy__(...) | | __format__(...) | NumPy array scalar formatter | | __getitem__(self, key, /) | Return self[key]. | | __reduce__(...) | Helper for pickle. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. ### class matrix | matrix(data, dtype=None, copy=True) | | matrix(data, dtype=None, copy=True) | | .. note:: It is no longer recommended to use this class, even for linear | algebra. Instead use regular arrays. The class may be removed | in the future. | | Returns a matrix from an array-like object, or from a string of data. | A matrix is a specialized 2-D array that retains its 2-D nature | through operations. It has certain special operators, such as ``*`` | (matrix multiplication) and ``**`` (matrix power). | | Parameters | ---------- | data : array_like or string | If `data` is a string, it is interpreted as a matrix with commas | or spaces separating columns, and semicolons separating rows. | dtype : data-type | Data-type of the output matrix. | copy : bool | If `data` is already an `ndarray`, then this flag determines | whether the data is copied (the default), or whether a view is | constructed. | | See Also | -------- | array | | Examples | -------- | >>> a = np.matrix('1 2; 3 4') | >>> a | matrix([[1, 2], | [3, 4]]) | | >>> np.matrix([[1, 2], [3, 4]]) | matrix([[1, 2], | [3, 4]]) | | Method resolution order: | matrix | ndarray | builtins.object | | Methods defined here: | | __array_finalize__(self, obj) | None. | | __getitem__(self, index) | Return self[key]. | | __imul__(self, other) | Return self*=value. | | __ipow__(self, other) | Return self**=value. | | __mul__(self, other) | Return self*value. | | __pow__(self, other) | Return pow(self, value, mod). | | __rmul__(self, other) | Return value*self. | | __rpow__(self, other) | Return pow(value, self, mod). | | all(self, axis=None, out=None) | Test whether all matrix elements along a given axis evaluate to True. | | Parameters | ---------- | See `numpy.all` for complete descriptions | | See Also | -------- | numpy.all | | Notes | ----- | This is the same as `ndarray.all`, but it returns a `matrix` object. | | Examples | -------- | >>> x = np.matrix([np.arange(12)](https://www.chedong.com/phpMan.php/man/np.arange/12/markdown).reshape((3,4))); x | matrix([[ 0, 1, 2, 3], | [ 4, 5, 6, 7], | [ 8, 9, 10, 11]]) | >>> y = x[0]; y | matrix([[0, 1, 2, 3]]) | >>> (x == y) | matrix([[ True, True, True, True], | [False, False, False, False], | [False, False, False, False]]) | >>> (x == y).all() | False | >>> (x == y)[.all(0)](https://www.chedong.com/phpMan.php/man/.all/0/markdown) | matrix([[False, False, False, False]]) | >>> (x == y)[.all(1)](https://www.chedong.com/phpMan.php/man/.all/1/markdown) | matrix([[ True], | [False], | [False]]) | | any(self, axis=None, out=None) | Test whether any array element along a given axis evaluates to True. | | Refer to `numpy.any` for full documentation. | | Parameters | ---------- | axis : int, optional | Axis along which logical OR is performed | out : ndarray, optional | Output to existing array instead of creating new one, must have | same shape as expected output | | Returns | ------- | any : bool, ndarray | Returns a single bool if `axis` is ``None``; otherwise, | returns `ndarray` | | argmax(self, axis=None, out=None) | Indexes of the maximum values along an axis. | | Return the indexes of the first occurrences of the maximum values | along the specified axis. If axis is None, the index is for the | flattened matrix. | | Parameters | ---------- | See `numpy.argmax` for complete descriptions | | See Also | -------- | numpy.argmax | | Notes | ----- | This is the same as `ndarray.argmax`, but returns a `matrix` object | where `ndarray.argmax` would return an `ndarray`. | | Examples | -------- | >>> x = np.matrix([np.arange(12)](https://www.chedong.com/phpMan.php/man/np.arange/12/markdown).reshape((3,4))); x | matrix([[ 0, 1, 2, 3], | [ 4, 5, 6, 7], | [ 8, 9, 10, 11]]) | >>> x.argmax() | 11 | >>> [x.argmax(0)](https://www.chedong.com/phpMan.php/man/x.argmax/0/markdown) | matrix([[2, 2, 2, 2]]) | >>> [x.argmax(1)](https://www.chedong.com/phpMan.php/man/x.argmax/1/markdown) | matrix([[3], | [3], | [3]]) | | argmin(self, axis=None, out=None) | Indexes of the minimum values along an axis. | | Return the indexes of the first occurrences of the minimum values | along the specified axis. If axis is None, the index is for the | flattened matrix. | | Parameters | ---------- | See `numpy.argmin` for complete descriptions. | | See Also | -------- | numpy.argmin | | Notes | ----- | This is the same as `ndarray.argmin`, but returns a `matrix` object | where `ndarray.argmin` would return an `ndarray`. | | Examples | -------- | >>> x = -np.matrix([np.arange(12)](https://www.chedong.com/phpMan.php/man/np.arange/12/markdown).reshape((3,4))); x | matrix([[ 0, -1, -2, -3], | [ -4, -5, -6, -7], | [ -8, -9, -10, -11]]) | >>> x.argmin() | 11 | >>> [x.argmin(0)](https://www.chedong.com/phpMan.php/man/x.argmin/0/markdown) | matrix([[2, 2, 2, 2]]) | >>> [x.argmin(1)](https://www.chedong.com/phpMan.php/man/x.argmin/1/markdown) | matrix([[3], | [3], | [3]]) | | flatten(self, order='C') | Return a flattened copy of the matrix. | | All `N` elements of the matrix are placed into a single row. | | Parameters | ---------- | order : {'C', 'F', 'A', 'K'}, optional | 'C' means to flatten in row-major (C-style) order. 'F' means to | flatten in column-major (Fortran-style) order. 'A' means to | flatten in column-major order if `m` is Fortran *contiguous* in | memory, row-major order otherwise. 'K' means to flatten `m` in | the order the elements occur in memory. The default is 'C'. | | Returns | ------- | y : matrix | A copy of the matrix, flattened to a `(1, N)` matrix where `N` | is the number of elements in the original matrix. | | See Also | -------- | ravel : Return a flattened array. | flat : A 1-D flat iterator over the matrix. | | Examples | -------- | >>> m = np.matrix([[1,2], [3,4]]) | >>> m.flatten() | matrix([[1, 2, 3, 4]]) | >>> m.flatten('F') | matrix([[1, 3, 2, 4]]) | | getA = A(self) | Return `self` as an `ndarray` object. | | Equivalent to ``np.asarray(self)``. | | Parameters | ---------- | None | | Returns | ------- | ret : ndarray | `self` as an `ndarray` | | Examples | -------- | >>> x = np.matrix([np.arange(12)](https://www.chedong.com/phpMan.php/man/np.arange/12/markdown).reshape((3,4))); x | matrix([[ 0, 1, 2, 3], | [ 4, 5, 6, 7], | [ 8, 9, 10, 11]]) | >>> x.getA() | array([[ 0, 1, 2, 3], | [ 4, 5, 6, 7], | [ 8, 9, 10, 11]]) | | getA1 = A1(self) | Return `self` as a flattened `ndarray`. | | Equivalent to ``np.asarray(x).ravel()`` | | Parameters | ---------- | None | | Returns | ------- | ret : ndarray | `self`, 1-D, as an `ndarray` | | Examples | -------- | >>> x = np.matrix([np.arange(12)](https://www.chedong.com/phpMan.php/man/np.arange/12/markdown).reshape((3,4))); x | matrix([[ 0, 1, 2, 3], | [ 4, 5, 6, 7], | [ 8, 9, 10, 11]]) | >>> x.getA1() | array([ 0, 1, 2, ..., 9, 10, 11]) | | getH = H(self) | Returns the (complex) conjugate transpose of `self`. | | Equivalent to ``np.transpose(self)`` if `self` is real-valued. | | Parameters | ---------- | None | | Returns | ------- | ret : matrix object | complex conjugate transpose of `self` | | Examples | -------- | >>> x = np.matrix([np.arange(12)](https://www.chedong.com/phpMan.php/man/np.arange/12/markdown).reshape((3,4))) | >>> z = x - 1j*x; z | matrix([[ 0. +0.j, 1. -1.j, 2. -2.j, 3. -3.j], | [ 4. -4.j, 5. -5.j, 6. -6.j, 7. -7.j], | [ 8. -8.j, 9. -9.j, 10.-10.j, 11.-11.j]]) | >>> z.getH() | matrix([[ 0. -0.j, 4. +4.j, 8. +8.j], | [ 1. +1.j, 5. +5.j, 9. +9.j], | [ 2. +2.j, 6. +6.j, 10.+10.j], | [ 3. +3.j, 7. +7.j, 11.+11.j]]) | | getI = I(self) | Returns the (multiplicative) inverse of invertible `self`. | | Parameters | ---------- | None | | Returns | ------- | ret : matrix object | If `self` is non-singular, `ret` is such that ``ret * self`` == | ``self * ret`` == ``np.matrix(np.eye(self[0,:].size))`` all return | ``True``. | | Raises | ------ | numpy.linalg.LinAlgError: Singular matrix | If `self` is singular. | | See Also | -------- | linalg.inv | | Examples | -------- | >>> m = np.matrix('[1, 2; 3, 4]'); m | matrix([[1, 2], | [3, 4]]) | >>> m.getI() | matrix([[-2. , 1. ], | [ 1.5, -0.5]]) | >>> m.getI() * m | matrix([[ 1., 0.], # may vary | [ 0., 1.]]) | | getT = T(self) | Returns the transpose of the matrix. | | Does *not* conjugate! For the complex conjugate transpose, use ``.H``. | | Parameters | ---------- | None | | Returns | ------- | ret : matrix object | The (non-conjugated) transpose of the matrix. | | See Also | -------- | transpose, getH | | Examples | -------- | >>> m = np.matrix('[1, 2; 3, 4]') | >>> m | matrix([[1, 2], | [3, 4]]) | >>> m.getT() | matrix([[1, 3], | [2, 4]]) | | max(self, axis=None, out=None) | Return the maximum value along an axis. | | Parameters | ---------- | See `amax` for complete descriptions | | See Also | -------- | amax, ndarray.max | | Notes | ----- | This is the same as `ndarray.max`, but returns a `matrix` object | where `ndarray.max` would return an ndarray. | | Examples | -------- | >>> x = np.matrix([np.arange(12)](https://www.chedong.com/phpMan.php/man/np.arange/12/markdown).reshape((3,4))); x | matrix([[ 0, 1, 2, 3], | [ 4, 5, 6, 7], | [ 8, 9, 10, 11]]) | >>> x.max() | 11 | >>> [x.max(0)](https://www.chedong.com/phpMan.php/man/x.max/0/markdown) | matrix([[ 8, 9, 10, 11]]) | >>> [x.max(1)](https://www.chedong.com/phpMan.php/man/x.max/1/markdown) | matrix([[ 3], | [ 7], | [11]]) | | mean(self, axis=None, dtype=None, out=None) | Returns the average of the matrix elements along the given axis. | | Refer to `numpy.mean` for full documentation. | | See Also | -------- | numpy.mean | | Notes | ----- | Same as `ndarray.mean` except that, where that returns an `ndarray`, | this returns a `matrix` object. | | Examples | -------- | >>> x = np.matrix([np.arange(12)](https://www.chedong.com/phpMan.php/man/np.arange/12/markdown).reshape((3, 4))) | >>> x | matrix([[ 0, 1, 2, 3], | [ 4, 5, 6, 7], | [ 8, 9, 10, 11]]) | >>> x.mean() | 5.5 | >>> [x.mean(0)](https://www.chedong.com/phpMan.php/man/x.mean/0/markdown) | matrix([[4., 5., 6., 7.]]) | >>> [x.mean(1)](https://www.chedong.com/phpMan.php/man/x.mean/1/markdown) | matrix([[ 1.5], | [ 5.5], | [ 9.5]]) | | min(self, axis=None, out=None) | Return the minimum value along an axis. | | Parameters | ---------- | See `amin` for complete descriptions. | | See Also | -------- | amin, ndarray.min | | Notes | ----- | This is the same as `ndarray.min`, but returns a `matrix` object | where `ndarray.min` would return an ndarray. | | Examples | -------- | >>> x = -np.matrix([np.arange(12)](https://www.chedong.com/phpMan.php/man/np.arange/12/markdown).reshape((3,4))); x | matrix([[ 0, -1, -2, -3], | [ -4, -5, -6, -7], | [ -8, -9, -10, -11]]) | >>> x.min() | -11 | >>> [x.min(0)](https://www.chedong.com/phpMan.php/man/x.min/0/markdown) | matrix([[ -8, -9, -10, -11]]) | >>> [x.min(1)](https://www.chedong.com/phpMan.php/man/x.min/1/markdown) | matrix([[ -3], | [ -7], | [-11]]) | | prod(self, axis=None, dtype=None, out=None) | Return the product of the array elements over the given axis. | | Refer to `prod` for full documentation. | | See Also | -------- | prod, ndarray.prod | | Notes | ----- | Same as `ndarray.prod`, except, where that returns an `ndarray`, this | returns a `matrix` object instead. | | Examples | -------- | >>> x = np.matrix([np.arange(12)](https://www.chedong.com/phpMan.php/man/np.arange/12/markdown).reshape((3,4))); x | matrix([[ 0, 1, 2, 3], | [ 4, 5, 6, 7], | [ 8, 9, 10, 11]]) | >>> x.prod() | 0 | >>> [x.prod(0)](https://www.chedong.com/phpMan.php/man/x.prod/0/markdown) | matrix([[ 0, 45, 120, 231]]) | >>> [x.prod(1)](https://www.chedong.com/phpMan.php/man/x.prod/1/markdown) | matrix([[ 0], | [ 840], | [7920]]) | | ptp(self, axis=None, out=None) | Peak-to-peak (maximum - minimum) value along the given axis. | | Refer to `numpy.ptp` for full documentation. | | See Also | -------- | numpy.ptp | | Notes | ----- | Same as `ndarray.ptp`, except, where that would return an `ndarray` object, | this returns a `matrix` object. | | Examples | -------- | >>> x = np.matrix([np.arange(12)](https://www.chedong.com/phpMan.php/man/np.arange/12/markdown).reshape((3,4))); x | matrix([[ 0, 1, 2, 3], | [ 4, 5, 6, 7], | [ 8, 9, 10, 11]]) | >>> x.ptp() | 11 | >>> [x.ptp(0)](https://www.chedong.com/phpMan.php/man/x.ptp/0/markdown) | matrix([[8, 8, 8, 8]]) | >>> [x.ptp(1)](https://www.chedong.com/phpMan.php/man/x.ptp/1/markdown) | matrix([[3], | [3], | [3]]) | | ravel(self, order='C') | Return a flattened matrix. | | Refer to `numpy.ravel` for more documentation. | | Parameters | ---------- | order : {'C', 'F', 'A', 'K'}, optional | The elements of `m` are read using this index order. 'C' means to | index the elements in C-like order, with the last axis index | changing fastest, back to the first axis index changing slowest. | 'F' means to index the elements in Fortran-like index order, with | the first index changing fastest, and the last index changing | slowest. Note that the 'C' and 'F' options take no account of the | memory layout of the underlying array, and only refer to the order | of axis indexing. 'A' means to read the elements in Fortran-like | index order if `m` is Fortran *contiguous* in memory, C-like order | otherwise. 'K' means to read the elements in the order they occur | in memory, except for reversing the data when strides are negative. | By default, 'C' index order is used. | | Returns | ------- | ret : matrix | Return the matrix flattened to shape `(1, N)` where `N` | is the number of elements in the original matrix. | A copy is made only if necessary. | | See Also | -------- | matrix.flatten : returns a similar output matrix but always a copy | matrix.flat : a flat iterator on the array. | numpy.ravel : related function which returns an ndarray | | squeeze(self, axis=None) | Return a possibly reshaped matrix. | | Refer to `numpy.squeeze` for more documentation. | | Parameters | ---------- | axis : None or int or tuple of ints, optional | Selects a subset of the axes of length one in the shape. | If an axis is selected with shape entry greater than one, | an error is raised. | | Returns | ------- | squeezed : matrix | The matrix, but as a (1, N) matrix if it had shape (N, 1). | | See Also | -------- | numpy.squeeze : related function | | Notes | ----- | If `m` has a single column then that column is returned | as the single row of a matrix. Otherwise `m` is returned. | The returned matrix is always either `m` itself or a view into `m`. | Supplying an axis keyword argument will not affect the returned matrix | but it may cause an error to be raised. | | Examples | -------- | >>> c = np.matrix([[1], [2]]) | >>> c | matrix([[1], | [2]]) | >>> c.squeeze() | matrix([[1, 2]]) | >>> r = c.T | >>> r | matrix([[1, 2]]) | >>> r.squeeze() | matrix([[1, 2]]) | >>> m = np.matrix([[1, 2], [3, 4]]) | >>> m.squeeze() | matrix([[1, 2], | [3, 4]]) | | std(self, axis=None, dtype=None, out=None, ddof=0) | Return the standard deviation of the array elements along the given axis. | | Refer to `numpy.std` for full documentation. | | See Also | -------- | numpy.std | | Notes | ----- | This is the same as `ndarray.std`, except that where an `ndarray` would | be returned, a `matrix` object is returned instead. | | Examples | -------- | >>> x = np.matrix([np.arange(12)](https://www.chedong.com/phpMan.php/man/np.arange/12/markdown).reshape((3, 4))) | >>> x | matrix([[ 0, 1, 2, 3], | [ 4, 5, 6, 7], | [ 8, 9, 10, 11]]) | >>> x.std() | 3.4520525295346629 # may vary | >>> [x.std(0)](https://www.chedong.com/phpMan.php/man/x.std/0/markdown) | matrix([[ 3.26598632, 3.26598632, 3.26598632, 3.26598632]]) # may vary | >>> [x.std(1)](https://www.chedong.com/phpMan.php/man/x.std/1/markdown) | matrix([[ 1.11803399], | [ 1.11803399], | [ 1.11803399]]) | | sum(self, axis=None, dtype=None, out=None) | Returns the sum of the matrix elements, along the given axis. | | Refer to `numpy.sum` for full documentation. | | See Also | -------- | numpy.sum | | Notes | ----- | This is the same as `ndarray.sum`, except that where an `ndarray` would | be returned, a `matrix` object is returned instead. | | Examples | -------- | >>> x = np.matrix([[1, 2], [4, 3]]) | >>> x.sum() | 10 | >>> x.sum(axis=1) | matrix([[3], | [7]]) | >>> x.sum(axis=1, dtype='float') | matrix([[3.], | [7.]]) | >>> out = np.zeros((2, 1), dtype='float') | >>> x.sum(axis=1, dtype='float', out=np.asmatrix(out)) | matrix([[3.], | [7.]]) | | tolist(self) | Return the matrix as a (possibly nested) list. | | See `ndarray.tolist` for full documentation. | | See Also | -------- | ndarray.tolist | | Examples | -------- | >>> x = np.matrix([np.arange(12)](https://www.chedong.com/phpMan.php/man/np.arange/12/markdown).reshape((3,4))); x | matrix([[ 0, 1, 2, 3], | [ 4, 5, 6, 7], | [ 8, 9, 10, 11]]) | >>> x.tolist() | [[0, 1, 2, 3], [4, 5, 6, 7], [8, 9, 10, 11]] | | var(self, axis=None, dtype=None, out=None, ddof=0) | Returns the variance of the matrix elements, along the given axis. | | Refer to `numpy.var` for full documentation. | | See Also | -------- | numpy.var | | Notes | ----- | This is the same as `ndarray.var`, except that where an `ndarray` would | be returned, a `matrix` object is returned instead. | | Examples | -------- | >>> x = np.matrix([np.arange(12)](https://www.chedong.com/phpMan.php/man/np.arange/12/markdown).reshape((3, 4))) | >>> x | matrix([[ 0, 1, 2, 3], | [ 4, 5, 6, 7], | [ 8, 9, 10, 11]]) | >>> x.var() | 11.916666666666666 | >>> [x.var(0)](https://www.chedong.com/phpMan.php/man/x.var/0/markdown) | matrix([[ 10.66666667, 10.66666667, 10.66666667, 10.66666667]]) # may vary | >>> [x.var(1)](https://www.chedong.com/phpMan.php/man/x.var/1/markdown) | matrix([[1.25], | [1.25], | [1.25]]) | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(subtype, data, dtype=None, copy=True) | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Readonly properties defined here: | | A | Return `self` as an `ndarray` object. | | Equivalent to ``np.asarray(self)``. | | Parameters | ---------- | None | | Returns | ------- | ret : ndarray | `self` as an `ndarray` | | Examples | -------- | >>> x = np.matrix([np.arange(12)](https://www.chedong.com/phpMan.php/man/np.arange/12/markdown).reshape((3,4))); x | matrix([[ 0, 1, 2, 3], | [ 4, 5, 6, 7], | [ 8, 9, 10, 11]]) | >>> x.getA() | array([[ 0, 1, 2, 3], | [ 4, 5, 6, 7], | [ 8, 9, 10, 11]]) | | A1 | Return `self` as a flattened `ndarray`. | | Equivalent to ``np.asarray(x).ravel()`` | | Parameters | ---------- | None | | Returns | ------- | ret : ndarray | `self`, 1-D, as an `ndarray` | | Examples | -------- | >>> x = np.matrix([np.arange(12)](https://www.chedong.com/phpMan.php/man/np.arange/12/markdown).reshape((3,4))); x | matrix([[ 0, 1, 2, 3], | [ 4, 5, 6, 7], | [ 8, 9, 10, 11]]) | >>> x.getA1() | array([ 0, 1, 2, ..., 9, 10, 11]) | | H | Returns the (complex) conjugate transpose of `self`. | | Equivalent to ``np.transpose(self)`` if `self` is real-valued. | | Parameters | ---------- | None | | Returns | ------- | ret : matrix object | complex conjugate transpose of `self` | | Examples | -------- | >>> x = np.matrix([np.arange(12)](https://www.chedong.com/phpMan.php/man/np.arange/12/markdown).reshape((3,4))) | >>> z = x - 1j*x; z | matrix([[ 0. +0.j, 1. -1.j, 2. -2.j, 3. -3.j], | [ 4. -4.j, 5. -5.j, 6. -6.j, 7. -7.j], | [ 8. -8.j, 9. -9.j, 10.-10.j, 11.-11.j]]) | >>> z.getH() | matrix([[ 0. -0.j, 4. +4.j, 8. +8.j], | [ 1. +1.j, 5. +5.j, 9. +9.j], | [ 2. +2.j, 6. +6.j, 10.+10.j], | [ 3. +3.j, 7. +7.j, 11.+11.j]]) | | I | Returns the (multiplicative) inverse of invertible `self`. | | Parameters | ---------- | None | | Returns | ------- | ret : matrix object | If `self` is non-singular, `ret` is such that ``ret * self`` == | ``self * ret`` == ``np.matrix(np.eye(self[0,:].size))`` all return | ``True``. | | Raises | ------ | numpy.linalg.LinAlgError: Singular matrix | If `self` is singular. | | See Also | -------- | linalg.inv | | Examples | -------- | >>> m = np.matrix('[1, 2; 3, 4]'); m | matrix([[1, 2], | [3, 4]]) | >>> m.getI() | matrix([[-2. , 1. ], | [ 1.5, -0.5]]) | >>> m.getI() * m | matrix([[ 1., 0.], # may vary | [ 0., 1.]]) | | T | Returns the transpose of the matrix. | | Does *not* conjugate! For the complex conjugate transpose, use ``.H``. | | Parameters | ---------- | None | | Returns | ------- | ret : matrix object | The (non-conjugated) transpose of the matrix. | | See Also | -------- | transpose, getH | | Examples | -------- | >>> m = np.matrix('[1, 2; 3, 4]') | >>> m | matrix([[1, 2], | [3, 4]]) | >>> m.getT() | matrix([[1, 3], | [2, 4]]) | | ---------------------------------------------------------------------- | Data descriptors defined here: | | __dict__ | dictionary for instance variables (if defined) | | ---------------------------------------------------------------------- | Data and other attributes defined here: | | __annotations__ = {} | | __array_priority__ = 10.0 | | ---------------------------------------------------------------------- | Methods inherited from ndarray: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __and__(self, value, /) | Return self&value. | | __array__(...) | a.__array__([dtype], /) -> reference if type unchanged, copy otherwise. | | Returns either a new reference to self if dtype is not given or a new array | of provided data type if dtype is different from the current dtype of the | array. | | __array_function__(...) | | __array_prepare__(...) | a.__array_prepare__(obj) -> Object of same type as ndarray object obj. | | __array_ufunc__(...) | | __array_wrap__(...) | a.__array_wrap__(obj) -> Object of same type as ndarray object a. | | __bool__(self, /) | True if self else False | | __complex__(...) | | __contains__(self, key, /) | Return key in self. | | __copy__(...) | a.__copy__() | | Used if :func:`copy.copy` is called on an array. Returns a copy of the array. | | Equivalent to ``a.copy(order='K')``. | | __deepcopy__(...) | a.__deepcopy__(memo, /) -> Deep copy of array. | | Used if :func:`copy.deepcopy` is called on an array. | | __delitem__(self, key, /) | Delete self[key]. | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __format__(...) | Default object formatter. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __iadd__(self, value, /) | Return self+=value. | | __iand__(self, value, /) | Return self&=value. | | __ifloordiv__(self, value, /) | Return self//=value. | | __ilshift__(self, value, /) | Return self<<=value. | | __imatmul__(self, value, /) | Return self@=value. | | __imod__(self, value, /) | Return self%=value. | | __index__(self, /) | Return self converted to an integer, if self is suitable for use as an index into a list. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __ior__(self, value, /) | Return self|=value. | | __irshift__(self, value, /) | Return self>>=value. | | __isub__(self, value, /) | Return self-=value. | | __iter__(self, /) | Implement iter(self). | | __itruediv__(self, value, /) | Return self/=value. | | __ixor__(self, value, /) | Return self^=value. | | __le__(self, value, /) | Return self<=value. | | __len__(self, /) | Return len(self). | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __setitem__(self, key, value, /) | Set self[key] to value. | | __setstate__(...) | a.__setstate__(state, /) | | For unpickling. | | The `state` argument must be a sequence that contains the following | elements: | | Parameters | ---------- | version : int | optional pickle version. If omitted defaults to 0. | shape : tuple | dtype : data-type | isFortran : bool | rawdata : string or list | a binary string with the data (or a list if 'a' is an object array) | | __sizeof__(...) | Size of object in memory, in bytes. | | __str__(self, /) | Return str(self). | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | argpartition(...) | a.argpartition(kth, axis=-1, kind='introselect', order=None) | | Returns the indices that would partition this array. | | Refer to `numpy.argpartition` for full documentation. | | .. versionadded:: 1.8.0 | | See Also | -------- | numpy.argpartition : equivalent function | | argsort(...) | a.argsort(axis=-1, kind=None, order=None) | | Returns the indices that would sort this array. | | Refer to `numpy.argsort` for full documentation. | | See Also | -------- | numpy.argsort : equivalent function | | astype(...) | a.astype(dtype, order='K', casting='unsafe', subok=True, copy=True) | | Copy of the array, cast to a specified type. | | Parameters | ---------- | dtype : str or dtype | Typecode or data-type to which the array is cast. | order : {'C', 'F', 'A', 'K'}, optional | Controls the memory layout order of the result. | 'C' means C order, 'F' means Fortran order, 'A' | means 'F' order if all the arrays are Fortran contiguous, | 'C' order otherwise, and 'K' means as close to the | order the array elements appear in memory as possible. | Default is 'K'. | casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional | Controls what kind of data casting may occur. Defaults to 'unsafe' | for backwards compatibility. | | * 'no' means the data types should not be cast at all. | * 'equiv' means only byte-order changes are allowed. | * 'safe' means only casts which can preserve values are allowed. | * 'same_kind' means only safe casts or casts within a kind, | like float64 to float32, are allowed. | * 'unsafe' means any data conversions may be done. | subok : bool, optional | If True, then sub-classes will be passed-through (default), otherwise | the returned array will be forced to be a base-class array. | copy : bool, optional | By default, astype always returns a newly allocated array. If this | is set to false, and the `dtype`, `order`, and `subok` | requirements are satisfied, the input array is returned instead | of a copy. | | Returns | ------- | arr_t : ndarray | Unless `copy` is False and the other conditions for returning the input | array are satisfied (see description for `copy` input parameter), `arr_t` | is a new array of the same shape as the input array, with dtype, order | given by `dtype`, `order`. | | Notes | ----- | .. versionchanged:: 1.17.0 | Casting between a simple data type and a structured one is possible only | for "unsafe" casting. Casting to multiple fields is allowed, but | casting from multiple fields is not. | | .. versionchanged:: 1.9.0 | Casting from numeric to string types in 'safe' casting mode requires | that the string dtype length is long enough to store the max | integer/float value converted. | | Raises | ------ | ComplexWarning | When casting from complex to float or int. To avoid this, | one should use ``a.real.astype(t)``. | | Examples | -------- | >>> x = np.array([1, 2, 2.5]) | >>> x | array([1. , 2. , 2.5]) | | >>> x.astype(int) | array([1, 2, 2]) | | byteswap(...) | a.byteswap(inplace=False) | | Swap the bytes of the array elements | | Toggle between low-endian and big-endian data representation by | returning a byteswapped array, optionally swapped in-place. | Arrays of byte-strings are not swapped. The real and imaginary | parts of a complex number are swapped individually. | | Parameters | ---------- | inplace : bool, optional | If ``True``, swap bytes in-place, default is ``False``. | | Returns | ------- | out : ndarray | The byteswapped array. If `inplace` is ``True``, this is | a view to self. | | Examples | -------- | >>> A = np.array([1, 256, 8755], dtype=np.int16) | >>> list(map(hex, A)) | ['0x1', '0x100', '0x2233'] | >>> A.byteswap(inplace=True) | array([ 256, 1, 13090], dtype=int16) | >>> list(map(hex, A)) | ['0x100', '0x1', '0x3322'] | | Arrays of byte-strings are not swapped | | >>> A = np.array([b'ceg', b'fac']) | >>> A.byteswap() | array([b'ceg', b'fac'], dtype='|S3') | | ``A.newbyteorder().byteswap()`` produces an array with the same values | but different representation in memory | | >>> A = np.array([1, 2, 3]) | >>> A.view(np.uint8) | array([1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, | 0, 0], dtype=uint8) | >>> A.newbyteorder().byteswap(inplace=True) | array([1, 2, 3]) | >>> A.view(np.uint8) | array([0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, | 0, 3], dtype=uint8) | | choose(...) | a.choose(choices, out=None, mode='raise') | | Use an index array to construct a new array from a set of choices. | | Refer to `numpy.choose` for full documentation. | | See Also | -------- | numpy.choose : equivalent function | | clip(...) | a.clip(min=None, max=None, out=None, **kwargs) | | Return an array whose values are limited to ``[min, max]``. | One of max or min must be given. | | Refer to `numpy.clip` for full documentation. | | See Also | -------- | numpy.clip : equivalent function | | compress(...) | a.compress(condition, axis=None, out=None) | | Return selected slices of this array along given axis. | | Refer to `numpy.compress` for full documentation. | | See Also | -------- | numpy.compress : equivalent function | | conj(...) | a.conj() | | Complex-conjugate all elements. | | Refer to `numpy.conjugate` for full documentation. | | See Also | -------- | numpy.conjugate : equivalent function | | conjugate(...) | a.conjugate() | | Return the complex conjugate, element-wise. | | Refer to `numpy.conjugate` for full documentation. | | See Also | -------- | numpy.conjugate : equivalent function | | copy(...) | a.copy(order='C') | | Return a copy of the array. | | Parameters | ---------- | order : {'C', 'F', 'A', 'K'}, optional | Controls the memory layout of the copy. 'C' means C-order, | 'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous, | 'C' otherwise. 'K' means match the layout of `a` as closely | as possible. (Note that this function and :func:`numpy.copy` are very | similar but have different default values for their order= | arguments, and this function always passes sub-classes through.) | | See also | -------- | numpy.copy : Similar function with different default behavior | numpy.copyto | | Notes | ----- | This function is the preferred method for creating an array copy. The | function :func:`numpy.copy` is similar, but it defaults to using order 'K', | and will not pass sub-classes through by default. | | Examples | -------- | >>> x = np.array([[1,2,3],[4,5,6]], order='F') | | >>> y = x.copy() | | >>> [x.fill(0)](https://www.chedong.com/phpMan.php/man/x.fill/0/markdown) | | >>> x | array([[0, 0, 0], | [0, 0, 0]]) | | >>> y | array([[1, 2, 3], | [4, 5, 6]]) | | >>> y.flags['C_CONTIGUOUS'] | True | | cumprod(...) | a.cumprod(axis=None, dtype=None, out=None) | | Return the cumulative product of the elements along the given axis. | | Refer to `numpy.cumprod` for full documentation. | | See Also | -------- | numpy.cumprod : equivalent function | | cumsum(...) | a.cumsum(axis=None, dtype=None, out=None) | | Return the cumulative sum of the elements along the given axis. | | Refer to `numpy.cumsum` for full documentation. | | See Also | -------- | numpy.cumsum : equivalent function | | diagonal(...) | a.diagonal(offset=0, axis1=0, axis2=1) | | Return specified diagonals. In NumPy 1.9 the returned array is a | read-only view instead of a copy as in previous NumPy versions. In | a future version the read-only restriction will be removed. | | Refer to :func:`numpy.diagonal` for full documentation. | | See Also | -------- | numpy.diagonal : equivalent function | | dot(...) | a.dot(b, out=None) | | Dot product of two arrays. | | Refer to `numpy.dot` for full documentation. | | See Also | -------- | numpy.dot : equivalent function | | Examples | -------- | >>> a = [np.eye(2)](https://www.chedong.com/phpMan.php/man/np.eye/2/markdown) | >>> b = np.ones((2, 2)) * 2 | >>> a.dot(b) | array([[2., 2.], | [2., 2.]]) | | This array method can be conveniently chained: | | >>> a.dot(b).dot(b) | array([[8., 8.], | [8., 8.]]) | | dump(...) | a.dump(file) | | Dump a pickle of the array to the specified file. | The array can be read back with pickle.load or numpy.load. | | Parameters | ---------- | file : str or Path | A string naming the dump file. | | .. versionchanged:: 1.17.0 | `pathlib.Path` objects are now accepted. | | dumps(...) | a.dumps() | | Returns the pickle of the array as a string. | pickle.loads or numpy.loads will convert the string back to an array. | | Parameters | ---------- | None | | fill(...) | a.fill(value) | | Fill the array with a scalar value. | | Parameters | ---------- | value : scalar | All elements of `a` will be assigned this value. | | Examples | -------- | >>> a = np.array([1, 2]) | >>> [a.fill(0)](https://www.chedong.com/phpMan.php/man/a.fill/0/markdown) | >>> a | array([0, 0]) | >>> a = [np.empty(2)](https://www.chedong.com/phpMan.php/man/np.empty/2/markdown) | >>> [a.fill(1)](https://www.chedong.com/phpMan.php/man/a.fill/1/markdown) | >>> a | array([1., 1.]) | | getfield(...) | a.getfield(dtype, offset=0) | | Returns a field of the given array as a certain type. | | A field is a view of the array data with a given data-type. The values in | the view are determined by the given type and the offset into the current | array in bytes. The offset needs to be such that the view dtype fits in the | array dtype; for example an array of dtype complex128 has 16-byte elements. | If taking a view with a 32-bit integer (4 bytes), the offset needs to be | between 0 and 12 bytes. | | Parameters | ---------- | dtype : str or dtype | The data type of the view. The dtype size of the view can not be larger | than that of the array itself. | offset : int | Number of bytes to skip before beginning the element view. | | Examples | -------- | >>> x = np.diag([1.+1.j]*2) | >>> x[1, 1] = 2 + 4.j | >>> x | array([[1.+1.j, 0.+0.j], | [0.+0.j, 2.+4.j]]) | >>> x.getfield(np.float64) | array([[1., 0.], | [0., 2.]]) | | By choosing an offset of 8 bytes we can select the complex part of the | array for our view: | | >>> x.getfield(np.float64, offset=8) | array([[1., 0.], | [0., 4.]]) | | item(...) | a.item(*args) | | Copy an element of an array to a standard Python scalar and return it. | | Parameters | ---------- | \*args : Arguments (variable number and type) | | * none: in this case, the method only works for arrays | with one element (`a.size == 1`), which element is | copied into a standard Python scalar object and returned. | | * int_type: this argument is interpreted as a flat index into | the array, specifying which element to copy and return. | | * tuple of int_types: functions as does a single int_type argument, | except that the argument is interpreted as an nd-index into the | array. | | Returns | ------- | z : Standard Python scalar object | A copy of the specified element of the array as a suitable | Python scalar | | Notes | ----- | When the data type of `a` is longdouble or clongdouble, item() returns | a scalar array object because there is no available Python scalar that | would not lose information. Void arrays return a buffer object for item(), | unless fields are defined, in which case a tuple is returned. | | `item` is very similar to a[args], except, instead of an array scalar, | a standard Python scalar is returned. This can be useful for speeding up | access to elements of the array and doing arithmetic on elements of the | array using Python's optimized math. | | Examples | -------- | >>> [np.random.seed(123)](https://www.chedong.com/phpMan.php/man/np.random.seed/123/markdown) | >>> x = np.random.randint(9, size=(3, 3)) | >>> x | array([[2, 2, 6], | [1, 3, 6], | [1, 0, 1]]) | >>> [x.item(3)](https://www.chedong.com/phpMan.php/man/x.item/3/markdown) | 1 | >>> [x.item(7)](https://www.chedong.com/phpMan.php/man/x.item/7/markdown) | 0 | >>> x.item((0, 1)) | 2 | >>> x.item((2, 2)) | 1 | | itemset(...) | a.itemset(*args) | | Insert scalar into an array (scalar is cast to array's dtype, if possible) | | There must be at least 1 argument, and define the last argument | as *item*. Then, ``a.itemset(*args)`` is equivalent to but faster | than ``a[args] = item``. The item should be a scalar value and `args` | must select a single item in the array `a`. | | Parameters | ---------- | \*args : Arguments | If one argument: a scalar, only used in case `a` is of size 1. | If two arguments: the last argument is the value to be set | and must be a scalar, the first argument specifies a single array | element location. It is either an int or a tuple. | | Notes | ----- | Compared to indexing syntax, `itemset` provides some speed increase | for placing a scalar into a particular location in an `ndarray`, | if you must do this. However, generally this is discouraged: | among other problems, it complicates the appearance of the code. | Also, when using `itemset` (and `item`) inside a loop, be sure | to assign the methods to a local variable to avoid the attribute | look-up at each loop iteration. | | Examples | -------- | >>> [np.random.seed(123)](https://www.chedong.com/phpMan.php/man/np.random.seed/123/markdown) | >>> x = np.random.randint(9, size=(3, 3)) | >>> x | array([[2, 2, 6], | [1, 3, 6], | [1, 0, 1]]) | >>> x.itemset(4, 0) | >>> x.itemset((2, 2), 9) | >>> x | array([[2, 2, 6], | [1, 0, 6], | [1, 0, 9]]) | | newbyteorder(...) | arr.newbyteorder(new_order='S', /) | | Return the array with the same data viewed with a different byte order. | | Equivalent to:: | | arr.view([arr.dtype.newbytorder(new_order)](https://www.chedong.com/phpMan.php/man/arr.dtype.newbytorder/neworder/markdown)) | | Changes are also made in all fields and sub-arrays of the array data | type. | | | | Parameters | ---------- | new_order : string, optional | Byte order to force; a value from the byte order specifications | below. `new_order` codes can be any of: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order, equivalent to `sys.byteorder` | * {'|', 'I'} - ignore (no change to byte order) | | The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_arr : array | New array object with the dtype reflecting given change to the | byte order. | | nonzero(...) | a.nonzero() | | Return the indices of the elements that are non-zero. | | Refer to `numpy.nonzero` for full documentation. | | See Also | -------- | numpy.nonzero : equivalent function | | partition(...) | a.partition(kth, axis=-1, kind='introselect', order=None) | | Rearranges the elements in the array in such a way that the value of the | element in kth position is in the position it would be in a sorted array. | All elements smaller than the kth element are moved before this element and | all equal or greater are moved behind it. The ordering of the elements in | the two partitions is undefined. | | .. versionadded:: 1.8.0 | | Parameters | ---------- | kth : int or sequence of ints | Element index to partition by. The kth element value will be in its | final sorted position and all smaller elements will be moved before it | and all equal or greater elements behind it. | The order of all elements in the partitions is undefined. | If provided with a sequence of kth it will partition all elements | indexed by kth of them into their sorted position at once. | axis : int, optional | Axis along which to sort. Default is -1, which means sort along the | last axis. | kind : {'introselect'}, optional | Selection algorithm. Default is 'introselect'. | order : str or list of str, optional | When `a` is an array with fields defined, this argument specifies | which fields to compare first, second, etc. A single field can | be specified as a string, and not all fields need to be specified, | but unspecified fields will still be used, in the order in which | they come up in the dtype, to break ties. | | See Also | -------- | numpy.partition : Return a parititioned copy of an array. | argpartition : Indirect partition. | sort : Full sort. | | Notes | ----- | See ``np.partition`` for notes on the different algorithms. | | Examples | -------- | >>> a = np.array([3, 4, 2, 1]) | >>> [a.partition(3)](https://www.chedong.com/phpMan.php/man/a.partition/3/markdown) | >>> a | array([2, 1, 3, 4]) | | >>> a.partition((1, 3)) | >>> a | array([1, 2, 3, 4]) | | put(...) | a.put(indices, values, mode='raise') | | Set ``a.flat[n] = values[n]`` for all `n` in indices. | | Refer to `numpy.put` for full documentation. | | See Also | -------- | numpy.put : equivalent function | | repeat(...) | a.repeat(repeats, axis=None) | | Repeat elements of an array. | | Refer to `numpy.repeat` for full documentation. | | See Also | -------- | numpy.repeat : equivalent function | | reshape(...) | a.reshape(shape, order='C') | | Returns an array containing the same data with a new shape. | | Refer to `numpy.reshape` for full documentation. | | See Also | -------- | numpy.reshape : equivalent function | | Notes | ----- | Unlike the free function `numpy.reshape`, this method on `ndarray` allows | the elements of the shape parameter to be passed in as separate arguments. | For example, ``a.reshape(10, 11)`` is equivalent to | ``a.reshape((10, 11))``. | | resize(...) | a.resize(new_shape, refcheck=True) | | Change shape and size of array in-place. | | Parameters | ---------- | new_shape : tuple of ints, or `n` ints | Shape of resized array. | refcheck : bool, optional | If False, reference count will not be checked. Default is True. | | Returns | ------- | None | | Raises | ------ | ValueError | If `a` does not own its own data or references or views to it exist, | and the data memory must be changed. | PyPy only: will always raise if the data memory must be changed, since | there is no reliable way to determine if references or views to it | exist. | | SystemError | If the `order` keyword argument is specified. This behaviour is a | bug in NumPy. | | See Also | -------- | resize : Return a new array with the specified shape. | | Notes | ----- | This reallocates space for the data area if necessary. | | Only contiguous arrays (data elements consecutive in memory) can be | resized. | | The purpose of the reference count check is to make sure you | do not use this array as a buffer for another Python object and then | reallocate the memory. However, reference counts can increase in | other ways so if you are sure that you have not shared the memory | for this array with another Python object, then you may safely set | `refcheck` to False. | | Examples | -------- | Shrinking an array: array is flattened (in the order that the data are | stored in memory), resized, and reshaped: | | >>> a = np.array([[0, 1], [2, 3]], order='C') | >>> a.resize((2, 1)) | >>> a | array([[0], | [1]]) | | >>> a = np.array([[0, 1], [2, 3]], order='F') | >>> a.resize((2, 1)) | >>> a | array([[0], | [2]]) | | Enlarging an array: as above, but missing entries are filled with zeros: | | >>> b = np.array([[0, 1], [2, 3]]) | >>> b.resize(2, 3) # new_shape parameter doesn't have to be a tuple | >>> b | array([[0, 1, 2], | [3, 0, 0]]) | | Referencing an array prevents resizing... | | >>> c = a | >>> a.resize((1, 1)) | Traceback (most recent call last): | ... | ValueError: cannot resize an array that references or is referenced ... | | Unless `refcheck` is False: | | >>> a.resize((1, 1), refcheck=False) | >>> a | array([[0]]) | >>> c | array([[0]]) | | round(...) | a.round(decimals=0, out=None) | | Return `a` with each element rounded to the given number of decimals. | | Refer to `numpy.around` for full documentation. | | See Also | -------- | numpy.around : equivalent function | | searchsorted(...) | a.searchsorted(v, side='left', sorter=None) | | Find indices where elements of v should be inserted in a to maintain order. | | For full documentation, see `numpy.searchsorted` | | See Also | -------- | numpy.searchsorted : equivalent function | | setfield(...) | a.setfield(val, dtype, offset=0) | | Put a value into a specified place in a field defined by a data-type. | | Place `val` into `a`'s field defined by `dtype` and beginning `offset` | bytes into the field. | | Parameters | ---------- | val : object | Value to be placed in field. | dtype : dtype object | Data-type of the field in which to place `val`. | offset : int, optional | The number of bytes into the field at which to place `val`. | | Returns | ------- | None | | See Also | -------- | getfield | | Examples | -------- | >>> x = [np.eye(3)](https://www.chedong.com/phpMan.php/man/np.eye/3/markdown) | >>> x.getfield(np.float64) | array([[1., 0., 0.], | [0., 1., 0.], | [0., 0., 1.]]) | >>> x.setfield(3, np.int32) | >>> x.getfield(np.int32) | array([[3, 3, 3], | [3, 3, 3], | [3, 3, 3]], dtype=int32) | >>> x | array([[1.0e+000, 1.5e-323, 1.5e-323], | [1.5e-323, 1.0e+000, 1.5e-323], | [1.5e-323, 1.5e-323, 1.0e+000]]) | >>> x.setfield([np.eye(3)](https://www.chedong.com/phpMan.php/man/np.eye/3/markdown), np.int32) | >>> x | array([[1., 0., 0.], | [0., 1., 0.], | [0., 0., 1.]]) | | setflags(...) | a.setflags(write=None, align=None, uic=None) | | Set array flags WRITEABLE, ALIGNED, (WRITEBACKIFCOPY and UPDATEIFCOPY), | respectively. | | These Boolean-valued flags affect how numpy interprets the memory | area used by `a` (see Notes below). The ALIGNED flag can only | be set to True if the data is actually aligned according to the type. | The WRITEBACKIFCOPY and (deprecated) UPDATEIFCOPY flags can never be set | to True. The flag WRITEABLE can only be set to True if the array owns its | own memory, or the ultimate owner of the memory exposes a writeable buffer | interface, or is a string. (The exception for string is made so that | unpickling can be done without copying memory.) | | Parameters | ---------- | write : bool, optional | Describes whether or not `a` can be written to. | align : bool, optional | Describes whether or not `a` is aligned properly for its type. | uic : bool, optional | Describes whether or not `a` is a copy of another "base" array. | | Notes | ----- | Array flags provide information about how the memory area used | for the array is to be interpreted. There are 7 Boolean flags | in use, only four of which can be changed by the user: | WRITEBACKIFCOPY, UPDATEIFCOPY, WRITEABLE, and ALIGNED. | | WRITEABLE (W) the data area can be written to; | | ALIGNED (A) the data and strides are aligned appropriately for the hardware | (as determined by the compiler); | | UPDATEIFCOPY (U) (deprecated), replaced by WRITEBACKIFCOPY; | | WRITEBACKIFCOPY (X) this array is a copy of some other array (referenced | by .base). When the C-API function PyArray_ResolveWritebackIfCopy is | called, the base array will be updated with the contents of this array. | | All flags can be accessed using the single (upper case) letter as well | as the full name. | | Examples | -------- | >>> y = np.array([[3, 1, 7], | ... [2, 0, 0], | ... [8, 5, 9]]) | >>> y | array([[3, 1, 7], | [2, 0, 0], | [8, 5, 9]]) | >>> y.flags | C_CONTIGUOUS : True | F_CONTIGUOUS : False | OWNDATA : True | WRITEABLE : True | ALIGNED : True | WRITEBACKIFCOPY : False | UPDATEIFCOPY : False | >>> y.setflags(write=0, align=0) | >>> y.flags | C_CONTIGUOUS : True | F_CONTIGUOUS : False | OWNDATA : True | WRITEABLE : False | ALIGNED : False | WRITEBACKIFCOPY : False | UPDATEIFCOPY : False | >>> y.setflags(uic=1) | Traceback (most recent call last): | File "", line 1, in | ValueError: cannot set WRITEBACKIFCOPY flag to True | | sort(...) | a.sort(axis=-1, kind=None, order=None) | | Sort an array in-place. Refer to `numpy.sort` for full documentation. | | Parameters | ---------- | axis : int, optional | Axis along which to sort. Default is -1, which means sort along the | last axis. | kind : {'quicksort', 'mergesort', 'heapsort', 'stable'}, optional | Sorting algorithm. The default is 'quicksort'. Note that both 'stable' | and 'mergesort' use timsort under the covers and, in general, the | actual implementation will vary with datatype. The 'mergesort' option | is retained for backwards compatibility. | | .. versionchanged:: 1.15.0 | The 'stable' option was added. | | order : str or list of str, optional | When `a` is an array with fields defined, this argument specifies | which fields to compare first, second, etc. A single field can | be specified as a string, and not all fields need be specified, | but unspecified fields will still be used, in the order in which | they come up in the dtype, to break ties. | | See Also | -------- | numpy.sort : Return a sorted copy of an array. | numpy.argsort : Indirect sort. | numpy.lexsort : Indirect stable sort on multiple keys. | numpy.searchsorted : Find elements in sorted array. | numpy.partition: Partial sort. | | Notes | ----- | See `numpy.sort` for notes on the different sorting algorithms. | | Examples | -------- | >>> a = np.array([[1,4], [3,1]]) | >>> a.sort(axis=1) | >>> a | array([[1, 4], | [1, 3]]) | >>> a.sort(axis=0) | >>> a | array([[1, 3], | [1, 4]]) | | Use the `order` keyword to specify a field to use when sorting a | structured array: | | >>> a = np.array([('a', 2), ('c', 1)], dtype=[('x', 'S1'), ('y', int)]) | >>> a.sort(order='y') | >>> a | array([(b'c', 1), (b'a', 2)], | dtype=[('x', 'S1'), ('y', '>> x = np.array([[0, 1], [2, 3]], dtype='>> x.tobytes() | b'\x00\x00\x01\x00\x02\x00\x03\x00' | >>> x.tobytes('C') == x.tobytes() | True | >>> x.tobytes('F') | b'\x00\x00\x02\x00\x01\x00\x03\x00' | | tofile(...) | a.tofile(fid, sep="", format="%s") | | Write array to a file as text or binary (default). | | Data is always written in 'C' order, independent of the order of `a`. | The data produced by this method can be recovered using the function | fromfile(). | | Parameters | ---------- | fid : file or str or Path | An open file object, or a string containing a filename. | | .. versionchanged:: 1.17.0 | `pathlib.Path` objects are now accepted. | | sep : str | Separator between array items for text output. | If "" (empty), a binary file is written, equivalent to | ``file.write(a.tobytes())``. | format : str | Format string for text file output. | Each entry in the array is formatted to text by first converting | it to the closest Python type, and then using "format" % item. | | Notes | ----- | This is a convenience function for quick storage of array data. | Information on endianness and precision is lost, so this method is not a | good choice for files intended to archive data or transport data between | machines with different endianness. Some of these problems can be overcome | by outputting the data as text files, at the expense of speed and file | size. | | When fid is a file object, array contents are directly written to the | file, bypassing the file object's ``write`` method. As a result, tofile | cannot be used with files objects supporting compression (e.g., GzipFile) | or file-like objects that do not support ``fileno()`` (e.g., BytesIO). | | tostring(...) | a.tostring(order='C') | | A compatibility alias for `tobytes`, with exactly the same behavior. | | Despite its name, it returns `bytes` not `str`\ s. | | .. deprecated:: 1.19.0 | | trace(...) | a.trace(offset=0, axis1=0, axis2=1, dtype=None, out=None) | | Return the sum along diagonals of the array. | | Refer to `numpy.trace` for full documentation. | | See Also | -------- | numpy.trace : equivalent function | | transpose(...) | a.transpose(*axes) | | Returns a view of the array with axes transposed. | | For a 1-D array this has no effect, as a transposed vector is simply the | same vector. To convert a 1-D array into a 2D column vector, an additional | dimension must be added. `np.atleast2d(a).T` achieves this, as does | `a[:, np.newaxis]`. | For a 2-D array, this is a standard matrix transpose. | For an n-D array, if axes are given, their order indicates how the | axes are permuted (see Examples). If axes are not provided and | ``a.shape = (i[0], i[1], ... i[n-2], i[n-1])``, then | ``a.transpose().shape = (i[n-1], i[n-2], ... i[1], i[0])``. | | Parameters | ---------- | axes : None, tuple of ints, or `n` ints | | * None or no argument: reverses the order of the axes. | | * tuple of ints: `i` in the `j`-th place in the tuple means `a`'s | `i`-th axis becomes `a.transpose()`'s `j`-th axis. | | * `n` ints: same as an n-tuple of the same ints (this form is | intended simply as a "convenience" alternative to the tuple form) | | Returns | ------- | out : ndarray | View of `a`, with axes suitably permuted. | | See Also | -------- | transpose : Equivalent function | ndarray.T : Array property returning the array transposed. | ndarray.reshape : Give a new shape to an array without changing its data. | | Examples | -------- | >>> a = np.array([[1, 2], [3, 4]]) | >>> a | array([[1, 2], | [3, 4]]) | >>> a.transpose() | array([[1, 3], | [2, 4]]) | >>> a.transpose((1, 0)) | array([[1, 3], | [2, 4]]) | >>> a.transpose(1, 0) | array([[1, 3], | [2, 4]]) | | view(...) | a.view([dtype][, type]) | | New view of array with the same data. | | .. note:: | Passing None for ``dtype`` is different from omitting the parameter, | since the former invokes ``dtype(None)`` which is an alias for | ``dtype('float_')``. | | Parameters | ---------- | dtype : data-type or ndarray sub-class, optional | Data-type descriptor of the returned view, e.g., float32 or int16. | Omitting it results in the view having the same data-type as `a`. | This argument can also be specified as an ndarray sub-class, which | then specifies the type of the returned object (this is equivalent to | setting the ``type`` parameter). | type : Python type, optional | Type of the returned view, e.g., ndarray or matrix. Again, omission | of the parameter results in type preservation. | | Notes | ----- | ``a.view()`` is used two different ways: | | ``a.view(some_dtype)`` or ``a.view(dtype=some_dtype)`` constructs a view | of the array's memory with a different data-type. This can cause a | reinterpretation of the bytes of memory. | | ``[a.view(ndarray_subclass)](https://www.chedong.com/phpMan.php/man/a.view/ndarraysubclass/markdown)`` or ``a.view(type=ndarray_subclass)`` just | returns an instance of `ndarray_subclass` that looks at the same array | (same shape, dtype, etc.) This does not cause a reinterpretation of the | memory. | | For ``a.view(some_dtype)``, if ``some_dtype`` has a different number of | bytes per entry than the previous dtype (for example, converting a | regular array to a structured array), then the behavior of the view | cannot be predicted just from the superficial appearance of ``a`` (shown | by ``print(a)``). It also depends on exactly how ``a`` is stored in | memory. Therefore if ``a`` is C-ordered versus fortran-ordered, versus | defined as a slice or transpose, etc., the view may give different | results. | | | Examples | -------- | >>> x = np.array([(1, 2)], dtype=[('a', np.int8), ('b', np.int8)]) | | Viewing array data using a different type and dtype: | | >>> y = x.view(dtype=np.int16, type=np.matrix) | >>> y | matrix([[513]], dtype=int16) | >>> print(type(y)) | | | Creating a view on a structured array so it can be used in calculations | | >>> x = np.array([(1, 2),(3,4)], dtype=[('a', np.int8), ('b', np.int8)]) | >>> xv = x.view(dtype=np.int8).reshape(-1,2) | >>> xv | array([[1, 2], | [3, 4]], dtype=int8) | >>> [xv.mean(0)](https://www.chedong.com/phpMan.php/man/xv.mean/0/markdown) | array([2., 3.]) | | Making changes to the view changes the underlying array | | >>> xv[0,1] = 20 | >>> x | array([(1, 20), (3, 4)], dtype=[('a', 'i1'), ('b', 'i1')]) | | Using a view to convert an array to a recarray: | | >>> z = x.view(np.recarray) | >>> z.a | array([1, 3], dtype=int8) | | Views share data: | | >>> x[0] = (9, 10) | >>> z[0] | (9, 10) | | Views that change the dtype size (bytes per entry) should normally be | avoided on arrays defined by slices, transposes, fortran-ordering, etc.: | | >>> x = np.array([[1,2,3],[4,5,6]], dtype=np.int16) | >>> y = x[:, 0:2] | >>> y | array([[1, 2], | [4, 5]], dtype=int16) | >>> y.view(dtype=[('width', np.int16), ('length', np.int16)]) | Traceback (most recent call last): | ... | ValueError: To change to a dtype of a different size, the array must be C-contiguous | >>> z = y.copy() | >>> z.view(dtype=[('width', np.int16), ('length', np.int16)]) | array([[(1, 2)], | [(4, 5)]], dtype=[('width', '>> x = np.array([1,2,3,4]) | >>> x.base is None | True | | Slicing creates a view, whose memory is shared with x: | | >>> y = x[2:] | >>> y.base is x | True | | ctypes | An object to simplify the interaction of the array with the ctypes | module. | | This attribute creates an object that makes it easier to use arrays | when calling shared libraries with the ctypes module. The returned | object has, among others, data, shape, and strides attributes (see | Notes below) which themselves return ctypes objects that can be used | as arguments to a shared library. | | Parameters | ---------- | None | | Returns | ------- | c : Python object | Possessing attributes data, shape, strides, etc. | | See Also | -------- | numpy.ctypeslib | | Notes | ----- | Below are the public attributes of this object which were documented | in "Guide to NumPy" (we have omitted undocumented public attributes, | as well as documented private attributes): | | .. autoattribute:: numpy.core._internal._ctypes.data | :noindex: | | .. autoattribute:: numpy.core._internal._ctypes.shape | :noindex: | | .. autoattribute:: numpy.core._internal._ctypes.strides | :noindex: | | .. automethod:: numpy.core._internal._ctypes.data_as | :noindex: | | .. automethod:: numpy.core._internal._ctypes.shape_as | :noindex: | | .. automethod:: numpy.core._internal._ctypes.strides_as | :noindex: | | If the ctypes module is not available, then the ctypes attribute | of array objects still returns something useful, but ctypes objects | are not returned and errors may be raised instead. In particular, | the object will still have the ``as_parameter`` attribute which will | return an integer equal to the data attribute. | | Examples | -------- | >>> import ctypes | >>> x = np.array([[0, 1], [2, 3]], dtype=np.int32) | >>> x | array([[0, 1], | [2, 3]], dtype=int32) | >>> x.ctypes.data | 31962608 # may vary | >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)) | <__main__.LP_c_uint object at 0x7ff2fc1fc200> # may vary | >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)).contents | [c_uint(0)](https://www.chedong.com/phpMan.php/man/cuint/0/markdown) | >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint64)).contents | [c_ulong(4294967296)](https://www.chedong.com/phpMan.php/man/culong/4294967296/markdown) | >>> x.ctypes.shape | # may vary | >>> x.ctypes.strides | # may vary | | data | Python buffer object pointing to the start of the array's data. | | dtype | Data-type of the array's elements. | | Parameters | ---------- | None | | Returns | ------- | d : numpy dtype object | | See Also | -------- | numpy.dtype | | Examples | -------- | >>> x | array([[0, 1], | [2, 3]]) | >>> x.dtype | dtype('int32') | >>> type(x.dtype) | | | flags | Information about the memory layout of the array. | | Attributes | ---------- | C_CONTIGUOUS (C) | The data is in a single, C-style contiguous segment. | F_CONTIGUOUS (F) | The data is in a single, Fortran-style contiguous segment. | OWNDATA (O) | The array owns the memory it uses or borrows it from another object. | WRITEABLE (W) | The data area can be written to. Setting this to False locks | the data, making it read-only. A view (slice, etc.) inherits WRITEABLE | from its base array at creation time, but a view of a writeable | array may be subsequently locked while the base array remains writeable. | (The opposite is not true, in that a view of a locked array may not | be made writeable. However, currently, locking a base object does not | lock any views that already reference it, so under that circumstance it | is possible to alter the contents of a locked array via a previously | created writeable view onto it.) Attempting to change a non-writeable | array raises a RuntimeError exception. | ALIGNED (A) | The data and all elements are aligned appropriately for the hardware. | WRITEBACKIFCOPY (X) | This array is a copy of some other array. The C-API function | PyArray_ResolveWritebackIfCopy must be called before deallocating | to the base array will be updated with the contents of this array. | UPDATEIFCOPY (U) | (Deprecated, use WRITEBACKIFCOPY) This array is a copy of some other array. | When this array is | deallocated, the base array will be updated with the contents of | this array. | FNC | F_CONTIGUOUS and not C_CONTIGUOUS. | FORC | F_CONTIGUOUS or C_CONTIGUOUS (one-segment test). | BEHAVED (B) | ALIGNED and WRITEABLE. | CARRAY (CA) | BEHAVED and C_CONTIGUOUS. | FARRAY (FA) | BEHAVED and F_CONTIGUOUS and not C_CONTIGUOUS. | | Notes | ----- | The `flags` object can be accessed dictionary-like (as in ``a.flags['WRITEABLE']``), | or by using lowercased attribute names (as in ``a.flags.writeable``). Short flag | names are only supported in dictionary access. | | Only the WRITEBACKIFCOPY, UPDATEIFCOPY, WRITEABLE, and ALIGNED flags can be | changed by the user, via direct assignment to the attribute or dictionary | entry, or by calling `ndarray.setflags`. | | The array flags cannot be set arbitrarily: | | - UPDATEIFCOPY can only be set ``False``. | - WRITEBACKIFCOPY can only be set ``False``. | - ALIGNED can only be set ``True`` if the data is truly aligned. | - WRITEABLE can only be set ``True`` if the array owns its own memory | or the ultimate owner of the memory exposes a writeable buffer | interface or is a string. | | Arrays can be both C-style and Fortran-style contiguous simultaneously. | This is clear for 1-dimensional arrays, but can also be true for higher | dimensional arrays. | | Even for contiguous arrays a stride for a given dimension | ``arr.strides[dim]`` may be *arbitrary* if ``arr.shape[dim] == 1`` | or the array has no elements. | It does *not* generally hold that ``self.strides[-1] == self.itemsize`` | for C-style contiguous arrays or ``self.strides[0] == self.itemsize`` for | Fortran-style contiguous arrays is true. | | flat | A 1-D iterator over the array. | | This is a `numpy.flatiter` instance, which acts similarly to, but is not | a subclass of, Python's built-in iterator object. | | See Also | -------- | flatten : Return a copy of the array collapsed into one dimension. | | flatiter | | Examples | -------- | >>> x = np.arange(1, 7).reshape(2, 3) | >>> x | array([[1, 2, 3], | [4, 5, 6]]) | >>> x.flat[3] | 4 | >>> x.T | array([[1, 4], | [2, 5], | [3, 6]]) | >>> x.T.flat[3] | 5 | >>> type(x.flat) | | | An assignment example: | | >>> x.flat = 3; x | array([[3, 3, 3], | [3, 3, 3]]) | >>> x.flat[[1,4]] = 1; x | array([[3, 1, 3], | [3, 1, 3]]) | | imag | The imaginary part of the array. | | Examples | -------- | >>> x = np.sqrt([1+0j, 0+1j]) | >>> x.imag | array([ 0. , 0.70710678]) | >>> x.imag.dtype | dtype('float64') | | itemsize | Length of one array element in bytes. | | Examples | -------- | >>> x = np.array([1,2,3], dtype=np.float64) | >>> x.itemsize | 8 | >>> x = np.array([1,2,3], dtype=np.complex128) | >>> x.itemsize | 16 | | nbytes | Total bytes consumed by the elements of the array. | | Notes | ----- | Does not include memory consumed by non-element attributes of the | array object. | | Examples | -------- | >>> x = np.zeros((3,5,2), dtype=np.complex128) | >>> x.nbytes | 480 | >>> np.prod(x.shape) * x.itemsize | 480 | | ndim | Number of array dimensions. | | Examples | -------- | >>> x = np.array([1, 2, 3]) | >>> x.ndim | 1 | >>> y = np.zeros((2, 3, 4)) | >>> y.ndim | 3 | | real | The real part of the array. | | Examples | -------- | >>> x = np.sqrt([1+0j, 0+1j]) | >>> x.real | array([ 1. , 0.70710678]) | >>> x.real.dtype | dtype('float64') | | See Also | -------- | numpy.real : equivalent function | | shape | Tuple of array dimensions. | | The shape property is usually used to get the current shape of an array, | but may also be used to reshape the array in-place by assigning a tuple of | array dimensions to it. As with `numpy.reshape`, one of the new shape | dimensions can be -1, in which case its value is inferred from the size of | the array and the remaining dimensions. Reshaping an array in-place will | fail if a copy is required. | | Examples | -------- | >>> x = np.array([1, 2, 3, 4]) | >>> x.shape | (4,) | >>> y = np.zeros((2, 3, 4)) | >>> y.shape | (2, 3, 4) | >>> y.shape = (3, 8) | >>> y | array([[ 0., 0., 0., 0., 0., 0., 0., 0.], | [ 0., 0., 0., 0., 0., 0., 0., 0.], | [ 0., 0., 0., 0., 0., 0., 0., 0.]]) | >>> y.shape = (3, 6) | Traceback (most recent call last): | File "", line 1, in | ValueError: total size of new array must be unchanged | >>> np.zeros((4,2))[::2].shape = (-1,) | Traceback (most recent call last): | File "", line 1, in | AttributeError: Incompatible shape for in-place modification. Use | `.reshape()` to make a copy with the desired shape. | | See Also | -------- | numpy.reshape : similar function | ndarray.reshape : similar method | | size | Number of elements in the array. | | Equal to ``np.prod(a.shape)``, i.e., the product of the array's | dimensions. | | Notes | ----- | `a.size` returns a standard arbitrary precision Python integer. This | may not be the case with other methods of obtaining the same value | (like the suggested ``np.prod(a.shape)``, which returns an instance | of ``np.int_``), and may be relevant if the value is used further in | calculations that may overflow a fixed size integer type. | | Examples | -------- | >>> x = np.zeros((3, 5, 2), dtype=np.complex128) | >>> x.size | 30 | >>> np.prod(x.shape) | 30 | | strides | Tuple of bytes to step in each dimension when traversing an array. | | The byte offset of element ``(i[0], i[1], ..., i[n])`` in an array `a` | is:: | | offset = sum(np.array(i) * a.strides) | | A more detailed explanation of strides can be found in the | "ndarray.rst" file in the NumPy reference guide. | | Notes | ----- | Imagine an array of 32-bit integers (each 4 bytes):: | | x = np.array([[0, 1, 2, 3, 4], | [5, 6, 7, 8, 9]], dtype=np.int32) | | This array is stored in memory as 40 bytes, one after the other | (known as a contiguous block of memory). The strides of an array tell | us how many bytes we have to skip in memory to move to the next position | along a certain axis. For example, we have to skip 4 bytes (1 value) to | move to the next column, but 20 bytes (5 values) to get to the same | position in the next row. As such, the strides for the array `x` will be | ``(20, 4)``. | | See Also | -------- | numpy.lib.stride_tricks.as_strided | | Examples | -------- | >>> y = np.reshape(np.arange(2*3*4), (2,3,4)) | >>> y | array([[[ 0, 1, 2, 3], | [ 4, 5, 6, 7], | [ 8, 9, 10, 11]], | [[12, 13, 14, 15], | [16, 17, 18, 19], | [20, 21, 22, 23]]]) | >>> y.strides | (48, 16, 4) | >>> y[1,1,1] | 17 | >>> offset=sum(y.strides * np.array((1,1,1))) | >>> offset/y.itemsize | 17 | | >>> x = np.reshape(np.arange(5*6*7*8), (5,6,7,8)).transpose(2,3,1,0) | >>> x.strides | (32, 4, 224, 1344) | >>> i = np.array([3,5,2,2]) | >>> offset = sum(i * x.strides) | >>> x[3,5,2,2] | 813 | >>> offset / x.itemsize | 813 | | ---------------------------------------------------------------------- | Data and other attributes inherited from ndarray: | | __hash__ = None ### class memmap | memmap(filename, dtype=, mode='r+', offset=0, shape=None, order='C') | | Create a memory-map to an array stored in a *binary* file on disk. | | Memory-mapped files are used for accessing small segments of large files | on disk, without reading the entire file into memory. NumPy's | memmap's are array-like objects. This differs from Python's ``mmap`` | module, which uses file-like objects. | | This subclass of ndarray has some unpleasant interactions with | some operations, because it doesn't quite fit properly as a subclass. | An alternative to using this subclass is to create the ``mmap`` | object yourself, then create an ndarray with ndarray.__new__ directly, | passing the object created in its 'buffer=' parameter. | | This class may at some point be turned into a factory function | which returns a view into an mmap buffer. | | Flush the memmap instance to write the changes to the file. Currently there | is no API to close the underlying ``mmap``. It is tricky to ensure the | resource is actually closed, since it may be shared between different | memmap instances. | | | Parameters | ---------- | filename : str, file-like object, or pathlib.Path instance | The file name or file object to be used as the array data buffer. | dtype : data-type, optional | The data-type used to interpret the file contents. | Default is `uint8`. | mode : {'r+', 'r', 'w+', 'c'}, optional | The file is opened in this mode: | | +------+-------------------------------------------------------------+ | | 'r' | Open existing file for reading only. | | +------+-------------------------------------------------------------+ | | 'r+' | Open existing file for reading and writing. | | +------+-------------------------------------------------------------+ | | 'w+' | Create or overwrite existing file for reading and writing. | | +------+-------------------------------------------------------------+ | | 'c' | Copy-on-write: assignments affect data in memory, but | | | | changes are not saved to disk. The file on disk is | | | | read-only. | | +------+-------------------------------------------------------------+ | | Default is 'r+'. | offset : int, optional | In the file, array data starts at this offset. Since `offset` is | measured in bytes, it should normally be a multiple of the byte-size | of `dtype`. When ``mode != 'r'``, even positive offsets beyond end of | file are valid; The file will be extended to accommodate the | additional data. By default, ``memmap`` will start at the beginning of | the file, even if ``filename`` is a file pointer ``fp`` and | ``fp.tell() != 0``. | shape : tuple, optional | The desired shape of the array. If ``mode == 'r'`` and the number | of remaining bytes after `offset` is not a multiple of the byte-size | of `dtype`, you must specify `shape`. By default, the returned array | will be 1-D with the number of elements determined by file size | and data-type. | order : {'C', 'F'}, optional | Specify the order of the ndarray memory layout: | :term:`row-major`, C-style or :term:`column-major`, | Fortran-style. This only has an effect if the shape is | greater than 1-D. The default order is 'C'. | | Attributes | ---------- | filename : str or pathlib.Path instance | Path to the mapped file. | offset : int | Offset position in the file. | mode : str | File mode. | | Methods | ------- | flush | Flush any changes in memory to file on disk. | When you delete a memmap object, flush is called first to write | changes to disk. | | | See also | -------- | lib.format.open_memmap : Create or load a memory-mapped ``.npy`` file. | | Notes | ----- | The memmap object can be used anywhere an ndarray is accepted. | Given a memmap ``fp``, ``isinstance(fp, numpy.ndarray)`` returns | ``True``. | | Memory-mapped files cannot be larger than 2GB on 32-bit systems. | | When a memmap causes a file to be created or extended beyond its | current size in the filesystem, the contents of the new part are | unspecified. On systems with POSIX filesystem semantics, the extended | part will be filled with zero bytes. | | Examples | -------- | >>> data = np.arange(12, dtype='float32') | >>> data.resize((3,4)) | | This example uses a temporary file so that doctest doesn't write | files to your directory. You would use a 'normal' filename. | | >>> from tempfile import mkdtemp | >>> import os.path as path | >>> filename = path.join(mkdtemp(), 'newfile.dat') | | Create a memmap with dtype and shape that matches our data: | | >>> fp = np.memmap(filename, dtype='float32', mode='w+', shape=(3,4)) | >>> fp | memmap([[0., 0., 0., 0.], | [0., 0., 0., 0.], | [0., 0., 0., 0.]], dtype=float32) | | Write data to memmap array: | | >>> fp[:] = data[:] | >>> fp | memmap([[ 0., 1., 2., 3.], | [ 4., 5., 6., 7.], | [ 8., 9., 10., 11.]], dtype=float32) | | >>> fp.filename == path.abspath(filename) | True | | Flushes memory changes to disk in order to read them back | | >>> fp.flush() | | Load the memmap and verify data was stored: | | >>> newfp = np.memmap(filename, dtype='float32', mode='r', shape=(3,4)) | >>> newfp | memmap([[ 0., 1., 2., 3.], | [ 4., 5., 6., 7.], | [ 8., 9., 10., 11.]], dtype=float32) | | Read-only memmap: | | >>> fpr = np.memmap(filename, dtype='float32', mode='r', shape=(3,4)) | >>> fpr.flags.writeable | False | | Copy-on-write memmap: | | >>> fpc = np.memmap(filename, dtype='float32', mode='c', shape=(3,4)) | >>> fpc.flags.writeable | True | | It's possible to assign to copy-on-write array, but values are only | written into the memory copy of the array, and not written to disk: | | >>> fpc | memmap([[ 0., 1., 2., 3.], | [ 4., 5., 6., 7.], | [ 8., 9., 10., 11.]], dtype=float32) | >>> fpc[0,:] = 0 | >>> fpc | memmap([[ 0., 0., 0., 0.], | [ 4., 5., 6., 7.], | [ 8., 9., 10., 11.]], dtype=float32) | | File on disk is unchanged: | | >>> fpr | memmap([[ 0., 1., 2., 3.], | [ 4., 5., 6., 7.], | [ 8., 9., 10., 11.]], dtype=float32) | | Offset into a memmap: | | >>> fpo = np.memmap(filename, dtype='float32', mode='r', offset=16) | >>> fpo | memmap([ 4., 5., 6., 7., 8., 9., 10., 11.], dtype=float32) | | Method resolution order: | memmap | ndarray | builtins.object | | Methods defined here: | | __array_finalize__(self, obj) | None. | | __array_wrap__(self, arr, context=None) | a.__array_wrap__(obj) -> Object of same type as ndarray object a. | | __getitem__(self, index) | Return self[key]. | | flush(self) | Write any changes in the array to the file on disk. | | For further information, see `memmap`. | | Parameters | ---------- | None | | See Also | -------- | memmap | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(subtype, filename, dtype=, mode='r+', offset=0, shape=None, order='C') | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Data descriptors defined here: | | __dict__ | dictionary for instance variables (if defined) | | ---------------------------------------------------------------------- | Data and other attributes defined here: | | __array_priority__ = -100.0 | | ---------------------------------------------------------------------- | Methods inherited from ndarray: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __and__(self, value, /) | Return self&value. | | __array__(...) | a.__array__([dtype], /) -> reference if type unchanged, copy otherwise. | | Returns either a new reference to self if dtype is not given or a new array | of provided data type if dtype is different from the current dtype of the | array. | | __array_function__(...) | | __array_prepare__(...) | a.__array_prepare__(obj) -> Object of same type as ndarray object obj. | | __array_ufunc__(...) | | __bool__(self, /) | True if self else False | | __complex__(...) | | __contains__(self, key, /) | Return key in self. | | __copy__(...) | a.__copy__() | | Used if :func:`copy.copy` is called on an array. Returns a copy of the array. | | Equivalent to ``a.copy(order='K')``. | | __deepcopy__(...) | a.__deepcopy__(memo, /) -> Deep copy of array. | | Used if :func:`copy.deepcopy` is called on an array. | | __delitem__(self, key, /) | Delete self[key]. | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __format__(...) | Default object formatter. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __iadd__(self, value, /) | Return self+=value. | | __iand__(self, value, /) | Return self&=value. | | __ifloordiv__(self, value, /) | Return self//=value. | | __ilshift__(self, value, /) | Return self<<=value. | | __imatmul__(self, value, /) | Return self@=value. | | __imod__(self, value, /) | Return self%=value. | | __imul__(self, value, /) | Return self*=value. | | __index__(self, /) | Return self converted to an integer, if self is suitable for use as an index into a list. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __ior__(self, value, /) | Return self|=value. | | __ipow__(self, value, /) | Return self**=value. | | __irshift__(self, value, /) | Return self>>=value. | | __isub__(self, value, /) | Return self-=value. | | __iter__(self, /) | Implement iter(self). | | __itruediv__(self, value, /) | Return self/=value. | | __ixor__(self, value, /) | Return self^=value. | | __le__(self, value, /) | Return self<=value. | | __len__(self, /) | Return len(self). | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __setitem__(self, key, value, /) | Set self[key] to value. | | __setstate__(...) | a.__setstate__(state, /) | | For unpickling. | | The `state` argument must be a sequence that contains the following | elements: | | Parameters | ---------- | version : int | optional pickle version. If omitted defaults to 0. | shape : tuple | dtype : data-type | isFortran : bool | rawdata : string or list | a binary string with the data (or a list if 'a' is an object array) | | __sizeof__(...) | Size of object in memory, in bytes. | | __str__(self, /) | Return str(self). | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | all(...) | a.all(axis=None, out=None, keepdims=False, *, where=True) | | Returns True if all elements evaluate to True. | | Refer to `numpy.all` for full documentation. | | See Also | -------- | numpy.all : equivalent function | | any(...) | a.any(axis=None, out=None, keepdims=False, *, where=True) | | Returns True if any of the elements of `a` evaluate to True. | | Refer to `numpy.any` for full documentation. | | See Also | -------- | numpy.any : equivalent function | | argmax(...) | a.argmax(axis=None, out=None) | | Return indices of the maximum values along the given axis. | | Refer to `numpy.argmax` for full documentation. | | See Also | -------- | numpy.argmax : equivalent function | | argmin(...) | a.argmin(axis=None, out=None) | | Return indices of the minimum values along the given axis. | | Refer to `numpy.argmin` for detailed documentation. | | See Also | -------- | numpy.argmin : equivalent function | | argpartition(...) | a.argpartition(kth, axis=-1, kind='introselect', order=None) | | Returns the indices that would partition this array. | | Refer to `numpy.argpartition` for full documentation. | | .. versionadded:: 1.8.0 | | See Also | -------- | numpy.argpartition : equivalent function | | argsort(...) | a.argsort(axis=-1, kind=None, order=None) | | Returns the indices that would sort this array. | | Refer to `numpy.argsort` for full documentation. | | See Also | -------- | numpy.argsort : equivalent function | | astype(...) | a.astype(dtype, order='K', casting='unsafe', subok=True, copy=True) | | Copy of the array, cast to a specified type. | | Parameters | ---------- | dtype : str or dtype | Typecode or data-type to which the array is cast. | order : {'C', 'F', 'A', 'K'}, optional | Controls the memory layout order of the result. | 'C' means C order, 'F' means Fortran order, 'A' | means 'F' order if all the arrays are Fortran contiguous, | 'C' order otherwise, and 'K' means as close to the | order the array elements appear in memory as possible. | Default is 'K'. | casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional | Controls what kind of data casting may occur. Defaults to 'unsafe' | for backwards compatibility. | | * 'no' means the data types should not be cast at all. | * 'equiv' means only byte-order changes are allowed. | * 'safe' means only casts which can preserve values are allowed. | * 'same_kind' means only safe casts or casts within a kind, | like float64 to float32, are allowed. | * 'unsafe' means any data conversions may be done. | subok : bool, optional | If True, then sub-classes will be passed-through (default), otherwise | the returned array will be forced to be a base-class array. | copy : bool, optional | By default, astype always returns a newly allocated array. If this | is set to false, and the `dtype`, `order`, and `subok` | requirements are satisfied, the input array is returned instead | of a copy. | | Returns | ------- | arr_t : ndarray | Unless `copy` is False and the other conditions for returning the input | array are satisfied (see description for `copy` input parameter), `arr_t` | is a new array of the same shape as the input array, with dtype, order | given by `dtype`, `order`. | | Notes | ----- | .. versionchanged:: 1.17.0 | Casting between a simple data type and a structured one is possible only | for "unsafe" casting. Casting to multiple fields is allowed, but | casting from multiple fields is not. | | .. versionchanged:: 1.9.0 | Casting from numeric to string types in 'safe' casting mode requires | that the string dtype length is long enough to store the max | integer/float value converted. | | Raises | ------ | ComplexWarning | When casting from complex to float or int. To avoid this, | one should use ``a.real.astype(t)``. | | Examples | -------- | >>> x = np.array([1, 2, 2.5]) | >>> x | array([1. , 2. , 2.5]) | | >>> x.astype(int) | array([1, 2, 2]) | | byteswap(...) | a.byteswap(inplace=False) | | Swap the bytes of the array elements | | Toggle between low-endian and big-endian data representation by | returning a byteswapped array, optionally swapped in-place. | Arrays of byte-strings are not swapped. The real and imaginary | parts of a complex number are swapped individually. | | Parameters | ---------- | inplace : bool, optional | If ``True``, swap bytes in-place, default is ``False``. | | Returns | ------- | out : ndarray | The byteswapped array. If `inplace` is ``True``, this is | a view to self. | | Examples | -------- | >>> A = np.array([1, 256, 8755], dtype=np.int16) | >>> list(map(hex, A)) | ['0x1', '0x100', '0x2233'] | >>> A.byteswap(inplace=True) | array([ 256, 1, 13090], dtype=int16) | >>> list(map(hex, A)) | ['0x100', '0x1', '0x3322'] | | Arrays of byte-strings are not swapped | | >>> A = np.array([b'ceg', b'fac']) | >>> A.byteswap() | array([b'ceg', b'fac'], dtype='|S3') | | ``A.newbyteorder().byteswap()`` produces an array with the same values | but different representation in memory | | >>> A = np.array([1, 2, 3]) | >>> A.view(np.uint8) | array([1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, | 0, 0], dtype=uint8) | >>> A.newbyteorder().byteswap(inplace=True) | array([1, 2, 3]) | >>> A.view(np.uint8) | array([0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, | 0, 3], dtype=uint8) | | choose(...) | a.choose(choices, out=None, mode='raise') | | Use an index array to construct a new array from a set of choices. | | Refer to `numpy.choose` for full documentation. | | See Also | -------- | numpy.choose : equivalent function | | clip(...) | a.clip(min=None, max=None, out=None, **kwargs) | | Return an array whose values are limited to ``[min, max]``. | One of max or min must be given. | | Refer to `numpy.clip` for full documentation. | | See Also | -------- | numpy.clip : equivalent function | | compress(...) | a.compress(condition, axis=None, out=None) | | Return selected slices of this array along given axis. | | Refer to `numpy.compress` for full documentation. | | See Also | -------- | numpy.compress : equivalent function | | conj(...) | a.conj() | | Complex-conjugate all elements. | | Refer to `numpy.conjugate` for full documentation. | | See Also | -------- | numpy.conjugate : equivalent function | | conjugate(...) | a.conjugate() | | Return the complex conjugate, element-wise. | | Refer to `numpy.conjugate` for full documentation. | | See Also | -------- | numpy.conjugate : equivalent function | | copy(...) | a.copy(order='C') | | Return a copy of the array. | | Parameters | ---------- | order : {'C', 'F', 'A', 'K'}, optional | Controls the memory layout of the copy. 'C' means C-order, | 'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous, | 'C' otherwise. 'K' means match the layout of `a` as closely | as possible. (Note that this function and :func:`numpy.copy` are very | similar but have different default values for their order= | arguments, and this function always passes sub-classes through.) | | See also | -------- | numpy.copy : Similar function with different default behavior | numpy.copyto | | Notes | ----- | This function is the preferred method for creating an array copy. The | function :func:`numpy.copy` is similar, but it defaults to using order 'K', | and will not pass sub-classes through by default. | | Examples | -------- | >>> x = np.array([[1,2,3],[4,5,6]], order='F') | | >>> y = x.copy() | | >>> [x.fill(0)](https://www.chedong.com/phpMan.php/man/x.fill/0/markdown) | | >>> x | array([[0, 0, 0], | [0, 0, 0]]) | | >>> y | array([[1, 2, 3], | [4, 5, 6]]) | | >>> y.flags['C_CONTIGUOUS'] | True | | cumprod(...) | a.cumprod(axis=None, dtype=None, out=None) | | Return the cumulative product of the elements along the given axis. | | Refer to `numpy.cumprod` for full documentation. | | See Also | -------- | numpy.cumprod : equivalent function | | cumsum(...) | a.cumsum(axis=None, dtype=None, out=None) | | Return the cumulative sum of the elements along the given axis. | | Refer to `numpy.cumsum` for full documentation. | | See Also | -------- | numpy.cumsum : equivalent function | | diagonal(...) | a.diagonal(offset=0, axis1=0, axis2=1) | | Return specified diagonals. In NumPy 1.9 the returned array is a | read-only view instead of a copy as in previous NumPy versions. In | a future version the read-only restriction will be removed. | | Refer to :func:`numpy.diagonal` for full documentation. | | See Also | -------- | numpy.diagonal : equivalent function | | dot(...) | a.dot(b, out=None) | | Dot product of two arrays. | | Refer to `numpy.dot` for full documentation. | | See Also | -------- | numpy.dot : equivalent function | | Examples | -------- | >>> a = [np.eye(2)](https://www.chedong.com/phpMan.php/man/np.eye/2/markdown) | >>> b = np.ones((2, 2)) * 2 | >>> a.dot(b) | array([[2., 2.], | [2., 2.]]) | | This array method can be conveniently chained: | | >>> a.dot(b).dot(b) | array([[8., 8.], | [8., 8.]]) | | dump(...) | a.dump(file) | | Dump a pickle of the array to the specified file. | The array can be read back with pickle.load or numpy.load. | | Parameters | ---------- | file : str or Path | A string naming the dump file. | | .. versionchanged:: 1.17.0 | `pathlib.Path` objects are now accepted. | | dumps(...) | a.dumps() | | Returns the pickle of the array as a string. | pickle.loads or numpy.loads will convert the string back to an array. | | Parameters | ---------- | None | | fill(...) | a.fill(value) | | Fill the array with a scalar value. | | Parameters | ---------- | value : scalar | All elements of `a` will be assigned this value. | | Examples | -------- | >>> a = np.array([1, 2]) | >>> [a.fill(0)](https://www.chedong.com/phpMan.php/man/a.fill/0/markdown) | >>> a | array([0, 0]) | >>> a = [np.empty(2)](https://www.chedong.com/phpMan.php/man/np.empty/2/markdown) | >>> [a.fill(1)](https://www.chedong.com/phpMan.php/man/a.fill/1/markdown) | >>> a | array([1., 1.]) | | flatten(...) | a.flatten(order='C') | | Return a copy of the array collapsed into one dimension. | | Parameters | ---------- | order : {'C', 'F', 'A', 'K'}, optional | 'C' means to flatten in row-major (C-style) order. | 'F' means to flatten in column-major (Fortran- | style) order. 'A' means to flatten in column-major | order if `a` is Fortran *contiguous* in memory, | row-major order otherwise. 'K' means to flatten | `a` in the order the elements occur in memory. | The default is 'C'. | | Returns | ------- | y : ndarray | A copy of the input array, flattened to one dimension. | | See Also | -------- | ravel : Return a flattened array. | flat : A 1-D flat iterator over the array. | | Examples | -------- | >>> a = np.array([[1,2], [3,4]]) | >>> a.flatten() | array([1, 2, 3, 4]) | >>> a.flatten('F') | array([1, 3, 2, 4]) | | getfield(...) | a.getfield(dtype, offset=0) | | Returns a field of the given array as a certain type. | | A field is a view of the array data with a given data-type. The values in | the view are determined by the given type and the offset into the current | array in bytes. The offset needs to be such that the view dtype fits in the | array dtype; for example an array of dtype complex128 has 16-byte elements. | If taking a view with a 32-bit integer (4 bytes), the offset needs to be | between 0 and 12 bytes. | | Parameters | ---------- | dtype : str or dtype | The data type of the view. The dtype size of the view can not be larger | than that of the array itself. | offset : int | Number of bytes to skip before beginning the element view. | | Examples | -------- | >>> x = np.diag([1.+1.j]*2) | >>> x[1, 1] = 2 + 4.j | >>> x | array([[1.+1.j, 0.+0.j], | [0.+0.j, 2.+4.j]]) | >>> x.getfield(np.float64) | array([[1., 0.], | [0., 2.]]) | | By choosing an offset of 8 bytes we can select the complex part of the | array for our view: | | >>> x.getfield(np.float64, offset=8) | array([[1., 0.], | [0., 4.]]) | | item(...) | a.item(*args) | | Copy an element of an array to a standard Python scalar and return it. | | Parameters | ---------- | \*args : Arguments (variable number and type) | | * none: in this case, the method only works for arrays | with one element (`a.size == 1`), which element is | copied into a standard Python scalar object and returned. | | * int_type: this argument is interpreted as a flat index into | the array, specifying which element to copy and return. | | * tuple of int_types: functions as does a single int_type argument, | except that the argument is interpreted as an nd-index into the | array. | | Returns | ------- | z : Standard Python scalar object | A copy of the specified element of the array as a suitable | Python scalar | | Notes | ----- | When the data type of `a` is longdouble or clongdouble, item() returns | a scalar array object because there is no available Python scalar that | would not lose information. Void arrays return a buffer object for item(), | unless fields are defined, in which case a tuple is returned. | | `item` is very similar to a[args], except, instead of an array scalar, | a standard Python scalar is returned. This can be useful for speeding up | access to elements of the array and doing arithmetic on elements of the | array using Python's optimized math. | | Examples | -------- | >>> [np.random.seed(123)](https://www.chedong.com/phpMan.php/man/np.random.seed/123/markdown) | >>> x = np.random.randint(9, size=(3, 3)) | >>> x | array([[2, 2, 6], | [1, 3, 6], | [1, 0, 1]]) | >>> [x.item(3)](https://www.chedong.com/phpMan.php/man/x.item/3/markdown) | 1 | >>> [x.item(7)](https://www.chedong.com/phpMan.php/man/x.item/7/markdown) | 0 | >>> x.item((0, 1)) | 2 | >>> x.item((2, 2)) | 1 | | itemset(...) | a.itemset(*args) | | Insert scalar into an array (scalar is cast to array's dtype, if possible) | | There must be at least 1 argument, and define the last argument | as *item*. Then, ``a.itemset(*args)`` is equivalent to but faster | than ``a[args] = item``. The item should be a scalar value and `args` | must select a single item in the array `a`. | | Parameters | ---------- | \*args : Arguments | If one argument: a scalar, only used in case `a` is of size 1. | If two arguments: the last argument is the value to be set | and must be a scalar, the first argument specifies a single array | element location. It is either an int or a tuple. | | Notes | ----- | Compared to indexing syntax, `itemset` provides some speed increase | for placing a scalar into a particular location in an `ndarray`, | if you must do this. However, generally this is discouraged: | among other problems, it complicates the appearance of the code. | Also, when using `itemset` (and `item`) inside a loop, be sure | to assign the methods to a local variable to avoid the attribute | look-up at each loop iteration. | | Examples | -------- | >>> [np.random.seed(123)](https://www.chedong.com/phpMan.php/man/np.random.seed/123/markdown) | >>> x = np.random.randint(9, size=(3, 3)) | >>> x | array([[2, 2, 6], | [1, 3, 6], | [1, 0, 1]]) | >>> x.itemset(4, 0) | >>> x.itemset((2, 2), 9) | >>> x | array([[2, 2, 6], | [1, 0, 6], | [1, 0, 9]]) | | max(...) | a.max(axis=None, out=None, keepdims=False, initial=, where=True) | | Return the maximum along a given axis. | | Refer to `numpy.amax` for full documentation. | | See Also | -------- | numpy.amax : equivalent function | | mean(...) | a.mean(axis=None, dtype=None, out=None, keepdims=False, *, where=True) | | Returns the average of the array elements along given axis. | | Refer to `numpy.mean` for full documentation. | | See Also | -------- | numpy.mean : equivalent function | | min(...) | a.min(axis=None, out=None, keepdims=False, initial=, where=True) | | Return the minimum along a given axis. | | Refer to `numpy.amin` for full documentation. | | See Also | -------- | numpy.amin : equivalent function | | newbyteorder(...) | arr.newbyteorder(new_order='S', /) | | Return the array with the same data viewed with a different byte order. | | Equivalent to:: | | arr.view([arr.dtype.newbytorder(new_order)](https://www.chedong.com/phpMan.php/man/arr.dtype.newbytorder/neworder/markdown)) | | Changes are also made in all fields and sub-arrays of the array data | type. | | | | Parameters | ---------- | new_order : string, optional | Byte order to force; a value from the byte order specifications | below. `new_order` codes can be any of: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order, equivalent to `sys.byteorder` | * {'|', 'I'} - ignore (no change to byte order) | | The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_arr : array | New array object with the dtype reflecting given change to the | byte order. | | nonzero(...) | a.nonzero() | | Return the indices of the elements that are non-zero. | | Refer to `numpy.nonzero` for full documentation. | | See Also | -------- | numpy.nonzero : equivalent function | | partition(...) | a.partition(kth, axis=-1, kind='introselect', order=None) | | Rearranges the elements in the array in such a way that the value of the | element in kth position is in the position it would be in a sorted array. | All elements smaller than the kth element are moved before this element and | all equal or greater are moved behind it. The ordering of the elements in | the two partitions is undefined. | | .. versionadded:: 1.8.0 | | Parameters | ---------- | kth : int or sequence of ints | Element index to partition by. The kth element value will be in its | final sorted position and all smaller elements will be moved before it | and all equal or greater elements behind it. | The order of all elements in the partitions is undefined. | If provided with a sequence of kth it will partition all elements | indexed by kth of them into their sorted position at once. | axis : int, optional | Axis along which to sort. Default is -1, which means sort along the | last axis. | kind : {'introselect'}, optional | Selection algorithm. Default is 'introselect'. | order : str or list of str, optional | When `a` is an array with fields defined, this argument specifies | which fields to compare first, second, etc. A single field can | be specified as a string, and not all fields need to be specified, | but unspecified fields will still be used, in the order in which | they come up in the dtype, to break ties. | | See Also | -------- | numpy.partition : Return a parititioned copy of an array. | argpartition : Indirect partition. | sort : Full sort. | | Notes | ----- | See ``np.partition`` for notes on the different algorithms. | | Examples | -------- | >>> a = np.array([3, 4, 2, 1]) | >>> [a.partition(3)](https://www.chedong.com/phpMan.php/man/a.partition/3/markdown) | >>> a | array([2, 1, 3, 4]) | | >>> a.partition((1, 3)) | >>> a | array([1, 2, 3, 4]) | | prod(...) | a.prod(axis=None, dtype=None, out=None, keepdims=False, initial=1, where=True) | | Return the product of the array elements over the given axis | | Refer to `numpy.prod` for full documentation. | | See Also | -------- | numpy.prod : equivalent function | | ptp(...) | a.ptp(axis=None, out=None, keepdims=False) | | Peak to peak (maximum - minimum) value along a given axis. | | Refer to `numpy.ptp` for full documentation. | | See Also | -------- | numpy.ptp : equivalent function | | put(...) | a.put(indices, values, mode='raise') | | Set ``a.flat[n] = values[n]`` for all `n` in indices. | | Refer to `numpy.put` for full documentation. | | See Also | -------- | numpy.put : equivalent function | | ravel(...) | a.ravel([order]) | | Return a flattened array. | | Refer to `numpy.ravel` for full documentation. | | See Also | -------- | numpy.ravel : equivalent function | | ndarray.flat : a flat iterator on the array. | | repeat(...) | a.repeat(repeats, axis=None) | | Repeat elements of an array. | | Refer to `numpy.repeat` for full documentation. | | See Also | -------- | numpy.repeat : equivalent function | | reshape(...) | a.reshape(shape, order='C') | | Returns an array containing the same data with a new shape. | | Refer to `numpy.reshape` for full documentation. | | See Also | -------- | numpy.reshape : equivalent function | | Notes | ----- | Unlike the free function `numpy.reshape`, this method on `ndarray` allows | the elements of the shape parameter to be passed in as separate arguments. | For example, ``a.reshape(10, 11)`` is equivalent to | ``a.reshape((10, 11))``. | | resize(...) | a.resize(new_shape, refcheck=True) | | Change shape and size of array in-place. | | Parameters | ---------- | new_shape : tuple of ints, or `n` ints | Shape of resized array. | refcheck : bool, optional | If False, reference count will not be checked. Default is True. | | Returns | ------- | None | | Raises | ------ | ValueError | If `a` does not own its own data or references or views to it exist, | and the data memory must be changed. | PyPy only: will always raise if the data memory must be changed, since | there is no reliable way to determine if references or views to it | exist. | | SystemError | If the `order` keyword argument is specified. This behaviour is a | bug in NumPy. | | See Also | -------- | resize : Return a new array with the specified shape. | | Notes | ----- | This reallocates space for the data area if necessary. | | Only contiguous arrays (data elements consecutive in memory) can be | resized. | | The purpose of the reference count check is to make sure you | do not use this array as a buffer for another Python object and then | reallocate the memory. However, reference counts can increase in | other ways so if you are sure that you have not shared the memory | for this array with another Python object, then you may safely set | `refcheck` to False. | | Examples | -------- | Shrinking an array: array is flattened (in the order that the data are | stored in memory), resized, and reshaped: | | >>> a = np.array([[0, 1], [2, 3]], order='C') | >>> a.resize((2, 1)) | >>> a | array([[0], | [1]]) | | >>> a = np.array([[0, 1], [2, 3]], order='F') | >>> a.resize((2, 1)) | >>> a | array([[0], | [2]]) | | Enlarging an array: as above, but missing entries are filled with zeros: | | >>> b = np.array([[0, 1], [2, 3]]) | >>> b.resize(2, 3) # new_shape parameter doesn't have to be a tuple | >>> b | array([[0, 1, 2], | [3, 0, 0]]) | | Referencing an array prevents resizing... | | >>> c = a | >>> a.resize((1, 1)) | Traceback (most recent call last): | ... | ValueError: cannot resize an array that references or is referenced ... | | Unless `refcheck` is False: | | >>> a.resize((1, 1), refcheck=False) | >>> a | array([[0]]) | >>> c | array([[0]]) | | round(...) | a.round(decimals=0, out=None) | | Return `a` with each element rounded to the given number of decimals. | | Refer to `numpy.around` for full documentation. | | See Also | -------- | numpy.around : equivalent function | | searchsorted(...) | a.searchsorted(v, side='left', sorter=None) | | Find indices where elements of v should be inserted in a to maintain order. | | For full documentation, see `numpy.searchsorted` | | See Also | -------- | numpy.searchsorted : equivalent function | | setfield(...) | a.setfield(val, dtype, offset=0) | | Put a value into a specified place in a field defined by a data-type. | | Place `val` into `a`'s field defined by `dtype` and beginning `offset` | bytes into the field. | | Parameters | ---------- | val : object | Value to be placed in field. | dtype : dtype object | Data-type of the field in which to place `val`. | offset : int, optional | The number of bytes into the field at which to place `val`. | | Returns | ------- | None | | See Also | -------- | getfield | | Examples | -------- | >>> x = [np.eye(3)](https://www.chedong.com/phpMan.php/man/np.eye/3/markdown) | >>> x.getfield(np.float64) | array([[1., 0., 0.], | [0., 1., 0.], | [0., 0., 1.]]) | >>> x.setfield(3, np.int32) | >>> x.getfield(np.int32) | array([[3, 3, 3], | [3, 3, 3], | [3, 3, 3]], dtype=int32) | >>> x | array([[1.0e+000, 1.5e-323, 1.5e-323], | [1.5e-323, 1.0e+000, 1.5e-323], | [1.5e-323, 1.5e-323, 1.0e+000]]) | >>> x.setfield([np.eye(3)](https://www.chedong.com/phpMan.php/man/np.eye/3/markdown), np.int32) | >>> x | array([[1., 0., 0.], | [0., 1., 0.], | [0., 0., 1.]]) | | setflags(...) | a.setflags(write=None, align=None, uic=None) | | Set array flags WRITEABLE, ALIGNED, (WRITEBACKIFCOPY and UPDATEIFCOPY), | respectively. | | These Boolean-valued flags affect how numpy interprets the memory | area used by `a` (see Notes below). The ALIGNED flag can only | be set to True if the data is actually aligned according to the type. | The WRITEBACKIFCOPY and (deprecated) UPDATEIFCOPY flags can never be set | to True. The flag WRITEABLE can only be set to True if the array owns its | own memory, or the ultimate owner of the memory exposes a writeable buffer | interface, or is a string. (The exception for string is made so that | unpickling can be done without copying memory.) | | Parameters | ---------- | write : bool, optional | Describes whether or not `a` can be written to. | align : bool, optional | Describes whether or not `a` is aligned properly for its type. | uic : bool, optional | Describes whether or not `a` is a copy of another "base" array. | | Notes | ----- | Array flags provide information about how the memory area used | for the array is to be interpreted. There are 7 Boolean flags | in use, only four of which can be changed by the user: | WRITEBACKIFCOPY, UPDATEIFCOPY, WRITEABLE, and ALIGNED. | | WRITEABLE (W) the data area can be written to; | | ALIGNED (A) the data and strides are aligned appropriately for the hardware | (as determined by the compiler); | | UPDATEIFCOPY (U) (deprecated), replaced by WRITEBACKIFCOPY; | | WRITEBACKIFCOPY (X) this array is a copy of some other array (referenced | by .base). When the C-API function PyArray_ResolveWritebackIfCopy is | called, the base array will be updated with the contents of this array. | | All flags can be accessed using the single (upper case) letter as well | as the full name. | | Examples | -------- | >>> y = np.array([[3, 1, 7], | ... [2, 0, 0], | ... [8, 5, 9]]) | >>> y | array([[3, 1, 7], | [2, 0, 0], | [8, 5, 9]]) | >>> y.flags | C_CONTIGUOUS : True | F_CONTIGUOUS : False | OWNDATA : True | WRITEABLE : True | ALIGNED : True | WRITEBACKIFCOPY : False | UPDATEIFCOPY : False | >>> y.setflags(write=0, align=0) | >>> y.flags | C_CONTIGUOUS : True | F_CONTIGUOUS : False | OWNDATA : True | WRITEABLE : False | ALIGNED : False | WRITEBACKIFCOPY : False | UPDATEIFCOPY : False | >>> y.setflags(uic=1) | Traceback (most recent call last): | File "", line 1, in | ValueError: cannot set WRITEBACKIFCOPY flag to True | | sort(...) | a.sort(axis=-1, kind=None, order=None) | | Sort an array in-place. Refer to `numpy.sort` for full documentation. | | Parameters | ---------- | axis : int, optional | Axis along which to sort. Default is -1, which means sort along the | last axis. | kind : {'quicksort', 'mergesort', 'heapsort', 'stable'}, optional | Sorting algorithm. The default is 'quicksort'. Note that both 'stable' | and 'mergesort' use timsort under the covers and, in general, the | actual implementation will vary with datatype. The 'mergesort' option | is retained for backwards compatibility. | | .. versionchanged:: 1.15.0 | The 'stable' option was added. | | order : str or list of str, optional | When `a` is an array with fields defined, this argument specifies | which fields to compare first, second, etc. A single field can | be specified as a string, and not all fields need be specified, | but unspecified fields will still be used, in the order in which | they come up in the dtype, to break ties. | | See Also | -------- | numpy.sort : Return a sorted copy of an array. | numpy.argsort : Indirect sort. | numpy.lexsort : Indirect stable sort on multiple keys. | numpy.searchsorted : Find elements in sorted array. | numpy.partition: Partial sort. | | Notes | ----- | See `numpy.sort` for notes on the different sorting algorithms. | | Examples | -------- | >>> a = np.array([[1,4], [3,1]]) | >>> a.sort(axis=1) | >>> a | array([[1, 4], | [1, 3]]) | >>> a.sort(axis=0) | >>> a | array([[1, 3], | [1, 4]]) | | Use the `order` keyword to specify a field to use when sorting a | structured array: | | >>> a = np.array([('a', 2), ('c', 1)], dtype=[('x', 'S1'), ('y', int)]) | >>> a.sort(order='y') | >>> a | array([(b'c', 1), (b'a', 2)], | dtype=[('x', 'S1'), ('y', '>> x = np.array([[0, 1], [2, 3]], dtype='>> x.tobytes() | b'\x00\x00\x01\x00\x02\x00\x03\x00' | >>> x.tobytes('C') == x.tobytes() | True | >>> x.tobytes('F') | b'\x00\x00\x02\x00\x01\x00\x03\x00' | | tofile(...) | a.tofile(fid, sep="", format="%s") | | Write array to a file as text or binary (default). | | Data is always written in 'C' order, independent of the order of `a`. | The data produced by this method can be recovered using the function | fromfile(). | | Parameters | ---------- | fid : file or str or Path | An open file object, or a string containing a filename. | | .. versionchanged:: 1.17.0 | `pathlib.Path` objects are now accepted. | | sep : str | Separator between array items for text output. | If "" (empty), a binary file is written, equivalent to | ``file.write(a.tobytes())``. | format : str | Format string for text file output. | Each entry in the array is formatted to text by first converting | it to the closest Python type, and then using "format" % item. | | Notes | ----- | This is a convenience function for quick storage of array data. | Information on endianness and precision is lost, so this method is not a | good choice for files intended to archive data or transport data between | machines with different endianness. Some of these problems can be overcome | by outputting the data as text files, at the expense of speed and file | size. | | When fid is a file object, array contents are directly written to the | file, bypassing the file object's ``write`` method. As a result, tofile | cannot be used with files objects supporting compression (e.g., GzipFile) | or file-like objects that do not support ``fileno()`` (e.g., BytesIO). | | tolist(...) | a.tolist() | | Return the array as an ``a.ndim``-levels deep nested list of Python scalars. | | Return a copy of the array data as a (nested) Python list. | Data items are converted to the nearest compatible builtin Python type, via | the `~numpy.ndarray.item` function. | | If ``a.ndim`` is 0, then since the depth of the nested list is 0, it will | not be a list at all, but a simple Python scalar. | | Parameters | ---------- | none | | Returns | ------- | y : object, or list of object, or list of list of object, or ... | The possibly nested list of array elements. | | Notes | ----- | The array may be recreated via ``a = np.array(a.tolist())``, although this | may sometimes lose precision. | | Examples | -------- | For a 1D array, ``a.tolist()`` is almost the same as ``list(a)``, | except that ``tolist`` changes numpy scalars to Python scalars: | | >>> a = np.uint32([1, 2]) | >>> a_list = list(a) | >>> a_list | [1, 2] | >>> type(a_list[0]) | | >>> a_tolist = a.tolist() | >>> a_tolist | [1, 2] | >>> type(a_tolist[0]) | | | Additionally, for a 2D array, ``tolist`` applies recursively: | | >>> a = np.array([[1, 2], [3, 4]]) | >>> list(a) | [array([1, 2]), array([3, 4])] | >>> a.tolist() | [[1, 2], [3, 4]] | | The base case for this recursion is a 0D array: | | >>> a = [np.array(1)](https://www.chedong.com/phpMan.php/man/np.array/1/markdown) | >>> list(a) | Traceback (most recent call last): | ... | TypeError: iteration over a 0-d array | >>> a.tolist() | 1 | | tostring(...) | a.tostring(order='C') | | A compatibility alias for `tobytes`, with exactly the same behavior. | | Despite its name, it returns `bytes` not `str`\ s. | | .. deprecated:: 1.19.0 | | trace(...) | a.trace(offset=0, axis1=0, axis2=1, dtype=None, out=None) | | Return the sum along diagonals of the array. | | Refer to `numpy.trace` for full documentation. | | See Also | -------- | numpy.trace : equivalent function | | transpose(...) | a.transpose(*axes) | | Returns a view of the array with axes transposed. | | For a 1-D array this has no effect, as a transposed vector is simply the | same vector. To convert a 1-D array into a 2D column vector, an additional | dimension must be added. `np.atleast2d(a).T` achieves this, as does | `a[:, np.newaxis]`. | For a 2-D array, this is a standard matrix transpose. | For an n-D array, if axes are given, their order indicates how the | axes are permuted (see Examples). If axes are not provided and | ``a.shape = (i[0], i[1], ... i[n-2], i[n-1])``, then | ``a.transpose().shape = (i[n-1], i[n-2], ... i[1], i[0])``. | | Parameters | ---------- | axes : None, tuple of ints, or `n` ints | | * None or no argument: reverses the order of the axes. | | * tuple of ints: `i` in the `j`-th place in the tuple means `a`'s | `i`-th axis becomes `a.transpose()`'s `j`-th axis. | | * `n` ints: same as an n-tuple of the same ints (this form is | intended simply as a "convenience" alternative to the tuple form) | | Returns | ------- | out : ndarray | View of `a`, with axes suitably permuted. | | See Also | -------- | transpose : Equivalent function | ndarray.T : Array property returning the array transposed. | ndarray.reshape : Give a new shape to an array without changing its data. | | Examples | -------- | >>> a = np.array([[1, 2], [3, 4]]) | >>> a | array([[1, 2], | [3, 4]]) | >>> a.transpose() | array([[1, 3], | [2, 4]]) | >>> a.transpose((1, 0)) | array([[1, 3], | [2, 4]]) | >>> a.transpose(1, 0) | array([[1, 3], | [2, 4]]) | | var(...) | a.var(axis=None, dtype=None, out=None, ddof=0, keepdims=False, *, where=True) | | Returns the variance of the array elements, along given axis. | | Refer to `numpy.var` for full documentation. | | See Also | -------- | numpy.var : equivalent function | | view(...) | a.view([dtype][, type]) | | New view of array with the same data. | | .. note:: | Passing None for ``dtype`` is different from omitting the parameter, | since the former invokes ``dtype(None)`` which is an alias for | ``dtype('float_')``. | | Parameters | ---------- | dtype : data-type or ndarray sub-class, optional | Data-type descriptor of the returned view, e.g., float32 or int16. | Omitting it results in the view having the same data-type as `a`. | This argument can also be specified as an ndarray sub-class, which | then specifies the type of the returned object (this is equivalent to | setting the ``type`` parameter). | type : Python type, optional | Type of the returned view, e.g., ndarray or matrix. Again, omission | of the parameter results in type preservation. | | Notes | ----- | ``a.view()`` is used two different ways: | | ``a.view(some_dtype)`` or ``a.view(dtype=some_dtype)`` constructs a view | of the array's memory with a different data-type. This can cause a | reinterpretation of the bytes of memory. | | ``[a.view(ndarray_subclass)](https://www.chedong.com/phpMan.php/man/a.view/ndarraysubclass/markdown)`` or ``a.view(type=ndarray_subclass)`` just | returns an instance of `ndarray_subclass` that looks at the same array | (same shape, dtype, etc.) This does not cause a reinterpretation of the | memory. | | For ``a.view(some_dtype)``, if ``some_dtype`` has a different number of | bytes per entry than the previous dtype (for example, converting a | regular array to a structured array), then the behavior of the view | cannot be predicted just from the superficial appearance of ``a`` (shown | by ``print(a)``). It also depends on exactly how ``a`` is stored in | memory. Therefore if ``a`` is C-ordered versus fortran-ordered, versus | defined as a slice or transpose, etc., the view may give different | results. | | | Examples | -------- | >>> x = np.array([(1, 2)], dtype=[('a', np.int8), ('b', np.int8)]) | | Viewing array data using a different type and dtype: | | >>> y = x.view(dtype=np.int16, type=np.matrix) | >>> y | matrix([[513]], dtype=int16) | >>> print(type(y)) | | | Creating a view on a structured array so it can be used in calculations | | >>> x = np.array([(1, 2),(3,4)], dtype=[('a', np.int8), ('b', np.int8)]) | >>> xv = x.view(dtype=np.int8).reshape(-1,2) | >>> xv | array([[1, 2], | [3, 4]], dtype=int8) | >>> [xv.mean(0)](https://www.chedong.com/phpMan.php/man/xv.mean/0/markdown) | array([2., 3.]) | | Making changes to the view changes the underlying array | | >>> xv[0,1] = 20 | >>> x | array([(1, 20), (3, 4)], dtype=[('a', 'i1'), ('b', 'i1')]) | | Using a view to convert an array to a recarray: | | >>> z = x.view(np.recarray) | >>> z.a | array([1, 3], dtype=int8) | | Views share data: | | >>> x[0] = (9, 10) | >>> z[0] | (9, 10) | | Views that change the dtype size (bytes per entry) should normally be | avoided on arrays defined by slices, transposes, fortran-ordering, etc.: | | >>> x = np.array([[1,2,3],[4,5,6]], dtype=np.int16) | >>> y = x[:, 0:2] | >>> y | array([[1, 2], | [4, 5]], dtype=int16) | >>> y.view(dtype=[('width', np.int16), ('length', np.int16)]) | Traceback (most recent call last): | ... | ValueError: To change to a dtype of a different size, the array must be C-contiguous | >>> z = y.copy() | >>> z.view(dtype=[('width', np.int16), ('length', np.int16)]) | array([[(1, 2)], | [(4, 5)]], dtype=[('width', '>> x = np.array([[1.,2.],[3.,4.]]) | >>> x | array([[ 1., 2.], | [ 3., 4.]]) | >>> x.T | array([[ 1., 3.], | [ 2., 4.]]) | >>> x = np.array([1.,2.,3.,4.]) | >>> x | array([ 1., 2., 3., 4.]) | >>> x.T | array([ 1., 2., 3., 4.]) | | See Also | -------- | transpose | | __array_interface__ | Array protocol: Python side. | | __array_struct__ | Array protocol: C-struct side. | | base | Base object if memory is from some other object. | | Examples | -------- | The base of an array that owns its memory is None: | | >>> x = np.array([1,2,3,4]) | >>> x.base is None | True | | Slicing creates a view, whose memory is shared with x: | | >>> y = x[2:] | >>> y.base is x | True | | ctypes | An object to simplify the interaction of the array with the ctypes | module. | | This attribute creates an object that makes it easier to use arrays | when calling shared libraries with the ctypes module. The returned | object has, among others, data, shape, and strides attributes (see | Notes below) which themselves return ctypes objects that can be used | as arguments to a shared library. | | Parameters | ---------- | None | | Returns | ------- | c : Python object | Possessing attributes data, shape, strides, etc. | | See Also | -------- | numpy.ctypeslib | | Notes | ----- | Below are the public attributes of this object which were documented | in "Guide to NumPy" (we have omitted undocumented public attributes, | as well as documented private attributes): | | .. autoattribute:: numpy.core._internal._ctypes.data | :noindex: | | .. autoattribute:: numpy.core._internal._ctypes.shape | :noindex: | | .. autoattribute:: numpy.core._internal._ctypes.strides | :noindex: | | .. automethod:: numpy.core._internal._ctypes.data_as | :noindex: | | .. automethod:: numpy.core._internal._ctypes.shape_as | :noindex: | | .. automethod:: numpy.core._internal._ctypes.strides_as | :noindex: | | If the ctypes module is not available, then the ctypes attribute | of array objects still returns something useful, but ctypes objects | are not returned and errors may be raised instead. In particular, | the object will still have the ``as_parameter`` attribute which will | return an integer equal to the data attribute. | | Examples | -------- | >>> import ctypes | >>> x = np.array([[0, 1], [2, 3]], dtype=np.int32) | >>> x | array([[0, 1], | [2, 3]], dtype=int32) | >>> x.ctypes.data | 31962608 # may vary | >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)) | <__main__.LP_c_uint object at 0x7ff2fc1fc200> # may vary | >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)).contents | [c_uint(0)](https://www.chedong.com/phpMan.php/man/cuint/0/markdown) | >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint64)).contents | [c_ulong(4294967296)](https://www.chedong.com/phpMan.php/man/culong/4294967296/markdown) | >>> x.ctypes.shape | # may vary | >>> x.ctypes.strides | # may vary | | data | Python buffer object pointing to the start of the array's data. | | dtype | Data-type of the array's elements. | | Parameters | ---------- | None | | Returns | ------- | d : numpy dtype object | | See Also | -------- | numpy.dtype | | Examples | -------- | >>> x | array([[0, 1], | [2, 3]]) | >>> x.dtype | dtype('int32') | >>> type(x.dtype) | | | flags | Information about the memory layout of the array. | | Attributes | ---------- | C_CONTIGUOUS (C) | The data is in a single, C-style contiguous segment. | F_CONTIGUOUS (F) | The data is in a single, Fortran-style contiguous segment. | OWNDATA (O) | The array owns the memory it uses or borrows it from another object. | WRITEABLE (W) | The data area can be written to. Setting this to False locks | the data, making it read-only. A view (slice, etc.) inherits WRITEABLE | from its base array at creation time, but a view of a writeable | array may be subsequently locked while the base array remains writeable. | (The opposite is not true, in that a view of a locked array may not | be made writeable. However, currently, locking a base object does not | lock any views that already reference it, so under that circumstance it | is possible to alter the contents of a locked array via a previously | created writeable view onto it.) Attempting to change a non-writeable | array raises a RuntimeError exception. | ALIGNED (A) | The data and all elements are aligned appropriately for the hardware. | WRITEBACKIFCOPY (X) | This array is a copy of some other array. The C-API function | PyArray_ResolveWritebackIfCopy must be called before deallocating | to the base array will be updated with the contents of this array. | UPDATEIFCOPY (U) | (Deprecated, use WRITEBACKIFCOPY) This array is a copy of some other array. | When this array is | deallocated, the base array will be updated with the contents of | this array. | FNC | F_CONTIGUOUS and not C_CONTIGUOUS. | FORC | F_CONTIGUOUS or C_CONTIGUOUS (one-segment test). | BEHAVED (B) | ALIGNED and WRITEABLE. | CARRAY (CA) | BEHAVED and C_CONTIGUOUS. | FARRAY (FA) | BEHAVED and F_CONTIGUOUS and not C_CONTIGUOUS. | | Notes | ----- | The `flags` object can be accessed dictionary-like (as in ``a.flags['WRITEABLE']``), | or by using lowercased attribute names (as in ``a.flags.writeable``). Short flag | names are only supported in dictionary access. | | Only the WRITEBACKIFCOPY, UPDATEIFCOPY, WRITEABLE, and ALIGNED flags can be | changed by the user, via direct assignment to the attribute or dictionary | entry, or by calling `ndarray.setflags`. | | The array flags cannot be set arbitrarily: | | - UPDATEIFCOPY can only be set ``False``. | - WRITEBACKIFCOPY can only be set ``False``. | - ALIGNED can only be set ``True`` if the data is truly aligned. | - WRITEABLE can only be set ``True`` if the array owns its own memory | or the ultimate owner of the memory exposes a writeable buffer | interface or is a string. | | Arrays can be both C-style and Fortran-style contiguous simultaneously. | This is clear for 1-dimensional arrays, but can also be true for higher | dimensional arrays. | | Even for contiguous arrays a stride for a given dimension | ``arr.strides[dim]`` may be *arbitrary* if ``arr.shape[dim] == 1`` | or the array has no elements. | It does *not* generally hold that ``self.strides[-1] == self.itemsize`` | for C-style contiguous arrays or ``self.strides[0] == self.itemsize`` for | Fortran-style contiguous arrays is true. | | flat | A 1-D iterator over the array. | | This is a `numpy.flatiter` instance, which acts similarly to, but is not | a subclass of, Python's built-in iterator object. | | See Also | -------- | flatten : Return a copy of the array collapsed into one dimension. | | flatiter | | Examples | -------- | >>> x = np.arange(1, 7).reshape(2, 3) | >>> x | array([[1, 2, 3], | [4, 5, 6]]) | >>> x.flat[3] | 4 | >>> x.T | array([[1, 4], | [2, 5], | [3, 6]]) | >>> x.T.flat[3] | 5 | >>> type(x.flat) | | | An assignment example: | | >>> x.flat = 3; x | array([[3, 3, 3], | [3, 3, 3]]) | >>> x.flat[[1,4]] = 1; x | array([[3, 1, 3], | [3, 1, 3]]) | | imag | The imaginary part of the array. | | Examples | -------- | >>> x = np.sqrt([1+0j, 0+1j]) | >>> x.imag | array([ 0. , 0.70710678]) | >>> x.imag.dtype | dtype('float64') | | itemsize | Length of one array element in bytes. | | Examples | -------- | >>> x = np.array([1,2,3], dtype=np.float64) | >>> x.itemsize | 8 | >>> x = np.array([1,2,3], dtype=np.complex128) | >>> x.itemsize | 16 | | nbytes | Total bytes consumed by the elements of the array. | | Notes | ----- | Does not include memory consumed by non-element attributes of the | array object. | | Examples | -------- | >>> x = np.zeros((3,5,2), dtype=np.complex128) | >>> x.nbytes | 480 | >>> np.prod(x.shape) * x.itemsize | 480 | | ndim | Number of array dimensions. | | Examples | -------- | >>> x = np.array([1, 2, 3]) | >>> x.ndim | 1 | >>> y = np.zeros((2, 3, 4)) | >>> y.ndim | 3 | | real | The real part of the array. | | Examples | -------- | >>> x = np.sqrt([1+0j, 0+1j]) | >>> x.real | array([ 1. , 0.70710678]) | >>> x.real.dtype | dtype('float64') | | See Also | -------- | numpy.real : equivalent function | | shape | Tuple of array dimensions. | | The shape property is usually used to get the current shape of an array, | but may also be used to reshape the array in-place by assigning a tuple of | array dimensions to it. As with `numpy.reshape`, one of the new shape | dimensions can be -1, in which case its value is inferred from the size of | the array and the remaining dimensions. Reshaping an array in-place will | fail if a copy is required. | | Examples | -------- | >>> x = np.array([1, 2, 3, 4]) | >>> x.shape | (4,) | >>> y = np.zeros((2, 3, 4)) | >>> y.shape | (2, 3, 4) | >>> y.shape = (3, 8) | >>> y | array([[ 0., 0., 0., 0., 0., 0., 0., 0.], | [ 0., 0., 0., 0., 0., 0., 0., 0.], | [ 0., 0., 0., 0., 0., 0., 0., 0.]]) | >>> y.shape = (3, 6) | Traceback (most recent call last): | File "", line 1, in | ValueError: total size of new array must be unchanged | >>> np.zeros((4,2))[::2].shape = (-1,) | Traceback (most recent call last): | File "", line 1, in | AttributeError: Incompatible shape for in-place modification. Use | `.reshape()` to make a copy with the desired shape. | | See Also | -------- | numpy.reshape : similar function | ndarray.reshape : similar method | | size | Number of elements in the array. | | Equal to ``np.prod(a.shape)``, i.e., the product of the array's | dimensions. | | Notes | ----- | `a.size` returns a standard arbitrary precision Python integer. This | may not be the case with other methods of obtaining the same value | (like the suggested ``np.prod(a.shape)``, which returns an instance | of ``np.int_``), and may be relevant if the value is used further in | calculations that may overflow a fixed size integer type. | | Examples | -------- | >>> x = np.zeros((3, 5, 2), dtype=np.complex128) | >>> x.size | 30 | >>> np.prod(x.shape) | 30 | | strides | Tuple of bytes to step in each dimension when traversing an array. | | The byte offset of element ``(i[0], i[1], ..., i[n])`` in an array `a` | is:: | | offset = sum(np.array(i) * a.strides) | | A more detailed explanation of strides can be found in the | "ndarray.rst" file in the NumPy reference guide. | | Notes | ----- | Imagine an array of 32-bit integers (each 4 bytes):: | | x = np.array([[0, 1, 2, 3, 4], | [5, 6, 7, 8, 9]], dtype=np.int32) | | This array is stored in memory as 40 bytes, one after the other | (known as a contiguous block of memory). The strides of an array tell | us how many bytes we have to skip in memory to move to the next position | along a certain axis. For example, we have to skip 4 bytes (1 value) to | move to the next column, but 20 bytes (5 values) to get to the same | position in the next row. As such, the strides for the array `x` will be | ``(20, 4)``. | | See Also | -------- | numpy.lib.stride_tricks.as_strided | | Examples | -------- | >>> y = np.reshape(np.arange(2*3*4), (2,3,4)) | >>> y | array([[[ 0, 1, 2, 3], | [ 4, 5, 6, 7], | [ 8, 9, 10, 11]], | [[12, 13, 14, 15], | [16, 17, 18, 19], | [20, 21, 22, 23]]]) | >>> y.strides | (48, 16, 4) | >>> y[1,1,1] | 17 | >>> offset=sum(y.strides * np.array((1,1,1))) | >>> offset/y.itemsize | 17 | | >>> x = np.reshape(np.arange(5*6*7*8), (5,6,7,8)).transpose(2,3,1,0) | >>> x.strides | (32, 4, 224, 1344) | >>> i = np.array([3,5,2,2]) | >>> offset = sum(i * x.strides) | >>> x[3,5,2,2] | 813 | >>> offset / x.itemsize | 813 | | ---------------------------------------------------------------------- | Data and other attributes inherited from ndarray: | | __hash__ = None ### class ndarray | ndarray(shape, dtype=float, buffer=None, offset=0, | strides=None, order=None) | | An array object represents a multidimensional, homogeneous array | of fixed-size items. An associated data-type object describes the | format of each element in the array (its byte-order, how many bytes it | occupies in memory, whether it is an integer, a floating point number, | or something else, etc.) | | Arrays should be constructed using `array`, `zeros` or `empty` (refer | to the See Also section below). The parameters given here refer to | a low-level method (`ndarray(...)`) for instantiating an array. | | For more information, refer to the `numpy` module and examine the | methods and attributes of an array. | | Parameters | ---------- | (for the __new__ method; see Notes below) | | shape : tuple of ints | Shape of created array. | dtype : data-type, optional | Any object that can be interpreted as a numpy data type. | buffer : object exposing buffer interface, optional | Used to fill the array with data. | offset : int, optional | Offset of array data in buffer. | strides : tuple of ints, optional | Strides of data in memory. | order : {'C', 'F'}, optional | Row-major (C-style) or column-major (Fortran-style) order. | | Attributes | ---------- | T : ndarray | Transpose of the array. | data : buffer | The array's elements, in memory. | dtype : dtype object | Describes the format of the elements in the array. | flags : dict | Dictionary containing information related to memory use, e.g., | 'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc. | flat : numpy.flatiter object | Flattened version of the array as an iterator. The iterator | allows assignments, e.g., ``x.flat = 3`` (See `ndarray.flat` for | assignment examples; TODO). | imag : ndarray | Imaginary part of the array. | real : ndarray | Real part of the array. | size : int | Number of elements in the array. | itemsize : int | The memory use of each array element in bytes. | nbytes : int | The total number of bytes required to store the array data, | i.e., ``itemsize * size``. | ndim : int | The array's number of dimensions. | shape : tuple of ints | Shape of the array. | strides : tuple of ints | The step-size required to move from one element to the next in | memory. For example, a contiguous ``(3, 4)`` array of type | ``int16`` in C-order has strides ``(8, 2)``. This implies that | to move from element to element in memory requires jumps of 2 bytes. | To move from row-to-row, one needs to jump 8 bytes at a time | (``2 * 4``). | ctypes : ctypes object | Class containing properties of the array needed for interaction | with ctypes. | base : ndarray | If the array is a view into another array, that array is its `base` | (unless that array is also a view). The `base` array is where the | array data is actually stored. | | See Also | -------- | array : Construct an array. | zeros : Create an array, each element of which is zero. | empty : Create an array, but leave its allocated memory unchanged (i.e., | it contains "garbage"). | dtype : Create a data-type. | numpy.typing.NDArray : A :term:`generic ` version | of ndarray. | | Notes | ----- | There are two modes of creating an array using ``__new__``: | | 1. If `buffer` is None, then only `shape`, `dtype`, and `order` | are used. | 2. If `buffer` is an object exposing the buffer interface, then | all keywords are interpreted. | | No ``__init__`` method is needed because the array is fully initialized | after the ``__new__`` method. | | Examples | -------- | These examples illustrate the low-level `ndarray` constructor. Refer | to the `See Also` section above for easier ways of constructing an | ndarray. | | First mode, `buffer` is None: | | >>> np.ndarray(shape=(2,2), dtype=float, order='F') | array([[0.0e+000, 0.0e+000], # random | [ nan, 2.5e-323]]) | | Second mode: | | >>> np.ndarray((2,), buffer=np.array([1,2,3]), | ... offset=np.int_().itemsize, | ... dtype=int) # offset = 1*itemsize, i.e. skip first element | array([2, 3]) | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __and__(self, value, /) | Return self&value. | | __array__(...) | a.__array__([dtype], /) -> reference if type unchanged, copy otherwise. | | Returns either a new reference to self if dtype is not given or a new array | of provided data type if dtype is different from the current dtype of the | array. | | __array_function__(...) | | __array_prepare__(...) | a.__array_prepare__(obj) -> Object of same type as ndarray object obj. | | __array_ufunc__(...) | | __array_wrap__(...) | a.__array_wrap__(obj) -> Object of same type as ndarray object a. | | __bool__(self, /) | True if self else False | | __complex__(...) | | __contains__(self, key, /) | Return key in self. | | __copy__(...) | a.__copy__() | | Used if :func:`copy.copy` is called on an array. Returns a copy of the array. | | Equivalent to ``a.copy(order='K')``. | | __deepcopy__(...) | a.__deepcopy__(memo, /) -> Deep copy of array. | | Used if :func:`copy.deepcopy` is called on an array. | | __delitem__(self, key, /) | Delete self[key]. | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __format__(...) | Default object formatter. | | __ge__(self, value, /) | Return self>=value. | | __getitem__(self, key, /) | Return self[key]. | | __gt__(self, value, /) | Return self>value. | | __iadd__(self, value, /) | Return self+=value. | | __iand__(self, value, /) | Return self&=value. | | __ifloordiv__(self, value, /) | Return self//=value. | | __ilshift__(self, value, /) | Return self<<=value. | | __imatmul__(self, value, /) | Return self@=value. | | __imod__(self, value, /) | Return self%=value. | | __imul__(self, value, /) | Return self*=value. | | __index__(self, /) | Return self converted to an integer, if self is suitable for use as an index into a list. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __ior__(self, value, /) | Return self|=value. | | __ipow__(self, value, /) | Return self**=value. | | __irshift__(self, value, /) | Return self>>=value. | | __isub__(self, value, /) | Return self-=value. | | __iter__(self, /) | Implement iter(self). | | __itruediv__(self, value, /) | Return self/=value. | | __ixor__(self, value, /) | Return self^=value. | | __le__(self, value, /) | Return self<=value. | | __len__(self, /) | Return len(self). | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __setitem__(self, key, value, /) | Set self[key] to value. | | __setstate__(...) | a.__setstate__(state, /) | | For unpickling. | | The `state` argument must be a sequence that contains the following | elements: | | Parameters | ---------- | version : int | optional pickle version. If omitted defaults to 0. | shape : tuple | dtype : data-type | isFortran : bool | rawdata : string or list | a binary string with the data (or a list if 'a' is an object array) | | __sizeof__(...) | Size of object in memory, in bytes. | | __str__(self, /) | Return str(self). | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | all(...) | a.all(axis=None, out=None, keepdims=False, *, where=True) | | Returns True if all elements evaluate to True. | | Refer to `numpy.all` for full documentation. | | See Also | -------- | numpy.all : equivalent function | | any(...) | a.any(axis=None, out=None, keepdims=False, *, where=True) | | Returns True if any of the elements of `a` evaluate to True. | | Refer to `numpy.any` for full documentation. | | See Also | -------- | numpy.any : equivalent function | | argmax(...) | a.argmax(axis=None, out=None) | | Return indices of the maximum values along the given axis. | | Refer to `numpy.argmax` for full documentation. | | See Also | -------- | numpy.argmax : equivalent function | | argmin(...) | a.argmin(axis=None, out=None) | | Return indices of the minimum values along the given axis. | | Refer to `numpy.argmin` for detailed documentation. | | See Also | -------- | numpy.argmin : equivalent function | | argpartition(...) | a.argpartition(kth, axis=-1, kind='introselect', order=None) | | Returns the indices that would partition this array. | | Refer to `numpy.argpartition` for full documentation. | | .. versionadded:: 1.8.0 | | See Also | -------- | numpy.argpartition : equivalent function | | argsort(...) | a.argsort(axis=-1, kind=None, order=None) | | Returns the indices that would sort this array. | | Refer to `numpy.argsort` for full documentation. | | See Also | -------- | numpy.argsort : equivalent function | | astype(...) | a.astype(dtype, order='K', casting='unsafe', subok=True, copy=True) | | Copy of the array, cast to a specified type. | | Parameters | ---------- | dtype : str or dtype | Typecode or data-type to which the array is cast. | order : {'C', 'F', 'A', 'K'}, optional | Controls the memory layout order of the result. | 'C' means C order, 'F' means Fortran order, 'A' | means 'F' order if all the arrays are Fortran contiguous, | 'C' order otherwise, and 'K' means as close to the | order the array elements appear in memory as possible. | Default is 'K'. | casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional | Controls what kind of data casting may occur. Defaults to 'unsafe' | for backwards compatibility. | | * 'no' means the data types should not be cast at all. | * 'equiv' means only byte-order changes are allowed. | * 'safe' means only casts which can preserve values are allowed. | * 'same_kind' means only safe casts or casts within a kind, | like float64 to float32, are allowed. | * 'unsafe' means any data conversions may be done. | subok : bool, optional | If True, then sub-classes will be passed-through (default), otherwise | the returned array will be forced to be a base-class array. | copy : bool, optional | By default, astype always returns a newly allocated array. If this | is set to false, and the `dtype`, `order`, and `subok` | requirements are satisfied, the input array is returned instead | of a copy. | | Returns | ------- | arr_t : ndarray | Unless `copy` is False and the other conditions for returning the input | array are satisfied (see description for `copy` input parameter), `arr_t` | is a new array of the same shape as the input array, with dtype, order | given by `dtype`, `order`. | | Notes | ----- | .. versionchanged:: 1.17.0 | Casting between a simple data type and a structured one is possible only | for "unsafe" casting. Casting to multiple fields is allowed, but | casting from multiple fields is not. | | .. versionchanged:: 1.9.0 | Casting from numeric to string types in 'safe' casting mode requires | that the string dtype length is long enough to store the max | integer/float value converted. | | Raises | ------ | ComplexWarning | When casting from complex to float or int. To avoid this, | one should use ``a.real.astype(t)``. | | Examples | -------- | >>> x = np.array([1, 2, 2.5]) | >>> x | array([1. , 2. , 2.5]) | | >>> x.astype(int) | array([1, 2, 2]) | | byteswap(...) | a.byteswap(inplace=False) | | Swap the bytes of the array elements | | Toggle between low-endian and big-endian data representation by | returning a byteswapped array, optionally swapped in-place. | Arrays of byte-strings are not swapped. The real and imaginary | parts of a complex number are swapped individually. | | Parameters | ---------- | inplace : bool, optional | If ``True``, swap bytes in-place, default is ``False``. | | Returns | ------- | out : ndarray | The byteswapped array. If `inplace` is ``True``, this is | a view to self. | | Examples | -------- | >>> A = np.array([1, 256, 8755], dtype=np.int16) | >>> list(map(hex, A)) | ['0x1', '0x100', '0x2233'] | >>> A.byteswap(inplace=True) | array([ 256, 1, 13090], dtype=int16) | >>> list(map(hex, A)) | ['0x100', '0x1', '0x3322'] | | Arrays of byte-strings are not swapped | | >>> A = np.array([b'ceg', b'fac']) | >>> A.byteswap() | array([b'ceg', b'fac'], dtype='|S3') | | ``A.newbyteorder().byteswap()`` produces an array with the same values | but different representation in memory | | >>> A = np.array([1, 2, 3]) | >>> A.view(np.uint8) | array([1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, | 0, 0], dtype=uint8) | >>> A.newbyteorder().byteswap(inplace=True) | array([1, 2, 3]) | >>> A.view(np.uint8) | array([0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, | 0, 3], dtype=uint8) | | choose(...) | a.choose(choices, out=None, mode='raise') | | Use an index array to construct a new array from a set of choices. | | Refer to `numpy.choose` for full documentation. | | See Also | -------- | numpy.choose : equivalent function | | clip(...) | a.clip(min=None, max=None, out=None, **kwargs) | | Return an array whose values are limited to ``[min, max]``. | One of max or min must be given. | | Refer to `numpy.clip` for full documentation. | | See Also | -------- | numpy.clip : equivalent function | | compress(...) | a.compress(condition, axis=None, out=None) | | Return selected slices of this array along given axis. | | Refer to `numpy.compress` for full documentation. | | See Also | -------- | numpy.compress : equivalent function | | conj(...) | a.conj() | | Complex-conjugate all elements. | | Refer to `numpy.conjugate` for full documentation. | | See Also | -------- | numpy.conjugate : equivalent function | | conjugate(...) | a.conjugate() | | Return the complex conjugate, element-wise. | | Refer to `numpy.conjugate` for full documentation. | | See Also | -------- | numpy.conjugate : equivalent function | | copy(...) | a.copy(order='C') | | Return a copy of the array. | | Parameters | ---------- | order : {'C', 'F', 'A', 'K'}, optional | Controls the memory layout of the copy. 'C' means C-order, | 'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous, | 'C' otherwise. 'K' means match the layout of `a` as closely | as possible. (Note that this function and :func:`numpy.copy` are very | similar but have different default values for their order= | arguments, and this function always passes sub-classes through.) | | See also | -------- | numpy.copy : Similar function with different default behavior | numpy.copyto | | Notes | ----- | This function is the preferred method for creating an array copy. The | function :func:`numpy.copy` is similar, but it defaults to using order 'K', | and will not pass sub-classes through by default. | | Examples | -------- | >>> x = np.array([[1,2,3],[4,5,6]], order='F') | | >>> y = x.copy() | | >>> [x.fill(0)](https://www.chedong.com/phpMan.php/man/x.fill/0/markdown) | | >>> x | array([[0, 0, 0], | [0, 0, 0]]) | | >>> y | array([[1, 2, 3], | [4, 5, 6]]) | | >>> y.flags['C_CONTIGUOUS'] | True | | cumprod(...) | a.cumprod(axis=None, dtype=None, out=None) | | Return the cumulative product of the elements along the given axis. | | Refer to `numpy.cumprod` for full documentation. | | See Also | -------- | numpy.cumprod : equivalent function | | cumsum(...) | a.cumsum(axis=None, dtype=None, out=None) | | Return the cumulative sum of the elements along the given axis. | | Refer to `numpy.cumsum` for full documentation. | | See Also | -------- | numpy.cumsum : equivalent function | | diagonal(...) | a.diagonal(offset=0, axis1=0, axis2=1) | | Return specified diagonals. In NumPy 1.9 the returned array is a | read-only view instead of a copy as in previous NumPy versions. In | a future version the read-only restriction will be removed. | | Refer to :func:`numpy.diagonal` for full documentation. | | See Also | -------- | numpy.diagonal : equivalent function | | dot(...) | a.dot(b, out=None) | | Dot product of two arrays. | | Refer to `numpy.dot` for full documentation. | | See Also | -------- | numpy.dot : equivalent function | | Examples | -------- | >>> a = [np.eye(2)](https://www.chedong.com/phpMan.php/man/np.eye/2/markdown) | >>> b = np.ones((2, 2)) * 2 | >>> a.dot(b) | array([[2., 2.], | [2., 2.]]) | | This array method can be conveniently chained: | | >>> a.dot(b).dot(b) | array([[8., 8.], | [8., 8.]]) | | dump(...) | a.dump(file) | | Dump a pickle of the array to the specified file. | The array can be read back with pickle.load or numpy.load. | | Parameters | ---------- | file : str or Path | A string naming the dump file. | | .. versionchanged:: 1.17.0 | `pathlib.Path` objects are now accepted. | | dumps(...) | a.dumps() | | Returns the pickle of the array as a string. | pickle.loads or numpy.loads will convert the string back to an array. | | Parameters | ---------- | None | | fill(...) | a.fill(value) | | Fill the array with a scalar value. | | Parameters | ---------- | value : scalar | All elements of `a` will be assigned this value. | | Examples | -------- | >>> a = np.array([1, 2]) | >>> [a.fill(0)](https://www.chedong.com/phpMan.php/man/a.fill/0/markdown) | >>> a | array([0, 0]) | >>> a = [np.empty(2)](https://www.chedong.com/phpMan.php/man/np.empty/2/markdown) | >>> [a.fill(1)](https://www.chedong.com/phpMan.php/man/a.fill/1/markdown) | >>> a | array([1., 1.]) | | flatten(...) | a.flatten(order='C') | | Return a copy of the array collapsed into one dimension. | | Parameters | ---------- | order : {'C', 'F', 'A', 'K'}, optional | 'C' means to flatten in row-major (C-style) order. | 'F' means to flatten in column-major (Fortran- | style) order. 'A' means to flatten in column-major | order if `a` is Fortran *contiguous* in memory, | row-major order otherwise. 'K' means to flatten | `a` in the order the elements occur in memory. | The default is 'C'. | | Returns | ------- | y : ndarray | A copy of the input array, flattened to one dimension. | | See Also | -------- | ravel : Return a flattened array. | flat : A 1-D flat iterator over the array. | | Examples | -------- | >>> a = np.array([[1,2], [3,4]]) | >>> a.flatten() | array([1, 2, 3, 4]) | >>> a.flatten('F') | array([1, 3, 2, 4]) | | getfield(...) | a.getfield(dtype, offset=0) | | Returns a field of the given array as a certain type. | | A field is a view of the array data with a given data-type. The values in | the view are determined by the given type and the offset into the current | array in bytes. The offset needs to be such that the view dtype fits in the | array dtype; for example an array of dtype complex128 has 16-byte elements. | If taking a view with a 32-bit integer (4 bytes), the offset needs to be | between 0 and 12 bytes. | | Parameters | ---------- | dtype : str or dtype | The data type of the view. The dtype size of the view can not be larger | than that of the array itself. | offset : int | Number of bytes to skip before beginning the element view. | | Examples | -------- | >>> x = np.diag([1.+1.j]*2) | >>> x[1, 1] = 2 + 4.j | >>> x | array([[1.+1.j, 0.+0.j], | [0.+0.j, 2.+4.j]]) | >>> x.getfield(np.float64) | array([[1., 0.], | [0., 2.]]) | | By choosing an offset of 8 bytes we can select the complex part of the | array for our view: | | >>> x.getfield(np.float64, offset=8) | array([[1., 0.], | [0., 4.]]) | | item(...) | a.item(*args) | | Copy an element of an array to a standard Python scalar and return it. | | Parameters | ---------- | \*args : Arguments (variable number and type) | | * none: in this case, the method only works for arrays | with one element (`a.size == 1`), which element is | copied into a standard Python scalar object and returned. | | * int_type: this argument is interpreted as a flat index into | the array, specifying which element to copy and return. | | * tuple of int_types: functions as does a single int_type argument, | except that the argument is interpreted as an nd-index into the | array. | | Returns | ------- | z : Standard Python scalar object | A copy of the specified element of the array as a suitable | Python scalar | | Notes | ----- | When the data type of `a` is longdouble or clongdouble, item() returns | a scalar array object because there is no available Python scalar that | would not lose information. Void arrays return a buffer object for item(), | unless fields are defined, in which case a tuple is returned. | | `item` is very similar to a[args], except, instead of an array scalar, | a standard Python scalar is returned. This can be useful for speeding up | access to elements of the array and doing arithmetic on elements of the | array using Python's optimized math. | | Examples | -------- | >>> [np.random.seed(123)](https://www.chedong.com/phpMan.php/man/np.random.seed/123/markdown) | >>> x = np.random.randint(9, size=(3, 3)) | >>> x | array([[2, 2, 6], | [1, 3, 6], | [1, 0, 1]]) | >>> [x.item(3)](https://www.chedong.com/phpMan.php/man/x.item/3/markdown) | 1 | >>> [x.item(7)](https://www.chedong.com/phpMan.php/man/x.item/7/markdown) | 0 | >>> x.item((0, 1)) | 2 | >>> x.item((2, 2)) | 1 | | itemset(...) | a.itemset(*args) | | Insert scalar into an array (scalar is cast to array's dtype, if possible) | | There must be at least 1 argument, and define the last argument | as *item*. Then, ``a.itemset(*args)`` is equivalent to but faster | than ``a[args] = item``. The item should be a scalar value and `args` | must select a single item in the array `a`. | | Parameters | ---------- | \*args : Arguments | If one argument: a scalar, only used in case `a` is of size 1. | If two arguments: the last argument is the value to be set | and must be a scalar, the first argument specifies a single array | element location. It is either an int or a tuple. | | Notes | ----- | Compared to indexing syntax, `itemset` provides some speed increase | for placing a scalar into a particular location in an `ndarray`, | if you must do this. However, generally this is discouraged: | among other problems, it complicates the appearance of the code. | Also, when using `itemset` (and `item`) inside a loop, be sure | to assign the methods to a local variable to avoid the attribute | look-up at each loop iteration. | | Examples | -------- | >>> [np.random.seed(123)](https://www.chedong.com/phpMan.php/man/np.random.seed/123/markdown) | >>> x = np.random.randint(9, size=(3, 3)) | >>> x | array([[2, 2, 6], | [1, 3, 6], | [1, 0, 1]]) | >>> x.itemset(4, 0) | >>> x.itemset((2, 2), 9) | >>> x | array([[2, 2, 6], | [1, 0, 6], | [1, 0, 9]]) | | max(...) | a.max(axis=None, out=None, keepdims=False, initial=, where=True) | | Return the maximum along a given axis. | | Refer to `numpy.amax` for full documentation. | | See Also | -------- | numpy.amax : equivalent function | | mean(...) | a.mean(axis=None, dtype=None, out=None, keepdims=False, *, where=True) | | Returns the average of the array elements along given axis. | | Refer to `numpy.mean` for full documentation. | | See Also | -------- | numpy.mean : equivalent function | | min(...) | a.min(axis=None, out=None, keepdims=False, initial=, where=True) | | Return the minimum along a given axis. | | Refer to `numpy.amin` for full documentation. | | See Also | -------- | numpy.amin : equivalent function | | newbyteorder(...) | arr.newbyteorder(new_order='S', /) | | Return the array with the same data viewed with a different byte order. | | Equivalent to:: | | arr.view([arr.dtype.newbytorder(new_order)](https://www.chedong.com/phpMan.php/man/arr.dtype.newbytorder/neworder/markdown)) | | Changes are also made in all fields and sub-arrays of the array data | type. | | | | Parameters | ---------- | new_order : string, optional | Byte order to force; a value from the byte order specifications | below. `new_order` codes can be any of: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order, equivalent to `sys.byteorder` | * {'|', 'I'} - ignore (no change to byte order) | | The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_arr : array | New array object with the dtype reflecting given change to the | byte order. | | nonzero(...) | a.nonzero() | | Return the indices of the elements that are non-zero. | | Refer to `numpy.nonzero` for full documentation. | | See Also | -------- | numpy.nonzero : equivalent function | | partition(...) | a.partition(kth, axis=-1, kind='introselect', order=None) | | Rearranges the elements in the array in such a way that the value of the | element in kth position is in the position it would be in a sorted array. | All elements smaller than the kth element are moved before this element and | all equal or greater are moved behind it. The ordering of the elements in | the two partitions is undefined. | | .. versionadded:: 1.8.0 | | Parameters | ---------- | kth : int or sequence of ints | Element index to partition by. The kth element value will be in its | final sorted position and all smaller elements will be moved before it | and all equal or greater elements behind it. | The order of all elements in the partitions is undefined. | If provided with a sequence of kth it will partition all elements | indexed by kth of them into their sorted position at once. | axis : int, optional | Axis along which to sort. Default is -1, which means sort along the | last axis. | kind : {'introselect'}, optional | Selection algorithm. Default is 'introselect'. | order : str or list of str, optional | When `a` is an array with fields defined, this argument specifies | which fields to compare first, second, etc. A single field can | be specified as a string, and not all fields need to be specified, | but unspecified fields will still be used, in the order in which | they come up in the dtype, to break ties. | | See Also | -------- | numpy.partition : Return a parititioned copy of an array. | argpartition : Indirect partition. | sort : Full sort. | | Notes | ----- | See ``np.partition`` for notes on the different algorithms. | | Examples | -------- | >>> a = np.array([3, 4, 2, 1]) | >>> [a.partition(3)](https://www.chedong.com/phpMan.php/man/a.partition/3/markdown) | >>> a | array([2, 1, 3, 4]) | | >>> a.partition((1, 3)) | >>> a | array([1, 2, 3, 4]) | | prod(...) | a.prod(axis=None, dtype=None, out=None, keepdims=False, initial=1, where=True) | | Return the product of the array elements over the given axis | | Refer to `numpy.prod` for full documentation. | | See Also | -------- | numpy.prod : equivalent function | | ptp(...) | a.ptp(axis=None, out=None, keepdims=False) | | Peak to peak (maximum - minimum) value along a given axis. | | Refer to `numpy.ptp` for full documentation. | | See Also | -------- | numpy.ptp : equivalent function | | put(...) | a.put(indices, values, mode='raise') | | Set ``a.flat[n] = values[n]`` for all `n` in indices. | | Refer to `numpy.put` for full documentation. | | See Also | -------- | numpy.put : equivalent function | | ravel(...) | a.ravel([order]) | | Return a flattened array. | | Refer to `numpy.ravel` for full documentation. | | See Also | -------- | numpy.ravel : equivalent function | | ndarray.flat : a flat iterator on the array. | | repeat(...) | a.repeat(repeats, axis=None) | | Repeat elements of an array. | | Refer to `numpy.repeat` for full documentation. | | See Also | -------- | numpy.repeat : equivalent function | | reshape(...) | a.reshape(shape, order='C') | | Returns an array containing the same data with a new shape. | | Refer to `numpy.reshape` for full documentation. | | See Also | -------- | numpy.reshape : equivalent function | | Notes | ----- | Unlike the free function `numpy.reshape`, this method on `ndarray` allows | the elements of the shape parameter to be passed in as separate arguments. | For example, ``a.reshape(10, 11)`` is equivalent to | ``a.reshape((10, 11))``. | | resize(...) | a.resize(new_shape, refcheck=True) | | Change shape and size of array in-place. | | Parameters | ---------- | new_shape : tuple of ints, or `n` ints | Shape of resized array. | refcheck : bool, optional | If False, reference count will not be checked. Default is True. | | Returns | ------- | None | | Raises | ------ | ValueError | If `a` does not own its own data or references or views to it exist, | and the data memory must be changed. | PyPy only: will always raise if the data memory must be changed, since | there is no reliable way to determine if references or views to it | exist. | | SystemError | If the `order` keyword argument is specified. This behaviour is a | bug in NumPy. | | See Also | -------- | resize : Return a new array with the specified shape. | | Notes | ----- | This reallocates space for the data area if necessary. | | Only contiguous arrays (data elements consecutive in memory) can be | resized. | | The purpose of the reference count check is to make sure you | do not use this array as a buffer for another Python object and then | reallocate the memory. However, reference counts can increase in | other ways so if you are sure that you have not shared the memory | for this array with another Python object, then you may safely set | `refcheck` to False. | | Examples | -------- | Shrinking an array: array is flattened (in the order that the data are | stored in memory), resized, and reshaped: | | >>> a = np.array([[0, 1], [2, 3]], order='C') | >>> a.resize((2, 1)) | >>> a | array([[0], | [1]]) | | >>> a = np.array([[0, 1], [2, 3]], order='F') | >>> a.resize((2, 1)) | >>> a | array([[0], | [2]]) | | Enlarging an array: as above, but missing entries are filled with zeros: | | >>> b = np.array([[0, 1], [2, 3]]) | >>> b.resize(2, 3) # new_shape parameter doesn't have to be a tuple | >>> b | array([[0, 1, 2], | [3, 0, 0]]) | | Referencing an array prevents resizing... | | >>> c = a | >>> a.resize((1, 1)) | Traceback (most recent call last): | ... | ValueError: cannot resize an array that references or is referenced ... | | Unless `refcheck` is False: | | >>> a.resize((1, 1), refcheck=False) | >>> a | array([[0]]) | >>> c | array([[0]]) | | round(...) | a.round(decimals=0, out=None) | | Return `a` with each element rounded to the given number of decimals. | | Refer to `numpy.around` for full documentation. | | See Also | -------- | numpy.around : equivalent function | | searchsorted(...) | a.searchsorted(v, side='left', sorter=None) | | Find indices where elements of v should be inserted in a to maintain order. | | For full documentation, see `numpy.searchsorted` | | See Also | -------- | numpy.searchsorted : equivalent function | | setfield(...) | a.setfield(val, dtype, offset=0) | | Put a value into a specified place in a field defined by a data-type. | | Place `val` into `a`'s field defined by `dtype` and beginning `offset` | bytes into the field. | | Parameters | ---------- | val : object | Value to be placed in field. | dtype : dtype object | Data-type of the field in which to place `val`. | offset : int, optional | The number of bytes into the field at which to place `val`. | | Returns | ------- | None | | See Also | -------- | getfield | | Examples | -------- | >>> x = [np.eye(3)](https://www.chedong.com/phpMan.php/man/np.eye/3/markdown) | >>> x.getfield(np.float64) | array([[1., 0., 0.], | [0., 1., 0.], | [0., 0., 1.]]) | >>> x.setfield(3, np.int32) | >>> x.getfield(np.int32) | array([[3, 3, 3], | [3, 3, 3], | [3, 3, 3]], dtype=int32) | >>> x | array([[1.0e+000, 1.5e-323, 1.5e-323], | [1.5e-323, 1.0e+000, 1.5e-323], | [1.5e-323, 1.5e-323, 1.0e+000]]) | >>> x.setfield([np.eye(3)](https://www.chedong.com/phpMan.php/man/np.eye/3/markdown), np.int32) | >>> x | array([[1., 0., 0.], | [0., 1., 0.], | [0., 0., 1.]]) | | setflags(...) | a.setflags(write=None, align=None, uic=None) | | Set array flags WRITEABLE, ALIGNED, (WRITEBACKIFCOPY and UPDATEIFCOPY), | respectively. | | These Boolean-valued flags affect how numpy interprets the memory | area used by `a` (see Notes below). The ALIGNED flag can only | be set to True if the data is actually aligned according to the type. | The WRITEBACKIFCOPY and (deprecated) UPDATEIFCOPY flags can never be set | to True. The flag WRITEABLE can only be set to True if the array owns its | own memory, or the ultimate owner of the memory exposes a writeable buffer | interface, or is a string. (The exception for string is made so that | unpickling can be done without copying memory.) | | Parameters | ---------- | write : bool, optional | Describes whether or not `a` can be written to. | align : bool, optional | Describes whether or not `a` is aligned properly for its type. | uic : bool, optional | Describes whether or not `a` is a copy of another "base" array. | | Notes | ----- | Array flags provide information about how the memory area used | for the array is to be interpreted. There are 7 Boolean flags | in use, only four of which can be changed by the user: | WRITEBACKIFCOPY, UPDATEIFCOPY, WRITEABLE, and ALIGNED. | | WRITEABLE (W) the data area can be written to; | | ALIGNED (A) the data and strides are aligned appropriately for the hardware | (as determined by the compiler); | | UPDATEIFCOPY (U) (deprecated), replaced by WRITEBACKIFCOPY; | | WRITEBACKIFCOPY (X) this array is a copy of some other array (referenced | by .base). When the C-API function PyArray_ResolveWritebackIfCopy is | called, the base array will be updated with the contents of this array. | | All flags can be accessed using the single (upper case) letter as well | as the full name. | | Examples | -------- | >>> y = np.array([[3, 1, 7], | ... [2, 0, 0], | ... [8, 5, 9]]) | >>> y | array([[3, 1, 7], | [2, 0, 0], | [8, 5, 9]]) | >>> y.flags | C_CONTIGUOUS : True | F_CONTIGUOUS : False | OWNDATA : True | WRITEABLE : True | ALIGNED : True | WRITEBACKIFCOPY : False | UPDATEIFCOPY : False | >>> y.setflags(write=0, align=0) | >>> y.flags | C_CONTIGUOUS : True | F_CONTIGUOUS : False | OWNDATA : True | WRITEABLE : False | ALIGNED : False | WRITEBACKIFCOPY : False | UPDATEIFCOPY : False | >>> y.setflags(uic=1) | Traceback (most recent call last): | File "", line 1, in | ValueError: cannot set WRITEBACKIFCOPY flag to True | | sort(...) | a.sort(axis=-1, kind=None, order=None) | | Sort an array in-place. Refer to `numpy.sort` for full documentation. | | Parameters | ---------- | axis : int, optional | Axis along which to sort. Default is -1, which means sort along the | last axis. | kind : {'quicksort', 'mergesort', 'heapsort', 'stable'}, optional | Sorting algorithm. The default is 'quicksort'. Note that both 'stable' | and 'mergesort' use timsort under the covers and, in general, the | actual implementation will vary with datatype. The 'mergesort' option | is retained for backwards compatibility. | | .. versionchanged:: 1.15.0 | The 'stable' option was added. | | order : str or list of str, optional | When `a` is an array with fields defined, this argument specifies | which fields to compare first, second, etc. A single field can | be specified as a string, and not all fields need be specified, | but unspecified fields will still be used, in the order in which | they come up in the dtype, to break ties. | | See Also | -------- | numpy.sort : Return a sorted copy of an array. | numpy.argsort : Indirect sort. | numpy.lexsort : Indirect stable sort on multiple keys. | numpy.searchsorted : Find elements in sorted array. | numpy.partition: Partial sort. | | Notes | ----- | See `numpy.sort` for notes on the different sorting algorithms. | | Examples | -------- | >>> a = np.array([[1,4], [3,1]]) | >>> a.sort(axis=1) | >>> a | array([[1, 4], | [1, 3]]) | >>> a.sort(axis=0) | >>> a | array([[1, 3], | [1, 4]]) | | Use the `order` keyword to specify a field to use when sorting a | structured array: | | >>> a = np.array([('a', 2), ('c', 1)], dtype=[('x', 'S1'), ('y', int)]) | >>> a.sort(order='y') | >>> a | array([(b'c', 1), (b'a', 2)], | dtype=[('x', 'S1'), ('y', '>> x = np.array([[0, 1], [2, 3]], dtype='>> x.tobytes() | b'\x00\x00\x01\x00\x02\x00\x03\x00' | >>> x.tobytes('C') == x.tobytes() | True | >>> x.tobytes('F') | b'\x00\x00\x02\x00\x01\x00\x03\x00' | | tofile(...) | a.tofile(fid, sep="", format="%s") | | Write array to a file as text or binary (default). | | Data is always written in 'C' order, independent of the order of `a`. | The data produced by this method can be recovered using the function | fromfile(). | | Parameters | ---------- | fid : file or str or Path | An open file object, or a string containing a filename. | | .. versionchanged:: 1.17.0 | `pathlib.Path` objects are now accepted. | | sep : str | Separator between array items for text output. | If "" (empty), a binary file is written, equivalent to | ``file.write(a.tobytes())``. | format : str | Format string for text file output. | Each entry in the array is formatted to text by first converting | it to the closest Python type, and then using "format" % item. | | Notes | ----- | This is a convenience function for quick storage of array data. | Information on endianness and precision is lost, so this method is not a | good choice for files intended to archive data or transport data between | machines with different endianness. Some of these problems can be overcome | by outputting the data as text files, at the expense of speed and file | size. | | When fid is a file object, array contents are directly written to the | file, bypassing the file object's ``write`` method. As a result, tofile | cannot be used with files objects supporting compression (e.g., GzipFile) | or file-like objects that do not support ``fileno()`` (e.g., BytesIO). | | tolist(...) | a.tolist() | | Return the array as an ``a.ndim``-levels deep nested list of Python scalars. | | Return a copy of the array data as a (nested) Python list. | Data items are converted to the nearest compatible builtin Python type, via | the `~numpy.ndarray.item` function. | | If ``a.ndim`` is 0, then since the depth of the nested list is 0, it will | not be a list at all, but a simple Python scalar. | | Parameters | ---------- | none | | Returns | ------- | y : object, or list of object, or list of list of object, or ... | The possibly nested list of array elements. | | Notes | ----- | The array may be recreated via ``a = np.array(a.tolist())``, although this | may sometimes lose precision. | | Examples | -------- | For a 1D array, ``a.tolist()`` is almost the same as ``list(a)``, | except that ``tolist`` changes numpy scalars to Python scalars: | | >>> a = np.uint32([1, 2]) | >>> a_list = list(a) | >>> a_list | [1, 2] | >>> type(a_list[0]) | | >>> a_tolist = a.tolist() | >>> a_tolist | [1, 2] | >>> type(a_tolist[0]) | | | Additionally, for a 2D array, ``tolist`` applies recursively: | | >>> a = np.array([[1, 2], [3, 4]]) | >>> list(a) | [array([1, 2]), array([3, 4])] | >>> a.tolist() | [[1, 2], [3, 4]] | | The base case for this recursion is a 0D array: | | >>> a = [np.array(1)](https://www.chedong.com/phpMan.php/man/np.array/1/markdown) | >>> list(a) | Traceback (most recent call last): | ... | TypeError: iteration over a 0-d array | >>> a.tolist() | 1 | | tostring(...) | a.tostring(order='C') | | A compatibility alias for `tobytes`, with exactly the same behavior. | | Despite its name, it returns `bytes` not `str`\ s. | | .. deprecated:: 1.19.0 | | trace(...) | a.trace(offset=0, axis1=0, axis2=1, dtype=None, out=None) | | Return the sum along diagonals of the array. | | Refer to `numpy.trace` for full documentation. | | See Also | -------- | numpy.trace : equivalent function | | transpose(...) | a.transpose(*axes) | | Returns a view of the array with axes transposed. | | For a 1-D array this has no effect, as a transposed vector is simply the | same vector. To convert a 1-D array into a 2D column vector, an additional | dimension must be added. `np.atleast2d(a).T` achieves this, as does | `a[:, np.newaxis]`. | For a 2-D array, this is a standard matrix transpose. | For an n-D array, if axes are given, their order indicates how the | axes are permuted (see Examples). If axes are not provided and | ``a.shape = (i[0], i[1], ... i[n-2], i[n-1])``, then | ``a.transpose().shape = (i[n-1], i[n-2], ... i[1], i[0])``. | | Parameters | ---------- | axes : None, tuple of ints, or `n` ints | | * None or no argument: reverses the order of the axes. | | * tuple of ints: `i` in the `j`-th place in the tuple means `a`'s | `i`-th axis becomes `a.transpose()`'s `j`-th axis. | | * `n` ints: same as an n-tuple of the same ints (this form is | intended simply as a "convenience" alternative to the tuple form) | | Returns | ------- | out : ndarray | View of `a`, with axes suitably permuted. | | See Also | -------- | transpose : Equivalent function | ndarray.T : Array property returning the array transposed. | ndarray.reshape : Give a new shape to an array without changing its data. | | Examples | -------- | >>> a = np.array([[1, 2], [3, 4]]) | >>> a | array([[1, 2], | [3, 4]]) | >>> a.transpose() | array([[1, 3], | [2, 4]]) | >>> a.transpose((1, 0)) | array([[1, 3], | [2, 4]]) | >>> a.transpose(1, 0) | array([[1, 3], | [2, 4]]) | | var(...) | a.var(axis=None, dtype=None, out=None, ddof=0, keepdims=False, *, where=True) | | Returns the variance of the array elements, along given axis. | | Refer to `numpy.var` for full documentation. | | See Also | -------- | numpy.var : equivalent function | | view(...) | a.view([dtype][, type]) | | New view of array with the same data. | | .. note:: | Passing None for ``dtype`` is different from omitting the parameter, | since the former invokes ``dtype(None)`` which is an alias for | ``dtype('float_')``. | | Parameters | ---------- | dtype : data-type or ndarray sub-class, optional | Data-type descriptor of the returned view, e.g., float32 or int16. | Omitting it results in the view having the same data-type as `a`. | This argument can also be specified as an ndarray sub-class, which | then specifies the type of the returned object (this is equivalent to | setting the ``type`` parameter). | type : Python type, optional | Type of the returned view, e.g., ndarray or matrix. Again, omission | of the parameter results in type preservation. | | Notes | ----- | ``a.view()`` is used two different ways: | | ``a.view(some_dtype)`` or ``a.view(dtype=some_dtype)`` constructs a view | of the array's memory with a different data-type. This can cause a | reinterpretation of the bytes of memory. | | ``[a.view(ndarray_subclass)](https://www.chedong.com/phpMan.php/man/a.view/ndarraysubclass/markdown)`` or ``a.view(type=ndarray_subclass)`` just | returns an instance of `ndarray_subclass` that looks at the same array | (same shape, dtype, etc.) This does not cause a reinterpretation of the | memory. | | For ``a.view(some_dtype)``, if ``some_dtype`` has a different number of | bytes per entry than the previous dtype (for example, converting a | regular array to a structured array), then the behavior of the view | cannot be predicted just from the superficial appearance of ``a`` (shown | by ``print(a)``). It also depends on exactly how ``a`` is stored in | memory. Therefore if ``a`` is C-ordered versus fortran-ordered, versus | defined as a slice or transpose, etc., the view may give different | results. | | | Examples | -------- | >>> x = np.array([(1, 2)], dtype=[('a', np.int8), ('b', np.int8)]) | | Viewing array data using a different type and dtype: | | >>> y = x.view(dtype=np.int16, type=np.matrix) | >>> y | matrix([[513]], dtype=int16) | >>> print(type(y)) | | | Creating a view on a structured array so it can be used in calculations | | >>> x = np.array([(1, 2),(3,4)], dtype=[('a', np.int8), ('b', np.int8)]) | >>> xv = x.view(dtype=np.int8).reshape(-1,2) | >>> xv | array([[1, 2], | [3, 4]], dtype=int8) | >>> [xv.mean(0)](https://www.chedong.com/phpMan.php/man/xv.mean/0/markdown) | array([2., 3.]) | | Making changes to the view changes the underlying array | | >>> xv[0,1] = 20 | >>> x | array([(1, 20), (3, 4)], dtype=[('a', 'i1'), ('b', 'i1')]) | | Using a view to convert an array to a recarray: | | >>> z = x.view(np.recarray) | >>> z.a | array([1, 3], dtype=int8) | | Views share data: | | >>> x[0] = (9, 10) | >>> z[0] | (9, 10) | | Views that change the dtype size (bytes per entry) should normally be | avoided on arrays defined by slices, transposes, fortran-ordering, etc.: | | >>> x = np.array([[1,2,3],[4,5,6]], dtype=np.int16) | >>> y = x[:, 0:2] | >>> y | array([[1, 2], | [4, 5]], dtype=int16) | >>> y.view(dtype=[('width', np.int16), ('length', np.int16)]) | Traceback (most recent call last): | ... | ValueError: To change to a dtype of a different size, the array must be C-contiguous | >>> z = y.copy() | >>> z.view(dtype=[('width', np.int16), ('length', np.int16)]) | array([[(1, 2)], | [(4, 5)]], dtype=[('width', '>> x = np.array([[1.,2.],[3.,4.]]) | >>> x | array([[ 1., 2.], | [ 3., 4.]]) | >>> x.T | array([[ 1., 3.], | [ 2., 4.]]) | >>> x = np.array([1.,2.,3.,4.]) | >>> x | array([ 1., 2., 3., 4.]) | >>> x.T | array([ 1., 2., 3., 4.]) | | See Also | -------- | transpose | | __array_finalize__ | None. | | __array_interface__ | Array protocol: Python side. | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: C-struct side. | | base | Base object if memory is from some other object. | | Examples | -------- | The base of an array that owns its memory is None: | | >>> x = np.array([1,2,3,4]) | >>> x.base is None | True | | Slicing creates a view, whose memory is shared with x: | | >>> y = x[2:] | >>> y.base is x | True | | ctypes | An object to simplify the interaction of the array with the ctypes | module. | | This attribute creates an object that makes it easier to use arrays | when calling shared libraries with the ctypes module. The returned | object has, among others, data, shape, and strides attributes (see | Notes below) which themselves return ctypes objects that can be used | as arguments to a shared library. | | Parameters | ---------- | None | | Returns | ------- | c : Python object | Possessing attributes data, shape, strides, etc. | | See Also | -------- | numpy.ctypeslib | | Notes | ----- | Below are the public attributes of this object which were documented | in "Guide to NumPy" (we have omitted undocumented public attributes, | as well as documented private attributes): | | .. autoattribute:: numpy.core._internal._ctypes.data | :noindex: | | .. autoattribute:: numpy.core._internal._ctypes.shape | :noindex: | | .. autoattribute:: numpy.core._internal._ctypes.strides | :noindex: | | .. automethod:: numpy.core._internal._ctypes.data_as | :noindex: | | .. automethod:: numpy.core._internal._ctypes.shape_as | :noindex: | | .. automethod:: numpy.core._internal._ctypes.strides_as | :noindex: | | If the ctypes module is not available, then the ctypes attribute | of array objects still returns something useful, but ctypes objects | are not returned and errors may be raised instead. In particular, | the object will still have the ``as_parameter`` attribute which will | return an integer equal to the data attribute. | | Examples | -------- | >>> import ctypes | >>> x = np.array([[0, 1], [2, 3]], dtype=np.int32) | >>> x | array([[0, 1], | [2, 3]], dtype=int32) | >>> x.ctypes.data | 31962608 # may vary | >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)) | <__main__.LP_c_uint object at 0x7ff2fc1fc200> # may vary | >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)).contents | [c_uint(0)](https://www.chedong.com/phpMan.php/man/cuint/0/markdown) | >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint64)).contents | [c_ulong(4294967296)](https://www.chedong.com/phpMan.php/man/culong/4294967296/markdown) | >>> x.ctypes.shape | # may vary | >>> x.ctypes.strides | # may vary | | data | Python buffer object pointing to the start of the array's data. | | dtype | Data-type of the array's elements. | | Parameters | ---------- | None | | Returns | ------- | d : numpy dtype object | | See Also | -------- | numpy.dtype | | Examples | -------- | >>> x | array([[0, 1], | [2, 3]]) | >>> x.dtype | dtype('int32') | >>> type(x.dtype) | | | flags | Information about the memory layout of the array. | | Attributes | ---------- | C_CONTIGUOUS (C) | The data is in a single, C-style contiguous segment. | F_CONTIGUOUS (F) | The data is in a single, Fortran-style contiguous segment. | OWNDATA (O) | The array owns the memory it uses or borrows it from another object. | WRITEABLE (W) | The data area can be written to. Setting this to False locks | the data, making it read-only. A view (slice, etc.) inherits WRITEABLE | from its base array at creation time, but a view of a writeable | array may be subsequently locked while the base array remains writeable. | (The opposite is not true, in that a view of a locked array may not | be made writeable. However, currently, locking a base object does not | lock any views that already reference it, so under that circumstance it | is possible to alter the contents of a locked array via a previously | created writeable view onto it.) Attempting to change a non-writeable | array raises a RuntimeError exception. | ALIGNED (A) | The data and all elements are aligned appropriately for the hardware. | WRITEBACKIFCOPY (X) | This array is a copy of some other array. The C-API function | PyArray_ResolveWritebackIfCopy must be called before deallocating | to the base array will be updated with the contents of this array. | UPDATEIFCOPY (U) | (Deprecated, use WRITEBACKIFCOPY) This array is a copy of some other array. | When this array is | deallocated, the base array will be updated with the contents of | this array. | FNC | F_CONTIGUOUS and not C_CONTIGUOUS. | FORC | F_CONTIGUOUS or C_CONTIGUOUS (one-segment test). | BEHAVED (B) | ALIGNED and WRITEABLE. | CARRAY (CA) | BEHAVED and C_CONTIGUOUS. | FARRAY (FA) | BEHAVED and F_CONTIGUOUS and not C_CONTIGUOUS. | | Notes | ----- | The `flags` object can be accessed dictionary-like (as in ``a.flags['WRITEABLE']``), | or by using lowercased attribute names (as in ``a.flags.writeable``). Short flag | names are only supported in dictionary access. | | Only the WRITEBACKIFCOPY, UPDATEIFCOPY, WRITEABLE, and ALIGNED flags can be | changed by the user, via direct assignment to the attribute or dictionary | entry, or by calling `ndarray.setflags`. | | The array flags cannot be set arbitrarily: | | - UPDATEIFCOPY can only be set ``False``. | - WRITEBACKIFCOPY can only be set ``False``. | - ALIGNED can only be set ``True`` if the data is truly aligned. | - WRITEABLE can only be set ``True`` if the array owns its own memory | or the ultimate owner of the memory exposes a writeable buffer | interface or is a string. | | Arrays can be both C-style and Fortran-style contiguous simultaneously. | This is clear for 1-dimensional arrays, but can also be true for higher | dimensional arrays. | | Even for contiguous arrays a stride for a given dimension | ``arr.strides[dim]`` may be *arbitrary* if ``arr.shape[dim] == 1`` | or the array has no elements. | It does *not* generally hold that ``self.strides[-1] == self.itemsize`` | for C-style contiguous arrays or ``self.strides[0] == self.itemsize`` for | Fortran-style contiguous arrays is true. | | flat | A 1-D iterator over the array. | | This is a `numpy.flatiter` instance, which acts similarly to, but is not | a subclass of, Python's built-in iterator object. | | See Also | -------- | flatten : Return a copy of the array collapsed into one dimension. | | flatiter | | Examples | -------- | >>> x = np.arange(1, 7).reshape(2, 3) | >>> x | array([[1, 2, 3], | [4, 5, 6]]) | >>> x.flat[3] | 4 | >>> x.T | array([[1, 4], | [2, 5], | [3, 6]]) | >>> x.T.flat[3] | 5 | >>> type(x.flat) | | | An assignment example: | | >>> x.flat = 3; x | array([[3, 3, 3], | [3, 3, 3]]) | >>> x.flat[[1,4]] = 1; x | array([[3, 1, 3], | [3, 1, 3]]) | | imag | The imaginary part of the array. | | Examples | -------- | >>> x = np.sqrt([1+0j, 0+1j]) | >>> x.imag | array([ 0. , 0.70710678]) | >>> x.imag.dtype | dtype('float64') | | itemsize | Length of one array element in bytes. | | Examples | -------- | >>> x = np.array([1,2,3], dtype=np.float64) | >>> x.itemsize | 8 | >>> x = np.array([1,2,3], dtype=np.complex128) | >>> x.itemsize | 16 | | nbytes | Total bytes consumed by the elements of the array. | | Notes | ----- | Does not include memory consumed by non-element attributes of the | array object. | | Examples | -------- | >>> x = np.zeros((3,5,2), dtype=np.complex128) | >>> x.nbytes | 480 | >>> np.prod(x.shape) * x.itemsize | 480 | | ndim | Number of array dimensions. | | Examples | -------- | >>> x = np.array([1, 2, 3]) | >>> x.ndim | 1 | >>> y = np.zeros((2, 3, 4)) | >>> y.ndim | 3 | | real | The real part of the array. | | Examples | -------- | >>> x = np.sqrt([1+0j, 0+1j]) | >>> x.real | array([ 1. , 0.70710678]) | >>> x.real.dtype | dtype('float64') | | See Also | -------- | numpy.real : equivalent function | | shape | Tuple of array dimensions. | | The shape property is usually used to get the current shape of an array, | but may also be used to reshape the array in-place by assigning a tuple of | array dimensions to it. As with `numpy.reshape`, one of the new shape | dimensions can be -1, in which case its value is inferred from the size of | the array and the remaining dimensions. Reshaping an array in-place will | fail if a copy is required. | | Examples | -------- | >>> x = np.array([1, 2, 3, 4]) | >>> x.shape | (4,) | >>> y = np.zeros((2, 3, 4)) | >>> y.shape | (2, 3, 4) | >>> y.shape = (3, 8) | >>> y | array([[ 0., 0., 0., 0., 0., 0., 0., 0.], | [ 0., 0., 0., 0., 0., 0., 0., 0.], | [ 0., 0., 0., 0., 0., 0., 0., 0.]]) | >>> y.shape = (3, 6) | Traceback (most recent call last): | File "", line 1, in | ValueError: total size of new array must be unchanged | >>> np.zeros((4,2))[::2].shape = (-1,) | Traceback (most recent call last): | File "", line 1, in | AttributeError: Incompatible shape for in-place modification. Use | `.reshape()` to make a copy with the desired shape. | | See Also | -------- | numpy.reshape : similar function | ndarray.reshape : similar method | | size | Number of elements in the array. | | Equal to ``np.prod(a.shape)``, i.e., the product of the array's | dimensions. | | Notes | ----- | `a.size` returns a standard arbitrary precision Python integer. This | may not be the case with other methods of obtaining the same value | (like the suggested ``np.prod(a.shape)``, which returns an instance | of ``np.int_``), and may be relevant if the value is used further in | calculations that may overflow a fixed size integer type. | | Examples | -------- | >>> x = np.zeros((3, 5, 2), dtype=np.complex128) | >>> x.size | 30 | >>> np.prod(x.shape) | 30 | | strides | Tuple of bytes to step in each dimension when traversing an array. | | The byte offset of element ``(i[0], i[1], ..., i[n])`` in an array `a` | is:: | | offset = sum(np.array(i) * a.strides) | | A more detailed explanation of strides can be found in the | "ndarray.rst" file in the NumPy reference guide. | | Notes | ----- | Imagine an array of 32-bit integers (each 4 bytes):: | | x = np.array([[0, 1, 2, 3, 4], | [5, 6, 7, 8, 9]], dtype=np.int32) | | This array is stored in memory as 40 bytes, one after the other | (known as a contiguous block of memory). The strides of an array tell | us how many bytes we have to skip in memory to move to the next position | along a certain axis. For example, we have to skip 4 bytes (1 value) to | move to the next column, but 20 bytes (5 values) to get to the same | position in the next row. As such, the strides for the array `x` will be | ``(20, 4)``. | | See Also | -------- | numpy.lib.stride_tricks.as_strided | | Examples | -------- | >>> y = np.reshape(np.arange(2*3*4), (2,3,4)) | >>> y | array([[[ 0, 1, 2, 3], | [ 4, 5, 6, 7], | [ 8, 9, 10, 11]], | [[12, 13, 14, 15], | [16, 17, 18, 19], | [20, 21, 22, 23]]]) | >>> y.strides | (48, 16, 4) | >>> y[1,1,1] | 17 | >>> offset=sum(y.strides * np.array((1,1,1))) | >>> offset/y.itemsize | 17 | | >>> x = np.reshape(np.arange(5*6*7*8), (5,6,7,8)).transpose(2,3,1,0) | >>> x.strides | (32, 4, 224, 1344) | >>> i = np.array([3,5,2,2]) | >>> offset = sum(i * x.strides) | >>> x[3,5,2,2] | 813 | >>> offset / x.itemsize | 813 | | ---------------------------------------------------------------------- | Data and other attributes defined here: | | __hash__ = None ### class ndenumerate | ndenumerate(arr) | | Multidimensional index iterator. | | Return an iterator yielding pairs of array coordinates and values. | | Parameters | ---------- | arr : ndarray | Input array. | | See Also | -------- | ndindex, flatiter | | Examples | -------- | >>> a = np.array([[1, 2], [3, 4]]) | >>> for index, x in np.ndenumerate(a): | ... print(index, x) | (0, 0) 1 | (0, 1) 2 | (1, 0) 3 | (1, 1) 4 | | Methods defined here: | | __init__(self, arr) | Initialize self. See help(type(self)) for accurate signature. | | __iter__(self) | | __next__(self) | Standard iterator method, returns the index tuple and array value. | | Returns | ------- | coords : tuple of ints | The indices of the current iteration. | val : scalar | The array element of the current iteration. | | ---------------------------------------------------------------------- | Data descriptors defined here: | | __dict__ | dictionary for instance variables (if defined) | | __weakref__ | list of weak references to the object (if defined) ### class ndindex | ndindex(*shape) | | An N-dimensional iterator object to index arrays. | | Given the shape of an array, an `ndindex` instance iterates over | the N-dimensional index of the array. At each iteration a tuple | of indices is returned, the last dimension is iterated over first. | | Parameters | ---------- | shape : ints, or a single tuple of ints | The size of each dimension of the array can be passed as | individual parameters or as the elements of a tuple. | | See Also | -------- | ndenumerate, flatiter | | Examples | -------- | # dimensions as individual arguments | >>> for index in np.ndindex(3, 2, 1): | ... print(index) | (0, 0, 0) | (0, 1, 0) | (1, 0, 0) | (1, 1, 0) | (2, 0, 0) | (2, 1, 0) | | # same dimensions - but in a tuple (3, 2, 1) | >>> for index in np.ndindex((3, 2, 1)): | ... print(index) | (0, 0, 0) | (0, 1, 0) | (1, 0, 0) | (1, 1, 0) | (2, 0, 0) | (2, 1, 0) | | Methods defined here: | | __init__(self, *shape) | Initialize self. See help(type(self)) for accurate signature. | | __iter__(self) | | __next__(self) | Standard iterator method, updates the index and returns the index | tuple. | | Returns | ------- | val : tuple of ints | Returns a tuple containing the indices of the current | iteration. | | ndincr(self) | Increment the multi-dimensional index by one. | | This method is for backward compatibility only: do not use. | | .. deprecated:: 1.20.0 | This method has been advised against since numpy 1.8.0, but only | started emitting DeprecationWarning as of this version. | | ---------------------------------------------------------------------- | Data descriptors defined here: | | __dict__ | dictionary for instance variables (if defined) | | __weakref__ | list of weak references to the object (if defined) ### class nditer | nditer(op, flags=None, op_flags=None, op_dtypes=None, order='K', casting='safe', op_axes=None, itershape=None, buffersize=0) | | Efficient multi-dimensional iterator object to iterate over arrays. | To get started using this object, see the | :ref:`introductory guide to array iteration `. | | Parameters | ---------- | op : ndarray or sequence of array_like | The array(s) to iterate over. | | flags : sequence of str, optional | Flags to control the behavior of the iterator. | | * ``buffered`` enables buffering when required. | * ``c_index`` causes a C-order index to be tracked. | * ``f_index`` causes a Fortran-order index to be tracked. | * ``multi_index`` causes a multi-index, or a tuple of indices | with one per iteration dimension, to be tracked. | * ``common_dtype`` causes all the operands to be converted to | a common data type, with copying or buffering as necessary. | * ``copy_if_overlap`` causes the iterator to determine if read | operands have overlap with write operands, and make temporary | copies as necessary to avoid overlap. False positives (needless | copying) are possible in some cases. | * ``delay_bufalloc`` delays allocation of the buffers until | a reset() call is made. Allows ``allocate`` operands to | be initialized before their values are copied into the buffers. | * ``external_loop`` causes the ``values`` given to be | one-dimensional arrays with multiple values instead of | zero-dimensional arrays. | * ``grow_inner`` allows the ``value`` array sizes to be made | larger than the buffer size when both ``buffered`` and | ``external_loop`` is used. | * ``ranged`` allows the iterator to be restricted to a sub-range | of the iterindex values. | * ``refs_ok`` enables iteration of reference types, such as | object arrays. | * ``reduce_ok`` enables iteration of ``readwrite`` operands | which are broadcasted, also known as reduction operands. | * ``zerosize_ok`` allows `itersize` to be zero. | op_flags : list of list of str, optional | This is a list of flags for each operand. At minimum, one of | ``readonly``, ``readwrite``, or ``writeonly`` must be specified. | | * ``readonly`` indicates the operand will only be read from. | * ``readwrite`` indicates the operand will be read from and written to. | * ``writeonly`` indicates the operand will only be written to. | * ``no_broadcast`` prevents the operand from being broadcasted. | * ``contig`` forces the operand data to be contiguous. | * ``aligned`` forces the operand data to be aligned. | * ``nbo`` forces the operand data to be in native byte order. | * ``copy`` allows a temporary read-only copy if required. | * ``updateifcopy`` allows a temporary read-write copy if required. | * ``allocate`` causes the array to be allocated if it is None | in the ``op`` parameter. | * ``no_subtype`` prevents an ``allocate`` operand from using a subtype. | * ``arraymask`` indicates that this operand is the mask to use | for selecting elements when writing to operands with the | 'writemasked' flag set. The iterator does not enforce this, | but when writing from a buffer back to the array, it only | copies those elements indicated by this mask. | * ``writemasked`` indicates that only elements where the chosen | ``arraymask`` operand is True will be written to. | * ``overlap_assume_elementwise`` can be used to mark operands that are | accessed only in the iterator order, to allow less conservative | copying when ``copy_if_overlap`` is present. | op_dtypes : dtype or tuple of dtype(s), optional | The required data type(s) of the operands. If copying or buffering | is enabled, the data will be converted to/from their original types. | order : {'C', 'F', 'A', 'K'}, optional | Controls the iteration order. 'C' means C order, 'F' means | Fortran order, 'A' means 'F' order if all the arrays are Fortran | contiguous, 'C' order otherwise, and 'K' means as close to the | order the array elements appear in memory as possible. This also | affects the element memory order of ``allocate`` operands, as they | are allocated to be compatible with iteration order. | Default is 'K'. | casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional | Controls what kind of data casting may occur when making a copy | or buffering. Setting this to 'unsafe' is not recommended, | as it can adversely affect accumulations. | | * 'no' means the data types should not be cast at all. | * 'equiv' means only byte-order changes are allowed. | * 'safe' means only casts which can preserve values are allowed. | * 'same_kind' means only safe casts or casts within a kind, | like float64 to float32, are allowed. | * 'unsafe' means any data conversions may be done. | op_axes : list of list of ints, optional | If provided, is a list of ints or None for each operands. | The list of axes for an operand is a mapping from the dimensions | of the iterator to the dimensions of the operand. A value of | -1 can be placed for entries, causing that dimension to be | treated as `newaxis`. | itershape : tuple of ints, optional | The desired shape of the iterator. This allows ``allocate`` operands | with a dimension mapped by op_axes not corresponding to a dimension | of a different operand to get a value not equal to 1 for that | dimension. | buffersize : int, optional | When buffering is enabled, controls the size of the temporary | buffers. Set to 0 for the default value. | | Attributes | ---------- | dtypes : tuple of dtype(s) | The data types of the values provided in `value`. This may be | different from the operand data types if buffering is enabled. | Valid only before the iterator is closed. | finished : bool | Whether the iteration over the operands is finished or not. | has_delayed_bufalloc : bool | If True, the iterator was created with the ``delay_bufalloc`` flag, | and no reset() function was called on it yet. | has_index : bool | If True, the iterator was created with either the ``c_index`` or | the ``f_index`` flag, and the property `index` can be used to | retrieve it. | has_multi_index : bool | If True, the iterator was created with the ``multi_index`` flag, | and the property `multi_index` can be used to retrieve it. | index | When the ``c_index`` or ``f_index`` flag was used, this property | provides access to the index. Raises a ValueError if accessed | and ``has_index`` is False. | iterationneedsapi : bool | Whether iteration requires access to the Python API, for example | if one of the operands is an object array. | iterindex : int | An index which matches the order of iteration. | itersize : int | Size of the iterator. | itviews | Structured view(s) of `operands` in memory, matching the reordered | and optimized iterator access pattern. Valid only before the iterator | is closed. | multi_index | When the ``multi_index`` flag was used, this property | provides access to the index. Raises a ValueError if accessed | accessed and ``has_multi_index`` is False. | ndim : int | The dimensions of the iterator. | nop : int | The number of iterator operands. | operands : tuple of operand(s) | The array(s) to be iterated over. Valid only before the iterator is | closed. | shape : tuple of ints | Shape tuple, the shape of the iterator. | value | Value of ``operands`` at current iteration. Normally, this is a | tuple of array scalars, but if the flag ``external_loop`` is used, | it is a tuple of one dimensional arrays. | | Notes | ----- | `nditer` supersedes `flatiter`. The iterator implementation behind | `nditer` is also exposed by the NumPy C API. | | The Python exposure supplies two iteration interfaces, one which follows | the Python iterator protocol, and another which mirrors the C-style | do-while pattern. The native Python approach is better in most cases, but | if you need the coordinates or index of an iterator, use the C-style pattern. | | Examples | -------- | Here is how we might write an ``iter_add`` function, using the | Python iterator protocol: | | >>> def iter_add_py(x, y, out=None): | ... addop = np.add | ... it = np.nditer([x, y, out], [], | ... [['readonly'], ['readonly'], ['writeonly','allocate']]) | ... with it: | ... for (a, b, c) in it: | ... addop(a, b, out=c) | ... return it.operands[2] | | Here is the same function, but following the C-style pattern: | | >>> def iter_add(x, y, out=None): | ... addop = np.add | ... it = np.nditer([x, y, out], [], | ... [['readonly'], ['readonly'], ['writeonly','allocate']]) | ... with it: | ... while not it.finished: | ... addop(it[0], it[1], out=it[2]) | ... it.iternext() | ... return it.operands[2] | | Here is an example outer product function: | | >>> def outer_it(x, y, out=None): | ... mulop = np.multiply | ... it = np.nditer([x, y, out], ['external_loop'], | ... [['readonly'], ['readonly'], ['writeonly', 'allocate']], | ... op_axes=[list(range(x.ndim)) + [-1] * y.ndim, | ... [-1] * x.ndim + list(range(y.ndim)), | ... None]) | ... with it: | ... for (a, b, c) in it: | ... mulop(a, b, out=c) | ... return it.operands[2] | | >>> a = [np.arange(2)](https://www.chedong.com/phpMan.php/man/np.arange/2/markdown)+1 | >>> b = [np.arange(3)](https://www.chedong.com/phpMan.php/man/np.arange/3/markdown)+1 | >>> outer_it(a,b) | array([[1, 2, 3], | [2, 4, 6]]) | | Here is an example function which operates like a "lambda" ufunc: | | >>> def luf(lamdaexpr, *args, **kwargs): | ... '''luf(lambdaexpr, op1, ..., opn, out=None, order='K', casting='safe', buffersize=0)''' | ... nargs = len(args) | ... op = (kwargs.get('out',None),) + args | ... it = np.nditer(op, ['buffered','external_loop'], | ... [['writeonly','allocate','no_broadcast']] + | ... [['readonly','nbo','aligned']]*nargs, | ... order=kwargs.get('order','K'), | ... casting=kwargs.get('casting','safe'), | ... buffersize=kwargs.get('buffersize',0)) | ... while not it.finished: | ... it[0] = lamdaexpr(*it[1:]) | ... it.iternext() | ... return it.operands[0] | | >>> a = [np.arange(5)](https://www.chedong.com/phpMan.php/man/np.arange/5/markdown) | >>> b = [np.ones(5)](https://www.chedong.com/phpMan.php/man/np.ones/5/markdown) | >>> luf(lambda i,j:i*i + j/2, a, b) | array([ 0.5, 1.5, 4.5, 9.5, 16.5]) | | If operand flags `"writeonly"` or `"readwrite"` are used the | operands may be views into the original data with the | `WRITEBACKIFCOPY` flag. In this case `nditer` must be used as a | context manager or the `nditer.close` method must be called before | using the result. The temporary data will be written back to the | original data when the `__exit__` function is called but not before: | | >>> a = np.arange(6, dtype='i4')[::-2] | >>> with np.nditer(a, [], | ... [['writeonly', 'updateifcopy']], | ... casting='unsafe', | ... op_dtypes=[np.dtype('f4')]) as i: | ... x = i.operands[0] | ... x[:] = [-1, -2, -3] | ... # a still unchanged here | >>> a, x | (array([-1, -2, -3], dtype=int32), array([-1., -2., -3.], dtype=float32)) | | It is important to note that once the iterator is exited, dangling | references (like `x` in the example) may or may not share data with | the original data `a`. If writeback semantics were active, i.e. if | `x.base.flags.writebackifcopy` is `True`, then exiting the iterator | will sever the connection between `x` and `a`, writing to `x` will | no longer write to `a`. If writeback semantics are not active, then | `x.data` will still point at some part of `a.data`, and writing to | one will affect the other. | | Context management and the `close` method appeared in version 1.15.0. | | Methods defined here: | | __copy__(...) | | __delitem__(self, key, /) | Delete self[key]. | | __enter__(...) | | __exit__(...) | | __getitem__(self, key, /) | Return self[key]. | | __init__(self, /, *args, **kwargs) | Initialize self. See help(type(self)) for accurate signature. | | __iter__(self, /) | Implement iter(self). | | __len__(self, /) | Return len(self). | | __next__(self, /) | Implement next(self). | | __setitem__(self, key, value, /) | Set self[key] to value. | | close(...) | close() | | Resolve all writeback semantics in writeable operands. | | .. versionadded:: 1.15.0 | | See Also | -------- | | :ref:`nditer-context-manager` | | copy(...) | copy() | | Get a copy of the iterator in its current state. | | Examples | -------- | >>> x = [np.arange(10)](https://www.chedong.com/phpMan.php/man/np.arange/10/markdown) | >>> y = x + 1 | >>> it = np.nditer([x, y]) | >>> next(it) | ([array(0)](https://www.chedong.com/phpMan.php/man/array/0/markdown), [array(1)](https://www.chedong.com/phpMan.php/man/array/1/markdown)) | >>> it2 = it.copy() | >>> next(it2) | ([array(1)](https://www.chedong.com/phpMan.php/man/array/1/markdown), [array(2)](https://www.chedong.com/phpMan.php/man/array/2/markdown)) | | debug_print(...) | debug_print() | | Print the current state of the `nditer` instance and debug info to stdout. | | enable_external_loop(...) | enable_external_loop() | | When the "external_loop" was not used during construction, but | is desired, this modifies the iterator to behave as if the flag | was specified. | | iternext(...) | iternext() | | Check whether iterations are left, and perform a single internal iteration | without returning the result. Used in the C-style pattern do-while | pattern. For an example, see `nditer`. | | Returns | ------- | iternext : bool | Whether or not there are iterations left. | | remove_axis(...) | remove_axis(i) | | Removes axis `i` from the iterator. Requires that the flag "multi_index" | be enabled. | | remove_multi_index(...) | remove_multi_index() | | When the "multi_index" flag was specified, this removes it, allowing | the internal iteration structure to be optimized further. | | reset(...) | reset() | | Reset the iterator to its initial state. | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Data descriptors defined here: | | dtypes | | finished | | has_delayed_bufalloc | | has_index | | has_multi_index | | index | | iterationneedsapi | | iterindex | | iterrange | | itersize | | itviews | | multi_index | | ndim | | nop | | operands | operands[`Slice`] | | The array(s) to be iterated over. Valid only before the iterator is closed. | | shape | | value ### class number | Abstract base class of all numeric scalar types. | | Method resolution order: | number | generic | builtins.object | | Methods inherited from generic: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __and__(self, value, /) | Return self&value. | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __bool__(self, /) | True if self else False | | __copy__(...) | | __deepcopy__(...) | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __format__(...) | NumPy array scalar formatter | | __ge__(self, value, /) | Return self>=value. | | __getitem__(self, key, /) | Return self[key]. | | __gt__(self, value, /) | Return self>value. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __le__(self, value, /) | Return self<=value. | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. | | ---------------------------------------------------------------------- | Data and other attributes inherited from generic: | | __hash__ = None object0 = class object_(generic) | Any Python object. | | :Character code: ``'O'`` | | Method resolution order: | object_ | generic | builtins.object | | Methods defined here: | | __add__(self, value, /) | Return self+value. | | __call__(self, /, *args, **kwargs) | Call self as a function. | | __contains__(self, key, /) | Return key in self. | | __delattr__(self, name, /) | Implement delattr(self, name). | | __delitem__(self, key, /) | Delete self[key]. | | __eq__(self, value, /) | Return self==value. | | __ge__(self, value, /) | Return self>=value. | | __getattribute__(self, name, /) | Return getattr(self, name). | | __getitem__(self, key, /) | Return self[key]. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __iadd__(self, value, /) | Implement self+=value. | | __imul__(self, value, /) | Implement self*=value. | | __le__(self, value, /) | Return self<=value. | | __len__(self, /) | Return len(self). | | __lt__(self, value, /) | Return self>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. ### class object_ | Any Python object. | | :Character code: ``'O'`` | | Method resolution order: | object_ | generic | builtins.object | | Methods defined here: | | __add__(self, value, /) | Return self+value. | | __call__(self, /, *args, **kwargs) | Call self as a function. | | __contains__(self, key, /) | Return key in self. | | __delattr__(self, name, /) | Implement delattr(self, name). | | __delitem__(self, key, /) | Delete self[key]. | | __eq__(self, value, /) | Return self==value. | | __ge__(self, value, /) | Return self>=value. | | __getattribute__(self, name, /) | Return getattr(self, name). | | __getitem__(self, key, /) | Return self[key]. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __iadd__(self, value, /) | Implement self+=value. | | __imul__(self, value, /) | Implement self*=value. | | __le__(self, value, /) | Return self<=value. | | __len__(self, /) | Return len(self). | | __lt__(self, value, /) | Return self>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. ### class poly1d | poly1d(c_or_r, r=False, variable=None) | | A one-dimensional polynomial class. | | .. note:: | This forms part of the old polynomial API. Since version 1.4, the | new polynomial API defined in `numpy.polynomial` is preferred. | A summary of the differences can be found in the | :doc:`transition guide `. | | A convenience class, used to encapsulate "natural" operations on | polynomials so that said operations may take on their customary | form in code (see Examples). | | Parameters | ---------- | c_or_r : array_like | The polynomial's coefficients, in decreasing powers, or if | the value of the second parameter is True, the polynomial's | roots (values where the polynomial evaluates to 0). For example, | ``poly1d([1, 2, 3])`` returns an object that represents | :math:`x^2 + 2x + 3`, whereas ``poly1d([1, 2, 3], True)`` returns | one that represents :math:`(x-1)(x-2)(x-3) = x^3 - 6x^2 + 11x -6`. | r : bool, optional | If True, `c_or_r` specifies the polynomial's roots; the default | is False. | variable : str, optional | Changes the variable used when printing `p` from `x` to `variable` | (see Examples). | | Examples | -------- | Construct the polynomial :math:`x^2 + 2x + 3`: | | >>> p = np.poly1d([1, 2, 3]) | >>> print(np.poly1d(p)) | 2 | 1 x + 2 x + 3 | | Evaluate the polynomial at :math:`x = 0.5`: | | >>> p(0.5) | 4.25 | | Find the roots: | | >>> p.r | array([-1.+1.41421356j, -1.-1.41421356j]) | >>> p(p.r) | array([ -4.44089210e-16+0.j, -4.44089210e-16+0.j]) # may vary | | These numbers in the previous line represent (0, 0) to machine precision | | Show the coefficients: | | >>> p.c | array([1, 2, 3]) | | Display the order (the leading zero-coefficients are removed): | | >>> p.order | 2 | | Show the coefficient of the k-th power in the polynomial | (which is equivalent to ``p.c[-(i+1)]``): | | >>> p[1] | 2 | | Polynomials can be added, subtracted, multiplied, and divided | (returns quotient and remainder): | | >>> p * p | poly1d([ 1, 4, 10, 12, 9]) | | >>> (p**3 + 4) / p | (poly1d([ 1., 4., 10., 12., 9.]), poly1d([4.])) | | ``asarray(p)`` gives the coefficient array, so polynomials can be | used in all functions that accept arrays: | | >>> p**2 # square of polynomial | poly1d([ 1, 4, 10, 12, 9]) | | >>> np.square(p) # square of individual coefficients | array([1, 4, 9]) | | The variable used in the string representation of `p` can be modified, | using the `variable` parameter: | | >>> p = np.poly1d([1,2,3], variable='z') | >>> print(p) | 2 | 1 z + 2 z + 3 | | Construct a polynomial from its roots: | | >>> np.poly1d([1, 2], True) | poly1d([ 1., -3., 2.]) | | This is the same polynomial as obtained by: | | >>> np.poly1d([1, -1]) * np.poly1d([1, -2]) | poly1d([ 1, -3, 2]) | | Methods defined here: | | __add__(self, other) | | __array__(self, t=None) | | __call__(self, val) | Call self as a function. | | __div__(self, other) | | __eq__(self, other) | Return self==value. | | __getitem__(self, val) | | __init__(self, c_or_r, r=False, variable=None) | Initialize self. See help(type(self)) for accurate signature. | | __iter__(self) | | __len__(self) | | __mul__(self, other) | | __ne__(self, other) | Return self!=value. | | __neg__(self) | | __pos__(self) | | __pow__(self, val) | | __radd__(self, other) | | __rdiv__(self, other) | | __repr__(self) | Return repr(self). | | __rmul__(self, other) | | __rsub__(self, other) | | __rtruediv__ = __rdiv__(self, other) | | __setitem__(self, key, val) | | __str__(self) | Return str(self). | | __sub__(self, other) | | __truediv__ = __div__(self, other) | | deriv(self, m=1) | Return a derivative of this polynomial. | | Refer to `polyder` for full documentation. | | See Also | -------- | polyder : equivalent function | | integ(self, m=1, k=0) | Return an antiderivative (indefinite integral) of this polynomial. | | Refer to `polyint` for full documentation. | | See Also | -------- | polyint : equivalent function | | ---------------------------------------------------------------------- | Readonly properties defined here: | | o | The order or degree of the polynomial | | order | The order or degree of the polynomial | | r | The roots of the polynomial, where self(x) == 0 | | roots | The roots of the polynomial, where self(x) == 0 | | variable | The name of the polynomial variable | | ---------------------------------------------------------------------- | Data descriptors defined here: | | __dict__ | dictionary for instance variables (if defined) | | __weakref__ | list of weak references to the object (if defined) | | c | The polynomial coefficients | | coef | The polynomial coefficients | | coefficients | The polynomial coefficients | | coeffs | The polynomial coefficients | | ---------------------------------------------------------------------- | Data and other attributes defined here: | | __hash__ = None ### class recarray | recarray(shape, dtype=None, buf=None, offset=0, strides=None, formats=None, names=None, titles=None, byteorder=None, aligned=False, order='C') | | Construct an ndarray that allows field access using attributes. | | Arrays may have a data-types containing fields, analogous | to columns in a spread sheet. An example is ``[(x, int), (y, float)]``, | where each entry in the array is a pair of ``(int, float)``. Normally, | these attributes are accessed using dictionary lookups such as ``arr['x']`` | and ``arr['y']``. Record arrays allow the fields to be accessed as members | of the array, using ``arr.x`` and ``arr.y``. | | Parameters | ---------- | shape : tuple | Shape of output array. | dtype : data-type, optional | The desired data-type. By default, the data-type is determined | from `formats`, `names`, `titles`, `aligned` and `byteorder`. | formats : list of data-types, optional | A list containing the data-types for the different columns, e.g. | ``['i4', 'f8', 'i4']``. `formats` does *not* support the new | convention of using types directly, i.e. ``(int, float, int)``. | Note that `formats` must be a list, not a tuple. | Given that `formats` is somewhat limited, we recommend specifying | `dtype` instead. | names : tuple of str, optional | The name of each column, e.g. ``('x', 'y', 'z')``. | buf : buffer, optional | By default, a new array is created of the given shape and data-type. | If `buf` is specified and is an object exposing the buffer interface, | the array will use the memory from the existing buffer. In this case, | the `offset` and `strides` keywords are available. | | Other Parameters | ---------------- | titles : tuple of str, optional | Aliases for column names. For example, if `names` were | ``('x', 'y', 'z')`` and `titles` is | ``('x_coordinate', 'y_coordinate', 'z_coordinate')``, then | ``arr['x']`` is equivalent to both ``arr.x`` and ``arr.x_coordinate``. | byteorder : {'<', '>', '='}, optional | Byte-order for all fields. | aligned : bool, optional | Align the fields in memory as the C-compiler would. | strides : tuple of ints, optional | Buffer (`buf`) is interpreted according to these strides (strides | define how many bytes each array element, row, column, etc. | occupy in memory). | offset : int, optional | Start reading buffer (`buf`) from this offset onwards. | order : {'C', 'F'}, optional | Row-major (C-style) or column-major (Fortran-style) order. | | Returns | ------- | rec : recarray | Empty array of the given shape and type. | | See Also | -------- | core.records.fromrecords : Construct a record array from data. | record : fundamental data-type for `recarray`. | format_parser : determine a data-type from formats, names, titles. | | Notes | ----- | This constructor can be compared to ``empty``: it creates a new record | array but does not fill it with data. To create a record array from data, | use one of the following methods: | | 1. Create a standard ndarray and convert it to a record array, | using ``arr.view(np.recarray)`` | 2. Use the `buf` keyword. | 3. Use `np.rec.fromrecords`. | | Examples | -------- | Create an array with two fields, ``x`` and ``y``: | | >>> x = np.array([(1.0, 2), (3.0, 4)], dtype=[('x', '>> x | array([(1., 2), (3., 4)], dtype=[('x', '>> x['x'] | array([1., 3.]) | | View the array as a record array: | | >>> x = x.view(np.recarray) | | >>> x.x | array([1., 3.]) | | >>> x.y | array([2, 4]) | | Create a new, empty record array: | | >>> np.recarray((2,), | ... dtype=[('x', int), ('y', float), ('z', int)]) #doctest: +SKIP | rec.array([(-1073741821, 1.2249118382103472e-301, 24547520), | (3471280, 1.2134086255804012e-316, 0)], | dtype=[('x', ' reference if type unchanged, copy otherwise. | | Returns either a new reference to self if dtype is not given or a new array | of provided data type if dtype is different from the current dtype of the | array. | | __array_function__(...) | | __array_prepare__(...) | a.__array_prepare__(obj) -> Object of same type as ndarray object obj. | | __array_ufunc__(...) | | __array_wrap__(...) | a.__array_wrap__(obj) -> Object of same type as ndarray object a. | | __bool__(self, /) | True if self else False | | __complex__(...) | | __contains__(self, key, /) | Return key in self. | | __copy__(...) | a.__copy__() | | Used if :func:`copy.copy` is called on an array. Returns a copy of the array. | | Equivalent to ``a.copy(order='K')``. | | __deepcopy__(...) | a.__deepcopy__(memo, /) -> Deep copy of array. | | Used if :func:`copy.deepcopy` is called on an array. | | __delitem__(self, key, /) | Delete self[key]. | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __format__(...) | Default object formatter. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __iadd__(self, value, /) | Return self+=value. | | __iand__(self, value, /) | Return self&=value. | | __ifloordiv__(self, value, /) | Return self//=value. | | __ilshift__(self, value, /) | Return self<<=value. | | __imatmul__(self, value, /) | Return self@=value. | | __imod__(self, value, /) | Return self%=value. | | __imul__(self, value, /) | Return self*=value. | | __index__(self, /) | Return self converted to an integer, if self is suitable for use as an index into a list. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __ior__(self, value, /) | Return self|=value. | | __ipow__(self, value, /) | Return self**=value. | | __irshift__(self, value, /) | Return self>>=value. | | __isub__(self, value, /) | Return self-=value. | | __iter__(self, /) | Implement iter(self). | | __itruediv__(self, value, /) | Return self/=value. | | __ixor__(self, value, /) | Return self^=value. | | __le__(self, value, /) | Return self<=value. | | __len__(self, /) | Return len(self). | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __setitem__(self, key, value, /) | Set self[key] to value. | | __setstate__(...) | a.__setstate__(state, /) | | For unpickling. | | The `state` argument must be a sequence that contains the following | elements: | | Parameters | ---------- | version : int | optional pickle version. If omitted defaults to 0. | shape : tuple | dtype : data-type | isFortran : bool | rawdata : string or list | a binary string with the data (or a list if 'a' is an object array) | | __sizeof__(...) | Size of object in memory, in bytes. | | __str__(self, /) | Return str(self). | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | all(...) | a.all(axis=None, out=None, keepdims=False, *, where=True) | | Returns True if all elements evaluate to True. | | Refer to `numpy.all` for full documentation. | | See Also | -------- | numpy.all : equivalent function | | any(...) | a.any(axis=None, out=None, keepdims=False, *, where=True) | | Returns True if any of the elements of `a` evaluate to True. | | Refer to `numpy.any` for full documentation. | | See Also | -------- | numpy.any : equivalent function | | argmax(...) | a.argmax(axis=None, out=None) | | Return indices of the maximum values along the given axis. | | Refer to `numpy.argmax` for full documentation. | | See Also | -------- | numpy.argmax : equivalent function | | argmin(...) | a.argmin(axis=None, out=None) | | Return indices of the minimum values along the given axis. | | Refer to `numpy.argmin` for detailed documentation. | | See Also | -------- | numpy.argmin : equivalent function | | argpartition(...) | a.argpartition(kth, axis=-1, kind='introselect', order=None) | | Returns the indices that would partition this array. | | Refer to `numpy.argpartition` for full documentation. | | .. versionadded:: 1.8.0 | | See Also | -------- | numpy.argpartition : equivalent function | | argsort(...) | a.argsort(axis=-1, kind=None, order=None) | | Returns the indices that would sort this array. | | Refer to `numpy.argsort` for full documentation. | | See Also | -------- | numpy.argsort : equivalent function | | astype(...) | a.astype(dtype, order='K', casting='unsafe', subok=True, copy=True) | | Copy of the array, cast to a specified type. | | Parameters | ---------- | dtype : str or dtype | Typecode or data-type to which the array is cast. | order : {'C', 'F', 'A', 'K'}, optional | Controls the memory layout order of the result. | 'C' means C order, 'F' means Fortran order, 'A' | means 'F' order if all the arrays are Fortran contiguous, | 'C' order otherwise, and 'K' means as close to the | order the array elements appear in memory as possible. | Default is 'K'. | casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional | Controls what kind of data casting may occur. Defaults to 'unsafe' | for backwards compatibility. | | * 'no' means the data types should not be cast at all. | * 'equiv' means only byte-order changes are allowed. | * 'safe' means only casts which can preserve values are allowed. | * 'same_kind' means only safe casts or casts within a kind, | like float64 to float32, are allowed. | * 'unsafe' means any data conversions may be done. | subok : bool, optional | If True, then sub-classes will be passed-through (default), otherwise | the returned array will be forced to be a base-class array. | copy : bool, optional | By default, astype always returns a newly allocated array. If this | is set to false, and the `dtype`, `order`, and `subok` | requirements are satisfied, the input array is returned instead | of a copy. | | Returns | ------- | arr_t : ndarray | Unless `copy` is False and the other conditions for returning the input | array are satisfied (see description for `copy` input parameter), `arr_t` | is a new array of the same shape as the input array, with dtype, order | given by `dtype`, `order`. | | Notes | ----- | .. versionchanged:: 1.17.0 | Casting between a simple data type and a structured one is possible only | for "unsafe" casting. Casting to multiple fields is allowed, but | casting from multiple fields is not. | | .. versionchanged:: 1.9.0 | Casting from numeric to string types in 'safe' casting mode requires | that the string dtype length is long enough to store the max | integer/float value converted. | | Raises | ------ | ComplexWarning | When casting from complex to float or int. To avoid this, | one should use ``a.real.astype(t)``. | | Examples | -------- | >>> x = np.array([1, 2, 2.5]) | >>> x | array([1. , 2. , 2.5]) | | >>> x.astype(int) | array([1, 2, 2]) | | byteswap(...) | a.byteswap(inplace=False) | | Swap the bytes of the array elements | | Toggle between low-endian and big-endian data representation by | returning a byteswapped array, optionally swapped in-place. | Arrays of byte-strings are not swapped. The real and imaginary | parts of a complex number are swapped individually. | | Parameters | ---------- | inplace : bool, optional | If ``True``, swap bytes in-place, default is ``False``. | | Returns | ------- | out : ndarray | The byteswapped array. If `inplace` is ``True``, this is | a view to self. | | Examples | -------- | >>> A = np.array([1, 256, 8755], dtype=np.int16) | >>> list(map(hex, A)) | ['0x1', '0x100', '0x2233'] | >>> A.byteswap(inplace=True) | array([ 256, 1, 13090], dtype=int16) | >>> list(map(hex, A)) | ['0x100', '0x1', '0x3322'] | | Arrays of byte-strings are not swapped | | >>> A = np.array([b'ceg', b'fac']) | >>> A.byteswap() | array([b'ceg', b'fac'], dtype='|S3') | | ``A.newbyteorder().byteswap()`` produces an array with the same values | but different representation in memory | | >>> A = np.array([1, 2, 3]) | >>> A.view(np.uint8) | array([1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, | 0, 0], dtype=uint8) | >>> A.newbyteorder().byteswap(inplace=True) | array([1, 2, 3]) | >>> A.view(np.uint8) | array([0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, | 0, 3], dtype=uint8) | | choose(...) | a.choose(choices, out=None, mode='raise') | | Use an index array to construct a new array from a set of choices. | | Refer to `numpy.choose` for full documentation. | | See Also | -------- | numpy.choose : equivalent function | | clip(...) | a.clip(min=None, max=None, out=None, **kwargs) | | Return an array whose values are limited to ``[min, max]``. | One of max or min must be given. | | Refer to `numpy.clip` for full documentation. | | See Also | -------- | numpy.clip : equivalent function | | compress(...) | a.compress(condition, axis=None, out=None) | | Return selected slices of this array along given axis. | | Refer to `numpy.compress` for full documentation. | | See Also | -------- | numpy.compress : equivalent function | | conj(...) | a.conj() | | Complex-conjugate all elements. | | Refer to `numpy.conjugate` for full documentation. | | See Also | -------- | numpy.conjugate : equivalent function | | conjugate(...) | a.conjugate() | | Return the complex conjugate, element-wise. | | Refer to `numpy.conjugate` for full documentation. | | See Also | -------- | numpy.conjugate : equivalent function | | copy(...) | a.copy(order='C') | | Return a copy of the array. | | Parameters | ---------- | order : {'C', 'F', 'A', 'K'}, optional | Controls the memory layout of the copy. 'C' means C-order, | 'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous, | 'C' otherwise. 'K' means match the layout of `a` as closely | as possible. (Note that this function and :func:`numpy.copy` are very | similar but have different default values for their order= | arguments, and this function always passes sub-classes through.) | | See also | -------- | numpy.copy : Similar function with different default behavior | numpy.copyto | | Notes | ----- | This function is the preferred method for creating an array copy. The | function :func:`numpy.copy` is similar, but it defaults to using order 'K', | and will not pass sub-classes through by default. | | Examples | -------- | >>> x = np.array([[1,2,3],[4,5,6]], order='F') | | >>> y = x.copy() | | >>> [x.fill(0)](https://www.chedong.com/phpMan.php/man/x.fill/0/markdown) | | >>> x | array([[0, 0, 0], | [0, 0, 0]]) | | >>> y | array([[1, 2, 3], | [4, 5, 6]]) | | >>> y.flags['C_CONTIGUOUS'] | True | | cumprod(...) | a.cumprod(axis=None, dtype=None, out=None) | | Return the cumulative product of the elements along the given axis. | | Refer to `numpy.cumprod` for full documentation. | | See Also | -------- | numpy.cumprod : equivalent function | | cumsum(...) | a.cumsum(axis=None, dtype=None, out=None) | | Return the cumulative sum of the elements along the given axis. | | Refer to `numpy.cumsum` for full documentation. | | See Also | -------- | numpy.cumsum : equivalent function | | diagonal(...) | a.diagonal(offset=0, axis1=0, axis2=1) | | Return specified diagonals. In NumPy 1.9 the returned array is a | read-only view instead of a copy as in previous NumPy versions. In | a future version the read-only restriction will be removed. | | Refer to :func:`numpy.diagonal` for full documentation. | | See Also | -------- | numpy.diagonal : equivalent function | | dot(...) | a.dot(b, out=None) | | Dot product of two arrays. | | Refer to `numpy.dot` for full documentation. | | See Also | -------- | numpy.dot : equivalent function | | Examples | -------- | >>> a = [np.eye(2)](https://www.chedong.com/phpMan.php/man/np.eye/2/markdown) | >>> b = np.ones((2, 2)) * 2 | >>> a.dot(b) | array([[2., 2.], | [2., 2.]]) | | This array method can be conveniently chained: | | >>> a.dot(b).dot(b) | array([[8., 8.], | [8., 8.]]) | | dump(...) | a.dump(file) | | Dump a pickle of the array to the specified file. | The array can be read back with pickle.load or numpy.load. | | Parameters | ---------- | file : str or Path | A string naming the dump file. | | .. versionchanged:: 1.17.0 | `pathlib.Path` objects are now accepted. | | dumps(...) | a.dumps() | | Returns the pickle of the array as a string. | pickle.loads or numpy.loads will convert the string back to an array. | | Parameters | ---------- | None | | fill(...) | a.fill(value) | | Fill the array with a scalar value. | | Parameters | ---------- | value : scalar | All elements of `a` will be assigned this value. | | Examples | -------- | >>> a = np.array([1, 2]) | >>> [a.fill(0)](https://www.chedong.com/phpMan.php/man/a.fill/0/markdown) | >>> a | array([0, 0]) | >>> a = [np.empty(2)](https://www.chedong.com/phpMan.php/man/np.empty/2/markdown) | >>> [a.fill(1)](https://www.chedong.com/phpMan.php/man/a.fill/1/markdown) | >>> a | array([1., 1.]) | | flatten(...) | a.flatten(order='C') | | Return a copy of the array collapsed into one dimension. | | Parameters | ---------- | order : {'C', 'F', 'A', 'K'}, optional | 'C' means to flatten in row-major (C-style) order. | 'F' means to flatten in column-major (Fortran- | style) order. 'A' means to flatten in column-major | order if `a` is Fortran *contiguous* in memory, | row-major order otherwise. 'K' means to flatten | `a` in the order the elements occur in memory. | The default is 'C'. | | Returns | ------- | y : ndarray | A copy of the input array, flattened to one dimension. | | See Also | -------- | ravel : Return a flattened array. | flat : A 1-D flat iterator over the array. | | Examples | -------- | >>> a = np.array([[1,2], [3,4]]) | >>> a.flatten() | array([1, 2, 3, 4]) | >>> a.flatten('F') | array([1, 3, 2, 4]) | | getfield(...) | a.getfield(dtype, offset=0) | | Returns a field of the given array as a certain type. | | A field is a view of the array data with a given data-type. The values in | the view are determined by the given type and the offset into the current | array in bytes. The offset needs to be such that the view dtype fits in the | array dtype; for example an array of dtype complex128 has 16-byte elements. | If taking a view with a 32-bit integer (4 bytes), the offset needs to be | between 0 and 12 bytes. | | Parameters | ---------- | dtype : str or dtype | The data type of the view. The dtype size of the view can not be larger | than that of the array itself. | offset : int | Number of bytes to skip before beginning the element view. | | Examples | -------- | >>> x = np.diag([1.+1.j]*2) | >>> x[1, 1] = 2 + 4.j | >>> x | array([[1.+1.j, 0.+0.j], | [0.+0.j, 2.+4.j]]) | >>> x.getfield(np.float64) | array([[1., 0.], | [0., 2.]]) | | By choosing an offset of 8 bytes we can select the complex part of the | array for our view: | | >>> x.getfield(np.float64, offset=8) | array([[1., 0.], | [0., 4.]]) | | item(...) | a.item(*args) | | Copy an element of an array to a standard Python scalar and return it. | | Parameters | ---------- | \*args : Arguments (variable number and type) | | * none: in this case, the method only works for arrays | with one element (`a.size == 1`), which element is | copied into a standard Python scalar object and returned. | | * int_type: this argument is interpreted as a flat index into | the array, specifying which element to copy and return. | | * tuple of int_types: functions as does a single int_type argument, | except that the argument is interpreted as an nd-index into the | array. | | Returns | ------- | z : Standard Python scalar object | A copy of the specified element of the array as a suitable | Python scalar | | Notes | ----- | When the data type of `a` is longdouble or clongdouble, item() returns | a scalar array object because there is no available Python scalar that | would not lose information. Void arrays return a buffer object for item(), | unless fields are defined, in which case a tuple is returned. | | `item` is very similar to a[args], except, instead of an array scalar, | a standard Python scalar is returned. This can be useful for speeding up | access to elements of the array and doing arithmetic on elements of the | array using Python's optimized math. | | Examples | -------- | >>> [np.random.seed(123)](https://www.chedong.com/phpMan.php/man/np.random.seed/123/markdown) | >>> x = np.random.randint(9, size=(3, 3)) | >>> x | array([[2, 2, 6], | [1, 3, 6], | [1, 0, 1]]) | >>> [x.item(3)](https://www.chedong.com/phpMan.php/man/x.item/3/markdown) | 1 | >>> [x.item(7)](https://www.chedong.com/phpMan.php/man/x.item/7/markdown) | 0 | >>> x.item((0, 1)) | 2 | >>> x.item((2, 2)) | 1 | | itemset(...) | a.itemset(*args) | | Insert scalar into an array (scalar is cast to array's dtype, if possible) | | There must be at least 1 argument, and define the last argument | as *item*. Then, ``a.itemset(*args)`` is equivalent to but faster | than ``a[args] = item``. The item should be a scalar value and `args` | must select a single item in the array `a`. | | Parameters | ---------- | \*args : Arguments | If one argument: a scalar, only used in case `a` is of size 1. | If two arguments: the last argument is the value to be set | and must be a scalar, the first argument specifies a single array | element location. It is either an int or a tuple. | | Notes | ----- | Compared to indexing syntax, `itemset` provides some speed increase | for placing a scalar into a particular location in an `ndarray`, | if you must do this. However, generally this is discouraged: | among other problems, it complicates the appearance of the code. | Also, when using `itemset` (and `item`) inside a loop, be sure | to assign the methods to a local variable to avoid the attribute | look-up at each loop iteration. | | Examples | -------- | >>> [np.random.seed(123)](https://www.chedong.com/phpMan.php/man/np.random.seed/123/markdown) | >>> x = np.random.randint(9, size=(3, 3)) | >>> x | array([[2, 2, 6], | [1, 3, 6], | [1, 0, 1]]) | >>> x.itemset(4, 0) | >>> x.itemset((2, 2), 9) | >>> x | array([[2, 2, 6], | [1, 0, 6], | [1, 0, 9]]) | | max(...) | a.max(axis=None, out=None, keepdims=False, initial=, where=True) | | Return the maximum along a given axis. | | Refer to `numpy.amax` for full documentation. | | See Also | -------- | numpy.amax : equivalent function | | mean(...) | a.mean(axis=None, dtype=None, out=None, keepdims=False, *, where=True) | | Returns the average of the array elements along given axis. | | Refer to `numpy.mean` for full documentation. | | See Also | -------- | numpy.mean : equivalent function | | min(...) | a.min(axis=None, out=None, keepdims=False, initial=, where=True) | | Return the minimum along a given axis. | | Refer to `numpy.amin` for full documentation. | | See Also | -------- | numpy.amin : equivalent function | | newbyteorder(...) | arr.newbyteorder(new_order='S', /) | | Return the array with the same data viewed with a different byte order. | | Equivalent to:: | | arr.view([arr.dtype.newbytorder(new_order)](https://www.chedong.com/phpMan.php/man/arr.dtype.newbytorder/neworder/markdown)) | | Changes are also made in all fields and sub-arrays of the array data | type. | | | | Parameters | ---------- | new_order : string, optional | Byte order to force; a value from the byte order specifications | below. `new_order` codes can be any of: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order, equivalent to `sys.byteorder` | * {'|', 'I'} - ignore (no change to byte order) | | The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_arr : array | New array object with the dtype reflecting given change to the | byte order. | | nonzero(...) | a.nonzero() | | Return the indices of the elements that are non-zero. | | Refer to `numpy.nonzero` for full documentation. | | See Also | -------- | numpy.nonzero : equivalent function | | partition(...) | a.partition(kth, axis=-1, kind='introselect', order=None) | | Rearranges the elements in the array in such a way that the value of the | element in kth position is in the position it would be in a sorted array. | All elements smaller than the kth element are moved before this element and | all equal or greater are moved behind it. The ordering of the elements in | the two partitions is undefined. | | .. versionadded:: 1.8.0 | | Parameters | ---------- | kth : int or sequence of ints | Element index to partition by. The kth element value will be in its | final sorted position and all smaller elements will be moved before it | and all equal or greater elements behind it. | The order of all elements in the partitions is undefined. | If provided with a sequence of kth it will partition all elements | indexed by kth of them into their sorted position at once. | axis : int, optional | Axis along which to sort. Default is -1, which means sort along the | last axis. | kind : {'introselect'}, optional | Selection algorithm. Default is 'introselect'. | order : str or list of str, optional | When `a` is an array with fields defined, this argument specifies | which fields to compare first, second, etc. A single field can | be specified as a string, and not all fields need to be specified, | but unspecified fields will still be used, in the order in which | they come up in the dtype, to break ties. | | See Also | -------- | numpy.partition : Return a parititioned copy of an array. | argpartition : Indirect partition. | sort : Full sort. | | Notes | ----- | See ``np.partition`` for notes on the different algorithms. | | Examples | -------- | >>> a = np.array([3, 4, 2, 1]) | >>> [a.partition(3)](https://www.chedong.com/phpMan.php/man/a.partition/3/markdown) | >>> a | array([2, 1, 3, 4]) | | >>> a.partition((1, 3)) | >>> a | array([1, 2, 3, 4]) | | prod(...) | a.prod(axis=None, dtype=None, out=None, keepdims=False, initial=1, where=True) | | Return the product of the array elements over the given axis | | Refer to `numpy.prod` for full documentation. | | See Also | -------- | numpy.prod : equivalent function | | ptp(...) | a.ptp(axis=None, out=None, keepdims=False) | | Peak to peak (maximum - minimum) value along a given axis. | | Refer to `numpy.ptp` for full documentation. | | See Also | -------- | numpy.ptp : equivalent function | | put(...) | a.put(indices, values, mode='raise') | | Set ``a.flat[n] = values[n]`` for all `n` in indices. | | Refer to `numpy.put` for full documentation. | | See Also | -------- | numpy.put : equivalent function | | ravel(...) | a.ravel([order]) | | Return a flattened array. | | Refer to `numpy.ravel` for full documentation. | | See Also | -------- | numpy.ravel : equivalent function | | ndarray.flat : a flat iterator on the array. | | repeat(...) | a.repeat(repeats, axis=None) | | Repeat elements of an array. | | Refer to `numpy.repeat` for full documentation. | | See Also | -------- | numpy.repeat : equivalent function | | reshape(...) | a.reshape(shape, order='C') | | Returns an array containing the same data with a new shape. | | Refer to `numpy.reshape` for full documentation. | | See Also | -------- | numpy.reshape : equivalent function | | Notes | ----- | Unlike the free function `numpy.reshape`, this method on `ndarray` allows | the elements of the shape parameter to be passed in as separate arguments. | For example, ``a.reshape(10, 11)`` is equivalent to | ``a.reshape((10, 11))``. | | resize(...) | a.resize(new_shape, refcheck=True) | | Change shape and size of array in-place. | | Parameters | ---------- | new_shape : tuple of ints, or `n` ints | Shape of resized array. | refcheck : bool, optional | If False, reference count will not be checked. Default is True. | | Returns | ------- | None | | Raises | ------ | ValueError | If `a` does not own its own data or references or views to it exist, | and the data memory must be changed. | PyPy only: will always raise if the data memory must be changed, since | there is no reliable way to determine if references or views to it | exist. | | SystemError | If the `order` keyword argument is specified. This behaviour is a | bug in NumPy. | | See Also | -------- | resize : Return a new array with the specified shape. | | Notes | ----- | This reallocates space for the data area if necessary. | | Only contiguous arrays (data elements consecutive in memory) can be | resized. | | The purpose of the reference count check is to make sure you | do not use this array as a buffer for another Python object and then | reallocate the memory. However, reference counts can increase in | other ways so if you are sure that you have not shared the memory | for this array with another Python object, then you may safely set | `refcheck` to False. | | Examples | -------- | Shrinking an array: array is flattened (in the order that the data are | stored in memory), resized, and reshaped: | | >>> a = np.array([[0, 1], [2, 3]], order='C') | >>> a.resize((2, 1)) | >>> a | array([[0], | [1]]) | | >>> a = np.array([[0, 1], [2, 3]], order='F') | >>> a.resize((2, 1)) | >>> a | array([[0], | [2]]) | | Enlarging an array: as above, but missing entries are filled with zeros: | | >>> b = np.array([[0, 1], [2, 3]]) | >>> b.resize(2, 3) # new_shape parameter doesn't have to be a tuple | >>> b | array([[0, 1, 2], | [3, 0, 0]]) | | Referencing an array prevents resizing... | | >>> c = a | >>> a.resize((1, 1)) | Traceback (most recent call last): | ... | ValueError: cannot resize an array that references or is referenced ... | | Unless `refcheck` is False: | | >>> a.resize((1, 1), refcheck=False) | >>> a | array([[0]]) | >>> c | array([[0]]) | | round(...) | a.round(decimals=0, out=None) | | Return `a` with each element rounded to the given number of decimals. | | Refer to `numpy.around` for full documentation. | | See Also | -------- | numpy.around : equivalent function | | searchsorted(...) | a.searchsorted(v, side='left', sorter=None) | | Find indices where elements of v should be inserted in a to maintain order. | | For full documentation, see `numpy.searchsorted` | | See Also | -------- | numpy.searchsorted : equivalent function | | setfield(...) | a.setfield(val, dtype, offset=0) | | Put a value into a specified place in a field defined by a data-type. | | Place `val` into `a`'s field defined by `dtype` and beginning `offset` | bytes into the field. | | Parameters | ---------- | val : object | Value to be placed in field. | dtype : dtype object | Data-type of the field in which to place `val`. | offset : int, optional | The number of bytes into the field at which to place `val`. | | Returns | ------- | None | | See Also | -------- | getfield | | Examples | -------- | >>> x = [np.eye(3)](https://www.chedong.com/phpMan.php/man/np.eye/3/markdown) | >>> x.getfield(np.float64) | array([[1., 0., 0.], | [0., 1., 0.], | [0., 0., 1.]]) | >>> x.setfield(3, np.int32) | >>> x.getfield(np.int32) | array([[3, 3, 3], | [3, 3, 3], | [3, 3, 3]], dtype=int32) | >>> x | array([[1.0e+000, 1.5e-323, 1.5e-323], | [1.5e-323, 1.0e+000, 1.5e-323], | [1.5e-323, 1.5e-323, 1.0e+000]]) | >>> x.setfield([np.eye(3)](https://www.chedong.com/phpMan.php/man/np.eye/3/markdown), np.int32) | >>> x | array([[1., 0., 0.], | [0., 1., 0.], | [0., 0., 1.]]) | | setflags(...) | a.setflags(write=None, align=None, uic=None) | | Set array flags WRITEABLE, ALIGNED, (WRITEBACKIFCOPY and UPDATEIFCOPY), | respectively. | | These Boolean-valued flags affect how numpy interprets the memory | area used by `a` (see Notes below). The ALIGNED flag can only | be set to True if the data is actually aligned according to the type. | The WRITEBACKIFCOPY and (deprecated) UPDATEIFCOPY flags can never be set | to True. The flag WRITEABLE can only be set to True if the array owns its | own memory, or the ultimate owner of the memory exposes a writeable buffer | interface, or is a string. (The exception for string is made so that | unpickling can be done without copying memory.) | | Parameters | ---------- | write : bool, optional | Describes whether or not `a` can be written to. | align : bool, optional | Describes whether or not `a` is aligned properly for its type. | uic : bool, optional | Describes whether or not `a` is a copy of another "base" array. | | Notes | ----- | Array flags provide information about how the memory area used | for the array is to be interpreted. There are 7 Boolean flags | in use, only four of which can be changed by the user: | WRITEBACKIFCOPY, UPDATEIFCOPY, WRITEABLE, and ALIGNED. | | WRITEABLE (W) the data area can be written to; | | ALIGNED (A) the data and strides are aligned appropriately for the hardware | (as determined by the compiler); | | UPDATEIFCOPY (U) (deprecated), replaced by WRITEBACKIFCOPY; | | WRITEBACKIFCOPY (X) this array is a copy of some other array (referenced | by .base). When the C-API function PyArray_ResolveWritebackIfCopy is | called, the base array will be updated with the contents of this array. | | All flags can be accessed using the single (upper case) letter as well | as the full name. | | Examples | -------- | >>> y = np.array([[3, 1, 7], | ... [2, 0, 0], | ... [8, 5, 9]]) | >>> y | array([[3, 1, 7], | [2, 0, 0], | [8, 5, 9]]) | >>> y.flags | C_CONTIGUOUS : True | F_CONTIGUOUS : False | OWNDATA : True | WRITEABLE : True | ALIGNED : True | WRITEBACKIFCOPY : False | UPDATEIFCOPY : False | >>> y.setflags(write=0, align=0) | >>> y.flags | C_CONTIGUOUS : True | F_CONTIGUOUS : False | OWNDATA : True | WRITEABLE : False | ALIGNED : False | WRITEBACKIFCOPY : False | UPDATEIFCOPY : False | >>> y.setflags(uic=1) | Traceback (most recent call last): | File "", line 1, in | ValueError: cannot set WRITEBACKIFCOPY flag to True | | sort(...) | a.sort(axis=-1, kind=None, order=None) | | Sort an array in-place. Refer to `numpy.sort` for full documentation. | | Parameters | ---------- | axis : int, optional | Axis along which to sort. Default is -1, which means sort along the | last axis. | kind : {'quicksort', 'mergesort', 'heapsort', 'stable'}, optional | Sorting algorithm. The default is 'quicksort'. Note that both 'stable' | and 'mergesort' use timsort under the covers and, in general, the | actual implementation will vary with datatype. The 'mergesort' option | is retained for backwards compatibility. | | .. versionchanged:: 1.15.0 | The 'stable' option was added. | | order : str or list of str, optional | When `a` is an array with fields defined, this argument specifies | which fields to compare first, second, etc. A single field can | be specified as a string, and not all fields need be specified, | but unspecified fields will still be used, in the order in which | they come up in the dtype, to break ties. | | See Also | -------- | numpy.sort : Return a sorted copy of an array. | numpy.argsort : Indirect sort. | numpy.lexsort : Indirect stable sort on multiple keys. | numpy.searchsorted : Find elements in sorted array. | numpy.partition: Partial sort. | | Notes | ----- | See `numpy.sort` for notes on the different sorting algorithms. | | Examples | -------- | >>> a = np.array([[1,4], [3,1]]) | >>> a.sort(axis=1) | >>> a | array([[1, 4], | [1, 3]]) | >>> a.sort(axis=0) | >>> a | array([[1, 3], | [1, 4]]) | | Use the `order` keyword to specify a field to use when sorting a | structured array: | | >>> a = np.array([('a', 2), ('c', 1)], dtype=[('x', 'S1'), ('y', int)]) | >>> a.sort(order='y') | >>> a | array([(b'c', 1), (b'a', 2)], | dtype=[('x', 'S1'), ('y', '>> x = np.array([[0, 1], [2, 3]], dtype='>> x.tobytes() | b'\x00\x00\x01\x00\x02\x00\x03\x00' | >>> x.tobytes('C') == x.tobytes() | True | >>> x.tobytes('F') | b'\x00\x00\x02\x00\x01\x00\x03\x00' | | tofile(...) | a.tofile(fid, sep="", format="%s") | | Write array to a file as text or binary (default). | | Data is always written in 'C' order, independent of the order of `a`. | The data produced by this method can be recovered using the function | fromfile(). | | Parameters | ---------- | fid : file or str or Path | An open file object, or a string containing a filename. | | .. versionchanged:: 1.17.0 | `pathlib.Path` objects are now accepted. | | sep : str | Separator between array items for text output. | If "" (empty), a binary file is written, equivalent to | ``file.write(a.tobytes())``. | format : str | Format string for text file output. | Each entry in the array is formatted to text by first converting | it to the closest Python type, and then using "format" % item. | | Notes | ----- | This is a convenience function for quick storage of array data. | Information on endianness and precision is lost, so this method is not a | good choice for files intended to archive data or transport data between | machines with different endianness. Some of these problems can be overcome | by outputting the data as text files, at the expense of speed and file | size. | | When fid is a file object, array contents are directly written to the | file, bypassing the file object's ``write`` method. As a result, tofile | cannot be used with files objects supporting compression (e.g., GzipFile) | or file-like objects that do not support ``fileno()`` (e.g., BytesIO). | | tolist(...) | a.tolist() | | Return the array as an ``a.ndim``-levels deep nested list of Python scalars. | | Return a copy of the array data as a (nested) Python list. | Data items are converted to the nearest compatible builtin Python type, via | the `~numpy.ndarray.item` function. | | If ``a.ndim`` is 0, then since the depth of the nested list is 0, it will | not be a list at all, but a simple Python scalar. | | Parameters | ---------- | none | | Returns | ------- | y : object, or list of object, or list of list of object, or ... | The possibly nested list of array elements. | | Notes | ----- | The array may be recreated via ``a = np.array(a.tolist())``, although this | may sometimes lose precision. | | Examples | -------- | For a 1D array, ``a.tolist()`` is almost the same as ``list(a)``, | except that ``tolist`` changes numpy scalars to Python scalars: | | >>> a = np.uint32([1, 2]) | >>> a_list = list(a) | >>> a_list | [1, 2] | >>> type(a_list[0]) | | >>> a_tolist = a.tolist() | >>> a_tolist | [1, 2] | >>> type(a_tolist[0]) | | | Additionally, for a 2D array, ``tolist`` applies recursively: | | >>> a = np.array([[1, 2], [3, 4]]) | >>> list(a) | [array([1, 2]), array([3, 4])] | >>> a.tolist() | [[1, 2], [3, 4]] | | The base case for this recursion is a 0D array: | | >>> a = [np.array(1)](https://www.chedong.com/phpMan.php/man/np.array/1/markdown) | >>> list(a) | Traceback (most recent call last): | ... | TypeError: iteration over a 0-d array | >>> a.tolist() | 1 | | tostring(...) | a.tostring(order='C') | | A compatibility alias for `tobytes`, with exactly the same behavior. | | Despite its name, it returns `bytes` not `str`\ s. | | .. deprecated:: 1.19.0 | | trace(...) | a.trace(offset=0, axis1=0, axis2=1, dtype=None, out=None) | | Return the sum along diagonals of the array. | | Refer to `numpy.trace` for full documentation. | | See Also | -------- | numpy.trace : equivalent function | | transpose(...) | a.transpose(*axes) | | Returns a view of the array with axes transposed. | | For a 1-D array this has no effect, as a transposed vector is simply the | same vector. To convert a 1-D array into a 2D column vector, an additional | dimension must be added. `np.atleast2d(a).T` achieves this, as does | `a[:, np.newaxis]`. | For a 2-D array, this is a standard matrix transpose. | For an n-D array, if axes are given, their order indicates how the | axes are permuted (see Examples). If axes are not provided and | ``a.shape = (i[0], i[1], ... i[n-2], i[n-1])``, then | ``a.transpose().shape = (i[n-1], i[n-2], ... i[1], i[0])``. | | Parameters | ---------- | axes : None, tuple of ints, or `n` ints | | * None or no argument: reverses the order of the axes. | | * tuple of ints: `i` in the `j`-th place in the tuple means `a`'s | `i`-th axis becomes `a.transpose()`'s `j`-th axis. | | * `n` ints: same as an n-tuple of the same ints (this form is | intended simply as a "convenience" alternative to the tuple form) | | Returns | ------- | out : ndarray | View of `a`, with axes suitably permuted. | | See Also | -------- | transpose : Equivalent function | ndarray.T : Array property returning the array transposed. | ndarray.reshape : Give a new shape to an array without changing its data. | | Examples | -------- | >>> a = np.array([[1, 2], [3, 4]]) | >>> a | array([[1, 2], | [3, 4]]) | >>> a.transpose() | array([[1, 3], | [2, 4]]) | >>> a.transpose((1, 0)) | array([[1, 3], | [2, 4]]) | >>> a.transpose(1, 0) | array([[1, 3], | [2, 4]]) | | var(...) | a.var(axis=None, dtype=None, out=None, ddof=0, keepdims=False, *, where=True) | | Returns the variance of the array elements, along given axis. | | Refer to `numpy.var` for full documentation. | | See Also | -------- | numpy.var : equivalent function | | view(...) | a.view([dtype][, type]) | | New view of array with the same data. | | .. note:: | Passing None for ``dtype`` is different from omitting the parameter, | since the former invokes ``dtype(None)`` which is an alias for | ``dtype('float_')``. | | Parameters | ---------- | dtype : data-type or ndarray sub-class, optional | Data-type descriptor of the returned view, e.g., float32 or int16. | Omitting it results in the view having the same data-type as `a`. | This argument can also be specified as an ndarray sub-class, which | then specifies the type of the returned object (this is equivalent to | setting the ``type`` parameter). | type : Python type, optional | Type of the returned view, e.g., ndarray or matrix. Again, omission | of the parameter results in type preservation. | | Notes | ----- | ``a.view()`` is used two different ways: | | ``a.view(some_dtype)`` or ``a.view(dtype=some_dtype)`` constructs a view | of the array's memory with a different data-type. This can cause a | reinterpretation of the bytes of memory. | | ``[a.view(ndarray_subclass)](https://www.chedong.com/phpMan.php/man/a.view/ndarraysubclass/markdown)`` or ``a.view(type=ndarray_subclass)`` just | returns an instance of `ndarray_subclass` that looks at the same array | (same shape, dtype, etc.) This does not cause a reinterpretation of the | memory. | | For ``a.view(some_dtype)``, if ``some_dtype`` has a different number of | bytes per entry than the previous dtype (for example, converting a | regular array to a structured array), then the behavior of the view | cannot be predicted just from the superficial appearance of ``a`` (shown | by ``print(a)``). It also depends on exactly how ``a`` is stored in | memory. Therefore if ``a`` is C-ordered versus fortran-ordered, versus | defined as a slice or transpose, etc., the view may give different | results. | | | Examples | -------- | >>> x = np.array([(1, 2)], dtype=[('a', np.int8), ('b', np.int8)]) | | Viewing array data using a different type and dtype: | | >>> y = x.view(dtype=np.int16, type=np.matrix) | >>> y | matrix([[513]], dtype=int16) | >>> print(type(y)) | | | Creating a view on a structured array so it can be used in calculations | | >>> x = np.array([(1, 2),(3,4)], dtype=[('a', np.int8), ('b', np.int8)]) | >>> xv = x.view(dtype=np.int8).reshape(-1,2) | >>> xv | array([[1, 2], | [3, 4]], dtype=int8) | >>> [xv.mean(0)](https://www.chedong.com/phpMan.php/man/xv.mean/0/markdown) | array([2., 3.]) | | Making changes to the view changes the underlying array | | >>> xv[0,1] = 20 | >>> x | array([(1, 20), (3, 4)], dtype=[('a', 'i1'), ('b', 'i1')]) | | Using a view to convert an array to a recarray: | | >>> z = x.view(np.recarray) | >>> z.a | array([1, 3], dtype=int8) | | Views share data: | | >>> x[0] = (9, 10) | >>> z[0] | (9, 10) | | Views that change the dtype size (bytes per entry) should normally be | avoided on arrays defined by slices, transposes, fortran-ordering, etc.: | | >>> x = np.array([[1,2,3],[4,5,6]], dtype=np.int16) | >>> y = x[:, 0:2] | >>> y | array([[1, 2], | [4, 5]], dtype=int16) | >>> y.view(dtype=[('width', np.int16), ('length', np.int16)]) | Traceback (most recent call last): | ... | ValueError: To change to a dtype of a different size, the array must be C-contiguous | >>> z = y.copy() | >>> z.view(dtype=[('width', np.int16), ('length', np.int16)]) | array([[(1, 2)], | [(4, 5)]], dtype=[('width', '>> x = np.array([[1.,2.],[3.,4.]]) | >>> x | array([[ 1., 2.], | [ 3., 4.]]) | >>> x.T | array([[ 1., 3.], | [ 2., 4.]]) | >>> x = np.array([1.,2.,3.,4.]) | >>> x | array([ 1., 2., 3., 4.]) | >>> x.T | array([ 1., 2., 3., 4.]) | | See Also | -------- | transpose | | __array_interface__ | Array protocol: Python side. | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: C-struct side. | | base | Base object if memory is from some other object. | | Examples | -------- | The base of an array that owns its memory is None: | | >>> x = np.array([1,2,3,4]) | >>> x.base is None | True | | Slicing creates a view, whose memory is shared with x: | | >>> y = x[2:] | >>> y.base is x | True | | ctypes | An object to simplify the interaction of the array with the ctypes | module. | | This attribute creates an object that makes it easier to use arrays | when calling shared libraries with the ctypes module. The returned | object has, among others, data, shape, and strides attributes (see | Notes below) which themselves return ctypes objects that can be used | as arguments to a shared library. | | Parameters | ---------- | None | | Returns | ------- | c : Python object | Possessing attributes data, shape, strides, etc. | | See Also | -------- | numpy.ctypeslib | | Notes | ----- | Below are the public attributes of this object which were documented | in "Guide to NumPy" (we have omitted undocumented public attributes, | as well as documented private attributes): | | .. autoattribute:: numpy.core._internal._ctypes.data | :noindex: | | .. autoattribute:: numpy.core._internal._ctypes.shape | :noindex: | | .. autoattribute:: numpy.core._internal._ctypes.strides | :noindex: | | .. automethod:: numpy.core._internal._ctypes.data_as | :noindex: | | .. automethod:: numpy.core._internal._ctypes.shape_as | :noindex: | | .. automethod:: numpy.core._internal._ctypes.strides_as | :noindex: | | If the ctypes module is not available, then the ctypes attribute | of array objects still returns something useful, but ctypes objects | are not returned and errors may be raised instead. In particular, | the object will still have the ``as_parameter`` attribute which will | return an integer equal to the data attribute. | | Examples | -------- | >>> import ctypes | >>> x = np.array([[0, 1], [2, 3]], dtype=np.int32) | >>> x | array([[0, 1], | [2, 3]], dtype=int32) | >>> x.ctypes.data | 31962608 # may vary | >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)) | <__main__.LP_c_uint object at 0x7ff2fc1fc200> # may vary | >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint32)).contents | [c_uint(0)](https://www.chedong.com/phpMan.php/man/cuint/0/markdown) | >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_uint64)).contents | [c_ulong(4294967296)](https://www.chedong.com/phpMan.php/man/culong/4294967296/markdown) | >>> x.ctypes.shape | # may vary | >>> x.ctypes.strides | # may vary | | data | Python buffer object pointing to the start of the array's data. | | dtype | Data-type of the array's elements. | | Parameters | ---------- | None | | Returns | ------- | d : numpy dtype object | | See Also | -------- | numpy.dtype | | Examples | -------- | >>> x | array([[0, 1], | [2, 3]]) | >>> x.dtype | dtype('int32') | >>> type(x.dtype) | | | flags | Information about the memory layout of the array. | | Attributes | ---------- | C_CONTIGUOUS (C) | The data is in a single, C-style contiguous segment. | F_CONTIGUOUS (F) | The data is in a single, Fortran-style contiguous segment. | OWNDATA (O) | The array owns the memory it uses or borrows it from another object. | WRITEABLE (W) | The data area can be written to. Setting this to False locks | the data, making it read-only. A view (slice, etc.) inherits WRITEABLE | from its base array at creation time, but a view of a writeable | array may be subsequently locked while the base array remains writeable. | (The opposite is not true, in that a view of a locked array may not | be made writeable. However, currently, locking a base object does not | lock any views that already reference it, so under that circumstance it | is possible to alter the contents of a locked array via a previously | created writeable view onto it.) Attempting to change a non-writeable | array raises a RuntimeError exception. | ALIGNED (A) | The data and all elements are aligned appropriately for the hardware. | WRITEBACKIFCOPY (X) | This array is a copy of some other array. The C-API function | PyArray_ResolveWritebackIfCopy must be called before deallocating | to the base array will be updated with the contents of this array. | UPDATEIFCOPY (U) | (Deprecated, use WRITEBACKIFCOPY) This array is a copy of some other array. | When this array is | deallocated, the base array will be updated with the contents of | this array. | FNC | F_CONTIGUOUS and not C_CONTIGUOUS. | FORC | F_CONTIGUOUS or C_CONTIGUOUS (one-segment test). | BEHAVED (B) | ALIGNED and WRITEABLE. | CARRAY (CA) | BEHAVED and C_CONTIGUOUS. | FARRAY (FA) | BEHAVED and F_CONTIGUOUS and not C_CONTIGUOUS. | | Notes | ----- | The `flags` object can be accessed dictionary-like (as in ``a.flags['WRITEABLE']``), | or by using lowercased attribute names (as in ``a.flags.writeable``). Short flag | names are only supported in dictionary access. | | Only the WRITEBACKIFCOPY, UPDATEIFCOPY, WRITEABLE, and ALIGNED flags can be | changed by the user, via direct assignment to the attribute or dictionary | entry, or by calling `ndarray.setflags`. | | The array flags cannot be set arbitrarily: | | - UPDATEIFCOPY can only be set ``False``. | - WRITEBACKIFCOPY can only be set ``False``. | - ALIGNED can only be set ``True`` if the data is truly aligned. | - WRITEABLE can only be set ``True`` if the array owns its own memory | or the ultimate owner of the memory exposes a writeable buffer | interface or is a string. | | Arrays can be both C-style and Fortran-style contiguous simultaneously. | This is clear for 1-dimensional arrays, but can also be true for higher | dimensional arrays. | | Even for contiguous arrays a stride for a given dimension | ``arr.strides[dim]`` may be *arbitrary* if ``arr.shape[dim] == 1`` | or the array has no elements. | It does *not* generally hold that ``self.strides[-1] == self.itemsize`` | for C-style contiguous arrays or ``self.strides[0] == self.itemsize`` for | Fortran-style contiguous arrays is true. | | flat | A 1-D iterator over the array. | | This is a `numpy.flatiter` instance, which acts similarly to, but is not | a subclass of, Python's built-in iterator object. | | See Also | -------- | flatten : Return a copy of the array collapsed into one dimension. | | flatiter | | Examples | -------- | >>> x = np.arange(1, 7).reshape(2, 3) | >>> x | array([[1, 2, 3], | [4, 5, 6]]) | >>> x.flat[3] | 4 | >>> x.T | array([[1, 4], | [2, 5], | [3, 6]]) | >>> x.T.flat[3] | 5 | >>> type(x.flat) | | | An assignment example: | | >>> x.flat = 3; x | array([[3, 3, 3], | [3, 3, 3]]) | >>> x.flat[[1,4]] = 1; x | array([[3, 1, 3], | [3, 1, 3]]) | | imag | The imaginary part of the array. | | Examples | -------- | >>> x = np.sqrt([1+0j, 0+1j]) | >>> x.imag | array([ 0. , 0.70710678]) | >>> x.imag.dtype | dtype('float64') | | itemsize | Length of one array element in bytes. | | Examples | -------- | >>> x = np.array([1,2,3], dtype=np.float64) | >>> x.itemsize | 8 | >>> x = np.array([1,2,3], dtype=np.complex128) | >>> x.itemsize | 16 | | nbytes | Total bytes consumed by the elements of the array. | | Notes | ----- | Does not include memory consumed by non-element attributes of the | array object. | | Examples | -------- | >>> x = np.zeros((3,5,2), dtype=np.complex128) | >>> x.nbytes | 480 | >>> np.prod(x.shape) * x.itemsize | 480 | | ndim | Number of array dimensions. | | Examples | -------- | >>> x = np.array([1, 2, 3]) | >>> x.ndim | 1 | >>> y = np.zeros((2, 3, 4)) | >>> y.ndim | 3 | | real | The real part of the array. | | Examples | -------- | >>> x = np.sqrt([1+0j, 0+1j]) | >>> x.real | array([ 1. , 0.70710678]) | >>> x.real.dtype | dtype('float64') | | See Also | -------- | numpy.real : equivalent function | | shape | Tuple of array dimensions. | | The shape property is usually used to get the current shape of an array, | but may also be used to reshape the array in-place by assigning a tuple of | array dimensions to it. As with `numpy.reshape`, one of the new shape | dimensions can be -1, in which case its value is inferred from the size of | the array and the remaining dimensions. Reshaping an array in-place will | fail if a copy is required. | | Examples | -------- | >>> x = np.array([1, 2, 3, 4]) | >>> x.shape | (4,) | >>> y = np.zeros((2, 3, 4)) | >>> y.shape | (2, 3, 4) | >>> y.shape = (3, 8) | >>> y | array([[ 0., 0., 0., 0., 0., 0., 0., 0.], | [ 0., 0., 0., 0., 0., 0., 0., 0.], | [ 0., 0., 0., 0., 0., 0., 0., 0.]]) | >>> y.shape = (3, 6) | Traceback (most recent call last): | File "", line 1, in | ValueError: total size of new array must be unchanged | >>> np.zeros((4,2))[::2].shape = (-1,) | Traceback (most recent call last): | File "", line 1, in | AttributeError: Incompatible shape for in-place modification. Use | `.reshape()` to make a copy with the desired shape. | | See Also | -------- | numpy.reshape : similar function | ndarray.reshape : similar method | | size | Number of elements in the array. | | Equal to ``np.prod(a.shape)``, i.e., the product of the array's | dimensions. | | Notes | ----- | `a.size` returns a standard arbitrary precision Python integer. This | may not be the case with other methods of obtaining the same value | (like the suggested ``np.prod(a.shape)``, which returns an instance | of ``np.int_``), and may be relevant if the value is used further in | calculations that may overflow a fixed size integer type. | | Examples | -------- | >>> x = np.zeros((3, 5, 2), dtype=np.complex128) | >>> x.size | 30 | >>> np.prod(x.shape) | 30 | | strides | Tuple of bytes to step in each dimension when traversing an array. | | The byte offset of element ``(i[0], i[1], ..., i[n])`` in an array `a` | is:: | | offset = sum(np.array(i) * a.strides) | | A more detailed explanation of strides can be found in the | "ndarray.rst" file in the NumPy reference guide. | | Notes | ----- | Imagine an array of 32-bit integers (each 4 bytes):: | | x = np.array([[0, 1, 2, 3, 4], | [5, 6, 7, 8, 9]], dtype=np.int32) | | This array is stored in memory as 40 bytes, one after the other | (known as a contiguous block of memory). The strides of an array tell | us how many bytes we have to skip in memory to move to the next position | along a certain axis. For example, we have to skip 4 bytes (1 value) to | move to the next column, but 20 bytes (5 values) to get to the same | position in the next row. As such, the strides for the array `x` will be | ``(20, 4)``. | | See Also | -------- | numpy.lib.stride_tricks.as_strided | | Examples | -------- | >>> y = np.reshape(np.arange(2*3*4), (2,3,4)) | >>> y | array([[[ 0, 1, 2, 3], | [ 4, 5, 6, 7], | [ 8, 9, 10, 11]], | [[12, 13, 14, 15], | [16, 17, 18, 19], | [20, 21, 22, 23]]]) | >>> y.strides | (48, 16, 4) | >>> y[1,1,1] | 17 | >>> offset=sum(y.strides * np.array((1,1,1))) | >>> offset/y.itemsize | 17 | | >>> x = np.reshape(np.arange(5*6*7*8), (5,6,7,8)).transpose(2,3,1,0) | >>> x.strides | (32, 4, 224, 1344) | >>> i = np.array([3,5,2,2]) | >>> offset = sum(i * x.strides) | >>> x[3,5,2,2] | 813 | >>> offset / x.itemsize | 813 | | ---------------------------------------------------------------------- | Data and other attributes inherited from ndarray: | | __hash__ = None ### class record | A data-type scalar that allows field access as attribute lookup. | | Method resolution order: | record | void | flexible | generic | builtins.object | | Methods defined here: | | __getattribute__(self, attr) | Return getattr(self, name). | | __getitem__(self, indx) | Return self[key]. | | __repr__(self) | Return repr(self). | | __setattr__(self, attr, val) | Implement setattr(self, name, value). | | __str__(self) | Return str(self). | | pprint(self) | Pretty-print all fields. | | ---------------------------------------------------------------------- | Data descriptors defined here: | | __dict__ | dictionary for instance variables (if defined) | | __weakref__ | list of weak references to the object (if defined) | | ---------------------------------------------------------------------- | Methods inherited from void: | | __delitem__(self, key, /) | Delete self[key]. | | __eq__(self, value, /) | Return self==value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __le__(self, value, /) | Return self<=value. | | __len__(self, /) | Return len(self). | | __lt__(self, value, /) | Return self>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | data | Pointer to start of data. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. short = class int16(signedinteger) | Signed integer type, compatible with C ``short``. | | :Character code: ``'h'`` | :Canonical name: `numpy.short` | :Alias on this platform (Linux x86_64): `numpy.int16`: 16-bit signed integer (``-32_768`` to ``32_767``). | | Method resolution order: | int16 | signedinteger | integer | number | generic | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __and__(self, value, /) | Return self&value. | | __bool__(self, /) | True if self else False | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __index__(self, /) | Return self converted to an integer, if self is suitable for use as an index into a list. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __le__(self, value, /) | Return self<=value. | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __str__(self, /) | Return str(self). | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from integer: | | __round__(...) | | ---------------------------------------------------------------------- | Data descriptors inherited from integer: | | denominator | denominator of value (1) | | numerator | numerator of value (the value itself) | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __copy__(...) | | __deepcopy__(...) | | __format__(...) | NumPy array scalar formatter | | __getitem__(self, key, /) | Return self[key]. | | __reduce__(...) | Helper for pickle. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. ### class signedinteger | Abstract base class of all signed integer scalar types. | | Method resolution order: | signedinteger | integer | number | generic | builtins.object | | Methods inherited from integer: | | __round__(...) | | ---------------------------------------------------------------------- | Data descriptors inherited from integer: | | denominator | denominator of value (1) | | numerator | numerator of value (the value itself) | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __and__(self, value, /) | Return self&value. | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __bool__(self, /) | True if self else False | | __copy__(...) | | __deepcopy__(...) | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __format__(...) | NumPy array scalar formatter | | __ge__(self, value, /) | Return self>=value. | | __getitem__(self, key, /) | Return self[key]. | | __gt__(self, value, /) | Return self>value. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __le__(self, value, /) | Return self<=value. | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. | | ---------------------------------------------------------------------- | Data and other attributes inherited from generic: | | __hash__ = None single = class float32(floating) | Single-precision floating-point number type, compatible with C ``float``. | | :Character code: ``'f'`` | :Canonical name: `numpy.single` | :Alias on this platform (Linux x86_64): `numpy.float32`: 32-bit-precision floating-point number type: sign bit, 8 bits exponent, 23 bits mantissa. | | Method resolution order: | float32 | floating | inexact | number | generic | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __bool__(self, /) | True if self else False | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __int__(self, /) | int(self) | | __le__(self, value, /) | Return self<=value. | | __lt__(self, value, /) | Return self (int, int) | | Return a pair of integers, whose ratio is exactly equal to the original | floating point number, and with a positive denominator. | Raise `OverflowError` on infinities and a `ValueError` on NaNs. | | >>> np.single(10.0).as_integer_ratio() | (10, 1) | >>> np.single(0.0).as_integer_ratio() | (0, 1) | >>> np.single(-.25).as_integer_ratio() | (-1, 4) | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from floating: | | __round__(...) | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __and__(self, value, /) | Return self&value. | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __copy__(...) | | __deepcopy__(...) | | __format__(...) | NumPy array scalar formatter | | __getitem__(self, key, /) | Return self[key]. | | __invert__(self, /) | ~self | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. singlecomplex = class complex64(complexfloating) | Complex number type composed of two single-precision floating-point | numbers. | | :Character code: ``'F'`` | :Canonical name: `numpy.csingle` | :Alias: `numpy.singlecomplex` | :Alias on this platform (Linux x86_64): `numpy.complex64`: Complex number type composed of 2 32-bit-precision floating-point numbers. | | Method resolution order: | complex64 | complexfloating | inexact | number | generic | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __bool__(self, /) | True if self else False | | __complex__(...) | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __int__(self, /) | int(self) | | __le__(self, value, /) | Return self<=value. | | __lt__(self, value, /) | Return self>self. | | __rshift__(self, value, /) | Return self>>value. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. str0 = class str_(builtins.str, character) | A unicode string. | | When used in arrays, this type strips trailing null codepoints. | | Unlike the builtin `str`, this supports the :ref:`python:bufferobjects`, exposing its | contents as UCS4: | | >>> m = memoryview(np.str_("abc")) | >>> m.format | '3w' | >>> m.tobytes() | b'a\x00\x00\x00b\x00\x00\x00c\x00\x00\x00' | | :Character code: ``'U'`` | :Alias: `numpy.unicode_` | | Method resolution order: | str_ | builtins.str | character | flexible | generic | builtins.object | | Methods defined here: | | __eq__(self, value, /) | Return self==value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __le__(self, value, /) | Return self<=value. | | __lt__(self, value, /) | Return self int | | Return the number of non-overlapping occurrences of substring sub in | string S[start:end]. Optional arguments start and end are | interpreted as in slice notation. | | encode(self, /, encoding='utf-8', errors='strict') | Encode the string using the codec registered for encoding. | | encoding | The encoding in which to encode the string. | errors | The error handling scheme to use for encoding errors. | The default is 'strict' meaning that encoding errors raise a | UnicodeEncodeError. Other possible values are 'ignore', 'replace' and | 'xmlcharrefreplace' as well as any other name registered with | codecs.register_error that can handle UnicodeEncodeErrors. | | endswith(...) | S.endswith(suffix[, start[, end]]) -> bool | | Return True if S ends with the specified suffix, False otherwise. | With optional start, test S beginning at that position. | With optional end, stop comparing S at that position. | suffix can also be a tuple of strings to try. | | expandtabs(self, /, tabsize=8) | Return a copy where all tab characters are expanded using spaces. | | If tabsize is not given, a tab size of 8 characters is assumed. | | find(...) | S.find(sub[, start[, end]]) -> int | | Return the lowest index in S where substring sub is found, | such that sub is contained within S[start:end]. Optional | arguments start and end are interpreted as in slice notation. | | Return -1 on failure. | | format(...) | S.format(*args, **kwargs) -> str | | Return a formatted version of S, using substitutions from args and kwargs. | The substitutions are identified by braces ('{' and '}'). | | format_map(...) | S.format_map(mapping) -> str | | Return a formatted version of S, using substitutions from mapping. | The substitutions are identified by braces ('{' and '}'). | | index(...) | S.index(sub[, start[, end]]) -> int | | Return the lowest index in S where substring sub is found, | such that sub is contained within S[start:end]. Optional | arguments start and end are interpreted as in slice notation. | | Raises ValueError when the substring is not found. | | isalnum(self, /) | Return True if the string is an alpha-numeric string, False otherwise. | | A string is alpha-numeric if all characters in the string are alpha-numeric and | there is at least one character in the string. | | isalpha(self, /) | Return True if the string is an alphabetic string, False otherwise. | | A string is alphabetic if all characters in the string are alphabetic and there | is at least one character in the string. | | isascii(self, /) | Return True if all characters in the string are ASCII, False otherwise. | | ASCII characters have code points in the range U+0000-U+007F. | Empty string is ASCII too. | | isdecimal(self, /) | Return True if the string is a decimal string, False otherwise. | | A string is a decimal string if all characters in the string are decimal and | there is at least one character in the string. | | isdigit(self, /) | Return True if the string is a digit string, False otherwise. | | A string is a digit string if all characters in the string are digits and there | is at least one character in the string. | | isidentifier(self, /) | Return True if the string is a valid Python identifier, False otherwise. | | Call keyword.iskeyword(s) to test whether string s is a reserved identifier, | such as "def" or "class". | | islower(self, /) | Return True if the string is a lowercase string, False otherwise. | | A string is lowercase if all cased characters in the string are lowercase and | there is at least one cased character in the string. | | isnumeric(self, /) | Return True if the string is a numeric string, False otherwise. | | A string is numeric if all characters in the string are numeric and there is at | least one character in the string. | | isprintable(self, /) | Return True if the string is printable, False otherwise. | | A string is printable if all of its characters are considered printable in | repr() or if it is empty. | | isspace(self, /) | Return True if the string is a whitespace string, False otherwise. | | A string is whitespace if all characters in the string are whitespace and there | is at least one character in the string. | | istitle(self, /) | Return True if the string is a title-cased string, False otherwise. | | In a title-cased string, upper- and title-case characters may only | follow uncased characters and lowercase characters only cased ones. | | isupper(self, /) | Return True if the string is an uppercase string, False otherwise. | | A string is uppercase if all cased characters in the string are uppercase and | there is at least one cased character in the string. | | join(self, iterable, /) | Concatenate any number of strings. | | The string whose method is called is inserted in between each given string. | The result is returned as a new string. | | Example: '.'.join(['ab', 'pq', 'rs']) -> 'ab.pq.rs' | | ljust(self, width, fillchar=' ', /) | Return a left-justified string of length width. | | Padding is done using the specified fill character (default is a space). | | lower(self, /) | Return a copy of the string converted to lowercase. | | lstrip(self, chars=None, /) | Return a copy of the string with leading whitespace removed. | | If chars is given and not None, remove characters in chars instead. | | partition(self, sep, /) | Partition the string into three parts using the given separator. | | This will search for the separator in the string. If the separator is found, | returns a 3-tuple containing the part before the separator, the separator | itself, and the part after it. | | If the separator is not found, returns a 3-tuple containing the original string | and two empty strings. | | removeprefix(self, prefix, /) | Return a str with the given prefix string removed if present. | | If the string starts with the prefix string, return string[len(prefix):]. | Otherwise, return a copy of the original string. | | removesuffix(self, suffix, /) | Return a str with the given suffix string removed if present. | | If the string ends with the suffix string and that suffix is not empty, | return string[:-len(suffix)]. Otherwise, return a copy of the original | string. | | replace(self, old, new, count=-1, /) | Return a copy with all occurrences of substring old replaced by new. | | count | Maximum number of occurrences to replace. | -1 (the default value) means replace all occurrences. | | If the optional argument count is given, only the first count occurrences are | replaced. | | rfind(...) | S.rfind(sub[, start[, end]]) -> int | | Return the highest index in S where substring sub is found, | such that sub is contained within S[start:end]. Optional | arguments start and end are interpreted as in slice notation. | | Return -1 on failure. | | rindex(...) | S.rindex(sub[, start[, end]]) -> int | | Return the highest index in S where substring sub is found, | such that sub is contained within S[start:end]. Optional | arguments start and end are interpreted as in slice notation. | | Raises ValueError when the substring is not found. | | rjust(self, width, fillchar=' ', /) | Return a right-justified string of length width. | | Padding is done using the specified fill character (default is a space). | | rpartition(self, sep, /) | Partition the string into three parts using the given separator. | | This will search for the separator in the string, starting at the end. If | the separator is found, returns a 3-tuple containing the part before the | separator, the separator itself, and the part after it. | | If the separator is not found, returns a 3-tuple containing two empty strings | and the original string. | | rsplit(self, /, sep=None, maxsplit=-1) | Return a list of the substrings in the string, using sep as the separator string. | | sep | The separator used to split the string. | | When set to None (the default value), will split on any whitespace | character (including \\n \\r \\t \\f and spaces) and will discard | empty strings from the result. | maxsplit | Maximum number of splits (starting from the left). | -1 (the default value) means no limit. | | Splitting starts at the end of the string and works to the front. | | rstrip(self, chars=None, /) | Return a copy of the string with trailing whitespace removed. | | If chars is given and not None, remove characters in chars instead. | | split(self, /, sep=None, maxsplit=-1) | Return a list of the substrings in the string, using sep as the separator string. | | sep | The separator used to split the string. | | When set to None (the default value), will split on any whitespace | character (including \\n \\r \\t \\f and spaces) and will discard | empty strings from the result. | maxsplit | Maximum number of splits (starting from the left). | -1 (the default value) means no limit. | | Note, str.split() is mainly useful for data that has been intentionally | delimited. With natural text that includes punctuation, consider using | the regular expression module. | | splitlines(self, /, keepends=False) | Return a list of the lines in the string, breaking at line boundaries. | | Line breaks are not included in the resulting list unless keepends is given and | true. | | startswith(...) | S.startswith(prefix[, start[, end]]) -> bool | | Return True if S starts with the specified prefix, False otherwise. | With optional start, test S beginning at that position. | With optional end, stop comparing S at that position. | prefix can also be a tuple of strings to try. | | strip(self, chars=None, /) | Return a copy of the string with leading and trailing whitespace removed. | | If chars is given and not None, remove characters in chars instead. | | swapcase(self, /) | Convert uppercase characters to lowercase and lowercase characters to uppercase. | | title(self, /) | Return a version of the string where each word is titlecased. | | More specifically, words start with uppercased characters and all remaining | cased characters have lower case. | | translate(self, table, /) | Replace each character in the string using the given translation table. | | table | Translation table, which must be a mapping of Unicode ordinals to | Unicode ordinals, strings, or None. | | The table must implement lookup/indexing via __getitem__, for instance a | dictionary or list. If this operation raises LookupError, the character is | left untouched. Characters mapped to None are deleted. | | upper(self, /) | Return a copy of the string converted to uppercase. | | zfill(self, width, /) | Pad a numeric string with zeros on the left, to fill a field of the given width. | | The string is never truncated. | | ---------------------------------------------------------------------- | Static methods inherited from builtins.str: | | maketrans(...) | Return a translation table usable for str.translate(). | | If there is only one argument, it must be a dictionary mapping Unicode | ordinals (integers) or characters to Unicode ordinals, strings or None. | Character keys will be then converted to ordinals. | If there are two arguments, they must be strings of equal length, and | in the resulting dictionary, each character in x will be mapped to the | character at the same position in y. If there is a third argument, it | must be a string, whose characters will be mapped to None in the result. | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __abs__(self, /) | abs(self) | | __and__(self, value, /) | Return self&value. | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __bool__(self, /) | True if self else False | | __copy__(...) | | __deepcopy__(...) | | __divmod__(self, value, /) | Return divmod(self, value). | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. ### class str_ | A unicode string. | | When used in arrays, this type strips trailing null codepoints. | | Unlike the builtin `str`, this supports the :ref:`python:bufferobjects`, exposing its | contents as UCS4: | | >>> m = memoryview(np.str_("abc")) | >>> m.format | '3w' | >>> m.tobytes() | b'a\x00\x00\x00b\x00\x00\x00c\x00\x00\x00' | | :Character code: ``'U'`` | :Alias: `numpy.unicode_` | | Method resolution order: | str_ | builtins.str | character | flexible | generic | builtins.object | | Methods defined here: | | __eq__(self, value, /) | Return self==value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __le__(self, value, /) | Return self<=value. | | __lt__(self, value, /) | Return self int | | Return the number of non-overlapping occurrences of substring sub in | string S[start:end]. Optional arguments start and end are | interpreted as in slice notation. | | encode(self, /, encoding='utf-8', errors='strict') | Encode the string using the codec registered for encoding. | | encoding | The encoding in which to encode the string. | errors | The error handling scheme to use for encoding errors. | The default is 'strict' meaning that encoding errors raise a | UnicodeEncodeError. Other possible values are 'ignore', 'replace' and | 'xmlcharrefreplace' as well as any other name registered with | codecs.register_error that can handle UnicodeEncodeErrors. | | endswith(...) | S.endswith(suffix[, start[, end]]) -> bool | | Return True if S ends with the specified suffix, False otherwise. | With optional start, test S beginning at that position. | With optional end, stop comparing S at that position. | suffix can also be a tuple of strings to try. | | expandtabs(self, /, tabsize=8) | Return a copy where all tab characters are expanded using spaces. | | If tabsize is not given, a tab size of 8 characters is assumed. | | find(...) | S.find(sub[, start[, end]]) -> int | | Return the lowest index in S where substring sub is found, | such that sub is contained within S[start:end]. Optional | arguments start and end are interpreted as in slice notation. | | Return -1 on failure. | | format(...) | S.format(*args, **kwargs) -> str | | Return a formatted version of S, using substitutions from args and kwargs. | The substitutions are identified by braces ('{' and '}'). | | format_map(...) | S.format_map(mapping) -> str | | Return a formatted version of S, using substitutions from mapping. | The substitutions are identified by braces ('{' and '}'). | | index(...) | S.index(sub[, start[, end]]) -> int | | Return the lowest index in S where substring sub is found, | such that sub is contained within S[start:end]. Optional | arguments start and end are interpreted as in slice notation. | | Raises ValueError when the substring is not found. | | isalnum(self, /) | Return True if the string is an alpha-numeric string, False otherwise. | | A string is alpha-numeric if all characters in the string are alpha-numeric and | there is at least one character in the string. | | isalpha(self, /) | Return True if the string is an alphabetic string, False otherwise. | | A string is alphabetic if all characters in the string are alphabetic and there | is at least one character in the string. | | isascii(self, /) | Return True if all characters in the string are ASCII, False otherwise. | | ASCII characters have code points in the range U+0000-U+007F. | Empty string is ASCII too. | | isdecimal(self, /) | Return True if the string is a decimal string, False otherwise. | | A string is a decimal string if all characters in the string are decimal and | there is at least one character in the string. | | isdigit(self, /) | Return True if the string is a digit string, False otherwise. | | A string is a digit string if all characters in the string are digits and there | is at least one character in the string. | | isidentifier(self, /) | Return True if the string is a valid Python identifier, False otherwise. | | Call keyword.iskeyword(s) to test whether string s is a reserved identifier, | such as "def" or "class". | | islower(self, /) | Return True if the string is a lowercase string, False otherwise. | | A string is lowercase if all cased characters in the string are lowercase and | there is at least one cased character in the string. | | isnumeric(self, /) | Return True if the string is a numeric string, False otherwise. | | A string is numeric if all characters in the string are numeric and there is at | least one character in the string. | | isprintable(self, /) | Return True if the string is printable, False otherwise. | | A string is printable if all of its characters are considered printable in | repr() or if it is empty. | | isspace(self, /) | Return True if the string is a whitespace string, False otherwise. | | A string is whitespace if all characters in the string are whitespace and there | is at least one character in the string. | | istitle(self, /) | Return True if the string is a title-cased string, False otherwise. | | In a title-cased string, upper- and title-case characters may only | follow uncased characters and lowercase characters only cased ones. | | isupper(self, /) | Return True if the string is an uppercase string, False otherwise. | | A string is uppercase if all cased characters in the string are uppercase and | there is at least one cased character in the string. | | join(self, iterable, /) | Concatenate any number of strings. | | The string whose method is called is inserted in between each given string. | The result is returned as a new string. | | Example: '.'.join(['ab', 'pq', 'rs']) -> 'ab.pq.rs' | | ljust(self, width, fillchar=' ', /) | Return a left-justified string of length width. | | Padding is done using the specified fill character (default is a space). | | lower(self, /) | Return a copy of the string converted to lowercase. | | lstrip(self, chars=None, /) | Return a copy of the string with leading whitespace removed. | | If chars is given and not None, remove characters in chars instead. | | partition(self, sep, /) | Partition the string into three parts using the given separator. | | This will search for the separator in the string. If the separator is found, | returns a 3-tuple containing the part before the separator, the separator | itself, and the part after it. | | If the separator is not found, returns a 3-tuple containing the original string | and two empty strings. | | removeprefix(self, prefix, /) | Return a str with the given prefix string removed if present. | | If the string starts with the prefix string, return string[len(prefix):]. | Otherwise, return a copy of the original string. | | removesuffix(self, suffix, /) | Return a str with the given suffix string removed if present. | | If the string ends with the suffix string and that suffix is not empty, | return string[:-len(suffix)]. Otherwise, return a copy of the original | string. | | replace(self, old, new, count=-1, /) | Return a copy with all occurrences of substring old replaced by new. | | count | Maximum number of occurrences to replace. | -1 (the default value) means replace all occurrences. | | If the optional argument count is given, only the first count occurrences are | replaced. | | rfind(...) | S.rfind(sub[, start[, end]]) -> int | | Return the highest index in S where substring sub is found, | such that sub is contained within S[start:end]. Optional | arguments start and end are interpreted as in slice notation. | | Return -1 on failure. | | rindex(...) | S.rindex(sub[, start[, end]]) -> int | | Return the highest index in S where substring sub is found, | such that sub is contained within S[start:end]. Optional | arguments start and end are interpreted as in slice notation. | | Raises ValueError when the substring is not found. | | rjust(self, width, fillchar=' ', /) | Return a right-justified string of length width. | | Padding is done using the specified fill character (default is a space). | | rpartition(self, sep, /) | Partition the string into three parts using the given separator. | | This will search for the separator in the string, starting at the end. If | the separator is found, returns a 3-tuple containing the part before the | separator, the separator itself, and the part after it. | | If the separator is not found, returns a 3-tuple containing two empty strings | and the original string. | | rsplit(self, /, sep=None, maxsplit=-1) | Return a list of the substrings in the string, using sep as the separator string. | | sep | The separator used to split the string. | | When set to None (the default value), will split on any whitespace | character (including \\n \\r \\t \\f and spaces) and will discard | empty strings from the result. | maxsplit | Maximum number of splits (starting from the left). | -1 (the default value) means no limit. | | Splitting starts at the end of the string and works to the front. | | rstrip(self, chars=None, /) | Return a copy of the string with trailing whitespace removed. | | If chars is given and not None, remove characters in chars instead. | | split(self, /, sep=None, maxsplit=-1) | Return a list of the substrings in the string, using sep as the separator string. | | sep | The separator used to split the string. | | When set to None (the default value), will split on any whitespace | character (including \\n \\r \\t \\f and spaces) and will discard | empty strings from the result. | maxsplit | Maximum number of splits (starting from the left). | -1 (the default value) means no limit. | | Note, str.split() is mainly useful for data that has been intentionally | delimited. With natural text that includes punctuation, consider using | the regular expression module. | | splitlines(self, /, keepends=False) | Return a list of the lines in the string, breaking at line boundaries. | | Line breaks are not included in the resulting list unless keepends is given and | true. | | startswith(...) | S.startswith(prefix[, start[, end]]) -> bool | | Return True if S starts with the specified prefix, False otherwise. | With optional start, test S beginning at that position. | With optional end, stop comparing S at that position. | prefix can also be a tuple of strings to try. | | strip(self, chars=None, /) | Return a copy of the string with leading and trailing whitespace removed. | | If chars is given and not None, remove characters in chars instead. | | swapcase(self, /) | Convert uppercase characters to lowercase and lowercase characters to uppercase. | | title(self, /) | Return a version of the string where each word is titlecased. | | More specifically, words start with uppercased characters and all remaining | cased characters have lower case. | | translate(self, table, /) | Replace each character in the string using the given translation table. | | table | Translation table, which must be a mapping of Unicode ordinals to | Unicode ordinals, strings, or None. | | The table must implement lookup/indexing via __getitem__, for instance a | dictionary or list. If this operation raises LookupError, the character is | left untouched. Characters mapped to None are deleted. | | upper(self, /) | Return a copy of the string converted to uppercase. | | zfill(self, width, /) | Pad a numeric string with zeros on the left, to fill a field of the given width. | | The string is never truncated. | | ---------------------------------------------------------------------- | Static methods inherited from builtins.str: | | maketrans(...) | Return a translation table usable for str.translate(). | | If there is only one argument, it must be a dictionary mapping Unicode | ordinals (integers) or characters to Unicode ordinals, strings or None. | Character keys will be then converted to ordinals. | If there are two arguments, they must be strings of equal length, and | in the resulting dictionary, each character in x will be mapped to the | character at the same position in y. If there is a third argument, it | must be a string, whose characters will be mapped to None in the result. | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __abs__(self, /) | abs(self) | | __and__(self, value, /) | Return self&value. | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __bool__(self, /) | True if self else False | | __copy__(...) | | __deepcopy__(...) | | __divmod__(self, value, /) | Return divmod(self, value). | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. string_ = class bytes_(builtins.bytes, character) | A byte string. | | When used in arrays, this type strips trailing null bytes. | | :Character code: ``'S'`` | :Alias: `numpy.string_` | | Method resolution order: | bytes_ | builtins.bytes | character | flexible | generic | builtins.object | | Methods defined here: | | __eq__(self, value, /) | Return self==value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __le__(self, value, /) | Return self<=value. | | __lt__(self, value, /) | Return self copy of B | | Return a copy of B with only its first character capitalized (ASCII) | and the rest lower-cased. | | center(self, width, fillchar=b' ', /) | Return a centered string of length width. | | Padding is done using the specified fill character. | | count(...) | B.count(sub[, start[, end]]) -> int | | Return the number of non-overlapping occurrences of subsection sub in | bytes B[start:end]. Optional arguments start and end are interpreted | as in slice notation. | | decode(self, /, encoding='utf-8', errors='strict') | Decode the bytes using the codec registered for encoding. | | encoding | The encoding with which to decode the bytes. | errors | The error handling scheme to use for the handling of decoding errors. | The default is 'strict' meaning that decoding errors raise a | UnicodeDecodeError. Other possible values are 'ignore' and 'replace' | as well as any other name registered with codecs.register_error that | can handle UnicodeDecodeErrors. | | endswith(...) | B.endswith(suffix[, start[, end]]) -> bool | | Return True if B ends with the specified suffix, False otherwise. | With optional start, test B beginning at that position. | With optional end, stop comparing B at that position. | suffix can also be a tuple of bytes to try. | | expandtabs(self, /, tabsize=8) | Return a copy where all tab characters are expanded using spaces. | | If tabsize is not given, a tab size of 8 characters is assumed. | | find(...) | B.find(sub[, start[, end]]) -> int | | Return the lowest index in B where subsection sub is found, | such that sub is contained within B[start,end]. Optional | arguments start and end are interpreted as in slice notation. | | Return -1 on failure. | | hex(...) | Create a string of hexadecimal numbers from a bytes object. | | sep | An optional single character or byte to separate hex bytes. | bytes_per_sep | How many bytes between separators. Positive values count from the | right, negative values count from the left. | | Example: | >>> value = b'\xb9\x01\xef' | >>> value.hex() | 'b901ef' | >>> value.hex(':') | 'b9:01:ef' | >>> value.hex(':', 2) | 'b9:01ef' | >>> value.hex(':', -2) | 'b901:ef' | | index(...) | B.index(sub[, start[, end]]) -> int | | Return the lowest index in B where subsection sub is found, | such that sub is contained within B[start,end]. Optional | arguments start and end are interpreted as in slice notation. | | Raises ValueError when the subsection is not found. | | isalnum(...) | B.isalnum() -> bool | | Return True if all characters in B are alphanumeric | and there is at least one character in B, False otherwise. | | isalpha(...) | B.isalpha() -> bool | | Return True if all characters in B are alphabetic | and there is at least one character in B, False otherwise. | | isascii(...) | B.isascii() -> bool | | Return True if B is empty or all characters in B are ASCII, | False otherwise. | | isdigit(...) | B.isdigit() -> bool | | Return True if all characters in B are digits | and there is at least one character in B, False otherwise. | | islower(...) | B.islower() -> bool | | Return True if all cased characters in B are lowercase and there is | at least one cased character in B, False otherwise. | | isspace(...) | B.isspace() -> bool | | Return True if all characters in B are whitespace | and there is at least one character in B, False otherwise. | | istitle(...) | B.istitle() -> bool | | Return True if B is a titlecased string and there is at least one | character in B, i.e. uppercase characters may only follow uncased | characters and lowercase characters only cased ones. Return False | otherwise. | | isupper(...) | B.isupper() -> bool | | Return True if all cased characters in B are uppercase and there is | at least one cased character in B, False otherwise. | | join(self, iterable_of_bytes, /) | Concatenate any number of bytes objects. | | The bytes whose method is called is inserted in between each pair. | | The result is returned as a new bytes object. | | Example: b'.'.join([b'ab', b'pq', b'rs']) -> b'ab.pq.rs'. | | ljust(self, width, fillchar=b' ', /) | Return a left-justified string of length width. | | Padding is done using the specified fill character. | | lower(...) | B.lower() -> copy of B | | Return a copy of B with all ASCII characters converted to lowercase. | | lstrip(self, bytes=None, /) | Strip leading bytes contained in the argument. | | If the argument is omitted or None, strip leading ASCII whitespace. | | partition(self, sep, /) | Partition the bytes into three parts using the given separator. | | This will search for the separator sep in the bytes. If the separator is found, | returns a 3-tuple containing the part before the separator, the separator | itself, and the part after it. | | If the separator is not found, returns a 3-tuple containing the original bytes | object and two empty bytes objects. | | removeprefix(self, prefix, /) | Return a bytes object with the given prefix string removed if present. | | If the bytes starts with the prefix string, return bytes[len(prefix):]. | Otherwise, return a copy of the original bytes. | | removesuffix(self, suffix, /) | Return a bytes object with the given suffix string removed if present. | | If the bytes ends with the suffix string and that suffix is not empty, | return bytes[:-len(prefix)]. Otherwise, return a copy of the original | bytes. | | replace(self, old, new, count=-1, /) | Return a copy with all occurrences of substring old replaced by new. | | count | Maximum number of occurrences to replace. | -1 (the default value) means replace all occurrences. | | If the optional argument count is given, only the first count occurrences are | replaced. | | rfind(...) | B.rfind(sub[, start[, end]]) -> int | | Return the highest index in B where subsection sub is found, | such that sub is contained within B[start,end]. Optional | arguments start and end are interpreted as in slice notation. | | Return -1 on failure. | | rindex(...) | B.rindex(sub[, start[, end]]) -> int | | Return the highest index in B where subsection sub is found, | such that sub is contained within B[start,end]. Optional | arguments start and end are interpreted as in slice notation. | | Raise ValueError when the subsection is not found. | | rjust(self, width, fillchar=b' ', /) | Return a right-justified string of length width. | | Padding is done using the specified fill character. | | rpartition(self, sep, /) | Partition the bytes into three parts using the given separator. | | This will search for the separator sep in the bytes, starting at the end. If | the separator is found, returns a 3-tuple containing the part before the | separator, the separator itself, and the part after it. | | If the separator is not found, returns a 3-tuple containing two empty bytes | objects and the original bytes object. | | rsplit(self, /, sep=None, maxsplit=-1) | Return a list of the sections in the bytes, using sep as the delimiter. | | sep | The delimiter according which to split the bytes. | None (the default value) means split on ASCII whitespace characters | (space, tab, return, newline, formfeed, vertical tab). | maxsplit | Maximum number of splits to do. | -1 (the default value) means no limit. | | Splitting is done starting at the end of the bytes and working to the front. | | rstrip(self, bytes=None, /) | Strip trailing bytes contained in the argument. | | If the argument is omitted or None, strip trailing ASCII whitespace. | | split(self, /, sep=None, maxsplit=-1) | Return a list of the sections in the bytes, using sep as the delimiter. | | sep | The delimiter according which to split the bytes. | None (the default value) means split on ASCII whitespace characters | (space, tab, return, newline, formfeed, vertical tab). | maxsplit | Maximum number of splits to do. | -1 (the default value) means no limit. | | splitlines(self, /, keepends=False) | Return a list of the lines in the bytes, breaking at line boundaries. | | Line breaks are not included in the resulting list unless keepends is given and | true. | | startswith(...) | B.startswith(prefix[, start[, end]]) -> bool | | Return True if B starts with the specified prefix, False otherwise. | With optional start, test B beginning at that position. | With optional end, stop comparing B at that position. | prefix can also be a tuple of bytes to try. | | strip(self, bytes=None, /) | Strip leading and trailing bytes contained in the argument. | | If the argument is omitted or None, strip leading and trailing ASCII whitespace. | | swapcase(...) | B.swapcase() -> copy of B | | Return a copy of B with uppercase ASCII characters converted | to lowercase ASCII and vice versa. | | title(...) | B.title() -> copy of B | | Return a titlecased version of B, i.e. ASCII words start with uppercase | characters, all remaining cased characters have lowercase. | | translate(self, table, /, delete=b'') | Return a copy with each character mapped by the given translation table. | | table | Translation table, which must be a bytes object of length 256. | | All characters occurring in the optional argument delete are removed. | The remaining characters are mapped through the given translation table. | | upper(...) | B.upper() -> copy of B | | Return a copy of B with all ASCII characters converted to uppercase. | | zfill(self, width, /) | Pad a numeric string with zeros on the left, to fill a field of the given width. | | The original string is never truncated. | | ---------------------------------------------------------------------- | Class methods inherited from builtins.bytes: | | fromhex(string, /) from builtins.type | Create a bytes object from a string of hexadecimal numbers. | | Spaces between two numbers are accepted. | Example: bytes.fromhex('B9 01EF') -> b'\\xb9\\x01\\xef'. | | ---------------------------------------------------------------------- | Static methods inherited from builtins.bytes: | | maketrans(frm, to, /) | Return a translation table useable for the bytes or bytearray translate method. | | The returned table will be one where each byte in frm is mapped to the byte at | the same position in to. | | The bytes objects frm and to must be of the same length. | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __abs__(self, /) | abs(self) | | __and__(self, value, /) | Return self&value. | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __bool__(self, /) | True if self else False | | __copy__(...) | | __deepcopy__(...) | | __divmod__(self, value, /) | Return divmod(self, value). | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __format__(...) | NumPy array scalar formatter | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. ### class timedelta64 | A timedelta stored as a 64-bit integer. | | See :ref:`arrays.datetime` for more information. | | :Character code: ``'m'`` | | Method resolution order: | timedelta64 | signedinteger | integer | number | generic | builtins.object | | Methods defined here: | | __eq__(self, value, /) | Return self==value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __le__(self, value, /) | Return self<=value. | | __lt__(self, value, /) | Return self>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. ubyte = class uint8(unsignedinteger) | Unsigned integer type, compatible with C ``unsigned char``. | | :Character code: ``'B'`` | :Canonical name: `numpy.ubyte` | :Alias on this platform (Linux x86_64): `numpy.uint8`: 8-bit unsigned integer (``0`` to ``255``). | | Method resolution order: | uint8 | unsignedinteger | integer | number | generic | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __and__(self, value, /) | Return self&value. | | __bool__(self, /) | True if self else False | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __index__(self, /) | Return self converted to an integer, if self is suitable for use as an index into a list. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __le__(self, value, /) | Return self<=value. | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __str__(self, /) | Return str(self). | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from integer: | | __round__(...) | | ---------------------------------------------------------------------- | Data descriptors inherited from integer: | | denominator | denominator of value (1) | | numerator | numerator of value (the value itself) | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __copy__(...) | | __deepcopy__(...) | | __format__(...) | NumPy array scalar formatter | | __getitem__(self, key, /) | Return self[key]. | | __reduce__(...) | Helper for pickle. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. ### class ufunc | Functions that operate element by element on whole arrays. | | To see the documentation for a specific ufunc, use `info`. For | example, ``np.info(np.sin)``. Because ufuncs are written in C | (for speed) and linked into Python with NumPy's ufunc facility, | Python's help() function finds this page whenever help() is called | on a ufunc. | | A detailed explanation of ufuncs can be found in the docs for :ref:`ufuncs`. | | **Calling ufuncs:** ``op(*x[, out], where=True, **kwargs)`` | | Apply `op` to the arguments `*x` elementwise, broadcasting the arguments. | | The broadcasting rules are: | | * Dimensions of length 1 may be prepended to either array. | * Arrays may be repeated along dimensions of length 1. | | Parameters | ---------- | *x : array_like | Input arrays. | out : ndarray, None, or tuple of ndarray and None, optional | Alternate array object(s) in which to put the result; if provided, it | must have a shape that the inputs broadcast to. A tuple of arrays | (possible only as a keyword argument) must have length equal to the | number of outputs; use None for uninitialized outputs to be | allocated by the ufunc. | where : array_like, optional | This condition is broadcast over the input. At locations where the | condition is True, the `out` array will be set to the ufunc result. | Elsewhere, the `out` array will retain its original value. | Note that if an uninitialized `out` array is created via the default | ``out=None``, locations within it where the condition is False will | remain uninitialized. | **kwargs | For other keyword-only arguments, see the :ref:`ufunc docs `. | | Returns | ------- | r : ndarray or tuple of ndarray | `r` will have the shape that the arrays in `x` broadcast to; if `out` is | provided, it will be returned. If not, `r` will be allocated and | may contain uninitialized values. If the function has more than one | output, then the result will be a tuple of arrays. | | Methods defined here: | | __call__(self, /, *args, **kwargs) | Call self as a function. | | __repr__(self, /) | Return repr(self). | | __str__(self, /) | Return str(self). | | accumulate(...) | accumulate(array, axis=0, dtype=None, out=None) | | Accumulate the result of applying the operator to all elements. | | For a one-dimensional array, accumulate produces results equivalent to:: | | r = np.empty(len(A)) | t = op.identity # op = the ufunc being applied to A's elements | for i in range(len(A)): | t = op(t, A[i]) | r[i] = t | return r | | For example, add.accumulate() is equivalent to np.cumsum(). | | For a multi-dimensional array, accumulate is applied along only one | axis (axis zero by default; see Examples below) so repeated use is | necessary if one wants to accumulate over multiple axes. | | Parameters | ---------- | array : array_like | The array to act on. | axis : int, optional | The axis along which to apply the accumulation; default is zero. | dtype : data-type code, optional | The data-type used to represent the intermediate results. Defaults | to the data-type of the output array if such is provided, or the | the data-type of the input array if no output array is provided. | out : ndarray, None, or tuple of ndarray and None, optional | A location into which the result is stored. If not provided or None, | a freshly-allocated array is returned. For consistency with | ``ufunc.__call__``, if given as a keyword, this may be wrapped in a | 1-element tuple. | | .. versionchanged:: 1.13.0 | Tuples are allowed for keyword argument. | | Returns | ------- | r : ndarray | The accumulated values. If `out` was supplied, `r` is a reference to | `out`. | | Examples | -------- | 1-D array examples: | | >>> np.add.accumulate([2, 3, 5]) | array([ 2, 5, 10]) | >>> np.multiply.accumulate([2, 3, 5]) | array([ 2, 6, 30]) | | 2-D array examples: | | >>> I = [np.eye(2)](https://www.chedong.com/phpMan.php/man/np.eye/2/markdown) | >>> I | array([[1., 0.], | [0., 1.]]) | | Accumulate along axis 0 (rows), down columns: | | >>> np.add.accumulate(I, 0) | array([[1., 0.], | [1., 1.]]) | >>> np.add.accumulate(I) # no axis specified = axis zero | array([[1., 0.], | [1., 1.]]) | | Accumulate along axis 1 (columns), through rows: | | >>> np.add.accumulate(I, 1) | array([[1., 1.], | [0., 1.]]) | | at(...) | at(a, indices, b=None, /) | | Performs unbuffered in place operation on operand 'a' for elements | specified by 'indices'. For addition ufunc, this method is equivalent to | ``a[indices] += b``, except that results are accumulated for elements that | are indexed more than once. For example, ``a[[0,0]] += 1`` will only | increment the first element once because of buffering, whereas | ``add.at(a, [0,0], 1)`` will increment the first element twice. | | .. versionadded:: 1.8.0 | | Parameters | ---------- | a : array_like | The array to perform in place operation on. | indices : array_like or tuple | Array like index object or slice object for indexing into first | operand. If first operand has multiple dimensions, indices can be a | tuple of array like index objects or slice objects. | b : array_like | Second operand for ufuncs requiring two operands. Operand must be | broadcastable over first operand after indexing or slicing. | | Examples | -------- | Set items 0 and 1 to their negative values: | | >>> a = np.array([1, 2, 3, 4]) | >>> np.negative.at(a, [0, 1]) | >>> a | array([-1, -2, 3, 4]) | | Increment items 0 and 1, and increment item 2 twice: | | >>> a = np.array([1, 2, 3, 4]) | >>> np.add.at(a, [0, 1, 2, 2], 1) | >>> a | array([2, 3, 5, 4]) | | Add items 0 and 1 in first array to second array, | and store results in first array: | | >>> a = np.array([1, 2, 3, 4]) | >>> b = np.array([1, 2]) | >>> np.add.at(a, [0, 1], b) | >>> a | array([2, 4, 3, 4]) | | outer(...) | outer(A, B, /, **kwargs) | | Apply the ufunc `op` to all pairs (a, b) with a in `A` and b in `B`. | | Let ``M = A.ndim``, ``N = B.ndim``. Then the result, `C`, of | ``op.outer(A, B)`` is an array of dimension M + N such that: | | .. math:: C[i_0, ..., i_{M-1}, j_0, ..., j_{N-1}] = | op(A[i_0, ..., i_{M-1}], B[j_0, ..., j_{N-1}]) | | For `A` and `B` one-dimensional, this is equivalent to:: | | r = empty(len(A),len(B)) | for i in range(len(A)): | for j in range(len(B)): | r[i,j] = op(A[i], B[j]) # op = ufunc in question | | Parameters | ---------- | A : array_like | First array | B : array_like | Second array | kwargs : any | Arguments to pass on to the ufunc. Typically `dtype` or `out`. | See `ufunc` for a comprehensive overview of all available arguments. | | Returns | ------- | r : ndarray | Output array | | See Also | -------- | numpy.outer : A less powerful version of ``np.multiply.outer`` | that `ravel`\ s all inputs to 1D. This exists | primarily for compatibility with old code. | | tensordot : ``np.tensordot(a, b, axes=((), ()))`` and | ``np.multiply.outer(a, b)`` behave same for all | dimensions of a and b. | | Examples | -------- | >>> np.multiply.outer([1, 2, 3], [4, 5, 6]) | array([[ 4, 5, 6], | [ 8, 10, 12], | [12, 15, 18]]) | | A multi-dimensional example: | | >>> A = np.array([[1, 2, 3], [4, 5, 6]]) | >>> A.shape | (2, 3) | >>> B = np.array([[1, 2, 3, 4]]) | >>> B.shape | (1, 4) | >>> C = np.multiply.outer(A, B) | >>> C.shape; C | (2, 3, 1, 4) | array([[[[ 1, 2, 3, 4]], | [[ 2, 4, 6, 8]], | [[ 3, 6, 9, 12]]], | [[[ 4, 8, 12, 16]], | [[ 5, 10, 15, 20]], | [[ 6, 12, 18, 24]]]]) | | reduce(...) | reduce(array, axis=0, dtype=None, out=None, keepdims=False, initial=, where=True) | | Reduces `array`'s dimension by one, by applying ufunc along one axis. | | Let :math:`array.shape = (N_0, ..., N_i, ..., N_{M-1})`. Then | :math:`ufunc.reduce(array, axis=i)[k_0, ..,k_{i-1}, k_{i+1}, .., k_{M-1}]` = | the result of iterating `j` over :math:`range(N_i)`, cumulatively applying | ufunc to each :math:`array[k_0, ..,k_{i-1}, j, k_{i+1}, .., k_{M-1}]`. | For a one-dimensional array, reduce produces results equivalent to: | :: | | r = op.identity # op = ufunc | for i in range(len(A)): | r = op(r, A[i]) | return r | | For example, add.reduce() is equivalent to sum(). | | Parameters | ---------- | array : array_like | The array to act on. | axis : None or int or tuple of ints, optional | Axis or axes along which a reduction is performed. | The default (`axis` = 0) is perform a reduction over the first | dimension of the input array. `axis` may be negative, in | which case it counts from the last to the first axis. | | .. versionadded:: 1.7.0 | | If this is None, a reduction is performed over all the axes. | If this is a tuple of ints, a reduction is performed on multiple | axes, instead of a single axis or all the axes as before. | | For operations which are either not commutative or not associative, | doing a reduction over multiple axes is not well-defined. The | ufuncs do not currently raise an exception in this case, but will | likely do so in the future. | dtype : data-type code, optional | The type used to represent the intermediate results. Defaults | to the data-type of the output array if this is provided, or | the data-type of the input array if no output array is provided. | out : ndarray, None, or tuple of ndarray and None, optional | A location into which the result is stored. If not provided or None, | a freshly-allocated array is returned. For consistency with | ``ufunc.__call__``, if given as a keyword, this may be wrapped in a | 1-element tuple. | | .. versionchanged:: 1.13.0 | Tuples are allowed for keyword argument. | keepdims : bool, optional | If this is set to True, the axes which are reduced are left | in the result as dimensions with size one. With this option, | the result will broadcast correctly against the original `array`. | | .. versionadded:: 1.7.0 | initial : scalar, optional | The value with which to start the reduction. | If the ufunc has no identity or the dtype is object, this defaults | to None - otherwise it defaults to ufunc.identity. | If ``None`` is given, the first element of the reduction is used, | and an error is thrown if the reduction is empty. | | .. versionadded:: 1.15.0 | | where : array_like of bool, optional | A boolean array which is broadcasted to match the dimensions | of `array`, and selects elements to include in the reduction. Note | that for ufuncs like ``minimum`` that do not have an identity | defined, one has to pass in also ``initial``. | | .. versionadded:: 1.17.0 | | Returns | ------- | r : ndarray | The reduced array. If `out` was supplied, `r` is a reference to it. | | Examples | -------- | >>> np.multiply.reduce([2,3,5]) | 30 | | A multi-dimensional array example: | | >>> X = [np.arange(8)](https://www.chedong.com/phpMan.php/man/np.arange/8/markdown).reshape((2,2,2)) | >>> X | array([[[0, 1], | [2, 3]], | [[4, 5], | [6, 7]]]) | >>> np.add.reduce(X, 0) | array([[ 4, 6], | [ 8, 10]]) | >>> np.add.reduce(X) # confirm: default axis value is 0 | array([[ 4, 6], | [ 8, 10]]) | >>> np.add.reduce(X, 1) | array([[ 2, 4], | [10, 12]]) | >>> np.add.reduce(X, 2) | array([[ 1, 5], | [ 9, 13]]) | | You can use the ``initial`` keyword argument to initialize the reduction | with a different value, and ``where`` to select specific elements to include: | | >>> np.add.reduce([10], initial=5) | 15 | >>> np.add.reduce(np.ones((2, 2, 2)), axis=(0, 2), initial=10) | array([14., 14.]) | >>> a = np.array([10., np.nan, 10]) | >>> np.add.reduce(a, where=~np.isnan(a)) | 20.0 | | Allows reductions of empty arrays where they would normally fail, i.e. | for ufuncs without an identity. | | >>> np.minimum.reduce([], initial=np.inf) | inf | >>> np.minimum.reduce([[1., 2.], [3., 4.]], initial=10., where=[True, False]) | array([ 1., 10.]) | >>> np.minimum.reduce([]) | Traceback (most recent call last): | ... | ValueError: zero-size array to reduction operation minimum which has no identity | | reduceat(...) | reduceat(array, indices, axis=0, dtype=None, out=None) | | Performs a (local) reduce with specified slices over a single axis. | | For i in ``range(len(indices))``, `reduceat` computes | ``ufunc.reduce(array[indices[i]:indices[i+1]])``, which becomes the i-th | generalized "row" parallel to `axis` in the final result (i.e., in a | 2-D array, for example, if `axis = 0`, it becomes the i-th row, but if | `axis = 1`, it becomes the i-th column). There are three exceptions to this: | | * when ``i = len(indices) - 1`` (so for the last index), | ``indices[i+1] = array.shape[axis]``. | * if ``indices[i] >= indices[i + 1]``, the i-th generalized "row" is | simply ``array[indices[i]]``. | * if ``indices[i] >= len(array)`` or ``indices[i] < 0``, an error is raised. | | The shape of the output depends on the size of `indices`, and may be | larger than `array` (this happens if ``len(indices) > array.shape[axis]``). | | Parameters | ---------- | array : array_like | The array to act on. | indices : array_like | Paired indices, comma separated (not colon), specifying slices to | reduce. | axis : int, optional | The axis along which to apply the reduceat. | dtype : data-type code, optional | The type used to represent the intermediate results. Defaults | to the data type of the output array if this is provided, or | the data type of the input array if no output array is provided. | out : ndarray, None, or tuple of ndarray and None, optional | A location into which the result is stored. If not provided or None, | a freshly-allocated array is returned. For consistency with | ``ufunc.__call__``, if given as a keyword, this may be wrapped in a | 1-element tuple. | | .. versionchanged:: 1.13.0 | Tuples are allowed for keyword argument. | | Returns | ------- | r : ndarray | The reduced values. If `out` was supplied, `r` is a reference to | `out`. | | Notes | ----- | A descriptive example: | | If `array` is 1-D, the function `ufunc.accumulate(array)` is the same as | ``ufunc.reduceat(array, indices)[::2]`` where `indices` is | ``range(len(array) - 1)`` with a zero placed | in every other element: | ``indices = zeros(2 * len(array) - 1)``, | ``indices[[1::2](https://www.chedong.com/phpMan.php/perldoc/1%3A%3A2/markdown)] = range(1, len(array))``. | | Don't be fooled by this attribute's name: `reduceat(array)` is not | necessarily smaller than `array`. | | Examples | -------- | To take the running sum of four successive values: | | >>> np.add.reduceat([np.arange(8)](https://www.chedong.com/phpMan.php/man/np.arange/8/markdown),[0,4, 1,5, 2,6, 3,7])[::2] | array([ 6, 10, 14, 18]) | | A 2-D example: | | >>> x = np.linspace(0, 15, 16).reshape(4,4) | >>> x | array([[ 0., 1., 2., 3.], | [ 4., 5., 6., 7.], | [ 8., 9., 10., 11.], | [12., 13., 14., 15.]]) | | :: | | # reduce such that the result has the following five rows: | # [row1 + row2 + row3] | # [row4] | # [row2] | # [row3] | # [row1 + row2 + row3 + row4] | | >>> np.add.reduceat(x, [0, 3, 1, 2, 0]) | array([[12., 15., 18., 21.], | [12., 13., 14., 15.], | [ 4., 5., 6., 7.], | [ 8., 9., 10., 11.], | [24., 28., 32., 36.]]) | | :: | | # reduce such that result has the following two columns: | # [col1 * col2 * col3, col4] | | >>> np.multiply.reduceat(x, [0, 3], 1) | array([[ 0., 3.], | [ 120., 7.], | [ 720., 11.], | [2184., 15.]]) | | ---------------------------------------------------------------------- | Data descriptors defined here: | | identity | The identity value. | | Data attribute containing the identity element for the ufunc, if it has one. | If it does not, the attribute value is None. | | Examples | -------- | >>> np.add.identity | 0 | >>> np.multiply.identity | 1 | >>> np.power.identity | 1 | >>> print(np.exp.identity) | None | | nargs | The number of arguments. | | Data attribute containing the number of arguments the ufunc takes, including | optional ones. | | Notes | ----- | Typically this value will be one more than what you might expect because all | ufuncs take the optional "out" argument. | | Examples | -------- | >>> np.add.nargs | 3 | >>> np.multiply.nargs | 3 | >>> np.power.nargs | 3 | >>> np.exp.nargs | 2 | | nin | The number of inputs. | | Data attribute containing the number of arguments the ufunc treats as input. | | Examples | -------- | >>> np.add.nin | 2 | >>> np.multiply.nin | 2 | >>> np.power.nin | 2 | >>> np.exp.nin | 1 | | nout | The number of outputs. | | Data attribute containing the number of arguments the ufunc treats as output. | | Notes | ----- | Since all ufuncs can take output arguments, this will always be (at least) 1. | | Examples | -------- | >>> np.add.nout | 1 | >>> np.multiply.nout | 1 | >>> np.power.nout | 1 | >>> np.exp.nout | 1 | | ntypes | The number of types. | | The number of numerical NumPy types - of which there are 18 total - on which | the ufunc can operate. | | See Also | -------- | numpy.ufunc.types | | Examples | -------- | >>> np.add.ntypes | 18 | >>> np.multiply.ntypes | 18 | >>> np.power.ntypes | 17 | >>> np.exp.ntypes | 7 | >>> np.remainder.ntypes | 14 | | signature | Definition of the core elements a generalized ufunc operates on. | | The signature determines how the dimensions of each input/output array | are split into core and loop dimensions: | | 1. Each dimension in the signature is matched to a dimension of the | corresponding passed-in array, starting from the end of the shape tuple. | 2. Core dimensions assigned to the same label in the signature must have | exactly matching sizes, no broadcasting is performed. | 3. The core dimensions are removed from all inputs and the remaining | dimensions are broadcast together, defining the loop dimensions. | | Notes | ----- | Generalized ufuncs are used internally in many linalg functions, and in | the testing suite; the examples below are taken from these. | For ufuncs that operate on scalars, the signature is None, which is | equivalent to '()' for every argument. | | Examples | -------- | >>> np.core.umath_tests.matrix_multiply.signature | '(m,n),(n,p)->(m,p)' | >>> np.linalg._umath_linalg.det.signature | '(m,m)->()' | >>> np.add.signature is None | True # equivalent to '(),()->()' | | types | Returns a list with types grouped input->output. | | Data attribute listing the data-type "Domain-Range" groupings the ufunc can | deliver. The data-types are given using the character codes. | | See Also | -------- | numpy.ufunc.ntypes | | Examples | -------- | >>> np.add.types | ['??->?', 'bb->b', 'BB->B', 'hh->h', 'HH->H', 'ii->i', 'II->I', 'll->l', | 'LL->L', 'qq->q', 'QQ->Q', 'ff->f', 'dd->d', 'gg->g', 'FF->F', 'DD->D', | 'GG->G', 'OO->O'] | | >>> np.multiply.types | ['??->?', 'bb->b', 'BB->B', 'hh->h', 'HH->H', 'ii->i', 'II->I', 'll->l', | 'LL->L', 'qq->q', 'QQ->Q', 'ff->f', 'dd->d', 'gg->g', 'FF->F', 'DD->D', | 'GG->G', 'OO->O'] | | >>> np.power.types | ['bb->b', 'BB->B', 'hh->h', 'HH->H', 'ii->i', 'II->I', 'll->l', 'LL->L', | 'qq->q', 'QQ->Q', 'ff->f', 'dd->d', 'gg->g', 'FF->F', 'DD->D', 'GG->G', | 'OO->O'] | | >>> np.exp.types | ['f->f', 'd->d', 'g->g', 'F->F', 'D->D', 'G->G', 'O->O'] | | >>> np.remainder.types | ['bb->b', 'BB->B', 'hh->h', 'HH->H', 'ii->i', 'II->I', 'll->l', 'LL->L', | 'qq->q', 'QQ->Q', 'ff->f', 'dd->d', 'gg->g', 'OO->O'] uint = class uint64(unsignedinteger) | Unsigned integer type, compatible with C ``unsigned long``. | | :Character code: ``'L'`` | :Canonical name: `numpy.uint` | :Alias on this platform (Linux x86_64): `numpy.uint64`: 64-bit unsigned integer (``0`` to ``18_446_744_073_709_551_615``). | :Alias on this platform (Linux x86_64): `numpy.uintp`: Unsigned integer large enough to fit pointer, compatible with C ``uintptr_t``. | | Method resolution order: | uint64 | unsignedinteger | integer | number | generic | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __and__(self, value, /) | Return self&value. | | __bool__(self, /) | True if self else False | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __index__(self, /) | Return self converted to an integer, if self is suitable for use as an index into a list. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __le__(self, value, /) | Return self<=value. | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __str__(self, /) | Return str(self). | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from integer: | | __round__(...) | | ---------------------------------------------------------------------- | Data descriptors inherited from integer: | | denominator | denominator of value (1) | | numerator | numerator of value (the value itself) | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __copy__(...) | | __deepcopy__(...) | | __format__(...) | NumPy array scalar formatter | | __getitem__(self, key, /) | Return self[key]. | | __reduce__(...) | Helper for pickle. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. uint0 = class uint64(unsignedinteger) | Unsigned integer type, compatible with C ``unsigned long``. | | :Character code: ``'L'`` | :Canonical name: `numpy.uint` | :Alias on this platform (Linux x86_64): `numpy.uint64`: 64-bit unsigned integer (``0`` to ``18_446_744_073_709_551_615``). | :Alias on this platform (Linux x86_64): `numpy.uintp`: Unsigned integer large enough to fit pointer, compatible with C ``uintptr_t``. | | Method resolution order: | uint64 | unsignedinteger | integer | number | generic | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __and__(self, value, /) | Return self&value. | | __bool__(self, /) | True if self else False | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __index__(self, /) | Return self converted to an integer, if self is suitable for use as an index into a list. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __le__(self, value, /) | Return self<=value. | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __str__(self, /) | Return str(self). | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from integer: | | __round__(...) | | ---------------------------------------------------------------------- | Data descriptors inherited from integer: | | denominator | denominator of value (1) | | numerator | numerator of value (the value itself) | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __copy__(...) | | __deepcopy__(...) | | __format__(...) | NumPy array scalar formatter | | __getitem__(self, key, /) | Return self[key]. | | __reduce__(...) | Helper for pickle. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. ### class uint16 | Unsigned integer type, compatible with C ``unsigned short``. | | :Character code: ``'H'`` | :Canonical name: `numpy.ushort` | :Alias on this platform (Linux x86_64): `numpy.uint16`: 16-bit unsigned integer (``0`` to ``65_535``). | | Method resolution order: | uint16 | unsignedinteger | integer | number | generic | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __and__(self, value, /) | Return self&value. | | __bool__(self, /) | True if self else False | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __index__(self, /) | Return self converted to an integer, if self is suitable for use as an index into a list. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __le__(self, value, /) | Return self<=value. | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __str__(self, /) | Return str(self). | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from integer: | | __round__(...) | | ---------------------------------------------------------------------- | Data descriptors inherited from integer: | | denominator | denominator of value (1) | | numerator | numerator of value (the value itself) | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __copy__(...) | | __deepcopy__(...) | | __format__(...) | NumPy array scalar formatter | | __getitem__(self, key, /) | Return self[key]. | | __reduce__(...) | Helper for pickle. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. ### class uint32 | Unsigned integer type, compatible with C ``unsigned int``. | | :Character code: ``'I'`` | :Canonical name: `numpy.uintc` | :Alias on this platform (Linux x86_64): `numpy.uint32`: 32-bit unsigned integer (``0`` to ``4_294_967_295``). | | Method resolution order: | uint32 | unsignedinteger | integer | number | generic | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __and__(self, value, /) | Return self&value. | | __bool__(self, /) | True if self else False | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __index__(self, /) | Return self converted to an integer, if self is suitable for use as an index into a list. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __le__(self, value, /) | Return self<=value. | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __str__(self, /) | Return str(self). | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from integer: | | __round__(...) | | ---------------------------------------------------------------------- | Data descriptors inherited from integer: | | denominator | denominator of value (1) | | numerator | numerator of value (the value itself) | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __copy__(...) | | __deepcopy__(...) | | __format__(...) | NumPy array scalar formatter | | __getitem__(self, key, /) | Return self[key]. | | __reduce__(...) | Helper for pickle. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. ### class uint64 | Unsigned integer type, compatible with C ``unsigned long``. | | :Character code: ``'L'`` | :Canonical name: `numpy.uint` | :Alias on this platform (Linux x86_64): `numpy.uint64`: 64-bit unsigned integer (``0`` to ``18_446_744_073_709_551_615``). | :Alias on this platform (Linux x86_64): `numpy.uintp`: Unsigned integer large enough to fit pointer, compatible with C ``uintptr_t``. | | Method resolution order: | uint64 | unsignedinteger | integer | number | generic | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __and__(self, value, /) | Return self&value. | | __bool__(self, /) | True if self else False | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __index__(self, /) | Return self converted to an integer, if self is suitable for use as an index into a list. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __le__(self, value, /) | Return self<=value. | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __str__(self, /) | Return str(self). | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from integer: | | __round__(...) | | ---------------------------------------------------------------------- | Data descriptors inherited from integer: | | denominator | denominator of value (1) | | numerator | numerator of value (the value itself) | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __copy__(...) | | __deepcopy__(...) | | __format__(...) | NumPy array scalar formatter | | __getitem__(self, key, /) | Return self[key]. | | __reduce__(...) | Helper for pickle. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. ### class uint8 | Unsigned integer type, compatible with C ``unsigned char``. | | :Character code: ``'B'`` | :Canonical name: `numpy.ubyte` | :Alias on this platform (Linux x86_64): `numpy.uint8`: 8-bit unsigned integer (``0`` to ``255``). | | Method resolution order: | uint8 | unsignedinteger | integer | number | generic | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __and__(self, value, /) | Return self&value. | | __bool__(self, /) | True if self else False | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __index__(self, /) | Return self converted to an integer, if self is suitable for use as an index into a list. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __le__(self, value, /) | Return self<=value. | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __str__(self, /) | Return str(self). | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from integer: | | __round__(...) | | ---------------------------------------------------------------------- | Data descriptors inherited from integer: | | denominator | denominator of value (1) | | numerator | numerator of value (the value itself) | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __copy__(...) | | __deepcopy__(...) | | __format__(...) | NumPy array scalar formatter | | __getitem__(self, key, /) | Return self[key]. | | __reduce__(...) | Helper for pickle. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. uintc = class uint32(unsignedinteger) | Unsigned integer type, compatible with C ``unsigned int``. | | :Character code: ``'I'`` | :Canonical name: `numpy.uintc` | :Alias on this platform (Linux x86_64): `numpy.uint32`: 32-bit unsigned integer (``0`` to ``4_294_967_295``). | | Method resolution order: | uint32 | unsignedinteger | integer | number | generic | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __and__(self, value, /) | Return self&value. | | __bool__(self, /) | True if self else False | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __index__(self, /) | Return self converted to an integer, if self is suitable for use as an index into a list. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __le__(self, value, /) | Return self<=value. | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __str__(self, /) | Return str(self). | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from integer: | | __round__(...) | | ---------------------------------------------------------------------- | Data descriptors inherited from integer: | | denominator | denominator of value (1) | | numerator | numerator of value (the value itself) | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __copy__(...) | | __deepcopy__(...) | | __format__(...) | NumPy array scalar formatter | | __getitem__(self, key, /) | Return self[key]. | | __reduce__(...) | Helper for pickle. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. uintp = class uint64(unsignedinteger) | Unsigned integer type, compatible with C ``unsigned long``. | | :Character code: ``'L'`` | :Canonical name: `numpy.uint` | :Alias on this platform (Linux x86_64): `numpy.uint64`: 64-bit unsigned integer (``0`` to ``18_446_744_073_709_551_615``). | :Alias on this platform (Linux x86_64): `numpy.uintp`: Unsigned integer large enough to fit pointer, compatible with C ``uintptr_t``. | | Method resolution order: | uint64 | unsignedinteger | integer | number | generic | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __and__(self, value, /) | Return self&value. | | __bool__(self, /) | True if self else False | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __index__(self, /) | Return self converted to an integer, if self is suitable for use as an index into a list. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __le__(self, value, /) | Return self<=value. | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __str__(self, /) | Return str(self). | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from integer: | | __round__(...) | | ---------------------------------------------------------------------- | Data descriptors inherited from integer: | | denominator | denominator of value (1) | | numerator | numerator of value (the value itself) | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __copy__(...) | | __deepcopy__(...) | | __format__(...) | NumPy array scalar formatter | | __getitem__(self, key, /) | Return self[key]. | | __reduce__(...) | Helper for pickle. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. ### class ulonglong | Signed integer type, compatible with C ``unsigned long long``. | | :Character code: ``'Q'`` | | Method resolution order: | ulonglong | unsignedinteger | integer | number | generic | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __and__(self, value, /) | Return self&value. | | __bool__(self, /) | True if self else False | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __index__(self, /) | Return self converted to an integer, if self is suitable for use as an index into a list. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __le__(self, value, /) | Return self<=value. | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __str__(self, /) | Return str(self). | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from integer: | | __round__(...) | | ---------------------------------------------------------------------- | Data descriptors inherited from integer: | | denominator | denominator of value (1) | | numerator | numerator of value (the value itself) | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __copy__(...) | | __deepcopy__(...) | | __format__(...) | NumPy array scalar formatter | | __getitem__(self, key, /) | Return self[key]. | | __reduce__(...) | Helper for pickle. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. unicode_ = class str_(builtins.str, character) | A unicode string. | | When used in arrays, this type strips trailing null codepoints. | | Unlike the builtin `str`, this supports the :ref:`python:bufferobjects`, exposing its | contents as UCS4: | | >>> m = memoryview(np.str_("abc")) | >>> m.format | '3w' | >>> m.tobytes() | b'a\x00\x00\x00b\x00\x00\x00c\x00\x00\x00' | | :Character code: ``'U'`` | :Alias: `numpy.unicode_` | | Method resolution order: | str_ | builtins.str | character | flexible | generic | builtins.object | | Methods defined here: | | __eq__(self, value, /) | Return self==value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __le__(self, value, /) | Return self<=value. | | __lt__(self, value, /) | Return self int | | Return the number of non-overlapping occurrences of substring sub in | string S[start:end]. Optional arguments start and end are | interpreted as in slice notation. | | encode(self, /, encoding='utf-8', errors='strict') | Encode the string using the codec registered for encoding. | | encoding | The encoding in which to encode the string. | errors | The error handling scheme to use for encoding errors. | The default is 'strict' meaning that encoding errors raise a | UnicodeEncodeError. Other possible values are 'ignore', 'replace' and | 'xmlcharrefreplace' as well as any other name registered with | codecs.register_error that can handle UnicodeEncodeErrors. | | endswith(...) | S.endswith(suffix[, start[, end]]) -> bool | | Return True if S ends with the specified suffix, False otherwise. | With optional start, test S beginning at that position. | With optional end, stop comparing S at that position. | suffix can also be a tuple of strings to try. | | expandtabs(self, /, tabsize=8) | Return a copy where all tab characters are expanded using spaces. | | If tabsize is not given, a tab size of 8 characters is assumed. | | find(...) | S.find(sub[, start[, end]]) -> int | | Return the lowest index in S where substring sub is found, | such that sub is contained within S[start:end]. Optional | arguments start and end are interpreted as in slice notation. | | Return -1 on failure. | | format(...) | S.format(*args, **kwargs) -> str | | Return a formatted version of S, using substitutions from args and kwargs. | The substitutions are identified by braces ('{' and '}'). | | format_map(...) | S.format_map(mapping) -> str | | Return a formatted version of S, using substitutions from mapping. | The substitutions are identified by braces ('{' and '}'). | | index(...) | S.index(sub[, start[, end]]) -> int | | Return the lowest index in S where substring sub is found, | such that sub is contained within S[start:end]. Optional | arguments start and end are interpreted as in slice notation. | | Raises ValueError when the substring is not found. | | isalnum(self, /) | Return True if the string is an alpha-numeric string, False otherwise. | | A string is alpha-numeric if all characters in the string are alpha-numeric and | there is at least one character in the string. | | isalpha(self, /) | Return True if the string is an alphabetic string, False otherwise. | | A string is alphabetic if all characters in the string are alphabetic and there | is at least one character in the string. | | isascii(self, /) | Return True if all characters in the string are ASCII, False otherwise. | | ASCII characters have code points in the range U+0000-U+007F. | Empty string is ASCII too. | | isdecimal(self, /) | Return True if the string is a decimal string, False otherwise. | | A string is a decimal string if all characters in the string are decimal and | there is at least one character in the string. | | isdigit(self, /) | Return True if the string is a digit string, False otherwise. | | A string is a digit string if all characters in the string are digits and there | is at least one character in the string. | | isidentifier(self, /) | Return True if the string is a valid Python identifier, False otherwise. | | Call keyword.iskeyword(s) to test whether string s is a reserved identifier, | such as "def" or "class". | | islower(self, /) | Return True if the string is a lowercase string, False otherwise. | | A string is lowercase if all cased characters in the string are lowercase and | there is at least one cased character in the string. | | isnumeric(self, /) | Return True if the string is a numeric string, False otherwise. | | A string is numeric if all characters in the string are numeric and there is at | least one character in the string. | | isprintable(self, /) | Return True if the string is printable, False otherwise. | | A string is printable if all of its characters are considered printable in | repr() or if it is empty. | | isspace(self, /) | Return True if the string is a whitespace string, False otherwise. | | A string is whitespace if all characters in the string are whitespace and there | is at least one character in the string. | | istitle(self, /) | Return True if the string is a title-cased string, False otherwise. | | In a title-cased string, upper- and title-case characters may only | follow uncased characters and lowercase characters only cased ones. | | isupper(self, /) | Return True if the string is an uppercase string, False otherwise. | | A string is uppercase if all cased characters in the string are uppercase and | there is at least one cased character in the string. | | join(self, iterable, /) | Concatenate any number of strings. | | The string whose method is called is inserted in between each given string. | The result is returned as a new string. | | Example: '.'.join(['ab', 'pq', 'rs']) -> 'ab.pq.rs' | | ljust(self, width, fillchar=' ', /) | Return a left-justified string of length width. | | Padding is done using the specified fill character (default is a space). | | lower(self, /) | Return a copy of the string converted to lowercase. | | lstrip(self, chars=None, /) | Return a copy of the string with leading whitespace removed. | | If chars is given and not None, remove characters in chars instead. | | partition(self, sep, /) | Partition the string into three parts using the given separator. | | This will search for the separator in the string. If the separator is found, | returns a 3-tuple containing the part before the separator, the separator | itself, and the part after it. | | If the separator is not found, returns a 3-tuple containing the original string | and two empty strings. | | removeprefix(self, prefix, /) | Return a str with the given prefix string removed if present. | | If the string starts with the prefix string, return string[len(prefix):]. | Otherwise, return a copy of the original string. | | removesuffix(self, suffix, /) | Return a str with the given suffix string removed if present. | | If the string ends with the suffix string and that suffix is not empty, | return string[:-len(suffix)]. Otherwise, return a copy of the original | string. | | replace(self, old, new, count=-1, /) | Return a copy with all occurrences of substring old replaced by new. | | count | Maximum number of occurrences to replace. | -1 (the default value) means replace all occurrences. | | If the optional argument count is given, only the first count occurrences are | replaced. | | rfind(...) | S.rfind(sub[, start[, end]]) -> int | | Return the highest index in S where substring sub is found, | such that sub is contained within S[start:end]. Optional | arguments start and end are interpreted as in slice notation. | | Return -1 on failure. | | rindex(...) | S.rindex(sub[, start[, end]]) -> int | | Return the highest index in S where substring sub is found, | such that sub is contained within S[start:end]. Optional | arguments start and end are interpreted as in slice notation. | | Raises ValueError when the substring is not found. | | rjust(self, width, fillchar=' ', /) | Return a right-justified string of length width. | | Padding is done using the specified fill character (default is a space). | | rpartition(self, sep, /) | Partition the string into three parts using the given separator. | | This will search for the separator in the string, starting at the end. If | the separator is found, returns a 3-tuple containing the part before the | separator, the separator itself, and the part after it. | | If the separator is not found, returns a 3-tuple containing two empty strings | and the original string. | | rsplit(self, /, sep=None, maxsplit=-1) | Return a list of the substrings in the string, using sep as the separator string. | | sep | The separator used to split the string. | | When set to None (the default value), will split on any whitespace | character (including \\n \\r \\t \\f and spaces) and will discard | empty strings from the result. | maxsplit | Maximum number of splits (starting from the left). | -1 (the default value) means no limit. | | Splitting starts at the end of the string and works to the front. | | rstrip(self, chars=None, /) | Return a copy of the string with trailing whitespace removed. | | If chars is given and not None, remove characters in chars instead. | | split(self, /, sep=None, maxsplit=-1) | Return a list of the substrings in the string, using sep as the separator string. | | sep | The separator used to split the string. | | When set to None (the default value), will split on any whitespace | character (including \\n \\r \\t \\f and spaces) and will discard | empty strings from the result. | maxsplit | Maximum number of splits (starting from the left). | -1 (the default value) means no limit. | | Note, str.split() is mainly useful for data that has been intentionally | delimited. With natural text that includes punctuation, consider using | the regular expression module. | | splitlines(self, /, keepends=False) | Return a list of the lines in the string, breaking at line boundaries. | | Line breaks are not included in the resulting list unless keepends is given and | true. | | startswith(...) | S.startswith(prefix[, start[, end]]) -> bool | | Return True if S starts with the specified prefix, False otherwise. | With optional start, test S beginning at that position. | With optional end, stop comparing S at that position. | prefix can also be a tuple of strings to try. | | strip(self, chars=None, /) | Return a copy of the string with leading and trailing whitespace removed. | | If chars is given and not None, remove characters in chars instead. | | swapcase(self, /) | Convert uppercase characters to lowercase and lowercase characters to uppercase. | | title(self, /) | Return a version of the string where each word is titlecased. | | More specifically, words start with uppercased characters and all remaining | cased characters have lower case. | | translate(self, table, /) | Replace each character in the string using the given translation table. | | table | Translation table, which must be a mapping of Unicode ordinals to | Unicode ordinals, strings, or None. | | The table must implement lookup/indexing via __getitem__, for instance a | dictionary or list. If this operation raises LookupError, the character is | left untouched. Characters mapped to None are deleted. | | upper(self, /) | Return a copy of the string converted to uppercase. | | zfill(self, width, /) | Pad a numeric string with zeros on the left, to fill a field of the given width. | | The string is never truncated. | | ---------------------------------------------------------------------- | Static methods inherited from builtins.str: | | maketrans(...) | Return a translation table usable for str.translate(). | | If there is only one argument, it must be a dictionary mapping Unicode | ordinals (integers) or characters to Unicode ordinals, strings or None. | Character keys will be then converted to ordinals. | If there are two arguments, they must be strings of equal length, and | in the resulting dictionary, each character in x will be mapped to the | character at the same position in y. If there is a third argument, it | must be a string, whose characters will be mapped to None in the result. | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __abs__(self, /) | abs(self) | | __and__(self, value, /) | Return self&value. | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __bool__(self, /) | True if self else False | | __copy__(...) | | __deepcopy__(...) | | __divmod__(self, value, /) | Return divmod(self, value). | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. ### class unsignedinteger | Abstract base class of all unsigned integer scalar types. | | Method resolution order: | unsignedinteger | integer | number | generic | builtins.object | | Methods inherited from integer: | | __round__(...) | | ---------------------------------------------------------------------- | Data descriptors inherited from integer: | | denominator | denominator of value (1) | | numerator | numerator of value (the value itself) | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __and__(self, value, /) | Return self&value. | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __bool__(self, /) | True if self else False | | __copy__(...) | | __deepcopy__(...) | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __format__(...) | NumPy array scalar formatter | | __ge__(self, value, /) | Return self>=value. | | __getitem__(self, key, /) | Return self[key]. | | __gt__(self, value, /) | Return self>value. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __le__(self, value, /) | Return self<=value. | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. | | ---------------------------------------------------------------------- | Data and other attributes inherited from generic: | | __hash__ = None ushort = class uint16(unsignedinteger) | Unsigned integer type, compatible with C ``unsigned short``. | | :Character code: ``'H'`` | :Canonical name: `numpy.ushort` | :Alias on this platform (Linux x86_64): `numpy.uint16`: 16-bit unsigned integer (``0`` to ``65_535``). | | Method resolution order: | uint16 | unsignedinteger | integer | number | generic | builtins.object | | Methods defined here: | | __abs__(self, /) | abs(self) | | __add__(self, value, /) | Return self+value. | | __and__(self, value, /) | Return self&value. | | __bool__(self, /) | True if self else False | | __divmod__(self, value, /) | Return divmod(self, value). | | __eq__(self, value, /) | Return self==value. | | __float__(self, /) | float(self) | | __floordiv__(self, value, /) | Return self//value. | | __ge__(self, value, /) | Return self>=value. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __index__(self, /) | Return self converted to an integer, if self is suitable for use as an index into a list. | | __int__(self, /) | int(self) | | __invert__(self, /) | ~self | | __le__(self, value, /) | Return self<=value. | | __lshift__(self, value, /) | Return self<>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __str__(self, /) | Return str(self). | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | ---------------------------------------------------------------------- | Static methods defined here: | | __new__(*args, **kwargs) from builtins.type | Create and return a new object. See help(type) for accurate signature. | | ---------------------------------------------------------------------- | Methods inherited from integer: | | __round__(...) | | ---------------------------------------------------------------------- | Data descriptors inherited from integer: | | denominator | denominator of value (1) | | numerator | numerator of value (the value itself) | | ---------------------------------------------------------------------- | Methods inherited from generic: | | __array__(...) | sc.__array__(dtype) return 0-dim array from scalar with specified dtype | | __array_wrap__(...) | sc.__array_wrap__(obj) return scalar from array | | __copy__(...) | | __deepcopy__(...) | | __format__(...) | NumPy array scalar formatter | | __getitem__(self, key, /) | Return self[key]. | | __reduce__(...) | Helper for pickle. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | getfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.getfield`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setfield(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setfield`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | base | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.base`. | | data | Pointer to start of data. | | dtype | Get array data-descriptor. | | flags | The integer value of flags. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. ### class vectorize | vectorize(pyfunc, otypes=None, doc=None, excluded=None, cache=False, signature=None) | | vectorize(pyfunc, otypes=None, doc=None, excluded=None, cache=False, | signature=None) | | Generalized function class. | | Define a vectorized function which takes a nested sequence of objects or | numpy arrays as inputs and returns a single numpy array or a tuple of numpy | arrays. The vectorized function evaluates `pyfunc` over successive tuples | of the input arrays like the python map function, except it uses the | broadcasting rules of numpy. | | The data type of the output of `vectorized` is determined by calling | the function with the first element of the input. This can be avoided | by specifying the `otypes` argument. | | Parameters | ---------- | pyfunc : callable | A python function or method. | otypes : str or list of dtypes, optional | The output data type. It must be specified as either a string of | typecode characters or a list of data type specifiers. There should | be one data type specifier for each output. | doc : str, optional | The docstring for the function. If None, the docstring will be the | ``pyfunc.__doc__``. | excluded : set, optional | Set of strings or integers representing the positional or keyword | arguments for which the function will not be vectorized. These will be | passed directly to `pyfunc` unmodified. | | .. versionadded:: 1.7.0 | | cache : bool, optional | If `True`, then cache the first function call that determines the number | of outputs if `otypes` is not provided. | | .. versionadded:: 1.7.0 | | signature : string, optional | Generalized universal function signature, e.g., ``(m,n),(n)->(m)`` for | vectorized matrix-vector multiplication. If provided, ``pyfunc`` will | be called with (and expected to return) arrays with shapes given by the | size of corresponding core dimensions. By default, ``pyfunc`` is | assumed to take scalars as input and output. | | .. versionadded:: 1.12.0 | | Returns | ------- | vectorized : callable | Vectorized function. | | See Also | -------- | frompyfunc : Takes an arbitrary Python function and returns a ufunc | | Notes | ----- | The `vectorize` function is provided primarily for convenience, not for | performance. The implementation is essentially a for loop. | | If `otypes` is not specified, then a call to the function with the | first argument will be used to determine the number of outputs. The | results of this call will be cached if `cache` is `True` to prevent | calling the function twice. However, to implement the cache, the | original function must be wrapped which will slow down subsequent | calls, so only do this if your function is expensive. | | The new keyword argument interface and `excluded` argument support | further degrades performance. | | References | ---------- | .. [1] :doc:`/reference/c-api/generalized-ufuncs` | | Examples | -------- | >>> def myfunc(a, b): | ... "Return a-b if a>b, otherwise return a+b" | ... if a > b: | ... return a - b | ... else: | ... return a + b | | >>> vfunc = np.vectorize(myfunc) | >>> vfunc([1, 2, 3, 4], 2) | array([3, 4, 1, 2]) | | The docstring is taken from the input function to `vectorize` unless it | is specified: | | >>> vfunc.__doc__ | 'Return a-b if a>b, otherwise return a+b' | >>> vfunc = np.vectorize(myfunc, doc='Vectorized `myfunc`') | >>> vfunc.__doc__ | 'Vectorized `myfunc`' | | The output type is determined by evaluating the first element of the input, | unless it is specified: | | >>> out = vfunc([1, 2, 3, 4], 2) | >>> type(out[0]) | | >>> vfunc = np.vectorize(myfunc, otypes=[float]) | >>> out = vfunc([1, 2, 3, 4], 2) | >>> type(out[0]) | | | The `excluded` argument can be used to prevent vectorizing over certain | arguments. This can be useful for array-like arguments of a fixed length | such as the coefficients for a polynomial as in `polyval`: | | >>> def mypolyval(p, x): | ... _p = list(p) | ... res = [_p.pop(0)](https://www.chedong.com/phpMan.php/man/p.pop/0/markdown) | ... while _p: | ... res = res*x + [_p.pop(0)](https://www.chedong.com/phpMan.php/man/p.pop/0/markdown) | ... return res | >>> vpolyval = np.vectorize(mypolyval, excluded=['p']) | >>> vpolyval(p=[1, 2, 3], x=[0, 1]) | array([3, 6]) | | Positional arguments may also be excluded by specifying their position: | | >>> [vpolyval.excluded.add(0)](https://www.chedong.com/phpMan.php/man/vpolyval.excluded.add/0/markdown) | >>> vpolyval([1, 2, 3], x=[0, 1]) | array([3, 6]) | | The `signature` argument allows for vectorizing functions that act on | non-scalar arrays of fixed length. For example, you can use it for a | vectorized calculation of Pearson correlation coefficient and its p-value: | | >>> import scipy.stats | >>> pearsonr = np.vectorize(scipy.stats.pearsonr, | ... signature='(n),(n)->(),()') | >>> pearsonr([[0, 1, 2, 3]], [[1, 2, 3, 4], [4, 3, 2, 1]]) | (array([ 1., -1.]), array([ 0., 0.])) | | Or for a vectorized convolution: | | >>> convolve = np.vectorize(np.convolve, signature='(n),(m)->(k)') | >>> convolve([np.eye(4)](https://www.chedong.com/phpMan.php/man/np.eye/4/markdown), [1, 2, 1]) | array([[1., 2., 1., 0., 0., 0.], | [0., 1., 2., 1., 0., 0.], | [0., 0., 1., 2., 1., 0.], | [0., 0., 0., 1., 2., 1.]]) | | Methods defined here: | | __call__(self, *args, **kwargs) | Return arrays with the results of `pyfunc` broadcast (vectorized) over | `args` and `kwargs` not in `excluded`. | | __init__(self, pyfunc, otypes=None, doc=None, excluded=None, cache=False, signature=None) | Initialize self. See help(type(self)) for accurate signature. | | ---------------------------------------------------------------------- | Data descriptors defined here: | | __dict__ | dictionary for instance variables (if defined) | | __weakref__ | list of weak references to the object (if defined) ### class void | Either an opaque sequence of bytes, or a structure. | | >>> np.void(b'abcd') | void(b'\x61\x62\x63\x64') | | Structured `void` scalars can only be constructed via extraction from :ref:`structured_arrays`: | | >>> arr = np.array((1, 2), dtype=[('x', np.int8), ('y', np.int8)]) | >>> arr[()] | (1, 2) # looks like a tuple, but is `np.void` | | :Character code: ``'V'`` | | Method resolution order: | void | flexible | generic | builtins.object | | Methods defined here: | | __delitem__(self, key, /) | Delete self[key]. | | __eq__(self, value, /) | Return self==value. | | __ge__(self, value, /) | Return self>=value. | | __getitem__(self, key, /) | Return self[key]. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __le__(self, value, /) | Return self<=value. | | __len__(self, /) | Return len(self). | | __lt__(self, value, /) | Return self>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | data | Pointer to start of data. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. void0 = class void(flexible) | Either an opaque sequence of bytes, or a structure. | | >>> np.void(b'abcd') | void(b'\x61\x62\x63\x64') | | Structured `void` scalars can only be constructed via extraction from :ref:`structured_arrays`: | | >>> arr = np.array((1, 2), dtype=[('x', np.int8), ('y', np.int8)]) | >>> arr[()] | (1, 2) # looks like a tuple, but is `np.void` | | :Character code: ``'V'`` | | Method resolution order: | void | flexible | generic | builtins.object | | Methods defined here: | | __delitem__(self, key, /) | Delete self[key]. | | __eq__(self, value, /) | Return self==value. | | __ge__(self, value, /) | Return self>=value. | | __getitem__(self, key, /) | Return self[key]. | | __gt__(self, value, /) | Return self>value. | | __hash__(self, /) | Return hash(self). | | __le__(self, value, /) | Return self<=value. | | __len__(self, /) | Return len(self). | | __lt__(self, value, /) | Return self>self. | | __rshift__(self, value, /) | Return self>>value. | | __rsub__(self, value, /) | Return value-self. | | __rtruediv__(self, value, /) | Return value/self. | | __rxor__(self, value, /) | Return value^self. | | __setstate__(...) | | __sizeof__(...) | Size of object in memory, in bytes. | | __sub__(self, value, /) | Return self-value. | | __truediv__(self, value, /) | Return self/value. | | __xor__(self, value, /) | Return self^value. | | all(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.all`. | | any(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.any`. | | argmax(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmax`. | | argmin(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argmin`. | | argsort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.argsort`. | | astype(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.astype`. | | byteswap(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.byteswap`. | | choose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.choose`. | | clip(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.clip`. | | compress(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.compress`. | | conj(...) | | conjugate(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.conjugate`. | | copy(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.copy`. | | cumprod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumprod`. | | cumsum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.cumsum`. | | diagonal(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.diagonal`. | | dump(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dump`. | | dumps(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.dumps`. | | fill(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.fill`. | | flatten(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.flatten`. | | item(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.item`. | | itemset(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.itemset`. | | max(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.max`. | | mean(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.mean`. | | min(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.min`. | | newbyteorder(...) | newbyteorder(new_order='S', /) | | Return a new `dtype` with a different byte order. | | Changes are also made in all fields and sub-arrays of the data type. | | The `new_order` code can be any from the following: | | * 'S' - swap dtype from current to opposite endian | * {'<', 'little'} - little endian | * {'>', 'big'} - big endian | * '=' - native order | * {'|', 'I'} - ignore (no change to byte order) | | Parameters | ---------- | new_order : str, optional | Byte order to force; a value from the byte order specifications | above. The default value ('S') results in swapping the current | byte order. | | | Returns | ------- | new_dtype : dtype | New `dtype` object with the given change to the byte order. | | nonzero(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.nonzero`. | | prod(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.prod`. | | ptp(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ptp`. | | put(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.put`. | | ravel(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.ravel`. | | repeat(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.repeat`. | | reshape(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.reshape`. | | resize(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.resize`. | | round(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.round`. | | searchsorted(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.searchsorted`. | | setflags(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.setflags`. | | sort(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sort`. | | squeeze(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.squeeze`. | | std(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.std`. | | sum(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.sum`. | | swapaxes(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.swapaxes`. | | take(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.take`. | | tobytes(...) | | tofile(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tofile`. | | tolist(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tolist`. | | tostring(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.tostring`. | | trace(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.trace`. | | transpose(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.transpose`. | | var(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.var`. | | view(...) | Scalar method identical to the corresponding array attribute. | | Please see `ndarray.view`. | | ---------------------------------------------------------------------- | Data descriptors inherited from generic: | | T | Scalar attribute identical to the corresponding array attribute. | | Please see `ndarray.T`. | | __array_interface__ | Array protocol: Python side | | __array_priority__ | Array priority. | | __array_struct__ | Array protocol: struct | | data | Pointer to start of data. | | flat | A 1-D view of the scalar. | | imag | The imaginary part of the scalar. | | itemsize | The length of one element in bytes. | | nbytes | The length of the scalar in bytes. | | ndim | The number of array dimensions. | | real | The real part of the scalar. | | shape | Tuple of array dimensions. | | size | The number of elements in the gentype. | | strides | Tuple of bytes steps in each dimension. ## FUNCTIONS __dir__() __getattr__(attr) # module level getattr is only supported in 3.7 onwards # _add_newdoc_ufunc(...) add_ufunc_docstring(ufunc, new_docstring) Replace the docstring for a ufunc with new_docstring. This method will only work if the current docstring for the ufunc is NULL. (At the C level, i.e. when ufunc->doc is NULL.) Parameters ---------- ufunc : numpy.ufunc A ufunc whose current doc is NULL. new_docstring : string The new docstring for the ufunc. Notes ----- This method allocates memory for new_docstring on the heap. Technically this creates a mempory leak, since this memory will not be reclaimed until the end of the program even if the ufunc itself is removed. However this will only be a problem if the user is repeatedly creating ufuncs with no documentation, adding documentation via add_newdoc_ufunc, and then throwing away the ufunc. ### add_docstring add_docstring(obj, docstring) Add a docstring to a built-in obj if possible. If the obj already has a docstring raise a RuntimeError If this routine does not know how to add a docstring to the object raise a TypeError ### add_newdoc Add documentation to an existing object, typically one defined in C The purpose is to allow easier editing of the docstrings without requiring a re-compile. This exists primarily for internal use within numpy itself. Parameters ---------- place : str The absolute name of the module to import from obj : str The name of the object to add documentation to, typically a class or function name doc : {str, Tuple[str, str], List[Tuple[str, str]]} If a string, the documentation to apply to `obj` If a tuple, then the first element is interpreted as an attribute of `obj` and the second as the docstring to apply - ``(method, docstring)`` If a list, then each element of the list should be a tuple of length two - ``[(method1, docstring1), (method2, docstring2), ...]`` warn_on_python : bool If True, the default, emit `UserWarning` if this is used to attach documentation to a pure-python object. Notes ----- This routine never raises an error if the docstring can't be written, but will raise an error if the object being documented does not exist. This routine cannot modify read-only docstrings, as appear in new-style classes or built-in functions. Because this routine never raises an error the caller must check manually that the docstrings were changed. Since this function grabs the ``char *`` from a c-level str object and puts it into the ``tp_doc`` slot of the type of `obj`, it violates a number of C-API best-practices, by: - modifying a `PyTypeObject` after calling `PyType_Ready` - calling `Py_INCREF` on the str and losing the reference, so the str will never be released If possible it should be avoided. add_newdoc_ufunc = _add_newdoc_ufunc(...) add_ufunc_docstring(ufunc, new_docstring) Replace the docstring for a ufunc with new_docstring. This method will only work if the current docstring for the ufunc is NULL. (At the C level, i.e. when ufunc->doc is NULL.) Parameters ---------- ufunc : numpy.ufunc A ufunc whose current doc is NULL. new_docstring : string The new docstring for the ufunc. Notes ----- This method allocates memory for new_docstring on the heap. Technically this creates a mempory leak, since this memory will not be reclaimed until the end of the program even if the ufunc itself is removed. However this will only be a problem if the user is repeatedly creating ufuncs with no documentation, adding documentation via add_newdoc_ufunc, and then throwing away the ufunc. ### alen Return the length of the first dimension of the input array. .. deprecated:: 1.18 `numpy.alen` is deprecated, use `len` instead. Parameters ---------- a : array_like Input array. Returns ------- alen : int Length of the first dimension of `a`. See Also -------- shape, size Examples -------- >>> a = np.zeros((7,4,5)) >>> a.shape[0] 7 >>> np.alen(a) 7 ### all Test whether all array elements along a given axis evaluate to True. Parameters ---------- a : array_like Input array or object that can be converted to an array. axis : None or int or tuple of ints, optional Axis or axes along which a logical AND reduction is performed. The default (``axis=None``) is to perform a logical AND over all the dimensions of the input array. `axis` may be negative, in which case it counts from the last to the first axis. .. versionadded:: 1.7.0 If this is a tuple of ints, a reduction is performed on multiple axes, instead of a single axis or all the axes as before. out : ndarray, optional Alternate output array in which to place the result. It must have the same shape as the expected output and its type is preserved (e.g., if ``dtype(out)`` is float, the result will consist of 0.0's and 1.0's). See :ref:`ufuncs-output-type` for more details. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array. If the default value is passed, then `keepdims` will not be passed through to the `all` method of sub-classes of `ndarray`, however any non-default value will be. If the sub-class' method does not implement `keepdims` any exceptions will be raised. where : array_like of bool, optional Elements to include in checking for all `True` values. See `~numpy.ufunc.reduce` for details. .. versionadded:: 1.20.0 Returns ------- all : ndarray, bool A new boolean or array is returned unless `out` is specified, in which case a reference to `out` is returned. See Also -------- ndarray.all : equivalent method any : Test whether any element along a given axis evaluates to True. Notes ----- Not a Number (NaN), positive infinity and negative infinity evaluate to `True` because these are not equal to zero. Examples -------- >>> np.all([[True,False],[True,True]]) False >>> np.all([[True,False],[True,True]], axis=0) array([ True, False]) >>> np.all([-1, 4, 5]) True >>> np.all([1.0, np.nan]) True >>> np.all([[True, True], [False, True]], where=[[True], [False]]) True >>> o=np.array(False) >>> z=np.all([-1, 4, 5], out=o) >>> id(z), id(o), z (28293632, 28293632, array(True)) # may vary ### allclose Returns True if two arrays are element-wise equal within a tolerance. The tolerance values are positive, typically very small numbers. The relative difference (`rtol` * abs(`b`)) and the absolute difference `atol` are added together to compare against the absolute difference between `a` and `b`. NaNs are treated as equal if they are in the same place and if ``equal_nan=True``. Infs are treated as equal if they are in the same place and of the same sign in both arrays. Parameters ---------- a, b : array_like Input arrays to compare. rtol : float The relative tolerance parameter (see Notes). atol : float The absolute tolerance parameter (see Notes). equal_nan : bool Whether to compare NaN's as equal. If True, NaN's in `a` will be considered equal to NaN's in `b` in the output array. .. versionadded:: 1.10.0 Returns ------- allclose : bool Returns True if the two arrays are equal within the given tolerance; False otherwise. See Also -------- isclose, all, any, equal Notes ----- If the following equation is element-wise True, then allclose returns True. absolute(`a` - `b`) <= (`atol` + `rtol` * absolute(`b`)) The above equation is not symmetric in `a` and `b`, so that ``allclose(a, b)`` might be different from ``allclose(b, a)`` in some rare cases. The comparison of `a` and `b` uses standard broadcasting, which means that `a` and `b` need not have the same shape in order for ``allclose(a, b)`` to evaluate to True. The same is true for `equal` but not `array_equal`. `allclose` is not defined for non-numeric data types. Examples -------- >>> np.allclose([1e10,1e-7], [1.00001e10,1e-8]) False >>> np.allclose([1e10,1e-8], [1.00001e10,1e-9]) True >>> np.allclose([1e10,1e-8], [1.0001e10,1e-9]) False >>> np.allclose([1.0, np.nan], [1.0, np.nan]) False >>> np.allclose([1.0, np.nan], [1.0, np.nan], equal_nan=True) True ### alltrue Check if all elements of input array are true. See Also -------- numpy.all : Equivalent function; see for details. ### amax Return the maximum of an array or maximum along an axis. Parameters ---------- a : array_like Input data. axis : None or int or tuple of ints, optional Axis or axes along which to operate. By default, flattened input is used. .. versionadded:: 1.7.0 If this is a tuple of ints, the maximum is selected over multiple axes, instead of a single axis or all the axes as before. out : ndarray, optional Alternative output array in which to place the result. Must be of the same shape and buffer length as the expected output. See :ref:`ufuncs-output-type` for more details. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array. If the default value is passed, then `keepdims` will not be passed through to the `amax` method of sub-classes of `ndarray`, however any non-default value will be. If the sub-class' method does not implement `keepdims` any exceptions will be raised. initial : scalar, optional The minimum value of an output element. Must be present to allow computation on empty slice. See `~numpy.ufunc.reduce` for details. .. versionadded:: 1.15.0 where : array_like of bool, optional Elements to compare for the maximum. See `~numpy.ufunc.reduce` for details. .. versionadded:: 1.17.0 Returns ------- amax : ndarray or scalar Maximum of `a`. If `axis` is None, the result is a scalar value. If `axis` is given, the result is an array of dimension ``a.ndim - 1``. See Also -------- amin : The minimum value of an array along a given axis, propagating any NaNs. nanmax : The maximum value of an array along a given axis, ignoring any NaNs. maximum : Element-wise maximum of two arrays, propagating any NaNs. fmax : Element-wise maximum of two arrays, ignoring any NaNs. argmax : Return the indices of the maximum values. nanmin, minimum, fmin Notes ----- NaN values are propagated, that is if at least one item is NaN, the corresponding max value will be NaN as well. To ignore NaN values (MATLAB behavior), please use nanmax. Don't use `amax` for element-wise comparison of 2 arrays; when ``a.shape[0]`` is 2, ``maximum(a[0], a[1])`` is faster than ``amax(a, axis=0)``. Examples -------- >>> a = [np.arange(4)](https://www.chedong.com/phpMan.php/man/np.arange/4/markdown).reshape((2,2)) >>> a array([[0, 1], [2, 3]]) >>> np.amax(a) # Maximum of the flattened array 3 >>> np.amax(a, axis=0) # Maxima along the first axis array([2, 3]) >>> np.amax(a, axis=1) # Maxima along the second axis array([1, 3]) >>> np.amax(a, where=[False, True], initial=-1, axis=0) array([-1, 3]) >>> b = np.arange(5, dtype=float) >>> b[2] = np.NaN >>> np.amax(b) nan >>> np.amax(b, where=~np.isnan(b), initial=-1) 4.0 >>> np.nanmax(b) 4.0 You can use an initial value to compute the maximum of an empty slice, or to initialize it to a different value: >>> np.max([[-50], [10]], axis=-1, initial=0) array([ 0, 10]) Notice that the initial value is used as one of the elements for which the maximum is determined, unlike for the default argument Python's max function, which is only used for empty iterables. >>> np.max([5], initial=6) 6 >>> max([5], default=6) 5 ### amin Return the minimum of an array or minimum along an axis. Parameters ---------- a : array_like Input data. axis : None or int or tuple of ints, optional Axis or axes along which to operate. By default, flattened input is used. .. versionadded:: 1.7.0 If this is a tuple of ints, the minimum is selected over multiple axes, instead of a single axis or all the axes as before. out : ndarray, optional Alternative output array in which to place the result. Must be of the same shape and buffer length as the expected output. See :ref:`ufuncs-output-type` for more details. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array. If the default value is passed, then `keepdims` will not be passed through to the `amin` method of sub-classes of `ndarray`, however any non-default value will be. If the sub-class' method does not implement `keepdims` any exceptions will be raised. initial : scalar, optional The maximum value of an output element. Must be present to allow computation on empty slice. See `~numpy.ufunc.reduce` for details. .. versionadded:: 1.15.0 where : array_like of bool, optional Elements to compare for the minimum. See `~numpy.ufunc.reduce` for details. .. versionadded:: 1.17.0 Returns ------- amin : ndarray or scalar Minimum of `a`. If `axis` is None, the result is a scalar value. If `axis` is given, the result is an array of dimension ``a.ndim - 1``. See Also -------- amax : The maximum value of an array along a given axis, propagating any NaNs. nanmin : The minimum value of an array along a given axis, ignoring any NaNs. minimum : Element-wise minimum of two arrays, propagating any NaNs. fmin : Element-wise minimum of two arrays, ignoring any NaNs. argmin : Return the indices of the minimum values. nanmax, maximum, fmax Notes ----- NaN values are propagated, that is if at least one item is NaN, the corresponding min value will be NaN as well. To ignore NaN values (MATLAB behavior), please use nanmin. Don't use `amin` for element-wise comparison of 2 arrays; when ``a.shape[0]`` is 2, ``minimum(a[0], a[1])`` is faster than ``amin(a, axis=0)``. Examples -------- >>> a = [np.arange(4)](https://www.chedong.com/phpMan.php/man/np.arange/4/markdown).reshape((2,2)) >>> a array([[0, 1], [2, 3]]) >>> np.amin(a) # Minimum of the flattened array 0 >>> np.amin(a, axis=0) # Minima along the first axis array([0, 1]) >>> np.amin(a, axis=1) # Minima along the second axis array([0, 2]) >>> np.amin(a, where=[False, True], initial=10, axis=0) array([10, 1]) >>> b = np.arange(5, dtype=float) >>> b[2] = np.NaN >>> np.amin(b) nan >>> np.amin(b, where=~np.isnan(b), initial=10) 0.0 >>> np.nanmin(b) 0.0 >>> np.min([[-50], [10]], axis=-1, initial=0) array([-50, 0]) Notice that the initial value is used as one of the elements for which the minimum is determined, unlike for the default argument Python's max function, which is only used for empty iterables. Notice that this isn't the same as Python's ``default`` argument. >>> np.min([6], initial=5) 5 >>> min([6], default=5) 6 ### angle Return the angle of the complex argument. Parameters ---------- z : array_like A complex number or sequence of complex numbers. deg : bool, optional Return angle in degrees if True, radians if False (default). Returns ------- angle : ndarray or scalar The counterclockwise angle from the positive real axis on the complex plane in the range ``(-pi, pi]``, with dtype as numpy.float64. .. versionchanged:: 1.16.0 This function works on subclasses of ndarray like `ma.array`. See Also -------- arctan2 absolute Notes ----- Although the angle of the complex number 0 is undefined, ``[numpy.angle(0)](https://www.chedong.com/phpMan.php/man/numpy.angle/0/markdown)`` returns the value 0. Examples -------- >>> np.angle([1.0, 1.0j, 1+1j]) # in radians array([ 0. , 1.57079633, 0.78539816]) # may vary >>> np.angle(1+1j, deg=True) # in degrees 45.0 ### any Test whether any array element along a given axis evaluates to True. Returns single boolean unless `axis` is not ``None`` Parameters ---------- a : array_like Input array or object that can be converted to an array. axis : None or int or tuple of ints, optional Axis or axes along which a logical OR reduction is performed. The default (``axis=None``) is to perform a logical OR over all the dimensions of the input array. `axis` may be negative, in which case it counts from the last to the first axis. .. versionadded:: 1.7.0 If this is a tuple of ints, a reduction is performed on multiple axes, instead of a single axis or all the axes as before. out : ndarray, optional Alternate output array in which to place the result. It must have the same shape as the expected output and its type is preserved (e.g., if it is of type float, then it will remain so, returning 1.0 for True and 0.0 for False, regardless of the type of `a`). See :ref:`ufuncs-output-type` for more details. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array. If the default value is passed, then `keepdims` will not be passed through to the `any` method of sub-classes of `ndarray`, however any non-default value will be. If the sub-class' method does not implement `keepdims` any exceptions will be raised. where : array_like of bool, optional Elements to include in checking for any `True` values. See `~numpy.ufunc.reduce` for details. .. versionadded:: 1.20.0 Returns ------- any : bool or ndarray A new boolean or `ndarray` is returned unless `out` is specified, in which case a reference to `out` is returned. See Also -------- ndarray.any : equivalent method all : Test whether all elements along a given axis evaluate to True. Notes ----- Not a Number (NaN), positive infinity and negative infinity evaluate to `True` because these are not equal to zero. Examples -------- >>> np.any([[True, False], [True, True]]) True >>> np.any([[True, False], [False, False]], axis=0) array([ True, False]) >>> np.any([-1, 0, 5]) True >>> np.any(np.nan) True >>> np.any([[True, False], [False, False]], where=[[False], [True]]) False >>> o=np.array(False) >>> z=np.any([-1, 4, 5], out=o) >>> z, o (array(True), array(True)) >>> # Check now that z is a reference to o >>> z is o True >>> id(z), id(o) # identity of z and o # doctest: +SKIP (191614240, 191614240) ### append Append values to the end of an array. Parameters ---------- arr : array_like Values are appended to a copy of this array. values : array_like These values are appended to a copy of `arr`. It must be of the correct shape (the same shape as `arr`, excluding `axis`). If `axis` is not specified, `values` can be any shape and will be flattened before use. axis : int, optional The axis along which `values` are appended. If `axis` is not given, both `arr` and `values` are flattened before use. Returns ------- append : ndarray A copy of `arr` with `values` appended to `axis`. Note that `append` does not occur in-place: a new array is allocated and filled. If `axis` is None, `out` is a flattened array. See Also -------- insert : Insert elements into an array. delete : Delete elements from an array. Examples -------- >>> np.append([1, 2, 3], [[4, 5, 6], [7, 8, 9]]) array([1, 2, 3, ..., 7, 8, 9]) When `axis` is specified, `values` must have the correct shape. >>> np.append([[1, 2, 3], [4, 5, 6]], [[7, 8, 9]], axis=0) array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) >>> np.append([[1, 2, 3], [4, 5, 6]], [7, 8, 9], axis=0) Traceback (most recent call last): ... ValueError: all the input arrays must have same number of dimensions, but the array at index 0 has 2 dimension(s) and the array at index 1 has 1 dimension(s) ### apply_along_axis Apply a function to 1-D slices along the given axis. Execute `func1d(a, *args, **kwargs)` where `func1d` operates on 1-D arrays and `a` is a 1-D slice of `arr` along `axis`. This is equivalent to (but faster than) the following use of `ndindex` and `s_`, which sets each of ``ii``, ``jj``, and ``kk`` to a tuple of indices:: Ni, Nk = a.shape[:axis], a.shape[axis+1:] for ii in ndindex(Ni): for kk in ndindex(Nk): f = func1d(arr[ii + s_[:,] + kk]) Nj = f.shape for jj in ndindex(Nj): out[ii + jj + kk] = f[jj] Equivalently, eliminating the inner loop, this can be expressed as:: Ni, Nk = a.shape[:axis], a.shape[axis+1:] for ii in ndindex(Ni): for kk in ndindex(Nk): out[ii + s_[...,] + kk] = func1d(arr[ii + s_[:,] + kk]) Parameters ---------- func1d : function (M,) -> (Nj...) This function should accept 1-D arrays. It is applied to 1-D slices of `arr` along the specified axis. axis : integer Axis along which `arr` is sliced. arr : ndarray (Ni..., M, Nk...) Input array. args : any Additional arguments to `func1d`. kwargs : any Additional named arguments to `func1d`. .. versionadded:: 1.9.0 Returns ------- out : ndarray (Ni..., Nj..., Nk...) The output array. The shape of `out` is identical to the shape of `arr`, except along the `axis` dimension. This axis is removed, and replaced with new dimensions equal to the shape of the return value of `func1d`. So if `func1d` returns a scalar `out` will have one fewer dimensions than `arr`. See Also -------- apply_over_axes : Apply a function repeatedly over multiple axes. Examples -------- >>> def my_func(a): ... """Average first and last element of a 1-D array""" ... return (a[0] + a[-1]) * 0.5 >>> b = np.array([[1,2,3], [4,5,6], [7,8,9]]) >>> np.apply_along_axis(my_func, 0, b) array([4., 5., 6.]) >>> np.apply_along_axis(my_func, 1, b) array([2., 5., 8.]) For a function that returns a 1D array, the number of dimensions in `outarr` is the same as `arr`. >>> b = np.array([[8,1,7], [4,3,9], [5,2,6]]) >>> np.apply_along_axis(sorted, 1, b) array([[1, 7, 8], [3, 4, 9], [2, 5, 6]]) For a function that returns a higher dimensional array, those dimensions are inserted in place of the `axis` dimension. >>> b = np.array([[1,2,3], [4,5,6], [7,8,9]]) >>> np.apply_along_axis(np.diag, -1, b) array([[[1, 0, 0], [0, 2, 0], [0, 0, 3]], [[4, 0, 0], [0, 5, 0], [0, 0, 6]], [[7, 0, 0], [0, 8, 0], [0, 0, 9]]]) ### apply_over_axes Apply a function repeatedly over multiple axes. `func` is called as `res = func(a, axis)`, where `axis` is the first element of `axes`. The result `res` of the function call must have either the same dimensions as `a` or one less dimension. If `res` has one less dimension than `a`, a dimension is inserted before `axis`. The call to `func` is then repeated for each axis in `axes`, with `res` as the first argument. Parameters ---------- func : function This function must take two arguments, `func(a, axis)`. a : array_like Input array. axes : array_like Axes over which `func` is applied; the elements must be integers. Returns ------- apply_over_axis : ndarray The output array. The number of dimensions is the same as `a`, but the shape can be different. This depends on whether `func` changes the shape of its output with respect to its input. See Also -------- apply_along_axis : Apply a function to 1-D slices of an array along the given axis. Notes ----- This function is equivalent to tuple axis arguments to reorderable ufuncs with keepdims=True. Tuple axis arguments to ufuncs have been available since version 1.7.0. Examples -------- >>> a = [np.arange(24)](https://www.chedong.com/phpMan.php/man/np.arange/24/markdown).reshape(2,3,4) >>> a array([[[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]], [[12, 13, 14, 15], [16, 17, 18, 19], [20, 21, 22, 23]]]) Sum over axes 0 and 2. The result has same number of dimensions as the original array: >>> np.apply_over_axes(np.sum, a, [0,2]) array([[[ 60], [ 92], [124]]]) Tuple axis arguments to ufuncs are equivalent: >>> np.sum(a, axis=(0,2), keepdims=True) array([[[ 60], [ 92], [124]]]) ### arange arange([start,] stop[, step,], dtype=None, *, like=None) Return evenly spaced values within a given interval. Values are generated within the half-open interval ``[start, stop)`` (in other words, the interval including `start` but excluding `stop`). For integer arguments the function is equivalent to the Python built-in `range` function, but returns an ndarray rather than a list. When using a non-integer step, such as 0.1, the results will often not be consistent. It is better to use `numpy.linspace` for these cases. Parameters ---------- start : integer or real, optional Start of interval. The interval includes this value. The default start value is 0. stop : integer or real End of interval. The interval does not include this value, except in some cases where `step` is not an integer and floating point round-off affects the length of `out`. step : integer or real, optional Spacing between values. For any output `out`, this is the distance between two adjacent values, ``out[i+1] - out[i]``. The default step size is 1. If `step` is specified as a position argument, `start` must also be given. dtype : dtype The type of the output array. If `dtype` is not given, infer the data type from the other input arguments. like : array_like Reference object to allow the creation of arrays which are not NumPy arrays. If an array-like passed in as ``like`` supports the ``__array_function__`` protocol, the result will be defined by it. In this case, it ensures the creation of an array object compatible with that passed in via this argument. .. versionadded:: 1.20.0 Returns ------- arange : ndarray Array of evenly spaced values. For floating point arguments, the length of the result is ``ceil((stop - start)/step)``. Because of floating point overflow, this rule may result in the last element of `out` being greater than `stop`. See Also -------- numpy.linspace : Evenly spaced numbers with careful handling of endpoints. numpy.ogrid: Arrays of evenly spaced numbers in N-dimensions. numpy.mgrid: Grid-shaped arrays of evenly spaced numbers in N-dimensions. Examples -------- >>> [np.arange(3)](https://www.chedong.com/phpMan.php/man/np.arange/3/markdown) array([0, 1, 2]) >>> np.arange(3.0) array([ 0., 1., 2.]) >>> np.arange(3,7) array([3, 4, 5, 6]) >>> np.arange(3,7,2) array([3, 5]) ### argmax Returns the indices of the maximum values along an axis. Parameters ---------- a : array_like Input array. axis : int, optional By default, the index is into the flattened array, otherwise along the specified axis. out : array, optional If provided, the result will be inserted into this array. It should be of the appropriate shape and dtype. Returns ------- index_array : ndarray of ints Array of indices into the array. It has the same shape as `a.shape` with the dimension along `axis` removed. See Also -------- ndarray.argmax, argmin amax : The maximum value along a given axis. unravel_index : Convert a flat index into an index tuple. take_along_axis : Apply ``np.expand_dims(index_array, axis)`` from argmax to an array as if by calling max. Notes ----- In case of multiple occurrences of the maximum values, the indices corresponding to the first occurrence are returned. Examples -------- >>> a = [np.arange(6)](https://www.chedong.com/phpMan.php/man/np.arange/6/markdown).reshape(2,3) + 10 >>> a array([[10, 11, 12], [13, 14, 15]]) >>> np.argmax(a) 5 >>> np.argmax(a, axis=0) array([1, 1, 1]) >>> np.argmax(a, axis=1) array([2, 2]) Indexes of the maximal elements of a N-dimensional array: >>> ind = np.unravel_index(np.argmax(a, axis=None), a.shape) >>> ind (1, 2) >>> a[ind] 15 >>> b = [np.arange(6)](https://www.chedong.com/phpMan.php/man/np.arange/6/markdown) >>> b[1] = 5 >>> b array([0, 5, 2, 3, 4, 5]) >>> np.argmax(b) # Only the first occurrence is returned. 1 >>> x = np.array([[4,2,3], [1,0,3]]) >>> index_array = np.argmax(x, axis=-1) >>> # Same as np.max(x, axis=-1, keepdims=True) >>> np.take_along_axis(x, np.expand_dims(index_array, axis=-1), axis=-1) array([[4], [3]]) >>> # Same as np.max(x, axis=-1) >>> np.take_along_axis(x, np.expand_dims(index_array, axis=-1), axis=-1).squeeze(axis=-1) array([4, 3]) ### argmin Returns the indices of the minimum values along an axis. Parameters ---------- a : array_like Input array. axis : int, optional By default, the index is into the flattened array, otherwise along the specified axis. out : array, optional If provided, the result will be inserted into this array. It should be of the appropriate shape and dtype. Returns ------- index_array : ndarray of ints Array of indices into the array. It has the same shape as `a.shape` with the dimension along `axis` removed. See Also -------- ndarray.argmin, argmax amin : The minimum value along a given axis. unravel_index : Convert a flat index into an index tuple. take_along_axis : Apply ``np.expand_dims(index_array, axis)`` from argmin to an array as if by calling min. Notes ----- In case of multiple occurrences of the minimum values, the indices corresponding to the first occurrence are returned. Examples -------- >>> a = [np.arange(6)](https://www.chedong.com/phpMan.php/man/np.arange/6/markdown).reshape(2,3) + 10 >>> a array([[10, 11, 12], [13, 14, 15]]) >>> np.argmin(a) 0 >>> np.argmin(a, axis=0) array([0, 0, 0]) >>> np.argmin(a, axis=1) array([0, 0]) Indices of the minimum elements of a N-dimensional array: >>> ind = np.unravel_index(np.argmin(a, axis=None), a.shape) >>> ind (0, 0) >>> a[ind] 10 >>> b = [np.arange(6)](https://www.chedong.com/phpMan.php/man/np.arange/6/markdown) + 10 >>> b[4] = 10 >>> b array([10, 11, 12, 13, 10, 15]) >>> np.argmin(b) # Only the first occurrence is returned. 0 >>> x = np.array([[4,2,3], [1,0,3]]) >>> index_array = np.argmin(x, axis=-1) >>> # Same as np.min(x, axis=-1, keepdims=True) >>> np.take_along_axis(x, np.expand_dims(index_array, axis=-1), axis=-1) array([[2], [0]]) >>> # Same as np.max(x, axis=-1) >>> np.take_along_axis(x, np.expand_dims(index_array, axis=-1), axis=-1).squeeze(axis=-1) array([2, 0]) ### argpartition Perform an indirect partition along the given axis using the algorithm specified by the `kind` keyword. It returns an array of indices of the same shape as `a` that index data along the given axis in partitioned order. .. versionadded:: 1.8.0 Parameters ---------- a : array_like Array to sort. kth : int or sequence of ints Element index to partition by. The k-th element will be in its final sorted position and all smaller elements will be moved before it and all larger elements behind it. The order all elements in the partitions is undefined. If provided with a sequence of k-th it will partition all of them into their sorted position at once. axis : int or None, optional Axis along which to sort. The default is -1 (the last axis). If None, the flattened array is used. kind : {'introselect'}, optional Selection algorithm. Default is 'introselect' order : str or list of str, optional When `a` is an array with fields defined, this argument specifies which fields to compare first, second, etc. A single field can be specified as a string, and not all fields need be specified, but unspecified fields will still be used, in the order in which they come up in the dtype, to break ties. Returns ------- index_array : ndarray, int Array of indices that partition `a` along the specified axis. If `a` is one-dimensional, ``a[index_array]`` yields a partitioned `a`. More generally, ``np.take_along_axis(a, index_array, axis=a)`` always yields the partitioned `a`, irrespective of dimensionality. See Also -------- partition : Describes partition algorithms used. ndarray.partition : Inplace partition. argsort : Full indirect sort. take_along_axis : Apply ``index_array`` from argpartition to an array as if by calling partition. Notes ----- See `partition` for notes on the different selection algorithms. Examples -------- One dimensional array: >>> x = np.array([3, 4, 2, 1]) >>> x[np.argpartition(x, 3)] array([2, 1, 3, 4]) >>> x[np.argpartition(x, (1, 3))] array([1, 2, 3, 4]) >>> x = [3, 4, 2, 1] >>> np.array(x)[np.argpartition(x, 3)] array([2, 1, 3, 4]) Multi-dimensional array: >>> x = np.array([[3, 4, 2], [1, 3, 1]]) >>> index_array = np.argpartition(x, kth=1, axis=-1) >>> np.take_along_axis(x, index_array, axis=-1) # same as np.partition(x, kth=1) array([[2, 3, 4], [1, 1, 3]]) ### argsort Returns the indices that would sort an array. Perform an indirect sort along the given axis using the algorithm specified by the `kind` keyword. It returns an array of indices of the same shape as `a` that index data along the given axis in sorted order. Parameters ---------- a : array_like Array to sort. axis : int or None, optional Axis along which to sort. The default is -1 (the last axis). If None, the flattened array is used. kind : {'quicksort', 'mergesort', 'heapsort', 'stable'}, optional Sorting algorithm. The default is 'quicksort'. Note that both 'stable' and 'mergesort' use timsort under the covers and, in general, the actual implementation will vary with data type. The 'mergesort' option is retained for backwards compatibility. .. versionchanged:: 1.15.0. The 'stable' option was added. order : str or list of str, optional When `a` is an array with fields defined, this argument specifies which fields to compare first, second, etc. A single field can be specified as a string, and not all fields need be specified, but unspecified fields will still be used, in the order in which they come up in the dtype, to break ties. Returns ------- index_array : ndarray, int Array of indices that sort `a` along the specified `axis`. If `a` is one-dimensional, ``a[index_array]`` yields a sorted `a`. More generally, ``np.take_along_axis(a, index_array, axis=axis)`` always yields the sorted `a`, irrespective of dimensionality. See Also -------- sort : Describes sorting algorithms used. lexsort : Indirect stable sort with multiple keys. ndarray.sort : Inplace sort. argpartition : Indirect partial sort. take_along_axis : Apply ``index_array`` from argsort to an array as if by calling sort. Notes ----- See `sort` for notes on the different sorting algorithms. As of NumPy 1.4.0 `argsort` works with real/complex arrays containing nan values. The enhanced sort order is documented in `sort`. Examples -------- One dimensional array: >>> x = np.array([3, 1, 2]) >>> np.argsort(x) array([1, 2, 0]) Two-dimensional array: >>> x = np.array([[0, 3], [2, 2]]) >>> x array([[0, 3], [2, 2]]) >>> ind = np.argsort(x, axis=0) # sorts along first axis (down) >>> ind array([[0, 1], [1, 0]]) >>> np.take_along_axis(x, ind, axis=0) # same as np.sort(x, axis=0) array([[0, 2], [2, 3]]) >>> ind = np.argsort(x, axis=1) # sorts along last axis (across) >>> ind array([[0, 1], [0, 1]]) >>> np.take_along_axis(x, ind, axis=1) # same as np.sort(x, axis=1) array([[0, 3], [2, 2]]) Indices of the sorted elements of a N-dimensional array: >>> ind = np.unravel_index(np.argsort(x, axis=None), x.shape) >>> ind (array([0, 1, 1, 0]), array([0, 0, 1, 1])) >>> x[ind] # same as np.sort(x, axis=None) array([0, 2, 2, 3]) Sorting with keys: >>> x = np.array([(1, 0), (0, 1)], dtype=[('x', '>> x array([(1, 0), (0, 1)], dtype=[('x', '>> np.argsort(x, order=('x','y')) array([1, 0]) >>> np.argsort(x, order=('y','x')) array([0, 1]) ### argwhere Find the indices of array elements that are non-zero, grouped by element. Parameters ---------- a : array_like Input data. Returns ------- index_array : (N, a.ndim) ndarray Indices of elements that are non-zero. Indices are grouped by element. This array will have shape ``(N, a.ndim)`` where ``N`` is the number of non-zero items. See Also -------- where, nonzero Notes ----- ``np.argwhere(a)`` is almost the same as ``np.transpose(np.nonzero(a))``, but produces a result of the correct shape for a 0D array. The output of ``argwhere`` is not suitable for indexing arrays. For this purpose use ``nonzero(a)`` instead. Examples -------- >>> x = [np.arange(6)](https://www.chedong.com/phpMan.php/man/np.arange/6/markdown).reshape(2,3) >>> x array([[0, 1, 2], [3, 4, 5]]) >>> np.argwhere(x>1) array([[0, 2], [1, 0], [1, 1], [1, 2]]) ### around Evenly round to the given number of decimals. Parameters ---------- a : array_like Input data. decimals : int, optional Number of decimal places to round to (default: 0). If decimals is negative, it specifies the number of positions to the left of the decimal point. out : ndarray, optional Alternative output array in which to place the result. It must have the same shape as the expected output, but the type of the output values will be cast if necessary. See :ref:`ufuncs-output-type` for more details. Returns ------- rounded_array : ndarray An array of the same type as `a`, containing the rounded values. Unless `out` was specified, a new array is created. A reference to the result is returned. The real and imaginary parts of complex numbers are rounded separately. The result of rounding a float is a float. See Also -------- ndarray.round : equivalent method ceil, fix, floor, rint, trunc Notes ----- For values exactly halfway between rounded decimal values, NumPy rounds to the nearest even value. Thus 1.5 and 2.5 round to 2.0, -0.5 and 0.5 round to 0.0, etc. ``np.around`` uses a fast but sometimes inexact algorithm to round floating-point datatypes. For positive `decimals` it is equivalent to ``np.true_divide(np.rint(a * 10**decimals), 10**decimals)``, which has error due to the inexact representation of decimal fractions in the IEEE floating point standard [1]_ and errors introduced when scaling by powers of ten. For instance, note the extra "1" in the following: >>> np.round(56294995342131.5, 3) 56294995342131.51 If your goal is to print such values with a fixed number of decimals, it is preferable to use numpy's float printing routines to limit the number of printed decimals: >>> np.format_float_positional(56294995342131.5, precision=3) '56294995342131.5' The float printing routines use an accurate but much more computationally demanding algorithm to compute the number of digits after the decimal point. Alternatively, Python's builtin `round` function uses a more accurate but slower algorithm for 64-bit floating point values: >>> round(56294995342131.5, 3) 56294995342131.5 >>> np.round(16.055, 2), round(16.055, 2) # equals 16.0549999999999997 (16.06, 16.05) References ---------- .. [1] "Lecture Notes on the Status of IEEE 754", William Kahan, .. [2] "How Futile are Mindless Assessments of Roundoff in Floating-Point Computation?", William Kahan, Examples -------- >>> np.around([0.37, 1.64]) array([0., 2.]) >>> np.around([0.37, 1.64], decimals=1) array([0.4, 1.6]) >>> np.around([.5, 1.5, 2.5, 3.5, 4.5]) # rounds to nearest even value array([0., 2., 2., 4., 4.]) >>> np.around([1,2,3,11], decimals=1) # ndarray of ints is returned array([ 1, 2, 3, 11]) >>> np.around([1,2,3,11], decimals=-1) array([ 0, 0, 0, 10]) ### array array(object, dtype=None, *, copy=True, order='K', subok=False, ndmin=0, like=None) Create an array. Parameters ---------- object : array_like An array, any object exposing the array interface, an object whose __array__ method returns an array, or any (nested) sequence. dtype : data-type, optional The desired data-type for the array. If not given, then the type will be determined as the minimum type required to hold the objects in the sequence. copy : bool, optional If true (default), then the object is copied. Otherwise, a copy will only be made if __array__ returns a copy, if obj is a nested sequence, or if a copy is needed to satisfy any of the other requirements (`dtype`, `order`, etc.). order : {'K', 'A', 'C', 'F'}, optional Specify the memory layout of the array. If object is not an array, the newly created array will be in C order (row major) unless 'F' is specified, in which case it will be in Fortran order (column major). If object is an array the following holds. ===== ========= =================================================== order no copy copy=True ===== ========= =================================================== 'K' unchanged F & C order preserved, otherwise most similar order 'A' unchanged F order if input is F and not C, otherwise C order 'C' C order C order 'F' F order F order ===== ========= =================================================== When ``copy=False`` and a copy is made for other reasons, the result is the same as if ``copy=True``, with some exceptions for 'A', see the Notes section. The default order is 'K'. subok : bool, optional If True, then sub-classes will be passed-through, otherwise the returned array will be forced to be a base-class array (default). ndmin : int, optional Specifies the minimum number of dimensions that the resulting array should have. Ones will be pre-pended to the shape as needed to meet this requirement. like : array_like Reference object to allow the creation of arrays which are not NumPy arrays. If an array-like passed in as ``like`` supports the ``__array_function__`` protocol, the result will be defined by it. In this case, it ensures the creation of an array object compatible with that passed in via this argument. .. versionadded:: 1.20.0 Returns ------- out : ndarray An array object satisfying the specified requirements. See Also -------- empty_like : Return an empty array with shape and type of input. ones_like : Return an array of ones with shape and type of input. zeros_like : Return an array of zeros with shape and type of input. full_like : Return a new array with shape of input filled with value. empty : Return a new uninitialized array. ones : Return a new array setting values to one. zeros : Return a new array setting values to zero. full : Return a new array of given shape filled with value. Notes ----- When order is 'A' and `object` is an array in neither 'C' nor 'F' order, and a copy is forced by a change in dtype, then the order of the result is not necessarily 'C' as expected. This is likely a bug. Examples -------- >>> np.array([1, 2, 3]) array([1, 2, 3]) Upcasting: >>> np.array([1, 2, 3.0]) array([ 1., 2., 3.]) More than one dimension: >>> np.array([[1, 2], [3, 4]]) array([[1, 2], [3, 4]]) Minimum dimensions 2: >>> np.array([1, 2, 3], ndmin=2) array([[1, 2, 3]]) Type provided: >>> np.array([1, 2, 3], dtype=complex) array([ 1.+0.j, 2.+0.j, 3.+0.j]) Data-type consisting of more than one element: >>> x = np.array([(1,2),(3,4)],dtype=[('a','>> x['a'] array([1, 3]) Creating an array from sub-classes: >>> np.array(np.mat('1 2; 3 4')) array([[1, 2], [3, 4]]) >>> np.array(np.mat('1 2; 3 4'), subok=True) matrix([[1, 2], [3, 4]]) ### array2string Return a string representation of an array. Parameters ---------- a : ndarray Input array. max_line_width : int, optional Inserts newlines if text is longer than `max_line_width`. Defaults to ``numpy.get_printoptions()['linewidth']``. precision : int or None, optional Floating point precision. Defaults to ``numpy.get_printoptions()['precision']``. suppress_small : bool, optional Represent numbers "very close" to zero as zero; default is False. Very close is defined by precision: if the precision is 8, e.g., numbers smaller (in absolute value) than 5e-9 are represented as zero. Defaults to ``numpy.get_printoptions()['suppress']``. separator : str, optional Inserted between elements. prefix : str, optional suffix : str, optional The length of the prefix and suffix strings are used to respectively align and wrap the output. An array is typically printed as:: prefix + array2string(a) + suffix The output is left-padded by the length of the prefix string, and wrapping is forced at the column ``max_line_width - len(suffix)``. It should be noted that the content of prefix and suffix strings are not included in the output. style : _NoValue, optional Has no effect, do not use. .. deprecated:: 1.14.0 formatter : dict of callables, optional If not None, the keys should indicate the type(s) that the respective formatting function applies to. Callables should return a string. Types that are not specified (by their corresponding keys) are handled by the default formatters. Individual types for which a formatter can be set are: - 'bool' - 'int' - 'timedelta' : a `numpy.timedelta64` - 'datetime' : a `numpy.datetime64` - 'float' - 'longfloat' : 128-bit floats - 'complexfloat' - 'longcomplexfloat' : composed of two 128-bit floats - 'void' : type `numpy.void` - 'numpystr' : types `numpy.string_` and `numpy.unicode_` Other keys that can be used to set a group of types at once are: - 'all' : sets all types - 'int_kind' : sets 'int' - 'float_kind' : sets 'float' and 'longfloat' - 'complex_kind' : sets 'complexfloat' and 'longcomplexfloat' - 'str_kind' : sets 'numpystr' threshold : int, optional Total number of array elements which trigger summarization rather than full repr. Defaults to ``numpy.get_printoptions()['threshold']``. edgeitems : int, optional Number of array items in summary at beginning and end of each dimension. Defaults to ``numpy.get_printoptions()['edgeitems']``. sign : string, either '-', '+', or ' ', optional Controls printing of the sign of floating-point types. If '+', always print the sign of positive values. If ' ', always prints a space (whitespace character) in the sign position of positive values. If '-', omit the sign character of positive values. Defaults to ``numpy.get_printoptions()['sign']``. floatmode : str, optional Controls the interpretation of the `precision` option for floating-point types. Defaults to ``numpy.get_printoptions()['floatmode']``. Can take the following values: - 'fixed': Always print exactly `precision` fractional digits, even if this would print more or fewer digits than necessary to specify the value uniquely. - 'unique': Print the minimum number of fractional digits necessary to represent each value uniquely. Different elements may have a different number of digits. The value of the `precision` option is ignored. - 'maxprec': Print at most `precision` fractional digits, but if an element can be uniquely represented with fewer digits only print it with that many. - 'maxprec_equal': Print at most `precision` fractional digits, but if every element in the array can be uniquely represented with an equal number of fewer digits, use that many digits for all elements. legacy : string or `False`, optional If set to the string `'1.13'` enables 1.13 legacy printing mode. This approximates numpy 1.13 print output by including a space in the sign position of floats and different behavior for 0d arrays. If set to `False`, disables legacy mode. Unrecognized strings will be ignored with a warning for forward compatibility. .. versionadded:: 1.14.0 Returns ------- array_str : str String representation of the array. Raises ------ TypeError if a callable in `formatter` does not return a string. See Also -------- array_str, array_repr, set_printoptions, get_printoptions Notes ----- If a formatter is specified for a certain type, the `precision` keyword is ignored for that type. This is a very flexible function; `array_repr` and `array_str` are using `array2string` internally so keywords with the same name should work identically in all three functions. Examples -------- >>> x = np.array([1e-16,1,2,3]) >>> np.array2string(x, precision=2, separator=',', ... suppress_small=True) '[0.,1.,2.,3.]' >>> x = np.arange(3.) >>> np.array2string(x, formatter={'float_kind':lambda x: "%.2f" % x}) '[0.00 1.00 2.00]' >>> x = [np.arange(3)](https://www.chedong.com/phpMan.php/man/np.arange/3/markdown) >>> np.array2string(x, formatter={'int':lambda x: hex(x)}) '[0x0 0x1 0x2]' ### array_equal True if two arrays have the same shape and elements, False otherwise. Parameters ---------- a1, a2 : array_like Input arrays. equal_nan : bool Whether to compare NaN's as equal. If the dtype of a1 and a2 is complex, values will be considered equal if either the real or the imaginary component of a given value is ``nan``. .. versionadded:: 1.19.0 Returns ------- b : bool Returns True if the arrays are equal. See Also -------- allclose: Returns True if two arrays are element-wise equal within a tolerance. array_equiv: Returns True if input arrays are shape consistent and all elements equal. Examples -------- >>> np.array_equal([1, 2], [1, 2]) True >>> np.array_equal(np.array([1, 2]), np.array([1, 2])) True >>> np.array_equal([1, 2], [1, 2, 3]) False >>> np.array_equal([1, 2], [1, 4]) False >>> a = np.array([1, np.nan]) >>> np.array_equal(a, a) False >>> np.array_equal(a, a, equal_nan=True) True When ``equal_nan`` is True, complex values with nan components are considered equal if either the real *or* the imaginary components are nan. >>> a = np.array([1 + 1j]) >>> b = a.copy() >>> a.real = np.nan >>> b.imag = np.nan >>> np.array_equal(a, b, equal_nan=True) True ### array_equiv Returns True if input arrays are shape consistent and all elements equal. Shape consistent means they are either the same shape, or one input array can be broadcasted to create the same shape as the other one. Parameters ---------- a1, a2 : array_like Input arrays. Returns ------- out : bool True if equivalent, False otherwise. Examples -------- >>> np.array_equiv([1, 2], [1, 2]) True >>> np.array_equiv([1, 2], [1, 3]) False Showing the shape equivalence: >>> np.array_equiv([1, 2], [[1, 2], [1, 2]]) True >>> np.array_equiv([1, 2], [[1, 2, 1, 2], [1, 2, 1, 2]]) False >>> np.array_equiv([1, 2], [[1, 2], [1, 3]]) False ### array_repr Return the string representation of an array. Parameters ---------- arr : ndarray Input array. max_line_width : int, optional Inserts newlines if text is longer than `max_line_width`. Defaults to ``numpy.get_printoptions()['linewidth']``. precision : int, optional Floating point precision. Defaults to ``numpy.get_printoptions()['precision']``. suppress_small : bool, optional Represent numbers "very close" to zero as zero; default is False. Very close is defined by precision: if the precision is 8, e.g., numbers smaller (in absolute value) than 5e-9 are represented as zero. Defaults to ``numpy.get_printoptions()['suppress']``. Returns ------- string : str The string representation of an array. See Also -------- array_str, array2string, set_printoptions Examples -------- >>> np.array_repr(np.array([1,2])) 'array([1, 2])' >>> np.array_repr(np.ma.array([0.])) 'MaskedArray([0.])' >>> np.array_repr(np.array([], np.int32)) 'array([], dtype=int32)' >>> x = np.array([1e-6, 4e-7, 2, 3]) >>> np.array_repr(x, precision=6, suppress_small=True) 'array([0.000001, 0. , 2. , 3. ])' ### array_split Split an array into multiple sub-arrays. Please refer to the ``split`` documentation. The only difference between these functions is that ``array_split`` allows `indices_or_sections` to be an integer that does *not* equally divide the axis. For an array of length l that should be split into n sections, it returns l % n sub-arrays of size l//n + 1 and the rest of size l//n. See Also -------- split : Split array into multiple sub-arrays of equal size. Examples -------- >>> x = np.arange(8.0) >>> np.array_split(x, 3) [array([0., 1., 2.]), array([3., 4., 5.]), array([6., 7.])] >>> x = [np.arange(9)](https://www.chedong.com/phpMan.php/man/np.arange/9/markdown) >>> np.array_split(x, 4) [array([0, 1, 2]), array([3, 4]), array([5, 6]), array([7, 8])] ### array_str Return a string representation of the data in an array. The data in the array is returned as a single string. This function is similar to `array_repr`, the difference being that `array_repr` also returns information on the kind of array and its data type. Parameters ---------- a : ndarray Input array. max_line_width : int, optional Inserts newlines if text is longer than `max_line_width`. Defaults to ``numpy.get_printoptions()['linewidth']``. precision : int, optional Floating point precision. Defaults to ``numpy.get_printoptions()['precision']``. suppress_small : bool, optional Represent numbers "very close" to zero as zero; default is False. Very close is defined by precision: if the precision is 8, e.g., numbers smaller (in absolute value) than 5e-9 are represented as zero. Defaults to ``numpy.get_printoptions()['suppress']``. See Also -------- array2string, array_repr, set_printoptions Examples -------- >>> np.array_str([np.arange(3)](https://www.chedong.com/phpMan.php/man/np.arange/3/markdown)) '[0 1 2]' ### asanyarray asanyarray(a, dtype=None, order=None, *, like=None) Convert the input to an ndarray, but pass ndarray subclasses through. Parameters ---------- a : array_like Input data, in any form that can be converted to an array. This includes scalars, lists, lists of tuples, tuples, tuples of tuples, tuples of lists, and ndarrays. dtype : data-type, optional By default, the data-type is inferred from the input data. order : {'C', 'F', 'A', 'K'}, optional Memory layout. 'A' and 'K' depend on the order of input array a. 'C' row-major (C-style), 'F' column-major (Fortran-style) memory representation. 'A' (any) means 'F' if `a` is Fortran contiguous, 'C' otherwise 'K' (keep) preserve input order Defaults to 'C'. like : array_like Reference object to allow the creation of arrays which are not NumPy arrays. If an array-like passed in as ``like`` supports the ``__array_function__`` protocol, the result will be defined by it. In this case, it ensures the creation of an array object compatible with that passed in via this argument. .. versionadded:: 1.20.0 Returns ------- out : ndarray or an ndarray subclass Array interpretation of `a`. If `a` is an ndarray or a subclass of ndarray, it is returned as-is and no copy is performed. See Also -------- asarray : Similar function which always returns ndarrays. ascontiguousarray : Convert input to a contiguous array. asfarray : Convert input to a floating point ndarray. asfortranarray : Convert input to an ndarray with column-major memory order. asarray_chkfinite : Similar function which checks input for NaNs and Infs. fromiter : Create an array from an iterator. fromfunction : Construct an array by executing a function on grid positions. Examples -------- Convert a list into an array: >>> a = [1, 2] >>> np.asanyarray(a) array([1, 2]) Instances of `ndarray` subclasses are passed through as-is: >>> a = np.array([(1.0, 2), (3.0, 4)], dtype='f4,i4').view(np.recarray) >>> np.asanyarray(a) is a True ### asarray asarray(a, dtype=None, order=None, *, like=None) Convert the input to an array. Parameters ---------- a : array_like Input data, in any form that can be converted to an array. This includes lists, lists of tuples, tuples, tuples of tuples, tuples of lists and ndarrays. dtype : data-type, optional By default, the data-type is inferred from the input data. order : {'C', 'F', 'A', 'K'}, optional Memory layout. 'A' and 'K' depend on the order of input array a. 'C' row-major (C-style), 'F' column-major (Fortran-style) memory representation. 'A' (any) means 'F' if `a` is Fortran contiguous, 'C' otherwise 'K' (keep) preserve input order Defaults to 'C'. like : array_like Reference object to allow the creation of arrays which are not NumPy arrays. If an array-like passed in as ``like`` supports the ``__array_function__`` protocol, the result will be defined by it. In this case, it ensures the creation of an array object compatible with that passed in via this argument. .. versionadded:: 1.20.0 Returns ------- out : ndarray Array interpretation of `a`. No copy is performed if the input is already an ndarray with matching dtype and order. If `a` is a subclass of ndarray, a base class ndarray is returned. See Also -------- asanyarray : Similar function which passes through subclasses. ascontiguousarray : Convert input to a contiguous array. asfarray : Convert input to a floating point ndarray. asfortranarray : Convert input to an ndarray with column-major memory order. asarray_chkfinite : Similar function which checks input for NaNs and Infs. fromiter : Create an array from an iterator. fromfunction : Construct an array by executing a function on grid positions. Examples -------- Convert a list into an array: >>> a = [1, 2] >>> np.asarray(a) array([1, 2]) Existing arrays are not copied: >>> a = np.array([1, 2]) >>> np.asarray(a) is a True If `dtype` is set, array is copied only if dtype does not match: >>> a = np.array([1, 2], dtype=np.float32) >>> np.asarray(a, dtype=np.float32) is a True >>> np.asarray(a, dtype=np.float64) is a False Contrary to `asanyarray`, ndarray subclasses are not passed through: >>> issubclass(np.recarray, np.ndarray) True >>> a = np.array([(1.0, 2), (3.0, 4)], dtype='f4,i4').view(np.recarray) >>> np.asarray(a) is a False >>> np.asanyarray(a) is a True ### asarray_chkfinite Convert the input to an array, checking for NaNs or Infs. Parameters ---------- a : array_like Input data, in any form that can be converted to an array. This includes lists, lists of tuples, tuples, tuples of tuples, tuples of lists and ndarrays. Success requires no NaNs or Infs. dtype : data-type, optional By default, the data-type is inferred from the input data. order : {'C', 'F', 'A', 'K'}, optional Memory layout. 'A' and 'K' depend on the order of input array a. 'C' row-major (C-style), 'F' column-major (Fortran-style) memory representation. 'A' (any) means 'F' if `a` is Fortran contiguous, 'C' otherwise 'K' (keep) preserve input order Defaults to 'C'. Returns ------- out : ndarray Array interpretation of `a`. No copy is performed if the input is already an ndarray. If `a` is a subclass of ndarray, a base class ndarray is returned. Raises ------ ValueError Raises ValueError if `a` contains NaN (Not a Number) or Inf (Infinity). See Also -------- asarray : Create and array. asanyarray : Similar function which passes through subclasses. ascontiguousarray : Convert input to a contiguous array. asfarray : Convert input to a floating point ndarray. asfortranarray : Convert input to an ndarray with column-major memory order. fromiter : Create an array from an iterator. fromfunction : Construct an array by executing a function on grid positions. Examples -------- Convert a list into an array. If all elements are finite ``asarray_chkfinite`` is identical to ``asarray``. >>> a = [1, 2] >>> np.asarray_chkfinite(a, dtype=float) array([1., 2.]) Raises ValueError if array_like contains Nans or Infs. >>> a = [1, 2, np.inf] >>> try: ... np.asarray_chkfinite(a) ... except ValueError: ... print('ValueError') ... ValueError ### ascontiguousarray ascontiguousarray(a, dtype=None, *, like=None) Return a contiguous array (ndim >= 1) in memory (C order). Parameters ---------- a : array_like Input array. dtype : str or dtype object, optional Data-type of returned array. like : array_like Reference object to allow the creation of arrays which are not NumPy arrays. If an array-like passed in as ``like`` supports the ``__array_function__`` protocol, the result will be defined by it. In this case, it ensures the creation of an array object compatible with that passed in via this argument. .. versionadded:: 1.20.0 Returns ------- out : ndarray Contiguous array of same shape and content as `a`, with type `dtype` if specified. See Also -------- asfortranarray : Convert input to an ndarray with column-major memory order. require : Return an ndarray that satisfies requirements. ndarray.flags : Information about the memory layout of the array. Examples -------- >>> x = [np.arange(6)](https://www.chedong.com/phpMan.php/man/np.arange/6/markdown).reshape(2,3) >>> np.ascontiguousarray(x, dtype=np.float32) array([[0., 1., 2.], [3., 4., 5.]], dtype=float32) >>> x.flags['C_CONTIGUOUS'] True Note: This function returns an array with at least one-dimension (1-d) so it will not preserve 0-d arrays. ### asfarray Return an array converted to a float type. Parameters ---------- a : array_like The input array. dtype : str or dtype object, optional Float type code to coerce input array `a`. If `dtype` is one of the 'int' dtypes, it is replaced with float64. Returns ------- out : ndarray The input `a` as a float ndarray. Examples -------- >>> np.asfarray([2, 3]) array([2., 3.]) >>> np.asfarray([2, 3], dtype='float') array([2., 3.]) >>> np.asfarray([2, 3], dtype='int8') array([2., 3.]) ### asfortranarray asfortranarray(a, dtype=None, *, like=None) Return an array (ndim >= 1) laid out in Fortran order in memory. Parameters ---------- a : array_like Input array. dtype : str or dtype object, optional By default, the data-type is inferred from the input data. like : array_like Reference object to allow the creation of arrays which are not NumPy arrays. If an array-like passed in as ``like`` supports the ``__array_function__`` protocol, the result will be defined by it. In this case, it ensures the creation of an array object compatible with that passed in via this argument. .. versionadded:: 1.20.0 Returns ------- out : ndarray The input `a` in Fortran, or column-major, order. See Also -------- ascontiguousarray : Convert input to a contiguous (C order) array. asanyarray : Convert input to an ndarray with either row or column-major memory order. require : Return an ndarray that satisfies requirements. ndarray.flags : Information about the memory layout of the array. Examples -------- >>> x = [np.arange(6)](https://www.chedong.com/phpMan.php/man/np.arange/6/markdown).reshape(2,3) >>> y = np.asfortranarray(x) >>> x.flags['F_CONTIGUOUS'] False >>> y.flags['F_CONTIGUOUS'] True Note: This function returns an array with at least one-dimension (1-d) so it will not preserve 0-d arrays. ### asmatrix Interpret the input as a matrix. Unlike `matrix`, `asmatrix` does not make a copy if the input is already a matrix or an ndarray. Equivalent to ``matrix(data, copy=False)``. Parameters ---------- data : array_like Input data. dtype : data-type Data-type of the output matrix. Returns ------- mat : matrix `data` interpreted as a matrix. Examples -------- >>> x = np.array([[1, 2], [3, 4]]) >>> m = np.asmatrix(x) >>> x[0,0] = 5 >>> m matrix([[5, 2], [3, 4]]) ### asscalar Convert an array of size 1 to its scalar equivalent. .. deprecated:: 1.16 Deprecated, use `numpy.ndarray.item()` instead. Parameters ---------- a : ndarray Input array of size 1. Returns ------- out : scalar Scalar representation of `a`. The output data type is the same type returned by the input's `item` method. Examples -------- >>> np.asscalar(np.array([24])) 24 ### atleast_1d Convert inputs to arrays with at least one dimension. Scalar inputs are converted to 1-dimensional arrays, whilst higher-dimensional inputs are preserved. Parameters ---------- arys1, arys2, ... : array_like One or more input arrays. Returns ------- ret : ndarray An array, or list of arrays, each with ``a.ndim >= 1``. Copies are made only if necessary. See Also -------- atleast_2d, atleast_3d Examples -------- >>> np.atleast_1d(1.0) array([1.]) >>> x = np.arange(9.0).reshape(3,3) >>> np.atleast_1d(x) array([[0., 1., 2.], [3., 4., 5.], [6., 7., 8.]]) >>> np.atleast_1d(x) is x True >>> np.atleast_1d(1, [3, 4]) [array([1]), array([3, 4])] ### atleast_2d View inputs as arrays with at least two dimensions. Parameters ---------- arys1, arys2, ... : array_like One or more array-like sequences. Non-array inputs are converted to arrays. Arrays that already have two or more dimensions are preserved. Returns ------- res, res2, ... : ndarray An array, or list of arrays, each with ``a.ndim >= 2``. Copies are avoided where possible, and views with two or more dimensions are returned. See Also -------- atleast_1d, atleast_3d Examples -------- >>> np.atleast_2d(3.0) array([[3.]]) >>> x = np.arange(3.0) >>> np.atleast_2d(x) array([[0., 1., 2.]]) >>> np.atleast_2d(x).base is x True >>> np.atleast_2d(1, [1, 2], [[1, 2]]) [array([[1]]), array([[1, 2]]), array([[1, 2]])] ### atleast_3d View inputs as arrays with at least three dimensions. Parameters ---------- arys1, arys2, ... : array_like One or more array-like sequences. Non-array inputs are converted to arrays. Arrays that already have three or more dimensions are preserved. Returns ------- res1, res2, ... : ndarray An array, or list of arrays, each with ``a.ndim >= 3``. Copies are avoided where possible, and views with three or more dimensions are returned. For example, a 1-D array of shape ``(N,)`` becomes a view of shape ``(1, N, 1)``, and a 2-D array of shape ``(M, N)`` becomes a view of shape ``(M, N, 1)``. See Also -------- atleast_1d, atleast_2d Examples -------- >>> np.atleast_3d(3.0) array([[[3.]]]) >>> x = np.arange(3.0) >>> np.atleast_3d(x).shape (1, 3, 1) >>> x = np.arange(12.0).reshape(4,3) >>> np.atleast_3d(x).shape (4, 3, 1) >>> np.atleast_3d(x).base is x.base # x is a reshape, so not base itself True >>> for arr in np.atleast_3d([1, 2], [[1, 2]], [[[1, 2]]]): ... print(arr, arr.shape) # doctest: +SKIP ... [[[1] [2]]] (1, 2, 1) [[[1] [2]]] (1, 2, 1) [[[1 2]]] (1, 1, 2) ### average Compute the weighted average along the specified axis. Parameters ---------- a : array_like Array containing data to be averaged. If `a` is not an array, a conversion is attempted. axis : None or int or tuple of ints, optional Axis or axes along which to average `a`. The default, axis=None, will average over all of the elements of the input array. If axis is negative it counts from the last to the first axis. .. versionadded:: 1.7.0 If axis is a tuple of ints, averaging is performed on all of the axes specified in the tuple instead of a single axis or all the axes as before. weights : array_like, optional An array of weights associated with the values in `a`. Each value in `a` contributes to the average according to its associated weight. The weights array can either be 1-D (in which case its length must be the size of `a` along the given axis) or of the same shape as `a`. If `weights=None`, then all data in `a` are assumed to have a weight equal to one. The 1-D calculation is:: avg = sum(a * weights) / sum(weights) The only constraint on `weights` is that `sum(weights)` must not be 0. returned : bool, optional Default is `False`. If `True`, the tuple (`average`, `sum_of_weights`) is returned, otherwise only the average is returned. If `weights=None`, `sum_of_weights` is equivalent to the number of elements over which the average is taken. Returns ------- retval, [sum_of_weights] : array_type or double Return the average along the specified axis. When `returned` is `True`, return a tuple with the average as the first element and the sum of the weights as the second element. `sum_of_weights` is of the same type as `retval`. The result dtype follows a genereal pattern. If `weights` is None, the result dtype will be that of `a` , or ``float64`` if `a` is integral. Otherwise, if `weights` is not None and `a` is non- integral, the result type will be the type of lowest precision capable of representing values of both `a` and `weights`. If `a` happens to be integral, the previous rules still applies but the result dtype will at least be ``float64``. Raises ------ ZeroDivisionError When all weights along axis are zero. See `numpy.ma.average` for a version robust to this type of error. TypeError When the length of 1D `weights` is not the same as the shape of `a` along axis. See Also -------- mean ma.average : average for masked arrays -- useful if your data contains "missing" values numpy.result_type : Returns the type that results from applying the numpy type promotion rules to the arguments. Examples -------- >>> data = np.arange(1, 5) >>> data array([1, 2, 3, 4]) >>> np.average(data) 2.5 >>> np.average(np.arange(1, 11), weights=np.arange(10, 0, -1)) 4.0 >>> data = [np.arange(6)](https://www.chedong.com/phpMan.php/man/np.arange/6/markdown).reshape((3,2)) >>> data array([[0, 1], [2, 3], [4, 5]]) >>> np.average(data, axis=1, weights=[1./4, 3./4]) array([0.75, 2.75, 4.75]) >>> np.average(data, weights=[1./4, 3./4]) Traceback (most recent call last): ... TypeError: Axis must be specified when shapes of a and weights differ. >>> a = np.ones(5, dtype=np.float128) >>> w = np.ones(5, dtype=np.complex64) >>> avg = np.average(a, weights=w) >>> print(avg.dtype) complex256 ### bartlett Return the Bartlett window. The Bartlett window is very similar to a triangular window, except that the end points are at zero. It is often used in signal processing for tapering a signal, without generating too much ripple in the frequency domain. Parameters ---------- M : int Number of points in the output window. If zero or less, an empty array is returned. Returns ------- out : array The triangular window, with the maximum value normalized to one (the value one appears only if the number of samples is odd), with the first and last samples equal to zero. See Also -------- blackman, hamming, hanning, kaiser Notes ----- The Bartlett window is defined as .. math:: [w(n)](https://www.chedong.com/phpMan.php/man/w/n/markdown) = \frac{2}{M-1} \left( \frac{M-1}{2} - \left|n - \frac{M-1}{2}\right| \right) Most references to the Bartlett window come from the signal processing literature, where it is used as one of many windowing functions for smoothing values. Note that convolution with this window produces linear interpolation. It is also known as an apodization (which means"removing the foot", i.e. smoothing discontinuities at the beginning and end of the sampled signal) or tapering function. The fourier transform of the Bartlett is the product of two sinc functions. Note the excellent discussion in Kanasewich. References ---------- .. [1] M.S. Bartlett, "Periodogram Analysis and Continuous Spectra", Biometrika 37, 1-16, 1950. .. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics", The University of Alberta Press, 1975, pp. 109-110. .. [3] A.V. Oppenheim and R.W. Schafer, "Discrete-Time Signal Processing", Prentice-Hall, 1999, pp. 468-471. .. [4] Wikipedia, "Window function", .. [5] W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling, "Numerical Recipes", Cambridge University Press, 1986, page 429. Examples -------- >>> import matplotlib.pyplot as plt >>> [np.bartlett(12)](https://www.chedong.com/phpMan.php/man/np.bartlett/12/markdown) array([ 0. , 0.18181818, 0.36363636, 0.54545455, 0.72727273, # may vary 0.90909091, 0.90909091, 0.72727273, 0.54545455, 0.36363636, 0.18181818, 0. ]) Plot the window and its frequency response (requires SciPy and matplotlib): >>> from numpy.fft import fft, fftshift >>> window = [np.bartlett(51)](https://www.chedong.com/phpMan.php/man/np.bartlett/51/markdown) >>> plt.plot(window) [] >>> plt.title("Bartlett window") Text(0.5, 1.0, 'Bartlett window') >>> plt.ylabel("Amplitude") Text(0, 0.5, 'Amplitude') >>> plt.xlabel("Sample") Text(0.5, 0, 'Sample') >>> plt.show() >>> plt.figure()
>>> A = fft(window, 2048) / 25.5 >>> mag = np.abs(fftshift(A)) >>> freq = np.linspace(-0.5, 0.5, len(A)) >>> with np.errstate(divide='ignore', invalid='ignore'): ... response = 20 * np.log10(mag) ... >>> response = np.clip(response, -100, 100) >>> plt.plot(freq, response) [] >>> plt.title("Frequency response of Bartlett window") Text(0.5, 1.0, 'Frequency response of Bartlett window') >>> plt.ylabel("Magnitude [dB]") Text(0, 0.5, 'Magnitude [dB]') >>> plt.xlabel("Normalized frequency [cycles per sample]") Text(0.5, 0, 'Normalized frequency [cycles per sample]') >>> _ = plt.axis('tight') >>> plt.show() ### base_repr Return a string representation of a number in the given base system. Parameters ---------- number : int The value to convert. Positive and negative values are handled. base : int, optional Convert `number` to the `base` number system. The valid range is 2-36, the default value is 2. padding : int, optional Number of zeros padded on the left. Default is 0 (no padding). Returns ------- out : str String representation of `number` in `base` system. See Also -------- binary_repr : Faster version of `base_repr` for base 2. Examples -------- >>> [np.base_repr(5)](https://www.chedong.com/phpMan.php/man/np.baserepr/5/markdown) '101' >>> np.base_repr(6, 5) '11' >>> np.base_repr(7, base=5, padding=3) '00012' >>> np.base_repr(10, base=16) 'A' >>> np.base_repr(32, base=16) '20' ### binary_repr Return the binary representation of the input number as a string. For negative numbers, if width is not given, a minus sign is added to the front. If width is given, the two's complement of the number is returned, with respect to that width. In a two's-complement system negative numbers are represented by the two's complement of the absolute value. This is the most common method of representing signed integers on computers [1]_. A N-bit two's-complement system can represent every integer in the range :math:`-2^{N-1}` to :math:`+2^{N-1}-1`. Parameters ---------- num : int Only an integer decimal number can be used. width : int, optional The length of the returned string if `num` is positive, or the length of the two's complement if `num` is negative, provided that `width` is at least a sufficient number of bits for `num` to be represented in the designated form. If the `width` value is insufficient, it will be ignored, and `num` will be returned in binary (`num` > 0) or two's complement (`num` < 0) form with its width equal to the minimum number of bits needed to represent the number in the designated form. This behavior is deprecated and will later raise an error. .. deprecated:: 1.12.0 Returns ------- bin : str Binary representation of `num` or two's complement of `num`. See Also -------- base_repr: Return a string representation of a number in the given base system. bin: Python's built-in binary representation generator of an integer. Notes ----- `binary_repr` is equivalent to using `base_repr` with base 2, but about 25x faster. References ---------- .. [1] Wikipedia, "Two's complement", 's_complement Examples -------- >>> [np.binary_repr(3)](https://www.chedong.com/phpMan.php/man/np.binaryrepr/3/markdown) '11' >>> np.binary_repr(-3) '-11' >>> np.binary_repr(3, width=4) '0011' The two's complement is returned when the input number is negative and width is specified: >>> np.binary_repr(-3, width=3) '101' >>> np.binary_repr(-3, width=5) '11101' ### bincount bincount(x, weights=None, minlength=0) Count number of occurrences of each value in array of non-negative ints. The number of bins (of size 1) is one larger than the largest value in `x`. If `minlength` is specified, there will be at least this number of bins in the output array (though it will be longer if necessary, depending on the contents of `x`). Each bin gives the number of occurrences of its index value in `x`. If `weights` is specified the input array is weighted by it, i.e. if a value ``n`` is found at position ``i``, ``out[n] += weight[i]`` instead of ``out[n] += 1``. Parameters ---------- x : array_like, 1 dimension, nonnegative ints Input array. weights : array_like, optional Weights, array of the same shape as `x`. minlength : int, optional A minimum number of bins for the output array. .. versionadded:: 1.6.0 Returns ------- out : ndarray of ints The result of binning the input array. The length of `out` is equal to ``np.amax(x)+1``. Raises ------ ValueError If the input is not 1-dimensional, or contains elements with negative values, or if `minlength` is negative. TypeError If the type of the input is float or complex. See Also -------- histogram, digitize, unique Examples -------- >>> np.bincount([np.arange(5)](https://www.chedong.com/phpMan.php/man/np.arange/5/markdown)) array([1, 1, 1, 1, 1]) >>> np.bincount(np.array([0, 1, 1, 3, 2, 1, 7])) array([1, 3, 1, 1, 0, 0, 0, 1]) >>> x = np.array([0, 1, 1, 3, 2, 1, 7, 23]) >>> np.bincount(x).size == np.amax(x)+1 True The input array needs to be of integer dtype, otherwise a TypeError is raised: >>> np.bincount(np.arange(5, dtype=float)) Traceback (most recent call last): ... TypeError: Cannot cast array data from dtype('float64') to dtype('int64') according to the rule 'safe' A possible use of ``bincount`` is to perform sums over variable-size chunks of an array, using the ``weights`` keyword. >>> w = np.array([0.3, 0.5, 0.2, 0.7, 1., -0.6]) # weights >>> x = np.array([0, 1, 1, 2, 2, 2]) >>> np.bincount(x, weights=w) array([ 0.3, 0.7, 1.1]) ### blackman Return the Blackman window. The Blackman window is a taper formed by using the first three terms of a summation of cosines. It was designed to have close to the minimal leakage possible. It is close to optimal, only slightly worse than a Kaiser window. Parameters ---------- M : int Number of points in the output window. If zero or less, an empty array is returned. Returns ------- out : ndarray The window, with the maximum value normalized to one (the value one appears only if the number of samples is odd). See Also -------- bartlett, hamming, hanning, kaiser Notes ----- The Blackman window is defined as .. math:: [w(n)](https://www.chedong.com/phpMan.php/man/w/n/markdown) = 0.42 - 0.5 \cos(2\pi n/M) + 0.08 \cos(4\pi n/M) Most references to the Blackman window come from the signal processing literature, where it is used as one of many windowing functions for smoothing values. It is also known as an apodization (which means "removing the foot", i.e. smoothing discontinuities at the beginning and end of the sampled signal) or tapering function. It is known as a "near optimal" tapering function, almost as good (by some measures) as the kaiser window. References ---------- Blackman, R.B. and Tukey, J.W., (1958) The measurement of power spectra, Dover Publications, New York. Oppenheim, A.V., and R.W. Schafer. Discrete-Time Signal Processing. Upper Saddle River, NJ: Prentice-Hall, 1999, pp. 468-471. Examples -------- >>> import matplotlib.pyplot as plt >>> [np.blackman(12)](https://www.chedong.com/phpMan.php/man/np.blackman/12/markdown) array([-1.38777878e-17, 3.26064346e-02, 1.59903635e-01, # may vary 4.14397981e-01, 7.36045180e-01, 9.67046769e-01, 9.67046769e-01, 7.36045180e-01, 4.14397981e-01, 1.59903635e-01, 3.26064346e-02, -1.38777878e-17]) Plot the window and the frequency response: >>> from numpy.fft import fft, fftshift >>> window = [np.blackman(51)](https://www.chedong.com/phpMan.php/man/np.blackman/51/markdown) >>> plt.plot(window) [] >>> plt.title("Blackman window") Text(0.5, 1.0, 'Blackman window') >>> plt.ylabel("Amplitude") Text(0, 0.5, 'Amplitude') >>> plt.xlabel("Sample") Text(0.5, 0, 'Sample') >>> plt.show() >>> plt.figure()
>>> A = fft(window, 2048) / 25.5 >>> mag = np.abs(fftshift(A)) >>> freq = np.linspace(-0.5, 0.5, len(A)) >>> with np.errstate(divide='ignore', invalid='ignore'): ... response = 20 * np.log10(mag) ... >>> response = np.clip(response, -100, 100) >>> plt.plot(freq, response) [] >>> plt.title("Frequency response of Blackman window") Text(0.5, 1.0, 'Frequency response of Blackman window') >>> plt.ylabel("Magnitude [dB]") Text(0, 0.5, 'Magnitude [dB]') >>> plt.xlabel("Normalized frequency [cycles per sample]") Text(0.5, 0, 'Normalized frequency [cycles per sample]') >>> _ = plt.axis('tight') >>> plt.show() ### block Assemble an nd-array from nested lists of blocks. Blocks in the innermost lists are concatenated (see `concatenate`) along the last dimension (-1), then these are concatenated along the second-last dimension (-2), and so on until the outermost list is reached. Blocks can be of any dimension, but will not be broadcasted using the normal rules. Instead, leading axes of size 1 are inserted, to make ``block.ndim`` the same for all blocks. This is primarily useful for working with scalars, and means that code like ``np.block([v, 1])`` is valid, where ``v.ndim == 1``. When the nested list is two levels deep, this allows block matrices to be constructed from their components. .. versionadded:: 1.13.0 Parameters ---------- arrays : nested list of array_like or scalars (but not tuples) If passed a single ndarray or scalar (a nested list of depth 0), this is returned unmodified (and not copied). Elements shapes must match along the appropriate axes (without broadcasting), but leading 1s will be prepended to the shape as necessary to make the dimensions match. Returns ------- block_array : ndarray The array assembled from the given blocks. The dimensionality of the output is equal to the greatest of: * the dimensionality of all the inputs * the depth to which the input list is nested Raises ------ ValueError * If list depths are mismatched - for instance, ``[[a, b], c]`` is illegal, and should be spelt ``[[a, b], [c]]`` * If lists are empty - for instance, ``[[a, b], []]`` See Also -------- concatenate : Join a sequence of arrays along an existing axis. stack : Join a sequence of arrays along a new axis. vstack : Stack arrays in sequence vertically (row wise). hstack : Stack arrays in sequence horizontally (column wise). dstack : Stack arrays in sequence depth wise (along third axis). column_stack : Stack 1-D arrays as columns into a 2-D array. vsplit : Split an array into multiple sub-arrays vertically (row-wise). Notes ----- When called with only scalars, ``np.block`` is equivalent to an ndarray call. So ``np.block([[1, 2], [3, 4]])`` is equivalent to ``np.array([[1, 2], [3, 4]])``. This function does not enforce that the blocks lie on a fixed grid. ``np.block([[a, b], [c, d]])`` is not restricted to arrays of the form:: AAAbb AAAbb cccDD But is also allowed to produce, for some ``a, b, c, d``:: AAAbb AAAbb cDDDD Since concatenation happens along the last axis first, `block` is _not_ capable of producing the following directly:: AAAbb cccbb cccDD Matlab's "square bracket stacking", ``[A, B, ...; p, q, ...]``, is equivalent to ``np.block([[A, B, ...], [p, q, ...]])``. Examples -------- The most common use of this function is to build a block matrix >>> A = [np.eye(2)](https://www.chedong.com/phpMan.php/man/np.eye/2/markdown) * 2 >>> B = [np.eye(3)](https://www.chedong.com/phpMan.php/man/np.eye/3/markdown) * 3 >>> np.block([ ... [A, np.zeros((2, 3))], ... [np.ones((3, 2)), B ] ... ]) array([[2., 0., 0., 0., 0.], [0., 2., 0., 0., 0.], [1., 1., 3., 0., 0.], [1., 1., 0., 3., 0.], [1., 1., 0., 0., 3.]]) With a list of depth 1, `block` can be used as `hstack` >>> np.block([1, 2, 3]) # hstack([1, 2, 3]) array([1, 2, 3]) >>> a = np.array([1, 2, 3]) >>> b = np.array([4, 5, 6]) >>> np.block([a, b, 10]) # hstack([a, b, 10]) array([ 1, 2, 3, 4, 5, 6, 10]) >>> A = np.ones((2, 2), int) >>> B = 2 * A >>> np.block([A, B]) # hstack([A, B]) array([[1, 1, 2, 2], [1, 1, 2, 2]]) With a list of depth 2, `block` can be used in place of `vstack`: >>> a = np.array([1, 2, 3]) >>> b = np.array([4, 5, 6]) >>> np.block([[a], [b]]) # vstack([a, b]) array([[1, 2, 3], [4, 5, 6]]) >>> A = np.ones((2, 2), int) >>> B = 2 * A >>> np.block([[A], [B]]) # vstack([A, B]) array([[1, 1], [1, 1], [2, 2], [2, 2]]) It can also be used in places of `atleast_1d` and `atleast_2d` >>> a = [np.array(0)](https://www.chedong.com/phpMan.php/man/np.array/0/markdown) >>> b = np.array([1]) >>> np.block([a]) # atleast_1d(a) array([0]) >>> np.block([b]) # atleast_1d(b) array([1]) >>> np.block([[a]]) # atleast_2d(a) array([[0]]) >>> np.block([[b]]) # atleast_2d(b) array([[1]]) ### bmat Build a matrix object from a string, nested sequence, or array. Parameters ---------- obj : str or array_like Input data. If a string, variables in the current scope may be referenced by name. ldict : dict, optional A dictionary that replaces local operands in current frame. Ignored if `obj` is not a string or `gdict` is None. gdict : dict, optional A dictionary that replaces global operands in current frame. Ignored if `obj` is not a string. Returns ------- out : matrix Returns a matrix object, which is a specialized 2-D array. See Also -------- block : A generalization of this function for N-d arrays, that returns normal ndarrays. Examples -------- >>> A = np.mat('1 1; 1 1') >>> B = np.mat('2 2; 2 2') >>> C = np.mat('3 4; 5 6') >>> D = np.mat('7 8; 9 0') All the following expressions construct the same block matrix: >>> np.bmat([[A, B], [C, D]]) matrix([[1, 1, 2, 2], [1, 1, 2, 2], [3, 4, 7, 8], [5, 6, 9, 0]]) >>> np.bmat(np.r_[np.c_[A, B], np.c_[C, D]]) matrix([[1, 1, 2, 2], [1, 1, 2, 2], [3, 4, 7, 8], [5, 6, 9, 0]]) >>> np.bmat('A,B; C,D') matrix([[1, 1, 2, 2], [1, 1, 2, 2], [3, 4, 7, 8], [5, 6, 9, 0]]) ### broadcast_arrays Broadcast any number of arrays against each other. Parameters ---------- `*args` : array_likes The arrays to broadcast. subok : bool, optional If True, then sub-classes will be passed-through, otherwise the returned arrays will be forced to be a base-class array (default). Returns ------- broadcasted : list of arrays These arrays are views on the original arrays. They are typically not contiguous. Furthermore, more than one element of a broadcasted array may refer to a single memory location. If you need to write to the arrays, make copies first. While you can set the ``writable`` flag True, writing to a single output value may end up changing more than one location in the output array. .. deprecated:: 1.17 The output is currently marked so that if written to, a deprecation warning will be emitted. A future version will set the ``writable`` flag False so writing to it will raise an error. See Also -------- broadcast broadcast_to broadcast_shapes Examples -------- >>> x = np.array([[1,2,3]]) >>> y = np.array([[4],[5]]) >>> np.broadcast_arrays(x, y) [array([[1, 2, 3], [1, 2, 3]]), array([[4, 4, 4], [5, 5, 5]])] Here is a useful idiom for getting contiguous copies instead of non-contiguous views. >>> [np.array(a) for a in np.broadcast_arrays(x, y)] [array([[1, 2, 3], [1, 2, 3]]), array([[4, 4, 4], [5, 5, 5]])] ### broadcast_shapes Broadcast the input shapes into a single shape. :ref:`Learn more about broadcasting here `. .. versionadded:: 1.20.0 Parameters ---------- `*args` : tuples of ints, or ints The shapes to be broadcast against each other. Returns ------- tuple Broadcasted shape. Raises ------ ValueError If the shapes are not compatible and cannot be broadcast according to NumPy's broadcasting rules. See Also -------- broadcast broadcast_arrays broadcast_to Examples -------- >>> np.broadcast_shapes((1, 2), (3, 1), (3, 2)) (3, 2) >>> np.broadcast_shapes((6, 7), (5, 6, 1), (7,), (5, 1, 7)) (5, 6, 7) ### broadcast_to Broadcast an array to a new shape. Parameters ---------- array : array_like The array to broadcast. shape : tuple The shape of the desired array. subok : bool, optional If True, then sub-classes will be passed-through, otherwise the returned array will be forced to be a base-class array (default). Returns ------- broadcast : array A readonly view on the original array with the given shape. It is typically not contiguous. Furthermore, more than one element of a broadcasted array may refer to a single memory location. Raises ------ ValueError If the array is not compatible with the new shape according to NumPy's broadcasting rules. See Also -------- broadcast broadcast_arrays broadcast_shapes Notes ----- .. versionadded:: 1.10.0 Examples -------- >>> x = np.array([1, 2, 3]) >>> np.broadcast_to(x, (3, 3)) array([[1, 2, 3], [1, 2, 3], [1, 2, 3]]) ### busday_count busday_count(begindates, enddates, weekmask='1111100', holidays=[], busdaycal=None, out=None) Counts the number of valid days between `begindates` and `enddates`, not including the day of `enddates`. If ``enddates`` specifies a date value that is earlier than the corresponding ``begindates`` date value, the count will be negative. .. versionadded:: 1.7.0 Parameters ---------- begindates : array_like of datetime64[D] The array of the first dates for counting. enddates : array_like of datetime64[D] The array of the end dates for counting, which are excluded from the count themselves. weekmask : str or array_like of bool, optional A seven-element array indicating which of Monday through Sunday are valid days. May be specified as a length-seven list or array, like [1,1,1,1,1,0,0]; a length-seven string, like '1111100'; or a string like "Mon Tue Wed Thu Fri", made up of 3-character abbreviations for weekdays, optionally separated by white space. Valid abbreviations are: Mon Tue Wed Thu Fri Sat Sun holidays : array_like of datetime64[D], optional An array of dates to consider as invalid dates. They may be specified in any order, and NaT (not-a-time) dates are ignored. This list is saved in a normalized form that is suited for fast calculations of valid days. busdaycal : busdaycalendar, optional A `busdaycalendar` object which specifies the valid days. If this parameter is provided, neither weekmask nor holidays may be provided. out : array of int, optional If provided, this array is filled with the result. Returns ------- out : array of int An array with a shape from broadcasting ``begindates`` and ``enddates`` together, containing the number of valid days between the begin and end dates. See Also -------- busdaycalendar : An object that specifies a custom set of valid days. is_busday : Returns a boolean array indicating valid days. busday_offset : Applies an offset counted in valid days. Examples -------- >>> # Number of weekdays in January 2011 ... np.busday_count('2011-01', '2011-02') 21 >>> # Number of weekdays in 2011 >>> np.busday_count('2011', '2012') 260 >>> # Number of Saturdays in 2011 ... np.busday_count('2011', '2012', weekmask='Sat') 53 ### busday_offset busday_offset(dates, offsets, roll='raise', weekmask='1111100', holidays=None, busdaycal=None, out=None) First adjusts the date to fall on a valid day according to the ``roll`` rule, then applies offsets to the given dates counted in valid days. .. versionadded:: 1.7.0 Parameters ---------- dates : array_like of datetime64[D] The array of dates to process. offsets : array_like of int The array of offsets, which is broadcast with ``dates``. roll : {'raise', 'nat', 'forward', 'following', 'backward', 'preceding', 'modifiedfollowing', 'modifiedpreceding'}, optional How to treat dates that do not fall on a valid day. The default is 'raise'. * 'raise' means to raise an exception for an invalid day. * 'nat' means to return a NaT (not-a-time) for an invalid day. * 'forward' and 'following' mean to take the first valid day later in time. * 'backward' and 'preceding' mean to take the first valid day earlier in time. * 'modifiedfollowing' means to take the first valid day later in time unless it is across a Month boundary, in which case to take the first valid day earlier in time. * 'modifiedpreceding' means to take the first valid day earlier in time unless it is across a Month boundary, in which case to take the first valid day later in time. weekmask : str or array_like of bool, optional A seven-element array indicating which of Monday through Sunday are valid days. May be specified as a length-seven list or array, like [1,1,1,1,1,0,0]; a length-seven string, like '1111100'; or a string like "Mon Tue Wed Thu Fri", made up of 3-character abbreviations for weekdays, optionally separated by white space. Valid abbreviations are: Mon Tue Wed Thu Fri Sat Sun holidays : array_like of datetime64[D], optional An array of dates to consider as invalid dates. They may be specified in any order, and NaT (not-a-time) dates are ignored. This list is saved in a normalized form that is suited for fast calculations of valid days. busdaycal : busdaycalendar, optional A `busdaycalendar` object which specifies the valid days. If this parameter is provided, neither weekmask nor holidays may be provided. out : array of datetime64[D], optional If provided, this array is filled with the result. Returns ------- out : array of datetime64[D] An array with a shape from broadcasting ``dates`` and ``offsets`` together, containing the dates with offsets applied. See Also -------- busdaycalendar : An object that specifies a custom set of valid days. is_busday : Returns a boolean array indicating valid days. busday_count : Counts how many valid days are in a half-open date range. Examples -------- >>> # First business day in October 2011 (not accounting for holidays) ... np.busday_offset('2011-10', 0, roll='forward') numpy.datetime64('2011-10-03') >>> # Last business day in February 2012 (not accounting for holidays) ... np.busday_offset('2012-03', -1, roll='forward') numpy.datetime64('2012-02-29') >>> # Third Wednesday in January 2011 ... np.busday_offset('2011-01', 2, roll='forward', weekmask='Wed') numpy.datetime64('2011-01-19') >>> # 2012 Mother's Day in Canada and the U.S. ... np.busday_offset('2012-05', 1, roll='forward', weekmask='Sun') numpy.datetime64('2012-05-13') >>> # First business day on or after a date ... np.busday_offset('2011-03-20', 0, roll='forward') numpy.datetime64('2011-03-21') >>> np.busday_offset('2011-03-22', 0, roll='forward') numpy.datetime64('2011-03-22') >>> # First business day after a date ... np.busday_offset('2011-03-20', 1, roll='backward') numpy.datetime64('2011-03-21') >>> np.busday_offset('2011-03-22', 1, roll='backward') numpy.datetime64('2011-03-23') ### byte_bounds Returns pointers to the end-points of an array. Parameters ---------- a : ndarray Input array. It must conform to the Python-side of the array interface. Returns ------- (low, high) : tuple of 2 integers The first integer is the first byte of the array, the second integer is just past the last byte of the array. If `a` is not contiguous it will not use every byte between the (`low`, `high`) values. Examples -------- >>> I = np.eye(2, dtype='f'); I.dtype dtype('float32') >>> low, high = np.byte_bounds(I) >>> high - low == I.size*I.itemsize True >>> I = [np.eye(2)](https://www.chedong.com/phpMan.php/man/np.eye/2/markdown); I.dtype dtype('float64') >>> low, high = np.byte_bounds(I) >>> high - low == I.size*I.itemsize True ### can_cast can_cast(from_, to, casting='safe') Returns True if cast between data types can occur according to the casting rule. If from is a scalar or array scalar, also returns True if the scalar value can be cast without overflow or truncation to an integer. Parameters ---------- from_ : dtype, dtype specifier, scalar, or array Data type, scalar, or array to cast from. to : dtype or dtype specifier Data type to cast to. casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional Controls what kind of data casting may occur. * 'no' means the data types should not be cast at all. * 'equiv' means only byte-order changes are allowed. * 'safe' means only casts which can preserve values are allowed. * 'same_kind' means only safe casts or casts within a kind, like float64 to float32, are allowed. * 'unsafe' means any data conversions may be done. Returns ------- out : bool True if cast can occur according to the casting rule. Notes ----- .. versionchanged:: 1.17.0 Casting between a simple data type and a structured one is possible only for "unsafe" casting. Casting to multiple fields is allowed, but casting from multiple fields is not. .. versionchanged:: 1.9.0 Casting from numeric to string types in 'safe' casting mode requires that the string dtype length is long enough to store the maximum integer/float value converted. See also -------- dtype, result_type Examples -------- Basic examples >>> np.can_cast(np.int32, np.int64) True >>> np.can_cast(np.float64, complex) True >>> np.can_cast(complex, float) False >>> np.can_cast('i8', 'f8') True >>> np.can_cast('i8', 'f4') False >>> np.can_cast('i4', 'S4') False Casting scalars >>> np.can_cast(100, 'i1') True >>> np.can_cast(150, 'i1') False >>> np.can_cast(150, 'u1') True >>> np.can_cast(3.5e100, np.float32) False >>> np.can_cast(1000.0, np.float32) True Array scalar checks the value, array does not >>> np.can_cast(np.array(1000.0), np.float32) True >>> np.can_cast(np.array([1000.0]), np.float32) False Using the casting rules >>> np.can_cast('i8', 'i8', 'no') True >>> np.can_cast('i8', 'no') False >>> np.can_cast('i8', 'equiv') True >>> np.can_cast('i8', 'equiv') False >>> np.can_cast('i8', 'safe') True >>> np.can_cast('i4', 'safe') False >>> np.can_cast('i4', 'same_kind') True >>> np.can_cast('u4', 'same_kind') False >>> np.can_cast('u4', 'unsafe') True ### choose Construct an array from an index array and a list of arrays to choose from. First of all, if confused or uncertain, definitely look at the Examples - in its full generality, this function is less simple than it might seem from the following code description (below ndi = `numpy.lib.index_tricks`): ``np.choose(a,c) == np.array([c[a[I]][I] for I in ndi.ndindex(a.shape)])``. But this omits some subtleties. Here is a fully general summary: Given an "index" array (`a`) of integers and a sequence of ``n`` arrays (`choices`), `a` and each choice array are first broadcast, as necessary, to arrays of a common shape; calling these *Ba* and *Bchoices[i], i = 0,...,n-1* we have that, necessarily, ``Ba.shape == Bchoices[i].shape`` for each ``i``. Then, a new array with shape ``Ba.shape`` is created as follows: * if ``mode='raise'`` (the default), then, first of all, each element of ``a`` (and thus ``Ba``) must be in the range ``[0, n-1]``; now, suppose that ``i`` (in that range) is the value at the ``(j0, j1, ..., jm)`` position in ``Ba`` - then the value at the same position in the new array is the value in ``Bchoices[i]`` at that same position; * if ``mode='wrap'``, values in `a` (and thus `Ba`) may be any (signed) integer; modular arithmetic is used to map integers outside the range `[0, n-1]` back into that range; and then the new array is constructed as above; * if ``mode='clip'``, values in `a` (and thus ``Ba``) may be any (signed) integer; negative integers are mapped to 0; values greater than ``n-1`` are mapped to ``n-1``; and then the new array is constructed as above. Parameters ---------- a : int array This array must contain integers in ``[0, n-1]``, where ``n`` is the number of choices, unless ``mode=wrap`` or ``mode=clip``, in which cases any integers are permissible. choices : sequence of arrays Choice arrays. `a` and all of the choices must be broadcastable to the same shape. If `choices` is itself an array (not recommended), then its outermost dimension (i.e., the one corresponding to ``choices.shape[0]``) is taken as defining the "sequence". out : array, optional If provided, the result will be inserted into this array. It should be of the appropriate shape and dtype. Note that `out` is always buffered if ``mode='raise'``; use other modes for better performance. mode : {'raise' (default), 'wrap', 'clip'}, optional Specifies how indices outside ``[0, n-1]`` will be treated: * 'raise' : an exception is raised * 'wrap' : value becomes value mod ``n`` * 'clip' : values < 0 are mapped to 0, values > n-1 are mapped to n-1 Returns ------- merged_array : array The merged result. Raises ------ ValueError: shape mismatch If `a` and each choice array are not all broadcastable to the same shape. See Also -------- ndarray.choose : equivalent method numpy.take_along_axis : Preferable if `choices` is an array Notes ----- To reduce the chance of misinterpretation, even though the following "abuse" is nominally supported, `choices` should neither be, nor be thought of as, a single array, i.e., the outermost sequence-like container should be either a list or a tuple. Examples -------- >>> choices = [[0, 1, 2, 3], [10, 11, 12, 13], ... [20, 21, 22, 23], [30, 31, 32, 33]] >>> np.choose([2, 3, 1, 0], choices ... # the first element of the result will be the first element of the ... # third (2+1) "array" in choices, namely, 20; the second element ... # will be the second element of the fourth (3+1) choice array, i.e., ... # 31, etc. ... ) array([20, 31, 12, 3]) >>> np.choose([2, 4, 1, 0], choices, mode='clip') # 4 goes to 3 (4-1) array([20, 31, 12, 3]) >>> # because there are 4 choice arrays >>> np.choose([2, 4, 1, 0], choices, mode='wrap') # 4 goes to (4 mod 4) array([20, 1, 12, 3]) >>> # i.e., 0 A couple examples illustrating how choose broadcasts: >>> a = [[1, 0, 1], [0, 1, 0], [1, 0, 1]] >>> choices = [-10, 10] >>> np.choose(a, choices) array([[ 10, -10, 10], [-10, 10, -10], [ 10, -10, 10]]) >>> # With thanks to Anne Archibald >>> a = np.array([0, 1]).reshape((2,1,1)) >>> c1 = np.array([1, 2, 3]).reshape((1,3,1)) >>> c2 = np.array([-1, -2, -3, -4, -5]).reshape((1,1,5)) >>> np.choose(a, (c1, c2)) # result is 2x3x5, res[0,:,:]=c1, res[1,:,:]=c2 array([[[ 1, 1, 1, 1, 1], [ 2, 2, 2, 2, 2], [ 3, 3, 3, 3, 3]], [[-1, -2, -3, -4, -5], [-1, -2, -3, -4, -5], [-1, -2, -3, -4, -5]]]) ### clip Clip (limit) the values in an array. Given an interval, values outside the interval are clipped to the interval edges. For example, if an interval of ``[0, 1]`` is specified, values smaller than 0 become 0, and values larger than 1 become 1. Equivalent to but faster than ``np.minimum(a_max, np.maximum(a, a_min))``. No check is performed to ensure ``a_min < a_max``. Parameters ---------- a : array_like Array containing elements to clip. a_min, a_max : array_like or None Minimum and maximum value. If ``None``, clipping is not performed on the corresponding edge. Only one of `a_min` and `a_max` may be ``None``. Both are broadcast against `a`. out : ndarray, optional The results will be placed in this array. It may be the input array for in-place clipping. `out` must be of the right shape to hold the output. Its type is preserved. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. .. versionadded:: 1.17.0 Returns ------- clipped_array : ndarray An array with the elements of `a`, but where values < `a_min` are replaced with `a_min`, and those > `a_max` with `a_max`. See Also -------- :ref:`ufuncs-output-type` Notes ----- When `a_min` is greater than `a_max`, `clip` returns an array in which all values are equal to `a_max`, as shown in the second example. Examples -------- >>> a = [np.arange(10)](https://www.chedong.com/phpMan.php/man/np.arange/10/markdown) >>> a array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) >>> np.clip(a, 1, 8) array([1, 1, 2, 3, 4, 5, 6, 7, 8, 8]) >>> np.clip(a, 8, 1) array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) >>> np.clip(a, 3, 6, out=a) array([3, 3, 3, 3, 4, 5, 6, 6, 6, 6]) >>> a array([3, 3, 3, 3, 4, 5, 6, 6, 6, 6]) >>> a = [np.arange(10)](https://www.chedong.com/phpMan.php/man/np.arange/10/markdown) >>> a array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) >>> np.clip(a, [3, 4, 1, 1, 1, 4, 4, 4, 4, 4], 8) array([3, 4, 2, 3, 4, 5, 6, 7, 8, 8]) ### column_stack Stack 1-D arrays as columns into a 2-D array. Take a sequence of 1-D arrays and stack them as columns to make a single 2-D array. 2-D arrays are stacked as-is, just like with `hstack`. 1-D arrays are turned into 2-D columns first. Parameters ---------- tup : sequence of 1-D or 2-D arrays. Arrays to stack. All of them must have the same first dimension. Returns ------- stacked : 2-D array The array formed by stacking the given arrays. See Also -------- stack, hstack, vstack, concatenate Examples -------- >>> a = np.array((1,2,3)) >>> b = np.array((2,3,4)) >>> np.column_stack((a,b)) array([[1, 2], [2, 3], [3, 4]]) ### common_type Return a scalar type which is common to the input arrays. The return type will always be an inexact (i.e. floating point) scalar type, even if all the arrays are integer arrays. If one of the inputs is an integer array, the minimum precision type that is returned is a 64-bit floating point dtype. All input arrays except int64 and uint64 can be safely cast to the returned dtype without loss of information. Parameters ---------- array1, array2, ... : ndarrays Input arrays. Returns ------- out : data type code Data type code. See Also -------- dtype, mintypecode Examples -------- >>> np.common_type(np.arange(2, dtype=np.float32)) >>> np.common_type(np.arange(2, dtype=np.float32), [np.arange(2)](https://www.chedong.com/phpMan.php/man/np.arange/2/markdown)) >>> np.common_type([np.arange(4)](https://www.chedong.com/phpMan.php/man/np.arange/4/markdown), np.array([45, 6.j]), np.array([45.0])) ### compare_chararrays compare_chararrays(a, b, cmp_op, rstrip) Performs element-wise comparison of two string arrays using the comparison operator specified by `cmp_op`. Parameters ---------- a, b : array_like Arrays to be compared. cmp_op : {"<", "<=", "==", ">=", ">", "!="} Type of comparison. rstrip : Boolean If True, the spaces at the end of Strings are removed before the comparison. Returns ------- out : ndarray The output array of type Boolean with the same shape as a and b. Raises ------ ValueError If `cmp_op` is not valid. TypeError If at least one of `a` or `b` is a non-string array Examples -------- >>> a = np.array(["a", "b", "cde"]) >>> b = np.array(["a", "a", "dec"]) >>> np.compare_chararrays(a, b, ">", True) array([False, True, False]) ### compress Return selected slices of an array along given axis. When working along a given axis, a slice along that axis is returned in `output` for each index where `condition` evaluates to True. When working on a 1-D array, `compress` is equivalent to `extract`. Parameters ---------- condition : 1-D array of bools Array that selects which entries to return. If len(condition) is less than the size of `a` along the given axis, then output is truncated to the length of the condition array. a : array_like Array from which to extract a part. axis : int, optional Axis along which to take slices. If None (default), work on the flattened array. out : ndarray, optional Output array. Its type is preserved and it must be of the right shape to hold the output. Returns ------- compressed_array : ndarray A copy of `a` without the slices along axis for which `condition` is false. See Also -------- take, choose, diag, diagonal, select ndarray.compress : Equivalent method in ndarray extract : Equivalent method when working on 1-D arrays :ref:`ufuncs-output-type` Examples -------- >>> a = np.array([[1, 2], [3, 4], [5, 6]]) >>> a array([[1, 2], [3, 4], [5, 6]]) >>> np.compress([0, 1], a, axis=0) array([[3, 4]]) >>> np.compress([False, True, True], a, axis=0) array([[3, 4], [5, 6]]) >>> np.compress([False, True], a, axis=1) array([[2], [4], [6]]) Working on the flattened array does not return slices along an axis but selects elements. >>> np.compress([False, True], a) array([2]) ### concatenate concatenate((a1, a2, ...), axis=0, out=None, dtype=None, casting="same_kind") Join a sequence of arrays along an existing axis. Parameters ---------- a1, a2, ... : sequence of array_like The arrays must have the same shape, except in the dimension corresponding to `axis` (the first, by default). axis : int, optional The axis along which the arrays will be joined. If axis is None, arrays are flattened before use. Default is 0. out : ndarray, optional If provided, the destination to place the result. The shape must be correct, matching that of what concatenate would have returned if no out argument were specified. dtype : str or dtype If provided, the destination array will have this dtype. Cannot be provided together with `out`. .. versionadded:: 1.20.0 casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional Controls what kind of data casting may occur. Defaults to 'same_kind'. .. versionadded:: 1.20.0 Returns ------- res : ndarray The concatenated array. See Also -------- ma.concatenate : Concatenate function that preserves input masks. array_split : Split an array into multiple sub-arrays of equal or near-equal size. split : Split array into a list of multiple sub-arrays of equal size. hsplit : Split array into multiple sub-arrays horizontally (column wise). vsplit : Split array into multiple sub-arrays vertically (row wise). dsplit : Split array into multiple sub-arrays along the 3rd axis (depth). stack : Stack a sequence of arrays along a new axis. block : Assemble arrays from blocks. hstack : Stack arrays in sequence horizontally (column wise). vstack : Stack arrays in sequence vertically (row wise). dstack : Stack arrays in sequence depth wise (along third dimension). column_stack : Stack 1-D arrays as columns into a 2-D array. Notes ----- When one or more of the arrays to be concatenated is a MaskedArray, this function will return a MaskedArray object instead of an ndarray, but the input masks are *not* preserved. In cases where a MaskedArray is expected as input, use the ma.concatenate function from the masked array module instead. Examples -------- >>> a = np.array([[1, 2], [3, 4]]) >>> b = np.array([[5, 6]]) >>> np.concatenate((a, b), axis=0) array([[1, 2], [3, 4], [5, 6]]) >>> np.concatenate((a, b.T), axis=1) array([[1, 2, 5], [3, 4, 6]]) >>> np.concatenate((a, b), axis=None) array([1, 2, 3, 4, 5, 6]) This function will not preserve masking of MaskedArray inputs. >>> a = [np.ma.arange(3)](https://www.chedong.com/phpMan.php/man/np.ma.arange/3/markdown) >>> a[1] = np.ma.masked >>> b = np.arange(2, 5) >>> a masked_array(data=[0, --, 2], mask=[False, True, False], fill_value=999999) >>> b array([2, 3, 4]) >>> np.concatenate([a, b]) masked_array(data=[0, 1, 2, 2, 3, 4], mask=False, fill_value=999999) >>> np.ma.concatenate([a, b]) masked_array(data=[0, --, 2, 2, 3, 4], mask=[False, True, False, False, False, False], fill_value=999999) ### convolve Returns the discrete, linear convolution of two one-dimensional sequences. The convolution operator is often seen in signal processing, where it models the effect of a linear time-invariant system on a signal [1]_. In probability theory, the sum of two independent random variables is distributed according to the convolution of their individual distributions. If `v` is longer than `a`, the arrays are swapped before computation. Parameters ---------- a : (N,) array_like First one-dimensional input array. v : (M,) array_like Second one-dimensional input array. mode : {'full', 'valid', 'same'}, optional 'full': By default, mode is 'full'. This returns the convolution at each point of overlap, with an output shape of (N+M-1,). At the end-points of the convolution, the signals do not overlap completely, and boundary effects may be seen. 'same': Mode 'same' returns output of length ``max(M, N)``. Boundary effects are still visible. 'valid': Mode 'valid' returns output of length ``max(M, N) - min(M, N) + 1``. The convolution product is only given for points where the signals overlap completely. Values outside the signal boundary have no effect. Returns ------- out : ndarray Discrete, linear convolution of `a` and `v`. See Also -------- scipy.signal.fftconvolve : Convolve two arrays using the Fast Fourier Transform. scipy.linalg.toeplitz : Used to construct the convolution operator. polymul : Polynomial multiplication. Same output as convolve, but also accepts poly1d objects as input. Notes ----- The discrete convolution operation is defined as .. math:: (a * v)[n] = \sum_{m = -\infty}^{\infty} a[m] v[n - m] It can be shown that a convolution :math:`x(t) * y(t)` in time/space is equivalent to the multiplication :math:`X(f) Y(f)` in the Fourier domain, after appropriate padding (padding is necessary to prevent circular convolution). Since multiplication is more efficient (faster) than convolution, the function `scipy.signal.fftconvolve` exploits the FFT to calculate the convolution of large data-sets. References ---------- .. [1] Wikipedia, "Convolution", Examples -------- Note how the convolution operator flips the second array before "sliding" the two across one another: >>> np.convolve([1, 2, 3], [0, 1, 0.5]) array([0. , 1. , 2.5, 4. , 1.5]) Only return the middle values of the convolution. Contains boundary effects, where zeros are taken into account: >>> np.convolve([1,2,3],[0,1,0.5], 'same') array([1. , 2.5, 4. ]) The two arrays are of the same length, so there is only one position where they completely overlap: >>> np.convolve([1,2,3],[0,1,0.5], 'valid') array([2.5]) ### copy Return an array copy of the given object. Parameters ---------- a : array_like Input data. order : {'C', 'F', 'A', 'K'}, optional Controls the memory layout of the copy. 'C' means C-order, 'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous, 'C' otherwise. 'K' means match the layout of `a` as closely as possible. (Note that this function and :meth:`ndarray.copy` are very similar, but have different default values for their order= arguments.) subok : bool, optional If True, then sub-classes will be passed-through, otherwise the returned array will be forced to be a base-class array (defaults to False). .. versionadded:: 1.19.0 Returns ------- arr : ndarray Array interpretation of `a`. See Also -------- ndarray.copy : Preferred method for creating an array copy Notes ----- This is equivalent to: >>> np.array(a, copy=True) #doctest: +SKIP Examples -------- Create an array x, with a reference y and a copy z: >>> x = np.array([1, 2, 3]) >>> y = x >>> z = np.copy(x) Note that, when we modify x, y changes, but not z: >>> x[0] = 10 >>> x[0] == y[0] True >>> x[0] == z[0] False Note that np.copy is a shallow copy and will not copy object elements within arrays. This is mainly important for arrays containing Python objects. The new array will contain the same object which may lead to surprises if that object can be modified (is mutable): >>> a = np.array([1, 'm', [2, 3, 4]], dtype=object) >>> b = np.copy(a) >>> b[2][0] = 10 >>> a array([1, 'm', list([10, 3, 4])], dtype=object) To ensure all elements within an ``object`` array are copied, use `copy.deepcopy`: >>> import copy >>> a = np.array([1, 'm', [2, 3, 4]], dtype=object) >>> c = copy.deepcopy(a) >>> c[2][0] = 10 >>> c array([1, 'm', list([10, 3, 4])], dtype=object) >>> a array([1, 'm', list([2, 3, 4])], dtype=object) ### copyto copyto(dst, src, casting='same_kind', where=True) Copies values from one array to another, broadcasting as necessary. Raises a TypeError if the `casting` rule is violated, and if `where` is provided, it selects which elements to copy. .. versionadded:: 1.7.0 Parameters ---------- dst : ndarray The array into which values are copied. src : array_like The array from which values are copied. casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional Controls what kind of data casting may occur when copying. * 'no' means the data types should not be cast at all. * 'equiv' means only byte-order changes are allowed. * 'safe' means only casts which can preserve values are allowed. * 'same_kind' means only safe casts or casts within a kind, like float64 to float32, are allowed. * 'unsafe' means any data conversions may be done. where : array_like of bool, optional A boolean array which is broadcasted to match the dimensions of `dst`, and selects elements to copy from `src` to `dst` wherever it contains the value True. ### corrcoef Return Pearson product-moment correlation coefficients. Please refer to the documentation for `cov` for more detail. The relationship between the correlation coefficient matrix, `R`, and the covariance matrix, `C`, is .. math:: R_{ij} = \frac{ C_{ij} } { \sqrt{ C_{ii} * C_{jj} } } The values of `R` are between -1 and 1, inclusive. Parameters ---------- x : array_like A 1-D or 2-D array containing multiple variables and observations. Each row of `x` represents a variable, and each column a single observation of all those variables. Also see `rowvar` below. y : array_like, optional An additional set of variables and observations. `y` has the same shape as `x`. rowvar : bool, optional If `rowvar` is True (default), then each row represents a variable, with observations in the columns. Otherwise, the relationship is transposed: each column represents a variable, while the rows contain observations. bias : _NoValue, optional Has no effect, do not use. .. deprecated:: 1.10.0 ddof : _NoValue, optional Has no effect, do not use. .. deprecated:: 1.10.0 dtype : data-type, optional Data-type of the result. By default, the return data-type will have at least `numpy.float64` precision. .. versionadded:: 1.20 Returns ------- R : ndarray The correlation coefficient matrix of the variables. See Also -------- cov : Covariance matrix Notes ----- Due to floating point rounding the resulting array may not be Hermitian, the diagonal elements may not be 1, and the elements may not satisfy the inequality abs(a) <= 1. The real and imaginary parts are clipped to the interval [-1, 1] in an attempt to improve on that situation but is not much help in the complex case. This function accepts but discards arguments `bias` and `ddof`. This is for backwards compatibility with previous versions of this function. These arguments had no effect on the return values of the function and can be safely ignored in this and previous versions of numpy. Examples -------- In this example we generate two random arrays, ``xarr`` and ``yarr``, and compute the row-wise and column-wise Pearson correlation coefficients, ``R``. Since ``rowvar`` is true by default, we first find the row-wise Pearson correlation coefficients between the variables of ``xarr``. >>> import numpy as np >>> rng = np.random.default_rng(seed=42) >>> xarr = rng.random((3, 3)) >>> xarr array([[0.77395605, 0.43887844, 0.85859792], [0.69736803, 0.09417735, 0.97562235], [0.7611397 , 0.78606431, 0.12811363]]) >>> R1 = np.corrcoef(xarr) >>> R1 array([[ 1. , 0.99256089, -0.68080986], [ 0.99256089, 1. , -0.76492172], [-0.68080986, -0.76492172, 1. ]]) If we add another set of variables and observations ``yarr``, we can compute the row-wise Pearson correlation coefficients between the variables in ``xarr`` and ``yarr``. >>> yarr = rng.random((3, 3)) >>> yarr array([[0.45038594, 0.37079802, 0.92676499], [0.64386512, 0.82276161, 0.4434142 ], [0.22723872, 0.55458479, 0.06381726]]) >>> R2 = np.corrcoef(xarr, yarr) >>> R2 array([[ 1. , 0.99256089, -0.68080986, 0.75008178, -0.934284 , -0.99004057], [ 0.99256089, 1. , -0.76492172, 0.82502011, -0.97074098, -0.99981569], [-0.68080986, -0.76492172, 1. , -0.99507202, 0.89721355, 0.77714685], [ 0.75008178, 0.82502011, -0.99507202, 1. , -0.93657855, -0.83571711], [-0.934284 , -0.97074098, 0.89721355, -0.93657855, 1. , 0.97517215], [-0.99004057, -0.99981569, 0.77714685, -0.83571711, 0.97517215, 1. ]]) Finally if we use the option ``rowvar=False``, the columns are now being treated as the variables and we will find the column-wise Pearson correlation coefficients between variables in ``xarr`` and ``yarr``. >>> R3 = np.corrcoef(xarr, yarr, rowvar=False) >>> R3 array([[ 1. , 0.77598074, -0.47458546, -0.75078643, -0.9665554 , 0.22423734], [ 0.77598074, 1. , -0.92346708, -0.99923895, -0.58826587, -0.44069024], [-0.47458546, -0.92346708, 1. , 0.93773029, 0.23297648, 0.75137473], [-0.75078643, -0.99923895, 0.93773029, 1. , 0.55627469, 0.47536961], [-0.9665554 , -0.58826587, 0.23297648, 0.55627469, 1. , -0.46666491], [ 0.22423734, -0.44069024, 0.75137473, 0.47536961, -0.46666491, 1. ]]) ### correlate Cross-correlation of two 1-dimensional sequences. This function computes the correlation as generally defined in signal processing texts:: c_{av}[k] = sum_n a[n+k] * conj(v[n]) with a and v sequences being zero-padded where necessary and conj being the conjugate. Parameters ---------- a, v : array_like Input sequences. mode : {'valid', 'same', 'full'}, optional Refer to the `convolve` docstring. Note that the default is 'valid', unlike `convolve`, which uses 'full'. old_behavior : bool `old_behavior` was removed in NumPy 1.10. If you need the old behavior, use `multiarray.correlate`. Returns ------- out : ndarray Discrete cross-correlation of `a` and `v`. See Also -------- convolve : Discrete, linear convolution of two one-dimensional sequences. multiarray.correlate : Old, no conjugate, version of correlate. scipy.signal.correlate : uses FFT which has superior performance on large arrays. Notes ----- The definition of correlation above is not unique and sometimes correlation may be defined differently. Another common definition is:: c'_{av}[k] = sum_n a[n] conj(v[n+k]) which is related to ``c_{av}[k]`` by ``c'_{av}[k] = c_{av}[-k]``. `numpy.correlate` may perform slowly in large arrays (i.e. n = 1e5) because it does not use the FFT to compute the convolution; in that case, `scipy.signal.correlate` might be preferable. Examples -------- >>> np.correlate([1, 2, 3], [0, 1, 0.5]) array([3.5]) >>> np.correlate([1, 2, 3], [0, 1, 0.5], "same") array([2. , 3.5, 3. ]) >>> np.correlate([1, 2, 3], [0, 1, 0.5], "full") array([0.5, 2. , 3.5, 3. , 0. ]) Using complex sequences: >>> np.correlate([1+1j, 2, 3-1j], [0, 1, 0.5j], 'full') array([ 0.5-0.5j, 1.0+0.j , 1.5-1.5j, 3.0-1.j , 0.0+0.j ]) Note that you get the time reversed, complex conjugated result when the two input sequences change places, i.e., ``c_{va}[k] = c^{*}_{av}[-k]``: >>> np.correlate([0, 1, 0.5j], [1+1j, 2, 3-1j], 'full') array([ 0.0+0.j , 3.0+1.j , 1.5+1.5j, 1.0+0.j , 0.5+0.5j]) ### count_nonzero Counts the number of non-zero values in the array ``a``. The word "non-zero" is in reference to the Python 2.x built-in method ``__nonzero__()`` (renamed ``__bool__()`` in Python 3.x) of Python objects that tests an object's "truthfulness". For example, any number is considered truthful if it is nonzero, whereas any string is considered truthful if it is not the empty string. Thus, this function (recursively) counts how many elements in ``a`` (and in sub-arrays thereof) have their ``__nonzero__()`` or ``__bool__()`` method evaluated to ``True``. Parameters ---------- a : array_like The array for which to count non-zeros. axis : int or tuple, optional Axis or tuple of axes along which to count non-zeros. Default is None, meaning that non-zeros will be counted along a flattened version of ``a``. .. versionadded:: 1.12.0 keepdims : bool, optional If this is set to True, the axes that are counted are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array. .. versionadded:: 1.19.0 Returns ------- count : int or array of int Number of non-zero values in the array along a given axis. Otherwise, the total number of non-zero values in the array is returned. See Also -------- nonzero : Return the coordinates of all the non-zero values. Examples -------- >>> np.count_nonzero([np.eye(4)](https://www.chedong.com/phpMan.php/man/np.eye/4/markdown)) 4 >>> a = np.array([[0, 1, 7, 0], ... [3, 0, 2, 19]]) >>> np.count_nonzero(a) 5 >>> np.count_nonzero(a, axis=0) array([1, 1, 2, 1]) >>> np.count_nonzero(a, axis=1) array([2, 3]) >>> np.count_nonzero(a, axis=1, keepdims=True) array([[2], [3]]) ### cov Estimate a covariance matrix, given data and weights. Covariance indicates the level to which two variables vary together. If we examine N-dimensional samples, :math:`X = [x_1, x_2, ... x_N]^T`, then the covariance matrix element :math:`C_{ij}` is the covariance of :math:`x_i` and :math:`x_j`. The element :math:`C_{ii}` is the variance of :math:`x_i`. See the notes for an outline of the algorithm. Parameters ---------- m : array_like A 1-D or 2-D array containing multiple variables and observations. Each row of `m` represents a variable, and each column a single observation of all those variables. Also see `rowvar` below. y : array_like, optional An additional set of variables and observations. `y` has the same form as that of `m`. rowvar : bool, optional If `rowvar` is True (default), then each row represents a variable, with observations in the columns. Otherwise, the relationship is transposed: each column represents a variable, while the rows contain observations. bias : bool, optional Default normalization (False) is by ``(N - 1)``, where ``N`` is the number of observations given (unbiased estimate). If `bias` is True, then normalization is by ``N``. These values can be overridden by using the keyword ``ddof`` in numpy versions >= 1.5. ddof : int, optional If not ``None`` the default value implied by `bias` is overridden. Note that ``ddof=1`` will return the unbiased estimate, even if both `fweights` and `aweights` are specified, and ``ddof=0`` will return the simple average. See the notes for the details. The default value is ``None``. .. versionadded:: 1.5 fweights : array_like, int, optional 1-D array of integer frequency weights; the number of times each observation vector should be repeated. .. versionadded:: 1.10 aweights : array_like, optional 1-D array of observation vector weights. These relative weights are typically large for observations considered "important" and smaller for observations considered less "important". If ``ddof=0`` the array of weights can be used to assign probabilities to observation vectors. .. versionadded:: 1.10 dtype : data-type, optional Data-type of the result. By default, the return data-type will have at least `numpy.float64` precision. .. versionadded:: 1.20 Returns ------- out : ndarray The covariance matrix of the variables. See Also -------- corrcoef : Normalized covariance matrix Notes ----- Assume that the observations are in the columns of the observation array `m` and let ``f = fweights`` and ``a = aweights`` for brevity. The steps to compute the weighted covariance are as follows:: >>> m = np.arange(10, dtype=np.float64) >>> f = [np.arange(10)](https://www.chedong.com/phpMan.php/man/np.arange/10/markdown) * 2 >>> a = [np.arange(10)](https://www.chedong.com/phpMan.php/man/np.arange/10/markdown) ** 2. >>> ddof = 1 >>> w = f * a >>> v1 = np.sum(w) >>> v2 = np.sum(w * a) >>> m -= np.sum(m * w, axis=None, keepdims=True) / v1 >>> cov = np.dot(m * w, m.T) * v1 / (v1**2 - ddof * v2) Note that when ``a == 1``, the normalization factor ``v1 / (v1**2 - ddof * v2)`` goes over to ``1 / (np.sum(f) - ddof)`` as it should. Examples -------- Consider two variables, :math:`x_0` and :math:`x_1`, which correlate perfectly, but in opposite directions: >>> x = np.array([[0, 2], [1, 1], [2, 0]]).T >>> x array([[0, 1, 2], [2, 1, 0]]) Note how :math:`x_0` increases while :math:`x_1` decreases. The covariance matrix shows this clearly: >>> np.cov(x) array([[ 1., -1.], [-1., 1.]]) Note that element :math:`C_{0,1}`, which shows the correlation between :math:`x_0` and :math:`x_1`, is negative. Further, note how `x` and `y` are combined: >>> x = [-2.1, -1, 4.3] >>> y = [3, 1.1, 0.12] >>> X = np.stack((x, y), axis=0) >>> np.cov(X) array([[11.71 , -4.286 ], # may vary [-4.286 , 2.144133]]) >>> np.cov(x, y) array([[11.71 , -4.286 ], # may vary [-4.286 , 2.144133]]) >>> np.cov(x) array(11.71) ### cross Return the cross product of two (arrays of) vectors. The cross product of `a` and `b` in :math:`R^3` is a vector perpendicular to both `a` and `b`. If `a` and `b` are arrays of vectors, the vectors are defined by the last axis of `a` and `b` by default, and these axes can have dimensions 2 or 3. Where the dimension of either `a` or `b` is 2, the third component of the input vector is assumed to be zero and the cross product calculated accordingly. In cases where both input vectors have dimension 2, the z-component of the cross product is returned. Parameters ---------- a : array_like Components of the first vector(s). b : array_like Components of the second vector(s). axisa : int, optional Axis of `a` that defines the vector(s). By default, the last axis. axisb : int, optional Axis of `b` that defines the vector(s). By default, the last axis. axisc : int, optional Axis of `c` containing the cross product vector(s). Ignored if both input vectors have dimension 2, as the return is scalar. By default, the last axis. axis : int, optional If defined, the axis of `a`, `b` and `c` that defines the vector(s) and cross product(s). Overrides `axisa`, `axisb` and `axisc`. Returns ------- c : ndarray Vector cross product(s). Raises ------ ValueError When the dimension of the vector(s) in `a` and/or `b` does not equal 2 or 3. See Also -------- inner : Inner product outer : Outer product. ix_ : Construct index arrays. Notes ----- .. versionadded:: 1.9.0 Supports full broadcasting of the inputs. Examples -------- Vector cross-product. >>> x = [1, 2, 3] >>> y = [4, 5, 6] >>> np.cross(x, y) array([-3, 6, -3]) One vector with dimension 2. >>> x = [1, 2] >>> y = [4, 5, 6] >>> np.cross(x, y) array([12, -6, -3]) Equivalently: >>> x = [1, 2, 0] >>> y = [4, 5, 6] >>> np.cross(x, y) array([12, -6, -3]) Both vectors with dimension 2. >>> x = [1,2] >>> y = [4,5] >>> np.cross(x, y) array(-3) Multiple vector cross-products. Note that the direction of the cross product vector is defined by the `right-hand rule`. >>> x = np.array([[1,2,3], [4,5,6]]) >>> y = np.array([[4,5,6], [1,2,3]]) >>> np.cross(x, y) array([[-3, 6, -3], [ 3, -6, 3]]) The orientation of `c` can be changed using the `axisc` keyword. >>> np.cross(x, y, axisc=0) array([[-3, 3], [ 6, -6], [-3, 3]]) Change the vector definition of `x` and `y` using `axisa` and `axisb`. >>> x = np.array([[1,2,3], [4,5,6], [7, 8, 9]]) >>> y = np.array([[7, 8, 9], [4,5,6], [1,2,3]]) >>> np.cross(x, y) array([[ -6, 12, -6], [ 0, 0, 0], [ 6, -12, 6]]) >>> np.cross(x, y, axisa=0, axisb=0) array([[-24, 48, -24], [-30, 60, -30], [-36, 72, -36]]) ### cumprod Return the cumulative product of elements along a given axis. Parameters ---------- a : array_like Input array. axis : int, optional Axis along which the cumulative product is computed. By default the input is flattened. dtype : dtype, optional Type of the returned array, as well as of the accumulator in which the elements are multiplied. If *dtype* is not specified, it defaults to the dtype of `a`, unless `a` has an integer dtype with a precision less than that of the default platform integer. In that case, the default platform integer is used instead. out : ndarray, optional Alternative output array in which to place the result. It must have the same shape and buffer length as the expected output but the type of the resulting values will be cast if necessary. Returns ------- cumprod : ndarray A new array holding the result is returned unless `out` is specified, in which case a reference to out is returned. See Also -------- :ref:`ufuncs-output-type` Notes ----- Arithmetic is modular when using integer types, and no error is raised on overflow. Examples -------- >>> a = np.array([1,2,3]) >>> np.cumprod(a) # intermediate results 1, 1*2 ... # total product 1*2*3 = 6 array([1, 2, 6]) >>> a = np.array([[1, 2, 3], [4, 5, 6]]) >>> np.cumprod(a, dtype=float) # specify type of output array([ 1., 2., 6., 24., 120., 720.]) The cumulative product for each column (i.e., over the rows) of `a`: >>> np.cumprod(a, axis=0) array([[ 1, 2, 3], [ 4, 10, 18]]) The cumulative product for each row (i.e. over the columns) of `a`: >>> np.cumprod(a,axis=1) array([[ 1, 2, 6], [ 4, 20, 120]]) ### cumproduct Return the cumulative product over the given axis. See Also -------- cumprod : equivalent function; see for details. ### cumsum Return the cumulative sum of the elements along a given axis. Parameters ---------- a : array_like Input array. axis : int, optional Axis along which the cumulative sum is computed. The default (None) is to compute the cumsum over the flattened array. dtype : dtype, optional Type of the returned array and of the accumulator in which the elements are summed. If `dtype` is not specified, it defaults to the dtype of `a`, unless `a` has an integer dtype with a precision less than that of the default platform integer. In that case, the default platform integer is used. out : ndarray, optional Alternative output array in which to place the result. It must have the same shape and buffer length as the expected output but the type will be cast if necessary. See :ref:`ufuncs-output-type` for more details. Returns ------- cumsum_along_axis : ndarray. A new array holding the result is returned unless `out` is specified, in which case a reference to `out` is returned. The result has the same size as `a`, and the same shape as `a` if `axis` is not None or `a` is a 1-d array. See Also -------- sum : Sum array elements. trapz : Integration of array values using the composite trapezoidal rule. diff : Calculate the n-th discrete difference along given axis. Notes ----- Arithmetic is modular when using integer types, and no error is raised on overflow. ``cumsum(a)[-1]`` may not be equal to ``sum(a)`` for floating-point values since ``sum`` may use a pairwise summation routine, reducing the roundoff-error. See `sum` for more information. Examples -------- >>> a = np.array([[1,2,3], [4,5,6]]) >>> a array([[1, 2, 3], [4, 5, 6]]) >>> np.cumsum(a) array([ 1, 3, 6, 10, 15, 21]) >>> np.cumsum(a, dtype=float) # specifies type of output value(s) array([ 1., 3., 6., 10., 15., 21.]) >>> np.cumsum(a,axis=0) # sum over rows for each of the 3 columns array([[1, 2, 3], [5, 7, 9]]) >>> np.cumsum(a,axis=1) # sum over columns for each of the 2 rows array([[ 1, 3, 6], [ 4, 9, 15]]) ``cumsum(b)[-1]`` may not be equal to ``sum(b)`` >>> b = np.array([1, 2e-9, 3e-9] * 1000000) >>> b.cumsum()[-1] 1000000.0050045159 >>> b.sum() 1000000.0050000029 ### datetime_as_string datetime_as_string(arr, unit=None, timezone='naive', casting='same_kind') Convert an array of datetimes into an array of strings. Parameters ---------- arr : array_like of datetime64 The array of UTC timestamps to format. unit : str One of None, 'auto', or a :ref:`datetime unit `. timezone : {'naive', 'UTC', 'local'} or tzinfo Timezone information to use when displaying the datetime. If 'UTC', end with a Z to indicate UTC time. If 'local', convert to the local timezone first, and suffix with a +-#### timezone offset. If a tzinfo object, then do as with 'local', but use the specified timezone. casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'} Casting to allow when changing between datetime units. Returns ------- str_arr : ndarray An array of strings the same shape as `arr`. Examples -------- >>> import pytz >>> d = np.arange('2002-10-27T04:30', 4*60, 60, dtype='M8[m]') >>> d array(['2002-10-27T04:30', '2002-10-27T05:30', '2002-10-27T06:30', '2002-10-27T07:30'], dtype='datetime64[m]') Setting the timezone to UTC shows the same information, but with a Z suffix >>> np.datetime_as_string(d, timezone='UTC') array(['2002-10-27T04:30Z', '2002-10-27T05:30Z', '2002-10-27T06:30Z', '2002-10-27T07:30Z'], dtype='>> np.datetime_as_string(d, timezone=pytz.timezone('US/Eastern')) array(['2002-10-27T00:30-0400', '2002-10-27T01:30-0400', '2002-10-27T01:30-0500', '2002-10-27T02:30-0500'], dtype='>> np.datetime_as_string(d, unit='h') array(['2002-10-27T04', '2002-10-27T05', '2002-10-27T06', '2002-10-27T07'], dtype='>> np.datetime_as_string(d, unit='s') array(['2002-10-27T04:30:00', '2002-10-27T05:30:00', '2002-10-27T06:30:00', '2002-10-27T07:30:00'], dtype='>> np.datetime_as_string(d, unit='h', casting='safe') Traceback (most recent call last): ... TypeError: Cannot create a datetime string as units 'h' from a NumPy datetime with units 'm' according to the rule 'safe' ### datetime_data datetime_data(dtype, /) Get information about the step size of a date or time type. The returned tuple can be passed as the second argument of `numpy.datetime64` and `numpy.timedelta64`. Parameters ---------- dtype : dtype The dtype object, which must be a `datetime64` or `timedelta64` type. Returns ------- unit : str The :ref:`datetime unit ` on which this dtype is based. count : int The number of base units in a step. Examples -------- >>> dt_25s = np.dtype('timedelta64[25s]') >>> np.datetime_data(dt_25s) ('s', 25) >>> np.array(10, dt_25s).astype('timedelta64[s]') array(250, dtype='timedelta64[s]') The result can be used to construct a datetime that uses the same units as a timedelta >>> np.datetime64('2010', np.datetime_data(dt_25s)) numpy.datetime64('2010-01-01T00:00:00','25s') ### delete Return a new array with sub-arrays along an axis deleted. For a one dimensional array, this returns those entries not returned by `arr[obj]`. Parameters ---------- arr : array_like Input array. obj : slice, int or array of ints Indicate indices of sub-arrays to remove along the specified axis. .. versionchanged:: 1.19.0 Boolean indices are now treated as a mask of elements to remove, rather than being cast to the integers 0 and 1. axis : int, optional The axis along which to delete the subarray defined by `obj`. If `axis` is None, `obj` is applied to the flattened array. Returns ------- out : ndarray A copy of `arr` with the elements specified by `obj` removed. Note that `delete` does not occur in-place. If `axis` is None, `out` is a flattened array. See Also -------- insert : Insert elements into an array. append : Append elements at the end of an array. Notes ----- Often it is preferable to use a boolean mask. For example: >>> arr = [np.arange(12)](https://www.chedong.com/phpMan.php/man/np.arange/12/markdown) + 1 >>> mask = np.ones(len(arr), dtype=bool) >>> mask[[0,2,4]] = False >>> result = arr[mask,...] Is equivalent to `np.delete(arr, [0,2,4], axis=0)`, but allows further use of `mask`. Examples -------- >>> arr = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]]) >>> arr array([[ 1, 2, 3, 4], [ 5, 6, 7, 8], [ 9, 10, 11, 12]]) >>> np.delete(arr, 1, 0) array([[ 1, 2, 3, 4], [ 9, 10, 11, 12]]) >>> np.delete(arr, np.s_[::2], 1) array([[ 2, 4], [ 6, 8], [10, 12]]) >>> np.delete(arr, [1,3,5], None) array([ 1, 3, 5, 7, 8, 9, 10, 11, 12]) ### deprecate Issues a DeprecationWarning, adds warning to `old_name`'s docstring, rebinds ``old_name.__name__`` and returns the new function object. This function may also be used as a decorator. Parameters ---------- func : function The function to be deprecated. old_name : str, optional The name of the function to be deprecated. Default is None, in which case the name of `func` is used. new_name : str, optional The new name for the function. Default is None, in which case the deprecation message is that `old_name` is deprecated. If given, the deprecation message is that `old_name` is deprecated and `new_name` should be used instead. message : str, optional Additional explanation of the deprecation. Displayed in the docstring after the warning. Returns ------- old_func : function The deprecated function. Examples -------- Note that ``olduint`` returns a value after printing Deprecation Warning: >>> olduint = np.deprecate(np.uint) DeprecationWarning: `uint64` is deprecated! # may vary >>> [olduint(6)](https://www.chedong.com/phpMan.php/man/olduint/6/markdown) 6 ### deprecate_with_doc Deprecates a function and includes the deprecation in its docstring. This function is used as a decorator. It returns an object that can be used to issue a DeprecationWarning, by passing the to-be decorated function as argument, this adds warning to the to-be decorated function's docstring and returns the new function object. See Also -------- deprecate : Decorate a function such that it issues a `DeprecationWarning` Parameters ---------- msg : str Additional explanation of the deprecation. Displayed in the docstring after the warning. Returns ------- obj : object ### diag Extract a diagonal or construct a diagonal array. See the more detailed documentation for ``numpy.diagonal`` if you use this function to extract a diagonal and wish to write to the resulting array; whether it returns a copy or a view depends on what version of numpy you are using. Parameters ---------- v : array_like If `v` is a 2-D array, return a copy of its `k`-th diagonal. If `v` is a 1-D array, return a 2-D array with `v` on the `k`-th diagonal. k : int, optional Diagonal in question. The default is 0. Use `k>0` for diagonals above the main diagonal, and `k<0` for diagonals below the main diagonal. Returns ------- out : ndarray The extracted diagonal or constructed diagonal array. See Also -------- diagonal : Return specified diagonals. diagflat : Create a 2-D array with the flattened input as a diagonal. trace : Sum along diagonals. triu : Upper triangle of an array. tril : Lower triangle of an array. Examples -------- >>> x = [np.arange(9)](https://www.chedong.com/phpMan.php/man/np.arange/9/markdown).reshape((3,3)) >>> x array([[0, 1, 2], [3, 4, 5], [6, 7, 8]]) >>> np.diag(x) array([0, 4, 8]) >>> np.diag(x, k=1) array([1, 5]) >>> np.diag(x, k=-1) array([3, 7]) >>> np.diag(np.diag(x)) array([[0, 0, 0], [0, 4, 0], [0, 0, 8]]) ### diag_indices Return the indices to access the main diagonal of an array. This returns a tuple of indices that can be used to access the main diagonal of an array `a` with ``a.ndim >= 2`` dimensions and shape (n, n, ..., n). For ``a.ndim = 2`` this is the usual diagonal, for ``a.ndim > 2`` this is the set of indices to access ``a[i, i, ..., i]`` for ``i = [0..n-1]``. Parameters ---------- n : int The size, along each dimension, of the arrays for which the returned indices can be used. ndim : int, optional The number of dimensions. See Also -------- diag_indices_from Notes ----- .. versionadded:: 1.4.0 Examples -------- Create a set of indices to access the diagonal of a (4, 4) array: >>> di = [np.diag_indices(4)](https://www.chedong.com/phpMan.php/man/np.diagindices/4/markdown) >>> di (array([0, 1, 2, 3]), array([0, 1, 2, 3])) >>> a = [np.arange(16)](https://www.chedong.com/phpMan.php/man/np.arange/16/markdown).reshape(4, 4) >>> a array([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11], [12, 13, 14, 15]]) >>> a[di] = 100 >>> a array([[100, 1, 2, 3], [ 4, 100, 6, 7], [ 8, 9, 100, 11], [ 12, 13, 14, 100]]) Now, we create indices to manipulate a 3-D array: >>> d3 = np.diag_indices(2, 3) >>> d3 (array([0, 1]), array([0, 1]), array([0, 1])) And use it to set the diagonal of an array of zeros to 1: >>> a = np.zeros((2, 2, 2), dtype=int) >>> a[d3] = 1 >>> a array([[[1, 0], [0, 0]], [[0, 0], [0, 1]]]) ### diag_indices_from Return the indices to access the main diagonal of an n-dimensional array. See `diag_indices` for full details. Parameters ---------- arr : array, at least 2-D See Also -------- diag_indices Notes ----- .. versionadded:: 1.4.0 ### diagflat Create a two-dimensional array with the flattened input as a diagonal. Parameters ---------- v : array_like Input data, which is flattened and set as the `k`-th diagonal of the output. k : int, optional Diagonal to set; 0, the default, corresponds to the "main" diagonal, a positive (negative) `k` giving the number of the diagonal above (below) the main. Returns ------- out : ndarray The 2-D output array. See Also -------- diag : MATLAB work-alike for 1-D and 2-D arrays. diagonal : Return specified diagonals. trace : Sum along diagonals. Examples -------- >>> np.diagflat([[1,2], [3,4]]) array([[1, 0, 0, 0], [0, 2, 0, 0], [0, 0, 3, 0], [0, 0, 0, 4]]) >>> np.diagflat([1,2], 1) array([[0, 1, 0], [0, 0, 2], [0, 0, 0]]) ### diagonal Return specified diagonals. If `a` is 2-D, returns the diagonal of `a` with the given offset, i.e., the collection of elements of the form ``a[i, i+offset]``. If `a` has more than two dimensions, then the axes specified by `axis1` and `axis2` are used to determine the 2-D sub-array whose diagonal is returned. The shape of the resulting array can be determined by removing `axis1` and `axis2` and appending an index to the right equal to the size of the resulting diagonals. In versions of NumPy prior to 1.7, this function always returned a new, independent array containing a copy of the values in the diagonal. In NumPy 1.7 and 1.8, it continues to return a copy of the diagonal, but depending on this fact is deprecated. Writing to the resulting array continues to work as it used to, but a FutureWarning is issued. Starting in NumPy 1.9 it returns a read-only view on the original array. Attempting to write to the resulting array will produce an error. In some future release, it will return a read/write view and writing to the returned array will alter your original array. The returned array will have the same type as the input array. If you don't write to the array returned by this function, then you can just ignore all of the above. If you depend on the current behavior, then we suggest copying the returned array explicitly, i.e., use ``np.diagonal(a).copy()`` instead of just ``np.diagonal(a)``. This will work with both past and future versions of NumPy. Parameters ---------- a : array_like Array from which the diagonals are taken. offset : int, optional Offset of the diagonal from the main diagonal. Can be positive or negative. Defaults to main diagonal (0). axis1 : int, optional Axis to be used as the first axis of the 2-D sub-arrays from which the diagonals should be taken. Defaults to first axis (0). axis2 : int, optional Axis to be used as the second axis of the 2-D sub-arrays from which the diagonals should be taken. Defaults to second axis (1). Returns ------- array_of_diagonals : ndarray If `a` is 2-D, then a 1-D array containing the diagonal and of the same type as `a` is returned unless `a` is a `matrix`, in which case a 1-D array rather than a (2-D) `matrix` is returned in order to maintain backward compatibility. If ``a.ndim > 2``, then the dimensions specified by `axis1` and `axis2` are removed, and a new axis inserted at the end corresponding to the diagonal. Raises ------ ValueError If the dimension of `a` is less than 2. See Also -------- diag : MATLAB work-a-like for 1-D and 2-D arrays. diagflat : Create diagonal arrays. trace : Sum along diagonals. Examples -------- >>> a = [np.arange(4)](https://www.chedong.com/phpMan.php/man/np.arange/4/markdown).reshape(2,2) >>> a array([[0, 1], [2, 3]]) >>> a.diagonal() array([0, 3]) >>> [a.diagonal(1)](https://www.chedong.com/phpMan.php/man/a.diagonal/1/markdown) array([1]) A 3-D example: >>> a = [np.arange(8)](https://www.chedong.com/phpMan.php/man/np.arange/8/markdown).reshape(2,2,2); a array([[[0, 1], [2, 3]], [[4, 5], [6, 7]]]) >>> a.diagonal(0, # Main diagonals of two arrays created by skipping ... 0, # across the outer(left)-most axis last and ... 1) # the "middle" (row) axis first. array([[0, 6], [1, 7]]) The sub-arrays whose main diagonals we just obtained; note that each corresponds to fixing the right-most (column) axis, and that the diagonals are "packed" in rows. >>> a[:,:,0] # main diagonal is [0 6] array([[0, 2], [4, 6]]) >>> a[:,:,1] # main diagonal is [1 7] array([[1, 3], [5, 7]]) The anti-diagonal can be obtained by reversing the order of elements using either `numpy.flipud` or `numpy.fliplr`. >>> a = [np.arange(9)](https://www.chedong.com/phpMan.php/man/np.arange/9/markdown).reshape(3, 3) >>> a array([[0, 1, 2], [3, 4, 5], [6, 7, 8]]) >>> np.fliplr(a).diagonal() # Horizontal flip array([2, 4, 6]) >>> np.flipud(a).diagonal() # Vertical flip array([6, 4, 2]) Note that the order in which the diagonal is retrieved varies depending on the flip function. ### diff Calculate the n-th discrete difference along the given axis. The first difference is given by ``out[i] = a[i+1] - a[i]`` along the given axis, higher differences are calculated by using `diff` recursively. Parameters ---------- a : array_like Input array n : int, optional The number of times values are differenced. If zero, the input is returned as-is. axis : int, optional The axis along which the difference is taken, default is the last axis. prepend, append : array_like, optional Values to prepend or append to `a` along axis prior to performing the difference. Scalar values are expanded to arrays with length 1 in the direction of axis and the shape of the input array in along all other axes. Otherwise the dimension and shape must match `a` except along axis. .. versionadded:: 1.16.0 Returns ------- diff : ndarray The n-th differences. The shape of the output is the same as `a` except along `axis` where the dimension is smaller by `n`. The type of the output is the same as the type of the difference between any two elements of `a`. This is the same as the type of `a` in most cases. A notable exception is `datetime64`, which results in a `timedelta64` output array. See Also -------- gradient, ediff1d, cumsum Notes ----- Type is preserved for boolean arrays, so the result will contain `False` when consecutive elements are the same and `True` when they differ. For unsigned integer arrays, the results will also be unsigned. This should not be surprising, as the result is consistent with calculating the difference directly: >>> u8_arr = np.array([1, 0], dtype=np.uint8) >>> np.diff(u8_arr) array([255], dtype=uint8) >>> u8_arr[1,...] - u8_arr[0,...] 255 If this is not desirable, then the array should be cast to a larger integer type first: >>> i16_arr = u8_arr.astype(np.int16) >>> np.diff(i16_arr) array([-1], dtype=int16) Examples -------- >>> x = np.array([1, 2, 4, 7, 0]) >>> np.diff(x) array([ 1, 2, 3, -7]) >>> np.diff(x, n=2) array([ 1, 1, -10]) >>> x = np.array([[1, 3, 6, 10], [0, 5, 6, 8]]) >>> np.diff(x) array([[2, 3, 4], [5, 1, 2]]) >>> np.diff(x, axis=0) array([[-1, 2, 0, -2]]) >>> x = np.arange('1066-10-13', '1066-10-16', dtype=np.datetime64) >>> np.diff(x) array([1, 1], dtype='timedelta64[D]') ### digitize Return the indices of the bins to which each value in input array belongs. ========= ============= ============================ `right` order of bins returned index `i` satisfies ========= ============= ============================ ``False`` increasing ``bins[i-1] <= x < bins[i]`` ``True`` increasing ``bins[i-1] < x <= bins[i]`` ``False`` decreasing ``bins[i-1] > x >= bins[i]`` ``True`` decreasing ``bins[i-1] >= x > bins[i]`` ========= ============= ============================ If values in `x` are beyond the bounds of `bins`, 0 or ``len(bins)`` is returned as appropriate. Parameters ---------- x : array_like Input array to be binned. Prior to NumPy 1.10.0, this array had to be 1-dimensional, but can now have any shape. bins : array_like Array of bins. It has to be 1-dimensional and monotonic. right : bool, optional Indicating whether the intervals include the right or the left bin edge. Default behavior is (right==False) indicating that the interval does not include the right edge. The left bin end is open in this case, i.e., bins[i-1] <= x < bins[i] is the default behavior for monotonically increasing bins. Returns ------- indices : ndarray of ints Output array of indices, of same shape as `x`. Raises ------ ValueError If `bins` is not monotonic. TypeError If the type of the input is complex. See Also -------- bincount, histogram, unique, searchsorted Notes ----- If values in `x` are such that they fall outside the bin range, attempting to index `bins` with the indices that `digitize` returns will result in an IndexError. .. versionadded:: 1.10.0 `np.digitize` is implemented in terms of `np.searchsorted`. This means that a binary search is used to bin the values, which scales much better for larger number of bins than the previous linear search. It also removes the requirement for the input array to be 1-dimensional. For monotonically _increasing_ `bins`, the following are equivalent:: np.digitize(x, bins, right=True) np.searchsorted(bins, x, side='left') Note that as the order of the arguments are reversed, the side must be too. The `searchsorted` call is marginally faster, as it does not do any monotonicity checks. Perhaps more importantly, it supports all dtypes. Examples -------- >>> x = np.array([0.2, 6.4, 3.0, 1.6]) >>> bins = np.array([0.0, 1.0, 2.5, 4.0, 10.0]) >>> inds = np.digitize(x, bins) >>> inds array([1, 4, 3, 2]) >>> for n in range(x.size): ... print(bins[inds[n]-1], "<=", x[n], "<", bins[inds[n]]) ... 0.0 <= 0.2 < 1.0 4.0 <= 6.4 < 10.0 2.5 <= 3.0 < 4.0 1.0 <= 1.6 < 2.5 >>> x = np.array([1.2, 10.0, 12.4, 15.5, 20.]) >>> bins = np.array([0, 5, 10, 15, 20]) >>> np.digitize(x,bins,right=True) array([1, 2, 3, 4, 4]) >>> np.digitize(x,bins,right=False) array([1, 3, 3, 4, 5]) ### disp Display a message on a device. Parameters ---------- mesg : str Message to display. device : object Device to write message. If None, defaults to ``sys.stdout`` which is very similar to ``print``. `device` needs to have ``write()`` and ``flush()`` methods. linefeed : bool, optional Option whether to print a line feed or not. Defaults to True. Raises ------ AttributeError If `device` does not have a ``write()`` or ``flush()`` method. Examples -------- Besides ``sys.stdout``, a file-like object can also be used as it has both required methods: >>> from io import StringIO >>> buf = StringIO() >>> np.disp(u'"Display" in a file', device=buf) >>> buf.getvalue() '"Display" in a file\n' ### dot dot(a, b, out=None) Dot product of two arrays. Specifically, - If both `a` and `b` are 1-D arrays, it is inner product of vectors (without complex conjugation). - If both `a` and `b` are 2-D arrays, it is matrix multiplication, but using :func:`matmul` or ``a @ b`` is preferred. - If either `a` or `b` is 0-D (scalar), it is equivalent to :func:`multiply` and using ``numpy.multiply(a, b)`` or ``a * b`` is preferred. - If `a` is an N-D array and `b` is a 1-D array, it is a sum product over the last axis of `a` and `b`. - If `a` is an N-D array and `b` is an M-D array (where ``M>=2``), it is a sum product over the last axis of `a` and the second-to-last axis of `b`:: dot(a, b)[i,j,k,m] = sum(a[i,j,:] * b[k,:,m]) Parameters ---------- a : array_like First argument. b : array_like Second argument. out : ndarray, optional Output argument. This must have the exact kind that would be returned if it was not used. In particular, it must have the right type, must be C-contiguous, and its dtype must be the dtype that would be returned for `dot(a,b)`. This is a performance feature. Therefore, if these conditions are not met, an exception is raised, instead of attempting to be flexible. Returns ------- output : ndarray Returns the dot product of `a` and `b`. If `a` and `b` are both scalars or both 1-D arrays then a scalar is returned; otherwise an array is returned. If `out` is given, then it is returned. Raises ------ ValueError If the last dimension of `a` is not the same size as the second-to-last dimension of `b`. See Also -------- vdot : Complex-conjugating dot product. tensordot : Sum products over arbitrary axes. einsum : Einstein summation convention. matmul : '@' operator as method with out parameter. linalg.multi_dot : Chained dot product. Examples -------- >>> np.dot(3, 4) 12 Neither argument is complex-conjugated: >>> np.dot([2j, 3j], [2j, 3j]) (-13+0j) For 2-D arrays it is the matrix product: >>> a = [[1, 0], [0, 1]] >>> b = [[4, 1], [2, 2]] >>> np.dot(a, b) array([[4, 1], [2, 2]]) >>> a = np.arange(3*4*5*6).reshape((3,4,5,6)) >>> b = np.arange(3*4*5*6)[::-1].reshape((5,4,6,3)) >>> np.dot(a, b)[2,3,2,1,2,2] 499128 >>> sum(a[2,3,2,:] * b[1,2,:,2]) 499128 ### dsplit Split array into multiple sub-arrays along the 3rd axis (depth). Please refer to the `split` documentation. `dsplit` is equivalent to `split` with ``axis=2``, the array is always split along the third axis provided the array dimension is greater than or equal to 3. See Also -------- split : Split an array into multiple sub-arrays of equal size. Examples -------- >>> x = np.arange(16.0).reshape(2, 2, 4) >>> x array([[[ 0., 1., 2., 3.], [ 4., 5., 6., 7.]], [[ 8., 9., 10., 11.], [12., 13., 14., 15.]]]) >>> np.dsplit(x, 2) [array([[[ 0., 1.], [ 4., 5.]], [[ 8., 9.], [12., 13.]]]), array([[[ 2., 3.], [ 6., 7.]], [[10., 11.], [14., 15.]]])] >>> np.dsplit(x, np.array([3, 6])) [array([[[ 0., 1., 2.], [ 4., 5., 6.]], [[ 8., 9., 10.], [12., 13., 14.]]]), array([[[ 3.], [ 7.]], [[11.], [15.]]]), array([], shape=(2, 2, 0), dtype=float64)] ### dstack Stack arrays in sequence depth wise (along third axis). This is equivalent to concatenation along the third axis after 2-D arrays of shape `(M,N)` have been reshaped to `(M,N,1)` and 1-D arrays of shape `(N,)` have been reshaped to `(1,N,1)`. Rebuilds arrays divided by `dsplit`. This function makes most sense for arrays with up to 3 dimensions. For instance, for pixel-data with a height (first axis), width (second axis), and r/g/b channels (third axis). The functions `concatenate`, `stack` and `block` provide more general stacking and concatenation operations. Parameters ---------- tup : sequence of arrays The arrays must have the same shape along all but the third axis. 1-D or 2-D arrays must have the same shape. Returns ------- stacked : ndarray The array formed by stacking the given arrays, will be at least 3-D. See Also -------- concatenate : Join a sequence of arrays along an existing axis. stack : Join a sequence of arrays along a new axis. block : Assemble an nd-array from nested lists of blocks. vstack : Stack arrays in sequence vertically (row wise). hstack : Stack arrays in sequence horizontally (column wise). column_stack : Stack 1-D arrays as columns into a 2-D array. dsplit : Split array along third axis. Examples -------- >>> a = np.array((1,2,3)) >>> b = np.array((2,3,4)) >>> np.dstack((a,b)) array([[[1, 2], [2, 3], [3, 4]]]) >>> a = np.array([[1],[2],[3]]) >>> b = np.array([[2],[3],[4]]) >>> np.dstack((a,b)) array([[[1, 2]], [[2, 3]], [[3, 4]]]) ### ediff1d The differences between consecutive elements of an array. Parameters ---------- ary : array_like If necessary, will be flattened before the differences are taken. to_end : array_like, optional Number(s) to append at the end of the returned differences. to_begin : array_like, optional Number(s) to prepend at the beginning of the returned differences. Returns ------- ediff1d : ndarray The differences. Loosely, this is ``ary.flat[1:] - ary.flat[:-1]``. See Also -------- diff, gradient Notes ----- When applied to masked arrays, this function drops the mask information if the `to_begin` and/or `to_end` parameters are used. Examples -------- >>> x = np.array([1, 2, 4, 7, 0]) >>> np.ediff1d(x) array([ 1, 2, 3, -7]) >>> np.ediff1d(x, to_begin=-99, to_end=np.array([88, 99])) array([-99, 1, 2, ..., -7, 88, 99]) The returned array is always 1D. >>> y = [[1, 2, 4], [1, 6, 24]] >>> np.ediff1d(y) array([ 1, 2, -3, 5, 18]) ### einsum einsum(subscripts, *operands, out=None, dtype=None, order='K', casting='safe', optimize=False) Evaluates the Einstein summation convention on the operands. Using the Einstein summation convention, many common multi-dimensional, linear algebraic array operations can be represented in a simple fashion. In *implicit* mode `einsum` computes these values. In *explicit* mode, `einsum` provides further flexibility to compute other array operations that might not be considered classical Einstein summation operations, by disabling, or forcing summation over specified subscript labels. See the notes and examples for clarification. Parameters ---------- subscripts : str Specifies the subscripts for summation as comma separated list of subscript labels. An implicit (classical Einstein summation) calculation is performed unless the explicit indicator '->' is included as well as subscript labels of the precise output form. operands : list of array_like These are the arrays for the operation. out : ndarray, optional If provided, the calculation is done into this array. dtype : {data-type, None}, optional If provided, forces the calculation to use the data type specified. Note that you may have to also give a more liberal `casting` parameter to allow the conversions. Default is None. order : {'C', 'F', 'A', 'K'}, optional Controls the memory layout of the output. 'C' means it should be C contiguous. 'F' means it should be Fortran contiguous, 'A' means it should be 'F' if the inputs are all 'F', 'C' otherwise. 'K' means it should be as close to the layout as the inputs as is possible, including arbitrarily permuted axes. Default is 'K'. casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional Controls what kind of data casting may occur. Setting this to 'unsafe' is not recommended, as it can adversely affect accumulations. * 'no' means the data types should not be cast at all. * 'equiv' means only byte-order changes are allowed. * 'safe' means only casts which can preserve values are allowed. * 'same_kind' means only safe casts or casts within a kind, like float64 to float32, are allowed. * 'unsafe' means any data conversions may be done. Default is 'safe'. optimize : {False, True, 'greedy', 'optimal'}, optional Controls if intermediate optimization should occur. No optimization will occur if False and True will default to the 'greedy' algorithm. Also accepts an explicit contraction list from the ``np.einsum_path`` function. See ``np.einsum_path`` for more details. Defaults to False. Returns ------- output : ndarray The calculation based on the Einstein summation convention. See Also -------- einsum_path, dot, inner, outer, tensordot, linalg.multi_dot einops : similar verbose interface is provided by `einops <>`_ package to cover additional operations: transpose, reshape/flatten, repeat/tile, squeeze/unsqueeze and reductions. opt_einsum : `opt_einsum <>`_ optimizes contraction order for einsum-like expressions in backend-agnostic manner. Notes ----- .. versionadded:: 1.6.0 The Einstein summation convention can be used to compute many multi-dimensional, linear algebraic array operations. `einsum` provides a succinct way of representing these. A non-exhaustive list of these operations, which can be computed by `einsum`, is shown below along with examples: * Trace of an array, :py:func:`numpy.trace`. * Return a diagonal, :py:func:`numpy.diag`. * Array axis summations, :py:func:`numpy.sum`. * Transpositions and permutations, :py:func:`numpy.transpose`. * Matrix multiplication and dot product, :py:func:`numpy.matmul` :py:func:`numpy.dot`. * Vector inner and outer products, :py:func:`numpy.inner` :py:func:`numpy.outer`. * Broadcasting, element-wise and scalar multiplication, :py:func:`numpy.multiply`. * Tensor contractions, :py:func:`numpy.tensordot`. * Chained array operations, in efficient calculation order, :py:func:`numpy.einsum_path`. The subscripts string is a comma-separated list of subscript labels, where each label refers to a dimension of the corresponding operand. Whenever a label is repeated it is summed, so ``np.einsum('i,i', a, b)`` is equivalent to :py:func:`np.inner(a,b) `. If a label appears only once, it is not summed, so ``np.einsum('i', a)`` produces a view of ``a`` with no changes. A further example ``np.einsum('ij,jk', a, b)`` describes traditional matrix multiplication and is equivalent to :py:func:`np.matmul(a,b) `. Repeated subscript labels in one operand take the diagonal. For example, ``np.einsum('ii', a)`` is equivalent to :py:func:`np.trace(a) `. In *implicit mode*, the chosen subscripts are important since the axes of the output are reordered alphabetically. This means that ``np.einsum('ij', a)`` doesn't affect a 2D array, while ``np.einsum('ji', a)`` takes its transpose. Additionally, ``np.einsum('ij,jk', a, b)`` returns a matrix multiplication, while, ``np.einsum('ij,jh', a, b)`` returns the transpose of the multiplication since subscript 'h' precedes subscript 'i'. In *explicit mode* the output can be directly controlled by specifying output subscript labels. This requires the identifier '->' as well as the list of output subscript labels. This feature increases the flexibility of the function since summing can be disabled or forced when required. The call ``np.einsum('i->', a)`` is like :py:func:`np.sum(a, axis=-1) `, and ``np.einsum('ii->i', a)`` is like :py:func:`np.diag(a) `. The difference is that `einsum` does not allow broadcasting by default. Additionally ``np.einsum('ij,jh->ih', a, b)`` directly specifies the order of the output subscript labels and therefore returns matrix multiplication, unlike the example above in implicit mode. To enable and control broadcasting, use an ellipsis. Default NumPy-style broadcasting is done by adding an ellipsis to the left of each term, like ``np.einsum('...ii->...i', a)``. To take the trace along the first and last axes, you can do ``np.einsum('i...i', a)``, or to do a matrix-matrix product with the left-most indices instead of rightmost, one can do ``np.einsum('ij...,jk...->ik...', a, b)``. When there is only one operand, no axes are summed, and no output parameter is provided, a view into the operand is returned instead of a new array. Thus, taking the diagonal as ``np.einsum('ii->i', a)`` produces a view (changed in version 1.10.0). `einsum` also provides an alternative way to provide the subscripts and operands as ``einsum(op0, sublist0, op1, sublist1, ..., [sublistout])``. If the output shape is not provided in this format `einsum` will be calculated in implicit mode, otherwise it will be performed explicitly. The examples below have corresponding `einsum` calls with the two parameter methods. .. versionadded:: 1.10.0 Views returned from einsum are now writeable whenever the input array is writeable. For example, ``np.einsum('ijk...->kji...', a)`` will now have the same effect as :py:func:`np.swapaxes(a, 0, 2) ` and ``np.einsum('ii->i', a)`` will return a writeable view of the diagonal of a 2D array. .. versionadded:: 1.12.0 Added the ``optimize`` argument which will optimize the contraction order of an einsum expression. For a contraction with three or more operands this can greatly increase the computational efficiency at the cost of a larger memory footprint during computation. Typically a 'greedy' algorithm is applied which empirical tests have shown returns the optimal path in the majority of cases. In some cases 'optimal' will return the superlative path through a more expensive, exhaustive search. For iterative calculations it may be advisable to calculate the optimal path once and reuse that path by supplying it as an argument. An example is given below. See :py:func:`numpy.einsum_path` for more details. Examples -------- >>> a = [np.arange(25)](https://www.chedong.com/phpMan.php/man/np.arange/25/markdown).reshape(5,5) >>> b = [np.arange(5)](https://www.chedong.com/phpMan.php/man/np.arange/5/markdown) >>> c = [np.arange(6)](https://www.chedong.com/phpMan.php/man/np.arange/6/markdown).reshape(2,3) Trace of a matrix: >>> np.einsum('ii', a) 60 >>> np.einsum(a, [0,0]) 60 >>> np.trace(a) 60 Extract the diagonal (requires explicit form): >>> np.einsum('ii->i', a) array([ 0, 6, 12, 18, 24]) >>> np.einsum(a, [0,0], [0]) array([ 0, 6, 12, 18, 24]) >>> np.diag(a) array([ 0, 6, 12, 18, 24]) Sum over an axis (requires explicit form): >>> np.einsum('ij->i', a) array([ 10, 35, 60, 85, 110]) >>> np.einsum(a, [0,1], [0]) array([ 10, 35, 60, 85, 110]) >>> np.sum(a, axis=1) array([ 10, 35, 60, 85, 110]) For higher dimensional arrays summing a single axis can be done with ellipsis: >>> np.einsum('...j->...', a) array([ 10, 35, 60, 85, 110]) >>> np.einsum(a, [Ellipsis,1], [Ellipsis]) array([ 10, 35, 60, 85, 110]) Compute a matrix transpose, or reorder any number of axes: >>> np.einsum('ji', c) array([[0, 3], [1, 4], [2, 5]]) >>> np.einsum('ij->ji', c) array([[0, 3], [1, 4], [2, 5]]) >>> np.einsum(c, [1,0]) array([[0, 3], [1, 4], [2, 5]]) >>> np.transpose(c) array([[0, 3], [1, 4], [2, 5]]) Vector inner products: >>> np.einsum('i,i', b, b) 30 >>> np.einsum(b, [0], b, [0]) 30 >>> np.inner(b,b) 30 Matrix vector multiplication: >>> np.einsum('ij,j', a, b) array([ 30, 80, 130, 180, 230]) >>> np.einsum(a, [0,1], b, [1]) array([ 30, 80, 130, 180, 230]) >>> np.dot(a, b) array([ 30, 80, 130, 180, 230]) >>> np.einsum('...j,j', a, b) array([ 30, 80, 130, 180, 230]) Broadcasting and scalar multiplication: >>> np.einsum('..., ...', 3, c) array([[ 0, 3, 6], [ 9, 12, 15]]) >>> np.einsum(',ij', 3, c) array([[ 0, 3, 6], [ 9, 12, 15]]) >>> np.einsum(3, [Ellipsis], c, [Ellipsis]) array([[ 0, 3, 6], [ 9, 12, 15]]) >>> np.multiply(3, c) array([[ 0, 3, 6], [ 9, 12, 15]]) Vector outer product: >>> np.einsum('i,j', [np.arange(2)](https://www.chedong.com/phpMan.php/man/np.arange/2/markdown)+1, b) array([[0, 1, 2, 3, 4], [0, 2, 4, 6, 8]]) >>> np.einsum([np.arange(2)](https://www.chedong.com/phpMan.php/man/np.arange/2/markdown)+1, [0], b, [1]) array([[0, 1, 2, 3, 4], [0, 2, 4, 6, 8]]) >>> np.outer([np.arange(2)](https://www.chedong.com/phpMan.php/man/np.arange/2/markdown)+1, b) array([[0, 1, 2, 3, 4], [0, 2, 4, 6, 8]]) Tensor contraction: >>> a = np.arange(60.).reshape(3,4,5) >>> b = np.arange(24.).reshape(4,3,2) >>> np.einsum('ijk,jil->kl', a, b) array([[4400., 4730.], [4532., 4874.], [4664., 5018.], [4796., 5162.], [4928., 5306.]]) >>> np.einsum(a, [0,1,2], b, [1,0,3], [2,3]) array([[4400., 4730.], [4532., 4874.], [4664., 5018.], [4796., 5162.], [4928., 5306.]]) >>> np.tensordot(a,b, axes=([1,0],[0,1])) array([[4400., 4730.], [4532., 4874.], [4664., 5018.], [4796., 5162.], [4928., 5306.]]) Writeable returned arrays (since version 1.10.0): >>> a = np.zeros((3, 3)) >>> np.einsum('ii->i', a)[:] = 1 >>> a array([[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]]) Example of ellipsis use: >>> a = [np.arange(6)](https://www.chedong.com/phpMan.php/man/np.arange/6/markdown).reshape((3,2)) >>> b = [np.arange(12)](https://www.chedong.com/phpMan.php/man/np.arange/12/markdown).reshape((4,3)) >>> np.einsum('ki,jk->ij', a, b) array([[10, 28, 46, 64], [13, 40, 67, 94]]) >>> np.einsum('ki,...k->i...', a, b) array([[10, 28, 46, 64], [13, 40, 67, 94]]) >>> np.einsum('k...,jk', a, b) array([[10, 28, 46, 64], [13, 40, 67, 94]]) Chained array operations. For more complicated contractions, speed ups might be achieved by repeatedly computing a 'greedy' path or pre-computing the 'optimal' path and repeatedly applying it, using an `einsum_path` insertion (since version 1.12.0). Performance improvements can be particularly significant with larger arrays: >>> a = [np.ones(64)](https://www.chedong.com/phpMan.php/man/np.ones/64/markdown).reshape(2,4,8) Basic `einsum`: ~1520ms (benchmarked on 3.1GHz Intel i5.) >>> for iteration in [range(500)](https://www.chedong.com/phpMan.php/man/range/500/markdown): ... _ = np.einsum('ijk,ilm,njm,nlk,abc->',a,a,a,a,a) Sub-optimal `einsum` (due to repeated path calculation time): ~330ms >>> for iteration in [range(500)](https://www.chedong.com/phpMan.php/man/range/500/markdown): ... _ = np.einsum('ijk,ilm,njm,nlk,abc->',a,a,a,a,a, optimize='optimal') Greedy `einsum` (faster optimal path approximation): ~160ms >>> for iteration in [range(500)](https://www.chedong.com/phpMan.php/man/range/500/markdown): ... _ = np.einsum('ijk,ilm,njm,nlk,abc->',a,a,a,a,a, optimize='greedy') Optimal `einsum` (best usage pattern in some use cases): ~110ms >>> path = np.einsum_path('ijk,ilm,njm,nlk,abc->',a,a,a,a,a, optimize='optimal')[0] >>> for iteration in [range(500)](https://www.chedong.com/phpMan.php/man/range/500/markdown): ... _ = np.einsum('ijk,ilm,njm,nlk,abc->',a,a,a,a,a, optimize=path) ### einsum_path einsum_path(subscripts, *operands, optimize='greedy') Evaluates the lowest cost contraction order for an einsum expression by considering the creation of intermediate arrays. Parameters ---------- subscripts : str Specifies the subscripts for summation. *operands : list of array_like These are the arrays for the operation. optimize : {bool, list, tuple, 'greedy', 'optimal'} Choose the type of path. If a tuple is provided, the second argument is assumed to be the maximum intermediate size created. If only a single argument is provided the largest input or output array size is used as a maximum intermediate size. * if a list is given that starts with ``einsum_path``, uses this as the contraction path * if False no optimization is taken * if True defaults to the 'greedy' algorithm * 'optimal' An algorithm that combinatorially explores all possible ways of contracting the listed tensors and choosest the least costly path. Scales exponentially with the number of terms in the contraction. * 'greedy' An algorithm that chooses the best pair contraction at each step. Effectively, this algorithm searches the largest inner, Hadamard, and then outer products at each step. Scales cubically with the number of terms in the contraction. Equivalent to the 'optimal' path for most contractions. Default is 'greedy'. Returns ------- path : list of tuples A list representation of the einsum path. string_repr : str A printable representation of the einsum path. Notes ----- The resulting path indicates which terms of the input contraction should be contracted first, the result of this contraction is then appended to the end of the contraction list. This list can then be iterated over until all intermediate contractions are complete. See Also -------- einsum, linalg.multi_dot Examples -------- We can begin with a chain dot example. In this case, it is optimal to contract the ``b`` and ``c`` tensors first as represented by the first element of the path ``(1, 2)``. The resulting tensor is added to the end of the contraction and the remaining contraction ``(0, 1)`` is then completed. >>> [np.random.seed(123)](https://www.chedong.com/phpMan.php/man/np.random.seed/123/markdown) >>> a = np.random.rand(2, 2) >>> b = np.random.rand(2, 5) >>> c = np.random.rand(5, 2) >>> path_info = np.einsum_path('ij,jk,kl->il', a, b, c, optimize='greedy') >>> print(path_info[0]) ['einsum_path', (1, 2), (0, 1)] >>> print(path_info[1]) Complete contraction: ij,jk,kl->il # may vary Naive scaling: 4 Optimized scaling: 3 Naive FLOP count: 1.600e+02 Optimized FLOP count: 5.600e+01 Theoretical speedup: 2.857 Largest intermediate: 4.000e+00 elements ------------------------------------------------------------------------- scaling current remaining ------------------------------------------------------------------------- 3 kl,jk->jl ij,jl->il 3 jl,ij->il il->il A more complex index transformation example. >>> I = np.random.rand(10, 10, 10, 10) >>> C = np.random.rand(10, 10) >>> path_info = np.einsum_path('ea,fb,abcd,gc,hd->efgh', C, C, I, C, C, ... optimize='greedy') >>> print(path_info[0]) ['einsum_path', (0, 2), (0, 3), (0, 2), (0, 1)] >>> print(path_info[1]) Complete contraction: ea,fb,abcd,gc,hd->efgh # may vary Naive scaling: 8 Optimized scaling: 5 Naive FLOP count: 8.000e+08 Optimized FLOP count: 8.000e+05 Theoretical speedup: 1000.000 Largest intermediate: 1.000e+04 elements -------------------------------------------------------------------------- scaling current remaining -------------------------------------------------------------------------- 5 abcd,ea->bcde fb,gc,hd,bcde->efgh 5 bcde,fb->cdef gc,hd,cdef->efgh 5 cdef,gc->defg hd,defg->efgh 5 defg,hd->efgh efgh->efgh ### empty empty(shape, dtype=float, order='C', *, like=None) Return a new array of given shape and type, without initializing entries. Parameters ---------- shape : int or tuple of int Shape of the empty array, e.g., ``(2, 3)`` or ``2``. dtype : data-type, optional Desired output data-type for the array, e.g, `numpy.int8`. Default is `numpy.float64`. order : {'C', 'F'}, optional, default: 'C' Whether to store multi-dimensional data in row-major (C-style) or column-major (Fortran-style) order in memory. like : array_like Reference object to allow the creation of arrays which are not NumPy arrays. If an array-like passed in as ``like`` supports the ``__array_function__`` protocol, the result will be defined by it. In this case, it ensures the creation of an array object compatible with that passed in via this argument. .. versionadded:: 1.20.0 Returns ------- out : ndarray Array of uninitialized (arbitrary) data of the given shape, dtype, and order. Object arrays will be initialized to None. See Also -------- empty_like : Return an empty array with shape and type of input. ones : Return a new array setting values to one. zeros : Return a new array setting values to zero. full : Return a new array of given shape filled with value. Notes ----- `empty`, unlike `zeros`, does not set the array values to zero, and may therefore be marginally faster. On the other hand, it requires the user to manually set all the values in the array, and should be used with caution. Examples -------- >>> np.empty([2, 2]) array([[ -9.74499359e+001, 6.69583040e-309], [ 2.13182611e-314, 3.06959433e-309]]) #uninitialized >>> np.empty([2, 2], dtype=int) array([[-1073741821, -1067949133], [ 496041986, 19249760]]) #uninitialized ### empty_like empty_like(prototype, dtype=None, order='K', subok=True, shape=None) Return a new array with the same shape and type as a given array. Parameters ---------- prototype : array_like The shape and data-type of `prototype` define these same attributes of the returned array. dtype : data-type, optional Overrides the data type of the result. .. versionadded:: 1.6.0 order : {'C', 'F', 'A', or 'K'}, optional Overrides the memory layout of the result. 'C' means C-order, 'F' means F-order, 'A' means 'F' if `prototype` is Fortran contiguous, 'C' otherwise. 'K' means match the layout of `prototype` as closely as possible. .. versionadded:: 1.6.0 subok : bool, optional. If True, then the newly created array will use the sub-class type of `prototype`, otherwise it will be a base-class array. Defaults to True. shape : int or sequence of ints, optional. Overrides the shape of the result. If order='K' and the number of dimensions is unchanged, will try to keep order, otherwise, order='C' is implied. .. versionadded:: 1.17.0 Returns ------- out : ndarray Array of uninitialized (arbitrary) data with the same shape and type as `prototype`. See Also -------- ones_like : Return an array of ones with shape and type of input. zeros_like : Return an array of zeros with shape and type of input. full_like : Return a new array with shape of input filled with value. empty : Return a new uninitialized array. Notes ----- This function does *not* initialize the returned array; to do that use `zeros_like` or `ones_like` instead. It may be marginally faster than the functions that do set the array values. Examples -------- >>> a = ([1,2,3], [4,5,6]) # a is array-like >>> np.empty_like(a) array([[-1073741821, -1073741821, 3], # uninitialized [ 0, 0, -1073741821]]) >>> a = np.array([[1., 2., 3.],[4.,5.,6.]]) >>> np.empty_like(a) array([[ -2.00000715e+000, 1.48219694e-323, -2.00000572e+000], # uninitialized [ 4.38791518e-305, -2.00000715e+000, 4.17269252e-309]]) ### expand_dims Expand the shape of an array. Insert a new axis that will appear at the `axis` position in the expanded array shape. Parameters ---------- a : array_like Input array. axis : int or tuple of ints Position in the expanded axes where the new axis (or axes) is placed. .. deprecated:: 1.13.0 Passing an axis where ``axis > a.ndim`` will be treated as ``axis == a.ndim``, and passing ``axis < -a.ndim - 1`` will be treated as ``axis == 0``. This behavior is deprecated. .. versionchanged:: 1.18.0 A tuple of axes is now supported. Out of range axes as described above are now forbidden and raise an `AxisError`. Returns ------- result : ndarray View of `a` with the number of dimensions increased. See Also -------- squeeze : The inverse operation, removing singleton dimensions reshape : Insert, remove, and combine dimensions, and resize existing ones doc.indexing, atleast_1d, atleast_2d, atleast_3d Examples -------- >>> x = np.array([1, 2]) >>> x.shape (2,) The following is equivalent to ``x[np.newaxis, :]`` or ``x[np.newaxis]``: >>> y = np.expand_dims(x, axis=0) >>> y array([[1, 2]]) >>> y.shape (1, 2) The following is equivalent to ``x[:, np.newaxis]``: >>> y = np.expand_dims(x, axis=1) >>> y array([[1], [2]]) >>> y.shape (2, 1) ``axis`` may also be a tuple: >>> y = np.expand_dims(x, axis=(0, 1)) >>> y array([[[1, 2]]]) >>> y = np.expand_dims(x, axis=(2, 0)) >>> y array([[[1], [2]]]) Note that some examples may use ``None`` instead of ``np.newaxis``. These are the same objects: >>> np.newaxis is None True ### extract Return the elements of an array that satisfy some condition. This is equivalent to ``np.compress(ravel(condition), ravel(arr))``. If `condition` is boolean ``np.extract`` is equivalent to ``arr[condition]``. Note that `place` does the exact opposite of `extract`. Parameters ---------- condition : array_like An array whose nonzero or True entries indicate the elements of `arr` to extract. arr : array_like Input array of the same size as `condition`. Returns ------- extract : ndarray Rank 1 array of values from `arr` where `condition` is True. See Also -------- take, put, copyto, compress, place Examples -------- >>> arr = [np.arange(12)](https://www.chedong.com/phpMan.php/man/np.arange/12/markdown).reshape((3, 4)) >>> arr array([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11]]) >>> condition = np.mod(arr, 3)==0 >>> condition array([[ True, False, False, True], [False, False, True, False], [False, True, False, False]]) >>> np.extract(condition, arr) array([0, 3, 6, 9]) If `condition` is boolean: >>> arr[condition] array([0, 3, 6, 9]) ### eye Return a 2-D array with ones on the diagonal and zeros elsewhere. Parameters ---------- N : int Number of rows in the output. M : int, optional Number of columns in the output. If None, defaults to `N`. k : int, optional Index of the diagonal: 0 (the default) refers to the main diagonal, a positive value refers to an upper diagonal, and a negative value to a lower diagonal. dtype : data-type, optional Data-type of the returned array. order : {'C', 'F'}, optional Whether the output should be stored in row-major (C-style) or column-major (Fortran-style) order in memory. .. versionadded:: 1.14.0 like : array_like Reference object to allow the creation of arrays which are not NumPy arrays. If an array-like passed in as ``like`` supports the ``__array_function__`` protocol, the result will be defined by it. In this case, it ensures the creation of an array object compatible with that passed in via this argument. .. versionadded:: 1.20.0 Returns ------- I : ndarray of shape (N,M) An array where all elements are equal to zero, except for the `k`-th diagonal, whose values are equal to one. See Also -------- identity : (almost) equivalent function diag : diagonal 2-D array from a 1-D array specified by the user. Examples -------- >>> np.eye(2, dtype=int) array([[1, 0], [0, 1]]) >>> np.eye(3, k=1) array([[0., 1., 0.], [0., 0., 1.], [0., 0., 0.]]) fastCopyAndTranspose = _fastCopyAndTranspose(...) _fastCopyAndTranspose(a) ### fill_diagonal Fill the main diagonal of the given array of any dimensionality. For an array `a` with ``a.ndim >= 2``, the diagonal is the list of locations with indices ``a[i, ..., i]`` all identical. This function modifies the input array in-place, it does not return a value. Parameters ---------- a : array, at least 2-D. Array whose diagonal is to be filled, it gets modified in-place. val : scalar or array_like Value(s) to write on the diagonal. If `val` is scalar, the value is written along the diagonal. If array-like, the flattened `val` is written along the diagonal, repeating if necessary to fill all diagonal entries. wrap : bool For tall matrices in NumPy version up to 1.6.2, the diagonal "wrapped" after N columns. You can have this behavior with this option. This affects only tall matrices. See also -------- diag_indices, diag_indices_from Notes ----- .. versionadded:: 1.4.0 This functionality can be obtained via `diag_indices`, but internally this version uses a much faster implementation that never constructs the indices and uses simple slicing. Examples -------- >>> a = np.zeros((3, 3), int) >>> np.fill_diagonal(a, 5) >>> a array([[5, 0, 0], [0, 5, 0], [0, 0, 5]]) The same function can operate on a 4-D array: >>> a = np.zeros((3, 3, 3, 3), int) >>> np.fill_diagonal(a, 4) We only show a few blocks for clarity: >>> a[0, 0] array([[4, 0, 0], [0, 0, 0], [0, 0, 0]]) >>> a[1, 1] array([[0, 0, 0], [0, 4, 0], [0, 0, 0]]) >>> a[2, 2] array([[0, 0, 0], [0, 0, 0], [0, 0, 4]]) The wrap option affects only tall matrices: >>> # tall matrices no wrap >>> a = np.zeros((5, 3), int) >>> np.fill_diagonal(a, 4) >>> a array([[4, 0, 0], [0, 4, 0], [0, 0, 4], [0, 0, 0], [0, 0, 0]]) >>> # tall matrices wrap >>> a = np.zeros((5, 3), int) >>> np.fill_diagonal(a, 4, wrap=True) >>> a array([[4, 0, 0], [0, 4, 0], [0, 0, 4], [0, 0, 0], [4, 0, 0]]) >>> # wide matrices >>> a = np.zeros((3, 5), int) >>> np.fill_diagonal(a, 4, wrap=True) >>> a array([[4, 0, 0, 0, 0], [0, 4, 0, 0, 0], [0, 0, 4, 0, 0]]) The anti-diagonal can be filled by reversing the order of elements using either `numpy.flipud` or `numpy.fliplr`. >>> a = np.zeros((3, 3), int); >>> np.fill_diagonal(np.fliplr(a), [1,2,3]) # Horizontal flip >>> a array([[0, 0, 1], [0, 2, 0], [3, 0, 0]]) >>> np.fill_diagonal(np.flipud(a), [1,2,3]) # Vertical flip >>> a array([[0, 0, 3], [0, 2, 0], [1, 0, 0]]) Note that the order in which the diagonal is filled varies depending on the flip function. ### find_common_type Determine common type following standard coercion rules. Parameters ---------- array_types : sequence A list of dtypes or dtype convertible objects representing arrays. scalar_types : sequence A list of dtypes or dtype convertible objects representing scalars. Returns ------- datatype : dtype The common data type, which is the maximum of `array_types` ignoring `scalar_types`, unless the maximum of `scalar_types` is of a different kind (`dtype.kind`). If the kind is not understood, then None is returned. See Also -------- dtype, common_type, can_cast, mintypecode Examples -------- >>> np.find_common_type([], [np.int64, np.float32, complex]) dtype('complex128') >>> np.find_common_type([np.int64, np.float32], []) dtype('float64') The standard casting rules ensure that a scalar cannot up-cast an array unless the scalar is of a fundamentally different kind of data (i.e. under a different hierarchy in the data type hierarchy) then the array: >>> np.find_common_type([np.float32], [np.int64, np.float64]) dtype('float32') Complex is of a different type, so it up-casts the float in the `array_types` argument: >>> np.find_common_type([np.float32], [complex]) dtype('complex128') Type specifier strings are convertible to dtypes and can therefore be used instead of dtypes: >>> np.find_common_type(['f4', 'f4', 'i4'], ['c8']) dtype('complex128') ### fix Round to nearest integer towards zero. Round an array of floats element-wise to nearest integer towards zero. The rounded values are returned as floats. Parameters ---------- x : array_like An array of floats to be rounded out : ndarray, optional A location into which the result is stored. If provided, it must have a shape that the input broadcasts to. If not provided or None, a freshly-allocated array is returned. Returns ------- out : ndarray of floats A float array with the same dimensions as the input. If second argument is not supplied then a float array is returned with the rounded values. If a second argument is supplied the result is stored there. The return value `out` is then a reference to that array. See Also -------- rint, trunc, floor, ceil around : Round to given number of decimals Examples -------- >>> np.fix(3.14) 3.0 >>> [np.fix(3)](https://www.chedong.com/phpMan.php/man/np.fix/3/markdown) 3.0 >>> np.fix([2.1, 2.9, -2.1, -2.9]) array([ 2., 2., -2., -2.]) ### flatnonzero Return indices that are non-zero in the flattened version of a. This is equivalent to np.nonzero(np.ravel(a))[0]. Parameters ---------- a : array_like Input data. Returns ------- res : ndarray Output array, containing the indices of the elements of `a.ravel()` that are non-zero. See Also -------- nonzero : Return the indices of the non-zero elements of the input array. ravel : Return a 1-D array containing the elements of the input array. Examples -------- >>> x = np.arange(-2, 3) >>> x array([-2, -1, 0, 1, 2]) >>> np.flatnonzero(x) array([0, 1, 3, 4]) Use the indices of the non-zero elements as an index array to extract these elements: >>> x.ravel()[np.flatnonzero(x)] array([-2, -1, 1, 2]) ### flip Reverse the order of elements in an array along the given axis. The shape of the array is preserved, but the elements are reordered. .. versionadded:: 1.12.0 Parameters ---------- m : array_like Input array. axis : None or int or tuple of ints, optional Axis or axes along which to flip over. The default, axis=None, will flip over all of the axes of the input array. If axis is negative it counts from the last to the first axis. If axis is a tuple of ints, flipping is performed on all of the axes specified in the tuple. .. versionchanged:: 1.15.0 None and tuples of axes are supported Returns ------- out : array_like A view of `m` with the entries of axis reversed. Since a view is returned, this operation is done in constant time. See Also -------- flipud : Flip an array vertically (axis=0). fliplr : Flip an array horizontally (axis=1). Notes ----- flip(m, 0) is equivalent to flipud(m). flip(m, 1) is equivalent to fliplr(m). flip(m, n) corresponds to ``m[...,::-1,...]`` with ``::-1`` at position n. flip(m) corresponds to ``m[::-1,::-1,...,::-1]`` with ``::-1`` at all positions. flip(m, (0, 1)) corresponds to ``m[::-1,::-1,...]`` with ``::-1`` at position 0 and position 1. Examples -------- >>> A = [np.arange(8)](https://www.chedong.com/phpMan.php/man/np.arange/8/markdown).reshape((2,2,2)) >>> A array([[[0, 1], [2, 3]], [[4, 5], [6, 7]]]) >>> np.flip(A, 0) array([[[4, 5], [6, 7]], [[0, 1], [2, 3]]]) >>> np.flip(A, 1) array([[[2, 3], [0, 1]], [[6, 7], [4, 5]]]) >>> np.flip(A) array([[[7, 6], [5, 4]], [[3, 2], [1, 0]]]) >>> np.flip(A, (0, 2)) array([[[5, 4], [7, 6]], [[1, 0], [3, 2]]]) >>> A = np.random.randn(3,4,5) >>> np.all(np.flip(A,2) == A[:,:,::-1,...]) True ### fliplr Reverse the order of elements along axis 1 (left/right). For a 2-D array, this flips the entries in each row in the left/right direction. Columns are preserved, but appear in a different order than before. Parameters ---------- m : array_like Input array, must be at least 2-D. Returns ------- f : ndarray A view of `m` with the columns reversed. Since a view is returned, this operation is :math:`\mathcal [O(1)](https://www.chedong.com/phpMan.php/man/O/1/markdown)`. See Also -------- flipud : Flip array in the up/down direction. flip : Flip array in one or more dimesions. rot90 : Rotate array counterclockwise. Notes ----- Equivalent to ``m[:,::-1]`` or ``np.flip(m, axis=1)``. Requires the array to be at least 2-D. Examples -------- >>> A = np.diag([1.,2.,3.]) >>> A array([[1., 0., 0.], [0., 2., 0.], [0., 0., 3.]]) >>> np.fliplr(A) array([[0., 0., 1.], [0., 2., 0.], [3., 0., 0.]]) >>> A = np.random.randn(2,3,5) >>> np.all(np.fliplr(A) == A[:,::-1,...]) True ### flipud Reverse the order of elements along axis 0 (up/down). For a 2-D array, this flips the entries in each column in the up/down direction. Rows are preserved, but appear in a different order than before. Parameters ---------- m : array_like Input array. Returns ------- out : array_like A view of `m` with the rows reversed. Since a view is returned, this operation is :math:`\mathcal [O(1)](https://www.chedong.com/phpMan.php/man/O/1/markdown)`. See Also -------- fliplr : Flip array in the left/right direction. flip : Flip array in one or more dimesions. rot90 : Rotate array counterclockwise. Notes ----- Equivalent to ``m[::-1, ...]`` or ``np.flip(m, axis=0)``. Requires the array to be at least 1-D. Examples -------- >>> A = np.diag([1.0, 2, 3]) >>> A array([[1., 0., 0.], [0., 2., 0.], [0., 0., 3.]]) >>> np.flipud(A) array([[0., 0., 3.], [0., 2., 0.], [1., 0., 0.]]) >>> A = np.random.randn(2,3,5) >>> np.all(np.flipud(A) == A[::-1,...]) True >>> np.flipud([1,2]) array([2, 1]) ### format_float_positional Format a floating-point scalar as a decimal string in positional notation. Provides control over rounding, trimming and padding. Uses and assumes IEEE unbiased rounding. Uses the "Dragon4" algorithm. Parameters ---------- x : python float or numpy floating scalar Value to format. precision : non-negative integer or None, optional Maximum number of digits to print. May be None if `unique` is `True`, but must be an integer if unique is `False`. unique : boolean, optional If `True`, use a digit-generation strategy which gives the shortest representation which uniquely identifies the floating-point number from other values of the same type, by judicious rounding. If `precision` is given fewer digits than necessary can be printed, or if `min_digits` is given more can be printed, in which cases the last digit is rounded with unbiased rounding. If `False`, digits are generated as if printing an infinite-precision value and stopping after `precision` digits, rounding the remaining value with unbiased rounding fractional : boolean, optional If `True`, the cutoffs of `precision` and `min_digits` refer to the total number of digits after the decimal point, including leading zeros. If `False`, `precision` and `min_digits` refer to the total number of significant digits, before or after the decimal point, ignoring leading zeros. trim : one of 'k', '.', '0', '-', optional Controls post-processing trimming of trailing digits, as follows: * 'k' : keep trailing zeros, keep decimal point (no trimming) * '.' : trim all trailing zeros, leave decimal point * '0' : trim all but the zero before the decimal point. Insert the zero if it is missing. * '-' : trim trailing zeros and any trailing decimal point sign : boolean, optional Whether to show the sign for positive values. pad_left : non-negative integer, optional Pad the left side of the string with whitespace until at least that many characters are to the left of the decimal point. pad_right : non-negative integer, optional Pad the right side of the string with whitespace until at least that many characters are to the right of the decimal point. min_digits : non-negative integer or None, optional Minimum number of digits to print. Only has an effect if `unique=True` in which case additional digits past those necessary to uniquely identify the value may be printed, rounding the last additional digit. -- versionadded:: 1.21.0 Returns ------- rep : string The string representation of the floating point value See Also -------- format_float_scientific Examples -------- >>> np.format_float_positional(np.float32(np.pi)) '3.1415927' >>> np.format_float_positional(np.float16(np.pi)) '3.14' >>> np.format_float_positional(np.float16(0.3)) '0.3' >>> np.format_float_positional(np.float16(0.3), unique=False, precision=10) '0.3000488281' ### format_float_scientific Format a floating-point scalar as a decimal string in scientific notation. Provides control over rounding, trimming and padding. Uses and assumes IEEE unbiased rounding. Uses the "Dragon4" algorithm. Parameters ---------- x : python float or numpy floating scalar Value to format. precision : non-negative integer or None, optional Maximum number of digits to print. May be None if `unique` is `True`, but must be an integer if unique is `False`. unique : boolean, optional If `True`, use a digit-generation strategy which gives the shortest representation which uniquely identifies the floating-point number from other values of the same type, by judicious rounding. If `precision` is given fewer digits than necessary can be printed. If `min_digits` is given more can be printed, in which cases the last digit is rounded with unbiased rounding. If `False`, digits are generated as if printing an infinite-precision value and stopping after `precision` digits, rounding the remaining value with unbiased rounding trim : one of 'k', '.', '0', '-', optional Controls post-processing trimming of trailing digits, as follows: * 'k' : keep trailing zeros, keep decimal point (no trimming) * '.' : trim all trailing zeros, leave decimal point * '0' : trim all but the zero before the decimal point. Insert the zero if it is missing. * '-' : trim trailing zeros and any trailing decimal point sign : boolean, optional Whether to show the sign for positive values. pad_left : non-negative integer, optional Pad the left side of the string with whitespace until at least that many characters are to the left of the decimal point. exp_digits : non-negative integer, optional Pad the exponent with zeros until it contains at least this many digits. If omitted, the exponent will be at least 2 digits. min_digits : non-negative integer or None, optional Minimum number of digits to print. This only has an effect for `unique=True`. In that case more digits than necessary to uniquely identify the value may be printed and rounded unbiased. -- versionadded:: 1.21.0 Returns ------- rep : string The string representation of the floating point value See Also -------- format_float_positional Examples -------- >>> np.format_float_scientific(np.float32(np.pi)) '3.1415927e+00' >>> s = np.float32(1.23e24) >>> np.format_float_scientific(s, unique=False, precision=15) '1.230000071797338e+24' >>> np.format_float_scientific(s, exp_digits=4) '1.23e+0024' ### frombuffer frombuffer(buffer, dtype=float, count=-1, offset=0, *, like=None) Interpret a buffer as a 1-dimensional array. Parameters ---------- buffer : buffer_like An object that exposes the buffer interface. dtype : data-type, optional Data-type of the returned array; default: float. count : int, optional Number of items to read. ``-1`` means all data in the buffer. offset : int, optional Start reading the buffer from this offset (in bytes); default: 0. like : array_like Reference object to allow the creation of arrays which are not NumPy arrays. If an array-like passed in as ``like`` supports the ``__array_function__`` protocol, the result will be defined by it. In this case, it ensures the creation of an array object compatible with that passed in via this argument. .. versionadded:: 1.20.0 Notes ----- If the buffer has data that is not in machine byte-order, this should be specified as part of the data-type, e.g.:: >>> dt = np.dtype(int) >>> dt = dt.newbyteorder('>') >>> np.frombuffer(buf, dtype=dt) # doctest: +SKIP The data of the resulting array will not be byteswapped, but will be interpreted correctly. Examples -------- >>> s = b'hello world' >>> np.frombuffer(s, dtype='S1', count=5, offset=6) array([b'w', b'o', b'r', b'l', b'd'], dtype='|S1') >>> np.frombuffer(b'\x01\x02', dtype=np.uint8) array([1, 2], dtype=uint8) >>> np.frombuffer(b'\x01\x02\x03\x04\x05', dtype=np.uint8, count=3) array([1, 2, 3], dtype=uint8) ### fromfile fromfile(file, dtype=float, count=-1, sep='', offset=0, *, like=None) Construct an array from data in a text or binary file. A highly efficient way of reading binary data with a known data-type, as well as parsing simply formatted text files. Data written using the `tofile` method can be read using this function. Parameters ---------- file : file or str or Path Open file object or filename. .. versionchanged:: 1.17.0 `pathlib.Path` objects are now accepted. dtype : data-type Data type of the returned array. For binary files, it is used to determine the size and byte-order of the items in the file. Most builtin numeric types are supported and extension types may be supported. .. versionadded:: 1.18.0 Complex dtypes. count : int Number of items to read. ``-1`` means all items (i.e., the complete file). sep : str Separator between items if file is a text file. Empty ("") separator means the file should be treated as binary. Spaces (" ") in the separator match zero or more whitespace characters. A separator consisting only of spaces must match at least one whitespace. offset : int The offset (in bytes) from the file's current position. Defaults to 0. Only permitted for binary files. .. versionadded:: 1.17.0 like : array_like Reference object to allow the creation of arrays which are not NumPy arrays. If an array-like passed in as ``like`` supports the ``__array_function__`` protocol, the result will be defined by it. In this case, it ensures the creation of an array object compatible with that passed in via this argument. .. versionadded:: 1.20.0 See also -------- load, save ndarray.tofile loadtxt : More flexible way of loading data from a text file. Notes ----- Do not rely on the combination of `tofile` and `fromfile` for data storage, as the binary files generated are not platform independent. In particular, no byte-order or data-type information is saved. Data can be stored in the platform independent ``.npy`` format using `save` and `load` instead. Examples -------- Construct an ndarray: >>> dt = np.dtype([('time', [('min', np.int64), ('sec', np.int64)]), ... ('temp', float)]) >>> x = np.zeros((1,), dtype=dt) >>> x['time']['min'] = 10; x['temp'] = 98.25 >>> x array([((10, 0), 98.25)], dtype=[('time', [('min', '>> import tempfile >>> fname = tempfile.mkstemp()[1] >>> x.tofile(fname) Read the raw data from disk: >>> np.fromfile(fname, dtype=dt) array([((10, 0), 98.25)], dtype=[('time', [('min', '>> np.save(fname, x) >>> np.load(fname + '.npy') array([((10, 0), 98.25)], dtype=[('time', [('min', '>> np.fromfunction(lambda i, j: i == j, (3, 3), dtype=int) array([[ True, False, False], [False, True, False], [False, False, True]]) >>> np.fromfunction(lambda i, j: i + j, (3, 3), dtype=int) array([[0, 1, 2], [1, 2, 3], [2, 3, 4]]) ### fromiter fromiter(iter, dtype, count=-1, *, like=None) Create a new 1-dimensional array from an iterable object. Parameters ---------- iter : iterable object An iterable object providing data for the array. dtype : data-type The data-type of the returned array. count : int, optional The number of items to read from *iterable*. The default is -1, which means all data is read. like : array_like Reference object to allow the creation of arrays which are not NumPy arrays. If an array-like passed in as ``like`` supports the ``__array_function__`` protocol, the result will be defined by it. In this case, it ensures the creation of an array object compatible with that passed in via this argument. .. versionadded:: 1.20.0 Returns ------- out : ndarray The output array. Notes ----- Specify `count` to improve performance. It allows ``fromiter`` to pre-allocate the output array, instead of resizing it on demand. Examples -------- >>> iterable = (x*x for x in [range(5)](https://www.chedong.com/phpMan.php/man/range/5/markdown)) >>> np.fromiter(iterable, float) array([ 0., 1., 4., 9., 16.]) ### frompyfunc frompyfunc(func, nin, nout, *[, identity]) Takes an arbitrary Python function and returns a NumPy ufunc. Can be used, for example, to add broadcasting to a built-in Python function (see Examples section). Parameters ---------- func : Python function object An arbitrary Python function. nin : int The number of input arguments. nout : int The number of objects returned by `func`. identity : object, optional The value to use for the `~numpy.ufunc.identity` attribute of the resulting object. If specified, this is equivalent to setting the underlying C ``identity`` field to ``PyUFunc_IdentityValue``. If omitted, the identity is set to ``PyUFunc_None``. Note that this is _not_ equivalent to setting the identity to ``None``, which implies the operation is reorderable. Returns ------- out : ufunc Returns a NumPy universal function (``ufunc``) object. See Also -------- vectorize : Evaluates pyfunc over input arrays using broadcasting rules of numpy. Notes ----- The returned ufunc always returns PyObject arrays. Examples -------- Use frompyfunc to add broadcasting to the Python function ``oct``: >>> oct_array = np.frompyfunc(oct, 1, 1) >>> oct_array(np.array((10, 30, 100))) array(['0o12', '0o36', '0o144'], dtype=object) >>> np.array(([oct(10)](https://www.chedong.com/phpMan.php/man/oct/10/markdown), [oct(30)](https://www.chedong.com/phpMan.php/man/oct/30/markdown), [oct(100)](https://www.chedong.com/phpMan.php/man/oct/100/markdown))) # for comparison array(['0o12', '0o36', '0o144'], dtype='>> f = open('test.dat', 'w') >>> _ = f.write("1312 foo\n1534 bar\n444 qux") >>> f.close() >>> regexp = r"(\d+)\s+(...)" # match [digits, whitespace, anything] >>> output = np.fromregex('test.dat', regexp, ... [('num', np.int64), ('key', 'S3')]) >>> output array([(1312, b'foo'), (1534, b'bar'), ( 444, b'qux')], dtype=[('num', '>> output['num'] array([1312, 1534, 444]) ### fromstring fromstring(string, dtype=float, count=-1, sep='', *, like=None) A new 1-D array initialized from text data in a string. Parameters ---------- string : str A string containing the data. dtype : data-type, optional The data type of the array; default: float. For binary input data, the data must be in exactly this format. Most builtin numeric types are supported and extension types may be supported. .. versionadded:: 1.18.0 Complex dtypes. count : int, optional Read this number of `dtype` elements from the data. If this is negative (the default), the count will be determined from the length of the data. sep : str, optional The string separating numbers in the data; extra whitespace between elements is also ignored. .. deprecated:: 1.14 Passing ``sep=''``, the default, is deprecated since it will trigger the deprecated binary mode of this function. This mode interprets `string` as binary bytes, rather than ASCII text with decimal numbers, an operation which is better spelt ``frombuffer(string, dtype, count)``. If `string` contains unicode text, the binary mode of `fromstring` will first encode it into bytes using either utf-8 (python 3) or the default encoding (python 2), neither of which produce sane results. like : array_like Reference object to allow the creation of arrays which are not NumPy arrays. If an array-like passed in as ``like`` supports the ``__array_function__`` protocol, the result will be defined by it. In this case, it ensures the creation of an array object compatible with that passed in via this argument. .. versionadded:: 1.20.0 Returns ------- arr : ndarray The constructed array. Raises ------ ValueError If the string is not the correct size to satisfy the requested `dtype` and `count`. See Also -------- frombuffer, fromfile, fromiter Examples -------- >>> np.fromstring('1 2', dtype=int, sep=' ') array([1, 2]) >>> np.fromstring('1, 2', dtype=int, sep=',') array([1, 2]) ### full Return a new array of given shape and type, filled with `fill_value`. Parameters ---------- shape : int or sequence of ints Shape of the new array, e.g., ``(2, 3)`` or ``2``. fill_value : scalar or array_like Fill value. dtype : data-type, optional The desired data-type for the array The default, None, means ``np.array(fill_value).dtype``. order : {'C', 'F'}, optional Whether to store multidimensional data in C- or Fortran-contiguous (row- or column-wise) order in memory. like : array_like Reference object to allow the creation of arrays which are not NumPy arrays. If an array-like passed in as ``like`` supports the ``__array_function__`` protocol, the result will be defined by it. In this case, it ensures the creation of an array object compatible with that passed in via this argument. .. versionadded:: 1.20.0 Returns ------- out : ndarray Array of `fill_value` with the given shape, dtype, and order. See Also -------- full_like : Return a new array with shape of input filled with value. empty : Return a new uninitialized array. ones : Return a new array setting values to one. zeros : Return a new array setting values to zero. Examples -------- >>> np.full((2, 2), np.inf) array([[inf, inf], [inf, inf]]) >>> np.full((2, 2), 10) array([[10, 10], [10, 10]]) >>> np.full((2, 2), [1, 2]) array([[1, 2], [1, 2]]) ### full_like Return a full array with the same shape and type as a given array. Parameters ---------- a : array_like The shape and data-type of `a` define these same attributes of the returned array. fill_value : scalar Fill value. dtype : data-type, optional Overrides the data type of the result. order : {'C', 'F', 'A', or 'K'}, optional Overrides the memory layout of the result. 'C' means C-order, 'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous, 'C' otherwise. 'K' means match the layout of `a` as closely as possible. subok : bool, optional. If True, then the newly created array will use the sub-class type of `a`, otherwise it will be a base-class array. Defaults to True. shape : int or sequence of ints, optional. Overrides the shape of the result. If order='K' and the number of dimensions is unchanged, will try to keep order, otherwise, order='C' is implied. .. versionadded:: 1.17.0 Returns ------- out : ndarray Array of `fill_value` with the same shape and type as `a`. See Also -------- empty_like : Return an empty array with shape and type of input. ones_like : Return an array of ones with shape and type of input. zeros_like : Return an array of zeros with shape and type of input. full : Return a new array of given shape filled with value. Examples -------- >>> x = np.arange(6, dtype=int) >>> np.full_like(x, 1) array([1, 1, 1, 1, 1, 1]) >>> np.full_like(x, 0.1) array([0, 0, 0, 0, 0, 0]) >>> np.full_like(x, 0.1, dtype=np.double) array([0.1, 0.1, 0.1, 0.1, 0.1, 0.1]) >>> np.full_like(x, np.nan, dtype=np.double) array([nan, nan, nan, nan, nan, nan]) >>> y = np.arange(6, dtype=np.double) >>> np.full_like(y, 0.1) array([0.1, 0.1, 0.1, 0.1, 0.1, 0.1]) ### genfromtxt Load data from a text file, with missing values handled as specified. Each line past the first `skip_header` lines is split at the `delimiter` character, and characters following the `comments` character are discarded. Parameters ---------- fname : file, str, pathlib.Path, list of str, generator File, filename, list, or generator to read. If the filename extension is `.gz` or `.bz2`, the file is first decompressed. Note that generators must return byte strings. The strings in a list or produced by a generator are treated as lines. dtype : dtype, optional Data type of the resulting array. If None, the dtypes will be determined by the contents of each column, individually. comments : str, optional The character used to indicate the start of a comment. All the characters occurring on a line after a comment are discarded. delimiter : str, int, or sequence, optional The string used to separate values. By default, any consecutive whitespaces act as delimiter. An integer or sequence of integers can also be provided as width(s) of each field. skiprows : int, optional `skiprows` was removed in numpy 1.10. Please use `skip_header` instead. skip_header : int, optional The number of lines to skip at the beginning of the file. skip_footer : int, optional The number of lines to skip at the end of the file. converters : variable, optional The set of functions that convert the data of a column to a value. The converters can also be used to provide a default value for missing data: ``converters = {3: lambda s: float(s or 0)}``. missing : variable, optional `missing` was removed in numpy 1.10. Please use `missing_values` instead. missing_values : variable, optional The set of strings corresponding to missing data. filling_values : variable, optional The set of values to be used as default when the data are missing. usecols : sequence, optional Which columns to read, with 0 being the first. For example, ``usecols = (1, 4, 5)`` will extract the 2nd, 5th and 6th columns. names : {None, True, str, sequence}, optional If `names` is True, the field names are read from the first line after the first `skip_header` lines. This line can optionally be preceeded by a comment delimiter. If `names` is a sequence or a single-string of comma-separated names, the names will be used to define the field names in a structured dtype. If `names` is None, the names of the dtype fields will be used, if any. excludelist : sequence, optional A list of names to exclude. This list is appended to the default list ['return','file','print']. Excluded names are appended with an underscore: for example, `file` would become `file_`. deletechars : str, optional A string combining invalid characters that must be deleted from the names. defaultfmt : str, optional A format used to define default field names, such as "f%i" or "f_%02i". autostrip : bool, optional Whether to automatically strip white spaces from the variables. replace_space : char, optional Character(s) used in replacement of white spaces in the variable names. By default, use a '_'. case_sensitive : {True, False, 'upper', 'lower'}, optional If True, field names are case sensitive. If False or 'upper', field names are converted to upper case. If 'lower', field names are converted to lower case. unpack : bool, optional If True, the returned array is transposed, so that arguments may be unpacked using ``x, y, z = genfromtxt(...)``. When used with a structured data-type, arrays are returned for each field. Default is False. usemask : bool, optional If True, return a masked array. If False, return a regular array. loose : bool, optional If True, do not raise errors for invalid values. invalid_raise : bool, optional If True, an exception is raised if an inconsistency is detected in the number of columns. If False, a warning is emitted and the offending lines are skipped. max_rows : int, optional The maximum number of rows to read. Must not be used with skip_footer at the same time. If given, the value must be at least 1. Default is to read the entire file. .. versionadded:: 1.10.0 encoding : str, optional Encoding used to decode the inputfile. Does not apply when `fname` is a file object. The special value 'bytes' enables backward compatibility workarounds that ensure that you receive byte arrays when possible and passes latin1 encoded strings to converters. Override this value to receive unicode arrays and pass strings as input to converters. If set to None the system default is used. The default value is 'bytes'. .. versionadded:: 1.14.0 like : array_like Reference object to allow the creation of arrays which are not NumPy arrays. If an array-like passed in as ``like`` supports the ``__array_function__`` protocol, the result will be defined by it. In this case, it ensures the creation of an array object compatible with that passed in via this argument. .. versionadded:: 1.20.0 Returns ------- out : ndarray Data read from the text file. If `usemask` is True, this is a masked array. See Also -------- numpy.loadtxt : equivalent function when no data is missing. Notes ----- * When spaces are used as delimiters, or when no delimiter has been given as input, there should not be any missing data between two fields. * When the variables are named (either by a flexible dtype or with `names`), there must not be any header in the file (else a ValueError exception is raised). * Individual values are not stripped of spaces by default. When using a custom converter, make sure the function does remove spaces. References ---------- .. [1] NumPy User Guide, section `I/O with NumPy <>`_. Examples -------- >>> from io import StringIO >>> import numpy as np Comma delimited file with mixed dtype >>> s = StringIO(u"1,1.3,abcde") >>> data = np.genfromtxt(s, dtype=[('myint','i8'),('myfloat','f8'), ... ('mystring','S5')], delimiter=",") >>> data array((1, 1.3, b'abcde'), dtype=[('myint', '>> _ = [s.seek(0)](https://www.chedong.com/phpMan.php/man/s.seek/0/markdown) # needed for StringIO example only >>> data = np.genfromtxt(s, dtype=None, ... names = ['myint','myfloat','mystring'], delimiter=",") >>> data array((1, 1.3, b'abcde'), dtype=[('myint', '>> _ = [s.seek(0)](https://www.chedong.com/phpMan.php/man/s.seek/0/markdown) >>> data = np.genfromtxt(s, dtype="i8,f8,S5", ... names=['myint','myfloat','mystring'], delimiter=",") >>> data array((1, 1.3, b'abcde'), dtype=[('myint', '>> s = StringIO(u"11.3abcde") >>> data = np.genfromtxt(s, dtype=None, names=['intvar','fltvar','strvar'], ... delimiter=[1,3,5]) >>> data array((1, 1.3, b'abcde'), dtype=[('intvar', '>> f = StringIO(''' ... text,# of chars ... hello world,11 ... numpy,5''') >>> np.genfromtxt(f, dtype='S12,S12', delimiter=',') array([(b'text', b''), (b'hello world', b'11'), (b'numpy', b'5')], dtype=[('f0', 'S12'), ('f1', 'S12')]) ### geomspace Return numbers spaced evenly on a log scale (a geometric progression). This is similar to `logspace`, but with endpoints specified directly. Each output sample is a constant multiple of the previous. .. versionchanged:: 1.16.0 Non-scalar `start` and `stop` are now supported. Parameters ---------- start : array_like The starting value of the sequence. stop : array_like The final value of the sequence, unless `endpoint` is False. In that case, ``num + 1`` values are spaced over the interval in log-space, of which all but the last (a sequence of length `num`) are returned. num : integer, optional Number of samples to generate. Default is 50. endpoint : boolean, optional If true, `stop` is the last sample. Otherwise, it is not included. Default is True. dtype : dtype The type of the output array. If `dtype` is not given, the data type is inferred from `start` and `stop`. The inferred dtype will never be an integer; `float` is chosen even if the arguments would produce an array of integers. axis : int, optional The axis in the result to store the samples. Relevant only if start or stop are array-like. By default (0), the samples will be along a new axis inserted at the beginning. Use -1 to get an axis at the end. .. versionadded:: 1.16.0 Returns ------- samples : ndarray `num` samples, equally spaced on a log scale. See Also -------- logspace : Similar to geomspace, but with endpoints specified using log and base. linspace : Similar to geomspace, but with arithmetic instead of geometric progression. arange : Similar to linspace, with the step size specified instead of the number of samples. Notes ----- If the inputs or dtype are complex, the output will follow a logarithmic spiral in the complex plane. (There are an infinite number of spirals passing through two points; the output will follow the shortest such path.) Examples -------- >>> np.geomspace(1, 1000, num=4) array([ 1., 10., 100., 1000.]) >>> np.geomspace(1, 1000, num=3, endpoint=False) array([ 1., 10., 100.]) >>> np.geomspace(1, 1000, num=4, endpoint=False) array([ 1. , 5.62341325, 31.6227766 , 177.827941 ]) >>> np.geomspace(1, 256, num=9) array([ 1., 2., 4., 8., 16., 32., 64., 128., 256.]) Note that the above may not produce exact integers: >>> np.geomspace(1, 256, num=9, dtype=int) array([ 1, 2, 4, 7, 16, 32, 63, 127, 256]) >>> np.around(np.geomspace(1, 256, num=9)).astype(int) array([ 1, 2, 4, 8, 16, 32, 64, 128, 256]) Negative, decreasing, and complex inputs are allowed: >>> np.geomspace(1000, 1, num=4) array([1000., 100., 10., 1.]) >>> np.geomspace(-1000, -1, num=4) array([-1000., -100., -10., -1.]) >>> np.geomspace(1j, 1000j, num=4) # Straight line array([0. +1.j, 0. +10.j, 0. +100.j, 0.+1000.j]) >>> np.geomspace(-1+0j, 1+0j, num=5) # Circle array([-1.00000000e+00+1.22464680e-16j, -7.07106781e-01+7.07106781e-01j, 6.12323400e-17+1.00000000e+00j, 7.07106781e-01+7.07106781e-01j, 1.00000000e+00+0.00000000e+00j]) Graphical illustration of `endpoint` parameter: >>> import matplotlib.pyplot as plt >>> N = 10 >>> y = np.zeros(N) >>> plt.semilogx(np.geomspace(1, 1000, N, endpoint=True), y + 1, 'o') [] >>> plt.semilogx(np.geomspace(1, 1000, N, endpoint=False), y + 2, 'o') [] >>> plt.axis([0.5, 2000, 0, 3]) [0.5, 2000, 0, 3] >>> plt.grid(True, color='0.7', linestyle='-', which='both', axis='both') >>> plt.show() ### get_array_wrap Find the wrapper for the array with the highest priority. In case of ties, leftmost wins. If no wrapper is found, return None ### get_include Return the directory that contains the NumPy \*.h header files. Extension modules that need to compile against NumPy should use this function to locate the appropriate include directory. Notes ----- When using ``distutils``, for example in ``setup.py``. :: import numpy as np ... Extension('extension_name', ... include_dirs=[np.get_include()]) ... ### get_printoptions Return the current print options. Returns ------- print_opts : dict Dictionary of current print options with keys - precision : int - threshold : int - edgeitems : int - linewidth : int - suppress : bool - nanstr : str - infstr : str - formatter : dict of callables - sign : str For a full description of these options, see `set_printoptions`. See Also -------- set_printoptions, printoptions, set_string_function ### getbufsize Return the size of the buffer used in ufuncs. Returns ------- getbufsize : int Size of ufunc buffer in bytes. ### geterr Get the current way of handling floating-point errors. Returns ------- res : dict A dictionary with keys "divide", "over", "under", and "invalid", whose values are from the strings "ignore", "print", "log", "warn", "raise", and "call". The keys represent possible floating-point exceptions, and the values define how these exceptions are handled. See Also -------- geterrcall, seterr, seterrcall Notes ----- For complete documentation of the types of floating-point exceptions and treatment options, see `seterr`. Examples -------- >>> np.geterr() {'divide': 'warn', 'over': 'warn', 'under': 'ignore', 'invalid': 'warn'} >>> np.arange(3.) / np.arange(3.) array([nan, 1., 1.]) >>> oldsettings = np.seterr(all='warn', over='raise') >>> np.geterr() {'divide': 'warn', 'over': 'raise', 'under': 'warn', 'invalid': 'warn'} >>> np.arange(3.) / np.arange(3.) array([nan, 1., 1.]) ### geterrcall Return the current callback function used on floating-point errors. When the error handling for a floating-point error (one of "divide", "over", "under", or "invalid") is set to 'call' or 'log', the function that is called or the log instance that is written to is returned by `geterrcall`. This function or log instance has been set with `seterrcall`. Returns ------- errobj : callable, log instance or None The current error handler. If no handler was set through `seterrcall`, ``None`` is returned. See Also -------- seterrcall, seterr, geterr Notes ----- For complete documentation of the types of floating-point exceptions and treatment options, see `seterr`. Examples -------- >>> np.geterrcall() # we did not yet set a handler, returns None >>> oldsettings = np.seterr(all='call') >>> def err_handler(type, flag): ... print("Floating point error (%s), with flag %s" % (type, flag)) >>> oldhandler = np.seterrcall(err_handler) >>> np.array([1, 2, 3]) / 0.0 Floating point error (divide by zero), with flag 1 array([inf, inf, inf]) >>> cur_handler = np.geterrcall() >>> cur_handler is err_handler True ### geterrobj geterrobj() Return the current object that defines floating-point error handling. The error object contains all information that defines the error handling behavior in NumPy. `geterrobj` is used internally by the other functions that get and set error handling behavior (`geterr`, `seterr`, `geterrcall`, `seterrcall`). Returns ------- errobj : list The error object, a list containing three elements: [internal numpy buffer size, error mask, error callback function]. The error mask is a single integer that holds the treatment information on all four floating point errors. The information for each error type is contained in three bits of the integer. If we print it in base 8, we can see what treatment is set for "invalid", "under", "over", and "divide" (in that order). The printed string can be interpreted with * 0 : 'ignore' * 1 : 'warn' * 2 : 'raise' * 3 : 'call' * 4 : 'print' * 5 : 'log' See Also -------- seterrobj, seterr, geterr, seterrcall, geterrcall getbufsize, setbufsize Notes ----- For complete documentation of the types of floating-point exceptions and treatment options, see `seterr`. Examples -------- >>> np.geterrobj() # first get the defaults [8192, 521, None] >>> def err_handler(type, flag): ... print("Floating point error (%s), with flag %s" % (type, flag)) ... >>> old_bufsize = [np.setbufsize(20000)](https://www.chedong.com/phpMan.php/man/np.setbufsize/20000/markdown) >>> old_err = np.seterr(divide='raise') >>> old_handler = np.seterrcall(err_handler) >>> np.geterrobj() [8192, 521, ] >>> old_err = np.seterr(all='ignore') >>> np.base_repr(np.geterrobj()[1], 8) '0' >>> old_err = np.seterr(divide='warn', over='log', under='call', ... invalid='print') >>> np.base_repr(np.geterrobj()[1], 8) '4351' ### gradient Return the gradient of an N-dimensional array. The gradient is computed using second order accurate central differences in the interior points and either first or second order accurate one-sides (forward or backwards) differences at the boundaries. The returned gradient hence has the same shape as the input array. Parameters ---------- f : array_like An N-dimensional array containing samples of a scalar function. varargs : list of scalar or array, optional Spacing between f values. Default unitary spacing for all dimensions. Spacing can be specified using: 1. single scalar to specify a sample distance for all dimensions. 2. N scalars to specify a constant sample distance for each dimension. i.e. `dx`, `dy`, `dz`, ... 3. N arrays to specify the coordinates of the values along each dimension of F. The length of the array must match the size of the corresponding dimension 4. Any combination of N scalars/arrays with the meaning of 2. and 3. If `axis` is given, the number of varargs must equal the number of axes. Default: 1. edge_order : {1, 2}, optional Gradient is calculated using N-th order accurate differences at the boundaries. Default: 1. .. versionadded:: 1.9.1 axis : None or int or tuple of ints, optional Gradient is calculated only along the given axis or axes The default (axis = None) is to calculate the gradient for all the axes of the input array. axis may be negative, in which case it counts from the last to the first axis. .. versionadded:: 1.11.0 Returns ------- gradient : ndarray or list of ndarray A list of ndarrays (or a single ndarray if there is only one dimension) corresponding to the derivatives of f with respect to each dimension. Each derivative has the same shape as f. Examples -------- >>> f = np.array([1, 2, 4, 7, 11, 16], dtype=float) >>> np.gradient(f) array([1. , 1.5, 2.5, 3.5, 4.5, 5. ]) >>> np.gradient(f, 2) array([0.5 , 0.75, 1.25, 1.75, 2.25, 2.5 ]) Spacing can be also specified with an array that represents the coordinates of the values F along the dimensions. For instance a uniform spacing: >>> x = np.arange(f.size) >>> np.gradient(f, x) array([1. , 1.5, 2.5, 3.5, 4.5, 5. ]) Or a non uniform one: >>> x = np.array([0., 1., 1.5, 3.5, 4., 6.], dtype=float) >>> np.gradient(f, x) array([1. , 3. , 3.5, 6.7, 6.9, 2.5]) For two dimensional arrays, the return will be two arrays ordered by axis. In this example the first array stands for the gradient in rows and the second one in columns direction: >>> np.gradient(np.array([[1, 2, 6], [3, 4, 5]], dtype=float)) [array([[ 2., 2., -1.], [ 2., 2., -1.]]), array([[1. , 2.5, 4. ], [1. , 1. , 1. ]])] In this example the spacing is also specified: uniform for axis=0 and non uniform for axis=1 >>> dx = 2. >>> y = [1., 1.5, 3.5] >>> np.gradient(np.array([[1, 2, 6], [3, 4, 5]], dtype=float), dx, y) [array([[ 1. , 1. , -0.5], [ 1. , 1. , -0.5]]), array([[2. , 2. , 2. ], [2. , 1.7, 0.5]])] It is possible to specify how boundaries are treated using `edge_order` >>> x = np.array([0, 1, 2, 3, 4]) >>> f = x**2 >>> np.gradient(f, edge_order=1) array([1., 2., 4., 6., 7.]) >>> np.gradient(f, edge_order=2) array([0., 2., 4., 6., 8.]) The `axis` keyword can be used to specify a subset of axes of which the gradient is calculated >>> np.gradient(np.array([[1, 2, 6], [3, 4, 5]], dtype=float), axis=0) array([[ 2., 2., -1.], [ 2., 2., -1.]]) Notes ----- Assuming that :math:`f\in C^{3}` (i.e., :math:`f` has at least 3 continuous derivatives) and let :math:`h_{*}` be a non-homogeneous stepsize, we minimize the "consistency error" :math:`\eta_{i}` between the true gradient and its estimate from a linear combination of the neighboring grid-points: .. math:: \eta_{i} = f_{i}^{\left(1\right)} - \left[ \alpha f\left(x_{i}\right) + \beta f\left(x_{i} + h_{d}\right) + \gamma f\left(x_{i}-h_{s}\right) \right] By substituting :math:`f(x_{i} + h_{d})` and :math:`f(x_{i} - h_{s})` with their Taylor series expansion, this translates into solving the following the linear system: .. math:: \left\{ \begin{array}{r} \alpha+\beta+\gamma=0 \\ \beta h_{d}-\gamma h_{s}=1 \\ \beta h_{d}^{2}+\gamma h_{s}^{2}=0 \end{array} \right. The resulting approximation of :math:`f_{i}^{(1)}` is the following: .. math:: \hat f_{i}^{(1)} = \frac{ h_{s}^{2}f\left(x_{i} + h_{d}\right) + \left(h_{d}^{2} - h_{s}^{2}\right)f\left(x_{i}\right) - h_{d}^{2}f\left(x_{i}-h_{s}\right)} { h_{s}h_{d}\left(h_{d} + h_{s}\right)} + \mathcal{O}\left(\frac{h_{d}h_{s}^{2} + h_{s}h_{d}^{2}}{h_{d} + h_{s}}\right) It is worth noting that if :math:`h_{s}=h_{d}` (i.e., data are evenly spaced) we find the standard second order approximation: .. math:: \hat f_{i}^{(1)}= \frac{f\left(x_{i+1}\right) - f\left(x_{i-1}\right)}{2h} + \mathcal{O}\left(h^{2}\right) With a similar procedure the forward/backward approximations used for boundaries can be derived. References ---------- .. [1] Quarteroni A., Sacco R., Saleri F. (2007) Numerical Mathematics (Texts in Applied Mathematics). New York: Springer. .. [2] Durran D. R. (1999) Numerical Methods for Wave Equations in Geophysical Fluid Dynamics. New York: Springer. .. [3] Fornberg B. (1988) Generation of Finite Difference Formulas on Arbitrarily Spaced Grids, Mathematics of Computation 51, no. 184 : 699-706. `PDF < S0025-5718-1988-0935077-0/S0025-5718-1988-0935077-0.pdf>`_. ### hamming Return the Hamming window. The Hamming window is a taper formed by using a weighted cosine. Parameters ---------- M : int Number of points in the output window. If zero or less, an empty array is returned. Returns ------- out : ndarray The window, with the maximum value normalized to one (the value one appears only if the number of samples is odd). See Also -------- bartlett, blackman, hanning, kaiser Notes ----- The Hamming window is defined as .. math:: [w(n)](https://www.chedong.com/phpMan.php/man/w/n/markdown) = 0.54 - 0.46cos\left(\frac{2\pi{n}}{M-1}\right) \qquad 0 \leq n \leq M-1 The Hamming was named for R. W. Hamming, an associate of J. W. Tukey and is described in Blackman and Tukey. It was recommended for smoothing the truncated autocovariance function in the time domain. Most references to the Hamming window come from the signal processing literature, where it is used as one of many windowing functions for smoothing values. It is also known as an apodization (which means "removing the foot", i.e. smoothing discontinuities at the beginning and end of the sampled signal) or tapering function. References ---------- .. [1] Blackman, R.B. and Tukey, J.W., (1958) The measurement of power spectra, Dover Publications, New York. .. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics", The University of Alberta Press, 1975, pp. 109-110. .. [3] Wikipedia, "Window function", .. [4] W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling, "Numerical Recipes", Cambridge University Press, 1986, page 425. Examples -------- >>> [np.hamming(12)](https://www.chedong.com/phpMan.php/man/np.hamming/12/markdown) array([ 0.08 , 0.15302337, 0.34890909, 0.60546483, 0.84123594, # may vary 0.98136677, 0.98136677, 0.84123594, 0.60546483, 0.34890909, 0.15302337, 0.08 ]) Plot the window and the frequency response: >>> import matplotlib.pyplot as plt >>> from numpy.fft import fft, fftshift >>> window = [np.hamming(51)](https://www.chedong.com/phpMan.php/man/np.hamming/51/markdown) >>> plt.plot(window) [] >>> plt.title("Hamming window") Text(0.5, 1.0, 'Hamming window') >>> plt.ylabel("Amplitude") Text(0, 0.5, 'Amplitude') >>> plt.xlabel("Sample") Text(0.5, 0, 'Sample') >>> plt.show() >>> plt.figure()
>>> A = fft(window, 2048) / 25.5 >>> mag = np.abs(fftshift(A)) >>> freq = np.linspace(-0.5, 0.5, len(A)) >>> response = 20 * np.log10(mag) >>> response = np.clip(response, -100, 100) >>> plt.plot(freq, response) [] >>> plt.title("Frequency response of Hamming window") Text(0.5, 1.0, 'Frequency response of Hamming window') >>> plt.ylabel("Magnitude [dB]") Text(0, 0.5, 'Magnitude [dB]') >>> plt.xlabel("Normalized frequency [cycles per sample]") Text(0.5, 0, 'Normalized frequency [cycles per sample]') >>> plt.axis('tight') ... >>> plt.show() ### hanning Return the Hanning window. The Hanning window is a taper formed by using a weighted cosine. Parameters ---------- M : int Number of points in the output window. If zero or less, an empty array is returned. Returns ------- out : ndarray, shape(M,) The window, with the maximum value normalized to one (the value one appears only if `M` is odd). See Also -------- bartlett, blackman, hamming, kaiser Notes ----- The Hanning window is defined as .. math:: [w(n)](https://www.chedong.com/phpMan.php/man/w/n/markdown) = 0.5 - 0.5cos\left(\frac{2\pi{n}}{M-1}\right) \qquad 0 \leq n \leq M-1 The Hanning was named for Julius von Hann, an Austrian meteorologist. It is also known as the Cosine Bell. Some authors prefer that it be called a Hann window, to help avoid confusion with the very similar Hamming window. Most references to the Hanning window come from the signal processing literature, where it is used as one of many windowing functions for smoothing values. It is also known as an apodization (which means "removing the foot", i.e. smoothing discontinuities at the beginning and end of the sampled signal) or tapering function. References ---------- .. [1] Blackman, R.B. and Tukey, J.W., (1958) The measurement of power spectra, Dover Publications, New York. .. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics", The University of Alberta Press, 1975, pp. 106-108. .. [3] Wikipedia, "Window function", .. [4] W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling, "Numerical Recipes", Cambridge University Press, 1986, page 425. Examples -------- >>> [np.hanning(12)](https://www.chedong.com/phpMan.php/man/np.hanning/12/markdown) array([0. , 0.07937323, 0.29229249, 0.57115742, 0.82743037, 0.97974649, 0.97974649, 0.82743037, 0.57115742, 0.29229249, 0.07937323, 0. ]) Plot the window and its frequency response: >>> import matplotlib.pyplot as plt >>> from numpy.fft import fft, fftshift >>> window = [np.hanning(51)](https://www.chedong.com/phpMan.php/man/np.hanning/51/markdown) >>> plt.plot(window) [] >>> plt.title("Hann window") Text(0.5, 1.0, 'Hann window') >>> plt.ylabel("Amplitude") Text(0, 0.5, 'Amplitude') >>> plt.xlabel("Sample") Text(0.5, 0, 'Sample') >>> plt.show() >>> plt.figure()
>>> A = fft(window, 2048) / 25.5 >>> mag = np.abs(fftshift(A)) >>> freq = np.linspace(-0.5, 0.5, len(A)) >>> with np.errstate(divide='ignore', invalid='ignore'): ... response = 20 * np.log10(mag) ... >>> response = np.clip(response, -100, 100) >>> plt.plot(freq, response) [] >>> plt.title("Frequency response of the Hann window") Text(0.5, 1.0, 'Frequency response of the Hann window') >>> plt.ylabel("Magnitude [dB]") Text(0, 0.5, 'Magnitude [dB]') >>> plt.xlabel("Normalized frequency [cycles per sample]") Text(0.5, 0, 'Normalized frequency [cycles per sample]') >>> plt.axis('tight') ... >>> plt.show() ### histogram Compute the histogram of a dataset. Parameters ---------- a : array_like Input data. The histogram is computed over the flattened array. bins : int or sequence of scalars or str, optional If `bins` is an int, it defines the number of equal-width bins in the given range (10, by default). If `bins` is a sequence, it defines a monotonically increasing array of bin edges, including the rightmost edge, allowing for non-uniform bin widths. .. versionadded:: 1.11.0 If `bins` is a string, it defines the method used to calculate the optimal bin width, as defined by `histogram_bin_edges`. range : (float, float), optional The lower and upper range of the bins. If not provided, range is simply ``(a.min(), a.max())``. Values outside the range are ignored. The first element of the range must be less than or equal to the second. `range` affects the automatic bin computation as well. While bin width is computed to be optimal based on the actual data within `range`, the bin count will fill the entire range including portions containing no data. normed : bool, optional .. deprecated:: 1.6.0 This is equivalent to the `density` argument, but produces incorrect results for unequal bin widths. It should not be used. .. versionchanged:: 1.15.0 DeprecationWarnings are actually emitted. weights : array_like, optional An array of weights, of the same shape as `a`. Each value in `a` only contributes its associated weight towards the bin count (instead of 1). If `density` is True, the weights are normalized, so that the integral of the density over the range remains 1. density : bool, optional If ``False``, the result will contain the number of samples in each bin. If ``True``, the result is the value of the probability *density* function at the bin, normalized such that the *integral* over the range is 1. Note that the sum of the histogram values will not be equal to 1 unless bins of unity width are chosen; it is not a probability *mass* function. Overrides the ``normed`` keyword if given. Returns ------- hist : array The values of the histogram. See `density` and `weights` for a description of the possible semantics. bin_edges : array of dtype float Return the bin edges ``(length(hist)+1)``. See Also -------- histogramdd, bincount, searchsorted, digitize, histogram_bin_edges Notes ----- All but the last (righthand-most) bin is half-open. In other words, if `bins` is:: [1, 2, 3, 4] then the first bin is ``[1, 2)`` (including 1, but excluding 2) and the second ``[2, 3)``. The last bin, however, is ``[3, 4]``, which *includes* 4. Examples -------- >>> np.histogram([1, 2, 1], bins=[0, 1, 2, 3]) (array([0, 2, 1]), array([0, 1, 2, 3])) >>> np.histogram([np.arange(4)](https://www.chedong.com/phpMan.php/man/np.arange/4/markdown), bins=[np.arange(5)](https://www.chedong.com/phpMan.php/man/np.arange/5/markdown), density=True) (array([0.25, 0.25, 0.25, 0.25]), array([0, 1, 2, 3, 4])) >>> np.histogram([[1, 2, 1], [1, 0, 1]], bins=[0,1,2,3]) (array([1, 4, 1]), array([0, 1, 2, 3])) >>> a = [np.arange(5)](https://www.chedong.com/phpMan.php/man/np.arange/5/markdown) >>> hist, bin_edges = np.histogram(a, density=True) >>> hist array([0.5, 0. , 0.5, 0. , 0. , 0.5, 0. , 0.5, 0. , 0.5]) >>> hist.sum() 2.4999999999999996 >>> np.sum(hist * np.diff(bin_edges)) 1.0 .. versionadded:: 1.11.0 Automated Bin Selection Methods example, using 2 peak random data with 2000 points: >>> import matplotlib.pyplot as plt >>> rng = [np.random.RandomState(10)](https://www.chedong.com/phpMan.php/man/np.random.RandomState/10/markdown) # deterministic random data >>> a = np.hstack((rng.normal(size=1000), ... rng.normal(loc=5, scale=2, size=1000))) >>> _ = plt.hist(a, bins='auto') # arguments are passed to np.histogram >>> plt.title("Histogram with 'auto' bins") Text(0.5, 1.0, "Histogram with 'auto' bins") >>> plt.show() ### histogram2d Compute the bi-dimensional histogram of two data samples. Parameters ---------- x : array_like, shape (N,) An array containing the x coordinates of the points to be histogrammed. y : array_like, shape (N,) An array containing the y coordinates of the points to be histogrammed. bins : int or array_like or [int, int] or [array, array], optional The bin specification: * If int, the number of bins for the two dimensions (nx=ny=bins). * If array_like, the bin edges for the two dimensions (x_edges=y_edges=bins). * If [int, int], the number of bins in each dimension (nx, ny = bins). * If [array, array], the bin edges in each dimension (x_edges, y_edges = bins). * A combination [int, array] or [array, int], where int is the number of bins and array is the bin edges. range : array_like, shape(2,2), optional The leftmost and rightmost edges of the bins along each dimension (if not specified explicitly in the `bins` parameters): ``[[xmin, xmax], [ymin, ymax]]``. All values outside of this range will be considered outliers and not tallied in the histogram. density : bool, optional If False, the default, returns the number of samples in each bin. If True, returns the probability *density* function at the bin, ``bin_count / sample_count / bin_area``. normed : bool, optional An alias for the density argument that behaves identically. To avoid confusion with the broken normed argument to `histogram`, `density` should be preferred. weights : array_like, shape(N,), optional An array of values ``w_i`` weighing each sample ``(x_i, y_i)``. Weights are normalized to 1 if `normed` is True. If `normed` is False, the values of the returned histogram are equal to the sum of the weights belonging to the samples falling into each bin. Returns ------- H : ndarray, shape(nx, ny) The bi-dimensional histogram of samples `x` and `y`. Values in `x` are histogrammed along the first dimension and values in `y` are histogrammed along the second dimension. xedges : ndarray, shape(nx+1,) The bin edges along the first dimension. yedges : ndarray, shape(ny+1,) The bin edges along the second dimension. See Also -------- histogram : 1D histogram histogramdd : Multidimensional histogram Notes ----- When `normed` is True, then the returned histogram is the sample density, defined such that the sum over bins of the product ``bin_value * bin_area`` is 1. Please note that the histogram does not follow the Cartesian convention where `x` values are on the abscissa and `y` values on the ordinate axis. Rather, `x` is histogrammed along the first dimension of the array (vertical), and `y` along the second dimension of the array (horizontal). This ensures compatibility with `histogramdd`. Examples -------- >>> from matplotlib.image import NonUniformImage >>> import matplotlib.pyplot as plt Construct a 2-D histogram with variable bin width. First define the bin edges: >>> xedges = [0, 1, 3, 5] >>> yedges = [0, 2, 3, 4, 6] Next we create a histogram H with random bin content: >>> x = np.random.normal(2, 1, 100) >>> y = np.random.normal(1, 1, 100) >>> H, xedges, yedges = np.histogram2d(x, y, bins=(xedges, yedges)) >>> # Histogram does not follow Cartesian convention (see Notes), >>> # therefore transpose H for visualization purposes. >>> H = H.T :func:`imshow ` can only display square bins: >>> fig = plt.figure(figsize=(7, 3)) >>> ax = fig.add_subplot(131, title='imshow: square bins') >>> plt.imshow(H, interpolation='nearest', origin='lower', ... extent=[xedges[0], xedges[-1], yedges[0], yedges[-1]]) :func:`pcolormesh ` can display actual edges: >>> ax = fig.add_subplot(132, title='pcolormesh: actual edges', ... aspect='equal') >>> X, Y = np.meshgrid(xedges, yedges) >>> ax.pcolormesh(X, Y, H) :class:`NonUniformImage ` can be used to display actual bin edges with interpolation: >>> ax = fig.add_subplot(133, title='NonUniformImage: interpolated', ... aspect='equal', xlim=xedges[[0, -1]], ylim=yedges[[0, -1]]) >>> im = NonUniformImage(ax, interpolation='bilinear') >>> xcenters = (xedges[:-1] + xedges[1:]) / 2 >>> ycenters = (yedges[:-1] + yedges[1:]) / 2 >>> im.set_data(xcenters, ycenters, H) >>> ax.images.append(im) >>> plt.show() ### histogram_bin_edges Function to calculate only the edges of the bins used by the `histogram` function. Parameters ---------- a : array_like Input data. The histogram is computed over the flattened array. bins : int or sequence of scalars or str, optional If `bins` is an int, it defines the number of equal-width bins in the given range (10, by default). If `bins` is a sequence, it defines the bin edges, including the rightmost edge, allowing for non-uniform bin widths. If `bins` is a string from the list below, `histogram_bin_edges` will use the method chosen to calculate the optimal bin width and consequently the number of bins (see `Notes` for more detail on the estimators) from the data that falls within the requested range. While the bin width will be optimal for the actual data in the range, the number of bins will be computed to fill the entire range, including the empty portions. For visualisation, using the 'auto' option is suggested. Weighted data is not supported for automated bin size selection. 'auto' Maximum of the 'sturges' and 'fd' estimators. Provides good all around performance. 'fd' (Freedman Diaconis Estimator) Robust (resilient to outliers) estimator that takes into account data variability and data size. 'doane' An improved version of Sturges' estimator that works better with non-normal datasets. 'scott' Less robust estimator that that takes into account data variability and data size. 'stone' Estimator based on leave-one-out cross-validation estimate of the integrated squared error. Can be regarded as a generalization of Scott's rule. 'rice' Estimator does not take variability into account, only data size. Commonly overestimates number of bins required. 'sturges' R's default method, only accounts for data size. Only optimal for gaussian data and underestimates number of bins for large non-gaussian datasets. 'sqrt' Square root (of data size) estimator, used by Excel and other programs for its speed and simplicity. range : (float, float), optional The lower and upper range of the bins. If not provided, range is simply ``(a.min(), a.max())``. Values outside the range are ignored. The first element of the range must be less than or equal to the second. `range` affects the automatic bin computation as well. While bin width is computed to be optimal based on the actual data within `range`, the bin count will fill the entire range including portions containing no data. weights : array_like, optional An array of weights, of the same shape as `a`. Each value in `a` only contributes its associated weight towards the bin count (instead of 1). This is currently not used by any of the bin estimators, but may be in the future. Returns ------- bin_edges : array of dtype float The edges to pass into `histogram` See Also -------- histogram Notes ----- The methods to estimate the optimal number of bins are well founded in literature, and are inspired by the choices R provides for histogram visualisation. Note that having the number of bins proportional to :math:`n^{1/3}` is asymptotically optimal, which is why it appears in most estimators. These are simply plug-in methods that give good starting points for number of bins. In the equations below, :math:`h` is the binwidth and :math:`n_h` is the number of bins. All estimators that compute bin counts are recast to bin width using the `ptp` of the data. The final bin count is obtained from ``np.round(np.ceil(range / h))``. The final bin width is often less than what is returned by the estimators below. 'auto' (maximum of the 'sturges' and 'fd' estimators) A compromise to get a good value. For small datasets the Sturges value will usually be chosen, while larger datasets will usually default to FD. Avoids the overly conservative behaviour of FD and Sturges for small and large datasets respectively. Switchover point is usually :math:`a.size \approx 1000`. 'fd' (Freedman Diaconis Estimator) .. math:: h = 2 \frac{IQR}{n^{1/3}} The binwidth is proportional to the interquartile range (IQR) and inversely proportional to cube root of a.size. Can be too conservative for small datasets, but is quite good for large datasets. The IQR is very robust to outliers. 'scott' .. math:: h = \sigma \sqrt[3]{\frac{24 * \sqrt{\pi}}{n}} The binwidth is proportional to the standard deviation of the data and inversely proportional to cube root of ``x.size``. Can be too conservative for small datasets, but is quite good for large datasets. The standard deviation is not very robust to outliers. Values are very similar to the Freedman-Diaconis estimator in the absence of outliers. 'rice' .. math:: n_h = 2n^{1/3} The number of bins is only proportional to cube root of ``a.size``. It tends to overestimate the number of bins and it does not take into account data variability. 'sturges' .. math:: n_h = \log _{2}n+1 The number of bins is the base 2 log of ``a.size``. This estimator assumes normality of data and is too conservative for larger, non-normal datasets. This is the default method in R's ``hist`` method. 'doane' .. math:: n_h = 1 + \log_{2}(n) + \log_{2}(1 + \frac{|g_1|}{\sigma_{g_1}}) g_1 = mean[(\frac{x - \mu}{\sigma})^3] \sigma_{g_1} = \sqrt{\frac{6(n - 2)}{(n + 1)(n + 3)}} An improved version of Sturges' formula that produces better estimates for non-normal datasets. This estimator attempts to account for the skew of the data. 'sqrt' .. math:: n_h = \sqrt n The simplest and fastest estimator. Only takes into account the data size. Examples -------- >>> arr = np.array([0, 0, 0, 1, 2, 3, 3, 4, 5]) >>> np.histogram_bin_edges(arr, bins='auto', range=(0, 1)) array([0. , 0.25, 0.5 , 0.75, 1. ]) >>> np.histogram_bin_edges(arr, bins=2) array([0. , 2.5, 5. ]) For consistency with histogram, an array of pre-computed bins is passed through unmodified: >>> np.histogram_bin_edges(arr, [1, 2]) array([1, 2]) This function allows one set of bins to be computed, and reused across multiple histograms: >>> shared_bins = np.histogram_bin_edges(arr, bins='auto') >>> shared_bins array([0., 1., 2., 3., 4., 5.]) >>> group_id = np.array([0, 1, 1, 0, 1, 1, 0, 1, 1]) >>> hist_0, _ = np.histogram(arr[group_id == 0], bins=shared_bins) >>> hist_1, _ = np.histogram(arr[group_id == 1], bins=shared_bins) >>> hist_0; hist_1 array([1, 1, 0, 1, 0]) array([2, 0, 1, 1, 2]) Which gives more easily comparable results than using separate bins for each histogram: >>> hist_0, bins_0 = np.histogram(arr[group_id == 0], bins='auto') >>> hist_1, bins_1 = np.histogram(arr[group_id == 1], bins='auto') >>> hist_0; hist_1 array([1, 1, 1]) array([2, 1, 1, 2]) >>> bins_0; bins_1 array([0., 1., 2., 3.]) array([0. , 1.25, 2.5 , 3.75, 5. ]) ### histogramdd Compute the multidimensional histogram of some data. Parameters ---------- sample : (N, D) array, or (D, N) array_like The data to be histogrammed. Note the unusual interpretation of sample when an array_like: * When an array, each row is a coordinate in a D-dimensional space - such as ``histogramdd(np.array([p1, p2, p3]))``. * When an array_like, each element is the list of values for single coordinate - such as ``histogramdd((X, Y, Z))``. The first form should be preferred. bins : sequence or int, optional The bin specification: * A sequence of arrays describing the monotonically increasing bin edges along each dimension. * The number of bins for each dimension (nx, ny, ... =bins) * The number of bins for all dimensions (nx=ny=...=bins). range : sequence, optional A sequence of length D, each an optional (lower, upper) tuple giving the outer bin edges to be used if the edges are not given explicitly in `bins`. An entry of None in the sequence results in the minimum and maximum values being used for the corresponding dimension. The default, None, is equivalent to passing a tuple of D None values. density : bool, optional If False, the default, returns the number of samples in each bin. If True, returns the probability *density* function at the bin, ``bin_count / sample_count / bin_volume``. normed : bool, optional An alias for the density argument that behaves identically. To avoid confusion with the broken normed argument to `histogram`, `density` should be preferred. weights : (N,) array_like, optional An array of values `w_i` weighing each sample `(x_i, y_i, z_i, ...)`. Weights are normalized to 1 if normed is True. If normed is False, the values of the returned histogram are equal to the sum of the weights belonging to the samples falling into each bin. Returns ------- H : ndarray The multidimensional histogram of sample x. See normed and weights for the different possible semantics. edges : list A list of D arrays describing the bin edges for each dimension. See Also -------- histogram: 1-D histogram histogram2d: 2-D histogram Examples -------- >>> r = np.random.randn(100,3) >>> H, edges = np.histogramdd(r, bins = (5, 8, 4)) >>> H.shape, edges[0].size, edges[1].size, edges[2].size ((5, 8, 4), 6, 9, 5) ### hsplit Split an array into multiple sub-arrays horizontally (column-wise). Please refer to the `split` documentation. `hsplit` is equivalent to `split` with ``axis=1``, the array is always split along the second axis regardless of the array dimension. See Also -------- split : Split an array into multiple sub-arrays of equal size. Examples -------- >>> x = np.arange(16.0).reshape(4, 4) >>> x array([[ 0., 1., 2., 3.], [ 4., 5., 6., 7.], [ 8., 9., 10., 11.], [12., 13., 14., 15.]]) >>> np.hsplit(x, 2) [array([[ 0., 1.], [ 4., 5.], [ 8., 9.], [12., 13.]]), array([[ 2., 3.], [ 6., 7.], [10., 11.], [14., 15.]])] >>> np.hsplit(x, np.array([3, 6])) [array([[ 0., 1., 2.], [ 4., 5., 6.], [ 8., 9., 10.], [12., 13., 14.]]), array([[ 3.], [ 7.], [11.], [15.]]), array([], shape=(4, 0), dtype=float64)] With a higher dimensional array the split is still along the second axis. >>> x = np.arange(8.0).reshape(2, 2, 2) >>> x array([[[0., 1.], [2., 3.]], [[4., 5.], [6., 7.]]]) >>> np.hsplit(x, 2) [array([[[0., 1.]], [[4., 5.]]]), array([[[2., 3.]], [[6., 7.]]])] ### hstack Stack arrays in sequence horizontally (column wise). This is equivalent to concatenation along the second axis, except for 1-D arrays where it concatenates along the first axis. Rebuilds arrays divided by `hsplit`. This function makes most sense for arrays with up to 3 dimensions. For instance, for pixel-data with a height (first axis), width (second axis), and r/g/b channels (third axis). The functions `concatenate`, `stack` and `block` provide more general stacking and concatenation operations. Parameters ---------- tup : sequence of ndarrays The arrays must have the same shape along all but the second axis, except 1-D arrays which can be any length. Returns ------- stacked : ndarray The array formed by stacking the given arrays. See Also -------- concatenate : Join a sequence of arrays along an existing axis. stack : Join a sequence of arrays along a new axis. block : Assemble an nd-array from nested lists of blocks. vstack : Stack arrays in sequence vertically (row wise). dstack : Stack arrays in sequence depth wise (along third axis). column_stack : Stack 1-D arrays as columns into a 2-D array. hsplit : Split an array into multiple sub-arrays horizontally (column-wise). Examples -------- >>> a = np.array((1,2,3)) >>> b = np.array((4,5,6)) >>> np.hstack((a,b)) array([1, 2, 3, 4, 5, 6]) >>> a = np.array([[1],[2],[3]]) >>> b = np.array([[4],[5],[6]]) >>> np.hstack((a,b)) array([[1, 4], [2, 5], [3, 6]]) ### i0 Modified Bessel function of the first kind, order 0. Usually denoted :math:`I_0`. Parameters ---------- x : array_like of float Argument of the Bessel function. Returns ------- out : ndarray, shape = x.shape, dtype = float The modified Bessel function evaluated at each of the elements of `x`. See Also -------- scipy.special.i0, scipy.special.iv, scipy.special.ive Notes ----- The scipy implementation is recommended over this function: it is a proper ufunc written in C, and more than an order of magnitude faster. We use the algorithm published by Clenshaw [1]_ and referenced by Abramowitz and Stegun [2]_, for which the function domain is partitioned into the two intervals [0,8] and (8,inf), and Chebyshev polynomial expansions are employed in each interval. Relative error on the domain [0,30] using IEEE arithmetic is documented [3]_ as having a peak of 5.8e-16 with an rms of 1.4e-16 (n = 30000). References ---------- .. [1] C. W. Clenshaw, "Chebyshev series for mathematical functions", in *National Physical Laboratory Mathematical Tables*, vol. 5, London: Her Majesty's Stationery Office, 1962. .. [2] M. Abramowitz and I. A. Stegun, *Handbook of Mathematical Functions*, 10th printing, New York: Dover, 1964, pp. 379. .. [3] Examples -------- >>> np.i0(0.) array(1.0) >>> np.i0([0, 1, 2, 3]) array([1. , 1.26606588, 2.2795853 , 4.88079259]) ### identity Return the identity array. The identity array is a square array with ones on the main diagonal. Parameters ---------- n : int Number of rows (and columns) in `n` x `n` output. dtype : data-type, optional Data-type of the output. Defaults to ``float``. like : array_like Reference object to allow the creation of arrays which are not NumPy arrays. If an array-like passed in as ``like`` supports the ``__array_function__`` protocol, the result will be defined by it. In this case, it ensures the creation of an array object compatible with that passed in via this argument. .. versionadded:: 1.20.0 Returns ------- out : ndarray `n` x `n` array with its main diagonal set to one, and all other elements 0. Examples -------- >>> [np.identity(3)](https://www.chedong.com/phpMan.php/man/np.identity/3/markdown) array([[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]]) ### imag Return the imaginary part of the complex argument. Parameters ---------- val : array_like Input array. Returns ------- out : ndarray or scalar The imaginary component of the complex argument. If `val` is real, the type of `val` is used for the output. If `val` has complex elements, the returned type is float. See Also -------- real, angle, real_if_close Examples -------- >>> a = np.array([1+2j, 3+4j, 5+6j]) >>> a.imag array([2., 4., 6.]) >>> a.imag = np.array([8, 10, 12]) >>> a array([1. +8.j, 3.+10.j, 5.+12.j]) >>> np.imag(1 + 1j) 1.0 ### in1d Test whether each element of a 1-D array is also present in a second array. Returns a boolean array the same length as `ar1` that is True where an element of `ar1` is in `ar2` and False otherwise. We recommend using :func:`isin` instead of `in1d` for new code. Parameters ---------- ar1 : (M,) array_like Input array. ar2 : array_like The values against which to test each value of `ar1`. assume_unique : bool, optional If True, the input arrays are both assumed to be unique, which can speed up the calculation. Default is False. invert : bool, optional If True, the values in the returned array are inverted (that is, False where an element of `ar1` is in `ar2` and True otherwise). Default is False. ``np.in1d(a, b, invert=True)`` is equivalent to (but is faster than) ``np.invert(in1d(a, b))``. .. versionadded:: 1.8.0 Returns ------- in1d : (M,) ndarray, bool The values `ar1[in1d]` are in `ar2`. See Also -------- isin : Version of this function that preserves the shape of ar1. numpy.lib.arraysetops : Module with a number of other functions for performing set operations on arrays. Notes ----- `in1d` can be considered as an element-wise function version of the python keyword `in`, for 1-D sequences. ``in1d(a, b)`` is roughly equivalent to ``np.array([item in b for item in a])``. However, this idea fails if `ar2` is a set, or similar (non-sequence) container: As ``ar2`` is converted to an array, in those cases ``asarray(ar2)`` is an object array rather than the expected array of contained values. .. versionadded:: 1.4.0 Examples -------- >>> test = np.array([0, 1, 2, 5, 0]) >>> states = [0, 2] >>> mask = np.in1d(test, states) >>> mask array([ True, False, True, False, True]) >>> test[mask] array([0, 2, 0]) >>> mask = np.in1d(test, states, invert=True) >>> mask array([False, True, False, True, False]) >>> test[mask] array([1, 5]) ### indices Return an array representing the indices of a grid. Compute an array where the subarrays contain index values 0, 1, ... varying only along the corresponding axis. Parameters ---------- dimensions : sequence of ints The shape of the grid. dtype : dtype, optional Data type of the result. sparse : boolean, optional Return a sparse representation of the grid instead of a dense representation. Default is False. .. versionadded:: 1.17 Returns ------- grid : one ndarray or tuple of ndarrays If sparse is False: Returns one array of grid indices, ``grid.shape = (len(dimensions),) + tuple(dimensions)``. If sparse is True: Returns a tuple of arrays, with ``grid[i].shape = (1, ..., 1, dimensions[i], 1, ..., 1)`` with dimensions[i] in the ith place See Also -------- mgrid, ogrid, meshgrid Notes ----- The output shape in the dense case is obtained by prepending the number of dimensions in front of the tuple of dimensions, i.e. if `dimensions` is a tuple ``(r0, ..., rN-1)`` of length ``N``, the output shape is ``(N, r0, ..., rN-1)``. The subarrays ``grid[k]`` contains the N-D array of indices along the ``k-th`` axis. Explicitly:: grid[k, i0, i1, ..., iN-1] = ik Examples -------- >>> grid = np.indices((2, 3)) >>> grid.shape (2, 2, 3) >>> grid[0] # row indices array([[0, 0, 0], [1, 1, 1]]) >>> grid[1] # column indices array([[0, 1, 2], [0, 1, 2]]) The indices can be used as an index into an array. >>> x = [np.arange(20)](https://www.chedong.com/phpMan.php/man/np.arange/20/markdown).reshape(5, 4) >>> row, col = np.indices((2, 3)) >>> x[row, col] array([[0, 1, 2], [4, 5, 6]]) Note that it would be more straightforward in the above example to extract the required elements directly with ``x[:2, :3]``. If sparse is set to true, the grid will be returned in a sparse representation. >>> i, j = np.indices((2, 3), sparse=True) >>> i.shape (2, 1) >>> j.shape (1, 3) >>> i # row indices array([[0], [1]]) >>> j # column indices array([[0, 1, 2]]) ### info Get help information for a function, class, or module. Parameters ---------- object : object or str, optional Input object or name to get information about. If `object` is a numpy object, its docstring is given. If it is a string, available modules are searched for matching objects. If None, information about `info` itself is returned. maxwidth : int, optional Printing width. output : file like object, optional File like object that the output is written to, default is ``stdout``. The object has to be opened in 'w' or 'a' mode. toplevel : str, optional Start search at this level. See Also -------- source, lookfor Notes ----- When used interactively with an object, ``np.info(obj)`` is equivalent to ``help(obj)`` on the Python prompt or ``obj?`` on the IPython prompt. Examples -------- >>> np.info(np.polyval) # doctest: +SKIP polyval(p, x) Evaluate the polynomial p at x. ... When using a string for `object` it is possible to get multiple results. >>> np.info('fft') # doctest: +SKIP *** Found in numpy *** Core FFT routines ... *** Found in numpy.fft *** fft(a, n=None, axis=-1) ... *** Repeat reference found in numpy.fft.fftpack *** *** Total of 3 references found. *** ### inner inner(a, b) Inner product of two arrays. Ordinary inner product of vectors for 1-D arrays (without complex conjugation), in higher dimensions a sum product over the last axes. Parameters ---------- a, b : array_like If `a` and `b` are nonscalar, their last dimensions must match. Returns ------- out : ndarray If `a` and `b` are both scalars or both 1-D arrays then a scalar is returned; otherwise an array is returned. ``out.shape = (*a.shape[:-1], *b.shape[:-1])`` Raises ------ ValueError If both `a` and `b` are nonscalar and their last dimensions have different sizes. See Also -------- tensordot : Sum products over arbitrary axes. dot : Generalised matrix product, using second last dimension of `b`. einsum : Einstein summation convention. Notes ----- For vectors (1-D arrays) it computes the ordinary inner-product:: np.inner(a, b) = sum(a[:]*b[:]) More generally, if `ndim(a) = r > 0` and `ndim(b) = s > 0`:: np.inner(a, b) = np.tensordot(a, b, axes=(-1,-1)) or explicitly:: np.inner(a, b)[i0,...,ir-2,j0,...,js-2] = sum(a[i0,...,ir-2,:]*b[j0,...,js-2,:]) In addition `a` or `b` may be scalars, in which case:: np.inner(a,b) = a*b Examples -------- Ordinary inner product for vectors: >>> a = np.array([1,2,3]) >>> b = np.array([0,1,0]) >>> np.inner(a, b) 2 Some multidimensional examples: >>> a = [np.arange(24)](https://www.chedong.com/phpMan.php/man/np.arange/24/markdown).reshape((2,3,4)) >>> b = [np.arange(4)](https://www.chedong.com/phpMan.php/man/np.arange/4/markdown) >>> c = np.inner(a, b) >>> c.shape (2, 3) >>> c array([[ 14, 38, 62], [ 86, 110, 134]]) >>> a = [np.arange(2)](https://www.chedong.com/phpMan.php/man/np.arange/2/markdown).reshape((1,1,2)) >>> b = [np.arange(6)](https://www.chedong.com/phpMan.php/man/np.arange/6/markdown).reshape((3,2)) >>> c = np.inner(a, b) >>> c.shape (1, 1, 3) >>> c array([[[1, 3, 5]]]) An example where `b` is a scalar: >>> np.inner([np.eye(2)](https://www.chedong.com/phpMan.php/man/np.eye/2/markdown), 7) array([[7., 0.], [0., 7.]]) ### insert Insert values along the given axis before the given indices. Parameters ---------- arr : array_like Input array. obj : int, slice or sequence of ints Object that defines the index or indices before which `values` is inserted. .. versionadded:: 1.8.0 Support for multiple insertions when `obj` is a single scalar or a sequence with one element (similar to calling insert multiple times). values : array_like Values to insert into `arr`. If the type of `values` is different from that of `arr`, `values` is converted to the type of `arr`. `values` should be shaped so that ``arr[...,obj,...] = values`` is legal. axis : int, optional Axis along which to insert `values`. If `axis` is None then `arr` is flattened first. Returns ------- out : ndarray A copy of `arr` with `values` inserted. Note that `insert` does not occur in-place: a new array is returned. If `axis` is None, `out` is a flattened array. See Also -------- append : Append elements at the end of an array. concatenate : Join a sequence of arrays along an existing axis. delete : Delete elements from an array. Notes ----- Note that for higher dimensional inserts `obj=0` behaves very different from `obj=[0]` just like `arr[:,0,:] = values` is different from `arr[:,[0],:] = values`. Examples -------- >>> a = np.array([[1, 1], [2, 2], [3, 3]]) >>> a array([[1, 1], [2, 2], [3, 3]]) >>> np.insert(a, 1, 5) array([1, 5, 1, ..., 2, 3, 3]) >>> np.insert(a, 1, 5, axis=1) array([[1, 5, 1], [2, 5, 2], [3, 5, 3]]) Difference between sequence and scalars: >>> np.insert(a, [1], [[1],[2],[3]], axis=1) array([[1, 1, 1], [2, 2, 2], [3, 3, 3]]) >>> np.array_equal(np.insert(a, 1, [1, 2, 3], axis=1), ... np.insert(a, [1], [[1],[2],[3]], axis=1)) True >>> b = a.flatten() >>> b array([1, 1, 2, 2, 3, 3]) >>> np.insert(b, [2, 2], [5, 6]) array([1, 1, 5, ..., 2, 3, 3]) >>> np.insert(b, slice(2, 4), [5, 6]) array([1, 1, 5, ..., 2, 3, 3]) >>> np.insert(b, [2, 2], [7.13, False]) # type casting array([1, 1, 7, ..., 2, 3, 3]) >>> x = [np.arange(8)](https://www.chedong.com/phpMan.php/man/np.arange/8/markdown).reshape(2, 4) >>> idx = (1, 3) >>> np.insert(x, idx, 999, axis=1) array([[ 0, 999, 1, 2, 999, 3], [ 4, 999, 5, 6, 999, 7]]) ### interp One-dimensional linear interpolation for monotonically increasing sample points. Returns the one-dimensional piecewise linear interpolant to a function with given discrete data points (`xp`, `fp`), evaluated at `x`. Parameters ---------- x : array_like The x-coordinates at which to evaluate the interpolated values. xp : 1-D sequence of floats The x-coordinates of the data points, must be increasing if argument `period` is not specified. Otherwise, `xp` is internally sorted after normalizing the periodic boundaries with ``xp = xp % period``. fp : 1-D sequence of float or complex The y-coordinates of the data points, same length as `xp`. left : optional float or complex corresponding to fp Value to return for `x < xp[0]`, default is `fp[0]`. right : optional float or complex corresponding to fp Value to return for `x > xp[-1]`, default is `fp[-1]`. period : None or float, optional A period for the x-coordinates. This parameter allows the proper interpolation of angular x-coordinates. Parameters `left` and `right` are ignored if `period` is specified. .. versionadded:: 1.10.0 Returns ------- y : float or complex (corresponding to fp) or ndarray The interpolated values, same shape as `x`. Raises ------ ValueError If `xp` and `fp` have different length If `xp` or `fp` are not 1-D sequences If `period == 0` See Also -------- scipy.interpolate Warnings -------- The x-coordinate sequence is expected to be increasing, but this is not explicitly enforced. However, if the sequence `xp` is non-increasing, interpolation results are meaningless. Note that, since NaN is unsortable, `xp` also cannot contain NaNs. A simple check for `xp` being strictly increasing is:: np.all(np.diff(xp) > 0) Examples -------- >>> xp = [1, 2, 3] >>> fp = [3, 2, 0] >>> np.interp(2.5, xp, fp) 1.0 >>> np.interp([0, 1, 1.5, 2.72, 3.14], xp, fp) array([3. , 3. , 2.5 , 0.56, 0. ]) >>> UNDEF = -99.0 >>> np.interp(3.14, xp, fp, right=UNDEF) -99.0 Plot an interpolant to the sine function: >>> x = np.linspace(0, 2*np.pi, 10) >>> y = np.sin(x) >>> xvals = np.linspace(0, 2*np.pi, 50) >>> yinterp = np.interp(xvals, x, y) >>> import matplotlib.pyplot as plt >>> plt.plot(x, y, 'o') [] >>> plt.plot(xvals, yinterp, '-x') [] >>> plt.show() Interpolation with periodic x-coordinates: >>> x = [-180, -170, -185, 185, -10, -5, 0, 365] >>> xp = [190, -190, 350, -350] >>> fp = [5, 10, 3, 4] >>> np.interp(x, xp, fp, period=360) array([7.5 , 5. , 8.75, 6.25, 3. , 3.25, 3.5 , 3.75]) Complex interpolation: >>> x = [1.5, 4.0] >>> xp = [2,3,5] >>> fp = [1.0j, 0, 2+3j] >>> np.interp(x, xp, fp) array([0.+1.j , 1.+1.5j]) ### intersect1d Find the intersection of two arrays. Return the sorted, unique values that are in both of the input arrays. Parameters ---------- ar1, ar2 : array_like Input arrays. Will be flattened if not already 1D. assume_unique : bool If True, the input arrays are both assumed to be unique, which can speed up the calculation. If True but ``ar1`` or ``ar2`` are not unique, incorrect results and out-of-bounds indices could result. Default is False. return_indices : bool If True, the indices which correspond to the intersection of the two arrays are returned. The first instance of a value is used if there are multiple. Default is False. .. versionadded:: 1.15.0 Returns ------- intersect1d : ndarray Sorted 1D array of common and unique elements. comm1 : ndarray The indices of the first occurrences of the common values in `ar1`. Only provided if `return_indices` is True. comm2 : ndarray The indices of the first occurrences of the common values in `ar2`. Only provided if `return_indices` is True. See Also -------- numpy.lib.arraysetops : Module with a number of other functions for performing set operations on arrays. Examples -------- >>> np.intersect1d([1, 3, 4, 3], [3, 1, 2, 1]) array([1, 3]) To intersect more than two arrays, use functools.reduce: >>> from functools import reduce >>> reduce(np.intersect1d, ([1, 3, 4, 3], [3, 1, 2, 1], [6, 3, 4, 2])) array([3]) To return the indices of the values common to the input arrays along with the intersected values: >>> x = np.array([1, 1, 2, 3, 4]) >>> y = np.array([2, 1, 4, 6]) >>> xy, x_ind, y_ind = np.intersect1d(x, y, return_indices=True) >>> x_ind, y_ind (array([0, 2, 4]), array([1, 0, 2])) >>> xy, x[x_ind], y[y_ind] (array([1, 2, 4]), array([1, 2, 4]), array([1, 2, 4])) ### is_busday is_busday(dates, weekmask='1111100', holidays=None, busdaycal=None, out=None) Calculates which of the given dates are valid days, and which are not. .. versionadded:: 1.7.0 Parameters ---------- dates : array_like of datetime64[D] The array of dates to process. weekmask : str or array_like of bool, optional A seven-element array indicating which of Monday through Sunday are valid days. May be specified as a length-seven list or array, like [1,1,1,1,1,0,0]; a length-seven string, like '1111100'; or a string like "Mon Tue Wed Thu Fri", made up of 3-character abbreviations for weekdays, optionally separated by white space. Valid abbreviations are: Mon Tue Wed Thu Fri Sat Sun holidays : array_like of datetime64[D], optional An array of dates to consider as invalid dates. They may be specified in any order, and NaT (not-a-time) dates are ignored. This list is saved in a normalized form that is suited for fast calculations of valid days. busdaycal : busdaycalendar, optional A `busdaycalendar` object which specifies the valid days. If this parameter is provided, neither weekmask nor holidays may be provided. out : array of bool, optional If provided, this array is filled with the result. Returns ------- out : array of bool An array with the same shape as ``dates``, containing True for each valid day, and False for each invalid day. See Also -------- busdaycalendar : An object that specifies a custom set of valid days. busday_offset : Applies an offset counted in valid days. busday_count : Counts how many valid days are in a half-open date range. Examples -------- >>> # The weekdays are Friday, Saturday, and Monday ... np.is_busday(['2011-07-01', '2011-07-02', '2011-07-18'], ... holidays=['2011-07-01', '2011-07-04', '2011-07-17']) array([False, False, True]) ### isclose Returns a boolean array where two arrays are element-wise equal within a tolerance. The tolerance values are positive, typically very small numbers. The relative difference (`rtol` * abs(`b`)) and the absolute difference `atol` are added together to compare against the absolute difference between `a` and `b`. .. warning:: The default `atol` is not appropriate for comparing numbers that are much smaller than one (see Notes). Parameters ---------- a, b : array_like Input arrays to compare. rtol : float The relative tolerance parameter (see Notes). atol : float The absolute tolerance parameter (see Notes). equal_nan : bool Whether to compare NaN's as equal. If True, NaN's in `a` will be considered equal to NaN's in `b` in the output array. Returns ------- y : array_like Returns a boolean array of where `a` and `b` are equal within the given tolerance. If both `a` and `b` are scalars, returns a single boolean value. See Also -------- allclose math.isclose Notes ----- .. versionadded:: 1.7.0 For finite values, isclose uses the following equation to test whether two floating point values are equivalent. absolute(`a` - `b`) <= (`atol` + `rtol` * absolute(`b`)) Unlike the built-in `math.isclose`, the above equation is not symmetric in `a` and `b` -- it assumes `b` is the reference value -- so that `isclose(a, b)` might be different from `isclose(b, a)`. Furthermore, the default value of atol is not zero, and is used to determine what small values should be considered close to zero. The default value is appropriate for expected values of order unity: if the expected values are significantly smaller than one, it can result in false positives. `atol` should be carefully selected for the use case at hand. A zero value for `atol` will result in `False` if either `a` or `b` is zero. `isclose` is not defined for non-numeric data types. Examples -------- >>> np.isclose([1e10,1e-7], [1.00001e10,1e-8]) array([ True, False]) >>> np.isclose([1e10,1e-8], [1.00001e10,1e-9]) array([ True, True]) >>> np.isclose([1e10,1e-8], [1.0001e10,1e-9]) array([False, True]) >>> np.isclose([1.0, np.nan], [1.0, np.nan]) array([ True, False]) >>> np.isclose([1.0, np.nan], [1.0, np.nan], equal_nan=True) array([ True, True]) >>> np.isclose([1e-8, 1e-7], [0.0, 0.0]) array([ True, False]) >>> np.isclose([1e-100, 1e-7], [0.0, 0.0], atol=0.0) array([False, False]) >>> np.isclose([1e-10, 1e-10], [1e-20, 0.0]) array([ True, True]) >>> np.isclose([1e-10, 1e-10], [1e-20, 0.999999e-10], atol=0.0) array([False, True]) ### iscomplex Returns a bool array, where True if input element is complex. What is tested is whether the input has a non-zero imaginary part, not if the input type is complex. Parameters ---------- x : array_like Input array. Returns ------- out : ndarray of bools Output array. See Also -------- isreal iscomplexobj : Return True if x is a complex type or an array of complex numbers. Examples -------- >>> np.iscomplex([1+1j, 1+0j, 4.5, 3, 2, 2j]) array([ True, False, False, False, False, True]) ### iscomplexobj Check for a complex type or an array of complex numbers. The type of the input is checked, not the value. Even if the input has an imaginary part equal to zero, `iscomplexobj` evaluates to True. Parameters ---------- x : any The input can be of any type and shape. Returns ------- iscomplexobj : bool The return value, True if `x` is of a complex type or has at least one complex element. See Also -------- isrealobj, iscomplex Examples -------- >>> [np.iscomplexobj(1)](https://www.chedong.com/phpMan.php/man/np.iscomplexobj/1/markdown) False >>> np.iscomplexobj(1+0j) True >>> np.iscomplexobj([3, 1+0j, True]) True ### isfortran Check if the array is Fortran contiguous but *not* C contiguous. This function is obsolete and, because of changes due to relaxed stride checking, its return value for the same array may differ for versions of NumPy >= 1.10.0 and previous versions. If you only want to check if an array is Fortran contiguous use ``a.flags.f_contiguous`` instead. Parameters ---------- a : ndarray Input array. Returns ------- isfortran : bool Returns True if the array is Fortran contiguous but *not* C contiguous. Examples -------- np.array allows to specify whether the array is written in C-contiguous order (last index varies the fastest), or FORTRAN-contiguous order in memory (first index varies the fastest). >>> a = np.array([[1, 2, 3], [4, 5, 6]], order='C') >>> a array([[1, 2, 3], [4, 5, 6]]) >>> np.isfortran(a) False >>> b = np.array([[1, 2, 3], [4, 5, 6]], order='F') >>> b array([[1, 2, 3], [4, 5, 6]]) >>> np.isfortran(b) True The transpose of a C-ordered array is a FORTRAN-ordered array. >>> a = np.array([[1, 2, 3], [4, 5, 6]], order='C') >>> a array([[1, 2, 3], [4, 5, 6]]) >>> np.isfortran(a) False >>> b = a.T >>> b array([[1, 4], [2, 5], [3, 6]]) >>> np.isfortran(b) True C-ordered arrays evaluate as False even if they are also FORTRAN-ordered. >>> np.isfortran(np.array([1, 2], order='F')) False ### isin Calculates `element in test_elements`, broadcasting over `element` only. Returns a boolean array of the same shape as `element` that is True where an element of `element` is in `test_elements` and False otherwise. Parameters ---------- element : array_like Input array. test_elements : array_like The values against which to test each value of `element`. This argument is flattened if it is an array or array_like. See notes for behavior with non-array-like parameters. assume_unique : bool, optional If True, the input arrays are both assumed to be unique, which can speed up the calculation. Default is False. invert : bool, optional If True, the values in the returned array are inverted, as if calculating `element not in test_elements`. Default is False. ``np.isin(a, b, invert=True)`` is equivalent to (but faster than) ``np.invert(np.isin(a, b))``. Returns ------- isin : ndarray, bool Has the same shape as `element`. The values `element[isin]` are in `test_elements`. See Also -------- in1d : Flattened version of this function. numpy.lib.arraysetops : Module with a number of other functions for performing set operations on arrays. Notes ----- `isin` is an element-wise function version of the python keyword `in`. ``isin(a, b)`` is roughly equivalent to ``np.array([item in b for item in a])`` if `a` and `b` are 1-D sequences. `element` and `test_elements` are converted to arrays if they are not already. If `test_elements` is a set (or other non-sequence collection) it will be converted to an object array with one element, rather than an array of the values contained in `test_elements`. This is a consequence of the `array` constructor's way of handling non-sequence collections. Converting the set to a list usually gives the desired behavior. .. versionadded:: 1.13.0 Examples -------- >>> element = 2*[np.arange(4)](https://www.chedong.com/phpMan.php/man/np.arange/4/markdown).reshape((2, 2)) >>> element array([[0, 2], [4, 6]]) >>> test_elements = [1, 2, 4, 8] >>> mask = np.isin(element, test_elements) >>> mask array([[False, True], [ True, False]]) >>> element[mask] array([2, 4]) The indices of the matched values can be obtained with `nonzero`: >>> np.nonzero(mask) (array([0, 1]), array([1, 0])) The test can also be inverted: >>> mask = np.isin(element, test_elements, invert=True) >>> mask array([[ True, False], [False, True]]) >>> element[mask] array([0, 6]) Because of how `array` handles sets, the following does not work as expected: >>> test_set = {1, 2, 4, 8} >>> np.isin(element, test_set) array([[False, False], [False, False]]) Casting the set to a list gives the expected result: >>> np.isin(element, list(test_set)) array([[False, True], [ True, False]]) ### isneginf Test element-wise for negative infinity, return result as bool array. Parameters ---------- x : array_like The input array. out : array_like, optional A location into which the result is stored. If provided, it must have a shape that the input broadcasts to. If not provided or None, a freshly-allocated boolean array is returned. Returns ------- out : ndarray A boolean array with the same dimensions as the input. If second argument is not supplied then a numpy boolean array is returned with values True where the corresponding element of the input is negative infinity and values False where the element of the input is not negative infinity. If a second argument is supplied the result is stored there. If the type of that array is a numeric type the result is represented as zeros and ones, if the type is boolean then as False and True. The return value `out` is then a reference to that array. See Also -------- isinf, isposinf, isnan, isfinite Notes ----- NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754). Errors result if the second argument is also supplied when x is a scalar input, if first and second arguments have different shapes, or if the first argument has complex values. Examples -------- >>> np.isneginf(np.NINF) True >>> np.isneginf(np.inf) False >>> np.isneginf(np.PINF) False >>> np.isneginf([-np.inf, 0., np.inf]) array([ True, False, False]) >>> x = np.array([-np.inf, 0., np.inf]) >>> y = np.array([2, 2, 2]) >>> np.isneginf(x, y) array([1, 0, 0]) >>> y array([1, 0, 0]) ### isposinf Test element-wise for positive infinity, return result as bool array. Parameters ---------- x : array_like The input array. out : array_like, optional A location into which the result is stored. If provided, it must have a shape that the input broadcasts to. If not provided or None, a freshly-allocated boolean array is returned. Returns ------- out : ndarray A boolean array with the same dimensions as the input. If second argument is not supplied then a boolean array is returned with values True where the corresponding element of the input is positive infinity and values False where the element of the input is not positive infinity. If a second argument is supplied the result is stored there. If the type of that array is a numeric type the result is represented as zeros and ones, if the type is boolean then as False and True. The return value `out` is then a reference to that array. See Also -------- isinf, isneginf, isfinite, isnan Notes ----- NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754). Errors result if the second argument is also supplied when x is a scalar input, if first and second arguments have different shapes, or if the first argument has complex values Examples -------- >>> np.isposinf(np.PINF) True >>> np.isposinf(np.inf) True >>> np.isposinf(np.NINF) False >>> np.isposinf([-np.inf, 0., np.inf]) array([False, False, True]) >>> x = np.array([-np.inf, 0., np.inf]) >>> y = np.array([2, 2, 2]) >>> np.isposinf(x, y) array([0, 0, 1]) >>> y array([0, 0, 1]) ### isreal Returns a bool array, where True if input element is real. If element has complex type with zero complex part, the return value for that element is True. Parameters ---------- x : array_like Input array. Returns ------- out : ndarray, bool Boolean array of same shape as `x`. Notes ----- `isreal` may behave unexpectedly for string or object arrays (see examples) See Also -------- iscomplex isrealobj : Return True if x is not a complex type. Examples -------- >>> a = np.array([1+1j, 1+0j, 4.5, 3, 2, 2j], dtype=complex) >>> np.isreal(a) array([False, True, True, True, True, False]) The function does not work on string arrays. >>> a = np.array([2j, "a"], dtype="U") >>> np.isreal(a) # Warns about non-elementwise comparison False Returns True for all elements in input array of ``dtype=object`` even if any of the elements is complex. >>> a = np.array([1, "2", 3+4j], dtype=object) >>> np.isreal(a) array([ True, True, True]) isreal should not be used with object arrays >>> a = np.array([1+2j, 2+1j], dtype=object) >>> np.isreal(a) array([ True, True]) ### isrealobj Return True if x is a not complex type or an array of complex numbers. The type of the input is checked, not the value. So even if the input has an imaginary part equal to zero, `isrealobj` evaluates to False if the data type is complex. Parameters ---------- x : any The input can be of any type and shape. Returns ------- y : bool The return value, False if `x` is of a complex type. See Also -------- iscomplexobj, isreal Notes ----- The function is only meant for arrays with numerical values but it accepts all other objects. Since it assumes array input, the return value of other objects may be True. >>> np.isrealobj('A string') True >>> np.isrealobj(False) True >>> np.isrealobj(None) True Examples -------- >>> [np.isrealobj(1)](https://www.chedong.com/phpMan.php/man/np.isrealobj/1/markdown) True >>> np.isrealobj(1+0j) False >>> np.isrealobj([3, 1+0j, True]) False ### isscalar Returns True if the type of `element` is a scalar type. Parameters ---------- element : any Input argument, can be of any type and shape. Returns ------- val : bool True if `element` is a scalar type, False if it is not. See Also -------- ndim : Get the number of dimensions of an array Notes ----- If you need a stricter way to identify a *numerical* scalar, use ``isinstance(x, numbers.Number)``, as that returns ``False`` for most non-numerical elements such as strings. In most cases ``np.ndim(x) == 0`` should be used instead of this function, as that will also return true for 0d arrays. This is how numpy overloads functions in the style of the ``dx`` arguments to `gradient` and the ``bins`` argument to `histogram`. Some key differences: +--------------------------------------+---------------+-------------------+ | x |``isscalar(x)``|``np.ndim(x) == 0``| +======================================+===============+===================+ | PEP 3141 numeric objects (including | ``True`` | ``True`` | | builtins) | | | +--------------------------------------+---------------+-------------------+ | builtin string and buffer objects | ``True`` | ``True`` | +--------------------------------------+---------------+-------------------+ | other builtin objects, like | ``False`` | ``True`` | | `pathlib.Path`, `Exception`, | | | | the result of `re.compile` | | | +--------------------------------------+---------------+-------------------+ | third-party objects like | ``False`` | ``True`` | | `matplotlib.figure.Figure` | | | +--------------------------------------+---------------+-------------------+ | zero-dimensional numpy arrays | ``False`` | ``True`` | +--------------------------------------+---------------+-------------------+ | other numpy arrays | ``False`` | ``False`` | +--------------------------------------+---------------+-------------------+ | `list`, `tuple`, and other sequence | ``False`` | ``False`` | | objects | | | +--------------------------------------+---------------+-------------------+ Examples -------- >>> np.isscalar(3.1) True >>> np.isscalar(np.array(3.1)) False >>> np.isscalar([3.1]) False >>> np.isscalar(False) True >>> np.isscalar('numpy') True NumPy supports PEP 3141 numbers: >>> from fractions import Fraction >>> np.isscalar(Fraction(5, 17)) True >>> from numbers import Number >>> np.isscalar(Number()) True ### issctype Determines whether the given object represents a scalar data-type. Parameters ---------- rep : any If `rep` is an instance of a scalar dtype, True is returned. If not, False is returned. Returns ------- out : bool Boolean result of check whether `rep` is a scalar dtype. See Also -------- issubsctype, issubdtype, obj2sctype, sctype2char Examples -------- >>> np.issctype(np.int32) True >>> np.issctype(list) False >>> np.issctype(1.1) False Strings are also a scalar type: >>> np.issctype(np.dtype('str')) True ### issubclass_ Determine if a class is a subclass of a second class. `issubclass_` is equivalent to the Python built-in ``issubclass``, except that it returns False instead of raising a TypeError if one of the arguments is not a class. Parameters ---------- arg1 : class Input class. True is returned if `arg1` is a subclass of `arg2`. arg2 : class or tuple of classes. Input class. If a tuple of classes, True is returned if `arg1` is a subclass of any of the tuple elements. Returns ------- out : bool Whether `arg1` is a subclass of `arg2` or not. See Also -------- issubsctype, issubdtype, issctype Examples -------- >>> np.issubclass_(np.int32, int) False >>> np.issubclass_(np.int32, float) False >>> np.issubclass_(np.float64, float) True ### issubdtype Returns True if first argument is a typecode lower/equal in type hierarchy. This is like the builtin :func:`issubclass`, but for `dtype`\ s. Parameters ---------- arg1, arg2 : dtype_like `dtype` or object coercible to one Returns ------- out : bool See Also -------- :ref:`arrays.scalars` : Overview of the numpy type hierarchy. issubsctype, issubclass_ Examples -------- `issubdtype` can be used to check the type of arrays: >>> ints = np.array([1, 2, 3], dtype=np.int32) >>> np.issubdtype(ints.dtype, np.integer) True >>> np.issubdtype(ints.dtype, np.floating) False >>> floats = np.array([1, 2, 3], dtype=np.float32) >>> np.issubdtype(floats.dtype, np.integer) False >>> np.issubdtype(floats.dtype, np.floating) True Similar types of different sizes are not subdtypes of each other: >>> np.issubdtype(np.float64, np.float32) False >>> np.issubdtype(np.float32, np.float64) False but both are subtypes of `floating`: >>> np.issubdtype(np.float64, np.floating) True >>> np.issubdtype(np.float32, np.floating) True For convenience, dtype-like objects are allowed too: >>> np.issubdtype('S1', np.string_) True >>> np.issubdtype('i4', np.signedinteger) True ### issubsctype Determine if the first argument is a subclass of the second argument. Parameters ---------- arg1, arg2 : dtype or dtype specifier Data-types. Returns ------- out : bool The result. See Also -------- issctype, issubdtype, obj2sctype Examples -------- >>> np.issubsctype('S8', str) False >>> np.issubsctype(np.array([1]), int) True >>> np.issubsctype(np.array([1]), float) False ### iterable Check whether or not an object can be iterated over. Parameters ---------- y : object Input object. Returns ------- b : bool Return ``True`` if the object has an iterator method or is a sequence and ``False`` otherwise. Examples -------- >>> np.iterable([1, 2, 3]) True >>> [np.iterable(2)](https://www.chedong.com/phpMan.php/man/np.iterable/2/markdown) False ### ix_ Construct an open mesh from multiple sequences. This function takes N 1-D sequences and returns N outputs with N dimensions each, such that the shape is 1 in all but one dimension and the dimension with the non-unit shape value cycles through all N dimensions. Using `ix_` one can quickly construct index arrays that will index the cross product. ``a[np.ix_([1,3],[2,5])]`` returns the array ``[[a[1,2] a[1,5]], [a[3,2] a[3,5]]]``. Parameters ---------- args : 1-D sequences Each sequence should be of integer or boolean type. Boolean sequences will be interpreted as boolean masks for the corresponding dimension (equivalent to passing in ``np.nonzero(boolean_sequence)``). Returns ------- out : tuple of ndarrays N arrays with N dimensions each, with N the number of input sequences. Together these arrays form an open mesh. See Also -------- ogrid, mgrid, meshgrid Examples -------- >>> a = [np.arange(10)](https://www.chedong.com/phpMan.php/man/np.arange/10/markdown).reshape(2, 5) >>> a array([[0, 1, 2, 3, 4], [5, 6, 7, 8, 9]]) >>> ixgrid = np.ix_([0, 1], [2, 4]) >>> ixgrid (array([[0], [1]]), array([[2, 4]])) >>> ixgrid[0].shape, ixgrid[1].shape ((2, 1), (1, 2)) >>> a[ixgrid] array([[2, 4], [7, 9]]) >>> ixgrid = np.ix_([True, True], [2, 4]) >>> a[ixgrid] array([[2, 4], [7, 9]]) >>> ixgrid = np.ix_([True, True], [False, False, True, False, True]) >>> a[ixgrid] array([[2, 4], [7, 9]]) ### kaiser Return the Kaiser window. The Kaiser window is a taper formed by using a Bessel function. Parameters ---------- M : int Number of points in the output window. If zero or less, an empty array is returned. beta : float Shape parameter for window. Returns ------- out : array The window, with the maximum value normalized to one (the value one appears only if the number of samples is odd). See Also -------- bartlett, blackman, hamming, hanning Notes ----- The Kaiser window is defined as .. math:: [w(n)](https://www.chedong.com/phpMan.php/man/w/n/markdown) = I_0\left( \beta \sqrt{1-\frac{4n^2}{(M-1)^2}} \right)/I_0(\beta) with .. math:: \quad -\frac{M-1}{2} \leq n \leq \frac{M-1}{2}, where :math:`I_0` is the modified zeroth-order Bessel function. The Kaiser was named for Jim Kaiser, who discovered a simple approximation to the DPSS window based on Bessel functions. The Kaiser window is a very good approximation to the Digital Prolate Spheroidal Sequence, or Slepian window, which is the transform which maximizes the energy in the main lobe of the window relative to total energy. The Kaiser can approximate many other windows by varying the beta parameter. ==== ======================= beta Window shape ==== ======================= 0 Rectangular 5 Similar to a Hamming 6 Similar to a Hanning 8.6 Similar to a Blackman ==== ======================= A beta value of 14 is probably a good starting point. Note that as beta gets large, the window narrows, and so the number of samples needs to be large enough to sample the increasingly narrow spike, otherwise NaNs will get returned. Most references to the Kaiser window come from the signal processing literature, where it is used as one of many windowing functions for smoothing values. It is also known as an apodization (which means "removing the foot", i.e. smoothing discontinuities at the beginning and end of the sampled signal) or tapering function. References ---------- .. [1] J. F. Kaiser, "Digital Filters" - Ch 7 in "Systems analysis by digital computer", Editors: F.F. Kuo and J.F. Kaiser, p 218-285. John Wiley and Sons, New York, (1966). .. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics", The University of Alberta Press, 1975, pp. 177-178. .. [3] Wikipedia, "Window function", Examples -------- >>> import matplotlib.pyplot as plt >>> np.kaiser(12, 14) array([7.72686684e-06, 3.46009194e-03, 4.65200189e-02, # may vary 2.29737120e-01, 5.99885316e-01, 9.45674898e-01, 9.45674898e-01, 5.99885316e-01, 2.29737120e-01, 4.65200189e-02, 3.46009194e-03, 7.72686684e-06]) Plot the window and the frequency response: >>> from numpy.fft import fft, fftshift >>> window = np.kaiser(51, 14) >>> plt.plot(window) [] >>> plt.title("Kaiser window") Text(0.5, 1.0, 'Kaiser window') >>> plt.ylabel("Amplitude") Text(0, 0.5, 'Amplitude') >>> plt.xlabel("Sample") Text(0.5, 0, 'Sample') >>> plt.show() >>> plt.figure()
>>> A = fft(window, 2048) / 25.5 >>> mag = np.abs(fftshift(A)) >>> freq = np.linspace(-0.5, 0.5, len(A)) >>> response = 20 * np.log10(mag) >>> response = np.clip(response, -100, 100) >>> plt.plot(freq, response) [] >>> plt.title("Frequency response of Kaiser window") Text(0.5, 1.0, 'Frequency response of Kaiser window') >>> plt.ylabel("Magnitude [dB]") Text(0, 0.5, 'Magnitude [dB]') >>> plt.xlabel("Normalized frequency [cycles per sample]") Text(0.5, 0, 'Normalized frequency [cycles per sample]') >>> plt.axis('tight') (-0.5, 0.5, -100.0, ...) # may vary >>> plt.show() ### kron Kronecker product of two arrays. Computes the Kronecker product, a composite array made of blocks of the second array scaled by the first. Parameters ---------- a, b : array_like Returns ------- out : ndarray See Also -------- outer : The outer product Notes ----- The function assumes that the number of dimensions of `a` and `b` are the same, if necessary prepending the smallest with ones. If ``a.shape = (r0,r1,..,rN)`` and ``b.shape = (s0,s1,...,sN)``, the Kronecker product has shape ``(r0*s0, r1*s1, ..., rN*SN)``. The elements are products of elements from `a` and `b`, organized explicitly by:: kron(a,b)[k0,k1,...,kN] = a[i0,i1,...,iN] * b[j0,j1,...,jN] where:: kt = it * st + jt, t = 0,...,N In the common 2-D case (N=1), the block structure can be visualized:: [[ a[0,0]*b, a[0,1]*b, ... , a[0,-1]*b ], [ ... ... ], [ a[-1,0]*b, a[-1,1]*b, ... , a[-1,-1]*b ]] Examples -------- >>> np.kron([1,10,100], [5,6,7]) array([ 5, 6, 7, ..., 500, 600, 700]) >>> np.kron([5,6,7], [1,10,100]) array([ 5, 50, 500, ..., 7, 70, 700]) >>> np.kron([np.eye(2)](https://www.chedong.com/phpMan.php/man/np.eye/2/markdown), np.ones((2,2))) array([[1., 1., 0., 0.], [1., 1., 0., 0.], [0., 0., 1., 1.], [0., 0., 1., 1.]]) >>> a = [np.arange(100)](https://www.chedong.com/phpMan.php/man/np.arange/100/markdown).reshape((2,5,2,5)) >>> b = [np.arange(24)](https://www.chedong.com/phpMan.php/man/np.arange/24/markdown).reshape((2,3,4)) >>> c = np.kron(a,b) >>> c.shape (2, 10, 6, 20) >>> I = (1,3,0,2) >>> J = (0,2,1) >>> J1 = (0,) + J # extend to ndim=4 >>> S1 = (1,) + b.shape >>> K = tuple(np.array(I) * np.array(S1) + np.array(J1)) >>> c[K] == a[I]*b[J] True ### lexsort lexsort(keys, axis=-1) Perform an indirect stable sort using a sequence of keys. Given multiple sorting keys, which can be interpreted as columns in a spreadsheet, lexsort returns an array of integer indices that describes the sort order by multiple columns. The last key in the sequence is used for the primary sort order, the second-to-last key for the secondary sort order, and so on. The keys argument must be a sequence of objects that can be converted to arrays of the same shape. If a 2D array is provided for the keys argument, its rows are interpreted as the sorting keys and sorting is according to the last row, second last row etc. Parameters ---------- keys : (k, N) array or tuple containing k (N,)-shaped sequences The `k` different "columns" to be sorted. The last column (or row if `keys` is a 2D array) is the primary sort key. axis : int, optional Axis to be indirectly sorted. By default, sort over the last axis. Returns ------- indices : (N,) ndarray of ints Array of indices that sort the keys along the specified axis. See Also -------- argsort : Indirect sort. ndarray.sort : In-place sort. sort : Return a sorted copy of an array. Examples -------- Sort names: first by surname, then by name. >>> surnames = ('Hertz', 'Galilei', 'Hertz') >>> first_names = ('Heinrich', 'Galileo', 'Gustav') >>> ind = np.lexsort((first_names, surnames)) >>> ind array([1, 2, 0]) >>> [surnames[i] + ", " + first_names[i] for i in ind] ['Galilei, Galileo', 'Hertz, Gustav', 'Hertz, Heinrich'] Sort two columns of numbers: >>> a = [1,5,1,4,3,4,4] # First column >>> b = [9,4,0,4,0,2,1] # Second column >>> ind = np.lexsort((b,a)) # Sort by a, then by b >>> ind array([2, 0, 4, 6, 5, 3, 1]) >>> [(a[i],b[i]) for i in ind] [(1, 0), (1, 9), (3, 0), (4, 1), (4, 2), (4, 4), (5, 4)] Note that sorting is first according to the elements of ``a``. Secondary sorting is according to the elements of ``b``. A normal ``argsort`` would have yielded: >>> [(a[i],b[i]) for i in np.argsort(a)] [(1, 9), (1, 0), (3, 0), (4, 4), (4, 2), (4, 1), (5, 4)] Structured arrays are sorted lexically by ``argsort``: >>> x = np.array([(1,9), (5,4), (1,0), (4,4), (3,0), (4,2), (4,1)], ... dtype=np.dtype([('x', int), ('y', int)])) >>> np.argsort(x) # or np.argsort(x, order=('x', 'y')) array([2, 0, 4, 6, 5, 3, 1]) ### linspace Return evenly spaced numbers over a specified interval. Returns `num` evenly spaced samples, calculated over the interval [`start`, `stop`]. The endpoint of the interval can optionally be excluded. .. versionchanged:: 1.16.0 Non-scalar `start` and `stop` are now supported. .. versionchanged:: 1.20.0 Values are rounded towards ``-inf`` instead of ``0`` when an integer ``dtype`` is specified. The old behavior can still be obtained with ``np.linspace(start, stop, num).astype(int)`` Parameters ---------- start : array_like The starting value of the sequence. stop : array_like The end value of the sequence, unless `endpoint` is set to False. In that case, the sequence consists of all but the last of ``num + 1`` evenly spaced samples, so that `stop` is excluded. Note that the step size changes when `endpoint` is False. num : int, optional Number of samples to generate. Default is 50. Must be non-negative. endpoint : bool, optional If True, `stop` is the last sample. Otherwise, it is not included. Default is True. retstep : bool, optional If True, return (`samples`, `step`), where `step` is the spacing between samples. dtype : dtype, optional The type of the output array. If `dtype` is not given, the data type is inferred from `start` and `stop`. The inferred dtype will never be an integer; `float` is chosen even if the arguments would produce an array of integers. .. versionadded:: 1.9.0 axis : int, optional The axis in the result to store the samples. Relevant only if start or stop are array-like. By default (0), the samples will be along a new axis inserted at the beginning. Use -1 to get an axis at the end. .. versionadded:: 1.16.0 Returns ------- samples : ndarray There are `num` equally spaced samples in the closed interval ``[start, stop]`` or the half-open interval ``[start, stop)`` (depending on whether `endpoint` is True or False). step : float, optional Only returned if `retstep` is True Size of spacing between samples. See Also -------- arange : Similar to `linspace`, but uses a step size (instead of the number of samples). geomspace : Similar to `linspace`, but with numbers spaced evenly on a log scale (a geometric progression). logspace : Similar to `geomspace`, but with the end points specified as logarithms. Examples -------- >>> np.linspace(2.0, 3.0, num=5) array([2. , 2.25, 2.5 , 2.75, 3. ]) >>> np.linspace(2.0, 3.0, num=5, endpoint=False) array([2. , 2.2, 2.4, 2.6, 2.8]) >>> np.linspace(2.0, 3.0, num=5, retstep=True) (array([2. , 2.25, 2.5 , 2.75, 3. ]), 0.25) Graphical illustration: >>> import matplotlib.pyplot as plt >>> N = 8 >>> y = np.zeros(N) >>> x1 = np.linspace(0, 10, N, endpoint=True) >>> x2 = np.linspace(0, 10, N, endpoint=False) >>> plt.plot(x1, y, 'o') [] >>> plt.plot(x2, y + 0.5, 'o') [] >>> plt.ylim([-0.5, 1]) (-0.5, 1) >>> plt.show() ### load Load arrays or pickled objects from ``.npy``, ``.npz`` or pickled files. .. warning:: Loading files that contain object arrays uses the ``pickle`` module, which is not secure against erroneous or maliciously constructed data. Consider passing ``allow_pickle=False`` to load data that is known not to contain object arrays for the safer handling of untrusted sources. Parameters ---------- file : file-like object, string, or pathlib.Path The file to read. File-like objects must support the ``seek()`` and ``read()`` methods. Pickled files require that the file-like object support the ``readline()`` method as well. mmap_mode : {None, 'r+', 'r', 'w+', 'c'}, optional If not None, then memory-map the file, using the given mode (see `numpy.memmap` for a detailed description of the modes). A memory-mapped array is kept on disk. However, it can be accessed and sliced like any ndarray. Memory mapping is especially useful for accessing small fragments of large files without reading the entire file into memory. allow_pickle : bool, optional Allow loading pickled object arrays stored in npy files. Reasons for disallowing pickles include security, as loading pickled data can execute arbitrary code. If pickles are disallowed, loading object arrays will fail. Default: False .. versionchanged:: 1.16.3 Made default False in response to CVE-2019-6446. fix_imports : bool, optional Only useful when loading Python 2 generated pickled files on Python 3, which includes npy/npz files containing object arrays. If `fix_imports` is True, pickle will try to map the old Python 2 names to the new names used in Python 3. encoding : str, optional What encoding to use when reading Python 2 strings. Only useful when loading Python 2 generated pickled files in Python 3, which includes npy/npz files containing object arrays. Values other than 'latin1', 'ASCII', and 'bytes' are not allowed, as they can corrupt numerical data. Default: 'ASCII' Returns ------- result : array, tuple, dict, etc. Data stored in the file. For ``.npz`` files, the returned instance of NpzFile class must be closed to avoid leaking file descriptors. Raises ------ IOError If the input file does not exist or cannot be read. ValueError The file contains an object array, but allow_pickle=False given. See Also -------- save, savez, savez_compressed, loadtxt memmap : Create a memory-map to an array stored in a file on disk. lib.format.open_memmap : Create or load a memory-mapped ``.npy`` file. Notes ----- - If the file contains pickle data, then whatever object is stored in the pickle is returned. - If the file is a ``.npy`` file, then a single array is returned. - If the file is a ``.npz`` file, then a dictionary-like object is returned, containing ``{filename: array}`` key-value pairs, one for each file in the archive. - If the file is a ``.npz`` file, the returned value supports the context manager protocol in a similar fashion to the open function:: with load('foo.npz') as data: a = data['a'] The underlying file descriptor is closed when exiting the 'with' block. Examples -------- Store data to disk, and load it again: >>> np.save('/tmp/123', np.array([[1, 2, 3], [4, 5, 6]])) >>> np.load('/tmp/123.npy') array([[1, 2, 3], [4, 5, 6]]) Store compressed data to disk, and load it again: >>> a=np.array([[1, 2, 3], [4, 5, 6]]) >>> b=np.array([1, 2]) >>> np.savez('/tmp/123.npz', a=a, b=b) >>> data = np.load('/tmp/123.npz') >>> data['a'] array([[1, 2, 3], [4, 5, 6]]) >>> data['b'] array([1, 2]) >>> data.close() Mem-map the stored array, and then access the second row directly from disk: >>> X = np.load('/tmp/123.npy', mmap_mode='r') >>> X[1, :] memmap([4, 5, 6]) ### loads ### loadtxt Load data from a text file. Each row in the text file must have the same number of values. Parameters ---------- fname : file, str, or pathlib.Path File, filename, or generator to read. If the filename extension is ``.gz`` or ``.bz2``, the file is first decompressed. Note that generators should return byte strings. dtype : data-type, optional Data-type of the resulting array; default: float. If this is a structured data-type, the resulting array will be 1-dimensional, and each row will be interpreted as an element of the array. In this case, the number of columns used must match the number of fields in the data-type. comments : str or sequence of str, optional The characters or list of characters used to indicate the start of a comment. None implies no comments. For backwards compatibility, byte strings will be decoded as 'latin1'. The default is '#'. delimiter : str, optional The string used to separate values. For backwards compatibility, byte strings will be decoded as 'latin1'. The default is whitespace. converters : dict, optional A dictionary mapping column number to a function that will parse the column string into the desired value. E.g., if column 0 is a date string: ``converters = {0: datestr2num}``. Converters can also be used to provide a default value for missing data (but see also `genfromtxt`): ``converters = {3: lambda s: float(s.strip() or 0)}``. Default: None. skiprows : int, optional Skip the first `skiprows` lines, including comments; default: 0. usecols : int or sequence, optional Which columns to read, with 0 being the first. For example, ``usecols = (1,4,5)`` will extract the 2nd, 5th and 6th columns. The default, None, results in all columns being read. .. versionchanged:: 1.11.0 When a single column has to be read it is possible to use an integer instead of a tuple. E.g ``usecols = 3`` reads the fourth column the same way as ``usecols = (3,)`` would. unpack : bool, optional If True, the returned array is transposed, so that arguments may be unpacked using ``x, y, z = loadtxt(...)``. When used with a structured data-type, arrays are returned for each field. Default is False. ndmin : int, optional The returned array will have at least `ndmin` dimensions. Otherwise mono-dimensional axes will be squeezed. Legal values: 0 (default), 1 or 2. .. versionadded:: 1.6.0 encoding : str, optional Encoding used to decode the inputfile. Does not apply to input streams. The special value 'bytes' enables backward compatibility workarounds that ensures you receive byte arrays as results if possible and passes 'latin1' encoded strings to converters. Override this value to receive unicode arrays and pass strings as input to converters. If set to None the system default is used. The default value is 'bytes'. .. versionadded:: 1.14.0 max_rows : int, optional Read `max_rows` lines of content after `skiprows` lines. The default is to read all the lines. .. versionadded:: 1.16.0 like : array_like Reference object to allow the creation of arrays which are not NumPy arrays. If an array-like passed in as ``like`` supports the ``__array_function__`` protocol, the result will be defined by it. In this case, it ensures the creation of an array object compatible with that passed in via this argument. .. versionadded:: 1.20.0 Returns ------- out : ndarray Data read from the text file. See Also -------- load, fromstring, fromregex genfromtxt : Load data with missing values handled as specified. scipy.io.loadmat : reads MATLAB data files Notes ----- This function aims to be a fast reader for simply formatted files. The `genfromtxt` function provides more sophisticated handling of, e.g., lines with missing values. .. versionadded:: 1.10.0 The strings produced by the Python float.hex method can be used as input for floats. Examples -------- >>> from io import StringIO # StringIO behaves like a file object >>> c = StringIO("0 1\n2 3") >>> np.loadtxt(c) array([[0., 1.], [2., 3.]]) >>> d = StringIO("M 21 72\nF 35 58") >>> np.loadtxt(d, dtype={'names': ('gender', 'age', 'weight'), ... 'formats': ('S1', 'i4', 'f4')}) array([(b'M', 21, 72.), (b'F', 35, 58.)], dtype=[('gender', 'S1'), ('age', '>> c = StringIO("1,0,2\n3,0,4") >>> x, y = np.loadtxt(c, delimiter=',', usecols=(0, 2), unpack=True) >>> x array([1., 3.]) >>> y array([2., 4.]) This example shows how `converters` can be used to convert a field with a trailing minus sign into a negative number. >>> s = StringIO('10.01 31.25-\n19.22 64.31\n17.57- 63.94') >>> def conv(fld): ... return -float(fld[:-1]) if fld.endswith(b'-') else float(fld) ... >>> np.loadtxt(s, converters={0: conv, 1: conv}) array([[ 10.01, -31.25], [ 19.22, 64.31], [-17.57, 63.94]]) ### logspace Return numbers spaced evenly on a log scale. In linear space, the sequence starts at ``base ** start`` (`base` to the power of `start`) and ends with ``base ** stop`` (see `endpoint` below). .. versionchanged:: 1.16.0 Non-scalar `start` and `stop` are now supported. Parameters ---------- start : array_like ``base ** start`` is the starting value of the sequence. stop : array_like ``base ** stop`` is the final value of the sequence, unless `endpoint` is False. In that case, ``num + 1`` values are spaced over the interval in log-space, of which all but the last (a sequence of length `num`) are returned. num : integer, optional Number of samples to generate. Default is 50. endpoint : boolean, optional If true, `stop` is the last sample. Otherwise, it is not included. Default is True. base : array_like, optional The base of the log space. The step size between the elements in ``ln(samples) / ln(base)`` (or ``log_base(samples)``) is uniform. Default is 10.0. dtype : dtype The type of the output array. If `dtype` is not given, the data type is inferred from `start` and `stop`. The inferred type will never be an integer; `float` is chosen even if the arguments would produce an array of integers. axis : int, optional The axis in the result to store the samples. Relevant only if start or stop are array-like. By default (0), the samples will be along a new axis inserted at the beginning. Use -1 to get an axis at the end. .. versionadded:: 1.16.0 Returns ------- samples : ndarray `num` samples, equally spaced on a log scale. See Also -------- arange : Similar to linspace, with the step size specified instead of the number of samples. Note that, when used with a float endpoint, the endpoint may or may not be included. linspace : Similar to logspace, but with the samples uniformly distributed in linear space, instead of log space. geomspace : Similar to logspace, but with endpoints specified directly. Notes ----- Logspace is equivalent to the code >>> y = np.linspace(start, stop, num=num, endpoint=endpoint) ... # doctest: +SKIP >>> power(base, y).astype(dtype) ... # doctest: +SKIP Examples -------- >>> np.logspace(2.0, 3.0, num=4) array([ 100. , 215.443469 , 464.15888336, 1000. ]) >>> np.logspace(2.0, 3.0, num=4, endpoint=False) array([100. , 177.827941 , 316.22776602, 562.34132519]) >>> np.logspace(2.0, 3.0, num=4, base=2.0) array([4. , 5.0396842 , 6.34960421, 8. ]) Graphical illustration: >>> import matplotlib.pyplot as plt >>> N = 10 >>> x1 = np.logspace(0.1, 1, N, endpoint=True) >>> x2 = np.logspace(0.1, 1, N, endpoint=False) >>> y = np.zeros(N) >>> plt.plot(x1, y, 'o') [] >>> plt.plot(x2, y + 0.5, 'o') [] >>> plt.ylim([-0.5, 1]) (-0.5, 1) >>> plt.show() ### lookfor Do a keyword search on docstrings. A list of objects that matched the search is displayed, sorted by relevance. All given keywords need to be found in the docstring for it to be returned as a result, but the order does not matter. Parameters ---------- what : str String containing words to look for. module : str or list, optional Name of module(s) whose docstrings to go through. import_modules : bool, optional Whether to import sub-modules in packages. Default is True. regenerate : bool, optional Whether to re-generate the docstring cache. Default is False. output : file-like, optional File-like object to write the output to. If omitted, use a pager. See Also -------- source, info Notes ----- Relevance is determined only roughly, by checking if the keywords occur in the function name, at the start of a docstring, etc. Examples -------- >>> np.lookfor('binary representation') # doctest: +SKIP Search results for 'binary representation' ------------------------------------------ numpy.binary_repr Return the binary representation of the input number as a string. numpy.core.setup_common.long_double_representation Given a binary dump as given by GNU od -b, look for long double numpy.base_repr Return a string representation of a number in the given base system. ... ### mafromtxt Load ASCII data stored in a text file and return a masked array. .. deprecated:: 1.17 np.mafromtxt is a deprecated alias of `genfromtxt` which overwrites the ``usemask`` argument with `True` even when explicitly called as ``mafromtxt(..., usemask=False)``. Use `genfromtxt` instead. Parameters ---------- fname, kwargs : For a description of input parameters, see `genfromtxt`. See Also -------- numpy.genfromtxt : generic function to load ASCII data. ### mask_indices Return the indices to access (n, n) arrays, given a masking function. Assume `mask_func` is a function that, for a square array a of size ``(n, n)`` with a possible offset argument `k`, when called as ``mask_func(a, k)`` returns a new array with zeros in certain locations (functions like `triu` or `tril` do precisely this). Then this function returns the indices where the non-zero values would be located. Parameters ---------- n : int The returned indices will be valid to access arrays of shape (n, n). mask_func : callable A function whose call signature is similar to that of `triu`, `tril`. That is, ``mask_func(x, k)`` returns a boolean array, shaped like `x`. `k` is an optional argument to the function. k : scalar An optional argument which is passed through to `mask_func`. Functions like `triu`, `tril` take a second argument that is interpreted as an offset. Returns ------- indices : tuple of arrays. The `n` arrays of indices corresponding to the locations where ``mask_func(np.ones((n, n)), k)`` is True. See Also -------- triu, tril, triu_indices, tril_indices Notes ----- .. versionadded:: 1.4.0 Examples -------- These are the indices that would allow you to access the upper triangular part of any 3x3 array: >>> iu = np.mask_indices(3, np.triu) For example, if `a` is a 3x3 array: >>> a = [np.arange(9)](https://www.chedong.com/phpMan.php/man/np.arange/9/markdown).reshape(3, 3) >>> a array([[0, 1, 2], [3, 4, 5], [6, 7, 8]]) >>> a[iu] array([0, 1, 2, 4, 5, 8]) An offset can be passed also to the masking function. This gets us the indices starting on the first diagonal right of the main one: >>> iu1 = np.mask_indices(3, np.triu, 1) with which we now extract only three elements: >>> a[iu1] array([1, 2, 5]) mat = asmatrix(data, dtype=None) Interpret the input as a matrix. Unlike `matrix`, `asmatrix` does not make a copy if the input is already a matrix or an ndarray. Equivalent to ``matrix(data, copy=False)``. Parameters ---------- data : array_like Input data. dtype : data-type Data-type of the output matrix. Returns ------- mat : matrix `data` interpreted as a matrix. Examples -------- >>> x = np.array([[1, 2], [3, 4]]) >>> m = np.asmatrix(x) >>> x[0,0] = 5 >>> m matrix([[5, 2], [3, 4]]) ### maximum_sctype Return the scalar type of highest precision of the same kind as the input. Parameters ---------- t : dtype or dtype specifier The input data type. This can be a `dtype` object or an object that is convertible to a `dtype`. Returns ------- out : dtype The highest precision data type of the same kind (`dtype.kind`) as `t`. See Also -------- obj2sctype, mintypecode, sctype2char dtype Examples -------- >>> np.maximum_sctype(int) >>> np.maximum_sctype(np.uint8) >>> np.maximum_sctype(complex) # may vary >>> np.maximum_sctype(str) >>> np.maximum_sctype('i2') >>> np.maximum_sctype('f4') # may vary ### may_share_memory may_share_memory(a, b, max_work=None) Determine if two arrays might share memory A return of True does not necessarily mean that the two arrays share any element. It just means that they *might*. Only the memory bounds of a and b are checked by default. Parameters ---------- a, b : ndarray Input arrays max_work : int, optional Effort to spend on solving the overlap problem. See `shares_memory` for details. Default for ``may_share_memory`` is to do a bounds check. Returns ------- out : bool See Also -------- shares_memory Examples -------- >>> np.may_share_memory(np.array([1,2]), np.array([5,8,9])) False >>> x = np.zeros([3, 4]) >>> np.may_share_memory(x[:,0], x[:,1]) True ### mean Compute the arithmetic mean along the specified axis. Returns the average of the array elements. The average is taken over the flattened array by default, otherwise over the specified axis. `float64` intermediate and return values are used for integer inputs. Parameters ---------- a : array_like Array containing numbers whose mean is desired. If `a` is not an array, a conversion is attempted. axis : None or int or tuple of ints, optional Axis or axes along which the means are computed. The default is to compute the mean of the flattened array. .. versionadded:: 1.7.0 If this is a tuple of ints, a mean is performed over multiple axes, instead of a single axis or all the axes as before. dtype : data-type, optional Type to use in computing the mean. For integer inputs, the default is `float64`; for floating point inputs, it is the same as the input dtype. out : ndarray, optional Alternate output array in which to place the result. The default is ``None``; if provided, it must have the same shape as the expected output, but the type will be cast if necessary. See :ref:`ufuncs-output-type` for more details. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array. If the default value is passed, then `keepdims` will not be passed through to the `mean` method of sub-classes of `ndarray`, however any non-default value will be. If the sub-class' method does not implement `keepdims` any exceptions will be raised. where : array_like of bool, optional Elements to include in the mean. See `~numpy.ufunc.reduce` for details. .. versionadded:: 1.20.0 Returns ------- m : ndarray, see dtype parameter above If `out=None`, returns a new array containing the mean values, otherwise a reference to the output array is returned. See Also -------- average : Weighted average std, var, nanmean, nanstd, nanvar Notes ----- The arithmetic mean is the sum of the elements along the axis divided by the number of elements. Note that for floating-point input, the mean is computed using the same precision the input has. Depending on the input data, this can cause the results to be inaccurate, especially for `float32` (see example below). Specifying a higher-precision accumulator using the `dtype` keyword can alleviate this issue. By default, `float16` results are computed using `float32` intermediates for extra precision. Examples -------- >>> a = np.array([[1, 2], [3, 4]]) >>> np.mean(a) 2.5 >>> np.mean(a, axis=0) array([2., 3.]) >>> np.mean(a, axis=1) array([1.5, 3.5]) In single precision, `mean` can be inaccurate: >>> a = np.zeros((2, 512*512), dtype=np.float32) >>> a[0, :] = 1.0 >>> a[1, :] = 0.1 >>> np.mean(a) 0.54999924 Computing the mean in float64 is more accurate: >>> np.mean(a, dtype=np.float64) 0.55000000074505806 # may vary Specifying a where argument: >>> a = np.array([[5, 9, 13], [14, 10, 12], [11, 15, 19]]) >>> np.mean(a) 12.0 >>> np.mean(a, where=[[True], [False], [False]]) 9.0 ### median Compute the median along the specified axis. Returns the median of the array elements. Parameters ---------- a : array_like Input array or object that can be converted to an array. axis : {int, sequence of int, None}, optional Axis or axes along which the medians are computed. The default is to compute the median along a flattened version of the array. A sequence of axes is supported since version 1.9.0. out : ndarray, optional Alternative output array in which to place the result. It must have the same shape and buffer length as the expected output, but the type (of the output) will be cast if necessary. overwrite_input : bool, optional If True, then allow use of memory of input array `a` for calculations. The input array will be modified by the call to `median`. This will save memory when you do not need to preserve the contents of the input array. Treat the input as undefined, but it will probably be fully or partially sorted. Default is False. If `overwrite_input` is ``True`` and `a` is not already an `ndarray`, an error will be raised. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `arr`. .. versionadded:: 1.9.0 Returns ------- median : ndarray A new array holding the result. If the input contains integers or floats smaller than ``float64``, then the output data-type is ``np.float64``. Otherwise, the data-type of the output is the same as that of the input. If `out` is specified, that array is returned instead. See Also -------- mean, percentile Notes ----- Given a vector ``V`` of length ``N``, the median of ``V`` is the middle value of a sorted copy of ``V``, ``V_sorted`` - i e., ``V_sorted[(N-1)/2]``, when ``N`` is odd, and the average of the two middle values of ``V_sorted`` when ``N`` is even. Examples -------- >>> a = np.array([[10, 7, 4], [3, 2, 1]]) >>> a array([[10, 7, 4], [ 3, 2, 1]]) >>> np.median(a) 3.5 >>> np.median(a, axis=0) array([6.5, 4.5, 2.5]) >>> np.median(a, axis=1) array([7., 2.]) >>> m = np.median(a, axis=0) >>> out = np.zeros_like(m) >>> np.median(a, axis=0, out=m) array([6.5, 4.5, 2.5]) >>> m array([6.5, 4.5, 2.5]) >>> b = a.copy() >>> np.median(b, axis=1, overwrite_input=True) array([7., 2.]) >>> assert not np.all(a==b) >>> b = a.copy() >>> np.median(b, axis=None, overwrite_input=True) 3.5 >>> assert not np.all(a==b) ### meshgrid Return coordinate matrices from coordinate vectors. Make N-D coordinate arrays for vectorized evaluations of N-D scalar/vector fields over N-D grids, given one-dimensional coordinate arrays x1, x2,..., xn. .. versionchanged:: 1.9 1-D and 0-D cases are allowed. Parameters ---------- x1, x2,..., xn : array_like 1-D arrays representing the coordinates of a grid. indexing : {'xy', 'ij'}, optional Cartesian ('xy', default) or matrix ('ij') indexing of output. See Notes for more details. .. versionadded:: 1.7.0 sparse : bool, optional If True a sparse grid is returned in order to conserve memory. Default is False. .. versionadded:: 1.7.0 copy : bool, optional If False, a view into the original arrays are returned in order to conserve memory. Default is True. Please note that ``sparse=False, copy=False`` will likely return non-contiguous arrays. Furthermore, more than one element of a broadcast array may refer to a single memory location. If you need to write to the arrays, make copies first. .. versionadded:: 1.7.0 Returns ------- X1, X2,..., XN : ndarray For vectors `x1`, `x2`,..., 'xn' with lengths ``Ni=len(xi)`` , return ``(N1, N2, N3,...Nn)`` shaped arrays if indexing='ij' or ``(N2, N1, N3,...Nn)`` shaped arrays if indexing='xy' with the elements of `xi` repeated to fill the matrix along the first dimension for `x1`, the second for `x2` and so on. Notes ----- This function supports both indexing conventions through the indexing keyword argument. Giving the string 'ij' returns a meshgrid with matrix indexing, while 'xy' returns a meshgrid with Cartesian indexing. In the 2-D case with inputs of length M and N, the outputs are of shape (N, M) for 'xy' indexing and (M, N) for 'ij' indexing. In the 3-D case with inputs of length M, N and P, outputs are of shape (N, M, P) for 'xy' indexing and (M, N, P) for 'ij' indexing. The difference is illustrated by the following code snippet:: xv, yv = np.meshgrid(x, y, sparse=False, indexing='ij') for i in [range(nx)](https://www.chedong.com/phpMan.php/man/range/nx/markdown): for j in [range(ny)](https://www.chedong.com/phpMan.php/man/range/ny/markdown): # treat xv[i,j], yv[i,j] xv, yv = np.meshgrid(x, y, sparse=False, indexing='xy') for i in [range(nx)](https://www.chedong.com/phpMan.php/man/range/nx/markdown): for j in [range(ny)](https://www.chedong.com/phpMan.php/man/range/ny/markdown): # treat xv[j,i], yv[j,i] In the 1-D and 0-D case, the indexing and sparse keywords have no effect. See Also -------- mgrid : Construct a multi-dimensional "meshgrid" using indexing notation. ogrid : Construct an open multi-dimensional "meshgrid" using indexing notation. Examples -------- >>> nx, ny = (3, 2) >>> x = np.linspace(0, 1, nx) >>> y = np.linspace(0, 1, ny) >>> xv, yv = np.meshgrid(x, y) >>> xv array([[0. , 0.5, 1. ], [0. , 0.5, 1. ]]) >>> yv array([[0., 0., 0.], [1., 1., 1.]]) >>> xv, yv = np.meshgrid(x, y, sparse=True) # make sparse output arrays >>> xv array([[0. , 0.5, 1. ]]) >>> yv array([[0.], [1.]]) `meshgrid` is very useful to evaluate functions on a grid. >>> import matplotlib.pyplot as plt >>> x = np.arange(-5, 5, 0.1) >>> y = np.arange(-5, 5, 0.1) >>> xx, yy = np.meshgrid(x, y, sparse=True) >>> z = np.sin(xx**2 + yy**2) / (xx**2 + yy**2) >>> h = plt.contourf(x, y, z) >>> plt.axis('scaled') >>> plt.show() ### min_scalar_type min_scalar_type(a) For scalar ``a``, returns the data type with the smallest size and smallest scalar kind which can hold its value. For non-scalar array ``a``, returns the vector's dtype unmodified. Floating point values are not demoted to integers, and complex values are not demoted to floats. Parameters ---------- a : scalar or array_like The value whose minimal data type is to be found. Returns ------- out : dtype The minimal data type. Notes ----- .. versionadded:: 1.6.0 See Also -------- result_type, promote_types, dtype, can_cast Examples -------- >>> [np.min_scalar_type(10)](https://www.chedong.com/phpMan.php/man/np.minscalartype/10/markdown) dtype('uint8') >>> np.min_scalar_type(-260) dtype('int16') >>> np.min_scalar_type(3.1) dtype('float16') >>> [np.min_scalar_type(1e50)](https://www.chedong.com/phpMan.php/man/np.minscalartype/1e50/markdown) dtype('float64') >>> np.min_scalar_type(np.arange(4,dtype='f8')) dtype('float64') ### mintypecode Return the character for the minimum-size type to which given types can be safely cast. The returned type character must represent the smallest size dtype such that an array of the returned type can handle the data from an array of all types in `typechars` (or if `typechars` is an array, then its dtype.char). Parameters ---------- typechars : list of str or array_like If a list of strings, each string should represent a dtype. If array_like, the character representation of the array dtype is used. typeset : str or list of str, optional The set of characters that the returned character is chosen from. The default set is 'GDFgdf'. default : str, optional The default character, this is returned if none of the characters in `typechars` matches a character in `typeset`. Returns ------- typechar : str The character representing the minimum-size type that was found. See Also -------- dtype, sctype2char, maximum_sctype Examples -------- >>> np.mintypecode(['d', 'f', 'S']) 'd' >>> x = np.array([1.1, 2-3.j]) >>> np.mintypecode(x) 'D' >>> np.mintypecode('abceh', default='G') 'G' ### moveaxis Move axes of an array to new positions. Other axes remain in their original order. .. versionadded:: 1.11.0 Parameters ---------- a : np.ndarray The array whose axes should be reordered. source : int or sequence of int Original positions of the axes to move. These must be unique. destination : int or sequence of int Destination positions for each of the original axes. These must also be unique. Returns ------- result : np.ndarray Array with moved axes. This array is a view of the input array. See Also -------- transpose : Permute the dimensions of an array. swapaxes : Interchange two axes of an array. Examples -------- >>> x = np.zeros((3, 4, 5)) >>> np.moveaxis(x, 0, -1).shape (4, 5, 3) >>> np.moveaxis(x, -1, 0).shape (5, 3, 4) These all achieve the same result: >>> np.transpose(x).shape (5, 4, 3) >>> np.swapaxes(x, 0, -1).shape (5, 4, 3) >>> np.moveaxis(x, [0, 1], [-1, -2]).shape (5, 4, 3) >>> np.moveaxis(x, [0, 1, 2], [-1, -2, -3]).shape (5, 4, 3) ### msort Return a copy of an array sorted along the first axis. Parameters ---------- a : array_like Array to be sorted. Returns ------- sorted_array : ndarray Array of the same type and shape as `a`. See Also -------- sort Notes ----- ``np.msort(a)`` is equivalent to ``np.sort(a, axis=0)``. ### nan_to_num Replace NaN with zero and infinity with large finite numbers (default behaviour) or with the numbers defined by the user using the `nan`, `posinf` and/or `neginf` keywords. If `x` is inexact, NaN is replaced by zero or by the user defined value in `nan` keyword, infinity is replaced by the largest finite floating point values representable by ``x.dtype`` or by the user defined value in `posinf` keyword and -infinity is replaced by the most negative finite floating point values representable by ``x.dtype`` or by the user defined value in `neginf` keyword. For complex dtypes, the above is applied to each of the real and imaginary components of `x` separately. If `x` is not inexact, then no replacements are made. Parameters ---------- x : scalar or array_like Input data. copy : bool, optional Whether to create a copy of `x` (True) or to replace values in-place (False). The in-place operation only occurs if casting to an array does not require a copy. Default is True. .. versionadded:: 1.13 nan : int, float, optional Value to be used to fill NaN values. If no value is passed then NaN values will be replaced with 0.0. .. versionadded:: 1.17 posinf : int, float, optional Value to be used to fill positive infinity values. If no value is passed then positive infinity values will be replaced with a very large number. .. versionadded:: 1.17 neginf : int, float, optional Value to be used to fill negative infinity values. If no value is passed then negative infinity values will be replaced with a very small (or negative) number. .. versionadded:: 1.17 Returns ------- out : ndarray `x`, with the non-finite values replaced. If `copy` is False, this may be `x` itself. See Also -------- isinf : Shows which elements are positive or negative infinity. isneginf : Shows which elements are negative infinity. isposinf : Shows which elements are positive infinity. isnan : Shows which elements are Not a Number (NaN). isfinite : Shows which elements are finite (not NaN, not infinity) Notes ----- NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754). This means that Not a Number is not equivalent to infinity. Examples -------- >>> np.nan_to_num(np.inf) 1.7976931348623157e+308 >>> np.nan_to_num(-np.inf) -1.7976931348623157e+308 >>> np.nan_to_num(np.nan) 0.0 >>> x = np.array([np.inf, -np.inf, np.nan, -128, 128]) >>> np.nan_to_num(x) array([ 1.79769313e+308, -1.79769313e+308, 0.00000000e+000, # may vary -1.28000000e+002, 1.28000000e+002]) >>> np.nan_to_num(x, nan=-9999, posinf=33333333, neginf=33333333) array([ 3.3333333e+07, 3.3333333e+07, -9.9990000e+03, -1.2800000e+02, 1.2800000e+02]) >>> y = np.array([complex(np.inf, np.nan), np.nan, complex(np.nan, np.inf)]) array([ 1.79769313e+308, -1.79769313e+308, 0.00000000e+000, # may vary -1.28000000e+002, 1.28000000e+002]) >>> np.nan_to_num(y) array([ 1.79769313e+308 +0.00000000e+000j, # may vary 0.00000000e+000 +0.00000000e+000j, 0.00000000e+000 +1.79769313e+308j]) >>> np.nan_to_num(y, nan=111111, posinf=222222) array([222222.+111111.j, 111111. +0.j, 111111.+222222.j]) ### nanargmax Return the indices of the maximum values in the specified axis ignoring NaNs. For all-NaN slices ``ValueError`` is raised. Warning: the results cannot be trusted if a slice contains only NaNs and -Infs. Parameters ---------- a : array_like Input data. axis : int, optional Axis along which to operate. By default flattened input is used. Returns ------- index_array : ndarray An array of indices or a single index value. See Also -------- argmax, nanargmin Examples -------- >>> a = np.array([[np.nan, 4], [2, 3]]) >>> np.argmax(a) 0 >>> np.nanargmax(a) 1 >>> np.nanargmax(a, axis=0) array([1, 0]) >>> np.nanargmax(a, axis=1) array([1, 1]) ### nanargmin Return the indices of the minimum values in the specified axis ignoring NaNs. For all-NaN slices ``ValueError`` is raised. Warning: the results cannot be trusted if a slice contains only NaNs and Infs. Parameters ---------- a : array_like Input data. axis : int, optional Axis along which to operate. By default flattened input is used. Returns ------- index_array : ndarray An array of indices or a single index value. See Also -------- argmin, nanargmax Examples -------- >>> a = np.array([[np.nan, 4], [2, 3]]) >>> np.argmin(a) 0 >>> np.nanargmin(a) 2 >>> np.nanargmin(a, axis=0) array([1, 1]) >>> np.nanargmin(a, axis=1) array([1, 0]) ### nancumprod Return the cumulative product of array elements over a given axis treating Not a Numbers (NaNs) as one. The cumulative product does not change when NaNs are encountered and leading NaNs are replaced by ones. Ones are returned for slices that are all-NaN or empty. .. versionadded:: 1.12.0 Parameters ---------- a : array_like Input array. axis : int, optional Axis along which the cumulative product is computed. By default the input is flattened. dtype : dtype, optional Type of the returned array, as well as of the accumulator in which the elements are multiplied. If *dtype* is not specified, it defaults to the dtype of `a`, unless `a` has an integer dtype with a precision less than that of the default platform integer. In that case, the default platform integer is used instead. out : ndarray, optional Alternative output array in which to place the result. It must have the same shape and buffer length as the expected output but the type of the resulting values will be cast if necessary. Returns ------- nancumprod : ndarray A new array holding the result is returned unless `out` is specified, in which case it is returned. See Also -------- numpy.cumprod : Cumulative product across array propagating NaNs. isnan : Show which elements are NaN. Examples -------- >>> [np.nancumprod(1)](https://www.chedong.com/phpMan.php/man/np.nancumprod/1/markdown) array([1]) >>> np.nancumprod([1]) array([1]) >>> np.nancumprod([1, np.nan]) array([1., 1.]) >>> a = np.array([[1, 2], [3, np.nan]]) >>> np.nancumprod(a) array([1., 2., 6., 6.]) >>> np.nancumprod(a, axis=0) array([[1., 2.], [3., 2.]]) >>> np.nancumprod(a, axis=1) array([[1., 2.], [3., 3.]]) ### nancumsum Return the cumulative sum of array elements over a given axis treating Not a Numbers (NaNs) as zero. The cumulative sum does not change when NaNs are encountered and leading NaNs are replaced by zeros. Zeros are returned for slices that are all-NaN or empty. .. versionadded:: 1.12.0 Parameters ---------- a : array_like Input array. axis : int, optional Axis along which the cumulative sum is computed. The default (None) is to compute the cumsum over the flattened array. dtype : dtype, optional Type of the returned array and of the accumulator in which the elements are summed. If `dtype` is not specified, it defaults to the dtype of `a`, unless `a` has an integer dtype with a precision less than that of the default platform integer. In that case, the default platform integer is used. out : ndarray, optional Alternative output array in which to place the result. It must have the same shape and buffer length as the expected output but the type will be cast if necessary. See :ref:`ufuncs-output-type` for more details. Returns ------- nancumsum : ndarray. A new array holding the result is returned unless `out` is specified, in which it is returned. The result has the same size as `a`, and the same shape as `a` if `axis` is not None or `a` is a 1-d array. See Also -------- numpy.cumsum : Cumulative sum across array propagating NaNs. isnan : Show which elements are NaN. Examples -------- >>> [np.nancumsum(1)](https://www.chedong.com/phpMan.php/man/np.nancumsum/1/markdown) array([1]) >>> np.nancumsum([1]) array([1]) >>> np.nancumsum([1, np.nan]) array([1., 1.]) >>> a = np.array([[1, 2], [3, np.nan]]) >>> np.nancumsum(a) array([1., 3., 6., 6.]) >>> np.nancumsum(a, axis=0) array([[1., 2.], [4., 2.]]) >>> np.nancumsum(a, axis=1) array([[1., 3.], [3., 3.]]) ### nanmax Return the maximum of an array or maximum along an axis, ignoring any NaNs. When all-NaN slices are encountered a ``RuntimeWarning`` is raised and NaN is returned for that slice. Parameters ---------- a : array_like Array containing numbers whose maximum is desired. If `a` is not an array, a conversion is attempted. axis : {int, tuple of int, None}, optional Axis or axes along which the maximum is computed. The default is to compute the maximum of the flattened array. out : ndarray, optional Alternate output array in which to place the result. The default is ``None``; if provided, it must have the same shape as the expected output, but the type will be cast if necessary. See :ref:`ufuncs-output-type` for more details. .. versionadded:: 1.8.0 keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `a`. If the value is anything but the default, then `keepdims` will be passed through to the `max` method of sub-classes of `ndarray`. If the sub-classes methods does not implement `keepdims` any exceptions will be raised. .. versionadded:: 1.8.0 Returns ------- nanmax : ndarray An array with the same shape as `a`, with the specified axis removed. If `a` is a 0-d array, or if axis is None, an ndarray scalar is returned. The same dtype as `a` is returned. See Also -------- nanmin : The minimum value of an array along a given axis, ignoring any NaNs. amax : The maximum value of an array along a given axis, propagating any NaNs. fmax : Element-wise maximum of two arrays, ignoring any NaNs. maximum : Element-wise maximum of two arrays, propagating any NaNs. isnan : Shows which elements are Not a Number (NaN). isfinite: Shows which elements are neither NaN nor infinity. amin, fmin, minimum Notes ----- NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754). This means that Not a Number is not equivalent to infinity. Positive infinity is treated as a very large number and negative infinity is treated as a very small (i.e. negative) number. If the input has a integer type the function is equivalent to np.max. Examples -------- >>> a = np.array([[1, 2], [3, np.nan]]) >>> np.nanmax(a) 3.0 >>> np.nanmax(a, axis=0) array([3., 2.]) >>> np.nanmax(a, axis=1) array([2., 3.]) When positive infinity and negative infinity are present: >>> np.nanmax([1, 2, np.nan, np.NINF]) 2.0 >>> np.nanmax([1, 2, np.nan, np.inf]) inf ### nanmean Compute the arithmetic mean along the specified axis, ignoring NaNs. Returns the average of the array elements. The average is taken over the flattened array by default, otherwise over the specified axis. `float64` intermediate and return values are used for integer inputs. For all-NaN slices, NaN is returned and a `RuntimeWarning` is raised. .. versionadded:: 1.8.0 Parameters ---------- a : array_like Array containing numbers whose mean is desired. If `a` is not an array, a conversion is attempted. axis : {int, tuple of int, None}, optional Axis or axes along which the means are computed. The default is to compute the mean of the flattened array. dtype : data-type, optional Type to use in computing the mean. For integer inputs, the default is `float64`; for inexact inputs, it is the same as the input dtype. out : ndarray, optional Alternate output array in which to place the result. The default is ``None``; if provided, it must have the same shape as the expected output, but the type will be cast if necessary. See :ref:`ufuncs-output-type` for more details. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `a`. If the value is anything but the default, then `keepdims` will be passed through to the `mean` or `sum` methods of sub-classes of `ndarray`. If the sub-classes methods does not implement `keepdims` any exceptions will be raised. Returns ------- m : ndarray, see dtype parameter above If `out=None`, returns a new array containing the mean values, otherwise a reference to the output array is returned. Nan is returned for slices that contain only NaNs. See Also -------- average : Weighted average mean : Arithmetic mean taken while not ignoring NaNs var, nanvar Notes ----- The arithmetic mean is the sum of the non-NaN elements along the axis divided by the number of non-NaN elements. Note that for floating-point input, the mean is computed using the same precision the input has. Depending on the input data, this can cause the results to be inaccurate, especially for `float32`. Specifying a higher-precision accumulator using the `dtype` keyword can alleviate this issue. Examples -------- >>> a = np.array([[1, np.nan], [3, 4]]) >>> np.nanmean(a) 2.6666666666666665 >>> np.nanmean(a, axis=0) array([2., 4.]) >>> np.nanmean(a, axis=1) array([1., 3.5]) # may vary ### nanmedian Compute the median along the specified axis, while ignoring NaNs. Returns the median of the array elements. .. versionadded:: 1.9.0 Parameters ---------- a : array_like Input array or object that can be converted to an array. axis : {int, sequence of int, None}, optional Axis or axes along which the medians are computed. The default is to compute the median along a flattened version of the array. A sequence of axes is supported since version 1.9.0. out : ndarray, optional Alternative output array in which to place the result. It must have the same shape and buffer length as the expected output, but the type (of the output) will be cast if necessary. overwrite_input : bool, optional If True, then allow use of memory of input array `a` for calculations. The input array will be modified by the call to `median`. This will save memory when you do not need to preserve the contents of the input array. Treat the input as undefined, but it will probably be fully or partially sorted. Default is False. If `overwrite_input` is ``True`` and `a` is not already an `ndarray`, an error will be raised. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `a`. If this is anything but the default value it will be passed through (in the special case of an empty array) to the `mean` function of the underlying array. If the array is a sub-class and `mean` does not have the kwarg `keepdims` this will raise a RuntimeError. Returns ------- median : ndarray A new array holding the result. If the input contains integers or floats smaller than ``float64``, then the output data-type is ``np.float64``. Otherwise, the data-type of the output is the same as that of the input. If `out` is specified, that array is returned instead. See Also -------- mean, median, percentile Notes ----- Given a vector ``V`` of length ``N``, the median of ``V`` is the middle value of a sorted copy of ``V``, ``V_sorted`` - i.e., ``V_sorted[(N-1)/2]``, when ``N`` is odd and the average of the two middle values of ``V_sorted`` when ``N`` is even. Examples -------- >>> a = np.array([[10.0, 7, 4], [3, 2, 1]]) >>> a[0, 1] = np.nan >>> a array([[10., nan, 4.], [ 3., 2., 1.]]) >>> np.median(a) nan >>> np.nanmedian(a) 3.0 >>> np.nanmedian(a, axis=0) array([6.5, 2. , 2.5]) >>> np.median(a, axis=1) array([nan, 2.]) >>> b = a.copy() >>> np.nanmedian(b, axis=1, overwrite_input=True) array([7., 2.]) >>> assert not np.all(a==b) >>> b = a.copy() >>> np.nanmedian(b, axis=None, overwrite_input=True) 3.0 >>> assert not np.all(a==b) ### nanmin Return minimum of an array or minimum along an axis, ignoring any NaNs. When all-NaN slices are encountered a ``RuntimeWarning`` is raised and Nan is returned for that slice. Parameters ---------- a : array_like Array containing numbers whose minimum is desired. If `a` is not an array, a conversion is attempted. axis : {int, tuple of int, None}, optional Axis or axes along which the minimum is computed. The default is to compute the minimum of the flattened array. out : ndarray, optional Alternate output array in which to place the result. The default is ``None``; if provided, it must have the same shape as the expected output, but the type will be cast if necessary. See :ref:`ufuncs-output-type` for more details. .. versionadded:: 1.8.0 keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `a`. If the value is anything but the default, then `keepdims` will be passed through to the `min` method of sub-classes of `ndarray`. If the sub-classes methods does not implement `keepdims` any exceptions will be raised. .. versionadded:: 1.8.0 Returns ------- nanmin : ndarray An array with the same shape as `a`, with the specified axis removed. If `a` is a 0-d array, or if axis is None, an ndarray scalar is returned. The same dtype as `a` is returned. See Also -------- nanmax : The maximum value of an array along a given axis, ignoring any NaNs. amin : The minimum value of an array along a given axis, propagating any NaNs. fmin : Element-wise minimum of two arrays, ignoring any NaNs. minimum : Element-wise minimum of two arrays, propagating any NaNs. isnan : Shows which elements are Not a Number (NaN). isfinite: Shows which elements are neither NaN nor infinity. amax, fmax, maximum Notes ----- NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754). This means that Not a Number is not equivalent to infinity. Positive infinity is treated as a very large number and negative infinity is treated as a very small (i.e. negative) number. If the input has a integer type the function is equivalent to np.min. Examples -------- >>> a = np.array([[1, 2], [3, np.nan]]) >>> np.nanmin(a) 1.0 >>> np.nanmin(a, axis=0) array([1., 2.]) >>> np.nanmin(a, axis=1) array([1., 3.]) When positive infinity and negative infinity are present: >>> np.nanmin([1, 2, np.nan, np.inf]) 1.0 >>> np.nanmin([1, 2, np.nan, np.NINF]) ### -inf ### nanpercentile Compute the qth percentile of the data along the specified axis, while ignoring nan values. Returns the qth percentile(s) of the array elements. .. versionadded:: 1.9.0 Parameters ---------- a : array_like Input array or object that can be converted to an array, containing nan values to be ignored. q : array_like of float Percentile or sequence of percentiles to compute, which must be between 0 and 100 inclusive. axis : {int, tuple of int, None}, optional Axis or axes along which the percentiles are computed. The default is to compute the percentile(s) along a flattened version of the array. out : ndarray, optional Alternative output array in which to place the result. It must have the same shape and buffer length as the expected output, but the type (of the output) will be cast if necessary. overwrite_input : bool, optional If True, then allow the input array `a` to be modified by intermediate calculations, to save memory. In this case, the contents of the input `a` after this function completes is undefined. interpolation : {'linear', 'lower', 'higher', 'midpoint', 'nearest'} This optional parameter specifies the interpolation method to use when the desired percentile lies between two data points ``i < j``: * 'linear': ``i + (j - i) * fraction``, where ``fraction`` is the fractional part of the index surrounded by ``i`` and ``j``. * 'lower': ``i``. * 'higher': ``j``. * 'nearest': ``i`` or ``j``, whichever is nearest. * 'midpoint': ``(i + j) / 2``. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original array `a`. If this is anything but the default value it will be passed through (in the special case of an empty array) to the `mean` function of the underlying array. If the array is a sub-class and `mean` does not have the kwarg `keepdims` this will raise a RuntimeError. Returns ------- percentile : scalar or ndarray If `q` is a single percentile and `axis=None`, then the result is a scalar. If multiple percentiles are given, first axis of the result corresponds to the percentiles. The other axes are the axes that remain after the reduction of `a`. If the input contains integers or floats smaller than ``float64``, the output data-type is ``float64``. Otherwise, the output data-type is the same as that of the input. If `out` is specified, that array is returned instead. See Also -------- nanmean nanmedian : equivalent to ``nanpercentile(..., 50)`` percentile, median, mean nanquantile : equivalent to nanpercentile, but with q in the range [0, 1]. Notes ----- Given a vector ``V`` of length ``N``, the ``q``-th percentile of ``V`` is the value ``q/100`` of the way from the minimum to the maximum in a sorted copy of ``V``. The values and distances of the two nearest neighbors as well as the `interpolation` parameter will determine the percentile if the normalized ranking does not match the location of ``q`` exactly. This function is the same as the median if ``q=50``, the same as the minimum if ``q=0`` and the same as the maximum if ``q=100``. Examples -------- >>> a = np.array([[10., 7., 4.], [3., 2., 1.]]) >>> a[0][1] = np.nan >>> a array([[10., nan, 4.], [ 3., 2., 1.]]) >>> np.percentile(a, 50) nan >>> np.nanpercentile(a, 50) 3.0 >>> np.nanpercentile(a, 50, axis=0) array([6.5, 2. , 2.5]) >>> np.nanpercentile(a, 50, axis=1, keepdims=True) array([[7.], [2.]]) >>> m = np.nanpercentile(a, 50, axis=0) >>> out = np.zeros_like(m) >>> np.nanpercentile(a, 50, axis=0, out=out) array([6.5, 2. , 2.5]) >>> m array([6.5, 2. , 2.5]) >>> b = a.copy() >>> np.nanpercentile(b, 50, axis=1, overwrite_input=True) array([7., 2.]) >>> assert not np.all(a==b) ### nanprod Return the product of array elements over a given axis treating Not a Numbers (NaNs) as ones. One is returned for slices that are all-NaN or empty. .. versionadded:: 1.10.0 Parameters ---------- a : array_like Array containing numbers whose product is desired. If `a` is not an array, a conversion is attempted. axis : {int, tuple of int, None}, optional Axis or axes along which the product is computed. The default is to compute the product of the flattened array. dtype : data-type, optional The type of the returned array and of the accumulator in which the elements are summed. By default, the dtype of `a` is used. An exception is when `a` has an integer type with less precision than the platform (u)intp. In that case, the default will be either (u)int32 or (u)int64 depending on whether the platform is 32 or 64 bits. For inexact inputs, dtype must be inexact. out : ndarray, optional Alternate output array in which to place the result. The default is ``None``. If provided, it must have the same shape as the expected output, but the type will be cast if necessary. See :ref:`ufuncs-output-type` for more details. The casting of NaN to integer can yield unexpected results. keepdims : bool, optional If True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `arr`. Returns ------- nanprod : ndarray A new array holding the result is returned unless `out` is specified, in which case it is returned. See Also -------- numpy.prod : Product across array propagating NaNs. isnan : Show which elements are NaN. Examples -------- >>> [np.nanprod(1)](https://www.chedong.com/phpMan.php/man/np.nanprod/1/markdown) 1 >>> np.nanprod([1]) 1 >>> np.nanprod([1, np.nan]) 1.0 >>> a = np.array([[1, 2], [3, np.nan]]) >>> np.nanprod(a) 6.0 >>> np.nanprod(a, axis=0) array([3., 2.]) ### nanquantile Compute the qth quantile of the data along the specified axis, while ignoring nan values. Returns the qth quantile(s) of the array elements. .. versionadded:: 1.15.0 Parameters ---------- a : array_like Input array or object that can be converted to an array, containing nan values to be ignored q : array_like of float Quantile or sequence of quantiles to compute, which must be between 0 and 1 inclusive. axis : {int, tuple of int, None}, optional Axis or axes along which the quantiles are computed. The default is to compute the quantile(s) along a flattened version of the array. out : ndarray, optional Alternative output array in which to place the result. It must have the same shape and buffer length as the expected output, but the type (of the output) will be cast if necessary. overwrite_input : bool, optional If True, then allow the input array `a` to be modified by intermediate calculations, to save memory. In this case, the contents of the input `a` after this function completes is undefined. interpolation : {'linear', 'lower', 'higher', 'midpoint', 'nearest'} This optional parameter specifies the interpolation method to use when the desired quantile lies between two data points ``i < j``: * linear: ``i + (j - i) * fraction``, where ``fraction`` is the fractional part of the index surrounded by ``i`` and ``j``. * lower: ``i``. * higher: ``j``. * nearest: ``i`` or ``j``, whichever is nearest. * midpoint: ``(i + j) / 2``. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original array `a`. If this is anything but the default value it will be passed through (in the special case of an empty array) to the `mean` function of the underlying array. If the array is a sub-class and `mean` does not have the kwarg `keepdims` this will raise a RuntimeError. Returns ------- quantile : scalar or ndarray If `q` is a single percentile and `axis=None`, then the result is a scalar. If multiple quantiles are given, first axis of the result corresponds to the quantiles. The other axes are the axes that remain after the reduction of `a`. If the input contains integers or floats smaller than ``float64``, the output data-type is ``float64``. Otherwise, the output data-type is the same as that of the input. If `out` is specified, that array is returned instead. See Also -------- quantile nanmean, nanmedian nanmedian : equivalent to ``nanquantile(..., 0.5)`` nanpercentile : same as nanquantile, but with q in the range [0, 100]. Examples -------- >>> a = np.array([[10., 7., 4.], [3., 2., 1.]]) >>> a[0][1] = np.nan >>> a array([[10., nan, 4.], [ 3., 2., 1.]]) >>> np.quantile(a, 0.5) nan >>> np.nanquantile(a, 0.5) 3.0 >>> np.nanquantile(a, 0.5, axis=0) array([6.5, 2. , 2.5]) >>> np.nanquantile(a, 0.5, axis=1, keepdims=True) array([[7.], [2.]]) >>> m = np.nanquantile(a, 0.5, axis=0) >>> out = np.zeros_like(m) >>> np.nanquantile(a, 0.5, axis=0, out=out) array([6.5, 2. , 2.5]) >>> m array([6.5, 2. , 2.5]) >>> b = a.copy() >>> np.nanquantile(b, 0.5, axis=1, overwrite_input=True) array([7., 2.]) >>> assert not np.all(a==b) ### nanstd Compute the standard deviation along the specified axis, while ignoring NaNs. Returns the standard deviation, a measure of the spread of a distribution, of the non-NaN array elements. The standard deviation is computed for the flattened array by default, otherwise over the specified axis. For all-NaN slices or slices with zero degrees of freedom, NaN is returned and a `RuntimeWarning` is raised. .. versionadded:: 1.8.0 Parameters ---------- a : array_like Calculate the standard deviation of the non-NaN values. axis : {int, tuple of int, None}, optional Axis or axes along which the standard deviation is computed. The default is to compute the standard deviation of the flattened array. dtype : dtype, optional Type to use in computing the standard deviation. For arrays of integer type the default is float64, for arrays of float types it is the same as the array type. out : ndarray, optional Alternative output array in which to place the result. It must have the same shape as the expected output but the type (of the calculated values) will be cast if necessary. ddof : int, optional Means Delta Degrees of Freedom. The divisor used in calculations is ``N - ddof``, where ``N`` represents the number of non-NaN elements. By default `ddof` is zero. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `a`. If this value is anything but the default it is passed through as-is to the relevant functions of the sub-classes. If these functions do not have a `keepdims` kwarg, a RuntimeError will be raised. Returns ------- standard_deviation : ndarray, see dtype parameter above. If `out` is None, return a new array containing the standard deviation, otherwise return a reference to the output array. If ddof is >= the number of non-NaN elements in a slice or the slice contains only NaNs, then the result for that slice is NaN. See Also -------- var, mean, std nanvar, nanmean :ref:`ufuncs-output-type` Notes ----- The standard deviation is the square root of the average of the squared deviations from the mean: ``std = sqrt(mean(abs(x - x.mean())**2))``. The average squared deviation is normally calculated as ``x.sum() / N``, where ``N = len(x)``. If, however, `ddof` is specified, the divisor ``N - ddof`` is used instead. In standard statistical practice, ``ddof=1`` provides an unbiased estimator of the variance of the infinite population. ``ddof=0`` provides a maximum likelihood estimate of the variance for normally distributed variables. The standard deviation computed in this function is the square root of the estimated variance, so even with ``ddof=1``, it will not be an unbiased estimate of the standard deviation per se. Note that, for complex numbers, `std` takes the absolute value before squaring, so that the result is always real and nonnegative. For floating-point input, the *std* is computed using the same precision the input has. Depending on the input data, this can cause the results to be inaccurate, especially for float32 (see example below). Specifying a higher-accuracy accumulator using the `dtype` keyword can alleviate this issue. Examples -------- >>> a = np.array([[1, np.nan], [3, 4]]) >>> np.nanstd(a) 1.247219128924647 >>> np.nanstd(a, axis=0) array([1., 0.]) >>> np.nanstd(a, axis=1) array([0., 0.5]) # may vary ### nansum Return the sum of array elements over a given axis treating Not a Numbers (NaNs) as zero. In NumPy versions <= 1.9.0 Nan is returned for slices that are all-NaN or empty. In later versions zero is returned. Parameters ---------- a : array_like Array containing numbers whose sum is desired. If `a` is not an array, a conversion is attempted. axis : {int, tuple of int, None}, optional Axis or axes along which the sum is computed. The default is to compute the sum of the flattened array. dtype : data-type, optional The type of the returned array and of the accumulator in which the elements are summed. By default, the dtype of `a` is used. An exception is when `a` has an integer type with less precision than the platform (u)intp. In that case, the default will be either (u)int32 or (u)int64 depending on whether the platform is 32 or 64 bits. For inexact inputs, dtype must be inexact. .. versionadded:: 1.8.0 out : ndarray, optional Alternate output array in which to place the result. The default is ``None``. If provided, it must have the same shape as the expected output, but the type will be cast if necessary. See :ref:`ufuncs-output-type` for more details. The casting of NaN to integer can yield unexpected results. .. versionadded:: 1.8.0 keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `a`. If the value is anything but the default, then `keepdims` will be passed through to the `mean` or `sum` methods of sub-classes of `ndarray`. If the sub-classes methods does not implement `keepdims` any exceptions will be raised. .. versionadded:: 1.8.0 Returns ------- nansum : ndarray. A new array holding the result is returned unless `out` is specified, in which it is returned. The result has the same size as `a`, and the same shape as `a` if `axis` is not None or `a` is a 1-d array. See Also -------- numpy.sum : Sum across array propagating NaNs. isnan : Show which elements are NaN. isfinite : Show which elements are not NaN or +/-inf. Notes ----- If both positive and negative infinity are present, the sum will be Not A Number (NaN). Examples -------- >>> [np.nansum(1)](https://www.chedong.com/phpMan.php/man/np.nansum/1/markdown) 1 >>> np.nansum([1]) 1 >>> np.nansum([1, np.nan]) 1.0 >>> a = np.array([[1, 1], [1, np.nan]]) >>> np.nansum(a) 3.0 >>> np.nansum(a, axis=0) array([2., 1.]) >>> np.nansum([1, np.nan, np.inf]) inf >>> np.nansum([1, np.nan, np.NINF]) ### -inf >>> from numpy.testing import suppress_warnings >>> with suppress_warnings() as sup: ... sup.filter(RuntimeWarning) ... np.nansum([1, np.nan, np.inf, -np.inf]) # both +/- infinity present nan ### nanvar Compute the variance along the specified axis, while ignoring NaNs. Returns the variance of the array elements, a measure of the spread of a distribution. The variance is computed for the flattened array by default, otherwise over the specified axis. For all-NaN slices or slices with zero degrees of freedom, NaN is returned and a `RuntimeWarning` is raised. .. versionadded:: 1.8.0 Parameters ---------- a : array_like Array containing numbers whose variance is desired. If `a` is not an array, a conversion is attempted. axis : {int, tuple of int, None}, optional Axis or axes along which the variance is computed. The default is to compute the variance of the flattened array. dtype : data-type, optional Type to use in computing the variance. For arrays of integer type the default is `float64`; for arrays of float types it is the same as the array type. out : ndarray, optional Alternate output array in which to place the result. It must have the same shape as the expected output, but the type is cast if necessary. ddof : int, optional "Delta Degrees of Freedom": the divisor used in the calculation is ``N - ddof``, where ``N`` represents the number of non-NaN elements. By default `ddof` is zero. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `a`. Returns ------- variance : ndarray, see dtype parameter above If `out` is None, return a new array containing the variance, otherwise return a reference to the output array. If ddof is >= the number of non-NaN elements in a slice or the slice contains only NaNs, then the result for that slice is NaN. See Also -------- std : Standard deviation mean : Average var : Variance while not ignoring NaNs nanstd, nanmean :ref:`ufuncs-output-type` Notes ----- The variance is the average of the squared deviations from the mean, i.e., ``var = mean(abs(x - x.mean())**2)``. The mean is normally calculated as ``x.sum() / N``, where ``N = len(x)``. If, however, `ddof` is specified, the divisor ``N - ddof`` is used instead. In standard statistical practice, ``ddof=1`` provides an unbiased estimator of the variance of a hypothetical infinite population. ``ddof=0`` provides a maximum likelihood estimate of the variance for normally distributed variables. Note that for complex numbers, the absolute value is taken before squaring, so that the result is always real and nonnegative. For floating-point input, the variance is computed using the same precision the input has. Depending on the input data, this can cause the results to be inaccurate, especially for `float32` (see example below). Specifying a higher-accuracy accumulator using the ``dtype`` keyword can alleviate this issue. For this function to work on sub-classes of ndarray, they must define `sum` with the kwarg `keepdims` Examples -------- >>> a = np.array([[1, np.nan], [3, 4]]) >>> np.nanvar(a) 1.5555555555555554 >>> np.nanvar(a, axis=0) array([1., 0.]) >>> np.nanvar(a, axis=1) array([0., 0.25]) # may vary ### ndfromtxt Load ASCII data stored in a file and return it as a single array. .. deprecated:: 1.17 ndfromtxt` is a deprecated alias of `genfromtxt` which overwrites the ``usemask`` argument with `False` even when explicitly called as ``ndfromtxt(..., usemask=True)``. Use `genfromtxt` instead. Parameters ---------- fname, kwargs : For a description of input parameters, see `genfromtxt`. See Also -------- numpy.genfromtxt : generic function. ### ndim Return the number of dimensions of an array. Parameters ---------- a : array_like Input array. If it is not already an ndarray, a conversion is attempted. Returns ------- number_of_dimensions : int The number of dimensions in `a`. Scalars are zero-dimensional. See Also -------- ndarray.ndim : equivalent method shape : dimensions of array ndarray.shape : dimensions of array Examples -------- >>> np.ndim([[1,2,3],[4,5,6]]) 2 >>> np.ndim(np.array([[1,2,3],[4,5,6]])) 2 >>> [np.ndim(1)](https://www.chedong.com/phpMan.php/man/np.ndim/1/markdown) 0 ### nested_iters Create nditers for use in nested loops Create a tuple of `nditer` objects which iterate in nested loops over different axes of the op argument. The first iterator is used in the outermost loop, the last in the innermost loop. Advancing one will change the subsequent iterators to point at its new element. Parameters ---------- op : ndarray or sequence of array_like The array(s) to iterate over. axes : list of list of int Each item is used as an "op_axes" argument to an nditer flags, op_flags, op_dtypes, order, casting, buffersize (optional) See `nditer` parameters of the same name Returns ------- iters : tuple of nditer An nditer for each item in `axes`, outermost first See Also -------- nditer Examples -------- Basic usage. Note how y is the "flattened" version of [a[:, 0, :], a[:, 1, 0], a[:, 2, :]] since we specified the first iter's axes as [1] >>> a = [np.arange(12)](https://www.chedong.com/phpMan.php/man/np.arange/12/markdown).reshape(2, 3, 2) >>> i, j = np.nested_iters(a, [[1], [0, 2]], flags=["multi_index"]) >>> for x in i: ... print(i.multi_index) ... for y in j: ... print('', j.multi_index, y) (0,) (0, 0) 0 (0, 1) 1 (1, 0) 6 (1, 1) 7 (1,) (0, 0) 2 (0, 1) 3 (1, 0) 8 (1, 1) 9 (2,) (0, 0) 4 (0, 1) 5 (1, 0) 10 (1, 1) 11 ### nonzero Return the indices of the elements that are non-zero. Returns a tuple of arrays, one for each dimension of `a`, containing the indices of the non-zero elements in that dimension. The values in `a` are always tested and returned in row-major, C-style order. To group the indices by element, rather than dimension, use `argwhere`, which returns a row for each non-zero element. .. note:: When called on a zero-d array or scalar, ``nonzero(a)`` is treated as ``nonzero(atleast_1d(a))``. .. deprecated:: 1.17.0 Use `atleast_1d` explicitly if this behavior is deliberate. Parameters ---------- a : array_like Input array. Returns ------- tuple_of_arrays : tuple Indices of elements that are non-zero. See Also -------- flatnonzero : Return indices that are non-zero in the flattened version of the input array. ndarray.nonzero : Equivalent ndarray method. count_nonzero : Counts the number of non-zero elements in the input array. Notes ----- While the nonzero values can be obtained with ``a[nonzero(a)]``, it is recommended to use ``x[x.astype(bool)]`` or ``x[x != 0]`` instead, which will correctly handle 0-d arrays. Examples -------- >>> x = np.array([[3, 0, 0], [0, 4, 0], [5, 6, 0]]) >>> x array([[3, 0, 0], [0, 4, 0], [5, 6, 0]]) >>> np.nonzero(x) (array([0, 1, 2, 2]), array([0, 1, 0, 1])) >>> x[np.nonzero(x)] array([3, 4, 5, 6]) >>> np.transpose(np.nonzero(x)) array([[0, 0], [1, 1], [2, 0], [2, 1]]) A common use for ``nonzero`` is to find the indices of an array, where a condition is True. Given an array `a`, the condition `a` > 3 is a boolean array and since False is interpreted as 0, np.nonzero(a > 3) yields the indices of the `a` where the condition is true. >>> a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) >>> a > 3 array([[False, False, False], [ True, True, True], [ True, True, True]]) >>> np.nonzero(a > 3) (array([1, 1, 1, 2, 2, 2]), array([0, 1, 2, 0, 1, 2])) Using this result to index `a` is equivalent to using the mask directly: >>> a[np.nonzero(a > 3)] array([4, 5, 6, 7, 8, 9]) >>> a[a > 3] # prefer this spelling array([4, 5, 6, 7, 8, 9]) ``nonzero`` can also be called as a method of the array. >>> (a > 3).nonzero() (array([1, 1, 1, 2, 2, 2]), array([0, 1, 2, 0, 1, 2])) ### obj2sctype Return the scalar dtype or NumPy equivalent of Python type of an object. Parameters ---------- rep : any The object of which the type is returned. default : any, optional If given, this is returned for objects whose types can not be determined. If not given, None is returned for those objects. Returns ------- dtype : dtype or Python type The data type of `rep`. See Also -------- sctype2char, issctype, issubsctype, issubdtype, maximum_sctype Examples -------- >>> np.obj2sctype(np.int32) >>> np.obj2sctype(np.array([1., 2.])) >>> np.obj2sctype(np.array([1.j])) >>> np.obj2sctype(dict) >>> np.obj2sctype('string') >>> np.obj2sctype(1, default=list) ### ones Return a new array of given shape and type, filled with ones. Parameters ---------- shape : int or sequence of ints Shape of the new array, e.g., ``(2, 3)`` or ``2``. dtype : data-type, optional The desired data-type for the array, e.g., `numpy.int8`. Default is `numpy.float64`. order : {'C', 'F'}, optional, default: C Whether to store multi-dimensional data in row-major (C-style) or column-major (Fortran-style) order in memory. like : array_like Reference object to allow the creation of arrays which are not NumPy arrays. If an array-like passed in as ``like`` supports the ``__array_function__`` protocol, the result will be defined by it. In this case, it ensures the creation of an array object compatible with that passed in via this argument. .. versionadded:: 1.20.0 Returns ------- out : ndarray Array of ones with the given shape, dtype, and order. See Also -------- ones_like : Return an array of ones with shape and type of input. empty : Return a new uninitialized array. zeros : Return a new array setting values to zero. full : Return a new array of given shape filled with value. Examples -------- >>> [np.ones(5)](https://www.chedong.com/phpMan.php/man/np.ones/5/markdown) array([1., 1., 1., 1., 1.]) >>> np.ones((5,), dtype=int) array([1, 1, 1, 1, 1]) >>> np.ones((2, 1)) array([[1.], [1.]]) >>> s = (2,2) >>> np.ones(s) array([[1., 1.], [1., 1.]]) ### ones_like Return an array of ones with the same shape and type as a given array. Parameters ---------- a : array_like The shape and data-type of `a` define these same attributes of the returned array. dtype : data-type, optional Overrides the data type of the result. .. versionadded:: 1.6.0 order : {'C', 'F', 'A', or 'K'}, optional Overrides the memory layout of the result. 'C' means C-order, 'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous, 'C' otherwise. 'K' means match the layout of `a` as closely as possible. .. versionadded:: 1.6.0 subok : bool, optional. If True, then the newly created array will use the sub-class type of `a`, otherwise it will be a base-class array. Defaults to True. shape : int or sequence of ints, optional. Overrides the shape of the result. If order='K' and the number of dimensions is unchanged, will try to keep order, otherwise, order='C' is implied. .. versionadded:: 1.17.0 Returns ------- out : ndarray Array of ones with the same shape and type as `a`. See Also -------- empty_like : Return an empty array with shape and type of input. zeros_like : Return an array of zeros with shape and type of input. full_like : Return a new array with shape of input filled with value. ones : Return a new array setting values to one. Examples -------- >>> x = [np.arange(6)](https://www.chedong.com/phpMan.php/man/np.arange/6/markdown) >>> x = x.reshape((2, 3)) >>> x array([[0, 1, 2], [3, 4, 5]]) >>> np.ones_like(x) array([[1, 1, 1], [1, 1, 1]]) >>> y = np.arange(3, dtype=float) >>> y array([0., 1., 2.]) >>> np.ones_like(y) array([1., 1., 1.]) ### outer Compute the outer product of two vectors. Given two vectors, ``a = [a0, a1, ..., aM]`` and ``b = [b0, b1, ..., bN]``, the outer product [1]_ is:: [[a0*b0 a0*b1 ... a0*bN ] [a1*b0 . [ ... . [aM*b0 aM*bN ]] Parameters ---------- a : (M,) array_like First input vector. Input is flattened if not already 1-dimensional. b : (N,) array_like Second input vector. Input is flattened if not already 1-dimensional. out : (M, N) ndarray, optional A location where the result is stored .. versionadded:: 1.9.0 Returns ------- out : (M, N) ndarray ``out[i, j] = a[i] * b[j]`` See also -------- inner einsum : ``einsum('i,j->ij', a.ravel(), b.ravel())`` is the equivalent. ufunc.outer : A generalization to dimensions other than 1D and other operations. ``np.multiply.outer(a.ravel(), b.ravel())`` is the equivalent. tensordot : ``np.tensordot(a.ravel(), b.ravel(), axes=((), ()))`` is the equivalent. References ---------- .. [1] : G. H. Golub and C. F. Van Loan, *Matrix Computations*, 3rd ed., Baltimore, MD, Johns Hopkins University Press, 1996, pg. 8. Examples -------- Make a (*very* coarse) grid for computing a Mandelbrot set: >>> rl = np.outer(np.ones((5,)), np.linspace(-2, 2, 5)) >>> rl array([[-2., -1., 0., 1., 2.], [-2., -1., 0., 1., 2.], [-2., -1., 0., 1., 2.], [-2., -1., 0., 1., 2.], [-2., -1., 0., 1., 2.]]) >>> im = np.outer(1j*np.linspace(2, -2, 5), np.ones((5,))) >>> im array([[0.+2.j, 0.+2.j, 0.+2.j, 0.+2.j, 0.+2.j], [0.+1.j, 0.+1.j, 0.+1.j, 0.+1.j, 0.+1.j], [0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j], [0.-1.j, 0.-1.j, 0.-1.j, 0.-1.j, 0.-1.j], [0.-2.j, 0.-2.j, 0.-2.j, 0.-2.j, 0.-2.j]]) >>> grid = rl + im >>> grid array([[-2.+2.j, -1.+2.j, 0.+2.j, 1.+2.j, 2.+2.j], [-2.+1.j, -1.+1.j, 0.+1.j, 1.+1.j, 2.+1.j], [-2.+0.j, -1.+0.j, 0.+0.j, 1.+0.j, 2.+0.j], [-2.-1.j, -1.-1.j, 0.-1.j, 1.-1.j, 2.-1.j], [-2.-2.j, -1.-2.j, 0.-2.j, 1.-2.j, 2.-2.j]]) An example using a "vector" of letters: >>> x = np.array(['a', 'b', 'c'], dtype=object) >>> np.outer(x, [1, 2, 3]) array([['a', 'aa', 'aaa'], ['b', 'bb', 'bbb'], ['c', 'cc', 'ccc']], dtype=object) ### packbits packbits(a, axis=None, bitorder='big') Packs the elements of a binary-valued array into bits in a uint8 array. The result is padded to full bytes by inserting zero bits at the end. Parameters ---------- a : array_like An array of integers or booleans whose elements should be packed to bits. axis : int, optional The dimension over which bit-packing is done. ``None`` implies packing the flattened array. bitorder : {'big', 'little'}, optional The order of the input bits. 'big' will mimic bin(val), ``[0, 0, 0, 0, 0, 0, 1, 1] => 3 = 0b00000011``, 'little' will reverse the order so ``[1, 1, 0, 0, 0, 0, 0, 0] => 3``. Defaults to 'big'. .. versionadded:: 1.17.0 Returns ------- packed : ndarray Array of type uint8 whose elements represent bits corresponding to the logical (0 or nonzero) value of the input elements. The shape of `packed` has the same number of dimensions as the input (unless `axis` is None, in which case the output is 1-D). See Also -------- unpackbits: Unpacks elements of a uint8 array into a binary-valued output array. Examples -------- >>> a = np.array([[[1,0,1], ... [0,1,0]], ... [[1,1,0], ... [0,0,1]]]) >>> b = np.packbits(a, axis=-1) >>> b array([[[160], [ 64]], [[192], [ 32]]], dtype=uint8) Note that in binary 160 = 1010 0000, 64 = 0100 0000, 192 = 1100 0000, and 32 = 0010 0000. ### pad Pad an array. Parameters ---------- array : array_like of rank N The array to pad. pad_width : {sequence, array_like, int} Number of values padded to the edges of each axis. ((before_1, after_1), ... (before_N, after_N)) unique pad widths for each axis. ((before, after),) yields same before and after pad for each axis. (pad,) or int is a shortcut for before = after = pad width for all axes. mode : str or function, optional One of the following string values or a user supplied function. 'constant' (default) Pads with a constant value. 'edge' Pads with the edge values of array. 'linear_ramp' Pads with the linear ramp between end_value and the array edge value. 'maximum' Pads with the maximum value of all or part of the vector along each axis. 'mean' Pads with the mean value of all or part of the vector along each axis. 'median' Pads with the median value of all or part of the vector along each axis. 'minimum' Pads with the minimum value of all or part of the vector along each axis. 'reflect' Pads with the reflection of the vector mirrored on the first and last values of the vector along each axis. 'symmetric' Pads with the reflection of the vector mirrored along the edge of the array. 'wrap' Pads with the wrap of the vector along the axis. The first values are used to pad the end and the end values are used to pad the beginning. 'empty' Pads with undefined values. .. versionadded:: 1.17 Padding function, see Notes. stat_length : sequence or int, optional Used in 'maximum', 'mean', 'median', and 'minimum'. Number of values at edge of each axis used to calculate the statistic value. ((before_1, after_1), ... (before_N, after_N)) unique statistic lengths for each axis. ((before, after),) yields same before and after statistic lengths for each axis. (stat_length,) or int is a shortcut for before = after = statistic length for all axes. Default is ``None``, to use the entire axis. constant_values : sequence or scalar, optional Used in 'constant'. The values to set the padded values for each axis. ``((before_1, after_1), ... (before_N, after_N))`` unique pad constants for each axis. ``((before, after),)`` yields same before and after constants for each axis. ``(constant,)`` or ``constant`` is a shortcut for ``before = after = constant`` for all axes. Default is 0. end_values : sequence or scalar, optional Used in 'linear_ramp'. The values used for the ending value of the linear_ramp and that will form the edge of the padded array. ``((before_1, after_1), ... (before_N, after_N))`` unique end values for each axis. ``((before, after),)`` yields same before and after end values for each axis. ``(constant,)`` or ``constant`` is a shortcut for ``before = after = constant`` for all axes. Default is 0. reflect_type : {'even', 'odd'}, optional Used in 'reflect', and 'symmetric'. The 'even' style is the default with an unaltered reflection around the edge value. For the 'odd' style, the extended part of the array is created by subtracting the reflected values from two times the edge value. Returns ------- pad : ndarray Padded array of rank equal to `array` with shape increased according to `pad_width`. Notes ----- .. versionadded:: 1.7.0 For an array with rank greater than 1, some of the padding of later axes is calculated from padding of previous axes. This is easiest to think about with a rank 2 array where the corners of the padded array are calculated by using padded values from the first axis. The padding function, if used, should modify a rank 1 array in-place. It has the following signature:: padding_func(vector, iaxis_pad_width, iaxis, kwargs) where vector : ndarray A rank 1 array already padded with zeros. Padded values are vector[:iaxis_pad_width[0]] and vector[-iaxis_pad_width[1]:]. iaxis_pad_width : tuple A 2-tuple of ints, iaxis_pad_width[0] represents the number of values padded at the beginning of vector where iaxis_pad_width[1] represents the number of values padded at the end of vector. iaxis : int The axis currently being calculated. kwargs : dict Any keyword arguments the function requires. Examples -------- >>> a = [1, 2, 3, 4, 5] >>> np.pad(a, (2, 3), 'constant', constant_values=(4, 6)) array([4, 4, 1, ..., 6, 6, 6]) >>> np.pad(a, (2, 3), 'edge') array([1, 1, 1, ..., 5, 5, 5]) >>> np.pad(a, (2, 3), 'linear_ramp', end_values=(5, -4)) array([ 5, 3, 1, 2, 3, 4, 5, 2, -1, -4]) >>> np.pad(a, (2,), 'maximum') array([5, 5, 1, 2, 3, 4, 5, 5, 5]) >>> np.pad(a, (2,), 'mean') array([3, 3, 1, 2, 3, 4, 5, 3, 3]) >>> np.pad(a, (2,), 'median') array([3, 3, 1, 2, 3, 4, 5, 3, 3]) >>> a = [[1, 2], [3, 4]] >>> np.pad(a, ((3, 2), (2, 3)), 'minimum') array([[1, 1, 1, 2, 1, 1, 1], [1, 1, 1, 2, 1, 1, 1], [1, 1, 1, 2, 1, 1, 1], [1, 1, 1, 2, 1, 1, 1], [3, 3, 3, 4, 3, 3, 3], [1, 1, 1, 2, 1, 1, 1], [1, 1, 1, 2, 1, 1, 1]]) >>> a = [1, 2, 3, 4, 5] >>> np.pad(a, (2, 3), 'reflect') array([3, 2, 1, 2, 3, 4, 5, 4, 3, 2]) >>> np.pad(a, (2, 3), 'reflect', reflect_type='odd') array([-1, 0, 1, 2, 3, 4, 5, 6, 7, 8]) >>> np.pad(a, (2, 3), 'symmetric') array([2, 1, 1, 2, 3, 4, 5, 5, 4, 3]) >>> np.pad(a, (2, 3), 'symmetric', reflect_type='odd') array([0, 1, 1, 2, 3, 4, 5, 5, 6, 7]) >>> np.pad(a, (2, 3), 'wrap') array([4, 5, 1, 2, 3, 4, 5, 1, 2, 3]) >>> def pad_with(vector, pad_width, iaxis, kwargs): ... pad_value = kwargs.get('padder', 10) ... vector[:pad_width[0]] = pad_value ... vector[-pad_width[1]:] = pad_value >>> a = [np.arange(6)](https://www.chedong.com/phpMan.php/man/np.arange/6/markdown) >>> a = a.reshape((2, 3)) >>> np.pad(a, 2, pad_with) array([[10, 10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10, 10, 10], [10, 10, 0, 1, 2, 10, 10], [10, 10, 3, 4, 5, 10, 10], [10, 10, 10, 10, 10, 10, 10], [10, 10, 10, 10, 10, 10, 10]]) >>> np.pad(a, 2, pad_with, padder=100) array([[100, 100, 100, 100, 100, 100, 100], [100, 100, 100, 100, 100, 100, 100], [100, 100, 0, 1, 2, 100, 100], [100, 100, 3, 4, 5, 100, 100], [100, 100, 100, 100, 100, 100, 100], [100, 100, 100, 100, 100, 100, 100]]) ### partition Return a partitioned copy of an array. Creates a copy of the array with its elements rearranged in such a way that the value of the element in k-th position is in the position it would be in a sorted array. All elements smaller than the k-th element are moved before this element and all equal or greater are moved behind it. The ordering of the elements in the two partitions is undefined. .. versionadded:: 1.8.0 Parameters ---------- a : array_like Array to be sorted. kth : int or sequence of ints Element index to partition by. The k-th value of the element will be in its final sorted position and all smaller elements will be moved before it and all equal or greater elements behind it. The order of all elements in the partitions is undefined. If provided with a sequence of k-th it will partition all elements indexed by k-th of them into their sorted position at once. axis : int or None, optional Axis along which to sort. If None, the array is flattened before sorting. The default is -1, which sorts along the last axis. kind : {'introselect'}, optional Selection algorithm. Default is 'introselect'. order : str or list of str, optional When `a` is an array with fields defined, this argument specifies which fields to compare first, second, etc. A single field can be specified as a string. Not all fields need be specified, but unspecified fields will still be used, in the order in which they come up in the dtype, to break ties. Returns ------- partitioned_array : ndarray Array of the same type and shape as `a`. See Also -------- ndarray.partition : Method to sort an array in-place. argpartition : Indirect partition. sort : Full sorting Notes ----- The various selection algorithms are characterized by their average speed, worst case performance, work space size, and whether they are stable. A stable sort keeps items with the same key in the same relative order. The available algorithms have the following properties: ================= ======= ============= ============ ======= kind speed worst case work space stable ================= ======= ============= ============ ======= 'introselect' 1 [O(n)](https://www.chedong.com/phpMan.php/man/O/n/markdown) 0 no ================= ======= ============= ============ ======= All the partition algorithms make temporary copies of the data when partitioning along any but the last axis. Consequently, partitioning along the last axis is faster and uses less space than partitioning along any other axis. The sort order for complex numbers is lexicographic. If both the real and imaginary parts are non-nan then the order is determined by the real parts except when they are equal, in which case the order is determined by the imaginary parts. Examples -------- >>> a = np.array([3, 4, 2, 1]) >>> np.partition(a, 3) array([2, 1, 3, 4]) >>> np.partition(a, (1, 3)) array([1, 2, 3, 4]) ### percentile Compute the q-th percentile of the data along the specified axis. Returns the q-th percentile(s) of the array elements. Parameters ---------- a : array_like Input array or object that can be converted to an array. q : array_like of float Percentile or sequence of percentiles to compute, which must be between 0 and 100 inclusive. axis : {int, tuple of int, None}, optional Axis or axes along which the percentiles are computed. The default is to compute the percentile(s) along a flattened version of the array. .. versionchanged:: 1.9.0 A tuple of axes is supported out : ndarray, optional Alternative output array in which to place the result. It must have the same shape and buffer length as the expected output, but the type (of the output) will be cast if necessary. overwrite_input : bool, optional If True, then allow the input array `a` to be modified by intermediate calculations, to save memory. In this case, the contents of the input `a` after this function completes is undefined. interpolation : {'linear', 'lower', 'higher', 'midpoint', 'nearest'} This optional parameter specifies the interpolation method to use when the desired percentile lies between two data points ``i < j``: * 'linear': ``i + (j - i) * fraction``, where ``fraction`` is the fractional part of the index surrounded by ``i`` and ``j``. * 'lower': ``i``. * 'higher': ``j``. * 'nearest': ``i`` or ``j``, whichever is nearest. * 'midpoint': ``(i + j) / 2``. .. versionadded:: 1.9.0 keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original array `a`. .. versionadded:: 1.9.0 Returns ------- percentile : scalar or ndarray If `q` is a single percentile and `axis=None`, then the result is a scalar. If multiple percentiles are given, first axis of the result corresponds to the percentiles. The other axes are the axes that remain after the reduction of `a`. If the input contains integers or floats smaller than ``float64``, the output data-type is ``float64``. Otherwise, the output data-type is the same as that of the input. If `out` is specified, that array is returned instead. See Also -------- mean median : equivalent to ``percentile(..., 50)`` nanpercentile quantile : equivalent to percentile, except with q in the range [0, 1]. Notes ----- Given a vector ``V`` of length ``N``, the q-th percentile of ``V`` is the value ``q/100`` of the way from the minimum to the maximum in a sorted copy of ``V``. The values and distances of the two nearest neighbors as well as the `interpolation` parameter will determine the percentile if the normalized ranking does not match the location of ``q`` exactly. This function is the same as the median if ``q=50``, the same as the minimum if ``q=0`` and the same as the maximum if ``q=100``. Examples -------- >>> a = np.array([[10, 7, 4], [3, 2, 1]]) >>> a array([[10, 7, 4], [ 3, 2, 1]]) >>> np.percentile(a, 50) 3.5 >>> np.percentile(a, 50, axis=0) array([6.5, 4.5, 2.5]) >>> np.percentile(a, 50, axis=1) array([7., 2.]) >>> np.percentile(a, 50, axis=1, keepdims=True) array([[7.], [2.]]) >>> m = np.percentile(a, 50, axis=0) >>> out = np.zeros_like(m) >>> np.percentile(a, 50, axis=0, out=out) array([6.5, 4.5, 2.5]) >>> m array([6.5, 4.5, 2.5]) >>> b = a.copy() >>> np.percentile(b, 50, axis=1, overwrite_input=True) array([7., 2.]) >>> assert not np.all(a == b) The different types of interpolation can be visualized graphically: .. plot:: import matplotlib.pyplot as plt a = [np.arange(4)](https://www.chedong.com/phpMan.php/man/np.arange/4/markdown) p = np.linspace(0, 100, 6001) ax = plt.gca() lines = [ ('linear', None), ('higher', '--'), ('lower', '--'), ('nearest', '-.'), ('midpoint', '-.'), ] for interpolation, style in lines: ax.plot( p, np.percentile(a, p, interpolation=interpolation), label=interpolation, linestyle=style) ax.set( title='Interpolation methods for list: ' + str(a), xlabel='Percentile', ylabel='List item returned', yticks=a) ax.legend() plt.show() ### piecewise Evaluate a piecewise-defined function. Given a set of conditions and corresponding functions, evaluate each function on the input data wherever its condition is true. Parameters ---------- x : ndarray or scalar The input domain. condlist : list of bool arrays or bool scalars Each boolean array corresponds to a function in `funclist`. Wherever `condlist[i]` is True, `funclist[i](x)` is used as the output value. Each boolean array in `condlist` selects a piece of `x`, and should therefore be of the same shape as `x`. The length of `condlist` must correspond to that of `funclist`. If one extra function is given, i.e. if ``len(funclist) == len(condlist) + 1``, then that extra function is the default value, used wherever all conditions are false. funclist : list of callables, f(x,*args,**kw), or scalars Each function is evaluated over `x` wherever its corresponding condition is True. It should take a 1d array as input and give an 1d array or a scalar value as output. If, instead of a callable, a scalar is provided then a constant function (``lambda x: scalar``) is assumed. args : tuple, optional Any further arguments given to `piecewise` are passed to the functions upon execution, i.e., if called ``piecewise(..., ..., 1, 'a')``, then each function is called as ``f(x, 1, 'a')``. kw : dict, optional Keyword arguments used in calling `piecewise` are passed to the functions upon execution, i.e., if called ``piecewise(..., ..., alpha=1)``, then each function is called as ``f(x, alpha=1)``. Returns ------- out : ndarray The output is the same shape and type as x and is found by calling the functions in `funclist` on the appropriate portions of `x`, as defined by the boolean arrays in `condlist`. Portions not covered by any condition have a default value of 0. See Also -------- choose, select, where Notes ----- This is similar to choose or select, except that functions are evaluated on elements of `x` that satisfy the corresponding condition from `condlist`. The result is:: |-- |funclist[0](x[condlist[0]]) out = |funclist[1](x[condlist[1]]) |... |funclist[n2](x[condlist[n2]]) |-- Examples -------- Define the sigma function, which is -1 for ``x < 0`` and +1 for ``x >= 0``. >>> x = np.linspace(-2.5, 2.5, 6) >>> np.piecewise(x, [x < 0, x >= 0], [-1, 1]) array([-1., -1., -1., 1., 1., 1.]) Define the absolute value, which is ``-x`` for ``x <0`` and ``x`` for ``x >= 0``. >>> np.piecewise(x, [x < 0, x >= 0], [lambda x: -x, lambda x: x]) array([2.5, 1.5, 0.5, 0.5, 1.5, 2.5]) Apply the same function to a scalar value. >>> y = -2 >>> np.piecewise(y, [y < 0, y >= 0], [lambda x: -x, lambda x: x]) [array(2)](https://www.chedong.com/phpMan.php/man/array/2/markdown) ### place Change elements of an array based on conditional and input values. Similar to ``np.copyto(arr, vals, where=mask)``, the difference is that `place` uses the first N elements of `vals`, where N is the number of True values in `mask`, while `copyto` uses the elements where `mask` is True. Note that `extract` does the exact opposite of `place`. Parameters ---------- arr : ndarray Array to put data into. mask : array_like Boolean mask array. Must have the same size as `a`. vals : 1-D sequence Values to put into `a`. Only the first N elements are used, where N is the number of True values in `mask`. If `vals` is smaller than N, it will be repeated, and if elements of `a` are to be masked, this sequence must be non-empty. See Also -------- copyto, put, take, extract Examples -------- >>> arr = [np.arange(6)](https://www.chedong.com/phpMan.php/man/np.arange/6/markdown).reshape(2, 3) >>> np.place(arr, arr>2, [44, 55]) >>> arr array([[ 0, 1, 2], [44, 55, 44]]) ### poly Find the coefficients of a polynomial with the given sequence of roots. .. note:: This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in `numpy.polynomial` is preferred. A summary of the differences can be found in the :doc:`transition guide `. Returns the coefficients of the polynomial whose leading coefficient is one for the given sequence of zeros (multiple roots must be included in the sequence as many times as their multiplicity; see Examples). A square matrix (or array, which will be treated as a matrix) can also be given, in which case the coefficients of the characteristic polynomial of the matrix are returned. Parameters ---------- seq_of_zeros : array_like, shape (N,) or (N, N) A sequence of polynomial roots, or a square array or matrix object. Returns ------- c : ndarray 1D array of polynomial coefficients from highest to lowest degree: ``c[0] * x**(N) + c[1] * x**(N-1) + ... + c[N-1] * x + c[N]`` where c[0] always equals 1. Raises ------ ValueError If input is the wrong shape (the input must be a 1-D or square 2-D array). See Also -------- polyval : Compute polynomial values. roots : Return the roots of a polynomial. polyfit : Least squares polynomial fit. poly1d : A one-dimensional polynomial class. Notes ----- Specifying the roots of a polynomial still leaves one degree of freedom, typically represented by an undetermined leading coefficient. [1]_ In the case of this function, that coefficient - the first one in the returned array - is always taken as one. (If for some reason you have one other point, the only automatic way presently to leverage that information is to use ``polyfit``.) The characteristic polynomial, :math:`p_a(t)`, of an `n`-by-`n` matrix **A** is given by :math:`p_a(t) = \mathrm{det}(t\, \mathbf{I} - \mathbf{A})`, where **I** is the `n`-by-`n` identity matrix. [2]_ References ---------- .. [1] M. Sullivan and M. Sullivan, III, "Algebra and Trignometry, Enhanced With Graphing Utilities," Prentice-Hall, pg. 318, 1996. .. [2] G. Strang, "Linear Algebra and Its Applications, 2nd Edition," Academic Press, pg. 182, 1980. Examples -------- Given a sequence of a polynomial's zeros: >>> np.poly((0, 0, 0)) # Multiple root example array([1., 0., 0., 0.]) The line above represents z**3 + 0*z**2 + 0*z + 0. >>> np.poly((-1./2, 0, 1./2)) array([ 1. , 0. , -0.25, 0. ]) The line above represents z**3 - z/4 >>> np.poly(([np.random.random(1)](https://www.chedong.com/phpMan.php/man/np.random.random/1/markdown)[0], 0, [np.random.random(1)](https://www.chedong.com/phpMan.php/man/np.random.random/1/markdown)[0])) array([ 1. , -0.77086955, 0.08618131, 0. ]) # random Given a square array object: >>> P = np.array([[0, 1./3], [-1./2, 0]]) >>> np.poly(P) array([1. , 0. , 0.16666667]) Note how in all cases the leading coefficient is always 1. ### polyadd Find the sum of two polynomials. .. note:: This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in `numpy.polynomial` is preferred. A summary of the differences can be found in the :doc:`transition guide `. Returns the polynomial resulting from the sum of two input polynomials. Each input must be either a poly1d object or a 1D sequence of polynomial coefficients, from highest to lowest degree. Parameters ---------- a1, a2 : array_like or poly1d object Input polynomials. Returns ------- out : ndarray or poly1d object The sum of the inputs. If either input is a poly1d object, then the output is also a poly1d object. Otherwise, it is a 1D array of polynomial coefficients from highest to lowest degree. See Also -------- poly1d : A one-dimensional polynomial class. poly, polyadd, polyder, polydiv, polyfit, polyint, polysub, polyval Examples -------- >>> np.polyadd([1, 2], [9, 5, 4]) array([9, 6, 6]) Using poly1d objects: >>> p1 = np.poly1d([1, 2]) >>> p2 = np.poly1d([9, 5, 4]) >>> print(p1) 1 x + 2 >>> print(p2) 2 9 x + 5 x + 4 >>> print(np.polyadd(p1, p2)) 2 9 x + 6 x + 6 ### polyder Return the derivative of the specified order of a polynomial. .. note:: This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in `numpy.polynomial` is preferred. A summary of the differences can be found in the :doc:`transition guide `. Parameters ---------- p : poly1d or sequence Polynomial to differentiate. A sequence is interpreted as polynomial coefficients, see `poly1d`. m : int, optional Order of differentiation (default: 1) Returns ------- der : poly1d A new polynomial representing the derivative. See Also -------- polyint : Anti-derivative of a polynomial. poly1d : Class for one-dimensional polynomials. Examples -------- The derivative of the polynomial :math:`x^3 + x^2 + x^1 + 1` is: >>> p = np.poly1d([1,1,1,1]) >>> p2 = np.polyder(p) >>> p2 poly1d([3, 2, 1]) which evaluates to: >>> p2(2.) 17.0 We can verify this, approximating the derivative with ``(f(x + h) - f(x))/h``: >>> (p(2. + 0.001) - p(2.)) / 0.001 17.007000999997857 The fourth-order derivative of a 3rd-order polynomial is zero: >>> np.polyder(p, 2) poly1d([6, 2]) >>> np.polyder(p, 3) poly1d([6]) >>> np.polyder(p, 4) poly1d([0]) ### polydiv Returns the quotient and remainder of polynomial division. .. note:: This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in `numpy.polynomial` is preferred. A summary of the differences can be found in the :doc:`transition guide `. The input arrays are the coefficients (including any coefficients equal to zero) of the "numerator" (dividend) and "denominator" (divisor) polynomials, respectively. Parameters ---------- u : array_like or poly1d Dividend polynomial's coefficients. v : array_like or poly1d Divisor polynomial's coefficients. Returns ------- q : ndarray Coefficients, including those equal to zero, of the quotient. r : ndarray Coefficients, including those equal to zero, of the remainder. See Also -------- poly, polyadd, polyder, polydiv, polyfit, polyint, polymul, polysub polyval Notes ----- Both `u` and `v` must be 0-d or 1-d (ndim = 0 or 1), but `u.ndim` need not equal `v.ndim`. In other words, all four possible combinations - ``u.ndim = v.ndim = 0``, ``u.ndim = v.ndim = 1``, ``u.ndim = 1, v.ndim = 0``, and ``u.ndim = 0, v.ndim = 1`` - work. Examples -------- .. math:: \frac{3x^2 + 5x + 2}{2x + 1} = 1.5x + 1.75, remainder 0.25 >>> x = np.array([3.0, 5.0, 2.0]) >>> y = np.array([2.0, 1.0]) >>> np.polydiv(x, y) (array([1.5 , 1.75]), array([0.25])) ### polyfit Least squares polynomial fit. .. note:: This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in `numpy.polynomial` is preferred. A summary of the differences can be found in the :doc:`transition guide `. Fit a polynomial ``p(x) = p[0] * x**deg + ... + p[deg]`` of degree `deg` to points `(x, y)`. Returns a vector of coefficients `p` that minimises the squared error in the order `deg`, `deg-1`, ... `0`. The `Polynomial.fit ` class method is recommended for new code as it is more stable numerically. See the documentation of the method for more information. Parameters ---------- x : array_like, shape (M,) x-coordinates of the M sample points ``(x[i], y[i])``. y : array_like, shape (M,) or (M, K) y-coordinates of the sample points. Several data sets of sample points sharing the same x-coordinates can be fitted at once by passing in a 2D-array that contains one dataset per column. deg : int Degree of the fitting polynomial rcond : float, optional Relative condition number of the fit. Singular values smaller than this relative to the largest singular value will be ignored. The default value is len(x)*eps, where eps is the relative precision of the float type, about 2e-16 in most cases. full : bool, optional Switch determining nature of return value. When it is False (the default) just the coefficients are returned, when True diagnostic information from the singular value decomposition is also returned. w : array_like, shape (M,), optional Weights to apply to the y-coordinates of the sample points. For gaussian uncertainties, use 1/sigma (not 1/sigma**2). cov : bool or str, optional If given and not `False`, return not just the estimate but also its covariance matrix. By default, the covariance are scaled by chi2/dof, where dof = M - (deg + 1), i.e., the weights are presumed to be unreliable except in a relative sense and everything is scaled such that the reduced chi2 is unity. This scaling is omitted if ``cov='unscaled'``, as is relevant for the case that the weights are 1/sigma**2, with sigma known to be a reliable estimate of the uncertainty. Returns ------- p : ndarray, shape (deg + 1,) or (deg + 1, K) Polynomial coefficients, highest power first. If `y` was 2-D, the coefficients for `k`-th data set are in ``p[:,k]``. residuals, rank, singular_values, rcond Present only if `full` = True. Residuals is sum of squared residuals of the least-squares fit, the effective rank of the scaled Vandermonde coefficient matrix, its singular values, and the specified value of `rcond`. For more details, see `linalg.lstsq`. V : ndarray, shape (M,M) or (M,M,K) Present only if `full` = False and `cov`=True. The covariance matrix of the polynomial coefficient estimates. The diagonal of this matrix are the variance estimates for each coefficient. If y is a 2-D array, then the covariance matrix for the `k`-th data set are in ``V[:,:,k]`` Warns ----- RankWarning The rank of the coefficient matrix in the least-squares fit is deficient. The warning is only raised if `full` = False. The warnings can be turned off by >>> import warnings >>> warnings.simplefilter('ignore', np.RankWarning) See Also -------- polyval : Compute polynomial values. linalg.lstsq : Computes a least-squares fit. scipy.interpolate.UnivariateSpline : Computes spline fits. Notes ----- The solution minimizes the squared error .. math :: E = \sum_{j=0}^k |p(x_j) - y_j|^2 in the equations:: x[0]**n * p[0] + ... + x[0] * p[n-1] + p[n] = y[0] x[1]**n * p[0] + ... + x[1] * p[n-1] + p[n] = y[1] ... x[k]**n * p[0] + ... + x[k] * p[n-1] + p[n] = y[k] The coefficient matrix of the coefficients `p` is a Vandermonde matrix. `polyfit` issues a `RankWarning` when the least-squares fit is badly conditioned. This implies that the best fit is not well-defined due to numerical error. The results may be improved by lowering the polynomial degree or by replacing `x` by `x` - `x`.mean(). The `rcond` parameter can also be set to a value smaller than its default, but the resulting fit may be spurious: including contributions from the small singular values can add numerical noise to the result. Note that fitting polynomial coefficients is inherently badly conditioned when the degree of the polynomial is large or the interval of sample points is badly centered. The quality of the fit should always be checked in these cases. When polynomial fits are not satisfactory, splines may be a good alternative. References ---------- .. [1] Wikipedia, "Curve fitting", .. [2] Wikipedia, "Polynomial interpolation", Examples -------- >>> import warnings >>> x = np.array([0.0, 1.0, 2.0, 3.0, 4.0, 5.0]) >>> y = np.array([0.0, 0.8, 0.9, 0.1, -0.8, -1.0]) >>> z = np.polyfit(x, y, 3) >>> z array([ 0.08703704, -0.81349206, 1.69312169, -0.03968254]) # may vary It is convenient to use `poly1d` objects for dealing with polynomials: >>> p = np.poly1d(z) >>> p(0.5) 0.6143849206349179 # may vary >>> p(3.5) -0.34732142857143039 # may vary >>> [p(10)](https://www.chedong.com/phpMan.php/man/p/10/markdown) 22.579365079365115 # may vary High-order polynomials may oscillate wildly: >>> with warnings.catch_warnings(): ... warnings.simplefilter('ignore', np.RankWarning) ... p30 = np.poly1d(np.polyfit(x, y, 30)) ... >>> [p30(4)](https://www.chedong.com/phpMan.php/man/p30/4/markdown) -0.80000000000000204 # may vary >>> [p30(5)](https://www.chedong.com/phpMan.php/man/p30/5/markdown) -0.99999999999999445 # may vary >>> p30(4.5) -0.10547061179440398 # may vary Illustration: >>> import matplotlib.pyplot as plt >>> xp = np.linspace(-2, 6, 100) >>> _ = plt.plot(x, y, '.', xp, p(xp), '-', xp, p30(xp), '--') >>> plt.ylim(-2,2) (-2, 2) >>> plt.show() ### polyint Return an antiderivative (indefinite integral) of a polynomial. .. note:: This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in `numpy.polynomial` is preferred. A summary of the differences can be found in the :doc:`transition guide `. The returned order `m` antiderivative `P` of polynomial `p` satisfies :math:`\frac{d^m}{dx^m}P(x) = p(x)` and is defined up to `m - 1` integration constants `k`. The constants determine the low-order polynomial part .. math:: \frac{k_{m-1}}{0!} x^0 + \ldots + \frac{k_0}{(m-1)!}x^{m-1} of `P` so that :math:`P^{(j)}(0) = k_{m-j-1}`. Parameters ---------- p : array_like or poly1d Polynomial to integrate. A sequence is interpreted as polynomial coefficients, see `poly1d`. m : int, optional Order of the antiderivative. (Default: 1) k : list of `m` scalars or scalar, optional Integration constants. They are given in the order of integration: those corresponding to highest-order terms come first. If ``None`` (default), all constants are assumed to be zero. If `m = 1`, a single scalar can be given instead of a list. See Also -------- polyder : derivative of a polynomial poly1d.integ : equivalent method Examples -------- The defining property of the antiderivative: >>> p = np.poly1d([1,1,1]) >>> P = np.polyint(p) >>> P poly1d([ 0.33333333, 0.5 , 1. , 0. ]) # may vary >>> np.polyder(P) == p True The integration constants default to zero, but can be specified: >>> P = np.polyint(p, 3) >>> [P(0)](https://www.chedong.com/phpMan.php/man/P/0/markdown) 0.0 >>> np.polyder(P)(0) 0.0 >>> np.polyder(P, 2)(0) 0.0 >>> P = np.polyint(p, 3, k=[6,5,3]) >>> P poly1d([ 0.01666667, 0.04166667, 0.16666667, 3. , 5. , 3. ]) # may vary Note that 3 = 6 / 2!, and that the constants are given in the order of integrations. Constant of the highest-order polynomial term comes first: >>> np.polyder(P, 2)(0) 6.0 >>> np.polyder(P, 1)(0) 5.0 >>> [P(0)](https://www.chedong.com/phpMan.php/man/P/0/markdown) 3.0 ### polymul Find the product of two polynomials. .. note:: This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in `numpy.polynomial` is preferred. A summary of the differences can be found in the :doc:`transition guide `. Finds the polynomial resulting from the multiplication of the two input polynomials. Each input must be either a poly1d object or a 1D sequence of polynomial coefficients, from highest to lowest degree. Parameters ---------- a1, a2 : array_like or poly1d object Input polynomials. Returns ------- out : ndarray or poly1d object The polynomial resulting from the multiplication of the inputs. If either inputs is a poly1d object, then the output is also a poly1d object. Otherwise, it is a 1D array of polynomial coefficients from highest to lowest degree. See Also -------- poly1d : A one-dimensional polynomial class. poly, polyadd, polyder, polydiv, polyfit, polyint, polysub, polyval convolve : Array convolution. Same output as polymul, but has parameter for overlap mode. Examples -------- >>> np.polymul([1, 2, 3], [9, 5, 1]) array([ 9, 23, 38, 17, 3]) Using poly1d objects: >>> p1 = np.poly1d([1, 2, 3]) >>> p2 = np.poly1d([9, 5, 1]) >>> print(p1) 2 1 x + 2 x + 3 >>> print(p2) 2 9 x + 5 x + 1 >>> print(np.polymul(p1, p2)) 4 3 2 9 x + 23 x + 38 x + 17 x + 3 ### polysub Difference (subtraction) of two polynomials. .. note:: This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in `numpy.polynomial` is preferred. A summary of the differences can be found in the :doc:`transition guide `. Given two polynomials `a1` and `a2`, returns ``a1 - a2``. `a1` and `a2` can be either array_like sequences of the polynomials' coefficients (including coefficients equal to zero), or `poly1d` objects. Parameters ---------- a1, a2 : array_like or poly1d Minuend and subtrahend polynomials, respectively. Returns ------- out : ndarray or poly1d Array or `poly1d` object of the difference polynomial's coefficients. See Also -------- polyval, polydiv, polymul, polyadd Examples -------- .. math:: (2 x^2 + 10 x - 2) - (3 x^2 + 10 x -4) = (-x^2 + 2) >>> np.polysub([2, 10, -2], [3, 10, -4]) array([-1, 0, 2]) ### polyval Evaluate a polynomial at specific values. .. note:: This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in `numpy.polynomial` is preferred. A summary of the differences can be found in the :doc:`transition guide `. If `p` is of length N, this function returns the value: ``p[0]*x**(N-1) + p[1]*x**(N-2) + ... + p[N-2]*x + p[N-1]`` If `x` is a sequence, then ``p(x)`` is returned for each element of ``x``. If `x` is another polynomial then the composite polynomial ``p(x(t))`` is returned. Parameters ---------- p : array_like or poly1d object 1D array of polynomial coefficients (including coefficients equal to zero) from highest degree to the constant term, or an instance of poly1d. x : array_like or poly1d object A number, an array of numbers, or an instance of poly1d, at which to evaluate `p`. Returns ------- values : ndarray or poly1d If `x` is a poly1d instance, the result is the composition of the two polynomials, i.e., `x` is "substituted" in `p` and the simplified result is returned. In addition, the type of `x` - array_like or poly1d - governs the type of the output: `x` array_like => `values` array_like, `x` a poly1d object => `values` is also. See Also -------- poly1d: A polynomial class. Notes ----- Horner's scheme [1]_ is used to evaluate the polynomial. Even so, for polynomials of high degree the values may be inaccurate due to rounding errors. Use carefully. If `x` is a subtype of `ndarray` the return value will be of the same type. References ---------- .. [1] I. N. Bronshtein, K. A. Semendyayev, and K. A. Hirsch (Eng. trans. Ed.), *Handbook of Mathematics*, New York, Van Nostrand Reinhold Co., 1985, pg. 720. Examples -------- >>> np.polyval([3,0,1], 5) # 3 * 5**2 + 0 * 5**1 + 1 76 >>> np.polyval([3,0,1], [np.poly1d(5)](https://www.chedong.com/phpMan.php/man/np.poly1d/5/markdown)) poly1d([76]) >>> np.polyval(np.poly1d([3,0,1]), 5) 76 >>> np.polyval(np.poly1d([3,0,1]), [np.poly1d(5)](https://www.chedong.com/phpMan.php/man/np.poly1d/5/markdown)) poly1d([76]) ### printoptions Context manager for setting print options. Set print options for the scope of the `with` block, and restore the old options at the end. See `set_printoptions` for the full description of available options. Examples -------- >>> from numpy.testing import assert_equal >>> with np.printoptions(precision=2): ... np.array([2.0]) / 3 array([0.67]) The `as`-clause of the `with`-statement gives the current print options: >>> with np.printoptions(precision=2) as opts: ... assert_equal(opts, np.get_printoptions()) See Also -------- set_printoptions, get_printoptions ### prod Return the product of array elements over a given axis. Parameters ---------- a : array_like Input data. axis : None or int or tuple of ints, optional Axis or axes along which a product is performed. The default, axis=None, will calculate the product of all the elements in the input array. If axis is negative it counts from the last to the first axis. .. versionadded:: 1.7.0 If axis is a tuple of ints, a product is performed on all of the axes specified in the tuple instead of a single axis or all the axes as before. dtype : dtype, optional The type of the returned array, as well as of the accumulator in which the elements are multiplied. The dtype of `a` is used by default unless `a` has an integer dtype of less precision than the default platform integer. In that case, if `a` is signed then the platform integer is used while if `a` is unsigned then an unsigned integer of the same precision as the platform integer is used. out : ndarray, optional Alternative output array in which to place the result. It must have the same shape as the expected output, but the type of the output values will be cast if necessary. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array. If the default value is passed, then `keepdims` will not be passed through to the `prod` method of sub-classes of `ndarray`, however any non-default value will be. If the sub-class' method does not implement `keepdims` any exceptions will be raised. initial : scalar, optional The starting value for this product. See `~numpy.ufunc.reduce` for details. .. versionadded:: 1.15.0 where : array_like of bool, optional Elements to include in the product. See `~numpy.ufunc.reduce` for details. .. versionadded:: 1.17.0 Returns ------- product_along_axis : ndarray, see `dtype` parameter above. An array shaped as `a` but with the specified axis removed. Returns a reference to `out` if specified. See Also -------- ndarray.prod : equivalent method :ref:`ufuncs-output-type` Notes ----- Arithmetic is modular when using integer types, and no error is raised on overflow. That means that, on a 32-bit platform: >>> x = np.array([536870910, 536870910, 536870910, 536870910]) >>> np.prod(x) 16 # may vary The product of an empty array is the neutral element 1: >>> np.prod([]) 1.0 Examples -------- By default, calculate the product of all elements: >>> np.prod([1.,2.]) 2.0 Even when the input array is two-dimensional: >>> np.prod([[1.,2.],[3.,4.]]) 24.0 But we can also specify the axis over which to multiply: >>> np.prod([[1.,2.],[3.,4.]], axis=1) array([ 2., 12.]) Or select specific elements to include: >>> np.prod([1., np.nan, 3.], where=[True, False, True]) 3.0 If the type of `x` is unsigned, then the output type is the unsigned platform integer: >>> x = np.array([1, 2, 3], dtype=np.uint8) >>> np.prod(x).dtype == np.uint True If `x` is of a signed integer type, then the output type is the default platform integer: >>> x = np.array([1, 2, 3], dtype=np.int8) >>> np.prod(x).dtype == int True You can also start the product with a value other than one: >>> np.prod([1, 2], initial=5) 10 ### product Return the product of array elements over a given axis. See Also -------- prod : equivalent function; see for details. ### promote_types promote_types(type1, type2) Returns the data type with the smallest size and smallest scalar kind to which both ``type1`` and ``type2`` may be safely cast. The returned data type is always in native byte order. This function is symmetric, but rarely associative. Parameters ---------- type1 : dtype or dtype specifier First data type. type2 : dtype or dtype specifier Second data type. Returns ------- out : dtype The promoted data type. Notes ----- .. versionadded:: 1.6.0 Starting in NumPy 1.9, promote_types function now returns a valid string length when given an integer or float dtype as one argument and a string dtype as another argument. Previously it always returned the input string dtype, even if it wasn't long enough to store the max integer/float value converted to a string. See Also -------- result_type, dtype, can_cast Examples -------- >>> np.promote_types('f4', 'f8') dtype('float64') >>> np.promote_types('i8', 'f4') dtype('float64') >>> np.promote_types('>i8', '>> np.promote_types('i4', 'S8') dtype('S11') An example of a non-associative case: >>> p = np.promote_types >>> p('S', p('i1', 'u1')) dtype('S6') >>> p(p('S', 'i1'), 'u1') dtype('S4') ### ptp Range of values (maximum - minimum) along an axis. The name of the function comes from the acronym for 'peak to peak'. .. warning:: `ptp` preserves the data type of the array. This means the return value for an input of signed integers with n bits (e.g. `np.int8`, `np.int16`, etc) is also a signed integer with n bits. In that case, peak-to-peak values greater than ``2**(n-1)-1`` will be returned as negative values. An example with a work-around is shown below. Parameters ---------- a : array_like Input values. axis : None or int or tuple of ints, optional Axis along which to find the peaks. By default, flatten the array. `axis` may be negative, in which case it counts from the last to the first axis. .. versionadded:: 1.15.0 If this is a tuple of ints, a reduction is performed on multiple axes, instead of a single axis or all the axes as before. out : array_like Alternative output array in which to place the result. It must have the same shape and buffer length as the expected output, but the type of the output values will be cast if necessary. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array. If the default value is passed, then `keepdims` will not be passed through to the `ptp` method of sub-classes of `ndarray`, however any non-default value will be. If the sub-class' method does not implement `keepdims` any exceptions will be raised. Returns ------- ptp : ndarray A new array holding the result, unless `out` was specified, in which case a reference to `out` is returned. Examples -------- >>> x = np.array([[4, 9, 2, 10], ... [6, 9, 7, 12]]) >>> np.ptp(x, axis=1) array([8, 6]) >>> np.ptp(x, axis=0) array([2, 0, 5, 2]) >>> np.ptp(x) 10 This example shows that a negative value can be returned when the input is an array of signed integers. >>> y = np.array([[1, 127], ... [0, 127], ... [-1, 127], ... [-2, 127]], dtype=np.int8) >>> np.ptp(y, axis=1) array([ 126, 127, -128, -127], dtype=int8) A work-around is to use the `view()` method to view the result as unsigned integers with the same bit width: >>> np.ptp(y, axis=1).view(np.uint8) array([126, 127, 128, 129], dtype=uint8) ### put Replaces specified elements of an array with given values. The indexing works on the flattened target array. `put` is roughly equivalent to: :: a.flat[ind] = v Parameters ---------- a : ndarray Target array. ind : array_like Target indices, interpreted as integers. v : array_like Values to place in `a` at target indices. If `v` is shorter than `ind` it will be repeated as necessary. mode : {'raise', 'wrap', 'clip'}, optional Specifies how out-of-bounds indices will behave. * 'raise' -- raise an error (default) * 'wrap' -- wrap around * 'clip' -- clip to the range 'clip' mode means that all indices that are too large are replaced by the index that addresses the last element along that axis. Note that this disables indexing with negative numbers. In 'raise' mode, if an exception occurs the target array may still be modified. See Also -------- putmask, place put_along_axis : Put elements by matching the array and the index arrays Examples -------- >>> a = [np.arange(5)](https://www.chedong.com/phpMan.php/man/np.arange/5/markdown) >>> np.put(a, [0, 2], [-44, -55]) >>> a array([-44, 1, -55, 3, 4]) >>> a = [np.arange(5)](https://www.chedong.com/phpMan.php/man/np.arange/5/markdown) >>> np.put(a, 22, -5, mode='clip') >>> a array([ 0, 1, 2, 3, -5]) ### put_along_axis Put values into the destination array by matching 1d index and data slices. This iterates over matching 1d slices oriented along the specified axis in the index and data arrays, and uses the former to place values into the latter. These slices can be different lengths. Functions returning an index along an axis, like `argsort` and `argpartition`, produce suitable indices for this function. .. versionadded:: 1.15.0 Parameters ---------- arr : ndarray (Ni..., M, Nk...) Destination array. indices : ndarray (Ni..., J, Nk...) Indices to change along each 1d slice of `arr`. This must match the dimension of arr, but dimensions in Ni and Nj may be 1 to broadcast against `arr`. values : array_like (Ni..., J, Nk...) values to insert at those indices. Its shape and dimension are broadcast to match that of `indices`. axis : int The axis to take 1d slices along. If axis is None, the destination array is treated as if a flattened 1d view had been created of it. Notes ----- This is equivalent to (but faster than) the following use of `ndindex` and `s_`, which sets each of ``ii`` and ``kk`` to a tuple of indices:: Ni, M, Nk = a.shape[:axis], a.shape[axis], a.shape[axis+1:] J = indices.shape[axis] # Need not equal M for ii in ndindex(Ni): for kk in ndindex(Nk): a_1d = a [ii + s_[:,] + kk] indices_1d = indices[ii + s_[:,] + kk] values_1d = values [ii + s_[:,] + kk] for j in range(J): a_1d[indices_1d[j]] = values_1d[j] Equivalently, eliminating the inner loop, the last two lines would be:: a_1d[indices_1d] = values_1d See Also -------- take_along_axis : Take values from the input array by matching 1d index and data slices Examples -------- For this sample array >>> a = np.array([[10, 30, 20], [60, 40, 50]]) We can replace the maximum values with: >>> ai = np.expand_dims(np.argmax(a, axis=1), axis=1) >>> ai array([[1], [0]]) >>> np.put_along_axis(a, ai, 99, axis=1) >>> a array([[10, 99, 20], [99, 40, 50]]) ### putmask putmask(a, mask, values) Changes elements of an array based on conditional and input values. Sets ``a.flat[n] = values[n]`` for each n where ``mask.flat[n]==True``. If `values` is not the same size as `a` and `mask` then it will repeat. This gives behavior different from ``a[mask] = values``. Parameters ---------- a : ndarray Target array. mask : array_like Boolean mask array. It has to be the same shape as `a`. values : array_like Values to put into `a` where `mask` is True. If `values` is smaller than `a` it will be repeated. See Also -------- place, put, take, copyto Examples -------- >>> x = [np.arange(6)](https://www.chedong.com/phpMan.php/man/np.arange/6/markdown).reshape(2, 3) >>> np.putmask(x, x>2, x**2) >>> x array([[ 0, 1, 2], [ 9, 16, 25]]) If `values` is smaller than `a` it is repeated: >>> x = [np.arange(5)](https://www.chedong.com/phpMan.php/man/np.arange/5/markdown) >>> np.putmask(x, x>1, [-33, -44]) >>> x array([ 0, 1, -33, -44, -33]) ### quantile Compute the q-th quantile of the data along the specified axis. .. versionadded:: 1.15.0 Parameters ---------- a : array_like Input array or object that can be converted to an array. q : array_like of float Quantile or sequence of quantiles to compute, which must be between 0 and 1 inclusive. axis : {int, tuple of int, None}, optional Axis or axes along which the quantiles are computed. The default is to compute the quantile(s) along a flattened version of the array. out : ndarray, optional Alternative output array in which to place the result. It must have the same shape and buffer length as the expected output, but the type (of the output) will be cast if necessary. overwrite_input : bool, optional If True, then allow the input array `a` to be modified by intermediate calculations, to save memory. In this case, the contents of the input `a` after this function completes is undefined. interpolation : {'linear', 'lower', 'higher', 'midpoint', 'nearest'} This optional parameter specifies the interpolation method to use when the desired quantile lies between two data points ``i < j``: * linear: ``i + (j - i) * fraction``, where ``fraction`` is the fractional part of the index surrounded by ``i`` and ``j``. * lower: ``i``. * higher: ``j``. * nearest: ``i`` or ``j``, whichever is nearest. * midpoint: ``(i + j) / 2``. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original array `a`. Returns ------- quantile : scalar or ndarray If `q` is a single quantile and `axis=None`, then the result is a scalar. If multiple quantiles are given, first axis of the result corresponds to the quantiles. The other axes are the axes that remain after the reduction of `a`. If the input contains integers or floats smaller than ``float64``, the output data-type is ``float64``. Otherwise, the output data-type is the same as that of the input. If `out` is specified, that array is returned instead. See Also -------- mean percentile : equivalent to quantile, but with q in the range [0, 100]. median : equivalent to ``quantile(..., 0.5)`` nanquantile Notes ----- Given a vector ``V`` of length ``N``, the q-th quantile of ``V`` is the value ``q`` of the way from the minimum to the maximum in a sorted copy of ``V``. The values and distances of the two nearest neighbors as well as the `interpolation` parameter will determine the quantile if the normalized ranking does not match the location of ``q`` exactly. This function is the same as the median if ``q=0.5``, the same as the minimum if ``q=0.0`` and the same as the maximum if ``q=1.0``. Examples -------- >>> a = np.array([[10, 7, 4], [3, 2, 1]]) >>> a array([[10, 7, 4], [ 3, 2, 1]]) >>> np.quantile(a, 0.5) 3.5 >>> np.quantile(a, 0.5, axis=0) array([6.5, 4.5, 2.5]) >>> np.quantile(a, 0.5, axis=1) array([7., 2.]) >>> np.quantile(a, 0.5, axis=1, keepdims=True) array([[7.], [2.]]) >>> m = np.quantile(a, 0.5, axis=0) >>> out = np.zeros_like(m) >>> np.quantile(a, 0.5, axis=0, out=out) array([6.5, 4.5, 2.5]) >>> m array([6.5, 4.5, 2.5]) >>> b = a.copy() >>> np.quantile(b, 0.5, axis=1, overwrite_input=True) array([7., 2.]) >>> assert not np.all(a == b) ### ravel Return a contiguous flattened array. A 1-D array, containing the elements of the input, is returned. A copy is made only if needed. As of NumPy 1.10, the returned array will have the same type as the input array. (for example, a masked array will be returned for a masked array input) Parameters ---------- a : array_like Input array. The elements in `a` are read in the order specified by `order`, and packed as a 1-D array. order : {'C','F', 'A', 'K'}, optional The elements of `a` are read using this index order. 'C' means to index the elements in row-major, C-style order, with the last axis index changing fastest, back to the first axis index changing slowest. 'F' means to index the elements in column-major, Fortran-style order, with the first index changing fastest, and the last index changing slowest. Note that the 'C' and 'F' options take no account of the memory layout of the underlying array, and only refer to the order of axis indexing. 'A' means to read the elements in Fortran-like index order if `a` is Fortran *contiguous* in memory, C-like order otherwise. 'K' means to read the elements in the order they occur in memory, except for reversing the data when strides are negative. By default, 'C' index order is used. Returns ------- y : array_like y is an array of the same subtype as `a`, with shape ``(a.size,)``. Note that matrices are special cased for backward compatibility, if `a` is a matrix, then y is a 1-D ndarray. See Also -------- ndarray.flat : 1-D iterator over an array. ndarray.flatten : 1-D array copy of the elements of an array in row-major order. ndarray.reshape : Change the shape of an array without changing its data. Notes ----- In row-major, C-style order, in two dimensions, the row index varies the slowest, and the column index the quickest. This can be generalized to multiple dimensions, where row-major order implies that the index along the first axis varies slowest, and the index along the last quickest. The opposite holds for column-major, Fortran-style index ordering. When a view is desired in as many cases as possible, ``arr.reshape(-1)`` may be preferable. Examples -------- It is equivalent to ``reshape(-1, order=order)``. >>> x = np.array([[1, 2, 3], [4, 5, 6]]) >>> np.ravel(x) array([1, 2, 3, 4, 5, 6]) >>> x.reshape(-1) array([1, 2, 3, 4, 5, 6]) >>> np.ravel(x, order='F') array([1, 4, 2, 5, 3, 6]) When ``order`` is 'A', it will preserve the array's 'C' or 'F' ordering: >>> np.ravel(x.T) array([1, 4, 2, 5, 3, 6]) >>> np.ravel(x.T, order='A') array([1, 2, 3, 4, 5, 6]) When ``order`` is 'K', it will preserve orderings that are neither 'C' nor 'F', but won't reverse axes: >>> a = [np.arange(3)](https://www.chedong.com/phpMan.php/man/np.arange/3/markdown)[::-1]; a array([2, 1, 0]) >>> a.ravel(order='C') array([2, 1, 0]) >>> a.ravel(order='K') array([2, 1, 0]) >>> a = [np.arange(12)](https://www.chedong.com/phpMan.php/man/np.arange/12/markdown).reshape(2,3,2).swapaxes(1,2); a array([[[ 0, 2, 4], [ 1, 3, 5]], [[ 6, 8, 10], [ 7, 9, 11]]]) >>> a.ravel(order='C') array([ 0, 2, 4, 1, 3, 5, 6, 8, 10, 7, 9, 11]) >>> a.ravel(order='K') array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]) ### ravel_multi_index ravel_multi_index(multi_index, dims, mode='raise', order='C') Converts a tuple of index arrays into an array of flat indices, applying boundary modes to the multi-index. Parameters ---------- multi_index : tuple of array_like A tuple of integer arrays, one array for each dimension. dims : tuple of ints The shape of array into which the indices from ``multi_index`` apply. mode : {'raise', 'wrap', 'clip'}, optional Specifies how out-of-bounds indices are handled. Can specify either one mode or a tuple of modes, one mode per index. * 'raise' -- raise an error (default) * 'wrap' -- wrap around * 'clip' -- clip to the range In 'clip' mode, a negative index which would normally wrap will clip to 0 instead. order : {'C', 'F'}, optional Determines whether the multi-index should be viewed as indexing in row-major (C-style) or column-major (Fortran-style) order. Returns ------- raveled_indices : ndarray An array of indices into the flattened version of an array of dimensions ``dims``. See Also -------- unravel_index Notes ----- .. versionadded:: 1.6.0 Examples -------- >>> arr = np.array([[3,6,6],[4,5,1]]) >>> np.ravel_multi_index(arr, (7,6)) array([22, 41, 37]) >>> np.ravel_multi_index(arr, (7,6), order='F') array([31, 41, 13]) >>> np.ravel_multi_index(arr, (4,6), mode='clip') array([22, 23, 19]) >>> np.ravel_multi_index(arr, (4,4), mode=('clip','wrap')) array([12, 13, 13]) >>> np.ravel_multi_index((3,1,4,1), (6,7,8,9)) 1621 ### real Return the real part of the complex argument. Parameters ---------- val : array_like Input array. Returns ------- out : ndarray or scalar The real component of the complex argument. If `val` is real, the type of `val` is used for the output. If `val` has complex elements, the returned type is float. See Also -------- real_if_close, imag, angle Examples -------- >>> a = np.array([1+2j, 3+4j, 5+6j]) >>> a.real array([1., 3., 5.]) >>> a.real = 9 >>> a array([9.+2.j, 9.+4.j, 9.+6.j]) >>> a.real = np.array([9, 8, 7]) >>> a array([9.+2.j, 8.+4.j, 7.+6.j]) >>> np.real(1 + 1j) 1.0 ### real_if_close If input is complex with all imaginary parts close to zero, return real parts. "Close to zero" is defined as `tol` * (machine epsilon of the type for `a`). Parameters ---------- a : array_like Input array. tol : float Tolerance in machine epsilons for the complex part of the elements in the array. Returns ------- out : ndarray If `a` is real, the type of `a` is used for the output. If `a` has complex elements, the returned type is float. See Also -------- real, imag, angle Notes ----- Machine epsilon varies from machine to machine and between data types but Python floats on most platforms have a machine epsilon equal to 2.2204460492503131e-16. You can use 'np.finfo(float).eps' to print out the machine epsilon for floats. Examples -------- >>> np.finfo(float).eps 2.2204460492503131e-16 # may vary >>> np.real_if_close([2.1 + 4e-14j, 5.2 + 3e-15j], tol=1000) array([2.1, 5.2]) >>> np.real_if_close([2.1 + 4e-13j, 5.2 + 3e-15j], tol=1000) array([2.1+4.e-13j, 5.2 + 3e-15j]) ### recfromcsv Load ASCII data stored in a comma-separated file. The returned array is a record array (if ``usemask=False``, see `recarray`) or a masked record array (if ``usemask=True``, see `ma.mrecords.MaskedRecords`). Parameters ---------- fname, kwargs : For a description of input parameters, see `genfromtxt`. See Also -------- numpy.genfromtxt : generic function to load ASCII data. Notes ----- By default, `dtype` is None, which means that the data-type of the output array will be determined from the data. ### recfromtxt Load ASCII data from a file and return it in a record array. If ``usemask=False`` a standard `recarray` is returned, if ``usemask=True`` a MaskedRecords array is returned. Parameters ---------- fname, kwargs : For a description of input parameters, see `genfromtxt`. See Also -------- numpy.genfromtxt : generic function Notes ----- By default, `dtype` is None, which means that the data-type of the output array will be determined from the data. ### repeat Repeat elements of an array. Parameters ---------- a : array_like Input array. repeats : int or array of ints The number of repetitions for each element. `repeats` is broadcasted to fit the shape of the given axis. axis : int, optional The axis along which to repeat values. By default, use the flattened input array, and return a flat output array. Returns ------- repeated_array : ndarray Output array which has the same shape as `a`, except along the given axis. See Also -------- tile : Tile an array. unique : Find the unique elements of an array. Examples -------- >>> np.repeat(3, 4) array([3, 3, 3, 3]) >>> x = np.array([[1,2],[3,4]]) >>> np.repeat(x, 2) array([1, 1, 2, 2, 3, 3, 4, 4]) >>> np.repeat(x, 3, axis=1) array([[1, 1, 1, 2, 2, 2], [3, 3, 3, 4, 4, 4]]) >>> np.repeat(x, [1, 2], axis=0) array([[1, 2], [3, 4], [3, 4]]) ### require Return an ndarray of the provided type that satisfies requirements. This function is useful to be sure that an array with the correct flags is returned for passing to compiled code (perhaps through ctypes). Parameters ---------- a : array_like The object to be converted to a type-and-requirement-satisfying array. dtype : data-type The required data-type. If None preserve the current dtype. If your application requires the data to be in native byteorder, include a byteorder specification as a part of the dtype specification. requirements : str or list of str The requirements list can be any of the following * 'F_CONTIGUOUS' ('F') - ensure a Fortran-contiguous array * 'C_CONTIGUOUS' ('C') - ensure a C-contiguous array * 'ALIGNED' ('A') - ensure a data-type aligned array * 'WRITEABLE' ('W') - ensure a writable array * 'OWNDATA' ('O') - ensure an array that owns its own data * 'ENSUREARRAY', ('E') - ensure a base array, instead of a subclass like : array_like Reference object to allow the creation of arrays which are not NumPy arrays. If an array-like passed in as ``like`` supports the ``__array_function__`` protocol, the result will be defined by it. In this case, it ensures the creation of an array object compatible with that passed in via this argument. .. versionadded:: 1.20.0 Returns ------- out : ndarray Array with specified requirements and type if given. See Also -------- asarray : Convert input to an ndarray. asanyarray : Convert to an ndarray, but pass through ndarray subclasses. ascontiguousarray : Convert input to a contiguous array. asfortranarray : Convert input to an ndarray with column-major memory order. ndarray.flags : Information about the memory layout of the array. Notes ----- The returned array will be guaranteed to have the listed requirements by making a copy if needed. Examples -------- >>> x = [np.arange(6)](https://www.chedong.com/phpMan.php/man/np.arange/6/markdown).reshape(2,3) >>> x.flags C_CONTIGUOUS : True F_CONTIGUOUS : False OWNDATA : False WRITEABLE : True ALIGNED : True WRITEBACKIFCOPY : False UPDATEIFCOPY : False >>> y = np.require(x, dtype=np.float32, requirements=['A', 'O', 'W', 'F']) >>> y.flags C_CONTIGUOUS : False F_CONTIGUOUS : True OWNDATA : True WRITEABLE : True ALIGNED : True WRITEBACKIFCOPY : False UPDATEIFCOPY : False ### reshape Gives a new shape to an array without changing its data. Parameters ---------- a : array_like Array to be reshaped. newshape : int or tuple of ints The new shape should be compatible with the original shape. If an integer, then the result will be a 1-D array of that length. One shape dimension can be -1. In this case, the value is inferred from the length of the array and remaining dimensions. order : {'C', 'F', 'A'}, optional Read the elements of `a` using this index order, and place the elements into the reshaped array using this index order. 'C' means to read / write the elements using C-like index order, with the last axis index changing fastest, back to the first axis index changing slowest. 'F' means to read / write the elements using Fortran-like index order, with the first index changing fastest, and the last index changing slowest. Note that the 'C' and 'F' options take no account of the memory layout of the underlying array, and only refer to the order of indexing. 'A' means to read / write the elements in Fortran-like index order if `a` is Fortran *contiguous* in memory, C-like order otherwise. Returns ------- reshaped_array : ndarray This will be a new view object if possible; otherwise, it will be a copy. Note there is no guarantee of the *memory layout* (C- or Fortran- contiguous) of the returned array. See Also -------- ndarray.reshape : Equivalent method. Notes ----- It is not always possible to change the shape of an array without copying the data. If you want an error to be raised when the data is copied, you should assign the new shape to the shape attribute of the array:: >>> a = np.zeros((10, 2)) # A transpose makes the array non-contiguous >>> b = a.T # Taking a view makes it possible to modify the shape without modifying # the initial object. >>> c = b.view() >>> c.shape = (20) Traceback (most recent call last): ... AttributeError: Incompatible shape for in-place modification. Use `.reshape()` to make a copy with the desired shape. The `order` keyword gives the index ordering both for *fetching* the values from `a`, and then *placing* the values into the output array. For example, let's say you have an array: >>> a = [np.arange(6)](https://www.chedong.com/phpMan.php/man/np.arange/6/markdown).reshape((3, 2)) >>> a array([[0, 1], [2, 3], [4, 5]]) You can think of reshaping as first raveling the array (using the given index order), then inserting the elements from the raveled array into the new array using the same kind of index ordering as was used for the raveling. >>> np.reshape(a, (2, 3)) # C-like index ordering array([[0, 1, 2], [3, 4, 5]]) >>> np.reshape(np.ravel(a), (2, 3)) # equivalent to C ravel then C reshape array([[0, 1, 2], [3, 4, 5]]) >>> np.reshape(a, (2, 3), order='F') # Fortran-like index ordering array([[0, 4, 3], [2, 1, 5]]) >>> np.reshape(np.ravel(a, order='F'), (2, 3), order='F') array([[0, 4, 3], [2, 1, 5]]) Examples -------- >>> a = np.array([[1,2,3], [4,5,6]]) >>> np.reshape(a, 6) array([1, 2, 3, 4, 5, 6]) >>> np.reshape(a, 6, order='F') array([1, 4, 2, 5, 3, 6]) >>> np.reshape(a, (3,-1)) # the unspecified value is inferred to be 2 array([[1, 2], [3, 4], [5, 6]]) ### resize Return a new array with the specified shape. If the new array is larger than the original array, then the new array is filled with repeated copies of `a`. Note that this behavior is different from [a.resize(new_shape)](https://www.chedong.com/phpMan.php/man/a.resize/newshape/markdown) which fills with zeros instead of repeated copies of `a`. Parameters ---------- a : array_like Array to be resized. new_shape : int or tuple of int Shape of resized array. Returns ------- reshaped_array : ndarray The new array is formed from the data in the old array, repeated if necessary to fill out the required number of elements. The data are repeated iterating over the array in C-order. See Also -------- np.reshape : Reshape an array without changing the total size. np.pad : Enlarge and pad an array. np.repeat : Repeat elements of an array. ndarray.resize : resize an array in-place. Notes ----- When the total size of the array does not change `~numpy.reshape` should be used. In most other cases either indexing (to reduce the size) or padding (to increase the size) may be a more appropriate solution. Warning: This functionality does **not** consider axes separately, i.e. it does not apply interpolation/extrapolation. It fills the return array with the required number of elements, iterating over `a` in C-order, disregarding axes (and cycling back from the start if the new shape is larger). This functionality is therefore not suitable to resize images, or data where each axis represents a separate and distinct entity. Examples -------- >>> a=np.array([[0,1],[2,3]]) >>> np.resize(a,(2,3)) array([[0, 1, 2], [3, 0, 1]]) >>> np.resize(a,(1,4)) array([[0, 1, 2, 3]]) >>> np.resize(a,(2,4)) array([[0, 1, 2, 3], [0, 1, 2, 3]]) ### result_type result_type(*arrays_and_dtypes) Returns the type that results from applying the NumPy type promotion rules to the arguments. Type promotion in NumPy works similarly to the rules in languages like C++, with some slight differences. When both scalars and arrays are used, the array's type takes precedence and the actual value of the scalar is taken into account. For example, calculating 3*a, where a is an array of 32-bit floats, intuitively should result in a 32-bit float output. If the 3 is a 32-bit integer, the NumPy rules indicate it can't convert losslessly into a 32-bit float, so a 64-bit float should be the result type. By examining the value of the constant, '3', we see that it fits in an 8-bit integer, which can be cast losslessly into the 32-bit float. Parameters ---------- arrays_and_dtypes : list of arrays and dtypes The operands of some operation whose result type is needed. Returns ------- out : dtype The result type. See also -------- dtype, promote_types, min_scalar_type, can_cast Notes ----- .. versionadded:: 1.6.0 The specific algorithm used is as follows. Categories are determined by first checking which of boolean, integer (int/uint), or floating point (float/complex) the maximum kind of all the arrays and the scalars are. If there are only scalars or the maximum category of the scalars is higher than the maximum category of the arrays, the data types are combined with :func:`promote_types` to produce the return value. Otherwise, `min_scalar_type` is called on each array, and the resulting data types are all combined with :func:`promote_types` to produce the return value. The set of int values is not a subset of the uint values for types with the same number of bits, something not reflected in :func:`min_scalar_type`, but handled as a special case in `result_type`. Examples -------- >>> np.result_type(3, np.arange(7, dtype='i1')) dtype('int8') >>> np.result_type('i4', 'c8') dtype('complex128') >>> np.result_type(3.0, -2) dtype('float64') ### roll Roll array elements along a given axis. Elements that roll beyond the last position are re-introduced at the first. Parameters ---------- a : array_like Input array. shift : int or tuple of ints The number of places by which elements are shifted. If a tuple, then `axis` must be a tuple of the same size, and each of the given axes is shifted by the corresponding number. If an int while `axis` is a tuple of ints, then the same value is used for all given axes. axis : int or tuple of ints, optional Axis or axes along which elements are shifted. By default, the array is flattened before shifting, after which the original shape is restored. Returns ------- res : ndarray Output array, with the same shape as `a`. See Also -------- rollaxis : Roll the specified axis backwards, until it lies in a given position. Notes ----- .. versionadded:: 1.12.0 Supports rolling over multiple dimensions simultaneously. Examples -------- >>> x = [np.arange(10)](https://www.chedong.com/phpMan.php/man/np.arange/10/markdown) >>> np.roll(x, 2) array([8, 9, 0, 1, 2, 3, 4, 5, 6, 7]) >>> np.roll(x, -2) array([2, 3, 4, 5, 6, 7, 8, 9, 0, 1]) >>> x2 = np.reshape(x, (2,5)) >>> x2 array([[0, 1, 2, 3, 4], [5, 6, 7, 8, 9]]) >>> np.roll(x2, 1) array([[9, 0, 1, 2, 3], [4, 5, 6, 7, 8]]) >>> np.roll(x2, -1) array([[1, 2, 3, 4, 5], [6, 7, 8, 9, 0]]) >>> np.roll(x2, 1, axis=0) array([[5, 6, 7, 8, 9], [0, 1, 2, 3, 4]]) >>> np.roll(x2, -1, axis=0) array([[5, 6, 7, 8, 9], [0, 1, 2, 3, 4]]) >>> np.roll(x2, 1, axis=1) array([[4, 0, 1, 2, 3], [9, 5, 6, 7, 8]]) >>> np.roll(x2, -1, axis=1) array([[1, 2, 3, 4, 0], [6, 7, 8, 9, 5]]) ### rollaxis Roll the specified axis backwards, until it lies in a given position. This function continues to be supported for backward compatibility, but you should prefer `moveaxis`. The `moveaxis` function was added in NumPy 1.11. Parameters ---------- a : ndarray Input array. axis : int The axis to be rolled. The positions of the other axes do not change relative to one another. start : int, optional When ``start <= axis``, the axis is rolled back until it lies in this position. When ``start > axis``, the axis is rolled until it lies before this position. The default, 0, results in a "complete" roll. The following table describes how negative values of ``start`` are interpreted: .. table:: :align: left +-------------------+----------------------+ | ``start`` | Normalized ``start`` | +===================+======================+ | ``-(arr.ndim+1)`` | raise ``AxisError`` | +-------------------+----------------------+ | ``-arr.ndim`` | 0 | +-------------------+----------------------+ | |vdots| | |vdots| | +-------------------+----------------------+ | ``-1`` | ``arr.ndim-1`` | +-------------------+----------------------+ | ``0`` | ``0`` | +-------------------+----------------------+ | |vdots| | |vdots| | +-------------------+----------------------+ | ``arr.ndim`` | ``arr.ndim`` | +-------------------+----------------------+ | ``arr.ndim + 1`` | raise ``AxisError`` | +-------------------+----------------------+ .. |vdots| unicode:: U+22EE .. Vertical Ellipsis Returns ------- res : ndarray For NumPy >= 1.10.0 a view of `a` is always returned. For earlier NumPy versions a view of `a` is returned only if the order of the axes is changed, otherwise the input array is returned. See Also -------- moveaxis : Move array axes to new positions. roll : Roll the elements of an array by a number of positions along a given axis. Examples -------- >>> a = np.ones((3,4,5,6)) >>> np.rollaxis(a, 3, 1).shape (3, 6, 4, 5) >>> np.rollaxis(a, 2).shape (5, 3, 4, 6) >>> np.rollaxis(a, 1, 4).shape (3, 5, 6, 4) ### roots Return the roots of a polynomial with coefficients given in p. .. note:: This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in `numpy.polynomial` is preferred. A summary of the differences can be found in the :doc:`transition guide `. The values in the rank-1 array `p` are coefficients of a polynomial. If the length of `p` is n+1 then the polynomial is described by:: p[0] * x**n + p[1] * x**(n-1) + ... + p[n-1]*x + p[n] Parameters ---------- p : array_like Rank-1 array of polynomial coefficients. Returns ------- out : ndarray An array containing the roots of the polynomial. Raises ------ ValueError When `p` cannot be converted to a rank-1 array. See also -------- poly : Find the coefficients of a polynomial with a given sequence of roots. polyval : Compute polynomial values. polyfit : Least squares polynomial fit. poly1d : A one-dimensional polynomial class. Notes ----- The algorithm relies on computing the eigenvalues of the companion matrix [1]_. References ---------- .. [1] R. A. Horn & C. R. Johnson, *Matrix Analysis*. Cambridge, UK: Cambridge University Press, 1999, pp. 146-7. Examples -------- >>> coeff = [3.2, 2, 1] >>> np.roots(coeff) array([-0.3125+0.46351241j, -0.3125-0.46351241j]) ### rot90 Rotate an array by 90 degrees in the plane specified by axes. Rotation direction is from the first towards the second axis. Parameters ---------- m : array_like Array of two or more dimensions. k : integer Number of times the array is rotated by 90 degrees. axes: (2,) array_like The array is rotated in the plane defined by the axes. Axes must be different. .. versionadded:: 1.12.0 Returns ------- y : ndarray A rotated view of `m`. See Also -------- flip : Reverse the order of elements in an array along the given axis. fliplr : Flip an array horizontally. flipud : Flip an array vertically. Notes ----- rot90(m, k=1, axes=(1,0)) is the reverse of rot90(m, k=1, axes=(0,1)) rot90(m, k=1, axes=(1,0)) is equivalent to rot90(m, k=-1, axes=(0,1)) Examples -------- >>> m = np.array([[1,2],[3,4]], int) >>> m array([[1, 2], [3, 4]]) >>> np.rot90(m) array([[2, 4], [1, 3]]) >>> np.rot90(m, 2) array([[4, 3], [2, 1]]) >>> m = [np.arange(8)](https://www.chedong.com/phpMan.php/man/np.arange/8/markdown).reshape((2,2,2)) >>> np.rot90(m, 1, (1,2)) array([[[1, 3], [0, 2]], [[5, 7], [4, 6]]]) ### round_ Round an array to the given number of decimals. See Also -------- around : equivalent function; see for details. row_stack = vstack(tup) Stack arrays in sequence vertically (row wise). This is equivalent to concatenation along the first axis after 1-D arrays of shape `(N,)` have been reshaped to `(1,N)`. Rebuilds arrays divided by `vsplit`. This function makes most sense for arrays with up to 3 dimensions. For instance, for pixel-data with a height (first axis), width (second axis), and r/g/b channels (third axis). The functions `concatenate`, `stack` and `block` provide more general stacking and concatenation operations. Parameters ---------- tup : sequence of ndarrays The arrays must have the same shape along all but the first axis. 1-D arrays must have the same length. Returns ------- stacked : ndarray The array formed by stacking the given arrays, will be at least 2-D. See Also -------- concatenate : Join a sequence of arrays along an existing axis. stack : Join a sequence of arrays along a new axis. block : Assemble an nd-array from nested lists of blocks. hstack : Stack arrays in sequence horizontally (column wise). dstack : Stack arrays in sequence depth wise (along third axis). column_stack : Stack 1-D arrays as columns into a 2-D array. vsplit : Split an array into multiple sub-arrays vertically (row-wise). Examples -------- >>> a = np.array([1, 2, 3]) >>> b = np.array([4, 5, 6]) >>> np.vstack((a,b)) array([[1, 2, 3], [4, 5, 6]]) >>> a = np.array([[1], [2], [3]]) >>> b = np.array([[4], [5], [6]]) >>> np.vstack((a,b)) array([[1], [2], [3], [4], [5], [6]]) ### safe_eval Protected string evaluation. Evaluate a string containing a Python literal expression without allowing the execution of arbitrary non-literal code. Parameters ---------- source : str The string to evaluate. Returns ------- obj : object The result of evaluating `source`. Raises ------ SyntaxError If the code has invalid Python syntax, or if it contains non-literal code. Examples -------- >>> np.safe_eval('1') 1 >>> np.safe_eval('[1, 2, 3]') [1, 2, 3] >>> np.safe_eval('{"foo": ("bar", 10.0)}') {'foo': ('bar', 10.0)} >>> np.safe_eval('import os') Traceback (most recent call last): ... SyntaxError: invalid syntax >>> np.safe_eval('open("/home/user/.ssh/id_dsa").read()') Traceback (most recent call last): ... ValueError: malformed node or string: <_ast.Call object at 0x...> ### save Save an array to a binary file in NumPy ``.npy`` format. Parameters ---------- file : file, str, or pathlib.Path File or filename to which the data is saved. If file is a file-object, then the filename is unchanged. If file is a string or Path, a ``.npy`` extension will be appended to the filename if it does not already have one. arr : array_like Array data to be saved. allow_pickle : bool, optional Allow saving object arrays using Python pickles. Reasons for disallowing pickles include security (loading pickled data can execute arbitrary code) and portability (pickled objects may not be loadable on different Python installations, for example if the stored objects require libraries that are not available, and not all pickled data is compatible between Python 2 and Python 3). Default: True fix_imports : bool, optional Only useful in forcing objects in object arrays on Python 3 to be pickled in a Python 2 compatible way. If `fix_imports` is True, pickle will try to map the new Python 3 names to the old module names used in Python 2, so that the pickle data stream is readable with Python 2. See Also -------- savez : Save several arrays into a ``.npz`` archive savetxt, load Notes ----- For a description of the ``.npy`` format, see :py:mod:`numpy.lib.format`. Any data saved to the file is appended to the end of the file. Examples -------- >>> from tempfile import TemporaryFile >>> outfile = TemporaryFile() >>> x = [np.arange(10)](https://www.chedong.com/phpMan.php/man/np.arange/10/markdown) >>> np.save(outfile, x) >>> _ = [outfile.seek(0)](https://www.chedong.com/phpMan.php/man/outfile.seek/0/markdown) # Only needed here to simulate closing & reopening file >>> np.load(outfile) array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) >>> with open('test.npy', 'wb') as f: ... np.save(f, np.array([1, 2])) ... np.save(f, np.array([1, 3])) >>> with open('test.npy', 'rb') as f: ... a = np.load(f) ... b = np.load(f) >>> print(a, b) # [1 2] [1 3] ### savetxt Save an array to a text file. Parameters ---------- fname : filename or file handle If the filename ends in ``.gz``, the file is automatically saved in compressed gzip format. `loadtxt` understands gzipped files transparently. X : 1D or 2D array_like Data to be saved to a text file. fmt : str or sequence of strs, optional A single format (%10.5f), a sequence of formats, or a multi-format string, e.g. 'Iteration %d -- %10.5f', in which case `delimiter` is ignored. For complex `X`, the legal options for `fmt` are: * a single specifier, `fmt='%.4e'`, resulting in numbers formatted like `' (%s+%sj)' % (fmt, fmt)` * a full string specifying every real and imaginary part, e.g. `' %.4e %+.4ej %.4e %+.4ej %.4e %+.4ej'` for 3 columns * a list of specifiers, one per column - in this case, the real and imaginary part must have separate specifiers, e.g. `['%.3e + %.3ej', '(%.15e%+.15ej)']` for 2 columns delimiter : str, optional String or character separating columns. newline : str, optional String or character separating lines. .. versionadded:: 1.5.0 header : str, optional String that will be written at the beginning of the file. .. versionadded:: 1.7.0 footer : str, optional String that will be written at the end of the file. .. versionadded:: 1.7.0 comments : str, optional String that will be prepended to the ``header`` and ``footer`` strings, to mark them as comments. Default: '# ', as expected by e.g. ``numpy.loadtxt``. .. versionadded:: 1.7.0 encoding : {None, str}, optional Encoding used to encode the outputfile. Does not apply to output streams. If the encoding is something other than 'bytes' or 'latin1' you will not be able to load the file in NumPy versions < 1.14. Default is 'latin1'. .. versionadded:: 1.14.0 See Also -------- save : Save an array to a binary file in NumPy ``.npy`` format savez : Save several arrays into an uncompressed ``.npz`` archive savez_compressed : Save several arrays into a compressed ``.npz`` archive Notes ----- Further explanation of the `fmt` parameter (``%[flag]width[.precision]specifier``): flags: ``-`` : left justify ``+`` : Forces to precede result with + or -. ``0`` : Left pad the number with zeros instead of space (see width). width: Minimum number of characters to be printed. The value is not truncated if it has more characters. precision: - For integer specifiers (eg. ``d,i,o,x``), the minimum number of digits. - For ``e, E`` and ``f`` specifiers, the number of digits to print after the decimal point. - For ``g`` and ``G``, the maximum number of significant digits. - For ``s``, the maximum number of characters. specifiers: ``c`` : character ``d`` or ``i`` : signed decimal integer ``e`` or ``E`` : scientific notation with ``e`` or ``E``. ``f`` : decimal floating point ``g,G`` : use the shorter of ``e,E`` or ``f`` ``o`` : signed octal ``s`` : string of characters ``u`` : unsigned decimal integer ``x,X`` : unsigned hexadecimal integer This explanation of ``fmt`` is not complete, for an exhaustive specification see [1]_. References ---------- .. [1] `Format Specification Mini-Language <>`_, Python Documentation. Examples -------- >>> x = y = z = np.arange(0.0,5.0,1.0) >>> np.savetxt('test.out', x, delimiter=',') # X is an array >>> np.savetxt('test.out', (x,y,z)) # x,y,z equal sized 1D arrays >>> np.savetxt('test.out', x, fmt='%1.4e') # use exponential notation ### savez Save several arrays into a single file in uncompressed ``.npz`` format. Provide arrays as keyword arguments to store them under the corresponding name in the output file: ``savez(fn, x=x, y=y)``. If arrays are specified as positional arguments, i.e., ``savez(fn, x, y)``, their names will be `arr_0`, `arr_1`, etc. Parameters ---------- file : str or file Either the filename (string) or an open file (file-like object) where the data will be saved. If file is a string or a Path, the ``.npz`` extension will be appended to the filename if it is not already there. args : Arguments, optional Arrays to save to the file. Please use keyword arguments (see `kwds` below) to assign names to arrays. Arrays specified as args will be named "arr_0", "arr_1", and so on. kwds : Keyword arguments, optional Arrays to save to the file. Each array will be saved to the output file with its corresponding keyword name. Returns ------- None See Also -------- save : Save a single array to a binary file in NumPy format. savetxt : Save an array to a file as plain text. savez_compressed : Save several arrays into a compressed ``.npz`` archive Notes ----- The ``.npz`` file format is a zipped archive of files named after the variables they contain. The archive is not compressed and each file in the archive contains one variable in ``.npy`` format. For a description of the ``.npy`` format, see :py:mod:`numpy.lib.format`. When opening the saved ``.npz`` file with `load` a `NpzFile` object is returned. This is a dictionary-like object which can be queried for its list of arrays (with the ``.files`` attribute), and for the arrays themselves. When saving dictionaries, the dictionary keys become filenames inside the ZIP archive. Therefore, keys should be valid filenames. E.g., avoid keys that begin with ``/`` or contain ``.``. Examples -------- >>> from tempfile import TemporaryFile >>> outfile = TemporaryFile() >>> x = [np.arange(10)](https://www.chedong.com/phpMan.php/man/np.arange/10/markdown) >>> y = np.sin(x) Using `savez` with \*args, the arrays are saved with default names. >>> np.savez(outfile, x, y) >>> _ = [outfile.seek(0)](https://www.chedong.com/phpMan.php/man/outfile.seek/0/markdown) # Only needed here to simulate closing & reopening file >>> npzfile = np.load(outfile) >>> npzfile.files ['arr_0', 'arr_1'] >>> npzfile['arr_0'] array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) Using `savez` with \**kwds, the arrays are saved with the keyword names. >>> outfile = TemporaryFile() >>> np.savez(outfile, x=x, y=y) >>> _ = [outfile.seek(0)](https://www.chedong.com/phpMan.php/man/outfile.seek/0/markdown) >>> npzfile = np.load(outfile) >>> sorted(npzfile.files) ['x', 'y'] >>> npzfile['x'] array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) ### savez_compressed Save several arrays into a single file in compressed ``.npz`` format. Provide arrays as keyword arguments to store them under the corresponding name in the output file: ``savez(fn, x=x, y=y)``. If arrays are specified as positional arguments, i.e., ``savez(fn, x, y)``, their names will be `arr_0`, `arr_1`, etc. Parameters ---------- file : str or file Either the filename (string) or an open file (file-like object) where the data will be saved. If file is a string or a Path, the ``.npz`` extension will be appended to the filename if it is not already there. args : Arguments, optional Arrays to save to the file. Please use keyword arguments (see `kwds` below) to assign names to arrays. Arrays specified as args will be named "arr_0", "arr_1", and so on. kwds : Keyword arguments, optional Arrays to save to the file. Each array will be saved to the output file with its corresponding keyword name. Returns ------- None See Also -------- numpy.save : Save a single array to a binary file in NumPy format. numpy.savetxt : Save an array to a file as plain text. numpy.savez : Save several arrays into an uncompressed ``.npz`` file format numpy.load : Load the files created by savez_compressed. Notes ----- The ``.npz`` file format is a zipped archive of files named after the variables they contain. The archive is compressed with ``zipfile.ZIP_DEFLATED`` and each file in the archive contains one variable in ``.npy`` format. For a description of the ``.npy`` format, see :py:mod:`numpy.lib.format`. When opening the saved ``.npz`` file with `load` a `NpzFile` object is returned. This is a dictionary-like object which can be queried for its list of arrays (with the ``.files`` attribute), and for the arrays themselves. Examples -------- >>> test_array = np.random.rand(3, 2) >>> test_vector = [np.random.rand(4)](https://www.chedong.com/phpMan.php/man/np.random.rand/4/markdown) >>> np.savez_compressed('/tmp/123', a=test_array, b=test_vector) >>> loaded = np.load('/tmp/123.npz') >>> print(np.array_equal(test_array, loaded['a'])) True >>> print(np.array_equal(test_vector, loaded['b'])) True ### sctype2char Return the string representation of a scalar dtype. Parameters ---------- sctype : scalar dtype or object If a scalar dtype, the corresponding string character is returned. If an object, `sctype2char` tries to infer its scalar type and then return the corresponding string character. Returns ------- typechar : str The string character corresponding to the scalar type. Raises ------ ValueError If `sctype` is an object for which the type can not be inferred. See Also -------- obj2sctype, issctype, issubsctype, mintypecode Examples -------- >>> for sctype in [np.int32, np.double, np.complex_, np.string_, np.ndarray]: ... print(np.sctype2char(sctype)) l # may vary d D S O >>> x = np.array([1., 2-1.j]) >>> np.sctype2char(x) 'D' >>> np.sctype2char(list) 'O' ### searchsorted Find indices where elements should be inserted to maintain order. Find the indices into a sorted array `a` such that, if the corresponding elements in `v` were inserted before the indices, the order of `a` would be preserved. Assuming that `a` is sorted: ====== ============================ `side` returned index `i` satisfies ====== ============================ left ``a[i-1] < v <= a[i]`` right ``a[i-1] <= v < a[i]`` ====== ============================ Parameters ---------- a : 1-D array_like Input array. If `sorter` is None, then it must be sorted in ascending order, otherwise `sorter` must be an array of indices that sort it. v : array_like Values to insert into `a`. side : {'left', 'right'}, optional If 'left', the index of the first suitable location found is given. If 'right', return the last such index. If there is no suitable index, return either 0 or N (where N is the length of `a`). sorter : 1-D array_like, optional Optional array of integer indices that sort array a into ascending order. They are typically the result of argsort. .. versionadded:: 1.7.0 Returns ------- indices : array of ints Array of insertion points with the same shape as `v`. See Also -------- sort : Return a sorted copy of an array. histogram : Produce histogram from 1-D data. Notes ----- Binary search is used to find the required insertion points. As of NumPy 1.4.0 `searchsorted` works with real/complex arrays containing `nan` values. The enhanced sort order is documented in `sort`. This function uses the same algorithm as the builtin python `bisect.bisect_left` (``side='left'``) and `bisect.bisect_right` (``side='right'``) functions, which is also vectorized in the `v` argument. Examples -------- >>> np.searchsorted([1,2,3,4,5], 3) 2 >>> np.searchsorted([1,2,3,4,5], 3, side='right') 3 >>> np.searchsorted([1,2,3,4,5], [-10, 10, 2, 3]) array([0, 5, 1, 2]) ### select Return an array drawn from elements in choicelist, depending on conditions. Parameters ---------- condlist : list of bool ndarrays The list of conditions which determine from which array in `choicelist` the output elements are taken. When multiple conditions are satisfied, the first one encountered in `condlist` is used. choicelist : list of ndarrays The list of arrays from which the output elements are taken. It has to be of the same length as `condlist`. default : scalar, optional The element inserted in `output` when all conditions evaluate to False. Returns ------- output : ndarray The output at position m is the m-th element of the array in `choicelist` where the m-th element of the corresponding array in `condlist` is True. See Also -------- where : Return elements from one of two arrays depending on condition. take, choose, compress, diag, diagonal Examples -------- >>> x = [np.arange(10)](https://www.chedong.com/phpMan.php/man/np.arange/10/markdown) >>> condlist = [x<3, x>5] >>> choicelist = [x, x**2] >>> np.select(condlist, choicelist) array([ 0, 1, 2, ..., 49, 64, 81]) ### set_numeric_ops set_numeric_ops(op1=func1, op2=func2, ...) Set numerical operators for array objects. .. deprecated:: 1.16 For the general case, use :c:func:`PyUFunc_ReplaceLoopBySignature`. For ndarray subclasses, define the ``__array_ufunc__`` method and override the relevant ufunc. Parameters ---------- op1, op2, ... : callable Each ``op = func`` pair describes an operator to be replaced. For example, ``add = lambda x, y: np.add(x, y) % 5`` would replace addition by modulus 5 addition. Returns ------- saved_ops : list of callables A list of all operators, stored before making replacements. Notes ----- .. WARNING:: Use with care! Incorrect usage may lead to memory errors. A function replacing an operator cannot make use of that operator. For example, when replacing add, you may not use ``+``. Instead, directly call ufuncs. Examples -------- >>> def add_mod5(x, y): ... return np.add(x, y) % 5 ... >>> old_funcs = np.set_numeric_ops(add=add_mod5) >>> x = [np.arange(12)](https://www.chedong.com/phpMan.php/man/np.arange/12/markdown).reshape((3, 4)) >>> x + x array([[0, 2, 4, 1], [3, 0, 2, 4], [1, 3, 0, 2]]) >>> ignore = np.set_numeric_ops(**old_funcs) # restore operators ### set_printoptions Set printing options. These options determine the way floating point numbers, arrays and other NumPy objects are displayed. Parameters ---------- precision : int or None, optional Number of digits of precision for floating point output (default 8). May be None if `floatmode` is not `fixed`, to print as many digits as necessary to uniquely specify the value. threshold : int, optional Total number of array elements which trigger summarization rather than full repr (default 1000). To always use the full repr without summarization, pass `sys.maxsize`. edgeitems : int, optional Number of array items in summary at beginning and end of each dimension (default 3). linewidth : int, optional The number of characters per line for the purpose of inserting line breaks (default 75). suppress : bool, optional If True, always print floating point numbers using fixed point notation, in which case numbers equal to zero in the current precision will print as zero. If False, then scientific notation is used when absolute value of the smallest number is < 1e-4 or the ratio of the maximum absolute value to the minimum is > 1e3. The default is False. nanstr : str, optional String representation of floating point not-a-number (default nan). infstr : str, optional String representation of floating point infinity (default inf). sign : string, either '-', '+', or ' ', optional Controls printing of the sign of floating-point types. If '+', always print the sign of positive values. If ' ', always prints a space (whitespace character) in the sign position of positive values. If '-', omit the sign character of positive values. (default '-') formatter : dict of callables, optional If not None, the keys should indicate the type(s) that the respective formatting function applies to. Callables should return a string. Types that are not specified (by their corresponding keys) are handled by the default formatters. Individual types for which a formatter can be set are: - 'bool' - 'int' - 'timedelta' : a `numpy.timedelta64` - 'datetime' : a `numpy.datetime64` - 'float' - 'longfloat' : 128-bit floats - 'complexfloat' - 'longcomplexfloat' : composed of two 128-bit floats - 'numpystr' : types `numpy.string_` and `numpy.unicode_` - 'object' : `np.object_` arrays Other keys that can be used to set a group of types at once are: - 'all' : sets all types - 'int_kind' : sets 'int' - 'float_kind' : sets 'float' and 'longfloat' - 'complex_kind' : sets 'complexfloat' and 'longcomplexfloat' - 'str_kind' : sets 'numpystr' floatmode : str, optional Controls the interpretation of the `precision` option for floating-point types. Can take the following values (default maxprec_equal): * 'fixed': Always print exactly `precision` fractional digits, even if this would print more or fewer digits than necessary to specify the value uniquely. * 'unique': Print the minimum number of fractional digits necessary to represent each value uniquely. Different elements may have a different number of digits. The value of the `precision` option is ignored. * 'maxprec': Print at most `precision` fractional digits, but if an element can be uniquely represented with fewer digits only print it with that many. * 'maxprec_equal': Print at most `precision` fractional digits, but if every element in the array can be uniquely represented with an equal number of fewer digits, use that many digits for all elements. legacy : string or `False`, optional If set to the string `'1.13'` enables 1.13 legacy printing mode. This approximates numpy 1.13 print output by including a space in the sign position of floats and different behavior for 0d arrays. If set to `False`, disables legacy mode. Unrecognized strings will be ignored with a warning for forward compatibility. .. versionadded:: 1.14.0 See Also -------- get_printoptions, printoptions, set_string_function, array2string Notes ----- `formatter` is always reset with a call to `set_printoptions`. Use `printoptions` as a context manager to set the values temporarily. Examples -------- Floating point precision can be set: >>> np.set_printoptions(precision=4) >>> np.array([1.123456789]) [1.1235] Long arrays can be summarised: >>> np.set_printoptions(threshold=5) >>> [np.arange(10)](https://www.chedong.com/phpMan.php/man/np.arange/10/markdown) array([0, 1, 2, ..., 7, 8, 9]) Small results can be suppressed: >>> eps = np.finfo(float).eps >>> x = np.arange(4.) >>> x**2 - (x + eps)**2 array([-4.9304e-32, -4.4409e-16, 0.0000e+00, 0.0000e+00]) >>> np.set_printoptions(suppress=True) >>> x**2 - (x + eps)**2 array([-0., -0., 0., 0.]) A custom formatter can be used to display array elements as desired: >>> np.set_printoptions(formatter={'all':lambda x: 'int: '+str(-x)}) >>> x = [np.arange(3)](https://www.chedong.com/phpMan.php/man/np.arange/3/markdown) >>> x array([int: 0, int: -1, int: -2]) >>> np.set_printoptions() # formatter gets reset >>> x array([0, 1, 2]) To put back the default options, you can use: >>> np.set_printoptions(edgeitems=3, infstr='inf', ... linewidth=75, nanstr='nan', precision=8, ... suppress=False, threshold=1000, formatter=None) Also to temporarily override options, use `printoptions` as a context manager: >>> with np.printoptions(precision=2, suppress=True, threshold=5): ... np.linspace(0, 10, 10) array([ 0. , 1.11, 2.22, ..., 7.78, 8.89, 10. ]) ### set_string_function Set a Python function to be used when pretty printing arrays. Parameters ---------- f : function or None Function to be used to pretty print arrays. The function should expect a single array argument and return a string of the representation of the array. If None, the function is reset to the default NumPy function to print arrays. repr : bool, optional If True (default), the function for pretty printing (``__repr__``) is set, if False the function that returns the default string representation (``__str__``) is set. See Also -------- set_printoptions, get_printoptions Examples -------- >>> def pprint(arr): ... return 'HA! - What are you going to do now?' ... >>> np.set_string_function(pprint) >>> a = [np.arange(10)](https://www.chedong.com/phpMan.php/man/np.arange/10/markdown) >>> a HA! - What are you going to do now? >>> _ = a >>> # [0 1 2 3 4 5 6 7 8 9] We can reset the function to the default: >>> np.set_string_function(None) >>> a array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) `repr` affects either pretty printing or normal string representation. Note that ``__repr__`` is still affected by setting ``__str__`` because the width of each array element in the returned string becomes equal to the length of the result of ``__str__()``. >>> x = [np.arange(4)](https://www.chedong.com/phpMan.php/man/np.arange/4/markdown) >>> np.set_string_function(lambda x:'random', repr=False) >>> x.__str__() 'random' >>> x.__repr__() 'array([0, 1, 2, 3])' ### setbufsize Set the size of the buffer used in ufuncs. Parameters ---------- size : int Size of buffer. ### setdiff1d Find the set difference of two arrays. Return the unique values in `ar1` that are not in `ar2`. Parameters ---------- ar1 : array_like Input array. ar2 : array_like Input comparison array. assume_unique : bool If True, the input arrays are both assumed to be unique, which can speed up the calculation. Default is False. Returns ------- setdiff1d : ndarray 1D array of values in `ar1` that are not in `ar2`. The result is sorted when `assume_unique=False`, but otherwise only sorted if the input is sorted. See Also -------- numpy.lib.arraysetops : Module with a number of other functions for performing set operations on arrays. Examples -------- >>> a = np.array([1, 2, 3, 2, 4, 1]) >>> b = np.array([3, 4, 5, 6]) >>> np.setdiff1d(a, b) array([1, 2]) ### seterr Set how floating-point errors are handled. Note that operations on integer scalar types (such as `int16`) are handled like floating point, and are affected by these settings. Parameters ---------- all : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional Set treatment for all types of floating-point errors at once: - ignore: Take no action when the exception occurs. - warn: Print a `RuntimeWarning` (via the Python `warnings` module). - raise: Raise a `FloatingPointError`. - call: Call a function specified using the `seterrcall` function. - print: Print a warning directly to ``stdout``. - log: Record error in a Log object specified by `seterrcall`. The default is not to change the current behavior. divide : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional Treatment for division by zero. over : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional Treatment for floating-point overflow. under : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional Treatment for floating-point underflow. invalid : {'ignore', 'warn', 'raise', 'call', 'print', 'log'}, optional Treatment for invalid floating-point operation. Returns ------- old_settings : dict Dictionary containing the old settings. See also -------- seterrcall : Set a callback function for the 'call' mode. geterr, geterrcall, errstate Notes ----- The floating-point exceptions are defined in the IEEE 754 standard [1]_: - Division by zero: infinite result obtained from finite numbers. - Overflow: result too large to be expressed. - Underflow: result so close to zero that some precision was lost. - Invalid operation: result is not an expressible number, typically indicates that a NaN was produced. .. [1] Examples -------- >>> old_settings = np.seterr(all='ignore') #seterr to known value >>> np.seterr(over='raise') {'divide': 'ignore', 'over': 'ignore', 'under': 'ignore', 'invalid': 'ignore'} >>> np.seterr(**old_settings) # reset to default {'divide': 'ignore', 'over': 'raise', 'under': 'ignore', 'invalid': 'ignore'} >>> [np.int16(32000)](https://www.chedong.com/phpMan.php/man/np.int16/32000/markdown) * [np.int16(3)](https://www.chedong.com/phpMan.php/man/np.int16/3/markdown) 30464 >>> old_settings = np.seterr(all='warn', over='raise') >>> [np.int16(32000)](https://www.chedong.com/phpMan.php/man/np.int16/32000/markdown) * [np.int16(3)](https://www.chedong.com/phpMan.php/man/np.int16/3/markdown) Traceback (most recent call last): File "", line 1, in FloatingPointError: overflow encountered in short_scalars >>> old_settings = np.seterr(all='print') >>> np.geterr() {'divide': 'print', 'over': 'print', 'under': 'print', 'invalid': 'print'} >>> [np.int16(32000)](https://www.chedong.com/phpMan.php/man/np.int16/32000/markdown) * [np.int16(3)](https://www.chedong.com/phpMan.php/man/np.int16/3/markdown) 30464 ### seterrcall Set the floating-point error callback function or log object. There are two ways to capture floating-point error messages. The first is to set the error-handler to 'call', using `seterr`. Then, set the function to call using this function. The second is to set the error-handler to 'log', using `seterr`. Floating-point errors then trigger a call to the 'write' method of the provided object. Parameters ---------- func : callable f(err, flag) or object with write method Function to call upon floating-point errors ('call'-mode) or object whose 'write' method is used to log such message ('log'-mode). The call function takes two arguments. The first is a string describing the type of error (such as "divide by zero", "overflow", "underflow", or "invalid value"), and the second is the status flag. The flag is a byte, whose four least-significant bits indicate the type of error, one of "divide", "over", "under", "invalid":: [0 0 0 0 divide over under invalid] In other words, ``flags = divide + 2*over + 4*under + 8*invalid``. If an object is provided, its write method should take one argument, a string. Returns ------- h : callable, log instance or None The old error handler. See Also -------- seterr, geterr, geterrcall Examples -------- Callback upon error: >>> def err_handler(type, flag): ... print("Floating point error (%s), with flag %s" % (type, flag)) ... >>> saved_handler = np.seterrcall(err_handler) >>> save_err = np.seterr(all='call') >>> np.array([1, 2, 3]) / 0.0 Floating point error (divide by zero), with flag 1 array([inf, inf, inf]) >>> np.seterrcall(saved_handler) >>> np.seterr(**save_err) {'divide': 'call', 'over': 'call', 'under': 'call', 'invalid': 'call'} Log error message: >>> class Log: ... def write(self, msg): ... print("LOG: %s" % msg) ... >>> log = Log() >>> saved_handler = np.seterrcall(log) >>> save_err = np.seterr(all='log') >>> np.array([1, 2, 3]) / 0.0 LOG: Warning: divide by zero encountered in true_divide array([inf, inf, inf]) >>> np.seterrcall(saved_handler) >>> np.seterr(**save_err) {'divide': 'log', 'over': 'log', 'under': 'log', 'invalid': 'log'} ### seterrobj seterrobj(errobj) Set the object that defines floating-point error handling. The error object contains all information that defines the error handling behavior in NumPy. `seterrobj` is used internally by the other functions that set error handling behavior (`seterr`, `seterrcall`). Parameters ---------- errobj : list The error object, a list containing three elements: [internal numpy buffer size, error mask, error callback function]. The error mask is a single integer that holds the treatment information on all four floating point errors. The information for each error type is contained in three bits of the integer. If we print it in base 8, we can see what treatment is set for "invalid", "under", "over", and "divide" (in that order). The printed string can be interpreted with * 0 : 'ignore' * 1 : 'warn' * 2 : 'raise' * 3 : 'call' * 4 : 'print' * 5 : 'log' See Also -------- geterrobj, seterr, geterr, seterrcall, geterrcall getbufsize, setbufsize Notes ----- For complete documentation of the types of floating-point exceptions and treatment options, see `seterr`. Examples -------- >>> old_errobj = np.geterrobj() # first get the defaults >>> old_errobj [8192, 521, None] >>> def err_handler(type, flag): ... print("Floating point error (%s), with flag %s" % (type, flag)) ... >>> new_errobj = [20000, 12, err_handler] >>> [np.seterrobj(new_errobj)](https://www.chedong.com/phpMan.php/man/np.seterrobj/newerrobj/markdown) >>> np.base_repr(12, 8) # int for divide=4 ('print') and over=1 ('warn') '14' >>> np.geterr() {'over': 'warn', 'divide': 'print', 'invalid': 'ignore', 'under': 'ignore'} >>> np.geterrcall() is err_handler True ### setxor1d Find the set exclusive-or of two arrays. Return the sorted, unique values that are in only one (not both) of the input arrays. Parameters ---------- ar1, ar2 : array_like Input arrays. assume_unique : bool If True, the input arrays are both assumed to be unique, which can speed up the calculation. Default is False. Returns ------- setxor1d : ndarray Sorted 1D array of unique values that are in only one of the input arrays. Examples -------- >>> a = np.array([1, 2, 3, 2, 4]) >>> b = np.array([2, 3, 5, 7, 5]) >>> np.setxor1d(a,b) array([1, 4, 5, 7]) ### shape Return the shape of an array. Parameters ---------- a : array_like Input array. Returns ------- shape : tuple of ints The elements of the shape tuple give the lengths of the corresponding array dimensions. See Also -------- len ndarray.shape : Equivalent array method. Examples -------- >>> np.shape([np.eye(3)](https://www.chedong.com/phpMan.php/man/np.eye/3/markdown)) (3, 3) >>> np.shape([[1, 2]]) (1, 2) >>> np.shape([0]) (1,) >>> [np.shape(0)](https://www.chedong.com/phpMan.php/man/np.shape/0/markdown) () >>> a = np.array([(1, 2), (3, 4)], dtype=[('x', 'i4'), ('y', 'i4')]) >>> np.shape(a) (2,) >>> a.shape (2,) ### shares_memory shares_memory(a, b, max_work=None) Determine if two arrays share memory. .. warning:: This function can be exponentially slow for some inputs, unless `max_work` is set to a finite number or ``MAY_SHARE_BOUNDS``. If in doubt, use `numpy.may_share_memory` instead. Parameters ---------- a, b : ndarray Input arrays max_work : int, optional Effort to spend on solving the overlap problem (maximum number of candidate solutions to consider). The following special values are recognized: max_work=MAY_SHARE_EXACT (default) The problem is solved exactly. In this case, the function returns True only if there is an element shared between the arrays. Finding the exact solution may take extremely long in some cases. max_work=MAY_SHARE_BOUNDS Only the memory bounds of a and b are checked. Raises ------ numpy.TooHardError Exceeded max_work. Returns ------- out : bool See Also -------- may_share_memory Examples -------- >>> x = np.array([1, 2, 3, 4]) >>> np.shares_memory(x, np.array([5, 6, 7])) False >>> np.shares_memory(x[::2], x) True >>> np.shares_memory(x[::2], x[[1::2](https://www.chedong.com/phpMan.php/perldoc/1%3A%3A2/markdown)]) False Checking whether two arrays share memory is NP-complete, and runtime may increase exponentially in the number of dimensions. Hence, `max_work` should generally be set to a finite number, as it is possible to construct examples that take extremely long to run: >>> from numpy.lib.stride_tricks import as_strided >>> x = np.zeros([192163377], dtype=np.int8) >>> x1 = as_strided(x, strides=(36674, 61119, 85569), shape=(1049, 1049, 1049)) >>> x2 = as_strided(x[64023025:], strides=(12223, 12224, 1), shape=(1049, 1049, 1)) >>> np.shares_memory(x1, x2, max_work=1000) Traceback (most recent call last): ... numpy.TooHardError: Exceeded max_work Running ``np.shares_memory(x1, x2)`` without `max_work` set takes around 1 minute for this case. It is possible to find problems that take still significantly longer. show_config = show() Show libraries in the system on which NumPy was built. Print information about various resources (libraries, library directories, include directories, etc.) in the system on which NumPy was built. See Also -------- get_include : Returns the directory containing NumPy C header files. Notes ----- Classes specifying the information to be printed are defined in the `numpy.distutils.system_info` module. Information may include: * ``language``: language used to write the libraries (mostly C or f77) * ``libraries``: names of libraries found in the system * ``library_dirs``: directories containing the libraries * ``include_dirs``: directories containing library header files * ``src_dirs``: directories containing library source files * ``define_macros``: preprocessor macros used by ``distutils.setup`` * ``baseline``: minimum CPU features required * ``found``: dispatched features supported in the system * ``not found``: dispatched features that are not supported in the system Examples -------- >>> import numpy as np >>> np.show_config() blas_opt_info: language = c define_macros = [('HAVE_CBLAS', None)] libraries = ['openblas', 'openblas'] library_dirs = ['/usr/local/lib'] ### sinc Return the normalized sinc function. The sinc function is :math:`\sin(\pi x)/(\pi x)`. .. note:: Note the normalization factor of ``pi`` used in the definition. This is the most commonly used definition in signal processing. Use ``sinc(x / np.pi)`` to obtain the unnormalized sinc function :math:`\sin(x)/(x)` that is more common in mathematics. Parameters ---------- x : ndarray Array (possibly multi-dimensional) of values for which to to calculate ``sinc(x)``. Returns ------- out : ndarray ``sinc(x)``, which has the same shape as the input. Notes ----- ``[sinc(0)](https://www.chedong.com/phpMan.php/man/sinc/0/markdown)`` is the limit value 1. The name sinc is short for "sine cardinal" or "sinus cardinalis". The sinc function is used in various signal processing applications, including in anti-aliasing, in the construction of a Lanczos resampling filter, and in interpolation. For bandlimited interpolation of discrete-time signals, the ideal interpolation kernel is proportional to the sinc function. References ---------- .. [1] Weisstein, Eric W. "Sinc Function." From MathWorld--A Wolfram Web Resource. .. [2] Wikipedia, "Sinc function", Examples -------- >>> import matplotlib.pyplot as plt >>> x = np.linspace(-4, 4, 41) >>> np.sinc(x) array([-3.89804309e-17, -4.92362781e-02, -8.40918587e-02, # may vary -8.90384387e-02, -5.84680802e-02, 3.89804309e-17, 6.68206631e-02, 1.16434881e-01, 1.26137788e-01, 8.50444803e-02, -3.89804309e-17, -1.03943254e-01, -1.89206682e-01, -2.16236208e-01, -1.55914881e-01, 3.89804309e-17, 2.33872321e-01, 5.04551152e-01, 7.56826729e-01, 9.35489284e-01, 1.00000000e+00, 9.35489284e-01, 7.56826729e-01, 5.04551152e-01, 2.33872321e-01, 3.89804309e-17, -1.55914881e-01, -2.16236208e-01, -1.89206682e-01, -1.03943254e-01, -3.89804309e-17, 8.50444803e-02, 1.26137788e-01, 1.16434881e-01, 6.68206631e-02, 3.89804309e-17, -5.84680802e-02, -8.90384387e-02, -8.40918587e-02, -4.92362781e-02, -3.89804309e-17]) >>> plt.plot(x, np.sinc(x)) [] >>> plt.title("Sinc Function") Text(0.5, 1.0, 'Sinc Function') >>> plt.ylabel("Amplitude") Text(0, 0.5, 'Amplitude') >>> plt.xlabel("X") Text(0.5, 0, 'X') >>> plt.show() ### size Return the number of elements along a given axis. Parameters ---------- a : array_like Input data. axis : int, optional Axis along which the elements are counted. By default, give the total number of elements. Returns ------- element_count : int Number of elements along the specified axis. See Also -------- shape : dimensions of array ndarray.shape : dimensions of array ndarray.size : number of elements in array Examples -------- >>> a = np.array([[1,2,3],[4,5,6]]) >>> np.size(a) 6 >>> np.size(a,1) 3 >>> np.size(a,0) 2 ### sometrue Check whether some values are true. Refer to `any` for full documentation. See Also -------- any : equivalent function; see for details. ### sort Return a sorted copy of an array. Parameters ---------- a : array_like Array to be sorted. axis : int or None, optional Axis along which to sort. If None, the array is flattened before sorting. The default is -1, which sorts along the last axis. kind : {'quicksort', 'mergesort', 'heapsort', 'stable'}, optional Sorting algorithm. The default is 'quicksort'. Note that both 'stable' and 'mergesort' use timsort or radix sort under the covers and, in general, the actual implementation will vary with data type. The 'mergesort' option is retained for backwards compatibility. .. versionchanged:: 1.15.0. The 'stable' option was added. order : str or list of str, optional When `a` is an array with fields defined, this argument specifies which fields to compare first, second, etc. A single field can be specified as a string, and not all fields need be specified, but unspecified fields will still be used, in the order in which they come up in the dtype, to break ties. Returns ------- sorted_array : ndarray Array of the same type and shape as `a`. See Also -------- ndarray.sort : Method to sort an array in-place. argsort : Indirect sort. lexsort : Indirect stable sort on multiple keys. searchsorted : Find elements in a sorted array. partition : Partial sort. Notes ----- The various sorting algorithms are characterized by their average speed, worst case performance, work space size, and whether they are stable. A stable sort keeps items with the same key in the same relative order. The four algorithms implemented in NumPy have the following properties: =========== ======= ============= ============ ======== kind speed worst case work space stable =========== ======= ============= ============ ======== 'quicksort' 1 O(n^2) 0 no 'heapsort' 3 O(n*[log(n)](https://www.chedong.com/phpMan.php/man/log/n/markdown)) 0 no 'mergesort' 2 O(n*[log(n)](https://www.chedong.com/phpMan.php/man/log/n/markdown)) ~n/2 yes 'timsort' 2 O(n*[log(n)](https://www.chedong.com/phpMan.php/man/log/n/markdown)) ~n/2 yes =========== ======= ============= ============ ======== .. note:: The datatype determines which of 'mergesort' or 'timsort' is actually used, even if 'mergesort' is specified. User selection at a finer scale is not currently available. All the sort algorithms make temporary copies of the data when sorting along any but the last axis. Consequently, sorting along the last axis is faster and uses less space than sorting along any other axis. The sort order for complex numbers is lexicographic. If both the real and imaginary parts are non-nan then the order is determined by the real parts except when they are equal, in which case the order is determined by the imaginary parts. Previous to numpy 1.4.0 sorting real and complex arrays containing nan values led to undefined behaviour. In numpy versions >= 1.4.0 nan values are sorted to the end. The extended sort order is: * Real: [R, nan] * Complex: [R + Rj, R + nanj, nan + Rj, nan + nanj] where R is a non-nan real value. Complex values with the same nan placements are sorted according to the non-nan part if it exists. Non-nan values are sorted as before. .. versionadded:: 1.12.0 quicksort has been changed to `introsort <>`_. When sorting does not make enough progress it switches to `heapsort <>`_. This implementation makes quicksort O(n*[log(n)](https://www.chedong.com/phpMan.php/man/log/n/markdown)) in the worst case. 'stable' automatically chooses the best stable sorting algorithm for the data type being sorted. It, along with 'mergesort' is currently mapped to `timsort <>`_ or `radix sort <>`_ depending on the data type. API forward compatibility currently limits the ability to select the implementation and it is hardwired for the different data types. .. versionadded:: 1.17.0 Timsort is added for better performance on already or nearly sorted data. On random data timsort is almost identical to mergesort. It is now used for stable sort while quicksort is still the default sort if none is chosen. For timsort details, refer to `CPython listsort.txt <>`_. 'mergesort' and 'stable' are mapped to radix sort for integer data types. Radix sort is an [O(n)](https://www.chedong.com/phpMan.php/man/O/n/markdown) sort instead of O(n log n). .. versionchanged:: 1.18.0 NaT now sorts to the end of arrays for consistency with NaN. Examples -------- >>> a = np.array([[1,4],[3,1]]) >>> np.sort(a) # sort along the last axis array([[1, 4], [1, 3]]) >>> np.sort(a, axis=None) # sort the flattened array array([1, 1, 3, 4]) >>> np.sort(a, axis=0) # sort along the first axis array([[1, 1], [3, 4]]) Use the `order` keyword to specify a field to use when sorting a structured array: >>> dtype = [('name', 'S10'), ('height', float), ('age', int)] >>> values = [('Arthur', 1.8, 41), ('Lancelot', 1.9, 38), ... ('Galahad', 1.7, 38)] >>> a = np.array(values, dtype=dtype) # create a structured array >>> np.sort(a, order='height') # doctest: +SKIP array([('Galahad', 1.7, 38), ('Arthur', 1.8, 41), ('Lancelot', 1.8999999999999999, 38)], dtype=[('name', '|S10'), ('height', '>> np.sort(a, order=['age', 'height']) # doctest: +SKIP array([('Galahad', 1.7, 38), ('Lancelot', 1.8999999999999999, 38), ('Arthur', 1.8, 41)], dtype=[('name', '|S10'), ('height', '>> np.sort_complex([5, 3, 6, 2, 1]) array([1.+0.j, 2.+0.j, 3.+0.j, 5.+0.j, 6.+0.j]) >>> np.sort_complex([1 + 2j, 2 - 1j, 3 - 2j, 3 - 3j, 3 + 5j]) array([1.+2.j, 2.-1.j, 3.-3.j, 3.-2.j, 3.+5.j]) ### source Print or write to a file the source code for a NumPy object. The source code is only returned for objects written in Python. Many functions and classes are defined in C and will therefore not return useful information. Parameters ---------- object : numpy object Input object. This can be any object (function, class, module, ...). output : file object, optional If `output` not supplied then source code is printed to screen (sys.stdout). File object must be created with either write 'w' or append 'a' modes. See Also -------- lookfor, info Examples -------- >>> np.source(np.interp) #doctest: +SKIP In file: /usr/lib/python2.6/dist-packages/numpy/lib/function_base.py def interp(x, xp, fp, left=None, right=None): """.... (full docstring printed)""" if isinstance(x, (float, int, number)): return compiled_interp([x], xp, fp, left, right).item() else: return compiled_interp(x, xp, fp, left, right) The source code is only returned for objects written in Python. >>> np.source(np.array) #doctest: +SKIP Not available for this object. ### split Split an array into multiple sub-arrays as views into `ary`. Parameters ---------- ary : ndarray Array to be divided into sub-arrays. indices_or_sections : int or 1-D array If `indices_or_sections` is an integer, N, the array will be divided into N equal arrays along `axis`. If such a split is not possible, an error is raised. If `indices_or_sections` is a 1-D array of sorted integers, the entries indicate where along `axis` the array is split. For example, ``[2, 3]`` would, for ``axis=0``, result in - ary[:2] - ary[2:3] - ary[3:] If an index exceeds the dimension of the array along `axis`, an empty sub-array is returned correspondingly. axis : int, optional The axis along which to split, default is 0. Returns ------- sub-arrays : list of ndarrays A list of sub-arrays as views into `ary`. Raises ------ ValueError If `indices_or_sections` is given as an integer, but a split does not result in equal division. See Also -------- array_split : Split an array into multiple sub-arrays of equal or near-equal size. Does not raise an exception if an equal division cannot be made. hsplit : Split array into multiple sub-arrays horizontally (column-wise). vsplit : Split array into multiple sub-arrays vertically (row wise). dsplit : Split array into multiple sub-arrays along the 3rd axis (depth). concatenate : Join a sequence of arrays along an existing axis. stack : Join a sequence of arrays along a new axis. hstack : Stack arrays in sequence horizontally (column wise). vstack : Stack arrays in sequence vertically (row wise). dstack : Stack arrays in sequence depth wise (along third dimension). Examples -------- >>> x = np.arange(9.0) >>> np.split(x, 3) [array([0., 1., 2.]), array([3., 4., 5.]), array([6., 7., 8.])] >>> x = np.arange(8.0) >>> np.split(x, [3, 5, 6, 10]) [array([0., 1., 2.]), array([3., 4.]), array([5.]), array([6., 7.]), array([], dtype=float64)] ### squeeze Remove axes of length one from `a`. Parameters ---------- a : array_like Input data. axis : None or int or tuple of ints, optional .. versionadded:: 1.7.0 Selects a subset of the entries of length one in the shape. If an axis is selected with shape entry greater than one, an error is raised. Returns ------- squeezed : ndarray The input array, but with all or a subset of the dimensions of length 1 removed. This is always `a` itself or a view into `a`. Note that if all axes are squeezed, the result is a 0d array and not a scalar. Raises ------ ValueError If `axis` is not None, and an axis being squeezed is not of length 1 See Also -------- expand_dims : The inverse operation, adding entries of length one reshape : Insert, remove, and combine dimensions, and resize existing ones Examples -------- >>> x = np.array([[[0], [1], [2]]]) >>> x.shape (1, 3, 1) >>> np.squeeze(x).shape (3,) >>> np.squeeze(x, axis=0).shape (3, 1) >>> np.squeeze(x, axis=1).shape Traceback (most recent call last): ... ValueError: cannot select an axis to squeeze out which has size not equal to one >>> np.squeeze(x, axis=2).shape (1, 3) >>> x = np.array([[1234]]) >>> x.shape (1, 1) >>> np.squeeze(x) [array(1234)](https://www.chedong.com/phpMan.php/man/array/1234/markdown) # 0d array >>> np.squeeze(x).shape () >>> np.squeeze(x)[()] 1234 ### stack Join a sequence of arrays along a new axis. The ``axis`` parameter specifies the index of the new axis in the dimensions of the result. For example, if ``axis=0`` it will be the first dimension and if ``axis=-1`` it will be the last dimension. .. versionadded:: 1.10.0 Parameters ---------- arrays : sequence of array_like Each array must have the same shape. axis : int, optional The axis in the result array along which the input arrays are stacked. out : ndarray, optional If provided, the destination to place the result. The shape must be correct, matching that of what stack would have returned if no out argument were specified. Returns ------- stacked : ndarray The stacked array has one more dimension than the input arrays. See Also -------- concatenate : Join a sequence of arrays along an existing axis. block : Assemble an nd-array from nested lists of blocks. split : Split array into a list of multiple sub-arrays of equal size. Examples -------- >>> arrays = [np.random.randn(3, 4) for _ in [range(10)](https://www.chedong.com/phpMan.php/man/range/10/markdown)] >>> np.stack(arrays, axis=0).shape (10, 3, 4) >>> np.stack(arrays, axis=1).shape (3, 10, 4) >>> np.stack(arrays, axis=2).shape (3, 4, 10) >>> a = np.array([1, 2, 3]) >>> b = np.array([4, 5, 6]) >>> np.stack((a, b)) array([[1, 2, 3], [4, 5, 6]]) >>> np.stack((a, b), axis=-1) array([[1, 4], [2, 5], [3, 6]]) ### std Compute the standard deviation along the specified axis. Returns the standard deviation, a measure of the spread of a distribution, of the array elements. The standard deviation is computed for the flattened array by default, otherwise over the specified axis. Parameters ---------- a : array_like Calculate the standard deviation of these values. axis : None or int or tuple of ints, optional Axis or axes along which the standard deviation is computed. The default is to compute the standard deviation of the flattened array. .. versionadded:: 1.7.0 If this is a tuple of ints, a standard deviation is performed over multiple axes, instead of a single axis or all the axes as before. dtype : dtype, optional Type to use in computing the standard deviation. For arrays of integer type the default is float64, for arrays of float types it is the same as the array type. out : ndarray, optional Alternative output array in which to place the result. It must have the same shape as the expected output but the type (of the calculated values) will be cast if necessary. ddof : int, optional Means Delta Degrees of Freedom. The divisor used in calculations is ``N - ddof``, where ``N`` represents the number of elements. By default `ddof` is zero. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array. If the default value is passed, then `keepdims` will not be passed through to the `std` method of sub-classes of `ndarray`, however any non-default value will be. If the sub-class' method does not implement `keepdims` any exceptions will be raised. where : array_like of bool, optional Elements to include in the standard deviation. See `~numpy.ufunc.reduce` for details. .. versionadded:: 1.20.0 Returns ------- standard_deviation : ndarray, see dtype parameter above. If `out` is None, return a new array containing the standard deviation, otherwise return a reference to the output array. See Also -------- var, mean, nanmean, nanstd, nanvar :ref:`ufuncs-output-type` Notes ----- The standard deviation is the square root of the average of the squared deviations from the mean, i.e., ``std = sqrt(mean(x))``, where ``x = abs(a - a.mean())**2``. The average squared deviation is typically calculated as ``x.sum() / N``, where ``N = len(x)``. If, however, `ddof` is specified, the divisor ``N - ddof`` is used instead. In standard statistical practice, ``ddof=1`` provides an unbiased estimator of the variance of the infinite population. ``ddof=0`` provides a maximum likelihood estimate of the variance for normally distributed variables. The standard deviation computed in this function is the square root of the estimated variance, so even with ``ddof=1``, it will not be an unbiased estimate of the standard deviation per se. Note that, for complex numbers, `std` takes the absolute value before squaring, so that the result is always real and nonnegative. For floating-point input, the *std* is computed using the same precision the input has. Depending on the input data, this can cause the results to be inaccurate, especially for float32 (see example below). Specifying a higher-accuracy accumulator using the `dtype` keyword can alleviate this issue. Examples -------- >>> a = np.array([[1, 2], [3, 4]]) >>> np.std(a) 1.1180339887498949 # may vary >>> np.std(a, axis=0) array([1., 1.]) >>> np.std(a, axis=1) array([0.5, 0.5]) In single precision, std() can be inaccurate: >>> a = np.zeros((2, 512*512), dtype=np.float32) >>> a[0, :] = 1.0 >>> a[1, :] = 0.1 >>> np.std(a) 0.45000005 Computing the standard deviation in float64 is more accurate: >>> np.std(a, dtype=np.float64) 0.44999999925494177 # may vary Specifying a where argument: >>> a = np.array([[14, 8, 11, 10], [7, 9, 10, 11], [10, 15, 5, 10]]) >>> np.std(a) 2.614064523559687 # may vary >>> np.std(a, where=[[True], [True], [False]]) 2.0 ### sum Sum of array elements over a given axis. Parameters ---------- a : array_like Elements to sum. axis : None or int or tuple of ints, optional Axis or axes along which a sum is performed. The default, axis=None, will sum all of the elements of the input array. If axis is negative it counts from the last to the first axis. .. versionadded:: 1.7.0 If axis is a tuple of ints, a sum is performed on all of the axes specified in the tuple instead of a single axis or all the axes as before. dtype : dtype, optional The type of the returned array and of the accumulator in which the elements are summed. The dtype of `a` is used by default unless `a` has an integer dtype of less precision than the default platform integer. In that case, if `a` is signed then the platform integer is used while if `a` is unsigned then an unsigned integer of the same precision as the platform integer is used. out : ndarray, optional Alternative output array in which to place the result. It must have the same shape as the expected output, but the type of the output values will be cast if necessary. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array. If the default value is passed, then `keepdims` will not be passed through to the `sum` method of sub-classes of `ndarray`, however any non-default value will be. If the sub-class' method does not implement `keepdims` any exceptions will be raised. initial : scalar, optional Starting value for the sum. See `~numpy.ufunc.reduce` for details. .. versionadded:: 1.15.0 where : array_like of bool, optional Elements to include in the sum. See `~numpy.ufunc.reduce` for details. .. versionadded:: 1.17.0 Returns ------- sum_along_axis : ndarray An array with the same shape as `a`, with the specified axis removed. If `a` is a 0-d array, or if `axis` is None, a scalar is returned. If an output array is specified, a reference to `out` is returned. See Also -------- ndarray.sum : Equivalent method. add.reduce : Equivalent functionality of `add`. cumsum : Cumulative sum of array elements. trapz : Integration of array values using the composite trapezoidal rule. mean, average Notes ----- Arithmetic is modular when using integer types, and no error is raised on overflow. The sum of an empty array is the neutral element 0: >>> np.sum([]) 0.0 For floating point numbers the numerical precision of sum (and ``np.add.reduce``) is in general limited by directly adding each number individually to the result causing rounding errors in every step. However, often numpy will use a numerically better approach (partial pairwise summation) leading to improved precision in many use-cases. This improved precision is always provided when no ``axis`` is given. When ``axis`` is given, it will depend on which axis is summed. Technically, to provide the best speed possible, the improved precision is only used when the summation is along the fast axis in memory. Note that the exact precision may vary depending on other parameters. In contrast to NumPy, Python's ``math.fsum`` function uses a slower but more precise approach to summation. Especially when summing a large number of lower precision floating point numbers, such as ``float32``, numerical errors can become significant. In such cases it can be advisable to use `dtype="float64"` to use a higher precision for the output. Examples -------- >>> np.sum([0.5, 1.5]) 2.0 >>> np.sum([0.5, 0.7, 0.2, 1.5], dtype=np.int32) 1 >>> np.sum([[0, 1], [0, 5]]) 6 >>> np.sum([[0, 1], [0, 5]], axis=0) array([0, 6]) >>> np.sum([[0, 1], [0, 5]], axis=1) array([1, 5]) >>> np.sum([[0, 1], [np.nan, 5]], where=[False, True], axis=1) array([1., 5.]) If the accumulator is too small, overflow occurs: >>> np.ones(128, dtype=np.int8).sum(dtype=np.int8) -128 You can also start the sum with a value other than zero: >>> np.sum([10], initial=5) 15 ### swapaxes Interchange two axes of an array. Parameters ---------- a : array_like Input array. axis1 : int First axis. axis2 : int Second axis. Returns ------- a_swapped : ndarray For NumPy >= 1.10.0, if `a` is an ndarray, then a view of `a` is returned; otherwise a new array is created. For earlier NumPy versions a view of `a` is returned only if the order of the axes is changed, otherwise the input array is returned. Examples -------- >>> x = np.array([[1,2,3]]) >>> np.swapaxes(x,0,1) array([[1], [2], [3]]) >>> x = np.array([[[0,1],[2,3]],[[4,5],[6,7]]]) >>> x array([[[0, 1], [2, 3]], [[4, 5], [6, 7]]]) >>> np.swapaxes(x,0,2) array([[[0, 4], [2, 6]], [[1, 5], [3, 7]]]) ### take Take elements from an array along an axis. When axis is not None, this function does the same thing as "fancy" indexing (indexing arrays using arrays); however, it can be easier to use if you need elements along a given axis. A call such as ``np.take(arr, indices, axis=3)`` is equivalent to ``arr[:,:,:,indices,...]``. Explained without fancy indexing, this is equivalent to the following use of `ndindex`, which sets each of ``ii``, ``jj``, and ``kk`` to a tuple of indices:: Ni, Nk = a.shape[:axis], a.shape[axis+1:] Nj = indices.shape for ii in ndindex(Ni): for jj in ndindex(Nj): for kk in ndindex(Nk): out[ii + jj + kk] = a[ii + (indices[jj],) + kk] Parameters ---------- a : array_like (Ni..., M, Nk...) The source array. indices : array_like (Nj...) The indices of the values to extract. .. versionadded:: 1.8.0 Also allow scalars for indices. axis : int, optional The axis over which to select values. By default, the flattened input array is used. out : ndarray, optional (Ni..., Nj..., Nk...) If provided, the result will be placed in this array. It should be of the appropriate shape and dtype. Note that `out` is always buffered if `mode='raise'`; use other modes for better performance. mode : {'raise', 'wrap', 'clip'}, optional Specifies how out-of-bounds indices will behave. * 'raise' -- raise an error (default) * 'wrap' -- wrap around * 'clip' -- clip to the range 'clip' mode means that all indices that are too large are replaced by the index that addresses the last element along that axis. Note that this disables indexing with negative numbers. Returns ------- out : ndarray (Ni..., Nj..., Nk...) The returned array has the same type as `a`. See Also -------- compress : Take elements using a boolean mask ndarray.take : equivalent method take_along_axis : Take elements by matching the array and the index arrays Notes ----- By eliminating the inner loop in the description above, and using `s_` to build simple slice objects, `take` can be expressed in terms of applying fancy indexing to each 1-d slice:: Ni, Nk = a.shape[:axis], a.shape[axis+1:] for ii in ndindex(Ni): for kk in ndindex(Nj): out[ii + s_[...,] + kk] = a[ii + s_[:,] + kk][indices] For this reason, it is equivalent to (but faster than) the following use of `apply_along_axis`:: out = np.apply_along_axis(lambda a_1d: a_1d[indices], axis, a) Examples -------- >>> a = [4, 3, 5, 7, 6, 8] >>> indices = [0, 1, 4] >>> np.take(a, indices) array([4, 3, 6]) In this example if `a` is an ndarray, "fancy" indexing can be used. >>> a = np.array(a) >>> a[indices] array([4, 3, 6]) If `indices` is not one dimensional, the output also has these dimensions. >>> np.take(a, [[0, 1], [2, 3]]) array([[4, 3], [5, 7]]) ### take_along_axis Take values from the input array by matching 1d index and data slices. This iterates over matching 1d slices oriented along the specified axis in the index and data arrays, and uses the former to look up values in the latter. These slices can be different lengths. Functions returning an index along an axis, like `argsort` and `argpartition`, produce suitable indices for this function. .. versionadded:: 1.15.0 Parameters ---------- arr : ndarray (Ni..., M, Nk...) Source array indices : ndarray (Ni..., J, Nk...) Indices to take along each 1d slice of `arr`. This must match the dimension of arr, but dimensions Ni and Nj only need to broadcast against `arr`. axis : int The axis to take 1d slices along. If axis is None, the input array is treated as if it had first been flattened to 1d, for consistency with `sort` and `argsort`. Returns ------- out: ndarray (Ni..., J, Nk...) The indexed result. Notes ----- This is equivalent to (but faster than) the following use of `ndindex` and `s_`, which sets each of ``ii`` and ``kk`` to a tuple of indices:: Ni, M, Nk = a.shape[:axis], a.shape[axis], a.shape[axis+1:] J = indices.shape[axis] # Need not equal M out = np.empty(Ni + (J,) + Nk) for ii in ndindex(Ni): for kk in ndindex(Nk): a_1d = a [ii + s_[:,] + kk] indices_1d = indices[ii + s_[:,] + kk] out_1d = out [ii + s_[:,] + kk] for j in range(J): out_1d[j] = a_1d[indices_1d[j]] Equivalently, eliminating the inner loop, the last two lines would be:: out_1d[:] = a_1d[indices_1d] See Also -------- take : Take along an axis, using the same indices for every 1d slice put_along_axis : Put values into the destination array by matching 1d index and data slices Examples -------- For this sample array >>> a = np.array([[10, 30, 20], [60, 40, 50]]) We can sort either by using sort directly, or argsort and this function >>> np.sort(a, axis=1) array([[10, 20, 30], [40, 50, 60]]) >>> ai = np.argsort(a, axis=1); ai array([[0, 2, 1], [1, 2, 0]]) >>> np.take_along_axis(a, ai, axis=1) array([[10, 20, 30], [40, 50, 60]]) The same works for max and min, if you expand the dimensions: >>> np.expand_dims(np.max(a, axis=1), axis=1) array([[30], [60]]) >>> ai = np.expand_dims(np.argmax(a, axis=1), axis=1) >>> ai array([[1], [0]]) >>> np.take_along_axis(a, ai, axis=1) array([[30], [60]]) If we want to get the max and min at the same time, we can stack the indices first >>> ai_min = np.expand_dims(np.argmin(a, axis=1), axis=1) >>> ai_max = np.expand_dims(np.argmax(a, axis=1), axis=1) >>> ai = np.concatenate([ai_min, ai_max], axis=1) >>> ai array([[0, 1], [1, 0]]) >>> np.take_along_axis(a, ai, axis=1) array([[10, 30], [40, 60]]) ### tensordot Compute tensor dot product along specified axes. Given two tensors, `a` and `b`, and an array_like object containing two array_like objects, ``(a_axes, b_axes)``, sum the products of `a`'s and `b`'s elements (components) over the axes specified by ``a_axes`` and ``b_axes``. The third argument can be a single non-negative integer_like scalar, ``N``; if it is such, then the last ``N`` dimensions of `a` and the first ``N`` dimensions of `b` are summed over. Parameters ---------- a, b : array_like Tensors to "dot". axes : int or (2,) array_like * integer_like If an int N, sum over the last N axes of `a` and the first N axes of `b` in order. The sizes of the corresponding axes must match. * (2,) array_like Or, a list of axes to be summed over, first sequence applying to `a`, second to `b`. Both elements array_like must be of the same length. Returns ------- output : ndarray The tensor dot product of the input. See Also -------- dot, einsum Notes ----- Three common use cases are: * ``axes = 0`` : tensor product :math:`a\otimes b` * ``axes = 1`` : tensor dot product :math:`a\cdot b` * ``axes = 2`` : (default) tensor double contraction :math:`a:b` When `axes` is integer_like, the sequence for evaluation will be: first the -Nth axis in `a` and 0th axis in `b`, and the -1th axis in `a` and Nth axis in `b` last. When there is more than one axis to sum over - and they are not the last (first) axes of `a` (`b`) - the argument `axes` should consist of two sequences of the same length, with the first axis to sum over given first in both sequences, the second axis second, and so forth. The shape of the result consists of the non-contracted axes of the first tensor, followed by the non-contracted axes of the second. Examples -------- A "traditional" example: >>> a = np.arange(60.).reshape(3,4,5) >>> b = np.arange(24.).reshape(4,3,2) >>> c = np.tensordot(a,b, axes=([1,0],[0,1])) >>> c.shape (5, 2) >>> c array([[4400., 4730.], [4532., 4874.], [4664., 5018.], [4796., 5162.], [4928., 5306.]]) >>> # A slower but equivalent way of computing the same... >>> d = np.zeros((5,2)) >>> for i in [range(5)](https://www.chedong.com/phpMan.php/man/range/5/markdown): ... for j in [range(2)](https://www.chedong.com/phpMan.php/man/range/2/markdown): ... for k in [range(3)](https://www.chedong.com/phpMan.php/man/range/3/markdown): ... for n in [range(4)](https://www.chedong.com/phpMan.php/man/range/4/markdown): ... d[i,j] += a[k,n,i] * b[n,k,j] >>> c == d array([[ True, True], [ True, True], [ True, True], [ True, True], [ True, True]]) An extended example taking advantage of the overloading of + and \*: >>> a = np.array(range(1, 9)) >>> a.shape = (2, 2, 2) >>> A = np.array(('a', 'b', 'c', 'd'), dtype=object) >>> A.shape = (2, 2) >>> a; A array([[[1, 2], [3, 4]], [[5, 6], [7, 8]]]) array([['a', 'b'], ['c', 'd']], dtype=object) >>> np.tensordot(a, A) # third argument default is 2 for double-contraction array(['abbcccdddd', 'aaaaabbbbbbcccccccdddddddd'], dtype=object) >>> np.tensordot(a, A, 1) array([[['acc', 'bdd'], ['aaacccc', 'bbbdddd']], [['aaaaacccccc', 'bbbbbdddddd'], ['aaaaaaacccccccc', 'bbbbbbbdddddddd']]], dtype=object) >>> np.tensordot(a, A, 0) # tensor product (result too long to incl.) array([[[[['a', 'b'], ['c', 'd']], ... >>> np.tensordot(a, A, (0, 1)) array([[['abbbbb', 'cddddd'], ['aabbbbbb', 'ccdddddd']], [['aaabbbbbbb', 'cccddddddd'], ['aaaabbbbbbbb', 'ccccdddddddd']]], dtype=object) >>> np.tensordot(a, A, (2, 1)) array([[['abb', 'cdd'], ['aaabbbb', 'cccdddd']], [['aaaaabbbbbb', 'cccccdddddd'], ['aaaaaaabbbbbbbb', 'cccccccdddddddd']]], dtype=object) >>> np.tensordot(a, A, ((0, 1), (0, 1))) array(['abbbcccccddddddd', 'aabbbbccccccdddddddd'], dtype=object) >>> np.tensordot(a, A, ((2, 1), (1, 0))) array(['acccbbdddd', 'aaaaacccccccbbbbbbdddddddd'], dtype=object) ### tile Construct an array by repeating A the number of times given by reps. If `reps` has length ``d``, the result will have dimension of ``max(d, A.ndim)``. If ``A.ndim < d``, `A` is promoted to be d-dimensional by prepending new axes. So a shape (3,) array is promoted to (1, 3) for 2-D replication, or shape (1, 1, 3) for 3-D replication. If this is not the desired behavior, promote `A` to d-dimensions manually before calling this function. If ``A.ndim > d``, `reps` is promoted to `A`.ndim by pre-pending 1's to it. Thus for an `A` of shape (2, 3, 4, 5), a `reps` of (2, 2) is treated as (1, 1, 2, 2). Note : Although tile may be used for broadcasting, it is strongly recommended to use numpy's broadcasting operations and functions. Parameters ---------- A : array_like The input array. reps : array_like The number of repetitions of `A` along each axis. Returns ------- c : ndarray The tiled output array. See Also -------- repeat : Repeat elements of an array. broadcast_to : Broadcast an array to a new shape Examples -------- >>> a = np.array([0, 1, 2]) >>> np.tile(a, 2) array([0, 1, 2, 0, 1, 2]) >>> np.tile(a, (2, 2)) array([[0, 1, 2, 0, 1, 2], [0, 1, 2, 0, 1, 2]]) >>> np.tile(a, (2, 1, 2)) array([[[0, 1, 2, 0, 1, 2]], [[0, 1, 2, 0, 1, 2]]]) >>> b = np.array([[1, 2], [3, 4]]) >>> np.tile(b, 2) array([[1, 2, 1, 2], [3, 4, 3, 4]]) >>> np.tile(b, (2, 1)) array([[1, 2], [3, 4], [1, 2], [3, 4]]) >>> c = np.array([1,2,3,4]) >>> np.tile(c,(4,1)) array([[1, 2, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4]]) ### trace Return the sum along diagonals of the array. If `a` is 2-D, the sum along its diagonal with the given offset is returned, i.e., the sum of elements ``a[i,i+offset]`` for all i. If `a` has more than two dimensions, then the axes specified by axis1 and axis2 are used to determine the 2-D sub-arrays whose traces are returned. The shape of the resulting array is the same as that of `a` with `axis1` and `axis2` removed. Parameters ---------- a : array_like Input array, from which the diagonals are taken. offset : int, optional Offset of the diagonal from the main diagonal. Can be both positive and negative. Defaults to 0. axis1, axis2 : int, optional Axes to be used as the first and second axis of the 2-D sub-arrays from which the diagonals should be taken. Defaults are the first two axes of `a`. dtype : dtype, optional Determines the data-type of the returned array and of the accumulator where the elements are summed. If dtype has the value None and `a` is of integer type of precision less than the default integer precision, then the default integer precision is used. Otherwise, the precision is the same as that of `a`. out : ndarray, optional Array into which the output is placed. Its type is preserved and it must be of the right shape to hold the output. Returns ------- sum_along_diagonals : ndarray If `a` is 2-D, the sum along the diagonal is returned. If `a` has larger dimensions, then an array of sums along diagonals is returned. See Also -------- diag, diagonal, diagflat Examples -------- >>> np.trace([np.eye(3)](https://www.chedong.com/phpMan.php/man/np.eye/3/markdown)) 3.0 >>> a = [np.arange(8)](https://www.chedong.com/phpMan.php/man/np.arange/8/markdown).reshape((2,2,2)) >>> np.trace(a) array([6, 8]) >>> a = [np.arange(24)](https://www.chedong.com/phpMan.php/man/np.arange/24/markdown).reshape((2,2,2,3)) >>> np.trace(a).shape (2, 3) ### transpose Reverse or permute the axes of an array; returns the modified array. For an array a with two axes, transpose(a) gives the matrix transpose. Refer to `numpy.ndarray.transpose` for full documentation. Parameters ---------- a : array_like Input array. axes : tuple or list of ints, optional If specified, it must be a tuple or list which contains a permutation of [0,1,..,N-1] where N is the number of axes of a. The i'th axis of the returned array will correspond to the axis numbered ``axes[i]`` of the input. If not specified, defaults to ``range(a.ndim)[::-1]``, which reverses the order of the axes. Returns ------- p : ndarray `a` with its axes permuted. A view is returned whenever possible. See Also -------- ndarray.transpose : Equivalent method moveaxis argsort Notes ----- Use `transpose(a, argsort(axes))` to invert the transposition of tensors when using the `axes` keyword argument. Transposing a 1-D array returns an unchanged view of the original array. Examples -------- >>> x = [np.arange(4)](https://www.chedong.com/phpMan.php/man/np.arange/4/markdown).reshape((2,2)) >>> x array([[0, 1], [2, 3]]) >>> np.transpose(x) array([[0, 2], [1, 3]]) >>> x = np.ones((1, 2, 3)) >>> np.transpose(x, (1, 0, 2)).shape (2, 1, 3) >>> x = np.ones((2, 3, 4, 5)) >>> np.transpose(x).shape (5, 4, 3, 2) ### trapz Integrate along the given axis using the composite trapezoidal rule. If `x` is provided, the integration happens in sequence along its elements - they are not sorted. Integrate `y` (`x`) along each 1d slice on the given axis, compute :math:`\int y(x) dx`. When `x` is specified, this integrates along the parametric curve, computing :math:`\int_t y(t) dt = \int_t y(t) \left.\frac{dx}{dt}\right|_{x=x(t)} dt`. Parameters ---------- y : array_like Input array to integrate. x : array_like, optional The sample points corresponding to the `y` values. If `x` is None, the sample points are assumed to be evenly spaced `dx` apart. The default is None. dx : scalar, optional The spacing between sample points when `x` is None. The default is 1. axis : int, optional The axis along which to integrate. Returns ------- trapz : float or ndarray Definite integral of 'y' = n-dimensional array as approximated along a single axis by the trapezoidal rule. If 'y' is a 1-dimensional array, then the result is a float. If 'n' is greater than 1, then the result is an 'n-1' dimensional array. See Also -------- sum, cumsum Notes ----- Image [2]_ illustrates trapezoidal rule -- y-axis locations of points will be taken from `y` array, by default x-axis distances between points will be 1.0, alternatively they can be provided with `x` array or with `dx` scalar. Return value will be equal to combined area under the red lines. References ---------- .. [1] Wikipedia page: .. [2] Illustration image: Examples -------- >>> np.trapz([1,2,3]) 4.0 >>> np.trapz([1,2,3], x=[4,6,8]) 8.0 >>> np.trapz([1,2,3], dx=2) 8.0 Using a decreasing `x` corresponds to integrating in reverse: >>> np.trapz([1,2,3], x=[8,6,4]) -8.0 More generally `x` is used to integrate along a parametric curve. This finds the area of a circle, noting we repeat the sample which closes the curve: >>> theta = np.linspace(0, 2 * np.pi, num=1000, endpoint=True) >>> np.trapz(np.cos(theta), x=np.sin(theta)) 3.141571941375841 >>> a = [np.arange(6)](https://www.chedong.com/phpMan.php/man/np.arange/6/markdown).reshape(2, 3) >>> a array([[0, 1, 2], [3, 4, 5]]) >>> np.trapz(a, axis=0) array([1.5, 2.5, 3.5]) >>> np.trapz(a, axis=1) array([2., 8.]) ### tri An array with ones at and below the given diagonal and zeros elsewhere. Parameters ---------- N : int Number of rows in the array. M : int, optional Number of columns in the array. By default, `M` is taken equal to `N`. k : int, optional The sub-diagonal at and below which the array is filled. `k` = 0 is the main diagonal, while `k` < 0 is below it, and `k` > 0 is above. The default is 0. dtype : dtype, optional Data type of the returned array. The default is float. like : array_like Reference object to allow the creation of arrays which are not NumPy arrays. If an array-like passed in as ``like`` supports the ``__array_function__`` protocol, the result will be defined by it. In this case, it ensures the creation of an array object compatible with that passed in via this argument. .. versionadded:: 1.20.0 Returns ------- tri : ndarray of shape (N, M) Array with its lower triangle filled with ones and zero elsewhere; in other words ``T[i,j] == 1`` for ``j <= i + k``, 0 otherwise. Examples -------- >>> np.tri(3, 5, 2, dtype=int) array([[1, 1, 1, 0, 0], [1, 1, 1, 1, 0], [1, 1, 1, 1, 1]]) >>> np.tri(3, 5, -1) array([[0., 0., 0., 0., 0.], [1., 0., 0., 0., 0.], [1., 1., 0., 0., 0.]]) ### tril Lower triangle of an array. Return a copy of an array with elements above the `k`-th diagonal zeroed. Parameters ---------- m : array_like, shape (M, N) Input array. k : int, optional Diagonal above which to zero elements. `k = 0` (the default) is the main diagonal, `k < 0` is below it and `k > 0` is above. Returns ------- tril : ndarray, shape (M, N) Lower triangle of `m`, of same shape and data-type as `m`. See Also -------- triu : same thing, only for the upper triangle Examples -------- >>> np.tril([[1,2,3],[4,5,6],[7,8,9],[10,11,12]], -1) array([[ 0, 0, 0], [ 4, 0, 0], [ 7, 8, 0], [10, 11, 12]]) ### tril_indices Return the indices for the lower-triangle of an (n, m) array. Parameters ---------- n : int The row dimension of the arrays for which the returned indices will be valid. k : int, optional Diagonal offset (see `tril` for details). m : int, optional .. versionadded:: 1.9.0 The column dimension of the arrays for which the returned arrays will be valid. By default `m` is taken equal to `n`. Returns ------- inds : tuple of arrays The indices for the triangle. The returned tuple contains two arrays, each with the indices along one dimension of the array. See also -------- triu_indices : similar function, for upper-triangular. mask_indices : generic function accepting an arbitrary mask function. tril, triu Notes ----- .. versionadded:: 1.4.0 Examples -------- Compute two different sets of indices to access 4x4 arrays, one for the lower triangular part starting at the main diagonal, and one starting two diagonals further right: >>> il1 = [np.tril_indices(4)](https://www.chedong.com/phpMan.php/man/np.trilindices/4/markdown) >>> il2 = np.tril_indices(4, 2) Here is how they can be used with a sample array: >>> a = [np.arange(16)](https://www.chedong.com/phpMan.php/man/np.arange/16/markdown).reshape(4, 4) >>> a array([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11], [12, 13, 14, 15]]) Both for indexing: >>> a[il1] array([ 0, 4, 5, ..., 13, 14, 15]) And for assigning values: >>> a[il1] = -1 >>> a array([[-1, 1, 2, 3], [-1, -1, 6, 7], [-1, -1, -1, 11], [-1, -1, -1, -1]]) These cover almost the whole array (two diagonals right of the main one): >>> a[il2] = -10 >>> a array([[-10, -10, -10, 3], [-10, -10, -10, -10], [-10, -10, -10, -10], [-10, -10, -10, -10]]) ### tril_indices_from Return the indices for the lower-triangle of arr. See `tril_indices` for full details. Parameters ---------- arr : array_like The indices will be valid for square arrays whose dimensions are the same as arr. k : int, optional Diagonal offset (see `tril` for details). See Also -------- tril_indices, tril Notes ----- .. versionadded:: 1.4.0 ### trim_zeros Trim the leading and/or trailing zeros from a 1-D array or sequence. Parameters ---------- filt : 1-D array or sequence Input array. trim : str, optional A string with 'f' representing trim from front and 'b' to trim from back. Default is 'fb', trim zeros from both front and back of the array. Returns ------- trimmed : 1-D array or sequence The result of trimming the input. The input data type is preserved. Examples -------- >>> a = np.array((0, 0, 0, 1, 2, 3, 0, 2, 1, 0)) >>> np.trim_zeros(a) array([1, 2, 3, 0, 2, 1]) >>> np.trim_zeros(a, 'b') array([0, 0, 0, ..., 0, 2, 1]) The input data type is preserved, list/tuple in means list/tuple out. >>> np.trim_zeros([0, 1, 2, 0]) [1, 2] ### triu Upper triangle of an array. Return a copy of an array with the elements below the `k`-th diagonal zeroed. Please refer to the documentation for `tril` for further details. See Also -------- tril : lower triangle of an array Examples -------- >>> np.triu([[1,2,3],[4,5,6],[7,8,9],[10,11,12]], -1) array([[ 1, 2, 3], [ 4, 5, 6], [ 0, 8, 9], [ 0, 0, 12]]) ### triu_indices Return the indices for the upper-triangle of an (n, m) array. Parameters ---------- n : int The size of the arrays for which the returned indices will be valid. k : int, optional Diagonal offset (see `triu` for details). m : int, optional .. versionadded:: 1.9.0 The column dimension of the arrays for which the returned arrays will be valid. By default `m` is taken equal to `n`. Returns ------- inds : tuple, [shape(2)](https://www.chedong.com/phpMan.php/man/shape/2/markdown) of ndarrays, shape(`n`) The indices for the triangle. The returned tuple contains two arrays, each with the indices along one dimension of the array. Can be used to slice a ndarray of shape(`n`, `n`). See also -------- tril_indices : similar function, for lower-triangular. mask_indices : generic function accepting an arbitrary mask function. triu, tril Notes ----- .. versionadded:: 1.4.0 Examples -------- Compute two different sets of indices to access 4x4 arrays, one for the upper triangular part starting at the main diagonal, and one starting two diagonals further right: >>> iu1 = [np.triu_indices(4)](https://www.chedong.com/phpMan.php/man/np.triuindices/4/markdown) >>> iu2 = np.triu_indices(4, 2) Here is how they can be used with a sample array: >>> a = [np.arange(16)](https://www.chedong.com/phpMan.php/man/np.arange/16/markdown).reshape(4, 4) >>> a array([[ 0, 1, 2, 3], [ 4, 5, 6, 7], [ 8, 9, 10, 11], [12, 13, 14, 15]]) Both for indexing: >>> a[iu1] array([ 0, 1, 2, ..., 10, 11, 15]) And for assigning values: >>> a[iu1] = -1 >>> a array([[-1, -1, -1, -1], [ 4, -1, -1, -1], [ 8, 9, -1, -1], [12, 13, 14, -1]]) These cover only a small part of the whole array (two diagonals right of the main one): >>> a[iu2] = -10 >>> a array([[ -1, -1, -10, -10], [ 4, -1, -1, -10], [ 8, 9, -1, -1], [ 12, 13, 14, -1]]) ### triu_indices_from Return the indices for the upper-triangle of arr. See `triu_indices` for full details. Parameters ---------- arr : ndarray, shape(N, N) The indices will be valid for square arrays. k : int, optional Diagonal offset (see `triu` for details). Returns ------- triu_indices_from : tuple, [shape(2)](https://www.chedong.com/phpMan.php/man/shape/2/markdown) of ndarray, shape(N) Indices for the upper-triangle of `arr`. See Also -------- triu_indices, triu Notes ----- .. versionadded:: 1.4.0 ### typename Return a description for the given data type code. Parameters ---------- char : str Data type code. Returns ------- out : str Description of the input data type code. See Also -------- dtype, typecodes Examples -------- >>> typechars = ['S1', '?', 'B', 'D', 'G', 'F', 'I', 'H', 'L', 'O', 'Q', ... 'S', 'U', 'V', 'b', 'd', 'g', 'f', 'i', 'h', 'l', 'q'] >>> for typechar in typechars: ... print(typechar, ' : ', np.typename(typechar)) ... S1 : character ? : bool B : unsigned char D : complex double precision G : complex long double precision F : complex single precision I : unsigned integer H : unsigned short L : unsigned long integer O : object Q : unsigned long long integer S : string U : unicode V : void b : signed char d : double precision g : long precision f : single precision i : integer h : short l : long integer q : long long integer ### union1d Find the union of two arrays. Return the unique, sorted array of values that are in either of the two input arrays. Parameters ---------- ar1, ar2 : array_like Input arrays. They are flattened if they are not already 1D. Returns ------- union1d : ndarray Unique, sorted union of the input arrays. See Also -------- numpy.lib.arraysetops : Module with a number of other functions for performing set operations on arrays. Examples -------- >>> np.union1d([-1, 0, 1], [-2, 0, 2]) array([-2, -1, 0, 1, 2]) To find the union of more than two arrays, use functools.reduce: >>> from functools import reduce >>> reduce(np.union1d, ([1, 3, 4, 3], [3, 1, 2, 1], [6, 3, 4, 2])) array([1, 2, 3, 4, 6]) ### unique Find the unique elements of an array. Returns the sorted unique elements of an array. There are three optional outputs in addition to the unique elements: * the indices of the input array that give the unique values * the indices of the unique array that reconstruct the input array * the number of times each unique value comes up in the input array Parameters ---------- ar : array_like Input array. Unless `axis` is specified, this will be flattened if it is not already 1-D. return_index : bool, optional If True, also return the indices of `ar` (along the specified axis, if provided, or in the flattened array) that result in the unique array. return_inverse : bool, optional If True, also return the indices of the unique array (for the specified axis, if provided) that can be used to reconstruct `ar`. return_counts : bool, optional If True, also return the number of times each unique item appears in `ar`. .. versionadded:: 1.9.0 axis : int or None, optional The axis to operate on. If None, `ar` will be flattened. If an integer, the subarrays indexed by the given axis will be flattened and treated as the elements of a 1-D array with the dimension of the given axis, see the notes for more details. Object arrays or structured arrays that contain objects are not supported if the `axis` kwarg is used. The default is None. .. versionadded:: 1.13.0 Returns ------- unique : ndarray The sorted unique values. unique_indices : ndarray, optional The indices of the first occurrences of the unique values in the original array. Only provided if `return_index` is True. unique_inverse : ndarray, optional The indices to reconstruct the original array from the unique array. Only provided if `return_inverse` is True. unique_counts : ndarray, optional The number of times each of the unique values comes up in the original array. Only provided if `return_counts` is True. .. versionadded:: 1.9.0 See Also -------- numpy.lib.arraysetops : Module with a number of other functions for performing set operations on arrays. repeat : Repeat elements of an array. Notes ----- When an axis is specified the subarrays indexed by the axis are sorted. This is done by making the specified axis the first dimension of the array (move the axis to the first dimension to keep the order of the other axes) and then flattening the subarrays in C order. The flattened subarrays are then viewed as a structured type with each element given a label, with the effect that we end up with a 1-D array of structured types that can be treated in the same way as any other 1-D array. The result is that the flattened subarrays are sorted in lexicographic order starting with the first element. .. versionchanged: NumPy 1.21 If nan values are in the input array, a single nan is put to the end of the sorted unique values. Also for complex arrays all NaN values are considered equivalent (no matter whether the NaN is in the real or imaginary part). As the representant for the returned array the smallest one in the lexicographical order is chosen - see np.sort for how the lexicographical order is defined for complex arrays. Examples -------- >>> np.unique([1, 1, 2, 2, 3, 3]) array([1, 2, 3]) >>> a = np.array([[1, 1], [2, 3]]) >>> np.unique(a) array([1, 2, 3]) Return the unique rows of a 2D array >>> a = np.array([[1, 0, 0], [1, 0, 0], [2, 3, 4]]) >>> np.unique(a, axis=0) array([[1, 0, 0], [2, 3, 4]]) Return the indices of the original array that give the unique values: >>> a = np.array(['a', 'b', 'b', 'c', 'a']) >>> u, indices = np.unique(a, return_index=True) >>> u array(['a', 'b', 'c'], dtype='>> indices array([0, 1, 3]) >>> a[indices] array(['a', 'b', 'c'], dtype='>> a = np.array([1, 2, 6, 4, 2, 3, 2]) >>> u, indices = np.unique(a, return_inverse=True) >>> u array([1, 2, 3, 4, 6]) >>> indices array([0, 1, 4, 3, 1, 2, 1]) >>> u[indices] array([1, 2, 6, 4, 2, 3, 2]) Reconstruct the input values from the unique values and counts: >>> a = np.array([1, 2, 6, 4, 2, 3, 2]) >>> values, counts = np.unique(a, return_counts=True) >>> values array([1, 2, 3, 4, 6]) >>> counts array([1, 3, 1, 1, 1]) >>> np.repeat(values, counts) array([1, 2, 2, 2, 3, 4, 6]) # original order not preserved ### unpackbits unpackbits(a, axis=None, count=None, bitorder='big') Unpacks elements of a uint8 array into a binary-valued output array. Each element of `a` represents a bit-field that should be unpacked into a binary-valued output array. The shape of the output array is either 1-D (if `axis` is ``None``) or the same shape as the input array with unpacking done along the axis specified. Parameters ---------- a : ndarray, uint8 type Input array. axis : int, optional The dimension over which bit-unpacking is done. ``None`` implies unpacking the flattened array. count : int or None, optional The number of elements to unpack along `axis`, provided as a way of undoing the effect of packing a size that is not a multiple of eight. A non-negative number means to only unpack `count` bits. A negative number means to trim off that many bits from the end. ``None`` means to unpack the entire array (the default). Counts larger than the available number of bits will add zero padding to the output. Negative counts must not exceed the available number of bits. .. versionadded:: 1.17.0 bitorder : {'big', 'little'}, optional The order of the returned bits. 'big' will mimic bin(val), ``3 = 0b00000011 => [0, 0, 0, 0, 0, 0, 1, 1]``, 'little' will reverse the order to ``[1, 1, 0, 0, 0, 0, 0, 0]``. Defaults to 'big'. .. versionadded:: 1.17.0 Returns ------- unpacked : ndarray, uint8 type The elements are binary-valued (0 or 1). See Also -------- packbits : Packs the elements of a binary-valued array into bits in a uint8 array. Examples -------- >>> a = np.array([[2], [7], [23]], dtype=np.uint8) >>> a array([[ 2], [ 7], [23]], dtype=uint8) >>> b = np.unpackbits(a, axis=1) >>> b array([[0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 0, 1, 1, 1]], dtype=uint8) >>> c = np.unpackbits(a, axis=1, count=-3) >>> c array([[0, 0, 0, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 1, 0]], dtype=uint8) >>> p = np.packbits(b, axis=0) >>> np.unpackbits(p, axis=0) array([[0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 1, 0, 1, 1, 1], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0]], dtype=uint8) >>> np.array_equal(b, np.unpackbits(p, axis=0, count=b.shape[0])) True ### unravel_index unravel_index(indices, shape, order='C') Converts a flat index or array of flat indices into a tuple of coordinate arrays. Parameters ---------- indices : array_like An integer array whose elements are indices into the flattened version of an array of dimensions ``shape``. Before version 1.6.0, this function accepted just one index value. shape : tuple of ints The shape of the array to use for unraveling ``indices``. .. versionchanged:: 1.16.0 Renamed from ``dims`` to ``shape``. order : {'C', 'F'}, optional Determines whether the indices should be viewed as indexing in row-major (C-style) or column-major (Fortran-style) order. .. versionadded:: 1.6.0 Returns ------- unraveled_coords : tuple of ndarray Each array in the tuple has the same shape as the ``indices`` array. See Also -------- ravel_multi_index Examples -------- >>> np.unravel_index([22, 41, 37], (7,6)) (array([3, 6, 6]), array([4, 5, 1])) >>> np.unravel_index([31, 41, 13], (7,6), order='F') (array([3, 6, 6]), array([4, 5, 1])) >>> np.unravel_index(1621, (6,7,8,9)) (3, 1, 4, 1) ### unwrap Unwrap by taking the complement of large deltas with respect to the period. This unwraps a signal `p` by changing elements which have an absolute difference from their predecessor of more than ``max(discont, period/2)`` to their `period`-complementary values. For the default case where `period` is :math:`2\pi` and is `discont` is :math:`\pi`, this unwraps a radian phase `p` such that adjacent differences are never greater than :math:`\pi` by adding :math:`2k\pi` for some integer :math:`k`. Parameters ---------- p : array_like Input array. discont : float, optional Maximum discontinuity between values, default is ``period/2``. Values below ``period/2`` are treated as if they were ``period/2``. To have an effect different from the default, `discont` should be larger than ``period/2``. axis : int, optional Axis along which unwrap will operate, default is the last axis. period: float, optional Size of the range over which the input wraps. By default, it is ``2 pi``. .. versionadded:: 1.21.0 Returns ------- out : ndarray Output array. See Also -------- rad2deg, deg2rad Notes ----- If the discontinuity in `p` is smaller than ``period/2``, but larger than `discont`, no unwrapping is done because taking the complement would only make the discontinuity larger. Examples -------- >>> phase = np.linspace(0, np.pi, num=5) >>> phase[3:] += np.pi >>> phase array([ 0. , 0.78539816, 1.57079633, 5.49778714, 6.28318531]) # may vary >>> np.unwrap(phase) array([ 0. , 0.78539816, 1.57079633, -0.78539816, 0. ]) # may vary >>> np.unwrap([0, 1, 2, -1, 0], period=4) array([0, 1, 2, 3, 4]) >>> np.unwrap([ 1, 2, 3, 4, 5, 6, 1, 2, 3], period=6) array([1, 2, 3, 4, 5, 6, 7, 8, 9]) >>> np.unwrap([2, 3, 4, 5, 2, 3, 4, 5], period=4) array([2, 3, 4, 5, 6, 7, 8, 9]) >>> phase_deg = np.mod(np.linspace(0 ,720, 19), 360) - 180 >>> np.unwrap(phase_deg, period=360) array([-180., -140., -100., -60., -20., 20., 60., 100., 140., 180., 220., 260., 300., 340., 380., 420., 460., 500., 540.]) ### vander Generate a Vandermonde matrix. The columns of the output matrix are powers of the input vector. The order of the powers is determined by the `increasing` boolean argument. Specifically, when `increasing` is False, the `i`-th output column is the input vector raised element-wise to the power of ``N - i - 1``. Such a matrix with a geometric progression in each row is named for Alexandre- Theophile Vandermonde. Parameters ---------- x : array_like 1-D input array. N : int, optional Number of columns in the output. If `N` is not specified, a square array is returned (``N = len(x)``). increasing : bool, optional Order of the powers of the columns. If True, the powers increase from left to right, if False (the default) they are reversed. .. versionadded:: 1.9.0 Returns ------- out : ndarray Vandermonde matrix. If `increasing` is False, the first column is ``x^(N-1)``, the second ``x^(N-2)`` and so forth. If `increasing` is True, the columns are ``x^0, x^1, ..., x^(N-1)``. See Also -------- polynomial.polynomial.polyvander Examples -------- >>> x = np.array([1, 2, 3, 5]) >>> N = 3 >>> np.vander(x, N) array([[ 1, 1, 1], [ 4, 2, 1], [ 9, 3, 1], [25, 5, 1]]) >>> np.column_stack([x**(N-1-i) for i in range(N)]) array([[ 1, 1, 1], [ 4, 2, 1], [ 9, 3, 1], [25, 5, 1]]) >>> x = np.array([1, 2, 3, 5]) >>> np.vander(x) array([[ 1, 1, 1, 1], [ 8, 4, 2, 1], [ 27, 9, 3, 1], [125, 25, 5, 1]]) >>> np.vander(x, increasing=True) array([[ 1, 1, 1, 1], [ 1, 2, 4, 8], [ 1, 3, 9, 27], [ 1, 5, 25, 125]]) The determinant of a square Vandermonde matrix is the product of the differences between the values of the input vector: >>> np.linalg.det(np.vander(x)) 48.000000000000043 # may vary >>> (5-3)*(5-2)*(5-1)*(3-2)*(3-1)*(2-1) 48 ### var Compute the variance along the specified axis. Returns the variance of the array elements, a measure of the spread of a distribution. The variance is computed for the flattened array by default, otherwise over the specified axis. Parameters ---------- a : array_like Array containing numbers whose variance is desired. If `a` is not an array, a conversion is attempted. axis : None or int or tuple of ints, optional Axis or axes along which the variance is computed. The default is to compute the variance of the flattened array. .. versionadded:: 1.7.0 If this is a tuple of ints, a variance is performed over multiple axes, instead of a single axis or all the axes as before. dtype : data-type, optional Type to use in computing the variance. For arrays of integer type the default is `float64`; for arrays of float types it is the same as the array type. out : ndarray, optional Alternate output array in which to place the result. It must have the same shape as the expected output, but the type is cast if necessary. ddof : int, optional "Delta Degrees of Freedom": the divisor used in the calculation is ``N - ddof``, where ``N`` represents the number of elements. By default `ddof` is zero. keepdims : bool, optional If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array. If the default value is passed, then `keepdims` will not be passed through to the `var` method of sub-classes of `ndarray`, however any non-default value will be. If the sub-class' method does not implement `keepdims` any exceptions will be raised. where : array_like of bool, optional Elements to include in the variance. See `~numpy.ufunc.reduce` for details. .. versionadded:: 1.20.0 Returns ------- variance : ndarray, see dtype parameter above If ``out=None``, returns a new array containing the variance; otherwise, a reference to the output array is returned. See Also -------- std, mean, nanmean, nanstd, nanvar :ref:`ufuncs-output-type` Notes ----- The variance is the average of the squared deviations from the mean, i.e., ``var = mean(x)``, where ``x = abs(a - a.mean())**2``. The mean is typically calculated as ``x.sum() / N``, where ``N = len(x)``. If, however, `ddof` is specified, the divisor ``N - ddof`` is used instead. In standard statistical practice, ``ddof=1`` provides an unbiased estimator of the variance of a hypothetical infinite population. ``ddof=0`` provides a maximum likelihood estimate of the variance for normally distributed variables. Note that for complex numbers, the absolute value is taken before squaring, so that the result is always real and nonnegative. For floating-point input, the variance is computed using the same precision the input has. Depending on the input data, this can cause the results to be inaccurate, especially for `float32` (see example below). Specifying a higher-accuracy accumulator using the ``dtype`` keyword can alleviate this issue. Examples -------- >>> a = np.array([[1, 2], [3, 4]]) >>> np.var(a) 1.25 >>> np.var(a, axis=0) array([1., 1.]) >>> np.var(a, axis=1) array([0.25, 0.25]) In single precision, var() can be inaccurate: >>> a = np.zeros((2, 512*512), dtype=np.float32) >>> a[0, :] = 1.0 >>> a[1, :] = 0.1 >>> np.var(a) 0.20250003 Computing the variance in float64 is more accurate: >>> np.var(a, dtype=np.float64) 0.20249999932944759 # may vary >>> ((1-0.55)**2 + (0.1-0.55)**2)/2 0.2025 Specifying a where argument: >>> a = np.array([[14, 8, 11, 10], [7, 9, 10, 11], [10, 15, 5, 10]]) >>> np.var(a) 6.833333333333333 # may vary >>> np.var(a, where=[[True], [True], [False]]) 4.0 ### vdot vdot(a, b) Return the dot product of two vectors. The vdot(`a`, `b`) function handles complex numbers differently than dot(`a`, `b`). If the first argument is complex the complex conjugate of the first argument is used for the calculation of the dot product. Note that `vdot` handles multidimensional arrays differently than `dot`: it does *not* perform a matrix product, but flattens input arguments to 1-D vectors first. Consequently, it should only be used for vectors. Parameters ---------- a : array_like If `a` is complex the complex conjugate is taken before calculation of the dot product. b : array_like Second argument to the dot product. Returns ------- output : ndarray Dot product of `a` and `b`. Can be an int, float, or complex depending on the types of `a` and `b`. See Also -------- dot : Return the dot product without using the complex conjugate of the first argument. Examples -------- >>> a = np.array([1+2j,3+4j]) >>> b = np.array([5+6j,7+8j]) >>> np.vdot(a, b) (70-8j) >>> np.vdot(b, a) (70+8j) Note that higher-dimensional arrays are flattened! >>> a = np.array([[1, 4], [5, 6]]) >>> b = np.array([[4, 1], [2, 2]]) >>> np.vdot(a, b) 30 >>> np.vdot(b, a) 30 >>> 1*4 + 4*1 + 5*2 + 6*2 30 ### vsplit Split an array into multiple sub-arrays vertically (row-wise). Please refer to the ``split`` documentation. ``vsplit`` is equivalent to ``split`` with `axis=0` (default), the array is always split along the first axis regardless of the array dimension. See Also -------- split : Split an array into multiple sub-arrays of equal size. Examples -------- >>> x = np.arange(16.0).reshape(4, 4) >>> x array([[ 0., 1., 2., 3.], [ 4., 5., 6., 7.], [ 8., 9., 10., 11.], [12., 13., 14., 15.]]) >>> np.vsplit(x, 2) [array([[0., 1., 2., 3.], [4., 5., 6., 7.]]), array([[ 8., 9., 10., 11.], [12., 13., 14., 15.]])] >>> np.vsplit(x, np.array([3, 6])) [array([[ 0., 1., 2., 3.], [ 4., 5., 6., 7.], [ 8., 9., 10., 11.]]), array([[12., 13., 14., 15.]]), array([], shape=(0, 4), dtype=float64)] With a higher dimensional array the split is still along the first axis. >>> x = np.arange(8.0).reshape(2, 2, 2) >>> x array([[[0., 1.], [2., 3.]], [[4., 5.], [6., 7.]]]) >>> np.vsplit(x, 2) [array([[[0., 1.], [2., 3.]]]), array([[[4., 5.], [6., 7.]]])] ### vstack Stack arrays in sequence vertically (row wise). This is equivalent to concatenation along the first axis after 1-D arrays of shape `(N,)` have been reshaped to `(1,N)`. Rebuilds arrays divided by `vsplit`. This function makes most sense for arrays with up to 3 dimensions. For instance, for pixel-data with a height (first axis), width (second axis), and r/g/b channels (third axis). The functions `concatenate`, `stack` and `block` provide more general stacking and concatenation operations. Parameters ---------- tup : sequence of ndarrays The arrays must have the same shape along all but the first axis. 1-D arrays must have the same length. Returns ------- stacked : ndarray The array formed by stacking the given arrays, will be at least 2-D. See Also -------- concatenate : Join a sequence of arrays along an existing axis. stack : Join a sequence of arrays along a new axis. block : Assemble an nd-array from nested lists of blocks. hstack : Stack arrays in sequence horizontally (column wise). dstack : Stack arrays in sequence depth wise (along third axis). column_stack : Stack 1-D arrays as columns into a 2-D array. vsplit : Split an array into multiple sub-arrays vertically (row-wise). Examples -------- >>> a = np.array([1, 2, 3]) >>> b = np.array([4, 5, 6]) >>> np.vstack((a,b)) array([[1, 2, 3], [4, 5, 6]]) >>> a = np.array([[1], [2], [3]]) >>> b = np.array([[4], [5], [6]]) >>> np.vstack((a,b)) array([[1], [2], [3], [4], [5], [6]]) ### where where(condition, [x, y]) Return elements chosen from `x` or `y` depending on `condition`. .. note:: When only `condition` is provided, this function is a shorthand for ``np.asarray(condition).nonzero()``. Using `nonzero` directly should be preferred, as it behaves correctly for subclasses. The rest of this documentation covers only the case where all three arguments are provided. Parameters ---------- condition : array_like, bool Where True, yield `x`, otherwise yield `y`. x, y : array_like Values from which to choose. `x`, `y` and `condition` need to be broadcastable to some shape. Returns ------- out : ndarray An array with elements from `x` where `condition` is True, and elements from `y` elsewhere. See Also -------- choose nonzero : The function that is called when x and y are omitted Notes ----- If all the arrays are 1-D, `where` is equivalent to:: [xv if c else yv for c, xv, yv in zip(condition, x, y)] Examples -------- >>> a = [np.arange(10)](https://www.chedong.com/phpMan.php/man/np.arange/10/markdown) >>> a array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) >>> np.where(a < 5, a, 10*a) array([ 0, 1, 2, 3, 4, 50, 60, 70, 80, 90]) This can be used on multidimensional arrays too: >>> np.where([[True, False], [True, True]], ... [[1, 2], [3, 4]], ... [[9, 8], [7, 6]]) array([[1, 8], [3, 4]]) The shapes of x, y, and the condition are broadcast together: >>> x, y = np.ogrid[:3, :4] >>> np.where(x < y, x, 10 + y) # both x and 10+y are broadcast array([[10, 0, 0, 0], [10, 11, 1, 1], [10, 11, 12, 2]]) >>> a = np.array([[0, 1, 2], ... [0, 2, 4], ... [0, 3, 6]]) >>> np.where(a < 4, a, -1) # -1 is broadcast array([[ 0, 1, 2], [ 0, 2, -1], [ 0, 3, -1]]) ### who Print the NumPy arrays in the given dictionary. If there is no dictionary passed in or `vardict` is None then returns NumPy arrays in the globals() dictionary (all NumPy arrays in the namespace). Parameters ---------- vardict : dict, optional A dictionary possibly containing ndarrays. Default is globals(). Returns ------- out : None Returns 'None'. Notes ----- Prints out the name, shape, bytes and type of all of the ndarrays present in `vardict`. Examples -------- >>> a = [np.arange(10)](https://www.chedong.com/phpMan.php/man/np.arange/10/markdown) >>> b = [np.ones(20)](https://www.chedong.com/phpMan.php/man/np.ones/20/markdown) >>> np.who() Name Shape Bytes Type =========================================================== a 10 80 int64 b 20 160 float64 Upper bound on total bytes = 240 >>> d = {'x': np.arange(2.0), 'y': np.arange(3.0), 'txt': 'Some str', ... 'idx':5} >>> np.who(d) Name Shape Bytes Type =========================================================== x 2 16 float64 y 3 24 float64 Upper bound on total bytes = 40 ### zeros zeros(shape, dtype=float, order='C', *, like=None) Return a new array of given shape and type, filled with zeros. Parameters ---------- shape : int or tuple of ints Shape of the new array, e.g., ``(2, 3)`` or ``2``. dtype : data-type, optional The desired data-type for the array, e.g., `numpy.int8`. Default is `numpy.float64`. order : {'C', 'F'}, optional, default: 'C' Whether to store multi-dimensional data in row-major (C-style) or column-major (Fortran-style) order in memory. like : array_like Reference object to allow the creation of arrays which are not NumPy arrays. If an array-like passed in as ``like`` supports the ``__array_function__`` protocol, the result will be defined by it. In this case, it ensures the creation of an array object compatible with that passed in via this argument. .. versionadded:: 1.20.0 Returns ------- out : ndarray Array of zeros with the given shape, dtype, and order. See Also -------- zeros_like : Return an array of zeros with shape and type of input. empty : Return a new uninitialized array. ones : Return a new array setting values to one. full : Return a new array of given shape filled with value. Examples -------- >>> [np.zeros(5)](https://www.chedong.com/phpMan.php/man/np.zeros/5/markdown) array([ 0., 0., 0., 0., 0.]) >>> np.zeros((5,), dtype=int) array([0, 0, 0, 0, 0]) >>> np.zeros((2, 1)) array([[ 0.], [ 0.]]) >>> s = (2,2) >>> np.zeros(s) array([[ 0., 0.], [ 0., 0.]]) >>> np.zeros((2,), dtype=[('x', 'i4'), ('y', 'i4')]) # custom dtype array([(0, 0), (0, 0)], dtype=[('x', '>> x = [np.arange(6)](https://www.chedong.com/phpMan.php/man/np.arange/6/markdown) >>> x = x.reshape((2, 3)) >>> x array([[0, 1, 2], [3, 4, 5]]) >>> np.zeros_like(x) array([[0, 0, 0], [0, 0, 0]]) >>> y = np.arange(3, dtype=float) >>> y array([0., 1., 2.]) >>> np.zeros_like(y) array([0., 0., 0.]) ## DATA ALLOW_THREADS = 1 BUFSIZE = 8192 CLIP = 0 ERR_CALL = 3 ERR_DEFAULT = 521 ERR_IGNORE = 0 ERR_LOG = 5 ERR_PRINT = 4 ERR_RAISE = 2 ERR_WARN = 1 FLOATING_POINT_SUPPORT = 1 FPE_DIVIDEBYZERO = 1 FPE_INVALID = 8 FPE_OVERFLOW = 2 FPE_UNDERFLOW = 4 False_ = False Inf = inf Infinity = inf MAXDIMS = 32 MAY_SHARE_BOUNDS = 0 MAY_SHARE_EXACT = -1 NAN = nan NINF = -inf NZERO = -0.0 NaN = nan PINF = inf PZERO = 0.0 RAISE = 2 SHIFT_DIVIDEBYZERO = 0 SHIFT_INVALID = 9 SHIFT_OVERFLOW = 3 SHIFT_UNDERFLOW = 6 ScalarType = (, , , __NUMPY_SETUP__ = False __all__ = ['ModuleDeprecationWarning', 'VisibleDeprecationWarning', '_... __deprecated_attrs__ = {'bool': (, '`np.bool` is a depre... __expired_functions__ = {'fv': 'In accordance with NEP 32, the functio... __git_version__ = 'c3d0a09342c08c466984654bc4738af595fba896' absolute = absolute(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Calculate the absolute value element-wise. ``np.abs`` is a shorthand for this function. Parameters ---------- x : array_like Input array. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- absolute : ndarray An ndarray containing the absolute value of each element in `x`. For complex input, ``a + ib``, the absolute value is :math:`\sqrt{ a^2 + b^2 }`. This is a scalar if `x` is a scalar. Examples -------- >>> x = np.array([-1.2, 1.2]) >>> np.absolute(x) array([ 1.2, 1.2]) >>> np.absolute(1.2 + 1j) 1.5620499351813308 Plot the function over ``[-10, 10]``: >>> import matplotlib.pyplot as plt >>> x = np.linspace(start=-10, stop=10, num=101) >>> plt.plot(x, np.absolute(x)) >>> plt.show() Plot the function over the complex plane: >>> xx = x + 1j * x[:, np.newaxis] >>> plt.imshow(np.abs(xx), extent=[-10, 10, -10, 10], cmap='gray') >>> plt.show() The `abs` function can be used as a shorthand for ``np.absolute`` on ndarrays. >>> x = np.array([-1.2, 1.2]) >>> abs(x) array([1.2, 1.2]) add = add(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Add arguments element-wise. Parameters ---------- x1, x2 : array_like The arrays to be added. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- add : ndarray or scalar The sum of `x1` and `x2`, element-wise. This is a scalar if both `x1` and `x2` are scalars. Notes ----- Equivalent to `x1` + `x2` in terms of array broadcasting. Examples -------- >>> np.add(1.0, 4.0) 5.0 >>> x1 = np.arange(9.0).reshape((3, 3)) >>> x2 = np.arange(3.0) >>> np.add(x1, x2) array([[ 0., 2., 4.], [ 3., 5., 7.], [ 6., 8., 10.]]) The ``+`` operator can be used as a shorthand for ``np.add`` on ndarrays. >>> x1 = np.arange(9.0).reshape((3, 3)) >>> x2 = np.arange(3.0) >>> x1 + x2 array([[ 0., 2., 4.], [ 3., 5., 7.], [ 6., 8., 10.]]) arccos = arccos(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Trigonometric inverse cosine, element-wise. The inverse of `cos` so that, if ``y = cos(x)``, then ``x = arccos(y)``. Parameters ---------- x : array_like `x`-coordinate on the unit circle. For real arguments, the domain is [-1, 1]. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- angle : ndarray The angle of the ray intersecting the unit circle at the given `x`-coordinate in radians [0, pi]. This is a scalar if `x` is a scalar. See Also -------- cos, arctan, arcsin, emath.arccos Notes ----- `arccos` is a multivalued function: for each `x` there are infinitely many numbers `z` such that ``cos(z) = x``. The convention is to return the angle `z` whose real part lies in `[0, pi]`. For real-valued input data types, `arccos` always returns real output. For each value that cannot be expressed as a real number or infinity, it yields ``nan`` and sets the `invalid` floating point error flag. For complex-valued input, `arccos` is a complex analytic function that has branch cuts ``[-inf, -1]`` and `[1, inf]` and is continuous from above on the former and from below on the latter. The inverse `cos` is also known as `acos` or cos^-1. References ---------- M. Abramowitz and I.A. Stegun, "Handbook of Mathematical Functions", 10th printing, 1964, pp. 79. Examples -------- We expect the arccos of 1 to be 0, and of -1 to be pi: >>> np.arccos([1, -1]) array([ 0. , 3.14159265]) Plot arccos: >>> import matplotlib.pyplot as plt >>> x = np.linspace(-1, 1, num=100) >>> plt.plot(x, np.arccos(x)) >>> plt.axis('tight') >>> plt.show() arccosh = arccosh(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Inverse hyperbolic cosine, element-wise. Parameters ---------- x : array_like Input array. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- arccosh : ndarray Array of the same shape as `x`. This is a scalar if `x` is a scalar. See Also -------- cosh, arcsinh, sinh, arctanh, tanh Notes ----- `arccosh` is a multivalued function: for each `x` there are infinitely many numbers `z` such that `cosh(z) = x`. The convention is to return the `z` whose imaginary part lies in ``[-pi, pi]`` and the real part in ``[0, inf]``. For real-valued input data types, `arccosh` always returns real output. For each value that cannot be expressed as a real number or infinity, it yields ``nan`` and sets the `invalid` floating point error flag. For complex-valued input, `arccosh` is a complex analytical function that has a branch cut `[-inf, 1]` and is continuous from above on it. References ---------- .. [1] M. Abramowitz and I.A. Stegun, "Handbook of Mathematical Functions", 10th printing, 1964, pp. 86. .. [2] Wikipedia, "Inverse hyperbolic function", Examples -------- >>> np.arccosh([np.e, 10.0]) array([ 1.65745445, 2.99322285]) >>> [np.arccosh(1)](https://www.chedong.com/phpMan.php/man/np.arccosh/1/markdown) 0.0 arcsin = arcsin(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Inverse sine, element-wise. Parameters ---------- x : array_like `y`-coordinate on the unit circle. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- angle : ndarray The inverse sine of each element in `x`, in radians and in the closed interval ``[-pi/2, pi/2]``. This is a scalar if `x` is a scalar. See Also -------- sin, cos, arccos, tan, arctan, arctan2, emath.arcsin Notes ----- `arcsin` is a multivalued function: for each `x` there are infinitely many numbers `z` such that :math:`sin(z) = x`. The convention is to return the angle `z` whose real part lies in [-pi/2, pi/2]. For real-valued input data types, *arcsin* always returns real output. For each value that cannot be expressed as a real number or infinity, it yields ``nan`` and sets the `invalid` floating point error flag. For complex-valued input, `arcsin` is a complex analytic function that has, by convention, the branch cuts [-inf, -1] and [1, inf] and is continuous from above on the former and from below on the latter. The inverse sine is also known as `asin` or sin^{-1}. References ---------- Abramowitz, M. and Stegun, I. A., *Handbook of Mathematical Functions*, 10th printing, New York: Dover, 1964, pp. 79ff. Examples -------- >>> [np.arcsin(1)](https://www.chedong.com/phpMan.php/man/np.arcsin/1/markdown) # pi/2 1.5707963267948966 >>> np.arcsin(-1) # -pi/2 -1.5707963267948966 >>> [np.arcsin(0)](https://www.chedong.com/phpMan.php/man/np.arcsin/0/markdown) 0.0 arcsinh = arcsinh(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Inverse hyperbolic sine element-wise. Parameters ---------- x : array_like Input array. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- out : ndarray or scalar Array of the same shape as `x`. This is a scalar if `x` is a scalar. Notes ----- `arcsinh` is a multivalued function: for each `x` there are infinitely many numbers `z` such that `sinh(z) = x`. The convention is to return the `z` whose imaginary part lies in `[-pi/2, pi/2]`. For real-valued input data types, `arcsinh` always returns real output. For each value that cannot be expressed as a real number or infinity, it returns ``nan`` and sets the `invalid` floating point error flag. For complex-valued input, `arccos` is a complex analytical function that has branch cuts `[1j, infj]` and `[-1j, -infj]` and is continuous from the right on the former and from the left on the latter. The inverse hyperbolic sine is also known as `asinh` or ``sinh^-1``. References ---------- .. [1] M. Abramowitz and I.A. Stegun, "Handbook of Mathematical Functions", 10th printing, 1964, pp. 86. .. [2] Wikipedia, "Inverse hyperbolic function", Examples -------- >>> np.arcsinh(np.array([np.e, 10.0])) array([ 1.72538256, 2.99822295]) arctan = arctan(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Trigonometric inverse tangent, element-wise. The inverse of tan, so that if ``y = tan(x)`` then ``x = arctan(y)``. Parameters ---------- x : array_like out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- out : ndarray or scalar Out has the same shape as `x`. Its real part is in ``[-pi/2, pi/2]`` (``arctan(+/-inf)`` returns ``+/-pi/2``). This is a scalar if `x` is a scalar. See Also -------- arctan2 : The "four quadrant" arctan of the angle formed by (`x`, `y`) and the positive `x`-axis. angle : Argument of complex values. Notes ----- `arctan` is a multi-valued function: for each `x` there are infinitely many numbers `z` such that tan(`z`) = `x`. The convention is to return the angle `z` whose real part lies in [-pi/2, pi/2]. For real-valued input data types, `arctan` always returns real output. For each value that cannot be expressed as a real number or infinity, it yields ``nan`` and sets the `invalid` floating point error flag. For complex-valued input, `arctan` is a complex analytic function that has [``1j, infj``] and [``-1j, -infj``] as branch cuts, and is continuous from the left on the former and from the right on the latter. The inverse tangent is also known as `atan` or tan^{-1}. References ---------- Abramowitz, M. and Stegun, I. A., *Handbook of Mathematical Functions*, 10th printing, New York: Dover, 1964, pp. 79. Examples -------- We expect the arctan of 0 to be 0, and of 1 to be pi/4: >>> np.arctan([0, 1]) array([ 0. , 0.78539816]) >>> np.pi/4 0.78539816339744828 Plot arctan: >>> import matplotlib.pyplot as plt >>> x = np.linspace(-10, 10) >>> plt.plot(x, np.arctan(x)) >>> plt.axis('tight') >>> plt.show() arctan2 = arctan2(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Element-wise arc tangent of ``x1/x2`` choosing the quadrant correctly. The quadrant (i.e., branch) is chosen so that ``arctan2(x1, x2)`` is the signed angle in radians between the ray ending at the origin and passing through the point (1,0), and the ray ending at the origin and passing through the point (`x2`, `x1`). (Note the role reversal: the "`y`-coordinate" is the first function parameter, the "`x`-coordinate" is the second.) By IEEE convention, this function is defined for `x2` = +/-0 and for either or both of `x1` and `x2` = +/-inf (see Notes for specific values). This function is not defined for complex-valued arguments; for the so-called argument of complex values, use `angle`. Parameters ---------- x1 : array_like, real-valued `y`-coordinates. x2 : array_like, real-valued `x`-coordinates. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- angle : ndarray Array of angles in radians, in the range ``[-pi, pi]``. This is a scalar if both `x1` and `x2` are scalars. See Also -------- arctan, tan, angle Notes ----- *arctan2* is identical to the `atan2` function of the underlying C library. The following special values are defined in the C standard: [1]_ ====== ====== ================ `x1` `x2` `arctan2(x1,x2)` ====== ====== ================ +/- 0 +0 +/- 0 +/- 0 -0 +/- pi > 0 +/-inf +0 / +pi < 0 +/-inf -0 / -pi +/-inf +inf +/- (pi/4) +/-inf -inf +/- (3*pi/4) ====== ====== ================ Note that +0 and -0 are distinct floating point numbers, as are +inf and -inf. References ---------- .. [1] ISO/IEC standard 9899:1999, "Programming language C." Examples -------- Consider four points in different quadrants: >>> x = np.array([-1, +1, +1, -1]) >>> y = np.array([-1, -1, +1, +1]) >>> np.arctan2(y, x) * 180 / np.pi array([-135., -45., 45., 135.]) Note the order of the parameters. `arctan2` is defined also when `x2` = 0 and at several other special points, obtaining values in the range ``[-pi, pi]``: >>> np.arctan2([1., -1.], [0., 0.]) array([ 1.57079633, -1.57079633]) >>> np.arctan2([0., 0., np.inf], [+0., -0., np.inf]) array([ 0. , 3.14159265, 0.78539816]) arctanh = arctanh(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Inverse hyperbolic tangent element-wise. Parameters ---------- x : array_like Input array. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- out : ndarray or scalar Array of the same shape as `x`. This is a scalar if `x` is a scalar. See Also -------- emath.arctanh Notes ----- `arctanh` is a multivalued function: for each `x` there are infinitely many numbers `z` such that ``tanh(z) = x``. The convention is to return the `z` whose imaginary part lies in `[-pi/2, pi/2]`. For real-valued input data types, `arctanh` always returns real output. For each value that cannot be expressed as a real number or infinity, it yields ``nan`` and sets the `invalid` floating point error flag. For complex-valued input, `arctanh` is a complex analytical function that has branch cuts `[-1, -inf]` and `[1, inf]` and is continuous from above on the former and from below on the latter. The inverse hyperbolic tangent is also known as `atanh` or ``tanh^-1``. References ---------- .. [1] M. Abramowitz and I.A. Stegun, "Handbook of Mathematical Functions", 10th printing, 1964, pp. 86. .. [2] Wikipedia, "Inverse hyperbolic function", Examples -------- >>> np.arctanh([0, -0.5]) array([ 0. , -0.54930614]) bitwise_and = bitwise_and(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Compute the bit-wise AND of two arrays element-wise. Computes the bit-wise AND of the underlying binary representation of the integers in the input arrays. This ufunc implements the C/Python operator ``&``. Parameters ---------- x1, x2 : array_like Only integer and boolean types are handled. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- out : ndarray or scalar Result. This is a scalar if both `x1` and `x2` are scalars. See Also -------- logical_and bitwise_or bitwise_xor binary_repr : Return the binary representation of the input number as a string. Examples -------- The number 13 is represented by ``00001101``. Likewise, 17 is represented by ``00010001``. The bit-wise AND of 13 and 17 is therefore ``000000001``, or 1: >>> np.bitwise_and(13, 17) 1 >>> np.bitwise_and(14, 13) 12 >>> [np.binary_repr(12)](https://www.chedong.com/phpMan.php/man/np.binaryrepr/12/markdown) '1100' >>> np.bitwise_and([14,3], 13) array([12, 1]) >>> np.bitwise_and([11,7], [4,25]) array([0, 1]) >>> np.bitwise_and(np.array([2,5,255]), np.array([3,14,16])) array([ 2, 4, 16]) >>> np.bitwise_and([True, True], [False, True]) array([False, True]) The ``&`` operator can be used as a shorthand for ``np.bitwise_and`` on ndarrays. >>> x1 = np.array([2, 5, 255]) >>> x2 = np.array([3, 14, 16]) >>> x1 & x2 array([ 2, 4, 16]) bitwise_not = invert(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Compute bit-wise inversion, or bit-wise NOT, element-wise. Computes the bit-wise NOT of the underlying binary representation of the integers in the input arrays. This ufunc implements the C/Python operator ``~``. For signed integer inputs, the two's complement is returned. In a two's-complement system negative numbers are represented by the two's complement of the absolute value. This is the most common method of representing signed integers on computers [1]_. A N-bit two's-complement system can represent every integer in the range :math:`-2^{N-1}` to :math:`+2^{N-1}-1`. Parameters ---------- x : array_like Only integer and boolean types are handled. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- out : ndarray or scalar Result. This is a scalar if `x` is a scalar. See Also -------- bitwise_and, bitwise_or, bitwise_xor logical_not binary_repr : Return the binary representation of the input number as a string. Notes ----- `bitwise_not` is an alias for `invert`: >>> np.bitwise_not is np.invert True References ---------- .. [1] Wikipedia, "Two's complement", 's_complement Examples -------- We've seen that 13 is represented by ``00001101``. The invert or bit-wise NOT of 13 is then: >>> x = np.invert(np.array(13, dtype=np.uint8)) >>> x 242 >>> np.binary_repr(x, width=8) '11110010' The result depends on the bit-width: >>> x = np.invert(np.array(13, dtype=np.uint16)) >>> x 65522 >>> np.binary_repr(x, width=16) '1111111111110010' When using signed integer types the result is the two's complement of the result for the unsigned type: >>> np.invert(np.array([13], dtype=np.int8)) array([-14], dtype=int8) >>> np.binary_repr(-14, width=8) '11110010' Booleans are accepted as well: >>> np.invert(np.array([True, False])) array([False, True]) The ``~`` operator can be used as a shorthand for ``np.invert`` on ndarrays. >>> x1 = np.array([True, False]) >>> ~x1 array([False, True]) bitwise_or = bitwise_or(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Compute the bit-wise OR of two arrays element-wise. Computes the bit-wise OR of the underlying binary representation of the integers in the input arrays. This ufunc implements the C/Python operator ``|``. Parameters ---------- x1, x2 : array_like Only integer and boolean types are handled. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- out : ndarray or scalar Result. This is a scalar if both `x1` and `x2` are scalars. See Also -------- logical_or bitwise_and bitwise_xor binary_repr : Return the binary representation of the input number as a string. Examples -------- The number 13 has the binaray representation ``00001101``. Likewise, 16 is represented by ``00010000``. The bit-wise OR of 13 and 16 is then ``000111011``, or 29: >>> np.bitwise_or(13, 16) 29 >>> [np.binary_repr(29)](https://www.chedong.com/phpMan.php/man/np.binaryrepr/29/markdown) '11101' >>> np.bitwise_or(32, 2) 34 >>> np.bitwise_or([33, 4], 1) array([33, 5]) >>> np.bitwise_or([33, 4], [1, 2]) array([33, 6]) >>> np.bitwise_or(np.array([2, 5, 255]), np.array([4, 4, 4])) array([ 6, 5, 255]) >>> np.array([2, 5, 255]) | np.array([4, 4, 4]) array([ 6, 5, 255]) >>> np.bitwise_or(np.array([2, 5, 255, 2147483647], dtype=np.int32), ... np.array([4, 4, 4, 2147483647], dtype=np.int32)) array([ 6, 5, 255, 2147483647]) >>> np.bitwise_or([True, True], [False, True]) array([ True, True]) The ``|`` operator can be used as a shorthand for ``np.bitwise_or`` on ndarrays. >>> x1 = np.array([2, 5, 255]) >>> x2 = np.array([4, 4, 4]) >>> x1 | x2 array([ 6, 5, 255]) bitwise_xor = bitwise_xor(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Compute the bit-wise XOR of two arrays element-wise. Computes the bit-wise XOR of the underlying binary representation of the integers in the input arrays. This ufunc implements the C/Python operator ``^``. Parameters ---------- x1, x2 : array_like Only integer and boolean types are handled. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- out : ndarray or scalar Result. This is a scalar if both `x1` and `x2` are scalars. See Also -------- logical_xor bitwise_and bitwise_or binary_repr : Return the binary representation of the input number as a string. Examples -------- The number 13 is represented by ``00001101``. Likewise, 17 is represented by ``00010001``. The bit-wise XOR of 13 and 17 is therefore ``00011100``, or 28: >>> np.bitwise_xor(13, 17) 28 >>> [np.binary_repr(28)](https://www.chedong.com/phpMan.php/man/np.binaryrepr/28/markdown) '11100' >>> np.bitwise_xor(31, 5) 26 >>> np.bitwise_xor([31,3], 5) array([26, 6]) >>> np.bitwise_xor([31,3], [5,6]) array([26, 5]) >>> np.bitwise_xor([True, True], [False, True]) array([ True, False]) The ``^`` operator can be used as a shorthand for ``np.bitwise_xor`` on ndarrays. >>> x1 = np.array([True, True]) >>> x2 = np.array([False, True]) >>> x1 ^ x2 array([ True, False]) c_ = cast = {: at 0...y.int16'>: <... cbrt = cbrt(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Return the cube-root of an array, element-wise. .. versionadded:: 1.10.0 Parameters ---------- x : array_like The values whose cube-roots are required. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray An array of the same shape as `x`, containing the cube cube-root of each element in `x`. If `out` was provided, `y` is a reference to it. This is a scalar if `x` is a scalar. Examples -------- >>> np.cbrt([1,8,27]) array([ 1., 2., 3.]) ceil = ceil(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Return the ceiling of the input, element-wise. The ceil of the scalar `x` is the smallest integer `i`, such that ``i >= x``. It is often denoted as :math:`\lceil x \rceil`. Parameters ---------- x : array_like Input data. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray or scalar The ceiling of each element in `x`, with `float` dtype. This is a scalar if `x` is a scalar. See Also -------- floor, trunc, rint, fix Examples -------- >>> a = np.array([-1.7, -1.5, -0.2, 0.2, 1.5, 1.7, 2.0]) >>> np.ceil(a) array([-1., -1., -0., 1., 2., 2., 2.]) conj = conjugate(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Return the complex conjugate, element-wise. The complex conjugate of a complex number is obtained by changing the sign of its imaginary part. Parameters ---------- x : array_like Input value. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray The complex conjugate of `x`, with same dtype as `y`. This is a scalar if `x` is a scalar. Notes ----- `conj` is an alias for `conjugate`: >>> np.conj is np.conjugate True Examples -------- >>> np.conjugate(1+2j) (1-2j) >>> x = [np.eye(2)](https://www.chedong.com/phpMan.php/man/np.eye/2/markdown) + 1j * [np.eye(2)](https://www.chedong.com/phpMan.php/man/np.eye/2/markdown) >>> np.conjugate(x) array([[ 1.-1.j, 0.-0.j], [ 0.-0.j, 1.-1.j]]) conjugate = conjugate(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Return the complex conjugate, element-wise. The complex conjugate of a complex number is obtained by changing the sign of its imaginary part. Parameters ---------- x : array_like Input value. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray The complex conjugate of `x`, with same dtype as `y`. This is a scalar if `x` is a scalar. Notes ----- `conj` is an alias for `conjugate`: >>> np.conj is np.conjugate True Examples -------- >>> np.conjugate(1+2j) (1-2j) >>> x = [np.eye(2)](https://www.chedong.com/phpMan.php/man/np.eye/2/markdown) + 1j * [np.eye(2)](https://www.chedong.com/phpMan.php/man/np.eye/2/markdown) >>> np.conjugate(x) array([[ 1.-1.j, 0.-0.j], [ 0.-0.j, 1.-1.j]]) copysign = copysign(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Change the sign of x1 to that of x2, element-wise. If `x2` is a scalar, its sign will be copied to all elements of `x1`. Parameters ---------- x1 : array_like Values to change the sign of. x2 : array_like The sign of `x2` is copied to `x1`. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- out : ndarray or scalar The values of `x1` with the sign of `x2`. This is a scalar if both `x1` and `x2` are scalars. Examples -------- >>> np.copysign(1.3, -1) -1.3 >>> 1/np.copysign(0, 1) inf >>> 1/np.copysign(0, -1) ### -inf >>> np.copysign([-1, 0, 1], -1.1) array([-1., -0., -1.]) >>> np.copysign([-1, 0, 1], [np.arange(3)](https://www.chedong.com/phpMan.php/man/np.arange/3/markdown)-1) array([-1., 0., 1.]) cos = cos(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Cosine element-wise. Parameters ---------- x : array_like Input array in radians. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray The corresponding cosine values. This is a scalar if `x` is a scalar. Notes ----- If `out` is provided, the function writes the result into it, and returns a reference to `out`. (See Examples) References ---------- M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions. New York, NY: Dover, 1972. Examples -------- >>> np.cos(np.array([0, np.pi/2, np.pi])) array([ 1.00000000e+00, 6.12303177e-17, -1.00000000e+00]) >>> >>> # Example of providing the optional output parameter >>> out1 = np.array([0], dtype='d') >>> out2 = np.cos([0.1], out1) >>> out2 is out1 True >>> >>> # Example of ValueError due to provision of shape mis-matched `out` >>> np.cos(np.zeros((3,3)),np.zeros((2,2))) Traceback (most recent call last): File "", line 1, in ValueError: operands could not be broadcast together with shapes (3,3) (2,2) cosh = cosh(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Hyperbolic cosine, element-wise. Equivalent to ``1/2 * (np.exp(x) + np.exp(-x))`` and ``np.cos(1j*x)``. Parameters ---------- x : array_like Input array. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- out : ndarray or scalar Output array of same shape as `x`. This is a scalar if `x` is a scalar. Examples -------- >>> [np.cosh(0)](https://www.chedong.com/phpMan.php/man/np.cosh/0/markdown) 1.0 The hyperbolic cosine describes the shape of a hanging cable: >>> import matplotlib.pyplot as plt >>> x = np.linspace(-4, 4, 1000) >>> plt.plot(x, np.cosh(x)) >>> plt.show() deg2rad = deg2rad(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Convert angles from degrees to radians. Parameters ---------- x : array_like Angles in degrees. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray The corresponding angle in radians. This is a scalar if `x` is a scalar. See Also -------- rad2deg : Convert angles from radians to degrees. unwrap : Remove large jumps in angle by wrapping. Notes ----- .. versionadded:: 1.3.0 ``deg2rad(x)`` is ``x * pi / 180``. Examples -------- >>> [np.deg2rad(180)](https://www.chedong.com/phpMan.php/man/np.deg2rad/180/markdown) 3.1415926535897931 degrees = degrees(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Convert angles from radians to degrees. Parameters ---------- x : array_like Input array in radians. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray of floats The corresponding degree values; if `out` was supplied this is a reference to it. This is a scalar if `x` is a scalar. See Also -------- rad2deg : equivalent function Examples -------- Convert a radian array to degrees >>> rad = np.arange(12.)*np.pi/6 >>> np.degrees(rad) array([ 0., 30., 60., 90., 120., 150., 180., 210., 240., 270., 300., 330.]) >>> out = np.zeros((rad.shape)) >>> r = np.degrees(rad, out) >>> np.all(r == out) True divide = true_divide(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Returns a true division of the inputs, element-wise. Instead of the Python traditional 'floor division', this returns a true division. True division adjusts the output type to present the best answer, regardless of input types. Parameters ---------- x1 : array_like Dividend array. x2 : array_like Divisor array. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- out : ndarray or scalar This is a scalar if both `x1` and `x2` are scalars. Notes ----- In Python, ``//`` is the floor division operator and ``/`` the true division operator. The ``true_divide(x1, x2)`` function is equivalent to true division in Python. Examples -------- >>> x = [np.arange(5)](https://www.chedong.com/phpMan.php/man/np.arange/5/markdown) >>> np.true_divide(x, 4) array([ 0. , 0.25, 0.5 , 0.75, 1. ]) >>> x/4 array([ 0. , 0.25, 0.5 , 0.75, 1. ]) >>> x//4 array([0, 0, 0, 0, 1]) The ``/`` operator can be used as a shorthand for ``np.true_divide`` on ndarrays. >>> x = [np.arange(5)](https://www.chedong.com/phpMan.php/man/np.arange/5/markdown) >>> x / 4 array([0. , 0.25, 0.5 , 0.75, 1. ]) divmod = divmod(x1, x2[, out1, out2], / [, out=(None, None)], *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Return element-wise quotient and remainder simultaneously. .. versionadded:: 1.13.0 ``np.divmod(x, y)`` is equivalent to ``(x // y, x % y)``, but faster because it avoids redundant work. It is used to implement the Python built-in function ``divmod`` on NumPy arrays. Parameters ---------- x1 : array_like Dividend array. x2 : array_like Divisor array. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- out1 : ndarray Element-wise quotient resulting from floor division. This is a scalar if both `x1` and `x2` are scalars. out2 : ndarray Element-wise remainder from floor division. This is a scalar if both `x1` and `x2` are scalars. See Also -------- floor_divide : Equivalent to Python's ``//`` operator. remainder : Equivalent to Python's ``%`` operator. modf : Equivalent to ``divmod(x, 1)`` for positive ``x`` with the return values switched. Examples -------- >>> np.divmod([np.arange(5)](https://www.chedong.com/phpMan.php/man/np.arange/5/markdown), 3) (array([0, 0, 0, 1, 1]), array([0, 1, 2, 0, 1])) The `divmod` function can be used as a shorthand for ``np.divmod`` on ndarrays. >>> x = [np.arange(5)](https://www.chedong.com/phpMan.php/man/np.arange/5/markdown) >>> divmod(x, 3) (array([0, 0, 0, 1, 1]), array([0, 1, 2, 0, 1])) e = 2.718281828459045 equal = equal(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Return (x1 == x2) element-wise. Parameters ---------- x1, x2 : array_like Input arrays. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- out : ndarray or scalar Output array, element-wise comparison of `x1` and `x2`. Typically of type bool, unless ``dtype=object`` is passed. This is a scalar if both `x1` and `x2` are scalars. See Also -------- not_equal, greater_equal, less_equal, greater, less Examples -------- >>> np.equal([0, 1, 3], [np.arange(3)](https://www.chedong.com/phpMan.php/man/np.arange/3/markdown)) array([ True, True, False]) What is compared are values, not types. So an int (1) and an array of length one can evaluate as True: >>> np.equal(1, [np.ones(1)](https://www.chedong.com/phpMan.php/man/np.ones/1/markdown)) array([ True]) The ``==`` operator can be used as a shorthand for ``np.equal`` on ndarrays. >>> a = np.array([2, 4, 6]) >>> b = np.array([2, 4, 2]) >>> a == b array([ True, True, False]) euler_gamma = 0.5772156649015329 exp = exp(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Calculate the exponential of all elements in the input array. Parameters ---------- x : array_like Input values. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- out : ndarray or scalar Output array, element-wise exponential of `x`. This is a scalar if `x` is a scalar. See Also -------- expm1 : Calculate ``exp(x) - 1`` for all elements in the array. exp2 : Calculate ``2**x`` for all elements in the array. Notes ----- The irrational number ``e`` is also known as Euler's number. It is approximately 2.718281, and is the base of the natural logarithm, ``ln`` (this means that, if :math:`x = \ln y = \log_e y`, then :math:`e^x = y`. For real input, ``exp(x)`` is always positive. For complex arguments, ``x = a + ib``, we can write :math:`e^x = e^a e^{ib}`. The first term, :math:`e^a`, is already known (it is the real argument, described above). The second term, :math:`e^{ib}`, is :math:`\cos b + i \sin b`, a function with magnitude 1 and a periodic phase. References ---------- .. [1] Wikipedia, "Exponential function", .. [2] M. Abramovitz and I. A. Stegun, "Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables," Dover, 1964, p. 69, Examples -------- Plot the magnitude and phase of ``exp(x)`` in the complex plane: >>> import matplotlib.pyplot as plt >>> x = np.linspace(-2*np.pi, 2*np.pi, 100) >>> xx = x + 1j * x[:, np.newaxis] # a + ib over complex plane >>> out = np.exp(xx) >>> [plt.subplot(121)](https://www.chedong.com/phpMan.php/man/plt.subplot/121/markdown) >>> plt.imshow(np.abs(out), ... extent=[-2*np.pi, 2*np.pi, -2*np.pi, 2*np.pi], cmap='gray') >>> plt.title('Magnitude of exp(x)') >>> [plt.subplot(122)](https://www.chedong.com/phpMan.php/man/plt.subplot/122/markdown) >>> plt.imshow(np.angle(out), ... extent=[-2*np.pi, 2*np.pi, -2*np.pi, 2*np.pi], cmap='hsv') >>> plt.title('Phase (angle) of exp(x)') >>> plt.show() exp2 = exp2(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Calculate `2**p` for all `p` in the input array. Parameters ---------- x : array_like Input values. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- out : ndarray or scalar Element-wise 2 to the power `x`. This is a scalar if `x` is a scalar. See Also -------- power Notes ----- .. versionadded:: 1.3.0 Examples -------- >>> np.exp2([2, 3]) array([ 4., 8.]) expm1 = expm1(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Calculate ``exp(x) - 1`` for all elements in the array. Parameters ---------- x : array_like Input values. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- out : ndarray or scalar Element-wise exponential minus one: ``out = exp(x) - 1``. This is a scalar if `x` is a scalar. See Also -------- log1p : ``log(1 + x)``, the inverse of expm1. Notes ----- This function provides greater precision than ``exp(x) - 1`` for small values of ``x``. Examples -------- The true value of ``exp(1e-10) - 1`` is ``1.00000000005e-10`` to about 32 significant digits. This example shows the superiority of expm1 in this case. >>> np.expm1(1e-10) 1.00000000005e-10 >>> np.exp(1e-10) - 1 1.000000082740371e-10 fabs = fabs(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Compute the absolute values element-wise. This function returns the absolute values (positive magnitude) of the data in `x`. Complex values are not handled, use `absolute` to find the absolute values of complex data. Parameters ---------- x : array_like The array of numbers for which the absolute values are required. If `x` is a scalar, the result `y` will also be a scalar. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray or scalar The absolute values of `x`, the returned values are always floats. This is a scalar if `x` is a scalar. See Also -------- absolute : Absolute values including `complex` types. Examples -------- >>> np.fabs(-1) 1.0 >>> np.fabs([-1.2, 1.2]) array([ 1.2, 1.2]) float_power = float_power(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) First array elements raised to powers from second array, element-wise. Raise each base in `x1` to the positionally-corresponding power in `x2`. `x1` and `x2` must be broadcastable to the same shape. This differs from the power function in that integers, float16, and float32 are promoted to floats with a minimum precision of float64 so that the result is always inexact. The intent is that the function will return a usable result for negative powers and seldom overflow for positive powers. .. versionadded:: 1.12.0 Parameters ---------- x1 : array_like The bases. x2 : array_like The exponents. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray The bases in `x1` raised to the exponents in `x2`. This is a scalar if both `x1` and `x2` are scalars. See Also -------- power : power function that preserves type Examples -------- Cube each element in a list. >>> x1 = [range(6)](https://www.chedong.com/phpMan.php/man/range/6/markdown) >>> x1 [0, 1, 2, 3, 4, 5] >>> np.float_power(x1, 3) array([ 0., 1., 8., 27., 64., 125.]) Raise the bases to different exponents. >>> x2 = [1.0, 2.0, 3.0, 3.0, 2.0, 1.0] >>> np.float_power(x1, x2) array([ 0., 1., 8., 27., 16., 5.]) The effect of broadcasting. >>> x2 = np.array([[1, 2, 3, 3, 2, 1], [1, 2, 3, 3, 2, 1]]) >>> x2 array([[1, 2, 3, 3, 2, 1], [1, 2, 3, 3, 2, 1]]) >>> np.float_power(x1, x2) array([[ 0., 1., 8., 27., 16., 5.], [ 0., 1., 8., 27., 16., 5.]]) floor = floor(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Return the floor of the input, element-wise. The floor of the scalar `x` is the largest integer `i`, such that `i <= x`. It is often denoted as :math:`\lfloor x \rfloor`. Parameters ---------- x : array_like Input data. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray or scalar The floor of each element in `x`. This is a scalar if `x` is a scalar. See Also -------- ceil, trunc, rint, fix Notes ----- Some spreadsheet programs calculate the "floor-towards-zero", where ``floor(-2.5) == -2``. NumPy instead uses the definition of `floor` where `floor(-2.5) == -3`. The "floor-towards-zero" function is called ``fix`` in NumPy. Examples -------- >>> a = np.array([-1.7, -1.5, -0.2, 0.2, 1.5, 1.7, 2.0]) >>> np.floor(a) array([-2., -2., -1., 0., 1., 1., 2.]) floor_divide = floor_divide(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Return the largest integer smaller or equal to the division of the inputs. It is equivalent to the Python ``//`` operator and pairs with the Python ``%`` (`remainder`), function so that ``a = a % b + b * (a // b)`` up to roundoff. Parameters ---------- x1 : array_like Numerator. x2 : array_like Denominator. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray y = floor(`x1`/`x2`) This is a scalar if both `x1` and `x2` are scalars. See Also -------- remainder : Remainder complementary to floor_divide. divmod : Simultaneous floor division and remainder. divide : Standard division. floor : Round a number to the nearest integer toward minus infinity. ceil : Round a number to the nearest integer toward infinity. Examples -------- >>> np.floor_divide(7,3) 2 >>> np.floor_divide([1., 2., 3., 4.], 2.5) array([ 0., 0., 1., 1.]) The ``//`` operator can be used as a shorthand for ``np.floor_divide`` on ndarrays. >>> x1 = np.array([1., 2., 3., 4.]) >>> x1 // 2.5 array([0., 0., 1., 1.]) fmax = fmax(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Element-wise maximum of array elements. Compare two arrays and returns a new array containing the element-wise maxima. If one of the elements being compared is a NaN, then the non-nan element is returned. If both elements are NaNs then the first is returned. The latter distinction is important for complex NaNs, which are defined as at least one of the real or imaginary parts being a NaN. The net effect is that NaNs are ignored when possible. Parameters ---------- x1, x2 : array_like The arrays holding the elements to be compared. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray or scalar The maximum of `x1` and `x2`, element-wise. This is a scalar if both `x1` and `x2` are scalars. See Also -------- fmin : Element-wise minimum of two arrays, ignores NaNs. maximum : Element-wise maximum of two arrays, propagates NaNs. amax : The maximum value of an array along a given axis, propagates NaNs. nanmax : The maximum value of an array along a given axis, ignores NaNs. minimum, amin, nanmin Notes ----- .. versionadded:: 1.3.0 The fmax is equivalent to ``np.where(x1 >= x2, x1, x2)`` when neither x1 nor x2 are NaNs, but it is faster and does proper broadcasting. Examples -------- >>> np.fmax([2, 3, 4], [1, 5, 2]) array([ 2., 5., 4.]) >>> np.fmax([np.eye(2)](https://www.chedong.com/phpMan.php/man/np.eye/2/markdown), [0.5, 2]) array([[ 1. , 2. ], [ 0.5, 2. ]]) >>> np.fmax([np.nan, 0, np.nan],[0, np.nan, np.nan]) array([ 0., 0., nan]) fmin = fmin(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Element-wise minimum of array elements. Compare two arrays and returns a new array containing the element-wise minima. If one of the elements being compared is a NaN, then the non-nan element is returned. If both elements are NaNs then the first is returned. The latter distinction is important for complex NaNs, which are defined as at least one of the real or imaginary parts being a NaN. The net effect is that NaNs are ignored when possible. Parameters ---------- x1, x2 : array_like The arrays holding the elements to be compared. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray or scalar The minimum of `x1` and `x2`, element-wise. This is a scalar if both `x1` and `x2` are scalars. See Also -------- fmax : Element-wise maximum of two arrays, ignores NaNs. minimum : Element-wise minimum of two arrays, propagates NaNs. amin : The minimum value of an array along a given axis, propagates NaNs. nanmin : The minimum value of an array along a given axis, ignores NaNs. maximum, amax, nanmax Notes ----- .. versionadded:: 1.3.0 The fmin is equivalent to ``np.where(x1 <= x2, x1, x2)`` when neither x1 nor x2 are NaNs, but it is faster and does proper broadcasting. Examples -------- >>> np.fmin([2, 3, 4], [1, 5, 2]) array([1, 3, 2]) >>> np.fmin([np.eye(2)](https://www.chedong.com/phpMan.php/man/np.eye/2/markdown), [0.5, 2]) array([[ 0.5, 0. ], [ 0. , 1. ]]) >>> np.fmin([np.nan, 0, np.nan],[0, np.nan, np.nan]) array([ 0., 0., nan]) fmod = fmod(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Return the element-wise remainder of division. This is the NumPy implementation of the C library function fmod, the remainder has the same sign as the dividend `x1`. It is equivalent to the Matlab(TM) ``rem`` function and should not be confused with the Python modulus operator ``x1 % x2``. Parameters ---------- x1 : array_like Dividend. x2 : array_like Divisor. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : array_like The remainder of the division of `x1` by `x2`. This is a scalar if both `x1` and `x2` are scalars. See Also -------- remainder : Equivalent to the Python ``%`` operator. divide Notes ----- The result of the modulo operation for negative dividend and divisors is bound by conventions. For `fmod`, the sign of result is the sign of the dividend, while for `remainder` the sign of the result is the sign of the divisor. The `fmod` function is equivalent to the Matlab(TM) ``rem`` function. Examples -------- >>> np.fmod([-3, -2, -1, 1, 2, 3], 2) array([-1, 0, -1, 1, 0, 1]) >>> np.remainder([-3, -2, -1, 1, 2, 3], 2) array([1, 0, 1, 1, 0, 1]) >>> np.fmod([5, 3], [2, 2.]) array([ 1., 1.]) >>> a = np.arange(-3, 3).reshape(3, 2) >>> a array([[-3, -2], [-1, 0], [ 1, 2]]) >>> np.fmod(a, [2,2]) array([[-1, 0], [-1, 0], [ 1, 0]]) frexp = frexp(x[, out1, out2], / [, out=(None, None)], *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Decompose the elements of x into mantissa and twos exponent. Returns (`mantissa`, `exponent`), where `x = mantissa * 2**exponent``. The mantissa lies in the open interval(-1, 1), while the twos exponent is a signed integer. Parameters ---------- x : array_like Array of numbers to be decomposed. out1 : ndarray, optional Output array for the mantissa. Must have the same shape as `x`. out2 : ndarray, optional Output array for the exponent. Must have the same shape as `x`. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- mantissa : ndarray Floating values between -1 and 1. This is a scalar if `x` is a scalar. exponent : ndarray Integer exponents of 2. This is a scalar if `x` is a scalar. See Also -------- ldexp : Compute ``y = x1 * 2**x2``, the inverse of `frexp`. Notes ----- Complex dtypes are not supported, they will raise a TypeError. Examples -------- >>> x = [np.arange(9)](https://www.chedong.com/phpMan.php/man/np.arange/9/markdown) >>> y1, y2 = np.frexp(x) >>> y1 array([ 0. , 0.5 , 0.5 , 0.75 , 0.5 , 0.625, 0.75 , 0.875, 0.5 ]) >>> y2 array([0, 1, 2, 2, 3, 3, 3, 3, 4]) >>> y1 * 2**y2 array([ 0., 1., 2., 3., 4., 5., 6., 7., 8.]) gcd = gcd(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Returns the greatest common divisor of ``|x1|`` and ``|x2|`` Parameters ---------- x1, x2 : array_like, int Arrays of values. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). Returns ------- y : ndarray or scalar The greatest common divisor of the absolute value of the inputs This is a scalar if both `x1` and `x2` are scalars. See Also -------- lcm : The lowest common multiple Examples -------- >>> np.gcd(12, 20) 4 >>> np.gcd.reduce([15, 25, 35]) 5 >>> np.gcd([np.arange(6)](https://www.chedong.com/phpMan.php/man/np.arange/6/markdown), 20) array([20, 1, 2, 1, 4, 5]) greater = greater(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Return the truth value of (x1 > x2) element-wise. Parameters ---------- x1, x2 : array_like Input arrays. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- out : ndarray or scalar Output array, element-wise comparison of `x1` and `x2`. Typically of type bool, unless ``dtype=object`` is passed. This is a scalar if both `x1` and `x2` are scalars. See Also -------- greater_equal, less, less_equal, equal, not_equal Examples -------- >>> np.greater([4,2],[2,2]) array([ True, False]) The ``>`` operator can be used as a shorthand for ``np.greater`` on ndarrays. >>> a = np.array([4, 2]) >>> b = np.array([2, 2]) >>> a > b array([ True, False]) greater_equal = greater_equal(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Return the truth value of (x1 >= x2) element-wise. Parameters ---------- x1, x2 : array_like Input arrays. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- out : bool or ndarray of bool Output array, element-wise comparison of `x1` and `x2`. Typically of type bool, unless ``dtype=object`` is passed. This is a scalar if both `x1` and `x2` are scalars. See Also -------- greater, less, less_equal, equal, not_equal Examples -------- >>> np.greater_equal([4, 2, 1], [2, 2, 2]) array([ True, True, False]) The ``>=`` operator can be used as a shorthand for ``np.greater_equal`` on ndarrays. >>> a = np.array([4, 2, 1]) >>> b = np.array([2, 2, 2]) >>> a >= b array([ True, True, False]) heaviside = heaviside(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Compute the Heaviside step function. The Heaviside step function is defined as:: 0 if x1 < 0 heaviside(x1, x2) = x2 if x1 == 0 1 if x1 > 0 where `x2` is often taken to be 0.5, but 0 and 1 are also sometimes used. Parameters ---------- x1 : array_like Input values. x2 : array_like The value of the function when x1 is 0. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- out : ndarray or scalar The output array, element-wise Heaviside step function of `x1`. This is a scalar if both `x1` and `x2` are scalars. Notes ----- .. versionadded:: 1.13.0 References ---------- .. Wikipedia, "Heaviside step function", Examples -------- >>> np.heaviside([-1.5, 0, 2.0], 0.5) array([ 0. , 0.5, 1. ]) >>> np.heaviside([-1.5, 0, 2.0], 1) array([ 0., 1., 1.]) hypot = hypot(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Given the "legs" of a right triangle, return its hypotenuse. Equivalent to ``sqrt(x1**2 + x2**2)``, element-wise. If `x1` or `x2` is scalar_like (i.e., unambiguously cast-able to a scalar type), it is broadcast for use with each element of the other argument. (See Examples) Parameters ---------- x1, x2 : array_like Leg of the triangle(s). If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- z : ndarray The hypotenuse of the triangle(s). This is a scalar if both `x1` and `x2` are scalars. Examples -------- >>> np.hypot(3*np.ones((3, 3)), 4*np.ones((3, 3))) array([[ 5., 5., 5.], [ 5., 5., 5.], [ 5., 5., 5.]]) Example showing broadcast of scalar_like argument: >>> np.hypot(3*np.ones((3, 3)), [4]) array([[ 5., 5., 5.], [ 5., 5., 5.], [ 5., 5., 5.]]) index_exp = inf = inf infty = inf invert = invert(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Compute bit-wise inversion, or bit-wise NOT, element-wise. Computes the bit-wise NOT of the underlying binary representation of the integers in the input arrays. This ufunc implements the C/Python operator ``~``. For signed integer inputs, the two's complement is returned. In a two's-complement system negative numbers are represented by the two's complement of the absolute value. This is the most common method of representing signed integers on computers [1]_. A N-bit two's-complement system can represent every integer in the range :math:`-2^{N-1}` to :math:`+2^{N-1}-1`. Parameters ---------- x : array_like Only integer and boolean types are handled. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- out : ndarray or scalar Result. This is a scalar if `x` is a scalar. See Also -------- bitwise_and, bitwise_or, bitwise_xor logical_not binary_repr : Return the binary representation of the input number as a string. Notes ----- `bitwise_not` is an alias for `invert`: >>> np.bitwise_not is np.invert True References ---------- .. [1] Wikipedia, "Two's complement", 's_complement Examples -------- We've seen that 13 is represented by ``00001101``. The invert or bit-wise NOT of 13 is then: >>> x = np.invert(np.array(13, dtype=np.uint8)) >>> x 242 >>> np.binary_repr(x, width=8) '11110010' The result depends on the bit-width: >>> x = np.invert(np.array(13, dtype=np.uint16)) >>> x 65522 >>> np.binary_repr(x, width=16) '1111111111110010' When using signed integer types the result is the two's complement of the result for the unsigned type: >>> np.invert(np.array([13], dtype=np.int8)) array([-14], dtype=int8) >>> np.binary_repr(-14, width=8) '11110010' Booleans are accepted as well: >>> np.invert(np.array([True, False])) array([False, True]) The ``~`` operator can be used as a shorthand for ``np.invert`` on ndarrays. >>> x1 = np.array([True, False]) >>> ~x1 array([False, True]) isfinite = isfinite(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Test element-wise for finiteness (not infinity or not Not a Number). The result is returned as a boolean array. Parameters ---------- x : array_like Input values. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray, bool True where ``x`` is not positive infinity, negative infinity, or NaN; false otherwise. This is a scalar if `x` is a scalar. See Also -------- isinf, isneginf, isposinf, isnan Notes ----- Not a Number, positive infinity and negative infinity are considered to be non-finite. NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754). This means that Not a Number is not equivalent to infinity. Also that positive infinity is not equivalent to negative infinity. But infinity is equivalent to positive infinity. Errors result if the second argument is also supplied when `x` is a scalar input, or if first and second arguments have different shapes. Examples -------- >>> [np.isfinite(1)](https://www.chedong.com/phpMan.php/man/np.isfinite/1/markdown) True >>> [np.isfinite(0)](https://www.chedong.com/phpMan.php/man/np.isfinite/0/markdown) True >>> np.isfinite(np.nan) False >>> np.isfinite(np.inf) False >>> np.isfinite(np.NINF) False >>> np.isfinite([np.log(-1.),1.,[np.log(0)](https://www.chedong.com/phpMan.php/man/np.log/0/markdown)]) array([False, True, False]) >>> x = np.array([-np.inf, 0., np.inf]) >>> y = np.array([2, 2, 2]) >>> np.isfinite(x, y) array([0, 1, 0]) >>> y array([0, 1, 0]) isinf = isinf(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Test element-wise for positive or negative infinity. Returns a boolean array of the same shape as `x`, True where ``x == +/-inf``, otherwise False. Parameters ---------- x : array_like Input values out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : bool (scalar) or boolean ndarray True where ``x`` is positive or negative infinity, false otherwise. This is a scalar if `x` is a scalar. See Also -------- isneginf, isposinf, isnan, isfinite Notes ----- NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754). Errors result if the second argument is supplied when the first argument is a scalar, or if the first and second arguments have different shapes. Examples -------- >>> np.isinf(np.inf) True >>> np.isinf(np.nan) False >>> np.isinf(np.NINF) True >>> np.isinf([np.inf, -np.inf, 1.0, np.nan]) array([ True, True, False, False]) >>> x = np.array([-np.inf, 0., np.inf]) >>> y = np.array([2, 2, 2]) >>> np.isinf(x, y) array([1, 0, 1]) >>> y array([1, 0, 1]) isnan = isnan(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Test element-wise for NaN and return result as a boolean array. Parameters ---------- x : array_like Input array. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray or bool True where ``x`` is NaN, false otherwise. This is a scalar if `x` is a scalar. See Also -------- isinf, isneginf, isposinf, isfinite, isnat Notes ----- NumPy uses the IEEE Standard for Binary Floating-Point for Arithmetic (IEEE 754). This means that Not a Number is not equivalent to infinity. Examples -------- >>> np.isnan(np.nan) True >>> np.isnan(np.inf) False >>> np.isnan([np.log(-1.),1.,[np.log(0)](https://www.chedong.com/phpMan.php/man/np.log/0/markdown)]) array([ True, False, False]) isnat = isnat(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Test element-wise for NaT (not a time) and return result as a boolean array. .. versionadded:: 1.13.0 Parameters ---------- x : array_like Input array with datetime or timedelta data type. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray or bool True where ``x`` is NaT, false otherwise. This is a scalar if `x` is a scalar. See Also -------- isnan, isinf, isneginf, isposinf, isfinite Examples -------- >>> np.isnat(np.datetime64("NaT")) True >>> np.isnat(np.datetime64("2016-01-01")) False >>> np.isnat(np.array(["NaT", "2016-01-01"], dtype="datetime64[ns]")) array([ True, False]) lcm = lcm(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Returns the lowest common multiple of ``|x1|`` and ``|x2|`` Parameters ---------- x1, x2 : array_like, int Arrays of values. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). Returns ------- y : ndarray or scalar The lowest common multiple of the absolute value of the inputs This is a scalar if both `x1` and `x2` are scalars. See Also -------- gcd : The greatest common divisor Examples -------- >>> np.lcm(12, 20) 60 >>> np.lcm.reduce([3, 12, 20]) 60 >>> np.lcm.reduce([40, 12, 20]) 120 >>> np.lcm([np.arange(6)](https://www.chedong.com/phpMan.php/man/np.arange/6/markdown), 20) array([ 0, 20, 20, 60, 20, 20]) ldexp = ldexp(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Returns x1 * 2**x2, element-wise. The mantissas `x1` and twos exponents `x2` are used to construct floating point numbers ``x1 * 2**x2``. Parameters ---------- x1 : array_like Array of multipliers. x2 : array_like, int Array of twos exponents. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray or scalar The result of ``x1 * 2**x2``. This is a scalar if both `x1` and `x2` are scalars. See Also -------- frexp : Return (y1, y2) from ``x = y1 * 2**y2``, inverse to `ldexp`. Notes ----- Complex dtypes are not supported, they will raise a TypeError. `ldexp` is useful as the inverse of `frexp`, if used by itself it is more clear to simply use the expression ``x1 * 2**x2``. Examples -------- >>> np.ldexp(5, [np.arange(4)](https://www.chedong.com/phpMan.php/man/np.arange/4/markdown)) array([ 5., 10., 20., 40.], dtype=float16) >>> x = [np.arange(6)](https://www.chedong.com/phpMan.php/man/np.arange/6/markdown) >>> np.ldexp(*np.frexp(x)) array([ 0., 1., 2., 3., 4., 5.]) left_shift = left_shift(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Shift the bits of an integer to the left. Bits are shifted to the left by appending `x2` 0s at the right of `x1`. Since the internal representation of numbers is in binary format, this operation is equivalent to multiplying `x1` by ``2**x2``. Parameters ---------- x1 : array_like of integer type Input values. x2 : array_like of integer type Number of zeros to append to `x1`. Has to be non-negative. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- out : array of integer type Return `x1` with bits shifted `x2` times to the left. This is a scalar if both `x1` and `x2` are scalars. See Also -------- right_shift : Shift the bits of an integer to the right. binary_repr : Return the binary representation of the input number as a string. Examples -------- >>> [np.binary_repr(5)](https://www.chedong.com/phpMan.php/man/np.binaryrepr/5/markdown) '101' >>> np.left_shift(5, 2) 20 >>> [np.binary_repr(20)](https://www.chedong.com/phpMan.php/man/np.binaryrepr/20/markdown) '10100' >>> np.left_shift(5, [1,2,3]) array([10, 20, 40]) Note that the dtype of the second argument may change the dtype of the result and can lead to unexpected results in some cases (see :ref:`Casting Rules `): >>> a = np.left_shift([np.uint8(255)](https://www.chedong.com/phpMan.php/man/np.uint8/255/markdown), 1) # Expect 254 >>> print(a, type(a)) # Unexpected result due to upcasting 510 >>> b = np.left_shift([np.uint8(255)](https://www.chedong.com/phpMan.php/man/np.uint8/255/markdown), [np.uint8(1)](https://www.chedong.com/phpMan.php/man/np.uint8/1/markdown)) >>> print(b, type(b)) 254 The ``<<`` operator can be used as a shorthand for ``np.left_shift`` on ndarrays. >>> x1 = 5 >>> x2 = np.array([1, 2, 3]) >>> x1 << x2 array([10, 20, 40]) less = less(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Return the truth value of (x1 < x2) element-wise. Parameters ---------- x1, x2 : array_like Input arrays. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- out : ndarray or scalar Output array, element-wise comparison of `x1` and `x2`. Typically of type bool, unless ``dtype=object`` is passed. This is a scalar if both `x1` and `x2` are scalars. See Also -------- greater, less_equal, greater_equal, equal, not_equal Examples -------- >>> np.less([1, 2], [2, 2]) array([ True, False]) The ``<`` operator can be used as a shorthand for ``np.less`` on ndarrays. >>> a = np.array([1, 2]) >>> b = np.array([2, 2]) >>> a < b array([ True, False]) less_equal = less_equal(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Return the truth value of (x1 <= x2) element-wise. Parameters ---------- x1, x2 : array_like Input arrays. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- out : ndarray or scalar Output array, element-wise comparison of `x1` and `x2`. Typically of type bool, unless ``dtype=object`` is passed. This is a scalar if both `x1` and `x2` are scalars. See Also -------- greater, less, greater_equal, equal, not_equal Examples -------- >>> np.less_equal([4, 2, 1], [2, 2, 2]) array([False, True, True]) The ``<=`` operator can be used as a shorthand for ``np.less_equal`` on ndarrays. >>> a = np.array([4, 2, 1]) >>> b = np.array([2, 2, 2]) >>> a <= b array([False, True, True]) little_endian = True log = log(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Natural logarithm, element-wise. The natural logarithm `log` is the inverse of the exponential function, so that `log(exp(x)) = x`. The natural logarithm is logarithm in base `e`. Parameters ---------- x : array_like Input value. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray The natural logarithm of `x`, element-wise. This is a scalar if `x` is a scalar. See Also -------- log10, log2, log1p, emath.log Notes ----- Logarithm is a multivalued function: for each `x` there is an infinite number of `z` such that `exp(z) = x`. The convention is to return the `z` whose imaginary part lies in `[-pi, pi]`. For real-valued input data types, `log` always returns real output. For each value that cannot be expressed as a real number or infinity, it yields ``nan`` and sets the `invalid` floating point error flag. For complex-valued input, `log` is a complex analytical function that has a branch cut `[-inf, 0]` and is continuous from above on it. `log` handles the floating-point negative zero as an infinitesimal negative number, conforming to the C99 standard. References ---------- .. [1] M. Abramowitz and I.A. Stegun, "Handbook of Mathematical Functions", 10th printing, 1964, pp. 67. .. [2] Wikipedia, "Logarithm". Examples -------- >>> np.log([1, np.e, np.e**2, 0]) array([ 0., 1., 2., -Inf]) log10 = log10(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Return the base 10 logarithm of the input array, element-wise. Parameters ---------- x : array_like Input values. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray The logarithm to the base 10 of `x`, element-wise. NaNs are returned where x is negative. This is a scalar if `x` is a scalar. See Also -------- emath.log10 Notes ----- Logarithm is a multivalued function: for each `x` there is an infinite number of `z` such that `10**z = x`. The convention is to return the `z` whose imaginary part lies in `[-pi, pi]`. For real-valued input data types, `log10` always returns real output. For each value that cannot be expressed as a real number or infinity, it yields ``nan`` and sets the `invalid` floating point error flag. For complex-valued input, `log10` is a complex analytical function that has a branch cut `[-inf, 0]` and is continuous from above on it. `log10` handles the floating-point negative zero as an infinitesimal negative number, conforming to the C99 standard. References ---------- .. [1] M. Abramowitz and I.A. Stegun, "Handbook of Mathematical Functions", 10th printing, 1964, pp. 67. .. [2] Wikipedia, "Logarithm". Examples -------- >>> np.log10([1e-15, -3.]) array([-15., nan]) log1p = log1p(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Return the natural logarithm of one plus the input array, element-wise. Calculates ``log(1 + x)``. Parameters ---------- x : array_like Input values. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray Natural logarithm of `1 + x`, element-wise. This is a scalar if `x` is a scalar. See Also -------- expm1 : ``exp(x) - 1``, the inverse of `log1p`. Notes ----- For real-valued input, `log1p` is accurate also for `x` so small that `1 + x == 1` in floating-point accuracy. Logarithm is a multivalued function: for each `x` there is an infinite number of `z` such that `exp(z) = 1 + x`. The convention is to return the `z` whose imaginary part lies in `[-pi, pi]`. For real-valued input data types, `log1p` always returns real output. For each value that cannot be expressed as a real number or infinity, it yields ``nan`` and sets the `invalid` floating point error flag. For complex-valued input, `log1p` is a complex analytical function that has a branch cut `[-inf, -1]` and is continuous from above on it. `log1p` handles the floating-point negative zero as an infinitesimal negative number, conforming to the C99 standard. References ---------- .. [1] M. Abramowitz and I.A. Stegun, "Handbook of Mathematical Functions", 10th printing, 1964, pp. 67. .. [2] Wikipedia, "Logarithm". Examples -------- >>> np.log1p(1e-99) 1e-99 >>> np.log(1 + 1e-99) 0.0 log2 = log2(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Base-2 logarithm of `x`. Parameters ---------- x : array_like Input values. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray Base-2 logarithm of `x`. This is a scalar if `x` is a scalar. See Also -------- log, log10, log1p, emath.log2 Notes ----- .. versionadded:: 1.3.0 Logarithm is a multivalued function: for each `x` there is an infinite number of `z` such that `2**z = x`. The convention is to return the `z` whose imaginary part lies in `[-pi, pi]`. For real-valued input data types, `log2` always returns real output. For each value that cannot be expressed as a real number or infinity, it yields ``nan`` and sets the `invalid` floating point error flag. For complex-valued input, `log2` is a complex analytical function that has a branch cut `[-inf, 0]` and is continuous from above on it. `log2` handles the floating-point negative zero as an infinitesimal negative number, conforming to the C99 standard. Examples -------- >>> x = np.array([0, 1, 2, 2**4]) >>> np.log2(x) array([-Inf, 0., 1., 4.]) >>> xi = np.array([0+1.j, 1, 2+0.j, 4.j]) >>> np.log2(xi) array([ 0.+2.26618007j, 0.+0.j , 1.+0.j , 2.+2.26618007j]) logaddexp = logaddexp(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Logarithm of the sum of exponentiations of the inputs. Calculates ``log(exp(x1) + exp(x2))``. This function is useful in statistics where the calculated probabilities of events may be so small as to exceed the range of normal floating point numbers. In such cases the logarithm of the calculated probability is stored. This function allows adding probabilities stored in such a fashion. Parameters ---------- x1, x2 : array_like Input values. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- result : ndarray Logarithm of ``exp(x1) + exp(x2)``. This is a scalar if both `x1` and `x2` are scalars. See Also -------- logaddexp2: Logarithm of the sum of exponentiations of inputs in base 2. Notes ----- .. versionadded:: 1.3.0 Examples -------- >>> prob1 = np.log(1e-50) >>> prob2 = np.log(2.5e-50) >>> prob12 = np.logaddexp(prob1, prob2) >>> prob12 -113.87649168120691 >>> np.exp(prob12) 3.5000000000000057e-50 logaddexp2 = logaddexp2(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Logarithm of the sum of exponentiations of the inputs in base-2. Calculates ``log2(2**x1 + 2**x2)``. This function is useful in machine learning when the calculated probabilities of events may be so small as to exceed the range of normal floating point numbers. In such cases the base-2 logarithm of the calculated probability can be used instead. This function allows adding probabilities stored in such a fashion. Parameters ---------- x1, x2 : array_like Input values. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- result : ndarray Base-2 logarithm of ``2**x1 + 2**x2``. This is a scalar if both `x1` and `x2` are scalars. See Also -------- logaddexp: Logarithm of the sum of exponentiations of the inputs. Notes ----- .. versionadded:: 1.3.0 Examples -------- >>> prob1 = np.log2(1e-50) >>> prob2 = np.log2(2.5e-50) >>> prob12 = np.logaddexp2(prob1, prob2) >>> prob1, prob2, prob12 (-166.09640474436813, -164.77447664948076, -164.28904982231052) >>> 2**prob12 3.4999999999999914e-50 logical_and = logical_and(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Compute the truth value of x1 AND x2 element-wise. Parameters ---------- x1, x2 : array_like Input arrays. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray or bool Boolean result of the logical AND operation applied to the elements of `x1` and `x2`; the shape is determined by broadcasting. This is a scalar if both `x1` and `x2` are scalars. See Also -------- logical_or, logical_not, logical_xor bitwise_and Examples -------- >>> np.logical_and(True, False) False >>> np.logical_and([True, False], [False, False]) array([False, False]) >>> x = [np.arange(5)](https://www.chedong.com/phpMan.php/man/np.arange/5/markdown) >>> np.logical_and(x>1, x<4) array([False, False, True, True, False]) The ``&`` operator can be used as a shorthand for ``np.logical_and`` on boolean ndarrays. >>> a = np.array([True, False]) >>> b = np.array([False, False]) >>> a & b array([False, False]) logical_not = logical_not(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Compute the truth value of NOT x element-wise. Parameters ---------- x : array_like Logical NOT is applied to the elements of `x`. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : bool or ndarray of bool Boolean result with the same shape as `x` of the NOT operation on elements of `x`. This is a scalar if `x` is a scalar. See Also -------- logical_and, logical_or, logical_xor Examples -------- >>> [np.logical_not(3)](https://www.chedong.com/phpMan.php/man/np.logicalnot/3/markdown) False >>> np.logical_not([True, False, 0, 1]) array([False, True, True, False]) >>> x = [np.arange(5)](https://www.chedong.com/phpMan.php/man/np.arange/5/markdown) >>> np.logical_not(x<3) array([False, False, False, True, True]) logical_or = logical_or(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Compute the truth value of x1 OR x2 element-wise. Parameters ---------- x1, x2 : array_like Logical OR is applied to the elements of `x1` and `x2`. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray or bool Boolean result of the logical OR operation applied to the elements of `x1` and `x2`; the shape is determined by broadcasting. This is a scalar if both `x1` and `x2` are scalars. See Also -------- logical_and, logical_not, logical_xor bitwise_or Examples -------- >>> np.logical_or(True, False) True >>> np.logical_or([True, False], [False, False]) array([ True, False]) >>> x = [np.arange(5)](https://www.chedong.com/phpMan.php/man/np.arange/5/markdown) >>> np.logical_or(x < 1, x > 3) array([ True, False, False, False, True]) The ``|`` operator can be used as a shorthand for ``np.logical_or`` on boolean ndarrays. >>> a = np.array([True, False]) >>> b = np.array([False, False]) >>> a | b array([ True, False]) logical_xor = logical_xor(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Compute the truth value of x1 XOR x2, element-wise. Parameters ---------- x1, x2 : array_like Logical XOR is applied to the elements of `x1` and `x2`. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : bool or ndarray of bool Boolean result of the logical XOR operation applied to the elements of `x1` and `x2`; the shape is determined by broadcasting. This is a scalar if both `x1` and `x2` are scalars. See Also -------- logical_and, logical_or, logical_not, bitwise_xor Examples -------- >>> np.logical_xor(True, False) True >>> np.logical_xor([True, True, False, False], [True, False, True, False]) array([False, True, True, False]) >>> x = [np.arange(5)](https://www.chedong.com/phpMan.php/man/np.arange/5/markdown) >>> np.logical_xor(x < 1, x > 3) array([ True, False, False, False, True]) Simple example showing support of broadcasting >>> np.logical_xor(0, [np.eye(2)](https://www.chedong.com/phpMan.php/man/np.eye/2/markdown)) array([[ True, False], [False, True]]) matmul = matmul(x1, x2, /, out=None, *, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj, axes, axis]) Matrix product of two arrays. Parameters ---------- x1, x2 : array_like Input arrays, scalars not allowed. out : ndarray, optional A location into which the result is stored. If provided, it must have a shape that matches the signature `(n,k),(k,m)->(n,m)`. If not provided or None, a freshly-allocated array is returned. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. .. versionadded:: 1.16 Now handles ufunc kwargs Returns ------- y : ndarray The matrix product of the inputs. This is a scalar only when both x1, x2 are 1-d vectors. Raises ------ ValueError If the last dimension of `x1` is not the same size as the second-to-last dimension of `x2`. If a scalar value is passed in. See Also -------- vdot : Complex-conjugating dot product. tensordot : Sum products over arbitrary axes. einsum : Einstein summation convention. dot : alternative matrix product with different broadcasting rules. Notes ----- The behavior depends on the arguments in the following way. - If both arguments are 2-D they are multiplied like conventional matrices. - If either argument is N-D, N > 2, it is treated as a stack of matrices residing in the last two indexes and broadcast accordingly. - If the first argument is 1-D, it is promoted to a matrix by prepending a 1 to its dimensions. After matrix multiplication the prepended 1 is removed. - If the second argument is 1-D, it is promoted to a matrix by appending a 1 to its dimensions. After matrix multiplication the appended 1 is removed. ``matmul`` differs from ``dot`` in two important ways: - Multiplication by scalars is not allowed, use ``*`` instead. - Stacks of matrices are broadcast together as if the matrices were elements, respecting the signature ``(n,k),(k,m)->(n,m)``: >>> a = np.ones([9, 5, 7, 4]) >>> c = np.ones([9, 5, 4, 3]) >>> np.dot(a, c).shape (9, 5, 7, 9, 5, 3) >>> np.matmul(a, c).shape (9, 5, 7, 3) >>> # n is 7, k is 4, m is 3 The matmul function implements the semantics of the ``@`` operator introduced in Python 3.5 following :pep:`465`. Examples -------- For 2-D arrays it is the matrix product: >>> a = np.array([[1, 0], ... [0, 1]]) >>> b = np.array([[4, 1], ... [2, 2]]) >>> np.matmul(a, b) array([[4, 1], [2, 2]]) For 2-D mixed with 1-D, the result is the usual. >>> a = np.array([[1, 0], ... [0, 1]]) >>> b = np.array([1, 2]) >>> np.matmul(a, b) array([1, 2]) >>> np.matmul(b, a) array([1, 2]) Broadcasting is conventional for stacks of arrays >>> a = np.arange(2 * 2 * 4).reshape((2, 2, 4)) >>> b = np.arange(2 * 2 * 4).reshape((2, 4, 2)) >>> np.matmul(a,b).shape (2, 2, 2) >>> np.matmul(a, b)[0, 1, 1] 98 >>> sum(a[0, 1, :] * b[0 , :, 1]) 98 Vector, vector returns the scalar inner product, but neither argument is complex-conjugated: >>> np.matmul([2j, 3j], [2j, 3j]) (-13+0j) Scalar multiplication raises an error. >>> np.matmul([1,2], 3) Traceback (most recent call last): ... ValueError: matmul: Input operand 1 does not have enough dimensions ... The ``@`` operator can be used as a shorthand for ``np.matmul`` on ndarrays. >>> x1 = np.array([2j, 3j]) >>> x2 = np.array([2j, 3j]) >>> x1 @ x2 (-13+0j) .. versionadded:: 1.10.0 maximum = maximum(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Element-wise maximum of array elements. Compare two arrays and returns a new array containing the element-wise maxima. If one of the elements being compared is a NaN, then that element is returned. If both elements are NaNs then the first is returned. The latter distinction is important for complex NaNs, which are defined as at least one of the real or imaginary parts being a NaN. The net effect is that NaNs are propagated. Parameters ---------- x1, x2 : array_like The arrays holding the elements to be compared. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray or scalar The maximum of `x1` and `x2`, element-wise. This is a scalar if both `x1` and `x2` are scalars. See Also -------- minimum : Element-wise minimum of two arrays, propagates NaNs. fmax : Element-wise maximum of two arrays, ignores NaNs. amax : The maximum value of an array along a given axis, propagates NaNs. nanmax : The maximum value of an array along a given axis, ignores NaNs. fmin, amin, nanmin Notes ----- The maximum is equivalent to ``np.where(x1 >= x2, x1, x2)`` when neither x1 nor x2 are nans, but it is faster and does proper broadcasting. Examples -------- >>> np.maximum([2, 3, 4], [1, 5, 2]) array([2, 5, 4]) >>> np.maximum([np.eye(2)](https://www.chedong.com/phpMan.php/man/np.eye/2/markdown), [0.5, 2]) # broadcasting array([[ 1. , 2. ], [ 0.5, 2. ]]) >>> np.maximum([np.nan, 0, np.nan], [0, np.nan, np.nan]) array([nan, nan, nan]) >>> np.maximum(np.Inf, 1) inf mgrid = minimum = minimum(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Element-wise minimum of array elements. Compare two arrays and returns a new array containing the element-wise minima. If one of the elements being compared is a NaN, then that element is returned. If both elements are NaNs then the first is returned. The latter distinction is important for complex NaNs, which are defined as at least one of the real or imaginary parts being a NaN. The net effect is that NaNs are propagated. Parameters ---------- x1, x2 : array_like The arrays holding the elements to be compared. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray or scalar The minimum of `x1` and `x2`, element-wise. This is a scalar if both `x1` and `x2` are scalars. See Also -------- maximum : Element-wise maximum of two arrays, propagates NaNs. fmin : Element-wise minimum of two arrays, ignores NaNs. amin : The minimum value of an array along a given axis, propagates NaNs. nanmin : The minimum value of an array along a given axis, ignores NaNs. fmax, amax, nanmax Notes ----- The minimum is equivalent to ``np.where(x1 <= x2, x1, x2)`` when neither x1 nor x2 are NaNs, but it is faster and does proper broadcasting. Examples -------- >>> np.minimum([2, 3, 4], [1, 5, 2]) array([1, 3, 2]) >>> np.minimum([np.eye(2)](https://www.chedong.com/phpMan.php/man/np.eye/2/markdown), [0.5, 2]) # broadcasting array([[ 0.5, 0. ], [ 0. , 1. ]]) >>> np.minimum([np.nan, 0, np.nan],[0, np.nan, np.nan]) array([nan, nan, nan]) >>> np.minimum(-np.Inf, 1) ### -inf mod = remainder(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Return element-wise remainder of division. Computes the remainder complementary to the `floor_divide` function. It is equivalent to the Python modulus operator``x1 % x2`` and has the same sign as the divisor `x2`. The MATLAB function equivalent to ``np.remainder`` is ``mod``. .. warning:: This should not be confused with: * Python 3.7's `math.remainder` and C's ``remainder``, which computes the IEEE remainder, which are the complement to ``round(x1 / x2)``. * The MATLAB ``rem`` function and or the C ``%`` operator which is the complement to ``int(x1 / x2)``. Parameters ---------- x1 : array_like Dividend array. x2 : array_like Divisor array. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray The element-wise remainder of the quotient ``floor_divide(x1, x2)``. This is a scalar if both `x1` and `x2` are scalars. See Also -------- floor_divide : Equivalent of Python ``//`` operator. divmod : Simultaneous floor division and remainder. fmod : Equivalent of the MATLAB ``rem`` function. divide, floor Notes ----- Returns 0 when `x2` is 0 and both `x1` and `x2` are (arrays of) integers. ``mod`` is an alias of ``remainder``. Examples -------- >>> np.remainder([4, 7], [2, 3]) array([0, 1]) >>> np.remainder([np.arange(7)](https://www.chedong.com/phpMan.php/man/np.arange/7/markdown), 5) array([0, 1, 2, 3, 4, 0, 1]) The ``%`` operator can be used as a shorthand for ``np.remainder`` on ndarrays. >>> x1 = [np.arange(7)](https://www.chedong.com/phpMan.php/man/np.arange/7/markdown) >>> x1 % 5 array([0, 1, 2, 3, 4, 0, 1]) modf = modf(x[, out1, out2], / [, out=(None, None)], *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Return the fractional and integral parts of an array, element-wise. The fractional and integral parts are negative if the given number is negative. Parameters ---------- x : array_like Input array. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y1 : ndarray Fractional part of `x`. This is a scalar if `x` is a scalar. y2 : ndarray Integral part of `x`. This is a scalar if `x` is a scalar. Notes ----- For integer input the return values are floats. See Also -------- divmod : ``divmod(x, 1)`` is equivalent to ``modf`` with the return values switched, except it always has a positive remainder. Examples -------- >>> np.modf([0, 3.5]) (array([ 0. , 0.5]), array([ 0., 3.])) >>> np.modf(-0.5) (-0.5, -0) multiply = multiply(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Multiply arguments element-wise. Parameters ---------- x1, x2 : array_like Input arrays to be multiplied. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray The product of `x1` and `x2`, element-wise. This is a scalar if both `x1` and `x2` are scalars. Notes ----- Equivalent to `x1` * `x2` in terms of array broadcasting. Examples -------- >>> np.multiply(2.0, 4.0) 8.0 >>> x1 = np.arange(9.0).reshape((3, 3)) >>> x2 = np.arange(3.0) >>> np.multiply(x1, x2) array([[ 0., 1., 4.], [ 0., 4., 10.], [ 0., 7., 16.]]) The ``*`` operator can be used as a shorthand for ``np.multiply`` on ndarrays. >>> x1 = np.arange(9.0).reshape((3, 3)) >>> x2 = np.arange(3.0) >>> x1 * x2 array([[ 0., 1., 4.], [ 0., 4., 10.], [ 0., 7., 16.]]) nan = nan nbytes = {: 1, :....datetime6... negative = negative(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Numerical negative, element-wise. Parameters ---------- x : array_like or scalar Input array. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray or scalar Returned array or scalar: `y = -x`. This is a scalar if `x` is a scalar. Examples -------- >>> np.negative([1.,-1.]) array([-1., 1.]) The unary ``-`` operator can be used as a shorthand for ``np.negative`` on ndarrays. >>> x1 = np.array(([1., -1.])) >>> -x1 array([-1., 1.]) newaxis = None nextafter = nextafter(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Return the next floating-point value after x1 towards x2, element-wise. Parameters ---------- x1 : array_like Values to find the next representable value of. x2 : array_like The direction where to look for the next representable value of `x1`. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- out : ndarray or scalar The next representable values of `x1` in the direction of `x2`. This is a scalar if both `x1` and `x2` are scalars. Examples -------- >>> eps = np.finfo(np.float64).eps >>> np.nextafter(1, 2) == eps + 1 True >>> np.nextafter([1, 2], [2, 1]) == [eps + 1, 2 - eps] array([ True, True]) not_equal = not_equal(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Return (x1 != x2) element-wise. Parameters ---------- x1, x2 : array_like Input arrays. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- out : ndarray or scalar Output array, element-wise comparison of `x1` and `x2`. Typically of type bool, unless ``dtype=object`` is passed. This is a scalar if both `x1` and `x2` are scalars. See Also -------- equal, greater, greater_equal, less, less_equal Examples -------- >>> np.not_equal([1.,2.], [1., 3.]) array([False, True]) >>> np.not_equal([1, 2], [[1, 3],[1, 4]]) array([[False, True], [False, True]]) The ``!=`` operator can be used as a shorthand for ``np.not_equal`` on ndarrays. >>> a = np.array([1., 2.]) >>> b = np.array([1., 3.]) >>> a != b array([False, True]) ogrid = pi = 3.141592653589793 positive = positive(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Numerical positive, element-wise. .. versionadded:: 1.13.0 Parameters ---------- x : array_like or scalar Input array. Returns ------- y : ndarray or scalar Returned array or scalar: `y = +x`. This is a scalar if `x` is a scalar. Notes ----- Equivalent to `x.copy()`, but only defined for types that support arithmetic. Examples -------- >>> x1 = np.array(([1., -1.])) >>> np.positive(x1) array([ 1., -1.]) The unary ``+`` operator can be used as a shorthand for ``np.positive`` on ndarrays. >>> x1 = np.array(([1., -1.])) >>> +x1 array([ 1., -1.]) power = power(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) First array elements raised to powers from second array, element-wise. Raise each base in `x1` to the positionally-corresponding power in `x2`. `x1` and `x2` must be broadcastable to the same shape. Note that an integer type raised to a negative integer power will raise a ValueError. Parameters ---------- x1 : array_like The bases. x2 : array_like The exponents. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray The bases in `x1` raised to the exponents in `x2`. This is a scalar if both `x1` and `x2` are scalars. See Also -------- float_power : power function that promotes integers to float Examples -------- Cube each element in an array. >>> x1 = [np.arange(6)](https://www.chedong.com/phpMan.php/man/np.arange/6/markdown) >>> x1 [0, 1, 2, 3, 4, 5] >>> np.power(x1, 3) array([ 0, 1, 8, 27, 64, 125]) Raise the bases to different exponents. >>> x2 = [1.0, 2.0, 3.0, 3.0, 2.0, 1.0] >>> np.power(x1, x2) array([ 0., 1., 8., 27., 16., 5.]) The effect of broadcasting. >>> x2 = np.array([[1, 2, 3, 3, 2, 1], [1, 2, 3, 3, 2, 1]]) >>> x2 array([[1, 2, 3, 3, 2, 1], [1, 2, 3, 3, 2, 1]]) >>> np.power(x1, x2) array([[ 0, 1, 8, 27, 16, 5], [ 0, 1, 8, 27, 16, 5]]) The ``**`` operator can be used as a shorthand for ``np.power`` on ndarrays. >>> x2 = np.array([1, 2, 3, 3, 2, 1]) >>> x1 = [np.arange(6)](https://www.chedong.com/phpMan.php/man/np.arange/6/markdown) >>> x1 ** x2 array([ 0, 1, 8, 27, 16, 5]) r_ = rad2deg = rad2deg(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Convert angles from radians to degrees. Parameters ---------- x : array_like Angle in radians. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray The corresponding angle in degrees. This is a scalar if `x` is a scalar. See Also -------- deg2rad : Convert angles from degrees to radians. unwrap : Remove large jumps in angle by wrapping. Notes ----- .. versionadded:: 1.3.0 rad2deg(x) is ``180 * x / pi``. Examples -------- >>> np.rad2deg(np.pi/2) 90.0 radians = radians(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Convert angles from degrees to radians. Parameters ---------- x : array_like Input array in degrees. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray The corresponding radian values. This is a scalar if `x` is a scalar. See Also -------- deg2rad : equivalent function Examples -------- Convert a degree array to radians >>> deg = np.arange(12.) * 30. >>> np.radians(deg) array([ 0. , 0.52359878, 1.04719755, 1.57079633, 2.0943951 , 2.61799388, 3.14159265, 3.66519143, 4.1887902 , 4.71238898, 5.23598776, 5.75958653]) >>> out = np.zeros((deg.shape)) >>> ret = np.radians(deg, out) >>> ret is out True reciprocal = reciprocal(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Return the reciprocal of the argument, element-wise. Calculates ``1/x``. Parameters ---------- x : array_like Input array. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray Return array. This is a scalar if `x` is a scalar. Notes ----- .. note:: This function is not designed to work with integers. For integer arguments with absolute value larger than 1 the result is always zero because of the way Python handles integer division. For integer zero the result is an overflow. Examples -------- >>> np.reciprocal(2.) 0.5 >>> np.reciprocal([1, 2., 3.33]) array([ 1. , 0.5 , 0.3003003]) remainder = remainder(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Return element-wise remainder of division. Computes the remainder complementary to the `floor_divide` function. It is equivalent to the Python modulus operator``x1 % x2`` and has the same sign as the divisor `x2`. The MATLAB function equivalent to ``np.remainder`` is ``mod``. .. warning:: This should not be confused with: * Python 3.7's `math.remainder` and C's ``remainder``, which computes the IEEE remainder, which are the complement to ``round(x1 / x2)``. * The MATLAB ``rem`` function and or the C ``%`` operator which is the complement to ``int(x1 / x2)``. Parameters ---------- x1 : array_like Dividend array. x2 : array_like Divisor array. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray The element-wise remainder of the quotient ``floor_divide(x1, x2)``. This is a scalar if both `x1` and `x2` are scalars. See Also -------- floor_divide : Equivalent of Python ``//`` operator. divmod : Simultaneous floor division and remainder. fmod : Equivalent of the MATLAB ``rem`` function. divide, floor Notes ----- Returns 0 when `x2` is 0 and both `x1` and `x2` are (arrays of) integers. ``mod`` is an alias of ``remainder``. Examples -------- >>> np.remainder([4, 7], [2, 3]) array([0, 1]) >>> np.remainder([np.arange(7)](https://www.chedong.com/phpMan.php/man/np.arange/7/markdown), 5) array([0, 1, 2, 3, 4, 0, 1]) The ``%`` operator can be used as a shorthand for ``np.remainder`` on ndarrays. >>> x1 = [np.arange(7)](https://www.chedong.com/phpMan.php/man/np.arange/7/markdown) >>> x1 % 5 array([0, 1, 2, 3, 4, 0, 1]) right_shift = right_shift(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Shift the bits of an integer to the right. Bits are shifted to the right `x2`. Because the internal representation of numbers is in binary format, this operation is equivalent to dividing `x1` by ``2**x2``. Parameters ---------- x1 : array_like, int Input values. x2 : array_like, int Number of bits to remove at the right of `x1`. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- out : ndarray, int Return `x1` with bits shifted `x2` times to the right. This is a scalar if both `x1` and `x2` are scalars. See Also -------- left_shift : Shift the bits of an integer to the left. binary_repr : Return the binary representation of the input number as a string. Examples -------- >>> [np.binary_repr(10)](https://www.chedong.com/phpMan.php/man/np.binaryrepr/10/markdown) '1010' >>> np.right_shift(10, 1) 5 >>> [np.binary_repr(5)](https://www.chedong.com/phpMan.php/man/np.binaryrepr/5/markdown) '101' >>> np.right_shift(10, [1,2,3]) array([5, 2, 1]) The ``>>`` operator can be used as a shorthand for ``np.right_shift`` on ndarrays. >>> x1 = 10 >>> x2 = np.array([1,2,3]) >>> x1 >> x2 array([5, 2, 1]) rint = rint(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Round elements of the array to the nearest integer. Parameters ---------- x : array_like Input array. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- out : ndarray or scalar Output array is same shape and type as `x`. This is a scalar if `x` is a scalar. See Also -------- fix, ceil, floor, trunc Notes ----- For values exactly halfway between rounded decimal values, NumPy rounds to the nearest even value. Thus 1.5 and 2.5 round to 2.0, -0.5 and 0.5 round to 0.0, etc. Examples -------- >>> a = np.array([-1.7, -1.5, -0.2, 0.2, 1.5, 1.7, 2.0]) >>> np.rint(a) array([-2., -2., -0., 0., 2., 2., 2.]) s_ = sctypeDict = {'?': , 0: , 'b... sctypes = {'complex': [, sign(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Returns an element-wise indication of the sign of a number. The `sign` function returns ``-1 if x < 0, 0 if x==0, 1 if x > 0``. nan is returned for nan inputs. For complex inputs, the `sign` function returns ``sign(x.real) + 0j if x.real != 0 else sign(x.imag) + 0j``. complex(nan, 0) is returned for complex nan inputs. Parameters ---------- x : array_like Input values. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray The sign of `x`. This is a scalar if `x` is a scalar. Notes ----- There is more than one definition of sign in common use for complex numbers. The definition used here is equivalent to :math:`x/\sqrt{x*x}` which is different from a common alternative, :math:`x/|x|`. Examples -------- >>> np.sign([-5., 4.5]) array([-1., 1.]) >>> [np.sign(0)](https://www.chedong.com/phpMan.php/man/np.sign/0/markdown) 0 >>> np.sign(5-2j) (1+0j) signbit = signbit(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Returns element-wise True where signbit is set (less than zero). Parameters ---------- x : array_like The input value(s). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- result : ndarray of bool Output array, or reference to `out` if that was supplied. This is a scalar if `x` is a scalar. Examples -------- >>> np.signbit(-1.2) True >>> np.signbit(np.array([1, -2.3, 2.1])) array([False, True, False]) sin = sin(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Trigonometric sine, element-wise. Parameters ---------- x : array_like Angle, in radians (:math:`2 \pi` rad equals 360 degrees). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : array_like The sine of each element of x. This is a scalar if `x` is a scalar. See Also -------- arcsin, sinh, cos Notes ----- The sine is one of the fundamental functions of trigonometry (the mathematical study of triangles). Consider a circle of radius 1 centered on the origin. A ray comes in from the :math:`+x` axis, makes an angle at the origin (measured counter-clockwise from that axis), and departs from the origin. The :math:`y` coordinate of the outgoing ray's intersection with the unit circle is the sine of that angle. It ranges from -1 for :math:`x=3\pi / 2` to +1 for :math:`\pi / 2.` The function has zeroes where the angle is a multiple of :math:`\pi`. Sines of angles between :math:`\pi` and :math:`2\pi` are negative. The numerous properties of the sine and related functions are included in any standard trigonometry text. Examples -------- Print sine of one angle: >>> np.sin(np.pi/2.) 1.0 Print sines of an array of angles given in degrees: >>> np.sin(np.array((0., 30., 45., 60., 90.)) * np.pi / 180. ) array([ 0. , 0.5 , 0.70710678, 0.8660254 , 1. ]) Plot the sine function: >>> import matplotlib.pylab as plt >>> x = np.linspace(-np.pi, np.pi, 201) >>> plt.plot(x, np.sin(x)) >>> plt.xlabel('Angle [rad]') >>> plt.ylabel('sin(x)') >>> plt.axis('tight') >>> plt.show() sinh = sinh(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Hyperbolic sine, element-wise. Equivalent to ``1/2 * (np.exp(x) - np.exp(-x))`` or ``-1j * np.sin(1j*x)``. Parameters ---------- x : array_like Input array. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray The corresponding hyperbolic sine values. This is a scalar if `x` is a scalar. Notes ----- If `out` is provided, the function writes the result into it, and returns a reference to `out`. (See Examples) References ---------- M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions. New York, NY: Dover, 1972, pg. 83. Examples -------- >>> [np.sinh(0)](https://www.chedong.com/phpMan.php/man/np.sinh/0/markdown) 0.0 >>> np.sinh(np.pi*1j/2) 1j >>> np.sinh(np.pi*1j) # (exact value is 0) 1.2246063538223773e-016j >>> # Discrepancy due to vagaries of floating point arithmetic. >>> # Example of providing the optional output parameter >>> out1 = np.array([0], dtype='d') >>> out2 = np.sinh([0.1], out1) >>> out2 is out1 True >>> # Example of ValueError due to provision of shape mis-matched `out` >>> np.sinh(np.zeros((3,3)),np.zeros((2,2))) Traceback (most recent call last): File "", line 1, in ValueError: operands could not be broadcast together with shapes (3,3) (2,2) spacing = spacing(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Return the distance between x and the nearest adjacent number. Parameters ---------- x : array_like Values to find the spacing of. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- out : ndarray or scalar The spacing of values of `x`. This is a scalar if `x` is a scalar. Notes ----- It can be considered as a generalization of EPS: ``spacing([np.float64(1)](https://www.chedong.com/phpMan.php/man/np.float64/1/markdown)) == np.finfo(np.float64).eps``, and there should not be any representable number between ``x + spacing(x)`` and x for any finite x. Spacing of +- inf and NaN is NaN. Examples -------- >>> [np.spacing(1)](https://www.chedong.com/phpMan.php/man/np.spacing/1/markdown) == np.finfo(np.float64).eps True sqrt = sqrt(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Return the non-negative square-root of an array, element-wise. Parameters ---------- x : array_like The values whose square-roots are required. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray An array of the same shape as `x`, containing the positive square-root of each element in `x`. If any element in `x` is complex, a complex array is returned (and the square-roots of negative reals are calculated). If all of the elements in `x` are real, so is `y`, with negative elements returning ``nan``. If `out` was provided, `y` is a reference to it. This is a scalar if `x` is a scalar. See Also -------- lib.scimath.sqrt A version which returns complex numbers when given negative reals. Notes ----- *sqrt* has--consistent with common convention--as its branch cut the real "interval" [`-inf`, 0), and is continuous from above on it. A branch cut is a curve in the complex plane across which a given complex function fails to be continuous. Examples -------- >>> np.sqrt([1,4,9]) array([ 1., 2., 3.]) >>> np.sqrt([4, -1, -3+4J]) array([ 2.+0.j, 0.+1.j, 1.+2.j]) >>> np.sqrt([4, -1, np.inf]) array([ 2., nan, inf]) square = square(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Return the element-wise square of the input. Parameters ---------- x : array_like Input data. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- out : ndarray or scalar Element-wise `x*x`, of the same shape and dtype as `x`. This is a scalar if `x` is a scalar. See Also -------- numpy.linalg.matrix_power sqrt power Examples -------- >>> np.square([-1j, 1]) array([-1.-0.j, 1.+0.j]) subtract = subtract(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Subtract arguments, element-wise. Parameters ---------- x1, x2 : array_like The arrays to be subtracted from each other. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray The difference of `x1` and `x2`, element-wise. This is a scalar if both `x1` and `x2` are scalars. Notes ----- Equivalent to ``x1 - x2`` in terms of array broadcasting. Examples -------- >>> np.subtract(1.0, 4.0) -3.0 >>> x1 = np.arange(9.0).reshape((3, 3)) >>> x2 = np.arange(3.0) >>> np.subtract(x1, x2) array([[ 0., 0., 0.], [ 3., 3., 3.], [ 6., 6., 6.]]) The ``-`` operator can be used as a shorthand for ``np.subtract`` on ndarrays. >>> x1 = np.arange(9.0).reshape((3, 3)) >>> x2 = np.arange(3.0) >>> x1 - x2 array([[0., 0., 0.], [3., 3., 3.], [6., 6., 6.]]) tan = tan(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Compute tangent element-wise. Equivalent to ``np.sin(x)/np.cos(x)`` element-wise. Parameters ---------- x : array_like Input array. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray The corresponding tangent values. This is a scalar if `x` is a scalar. Notes ----- If `out` is provided, the function writes the result into it, and returns a reference to `out`. (See Examples) References ---------- M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions. New York, NY: Dover, 1972. Examples -------- >>> from math import pi >>> np.tan(np.array([-pi,pi/2,pi])) array([ 1.22460635e-16, 1.63317787e+16, -1.22460635e-16]) >>> >>> # Example of providing the optional output parameter illustrating >>> # that what is returned is a reference to said parameter >>> out1 = np.array([0], dtype='d') >>> out2 = np.cos([0.1], out1) >>> out2 is out1 True >>> >>> # Example of ValueError due to provision of shape mis-matched `out` >>> np.cos(np.zeros((3,3)),np.zeros((2,2))) Traceback (most recent call last): File "", line 1, in ValueError: operands could not be broadcast together with shapes (3,3) (2,2) tanh = tanh(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Compute hyperbolic tangent element-wise. Equivalent to ``np.sinh(x)/np.cosh(x)`` or ``-1j * np.tan(1j*x)``. Parameters ---------- x : array_like Input array. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray The corresponding hyperbolic tangent values. This is a scalar if `x` is a scalar. Notes ----- If `out` is provided, the function writes the result into it, and returns a reference to `out`. (See Examples) References ---------- .. [1] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions. New York, NY: Dover, 1972, pg. 83. .. [2] Wikipedia, "Hyperbolic function", Examples -------- >>> np.tanh((0, np.pi*1j, np.pi*1j/2)) array([ 0. +0.00000000e+00j, 0. -1.22460635e-16j, 0. +1.63317787e+16j]) >>> # Example of providing the optional output parameter illustrating >>> # that what is returned is a reference to said parameter >>> out1 = np.array([0], dtype='d') >>> out2 = np.tanh([0.1], out1) >>> out2 is out1 True >>> # Example of ValueError due to provision of shape mis-matched `out` >>> np.tanh(np.zeros((3,3)),np.zeros((2,2))) Traceback (most recent call last): File "", line 1, in ValueError: operands could not be broadcast together with shapes (3,3) (2,2) tracemalloc_domain = 389047 true_divide = true_divide(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Returns a true division of the inputs, element-wise. Instead of the Python traditional 'floor division', this returns a true division. True division adjusts the output type to present the best answer, regardless of input types. Parameters ---------- x1 : array_like Dividend array. x2 : array_like Divisor array. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which becomes the shape of the output). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- out : ndarray or scalar This is a scalar if both `x1` and `x2` are scalars. Notes ----- In Python, ``//`` is the floor division operator and ``/`` the true division operator. The ``true_divide(x1, x2)`` function is equivalent to true division in Python. Examples -------- >>> x = [np.arange(5)](https://www.chedong.com/phpMan.php/man/np.arange/5/markdown) >>> np.true_divide(x, 4) array([ 0. , 0.25, 0.5 , 0.75, 1. ]) >>> x/4 array([ 0. , 0.25, 0.5 , 0.75, 1. ]) >>> x//4 array([0, 0, 0, 0, 1]) The ``/`` operator can be used as a shorthand for ``np.true_divide`` on ndarrays. >>> x = [np.arange(5)](https://www.chedong.com/phpMan.php/man/np.arange/5/markdown) >>> x / 4 array([0. , 0.25, 0.5 , 0.75, 1. ]) trunc = trunc(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Return the truncated value of the input, element-wise. The truncated value of the scalar `x` is the nearest integer `i` which is closer to zero than `x` is. In short, the fractional part of the signed number `x` is discarded. Parameters ---------- x : array_like Input data. out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional This condition is broadcast over the input. At locations where the condition is True, the `out` array will be set to the ufunc result. Elsewhere, the `out` array will retain its original value. Note that if an uninitialized `out` array is created via the default ``out=None``, locations within it where the condition is False will remain uninitialized. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs `. Returns ------- y : ndarray or scalar The truncated value of each element in `x`. This is a scalar if `x` is a scalar. See Also -------- ceil, floor, rint, fix Notes ----- .. versionadded:: 1.3.0 Examples -------- >>> a = np.array([-1.7, -1.5, -0.2, 0.2, 1.5, 1.7, 2.0]) >>> np.trunc(a) array([-1., -1., -0., 0., 1., 1., 2.]) typecodes = {'All': '?bhilqpBHILQPefdgFDGSUVOMm', 'AllFloat': 'efdgFDG... ## VERSION 1.21.5 ## FILE /usr/lib/python3/dist-packages/numpy/__init__.py