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env-llmeval/lib/python3.10/site-packages/numpy/lib/__init__.py

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+"""
+**Note:** almost all functions in the ``numpy.lib`` namespace
+are also present in the main ``numpy`` namespace.  Please use the
+functions as ``np.<funcname>`` where possible.
+
+``numpy.lib`` is mostly a space for implementing functions that don't
+belong in core or in another NumPy submodule with a clear purpose
+(e.g. ``random``, ``fft``, ``linalg``, ``ma``).
+
+Most contains basic functions that are used by several submodules and are
+useful to have in the main name-space.
+
+"""
+
+# Public submodules
+# Note: recfunctions and (maybe) format are public too, but not imported
+from . import mixins
+from . import scimath as emath
+
+# Private submodules
+# load module names. See https://github.com/networkx/networkx/issues/5838
+from . import type_check
+from . import index_tricks
+from . import function_base
+from . import nanfunctions
+from . import shape_base
+from . import stride_tricks
+from . import twodim_base
+from . import ufunclike
+from . import histograms
+from . import polynomial
+from . import utils
+from . import arraysetops
+from . import npyio
+from . import arrayterator
+from . import arraypad
+from . import _version
+
+from .type_check import *
+from .index_tricks import *
+from .function_base import *
+from .nanfunctions import *
+from .shape_base import *
+from .stride_tricks import *
+from .twodim_base import *
+from .ufunclike import *
+from .histograms import *
+
+from .polynomial import *
+from .utils import *
+from .arraysetops import *
+from .npyio import *
+from .arrayterator import Arrayterator
+from .arraypad import *
+from ._version import *
+from numpy.core._multiarray_umath import tracemalloc_domain
+
+__all__ = ['emath', 'tracemalloc_domain', 'Arrayterator']
+__all__ += type_check.__all__
+__all__ += index_tricks.__all__
+__all__ += function_base.__all__
+__all__ += shape_base.__all__
+__all__ += stride_tricks.__all__
+__all__ += twodim_base.__all__
+__all__ += ufunclike.__all__
+__all__ += arraypad.__all__
+__all__ += polynomial.__all__
+__all__ += utils.__all__
+__all__ += arraysetops.__all__
+__all__ += npyio.__all__
+__all__ += nanfunctions.__all__
+__all__ += histograms.__all__
+
+from numpy._pytesttester import PytestTester
+test = PytestTester(__name__)
+del PytestTester
+
+def __getattr__(attr):
+    # Warn for reprecated attributes
+    import math
+    import warnings
+
+    if attr == 'math':
+        warnings.warn(
+            "`np.lib.math` is a deprecated alias for the standard library "
+            "`math` module (Deprecated Numpy 1.25). Replace usages of "
+            "`numpy.lib.math` with `math`", DeprecationWarning, stacklevel=2)
+        return math
+    else:
+        raise AttributeError("module {!r} has no attribute "
+                             "{!r}".format(__name__, attr))
+        

env-llmeval/lib/python3.10/site-packages/numpy/lib/__init__.pyi

@@ -0,0 +1,245 @@
+import math as math
+from typing import Any
+
+from numpy._pytesttester import PytestTester
+
+from numpy import (
+    ndenumerate as ndenumerate,
+    ndindex as ndindex,
+)
+
+from numpy.version import version
+
+from numpy.lib import (
+    format as format,
+    mixins as mixins,
+    scimath as scimath,
+    stride_tricks as stride_tricks,
+)
+
+from numpy.lib._version import (
+    NumpyVersion as NumpyVersion,
+)
+
+from numpy.lib.arraypad import (
+    pad as pad,
+)
+
+from numpy.lib.arraysetops import (
+    ediff1d as ediff1d,
+    intersect1d as intersect1d,
+    setxor1d as setxor1d,
+    union1d as union1d,
+    setdiff1d as setdiff1d,
+    unique as unique,
+    in1d as in1d,
+    isin as isin,
+)
+
+from numpy.lib.arrayterator import (
+    Arrayterator as Arrayterator,
+)
+
+from numpy.lib.function_base import (
+    select as select,
+    piecewise as piecewise,
+    trim_zeros as trim_zeros,
+    copy as copy,
+    iterable as iterable,
+    percentile as percentile,
+    diff as diff,
+    gradient as gradient,
+    angle as angle,
+    unwrap as unwrap,
+    sort_complex as sort_complex,
+    disp as disp,
+    flip as flip,
+    rot90 as rot90,
+    extract as extract,
+    place as place,
+    vectorize as vectorize,
+    asarray_chkfinite as asarray_chkfinite,
+    average as average,
+    bincount as bincount,
+    digitize as digitize,
+    cov as cov,
+    corrcoef as corrcoef,
+    median as median,
+    sinc as sinc,
+    hamming as hamming,
+    hanning as hanning,
+    bartlett as bartlett,
+    blackman as blackman,
+    kaiser as kaiser,
+    trapz as trapz,
+    i0 as i0,
+    add_newdoc as add_newdoc,
+    add_docstring as add_docstring,
+    meshgrid as meshgrid,
+    delete as delete,
+    insert as insert,
+    append as append,
+    interp as interp,
+    add_newdoc_ufunc as add_newdoc_ufunc,
+    quantile as quantile,
+)
+
+from numpy.lib.histograms import (
+    histogram_bin_edges as histogram_bin_edges,
+    histogram as histogram,
+    histogramdd as histogramdd,
+)
+
+from numpy.lib.index_tricks import (
+    ravel_multi_index as ravel_multi_index,
+    unravel_index as unravel_index,
+    mgrid as mgrid,
+    ogrid as ogrid,
+    r_ as r_,
+    c_ as c_,
+    s_ as s_,
+    index_exp as index_exp,
+    ix_ as ix_,
+    fill_diagonal as fill_diagonal,
+    diag_indices as diag_indices,
+    diag_indices_from as diag_indices_from,
+)
+
+from numpy.lib.nanfunctions import (
+    nansum as nansum,
+    nanmax as nanmax,
+    nanmin as nanmin,
+    nanargmax as nanargmax,
+    nanargmin as nanargmin,
+    nanmean as nanmean,
+    nanmedian as nanmedian,
+    nanpercentile as nanpercentile,
+    nanvar as nanvar,
+    nanstd as nanstd,
+    nanprod as nanprod,
+    nancumsum as nancumsum,
+    nancumprod as nancumprod,
+    nanquantile as nanquantile,
+)
+
+from numpy.lib.npyio import (
+    savetxt as savetxt,
+    loadtxt as loadtxt,
+    genfromtxt as genfromtxt,
+    recfromtxt as recfromtxt,
+    recfromcsv as recfromcsv,
+    load as load,
+    save as save,
+    savez as savez,
+    savez_compressed as savez_compressed,
+    packbits as packbits,
+    unpackbits as unpackbits,
+    fromregex as fromregex,
+    DataSource as DataSource,
+)
+
+from numpy.lib.polynomial import (
+    poly as poly,
+    roots as roots,
+    polyint as polyint,
+    polyder as polyder,
+    polyadd as polyadd,
+    polysub as polysub,
+    polymul as polymul,
+    polydiv as polydiv,
+    polyval as polyval,
+    polyfit as polyfit,
+    RankWarning as RankWarning,
+    poly1d as poly1d,
+)
+
+from numpy.lib.shape_base import (
+    column_stack as column_stack,
+    row_stack as row_stack,
+    dstack as dstack,
+    array_split as array_split,
+    split as split,
+    hsplit as hsplit,
+    vsplit as vsplit,
+    dsplit as dsplit,
+    apply_over_axes as apply_over_axes,
+    expand_dims as expand_dims,
+    apply_along_axis as apply_along_axis,
+    kron as kron,
+    tile as tile,
+    get_array_wrap as get_array_wrap,
+    take_along_axis as take_along_axis,
+    put_along_axis as put_along_axis,
+)
+
+from numpy.lib.stride_tricks import (
+    broadcast_to as broadcast_to,
+    broadcast_arrays as broadcast_arrays,
+    broadcast_shapes as broadcast_shapes,
+)
+
+from numpy.lib.twodim_base import (
+    diag as diag,
+    diagflat as diagflat,
+    eye as eye,
+    fliplr as fliplr,
+    flipud as flipud,
+    tri as tri,
+    triu as triu,
+    tril as tril,
+    vander as vander,
+    histogram2d as histogram2d,
+    mask_indices as mask_indices,
+    tril_indices as tril_indices,
+    tril_indices_from as tril_indices_from,
+    triu_indices as triu_indices,
+    triu_indices_from as triu_indices_from,
+)
+
+from numpy.lib.type_check import (
+    mintypecode as mintypecode,
+    asfarray as asfarray,
+    real as real,
+    imag as imag,
+    iscomplex as iscomplex,
+    isreal as isreal,
+    iscomplexobj as iscomplexobj,
+    isrealobj as isrealobj,
+    nan_to_num as nan_to_num,
+    real_if_close as real_if_close,
+    typename as typename,
+    common_type as common_type,
+)
+
+from numpy.lib.ufunclike import (
+    fix as fix,
+    isposinf as isposinf,
+    isneginf as isneginf,
+)
+
+from numpy.lib.utils import (
+    issubclass_ as issubclass_,
+    issubsctype as issubsctype,
+    issubdtype as issubdtype,
+    deprecate as deprecate,
+    deprecate_with_doc as deprecate_with_doc,
+    get_include as get_include,
+    info as info,
+    source as source,
+    who as who,
+    lookfor as lookfor,
+    byte_bounds as byte_bounds,
+    safe_eval as safe_eval,
+    show_runtime as show_runtime,
+)
+
+from numpy.core.multiarray import (
+    tracemalloc_domain as tracemalloc_domain,
+)
+
+__all__: list[str]
+__path__: list[str]
+test: PytestTester
+
+__version__ = version
+emath = scimath

env-llmeval/lib/python3.10/site-packages/numpy/lib/_datasource.py

@@ -0,0 +1,704 @@
+"""A file interface for handling local and remote data files.
+
+The goal of datasource is to abstract some of the file system operations
+when dealing with data files so the researcher doesn't have to know all the
+low-level details.  Through datasource, a researcher can obtain and use a
+file with one function call, regardless of location of the file.
+
+DataSource is meant to augment standard python libraries, not replace them.
+It should work seamlessly with standard file IO operations and the os
+module.
+
+DataSource files can originate locally or remotely:
+
+- local files : '/home/guido/src/local/data.txt'
+- URLs (http, ftp, ...) : 'http://www.scipy.org/not/real/data.txt'
+
+DataSource files can also be compressed or uncompressed.  Currently only
+gzip, bz2 and xz are supported.
+
+Example::
+
+    >>> # Create a DataSource, use os.curdir (default) for local storage.
+    >>> from numpy import DataSource
+    >>> ds = DataSource()
+    >>>
+    >>> # Open a remote file.
+    >>> # DataSource downloads the file, stores it locally in:
+    >>> #     './www.google.com/index.html'
+    >>> # opens the file and returns a file object.
+    >>> fp = ds.open('http://www.google.com/') # doctest: +SKIP
+    >>>
+    >>> # Use the file as you normally would
+    >>> fp.read() # doctest: +SKIP
+    >>> fp.close() # doctest: +SKIP
+
+"""
+import os
+import io
+
+from .._utils import set_module
+
+
+_open = open
+
+
+def _check_mode(mode, encoding, newline):
+    """Check mode and that encoding and newline are compatible.
+
+    Parameters
+    ----------
+    mode : str
+        File open mode.
+    encoding : str
+        File encoding.
+    newline : str
+        Newline for text files.
+
+    """
+    if "t" in mode:
+        if "b" in mode:
+            raise ValueError("Invalid mode: %r" % (mode,))
+    else:
+        if encoding is not None:
+            raise ValueError("Argument 'encoding' not supported in binary mode")
+        if newline is not None:
+            raise ValueError("Argument 'newline' not supported in binary mode")
+
+
+# Using a class instead of a module-level dictionary
+# to reduce the initial 'import numpy' overhead by
+# deferring the import of lzma, bz2 and gzip until needed
+
+# TODO: .zip support, .tar support?
+class _FileOpeners:
+    """
+    Container for different methods to open (un-)compressed files.
+
+    `_FileOpeners` contains a dictionary that holds one method for each
+    supported file format. Attribute lookup is implemented in such a way
+    that an instance of `_FileOpeners` itself can be indexed with the keys
+    of that dictionary. Currently uncompressed files as well as files
+    compressed with ``gzip``, ``bz2`` or ``xz`` compression are supported.
+
+    Notes
+    -----
+    `_file_openers`, an instance of `_FileOpeners`, is made available for
+    use in the `_datasource` module.
+
+    Examples
+    --------
+    >>> import gzip
+    >>> np.lib._datasource._file_openers.keys()
+    [None, '.bz2', '.gz', '.xz', '.lzma']
+    >>> np.lib._datasource._file_openers['.gz'] is gzip.open
+    True
+
+    """
+
+    def __init__(self):
+        self._loaded = False
+        self._file_openers = {None: io.open}
+
+    def _load(self):
+        if self._loaded:
+            return
+
+        try:
+            import bz2
+            self._file_openers[".bz2"] = bz2.open
+        except ImportError:
+            pass
+
+        try:
+            import gzip
+            self._file_openers[".gz"] = gzip.open
+        except ImportError:
+            pass
+
+        try:
+            import lzma
+            self._file_openers[".xz"] = lzma.open
+            self._file_openers[".lzma"] = lzma.open
+        except (ImportError, AttributeError):
+            # There are incompatible backports of lzma that do not have the
+            # lzma.open attribute, so catch that as well as ImportError.
+            pass
+
+        self._loaded = True
+
+    def keys(self):
+        """
+        Return the keys of currently supported file openers.
+
+        Parameters
+        ----------
+        None
+
+        Returns
+        -------
+        keys : list
+            The keys are None for uncompressed files and the file extension
+            strings (i.e. ``'.gz'``, ``'.xz'``) for supported compression
+            methods.
+
+        """
+        self._load()
+        return list(self._file_openers.keys())
+
+    def __getitem__(self, key):
+        self._load()
+        return self._file_openers[key]
+
+_file_openers = _FileOpeners()
+
+def open(path, mode='r', destpath=os.curdir, encoding=None, newline=None):
+    """
+    Open `path` with `mode` and return the file object.
+
+    If ``path`` is an URL, it will be downloaded, stored in the
+    `DataSource` `destpath` directory and opened from there.
+
+    Parameters
+    ----------
+    path : str
+        Local file path or URL to open.
+    mode : str, 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'.
+    destpath : str, 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.
+    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
+        The opened file.
+
+    Notes
+    -----
+    This is a convenience function that instantiates a `DataSource` and
+    returns the file object from ``DataSource.open(path)``.
+
+    """
+
+    ds = DataSource(destpath)
+    return ds.open(path, mode, encoding=encoding, newline=newline)
+
+
+@set_module('numpy')
+class DataSource:
+    """
+    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('http://www.google.com/index.html')
+        True
+
+    Temporary directories are deleted when the DataSource is deleted.
+
+    Examples
+    --------
+    ::
+
+        >>> ds = np.DataSource('/home/guido')
+        >>> urlname = 'http://www.google.com/'
+        >>> gfile = ds.open('http://www.google.com/')
+        >>> ds.abspath(urlname)
+        '/home/guido/www.google.com/index.html'
+
+        >>> ds = np.DataSource(None)  # use with temporary file
+        >>> ds.open('/home/guido/foobar.txt')
+        <open file '/home/guido.foobar.txt', mode 'r' at 0x91d4430>
+        >>> ds.abspath('/home/guido/foobar.txt')
+        '/tmp/.../home/guido/foobar.txt'
+
+    """
+
+    def __init__(self, destpath=os.curdir):
+        """Create a DataSource with a local path at destpath."""
+        if destpath:
+            self._destpath = os.path.abspath(destpath)
+            self._istmpdest = False
+        else:
+            import tempfile  # deferring import to improve startup time
+            self._destpath = tempfile.mkdtemp()
+            self._istmpdest = True
+
+    def __del__(self):
+        # Remove temp directories
+        if hasattr(self, '_istmpdest') and self._istmpdest:
+            import shutil
+
+            shutil.rmtree(self._destpath)
+
+    def _iszip(self, filename):
+        """Test if the filename is a zip file by looking at the file extension.
+
+        """
+        fname, ext = os.path.splitext(filename)
+        return ext in _file_openers.keys()
+
+    def _iswritemode(self, mode):
+        """Test if the given mode will open a file for writing."""
+
+        # Currently only used to test the bz2 files.
+        _writemodes = ("w", "+")
+        for c in mode:
+            if c in _writemodes:
+                return True
+        return False
+
+    def _splitzipext(self, filename):
+        """Split zip extension from filename and return filename.
+
+        Returns
+        -------
+        base, zip_ext : {tuple}
+
+        """
+
+        if self._iszip(filename):
+            return os.path.splitext(filename)
+        else:
+            return filename, None
+
+    def _possible_names(self, filename):
+        """Return a tuple containing compressed filename variations."""
+        names = [filename]
+        if not self._iszip(filename):
+            for zipext in _file_openers.keys():
+                if zipext:
+                    names.append(filename+zipext)
+        return names
+
+    def _isurl(self, path):
+        """Test if path is a net location.  Tests the scheme and netloc."""
+
+        # We do this here to reduce the 'import numpy' initial import time.
+        from urllib.parse import urlparse
+
+        # BUG : URLs require a scheme string ('http://') to be used.
+        #       www.google.com will fail.
+        #       Should we prepend the scheme for those that don't have it and
+        #       test that also?  Similar to the way we append .gz and test for
+        #       for compressed versions of files.
+
+        scheme, netloc, upath, uparams, uquery, ufrag = urlparse(path)
+        return bool(scheme and netloc)
+
+    def _cache(self, path):
+        """Cache the file specified by path.
+
+        Creates a copy of the file in the datasource cache.
+
+        """
+        # We import these here because importing them is slow and
+        # a significant fraction of numpy's total import time.
+        import shutil
+        from urllib.request import urlopen
+
+        upath = self.abspath(path)
+
+        # ensure directory exists
+        if not os.path.exists(os.path.dirname(upath)):
+            os.makedirs(os.path.dirname(upath))
+
+        # TODO: Doesn't handle compressed files!
+        if self._isurl(path):
+            with urlopen(path) as openedurl:
+                with _open(upath, 'wb') as f:
+                    shutil.copyfileobj(openedurl, f)
+        else:
+            shutil.copyfile(path, upath)
+        return upath
+
+    def _findfile(self, path):
+        """Searches for ``path`` and returns full path if found.
+
+        If path is an URL, _findfile will cache a local copy and return the
+        path to the cached file.  If path is a local file, _findfile will
+        return a path to that local file.
+
+        The search will include possible compressed versions of the file
+        and return the first occurrence found.
+
+        """
+
+        # Build list of possible local file paths
+        if not self._isurl(path):
+            # Valid local paths
+            filelist = self._possible_names(path)
+            # Paths in self._destpath
+            filelist += self._possible_names(self.abspath(path))
+        else:
+            # Cached URLs in self._destpath
+            filelist = self._possible_names(self.abspath(path))
+            # Remote URLs
+            filelist = filelist + self._possible_names(path)
+
+        for name in filelist:
+            if self.exists(name):
+                if self._isurl(name):
+                    name = self._cache(name)
+                return name
+        return None
+
+    def 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`.
+
+        """
+        # We do this here to reduce the 'import numpy' initial import time.
+        from urllib.parse import urlparse
+
+        # TODO:  This should be more robust.  Handles case where path includes
+        #        the destpath, but not other sub-paths. Failing case:
+        #        path = /home/guido/datafile.txt
+        #        destpath = /home/alex/
+        #        upath = self.abspath(path)
+        #        upath == '/home/alex/home/guido/datafile.txt'
+
+        # handle case where path includes self._destpath
+        splitpath = path.split(self._destpath, 2)
+        if len(splitpath) > 1:
+            path = splitpath[1]
+        scheme, netloc, upath, uparams, uquery, ufrag = urlparse(path)
+        netloc = self._sanitize_relative_path(netloc)
+        upath = self._sanitize_relative_path(upath)
+        return os.path.join(self._destpath, netloc, upath)
+
+    def _sanitize_relative_path(self, path):
+        """Return a sanitised relative path for which
+        os.path.abspath(os.path.join(base, path)).startswith(base)
+        """
+        last = None
+        path = os.path.normpath(path)
+        while path != last:
+            last = path
+            # Note: os.path.join treats '/' as os.sep on Windows
+            path = path.lstrip(os.sep).lstrip('/')
+            path = path.lstrip(os.pardir).lstrip('..')
+            drive, path = os.path.splitdrive(path)  # for Windows
+        return path
+
+    def 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.
+
+        """
+
+        # First test for local path
+        if os.path.exists(path):
+            return True
+
+        # We import this here because importing urllib is slow and
+        # a significant fraction of numpy's total import time.
+        from urllib.request import urlopen
+        from urllib.error import URLError
+
+        # Test cached url
+        upath = self.abspath(path)
+        if os.path.exists(upath):
+            return True
+
+        # Test remote url
+        if self._isurl(path):
+            try:
+                netfile = urlopen(path)
+                netfile.close()
+                del(netfile)
+                return True
+            except URLError:
+                return False
+        return False
+
+    def 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.
+
+        """
+
+        # TODO: There is no support for opening a file for writing which
+        #       doesn't exist yet (creating a file).  Should there be?
+
+        # TODO: Add a ``subdir`` parameter for specifying the subdirectory
+        #       used to store URLs in self._destpath.
+
+        if self._isurl(path) and self._iswritemode(mode):
+            raise ValueError("URLs are not writeable")
+
+        # NOTE: _findfile will fail on a new file opened for writing.
+        found = self._findfile(path)
+        if found:
+            _fname, ext = self._splitzipext(found)
+            if ext == 'bz2':
+                mode.replace("+", "")
+            return _file_openers[ext](found, mode=mode,
+                                      encoding=encoding, newline=newline)
+        else:
+            raise FileNotFoundError(f"{path} not found.")
+
+
+class Repository (DataSource):
+    """
+    Repository(baseurl, destpath='.')
+
+    A data repository where multiple DataSource's share a base
+    URL/directory.
+
+    `Repository` extends `DataSource` by prepending a base URL (or
+    directory) to all the files it handles. Use `Repository` when you will
+    be working with multiple files from one base URL.  Initialize
+    `Repository` with the base URL, then refer to each file by its filename
+    only.
+
+    Parameters
+    ----------
+    baseurl : str
+        Path to the local directory or remote location that contains the
+        data files.
+    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.
+
+    Examples
+    --------
+    To analyze all files in the repository, do something like this
+    (note: this is not self-contained code)::
+
+        >>> repos = np.lib._datasource.Repository('/home/user/data/dir/')
+        >>> for filename in filelist:
+        ...     fp = repos.open(filename)
+        ...     fp.analyze()
+        ...     fp.close()
+
+    Similarly you could use a URL for a repository::
+
+        >>> repos = np.lib._datasource.Repository('http://www.xyz.edu/data')
+
+    """
+
+    def __init__(self, baseurl, destpath=os.curdir):
+        """Create a Repository with a shared url or directory of baseurl."""
+        DataSource.__init__(self, destpath=destpath)
+        self._baseurl = baseurl
+
+    def __del__(self):
+        DataSource.__del__(self)
+
+    def _fullpath(self, path):
+        """Return complete path for path.  Prepends baseurl if necessary."""
+        splitpath = path.split(self._baseurl, 2)
+        if len(splitpath) == 1:
+            result = os.path.join(self._baseurl, path)
+        else:
+            result = path    # path contains baseurl already
+        return result
+
+    def _findfile(self, path):
+        """Extend DataSource method to prepend baseurl to ``path``."""
+        return DataSource._findfile(self, self._fullpath(path))
+
+    def abspath(self, path):
+        """
+        Return absolute path of file in the Repository 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. This may, but does not
+            have to, include the `baseurl` with which the `Repository` was
+            initialized.
+
+        Returns
+        -------
+        out : str
+            Complete path, including the `DataSource` destination directory.
+
+        """
+        return DataSource.abspath(self, self._fullpath(path))
+
+    def exists(self, path):
+        """
+        Test if path exists prepending Repository base URL to path.
+
+        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. This may, but does not
+            have to, include the `baseurl` with which the `Repository` was
+            initialized.
+
+        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.
+
+        """
+        return DataSource.exists(self, self._fullpath(path))
+
+    def open(self, path, mode='r', encoding=None, newline=None):
+        """
+        Open and return file-like object prepending Repository base URL.
+
+        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. This may, but does not have to,
+            include the `baseurl` with which the `Repository` was
+            initialized.
+        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.
+
+        """
+        return DataSource.open(self, self._fullpath(path), mode,
+                               encoding=encoding, newline=newline)
+
+    def listdir(self):
+        """
+        List files in the source Repository.
+
+        Returns
+        -------
+        files : list of str
+            List of file names (not containing a directory part).
+
+        Notes
+        -----
+        Does not currently work for remote repositories.
+
+        """
+        if self._isurl(self._baseurl):
+            raise NotImplementedError(
+                  "Directory listing of URLs, not supported yet.")
+        else:
+            return os.listdir(self._baseurl)

env-llmeval/lib/python3.10/site-packages/numpy/lib/_iotools.py

@@ -0,0 +1,897 @@
+"""A collection of functions designed to help I/O with ascii files.
+
+"""
+__docformat__ = "restructuredtext en"
+
+import numpy as np
+import numpy.core.numeric as nx
+from numpy.compat import asbytes, asunicode
+
+
+def _decode_line(line, encoding=None):
+    """Decode bytes from binary input streams.
+
+    Defaults to decoding from 'latin1'. That differs from the behavior of
+    np.compat.asunicode that decodes from 'ascii'.
+
+    Parameters
+    ----------
+    line : str or bytes
+         Line to be decoded.
+    encoding : str
+         Encoding used to decode `line`.
+
+    Returns
+    -------
+    decoded_line : str
+
+    """
+    if type(line) is bytes:
+        if encoding is None:
+            encoding = "latin1"
+        line = line.decode(encoding)
+
+    return line
+
+
+def _is_string_like(obj):
+    """
+    Check whether obj behaves like a string.
+    """
+    try:
+        obj + ''
+    except (TypeError, ValueError):
+        return False
+    return True
+
+
+def _is_bytes_like(obj):
+    """
+    Check whether obj behaves like a bytes object.
+    """
+    try:
+        obj + b''
+    except (TypeError, ValueError):
+        return False
+    return True
+
+
+def has_nested_fields(ndtype):
+    """
+    Returns whether one or several fields of a dtype are nested.
+
+    Parameters
+    ----------
+    ndtype : dtype
+        Data-type of a structured array.
+
+    Raises
+    ------
+    AttributeError
+        If `ndtype` does not have a `names` attribute.
+
+    Examples
+    --------
+    >>> dt = np.dtype([('name', 'S4'), ('x', float), ('y', float)])
+    >>> np.lib._iotools.has_nested_fields(dt)
+    False
+
+    """
+    for name in ndtype.names or ():
+        if ndtype[name].names is not None:
+            return True
+    return False
+
+
+def flatten_dtype(ndtype, flatten_base=False):
+    """
+    Unpack a structured data-type by collapsing nested fields and/or fields
+    with a shape.
+
+    Note that the field names are lost.
+
+    Parameters
+    ----------
+    ndtype : dtype
+        The datatype to collapse
+    flatten_base : bool, optional
+       If True, transform a field with a shape into several fields. Default is
+       False.
+
+    Examples
+    --------
+    >>> dt = np.dtype([('name', 'S4'), ('x', float), ('y', float),
+    ...                ('block', int, (2, 3))])
+    >>> np.lib._iotools.flatten_dtype(dt)
+    [dtype('S4'), dtype('float64'), dtype('float64'), dtype('int64')]
+    >>> np.lib._iotools.flatten_dtype(dt, flatten_base=True)
+    [dtype('S4'),
+     dtype('float64'),
+     dtype('float64'),
+     dtype('int64'),
+     dtype('int64'),
+     dtype('int64'),
+     dtype('int64'),
+     dtype('int64'),
+     dtype('int64')]
+
+    """
+    names = ndtype.names
+    if names is None:
+        if flatten_base:
+            return [ndtype.base] * int(np.prod(ndtype.shape))
+        return [ndtype.base]
+    else:
+        types = []
+        for field in names:
+            info = ndtype.fields[field]
+            flat_dt = flatten_dtype(info[0], flatten_base)
+            types.extend(flat_dt)
+        return types
+
+
+class LineSplitter:
+    """
+    Object to split a string at a given delimiter or at given places.
+
+    Parameters
+    ----------
+    delimiter : str, int, or sequence of ints, optional
+        If a string, character used to delimit consecutive fields.
+        If an integer or a sequence of integers, width(s) of each field.
+    comments : str, optional
+        Character used to mark the beginning of a comment. Default is '#'.
+    autostrip : bool, optional
+        Whether to strip each individual field. Default is True.
+
+    """
+
+    def autostrip(self, method):
+        """
+        Wrapper to strip each member of the output of `method`.
+
+        Parameters
+        ----------
+        method : function
+            Function that takes a single argument and returns a sequence of
+            strings.
+
+        Returns
+        -------
+        wrapped : function
+            The result of wrapping `method`. `wrapped` takes a single input
+            argument and returns a list of strings that are stripped of
+            white-space.
+
+        """
+        return lambda input: [_.strip() for _ in method(input)]
+
+    def __init__(self, delimiter=None, comments='#', autostrip=True,
+                 encoding=None):
+        delimiter = _decode_line(delimiter)
+        comments = _decode_line(comments)
+
+        self.comments = comments
+
+        # Delimiter is a character
+        if (delimiter is None) or isinstance(delimiter, str):
+            delimiter = delimiter or None
+            _handyman = self._delimited_splitter
+        # Delimiter is a list of field widths
+        elif hasattr(delimiter, '__iter__'):
+            _handyman = self._variablewidth_splitter
+            idx = np.cumsum([0] + list(delimiter))
+            delimiter = [slice(i, j) for (i, j) in zip(idx[:-1], idx[1:])]
+        # Delimiter is a single integer
+        elif int(delimiter):
+            (_handyman, delimiter) = (
+                    self._fixedwidth_splitter, int(delimiter))
+        else:
+            (_handyman, delimiter) = (self._delimited_splitter, None)
+        self.delimiter = delimiter
+        if autostrip:
+            self._handyman = self.autostrip(_handyman)
+        else:
+            self._handyman = _handyman
+        self.encoding = encoding
+
+    def _delimited_splitter(self, line):
+        """Chop off comments, strip, and split at delimiter. """
+        if self.comments is not None:
+            line = line.split(self.comments)[0]
+        line = line.strip(" \r\n")
+        if not line:
+            return []
+        return line.split(self.delimiter)
+
+    def _fixedwidth_splitter(self, line):
+        if self.comments is not None:
+            line = line.split(self.comments)[0]
+        line = line.strip("\r\n")
+        if not line:
+            return []
+        fixed = self.delimiter
+        slices = [slice(i, i + fixed) for i in range(0, len(line), fixed)]
+        return [line[s] for s in slices]
+
+    def _variablewidth_splitter(self, line):
+        if self.comments is not None:
+            line = line.split(self.comments)[0]
+        if not line:
+            return []
+        slices = self.delimiter
+        return [line[s] for s in slices]
+
+    def __call__(self, line):
+        return self._handyman(_decode_line(line, self.encoding))
+
+
+class NameValidator:
+    """
+    Object to validate a list of strings to use as field names.
+
+    The strings are stripped of any non alphanumeric character, and spaces
+    are replaced by '_'. During instantiation, the user can define a list
+    of names to exclude, as well as a list of invalid characters. Names in
+    the exclusion list are appended a '_' character.
+
+    Once an instance has been created, it can be called with a list of
+    names, and a list of valid names will be created.  The `__call__`
+    method accepts an optional keyword "default" that sets the default name
+    in case of ambiguity. By default this is 'f', so that names will
+    default to `f0`, `f1`, etc.
+
+    Parameters
+    ----------
+    excludelist : sequence, optional
+        A list of names to exclude. This list is appended to the default
+        list ['return', 'file', 'print']. Excluded names are appended an
+        underscore: for example, `file` becomes `file_` if supplied.
+    deletechars : str, optional
+        A string combining invalid characters that must be deleted from the
+        names.
+    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.
+
+        The default value is True.
+    replace_space : '_', optional
+        Character(s) used in replacement of white spaces.
+
+    Notes
+    -----
+    Calling an instance of `NameValidator` is the same as calling its
+    method `validate`.
+
+    Examples
+    --------
+    >>> validator = np.lib._iotools.NameValidator()
+    >>> validator(['file', 'field2', 'with space', 'CaSe'])
+    ('file_', 'field2', 'with_space', 'CaSe')
+
+    >>> validator = np.lib._iotools.NameValidator(excludelist=['excl'],
+    ...                                           deletechars='q',
+    ...                                           case_sensitive=False)
+    >>> validator(['excl', 'field2', 'no_q', 'with space', 'CaSe'])
+    ('EXCL', 'FIELD2', 'NO_Q', 'WITH_SPACE', 'CASE')
+
+    """
+
+    defaultexcludelist = ['return', 'file', 'print']
+    defaultdeletechars = set(r"""~!@#$%^&*()-=+~\|]}[{';: /?.>,<""")
+
+    def __init__(self, excludelist=None, deletechars=None,
+                 case_sensitive=None, replace_space='_'):
+        # Process the exclusion list ..
+        if excludelist is None:
+            excludelist = []
+        excludelist.extend(self.defaultexcludelist)
+        self.excludelist = excludelist
+        # Process the list of characters to delete
+        if deletechars is None:
+            delete = self.defaultdeletechars
+        else:
+            delete = set(deletechars)
+        delete.add('"')
+        self.deletechars = delete
+        # Process the case option .....
+        if (case_sensitive is None) or (case_sensitive is True):
+            self.case_converter = lambda x: x
+        elif (case_sensitive is False) or case_sensitive.startswith('u'):
+            self.case_converter = lambda x: x.upper()
+        elif case_sensitive.startswith('l'):
+            self.case_converter = lambda x: x.lower()
+        else:
+            msg = 'unrecognized case_sensitive value %s.' % case_sensitive
+            raise ValueError(msg)
+
+        self.replace_space = replace_space
+
+    def validate(self, names, defaultfmt="f%i", nbfields=None):
+        """
+        Validate a list of strings as field names for a structured array.
+
+        Parameters
+        ----------
+        names : sequence of str
+            Strings to be validated.
+        defaultfmt : str, optional
+            Default format string, used if validating a given string
+            reduces its length to zero.
+        nbfields : integer, optional
+            Final number of validated names, used to expand or shrink the
+            initial list of names.
+
+        Returns
+        -------
+        validatednames : list of str
+            The list of validated field names.
+
+        Notes
+        -----
+        A `NameValidator` instance can be called directly, which is the
+        same as calling `validate`. For examples, see `NameValidator`.
+
+        """
+        # Initial checks ..............
+        if (names is None):
+            if (nbfields is None):
+                return None
+            names = []
+        if isinstance(names, str):
+            names = [names, ]
+        if nbfields is not None:
+            nbnames = len(names)
+            if (nbnames < nbfields):
+                names = list(names) + [''] * (nbfields - nbnames)
+            elif (nbnames > nbfields):
+                names = names[:nbfields]
+        # Set some shortcuts ...........
+        deletechars = self.deletechars
+        excludelist = self.excludelist
+        case_converter = self.case_converter
+        replace_space = self.replace_space
+        # Initializes some variables ...
+        validatednames = []
+        seen = dict()
+        nbempty = 0
+
+        for item in names:
+            item = case_converter(item).strip()
+            if replace_space:
+                item = item.replace(' ', replace_space)
+            item = ''.join([c for c in item if c not in deletechars])
+            if item == '':
+                item = defaultfmt % nbempty
+                while item in names:
+                    nbempty += 1
+                    item = defaultfmt % nbempty
+                nbempty += 1
+            elif item in excludelist:
+                item += '_'
+            cnt = seen.get(item, 0)
+            if cnt > 0:
+                validatednames.append(item + '_%d' % cnt)
+            else:
+                validatednames.append(item)
+            seen[item] = cnt + 1
+        return tuple(validatednames)
+
+    def __call__(self, names, defaultfmt="f%i", nbfields=None):
+        return self.validate(names, defaultfmt=defaultfmt, nbfields=nbfields)
+
+
+def str2bool(value):
+    """
+    Tries to transform a string supposed to represent a boolean to a boolean.
+
+    Parameters
+    ----------
+    value : str
+        The string that is transformed to a boolean.
+
+    Returns
+    -------
+    boolval : bool
+        The boolean representation of `value`.
+
+    Raises
+    ------
+    ValueError
+        If the string is not 'True' or 'False' (case independent)
+
+    Examples
+    --------
+    >>> np.lib._iotools.str2bool('TRUE')
+    True
+    >>> np.lib._iotools.str2bool('false')
+    False
+
+    """
+    value = value.upper()
+    if value == 'TRUE':
+        return True
+    elif value == 'FALSE':
+        return False
+    else:
+        raise ValueError("Invalid boolean")
+
+
+class ConverterError(Exception):
+    """
+    Exception raised when an error occurs in a converter for string values.
+
+    """
+    pass
+
+
+class ConverterLockError(ConverterError):
+    """
+    Exception raised when an attempt is made to upgrade a locked converter.
+
+    """
+    pass
+
+
+class ConversionWarning(UserWarning):
+    """
+    Warning issued when a string converter has a problem.
+
+    Notes
+    -----
+    In `genfromtxt` a `ConversionWarning` is issued if raising exceptions
+    is explicitly suppressed with the "invalid_raise" keyword.
+
+    """
+    pass
+
+
+class StringConverter:
+    """
+    Factory class for function transforming a string into another object
+    (int, float).
+
+    After initialization, an instance can be called to transform a string
+    into another object. If the string is recognized as representing a
+    missing value, a default value is returned.
+
+    Attributes
+    ----------
+    func : function
+        Function used for the conversion.
+    default : any
+        Default value to return when the input corresponds to a missing
+        value.
+    type : type
+        Type of the output.
+    _status : int
+        Integer representing the order of the conversion.
+    _mapper : sequence of tuples
+        Sequence of tuples (dtype, function, default value) to evaluate in
+        order.
+    _locked : bool
+        Holds `locked` parameter.
+
+    Parameters
+    ----------
+    dtype_or_func : {None, dtype, function}, optional
+        If a `dtype`, specifies the input data type, used to define a basic
+        function and a default value for missing data. For example, when
+        `dtype` is float, the `func` attribute is set to `float` and the
+        default value to `np.nan`.  If a function, this function is used to
+        convert a string to another object. In this case, it is recommended
+        to give an associated default value as input.
+    default : any, optional
+        Value to return by default, that is, when the string to be
+        converted is flagged as missing. If not given, `StringConverter`
+        tries to supply a reasonable default value.
+    missing_values : {None, sequence of str}, optional
+        ``None`` or sequence of strings indicating a missing value. If ``None``
+        then missing values are indicated by empty entries. The default is
+        ``None``.
+    locked : bool, optional
+        Whether the StringConverter should be locked to prevent automatic
+        upgrade or not. Default is False.
+
+    """
+    _mapper = [(nx.bool_, str2bool, False),
+               (nx.int_, int, -1),]
+
+    # On 32-bit systems, we need to make sure that we explicitly include
+    # nx.int64 since ns.int_ is nx.int32.
+    if nx.dtype(nx.int_).itemsize < nx.dtype(nx.int64).itemsize:
+        _mapper.append((nx.int64, int, -1))
+
+    _mapper.extend([(nx.float64, float, nx.nan),
+                    (nx.complex128, complex, nx.nan + 0j),
+                    (nx.longdouble, nx.longdouble, nx.nan),
+                    # If a non-default dtype is passed, fall back to generic
+                    # ones (should only be used for the converter)
+                    (nx.integer, int, -1),
+                    (nx.floating, float, nx.nan),
+                    (nx.complexfloating, complex, nx.nan + 0j),
+                    # Last, try with the string types (must be last, because
+                    # `_mapper[-1]` is used as default in some cases)
+                    (nx.str_, asunicode, '???'),
+                    (nx.bytes_, asbytes, '???'),
+                    ])
+
+    @classmethod
+    def _getdtype(cls, val):
+        """Returns the dtype of the input variable."""
+        return np.array(val).dtype
+
+    @classmethod
+    def _getsubdtype(cls, val):
+        """Returns the type of the dtype of the input variable."""
+        return np.array(val).dtype.type
+
+    @classmethod
+    def _dtypeortype(cls, dtype):
+        """Returns dtype for datetime64 and type of dtype otherwise."""
+
+        # This is a bit annoying. We want to return the "general" type in most
+        # cases (ie. "string" rather than "S10"), but we want to return the
+        # specific type for datetime64 (ie. "datetime64[us]" rather than
+        # "datetime64").
+        if dtype.type == np.datetime64:
+            return dtype
+        return dtype.type
+
+    @classmethod
+    def upgrade_mapper(cls, func, default=None):
+        """
+        Upgrade the mapper of a StringConverter by adding a new function and
+        its corresponding default.
+
+        The input function (or sequence of functions) and its associated
+        default value (if any) is inserted in penultimate position of the
+        mapper.  The corresponding type is estimated from the dtype of the
+        default value.
+
+        Parameters
+        ----------
+        func : var
+            Function, or sequence of functions
+
+        Examples
+        --------
+        >>> import dateutil.parser
+        >>> import datetime
+        >>> dateparser = dateutil.parser.parse
+        >>> defaultdate = datetime.date(2000, 1, 1)
+        >>> StringConverter.upgrade_mapper(dateparser, default=defaultdate)
+        """
+        # Func is a single functions
+        if hasattr(func, '__call__'):
+            cls._mapper.insert(-1, (cls._getsubdtype(default), func, default))
+            return
+        elif hasattr(func, '__iter__'):
+            if isinstance(func[0], (tuple, list)):
+                for _ in func:
+                    cls._mapper.insert(-1, _)
+                return
+            if default is None:
+                default = [None] * len(func)
+            else:
+                default = list(default)
+                default.append([None] * (len(func) - len(default)))
+            for fct, dft in zip(func, default):
+                cls._mapper.insert(-1, (cls._getsubdtype(dft), fct, dft))
+
+    @classmethod
+    def _find_map_entry(cls, dtype):
+        # if a converter for the specific dtype is available use that
+        for i, (deftype, func, default_def) in enumerate(cls._mapper):
+            if dtype.type == deftype:
+                return i, (deftype, func, default_def)
+
+        # otherwise find an inexact match
+        for i, (deftype, func, default_def) in enumerate(cls._mapper):
+            if np.issubdtype(dtype.type, deftype):
+                return i, (deftype, func, default_def)
+
+        raise LookupError
+
+    def __init__(self, dtype_or_func=None, default=None, missing_values=None,
+                 locked=False):
+        # Defines a lock for upgrade
+        self._locked = bool(locked)
+        # No input dtype: minimal initialization
+        if dtype_or_func is None:
+            self.func = str2bool
+            self._status = 0
+            self.default = default or False
+            dtype = np.dtype('bool')
+        else:
+            # Is the input a np.dtype ?
+            try:
+                self.func = None
+                dtype = np.dtype(dtype_or_func)
+            except TypeError:
+                # dtype_or_func must be a function, then
+                if not hasattr(dtype_or_func, '__call__'):
+                    errmsg = ("The input argument `dtype` is neither a"
+                              " function nor a dtype (got '%s' instead)")
+                    raise TypeError(errmsg % type(dtype_or_func))
+                # Set the function
+                self.func = dtype_or_func
+                # If we don't have a default, try to guess it or set it to
+                # None
+                if default is None:
+                    try:
+                        default = self.func('0')
+                    except ValueError:
+                        default = None
+                dtype = self._getdtype(default)
+
+            # find the best match in our mapper
+            try:
+                self._status, (_, func, default_def) = self._find_map_entry(dtype)
+            except LookupError:
+                # no match
+                self.default = default
+                _, func, _ = self._mapper[-1]
+                self._status = 0
+            else:
+                # use the found default only if we did not already have one
+                if default is None:
+                    self.default = default_def
+                else:
+                    self.default = default
+
+            # If the input was a dtype, set the function to the last we saw
+            if self.func is None:
+                self.func = func
+
+            # If the status is 1 (int), change the function to
+            # something more robust.
+            if self.func == self._mapper[1][1]:
+                if issubclass(dtype.type, np.uint64):
+                    self.func = np.uint64
+                elif issubclass(dtype.type, np.int64):
+                    self.func = np.int64
+                else:
+                    self.func = lambda x: int(float(x))
+        # Store the list of strings corresponding to missing values.
+        if missing_values is None:
+            self.missing_values = {''}
+        else:
+            if isinstance(missing_values, str):
+                missing_values = missing_values.split(",")
+            self.missing_values = set(list(missing_values) + [''])
+
+        self._callingfunction = self._strict_call
+        self.type = self._dtypeortype(dtype)
+        self._checked = False
+        self._initial_default = default
+
+    def _loose_call(self, value):
+        try:
+            return self.func(value)
+        except ValueError:
+            return self.default
+
+    def _strict_call(self, value):
+        try:
+
+            # We check if we can convert the value using the current function
+            new_value = self.func(value)
+
+            # In addition to having to check whether func can convert the
+            # value, we also have to make sure that we don't get overflow
+            # errors for integers.
+            if self.func is int:
+                try:
+                    np.array(value, dtype=self.type)
+                except OverflowError:
+                    raise ValueError
+
+            # We're still here so we can now return the new value
+            return new_value
+
+        except ValueError:
+            if value.strip() in self.missing_values:
+                if not self._status:
+                    self._checked = False
+                return self.default
+            raise ValueError("Cannot convert string '%s'" % value)
+
+    def __call__(self, value):
+        return self._callingfunction(value)
+
+    def _do_upgrade(self):
+        # Raise an exception if we locked the converter...
+        if self._locked:
+            errmsg = "Converter is locked and cannot be upgraded"
+            raise ConverterLockError(errmsg)
+        _statusmax = len(self._mapper)
+        # Complains if we try to upgrade by the maximum
+        _status = self._status
+        if _status == _statusmax:
+            errmsg = "Could not find a valid conversion function"
+            raise ConverterError(errmsg)
+        elif _status < _statusmax - 1:
+            _status += 1
+        self.type, self.func, default = self._mapper[_status]
+        self._status = _status
+        if self._initial_default is not None:
+            self.default = self._initial_default
+        else:
+            self.default = default
+
+    def upgrade(self, value):
+        """
+        Find the best converter for a given string, and return the result.
+
+        The supplied string `value` is converted by testing different
+        converters in order. First the `func` method of the
+        `StringConverter` instance is tried, if this fails other available
+        converters are tried.  The order in which these other converters
+        are tried is determined by the `_status` attribute of the instance.
+
+        Parameters
+        ----------
+        value : str
+            The string to convert.
+
+        Returns
+        -------
+        out : any
+            The result of converting `value` with the appropriate converter.
+
+        """
+        self._checked = True
+        try:
+            return self._strict_call(value)
+        except ValueError:
+            self._do_upgrade()
+            return self.upgrade(value)
+
+    def iterupgrade(self, value):
+        self._checked = True
+        if not hasattr(value, '__iter__'):
+            value = (value,)
+        _strict_call = self._strict_call
+        try:
+            for _m in value:
+                _strict_call(_m)
+        except ValueError:
+            self._do_upgrade()
+            self.iterupgrade(value)
+
+    def update(self, func, default=None, testing_value=None,
+               missing_values='', locked=False):
+        """
+        Set StringConverter attributes directly.
+
+        Parameters
+        ----------
+        func : function
+            Conversion function.
+        default : any, optional
+            Value to return by default, that is, when the string to be
+            converted is flagged as missing. If not given,
+            `StringConverter` tries to supply a reasonable default value.
+        testing_value : str, optional
+            A string representing a standard input value of the converter.
+            This string is used to help defining a reasonable default
+            value.
+        missing_values : {sequence of str, None}, optional
+            Sequence of strings indicating a missing value. If ``None``, then
+            the existing `missing_values` are cleared. The default is `''`.
+        locked : bool, optional
+            Whether the StringConverter should be locked to prevent
+            automatic upgrade or not. Default is False.
+
+        Notes
+        -----
+        `update` takes the same parameters as the constructor of
+        `StringConverter`, except that `func` does not accept a `dtype`
+        whereas `dtype_or_func` in the constructor does.
+
+        """
+        self.func = func
+        self._locked = locked
+
+        # Don't reset the default to None if we can avoid it
+        if default is not None:
+            self.default = default
+            self.type = self._dtypeortype(self._getdtype(default))
+        else:
+            try:
+                tester = func(testing_value or '1')
+            except (TypeError, ValueError):
+                tester = None
+            self.type = self._dtypeortype(self._getdtype(tester))
+
+        # Add the missing values to the existing set or clear it.
+        if missing_values is None:
+            # Clear all missing values even though the ctor initializes it to
+            # set(['']) when the argument is None.
+            self.missing_values = set()
+        else:
+            if not np.iterable(missing_values):
+                missing_values = [missing_values]
+            if not all(isinstance(v, str) for v in missing_values):
+                raise TypeError("missing_values must be strings or unicode")
+            self.missing_values.update(missing_values)
+
+
+def easy_dtype(ndtype, names=None, defaultfmt="f%i", **validationargs):
+    """
+    Convenience function to create a `np.dtype` object.
+
+    The function processes the input `dtype` and matches it with the given
+    names.
+
+    Parameters
+    ----------
+    ndtype : var
+        Definition of the dtype. Can be any string or dictionary recognized
+        by the `np.dtype` function, or a sequence of types.
+    names : str or sequence, optional
+        Sequence of strings to use as field names for a structured dtype.
+        For convenience, `names` can be a string of a comma-separated list
+        of names.
+    defaultfmt : str, optional
+        Format string used to define missing names, such as ``"f%i"``
+        (default) or ``"fields_%02i"``.
+    validationargs : optional
+        A series of optional arguments used to initialize a
+        `NameValidator`.
+
+    Examples
+    --------
+    >>> np.lib._iotools.easy_dtype(float)
+    dtype('float64')
+    >>> np.lib._iotools.easy_dtype("i4, f8")
+    dtype([('f0', '<i4'), ('f1', '<f8')])
+    >>> np.lib._iotools.easy_dtype("i4, f8", defaultfmt="field_%03i")
+    dtype([('field_000', '<i4'), ('field_001', '<f8')])
+
+    >>> np.lib._iotools.easy_dtype((int, float, float), names="a,b,c")
+    dtype([('a', '<i8'), ('b', '<f8'), ('c', '<f8')])
+    >>> np.lib._iotools.easy_dtype(float, names="a,b,c")
+    dtype([('a', '<f8'), ('b', '<f8'), ('c', '<f8')])
+
+    """
+    try:
+        ndtype = np.dtype(ndtype)
+    except TypeError:
+        validate = NameValidator(**validationargs)
+        nbfields = len(ndtype)
+        if names is None:
+            names = [''] * len(ndtype)
+        elif isinstance(names, str):
+            names = names.split(",")
+        names = validate(names, nbfields=nbfields, defaultfmt=defaultfmt)
+        ndtype = np.dtype(dict(formats=ndtype, names=names))
+    else:
+        # Explicit names
+        if names is not None:
+            validate = NameValidator(**validationargs)
+            if isinstance(names, str):
+                names = names.split(",")
+            # Simple dtype: repeat to match the nb of names
+            if ndtype.names is None:
+                formats = tuple([ndtype.type] * len(names))
+                names = validate(names, defaultfmt=defaultfmt)
+                ndtype = np.dtype(list(zip(names, formats)))
+            # Structured dtype: just validate the names as needed
+            else:
+                ndtype.names = validate(names, nbfields=len(ndtype.names),
+                                        defaultfmt=defaultfmt)
+        # No implicit names
+        elif ndtype.names is not None:
+            validate = NameValidator(**validationargs)
+            # Default initial names : should we change the format ?
+            numbered_names = tuple("f%i" % i for i in range(len(ndtype.names)))
+            if ((ndtype.names == numbered_names) and (defaultfmt != "f%i")):
+                ndtype.names = validate([''] * len(ndtype.names),
+                                        defaultfmt=defaultfmt)
+            # Explicit initial names : just validate
+            else:
+                ndtype.names = validate(ndtype.names, defaultfmt=defaultfmt)
+    return ndtype

env-llmeval/lib/python3.10/site-packages/numpy/lib/_version.py

@@ -0,0 +1,155 @@
+"""Utility to compare (NumPy) version strings.
+
+The NumpyVersion class allows properly comparing numpy version strings.
+The LooseVersion and StrictVersion classes that distutils provides don't
+work; they don't recognize anything like alpha/beta/rc/dev versions.
+
+"""
+import re
+
+
+__all__ = ['NumpyVersion']
+
+
+class NumpyVersion():
+    """Parse and compare numpy version strings.
+
+    NumPy has the following versioning scheme (numbers given are examples; they
+    can be > 9 in principle):
+
+    - Released version: '1.8.0', '1.8.1', etc.
+    - Alpha: '1.8.0a1', '1.8.0a2', etc.
+    - Beta: '1.8.0b1', '1.8.0b2', etc.
+    - Release candidates: '1.8.0rc1', '1.8.0rc2', etc.
+    - Development versions: '1.8.0.dev-f1234afa' (git commit hash appended)
+    - Development versions after a1: '1.8.0a1.dev-f1234afa',
+                                     '1.8.0b2.dev-f1234afa',
+                                     '1.8.1rc1.dev-f1234afa', etc.
+    - Development versions (no git hash available): '1.8.0.dev-Unknown'
+
+    Comparing needs to be done against a valid version string or other
+    `NumpyVersion` instance. Note that all development versions of the same
+    (pre-)release compare equal.
+
+    .. versionadded:: 1.9.0
+
+    Parameters
+    ----------
+    vstring : str
+        NumPy version string (``np.__version__``).
+
+    Examples
+    --------
+    >>> from numpy.lib import NumpyVersion
+    >>> if NumpyVersion(np.__version__) < '1.7.0':
+    ...     print('skip')
+    >>> # skip
+
+    >>> NumpyVersion('1.7')  # raises ValueError, add ".0"
+    Traceback (most recent call last):
+        ...
+    ValueError: Not a valid numpy version string
+
+    """
+
+    def __init__(self, vstring):
+        self.vstring = vstring
+        ver_main = re.match(r'\d+\.\d+\.\d+', vstring)
+        if not ver_main:
+            raise ValueError("Not a valid numpy version string")
+
+        self.version = ver_main.group()
+        self.major, self.minor, self.bugfix = [int(x) for x in
+            self.version.split('.')]
+        if len(vstring) == ver_main.end():
+            self.pre_release = 'final'
+        else:
+            alpha = re.match(r'a\d', vstring[ver_main.end():])
+            beta = re.match(r'b\d', vstring[ver_main.end():])
+            rc = re.match(r'rc\d', vstring[ver_main.end():])
+            pre_rel = [m for m in [alpha, beta, rc] if m is not None]
+            if pre_rel:
+                self.pre_release = pre_rel[0].group()
+            else:
+                self.pre_release = ''
+
+        self.is_devversion = bool(re.search(r'.dev', vstring))
+
+    def _compare_version(self, other):
+        """Compare major.minor.bugfix"""
+        if self.major == other.major:
+            if self.minor == other.minor:
+                if self.bugfix == other.bugfix:
+                    vercmp = 0
+                elif self.bugfix > other.bugfix:
+                    vercmp = 1
+                else:
+                    vercmp = -1
+            elif self.minor > other.minor:
+                vercmp = 1
+            else:
+                vercmp = -1
+        elif self.major > other.major:
+            vercmp = 1
+        else:
+            vercmp = -1
+
+        return vercmp
+
+    def _compare_pre_release(self, other):
+        """Compare alpha/beta/rc/final."""
+        if self.pre_release == other.pre_release:
+            vercmp = 0
+        elif self.pre_release == 'final':
+            vercmp = 1
+        elif other.pre_release == 'final':
+            vercmp = -1
+        elif self.pre_release > other.pre_release:
+            vercmp = 1
+        else:
+            vercmp = -1
+
+        return vercmp
+
+    def _compare(self, other):
+        if not isinstance(other, (str, NumpyVersion)):
+            raise ValueError("Invalid object to compare with NumpyVersion.")
+
+        if isinstance(other, str):
+            other = NumpyVersion(other)
+
+        vercmp = self._compare_version(other)
+        if vercmp == 0:
+            # Same x.y.z version, check for alpha/beta/rc
+            vercmp = self._compare_pre_release(other)
+            if vercmp == 0:
+                # Same version and same pre-release, check if dev version
+                if self.is_devversion is other.is_devversion:
+                    vercmp = 0
+                elif self.is_devversion:
+                    vercmp = -1
+                else:
+                    vercmp = 1
+
+        return vercmp
+
+    def __lt__(self, other):
+        return self._compare(other) < 0
+
+    def __le__(self, other):
+        return self._compare(other) <= 0
+
+    def __eq__(self, other):
+        return self._compare(other) == 0
+
+    def __ne__(self, other):
+        return self._compare(other) != 0
+
+    def __gt__(self, other):
+        return self._compare(other) > 0
+
+    def __ge__(self, other):
+        return self._compare(other) >= 0
+
+    def __repr__(self):
+        return "NumpyVersion(%s)" % self.vstring

env-llmeval/lib/python3.10/site-packages/numpy/lib/_version.pyi

@@ -0,0 +1,17 @@
+__all__: list[str]
+
+class NumpyVersion:
+    vstring: str
+    version: str
+    major: int
+    minor: int
+    bugfix: int
+    pre_release: str
+    is_devversion: bool
+    def __init__(self, vstring: str) -> None: ...
+    def __lt__(self, other: str | NumpyVersion) -> bool: ...
+    def __le__(self, other: str | NumpyVersion) -> bool: ...
+    def __eq__(self, other: str | NumpyVersion) -> bool: ...  # type: ignore[override]
+    def __ne__(self, other: str | NumpyVersion) -> bool: ...  # type: ignore[override]
+    def __gt__(self, other: str | NumpyVersion) -> bool: ...
+    def __ge__(self, other: str | NumpyVersion) -> bool: ...

env-llmeval/lib/python3.10/site-packages/numpy/lib/arraypad.py

@@ -0,0 +1,882 @@
+"""
+The arraypad module contains a group of functions to pad values onto the edges
+of an n-dimensional array.
+
+"""
+import numpy as np
+from numpy.core.overrides import array_function_dispatch
+from numpy.lib.index_tricks import ndindex
+
+
+__all__ = ['pad']
+
+
+###############################################################################
+# Private utility functions.
+
+
+def _round_if_needed(arr, dtype):
+    """
+    Rounds arr inplace if destination dtype is integer.
+
+    Parameters
+    ----------
+    arr : ndarray
+        Input array.
+    dtype : dtype
+        The dtype of the destination array.
+    """
+    if np.issubdtype(dtype, np.integer):
+        arr.round(out=arr)
+
+
+def _slice_at_axis(sl, axis):
+    """
+    Construct tuple of slices to slice an array in the given dimension.
+
+    Parameters
+    ----------
+    sl : slice
+        The slice for the given dimension.
+    axis : int
+        The axis to which `sl` is applied. All other dimensions are left
+        "unsliced".
+
+    Returns
+    -------
+    sl : tuple of slices
+        A tuple with slices matching `shape` in length.
+
+    Examples
+    --------
+    >>> _slice_at_axis(slice(None, 3, -1), 1)
+    (slice(None, None, None), slice(None, 3, -1), (...,))
+    """
+    return (slice(None),) * axis + (sl,) + (...,)
+
+
+def _view_roi(array, original_area_slice, axis):
+    """
+    Get a view of the current region of interest during iterative padding.
+
+    When padding multiple dimensions iteratively corner values are
+    unnecessarily overwritten multiple times. This function reduces the
+    working area for the first dimensions so that corners are excluded.
+
+    Parameters
+    ----------
+    array : ndarray
+        The array with the region of interest.
+    original_area_slice : tuple of slices
+        Denotes the area with original values of the unpadded array.
+    axis : int
+        The currently padded dimension assuming that `axis` is padded before
+        `axis` + 1.
+
+    Returns
+    -------
+    roi : ndarray
+        The region of interest of the original `array`.
+    """
+    axis += 1
+    sl = (slice(None),) * axis + original_area_slice[axis:]
+    return array[sl]
+
+
+def _pad_simple(array, pad_width, fill_value=None):
+    """
+    Pad array on all sides with either a single value or undefined values.
+
+    Parameters
+    ----------
+    array : ndarray
+        Array to grow.
+    pad_width : sequence of tuple[int, int]
+        Pad width on both sides for each dimension in `arr`.
+    fill_value : scalar, optional
+        If provided the padded area is filled with this value, otherwise
+        the pad area left undefined.
+
+    Returns
+    -------
+    padded : ndarray
+        The padded array with the same dtype as`array`. Its order will default
+        to C-style if `array` is not F-contiguous.
+    original_area_slice : tuple
+        A tuple of slices pointing to the area of the original array.
+    """
+    # Allocate grown array
+    new_shape = tuple(
+        left + size + right
+        for size, (left, right) in zip(array.shape, pad_width)
+    )
+    order = 'F' if array.flags.fnc else 'C'  # Fortran and not also C-order
+    padded = np.empty(new_shape, dtype=array.dtype, order=order)
+
+    if fill_value is not None:
+        padded.fill(fill_value)
+
+    # Copy old array into correct space
+    original_area_slice = tuple(
+        slice(left, left + size)
+        for size, (left, right) in zip(array.shape, pad_width)
+    )
+    padded[original_area_slice] = array
+
+    return padded, original_area_slice
+
+
+def _set_pad_area(padded, axis, width_pair, value_pair):
+    """
+    Set empty-padded area in given dimension.
+
+    Parameters
+    ----------
+    padded : ndarray
+        Array with the pad area which is modified inplace.
+    axis : int
+        Dimension with the pad area to set.
+    width_pair : (int, int)
+        Pair of widths that mark the pad area on both sides in the given
+        dimension.
+    value_pair : tuple of scalars or ndarrays
+        Values inserted into the pad area on each side. It must match or be
+        broadcastable to the shape of `arr`.
+    """
+    left_slice = _slice_at_axis(slice(None, width_pair[0]), axis)
+    padded[left_slice] = value_pair[0]
+
+    right_slice = _slice_at_axis(
+        slice(padded.shape[axis] - width_pair[1], None), axis)
+    padded[right_slice] = value_pair[1]
+
+
+def _get_edges(padded, axis, width_pair):
+    """
+    Retrieve edge values from empty-padded array in given dimension.
+
+    Parameters
+    ----------
+    padded : ndarray
+        Empty-padded array.
+    axis : int
+        Dimension in which the edges are considered.
+    width_pair : (int, int)
+        Pair of widths that mark the pad area on both sides in the given
+        dimension.
+
+    Returns
+    -------
+    left_edge, right_edge : ndarray
+        Edge values of the valid area in `padded` in the given dimension. Its
+        shape will always match `padded` except for the dimension given by
+        `axis` which will have a length of 1.
+    """
+    left_index = width_pair[0]
+    left_slice = _slice_at_axis(slice(left_index, left_index + 1), axis)
+    left_edge = padded[left_slice]
+
+    right_index = padded.shape[axis] - width_pair[1]
+    right_slice = _slice_at_axis(slice(right_index - 1, right_index), axis)
+    right_edge = padded[right_slice]
+
+    return left_edge, right_edge
+
+
+def _get_linear_ramps(padded, axis, width_pair, end_value_pair):
+    """
+    Construct linear ramps for empty-padded array in given dimension.
+
+    Parameters
+    ----------
+    padded : ndarray
+        Empty-padded array.
+    axis : int
+        Dimension in which the ramps are constructed.
+    width_pair : (int, int)
+        Pair of widths that mark the pad area on both sides in the given
+        dimension.
+    end_value_pair : (scalar, scalar)
+        End values for the linear ramps which form the edge of the fully padded
+        array. These values are included in the linear ramps.
+
+    Returns
+    -------
+    left_ramp, right_ramp : ndarray
+        Linear ramps to set on both sides of `padded`.
+    """
+    edge_pair = _get_edges(padded, axis, width_pair)
+
+    left_ramp, right_ramp = (
+        np.linspace(
+            start=end_value,
+            stop=edge.squeeze(axis), # Dimension is replaced by linspace
+            num=width,
+            endpoint=False,
+            dtype=padded.dtype,
+            axis=axis
+        )
+        for end_value, edge, width in zip(
+            end_value_pair, edge_pair, width_pair
+        )
+    )
+        
+    # Reverse linear space in appropriate dimension
+    right_ramp = right_ramp[_slice_at_axis(slice(None, None, -1), axis)]
+
+    return left_ramp, right_ramp
+
+
+def _get_stats(padded, axis, width_pair, length_pair, stat_func):
+    """
+    Calculate statistic for the empty-padded array in given dimension.
+
+    Parameters
+    ----------
+    padded : ndarray
+        Empty-padded array.
+    axis : int
+        Dimension in which the statistic is calculated.
+    width_pair : (int, int)
+        Pair of widths that mark the pad area on both sides in the given
+        dimension.
+    length_pair : 2-element sequence of None or int
+        Gives the number of values in valid area from each side that is
+        taken into account when calculating the statistic. If None the entire
+        valid area in `padded` is considered.
+    stat_func : function
+        Function to compute statistic. The expected signature is
+        ``stat_func(x: ndarray, axis: int, keepdims: bool) -> ndarray``.
+
+    Returns
+    -------
+    left_stat, right_stat : ndarray
+        Calculated statistic for both sides of `padded`.
+    """
+    # Calculate indices of the edges of the area with original values
+    left_index = width_pair[0]
+    right_index = padded.shape[axis] - width_pair[1]
+    # as well as its length
+    max_length = right_index - left_index
+
+    # Limit stat_lengths to max_length
+    left_length, right_length = length_pair
+    if left_length is None or max_length < left_length:
+        left_length = max_length
+    if right_length is None or max_length < right_length:
+        right_length = max_length
+
+    if (left_length == 0 or right_length == 0) \
+            and stat_func in {np.amax, np.amin}:
+        # amax and amin can't operate on an empty array,
+        # raise a more descriptive warning here instead of the default one
+        raise ValueError("stat_length of 0 yields no value for padding")
+
+    # Calculate statistic for the left side
+    left_slice = _slice_at_axis(
+        slice(left_index, left_index + left_length), axis)
+    left_chunk = padded[left_slice]
+    left_stat = stat_func(left_chunk, axis=axis, keepdims=True)
+    _round_if_needed(left_stat, padded.dtype)
+
+    if left_length == right_length == max_length:
+        # return early as right_stat must be identical to left_stat
+        return left_stat, left_stat
+
+    # Calculate statistic for the right side
+    right_slice = _slice_at_axis(
+        slice(right_index - right_length, right_index), axis)
+    right_chunk = padded[right_slice]
+    right_stat = stat_func(right_chunk, axis=axis, keepdims=True)
+    _round_if_needed(right_stat, padded.dtype)
+
+    return left_stat, right_stat
+
+
+def _set_reflect_both(padded, axis, width_pair, method, include_edge=False):
+    """
+    Pad `axis` of `arr` with reflection.
+
+    Parameters
+    ----------
+    padded : ndarray
+        Input array of arbitrary shape.
+    axis : int
+        Axis along which to pad `arr`.
+    width_pair : (int, int)
+        Pair of widths that mark the pad area on both sides in the given
+        dimension.
+    method : str
+        Controls method of reflection; options are 'even' or 'odd'.
+    include_edge : bool
+        If true, edge value is included in reflection, otherwise the edge
+        value forms the symmetric axis to the reflection.
+
+    Returns
+    -------
+    pad_amt : tuple of ints, length 2
+        New index positions of padding to do along the `axis`. If these are
+        both 0, padding is done in this dimension.
+    """
+    left_pad, right_pad = width_pair
+    old_length = padded.shape[axis] - right_pad - left_pad
+
+    if include_edge:
+        # Edge is included, we need to offset the pad amount by 1
+        edge_offset = 1
+    else:
+        edge_offset = 0  # Edge is not included, no need to offset pad amount
+        old_length -= 1  # but must be omitted from the chunk
+
+    if left_pad > 0:
+        # Pad with reflected values on left side:
+        # First limit chunk size which can't be larger than pad area
+        chunk_length = min(old_length, left_pad)
+        # Slice right to left, stop on or next to edge, start relative to stop
+        stop = left_pad - edge_offset
+        start = stop + chunk_length
+        left_slice = _slice_at_axis(slice(start, stop, -1), axis)
+        left_chunk = padded[left_slice]
+
+        if method == "odd":
+            # Negate chunk and align with edge
+            edge_slice = _slice_at_axis(slice(left_pad, left_pad + 1), axis)
+            left_chunk = 2 * padded[edge_slice] - left_chunk
+
+        # Insert chunk into padded area
+        start = left_pad - chunk_length
+        stop = left_pad
+        pad_area = _slice_at_axis(slice(start, stop), axis)
+        padded[pad_area] = left_chunk
+        # Adjust pointer to left edge for next iteration
+        left_pad -= chunk_length
+
+    if right_pad > 0:
+        # Pad with reflected values on right side:
+        # First limit chunk size which can't be larger than pad area
+        chunk_length = min(old_length, right_pad)
+        # Slice right to left, start on or next to edge, stop relative to start
+        start = -right_pad + edge_offset - 2
+        stop = start - chunk_length
+        right_slice = _slice_at_axis(slice(start, stop, -1), axis)
+        right_chunk = padded[right_slice]
+
+        if method == "odd":
+            # Negate chunk and align with edge
+            edge_slice = _slice_at_axis(
+                slice(-right_pad - 1, -right_pad), axis)
+            right_chunk = 2 * padded[edge_slice] - right_chunk
+
+        # Insert chunk into padded area
+        start = padded.shape[axis] - right_pad
+        stop = start + chunk_length
+        pad_area = _slice_at_axis(slice(start, stop), axis)
+        padded[pad_area] = right_chunk
+        # Adjust pointer to right edge for next iteration
+        right_pad -= chunk_length
+
+    return left_pad, right_pad
+
+
+def _set_wrap_both(padded, axis, width_pair, original_period):
+    """
+    Pad `axis` of `arr` with wrapped values.
+
+    Parameters
+    ----------
+    padded : ndarray
+        Input array of arbitrary shape.
+    axis : int
+        Axis along which to pad `arr`.
+    width_pair : (int, int)
+        Pair of widths that mark the pad area on both sides in the given
+        dimension.
+    original_period : int
+        Original length of data on `axis` of `arr`.
+
+    Returns
+    -------
+    pad_amt : tuple of ints, length 2
+        New index positions of padding to do along the `axis`. If these are
+        both 0, padding is done in this dimension.
+    """
+    left_pad, right_pad = width_pair
+    period = padded.shape[axis] - right_pad - left_pad
+    # Avoid wrapping with only a subset of the original area by ensuring period
+    # can only be a multiple of the original area's length.
+    period = period // original_period * original_period
+
+    # If the current dimension of `arr` doesn't contain enough valid values
+    # (not part of the undefined pad area) we need to pad multiple times.
+    # Each time the pad area shrinks on both sides which is communicated with
+    # these variables.
+    new_left_pad = 0
+    new_right_pad = 0
+
+    if left_pad > 0:
+        # Pad with wrapped values on left side
+        # First slice chunk from left side of the non-pad area.
+        # Use min(period, left_pad) to ensure that chunk is not larger than
+        # pad area.
+        slice_end = left_pad + period
+        slice_start = slice_end - min(period, left_pad)
+        right_slice = _slice_at_axis(slice(slice_start, slice_end), axis)
+        right_chunk = padded[right_slice]
+
+        if left_pad > period:
+            # Chunk is smaller than pad area
+            pad_area = _slice_at_axis(slice(left_pad - period, left_pad), axis)
+            new_left_pad = left_pad - period
+        else:
+            # Chunk matches pad area
+            pad_area = _slice_at_axis(slice(None, left_pad), axis)
+        padded[pad_area] = right_chunk
+
+    if right_pad > 0:
+        # Pad with wrapped values on right side
+        # First slice chunk from right side of the non-pad area.
+        # Use min(period, right_pad) to ensure that chunk is not larger than
+        # pad area.
+        slice_start = -right_pad - period
+        slice_end = slice_start + min(period, right_pad)
+        left_slice = _slice_at_axis(slice(slice_start, slice_end), axis)
+        left_chunk = padded[left_slice]
+
+        if right_pad > period:
+            # Chunk is smaller than pad area
+            pad_area = _slice_at_axis(
+                slice(-right_pad, -right_pad + period), axis)
+            new_right_pad = right_pad - period
+        else:
+            # Chunk matches pad area
+            pad_area = _slice_at_axis(slice(-right_pad, None), axis)
+        padded[pad_area] = left_chunk
+
+    return new_left_pad, new_right_pad
+
+
+def _as_pairs(x, ndim, as_index=False):
+    """
+    Broadcast `x` to an array with the shape (`ndim`, 2).
+
+    A helper function for `pad` that prepares and validates arguments like
+    `pad_width` for iteration in pairs.
+
+    Parameters
+    ----------
+    x : {None, scalar, array-like}
+        The object to broadcast to the shape (`ndim`, 2).
+    ndim : int
+        Number of pairs the broadcasted `x` will have.
+    as_index : bool, optional
+        If `x` is not None, try to round each element of `x` to an integer
+        (dtype `np.intp`) and ensure every element is positive.
+
+    Returns
+    -------
+    pairs : nested iterables, shape (`ndim`, 2)
+        The broadcasted version of `x`.
+
+    Raises
+    ------
+    ValueError
+        If `as_index` is True and `x` contains negative elements.
+        Or if `x` is not broadcastable to the shape (`ndim`, 2).
+    """
+    if x is None:
+        # Pass through None as a special case, otherwise np.round(x) fails
+        # with an AttributeError
+        return ((None, None),) * ndim
+
+    x = np.array(x)
+    if as_index:
+        x = np.round(x).astype(np.intp, copy=False)
+
+    if x.ndim < 3:
+        # Optimization: Possibly use faster paths for cases where `x` has
+        # only 1 or 2 elements. `np.broadcast_to` could handle these as well
+        # but is currently slower
+
+        if x.size == 1:
+            # x was supplied as a single value
+            x = x.ravel()  # Ensure x[0] works for x.ndim == 0, 1, 2
+            if as_index and x < 0:
+                raise ValueError("index can't contain negative values")
+            return ((x[0], x[0]),) * ndim
+
+        if x.size == 2 and x.shape != (2, 1):
+            # x was supplied with a single value for each side
+            # but except case when each dimension has a single value
+            # which should be broadcasted to a pair,
+            # e.g. [[1], [2]] -> [[1, 1], [2, 2]] not [[1, 2], [1, 2]]
+            x = x.ravel()  # Ensure x[0], x[1] works
+            if as_index and (x[0] < 0 or x[1] < 0):
+                raise ValueError("index can't contain negative values")
+            return ((x[0], x[1]),) * ndim
+
+    if as_index and x.min() < 0:
+        raise ValueError("index can't contain negative values")
+
+    # Converting the array with `tolist` seems to improve performance
+    # when iterating and indexing the result (see usage in `pad`)
+    return np.broadcast_to(x, (ndim, 2)).tolist()
+
+
+def _pad_dispatcher(array, pad_width, mode=None, **kwargs):
+    return (array,)
+
+
+###############################################################################
+# Public functions
+
+
+@array_function_dispatch(_pad_dispatcher, module='numpy')
+def pad(array, pad_width, mode='constant', **kwargs):
+    """
+    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)`` or ``((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
+
+        <function>
+            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)`` or ``((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)`` or ``((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)`` or ``((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)
+    >>> 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]])
+    """
+    array = np.asarray(array)
+    pad_width = np.asarray(pad_width)
+
+    if not pad_width.dtype.kind == 'i':
+        raise TypeError('`pad_width` must be of integral type.')
+
+    # Broadcast to shape (array.ndim, 2)
+    pad_width = _as_pairs(pad_width, array.ndim, as_index=True)
+
+    if callable(mode):
+        # Old behavior: Use user-supplied function with np.apply_along_axis
+        function = mode
+        # Create a new zero padded array
+        padded, _ = _pad_simple(array, pad_width, fill_value=0)
+        # And apply along each axis
+
+        for axis in range(padded.ndim):
+            # Iterate using ndindex as in apply_along_axis, but assuming that
+            # function operates inplace on the padded array.
+
+            # view with the iteration axis at the end
+            view = np.moveaxis(padded, axis, -1)
+
+            # compute indices for the iteration axes, and append a trailing
+            # ellipsis to prevent 0d arrays decaying to scalars (gh-8642)
+            inds = ndindex(view.shape[:-1])
+            inds = (ind + (Ellipsis,) for ind in inds)
+            for ind in inds:
+                function(view[ind], pad_width[axis], axis, kwargs)
+
+        return padded
+
+    # Make sure that no unsupported keywords were passed for the current mode
+    allowed_kwargs = {
+        'empty': [], 'edge': [], 'wrap': [],
+        'constant': ['constant_values'],
+        'linear_ramp': ['end_values'],
+        'maximum': ['stat_length'],
+        'mean': ['stat_length'],
+        'median': ['stat_length'],
+        'minimum': ['stat_length'],
+        'reflect': ['reflect_type'],
+        'symmetric': ['reflect_type'],
+    }
+    try:
+        unsupported_kwargs = set(kwargs) - set(allowed_kwargs[mode])
+    except KeyError:
+        raise ValueError("mode '{}' is not supported".format(mode)) from None
+    if unsupported_kwargs:
+        raise ValueError("unsupported keyword arguments for mode '{}': {}"
+                         .format(mode, unsupported_kwargs))
+
+    stat_functions = {"maximum": np.amax, "minimum": np.amin,
+                      "mean": np.mean, "median": np.median}
+
+    # Create array with final shape and original values
+    # (padded area is undefined)
+    padded, original_area_slice = _pad_simple(array, pad_width)
+    # And prepare iteration over all dimensions
+    # (zipping may be more readable than using enumerate)
+    axes = range(padded.ndim)
+
+    if mode == "constant":
+        values = kwargs.get("constant_values", 0)
+        values = _as_pairs(values, padded.ndim)
+        for axis, width_pair, value_pair in zip(axes, pad_width, values):
+            roi = _view_roi(padded, original_area_slice, axis)
+            _set_pad_area(roi, axis, width_pair, value_pair)
+
+    elif mode == "empty":
+        pass  # Do nothing as _pad_simple already returned the correct result
+
+    elif array.size == 0:
+        # Only modes "constant" and "empty" can extend empty axes, all other
+        # modes depend on `array` not being empty
+        # -> ensure every empty axis is only "padded with 0"
+        for axis, width_pair in zip(axes, pad_width):
+            if array.shape[axis] == 0 and any(width_pair):
+                raise ValueError(
+                    "can't extend empty axis {} using modes other than "
+                    "'constant' or 'empty'".format(axis)
+                )
+        # passed, don't need to do anything more as _pad_simple already
+        # returned the correct result
+
+    elif mode == "edge":
+        for axis, width_pair in zip(axes, pad_width):
+            roi = _view_roi(padded, original_area_slice, axis)
+            edge_pair = _get_edges(roi, axis, width_pair)
+            _set_pad_area(roi, axis, width_pair, edge_pair)
+
+    elif mode == "linear_ramp":
+        end_values = kwargs.get("end_values", 0)
+        end_values = _as_pairs(end_values, padded.ndim)
+        for axis, width_pair, value_pair in zip(axes, pad_width, end_values):
+            roi = _view_roi(padded, original_area_slice, axis)
+            ramp_pair = _get_linear_ramps(roi, axis, width_pair, value_pair)
+            _set_pad_area(roi, axis, width_pair, ramp_pair)
+
+    elif mode in stat_functions:
+        func = stat_functions[mode]
+        length = kwargs.get("stat_length", None)
+        length = _as_pairs(length, padded.ndim, as_index=True)
+        for axis, width_pair, length_pair in zip(axes, pad_width, length):
+            roi = _view_roi(padded, original_area_slice, axis)
+            stat_pair = _get_stats(roi, axis, width_pair, length_pair, func)
+            _set_pad_area(roi, axis, width_pair, stat_pair)
+
+    elif mode in {"reflect", "symmetric"}:
+        method = kwargs.get("reflect_type", "even")
+        include_edge = True if mode == "symmetric" else False
+        for axis, (left_index, right_index) in zip(axes, pad_width):
+            if array.shape[axis] == 1 and (left_index > 0 or right_index > 0):
+                # Extending singleton dimension for 'reflect' is legacy
+                # behavior; it really should raise an error.
+                edge_pair = _get_edges(padded, axis, (left_index, right_index))
+                _set_pad_area(
+                    padded, axis, (left_index, right_index), edge_pair)
+                continue
+
+            roi = _view_roi(padded, original_area_slice, axis)
+            while left_index > 0 or right_index > 0:
+                # Iteratively pad until dimension is filled with reflected
+                # values. This is necessary if the pad area is larger than
+                # the length of the original values in the current dimension.
+                left_index, right_index = _set_reflect_both(
+                    roi, axis, (left_index, right_index),
+                    method, include_edge
+                )
+
+    elif mode == "wrap":
+        for axis, (left_index, right_index) in zip(axes, pad_width):
+            roi = _view_roi(padded, original_area_slice, axis)
+            original_period = padded.shape[axis] - right_index - left_index
+            while left_index > 0 or right_index > 0:
+                # Iteratively pad until dimension is filled with wrapped
+                # values. This is necessary if the pad area is larger than
+                # the length of the original values in the current dimension.
+                left_index, right_index = _set_wrap_both(
+                    roi, axis, (left_index, right_index), original_period)
+
+    return padded

env-llmeval/lib/python3.10/site-packages/numpy/lib/arraypad.pyi

@@ -0,0 +1,85 @@
+from typing import (
+    Literal as L,
+    Any,
+    overload,
+    TypeVar,
+    Protocol,
+)
+
+from numpy import generic
+
+from numpy._typing import (
+    ArrayLike,
+    NDArray,
+    _ArrayLikeInt,
+    _ArrayLike,
+)
+
+_SCT = TypeVar("_SCT", bound=generic)
+
+class _ModeFunc(Protocol):
+    def __call__(
+        self,
+        vector: NDArray[Any],
+        iaxis_pad_width: tuple[int, int],
+        iaxis: int,
+        kwargs: dict[str, Any],
+        /,
+    ) -> None: ...
+
+_ModeKind = L[
+    "constant",
+    "edge",
+    "linear_ramp",
+    "maximum",
+    "mean",
+    "median",
+    "minimum",
+    "reflect",
+    "symmetric",
+    "wrap",
+    "empty",
+]
+
+__all__: list[str]
+
+# TODO: In practice each keyword argument is exclusive to one or more
+# specific modes. Consider adding more overloads to express this in the future.
+
+# Expand `**kwargs` into explicit keyword-only arguments
+@overload
+def pad(
+    array: _ArrayLike[_SCT],
+    pad_width: _ArrayLikeInt,
+    mode: _ModeKind = ...,
+    *,
+    stat_length: None | _ArrayLikeInt = ...,
+    constant_values: ArrayLike = ...,
+    end_values: ArrayLike = ...,
+    reflect_type: L["odd", "even"] = ...,
+) -> NDArray[_SCT]: ...
+@overload
+def pad(
+    array: ArrayLike,
+    pad_width: _ArrayLikeInt,
+    mode: _ModeKind = ...,
+    *,
+    stat_length: None | _ArrayLikeInt = ...,
+    constant_values: ArrayLike = ...,
+    end_values: ArrayLike = ...,
+    reflect_type: L["odd", "even"] = ...,
+) -> NDArray[Any]: ...
+@overload
+def pad(
+    array: _ArrayLike[_SCT],
+    pad_width: _ArrayLikeInt,
+    mode: _ModeFunc,
+    **kwargs: Any,
+) -> NDArray[_SCT]: ...
+@overload
+def pad(
+    array: ArrayLike,
+    pad_width: _ArrayLikeInt,
+    mode: _ModeFunc,
+    **kwargs: Any,
+) -> NDArray[Any]: ...

env-llmeval/lib/python3.10/site-packages/numpy/lib/arraysetops.py

@@ -0,0 +1,981 @@
+"""
+Set operations for arrays based on sorting.
+
+Notes
+-----
+
+For floating point arrays, inaccurate results may appear due to usual round-off
+and floating point comparison issues.
+
+Speed could be gained in some operations by an implementation of
+`numpy.sort`, that can provide directly the permutation vectors, thus avoiding
+calls to `numpy.argsort`.
+
+Original author: Robert Cimrman
+
+"""
+import functools
+
+import numpy as np
+from numpy.core import overrides
+
+
+array_function_dispatch = functools.partial(
+    overrides.array_function_dispatch, module='numpy')
+
+
+__all__ = [
+    'ediff1d', 'intersect1d', 'setxor1d', 'union1d', 'setdiff1d', 'unique',
+    'in1d', 'isin'
+    ]
+
+
+def _ediff1d_dispatcher(ary, to_end=None, to_begin=None):
+    return (ary, to_end, to_begin)
+
+
+@array_function_dispatch(_ediff1d_dispatcher)
+def ediff1d(ary, to_end=None, to_begin=None):
+    """
+    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])
+
+    """
+    # force a 1d array
+    ary = np.asanyarray(ary).ravel()
+
+    # enforce that the dtype of `ary` is used for the output
+    dtype_req = ary.dtype
+
+    # fast track default case
+    if to_begin is None and to_end is None:
+        return ary[1:] - ary[:-1]
+
+    if to_begin is None:
+        l_begin = 0
+    else:
+        to_begin = np.asanyarray(to_begin)
+        if not np.can_cast(to_begin, dtype_req, casting="same_kind"):
+            raise TypeError("dtype of `to_begin` must be compatible "
+                            "with input `ary` under the `same_kind` rule.")
+
+        to_begin = to_begin.ravel()
+        l_begin = len(to_begin)
+
+    if to_end is None:
+        l_end = 0
+    else:
+        to_end = np.asanyarray(to_end)
+        if not np.can_cast(to_end, dtype_req, casting="same_kind"):
+            raise TypeError("dtype of `to_end` must be compatible "
+                            "with input `ary` under the `same_kind` rule.")
+
+        to_end = to_end.ravel()
+        l_end = len(to_end)
+
+    # do the calculation in place and copy to_begin and to_end
+    l_diff = max(len(ary) - 1, 0)
+    result = np.empty(l_diff + l_begin + l_end, dtype=ary.dtype)
+    result = ary.__array_wrap__(result)
+    if l_begin > 0:
+        result[:l_begin] = to_begin
+    if l_end > 0:
+        result[l_begin + l_diff:] = to_end
+    np.subtract(ary[1:], ary[:-1], result[l_begin:l_begin + l_diff])
+    return result
+
+
+def _unpack_tuple(x):
+    """ Unpacks one-element tuples for use as return values """
+    if len(x) == 1:
+        return x[0]
+    else:
+        return x
+
+
+def _unique_dispatcher(ar, return_index=None, return_inverse=None,
+                       return_counts=None, axis=None, *, equal_nan=None):
+    return (ar,)
+
+
+@array_function_dispatch(_unique_dispatcher)
+def unique(ar, return_index=False, return_inverse=False,
+           return_counts=False, axis=None, *, equal_nan=True):
+    """
+    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`.
+    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
+
+    equal_nan : bool, optional
+        If True, collapses multiple NaN values in the return array into one.
+
+        .. versionadded:: 1.24
+
+    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='<U1')
+    >>> indices
+    array([0, 1, 3])
+    >>> a[indices]
+    array(['a', 'b', 'c'], dtype='<U1')
+
+    Reconstruct the input array from the unique values and inverse:
+
+    >>> 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
+
+    """
+    ar = np.asanyarray(ar)
+    if axis is None:
+        ret = _unique1d(ar, return_index, return_inverse, return_counts, 
+                        equal_nan=equal_nan)
+        return _unpack_tuple(ret)
+
+    # axis was specified and not None
+    try:
+        ar = np.moveaxis(ar, axis, 0)
+    except np.AxisError:
+        # this removes the "axis1" or "axis2" prefix from the error message
+        raise np.AxisError(axis, ar.ndim) from None
+
+    # Must reshape to a contiguous 2D array for this to work...
+    orig_shape, orig_dtype = ar.shape, ar.dtype
+    ar = ar.reshape(orig_shape[0], np.prod(orig_shape[1:], dtype=np.intp))
+    ar = np.ascontiguousarray(ar)
+    dtype = [('f{i}'.format(i=i), ar.dtype) for i in range(ar.shape[1])]
+
+    # At this point, `ar` has shape `(n, m)`, and `dtype` is a structured
+    # data type with `m` fields where each field has the data type of `ar`.
+    # In the following, we create the array `consolidated`, which has
+    # shape `(n,)` with data type `dtype`.
+    try:
+        if ar.shape[1] > 0:
+            consolidated = ar.view(dtype)
+        else:
+            # If ar.shape[1] == 0, then dtype will be `np.dtype([])`, which is
+            # a data type with itemsize 0, and the call `ar.view(dtype)` will
+            # fail.  Instead, we'll use `np.empty` to explicitly create the
+            # array with shape `(len(ar),)`.  Because `dtype` in this case has
+            # itemsize 0, the total size of the result is still 0 bytes.
+            consolidated = np.empty(len(ar), dtype=dtype)
+    except TypeError as e:
+        # There's no good way to do this for object arrays, etc...
+        msg = 'The axis argument to unique is not supported for dtype {dt}'
+        raise TypeError(msg.format(dt=ar.dtype)) from e
+
+    def reshape_uniq(uniq):
+        n = len(uniq)
+        uniq = uniq.view(orig_dtype)
+        uniq = uniq.reshape(n, *orig_shape[1:])
+        uniq = np.moveaxis(uniq, 0, axis)
+        return uniq
+
+    output = _unique1d(consolidated, return_index,
+                       return_inverse, return_counts, equal_nan=equal_nan)
+    output = (reshape_uniq(output[0]),) + output[1:]
+    return _unpack_tuple(output)
+
+
+def _unique1d(ar, return_index=False, return_inverse=False,
+              return_counts=False, *, equal_nan=True):
+    """
+    Find the unique elements of an array, ignoring shape.
+    """
+    ar = np.asanyarray(ar).flatten()
+
+    optional_indices = return_index or return_inverse
+
+    if optional_indices:
+        perm = ar.argsort(kind='mergesort' if return_index else 'quicksort')
+        aux = ar[perm]
+    else:
+        ar.sort()
+        aux = ar
+    mask = np.empty(aux.shape, dtype=np.bool_)
+    mask[:1] = True
+    if (equal_nan and aux.shape[0] > 0 and aux.dtype.kind in "cfmM" and
+            np.isnan(aux[-1])):
+        if aux.dtype.kind == "c":  # for complex all NaNs are considered equivalent
+            aux_firstnan = np.searchsorted(np.isnan(aux), True, side='left')
+        else:
+            aux_firstnan = np.searchsorted(aux, aux[-1], side='left')
+        if aux_firstnan > 0:
+            mask[1:aux_firstnan] = (
+                aux[1:aux_firstnan] != aux[:aux_firstnan - 1])
+        mask[aux_firstnan] = True
+        mask[aux_firstnan + 1:] = False
+    else:
+        mask[1:] = aux[1:] != aux[:-1]
+
+    ret = (aux[mask],)
+    if return_index:
+        ret += (perm[mask],)
+    if return_inverse:
+        imask = np.cumsum(mask) - 1
+        inv_idx = np.empty(mask.shape, dtype=np.intp)
+        inv_idx[perm] = imask
+        ret += (inv_idx,)
+    if return_counts:
+        idx = np.concatenate(np.nonzero(mask) + ([mask.size],))
+        ret += (np.diff(idx),)
+    return ret
+
+
+def _intersect1d_dispatcher(
+        ar1, ar2, assume_unique=None, return_indices=None):
+    return (ar1, ar2)
+
+
+@array_function_dispatch(_intersect1d_dispatcher)
+def intersect1d(ar1, ar2, assume_unique=False, return_indices=False):
+    """
+    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]))
+
+    """
+    ar1 = np.asanyarray(ar1)
+    ar2 = np.asanyarray(ar2)
+
+    if not assume_unique:
+        if return_indices:
+            ar1, ind1 = unique(ar1, return_index=True)
+            ar2, ind2 = unique(ar2, return_index=True)
+        else:
+            ar1 = unique(ar1)
+            ar2 = unique(ar2)
+    else:
+        ar1 = ar1.ravel()
+        ar2 = ar2.ravel()
+
+    aux = np.concatenate((ar1, ar2))
+    if return_indices:
+        aux_sort_indices = np.argsort(aux, kind='mergesort')
+        aux = aux[aux_sort_indices]
+    else:
+        aux.sort()
+
+    mask = aux[1:] == aux[:-1]
+    int1d = aux[:-1][mask]
+
+    if return_indices:
+        ar1_indices = aux_sort_indices[:-1][mask]
+        ar2_indices = aux_sort_indices[1:][mask] - ar1.size
+        if not assume_unique:
+            ar1_indices = ind1[ar1_indices]
+            ar2_indices = ind2[ar2_indices]
+
+        return int1d, ar1_indices, ar2_indices
+    else:
+        return int1d
+
+
+def _setxor1d_dispatcher(ar1, ar2, assume_unique=None):
+    return (ar1, ar2)
+
+
+@array_function_dispatch(_setxor1d_dispatcher)
+def setxor1d(ar1, ar2, assume_unique=False):
+    """
+    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])
+
+    """
+    if not assume_unique:
+        ar1 = unique(ar1)
+        ar2 = unique(ar2)
+
+    aux = np.concatenate((ar1, ar2))
+    if aux.size == 0:
+        return aux
+
+    aux.sort()
+    flag = np.concatenate(([True], aux[1:] != aux[:-1], [True]))
+    return aux[flag[1:] & flag[:-1]]
+
+
+def _in1d_dispatcher(ar1, ar2, assume_unique=None, invert=None, *,
+                     kind=None):
+    return (ar1, ar2)
+
+
+@array_function_dispatch(_in1d_dispatcher)
+def in1d(ar1, ar2, assume_unique=False, invert=False, *, kind=None):
+    """
+    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))``.
+    kind : {None, 'sort', 'table'}, optional
+        The algorithm to use. This will not affect the final result,
+        but will affect the speed and memory use. The default, None,
+        will select automatically based on memory considerations.
+
+        * If 'sort', will use a mergesort-based approach. This will have
+          a memory usage of roughly 6 times the sum of the sizes of
+          `ar1` and `ar2`, not accounting for size of dtypes.
+        * If 'table', will use a lookup table approach similar
+          to a counting sort. This is only available for boolean and
+          integer arrays. This will have a memory usage of the
+          size of `ar1` plus the max-min value of `ar2`. `assume_unique`
+          has no effect when the 'table' option is used.
+        * If None, will automatically choose 'table' if
+          the required memory allocation is less than or equal to
+          6 times the sum of the sizes of `ar1` and `ar2`,
+          otherwise will use 'sort'. This is done to not use
+          a large amount of memory by default, even though
+          'table' may be faster in most cases. If 'table' is chosen,
+          `assume_unique` will have no effect.
+
+        .. 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.
+
+    Using ``kind='table'`` tends to be faster than `kind='sort'` if the
+    following relationship is true:
+    ``log10(len(ar2)) > (log10(max(ar2)-min(ar2)) - 2.27) / 0.927``,
+    but may use greater memory. The default value for `kind` will
+    be automatically selected based only on memory usage, so one may
+    manually set ``kind='table'`` if memory constraints can be relaxed.
+
+    .. 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])
+    """
+    # Ravel both arrays, behavior for the first array could be different
+    ar1 = np.asarray(ar1).ravel()
+    ar2 = np.asarray(ar2).ravel()
+
+    # Ensure that iteration through object arrays yields size-1 arrays
+    if ar2.dtype == object:
+        ar2 = ar2.reshape(-1, 1)
+
+    if kind not in {None, 'sort', 'table'}:
+        raise ValueError(
+            f"Invalid kind: '{kind}'. Please use None, 'sort' or 'table'.")
+
+    # Can use the table method if all arrays are integers or boolean:
+    is_int_arrays = all(ar.dtype.kind in ("u", "i", "b") for ar in (ar1, ar2))
+    use_table_method = is_int_arrays and kind in {None, 'table'}
+
+    if use_table_method:
+        if ar2.size == 0:
+            if invert:
+                return np.ones_like(ar1, dtype=bool)
+            else:
+                return np.zeros_like(ar1, dtype=bool)
+
+        # Convert booleans to uint8 so we can use the fast integer algorithm
+        if ar1.dtype == bool:
+            ar1 = ar1.astype(np.uint8)
+        if ar2.dtype == bool:
+            ar2 = ar2.astype(np.uint8)
+
+        ar2_min = np.min(ar2)
+        ar2_max = np.max(ar2)
+
+        ar2_range = int(ar2_max) - int(ar2_min)
+
+        # Constraints on whether we can actually use the table method:
+        #  1. Assert memory usage is not too large
+        below_memory_constraint = ar2_range <= 6 * (ar1.size + ar2.size)
+        #  2. Check overflows for (ar2 - ar2_min); dtype=ar2.dtype
+        range_safe_from_overflow = ar2_range <= np.iinfo(ar2.dtype).max
+        #  3. Check overflows for (ar1 - ar2_min); dtype=ar1.dtype
+        if ar1.size > 0:
+            ar1_min = np.min(ar1)
+            ar1_max = np.max(ar1)
+
+            # After masking, the range of ar1 is guaranteed to be
+            # within the range of ar2:
+            ar1_upper = min(int(ar1_max), int(ar2_max))
+            ar1_lower = max(int(ar1_min), int(ar2_min))
+
+            range_safe_from_overflow &= all((
+                ar1_upper - int(ar2_min) <= np.iinfo(ar1.dtype).max,
+                ar1_lower - int(ar2_min) >= np.iinfo(ar1.dtype).min
+            ))
+
+        # Optimal performance is for approximately
+        # log10(size) > (log10(range) - 2.27) / 0.927.
+        # However, here we set the requirement that by default
+        # the intermediate array can only be 6x
+        # the combined memory allocation of the original
+        # arrays. See discussion on 
+        # https://github.com/numpy/numpy/pull/12065.
+
+        if (
+            range_safe_from_overflow and 
+            (below_memory_constraint or kind == 'table')
+        ):
+
+            if invert:
+                outgoing_array = np.ones_like(ar1, dtype=bool)
+            else:
+                outgoing_array = np.zeros_like(ar1, dtype=bool)
+
+            # Make elements 1 where the integer exists in ar2
+            if invert:
+                isin_helper_ar = np.ones(ar2_range + 1, dtype=bool)
+                isin_helper_ar[ar2 - ar2_min] = 0
+            else:
+                isin_helper_ar = np.zeros(ar2_range + 1, dtype=bool)
+                isin_helper_ar[ar2 - ar2_min] = 1
+
+            # Mask out elements we know won't work
+            basic_mask = (ar1 <= ar2_max) & (ar1 >= ar2_min)
+            outgoing_array[basic_mask] = isin_helper_ar[ar1[basic_mask] -
+                                                        ar2_min]
+
+            return outgoing_array
+        elif kind == 'table':  # not range_safe_from_overflow
+            raise RuntimeError(
+                "You have specified kind='table', "
+                "but the range of values in `ar2` or `ar1` exceed the "
+                "maximum integer of the datatype. "
+                "Please set `kind` to None or 'sort'."
+            )
+    elif kind == 'table':
+        raise ValueError(
+            "The 'table' method is only "
+            "supported for boolean or integer arrays. "
+            "Please select 'sort' or None for kind."
+        )
+
+
+    # Check if one of the arrays may contain arbitrary objects
+    contains_object = ar1.dtype.hasobject or ar2.dtype.hasobject
+
+    # This code is run when
+    # a) the first condition is true, making the code significantly faster
+    # b) the second condition is true (i.e. `ar1` or `ar2` may contain
+    #    arbitrary objects), since then sorting is not guaranteed to work
+    if len(ar2) < 10 * len(ar1) ** 0.145 or contains_object:
+        if invert:
+            mask = np.ones(len(ar1), dtype=bool)
+            for a in ar2:
+                mask &= (ar1 != a)
+        else:
+            mask = np.zeros(len(ar1), dtype=bool)
+            for a in ar2:
+                mask |= (ar1 == a)
+        return mask
+
+    # Otherwise use sorting
+    if not assume_unique:
+        ar1, rev_idx = np.unique(ar1, return_inverse=True)
+        ar2 = np.unique(ar2)
+
+    ar = np.concatenate((ar1, ar2))
+    # We need this to be a stable sort, so always use 'mergesort'
+    # here. The values from the first array should always come before
+    # the values from the second array.
+    order = ar.argsort(kind='mergesort')
+    sar = ar[order]
+    if invert:
+        bool_ar = (sar[1:] != sar[:-1])
+    else:
+        bool_ar = (sar[1:] == sar[:-1])
+    flag = np.concatenate((bool_ar, [invert]))
+    ret = np.empty(ar.shape, dtype=bool)
+    ret[order] = flag
+
+    if assume_unique:
+        return ret[:len(ar1)]
+    else:
+        return ret[rev_idx]
+
+
+def _isin_dispatcher(element, test_elements, assume_unique=None, invert=None,
+                     *, kind=None):
+    return (element, test_elements)
+
+
+@array_function_dispatch(_isin_dispatcher)
+def isin(element, test_elements, assume_unique=False, invert=False, *,
+         kind=None):
+    """
+    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))``.
+    kind : {None, 'sort', 'table'}, optional
+        The algorithm to use. This will not affect the final result,
+        but will affect the speed and memory use. The default, None,
+        will select automatically based on memory considerations.
+
+        * If 'sort', will use a mergesort-based approach. This will have
+          a memory usage of roughly 6 times the sum of the sizes of
+          `ar1` and `ar2`, not accounting for size of dtypes.
+        * If 'table', will use a lookup table approach similar
+          to a counting sort. This is only available for boolean and
+          integer arrays. This will have a memory usage of the
+          size of `ar1` plus the max-min value of `ar2`. `assume_unique`
+          has no effect when the 'table' option is used.
+        * If None, will automatically choose 'table' if
+          the required memory allocation is less than or equal to
+          6 times the sum of the sizes of `ar1` and `ar2`,
+          otherwise will use 'sort'. This is done to not use
+          a large amount of memory by default, even though
+          'table' may be faster in most cases. If 'table' is chosen,
+          `assume_unique` will have no effect.
+
+
+    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.
+
+    Using ``kind='table'`` tends to be faster than `kind='sort'` if the
+    following relationship is true:
+    ``log10(len(ar2)) > (log10(max(ar2)-min(ar2)) - 2.27) / 0.927``,
+    but may use greater memory. The default value for `kind` will
+    be automatically selected based only on memory usage, so one may
+    manually set ``kind='table'`` if memory constraints can be relaxed.
+
+    .. versionadded:: 1.13.0
+
+    Examples
+    --------
+    >>> element = 2*np.arange(4).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]])
+    """
+    element = np.asarray(element)
+    return in1d(element, test_elements, assume_unique=assume_unique,
+                invert=invert, kind=kind).reshape(element.shape)
+
+
+def _union1d_dispatcher(ar1, ar2):
+    return (ar1, ar2)
+
+
+@array_function_dispatch(_union1d_dispatcher)
+def union1d(ar1, ar2):
+    """
+    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])
+    """
+    return unique(np.concatenate((ar1, ar2), axis=None))
+
+
+def _setdiff1d_dispatcher(ar1, ar2, assume_unique=None):
+    return (ar1, ar2)
+
+
+@array_function_dispatch(_setdiff1d_dispatcher)
+def setdiff1d(ar1, ar2, assume_unique=False):
+    """
+    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])
+
+    """
+    if assume_unique:
+        ar1 = np.asarray(ar1).ravel()
+    else:
+        ar1 = unique(ar1)
+        ar2 = unique(ar2)
+    return ar1[in1d(ar1, ar2, assume_unique=True, invert=True)]

env-llmeval/lib/python3.10/site-packages/numpy/lib/arraysetops.pyi

@@ -0,0 +1,362 @@
+from typing import (
+    Literal as L,
+    Any,
+    TypeVar,
+    overload,
+    SupportsIndex,
+)
+
+from numpy import (
+    generic,
+    number,
+    bool_,
+    ushort,
+    ubyte,
+    uintc,
+    uint,
+    ulonglong,
+    short,
+    int8,
+    byte,
+    intc,
+    int_,
+    intp,
+    longlong,
+    half,
+    single,
+    double,
+    longdouble,
+    csingle,
+    cdouble,
+    clongdouble,
+    timedelta64,
+    datetime64,
+    object_,
+    str_,
+    bytes_,
+    void,
+)
+
+from numpy._typing import (
+    ArrayLike,
+    NDArray,
+    _ArrayLike,
+    _ArrayLikeBool_co,
+    _ArrayLikeDT64_co,
+    _ArrayLikeTD64_co,
+    _ArrayLikeObject_co,
+    _ArrayLikeNumber_co,
+)
+
+_SCT = TypeVar("_SCT", bound=generic)
+_NumberType = TypeVar("_NumberType", bound=number[Any])
+
+# Explicitly set all allowed values to prevent accidental castings to
+# abstract dtypes (their common super-type).
+#
+# Only relevant if two or more arguments are parametrized, (e.g. `setdiff1d`)
+# which could result in, for example, `int64` and `float64`producing a
+# `number[_64Bit]` array
+_SCTNoCast = TypeVar(
+    "_SCTNoCast",
+    bool_,
+    ushort,
+    ubyte,
+    uintc,
+    uint,
+    ulonglong,
+    short,
+    byte,
+    intc,
+    int_,
+    longlong,
+    half,
+    single,
+    double,
+    longdouble,
+    csingle,
+    cdouble,
+    clongdouble,
+    timedelta64,
+    datetime64,
+    object_,
+    str_,
+    bytes_,
+    void,
+)
+
+__all__: list[str]
+
+@overload
+def ediff1d(
+    ary: _ArrayLikeBool_co,
+    to_end: None | ArrayLike = ...,
+    to_begin: None | ArrayLike = ...,
+) -> NDArray[int8]: ...
+@overload
+def ediff1d(
+    ary: _ArrayLike[_NumberType],
+    to_end: None | ArrayLike = ...,
+    to_begin: None | ArrayLike = ...,
+) -> NDArray[_NumberType]: ...
+@overload
+def ediff1d(
+    ary: _ArrayLikeNumber_co,
+    to_end: None | ArrayLike = ...,
+    to_begin: None | ArrayLike = ...,
+) -> NDArray[Any]: ...
+@overload
+def ediff1d(
+    ary: _ArrayLikeDT64_co | _ArrayLikeTD64_co,
+    to_end: None | ArrayLike = ...,
+    to_begin: None | ArrayLike = ...,
+) -> NDArray[timedelta64]: ...
+@overload
+def ediff1d(
+    ary: _ArrayLikeObject_co,
+    to_end: None | ArrayLike = ...,
+    to_begin: None | ArrayLike = ...,
+) -> NDArray[object_]: ...
+
+@overload
+def unique(
+    ar: _ArrayLike[_SCT],
+    return_index: L[False] = ...,
+    return_inverse: L[False] = ...,
+    return_counts: L[False] = ...,
+    axis: None | SupportsIndex = ...,
+    *,
+    equal_nan: bool = ...,
+) -> NDArray[_SCT]: ...
+@overload
+def unique(
+    ar: ArrayLike,
+    return_index: L[False] = ...,
+    return_inverse: L[False] = ...,
+    return_counts: L[False] = ...,
+    axis: None | SupportsIndex = ...,
+    *,
+    equal_nan: bool = ...,
+) -> NDArray[Any]: ...
+@overload
+def unique(
+    ar: _ArrayLike[_SCT],
+    return_index: L[True] = ...,
+    return_inverse: L[False] = ...,
+    return_counts: L[False] = ...,
+    axis: None | SupportsIndex = ...,
+    *,
+    equal_nan: bool = ...,
+) -> tuple[NDArray[_SCT], NDArray[intp]]: ...
+@overload
+def unique(
+    ar: ArrayLike,
+    return_index: L[True] = ...,
+    return_inverse: L[False] = ...,
+    return_counts: L[False] = ...,
+    axis: None | SupportsIndex = ...,
+    *,
+    equal_nan: bool = ...,
+) -> tuple[NDArray[Any], NDArray[intp]]: ...
+@overload
+def unique(
+    ar: _ArrayLike[_SCT],
+    return_index: L[False] = ...,
+    return_inverse: L[True] = ...,
+    return_counts: L[False] = ...,
+    axis: None | SupportsIndex = ...,
+    *,
+    equal_nan: bool = ...,
+) -> tuple[NDArray[_SCT], NDArray[intp]]: ...
+@overload
+def unique(
+    ar: ArrayLike,
+    return_index: L[False] = ...,
+    return_inverse: L[True] = ...,
+    return_counts: L[False] = ...,
+    axis: None | SupportsIndex = ...,
+    *,
+    equal_nan: bool = ...,
+) -> tuple[NDArray[Any], NDArray[intp]]: ...
+@overload
+def unique(
+    ar: _ArrayLike[_SCT],
+    return_index: L[False] = ...,
+    return_inverse: L[False] = ...,
+    return_counts: L[True] = ...,
+    axis: None | SupportsIndex = ...,
+    *,
+    equal_nan: bool = ...,
+) -> tuple[NDArray[_SCT], NDArray[intp]]: ...
+@overload
+def unique(
+    ar: ArrayLike,
+    return_index: L[False] = ...,
+    return_inverse: L[False] = ...,
+    return_counts: L[True] = ...,
+    axis: None | SupportsIndex = ...,
+    *,
+    equal_nan: bool = ...,
+) -> tuple[NDArray[Any], NDArray[intp]]: ...
+@overload
+def unique(
+    ar: _ArrayLike[_SCT],
+    return_index: L[True] = ...,
+    return_inverse: L[True] = ...,
+    return_counts: L[False] = ...,
+    axis: None | SupportsIndex = ...,
+    *,
+    equal_nan: bool = ...,
+) -> tuple[NDArray[_SCT], NDArray[intp], NDArray[intp]]: ...
+@overload
+def unique(
+    ar: ArrayLike,
+    return_index: L[True] = ...,
+    return_inverse: L[True] = ...,
+    return_counts: L[False] = ...,
+    axis: None | SupportsIndex = ...,
+    *,
+    equal_nan: bool = ...,
+) -> tuple[NDArray[Any], NDArray[intp], NDArray[intp]]: ...
+@overload
+def unique(
+    ar: _ArrayLike[_SCT],
+    return_index: L[True] = ...,
+    return_inverse: L[False] = ...,
+    return_counts: L[True] = ...,
+    axis: None | SupportsIndex = ...,
+    *,
+    equal_nan: bool = ...,
+) -> tuple[NDArray[_SCT], NDArray[intp], NDArray[intp]]: ...
+@overload
+def unique(
+    ar: ArrayLike,
+    return_index: L[True] = ...,
+    return_inverse: L[False] = ...,
+    return_counts: L[True] = ...,
+    axis: None | SupportsIndex = ...,
+    *,
+    equal_nan: bool = ...,
+) -> tuple[NDArray[Any], NDArray[intp], NDArray[intp]]: ...
+@overload
+def unique(
+    ar: _ArrayLike[_SCT],
+    return_index: L[False] = ...,
+    return_inverse: L[True] = ...,
+    return_counts: L[True] = ...,
+    axis: None | SupportsIndex = ...,
+    *,
+    equal_nan: bool = ...,
+) -> tuple[NDArray[_SCT], NDArray[intp], NDArray[intp]]: ...
+@overload
+def unique(
+    ar: ArrayLike,
+    return_index: L[False] = ...,
+    return_inverse: L[True] = ...,
+    return_counts: L[True] = ...,
+    axis: None | SupportsIndex = ...,
+    *,
+    equal_nan: bool = ...,
+) -> tuple[NDArray[Any], NDArray[intp], NDArray[intp]]: ...
+@overload
+def unique(
+    ar: _ArrayLike[_SCT],
+    return_index: L[True] = ...,
+    return_inverse: L[True] = ...,
+    return_counts: L[True] = ...,
+    axis: None | SupportsIndex = ...,
+    *,
+    equal_nan: bool = ...,
+) -> tuple[NDArray[_SCT], NDArray[intp], NDArray[intp], NDArray[intp]]: ...
+@overload
+def unique(
+    ar: ArrayLike,
+    return_index: L[True] = ...,
+    return_inverse: L[True] = ...,
+    return_counts: L[True] = ...,
+    axis: None | SupportsIndex = ...,
+    *,
+    equal_nan: bool = ...,
+) -> tuple[NDArray[Any], NDArray[intp], NDArray[intp], NDArray[intp]]: ...
+
+@overload
+def intersect1d(
+    ar1: _ArrayLike[_SCTNoCast],
+    ar2: _ArrayLike[_SCTNoCast],
+    assume_unique: bool = ...,
+    return_indices: L[False] = ...,
+) -> NDArray[_SCTNoCast]: ...
+@overload
+def intersect1d(
+    ar1: ArrayLike,
+    ar2: ArrayLike,
+    assume_unique: bool = ...,
+    return_indices: L[False] = ...,
+) -> NDArray[Any]: ...
+@overload
+def intersect1d(
+    ar1: _ArrayLike[_SCTNoCast],
+    ar2: _ArrayLike[_SCTNoCast],
+    assume_unique: bool = ...,
+    return_indices: L[True] = ...,
+) -> tuple[NDArray[_SCTNoCast], NDArray[intp], NDArray[intp]]: ...
+@overload
+def intersect1d(
+    ar1: ArrayLike,
+    ar2: ArrayLike,
+    assume_unique: bool = ...,
+    return_indices: L[True] = ...,
+) -> tuple[NDArray[Any], NDArray[intp], NDArray[intp]]: ...
+
+@overload
+def setxor1d(
+    ar1: _ArrayLike[_SCTNoCast],
+    ar2: _ArrayLike[_SCTNoCast],
+    assume_unique: bool = ...,
+) -> NDArray[_SCTNoCast]: ...
+@overload
+def setxor1d(
+    ar1: ArrayLike,
+    ar2: ArrayLike,
+    assume_unique: bool = ...,
+) -> NDArray[Any]: ...
+
+def in1d(
+    ar1: ArrayLike,
+    ar2: ArrayLike,
+    assume_unique: bool = ...,
+    invert: bool = ...,
+) -> NDArray[bool_]: ...
+
+def isin(
+    element: ArrayLike,
+    test_elements: ArrayLike,
+    assume_unique: bool = ...,
+    invert: bool = ...,
+    *,
+    kind: None | str = ...,
+) -> NDArray[bool_]: ...
+
+@overload
+def union1d(
+    ar1: _ArrayLike[_SCTNoCast],
+    ar2: _ArrayLike[_SCTNoCast],
+) -> NDArray[_SCTNoCast]: ...
+@overload
+def union1d(
+    ar1: ArrayLike,
+    ar2: ArrayLike,
+) -> NDArray[Any]: ...
+
+@overload
+def setdiff1d(
+    ar1: _ArrayLike[_SCTNoCast],
+    ar2: _ArrayLike[_SCTNoCast],
+    assume_unique: bool = ...,
+) -> NDArray[_SCTNoCast]: ...
+@overload
+def setdiff1d(
+    ar1: ArrayLike,
+    ar2: ArrayLike,
+    assume_unique: bool = ...,
+) -> NDArray[Any]: ...

env-llmeval/lib/python3.10/site-packages/numpy/lib/arrayterator.py

@@ -0,0 +1,219 @@
+"""
+A buffered iterator for big arrays.
+
+This module solves the problem of iterating over a big file-based array
+without having to read it into memory. The `Arrayterator` class wraps
+an array object, and when iterated it will return sub-arrays with at most
+a user-specified number of elements.
+
+"""
+from operator import mul
+from functools import reduce
+
+__all__ = ['Arrayterator']
+
+
+class Arrayterator:
+    """
+    Buffered iterator for big arrays.
+
+    `Arrayterator` creates a buffered iterator for reading big arrays in small
+    contiguous blocks. The class is useful for objects stored in the
+    file system. It allows iteration over the object *without* reading
+    everything in memory; instead, small blocks are read and iterated over.
+
+    `Arrayterator` can be used with any object that supports multidimensional
+    slices. This includes NumPy arrays, but also variables from
+    Scientific.IO.NetCDF or pynetcdf for example.
+
+    Parameters
+    ----------
+    var : array_like
+        The object to iterate over.
+    buf_size : int, optional
+        The buffer size. If `buf_size` is supplied, the maximum amount of
+        data that will be read into memory is `buf_size` elements.
+        Default is None, which will read as many element as possible
+        into memory.
+
+    Attributes
+    ----------
+    var
+    buf_size
+    start
+    stop
+    step
+    shape
+    flat
+
+    See Also
+    --------
+    ndenumerate : Multidimensional array iterator.
+    flatiter : Flat array iterator.
+    memmap : Create a memory-map to an array stored in a binary file on disk.
+
+    Notes
+    -----
+    The algorithm works by first finding a "running dimension", along which
+    the blocks will be extracted. Given an array of dimensions
+    ``(d1, d2, ..., dn)``, e.g. if `buf_size` is smaller than ``d1``, the
+    first dimension will be used. If, on the other hand,
+    ``d1 < buf_size < d1*d2`` the second dimension will be used, and so on.
+    Blocks are extracted along this dimension, and when the last block is
+    returned the process continues from the next dimension, until all
+    elements have been read.
+
+    Examples
+    --------
+    >>> a = np.arange(3 * 4 * 5 * 6).reshape(3, 4, 5, 6)
+    >>> a_itor = np.lib.Arrayterator(a, 2)
+    >>> a_itor.shape
+    (3, 4, 5, 6)
+
+    Now we can iterate over ``a_itor``, and it will return arrays of size
+    two. Since `buf_size` was smaller than any dimension, the first
+    dimension will be iterated over first:
+
+    >>> for subarr in a_itor:
+    ...     if not subarr.all():
+    ...         print(subarr, subarr.shape) # doctest: +SKIP
+    >>> # [[[[0 1]]]] (1, 1, 1, 2)
+
+    """
+
+    def __init__(self, var, buf_size=None):
+        self.var = var
+        self.buf_size = buf_size
+
+        self.start = [0 for dim in var.shape]
+        self.stop = [dim for dim in var.shape]
+        self.step = [1 for dim in var.shape]
+
+    def __getattr__(self, attr):
+        return getattr(self.var, attr)
+
+    def __getitem__(self, index):
+        """
+        Return a new arrayterator.
+
+        """
+        # Fix index, handling ellipsis and incomplete slices.
+        if not isinstance(index, tuple):
+            index = (index,)
+        fixed = []
+        length, dims = len(index), self.ndim
+        for slice_ in index:
+            if slice_ is Ellipsis:
+                fixed.extend([slice(None)] * (dims-length+1))
+                length = len(fixed)
+            elif isinstance(slice_, int):
+                fixed.append(slice(slice_, slice_+1, 1))
+            else:
+                fixed.append(slice_)
+        index = tuple(fixed)
+        if len(index) < dims:
+            index += (slice(None),) * (dims-len(index))
+
+        # Return a new arrayterator object.
+        out = self.__class__(self.var, self.buf_size)
+        for i, (start, stop, step, slice_) in enumerate(
+                zip(self.start, self.stop, self.step, index)):
+            out.start[i] = start + (slice_.start or 0)
+            out.step[i] = step * (slice_.step or 1)
+            out.stop[i] = start + (slice_.stop or stop-start)
+            out.stop[i] = min(stop, out.stop[i])
+        return out
+
+    def __array__(self):
+        """
+        Return corresponding data.
+
+        """
+        slice_ = tuple(slice(*t) for t in zip(
+                self.start, self.stop, self.step))
+        return self.var[slice_]
+
+    @property
+    def flat(self):
+        """
+        A 1-D flat iterator for Arrayterator objects.
+
+        This iterator returns elements of the array to be iterated over in
+        `Arrayterator` one by one. It is similar to `flatiter`.
+
+        See Also
+        --------
+        Arrayterator
+        flatiter
+
+        Examples
+        --------
+        >>> a = np.arange(3 * 4 * 5 * 6).reshape(3, 4, 5, 6)
+        >>> a_itor = np.lib.Arrayterator(a, 2)
+
+        >>> for subarr in a_itor.flat:
+        ...     if not subarr:
+        ...         print(subarr, type(subarr))
+        ...
+        0 <class 'numpy.int64'>
+
+        """
+        for block in self:
+            yield from block.flat
+
+    @property
+    def shape(self):
+        """
+        The shape of the array to be iterated over.
+
+        For an example, see `Arrayterator`.
+
+        """
+        return tuple(((stop-start-1)//step+1) for start, stop, step in
+                zip(self.start, self.stop, self.step))
+
+    def __iter__(self):
+        # Skip arrays with degenerate dimensions
+        if [dim for dim in self.shape if dim <= 0]:
+            return
+
+        start = self.start[:]
+        stop = self.stop[:]
+        step = self.step[:]
+        ndims = self.var.ndim
+
+        while True:
+            count = self.buf_size or reduce(mul, self.shape)
+
+            # iterate over each dimension, looking for the
+            # running dimension (ie, the dimension along which
+            # the blocks will be built from)
+            rundim = 0
+            for i in range(ndims-1, -1, -1):
+                # if count is zero we ran out of elements to read
+                # along higher dimensions, so we read only a single position
+                if count == 0:
+                    stop[i] = start[i]+1
+                elif count <= self.shape[i]:
+                    # limit along this dimension
+                    stop[i] = start[i] + count*step[i]
+                    rundim = i
+                else:
+                    # read everything along this dimension
+                    stop[i] = self.stop[i]
+                stop[i] = min(self.stop[i], stop[i])
+                count = count//self.shape[i]
+
+            # yield a block
+            slice_ = tuple(slice(*t) for t in zip(start, stop, step))
+            yield self.var[slice_]
+
+            # Update start position, taking care of overflow to
+            # other dimensions
+            start[rundim] = stop[rundim]  # start where we stopped
+            for i in range(ndims-1, 0, -1):
+                if start[i] >= self.stop[i]:
+                    start[i] = self.start[i]
+                    start[i-1] += self.step[i-1]
+            if start[0] >= self.stop[0]:
+                return

env-llmeval/lib/python3.10/site-packages/numpy/lib/format.py

@@ -0,0 +1,976 @@
+"""
+Binary serialization
+
+NPY format
+==========
+
+A simple format for saving numpy arrays to disk with the full
+information about them.
+
+The ``.npy`` format is the standard binary file format in NumPy for
+persisting a *single* arbitrary NumPy array on disk. The format stores all
+of the shape and dtype information necessary to reconstruct the array
+correctly even on another machine with a different architecture.
+The format is designed to be as simple as possible while achieving
+its limited goals.
+
+The ``.npz`` format is the standard format for persisting *multiple* NumPy
+arrays on disk. A ``.npz`` file is a zip file containing multiple ``.npy``
+files, one for each array.
+
+Capabilities
+------------
+
+- Can represent all NumPy arrays including nested record arrays and
+  object arrays.
+
+- Represents the data in its native binary form.
+
+- Supports Fortran-contiguous arrays directly.
+
+- Stores all of the necessary information to reconstruct the array
+  including shape and dtype on a machine of a different
+  architecture.  Both little-endian and big-endian arrays are
+  supported, and a file with little-endian numbers will yield
+  a little-endian array on any machine reading the file. The
+  types are described in terms of their actual sizes. For example,
+  if a machine with a 64-bit C "long int" writes out an array with
+  "long ints", a reading machine with 32-bit C "long ints" will yield
+  an array with 64-bit integers.
+
+- Is straightforward to reverse engineer. Datasets often live longer than
+  the programs that created them. A competent developer should be
+  able to create a solution in their preferred programming language to
+  read most ``.npy`` files that they have been given without much
+  documentation.
+
+- Allows memory-mapping of the data. See `open_memmap`.
+
+- Can be read from a filelike stream object instead of an actual file.
+
+- Stores object arrays, i.e. arrays containing elements that are arbitrary
+  Python objects. Files with object arrays are not to be mmapable, but
+  can be read and written to disk.
+
+Limitations
+-----------
+
+- Arbitrary subclasses of numpy.ndarray are not completely preserved.
+  Subclasses will be accepted for writing, but only the array data will
+  be written out. A regular numpy.ndarray object will be created
+  upon reading the file.
+
+.. warning::
+
+  Due to limitations in the interpretation of structured dtypes, dtypes
+  with fields with empty names will have the names replaced by 'f0', 'f1',
+  etc. Such arrays will not round-trip through the format entirely
+  accurately. The data is intact; only the field names will differ. We are
+  working on a fix for this. This fix will not require a change in the
+  file format. The arrays with such structures can still be saved and
+  restored, and the correct dtype may be restored by using the
+  ``loadedarray.view(correct_dtype)`` method.
+
+File extensions
+---------------
+
+We recommend using the ``.npy`` and ``.npz`` extensions for files saved
+in this format. This is by no means a requirement; applications may wish
+to use these file formats but use an extension specific to the
+application. In the absence of an obvious alternative, however,
+we suggest using ``.npy`` and ``.npz``.
+
+Version numbering
+-----------------
+
+The version numbering of these formats is independent of NumPy version
+numbering. If the format is upgraded, the code in `numpy.io` will still
+be able to read and write Version 1.0 files.
+
+Format Version 1.0
+------------------
+
+The first 6 bytes are a magic string: exactly ``\\x93NUMPY``.
+
+The next 1 byte is an unsigned byte: the major version number of the file
+format, e.g. ``\\x01``.
+
+The next 1 byte is an unsigned byte: the minor version number of the file
+format, e.g. ``\\x00``. Note: the version of the file format is not tied
+to the version of the numpy package.
+
+The next 2 bytes form a little-endian unsigned short int: the length of
+the header data HEADER_LEN.
+
+The next HEADER_LEN bytes form the header data describing the array's
+format. It is an ASCII string which contains a Python literal expression
+of a dictionary. It is terminated by a newline (``\\n``) and padded with
+spaces (``\\x20``) to make the total of
+``len(magic string) + 2 + len(length) + HEADER_LEN`` be evenly divisible
+by 64 for alignment purposes.
+
+The dictionary contains three keys:
+
+    "descr" : dtype.descr
+      An object that can be passed as an argument to the `numpy.dtype`
+      constructor to create the array's dtype.
+    "fortran_order" : bool
+      Whether the array data is Fortran-contiguous or not. Since
+      Fortran-contiguous arrays are a common form of non-C-contiguity,
+      we allow them to be written directly to disk for efficiency.
+    "shape" : tuple of int
+      The shape of the array.
+
+For repeatability and readability, the dictionary keys are sorted in
+alphabetic order. This is for convenience only. A writer SHOULD implement
+this if possible. A reader MUST NOT depend on this.
+
+Following the header comes the array data. If the dtype contains Python
+objects (i.e. ``dtype.hasobject is True``), then the data is a Python
+pickle of the array. Otherwise the data is the contiguous (either C-
+or Fortran-, depending on ``fortran_order``) bytes of the array.
+Consumers can figure out the number of bytes by multiplying the number
+of elements given by the shape (noting that ``shape=()`` means there is
+1 element) by ``dtype.itemsize``.
+
+Format Version 2.0
+------------------
+
+The version 1.0 format only allowed the array header to have a total size of
+65535 bytes.  This can be exceeded by structured arrays with a large number of
+columns.  The version 2.0 format extends the header size to 4 GiB.
+`numpy.save` will automatically save in 2.0 format if the data requires it,
+else it will always use the more compatible 1.0 format.
+
+The description of the fourth element of the header therefore has become:
+"The next 4 bytes form a little-endian unsigned int: the length of the header
+data HEADER_LEN."
+
+Format Version 3.0
+------------------
+
+This version replaces the ASCII string (which in practice was latin1) with
+a utf8-encoded string, so supports structured types with any unicode field
+names.
+
+Notes
+-----
+The ``.npy`` format, including motivation for creating it and a comparison of
+alternatives, is described in the
+:doc:`"npy-format" NEP <neps:nep-0001-npy-format>`, however details have
+evolved with time and this document is more current.
+
+"""
+import numpy
+import warnings
+from numpy.lib.utils import safe_eval, drop_metadata
+from numpy.compat import (
+    isfileobj, os_fspath, pickle
+    )
+
+
+__all__ = []
+
+
+EXPECTED_KEYS = {'descr', 'fortran_order', 'shape'}
+MAGIC_PREFIX = b'\x93NUMPY'
+MAGIC_LEN = len(MAGIC_PREFIX) + 2
+ARRAY_ALIGN = 64 # plausible values are powers of 2 between 16 and 4096
+BUFFER_SIZE = 2**18  # size of buffer for reading npz files in bytes
+# allow growth within the address space of a 64 bit machine along one axis
+GROWTH_AXIS_MAX_DIGITS = 21  # = len(str(8*2**64-1)) hypothetical int1 dtype
+
+# difference between version 1.0 and 2.0 is a 4 byte (I) header length
+# instead of 2 bytes (H) allowing storage of large structured arrays
+_header_size_info = {
+    (1, 0): ('<H', 'latin1'),
+    (2, 0): ('<I', 'latin1'),
+    (3, 0): ('<I', 'utf8'),
+}
+
+# Python's literal_eval is not actually safe for large inputs, since parsing
+# may become slow or even cause interpreter crashes.
+# This is an arbitrary, low limit which should make it safe in practice.
+_MAX_HEADER_SIZE = 10000
+
+def _check_version(version):
+    if version not in [(1, 0), (2, 0), (3, 0), None]:
+        msg = "we only support format version (1,0), (2,0), and (3,0), not %s"
+        raise ValueError(msg % (version,))
+
+def magic(major, minor):
+    """ Return the magic string for the given file format version.
+
+    Parameters
+    ----------
+    major : int in [0, 255]
+    minor : int in [0, 255]
+
+    Returns
+    -------
+    magic : str
+
+    Raises
+    ------
+    ValueError if the version cannot be formatted.
+    """
+    if major < 0 or major > 255:
+        raise ValueError("major version must be 0 <= major < 256")
+    if minor < 0 or minor > 255:
+        raise ValueError("minor version must be 0 <= minor < 256")
+    return MAGIC_PREFIX + bytes([major, minor])
+
+def read_magic(fp):
+    """ Read the magic string to get the version of the file format.
+
+    Parameters
+    ----------
+    fp : filelike object
+
+    Returns
+    -------
+    major : int
+    minor : int
+    """
+    magic_str = _read_bytes(fp, MAGIC_LEN, "magic string")
+    if magic_str[:-2] != MAGIC_PREFIX:
+        msg = "the magic string is not correct; expected %r, got %r"
+        raise ValueError(msg % (MAGIC_PREFIX, magic_str[:-2]))
+    major, minor = magic_str[-2:]
+    return major, minor
+
+
+def dtype_to_descr(dtype):
+    """
+    Get a serializable descriptor from the dtype.
+
+    The .descr attribute of a dtype object cannot be round-tripped through
+    the dtype() constructor. Simple types, like dtype('float32'), have
+    a descr which looks like a record array with one field with '' as
+    a name. The dtype() constructor interprets this as a request to give
+    a default name.  Instead, we construct descriptor that can be passed to
+    dtype().
+
+    Parameters
+    ----------
+    dtype : dtype
+        The dtype of the array that will be written to disk.
+
+    Returns
+    -------
+    descr : object
+        An object that can be passed to `numpy.dtype()` in order to
+        replicate the input dtype.
+
+    """
+    # NOTE: that drop_metadata may not return the right dtype e.g. for user
+    #       dtypes.  In that case our code below would fail the same, though.
+    new_dtype = drop_metadata(dtype)
+    if new_dtype is not dtype:
+        warnings.warn("metadata on a dtype is not saved to an npy/npz. "
+                      "Use another format (such as pickle) to store it.",
+                      UserWarning, stacklevel=2)
+    if dtype.names is not None:
+        # This is a record array. The .descr is fine.  XXX: parts of the
+        # record array with an empty name, like padding bytes, still get
+        # fiddled with. This needs to be fixed in the C implementation of
+        # dtype().
+        return dtype.descr
+    else:
+        return dtype.str
+
+def descr_to_dtype(descr):
+    """
+    Returns a dtype based off the given description.
+
+    This is essentially the reverse of `dtype_to_descr()`. It will remove
+    the valueless padding fields created by, i.e. simple fields like
+    dtype('float32'), and then convert the description to its corresponding
+    dtype.
+
+    Parameters
+    ----------
+    descr : object
+        The object retrieved by dtype.descr. Can be passed to
+        `numpy.dtype()` in order to replicate the input dtype.
+
+    Returns
+    -------
+    dtype : dtype
+        The dtype constructed by the description.
+
+    """
+    if isinstance(descr, str):
+        # No padding removal needed
+        return numpy.dtype(descr)
+    elif isinstance(descr, tuple):
+        # subtype, will always have a shape descr[1]
+        dt = descr_to_dtype(descr[0])
+        return numpy.dtype((dt, descr[1]))
+
+    titles = []
+    names = []
+    formats = []
+    offsets = []
+    offset = 0
+    for field in descr:
+        if len(field) == 2:
+            name, descr_str = field
+            dt = descr_to_dtype(descr_str)
+        else:
+            name, descr_str, shape = field
+            dt = numpy.dtype((descr_to_dtype(descr_str), shape))
+
+        # Ignore padding bytes, which will be void bytes with '' as name
+        # Once support for blank names is removed, only "if name == ''" needed)
+        is_pad = (name == '' and dt.type is numpy.void and dt.names is None)
+        if not is_pad:
+            title, name = name if isinstance(name, tuple) else (None, name)
+            titles.append(title)
+            names.append(name)
+            formats.append(dt)
+            offsets.append(offset)
+        offset += dt.itemsize
+
+    return numpy.dtype({'names': names, 'formats': formats, 'titles': titles,
+                        'offsets': offsets, 'itemsize': offset})
+
+def header_data_from_array_1_0(array):
+    """ Get the dictionary of header metadata from a numpy.ndarray.
+
+    Parameters
+    ----------
+    array : numpy.ndarray
+
+    Returns
+    -------
+    d : dict
+        This has the appropriate entries for writing its string representation
+        to the header of the file.
+    """
+    d = {'shape': array.shape}
+    if array.flags.c_contiguous:
+        d['fortran_order'] = False
+    elif array.flags.f_contiguous:
+        d['fortran_order'] = True
+    else:
+        # Totally non-contiguous data. We will have to make it C-contiguous
+        # before writing. Note that we need to test for C_CONTIGUOUS first
+        # because a 1-D array is both C_CONTIGUOUS and F_CONTIGUOUS.
+        d['fortran_order'] = False
+
+    d['descr'] = dtype_to_descr(array.dtype)
+    return d
+
+
+def _wrap_header(header, version):
+    """
+    Takes a stringified header, and attaches the prefix and padding to it
+    """
+    import struct
+    assert version is not None
+    fmt, encoding = _header_size_info[version]
+    header = header.encode(encoding)
+    hlen = len(header) + 1
+    padlen = ARRAY_ALIGN - ((MAGIC_LEN + struct.calcsize(fmt) + hlen) % ARRAY_ALIGN)
+    try:
+        header_prefix = magic(*version) + struct.pack(fmt, hlen + padlen)
+    except struct.error:
+        msg = "Header length {} too big for version={}".format(hlen, version)
+        raise ValueError(msg) from None
+
+    # Pad the header with spaces and a final newline such that the magic
+    # string, the header-length short and the header are aligned on a
+    # ARRAY_ALIGN byte boundary.  This supports memory mapping of dtypes
+    # aligned up to ARRAY_ALIGN on systems like Linux where mmap()
+    # offset must be page-aligned (i.e. the beginning of the file).
+    return header_prefix + header + b' '*padlen + b'\n'
+
+
+def _wrap_header_guess_version(header):
+    """
+    Like `_wrap_header`, but chooses an appropriate version given the contents
+    """
+    try:
+        return _wrap_header(header, (1, 0))
+    except ValueError:
+        pass
+
+    try:
+        ret = _wrap_header(header, (2, 0))
+    except UnicodeEncodeError:
+        pass
+    else:
+        warnings.warn("Stored array in format 2.0. It can only be"
+                      "read by NumPy >= 1.9", UserWarning, stacklevel=2)
+        return ret
+
+    header = _wrap_header(header, (3, 0))
+    warnings.warn("Stored array in format 3.0. It can only be "
+                  "read by NumPy >= 1.17", UserWarning, stacklevel=2)
+    return header
+
+
+def _write_array_header(fp, d, version=None):
+    """ Write the header for an array and returns the version used
+
+    Parameters
+    ----------
+    fp : filelike object
+    d : dict
+        This has the appropriate entries for writing its string representation
+        to the header of the file.
+    version : tuple or None
+        None means use oldest that works. Providing an explicit version will
+        raise a ValueError if the format does not allow saving this data.
+        Default: None
+    """
+    header = ["{"]
+    for key, value in sorted(d.items()):
+        # Need to use repr here, since we eval these when reading
+        header.append("'%s': %s, " % (key, repr(value)))
+    header.append("}")
+    header = "".join(header)
+
+    # Add some spare space so that the array header can be modified in-place
+    # when changing the array size, e.g. when growing it by appending data at
+    # the end.
+    shape = d['shape']
+    header += " " * ((GROWTH_AXIS_MAX_DIGITS - len(repr(
+        shape[-1 if d['fortran_order'] else 0]
+    ))) if len(shape) > 0 else 0)
+
+    if version is None:
+        header = _wrap_header_guess_version(header)
+    else:
+        header = _wrap_header(header, version)
+    fp.write(header)
+
+def write_array_header_1_0(fp, d):
+    """ Write the header for an array using the 1.0 format.
+
+    Parameters
+    ----------
+    fp : filelike object
+    d : dict
+        This has the appropriate entries for writing its string
+        representation to the header of the file.
+    """
+    _write_array_header(fp, d, (1, 0))
+
+
+def write_array_header_2_0(fp, d):
+    """ Write the header for an array using the 2.0 format.
+        The 2.0 format allows storing very large structured arrays.
+
+    .. versionadded:: 1.9.0
+
+    Parameters
+    ----------
+    fp : filelike object
+    d : dict
+        This has the appropriate entries for writing its string
+        representation to the header of the file.
+    """
+    _write_array_header(fp, d, (2, 0))
+
+def read_array_header_1_0(fp, max_header_size=_MAX_HEADER_SIZE):
+    """
+    Read an array header from a filelike object using the 1.0 file format
+    version.
+
+    This will leave the file object located just after the header.
+
+    Parameters
+    ----------
+    fp : filelike object
+        A file object or something with a `.read()` method like a file.
+
+    Returns
+    -------
+    shape : tuple of int
+        The shape of the array.
+    fortran_order : bool
+        The array data will be written out directly if it is either
+        C-contiguous or Fortran-contiguous. Otherwise, it will be made
+        contiguous before writing it out.
+    dtype : dtype
+        The dtype of the file's data.
+    max_header_size : int, optional
+        Maximum allowed size of the header.  Large headers may not be safe
+        to load securely and thus require explicitly passing a larger value.
+        See :py:func:`ast.literal_eval()` for details.
+
+    Raises
+    ------
+    ValueError
+        If the data is invalid.
+
+    """
+    return _read_array_header(
+            fp, version=(1, 0), max_header_size=max_header_size)
+
+def read_array_header_2_0(fp, max_header_size=_MAX_HEADER_SIZE):
+    """
+    Read an array header from a filelike object using the 2.0 file format
+    version.
+
+    This will leave the file object located just after the header.
+
+    .. versionadded:: 1.9.0
+
+    Parameters
+    ----------
+    fp : filelike object
+        A file object or something with a `.read()` method like a file.
+    max_header_size : int, optional
+        Maximum allowed size of the header.  Large headers may not be safe
+        to load securely and thus require explicitly passing a larger value.
+        See :py:func:`ast.literal_eval()` for details.
+
+    Returns
+    -------
+    shape : tuple of int
+        The shape of the array.
+    fortran_order : bool
+        The array data will be written out directly if it is either
+        C-contiguous or Fortran-contiguous. Otherwise, it will be made
+        contiguous before writing it out.
+    dtype : dtype
+        The dtype of the file's data.
+
+    Raises
+    ------
+    ValueError
+        If the data is invalid.
+
+    """
+    return _read_array_header(
+            fp, version=(2, 0), max_header_size=max_header_size)
+
+
+def _filter_header(s):
+    """Clean up 'L' in npz header ints.
+
+    Cleans up the 'L' in strings representing integers. Needed to allow npz
+    headers produced in Python2 to be read in Python3.
+
+    Parameters
+    ----------
+    s : string
+        Npy file header.
+
+    Returns
+    -------
+    header : str
+        Cleaned up header.
+
+    """
+    import tokenize
+    from io import StringIO
+
+    tokens = []
+    last_token_was_number = False
+    for token in tokenize.generate_tokens(StringIO(s).readline):
+        token_type = token[0]
+        token_string = token[1]
+        if (last_token_was_number and
+                token_type == tokenize.NAME and
+                token_string == "L"):
+            continue
+        else:
+            tokens.append(token)
+        last_token_was_number = (token_type == tokenize.NUMBER)
+    return tokenize.untokenize(tokens)
+
+
+def _read_array_header(fp, version, max_header_size=_MAX_HEADER_SIZE):
+    """
+    see read_array_header_1_0
+    """
+    # Read an unsigned, little-endian short int which has the length of the
+    # header.
+    import struct
+    hinfo = _header_size_info.get(version)
+    if hinfo is None:
+        raise ValueError("Invalid version {!r}".format(version))
+    hlength_type, encoding = hinfo
+
+    hlength_str = _read_bytes(fp, struct.calcsize(hlength_type), "array header length")
+    header_length = struct.unpack(hlength_type, hlength_str)[0]
+    header = _read_bytes(fp, header_length, "array header")
+    header = header.decode(encoding)
+    if len(header) > max_header_size:
+        raise ValueError(
+            f"Header info length ({len(header)}) is large and may not be safe "
+            "to load securely.\n"
+            "To allow loading, adjust `max_header_size` or fully trust "
+            "the `.npy` file using `allow_pickle=True`.\n"
+            "For safety against large resource use or crashes, sandboxing "
+            "may be necessary.")
+
+    # The header is a pretty-printed string representation of a literal
+    # Python dictionary with trailing newlines padded to a ARRAY_ALIGN byte
+    # boundary. The keys are strings.
+    #   "shape" : tuple of int
+    #   "fortran_order" : bool
+    #   "descr" : dtype.descr
+    # Versions (2, 0) and (1, 0) could have been created by a Python 2
+    # implementation before header filtering was implemented.
+    #
+    # For performance reasons, we try without _filter_header first though
+    try:
+        d = safe_eval(header)
+    except SyntaxError as e:
+        if version <= (2, 0):
+            header = _filter_header(header)
+            try:
+                d = safe_eval(header)
+            except SyntaxError as e2:
+                msg = "Cannot parse header: {!r}"
+                raise ValueError(msg.format(header)) from e2
+            else:
+                warnings.warn(
+                    "Reading `.npy` or `.npz` file required additional "
+                    "header parsing as it was created on Python 2. Save the "
+                    "file again to speed up loading and avoid this warning.",
+                    UserWarning, stacklevel=4)
+        else:
+            msg = "Cannot parse header: {!r}"
+            raise ValueError(msg.format(header)) from e
+    if not isinstance(d, dict):
+        msg = "Header is not a dictionary: {!r}"
+        raise ValueError(msg.format(d))
+
+    if EXPECTED_KEYS != d.keys():
+        keys = sorted(d.keys())
+        msg = "Header does not contain the correct keys: {!r}"
+        raise ValueError(msg.format(keys))
+
+    # Sanity-check the values.
+    if (not isinstance(d['shape'], tuple) or
+            not all(isinstance(x, int) for x in d['shape'])):
+        msg = "shape is not valid: {!r}"
+        raise ValueError(msg.format(d['shape']))
+    if not isinstance(d['fortran_order'], bool):
+        msg = "fortran_order is not a valid bool: {!r}"
+        raise ValueError(msg.format(d['fortran_order']))
+    try:
+        dtype = descr_to_dtype(d['descr'])
+    except TypeError as e:
+        msg = "descr is not a valid dtype descriptor: {!r}"
+        raise ValueError(msg.format(d['descr'])) from e
+
+    return d['shape'], d['fortran_order'], dtype
+
+def write_array(fp, array, version=None, allow_pickle=True, pickle_kwargs=None):
+    """
+    Write an array to an NPY file, including a header.
+
+    If the array is neither C-contiguous nor Fortran-contiguous AND the
+    file_like object is not a real file object, this function will have to
+    copy data in memory.
+
+    Parameters
+    ----------
+    fp : file_like object
+        An open, writable file object, or similar object with a
+        ``.write()`` method.
+    array : ndarray
+        The array to write to disk.
+    version : (int, int) or None, optional
+        The version number of the format. None means use the oldest
+        supported version that is able to store the data.  Default: None
+    allow_pickle : bool, optional
+        Whether to allow writing pickled data. Default: True
+    pickle_kwargs : dict, optional
+        Additional keyword arguments to pass to pickle.dump, excluding
+        'protocol'. These are only useful when pickling objects in object
+        arrays on Python 3 to Python 2 compatible format.
+
+    Raises
+    ------
+    ValueError
+        If the array cannot be persisted. This includes the case of
+        allow_pickle=False and array being an object array.
+    Various other errors
+        If the array contains Python objects as part of its dtype, the
+        process of pickling them may raise various errors if the objects
+        are not picklable.
+
+    """
+    _check_version(version)
+    _write_array_header(fp, header_data_from_array_1_0(array), version)
+
+    if array.itemsize == 0:
+        buffersize = 0
+    else:
+        # Set buffer size to 16 MiB to hide the Python loop overhead.
+        buffersize = max(16 * 1024 ** 2 // array.itemsize, 1)
+
+    if array.dtype.hasobject:
+        # We contain Python objects so we cannot write out the data
+        # directly.  Instead, we will pickle it out
+        if not allow_pickle:
+            raise ValueError("Object arrays cannot be saved when "
+                             "allow_pickle=False")
+        if pickle_kwargs is None:
+            pickle_kwargs = {}
+        pickle.dump(array, fp, protocol=3, **pickle_kwargs)
+    elif array.flags.f_contiguous and not array.flags.c_contiguous:
+        if isfileobj(fp):
+            array.T.tofile(fp)
+        else:
+            for chunk in numpy.nditer(
+                    array, flags=['external_loop', 'buffered', 'zerosize_ok'],
+                    buffersize=buffersize, order='F'):
+                fp.write(chunk.tobytes('C'))
+    else:
+        if isfileobj(fp):
+            array.tofile(fp)
+        else:
+            for chunk in numpy.nditer(
+                    array, flags=['external_loop', 'buffered', 'zerosize_ok'],
+                    buffersize=buffersize, order='C'):
+                fp.write(chunk.tobytes('C'))
+
+
+def read_array(fp, allow_pickle=False, pickle_kwargs=None, *,
+               max_header_size=_MAX_HEADER_SIZE):
+    """
+    Read an array from an NPY file.
+
+    Parameters
+    ----------
+    fp : file_like object
+        If this is not a real file object, then this may take extra memory
+        and time.
+    allow_pickle : bool, optional
+        Whether to allow writing pickled data. Default: False
+
+        .. versionchanged:: 1.16.3
+            Made default False in response to CVE-2019-6446.
+
+    pickle_kwargs : dict
+        Additional keyword arguments to pass to pickle.load. These are only
+        useful when loading object arrays saved on Python 2 when using
+        Python 3.
+    max_header_size : int, optional
+        Maximum allowed size of the header.  Large headers may not be safe
+        to load securely and thus require explicitly passing a larger value.
+        See :py:func:`ast.literal_eval()` for details.
+        This option is ignored when `allow_pickle` is passed.  In that case
+        the file is by definition trusted and the limit is unnecessary.
+
+    Returns
+    -------
+    array : ndarray
+        The array from the data on disk.
+
+    Raises
+    ------
+    ValueError
+        If the data is invalid, or allow_pickle=False and the file contains
+        an object array.
+
+    """
+    if allow_pickle:
+        # Effectively ignore max_header_size, since `allow_pickle` indicates
+        # that the input is fully trusted.
+        max_header_size = 2**64
+
+    version = read_magic(fp)
+    _check_version(version)
+    shape, fortran_order, dtype = _read_array_header(
+            fp, version, max_header_size=max_header_size)
+    if len(shape) == 0:
+        count = 1
+    else:
+        count = numpy.multiply.reduce(shape, dtype=numpy.int64)
+
+    # Now read the actual data.
+    if dtype.hasobject:
+        # The array contained Python objects. We need to unpickle the data.
+        if not allow_pickle:
+            raise ValueError("Object arrays cannot be loaded when "
+                             "allow_pickle=False")
+        if pickle_kwargs is None:
+            pickle_kwargs = {}
+        try:
+            array = pickle.load(fp, **pickle_kwargs)
+        except UnicodeError as err:
+            # Friendlier error message
+            raise UnicodeError("Unpickling a python object failed: %r\n"
+                               "You may need to pass the encoding= option "
+                               "to numpy.load" % (err,)) from err
+    else:
+        if isfileobj(fp):
+            # We can use the fast fromfile() function.
+            array = numpy.fromfile(fp, dtype=dtype, count=count)
+        else:
+            # This is not a real file. We have to read it the
+            # memory-intensive way.
+            # crc32 module fails on reads greater than 2 ** 32 bytes,
+            # breaking large reads from gzip streams. Chunk reads to
+            # BUFFER_SIZE bytes to avoid issue and reduce memory overhead
+            # of the read. In non-chunked case count < max_read_count, so
+            # only one read is performed.
+
+            # Use np.ndarray instead of np.empty since the latter does
+            # not correctly instantiate zero-width string dtypes; see
+            # https://github.com/numpy/numpy/pull/6430
+            array = numpy.ndarray(count, dtype=dtype)
+
+            if dtype.itemsize > 0:
+                # If dtype.itemsize == 0 then there's nothing more to read
+                max_read_count = BUFFER_SIZE // min(BUFFER_SIZE, dtype.itemsize)
+
+                for i in range(0, count, max_read_count):
+                    read_count = min(max_read_count, count - i)
+                    read_size = int(read_count * dtype.itemsize)
+                    data = _read_bytes(fp, read_size, "array data")
+                    array[i:i+read_count] = numpy.frombuffer(data, dtype=dtype,
+                                                             count=read_count)
+
+        if fortran_order:
+            array.shape = shape[::-1]
+            array = array.transpose()
+        else:
+            array.shape = shape
+
+    return array
+
+
+def open_memmap(filename, mode='r+', dtype=None, shape=None,
+                fortran_order=False, version=None, *,
+                max_header_size=_MAX_HEADER_SIZE):
+    """
+    Open a .npy file as a memory-mapped array.
+
+    This may be used to read an existing file or create a new one.
+
+    Parameters
+    ----------
+    filename : str or path-like
+        The name of the file on disk.  This may *not* be a file-like
+        object.
+    mode : str, optional
+        The mode in which to open the file; the default is 'r+'.  In
+        addition to the standard file modes, 'c' is also accepted to mean
+        "copy on write."  See `memmap` for the available mode strings.
+    dtype : data-type, optional
+        The data type of the array if we are creating a new file in "write"
+        mode, if not, `dtype` is ignored.  The default value is None, which
+        results in a data-type of `float64`.
+    shape : tuple of int
+        The shape of the array if we are creating a new file in "write"
+        mode, in which case this parameter is required.  Otherwise, this
+        parameter is ignored and is thus optional.
+    fortran_order : bool, optional
+        Whether the array should be Fortran-contiguous (True) or
+        C-contiguous (False, the default) if we are creating a new file in
+        "write" mode.
+    version : tuple of int (major, minor) or None
+        If the mode is a "write" mode, then this is the version of the file
+        format used to create the file.  None means use the oldest
+        supported version that is able to store the data.  Default: None
+    max_header_size : int, optional
+        Maximum allowed size of the header.  Large headers may not be safe
+        to load securely and thus require explicitly passing a larger value.
+        See :py:func:`ast.literal_eval()` for details.
+
+    Returns
+    -------
+    marray : memmap
+        The memory-mapped array.
+
+    Raises
+    ------
+    ValueError
+        If the data or the mode is invalid.
+    OSError
+        If the file is not found or cannot be opened correctly.
+
+    See Also
+    --------
+    numpy.memmap
+
+    """
+    if isfileobj(filename):
+        raise ValueError("Filename must be a string or a path-like object."
+                         "  Memmap cannot use existing file handles.")
+
+    if 'w' in mode:
+        # We are creating the file, not reading it.
+        # Check if we ought to create the file.
+        _check_version(version)
+        # Ensure that the given dtype is an authentic dtype object rather
+        # than just something that can be interpreted as a dtype object.
+        dtype = numpy.dtype(dtype)
+        if dtype.hasobject:
+            msg = "Array can't be memory-mapped: Python objects in dtype."
+            raise ValueError(msg)
+        d = dict(
+            descr=dtype_to_descr(dtype),
+            fortran_order=fortran_order,
+            shape=shape,
+        )
+        # If we got here, then it should be safe to create the file.
+        with open(os_fspath(filename), mode+'b') as fp:
+            _write_array_header(fp, d, version)
+            offset = fp.tell()
+    else:
+        # Read the header of the file first.
+        with open(os_fspath(filename), 'rb') as fp:
+            version = read_magic(fp)
+            _check_version(version)
+
+            shape, fortran_order, dtype = _read_array_header(
+                    fp, version, max_header_size=max_header_size)
+            if dtype.hasobject:
+                msg = "Array can't be memory-mapped: Python objects in dtype."
+                raise ValueError(msg)
+            offset = fp.tell()
+
+    if fortran_order:
+        order = 'F'
+    else:
+        order = 'C'
+
+    # We need to change a write-only mode to a read-write mode since we've
+    # already written data to the file.
+    if mode == 'w+':
+        mode = 'r+'
+
+    marray = numpy.memmap(filename, dtype=dtype, shape=shape, order=order,
+        mode=mode, offset=offset)
+
+    return marray
+
+
+def _read_bytes(fp, size, error_template="ran out of data"):
+    """
+    Read from file-like object until size bytes are read.
+    Raises ValueError if not EOF is encountered before size bytes are read.
+    Non-blocking objects only supported if they derive from io objects.
+
+    Required as e.g. ZipExtFile in python 2.6 can return less data than
+    requested.
+    """
+    data = bytes()
+    while True:
+        # io files (default in python3) return None or raise on
+        # would-block, python2 file will truncate, probably nothing can be
+        # done about that.  note that regular files can't be non-blocking
+        try:
+            r = fp.read(size - len(data))
+            data += r
+            if len(r) == 0 or len(data) == size:
+                break
+        except BlockingIOError:
+            pass
+    if len(data) != size:
+        msg = "EOF: reading %s, expected %d bytes got %d"
+        raise ValueError(msg % (error_template, size, len(data)))
+    else:
+        return data

env-llmeval/lib/python3.10/site-packages/numpy/lib/format.pyi

@@ -0,0 +1,22 @@
+from typing import Any, Literal, Final
+
+__all__: list[str]
+
+EXPECTED_KEYS: Final[set[str]]
+MAGIC_PREFIX: Final[bytes]
+MAGIC_LEN: Literal[8]
+ARRAY_ALIGN: Literal[64]
+BUFFER_SIZE: Literal[262144]  # 2**18
+
+def magic(major, minor): ...
+def read_magic(fp): ...
+def dtype_to_descr(dtype): ...
+def descr_to_dtype(descr): ...
+def header_data_from_array_1_0(array): ...
+def write_array_header_1_0(fp, d): ...
+def write_array_header_2_0(fp, d): ...
+def read_array_header_1_0(fp): ...
+def read_array_header_2_0(fp): ...
+def write_array(fp, array, version=..., allow_pickle=..., pickle_kwargs=...): ...
+def read_array(fp, allow_pickle=..., pickle_kwargs=...): ...
+def open_memmap(filename, mode=..., dtype=..., shape=..., fortran_order=..., version=...): ...

env-llmeval/lib/python3.10/site-packages/numpy/lib/function_base.pyi

@@ -0,0 +1,697 @@
+import sys
+from collections.abc import Sequence, Iterator, Callable, Iterable
+from typing import (
+    Literal as L,
+    Any,
+    TypeVar,
+    overload,
+    Protocol,
+    SupportsIndex,
+    SupportsInt,
+)
+
+if sys.version_info >= (3, 10):
+    from typing import TypeGuard
+else:
+    from typing_extensions import TypeGuard
+
+from numpy import (
+    vectorize as vectorize,
+    ufunc,
+    generic,
+    floating,
+    complexfloating,
+    intp,
+    float64,
+    complex128,
+    timedelta64,
+    datetime64,
+    object_,
+    _OrderKACF,
+)
+
+from numpy._typing import (
+    NDArray,
+    ArrayLike,
+    DTypeLike,
+    _ShapeLike,
+    _ScalarLike_co,
+    _DTypeLike,
+    _ArrayLike,
+    _ArrayLikeInt_co,
+    _ArrayLikeFloat_co,
+    _ArrayLikeComplex_co,
+    _ArrayLikeTD64_co,
+    _ArrayLikeDT64_co,
+    _ArrayLikeObject_co,
+    _FloatLike_co,
+    _ComplexLike_co,
+)
+
+from numpy.core.function_base import (
+    add_newdoc as add_newdoc,
+)
+
+from numpy.core.multiarray import (
+    add_docstring as add_docstring,
+    bincount as bincount,
+)
+
+from numpy.core.umath import _add_newdoc_ufunc
+
+_T = TypeVar("_T")
+_T_co = TypeVar("_T_co", covariant=True)
+_SCT = TypeVar("_SCT", bound=generic)
+_ArrayType = TypeVar("_ArrayType", bound=NDArray[Any])
+
+_2Tuple = tuple[_T, _T]
+
+class _TrimZerosSequence(Protocol[_T_co]):
+    def __len__(self) -> int: ...
+    def __getitem__(self, key: slice, /) -> _T_co: ...
+    def __iter__(self) -> Iterator[Any]: ...
+
+class _SupportsWriteFlush(Protocol):
+    def write(self, s: str, /) -> object: ...
+    def flush(self) -> object: ...
+
+__all__: list[str]
+
+# NOTE: This is in reality a re-export of `np.core.umath._add_newdoc_ufunc`
+def add_newdoc_ufunc(ufunc: ufunc, new_docstring: str, /) -> None: ...
+
+@overload
+def rot90(
+    m: _ArrayLike[_SCT],
+    k: int = ...,
+    axes: tuple[int, int] = ...,
+) -> NDArray[_SCT]: ...
+@overload
+def rot90(
+    m: ArrayLike,
+    k: int = ...,
+    axes: tuple[int, int] = ...,
+) -> NDArray[Any]: ...
+
+@overload
+def flip(m: _SCT, axis: None = ...) -> _SCT: ...
+@overload
+def flip(m: _ScalarLike_co, axis: None = ...) -> Any: ...
+@overload
+def flip(m: _ArrayLike[_SCT], axis: None | _ShapeLike = ...) -> NDArray[_SCT]: ...
+@overload
+def flip(m: ArrayLike, axis: None | _ShapeLike = ...) -> NDArray[Any]: ...
+
+def iterable(y: object) -> TypeGuard[Iterable[Any]]: ...
+
+@overload
+def average(
+    a: _ArrayLikeFloat_co,
+    axis: None = ...,
+    weights: None | _ArrayLikeFloat_co= ...,
+    returned: L[False] = ...,
+    keepdims: L[False] = ...,
+) -> floating[Any]: ...
+@overload
+def average(
+    a: _ArrayLikeComplex_co,
+    axis: None = ...,
+    weights: None | _ArrayLikeComplex_co = ...,
+    returned: L[False] = ...,
+    keepdims: L[False] = ...,
+) -> complexfloating[Any, Any]: ...
+@overload
+def average(
+    a: _ArrayLikeObject_co,
+    axis: None = ...,
+    weights: None | Any = ...,
+    returned: L[False] = ...,
+    keepdims: L[False] = ...,
+) -> Any: ...
+@overload
+def average(
+    a: _ArrayLikeFloat_co,
+    axis: None = ...,
+    weights: None | _ArrayLikeFloat_co= ...,
+    returned: L[True] = ...,
+    keepdims: L[False] = ...,
+) -> _2Tuple[floating[Any]]: ...
+@overload
+def average(
+    a: _ArrayLikeComplex_co,
+    axis: None = ...,
+    weights: None | _ArrayLikeComplex_co = ...,
+    returned: L[True] = ...,
+    keepdims: L[False] = ...,
+) -> _2Tuple[complexfloating[Any, Any]]: ...
+@overload
+def average(
+    a: _ArrayLikeObject_co,
+    axis: None = ...,
+    weights: None | Any = ...,
+    returned: L[True] = ...,
+    keepdims: L[False] = ...,
+) -> _2Tuple[Any]: ...
+@overload
+def average(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: None | _ShapeLike = ...,
+    weights: None | Any = ...,
+    returned: L[False] = ...,
+    keepdims: bool = ...,
+) -> Any: ...
+@overload
+def average(
+    a: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    axis: None | _ShapeLike = ...,
+    weights: None | Any = ...,
+    returned: L[True] = ...,
+    keepdims: bool = ...,
+) -> _2Tuple[Any]: ...
+
+@overload
+def asarray_chkfinite(
+    a: _ArrayLike[_SCT],
+    dtype: None = ...,
+    order: _OrderKACF = ...,
+) -> NDArray[_SCT]: ...
+@overload
+def asarray_chkfinite(
+    a: object,
+    dtype: None = ...,
+    order: _OrderKACF = ...,
+) -> NDArray[Any]: ...
+@overload
+def asarray_chkfinite(
+    a: Any,
+    dtype: _DTypeLike[_SCT],
+    order: _OrderKACF = ...,
+) -> NDArray[_SCT]: ...
+@overload
+def asarray_chkfinite(
+    a: Any,
+    dtype: DTypeLike,
+    order: _OrderKACF = ...,
+) -> NDArray[Any]: ...
+
+# TODO: Use PEP 612 `ParamSpec` once mypy supports `Concatenate`
+# xref python/mypy#8645
+@overload
+def piecewise(
+    x: _ArrayLike[_SCT],
+    condlist: ArrayLike,
+    funclist: Sequence[Any | Callable[..., Any]],
+    *args: Any,
+    **kw: Any,
+) -> NDArray[_SCT]: ...
+@overload
+def piecewise(
+    x: ArrayLike,
+    condlist: ArrayLike,
+    funclist: Sequence[Any | Callable[..., Any]],
+    *args: Any,
+    **kw: Any,
+) -> NDArray[Any]: ...
+
+def select(
+    condlist: Sequence[ArrayLike],
+    choicelist: Sequence[ArrayLike],
+    default: ArrayLike = ...,
+) -> NDArray[Any]: ...
+
+@overload
+def copy(
+    a: _ArrayType,
+    order: _OrderKACF,
+    subok: L[True],
+) -> _ArrayType: ...
+@overload
+def copy(
+    a: _ArrayType,
+    order: _OrderKACF = ...,
+    *,
+    subok: L[True],
+) -> _ArrayType: ...
+@overload
+def copy(
+    a: _ArrayLike[_SCT],
+    order: _OrderKACF = ...,
+    subok: L[False] = ...,
+) -> NDArray[_SCT]: ...
+@overload
+def copy(
+    a: ArrayLike,
+    order: _OrderKACF = ...,
+    subok: L[False] = ...,
+) -> NDArray[Any]: ...
+
+def gradient(
+    f: ArrayLike,
+    *varargs: ArrayLike,
+    axis: None | _ShapeLike = ...,
+    edge_order: L[1, 2] = ...,
+) -> Any: ...
+
+@overload
+def diff(
+    a: _T,
+    n: L[0],
+    axis: SupportsIndex = ...,
+    prepend: ArrayLike = ...,
+    append: ArrayLike = ...,
+) -> _T: ...
+@overload
+def diff(
+    a: ArrayLike,
+    n: int = ...,
+    axis: SupportsIndex = ...,
+    prepend: ArrayLike = ...,
+    append: ArrayLike = ...,
+) -> NDArray[Any]: ...
+
+@overload
+def interp(
+    x: _ArrayLikeFloat_co,
+    xp: _ArrayLikeFloat_co,
+    fp: _ArrayLikeFloat_co,
+    left: None | _FloatLike_co = ...,
+    right: None | _FloatLike_co = ...,
+    period: None | _FloatLike_co = ...,
+) -> NDArray[float64]: ...
+@overload
+def interp(
+    x: _ArrayLikeFloat_co,
+    xp: _ArrayLikeFloat_co,
+    fp: _ArrayLikeComplex_co,
+    left: None | _ComplexLike_co = ...,
+    right: None | _ComplexLike_co = ...,
+    period: None | _FloatLike_co = ...,
+) -> NDArray[complex128]: ...
+
+@overload
+def angle(z: _ComplexLike_co, deg: bool = ...) -> floating[Any]: ...
+@overload
+def angle(z: object_, deg: bool = ...) -> Any: ...
+@overload
+def angle(z: _ArrayLikeComplex_co, deg: bool = ...) -> NDArray[floating[Any]]: ...
+@overload
+def angle(z: _ArrayLikeObject_co, deg: bool = ...) -> NDArray[object_]: ...
+
+@overload
+def unwrap(
+    p: _ArrayLikeFloat_co,
+    discont: None | float = ...,
+    axis: int = ...,
+    *,
+    period: float = ...,
+) -> NDArray[floating[Any]]: ...
+@overload
+def unwrap(
+    p: _ArrayLikeObject_co,
+    discont: None | float = ...,
+    axis: int = ...,
+    *,
+    period: float = ...,
+) -> NDArray[object_]: ...
+
+def sort_complex(a: ArrayLike) -> NDArray[complexfloating[Any, Any]]: ...
+
+def trim_zeros(
+    filt: _TrimZerosSequence[_T],
+    trim: L["f", "b", "fb", "bf"] = ...,
+) -> _T: ...
+
+@overload
+def extract(condition: ArrayLike, arr: _ArrayLike[_SCT]) -> NDArray[_SCT]: ...
+@overload
+def extract(condition: ArrayLike, arr: ArrayLike) -> NDArray[Any]: ...
+
+def place(arr: NDArray[Any], mask: ArrayLike, vals: Any) -> None: ...
+
+def disp(
+    mesg: object,
+    device: None | _SupportsWriteFlush = ...,
+    linefeed: bool = ...,
+) -> None: ...
+
+@overload
+def cov(
+    m: _ArrayLikeFloat_co,
+    y: None | _ArrayLikeFloat_co = ...,
+    rowvar: bool = ...,
+    bias: bool = ...,
+    ddof: None | SupportsIndex | SupportsInt = ...,
+    fweights: None | ArrayLike = ...,
+    aweights: None | ArrayLike = ...,
+    *,
+    dtype: None = ...,
+) -> NDArray[floating[Any]]: ...
+@overload
+def cov(
+    m: _ArrayLikeComplex_co,
+    y: None | _ArrayLikeComplex_co = ...,
+    rowvar: bool = ...,
+    bias: bool = ...,
+    ddof: None | SupportsIndex | SupportsInt = ...,
+    fweights: None | ArrayLike = ...,
+    aweights: None | ArrayLike = ...,
+    *,
+    dtype: None = ...,
+) -> NDArray[complexfloating[Any, Any]]: ...
+@overload
+def cov(
+    m: _ArrayLikeComplex_co,
+    y: None | _ArrayLikeComplex_co = ...,
+    rowvar: bool = ...,
+    bias: bool = ...,
+    ddof: None | SupportsIndex | SupportsInt = ...,
+    fweights: None | ArrayLike = ...,
+    aweights: None | ArrayLike = ...,
+    *,
+    dtype: _DTypeLike[_SCT],
+) -> NDArray[_SCT]: ...
+@overload
+def cov(
+    m: _ArrayLikeComplex_co,
+    y: None | _ArrayLikeComplex_co = ...,
+    rowvar: bool = ...,
+    bias: bool = ...,
+    ddof: None | SupportsIndex | SupportsInt = ...,
+    fweights: None | ArrayLike = ...,
+    aweights: None | ArrayLike = ...,
+    *,
+    dtype: DTypeLike,
+) -> NDArray[Any]: ...
+
+# NOTE `bias` and `ddof` have been deprecated
+@overload
+def corrcoef(
+    m: _ArrayLikeFloat_co,
+    y: None | _ArrayLikeFloat_co = ...,
+    rowvar: bool = ...,
+    *,
+    dtype: None = ...,
+) -> NDArray[floating[Any]]: ...
+@overload
+def corrcoef(
+    m: _ArrayLikeComplex_co,
+    y: None | _ArrayLikeComplex_co = ...,
+    rowvar: bool = ...,
+    *,
+    dtype: None = ...,
+) -> NDArray[complexfloating[Any, Any]]: ...
+@overload
+def corrcoef(
+    m: _ArrayLikeComplex_co,
+    y: None | _ArrayLikeComplex_co = ...,
+    rowvar: bool = ...,
+    *,
+    dtype: _DTypeLike[_SCT],
+) -> NDArray[_SCT]: ...
+@overload
+def corrcoef(
+    m: _ArrayLikeComplex_co,
+    y: None | _ArrayLikeComplex_co = ...,
+    rowvar: bool = ...,
+    *,
+    dtype: DTypeLike,
+) -> NDArray[Any]: ...
+
+def blackman(M: _FloatLike_co) -> NDArray[floating[Any]]: ...
+
+def bartlett(M: _FloatLike_co) -> NDArray[floating[Any]]: ...
+
+def hanning(M: _FloatLike_co) -> NDArray[floating[Any]]: ...
+
+def hamming(M: _FloatLike_co) -> NDArray[floating[Any]]: ...
+
+def i0(x: _ArrayLikeFloat_co) -> NDArray[floating[Any]]: ...
+
+def kaiser(
+    M: _FloatLike_co,
+    beta: _FloatLike_co,
+) -> NDArray[floating[Any]]: ...
+
+@overload
+def sinc(x: _FloatLike_co) -> floating[Any]: ...
+@overload
+def sinc(x: _ComplexLike_co) -> complexfloating[Any, Any]: ...
+@overload
+def sinc(x: _ArrayLikeFloat_co) -> NDArray[floating[Any]]: ...
+@overload
+def sinc(x: _ArrayLikeComplex_co) -> NDArray[complexfloating[Any, Any]]: ...
+
+# NOTE: Deprecated
+# def msort(a: ArrayLike) -> NDArray[Any]: ...
+
+@overload
+def median(
+    a: _ArrayLikeFloat_co,
+    axis: None = ...,
+    out: None = ...,
+    overwrite_input: bool = ...,
+    keepdims: L[False] = ...,
+) -> floating[Any]: ...
+@overload
+def median(
+    a: _ArrayLikeComplex_co,
+    axis: None = ...,
+    out: None = ...,
+    overwrite_input: bool = ...,
+    keepdims: L[False] = ...,
+) -> complexfloating[Any, Any]: ...
+@overload
+def median(
+    a: _ArrayLikeTD64_co,
+    axis: None = ...,
+    out: None = ...,
+    overwrite_input: bool = ...,
+    keepdims: L[False] = ...,
+) -> timedelta64: ...
+@overload
+def median(
+    a: _ArrayLikeObject_co,
+    axis: None = ...,
+    out: None = ...,
+    overwrite_input: bool = ...,
+    keepdims: L[False] = ...,
+) -> Any: ...
+@overload
+def median(
+    a: _ArrayLikeFloat_co | _ArrayLikeComplex_co | _ArrayLikeTD64_co | _ArrayLikeObject_co,
+    axis: None | _ShapeLike = ...,
+    out: None = ...,
+    overwrite_input: bool = ...,
+    keepdims: bool = ...,
+) -> Any: ...
+@overload
+def median(
+    a: _ArrayLikeFloat_co | _ArrayLikeComplex_co | _ArrayLikeTD64_co | _ArrayLikeObject_co,
+    axis: None | _ShapeLike = ...,
+    out: _ArrayType = ...,
+    overwrite_input: bool = ...,
+    keepdims: bool = ...,
+) -> _ArrayType: ...
+
+_MethodKind = L[
+    "inverted_cdf",
+    "averaged_inverted_cdf",
+    "closest_observation",
+    "interpolated_inverted_cdf",
+    "hazen",
+    "weibull",
+    "linear",
+    "median_unbiased",
+    "normal_unbiased",
+    "lower",
+    "higher",
+    "midpoint",
+    "nearest",
+]
+
+@overload
+def percentile(
+    a: _ArrayLikeFloat_co,
+    q: _FloatLike_co,
+    axis: None = ...,
+    out: None = ...,
+    overwrite_input: bool = ...,
+    method: _MethodKind = ...,
+    keepdims: L[False] = ...,
+) -> floating[Any]: ...
+@overload
+def percentile(
+    a: _ArrayLikeComplex_co,
+    q: _FloatLike_co,
+    axis: None = ...,
+    out: None = ...,
+    overwrite_input: bool = ...,
+    method: _MethodKind = ...,
+    keepdims: L[False] = ...,
+) -> complexfloating[Any, Any]: ...
+@overload
+def percentile(
+    a: _ArrayLikeTD64_co,
+    q: _FloatLike_co,
+    axis: None = ...,
+    out: None = ...,
+    overwrite_input: bool = ...,
+    method: _MethodKind = ...,
+    keepdims: L[False] = ...,
+) -> timedelta64: ...
+@overload
+def percentile(
+    a: _ArrayLikeDT64_co,
+    q: _FloatLike_co,
+    axis: None = ...,
+    out: None = ...,
+    overwrite_input: bool = ...,
+    method: _MethodKind = ...,
+    keepdims: L[False] = ...,
+) -> datetime64: ...
+@overload
+def percentile(
+    a: _ArrayLikeObject_co,
+    q: _FloatLike_co,
+    axis: None = ...,
+    out: None = ...,
+    overwrite_input: bool = ...,
+    method: _MethodKind = ...,
+    keepdims: L[False] = ...,
+) -> Any: ...
+@overload
+def percentile(
+    a: _ArrayLikeFloat_co,
+    q: _ArrayLikeFloat_co,
+    axis: None = ...,
+    out: None = ...,
+    overwrite_input: bool = ...,
+    method: _MethodKind = ...,
+    keepdims: L[False] = ...,
+) -> NDArray[floating[Any]]: ...
+@overload
+def percentile(
+    a: _ArrayLikeComplex_co,
+    q: _ArrayLikeFloat_co,
+    axis: None = ...,
+    out: None = ...,
+    overwrite_input: bool = ...,
+    method: _MethodKind = ...,
+    keepdims: L[False] = ...,
+) -> NDArray[complexfloating[Any, Any]]: ...
+@overload
+def percentile(
+    a: _ArrayLikeTD64_co,
+    q: _ArrayLikeFloat_co,
+    axis: None = ...,
+    out: None = ...,
+    overwrite_input: bool = ...,
+    method: _MethodKind = ...,
+    keepdims: L[False] = ...,
+) -> NDArray[timedelta64]: ...
+@overload
+def percentile(
+    a: _ArrayLikeDT64_co,
+    q: _ArrayLikeFloat_co,
+    axis: None = ...,
+    out: None = ...,
+    overwrite_input: bool = ...,
+    method: _MethodKind = ...,
+    keepdims: L[False] = ...,
+) -> NDArray[datetime64]: ...
+@overload
+def percentile(
+    a: _ArrayLikeObject_co,
+    q: _ArrayLikeFloat_co,
+    axis: None = ...,
+    out: None = ...,
+    overwrite_input: bool = ...,
+    method: _MethodKind = ...,
+    keepdims: L[False] = ...,
+) -> NDArray[object_]: ...
+@overload
+def percentile(
+    a: _ArrayLikeComplex_co | _ArrayLikeTD64_co | _ArrayLikeTD64_co | _ArrayLikeObject_co,
+    q: _ArrayLikeFloat_co,
+    axis: None | _ShapeLike = ...,
+    out: None = ...,
+    overwrite_input: bool = ...,
+    method: _MethodKind = ...,
+    keepdims: bool = ...,
+) -> Any: ...
+@overload
+def percentile(
+    a: _ArrayLikeComplex_co | _ArrayLikeTD64_co | _ArrayLikeTD64_co | _ArrayLikeObject_co,
+    q: _ArrayLikeFloat_co,
+    axis: None | _ShapeLike = ...,
+    out: _ArrayType = ...,
+    overwrite_input: bool = ...,
+    method: _MethodKind = ...,
+    keepdims: bool = ...,
+) -> _ArrayType: ...
+
+# NOTE: Not an alias, but they do have identical signatures
+# (that we can reuse)
+quantile = percentile
+
+# TODO: Returns a scalar for <= 1D array-likes; returns an ndarray otherwise
+def trapz(
+    y: _ArrayLikeComplex_co | _ArrayLikeTD64_co | _ArrayLikeObject_co,
+    x: None | _ArrayLikeComplex_co | _ArrayLikeTD64_co | _ArrayLikeObject_co = ...,
+    dx: float = ...,
+    axis: SupportsIndex = ...,
+) -> Any: ...
+
+def meshgrid(
+    *xi: ArrayLike,
+    copy: bool = ...,
+    sparse: bool = ...,
+    indexing: L["xy", "ij"] = ...,
+) -> list[NDArray[Any]]: ...
+
+@overload
+def delete(
+    arr: _ArrayLike[_SCT],
+    obj: slice | _ArrayLikeInt_co,
+    axis: None | SupportsIndex = ...,
+) -> NDArray[_SCT]: ...
+@overload
+def delete(
+    arr: ArrayLike,
+    obj: slice | _ArrayLikeInt_co,
+    axis: None | SupportsIndex = ...,
+) -> NDArray[Any]: ...
+
+@overload
+def insert(
+    arr: _ArrayLike[_SCT],
+    obj: slice | _ArrayLikeInt_co,
+    values: ArrayLike,
+    axis: None | SupportsIndex = ...,
+) -> NDArray[_SCT]: ...
+@overload
+def insert(
+    arr: ArrayLike,
+    obj: slice | _ArrayLikeInt_co,
+    values: ArrayLike,
+    axis: None | SupportsIndex = ...,
+) -> NDArray[Any]: ...
+
+def append(
+    arr: ArrayLike,
+    values: ArrayLike,
+    axis: None | SupportsIndex = ...,
+) -> NDArray[Any]: ...
+
+@overload
+def digitize(
+    x: _FloatLike_co,
+    bins: _ArrayLikeFloat_co,
+    right: bool = ...,
+) -> intp: ...
+@overload
+def digitize(
+    x: _ArrayLikeFloat_co,
+    bins: _ArrayLikeFloat_co,
+    right: bool = ...,
+) -> NDArray[intp]: ...

env-llmeval/lib/python3.10/site-packages/numpy/lib/histograms.py

@@ -0,0 +1,1072 @@
+"""
+Histogram-related functions
+"""
+import contextlib
+import functools
+import operator
+import warnings
+
+import numpy as np
+from numpy.core import overrides
+
+__all__ = ['histogram', 'histogramdd', 'histogram_bin_edges']
+
+array_function_dispatch = functools.partial(
+    overrides.array_function_dispatch, module='numpy')
+
+# range is a keyword argument to many functions, so save the builtin so they can
+# use it.
+_range = range
+
+
+def _ptp(x):
+    """Peak-to-peak value of x.
+
+    This implementation avoids the problem of signed integer arrays having a
+    peak-to-peak value that cannot be represented with the array's data type.
+    This function returns an unsigned value for signed integer arrays.
+    """
+    return _unsigned_subtract(x.max(), x.min())
+
+
+def _hist_bin_sqrt(x, range):
+    """
+    Square root histogram bin estimator.
+
+    Bin width is inversely proportional to the data size. Used by many
+    programs for its simplicity.
+
+    Parameters
+    ----------
+    x : array_like
+        Input data that is to be histogrammed, trimmed to range. May not
+        be empty.
+
+    Returns
+    -------
+    h : An estimate of the optimal bin width for the given data.
+    """
+    del range  # unused
+    return _ptp(x) / np.sqrt(x.size)
+
+
+def _hist_bin_sturges(x, range):
+    """
+    Sturges histogram bin estimator.
+
+    A very simplistic estimator based on the assumption of normality of
+    the data. This estimator has poor performance for non-normal data,
+    which becomes especially obvious for large data sets. The estimate
+    depends only on size of the data.
+
+    Parameters
+    ----------
+    x : array_like
+        Input data that is to be histogrammed, trimmed to range. May not
+        be empty.
+
+    Returns
+    -------
+    h : An estimate of the optimal bin width for the given data.
+    """
+    del range  # unused
+    return _ptp(x) / (np.log2(x.size) + 1.0)
+
+
+def _hist_bin_rice(x, range):
+    """
+    Rice histogram bin estimator.
+
+    Another simple estimator with no normality assumption. It has better
+    performance for large data than Sturges, but tends to overestimate
+    the number of bins. The number of bins is proportional to the cube
+    root of data size (asymptotically optimal). The estimate depends
+    only on size of the data.
+
+    Parameters
+    ----------
+    x : array_like
+        Input data that is to be histogrammed, trimmed to range. May not
+        be empty.
+
+    Returns
+    -------
+    h : An estimate of the optimal bin width for the given data.
+    """
+    del range  # unused
+    return _ptp(x) / (2.0 * x.size ** (1.0 / 3))
+
+
+def _hist_bin_scott(x, range):
+    """
+    Scott histogram bin estimator.
+
+    The binwidth is proportional to the standard deviation of the data
+    and inversely proportional to the cube root of data size
+    (asymptotically optimal).
+
+    Parameters
+    ----------
+    x : array_like
+        Input data that is to be histogrammed, trimmed to range. May not
+        be empty.
+
+    Returns
+    -------
+    h : An estimate of the optimal bin width for the given data.
+    """
+    del range  # unused
+    return (24.0 * np.pi**0.5 / x.size)**(1.0 / 3.0) * np.std(x)
+
+
+def _hist_bin_stone(x, range):
+    """
+    Histogram bin estimator based on minimizing the estimated integrated squared error (ISE).
+
+    The number of bins is chosen by minimizing the estimated ISE against the unknown true distribution.
+    The ISE is estimated using cross-validation and can be regarded as a generalization of Scott's rule.
+    https://en.wikipedia.org/wiki/Histogram#Scott.27s_normal_reference_rule
+
+    This paper by Stone appears to be the origination of this rule.
+    http://digitalassets.lib.berkeley.edu/sdtr/ucb/text/34.pdf
+
+    Parameters
+    ----------
+    x : array_like
+        Input data that is to be histogrammed, trimmed to range. May not
+        be empty.
+    range : (float, float)
+        The lower and upper range of the bins.
+
+    Returns
+    -------
+    h : An estimate of the optimal bin width for the given data.
+    """
+
+    n = x.size
+    ptp_x = _ptp(x)
+    if n <= 1 or ptp_x == 0:
+        return 0
+
+    def jhat(nbins):
+        hh = ptp_x / nbins
+        p_k = np.histogram(x, bins=nbins, range=range)[0] / n
+        return (2 - (n + 1) * p_k.dot(p_k)) / hh
+
+    nbins_upper_bound = max(100, int(np.sqrt(n)))
+    nbins = min(_range(1, nbins_upper_bound + 1), key=jhat)
+    if nbins == nbins_upper_bound:
+        warnings.warn("The number of bins estimated may be suboptimal.",
+                      RuntimeWarning, stacklevel=3)
+    return ptp_x / nbins
+
+
+def _hist_bin_doane(x, range):
+    """
+    Doane's histogram bin estimator.
+
+    Improved version of Sturges' formula which works better for
+    non-normal data. See
+    stats.stackexchange.com/questions/55134/doanes-formula-for-histogram-binning
+
+    Parameters
+    ----------
+    x : array_like
+        Input data that is to be histogrammed, trimmed to range. May not
+        be empty.
+
+    Returns
+    -------
+    h : An estimate of the optimal bin width for the given data.
+    """
+    del range  # unused
+    if x.size > 2:
+        sg1 = np.sqrt(6.0 * (x.size - 2) / ((x.size + 1.0) * (x.size + 3)))
+        sigma = np.std(x)
+        if sigma > 0.0:
+            # These three operations add up to
+            # g1 = np.mean(((x - np.mean(x)) / sigma)**3)
+            # but use only one temp array instead of three
+            temp = x - np.mean(x)
+            np.true_divide(temp, sigma, temp)
+            np.power(temp, 3, temp)
+            g1 = np.mean(temp)
+            return _ptp(x) / (1.0 + np.log2(x.size) +
+                                    np.log2(1.0 + np.absolute(g1) / sg1))
+    return 0.0
+
+
+def _hist_bin_fd(x, range):
+    """
+    The Freedman-Diaconis histogram bin estimator.
+
+    The Freedman-Diaconis rule uses interquartile range (IQR) to
+    estimate binwidth. It is considered a variation of the Scott rule
+    with more robustness as the IQR is less affected by outliers than
+    the standard deviation. However, the IQR depends on fewer points
+    than the standard deviation, so it is less accurate, especially for
+    long tailed distributions.
+
+    If the IQR is 0, this function returns 0 for the bin width.
+    Binwidth is inversely proportional to the cube root of data size
+    (asymptotically optimal).
+
+    Parameters
+    ----------
+    x : array_like
+        Input data that is to be histogrammed, trimmed to range. May not
+        be empty.
+
+    Returns
+    -------
+    h : An estimate of the optimal bin width for the given data.
+    """
+    del range  # unused
+    iqr = np.subtract(*np.percentile(x, [75, 25]))
+    return 2.0 * iqr * x.size ** (-1.0 / 3.0)
+
+
+def _hist_bin_auto(x, range):
+    """
+    Histogram bin estimator that uses the minimum width of the
+    Freedman-Diaconis and Sturges estimators if the FD bin width is non-zero.
+    If the bin width from the FD estimator is 0, the Sturges estimator is used.
+
+    The FD estimator is usually the most robust method, but its width
+    estimate tends to be too large for small `x` and bad for data with limited
+    variance. The Sturges estimator is quite good for small (<1000) datasets
+    and is the default in the R language. This method gives good off-the-shelf
+    behaviour.
+
+    .. versionchanged:: 1.15.0
+    If there is limited variance the IQR can be 0, which results in the
+    FD bin width being 0 too. This is not a valid bin width, so
+    ``np.histogram_bin_edges`` chooses 1 bin instead, which may not be optimal.
+    If the IQR is 0, it's unlikely any variance-based estimators will be of
+    use, so we revert to the Sturges estimator, which only uses the size of the
+    dataset in its calculation.
+
+    Parameters
+    ----------
+    x : array_like
+        Input data that is to be histogrammed, trimmed to range. May not
+        be empty.
+
+    Returns
+    -------
+    h : An estimate of the optimal bin width for the given data.
+
+    See Also
+    --------
+    _hist_bin_fd, _hist_bin_sturges
+    """
+    fd_bw = _hist_bin_fd(x, range)
+    sturges_bw = _hist_bin_sturges(x, range)
+    del range  # unused
+    if fd_bw:
+        return min(fd_bw, sturges_bw)
+    else:
+        # limited variance, so we return a len dependent bw estimator
+        return sturges_bw
+
+# Private dict initialized at module load time
+_hist_bin_selectors = {'stone': _hist_bin_stone,
+                       'auto': _hist_bin_auto,
+                       'doane': _hist_bin_doane,
+                       'fd': _hist_bin_fd,
+                       'rice': _hist_bin_rice,
+                       'scott': _hist_bin_scott,
+                       'sqrt': _hist_bin_sqrt,
+                       'sturges': _hist_bin_sturges}
+
+
+def _ravel_and_check_weights(a, weights):
+    """ Check a and weights have matching shapes, and ravel both """
+    a = np.asarray(a)
+
+    # Ensure that the array is a "subtractable" dtype
+    if a.dtype == np.bool_:
+        warnings.warn("Converting input from {} to {} for compatibility."
+                      .format(a.dtype, np.uint8),
+                      RuntimeWarning, stacklevel=3)
+        a = a.astype(np.uint8)
+
+    if weights is not None:
+        weights = np.asarray(weights)
+        if weights.shape != a.shape:
+            raise ValueError(
+                'weights should have the same shape as a.')
+        weights = weights.ravel()
+    a = a.ravel()
+    return a, weights
+
+
+def _get_outer_edges(a, range):
+    """
+    Determine the outer bin edges to use, from either the data or the range
+    argument
+    """
+    if range is not None:
+        first_edge, last_edge = range
+        if first_edge > last_edge:
+            raise ValueError(
+                'max must be larger than min in range parameter.')
+        if not (np.isfinite(first_edge) and np.isfinite(last_edge)):
+            raise ValueError(
+                "supplied range of [{}, {}] is not finite".format(first_edge, last_edge))
+    elif a.size == 0:
+        # handle empty arrays. Can't determine range, so use 0-1.
+        first_edge, last_edge = 0, 1
+    else:
+        first_edge, last_edge = a.min(), a.max()
+        if not (np.isfinite(first_edge) and np.isfinite(last_edge)):
+            raise ValueError(
+                "autodetected range of [{}, {}] is not finite".format(first_edge, last_edge))
+
+    # expand empty range to avoid divide by zero
+    if first_edge == last_edge:
+        first_edge = first_edge - 0.5
+        last_edge = last_edge + 0.5
+
+    return first_edge, last_edge
+
+
+def _unsigned_subtract(a, b):
+    """
+    Subtract two values where a >= b, and produce an unsigned result
+
+    This is needed when finding the difference between the upper and lower
+    bound of an int16 histogram
+    """
+    # coerce to a single type
+    signed_to_unsigned = {
+        np.byte: np.ubyte,
+        np.short: np.ushort,
+        np.intc: np.uintc,
+        np.int_: np.uint,
+        np.longlong: np.ulonglong
+    }
+    dt = np.result_type(a, b)
+    try:
+        dt = signed_to_unsigned[dt.type]
+    except KeyError:
+        return np.subtract(a, b, dtype=dt)
+    else:
+        # we know the inputs are integers, and we are deliberately casting
+        # signed to unsigned
+        return np.subtract(a, b, casting='unsafe', dtype=dt)
+
+
+def _get_bin_edges(a, bins, range, weights):
+    """
+    Computes the bins used internally by `histogram`.
+
+    Parameters
+    ==========
+    a : ndarray
+        Ravelled data array
+    bins, range
+        Forwarded arguments from `histogram`.
+    weights : ndarray, optional
+        Ravelled weights array, or None
+
+    Returns
+    =======
+    bin_edges : ndarray
+        Array of bin edges
+    uniform_bins : (Number, Number, int):
+        The upper bound, lowerbound, and number of bins, used in the optimized
+        implementation of `histogram` that works on uniform bins.
+    """
+    # parse the overloaded bins argument
+    n_equal_bins = None
+    bin_edges = None
+
+    if isinstance(bins, str):
+        bin_name = bins
+        # if `bins` is a string for an automatic method,
+        # this will replace it with the number of bins calculated
+        if bin_name not in _hist_bin_selectors:
+            raise ValueError(
+                "{!r} is not a valid estimator for `bins`".format(bin_name))
+        if weights is not None:
+            raise TypeError("Automated estimation of the number of "
+                            "bins is not supported for weighted data")
+
+        first_edge, last_edge = _get_outer_edges(a, range)
+
+        # truncate the range if needed
+        if range is not None:
+            keep = (a >= first_edge)
+            keep &= (a <= last_edge)
+            if not np.logical_and.reduce(keep):
+                a = a[keep]
+
+        if a.size == 0:
+            n_equal_bins = 1
+        else:
+            # Do not call selectors on empty arrays
+            width = _hist_bin_selectors[bin_name](a, (first_edge, last_edge))
+            if width:
+                n_equal_bins = int(np.ceil(_unsigned_subtract(last_edge, first_edge) / width))
+            else:
+                # Width can be zero for some estimators, e.g. FD when
+                # the IQR of the data is zero.
+                n_equal_bins = 1
+
+    elif np.ndim(bins) == 0:
+        try:
+            n_equal_bins = operator.index(bins)
+        except TypeError as e:
+            raise TypeError(
+                '`bins` must be an integer, a string, or an array') from e
+        if n_equal_bins < 1:
+            raise ValueError('`bins` must be positive, when an integer')
+
+        first_edge, last_edge = _get_outer_edges(a, range)
+
+    elif np.ndim(bins) == 1:
+        bin_edges = np.asarray(bins)
+        if np.any(bin_edges[:-1] > bin_edges[1:]):
+            raise ValueError(
+                '`bins` must increase monotonically, when an array')
+
+    else:
+        raise ValueError('`bins` must be 1d, when an array')
+
+    if n_equal_bins is not None:
+        # gh-10322 means that type resolution rules are dependent on array
+        # shapes. To avoid this causing problems, we pick a type now and stick
+        # with it throughout.
+        bin_type = np.result_type(first_edge, last_edge, a)
+        if np.issubdtype(bin_type, np.integer):
+            bin_type = np.result_type(bin_type, float)
+
+        # bin edges must be computed
+        bin_edges = np.linspace(
+            first_edge, last_edge, n_equal_bins + 1,
+            endpoint=True, dtype=bin_type)
+        return bin_edges, (first_edge, last_edge, n_equal_bins)
+    else:
+        return bin_edges, None
+
+
+def _search_sorted_inclusive(a, v):
+    """
+    Like `searchsorted`, but where the last item in `v` is placed on the right.
+
+    In the context of a histogram, this makes the last bin edge inclusive
+    """
+    return np.concatenate((
+        a.searchsorted(v[:-1], 'left'),
+        a.searchsorted(v[-1:], 'right')
+    ))
+
+
+def _histogram_bin_edges_dispatcher(a, bins=None, range=None, weights=None):
+    return (a, bins, weights)
+
+
+@array_function_dispatch(_histogram_bin_edges_dispatcher)
+def histogram_bin_edges(a, bins=10, range=None, weights=None):
+    r"""
+    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 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}\left(1 + \frac{|g_1|}{\sigma_{g_1}}\right)
+
+            g_1 = mean\left[\left(\frac{x - \mu}{\sigma}\right)^3\right]
+
+            \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.  ])
+
+    """
+    a, weights = _ravel_and_check_weights(a, weights)
+    bin_edges, _ = _get_bin_edges(a, bins, range, weights)
+    return bin_edges
+
+
+def _histogram_dispatcher(
+        a, bins=None, range=None, density=None, weights=None):
+    return (a, bins, weights)
+
+
+@array_function_dispatch(_histogram_dispatcher)
+def histogram(a, bins=10, range=None, density=None, weights=None):
+    r"""
+    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.
+    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.
+
+    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), bins=np.arange(5), 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)
+    >>> 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)  # 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()
+
+    """
+    a, weights = _ravel_and_check_weights(a, weights)
+
+    bin_edges, uniform_bins = _get_bin_edges(a, bins, range, weights)
+
+    # Histogram is an integer or a float array depending on the weights.
+    if weights is None:
+        ntype = np.dtype(np.intp)
+    else:
+        ntype = weights.dtype
+
+    # We set a block size, as this allows us to iterate over chunks when
+    # computing histograms, to minimize memory usage.
+    BLOCK = 65536
+
+    # The fast path uses bincount, but that only works for certain types
+    # of weight
+    simple_weights = (
+        weights is None or
+        np.can_cast(weights.dtype, np.double) or
+        np.can_cast(weights.dtype, complex)
+    )
+
+    if uniform_bins is not None and simple_weights:
+        # Fast algorithm for equal bins
+        # We now convert values of a to bin indices, under the assumption of
+        # equal bin widths (which is valid here).
+        first_edge, last_edge, n_equal_bins = uniform_bins
+
+        # Initialize empty histogram
+        n = np.zeros(n_equal_bins, ntype)
+
+        # Pre-compute histogram scaling factor
+        norm_numerator = n_equal_bins
+        norm_denom = _unsigned_subtract(last_edge, first_edge)
+
+        # We iterate over blocks here for two reasons: the first is that for
+        # large arrays, it is actually faster (for example for a 10^8 array it
+        # is 2x as fast) and it results in a memory footprint 3x lower in the
+        # limit of large arrays.
+        for i in _range(0, len(a), BLOCK):
+            tmp_a = a[i:i+BLOCK]
+            if weights is None:
+                tmp_w = None
+            else:
+                tmp_w = weights[i:i + BLOCK]
+
+            # Only include values in the right range
+            keep = (tmp_a >= first_edge)
+            keep &= (tmp_a <= last_edge)
+            if not np.logical_and.reduce(keep):
+                tmp_a = tmp_a[keep]
+                if tmp_w is not None:
+                    tmp_w = tmp_w[keep]
+
+            # This cast ensures no type promotions occur below, which gh-10322
+            # make unpredictable. Getting it wrong leads to precision errors
+            # like gh-8123.
+            tmp_a = tmp_a.astype(bin_edges.dtype, copy=False)
+
+            # Compute the bin indices, and for values that lie exactly on
+            # last_edge we need to subtract one
+            f_indices = ((_unsigned_subtract(tmp_a, first_edge) / norm_denom)
+                         * norm_numerator)
+            indices = f_indices.astype(np.intp)
+            indices[indices == n_equal_bins] -= 1
+
+            # The index computation is not guaranteed to give exactly
+            # consistent results within ~1 ULP of the bin edges.
+            decrement = tmp_a < bin_edges[indices]
+            indices[decrement] -= 1
+            # The last bin includes the right edge. The other bins do not.
+            increment = ((tmp_a >= bin_edges[indices + 1])
+                         & (indices != n_equal_bins - 1))
+            indices[increment] += 1
+
+            # We now compute the histogram using bincount
+            if ntype.kind == 'c':
+                n.real += np.bincount(indices, weights=tmp_w.real,
+                                      minlength=n_equal_bins)
+                n.imag += np.bincount(indices, weights=tmp_w.imag,
+                                      minlength=n_equal_bins)
+            else:
+                n += np.bincount(indices, weights=tmp_w,
+                                 minlength=n_equal_bins).astype(ntype)
+    else:
+        # Compute via cumulative histogram
+        cum_n = np.zeros(bin_edges.shape, ntype)
+        if weights is None:
+            for i in _range(0, len(a), BLOCK):
+                sa = np.sort(a[i:i+BLOCK])
+                cum_n += _search_sorted_inclusive(sa, bin_edges)
+        else:
+            zero = np.zeros(1, dtype=ntype)
+            for i in _range(0, len(a), BLOCK):
+                tmp_a = a[i:i+BLOCK]
+                tmp_w = weights[i:i+BLOCK]
+                sorting_index = np.argsort(tmp_a)
+                sa = tmp_a[sorting_index]
+                sw = tmp_w[sorting_index]
+                cw = np.concatenate((zero, sw.cumsum()))
+                bin_index = _search_sorted_inclusive(sa, bin_edges)
+                cum_n += cw[bin_index]
+
+        n = np.diff(cum_n)
+
+    if density:
+        db = np.array(np.diff(bin_edges), float)
+        return n/db/n.sum(), bin_edges
+
+    return n, bin_edges
+
+
+def _histogramdd_dispatcher(sample, bins=None, range=None, density=None,
+                            weights=None):
+    if hasattr(sample, 'shape'):  # same condition as used in histogramdd
+        yield sample
+    else:
+        yield from sample
+    with contextlib.suppress(TypeError):
+        yield from bins
+    yield weights
+
+
+@array_function_dispatch(_histogramdd_dispatcher)
+def histogramdd(sample, bins=10, range=None, density=None, weights=None):
+    """
+    Compute the multidimensional histogram of some data.
+
+    Parameters
+    ----------
+    sample : (N, D) array, or (N, D) 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``.
+    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 density is True. If density 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 density 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)
+
+    """
+
+    try:
+        # Sample is an ND-array.
+        N, D = sample.shape
+    except (AttributeError, ValueError):
+        # Sample is a sequence of 1D arrays.
+        sample = np.atleast_2d(sample).T
+        N, D = sample.shape
+
+    nbin = np.empty(D, np.intp)
+    edges = D*[None]
+    dedges = D*[None]
+    if weights is not None:
+        weights = np.asarray(weights)
+
+    try:
+        M = len(bins)
+        if M != D:
+            raise ValueError(
+                'The dimension of bins must be equal to the dimension of the '
+                'sample x.')
+    except TypeError:
+        # bins is an integer
+        bins = D*[bins]
+
+    # normalize the range argument
+    if range is None:
+        range = (None,) * D
+    elif len(range) != D:
+        raise ValueError('range argument must have one entry per dimension')
+
+    # Create edge arrays
+    for i in _range(D):
+        if np.ndim(bins[i]) == 0:
+            if bins[i] < 1:
+                raise ValueError(
+                    '`bins[{}]` must be positive, when an integer'.format(i))
+            smin, smax = _get_outer_edges(sample[:,i], range[i])
+            try:
+                n = operator.index(bins[i])
+
+            except TypeError as e:
+                raise TypeError(
+                	"`bins[{}]` must be an integer, when a scalar".format(i)
+                ) from e
+
+            edges[i] = np.linspace(smin, smax, n + 1)
+        elif np.ndim(bins[i]) == 1:
+            edges[i] = np.asarray(bins[i])
+            if np.any(edges[i][:-1] > edges[i][1:]):
+                raise ValueError(
+                    '`bins[{}]` must be monotonically increasing, when an array'
+                    .format(i))
+        else:
+            raise ValueError(
+                '`bins[{}]` must be a scalar or 1d array'.format(i))
+
+        nbin[i] = len(edges[i]) + 1  # includes an outlier on each end
+        dedges[i] = np.diff(edges[i])
+
+    # Compute the bin number each sample falls into.
+    Ncount = tuple(
+        # avoid np.digitize to work around gh-11022
+        np.searchsorted(edges[i], sample[:, i], side='right')
+        for i in _range(D)
+    )
+
+    # Using digitize, values that fall on an edge are put in the right bin.
+    # For the rightmost bin, we want values equal to the right edge to be
+    # counted in the last bin, and not as an outlier.
+    for i in _range(D):
+        # Find which points are on the rightmost edge.
+        on_edge = (sample[:, i] == edges[i][-1])
+        # Shift these points one bin to the left.
+        Ncount[i][on_edge] -= 1
+
+    # Compute the sample indices in the flattened histogram matrix.
+    # This raises an error if the array is too large.
+    xy = np.ravel_multi_index(Ncount, nbin)
+
+    # Compute the number of repetitions in xy and assign it to the
+    # flattened histmat.
+    hist = np.bincount(xy, weights, minlength=nbin.prod())
+
+    # Shape into a proper matrix
+    hist = hist.reshape(nbin)
+
+    # This preserves the (bad) behavior observed in gh-7845, for now.
+    hist = hist.astype(float, casting='safe')
+
+    # Remove outliers (indices 0 and -1 for each dimension).
+    core = D*(slice(1, -1),)
+    hist = hist[core]
+
+    if density:
+        # calculate the probability density function
+        s = hist.sum()
+        for i in _range(D):
+            shape = np.ones(D, int)
+            shape[i] = nbin[i] - 2
+            hist = hist / dedges[i].reshape(shape)
+        hist /= s
+
+    if (hist.shape != nbin - 2).any():
+        raise RuntimeError(
+            "Internal Shape Error")
+    return hist, edges

env-llmeval/lib/python3.10/site-packages/numpy/lib/index_tricks.py

@@ -0,0 +1,1046 @@
+import functools
+import sys
+import math
+import warnings
+
+import numpy as np
+from .._utils import set_module
+import numpy.core.numeric as _nx
+from numpy.core.numeric import ScalarType, array
+from numpy.core.numerictypes import issubdtype
+
+import numpy.matrixlib as matrixlib
+from .function_base import diff
+from numpy.core.multiarray import ravel_multi_index, unravel_index
+from numpy.core import overrides, linspace
+from numpy.lib.stride_tricks import as_strided
+
+
+array_function_dispatch = functools.partial(
+    overrides.array_function_dispatch, module='numpy')
+
+
+__all__ = [
+    'ravel_multi_index', 'unravel_index', 'mgrid', 'ogrid', 'r_', 'c_',
+    's_', 'index_exp', 'ix_', 'ndenumerate', 'ndindex', 'fill_diagonal',
+    'diag_indices', 'diag_indices_from'
+]
+
+
+def _ix__dispatcher(*args):
+    return args
+
+
+@array_function_dispatch(_ix__dispatcher)
+def ix_(*args):
+    """
+    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).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]])
+
+    """
+    out = []
+    nd = len(args)
+    for k, new in enumerate(args):
+        if not isinstance(new, _nx.ndarray):
+            new = np.asarray(new)
+            if new.size == 0:
+                # Explicitly type empty arrays to avoid float default
+                new = new.astype(_nx.intp)
+        if new.ndim != 1:
+            raise ValueError("Cross index must be 1 dimensional")
+        if issubdtype(new.dtype, _nx.bool_):
+            new, = new.nonzero()
+        new = new.reshape((1,)*k + (new.size,) + (1,)*(nd-k-1))
+        out.append(new)
+    return tuple(out)
+
+
+class nd_grid:
+    """
+    Construct a multi-dimensional "meshgrid".
+
+    ``grid = nd_grid()`` creates an instance which will return a mesh-grid
+    when indexed.  The dimension and number of the output arrays are equal
+    to the number of indexing dimensions.  If the step length is not a
+    complex number, then the stop is not inclusive.
+
+    However, if the step length is a **complex number** (e.g. 5j), then the
+    integer part of its magnitude is interpreted as specifying the
+    number of points to create between the start and stop values, where
+    the stop value **is inclusive**.
+
+    If instantiated with an argument of ``sparse=True``, the mesh-grid is
+    open (or not fleshed out) so that only one-dimension of each returned
+    argument is greater than 1.
+
+    Parameters
+    ----------
+    sparse : bool, optional
+        Whether the grid is sparse or not. Default is False.
+
+    Notes
+    -----
+    Two instances of `nd_grid` are made available in the NumPy namespace,
+    `mgrid` and `ogrid`, approximately defined as::
+
+        mgrid = nd_grid(sparse=False)
+        ogrid = nd_grid(sparse=True)
+
+    Users should use these pre-defined instances instead of using `nd_grid`
+    directly.
+    """
+
+    def __init__(self, sparse=False):
+        self.sparse = sparse
+
+    def __getitem__(self, key):
+        try:
+            size = []
+            # Mimic the behavior of `np.arange` and use a data type
+            # which is at least as large as `np.int_`
+            num_list = [0]
+            for k in range(len(key)):
+                step = key[k].step
+                start = key[k].start
+                stop = key[k].stop
+                if start is None:
+                    start = 0
+                if step is None:
+                    step = 1
+                if isinstance(step, (_nx.complexfloating, complex)):
+                    step = abs(step)
+                    size.append(int(step))
+                else:
+                    size.append(
+                        int(math.ceil((stop - start) / (step*1.0))))
+                num_list += [start, stop, step]
+            typ = _nx.result_type(*num_list)
+            if self.sparse:
+                nn = [_nx.arange(_x, dtype=_t)
+                      for _x, _t in zip(size, (typ,)*len(size))]
+            else:
+                nn = _nx.indices(size, typ)
+            for k, kk in enumerate(key):
+                step = kk.step
+                start = kk.start
+                if start is None:
+                    start = 0
+                if step is None:
+                    step = 1
+                if isinstance(step, (_nx.complexfloating, complex)):
+                    step = int(abs(step))
+                    if step != 1:
+                        step = (kk.stop - start) / float(step - 1)
+                nn[k] = (nn[k]*step+start)
+            if self.sparse:
+                slobj = [_nx.newaxis]*len(size)
+                for k in range(len(size)):
+                    slobj[k] = slice(None, None)
+                    nn[k] = nn[k][tuple(slobj)]
+                    slobj[k] = _nx.newaxis
+            return nn
+        except (IndexError, TypeError):
+            step = key.step
+            stop = key.stop
+            start = key.start
+            if start is None:
+                start = 0
+            if isinstance(step, (_nx.complexfloating, complex)):
+                # Prevent the (potential) creation of integer arrays
+                step_float = abs(step)
+                step = length = int(step_float)
+                if step != 1:
+                    step = (key.stop-start)/float(step-1)
+                typ = _nx.result_type(start, stop, step_float)
+                return _nx.arange(0, length, 1, dtype=typ)*step + start
+            else:
+                return _nx.arange(start, stop, step)
+
+
+class MGridClass(nd_grid):
+    """
+    An instance which returns a dense multi-dimensional "meshgrid".
+
+    An instance which returns a dense (or fleshed out) mesh-grid
+    when indexed, so that each returned argument has the same shape.
+    The dimensions and number of the output arrays are equal to the
+    number of indexing dimensions.  If the step length is not a complex
+    number, then the stop is not inclusive.
+
+    However, if the step length is a **complex number** (e.g. 5j), then
+    the integer part of its magnitude is interpreted as specifying the
+    number of points to create between the start and stop values, where
+    the stop value **is inclusive**.
+
+    Returns
+    -------
+    mesh-grid `ndarrays` all of the same dimensions
+
+    See Also
+    --------
+    ogrid : like `mgrid` but returns open (not fleshed out) mesh grids
+    meshgrid: return coordinate matrices from coordinate vectors
+    r_ : array concatenator
+    :ref:`how-to-partition`
+
+    Examples
+    --------
+    >>> np.mgrid[0:5, 0:5]
+    array([[[0, 0, 0, 0, 0],
+            [1, 1, 1, 1, 1],
+            [2, 2, 2, 2, 2],
+            [3, 3, 3, 3, 3],
+            [4, 4, 4, 4, 4]],
+           [[0, 1, 2, 3, 4],
+            [0, 1, 2, 3, 4],
+            [0, 1, 2, 3, 4],
+            [0, 1, 2, 3, 4],
+            [0, 1, 2, 3, 4]]])
+    >>> np.mgrid[-1:1:5j]
+    array([-1. , -0.5,  0. ,  0.5,  1. ])
+
+    """
+
+    def __init__(self):
+        super().__init__(sparse=False)
+
+
+mgrid = MGridClass()
+
+
+class OGridClass(nd_grid):
+    """
+    An instance which returns an open multi-dimensional "meshgrid".
+
+    An instance which returns an open (i.e. not fleshed out) mesh-grid
+    when indexed, so that only one dimension of each returned array is
+    greater than 1.  The dimension and number of the output arrays are
+    equal to the number of indexing dimensions.  If the step length is
+    not a complex number, then the stop is not inclusive.
+
+    However, if the step length is a **complex number** (e.g. 5j), then
+    the integer part of its magnitude is interpreted as specifying the
+    number of points to create between the start and stop values, where
+    the stop value **is inclusive**.
+
+    Returns
+    -------
+    mesh-grid
+        `ndarrays` with only one dimension not equal to 1
+
+    See Also
+    --------
+    mgrid : like `ogrid` but returns dense (or fleshed out) mesh grids
+    meshgrid: return coordinate matrices from coordinate vectors
+    r_ : array concatenator
+    :ref:`how-to-partition`
+
+    Examples
+    --------
+    >>> from numpy import ogrid
+    >>> ogrid[-1:1:5j]
+    array([-1. , -0.5,  0. ,  0.5,  1. ])
+    >>> ogrid[0:5,0:5]
+    [array([[0],
+            [1],
+            [2],
+            [3],
+            [4]]), array([[0, 1, 2, 3, 4]])]
+
+    """
+
+    def __init__(self):
+        super().__init__(sparse=True)
+
+
+ogrid = OGridClass()
+
+
+class AxisConcatenator:
+    """
+    Translates slice objects to concatenation along an axis.
+
+    For detailed documentation on usage, see `r_`.
+    """
+    # allow ma.mr_ to override this
+    concatenate = staticmethod(_nx.concatenate)
+    makemat = staticmethod(matrixlib.matrix)
+
+    def __init__(self, axis=0, matrix=False, ndmin=1, trans1d=-1):
+        self.axis = axis
+        self.matrix = matrix
+        self.trans1d = trans1d
+        self.ndmin = ndmin
+
+    def __getitem__(self, key):
+        # handle matrix builder syntax
+        if isinstance(key, str):
+            frame = sys._getframe().f_back
+            mymat = matrixlib.bmat(key, frame.f_globals, frame.f_locals)
+            return mymat
+
+        if not isinstance(key, tuple):
+            key = (key,)
+
+        # copy attributes, since they can be overridden in the first argument
+        trans1d = self.trans1d
+        ndmin = self.ndmin
+        matrix = self.matrix
+        axis = self.axis
+
+        objs = []
+        # dtypes or scalars for weak scalar handling in result_type
+        result_type_objs = []
+
+        for k, item in enumerate(key):
+            scalar = False
+            if isinstance(item, slice):
+                step = item.step
+                start = item.start
+                stop = item.stop
+                if start is None:
+                    start = 0
+                if step is None:
+                    step = 1
+                if isinstance(step, (_nx.complexfloating, complex)):
+                    size = int(abs(step))
+                    newobj = linspace(start, stop, num=size)
+                else:
+                    newobj = _nx.arange(start, stop, step)
+                if ndmin > 1:
+                    newobj = array(newobj, copy=False, ndmin=ndmin)
+                    if trans1d != -1:
+                        newobj = newobj.swapaxes(-1, trans1d)
+            elif isinstance(item, str):
+                if k != 0:
+                    raise ValueError("special directives must be the "
+                                     "first entry.")
+                if item in ('r', 'c'):
+                    matrix = True
+                    col = (item == 'c')
+                    continue
+                if ',' in item:
+                    vec = item.split(',')
+                    try:
+                        axis, ndmin = [int(x) for x in vec[:2]]
+                        if len(vec) == 3:
+                            trans1d = int(vec[2])
+                        continue
+                    except Exception as e:
+                        raise ValueError(
+                            "unknown special directive {!r}".format(item)
+                        ) from e
+                try:
+                    axis = int(item)
+                    continue
+                except (ValueError, TypeError) as e:
+                    raise ValueError("unknown special directive") from e
+            elif type(item) in ScalarType:
+                scalar = True
+                newobj = item
+            else:
+                item_ndim = np.ndim(item)
+                newobj = array(item, copy=False, subok=True, ndmin=ndmin)
+                if trans1d != -1 and item_ndim < ndmin:
+                    k2 = ndmin - item_ndim
+                    k1 = trans1d
+                    if k1 < 0:
+                        k1 += k2 + 1
+                    defaxes = list(range(ndmin))
+                    axes = defaxes[:k1] + defaxes[k2:] + defaxes[k1:k2]
+                    newobj = newobj.transpose(axes)
+
+            objs.append(newobj)
+            if scalar:
+                result_type_objs.append(item)
+            else:
+                result_type_objs.append(newobj.dtype)
+
+        # Ensure that scalars won't up-cast unless warranted, for 0, drops
+        # through to error in concatenate.
+        if len(result_type_objs) != 0:
+            final_dtype = _nx.result_type(*result_type_objs)
+            # concatenate could do cast, but that can be overriden:
+            objs = [array(obj, copy=False, subok=True,
+                          ndmin=ndmin, dtype=final_dtype) for obj in objs]
+
+        res = self.concatenate(tuple(objs), axis=axis)
+
+        if matrix:
+            oldndim = res.ndim
+            res = self.makemat(res)
+            if oldndim == 1 and col:
+                res = res.T
+        return res
+
+    def __len__(self):
+        return 0
+
+# separate classes are used here instead of just making r_ = concatentor(0),
+# etc. because otherwise we couldn't get the doc string to come out right
+# in help(r_)
+
+
+class RClass(AxisConcatenator):
+    """
+    Translates slice objects to concatenation along the first axis.
+
+    This is a simple way to build up arrays quickly. There are two use cases.
+
+    1. If the index expression contains comma separated arrays, then stack
+       them along their first axis.
+    2. If the index expression contains slice notation or scalars then create
+       a 1-D array with a range indicated by the slice notation.
+
+    If slice notation is used, the syntax ``start:stop:step`` is equivalent
+    to ``np.arange(start, stop, step)`` inside of the brackets. However, if
+    ``step`` is an imaginary number (i.e. 100j) then its integer portion is
+    interpreted as a number-of-points desired and the start and stop are
+    inclusive. In other words ``start:stop:stepj`` is interpreted as
+    ``np.linspace(start, stop, step, endpoint=1)`` inside of the brackets.
+    After expansion of slice notation, all comma separated sequences are
+    concatenated together.
+
+    Optional character strings placed as the first element of the index
+    expression can be used to change the output. The strings 'r' or 'c' result
+    in matrix output. If the result is 1-D and 'r' is specified a 1 x N (row)
+    matrix is produced. If the result is 1-D and 'c' is specified, then a N x 1
+    (column) matrix is produced. If the result is 2-D then both provide the
+    same matrix result.
+
+    A string integer specifies which axis to stack multiple comma separated
+    arrays along. A string of two comma-separated integers allows indication
+    of the minimum number of dimensions to force each entry into as the
+    second integer (the axis to concatenate along is still the first integer).
+
+    A string with three comma-separated integers allows specification of the
+    axis to concatenate along, the minimum number of dimensions to force the
+    entries to, and which axis should contain the start of the arrays which
+    are less than the specified number of dimensions. In other words the third
+    integer allows you to specify where the 1's should be placed in the shape
+    of the arrays that have their shapes upgraded. By default, they are placed
+    in the front of the shape tuple. The third argument allows you to specify
+    where the start of the array should be instead. Thus, a third argument of
+    '0' would place the 1's at the end of the array shape. Negative integers
+    specify where in the new shape tuple the last dimension of upgraded arrays
+    should be placed, so the default is '-1'.
+
+    Parameters
+    ----------
+    Not a function, so takes no parameters
+
+
+    Returns
+    -------
+    A concatenated ndarray or matrix.
+
+    See Also
+    --------
+    concatenate : Join a sequence of arrays along an existing axis.
+    c_ : Translates slice objects to concatenation along the second axis.
+
+    Examples
+    --------
+    >>> np.r_[np.array([1,2,3]), 0, 0, np.array([4,5,6])]
+    array([1, 2, 3, ..., 4, 5, 6])
+    >>> np.r_[-1:1:6j, [0]*3, 5, 6]
+    array([-1. , -0.6, -0.2,  0.2,  0.6,  1. ,  0. ,  0. ,  0. ,  5. ,  6. ])
+
+    String integers specify the axis to concatenate along or the minimum
+    number of dimensions to force entries into.
+
+    >>> a = np.array([[0, 1, 2], [3, 4, 5]])
+    >>> np.r_['-1', a, a] # concatenate along last axis
+    array([[0, 1, 2, 0, 1, 2],
+           [3, 4, 5, 3, 4, 5]])
+    >>> np.r_['0,2', [1,2,3], [4,5,6]] # concatenate along first axis, dim>=2
+    array([[1, 2, 3],
+           [4, 5, 6]])
+
+    >>> np.r_['0,2,0', [1,2,3], [4,5,6]]
+    array([[1],
+           [2],
+           [3],
+           [4],
+           [5],
+           [6]])
+    >>> np.r_['1,2,0', [1,2,3], [4,5,6]]
+    array([[1, 4],
+           [2, 5],
+           [3, 6]])
+
+    Using 'r' or 'c' as a first string argument creates a matrix.
+
+    >>> np.r_['r',[1,2,3], [4,5,6]]
+    matrix([[1, 2, 3, 4, 5, 6]])
+
+    """
+
+    def __init__(self):
+        AxisConcatenator.__init__(self, 0)
+
+
+r_ = RClass()
+
+
+class CClass(AxisConcatenator):
+    """
+    Translates slice objects to concatenation along the second axis.
+
+    This is short-hand for ``np.r_['-1,2,0', index expression]``, which is
+    useful because of its common occurrence. In particular, arrays will be
+    stacked along their last axis after being upgraded to at least 2-D with
+    1's post-pended to the shape (column vectors made out of 1-D arrays).
+
+    See Also
+    --------
+    column_stack : Stack 1-D arrays as columns into a 2-D array.
+    r_ : For more detailed documentation.
+
+    Examples
+    --------
+    >>> np.c_[np.array([1,2,3]), np.array([4,5,6])]
+    array([[1, 4],
+           [2, 5],
+           [3, 6]])
+    >>> np.c_[np.array([[1,2,3]]), 0, 0, np.array([[4,5,6]])]
+    array([[1, 2, 3, ..., 4, 5, 6]])
+
+    """
+
+    def __init__(self):
+        AxisConcatenator.__init__(self, -1, ndmin=2, trans1d=0)
+
+
+c_ = CClass()
+
+
+@set_module('numpy')
+class ndenumerate:
+    """
+    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
+
+    """
+
+    def __init__(self, arr):
+        self.iter = np.asarray(arr).flat
+
+    def __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.
+
+        """
+        return self.iter.coords, next(self.iter)
+
+    def __iter__(self):
+        return self
+
+
+@set_module('numpy')
+class ndindex:
+    """
+    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)
+
+    """
+
+    def __init__(self, *shape):
+        if len(shape) == 1 and isinstance(shape[0], tuple):
+            shape = shape[0]
+        x = as_strided(_nx.zeros(1), shape=shape,
+                       strides=_nx.zeros_like(shape))
+        self._it = _nx.nditer(x, flags=['multi_index', 'zerosize_ok'],
+                              order='C')
+
+    def __iter__(self):
+        return self
+
+    def 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.
+        """
+        # NumPy 1.20.0, 2020-09-08
+        warnings.warn(
+            "`ndindex.ndincr()` is deprecated, use `next(ndindex)` instead",
+            DeprecationWarning, stacklevel=2)
+        next(self)
+
+    def __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.
+
+        """
+        next(self._it)
+        return self._it.multi_index
+
+
+# You can do all this with slice() plus a few special objects,
+# but there's a lot to remember. This version is simpler because
+# it uses the standard array indexing syntax.
+#
+# Written by Konrad Hinsen <[email protected]>
+# last revision: 1999-7-23
+#
+# Cosmetic changes by T. Oliphant 2001
+#
+#
+
+class IndexExpression:
+    """
+    A nicer way to build up index tuples for arrays.
+
+    .. note::
+       Use one of the two predefined instances `index_exp` or `s_`
+       rather than directly using `IndexExpression`.
+
+    For any index combination, including slicing and axis insertion,
+    ``a[indices]`` is the same as ``a[np.index_exp[indices]]`` for any
+    array `a`. However, ``np.index_exp[indices]`` can be used anywhere
+    in Python code and returns a tuple of slice objects that can be
+    used in the construction of complex index expressions.
+
+    Parameters
+    ----------
+    maketuple : bool
+        If True, always returns a tuple.
+
+    See Also
+    --------
+    index_exp : Predefined instance that always returns a tuple:
+       `index_exp = IndexExpression(maketuple=True)`.
+    s_ : Predefined instance without tuple conversion:
+       `s_ = IndexExpression(maketuple=False)`.
+
+    Notes
+    -----
+    You can do all this with `slice()` plus a few special objects,
+    but there's a lot to remember and this version is simpler because
+    it uses the standard array indexing syntax.
+
+    Examples
+    --------
+    >>> np.s_[2::2]
+    slice(2, None, 2)
+    >>> np.index_exp[2::2]
+    (slice(2, None, 2),)
+
+    >>> np.array([0, 1, 2, 3, 4])[np.s_[2::2]]
+    array([2, 4])
+
+    """
+
+    def __init__(self, maketuple):
+        self.maketuple = maketuple
+
+    def __getitem__(self, item):
+        if self.maketuple and not isinstance(item, tuple):
+            return (item,)
+        else:
+            return item
+
+
+index_exp = IndexExpression(maketuple=True)
+s_ = IndexExpression(maketuple=False)
+
+# End contribution from Konrad.
+
+
+# The following functions complement those in twodim_base, but are
+# applicable to N-dimensions.
+
+
+def _fill_diagonal_dispatcher(a, val, wrap=None):
+    return (a,)
+
+
+@array_function_dispatch(_fill_diagonal_dispatcher)
+def fill_diagonal(a, val, wrap=False):
+    """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.
+    """
+    if a.ndim < 2:
+        raise ValueError("array must be at least 2-d")
+    end = None
+    if a.ndim == 2:
+        # Explicit, fast formula for the common case.  For 2-d arrays, we
+        # accept rectangular ones.
+        step = a.shape[1] + 1
+        # This is needed to don't have tall matrix have the diagonal wrap.
+        if not wrap:
+            end = a.shape[1] * a.shape[1]
+    else:
+        # For more than d=2, the strided formula is only valid for arrays with
+        # all dimensions equal, so we check first.
+        if not np.all(diff(a.shape) == 0):
+            raise ValueError("All dimensions of input must be of equal length")
+        step = 1 + (np.cumprod(a.shape[:-1])).sum()
+
+    # Write the value out into the diagonal.
+    a.flat[:end:step] = val
+
+
+@set_module('numpy')
+def diag_indices(n, ndim=2):
+    """
+    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)
+    >>> di
+    (array([0, 1, 2, 3]), array([0, 1, 2, 3]))
+    >>> a = np.arange(16).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]]])
+
+    """
+    idx = np.arange(n)
+    return (idx,) * ndim
+
+
+def _diag_indices_from(arr):
+    return (arr,)
+
+
+@array_function_dispatch(_diag_indices_from)
+def diag_indices_from(arr):
+    """
+    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
+
+    Examples
+    --------
+    
+    Create a 4 by 4 array.
+
+    >>> a = np.arange(16).reshape(4, 4)
+    >>> a
+    array([[ 0,  1,  2,  3],
+           [ 4,  5,  6,  7],
+           [ 8,  9, 10, 11],
+           [12, 13, 14, 15]])
+    
+    Get the indices of the diagonal elements.
+
+    >>> di = np.diag_indices_from(a)
+    >>> di
+    (array([0, 1, 2, 3]), array([0, 1, 2, 3]))
+
+    >>> a[di]
+    array([ 0,  5, 10, 15])
+
+    This is simply syntactic sugar for diag_indices.
+
+    >>> np.diag_indices(a.shape[0])
+    (array([0, 1, 2, 3]), array([0, 1, 2, 3]))
+
+    """
+
+    if not arr.ndim >= 2:
+        raise ValueError("input array must be at least 2-d")
+    # For more than d=2, the strided formula is only valid for arrays with
+    # all dimensions equal, so we check first.
+    if not np.all(diff(arr.shape) == 0):
+        raise ValueError("All dimensions of input must be of equal length")
+
+    return diag_indices(arr.shape[0], arr.ndim)

env-llmeval/lib/python3.10/site-packages/numpy/lib/index_tricks.pyi

@@ -0,0 +1,162 @@
+from collections.abc import Sequence
+from typing import (
+    Any,
+    TypeVar,
+    Generic,
+    overload,
+    Literal,
+    SupportsIndex,
+)
+
+from numpy import (
+    # Circumvent a naming conflict with `AxisConcatenator.matrix`
+    matrix as _Matrix,
+    ndenumerate as ndenumerate,
+    ndindex as ndindex,
+    ndarray,
+    dtype,
+    integer,
+    str_,
+    bytes_,
+    bool_,
+    int_,
+    float_,
+    complex_,
+    intp,
+    _OrderCF,
+    _ModeKind,
+)
+from numpy._typing import (
+    # Arrays
+    ArrayLike,
+    _NestedSequence,
+    _FiniteNestedSequence,
+    NDArray,
+    _ArrayLikeInt,
+
+    # DTypes
+    DTypeLike,
+    _SupportsDType,
+
+    # Shapes
+    _ShapeLike,
+)
+
+from numpy.core.multiarray import (
+    unravel_index as unravel_index,
+    ravel_multi_index as ravel_multi_index,
+)
+
+_T = TypeVar("_T")
+_DType = TypeVar("_DType", bound=dtype[Any])
+_BoolType = TypeVar("_BoolType", Literal[True], Literal[False])
+_TupType = TypeVar("_TupType", bound=tuple[Any, ...])
+_ArrayType = TypeVar("_ArrayType", bound=ndarray[Any, Any])
+
+__all__: list[str]
+
+@overload
+def ix_(*args: _FiniteNestedSequence[_SupportsDType[_DType]]) -> tuple[ndarray[Any, _DType], ...]: ...
+@overload
+def ix_(*args: str | _NestedSequence[str]) -> tuple[NDArray[str_], ...]: ...
+@overload
+def ix_(*args: bytes | _NestedSequence[bytes]) -> tuple[NDArray[bytes_], ...]: ...
+@overload
+def ix_(*args: bool | _NestedSequence[bool]) -> tuple[NDArray[bool_], ...]: ...
+@overload
+def ix_(*args: int | _NestedSequence[int]) -> tuple[NDArray[int_], ...]: ...
+@overload
+def ix_(*args: float | _NestedSequence[float]) -> tuple[NDArray[float_], ...]: ...
+@overload
+def ix_(*args: complex | _NestedSequence[complex]) -> tuple[NDArray[complex_], ...]: ...
+
+class nd_grid(Generic[_BoolType]):
+    sparse: _BoolType
+    def __init__(self, sparse: _BoolType = ...) -> None: ...
+    @overload
+    def __getitem__(
+        self: nd_grid[Literal[False]],
+        key: slice | Sequence[slice],
+    ) -> NDArray[Any]: ...
+    @overload
+    def __getitem__(
+        self: nd_grid[Literal[True]],
+        key: slice | Sequence[slice],
+    ) -> list[NDArray[Any]]: ...
+
+class MGridClass(nd_grid[Literal[False]]):
+    def __init__(self) -> None: ...
+
+mgrid: MGridClass
+
+class OGridClass(nd_grid[Literal[True]]):
+    def __init__(self) -> None: ...
+
+ogrid: OGridClass
+
+class AxisConcatenator:
+    axis: int
+    matrix: bool
+    ndmin: int
+    trans1d: int
+    def __init__(
+        self,
+        axis: int = ...,
+        matrix: bool = ...,
+        ndmin: int = ...,
+        trans1d: int = ...,
+    ) -> None: ...
+    @staticmethod
+    @overload
+    def concatenate(  # type: ignore[misc]
+        *a: ArrayLike, axis: SupportsIndex = ..., out: None = ...
+    ) -> NDArray[Any]: ...
+    @staticmethod
+    @overload
+    def concatenate(
+        *a: ArrayLike, axis: SupportsIndex = ..., out: _ArrayType = ...
+    ) -> _ArrayType: ...
+    @staticmethod
+    def makemat(
+        data: ArrayLike, dtype: DTypeLike = ..., copy: bool = ...
+    ) -> _Matrix[Any, Any]: ...
+
+    # TODO: Sort out this `__getitem__` method
+    def __getitem__(self, key: Any) -> Any: ...
+
+class RClass(AxisConcatenator):
+    axis: Literal[0]
+    matrix: Literal[False]
+    ndmin: Literal[1]
+    trans1d: Literal[-1]
+    def __init__(self) -> None: ...
+
+r_: RClass
+
+class CClass(AxisConcatenator):
+    axis: Literal[-1]
+    matrix: Literal[False]
+    ndmin: Literal[2]
+    trans1d: Literal[0]
+    def __init__(self) -> None: ...
+
+c_: CClass
+
+class IndexExpression(Generic[_BoolType]):
+    maketuple: _BoolType
+    def __init__(self, maketuple: _BoolType) -> None: ...
+    @overload
+    def __getitem__(self, item: _TupType) -> _TupType: ...  # type: ignore[misc]
+    @overload
+    def __getitem__(self: IndexExpression[Literal[True]], item: _T) -> tuple[_T]: ...
+    @overload
+    def __getitem__(self: IndexExpression[Literal[False]], item: _T) -> _T: ...
+
+index_exp: IndexExpression[Literal[True]]
+s_: IndexExpression[Literal[False]]
+
+def fill_diagonal(a: ndarray[Any, Any], val: Any, wrap: bool = ...) -> None: ...
+def diag_indices(n: int, ndim: int = ...) -> tuple[NDArray[int_], ...]: ...
+def diag_indices_from(arr: ArrayLike) -> tuple[NDArray[int_], ...]: ...
+
+# NOTE: see `numpy/__init__.pyi` for `ndenumerate` and `ndindex`

env-llmeval/lib/python3.10/site-packages/numpy/lib/mixins.py

@@ -0,0 +1,177 @@
+"""Mixin classes for custom array types that don't inherit from ndarray."""
+from numpy.core import umath as um
+
+
+__all__ = ['NDArrayOperatorsMixin']
+
+
+def _disables_array_ufunc(obj):
+    """True when __array_ufunc__ is set to None."""
+    try:
+        return obj.__array_ufunc__ is None
+    except AttributeError:
+        return False
+
+
+def _binary_method(ufunc, name):
+    """Implement a forward binary method with a ufunc, e.g., __add__."""
+    def func(self, other):
+        if _disables_array_ufunc(other):
+            return NotImplemented
+        return ufunc(self, other)
+    func.__name__ = '__{}__'.format(name)
+    return func
+
+
+def _reflected_binary_method(ufunc, name):
+    """Implement a reflected binary method with a ufunc, e.g., __radd__."""
+    def func(self, other):
+        if _disables_array_ufunc(other):
+            return NotImplemented
+        return ufunc(other, self)
+    func.__name__ = '__r{}__'.format(name)
+    return func
+
+
+def _inplace_binary_method(ufunc, name):
+    """Implement an in-place binary method with a ufunc, e.g., __iadd__."""
+    def func(self, other):
+        return ufunc(self, other, out=(self,))
+    func.__name__ = '__i{}__'.format(name)
+    return func
+
+
+def _numeric_methods(ufunc, name):
+    """Implement forward, reflected and inplace binary methods with a ufunc."""
+    return (_binary_method(ufunc, name),
+            _reflected_binary_method(ufunc, name),
+            _inplace_binary_method(ufunc, name))
+
+
+def _unary_method(ufunc, name):
+    """Implement a unary special method with a ufunc."""
+    def func(self):
+        return ufunc(self)
+    func.__name__ = '__{}__'.format(name)
+    return func
+
+
+class NDArrayOperatorsMixin:
+    """Mixin defining all operator special methods using __array_ufunc__.
+
+    This class implements the special methods for almost all of Python's
+    builtin operators defined in the `operator` module, including comparisons
+    (``==``, ``>``, etc.) and arithmetic (``+``, ``*``, ``-``, etc.), by
+    deferring to the ``__array_ufunc__`` method, which subclasses must
+    implement.
+
+    It is useful for writing classes that do not inherit from `numpy.ndarray`,
+    but that should support arithmetic and numpy universal functions like
+    arrays as described in `A Mechanism for Overriding Ufuncs
+    <https://numpy.org/neps/nep-0013-ufunc-overrides.html>`_.
+
+    As an trivial example, consider this implementation of an ``ArrayLike``
+    class that simply wraps a NumPy array and ensures that the result of any
+    arithmetic operation is also an ``ArrayLike`` object::
+
+        class ArrayLike(np.lib.mixins.NDArrayOperatorsMixin):
+            def __init__(self, value):
+                self.value = np.asarray(value)
+
+            # One might also consider adding the built-in list type to this
+            # list, to support operations like np.add(array_like, list)
+            _HANDLED_TYPES = (np.ndarray, numbers.Number)
+
+            def __array_ufunc__(self, ufunc, method, *inputs, **kwargs):
+                out = kwargs.get('out', ())
+                for x in inputs + out:
+                    # Only support operations with instances of _HANDLED_TYPES.
+                    # Use ArrayLike instead of type(self) for isinstance to
+                    # allow subclasses that don't override __array_ufunc__ to
+                    # handle ArrayLike objects.
+                    if not isinstance(x, self._HANDLED_TYPES + (ArrayLike,)):
+                        return NotImplemented
+
+                # Defer to the implementation of the ufunc on unwrapped values.
+                inputs = tuple(x.value if isinstance(x, ArrayLike) else x
+                               for x in inputs)
+                if out:
+                    kwargs['out'] = tuple(
+                        x.value if isinstance(x, ArrayLike) else x
+                        for x in out)
+                result = getattr(ufunc, method)(*inputs, **kwargs)
+
+                if type(result) is tuple:
+                    # multiple return values
+                    return tuple(type(self)(x) for x in result)
+                elif method == 'at':
+                    # no return value
+                    return None
+                else:
+                    # one return value
+                    return type(self)(result)
+
+            def __repr__(self):
+                return '%s(%r)' % (type(self).__name__, self.value)
+
+    In interactions between ``ArrayLike`` objects and numbers or numpy arrays,
+    the result is always another ``ArrayLike``:
+
+        >>> x = ArrayLike([1, 2, 3])
+        >>> x - 1
+        ArrayLike(array([0, 1, 2]))
+        >>> 1 - x
+        ArrayLike(array([ 0, -1, -2]))
+        >>> np.arange(3) - x
+        ArrayLike(array([-1, -1, -1]))
+        >>> x - np.arange(3)
+        ArrayLike(array([1, 1, 1]))
+
+    Note that unlike ``numpy.ndarray``, ``ArrayLike`` does not allow operations
+    with arbitrary, unrecognized types. This ensures that interactions with
+    ArrayLike preserve a well-defined casting hierarchy.
+
+    .. versionadded:: 1.13
+    """
+    __slots__ = ()
+    # Like np.ndarray, this mixin class implements "Option 1" from the ufunc
+    # overrides NEP.
+
+    # comparisons don't have reflected and in-place versions
+    __lt__ = _binary_method(um.less, 'lt')
+    __le__ = _binary_method(um.less_equal, 'le')
+    __eq__ = _binary_method(um.equal, 'eq')
+    __ne__ = _binary_method(um.not_equal, 'ne')
+    __gt__ = _binary_method(um.greater, 'gt')
+    __ge__ = _binary_method(um.greater_equal, 'ge')
+
+    # numeric methods
+    __add__, __radd__, __iadd__ = _numeric_methods(um.add, 'add')
+    __sub__, __rsub__, __isub__ = _numeric_methods(um.subtract, 'sub')
+    __mul__, __rmul__, __imul__ = _numeric_methods(um.multiply, 'mul')
+    __matmul__, __rmatmul__, __imatmul__ = _numeric_methods(
+        um.matmul, 'matmul')
+    # Python 3 does not use __div__, __rdiv__, or __idiv__
+    __truediv__, __rtruediv__, __itruediv__ = _numeric_methods(
+        um.true_divide, 'truediv')
+    __floordiv__, __rfloordiv__, __ifloordiv__ = _numeric_methods(
+        um.floor_divide, 'floordiv')
+    __mod__, __rmod__, __imod__ = _numeric_methods(um.remainder, 'mod')
+    __divmod__ = _binary_method(um.divmod, 'divmod')
+    __rdivmod__ = _reflected_binary_method(um.divmod, 'divmod')
+    # __idivmod__ does not exist
+    # TODO: handle the optional third argument for __pow__?
+    __pow__, __rpow__, __ipow__ = _numeric_methods(um.power, 'pow')
+    __lshift__, __rlshift__, __ilshift__ = _numeric_methods(
+        um.left_shift, 'lshift')
+    __rshift__, __rrshift__, __irshift__ = _numeric_methods(
+        um.right_shift, 'rshift')
+    __and__, __rand__, __iand__ = _numeric_methods(um.bitwise_and, 'and')
+    __xor__, __rxor__, __ixor__ = _numeric_methods(um.bitwise_xor, 'xor')
+    __or__, __ror__, __ior__ = _numeric_methods(um.bitwise_or, 'or')
+
+    # unary methods
+    __neg__ = _unary_method(um.negative, 'neg')
+    __pos__ = _unary_method(um.positive, 'pos')
+    __abs__ = _unary_method(um.absolute, 'abs')
+    __invert__ = _unary_method(um.invert, 'invert')

env-llmeval/lib/python3.10/site-packages/numpy/lib/mixins.pyi

@@ -0,0 +1,74 @@
+from abc import ABCMeta, abstractmethod
+from typing import Literal as L, Any
+
+from numpy import ufunc
+
+__all__: list[str]
+
+# NOTE: `NDArrayOperatorsMixin` is not formally an abstract baseclass,
+# even though it's reliant on subclasses implementing `__array_ufunc__`
+
+# NOTE: The accepted input- and output-types of the various dunders are
+# completely dependent on how `__array_ufunc__` is implemented.
+# As such, only little type safety can be provided here.
+
+class NDArrayOperatorsMixin(metaclass=ABCMeta):
+    @abstractmethod
+    def __array_ufunc__(
+        self,
+        ufunc: ufunc,
+        method: L["__call__", "reduce", "reduceat", "accumulate", "outer", "inner"],
+        *inputs: Any,
+        **kwargs: Any,
+    ) -> Any: ...
+    def __lt__(self, other: Any) -> Any: ...
+    def __le__(self, other: Any) -> Any: ...
+    def __eq__(self, other: Any) -> Any: ...
+    def __ne__(self, other: Any) -> Any: ...
+    def __gt__(self, other: Any) -> Any: ...
+    def __ge__(self, other: Any) -> Any: ...
+    def __add__(self, other: Any) -> Any: ...
+    def __radd__(self, other: Any) -> Any: ...
+    def __iadd__(self, other: Any) -> Any: ...
+    def __sub__(self, other: Any) -> Any: ...
+    def __rsub__(self, other: Any) -> Any: ...
+    def __isub__(self, other: Any) -> Any: ...
+    def __mul__(self, other: Any) -> Any: ...
+    def __rmul__(self, other: Any) -> Any: ...
+    def __imul__(self, other: Any) -> Any: ...
+    def __matmul__(self, other: Any) -> Any: ...
+    def __rmatmul__(self, other: Any) -> Any: ...
+    def __imatmul__(self, other: Any) -> Any: ...
+    def __truediv__(self, other: Any) -> Any: ...
+    def __rtruediv__(self, other: Any) -> Any: ...
+    def __itruediv__(self, other: Any) -> Any: ...
+    def __floordiv__(self, other: Any) -> Any: ...
+    def __rfloordiv__(self, other: Any) -> Any: ...
+    def __ifloordiv__(self, other: Any) -> Any: ...
+    def __mod__(self, other: Any) -> Any: ...
+    def __rmod__(self, other: Any) -> Any: ...
+    def __imod__(self, other: Any) -> Any: ...
+    def __divmod__(self, other: Any) -> Any: ...
+    def __rdivmod__(self, other: Any) -> Any: ...
+    def __pow__(self, other: Any) -> Any: ...
+    def __rpow__(self, other: Any) -> Any: ...
+    def __ipow__(self, other: Any) -> Any: ...
+    def __lshift__(self, other: Any) -> Any: ...
+    def __rlshift__(self, other: Any) -> Any: ...
+    def __ilshift__(self, other: Any) -> Any: ...
+    def __rshift__(self, other: Any) -> Any: ...
+    def __rrshift__(self, other: Any) -> Any: ...
+    def __irshift__(self, other: Any) -> Any: ...
+    def __and__(self, other: Any) -> Any: ...
+    def __rand__(self, other: Any) -> Any: ...
+    def __iand__(self, other: Any) -> Any: ...
+    def __xor__(self, other: Any) -> Any: ...
+    def __rxor__(self, other: Any) -> Any: ...
+    def __ixor__(self, other: Any) -> Any: ...
+    def __or__(self, other: Any) -> Any: ...
+    def __ror__(self, other: Any) -> Any: ...
+    def __ior__(self, other: Any) -> Any: ...
+    def __neg__(self) -> Any: ...
+    def __pos__(self) -> Any: ...
+    def __abs__(self) -> Any: ...
+    def __invert__(self) -> Any: ...

env-llmeval/lib/python3.10/site-packages/numpy/lib/nanfunctions.py

@@ -0,0 +1,1887 @@
+"""
+Functions that ignore NaN.
+
+Functions
+---------
+
+- `nanmin` -- minimum non-NaN value
+- `nanmax` -- maximum non-NaN value
+- `nanargmin` -- index of minimum non-NaN value
+- `nanargmax` -- index of maximum non-NaN value
+- `nansum` -- sum of non-NaN values
+- `nanprod` -- product of non-NaN values
+- `nancumsum` -- cumulative sum of non-NaN values
+- `nancumprod` -- cumulative product of non-NaN values
+- `nanmean` -- mean of non-NaN values
+- `nanvar` -- variance of non-NaN values
+- `nanstd` -- standard deviation of non-NaN values
+- `nanmedian` -- median of non-NaN values
+- `nanquantile` -- qth quantile of non-NaN values
+- `nanpercentile` -- qth percentile of non-NaN values
+
+"""
+import functools
+import warnings
+import numpy as np
+from numpy.lib import function_base
+from numpy.core import overrides
+
+
+array_function_dispatch = functools.partial(
+    overrides.array_function_dispatch, module='numpy')
+
+
+__all__ = [
+    'nansum', 'nanmax', 'nanmin', 'nanargmax', 'nanargmin', 'nanmean',
+    'nanmedian', 'nanpercentile', 'nanvar', 'nanstd', 'nanprod',
+    'nancumsum', 'nancumprod', 'nanquantile'
+    ]
+
+
+def _nan_mask(a, out=None):
+    """
+    Parameters
+    ----------
+    a : array-like
+        Input array with at least 1 dimension.
+    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 and will prevent the allocation of a new array.
+
+    Returns
+    -------
+    y : bool ndarray or True
+        A bool array where ``np.nan`` positions are marked with ``False``
+        and other positions are marked with ``True``. If the type of ``a``
+        is such that it can't possibly contain ``np.nan``, returns ``True``.
+    """
+    # we assume that a is an array for this private function
+
+    if a.dtype.kind not in 'fc':
+        return True
+
+    y = np.isnan(a, out=out)
+    y = np.invert(y, out=y)
+    return y
+
+def _replace_nan(a, val):
+    """
+    If `a` is of inexact type, make a copy of `a`, replace NaNs with
+    the `val` value, and return the copy together with a boolean mask
+    marking the locations where NaNs were present. If `a` is not of
+    inexact type, do nothing and return `a` together with a mask of None.
+
+    Note that scalars will end up as array scalars, which is important
+    for using the result as the value of the out argument in some
+    operations.
+
+    Parameters
+    ----------
+    a : array-like
+        Input array.
+    val : float
+        NaN values are set to val before doing the operation.
+
+    Returns
+    -------
+    y : ndarray
+        If `a` is of inexact type, return a copy of `a` with the NaNs
+        replaced by the fill value, otherwise return `a`.
+    mask: {bool, None}
+        If `a` is of inexact type, return a boolean mask marking locations of
+        NaNs, otherwise return None.
+
+    """
+    a = np.asanyarray(a)
+
+    if a.dtype == np.object_:
+        # object arrays do not support `isnan` (gh-9009), so make a guess
+        mask = np.not_equal(a, a, dtype=bool)
+    elif issubclass(a.dtype.type, np.inexact):
+        mask = np.isnan(a)
+    else:
+        mask = None
+
+    if mask is not None:
+        a = np.array(a, subok=True, copy=True)
+        np.copyto(a, val, where=mask)
+
+    return a, mask
+
+
+def _copyto(a, val, mask):
+    """
+    Replace values in `a` with NaN where `mask` is True.  This differs from
+    copyto in that it will deal with the case where `a` is a numpy scalar.
+
+    Parameters
+    ----------
+    a : ndarray or numpy scalar
+        Array or numpy scalar some of whose values are to be replaced
+        by val.
+    val : numpy scalar
+        Value used a replacement.
+    mask : ndarray, scalar
+        Boolean array. Where True the corresponding element of `a` is
+        replaced by `val`. Broadcasts.
+
+    Returns
+    -------
+    res : ndarray, scalar
+        Array with elements replaced or scalar `val`.
+
+    """
+    if isinstance(a, np.ndarray):
+        np.copyto(a, val, where=mask, casting='unsafe')
+    else:
+        a = a.dtype.type(val)
+    return a
+
+
+def _remove_nan_1d(arr1d, overwrite_input=False):
+    """
+    Equivalent to arr1d[~arr1d.isnan()], but in a different order
+
+    Presumably faster as it incurs fewer copies
+
+    Parameters
+    ----------
+    arr1d : ndarray
+        Array to remove nans from
+    overwrite_input : bool
+        True if `arr1d` can be modified in place
+
+    Returns
+    -------
+    res : ndarray
+        Array with nan elements removed
+    overwrite_input : bool
+        True if `res` can be modified in place, given the constraint on the
+        input
+    """
+    if arr1d.dtype == object:
+        # object arrays do not support `isnan` (gh-9009), so make a guess
+        c = np.not_equal(arr1d, arr1d, dtype=bool)
+    else:
+        c = np.isnan(arr1d)
+
+    s = np.nonzero(c)[0]
+    if s.size == arr1d.size:
+        warnings.warn("All-NaN slice encountered", RuntimeWarning,
+                      stacklevel=6)
+        return arr1d[:0], True
+    elif s.size == 0:
+        return arr1d, overwrite_input
+    else:
+        if not overwrite_input:
+            arr1d = arr1d.copy()
+        # select non-nans at end of array
+        enonan = arr1d[-s.size:][~c[-s.size:]]
+        # fill nans in beginning of array with non-nans of end
+        arr1d[s[:enonan.size]] = enonan
+
+        return arr1d[:-s.size], True
+
+
+def _divide_by_count(a, b, out=None):
+    """
+    Compute a/b ignoring invalid results. If `a` is an array the division
+    is done in place. If `a` is a scalar, then its type is preserved in the
+    output. If out is None, then a is used instead so that the division
+    is in place. Note that this is only called with `a` an inexact type.
+
+    Parameters
+    ----------
+    a : {ndarray, numpy scalar}
+        Numerator. Expected to be of inexact type but not checked.
+    b : {ndarray, numpy scalar}
+        Denominator.
+    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.
+
+    Returns
+    -------
+    ret : {ndarray, numpy scalar}
+        The return value is a/b. If `a` was an ndarray the division is done
+        in place. If `a` is a numpy scalar, the division preserves its type.
+
+    """
+    with np.errstate(invalid='ignore', divide='ignore'):
+        if isinstance(a, np.ndarray):
+            if out is None:
+                return np.divide(a, b, out=a, casting='unsafe')
+            else:
+                return np.divide(a, b, out=out, casting='unsafe')
+        else:
+            if out is None:
+                # Precaution against reduced object arrays
+                try:
+                    return a.dtype.type(a / b)
+                except AttributeError:
+                    return a / b
+            else:
+                # This is questionable, but currently a numpy scalar can
+                # be output to a zero dimensional array.
+                return np.divide(a, b, out=out, casting='unsafe')
+
+
+def _nanmin_dispatcher(a, axis=None, out=None, keepdims=None,
+                       initial=None, where=None):
+    return (a, out)
+
+
+@array_function_dispatch(_nanmin_dispatcher)
+def nanmin(a, axis=None, out=None, keepdims=np._NoValue, initial=np._NoValue,
+           where=np._NoValue):
+    """
+    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
+    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:: 1.22.0
+    where : array_like of bool, optional
+        Elements to compare for the minimum. See `~numpy.ufunc.reduce`
+        for details.
+
+        .. versionadded:: 1.22.0
+
+    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
+
+    """
+    kwargs = {}
+    if keepdims is not np._NoValue:
+        kwargs['keepdims'] = keepdims
+    if initial is not np._NoValue:
+        kwargs['initial'] = initial
+    if where is not np._NoValue:
+        kwargs['where'] = where
+
+    if type(a) is np.ndarray and a.dtype != np.object_:
+        # Fast, but not safe for subclasses of ndarray, or object arrays,
+        # which do not implement isnan (gh-9009), or fmin correctly (gh-8975)
+        res = np.fmin.reduce(a, axis=axis, out=out, **kwargs)
+        if np.isnan(res).any():
+            warnings.warn("All-NaN slice encountered", RuntimeWarning,
+                          stacklevel=2)
+    else:
+        # Slow, but safe for subclasses of ndarray
+        a, mask = _replace_nan(a, +np.inf)
+        res = np.amin(a, axis=axis, out=out, **kwargs)
+        if mask is None:
+            return res
+
+        # Check for all-NaN axis
+        kwargs.pop("initial", None)
+        mask = np.all(mask, axis=axis, **kwargs)
+        if np.any(mask):
+            res = _copyto(res, np.nan, mask)
+            warnings.warn("All-NaN axis encountered", RuntimeWarning,
+                          stacklevel=2)
+    return res
+
+
+def _nanmax_dispatcher(a, axis=None, out=None, keepdims=None,
+                       initial=None, where=None):
+    return (a, out)
+
+
+@array_function_dispatch(_nanmax_dispatcher)
+def nanmax(a, axis=None, out=None, keepdims=np._NoValue, initial=np._NoValue,
+           where=np._NoValue):
+    """
+    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
+    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:: 1.22.0
+    where : array_like of bool, optional
+        Elements to compare for the maximum. See `~numpy.ufunc.reduce`
+        for details.
+
+        .. versionadded:: 1.22.0
+
+    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
+
+    """
+    kwargs = {}
+    if keepdims is not np._NoValue:
+        kwargs['keepdims'] = keepdims
+    if initial is not np._NoValue:
+        kwargs['initial'] = initial
+    if where is not np._NoValue:
+        kwargs['where'] = where
+
+    if type(a) is np.ndarray and a.dtype != np.object_:
+        # Fast, but not safe for subclasses of ndarray, or object arrays,
+        # which do not implement isnan (gh-9009), or fmax correctly (gh-8975)
+        res = np.fmax.reduce(a, axis=axis, out=out, **kwargs)
+        if np.isnan(res).any():
+            warnings.warn("All-NaN slice encountered", RuntimeWarning,
+                          stacklevel=2)
+    else:
+        # Slow, but safe for subclasses of ndarray
+        a, mask = _replace_nan(a, -np.inf)
+        res = np.amax(a, axis=axis, out=out, **kwargs)
+        if mask is None:
+            return res
+
+        # Check for all-NaN axis
+        kwargs.pop("initial", None)
+        mask = np.all(mask, axis=axis, **kwargs)
+        if np.any(mask):
+            res = _copyto(res, np.nan, mask)
+            warnings.warn("All-NaN axis encountered", RuntimeWarning,
+                          stacklevel=2)
+    return res
+
+
+def _nanargmin_dispatcher(a, axis=None, out=None, *, keepdims=None):
+    return (a,)
+
+
+@array_function_dispatch(_nanargmin_dispatcher)
+def nanargmin(a, axis=None, out=None, *, keepdims=np._NoValue):
+    """
+    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.
+    out : array, optional
+        If provided, the result will be inserted into this array. It should
+        be of the appropriate shape and dtype.
+
+        .. versionadded:: 1.22.0
+    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 array.
+
+        .. versionadded:: 1.22.0
+
+    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])
+
+    """
+    a, mask = _replace_nan(a, np.inf)
+    if mask is not None:
+        mask = np.all(mask, axis=axis)
+        if np.any(mask):
+            raise ValueError("All-NaN slice encountered")
+    res = np.argmin(a, axis=axis, out=out, keepdims=keepdims)
+    return res
+
+
+def _nanargmax_dispatcher(a, axis=None, out=None, *, keepdims=None):
+    return (a,)
+
+
+@array_function_dispatch(_nanargmax_dispatcher)
+def nanargmax(a, axis=None, out=None, *, keepdims=np._NoValue):
+    """
+    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.
+    out : array, optional
+        If provided, the result will be inserted into this array. It should
+        be of the appropriate shape and dtype.
+
+        .. versionadded:: 1.22.0
+    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 array.
+
+        .. versionadded:: 1.22.0
+
+    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])
+
+    """
+    a, mask = _replace_nan(a, -np.inf)
+    if mask is not None:
+        mask = np.all(mask, axis=axis)
+        if np.any(mask):
+            raise ValueError("All-NaN slice encountered")
+    res = np.argmax(a, axis=axis, out=out, keepdims=keepdims)
+    return res
+
+
+def _nansum_dispatcher(a, axis=None, dtype=None, out=None, keepdims=None,
+                       initial=None, where=None):
+    return (a, out)
+
+
+@array_function_dispatch(_nansum_dispatcher)
+def nansum(a, axis=None, dtype=None, out=None, keepdims=np._NoValue,
+           initial=np._NoValue, where=np._NoValue):
+    """
+    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
+    initial : scalar, optional
+        Starting value for the sum. See `~numpy.ufunc.reduce` for details.
+
+        .. versionadded:: 1.22.0
+    where : array_like of bool, optional
+        Elements to include in the sum. See `~numpy.ufunc.reduce` for details.
+
+        .. versionadded:: 1.22.0
+
+    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)
+    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
+
+    """
+    a, mask = _replace_nan(a, 0)
+    return np.sum(a, axis=axis, dtype=dtype, out=out, keepdims=keepdims,
+                  initial=initial, where=where)
+
+
+def _nanprod_dispatcher(a, axis=None, dtype=None, out=None, keepdims=None,
+                        initial=None, where=None):
+    return (a, out)
+
+
+@array_function_dispatch(_nanprod_dispatcher)
+def nanprod(a, axis=None, dtype=None, out=None, keepdims=np._NoValue,
+            initial=np._NoValue, where=np._NoValue):
+    """
+    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`.
+    initial : scalar, optional
+        The starting value for this product. See `~numpy.ufunc.reduce`
+        for details.
+
+        .. versionadded:: 1.22.0
+    where : array_like of bool, optional
+        Elements to include in the product. See `~numpy.ufunc.reduce`
+        for details.
+
+        .. versionadded:: 1.22.0
+
+    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)
+    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.])
+
+    """
+    a, mask = _replace_nan(a, 1)
+    return np.prod(a, axis=axis, dtype=dtype, out=out, keepdims=keepdims,
+                   initial=initial, where=where)
+
+
+def _nancumsum_dispatcher(a, axis=None, dtype=None, out=None):
+    return (a, out)
+
+
+@array_function_dispatch(_nancumsum_dispatcher)
+def nancumsum(a, axis=None, dtype=None, out=None):
+    """
+    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)
+    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.]])
+
+    """
+    a, mask = _replace_nan(a, 0)
+    return np.cumsum(a, axis=axis, dtype=dtype, out=out)
+
+
+def _nancumprod_dispatcher(a, axis=None, dtype=None, out=None):
+    return (a, out)
+
+
+@array_function_dispatch(_nancumprod_dispatcher)
+def nancumprod(a, axis=None, dtype=None, out=None):
+    """
+    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)
+    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.]])
+
+    """
+    a, mask = _replace_nan(a, 1)
+    return np.cumprod(a, axis=axis, dtype=dtype, out=out)
+
+
+def _nanmean_dispatcher(a, axis=None, dtype=None, out=None, keepdims=None,
+                        *, where=None):
+    return (a, out)
+
+
+@array_function_dispatch(_nanmean_dispatcher)
+def nanmean(a, axis=None, dtype=None, out=None, keepdims=np._NoValue,
+            *, where=np._NoValue):
+    """
+    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.
+    where : array_like of bool, optional
+        Elements to include in the mean. See `~numpy.ufunc.reduce` for details.
+
+        .. versionadded:: 1.22.0
+
+    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. 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
+
+    """
+    arr, mask = _replace_nan(a, 0)
+    if mask is None:
+        return np.mean(arr, axis=axis, dtype=dtype, out=out, keepdims=keepdims,
+                       where=where)
+
+    if dtype is not None:
+        dtype = np.dtype(dtype)
+    if dtype is not None and not issubclass(dtype.type, np.inexact):
+        raise TypeError("If a is inexact, then dtype must be inexact")
+    if out is not None and not issubclass(out.dtype.type, np.inexact):
+        raise TypeError("If a is inexact, then out must be inexact")
+
+    cnt = np.sum(~mask, axis=axis, dtype=np.intp, keepdims=keepdims,
+                 where=where)
+    tot = np.sum(arr, axis=axis, dtype=dtype, out=out, keepdims=keepdims,
+                 where=where)
+    avg = _divide_by_count(tot, cnt, out=out)
+
+    isbad = (cnt == 0)
+    if isbad.any():
+        warnings.warn("Mean of empty slice", RuntimeWarning, stacklevel=2)
+        # NaN is the only possible bad value, so no further
+        # action is needed to handle bad results.
+    return avg
+
+
+def _nanmedian1d(arr1d, overwrite_input=False):
+    """
+    Private function for rank 1 arrays. Compute the median ignoring NaNs.
+    See nanmedian for parameter usage
+    """
+    arr1d_parsed, overwrite_input = _remove_nan_1d(
+        arr1d, overwrite_input=overwrite_input,
+    )
+
+    if arr1d_parsed.size == 0:
+        # Ensure that a nan-esque scalar of the appropriate type (and unit)
+        # is returned for `timedelta64` and `complexfloating`
+        return arr1d[-1]
+
+    return np.median(arr1d_parsed, overwrite_input=overwrite_input)
+
+
+def _nanmedian(a, axis=None, out=None, overwrite_input=False):
+    """
+    Private function that doesn't support extended axis or keepdims.
+    These methods are extended to this function using _ureduce
+    See nanmedian for parameter usage
+
+    """
+    if axis is None or a.ndim == 1:
+        part = a.ravel()
+        if out is None:
+            return _nanmedian1d(part, overwrite_input)
+        else:
+            out[...] = _nanmedian1d(part, overwrite_input)
+            return out
+    else:
+        # for small medians use sort + indexing which is still faster than
+        # apply_along_axis
+        # benchmarked with shuffled (50, 50, x) containing a few NaN
+        if a.shape[axis] < 600:
+            return _nanmedian_small(a, axis, out, overwrite_input)
+        result = np.apply_along_axis(_nanmedian1d, axis, a, overwrite_input)
+        if out is not None:
+            out[...] = result
+        return result
+
+
+def _nanmedian_small(a, axis=None, out=None, overwrite_input=False):
+    """
+    sort + indexing median, faster for small medians along multiple
+    dimensions due to the high overhead of apply_along_axis
+
+    see nanmedian for parameter usage
+    """
+    a = np.ma.masked_array(a, np.isnan(a))
+    m = np.ma.median(a, axis=axis, overwrite_input=overwrite_input)
+    for i in range(np.count_nonzero(m.mask.ravel())):
+        warnings.warn("All-NaN slice encountered", RuntimeWarning,
+                      stacklevel=5)
+
+    fill_value = np.timedelta64("NaT") if m.dtype.kind == "m" else np.nan
+    if out is not None:
+        out[...] = m.filled(fill_value)
+        return out
+    return m.filled(fill_value)
+
+
+def _nanmedian_dispatcher(
+        a, axis=None, out=None, overwrite_input=None, keepdims=None):
+    return (a, out)
+
+
+@array_function_dispatch(_nanmedian_dispatcher)
+def nanmedian(a, axis=None, out=None, overwrite_input=False, keepdims=np._NoValue):
+    """
+    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)
+
+    """
+    a = np.asanyarray(a)
+    # apply_along_axis in _nanmedian doesn't handle empty arrays well,
+    # so deal them upfront
+    if a.size == 0:
+        return np.nanmean(a, axis, out=out, keepdims=keepdims)
+
+    return function_base._ureduce(a, func=_nanmedian, keepdims=keepdims,
+                                  axis=axis, out=out,
+                                  overwrite_input=overwrite_input)
+
+
+def _nanpercentile_dispatcher(
+        a, q, axis=None, out=None, overwrite_input=None,
+        method=None, keepdims=None, *, interpolation=None):
+    return (a, q, out)
+
+
+@array_function_dispatch(_nanpercentile_dispatcher)
+def nanpercentile(
+        a,
+        q,
+        axis=None,
+        out=None,
+        overwrite_input=False,
+        method="linear",
+        keepdims=np._NoValue,
+        *,
+        interpolation=None,
+):
+    """
+    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.
+    method : str, optional
+        This parameter specifies the method to use for estimating the
+        percentile.  There are many different methods, some unique to NumPy.
+        See the notes for explanation.  The options sorted by their R type
+        as summarized in the H&F paper [1]_ are:
+
+        1. 'inverted_cdf'
+        2. 'averaged_inverted_cdf'
+        3. 'closest_observation'
+        4. 'interpolated_inverted_cdf'
+        5. 'hazen'
+        6. 'weibull'
+        7. 'linear'  (default)
+        8. 'median_unbiased'
+        9. 'normal_unbiased'
+
+        The first three methods are discontinuous.  NumPy further defines the
+        following discontinuous variations of the default 'linear' (7.) option:
+
+        * 'lower'
+        * 'higher',
+        * 'midpoint'
+        * 'nearest'
+
+        .. versionchanged:: 1.22.0
+            This argument was previously called "interpolation" and only
+            offered the "linear" default and last four options.
+
+    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.
+
+    interpolation : str, optional
+        Deprecated name for the method keyword argument.
+
+        .. deprecated:: 1.22.0
+
+    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
+    --------
+    nanmean
+    nanmedian : equivalent to ``nanpercentile(..., 50)``
+    percentile, median, mean
+    nanquantile : equivalent to nanpercentile, except q in range [0, 1].
+
+    Notes
+    -----
+    For more information please see `numpy.percentile`
+
+    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)
+
+    References
+    ----------
+    .. [1] R. J. Hyndman and Y. Fan,
+       "Sample quantiles in statistical packages,"
+       The American Statistician, 50(4), pp. 361-365, 1996
+
+    """
+    if interpolation is not None:
+        method = function_base._check_interpolation_as_method(
+            method, interpolation, "nanpercentile")
+
+    a = np.asanyarray(a)
+    if a.dtype.kind == "c":
+        raise TypeError("a must be an array of real numbers")
+
+    q = np.true_divide(q, 100.0)
+    # undo any decay that the ufunc performed (see gh-13105)
+    q = np.asanyarray(q)
+    if not function_base._quantile_is_valid(q):
+        raise ValueError("Percentiles must be in the range [0, 100]")
+    return _nanquantile_unchecked(
+        a, q, axis, out, overwrite_input, method, keepdims)
+
+
+def _nanquantile_dispatcher(a, q, axis=None, out=None, overwrite_input=None,
+                            method=None, keepdims=None, *, interpolation=None):
+    return (a, q, out)
+
+
+@array_function_dispatch(_nanquantile_dispatcher)
+def nanquantile(
+        a,
+        q,
+        axis=None,
+        out=None,
+        overwrite_input=False,
+        method="linear",
+        keepdims=np._NoValue,
+        *,
+        interpolation=None,
+):
+    """
+    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
+        Probability or sequence of probabilities for the quantiles to compute.
+        Values 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.
+    method : str, optional
+        This parameter specifies the method to use for estimating the
+        quantile.  There are many different methods, some unique to NumPy.
+        See the notes for explanation.  The options sorted by their R type
+        as summarized in the H&F paper [1]_ are:
+
+        1. 'inverted_cdf'
+        2. 'averaged_inverted_cdf'
+        3. 'closest_observation'
+        4. 'interpolated_inverted_cdf'
+        5. 'hazen'
+        6. 'weibull'
+        7. 'linear'  (default)
+        8. 'median_unbiased'
+        9. 'normal_unbiased'
+
+        The first three methods are discontinuous.  NumPy further defines the
+        following discontinuous variations of the default 'linear' (7.) option:
+
+        * 'lower'
+        * 'higher',
+        * 'midpoint'
+        * 'nearest'
+
+        .. versionchanged:: 1.22.0
+            This argument was previously called "interpolation" and only
+            offered the "linear" default and last four options.
+
+    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.
+
+    interpolation : str, optional
+        Deprecated name for the method keyword argument.
+
+        .. deprecated:: 1.22.0
+
+    Returns
+    -------
+    quantile : scalar or ndarray
+        If `q` is a single probability and `axis=None`, then the result
+        is a scalar. If multiple probability levels 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].
+
+    Notes
+    -----
+    For more information please see `numpy.quantile`
+
+    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)
+
+    References
+    ----------
+    .. [1] R. J. Hyndman and Y. Fan,
+       "Sample quantiles in statistical packages,"
+       The American Statistician, 50(4), pp. 361-365, 1996
+
+    """
+
+    if interpolation is not None:
+        method = function_base._check_interpolation_as_method(
+            method, interpolation, "nanquantile")
+
+    a = np.asanyarray(a)
+    if a.dtype.kind == "c":
+        raise TypeError("a must be an array of real numbers")
+
+    q = np.asanyarray(q)
+    if not function_base._quantile_is_valid(q):
+        raise ValueError("Quantiles must be in the range [0, 1]")
+    return _nanquantile_unchecked(
+        a, q, axis, out, overwrite_input, method, keepdims)
+
+
+def _nanquantile_unchecked(
+        a,
+        q,
+        axis=None,
+        out=None,
+        overwrite_input=False,
+        method="linear",
+        keepdims=np._NoValue,
+):
+    """Assumes that q is in [0, 1], and is an ndarray"""
+    # apply_along_axis in _nanpercentile doesn't handle empty arrays well,
+    # so deal them upfront
+    if a.size == 0:
+        return np.nanmean(a, axis, out=out, keepdims=keepdims)
+    return function_base._ureduce(a,
+                                  func=_nanquantile_ureduce_func,
+                                  q=q,
+                                  keepdims=keepdims,
+                                  axis=axis,
+                                  out=out,
+                                  overwrite_input=overwrite_input,
+                                  method=method)
+
+
+def _nanquantile_ureduce_func(a, q, axis=None, out=None, overwrite_input=False,
+                              method="linear"):
+    """
+    Private function that doesn't support extended axis or keepdims.
+    These methods are extended to this function using _ureduce
+    See nanpercentile for parameter usage
+    """
+    if axis is None or a.ndim == 1:
+        part = a.ravel()
+        result = _nanquantile_1d(part, q, overwrite_input, method)
+    else:
+        result = np.apply_along_axis(_nanquantile_1d, axis, a, q,
+                                     overwrite_input, method)
+        # apply_along_axis fills in collapsed axis with results.
+        # Move that axis to the beginning to match percentile's
+        # convention.
+        if q.ndim != 0:
+            result = np.moveaxis(result, axis, 0)
+
+    if out is not None:
+        out[...] = result
+    return result
+
+
+def _nanquantile_1d(arr1d, q, overwrite_input=False, method="linear"):
+    """
+    Private function for rank 1 arrays. Compute quantile ignoring NaNs.
+    See nanpercentile for parameter usage
+    """
+    arr1d, overwrite_input = _remove_nan_1d(arr1d,
+        overwrite_input=overwrite_input)
+    if arr1d.size == 0:
+        # convert to scalar
+        return np.full(q.shape, np.nan, dtype=arr1d.dtype)[()]
+
+    return function_base._quantile_unchecked(
+        arr1d, q, overwrite_input=overwrite_input, method=method)
+
+
+def _nanvar_dispatcher(a, axis=None, dtype=None, out=None, ddof=None,
+                       keepdims=None, *, where=None):
+    return (a, out)
+
+
+@array_function_dispatch(_nanvar_dispatcher)
+def nanvar(a, axis=None, dtype=None, out=None, ddof=0, keepdims=np._NoValue,
+           *, where=np._NoValue):
+    """
+    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`.
+    where : array_like of bool, optional
+        Elements to include in the variance. See `~numpy.ufunc.reduce` for
+        details.
+
+        .. versionadded:: 1.22.0
+
+    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
+
+    """
+    arr, mask = _replace_nan(a, 0)
+    if mask is None:
+        return np.var(arr, axis=axis, dtype=dtype, out=out, ddof=ddof,
+                      keepdims=keepdims, where=where)
+
+    if dtype is not None:
+        dtype = np.dtype(dtype)
+    if dtype is not None and not issubclass(dtype.type, np.inexact):
+        raise TypeError("If a is inexact, then dtype must be inexact")
+    if out is not None and not issubclass(out.dtype.type, np.inexact):
+        raise TypeError("If a is inexact, then out must be inexact")
+
+    # Compute mean
+    if type(arr) is np.matrix:
+        _keepdims = np._NoValue
+    else:
+        _keepdims = True
+    # we need to special case matrix for reverse compatibility
+    # in order for this to work, these sums need to be called with
+    # keepdims=True, however matrix now raises an error in this case, but
+    # the reason that it drops the keepdims kwarg is to force keepdims=True
+    # so this used to work by serendipity.
+    cnt = np.sum(~mask, axis=axis, dtype=np.intp, keepdims=_keepdims,
+                 where=where)
+    avg = np.sum(arr, axis=axis, dtype=dtype, keepdims=_keepdims, where=where)
+    avg = _divide_by_count(avg, cnt)
+
+    # Compute squared deviation from mean.
+    np.subtract(arr, avg, out=arr, casting='unsafe', where=where)
+    arr = _copyto(arr, 0, mask)
+    if issubclass(arr.dtype.type, np.complexfloating):
+        sqr = np.multiply(arr, arr.conj(), out=arr, where=where).real
+    else:
+        sqr = np.multiply(arr, arr, out=arr, where=where)
+
+    # Compute variance.
+    var = np.sum(sqr, axis=axis, dtype=dtype, out=out, keepdims=keepdims,
+                 where=where)
+
+    # Precaution against reduced object arrays
+    try:
+        var_ndim = var.ndim
+    except AttributeError:
+        var_ndim = np.ndim(var)
+    if var_ndim < cnt.ndim:
+        # Subclasses of ndarray may ignore keepdims, so check here.
+        cnt = cnt.squeeze(axis)
+    dof = cnt - ddof
+    var = _divide_by_count(var, dof)
+
+    isbad = (dof <= 0)
+    if np.any(isbad):
+        warnings.warn("Degrees of freedom <= 0 for slice.", RuntimeWarning,
+                      stacklevel=2)
+        # NaN, inf, or negative numbers are all possible bad
+        # values, so explicitly replace them with NaN.
+        var = _copyto(var, np.nan, isbad)
+    return var
+
+
+def _nanstd_dispatcher(a, axis=None, dtype=None, out=None, ddof=None,
+                       keepdims=None, *, where=None):
+    return (a, out)
+
+
+@array_function_dispatch(_nanstd_dispatcher)
+def nanstd(a, axis=None, dtype=None, out=None, ddof=0, keepdims=np._NoValue,
+           *, where=np._NoValue):
+    """
+    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.
+    where : array_like of bool, optional
+        Elements to include in the standard deviation.
+        See `~numpy.ufunc.reduce` for details.
+
+        .. versionadded:: 1.22.0
+
+    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. 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
+
+    """
+    var = nanvar(a, axis=axis, dtype=dtype, out=out, ddof=ddof,
+                 keepdims=keepdims, where=where)
+    if isinstance(var, np.ndarray):
+        std = np.sqrt(var, out=var)
+    elif hasattr(var, 'dtype'):
+        std = var.dtype.type(np.sqrt(var))
+    else:
+        std = np.sqrt(var)
+    return std

env-llmeval/lib/python3.10/site-packages/numpy/lib/nanfunctions.pyi

@@ -0,0 +1,38 @@
+from numpy.core.fromnumeric import (
+    amin,
+    amax,
+    argmin,
+    argmax,
+    sum,
+    prod,
+    cumsum,
+    cumprod,
+    mean,
+    var,
+    std
+)
+
+from numpy.lib.function_base import (
+    median,
+    percentile,
+    quantile,
+)
+
+__all__: list[str]
+
+# NOTE: In reaility these functions are not aliases but distinct functions
+# with identical signatures.
+nanmin = amin
+nanmax = amax
+nanargmin = argmin
+nanargmax = argmax
+nansum = sum
+nanprod = prod
+nancumsum = cumsum
+nancumprod = cumprod
+nanmean = mean
+nanvar = var
+nanstd = std
+nanmedian = median
+nanpercentile = percentile
+nanquantile = quantile

env-llmeval/lib/python3.10/site-packages/numpy/lib/npyio.py

@@ -0,0 +1,2547 @@
+import os
+import re
+import functools
+import itertools
+import warnings
+import weakref
+import contextlib
+import operator
+from operator import itemgetter, index as opindex, methodcaller
+from collections.abc import Mapping
+
+import numpy as np
+from . import format
+from ._datasource import DataSource
+from numpy.core import overrides
+from numpy.core.multiarray import packbits, unpackbits
+from numpy.core._multiarray_umath import _load_from_filelike
+from numpy.core.overrides import set_array_function_like_doc, set_module
+from ._iotools import (
+    LineSplitter, NameValidator, StringConverter, ConverterError,
+    ConverterLockError, ConversionWarning, _is_string_like,
+    has_nested_fields, flatten_dtype, easy_dtype, _decode_line
+    )
+
+from numpy.compat import (
+    asbytes, asstr, asunicode, os_fspath, os_PathLike,
+    pickle
+    )
+
+
+__all__ = [
+    'savetxt', 'loadtxt', 'genfromtxt',
+    'recfromtxt', 'recfromcsv', 'load', 'save', 'savez',
+    'savez_compressed', 'packbits', 'unpackbits', 'fromregex', 'DataSource'
+    ]
+
+
+array_function_dispatch = functools.partial(
+    overrides.array_function_dispatch, module='numpy')
+
+
+class BagObj:
+    """
+    BagObj(obj)
+
+    Convert attribute look-ups to getitems on the object passed in.
+
+    Parameters
+    ----------
+    obj : class instance
+        Object on which attribute look-up is performed.
+
+    Examples
+    --------
+    >>> from numpy.lib.npyio import BagObj as BO
+    >>> class BagDemo:
+    ...     def __getitem__(self, key): # An instance of BagObj(BagDemo)
+    ...                                 # will call this method when any
+    ...                                 # attribute look-up is required
+    ...         result = "Doesn't matter what you want, "
+    ...         return result + "you're gonna get this"
+    ...
+    >>> demo_obj = BagDemo()
+    >>> bagobj = BO(demo_obj)
+    >>> bagobj.hello_there
+    "Doesn't matter what you want, you're gonna get this"
+    >>> bagobj.I_can_be_anything
+    "Doesn't matter what you want, you're gonna get this"
+
+    """
+
+    def __init__(self, obj):
+        # Use weakref to make NpzFile objects collectable by refcount
+        self._obj = weakref.proxy(obj)
+
+    def __getattribute__(self, key):
+        try:
+            return object.__getattribute__(self, '_obj')[key]
+        except KeyError:
+            raise AttributeError(key) from None
+
+    def __dir__(self):
+        """
+        Enables dir(bagobj) to list the files in an NpzFile.
+
+        This also enables tab-completion in an interpreter or IPython.
+        """
+        return list(object.__getattribute__(self, '_obj').keys())
+
+
+def zipfile_factory(file, *args, **kwargs):
+    """
+    Create a ZipFile.
+
+    Allows for Zip64, and the `file` argument can accept file, str, or
+    pathlib.Path objects. `args` and `kwargs` are passed to the zipfile.ZipFile
+    constructor.
+    """
+    if not hasattr(file, 'read'):
+        file = os_fspath(file)
+    import zipfile
+    kwargs['allowZip64'] = True
+    return zipfile.ZipFile(file, *args, **kwargs)
+
+
+class NpzFile(Mapping):
+    """
+    NpzFile(fid)
+
+    A dictionary-like object with lazy-loading of files in the zipped
+    archive provided on construction.
+
+    `NpzFile` is used to load files in the NumPy ``.npz`` data archive
+    format. It assumes that files in the archive have a ``.npy`` extension,
+    other files are ignored.
+
+    The arrays and file strings are lazily loaded on either
+    getitem access using ``obj['key']`` or attribute lookup using
+    ``obj.f.key``. A list of all files (without ``.npy`` extensions) can
+    be obtained with ``obj.files`` and the ZipFile object itself using
+    ``obj.zip``.
+
+    Attributes
+    ----------
+    files : list of str
+        List of all files in the archive with a ``.npy`` extension.
+    zip : ZipFile instance
+        The ZipFile object initialized with the zipped archive.
+    f : BagObj instance
+        An object on which attribute can be performed as an alternative
+        to getitem access on the `NpzFile` instance itself.
+    allow_pickle : bool, optional
+        Allow loading pickled data. Default: False
+
+        .. versionchanged:: 1.16.3
+            Made default False in response to CVE-2019-6446.
+
+    pickle_kwargs : dict, optional
+        Additional keyword arguments to pass on to pickle.load.
+        These are only useful when loading object arrays saved on
+        Python 2 when using Python 3.
+    max_header_size : int, optional
+        Maximum allowed size of the header.  Large headers may not be safe
+        to load securely and thus require explicitly passing a larger value.
+        See :py:func:`ast.literal_eval()` for details.
+        This option is ignored when `allow_pickle` is passed.  In that case
+        the file is by definition trusted and the limit is unnecessary.
+
+    Parameters
+    ----------
+    fid : file or str
+        The zipped archive to open. This is either a file-like object
+        or a string containing the path to the archive.
+    own_fid : bool, optional
+        Whether NpzFile should close the file handle.
+        Requires that `fid` is a file-like object.
+
+    Examples
+    --------
+    >>> from tempfile import TemporaryFile
+    >>> outfile = TemporaryFile()
+    >>> x = np.arange(10)
+    >>> y = np.sin(x)
+    >>> np.savez(outfile, x=x, y=y)
+    >>> _ = outfile.seek(0)
+
+    >>> npz = np.load(outfile)
+    >>> isinstance(npz, np.lib.npyio.NpzFile)
+    True
+    >>> npz
+    NpzFile 'object' with keys x, y
+    >>> sorted(npz.files)
+    ['x', 'y']
+    >>> npz['x']  # getitem access
+    array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
+    >>> npz.f.x  # attribute lookup
+    array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
+
+    """
+    # Make __exit__ safe if zipfile_factory raises an exception
+    zip = None
+    fid = None
+    _MAX_REPR_ARRAY_COUNT = 5
+
+    def __init__(self, fid, own_fid=False, allow_pickle=False,
+                 pickle_kwargs=None, *,
+                 max_header_size=format._MAX_HEADER_SIZE):
+        # Import is postponed to here since zipfile depends on gzip, an
+        # optional component of the so-called standard library.
+        _zip = zipfile_factory(fid)
+        self._files = _zip.namelist()
+        self.files = []
+        self.allow_pickle = allow_pickle
+        self.max_header_size = max_header_size
+        self.pickle_kwargs = pickle_kwargs
+        for x in self._files:
+            if x.endswith('.npy'):
+                self.files.append(x[:-4])
+            else:
+                self.files.append(x)
+        self.zip = _zip
+        self.f = BagObj(self)
+        if own_fid:
+            self.fid = fid
+
+    def __enter__(self):
+        return self
+
+    def __exit__(self, exc_type, exc_value, traceback):
+        self.close()
+
+    def close(self):
+        """
+        Close the file.
+
+        """
+        if self.zip is not None:
+            self.zip.close()
+            self.zip = None
+        if self.fid is not None:
+            self.fid.close()
+            self.fid = None
+        self.f = None  # break reference cycle
+
+    def __del__(self):
+        self.close()
+
+    # Implement the Mapping ABC
+    def __iter__(self):
+        return iter(self.files)
+
+    def __len__(self):
+        return len(self.files)
+
+    def __getitem__(self, key):
+        # FIXME: This seems like it will copy strings around
+        #   more than is strictly necessary.  The zipfile
+        #   will read the string and then
+        #   the format.read_array will copy the string
+        #   to another place in memory.
+        #   It would be better if the zipfile could read
+        #   (or at least uncompress) the data
+        #   directly into the array memory.
+        member = False
+        if key in self._files:
+            member = True
+        elif key in self.files:
+            member = True
+            key += '.npy'
+        if member:
+            bytes = self.zip.open(key)
+            magic = bytes.read(len(format.MAGIC_PREFIX))
+            bytes.close()
+            if magic == format.MAGIC_PREFIX:
+                bytes = self.zip.open(key)
+                return format.read_array(bytes,
+                                         allow_pickle=self.allow_pickle,
+                                         pickle_kwargs=self.pickle_kwargs,
+                                         max_header_size=self.max_header_size)
+            else:
+                return self.zip.read(key)
+        else:
+            raise KeyError(f"{key} is not a file in the archive")
+
+    def __contains__(self, key):
+        return (key in self._files or key in self.files)
+
+    def __repr__(self):
+        # Get filename or default to `object`
+        if isinstance(self.fid, str):
+            filename = self.fid
+        else:
+            filename = getattr(self.fid, "name", "object")
+
+        # Get the name of arrays
+        array_names = ', '.join(self.files[:self._MAX_REPR_ARRAY_COUNT])
+        if len(self.files) > self._MAX_REPR_ARRAY_COUNT:
+            array_names += "..."
+        return f"NpzFile {filename!r} with keys: {array_names}"
+
+
+@set_module('numpy')
+def load(file, mmap_mode=None, allow_pickle=False, fix_imports=True,
+         encoding='ASCII', *, max_header_size=format._MAX_HEADER_SIZE):
+    """
+    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 and must always
+        be opened in binary mode.  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'
+    max_header_size : int, optional
+        Maximum allowed size of the header.  Large headers may not be safe
+        to load securely and thus require explicitly passing a larger value.
+        See :py:func:`ast.literal_eval()` for details.
+        This option is ignored when `allow_pickle` is passed.  In that case
+        the file is by definition trusted and the limit is unnecessary.
+
+    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
+    ------
+    OSError
+        If the input file does not exist or cannot be read.
+    UnpicklingError
+        If ``allow_pickle=True``, but the file cannot be loaded as a pickle.
+    ValueError
+        The file contains an object array, but ``allow_pickle=False`` given.
+    EOFError
+        When calling ``np.load`` multiple times on the same file handle,
+        if all data has already been read
+
+    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])
+
+    """
+    if encoding not in ('ASCII', 'latin1', 'bytes'):
+        # The 'encoding' value for pickle also affects what encoding
+        # the serialized binary data of NumPy arrays is loaded
+        # in. Pickle does not pass on the encoding information to
+        # NumPy. The unpickling code in numpy.core.multiarray is
+        # written to assume that unicode data appearing where binary
+        # should be is in 'latin1'. 'bytes' is also safe, as is 'ASCII'.
+        #
+        # Other encoding values can corrupt binary data, and we
+        # purposefully disallow them. For the same reason, the errors=
+        # argument is not exposed, as values other than 'strict'
+        # result can similarly silently corrupt numerical data.
+        raise ValueError("encoding must be 'ASCII', 'latin1', or 'bytes'")
+
+    pickle_kwargs = dict(encoding=encoding, fix_imports=fix_imports)
+
+    with contextlib.ExitStack() as stack:
+        if hasattr(file, 'read'):
+            fid = file
+            own_fid = False
+        else:
+            fid = stack.enter_context(open(os_fspath(file), "rb"))
+            own_fid = True
+
+        # Code to distinguish from NumPy binary files and pickles.
+        _ZIP_PREFIX = b'PK\x03\x04'
+        _ZIP_SUFFIX = b'PK\x05\x06' # empty zip files start with this
+        N = len(format.MAGIC_PREFIX)
+        magic = fid.read(N)
+        if not magic:
+            raise EOFError("No data left in file")
+        # If the file size is less than N, we need to make sure not
+        # to seek past the beginning of the file
+        fid.seek(-min(N, len(magic)), 1)  # back-up
+        if magic.startswith(_ZIP_PREFIX) or magic.startswith(_ZIP_SUFFIX):
+            # zip-file (assume .npz)
+            # Potentially transfer file ownership to NpzFile
+            stack.pop_all()
+            ret = NpzFile(fid, own_fid=own_fid, allow_pickle=allow_pickle,
+                          pickle_kwargs=pickle_kwargs,
+                          max_header_size=max_header_size)
+            return ret
+        elif magic == format.MAGIC_PREFIX:
+            # .npy file
+            if mmap_mode:
+                if allow_pickle:
+                    max_header_size = 2**64
+                return format.open_memmap(file, mode=mmap_mode,
+                                          max_header_size=max_header_size)
+            else:
+                return format.read_array(fid, allow_pickle=allow_pickle,
+                                         pickle_kwargs=pickle_kwargs,
+                                         max_header_size=max_header_size)
+        else:
+            # Try a pickle
+            if not allow_pickle:
+                raise ValueError("Cannot load file containing pickled data "
+                                 "when allow_pickle=False")
+            try:
+                return pickle.load(fid, **pickle_kwargs)
+            except Exception as e:
+                raise pickle.UnpicklingError(
+                    f"Failed to interpret file {file!r} as a pickle") from e
+
+
+def _save_dispatcher(file, arr, allow_pickle=None, fix_imports=None):
+    return (arr,)
+
+
+@array_function_dispatch(_save_dispatcher)
+def save(file, arr, allow_pickle=True, fix_imports=True):
+    """
+    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)
+    >>> np.save(outfile, x)
+
+    >>> _ = outfile.seek(0) # 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]
+    """
+    if hasattr(file, 'write'):
+        file_ctx = contextlib.nullcontext(file)
+    else:
+        file = os_fspath(file)
+        if not file.endswith('.npy'):
+            file = file + '.npy'
+        file_ctx = open(file, "wb")
+
+    with file_ctx as fid:
+        arr = np.asanyarray(arr)
+        format.write_array(fid, arr, allow_pickle=allow_pickle,
+                           pickle_kwargs=dict(fix_imports=fix_imports))
+
+
+def _savez_dispatcher(file, *args, **kwds):
+    yield from args
+    yield from kwds.values()
+
+
+@array_function_dispatch(_savez_dispatcher)
+def savez(file, *args, **kwds):
+    """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.
+
+    Keys passed in `kwds` are used as filenames inside the ZIP archive.
+    Therefore, keys should be valid filenames; e.g., avoid keys that begin with
+    ``/`` or contain ``.``.
+
+    When naming variables with keyword arguments, it is not possible to name a
+    variable ``file``, as this would cause the ``file`` argument to be defined
+    twice in the call to ``savez``.
+
+    Examples
+    --------
+    >>> from tempfile import TemporaryFile
+    >>> outfile = TemporaryFile()
+    >>> x = np.arange(10)
+    >>> y = np.sin(x)
+
+    Using `savez` with \\*args, the arrays are saved with default names.
+
+    >>> np.savez(outfile, x, y)
+    >>> _ = outfile.seek(0) # 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)
+    >>> npzfile = np.load(outfile)
+    >>> sorted(npzfile.files)
+    ['x', 'y']
+    >>> npzfile['x']
+    array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
+
+    """
+    _savez(file, args, kwds, False)
+
+
+def _savez_compressed_dispatcher(file, *args, **kwds):
+    yield from args
+    yield from kwds.values()
+
+
+@array_function_dispatch(_savez_compressed_dispatcher)
+def savez_compressed(file, *args, **kwds):
+    """
+    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)
+    >>> 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
+
+    """
+    _savez(file, args, kwds, True)
+
+
+def _savez(file, args, kwds, compress, allow_pickle=True, pickle_kwargs=None):
+    # Import is postponed to here since zipfile depends on gzip, an optional
+    # component of the so-called standard library.
+    import zipfile
+
+    if not hasattr(file, 'write'):
+        file = os_fspath(file)
+        if not file.endswith('.npz'):
+            file = file + '.npz'
+
+    namedict = kwds
+    for i, val in enumerate(args):
+        key = 'arr_%d' % i
+        if key in namedict.keys():
+            raise ValueError(
+                "Cannot use un-named variables and keyword %s" % key)
+        namedict[key] = val
+
+    if compress:
+        compression = zipfile.ZIP_DEFLATED
+    else:
+        compression = zipfile.ZIP_STORED
+
+    zipf = zipfile_factory(file, mode="w", compression=compression)
+
+    for key, val in namedict.items():
+        fname = key + '.npy'
+        val = np.asanyarray(val)
+        # always force zip64, gh-10776
+        with zipf.open(fname, 'w', force_zip64=True) as fid:
+            format.write_array(fid, val,
+                               allow_pickle=allow_pickle,
+                               pickle_kwargs=pickle_kwargs)
+
+    zipf.close()
+
+
+def _ensure_ndmin_ndarray_check_param(ndmin):
+    """Just checks if the param ndmin is supported on
+        _ensure_ndmin_ndarray. It is intended to be used as
+        verification before running anything expensive.
+        e.g. loadtxt, genfromtxt
+    """
+    # Check correctness of the values of `ndmin`
+    if ndmin not in [0, 1, 2]:
+        raise ValueError(f"Illegal value of ndmin keyword: {ndmin}")
+
+def _ensure_ndmin_ndarray(a, *, ndmin: int):
+    """This is a helper function of loadtxt and genfromtxt to ensure
+        proper minimum dimension as requested
+
+        ndim : int. Supported values 1, 2, 3
+                    ^^ whenever this changes, keep in sync with
+                       _ensure_ndmin_ndarray_check_param
+    """
+    # Verify that the array has at least dimensions `ndmin`.
+    # Tweak the size and shape of the arrays - remove extraneous dimensions
+    if a.ndim > ndmin:
+        a = np.squeeze(a)
+    # and ensure we have the minimum number of dimensions asked for
+    # - has to be in this order for the odd case ndmin=1, a.squeeze().ndim=0
+    if a.ndim < ndmin:
+        if ndmin == 1:
+            a = np.atleast_1d(a)
+        elif ndmin == 2:
+            a = np.atleast_2d(a).T
+
+    return a
+
+
+# amount of lines loadtxt reads in one chunk, can be overridden for testing
+_loadtxt_chunksize = 50000
+
+
+def _check_nonneg_int(value, name="argument"):
+    try:
+        operator.index(value)
+    except TypeError:
+        raise TypeError(f"{name} must be an integer") from None
+    if value < 0:
+        raise ValueError(f"{name} must be nonnegative")
+
+
+def _preprocess_comments(iterable, comments, encoding):
+    """
+    Generator that consumes a line iterated iterable and strips out the
+    multiple (or multi-character) comments from lines.
+    This is a pre-processing step to achieve feature parity with loadtxt
+    (we assume that this feature is a nieche feature).
+    """
+    for line in iterable:
+        if isinstance(line, bytes):
+            # Need to handle conversion here, or the splitting would fail
+            line = line.decode(encoding)
+
+        for c in comments:
+            line = line.split(c, 1)[0]
+
+        yield line
+
+
+# The number of rows we read in one go if confronted with a parametric dtype
+_loadtxt_chunksize = 50000
+
+
+def _read(fname, *, delimiter=',', comment='#', quote='"',
+          imaginary_unit='j', usecols=None, skiplines=0,
+          max_rows=None, converters=None, ndmin=None, unpack=False,
+          dtype=np.float64, encoding="bytes"):
+    r"""
+    Read a NumPy array from a text file.
+
+    Parameters
+    ----------
+    fname : str or file object
+        The filename or the file to be read.
+    delimiter : str, optional
+        Field delimiter of the fields in line of the file.
+        Default is a comma, ','.  If None any sequence of whitespace is
+        considered a delimiter.
+    comment : str or sequence of str or None, optional
+        Character that begins a comment.  All text from the comment
+        character to the end of the line is ignored.
+        Multiple comments or multiple-character comment strings are supported,
+        but may be slower and `quote` must be empty if used.
+        Use None to disable all use of comments.
+    quote : str or None, optional
+        Character that is used to quote string fields. Default is '"'
+        (a double quote). Use None to disable quote support.
+    imaginary_unit : str, optional
+        Character that represent the imaginay unit `sqrt(-1)`.
+        Default is 'j'.
+    usecols : array_like, optional
+        A one-dimensional array of integer column numbers.  These are the
+        columns from the file to be included in the array.  If this value
+        is not given, all the columns are used.
+    skiplines : int, optional
+        Number of lines to skip before interpreting the data in the file.
+    max_rows : int, optional
+        Maximum number of rows of data to read.  Default is to read the
+        entire file.
+    converters : dict or callable, optional
+        A function to parse all columns strings into the desired value, or
+        a dictionary mapping column number to a parser function.
+        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, e.g. ``converters = lambda s: float(s.strip() or 0)`` will
+        convert empty fields to 0.
+        Default: None
+    ndmin : int, optional
+        Minimum dimension of the array returned.
+        Allowed values are 0, 1 or 2.  Default is 0.
+    unpack : bool, optional
+        If True, the returned array is transposed, so that arguments may be
+        unpacked using ``x, y, z = read(...)``.  When used with a structured
+        data-type, arrays are returned for each field.  Default is False.
+    dtype : numpy data type
+        A NumPy dtype instance, can be a structured dtype to map to the
+        columns of the file.
+    encoding : str, optional
+        Encoding used to decode the inputfile. The special value 'bytes'
+        (the default) enables backwards-compatible behavior for `converters`,
+        ensuring that inputs to the converter functions are encoded
+        bytes objects. The special value 'bytes' has no additional effect if
+        ``converters=None``. If encoding is ``'bytes'`` or ``None``, the
+        default system encoding is used.
+
+    Returns
+    -------
+    ndarray
+        NumPy array.
+
+    Examples
+    --------
+    First we create a file for the example.
+
+    >>> s1 = '1.0,2.0,3.0\n4.0,5.0,6.0\n'
+    >>> with open('example1.csv', 'w') as f:
+    ...     f.write(s1)
+    >>> a1 = read_from_filename('example1.csv')
+    >>> a1
+    array([[1., 2., 3.],
+           [4., 5., 6.]])
+
+    The second example has columns with different data types, so a
+    one-dimensional array with a structured data type is returned.
+    The tab character is used as the field delimiter.
+
+    >>> s2 = '1.0\t10\talpha\n2.3\t25\tbeta\n4.5\t16\tgamma\n'
+    >>> with open('example2.tsv', 'w') as f:
+    ...     f.write(s2)
+    >>> a2 = read_from_filename('example2.tsv', delimiter='\t')
+    >>> a2
+    array([(1. , 10, b'alpha'), (2.3, 25, b'beta'), (4.5, 16, b'gamma')],
+          dtype=[('f0', '<f8'), ('f1', 'u1'), ('f2', 'S5')])
+    """
+    # Handle special 'bytes' keyword for encoding
+    byte_converters = False
+    if encoding == 'bytes':
+        encoding = None
+        byte_converters = True
+
+    if dtype is None:
+        raise TypeError("a dtype must be provided.")
+    dtype = np.dtype(dtype)
+
+    read_dtype_via_object_chunks = None
+    if dtype.kind in 'SUM' and (
+            dtype == "S0" or dtype == "U0" or dtype == "M8" or dtype == 'm8'):
+        # This is a legacy "flexible" dtype.  We do not truly support
+        # parametric dtypes currently (no dtype discovery step in the core),
+        # but have to support these for backward compatibility.
+        read_dtype_via_object_chunks = dtype
+        dtype = np.dtype(object)
+
+    if usecols is not None:
+        # Allow usecols to be a single int or a sequence of ints, the C-code
+        # handles the rest
+        try:
+            usecols = list(usecols)
+        except TypeError:
+            usecols = [usecols]
+
+    _ensure_ndmin_ndarray_check_param(ndmin)
+
+    if comment is None:
+        comments = None
+    else:
+        # assume comments are a sequence of strings
+        if "" in comment:
+            raise ValueError(
+                "comments cannot be an empty string. Use comments=None to "
+                "disable comments."
+            )
+        comments = tuple(comment)
+        comment = None
+        if len(comments) == 0:
+            comments = None  # No comments at all
+        elif len(comments) == 1:
+            # If there is only one comment, and that comment has one character,
+            # the normal parsing can deal with it just fine.
+            if isinstance(comments[0], str) and len(comments[0]) == 1:
+                comment = comments[0]
+                comments = None
+        else:
+            # Input validation if there are multiple comment characters
+            if delimiter in comments:
+                raise TypeError(
+                    f"Comment characters '{comments}' cannot include the "
+                    f"delimiter '{delimiter}'"
+                )
+
+    # comment is now either a 1 or 0 character string or a tuple:
+    if comments is not None:
+        # Note: An earlier version support two character comments (and could
+        #       have been extended to multiple characters, we assume this is
+        #       rare enough to not optimize for.
+        if quote is not None:
+            raise ValueError(
+                "when multiple comments or a multi-character comment is "
+                "given, quotes are not supported.  In this case quotechar "
+                "must be set to None.")
+
+    if len(imaginary_unit) != 1:
+        raise ValueError('len(imaginary_unit) must be 1.')
+
+    _check_nonneg_int(skiplines)
+    if max_rows is not None:
+        _check_nonneg_int(max_rows)
+    else:
+        # Passing -1 to the C code means "read the entire file".
+        max_rows = -1
+
+    fh_closing_ctx = contextlib.nullcontext()
+    filelike = False
+    try:
+        if isinstance(fname, os.PathLike):
+            fname = os.fspath(fname)
+        if isinstance(fname, str):
+            fh = np.lib._datasource.open(fname, 'rt', encoding=encoding)
+            if encoding is None:
+                encoding = getattr(fh, 'encoding', 'latin1')
+
+            fh_closing_ctx = contextlib.closing(fh)
+            data = fh
+            filelike = True
+        else:
+            if encoding is None:
+                encoding = getattr(fname, 'encoding', 'latin1')
+            data = iter(fname)
+    except TypeError as e:
+        raise ValueError(
+            f"fname must be a string, filehandle, list of strings,\n"
+            f"or generator. Got {type(fname)} instead.") from e
+
+    with fh_closing_ctx:
+        if comments is not None:
+            if filelike:
+                data = iter(data)
+                filelike = False
+            data = _preprocess_comments(data, comments, encoding)
+
+        if read_dtype_via_object_chunks is None:
+            arr = _load_from_filelike(
+                data, delimiter=delimiter, comment=comment, quote=quote,
+                imaginary_unit=imaginary_unit,
+                usecols=usecols, skiplines=skiplines, max_rows=max_rows,
+                converters=converters, dtype=dtype,
+                encoding=encoding, filelike=filelike,
+                byte_converters=byte_converters)
+
+        else:
+            # This branch reads the file into chunks of object arrays and then
+            # casts them to the desired actual dtype.  This ensures correct
+            # string-length and datetime-unit discovery (like `arr.astype()`).
+            # Due to chunking, certain error reports are less clear, currently.
+            if filelike:
+                data = iter(data)  # cannot chunk when reading from file
+
+            c_byte_converters = False
+            if read_dtype_via_object_chunks == "S":
+                c_byte_converters = True  # Use latin1 rather than ascii
+
+            chunks = []
+            while max_rows != 0:
+                if max_rows < 0:
+                    chunk_size = _loadtxt_chunksize
+                else:
+                    chunk_size = min(_loadtxt_chunksize, max_rows)
+
+                next_arr = _load_from_filelike(
+                    data, delimiter=delimiter, comment=comment, quote=quote,
+                    imaginary_unit=imaginary_unit,
+                    usecols=usecols, skiplines=skiplines, max_rows=max_rows,
+                    converters=converters, dtype=dtype,
+                    encoding=encoding, filelike=filelike,
+                    byte_converters=byte_converters,
+                    c_byte_converters=c_byte_converters)
+                # Cast here already.  We hope that this is better even for
+                # large files because the storage is more compact.  It could
+                # be adapted (in principle the concatenate could cast).
+                chunks.append(next_arr.astype(read_dtype_via_object_chunks))
+
+                skiprows = 0  # Only have to skip for first chunk
+                if max_rows >= 0:
+                    max_rows -= chunk_size
+                if len(next_arr) < chunk_size:
+                    # There was less data than requested, so we are done.
+                    break
+
+            # Need at least one chunk, but if empty, the last one may have
+            # the wrong shape.
+            if len(chunks) > 1 and len(chunks[-1]) == 0:
+                del chunks[-1]
+            if len(chunks) == 1:
+                arr = chunks[0]
+            else:
+                arr = np.concatenate(chunks, axis=0)
+
+    # NOTE: ndmin works as advertised for structured dtypes, but normally
+    #       these would return a 1D result plus the structured dimension,
+    #       so ndmin=2 adds a third dimension even when no squeezing occurs.
+    #       A `squeeze=False` could be a better solution (pandas uses squeeze).
+    arr = _ensure_ndmin_ndarray(arr, ndmin=ndmin)
+
+    if arr.shape:
+        if arr.shape[0] == 0:
+            warnings.warn(
+                f'loadtxt: input contained no data: "{fname}"',
+                category=UserWarning,
+                stacklevel=3
+            )
+
+    if unpack:
+        # Unpack structured dtypes if requested:
+        dt = arr.dtype
+        if dt.names is not None:
+            # For structured arrays, return an array for each field.
+            return [arr[field] for field in dt.names]
+        else:
+            return arr.T
+    else:
+        return arr
+
+
+@set_array_function_like_doc
+@set_module('numpy')
+def loadtxt(fname, dtype=float, comments='#', delimiter=None,
+            converters=None, skiprows=0, usecols=None, unpack=False,
+            ndmin=0, encoding='bytes', max_rows=None, *, quotechar=None,
+            like=None):
+    r"""
+    Load data from a text file.
+
+    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 bytes or strings. The strings
+        in a list or produced by a generator are treated as lines.
+    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 or None, 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 character used to separate the values. For backwards compatibility,
+        byte strings will be decoded as 'latin1'. The default is whitespace.
+
+        .. versionchanged:: 1.23.0
+           Only single character delimiters are supported. Newline characters
+           cannot be used as the delimiter.
+
+    converters : dict or callable, optional
+        Converter functions to customize value parsing. If `converters` is
+        callable, the function is applied to all columns, else it must be a
+        dict that maps column number to a parser function.
+        See examples for further details.
+        Default: None.
+
+        .. versionchanged:: 1.23.0
+           The ability to pass a single callable to be applied to all columns
+           was added.
+
+    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` rows of content after `skiprows` lines. The default is
+        to read all the rows. Note that empty rows containing no data such as
+        empty lines and comment lines are not counted towards `max_rows`,
+        while such lines are counted in `skiprows`.
+
+        .. versionadded:: 1.16.0
+
+        .. versionchanged:: 1.23.0
+            Lines containing no data, including comment lines (e.g., lines
+            starting with '#' or as specified via `comments`) are not counted
+            towards `max_rows`.
+    quotechar : unicode character or None, optional
+        The character used to denote the start and end of a quoted item.
+        Occurrences of the delimiter or comment characters are ignored within
+        a quoted item. The default value is ``quotechar=None``, which means
+        quoting support is disabled.
+
+        If two consecutive instances of `quotechar` are found within a quoted
+        field, the first is treated as an escape character. See examples.
+
+        .. versionadded:: 1.23.0
+    ${ARRAY_FUNCTION_LIKE}
+
+        .. 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.
+
+    Each row in the input text file must have the same number of values to be
+    able to read all values. If all rows do not have same number of values, a
+    subset of up to n columns (where n is the least number of values present
+    in all rows) can be read by specifying the columns via `usecols`.
+
+    .. 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', '<i4'), ('weight', '<f4')])
+
+    >>> 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.])
+
+    The `converters` argument is used to specify functions to preprocess the
+    text prior to parsing. `converters` can be a dictionary that maps
+    preprocessing functions to each column:
+
+    >>> s = StringIO("1.618, 2.296\n3.141, 4.669\n")
+    >>> conv = {
+    ...     0: lambda x: np.floor(float(x)),  # conversion fn for column 0
+    ...     1: lambda x: np.ceil(float(x)),  # conversion fn for column 1
+    ... }
+    >>> np.loadtxt(s, delimiter=",", converters=conv)
+    array([[1., 3.],
+           [3., 5.]])
+
+    `converters` can be a callable instead of a dictionary, in which case it
+    is applied to all columns:
+
+    >>> s = StringIO("0xDE 0xAD\n0xC0 0xDE")
+    >>> import functools
+    >>> conv = functools.partial(int, base=16)
+    >>> np.loadtxt(s, converters=conv)
+    array([[222., 173.],
+           [192., 222.]])
+
+    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=conv)
+    array([[ 10.01, -31.25],
+           [ 19.22,  64.31],
+           [-17.57,  63.94]])
+
+    Using a callable as the converter can be particularly useful for handling
+    values with different formatting, e.g. floats with underscores:
+
+    >>> s = StringIO("1 2.7 100_000")
+    >>> np.loadtxt(s, converters=float)
+    array([1.e+00, 2.7e+00, 1.e+05])
+
+    This idea can be extended to automatically handle values specified in
+    many different formats:
+
+    >>> def conv(val):
+    ...     try:
+    ...         return float(val)
+    ...     except ValueError:
+    ...         return float.fromhex(val)
+    >>> s = StringIO("1, 2.5, 3_000, 0b4, 0x1.4000000000000p+2")
+    >>> np.loadtxt(s, delimiter=",", converters=conv, encoding=None)
+    array([1.0e+00, 2.5e+00, 3.0e+03, 1.8e+02, 5.0e+00])
+
+    Note that with the default ``encoding="bytes"``, the inputs to the
+    converter function are latin-1 encoded byte strings. To deactivate the
+    implicit encoding prior to conversion, use ``encoding=None``
+
+    >>> s = StringIO('10.01 31.25-\n19.22 64.31\n17.57- 63.94')
+    >>> conv = lambda x: -float(x[:-1]) if x.endswith('-') else float(x)
+    >>> np.loadtxt(s, converters=conv, encoding=None)
+    array([[ 10.01, -31.25],
+           [ 19.22,  64.31],
+           [-17.57,  63.94]])
+
+    Support for quoted fields is enabled with the `quotechar` parameter.
+    Comment and delimiter characters are ignored when they appear within a
+    quoted item delineated by `quotechar`:
+
+    >>> s = StringIO('"alpha, #42", 10.0\n"beta, #64", 2.0\n')
+    >>> dtype = np.dtype([("label", "U12"), ("value", float)])
+    >>> np.loadtxt(s, dtype=dtype, delimiter=",", quotechar='"')
+    array([('alpha, #42', 10.), ('beta, #64',  2.)],
+          dtype=[('label', '<U12'), ('value', '<f8')])
+
+    Quoted fields can be separated by multiple whitespace characters:
+
+    >>> s = StringIO('"alpha, #42"       10.0\n"beta, #64" 2.0\n')
+    >>> dtype = np.dtype([("label", "U12"), ("value", float)])
+    >>> np.loadtxt(s, dtype=dtype, delimiter=None, quotechar='"')
+    array([('alpha, #42', 10.), ('beta, #64',  2.)],
+          dtype=[('label', '<U12'), ('value', '<f8')])
+
+    Two consecutive quote characters within a quoted field are treated as a
+    single escaped character:
+
+    >>> s = StringIO('"Hello, my name is ""Monty""!"')
+    >>> np.loadtxt(s, dtype="U", delimiter=",", quotechar='"')
+    array('Hello, my name is "Monty"!', dtype='<U26')
+
+    Read subset of columns when all rows do not contain equal number of values:
+
+    >>> d = StringIO("1 2\n2 4\n3 9 12\n4 16 20")
+    >>> np.loadtxt(d, usecols=(0, 1))
+    array([[ 1.,  2.],
+           [ 2.,  4.],
+           [ 3.,  9.],
+           [ 4., 16.]])
+
+    """
+
+    if like is not None:
+        return _loadtxt_with_like(
+            like, fname, dtype=dtype, comments=comments, delimiter=delimiter,
+            converters=converters, skiprows=skiprows, usecols=usecols,
+            unpack=unpack, ndmin=ndmin, encoding=encoding,
+            max_rows=max_rows
+        )
+
+    if isinstance(delimiter, bytes):
+        delimiter.decode("latin1")
+
+    if dtype is None:
+        dtype = np.float64
+
+    comment = comments
+    # Control character type conversions for Py3 convenience
+    if comment is not None:
+        if isinstance(comment, (str, bytes)):
+            comment = [comment]
+        comment = [
+            x.decode('latin1') if isinstance(x, bytes) else x for x in comment]
+    if isinstance(delimiter, bytes):
+        delimiter = delimiter.decode('latin1')
+
+    arr = _read(fname, dtype=dtype, comment=comment, delimiter=delimiter,
+                converters=converters, skiplines=skiprows, usecols=usecols,
+                unpack=unpack, ndmin=ndmin, encoding=encoding,
+                max_rows=max_rows, quote=quotechar)
+
+    return arr
+
+
+_loadtxt_with_like = array_function_dispatch()(loadtxt)
+
+
+def _savetxt_dispatcher(fname, X, fmt=None, delimiter=None, newline=None,
+                        header=None, footer=None, comments=None,
+                        encoding=None):
+    return (X,)
+
+
+@array_function_dispatch(_savetxt_dispatcher)
+def savetxt(fname, X, fmt='%.18e', delimiter=' ', newline='\n', header='',
+            footer='', comments='# ', encoding=None):
+    """
+    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
+           <https://docs.python.org/library/string.html#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
+
+    """
+
+    # Py3 conversions first
+    if isinstance(fmt, bytes):
+        fmt = asstr(fmt)
+    delimiter = asstr(delimiter)
+
+    class WriteWrap:
+        """Convert to bytes on bytestream inputs.
+
+        """
+        def __init__(self, fh, encoding):
+            self.fh = fh
+            self.encoding = encoding
+            self.do_write = self.first_write
+
+        def close(self):
+            self.fh.close()
+
+        def write(self, v):
+            self.do_write(v)
+
+        def write_bytes(self, v):
+            if isinstance(v, bytes):
+                self.fh.write(v)
+            else:
+                self.fh.write(v.encode(self.encoding))
+
+        def write_normal(self, v):
+            self.fh.write(asunicode(v))
+
+        def first_write(self, v):
+            try:
+                self.write_normal(v)
+                self.write = self.write_normal
+            except TypeError:
+                # input is probably a bytestream
+                self.write_bytes(v)
+                self.write = self.write_bytes
+
+    own_fh = False
+    if isinstance(fname, os_PathLike):
+        fname = os_fspath(fname)
+    if _is_string_like(fname):
+        # datasource doesn't support creating a new file ...
+        open(fname, 'wt').close()
+        fh = np.lib._datasource.open(fname, 'wt', encoding=encoding)
+        own_fh = True
+    elif hasattr(fname, 'write'):
+        # wrap to handle byte output streams
+        fh = WriteWrap(fname, encoding or 'latin1')
+    else:
+        raise ValueError('fname must be a string or file handle')
+
+    try:
+        X = np.asarray(X)
+
+        # Handle 1-dimensional arrays
+        if X.ndim == 0 or X.ndim > 2:
+            raise ValueError(
+                "Expected 1D or 2D array, got %dD array instead" % X.ndim)
+        elif X.ndim == 1:
+            # Common case -- 1d array of numbers
+            if X.dtype.names is None:
+                X = np.atleast_2d(X).T
+                ncol = 1
+
+            # Complex dtype -- each field indicates a separate column
+            else:
+                ncol = len(X.dtype.names)
+        else:
+            ncol = X.shape[1]
+
+        iscomplex_X = np.iscomplexobj(X)
+        # `fmt` can be a string with multiple insertion points or a
+        # list of formats.  E.g. '%10.5f\t%10d' or ('%10.5f', '$10d')
+        if type(fmt) in (list, tuple):
+            if len(fmt) != ncol:
+                raise AttributeError('fmt has wrong shape.  %s' % str(fmt))
+            format = asstr(delimiter).join(map(asstr, fmt))
+        elif isinstance(fmt, str):
+            n_fmt_chars = fmt.count('%')
+            error = ValueError('fmt has wrong number of %% formats:  %s' % fmt)
+            if n_fmt_chars == 1:
+                if iscomplex_X:
+                    fmt = [' (%s+%sj)' % (fmt, fmt), ] * ncol
+                else:
+                    fmt = [fmt, ] * ncol
+                format = delimiter.join(fmt)
+            elif iscomplex_X and n_fmt_chars != (2 * ncol):
+                raise error
+            elif ((not iscomplex_X) and n_fmt_chars != ncol):
+                raise error
+            else:
+                format = fmt
+        else:
+            raise ValueError('invalid fmt: %r' % (fmt,))
+
+        if len(header) > 0:
+            header = header.replace('\n', '\n' + comments)
+            fh.write(comments + header + newline)
+        if iscomplex_X:
+            for row in X:
+                row2 = []
+                for number in row:
+                    row2.append(number.real)
+                    row2.append(number.imag)
+                s = format % tuple(row2) + newline
+                fh.write(s.replace('+-', '-'))
+        else:
+            for row in X:
+                try:
+                    v = format % tuple(row) + newline
+                except TypeError as e:
+                    raise TypeError("Mismatch between array dtype ('%s') and "
+                                    "format specifier ('%s')"
+                                    % (str(X.dtype), format)) from e
+                fh.write(v)
+
+        if len(footer) > 0:
+            footer = footer.replace('\n', '\n' + comments)
+            fh.write(comments + footer + newline)
+    finally:
+        if own_fh:
+            fh.close()
+
+
+@set_module('numpy')
+def fromregex(file, regexp, dtype, encoding=None):
+    r"""
+    Construct an array from a text file, using regular expression parsing.
+
+    The returned array is always a structured array, and is constructed from
+    all matches of the regular expression in the file. Groups in the regular
+    expression are converted to fields of the structured array.
+
+    Parameters
+    ----------
+    file : path or file
+        Filename or file object to read.
+
+        .. versionchanged:: 1.22.0
+            Now accepts `os.PathLike` implementations.
+    regexp : str or regexp
+        Regular expression used to parse the file.
+        Groups in the regular expression correspond to fields in the dtype.
+    dtype : dtype or list of dtypes
+        Dtype for the structured array; must be a structured datatype.
+    encoding : str, optional
+        Encoding used to decode the inputfile. Does not apply to input streams.
+
+        .. versionadded:: 1.14.0
+
+    Returns
+    -------
+    output : ndarray
+        The output array, containing the part of the content of `file` that
+        was matched by `regexp`. `output` is always a structured array.
+
+    Raises
+    ------
+    TypeError
+        When `dtype` is not a valid dtype for a structured array.
+
+    See Also
+    --------
+    fromstring, loadtxt
+
+    Notes
+    -----
+    Dtypes for structured arrays can be specified in several forms, but all
+    forms specify at least the data type and field name. For details see
+    `basics.rec`.
+
+    Examples
+    --------
+    >>> from io import StringIO
+    >>> text = StringIO("1312 foo\n1534  bar\n444   qux")
+
+    >>> regexp = r"(\d+)\s+(...)"  # match [digits, whitespace, anything]
+    >>> output = np.fromregex(text, regexp,
+    ...                       [('num', np.int64), ('key', 'S3')])
+    >>> output
+    array([(1312, b'foo'), (1534, b'bar'), ( 444, b'qux')],
+          dtype=[('num', '<i8'), ('key', 'S3')])
+    >>> output['num']
+    array([1312, 1534,  444])
+
+    """
+    own_fh = False
+    if not hasattr(file, "read"):
+        file = os.fspath(file)
+        file = np.lib._datasource.open(file, 'rt', encoding=encoding)
+        own_fh = True
+
+    try:
+        if not isinstance(dtype, np.dtype):
+            dtype = np.dtype(dtype)
+        if dtype.names is None:
+            raise TypeError('dtype must be a structured datatype.')
+
+        content = file.read()
+        if isinstance(content, bytes) and isinstance(regexp, str):
+            regexp = asbytes(regexp)
+        elif isinstance(content, str) and isinstance(regexp, bytes):
+            regexp = asstr(regexp)
+
+        if not hasattr(regexp, 'match'):
+            regexp = re.compile(regexp)
+        seq = regexp.findall(content)
+        if seq and not isinstance(seq[0], tuple):
+            # Only one group is in the regexp.
+            # Create the new array as a single data-type and then
+            #   re-interpret as a single-field structured array.
+            newdtype = np.dtype(dtype[dtype.names[0]])
+            output = np.array(seq, dtype=newdtype)
+            output.dtype = dtype
+        else:
+            output = np.array(seq, dtype=dtype)
+
+        return output
+    finally:
+        if own_fh:
+            file.close()
+
+
+#####--------------------------------------------------------------------------
+#---- --- ASCII functions ---
+#####--------------------------------------------------------------------------
+
+
+@set_array_function_like_doc
+@set_module('numpy')
+def genfromtxt(fname, dtype=float, comments='#', delimiter=None,
+               skip_header=0, skip_footer=0, converters=None,
+               missing_values=None, filling_values=None, usecols=None,
+               names=None, excludelist=None,
+               deletechars=''.join(sorted(NameValidator.defaultdeletechars)),
+               replace_space='_', autostrip=False, case_sensitive=True,
+               defaultfmt="f%i", unpack=None, usemask=False, loose=True,
+               invalid_raise=True, max_rows=None, encoding='bytes',
+               *, ndmin=0, like=None):
+    """
+    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 bytes or 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 preceded
+        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
+    ndmin : int, optional
+        Same parameter as `loadtxt`
+
+        .. versionadded:: 1.23.0
+    ${ARRAY_FUNCTION_LIKE}
+
+        .. 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
+           <https://docs.scipy.org/doc/numpy/user/basics.io.genfromtxt.html>`_.
+
+    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', '<i8'), ('myfloat', '<f8'), ('mystring', 'S5')])
+
+    Using dtype = None
+
+    >>> _ = s.seek(0) # 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', '<i8'), ('myfloat', '<f8'), ('mystring', 'S5')])
+
+    Specifying dtype and names
+
+    >>> _ = s.seek(0)
+    >>> data = np.genfromtxt(s, dtype="i8,f8,S5",
+    ... names=['myint','myfloat','mystring'], delimiter=",")
+    >>> data
+    array((1, 1.3, b'abcde'),
+          dtype=[('myint', '<i8'), ('myfloat', '<f8'), ('mystring', 'S5')])
+
+    An example with fixed-width columns
+
+    >>> 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', '<i8'), ('fltvar', '<f8'), ('strvar', 'S5')])
+
+    An example to show comments
+
+    >>> 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')])
+
+    """
+
+    if like is not None:
+        return _genfromtxt_with_like(
+            like, fname, dtype=dtype, comments=comments, delimiter=delimiter,
+            skip_header=skip_header, skip_footer=skip_footer,
+            converters=converters, missing_values=missing_values,
+            filling_values=filling_values, usecols=usecols, names=names,
+            excludelist=excludelist, deletechars=deletechars,
+            replace_space=replace_space, autostrip=autostrip,
+            case_sensitive=case_sensitive, defaultfmt=defaultfmt,
+            unpack=unpack, usemask=usemask, loose=loose,
+            invalid_raise=invalid_raise, max_rows=max_rows, encoding=encoding,
+            ndmin=ndmin,
+        )
+
+    _ensure_ndmin_ndarray_check_param(ndmin)
+
+    if max_rows is not None:
+        if skip_footer:
+            raise ValueError(
+                    "The keywords 'skip_footer' and 'max_rows' can not be "
+                    "specified at the same time.")
+        if max_rows < 1:
+            raise ValueError("'max_rows' must be at least 1.")
+
+    if usemask:
+        from numpy.ma import MaskedArray, make_mask_descr
+    # Check the input dictionary of converters
+    user_converters = converters or {}
+    if not isinstance(user_converters, dict):
+        raise TypeError(
+            "The input argument 'converter' should be a valid dictionary "
+            "(got '%s' instead)" % type(user_converters))
+
+    if encoding == 'bytes':
+        encoding = None
+        byte_converters = True
+    else:
+        byte_converters = False
+
+    # Initialize the filehandle, the LineSplitter and the NameValidator
+    if isinstance(fname, os_PathLike):
+        fname = os_fspath(fname)
+    if isinstance(fname, str):
+        fid = np.lib._datasource.open(fname, 'rt', encoding=encoding)
+        fid_ctx = contextlib.closing(fid)
+    else:
+        fid = fname
+        fid_ctx = contextlib.nullcontext(fid)
+    try:
+        fhd = iter(fid)
+    except TypeError as e:
+        raise TypeError(
+            "fname must be a string, a filehandle, a sequence of strings,\n"
+            f"or an iterator of strings. Got {type(fname)} instead."
+        ) from e
+    with fid_ctx:
+        split_line = LineSplitter(delimiter=delimiter, comments=comments,
+                                  autostrip=autostrip, encoding=encoding)
+        validate_names = NameValidator(excludelist=excludelist,
+                                       deletechars=deletechars,
+                                       case_sensitive=case_sensitive,
+                                       replace_space=replace_space)
+
+        # Skip the first `skip_header` rows
+        try:
+            for i in range(skip_header):
+                next(fhd)
+
+            # Keep on until we find the first valid values
+            first_values = None
+
+            while not first_values:
+                first_line = _decode_line(next(fhd), encoding)
+                if (names is True) and (comments is not None):
+                    if comments in first_line:
+                        first_line = (
+                            ''.join(first_line.split(comments)[1:]))
+                first_values = split_line(first_line)
+        except StopIteration:
+            # return an empty array if the datafile is empty
+            first_line = ''
+            first_values = []
+            warnings.warn('genfromtxt: Empty input file: "%s"' % fname, stacklevel=2)
+
+        # Should we take the first values as names ?
+        if names is True:
+            fval = first_values[0].strip()
+            if comments is not None:
+                if fval in comments:
+                    del first_values[0]
+
+        # Check the columns to use: make sure `usecols` is a list
+        if usecols is not None:
+            try:
+                usecols = [_.strip() for _ in usecols.split(",")]
+            except AttributeError:
+                try:
+                    usecols = list(usecols)
+                except TypeError:
+                    usecols = [usecols, ]
+        nbcols = len(usecols or first_values)
+
+        # Check the names and overwrite the dtype.names if needed
+        if names is True:
+            names = validate_names([str(_.strip()) for _ in first_values])
+            first_line = ''
+        elif _is_string_like(names):
+            names = validate_names([_.strip() for _ in names.split(',')])
+        elif names:
+            names = validate_names(names)
+        # Get the dtype
+        if dtype is not None:
+            dtype = easy_dtype(dtype, defaultfmt=defaultfmt, names=names,
+                               excludelist=excludelist,
+                               deletechars=deletechars,
+                               case_sensitive=case_sensitive,
+                               replace_space=replace_space)
+        # Make sure the names is a list (for 2.5)
+        if names is not None:
+            names = list(names)
+
+        if usecols:
+            for (i, current) in enumerate(usecols):
+                # if usecols is a list of names, convert to a list of indices
+                if _is_string_like(current):
+                    usecols[i] = names.index(current)
+                elif current < 0:
+                    usecols[i] = current + len(first_values)
+            # If the dtype is not None, make sure we update it
+            if (dtype is not None) and (len(dtype) > nbcols):
+                descr = dtype.descr
+                dtype = np.dtype([descr[_] for _ in usecols])
+                names = list(dtype.names)
+            # If `names` is not None, update the names
+            elif (names is not None) and (len(names) > nbcols):
+                names = [names[_] for _ in usecols]
+        elif (names is not None) and (dtype is not None):
+            names = list(dtype.names)
+
+        # Process the missing values ...............................
+        # Rename missing_values for convenience
+        user_missing_values = missing_values or ()
+        if isinstance(user_missing_values, bytes):
+            user_missing_values = user_missing_values.decode('latin1')
+
+        # Define the list of missing_values (one column: one list)
+        missing_values = [list(['']) for _ in range(nbcols)]
+
+        # We have a dictionary: process it field by field
+        if isinstance(user_missing_values, dict):
+            # Loop on the items
+            for (key, val) in user_missing_values.items():
+                # Is the key a string ?
+                if _is_string_like(key):
+                    try:
+                        # Transform it into an integer
+                        key = names.index(key)
+                    except ValueError:
+                        # We couldn't find it: the name must have been dropped
+                        continue
+                # Redefine the key as needed if it's a column number
+                if usecols:
+                    try:
+                        key = usecols.index(key)
+                    except ValueError:
+                        pass
+                # Transform the value as a list of string
+                if isinstance(val, (list, tuple)):
+                    val = [str(_) for _ in val]
+                else:
+                    val = [str(val), ]
+                # Add the value(s) to the current list of missing
+                if key is None:
+                    # None acts as default
+                    for miss in missing_values:
+                        miss.extend(val)
+                else:
+                    missing_values[key].extend(val)
+        # We have a sequence : each item matches a column
+        elif isinstance(user_missing_values, (list, tuple)):
+            for (value, entry) in zip(user_missing_values, missing_values):
+                value = str(value)
+                if value not in entry:
+                    entry.append(value)
+        # We have a string : apply it to all entries
+        elif isinstance(user_missing_values, str):
+            user_value = user_missing_values.split(",")
+            for entry in missing_values:
+                entry.extend(user_value)
+        # We have something else: apply it to all entries
+        else:
+            for entry in missing_values:
+                entry.extend([str(user_missing_values)])
+
+        # Process the filling_values ...............................
+        # Rename the input for convenience
+        user_filling_values = filling_values
+        if user_filling_values is None:
+            user_filling_values = []
+        # Define the default
+        filling_values = [None] * nbcols
+        # We have a dictionary : update each entry individually
+        if isinstance(user_filling_values, dict):
+            for (key, val) in user_filling_values.items():
+                if _is_string_like(key):
+                    try:
+                        # Transform it into an integer
+                        key = names.index(key)
+                    except ValueError:
+                        # We couldn't find it: the name must have been dropped,
+                        continue
+                # Redefine the key if it's a column number and usecols is defined
+                if usecols:
+                    try:
+                        key = usecols.index(key)
+                    except ValueError:
+                        pass
+                # Add the value to the list
+                filling_values[key] = val
+        # We have a sequence : update on a one-to-one basis
+        elif isinstance(user_filling_values, (list, tuple)):
+            n = len(user_filling_values)
+            if (n <= nbcols):
+                filling_values[:n] = user_filling_values
+            else:
+                filling_values = user_filling_values[:nbcols]
+        # We have something else : use it for all entries
+        else:
+            filling_values = [user_filling_values] * nbcols
+
+        # Initialize the converters ................................
+        if dtype is None:
+            # Note: we can't use a [...]*nbcols, as we would have 3 times the same
+            # ... converter, instead of 3 different converters.
+            converters = [StringConverter(None, missing_values=miss, default=fill)
+                          for (miss, fill) in zip(missing_values, filling_values)]
+        else:
+            dtype_flat = flatten_dtype(dtype, flatten_base=True)
+            # Initialize the converters
+            if len(dtype_flat) > 1:
+                # Flexible type : get a converter from each dtype
+                zipit = zip(dtype_flat, missing_values, filling_values)
+                converters = [StringConverter(dt, locked=True,
+                                              missing_values=miss, default=fill)
+                              for (dt, miss, fill) in zipit]
+            else:
+                # Set to a default converter (but w/ different missing values)
+                zipit = zip(missing_values, filling_values)
+                converters = [StringConverter(dtype, locked=True,
+                                              missing_values=miss, default=fill)
+                              for (miss, fill) in zipit]
+        # Update the converters to use the user-defined ones
+        uc_update = []
+        for (j, conv) in user_converters.items():
+            # If the converter is specified by column names, use the index instead
+            if _is_string_like(j):
+                try:
+                    j = names.index(j)
+                    i = j
+                except ValueError:
+                    continue
+            elif usecols:
+                try:
+                    i = usecols.index(j)
+                except ValueError:
+                    # Unused converter specified
+                    continue
+            else:
+                i = j
+            # Find the value to test - first_line is not filtered by usecols:
+            if len(first_line):
+                testing_value = first_values[j]
+            else:
+                testing_value = None
+            if conv is bytes:
+                user_conv = asbytes
+            elif byte_converters:
+                # converters may use decode to workaround numpy's old behaviour,
+                # so encode the string again before passing to the user converter
+                def tobytes_first(x, conv):
+                    if type(x) is bytes:
+                        return conv(x)
+                    return conv(x.encode("latin1"))
+                user_conv = functools.partial(tobytes_first, conv=conv)
+            else:
+                user_conv = conv
+            converters[i].update(user_conv, locked=True,
+                                 testing_value=testing_value,
+                                 default=filling_values[i],
+                                 missing_values=missing_values[i],)
+            uc_update.append((i, user_conv))
+        # Make sure we have the corrected keys in user_converters...
+        user_converters.update(uc_update)
+
+        # Fixme: possible error as following variable never used.
+        # miss_chars = [_.missing_values for _ in converters]
+
+        # Initialize the output lists ...
+        # ... rows
+        rows = []
+        append_to_rows = rows.append
+        # ... masks
+        if usemask:
+            masks = []
+            append_to_masks = masks.append
+        # ... invalid
+        invalid = []
+        append_to_invalid = invalid.append
+
+        # Parse each line
+        for (i, line) in enumerate(itertools.chain([first_line, ], fhd)):
+            values = split_line(line)
+            nbvalues = len(values)
+            # Skip an empty line
+            if nbvalues == 0:
+                continue
+            if usecols:
+                # Select only the columns we need
+                try:
+                    values = [values[_] for _ in usecols]
+                except IndexError:
+                    append_to_invalid((i + skip_header + 1, nbvalues))
+                    continue
+            elif nbvalues != nbcols:
+                append_to_invalid((i + skip_header + 1, nbvalues))
+                continue
+            # Store the values
+            append_to_rows(tuple(values))
+            if usemask:
+                append_to_masks(tuple([v.strip() in m
+                                       for (v, m) in zip(values,
+                                                         missing_values)]))
+            if len(rows) == max_rows:
+                break
+
+    # Upgrade the converters (if needed)
+    if dtype is None:
+        for (i, converter) in enumerate(converters):
+            current_column = [itemgetter(i)(_m) for _m in rows]
+            try:
+                converter.iterupgrade(current_column)
+            except ConverterLockError:
+                errmsg = "Converter #%i is locked and cannot be upgraded: " % i
+                current_column = map(itemgetter(i), rows)
+                for (j, value) in enumerate(current_column):
+                    try:
+                        converter.upgrade(value)
+                    except (ConverterError, ValueError):
+                        errmsg += "(occurred line #%i for value '%s')"
+                        errmsg %= (j + 1 + skip_header, value)
+                        raise ConverterError(errmsg)
+
+    # Check that we don't have invalid values
+    nbinvalid = len(invalid)
+    if nbinvalid > 0:
+        nbrows = len(rows) + nbinvalid - skip_footer
+        # Construct the error message
+        template = "    Line #%%i (got %%i columns instead of %i)" % nbcols
+        if skip_footer > 0:
+            nbinvalid_skipped = len([_ for _ in invalid
+                                     if _[0] > nbrows + skip_header])
+            invalid = invalid[:nbinvalid - nbinvalid_skipped]
+            skip_footer -= nbinvalid_skipped
+#
+#            nbrows -= skip_footer
+#            errmsg = [template % (i, nb)
+#                      for (i, nb) in invalid if i < nbrows]
+#        else:
+        errmsg = [template % (i, nb)
+                  for (i, nb) in invalid]
+        if len(errmsg):
+            errmsg.insert(0, "Some errors were detected !")
+            errmsg = "\n".join(errmsg)
+            # Raise an exception ?
+            if invalid_raise:
+                raise ValueError(errmsg)
+            # Issue a warning ?
+            else:
+                warnings.warn(errmsg, ConversionWarning, stacklevel=2)
+
+    # Strip the last skip_footer data
+    if skip_footer > 0:
+        rows = rows[:-skip_footer]
+        if usemask:
+            masks = masks[:-skip_footer]
+
+    # Convert each value according to the converter:
+    # We want to modify the list in place to avoid creating a new one...
+    if loose:
+        rows = list(
+            zip(*[[conv._loose_call(_r) for _r in map(itemgetter(i), rows)]
+                  for (i, conv) in enumerate(converters)]))
+    else:
+        rows = list(
+            zip(*[[conv._strict_call(_r) for _r in map(itemgetter(i), rows)]
+                  for (i, conv) in enumerate(converters)]))
+
+    # Reset the dtype
+    data = rows
+    if dtype is None:
+        # Get the dtypes from the types of the converters
+        column_types = [conv.type for conv in converters]
+        # Find the columns with strings...
+        strcolidx = [i for (i, v) in enumerate(column_types)
+                     if v == np.str_]
+
+        if byte_converters and strcolidx:
+            # convert strings back to bytes for backward compatibility
+            warnings.warn(
+                "Reading unicode strings without specifying the encoding "
+                "argument is deprecated. Set the encoding, use None for the "
+                "system default.",
+                np.VisibleDeprecationWarning, stacklevel=2)
+            def encode_unicode_cols(row_tup):
+                row = list(row_tup)
+                for i in strcolidx:
+                    row[i] = row[i].encode('latin1')
+                return tuple(row)
+
+            try:
+                data = [encode_unicode_cols(r) for r in data]
+            except UnicodeEncodeError:
+                pass
+            else:
+                for i in strcolidx:
+                    column_types[i] = np.bytes_
+
+        # Update string types to be the right length
+        sized_column_types = column_types[:]
+        for i, col_type in enumerate(column_types):
+            if np.issubdtype(col_type, np.character):
+                n_chars = max(len(row[i]) for row in data)
+                sized_column_types[i] = (col_type, n_chars)
+
+        if names is None:
+            # If the dtype is uniform (before sizing strings)
+            base = {
+                c_type
+                for c, c_type in zip(converters, column_types)
+                if c._checked}
+            if len(base) == 1:
+                uniform_type, = base
+                (ddtype, mdtype) = (uniform_type, bool)
+            else:
+                ddtype = [(defaultfmt % i, dt)
+                          for (i, dt) in enumerate(sized_column_types)]
+                if usemask:
+                    mdtype = [(defaultfmt % i, bool)
+                              for (i, dt) in enumerate(sized_column_types)]
+        else:
+            ddtype = list(zip(names, sized_column_types))
+            mdtype = list(zip(names, [bool] * len(sized_column_types)))
+        output = np.array(data, dtype=ddtype)
+        if usemask:
+            outputmask = np.array(masks, dtype=mdtype)
+    else:
+        # Overwrite the initial dtype names if needed
+        if names and dtype.names is not None:
+            dtype.names = names
+        # Case 1. We have a structured type
+        if len(dtype_flat) > 1:
+            # Nested dtype, eg [('a', int), ('b', [('b0', int), ('b1', 'f4')])]
+            # First, create the array using a flattened dtype:
+            # [('a', int), ('b1', int), ('b2', float)]
+            # Then, view the array using the specified dtype.
+            if 'O' in (_.char for _ in dtype_flat):
+                if has_nested_fields(dtype):
+                    raise NotImplementedError(
+                        "Nested fields involving objects are not supported...")
+                else:
+                    output = np.array(data, dtype=dtype)
+            else:
+                rows = np.array(data, dtype=[('', _) for _ in dtype_flat])
+                output = rows.view(dtype)
+            # Now, process the rowmasks the same way
+            if usemask:
+                rowmasks = np.array(
+                    masks, dtype=np.dtype([('', bool) for t in dtype_flat]))
+                # Construct the new dtype
+                mdtype = make_mask_descr(dtype)
+                outputmask = rowmasks.view(mdtype)
+        # Case #2. We have a basic dtype
+        else:
+            # We used some user-defined converters
+            if user_converters:
+                ishomogeneous = True
+                descr = []
+                for i, ttype in enumerate([conv.type for conv in converters]):
+                    # Keep the dtype of the current converter
+                    if i in user_converters:
+                        ishomogeneous &= (ttype == dtype.type)
+                        if np.issubdtype(ttype, np.character):
+                            ttype = (ttype, max(len(row[i]) for row in data))
+                        descr.append(('', ttype))
+                    else:
+                        descr.append(('', dtype))
+                # So we changed the dtype ?
+                if not ishomogeneous:
+                    # We have more than one field
+                    if len(descr) > 1:
+                        dtype = np.dtype(descr)
+                    # We have only one field: drop the name if not needed.
+                    else:
+                        dtype = np.dtype(ttype)
+            #
+            output = np.array(data, dtype)
+            if usemask:
+                if dtype.names is not None:
+                    mdtype = [(_, bool) for _ in dtype.names]
+                else:
+                    mdtype = bool
+                outputmask = np.array(masks, dtype=mdtype)
+    # Try to take care of the missing data we missed
+    names = output.dtype.names
+    if usemask and names:
+        for (name, conv) in zip(names, converters):
+            missing_values = [conv(_) for _ in conv.missing_values
+                              if _ != '']
+            for mval in missing_values:
+                outputmask[name] |= (output[name] == mval)
+    # Construct the final array
+    if usemask:
+        output = output.view(MaskedArray)
+        output._mask = outputmask
+
+    output = _ensure_ndmin_ndarray(output, ndmin=ndmin)
+
+    if unpack:
+        if names is None:
+            return output.T
+        elif len(names) == 1:
+            # squeeze single-name dtypes too
+            return output[names[0]]
+        else:
+            # For structured arrays with multiple fields,
+            # return an array for each field.
+            return [output[field] for field in names]
+    return output
+
+
+_genfromtxt_with_like = array_function_dispatch()(genfromtxt)
+
+
+def recfromtxt(fname, **kwargs):
+    """
+    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.
+
+    """
+    kwargs.setdefault("dtype", None)
+    usemask = kwargs.get('usemask', False)
+    output = genfromtxt(fname, **kwargs)
+    if usemask:
+        from numpy.ma.mrecords import MaskedRecords
+        output = output.view(MaskedRecords)
+    else:
+        output = output.view(np.recarray)
+    return output
+
+
+def recfromcsv(fname, **kwargs):
+    """
+    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.
+
+    """
+    # Set default kwargs for genfromtxt as relevant to csv import.
+    kwargs.setdefault("case_sensitive", "lower")
+    kwargs.setdefault("names", True)
+    kwargs.setdefault("delimiter", ",")
+    kwargs.setdefault("dtype", None)
+    output = genfromtxt(fname, **kwargs)
+
+    usemask = kwargs.get("usemask", False)
+    if usemask:
+        from numpy.ma.mrecords import MaskedRecords
+        output = output.view(MaskedRecords)
+    else:
+        output = output.view(np.recarray)
+    return output

env-llmeval/lib/python3.10/site-packages/numpy/lib/polynomial.py

@@ -0,0 +1,1453 @@
+"""
+Functions to operate on polynomials.
+
+"""
+__all__ = ['poly', 'roots', 'polyint', 'polyder', 'polyadd',
+           'polysub', 'polymul', 'polydiv', 'polyval', 'poly1d',
+           'polyfit', 'RankWarning']
+
+import functools
+import re
+import warnings
+
+from .._utils import set_module
+import numpy.core.numeric as NX
+
+from numpy.core import (isscalar, abs, finfo, atleast_1d, hstack, dot, array,
+                        ones)
+from numpy.core import overrides
+from numpy.lib.twodim_base import diag, vander
+from numpy.lib.function_base import trim_zeros
+from numpy.lib.type_check import iscomplex, real, imag, mintypecode
+from numpy.linalg import eigvals, lstsq, inv
+
+
+array_function_dispatch = functools.partial(
+    overrides.array_function_dispatch, module='numpy')
+
+
+@set_module('numpy')
+class RankWarning(UserWarning):
+    """
+    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`.
+
+    """
+    pass
+
+
+def _poly_dispatcher(seq_of_zeros):
+    return seq_of_zeros
+
+
+@array_function_dispatch(_poly_dispatcher)
+def poly(seq_of_zeros):
+    """
+    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 </reference/routines.polynomials>`.
+
+    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 Trigonometry,
+       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)[0], 0, np.random.random(1)[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.
+
+    """
+    seq_of_zeros = atleast_1d(seq_of_zeros)
+    sh = seq_of_zeros.shape
+
+    if len(sh) == 2 and sh[0] == sh[1] and sh[0] != 0:
+        seq_of_zeros = eigvals(seq_of_zeros)
+    elif len(sh) == 1:
+        dt = seq_of_zeros.dtype
+        # Let object arrays slip through, e.g. for arbitrary precision
+        if dt != object:
+            seq_of_zeros = seq_of_zeros.astype(mintypecode(dt.char))
+    else:
+        raise ValueError("input must be 1d or non-empty square 2d array.")
+
+    if len(seq_of_zeros) == 0:
+        return 1.0
+    dt = seq_of_zeros.dtype
+    a = ones((1,), dtype=dt)
+    for zero in seq_of_zeros:
+        a = NX.convolve(a, array([1, -zero], dtype=dt), mode='full')
+
+    if issubclass(a.dtype.type, NX.complexfloating):
+        # if complex roots are all complex conjugates, the roots are real.
+        roots = NX.asarray(seq_of_zeros, complex)
+        if NX.all(NX.sort(roots) == NX.sort(roots.conjugate())):
+            a = a.real.copy()
+
+    return a
+
+
+def _roots_dispatcher(p):
+    return p
+
+
+@array_function_dispatch(_roots_dispatcher)
+def roots(p):
+    """
+    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 </reference/routines.polynomials>`.
+
+    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])
+
+    """
+    # If input is scalar, this makes it an array
+    p = atleast_1d(p)
+    if p.ndim != 1:
+        raise ValueError("Input must be a rank-1 array.")
+
+    # find non-zero array entries
+    non_zero = NX.nonzero(NX.ravel(p))[0]
+
+    # Return an empty array if polynomial is all zeros
+    if len(non_zero) == 0:
+        return NX.array([])
+
+    # find the number of trailing zeros -- this is the number of roots at 0.
+    trailing_zeros = len(p) - non_zero[-1] - 1
+
+    # strip leading and trailing zeros
+    p = p[int(non_zero[0]):int(non_zero[-1])+1]
+
+    # casting: if incoming array isn't floating point, make it floating point.
+    if not issubclass(p.dtype.type, (NX.floating, NX.complexfloating)):
+        p = p.astype(float)
+
+    N = len(p)
+    if N > 1:
+        # build companion matrix and find its eigenvalues (the roots)
+        A = diag(NX.ones((N-2,), p.dtype), -1)
+        A[0,:] = -p[1:] / p[0]
+        roots = eigvals(A)
+    else:
+        roots = NX.array([])
+
+    # tack any zeros onto the back of the array
+    roots = hstack((roots, NX.zeros(trailing_zeros, roots.dtype)))
+    return roots
+
+
+def _polyint_dispatcher(p, m=None, k=None):
+    return (p,)
+
+
+@array_function_dispatch(_polyint_dispatcher)
+def polyint(p, m=1, k=None):
+    """
+    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 </reference/routines.polynomials>`.
+
+    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)
+    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)
+    3.0
+
+    """
+    m = int(m)
+    if m < 0:
+        raise ValueError("Order of integral must be positive (see polyder)")
+    if k is None:
+        k = NX.zeros(m, float)
+    k = atleast_1d(k)
+    if len(k) == 1 and m > 1:
+        k = k[0]*NX.ones(m, float)
+    if len(k) < m:
+        raise ValueError(
+              "k must be a scalar or a rank-1 array of length 1 or >m.")
+
+    truepoly = isinstance(p, poly1d)
+    p = NX.asarray(p)
+    if m == 0:
+        if truepoly:
+            return poly1d(p)
+        return p
+    else:
+        # Note: this must work also with object and integer arrays
+        y = NX.concatenate((p.__truediv__(NX.arange(len(p), 0, -1)), [k[0]]))
+        val = polyint(y, m - 1, k=k[1:])
+        if truepoly:
+            return poly1d(val)
+        return val
+
+
+def _polyder_dispatcher(p, m=None):
+    return (p,)
+
+
+@array_function_dispatch(_polyder_dispatcher)
+def polyder(p, m=1):
+    """
+    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 </reference/routines.polynomials>`.
+
+    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])
+
+    """
+    m = int(m)
+    if m < 0:
+        raise ValueError("Order of derivative must be positive (see polyint)")
+
+    truepoly = isinstance(p, poly1d)
+    p = NX.asarray(p)
+    n = len(p) - 1
+    y = p[:-1] * NX.arange(n, 0, -1)
+    if m == 0:
+        val = p
+    else:
+        val = polyder(y, m - 1)
+    if truepoly:
+        val = poly1d(val)
+    return val
+
+
+def _polyfit_dispatcher(x, y, deg, rcond=None, full=None, w=None, cov=None):
+    return (x, y, w)
+
+
+@array_function_dispatch(_polyfit_dispatcher)
+def polyfit(x, y, deg, rcond=None, full=False, w=None, cov=False):
+    """
+    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 </reference/routines.polynomials>`.
+
+    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 <numpy.polynomial.polynomial.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. If not None, the weight ``w[i]`` applies to the unsquared
+        residual ``y[i] - y_hat[i]`` at ``x[i]``. Ideally the weights are
+        chosen so that the errors of the products ``w[i]*y[i]`` all have the
+        same variance.  When using inverse-variance weighting, use
+        ``w[i] = 1/sigma(y[i])``.  The default value is None.
+    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
+        w = 1/sigma, 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
+        These values are only returned if ``full == True``
+
+        - residuals -- sum of squared residuals of the least squares fit
+        - rank -- the effective rank of the scaled Vandermonde
+           coefficient matrix
+        - singular_values -- singular values of the scaled Vandermonde
+           coefficient matrix
+        - rcond -- value of `rcond`.
+
+        For more details, see `numpy.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",
+           https://en.wikipedia.org/wiki/Curve_fitting
+    .. [2] Wikipedia, "Polynomial interpolation",
+           https://en.wikipedia.org/wiki/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)
+    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)
+    -0.80000000000000204 # may vary
+    >>> p30(5)
+    -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()
+
+    """
+    order = int(deg) + 1
+    x = NX.asarray(x) + 0.0
+    y = NX.asarray(y) + 0.0
+
+    # check arguments.
+    if deg < 0:
+        raise ValueError("expected deg >= 0")
+    if x.ndim != 1:
+        raise TypeError("expected 1D vector for x")
+    if x.size == 0:
+        raise TypeError("expected non-empty vector for x")
+    if y.ndim < 1 or y.ndim > 2:
+        raise TypeError("expected 1D or 2D array for y")
+    if x.shape[0] != y.shape[0]:
+        raise TypeError("expected x and y to have same length")
+
+    # set rcond
+    if rcond is None:
+        rcond = len(x)*finfo(x.dtype).eps
+
+    # set up least squares equation for powers of x
+    lhs = vander(x, order)
+    rhs = y
+
+    # apply weighting
+    if w is not None:
+        w = NX.asarray(w) + 0.0
+        if w.ndim != 1:
+            raise TypeError("expected a 1-d array for weights")
+        if w.shape[0] != y.shape[0]:
+            raise TypeError("expected w and y to have the same length")
+        lhs *= w[:, NX.newaxis]
+        if rhs.ndim == 2:
+            rhs *= w[:, NX.newaxis]
+        else:
+            rhs *= w
+
+    # scale lhs to improve condition number and solve
+    scale = NX.sqrt((lhs*lhs).sum(axis=0))
+    lhs /= scale
+    c, resids, rank, s = lstsq(lhs, rhs, rcond)
+    c = (c.T/scale).T  # broadcast scale coefficients
+
+    # warn on rank reduction, which indicates an ill conditioned matrix
+    if rank != order and not full:
+        msg = "Polyfit may be poorly conditioned"
+        warnings.warn(msg, RankWarning, stacklevel=2)
+
+    if full:
+        return c, resids, rank, s, rcond
+    elif cov:
+        Vbase = inv(dot(lhs.T, lhs))
+        Vbase /= NX.outer(scale, scale)
+        if cov == "unscaled":
+            fac = 1
+        else:
+            if len(x) <= order:
+                raise ValueError("the number of data points must exceed order "
+                                 "to scale the covariance matrix")
+            # note, this used to be: fac = resids / (len(x) - order - 2.0)
+            # it was deciced that the "- 2" (originally justified by "Bayesian
+            # uncertainty analysis") is not what the user expects
+            # (see gh-11196 and gh-11197)
+            fac = resids / (len(x) - order)
+        if y.ndim == 1:
+            return c, Vbase * fac
+        else:
+            return c, Vbase[:,:, NX.newaxis] * fac
+    else:
+        return c
+
+
+def _polyval_dispatcher(p, x):
+    return (p, x)
+
+
+@array_function_dispatch(_polyval_dispatcher)
+def polyval(p, x):
+    """
+    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 </reference/routines.polynomials>`.
+
+    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))
+    poly1d([76])
+    >>> np.polyval(np.poly1d([3,0,1]), 5)
+    76
+    >>> np.polyval(np.poly1d([3,0,1]), np.poly1d(5))
+    poly1d([76])
+
+    """
+    p = NX.asarray(p)
+    if isinstance(x, poly1d):
+        y = 0
+    else:
+        x = NX.asanyarray(x)
+        y = NX.zeros_like(x)
+    for pv in p:
+        y = y * x + pv
+    return y
+
+
+def _binary_op_dispatcher(a1, a2):
+    return (a1, a2)
+
+
+@array_function_dispatch(_binary_op_dispatcher)
+def polyadd(a1, a2):
+    """
+    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 </reference/routines.polynomials>`.
+
+    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
+
+    """
+    truepoly = (isinstance(a1, poly1d) or isinstance(a2, poly1d))
+    a1 = atleast_1d(a1)
+    a2 = atleast_1d(a2)
+    diff = len(a2) - len(a1)
+    if diff == 0:
+        val = a1 + a2
+    elif diff > 0:
+        zr = NX.zeros(diff, a1.dtype)
+        val = NX.concatenate((zr, a1)) + a2
+    else:
+        zr = NX.zeros(abs(diff), a2.dtype)
+        val = a1 + NX.concatenate((zr, a2))
+    if truepoly:
+        val = poly1d(val)
+    return val
+
+
+@array_function_dispatch(_binary_op_dispatcher)
+def polysub(a1, a2):
+    """
+    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 </reference/routines.polynomials>`.
+
+    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])
+
+    """
+    truepoly = (isinstance(a1, poly1d) or isinstance(a2, poly1d))
+    a1 = atleast_1d(a1)
+    a2 = atleast_1d(a2)
+    diff = len(a2) - len(a1)
+    if diff == 0:
+        val = a1 - a2
+    elif diff > 0:
+        zr = NX.zeros(diff, a1.dtype)
+        val = NX.concatenate((zr, a1)) - a2
+    else:
+        zr = NX.zeros(abs(diff), a2.dtype)
+        val = a1 - NX.concatenate((zr, a2))
+    if truepoly:
+        val = poly1d(val)
+    return val
+
+
+@array_function_dispatch(_binary_op_dispatcher)
+def polymul(a1, a2):
+    """
+    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 </reference/routines.polynomials>`.
+
+    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
+
+    """
+    truepoly = (isinstance(a1, poly1d) or isinstance(a2, poly1d))
+    a1, a2 = poly1d(a1), poly1d(a2)
+    val = NX.convolve(a1, a2)
+    if truepoly:
+        val = poly1d(val)
+    return val
+
+
+def _polydiv_dispatcher(u, v):
+    return (u, v)
+
+
+@array_function_dispatch(_polydiv_dispatcher)
+def polydiv(u, v):
+    """
+    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 </reference/routines.polynomials>`.
+
+    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]))
+
+    """
+    truepoly = (isinstance(u, poly1d) or isinstance(v, poly1d))
+    u = atleast_1d(u) + 0.0
+    v = atleast_1d(v) + 0.0
+    # w has the common type
+    w = u[0] + v[0]
+    m = len(u) - 1
+    n = len(v) - 1
+    scale = 1. / v[0]
+    q = NX.zeros((max(m - n + 1, 1),), w.dtype)
+    r = u.astype(w.dtype)
+    for k in range(0, m-n+1):
+        d = scale * r[k]
+        q[k] = d
+        r[k:k+n+1] -= d*v
+    while NX.allclose(r[0], 0, rtol=1e-14) and (r.shape[-1] > 1):
+        r = r[1:]
+    if truepoly:
+        return poly1d(q), poly1d(r)
+    return q, r
+
+_poly_mat = re.compile(r"\*\*([0-9]*)")
+def _raise_power(astr, wrap=70):
+    n = 0
+    line1 = ''
+    line2 = ''
+    output = ' '
+    while True:
+        mat = _poly_mat.search(astr, n)
+        if mat is None:
+            break
+        span = mat.span()
+        power = mat.groups()[0]
+        partstr = astr[n:span[0]]
+        n = span[1]
+        toadd2 = partstr + ' '*(len(power)-1)
+        toadd1 = ' '*(len(partstr)-1) + power
+        if ((len(line2) + len(toadd2) > wrap) or
+                (len(line1) + len(toadd1) > wrap)):
+            output += line1 + "\n" + line2 + "\n "
+            line1 = toadd1
+            line2 = toadd2
+        else:
+            line2 += partstr + ' '*(len(power)-1)
+            line1 += ' '*(len(partstr)-1) + power
+    output += line1 + "\n" + line2
+    return output + astr[n:]
+
+
+@set_module('numpy')
+class poly1d:
+    """
+    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 </reference/routines.polynomials>`.
+
+    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])
+
+    """
+    __hash__ = None
+
+    @property
+    def coeffs(self):
+        """ The polynomial coefficients """
+        return self._coeffs
+
+    @coeffs.setter
+    def coeffs(self, value):
+        # allowing this makes p.coeffs *= 2 legal
+        if value is not self._coeffs:
+            raise AttributeError("Cannot set attribute")
+
+    @property
+    def variable(self):
+        """ The name of the polynomial variable """
+        return self._variable
+
+    # calculated attributes
+    @property
+    def order(self):
+        """ The order or degree of the polynomial """
+        return len(self._coeffs) - 1
+
+    @property
+    def roots(self):
+        """ The roots of the polynomial, where self(x) == 0 """
+        return roots(self._coeffs)
+
+    # our internal _coeffs property need to be backed by __dict__['coeffs'] for
+    # scipy to work correctly.
+    @property
+    def _coeffs(self):
+        return self.__dict__['coeffs']
+    @_coeffs.setter
+    def _coeffs(self, coeffs):
+        self.__dict__['coeffs'] = coeffs
+
+    # alias attributes
+    r = roots
+    c = coef = coefficients = coeffs
+    o = order
+
+    def __init__(self, c_or_r, r=False, variable=None):
+        if isinstance(c_or_r, poly1d):
+            self._variable = c_or_r._variable
+            self._coeffs = c_or_r._coeffs
+
+            if set(c_or_r.__dict__) - set(self.__dict__):
+                msg = ("In the future extra properties will not be copied "
+                       "across when constructing one poly1d from another")
+                warnings.warn(msg, FutureWarning, stacklevel=2)
+                self.__dict__.update(c_or_r.__dict__)
+
+            if variable is not None:
+                self._variable = variable
+            return
+        if r:
+            c_or_r = poly(c_or_r)
+        c_or_r = atleast_1d(c_or_r)
+        if c_or_r.ndim > 1:
+            raise ValueError("Polynomial must be 1d only.")
+        c_or_r = trim_zeros(c_or_r, trim='f')
+        if len(c_or_r) == 0:
+            c_or_r = NX.array([0], dtype=c_or_r.dtype)
+        self._coeffs = c_or_r
+        if variable is None:
+            variable = 'x'
+        self._variable = variable
+
+    def __array__(self, t=None):
+        if t:
+            return NX.asarray(self.coeffs, t)
+        else:
+            return NX.asarray(self.coeffs)
+
+    def __repr__(self):
+        vals = repr(self.coeffs)
+        vals = vals[6:-1]
+        return "poly1d(%s)" % vals
+
+    def __len__(self):
+        return self.order
+
+    def __str__(self):
+        thestr = "0"
+        var = self.variable
+
+        # Remove leading zeros
+        coeffs = self.coeffs[NX.logical_or.accumulate(self.coeffs != 0)]
+        N = len(coeffs)-1
+
+        def fmt_float(q):
+            s = '%.4g' % q
+            if s.endswith('.0000'):
+                s = s[:-5]
+            return s
+
+        for k, coeff in enumerate(coeffs):
+            if not iscomplex(coeff):
+                coefstr = fmt_float(real(coeff))
+            elif real(coeff) == 0:
+                coefstr = '%sj' % fmt_float(imag(coeff))
+            else:
+                coefstr = '(%s + %sj)' % (fmt_float(real(coeff)),
+                                          fmt_float(imag(coeff)))
+
+            power = (N-k)
+            if power == 0:
+                if coefstr != '0':
+                    newstr = '%s' % (coefstr,)
+                else:
+                    if k == 0:
+                        newstr = '0'
+                    else:
+                        newstr = ''
+            elif power == 1:
+                if coefstr == '0':
+                    newstr = ''
+                elif coefstr == 'b':
+                    newstr = var
+                else:
+                    newstr = '%s %s' % (coefstr, var)
+            else:
+                if coefstr == '0':
+                    newstr = ''
+                elif coefstr == 'b':
+                    newstr = '%s**%d' % (var, power,)
+                else:
+                    newstr = '%s %s**%d' % (coefstr, var, power)
+
+            if k > 0:
+                if newstr != '':
+                    if newstr.startswith('-'):
+                        thestr = "%s - %s" % (thestr, newstr[1:])
+                    else:
+                        thestr = "%s + %s" % (thestr, newstr)
+            else:
+                thestr = newstr
+        return _raise_power(thestr)
+
+    def __call__(self, val):
+        return polyval(self.coeffs, val)
+
+    def __neg__(self):
+        return poly1d(-self.coeffs)
+
+    def __pos__(self):
+        return self
+
+    def __mul__(self, other):
+        if isscalar(other):
+            return poly1d(self.coeffs * other)
+        else:
+            other = poly1d(other)
+            return poly1d(polymul(self.coeffs, other.coeffs))
+
+    def __rmul__(self, other):
+        if isscalar(other):
+            return poly1d(other * self.coeffs)
+        else:
+            other = poly1d(other)
+            return poly1d(polymul(self.coeffs, other.coeffs))
+
+    def __add__(self, other):
+        other = poly1d(other)
+        return poly1d(polyadd(self.coeffs, other.coeffs))
+
+    def __radd__(self, other):
+        other = poly1d(other)
+        return poly1d(polyadd(self.coeffs, other.coeffs))
+
+    def __pow__(self, val):
+        if not isscalar(val) or int(val) != val or val < 0:
+            raise ValueError("Power to non-negative integers only.")
+        res = [1]
+        for _ in range(val):
+            res = polymul(self.coeffs, res)
+        return poly1d(res)
+
+    def __sub__(self, other):
+        other = poly1d(other)
+        return poly1d(polysub(self.coeffs, other.coeffs))
+
+    def __rsub__(self, other):
+        other = poly1d(other)
+        return poly1d(polysub(other.coeffs, self.coeffs))
+
+    def __div__(self, other):
+        if isscalar(other):
+            return poly1d(self.coeffs/other)
+        else:
+            other = poly1d(other)
+            return polydiv(self, other)
+
+    __truediv__ = __div__
+
+    def __rdiv__(self, other):
+        if isscalar(other):
+            return poly1d(other/self.coeffs)
+        else:
+            other = poly1d(other)
+            return polydiv(other, self)
+
+    __rtruediv__ = __rdiv__
+
+    def __eq__(self, other):
+        if not isinstance(other, poly1d):
+            return NotImplemented
+        if self.coeffs.shape != other.coeffs.shape:
+            return False
+        return (self.coeffs == other.coeffs).all()
+
+    def __ne__(self, other):
+        if not isinstance(other, poly1d):
+            return NotImplemented
+        return not self.__eq__(other)
+
+
+    def __getitem__(self, val):
+        ind = self.order - val
+        if val > self.order:
+            return self.coeffs.dtype.type(0)
+        if val < 0:
+            return self.coeffs.dtype.type(0)
+        return self.coeffs[ind]
+
+    def __setitem__(self, key, val):
+        ind = self.order - key
+        if key < 0:
+            raise ValueError("Does not support negative powers.")
+        if key > self.order:
+            zr = NX.zeros(key-self.order, self.coeffs.dtype)
+            self._coeffs = NX.concatenate((zr, self.coeffs))
+            ind = 0
+        self._coeffs[ind] = val
+        return
+
+    def __iter__(self):
+        return iter(self.coeffs)
+
+    def 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
+
+        """
+        return poly1d(polyint(self.coeffs, m=m, k=k))
+
+    def deriv(self, m=1):
+        """
+        Return a derivative of this polynomial.
+
+        Refer to `polyder` for full documentation.
+
+        See Also
+        --------
+        polyder : equivalent function
+
+        """
+        return poly1d(polyder(self.coeffs, m=m))
+
+# Stuff to do on module import
+
+warnings.simplefilter('always', RankWarning)

env-llmeval/lib/python3.10/site-packages/numpy/lib/polynomial.pyi

@@ -0,0 +1,303 @@
+from typing import (
+    Literal as L,
+    overload,
+    Any,
+    SupportsInt,
+    SupportsIndex,
+    TypeVar,
+    NoReturn,
+)
+
+from numpy import (
+    RankWarning as RankWarning,
+    poly1d as poly1d,
+    unsignedinteger,
+    signedinteger,
+    floating,
+    complexfloating,
+    bool_,
+    int32,
+    int64,
+    float64,
+    complex128,
+    object_,
+)
+
+from numpy._typing import (
+    NDArray,
+    ArrayLike,
+    _ArrayLikeBool_co,
+    _ArrayLikeUInt_co,
+    _ArrayLikeInt_co,
+    _ArrayLikeFloat_co,
+    _ArrayLikeComplex_co,
+    _ArrayLikeObject_co,
+)
+
+_T = TypeVar("_T")
+
+_2Tup = tuple[_T, _T]
+_5Tup = tuple[
+    _T,
+    NDArray[float64],
+    NDArray[int32],
+    NDArray[float64],
+    NDArray[float64],
+]
+
+__all__: list[str]
+
+def poly(seq_of_zeros: ArrayLike) -> NDArray[floating[Any]]: ...
+
+# Returns either a float or complex array depending on the input values.
+# See `np.linalg.eigvals`.
+def roots(p: ArrayLike) -> NDArray[complexfloating[Any, Any]] | NDArray[floating[Any]]: ...
+
+@overload
+def polyint(
+    p: poly1d,
+    m: SupportsInt | SupportsIndex = ...,
+    k: None | _ArrayLikeComplex_co | _ArrayLikeObject_co = ...,
+) -> poly1d: ...
+@overload
+def polyint(
+    p: _ArrayLikeFloat_co,
+    m: SupportsInt | SupportsIndex = ...,
+    k: None | _ArrayLikeFloat_co = ...,
+) -> NDArray[floating[Any]]: ...
+@overload
+def polyint(
+    p: _ArrayLikeComplex_co,
+    m: SupportsInt | SupportsIndex = ...,
+    k: None | _ArrayLikeComplex_co = ...,
+) -> NDArray[complexfloating[Any, Any]]: ...
+@overload
+def polyint(
+    p: _ArrayLikeObject_co,
+    m: SupportsInt | SupportsIndex = ...,
+    k: None | _ArrayLikeObject_co = ...,
+) -> NDArray[object_]: ...
+
+@overload
+def polyder(
+    p: poly1d,
+    m: SupportsInt | SupportsIndex = ...,
+) -> poly1d: ...
+@overload
+def polyder(
+    p: _ArrayLikeFloat_co,
+    m: SupportsInt | SupportsIndex = ...,
+) -> NDArray[floating[Any]]: ...
+@overload
+def polyder(
+    p: _ArrayLikeComplex_co,
+    m: SupportsInt | SupportsIndex = ...,
+) -> NDArray[complexfloating[Any, Any]]: ...
+@overload
+def polyder(
+    p: _ArrayLikeObject_co,
+    m: SupportsInt | SupportsIndex = ...,
+) -> NDArray[object_]: ...
+
+@overload
+def polyfit(
+    x: _ArrayLikeFloat_co,
+    y: _ArrayLikeFloat_co,
+    deg: SupportsIndex | SupportsInt,
+    rcond: None | float = ...,
+    full: L[False] = ...,
+    w: None | _ArrayLikeFloat_co = ...,
+    cov: L[False] = ...,
+) -> NDArray[float64]: ...
+@overload
+def polyfit(
+    x: _ArrayLikeComplex_co,
+    y: _ArrayLikeComplex_co,
+    deg: SupportsIndex | SupportsInt,
+    rcond: None | float = ...,
+    full: L[False] = ...,
+    w: None | _ArrayLikeFloat_co = ...,
+    cov: L[False] = ...,
+) -> NDArray[complex128]: ...
+@overload
+def polyfit(
+    x: _ArrayLikeFloat_co,
+    y: _ArrayLikeFloat_co,
+    deg: SupportsIndex | SupportsInt,
+    rcond: None | float = ...,
+    full: L[False] = ...,
+    w: None | _ArrayLikeFloat_co = ...,
+    cov: L[True, "unscaled"] = ...,
+) -> _2Tup[NDArray[float64]]: ...
+@overload
+def polyfit(
+    x: _ArrayLikeComplex_co,
+    y: _ArrayLikeComplex_co,
+    deg: SupportsIndex | SupportsInt,
+    rcond: None | float = ...,
+    full: L[False] = ...,
+    w: None | _ArrayLikeFloat_co = ...,
+    cov: L[True, "unscaled"] = ...,
+) -> _2Tup[NDArray[complex128]]: ...
+@overload
+def polyfit(
+    x: _ArrayLikeFloat_co,
+    y: _ArrayLikeFloat_co,
+    deg: SupportsIndex | SupportsInt,
+    rcond: None | float = ...,
+    full: L[True] = ...,
+    w: None | _ArrayLikeFloat_co = ...,
+    cov: bool | L["unscaled"] = ...,
+) -> _5Tup[NDArray[float64]]: ...
+@overload
+def polyfit(
+    x: _ArrayLikeComplex_co,
+    y: _ArrayLikeComplex_co,
+    deg: SupportsIndex | SupportsInt,
+    rcond: None | float = ...,
+    full: L[True] = ...,
+    w: None | _ArrayLikeFloat_co = ...,
+    cov: bool | L["unscaled"] = ...,
+) -> _5Tup[NDArray[complex128]]: ...
+
+@overload
+def polyval(
+    p: _ArrayLikeBool_co,
+    x: _ArrayLikeBool_co,
+) -> NDArray[int64]: ...
+@overload
+def polyval(
+    p: _ArrayLikeUInt_co,
+    x: _ArrayLikeUInt_co,
+) -> NDArray[unsignedinteger[Any]]: ...
+@overload
+def polyval(
+    p: _ArrayLikeInt_co,
+    x: _ArrayLikeInt_co,
+) -> NDArray[signedinteger[Any]]: ...
+@overload
+def polyval(
+    p: _ArrayLikeFloat_co,
+    x: _ArrayLikeFloat_co,
+) -> NDArray[floating[Any]]: ...
+@overload
+def polyval(
+    p: _ArrayLikeComplex_co,
+    x: _ArrayLikeComplex_co,
+) -> NDArray[complexfloating[Any, Any]]: ...
+@overload
+def polyval(
+    p: _ArrayLikeObject_co,
+    x: _ArrayLikeObject_co,
+) -> NDArray[object_]: ...
+
+@overload
+def polyadd(
+    a1: poly1d,
+    a2: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+) -> poly1d: ...
+@overload
+def polyadd(
+    a1: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    a2: poly1d,
+) -> poly1d: ...
+@overload
+def polyadd(
+    a1: _ArrayLikeBool_co,
+    a2: _ArrayLikeBool_co,
+) -> NDArray[bool_]: ...
+@overload
+def polyadd(
+    a1: _ArrayLikeUInt_co,
+    a2: _ArrayLikeUInt_co,
+) -> NDArray[unsignedinteger[Any]]: ...
+@overload
+def polyadd(
+    a1: _ArrayLikeInt_co,
+    a2: _ArrayLikeInt_co,
+) -> NDArray[signedinteger[Any]]: ...
+@overload
+def polyadd(
+    a1: _ArrayLikeFloat_co,
+    a2: _ArrayLikeFloat_co,
+) -> NDArray[floating[Any]]: ...
+@overload
+def polyadd(
+    a1: _ArrayLikeComplex_co,
+    a2: _ArrayLikeComplex_co,
+) -> NDArray[complexfloating[Any, Any]]: ...
+@overload
+def polyadd(
+    a1: _ArrayLikeObject_co,
+    a2: _ArrayLikeObject_co,
+) -> NDArray[object_]: ...
+
+@overload
+def polysub(
+    a1: poly1d,
+    a2: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+) -> poly1d: ...
+@overload
+def polysub(
+    a1: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    a2: poly1d,
+) -> poly1d: ...
+@overload
+def polysub(
+    a1: _ArrayLikeBool_co,
+    a2: _ArrayLikeBool_co,
+) -> NoReturn: ...
+@overload
+def polysub(
+    a1: _ArrayLikeUInt_co,
+    a2: _ArrayLikeUInt_co,
+) -> NDArray[unsignedinteger[Any]]: ...
+@overload
+def polysub(
+    a1: _ArrayLikeInt_co,
+    a2: _ArrayLikeInt_co,
+) -> NDArray[signedinteger[Any]]: ...
+@overload
+def polysub(
+    a1: _ArrayLikeFloat_co,
+    a2: _ArrayLikeFloat_co,
+) -> NDArray[floating[Any]]: ...
+@overload
+def polysub(
+    a1: _ArrayLikeComplex_co,
+    a2: _ArrayLikeComplex_co,
+) -> NDArray[complexfloating[Any, Any]]: ...
+@overload
+def polysub(
+    a1: _ArrayLikeObject_co,
+    a2: _ArrayLikeObject_co,
+) -> NDArray[object_]: ...
+
+# NOTE: Not an alias, but they do have the same signature (that we can reuse)
+polymul = polyadd
+
+@overload
+def polydiv(
+    u: poly1d,
+    v: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+) -> _2Tup[poly1d]: ...
+@overload
+def polydiv(
+    u: _ArrayLikeComplex_co | _ArrayLikeObject_co,
+    v: poly1d,
+) -> _2Tup[poly1d]: ...
+@overload
+def polydiv(
+    u: _ArrayLikeFloat_co,
+    v: _ArrayLikeFloat_co,
+) -> _2Tup[NDArray[floating[Any]]]: ...
+@overload
+def polydiv(
+    u: _ArrayLikeComplex_co,
+    v: _ArrayLikeComplex_co,
+) -> _2Tup[NDArray[complexfloating[Any, Any]]]: ...
+@overload
+def polydiv(
+    u: _ArrayLikeObject_co,
+    v: _ArrayLikeObject_co,
+) -> _2Tup[NDArray[Any]]: ...

env-llmeval/lib/python3.10/site-packages/numpy/lib/recfunctions.py

@@ -0,0 +1,1673 @@
+"""
+Collection of utilities to manipulate structured arrays.
+
+Most of these functions were initially implemented by John Hunter for
+matplotlib.  They have been rewritten and extended for convenience.
+
+"""
+import itertools
+import numpy as np
+import numpy.ma as ma
+from numpy import ndarray, recarray
+from numpy.ma import MaskedArray
+from numpy.ma.mrecords import MaskedRecords
+from numpy.core.overrides import array_function_dispatch
+from numpy.lib._iotools import _is_string_like
+
+_check_fill_value = np.ma.core._check_fill_value
+
+
+__all__ = [
+    'append_fields', 'apply_along_fields', 'assign_fields_by_name',
+    'drop_fields', 'find_duplicates', 'flatten_descr',
+    'get_fieldstructure', 'get_names', 'get_names_flat',
+    'join_by', 'merge_arrays', 'rec_append_fields',
+    'rec_drop_fields', 'rec_join', 'recursive_fill_fields',
+    'rename_fields', 'repack_fields', 'require_fields',
+    'stack_arrays', 'structured_to_unstructured', 'unstructured_to_structured',
+    ]
+
+
+def _recursive_fill_fields_dispatcher(input, output):
+    return (input, output)
+
+
+@array_function_dispatch(_recursive_fill_fields_dispatcher)
+def recursive_fill_fields(input, output):
+    """
+    Fills fields from output with fields from input,
+    with support for nested structures.
+
+    Parameters
+    ----------
+    input : ndarray
+        Input array.
+    output : ndarray
+        Output array.
+
+    Notes
+    -----
+    * `output` should be at least the same size as `input`
+
+    Examples
+    --------
+    >>> from numpy.lib import recfunctions as rfn
+    >>> a = np.array([(1, 10.), (2, 20.)], dtype=[('A', np.int64), ('B', np.float64)])
+    >>> b = np.zeros((3,), dtype=a.dtype)
+    >>> rfn.recursive_fill_fields(a, b)
+    array([(1, 10.), (2, 20.), (0,  0.)], dtype=[('A', '<i8'), ('B', '<f8')])
+
+    """
+    newdtype = output.dtype
+    for field in newdtype.names:
+        try:
+            current = input[field]
+        except ValueError:
+            continue
+        if current.dtype.names is not None:
+            recursive_fill_fields(current, output[field])
+        else:
+            output[field][:len(current)] = current
+    return output
+
+
+def _get_fieldspec(dtype):
+    """
+    Produce a list of name/dtype pairs corresponding to the dtype fields
+
+    Similar to dtype.descr, but the second item of each tuple is a dtype, not a
+    string. As a result, this handles subarray dtypes
+
+    Can be passed to the dtype constructor to reconstruct the dtype, noting that
+    this (deliberately) discards field offsets.
+
+    Examples
+    --------
+    >>> dt = np.dtype([(('a', 'A'), np.int64), ('b', np.double, 3)])
+    >>> dt.descr
+    [(('a', 'A'), '<i8'), ('b', '<f8', (3,))]
+    >>> _get_fieldspec(dt)
+    [(('a', 'A'), dtype('int64')), ('b', dtype(('<f8', (3,))))]
+
+    """
+    if dtype.names is None:
+        # .descr returns a nameless field, so we should too
+        return [('', dtype)]
+    else:
+        fields = ((name, dtype.fields[name]) for name in dtype.names)
+        # keep any titles, if present
+        return [
+            (name if len(f) == 2 else (f[2], name), f[0])
+            for name, f in fields
+        ]
+
+
+def get_names(adtype):
+    """
+    Returns the field names of the input datatype as a tuple. Input datatype
+    must have fields otherwise error is raised.
+
+    Parameters
+    ----------
+    adtype : dtype
+        Input datatype
+
+    Examples
+    --------
+    >>> from numpy.lib import recfunctions as rfn
+    >>> rfn.get_names(np.empty((1,), dtype=[('A', int)]).dtype)
+    ('A',)
+    >>> rfn.get_names(np.empty((1,), dtype=[('A',int), ('B', float)]).dtype)
+    ('A', 'B')
+    >>> adtype = np.dtype([('a', int), ('b', [('ba', int), ('bb', int)])])
+    >>> rfn.get_names(adtype)
+    ('a', ('b', ('ba', 'bb')))
+    """
+    listnames = []
+    names = adtype.names
+    for name in names:
+        current = adtype[name]
+        if current.names is not None:
+            listnames.append((name, tuple(get_names(current))))
+        else:
+            listnames.append(name)
+    return tuple(listnames)
+
+
+def get_names_flat(adtype):
+    """
+    Returns the field names of the input datatype as a tuple. Input datatype
+    must have fields otherwise error is raised.
+    Nested structure are flattened beforehand.
+
+    Parameters
+    ----------
+    adtype : dtype
+        Input datatype
+
+    Examples
+    --------
+    >>> from numpy.lib import recfunctions as rfn
+    >>> rfn.get_names_flat(np.empty((1,), dtype=[('A', int)]).dtype) is None
+    False
+    >>> rfn.get_names_flat(np.empty((1,), dtype=[('A',int), ('B', str)]).dtype)
+    ('A', 'B')
+    >>> adtype = np.dtype([('a', int), ('b', [('ba', int), ('bb', int)])])
+    >>> rfn.get_names_flat(adtype)
+    ('a', 'b', 'ba', 'bb')
+    """
+    listnames = []
+    names = adtype.names
+    for name in names:
+        listnames.append(name)
+        current = adtype[name]
+        if current.names is not None:
+            listnames.extend(get_names_flat(current))
+    return tuple(listnames)
+
+
+def flatten_descr(ndtype):
+    """
+    Flatten a structured data-type description.
+
+    Examples
+    --------
+    >>> from numpy.lib import recfunctions as rfn
+    >>> ndtype = np.dtype([('a', '<i4'), ('b', [('ba', '<f8'), ('bb', '<i4')])])
+    >>> rfn.flatten_descr(ndtype)
+    (('a', dtype('int32')), ('ba', dtype('float64')), ('bb', dtype('int32')))
+
+    """
+    names = ndtype.names
+    if names is None:
+        return (('', ndtype),)
+    else:
+        descr = []
+        for field in names:
+            (typ, _) = ndtype.fields[field]
+            if typ.names is not None:
+                descr.extend(flatten_descr(typ))
+            else:
+                descr.append((field, typ))
+        return tuple(descr)
+
+
+def _zip_dtype(seqarrays, flatten=False):
+    newdtype = []
+    if flatten:
+        for a in seqarrays:
+            newdtype.extend(flatten_descr(a.dtype))
+    else:
+        for a in seqarrays:
+            current = a.dtype
+            if current.names is not None and len(current.names) == 1:
+                # special case - dtypes of 1 field are flattened
+                newdtype.extend(_get_fieldspec(current))
+            else:
+                newdtype.append(('', current))
+    return np.dtype(newdtype)
+
+
+def _zip_descr(seqarrays, flatten=False):
+    """
+    Combine the dtype description of a series of arrays.
+
+    Parameters
+    ----------
+    seqarrays : sequence of arrays
+        Sequence of arrays
+    flatten : {boolean}, optional
+        Whether to collapse nested descriptions.
+    """
+    return _zip_dtype(seqarrays, flatten=flatten).descr
+
+
+def get_fieldstructure(adtype, lastname=None, parents=None,):
+    """
+    Returns a dictionary with fields indexing lists of their parent fields.
+
+    This function is used to simplify access to fields nested in other fields.
+
+    Parameters
+    ----------
+    adtype : np.dtype
+        Input datatype
+    lastname : optional
+        Last processed field name (used internally during recursion).
+    parents : dictionary
+        Dictionary of parent fields (used interbally during recursion).
+
+    Examples
+    --------
+    >>> from numpy.lib import recfunctions as rfn
+    >>> ndtype =  np.dtype([('A', int),
+    ...                     ('B', [('BA', int),
+    ...                            ('BB', [('BBA', int), ('BBB', int)])])])
+    >>> rfn.get_fieldstructure(ndtype)
+    ... # XXX: possible regression, order of BBA and BBB is swapped
+    {'A': [], 'B': [], 'BA': ['B'], 'BB': ['B'], 'BBA': ['B', 'BB'], 'BBB': ['B', 'BB']}
+
+    """
+    if parents is None:
+        parents = {}
+    names = adtype.names
+    for name in names:
+        current = adtype[name]
+        if current.names is not None:
+            if lastname:
+                parents[name] = [lastname, ]
+            else:
+                parents[name] = []
+            parents.update(get_fieldstructure(current, name, parents))
+        else:
+            lastparent = [_ for _ in (parents.get(lastname, []) or [])]
+            if lastparent:
+                lastparent.append(lastname)
+            elif lastname:
+                lastparent = [lastname, ]
+            parents[name] = lastparent or []
+    return parents
+
+
+def _izip_fields_flat(iterable):
+    """
+    Returns an iterator of concatenated fields from a sequence of arrays,
+    collapsing any nested structure.
+
+    """
+    for element in iterable:
+        if isinstance(element, np.void):
+            yield from _izip_fields_flat(tuple(element))
+        else:
+            yield element
+
+
+def _izip_fields(iterable):
+    """
+    Returns an iterator of concatenated fields from a sequence of arrays.
+
+    """
+    for element in iterable:
+        if (hasattr(element, '__iter__') and
+                not isinstance(element, str)):
+            yield from _izip_fields(element)
+        elif isinstance(element, np.void) and len(tuple(element)) == 1:
+            # this statement is the same from the previous expression
+            yield from _izip_fields(element)
+        else:
+            yield element
+
+
+def _izip_records(seqarrays, fill_value=None, flatten=True):
+    """
+    Returns an iterator of concatenated items from a sequence of arrays.
+
+    Parameters
+    ----------
+    seqarrays : sequence of arrays
+        Sequence of arrays.
+    fill_value : {None, integer}
+        Value used to pad shorter iterables.
+    flatten : {True, False},
+        Whether to
+    """
+
+    # Should we flatten the items, or just use a nested approach
+    if flatten:
+        zipfunc = _izip_fields_flat
+    else:
+        zipfunc = _izip_fields
+
+    for tup in itertools.zip_longest(*seqarrays, fillvalue=fill_value):
+        yield tuple(zipfunc(tup))
+
+
+def _fix_output(output, usemask=True, asrecarray=False):
+    """
+    Private function: return a recarray, a ndarray, a MaskedArray
+    or a MaskedRecords depending on the input parameters
+    """
+    if not isinstance(output, MaskedArray):
+        usemask = False
+    if usemask:
+        if asrecarray:
+            output = output.view(MaskedRecords)
+    else:
+        output = ma.filled(output)
+        if asrecarray:
+            output = output.view(recarray)
+    return output
+
+
+def _fix_defaults(output, defaults=None):
+    """
+    Update the fill_value and masked data of `output`
+    from the default given in a dictionary defaults.
+    """
+    names = output.dtype.names
+    (data, mask, fill_value) = (output.data, output.mask, output.fill_value)
+    for (k, v) in (defaults or {}).items():
+        if k in names:
+            fill_value[k] = v
+            data[k][mask[k]] = v
+    return output
+
+
+def _merge_arrays_dispatcher(seqarrays, fill_value=None, flatten=None,
+                             usemask=None, asrecarray=None):
+    return seqarrays
+
+
+@array_function_dispatch(_merge_arrays_dispatcher)
+def merge_arrays(seqarrays, fill_value=-1, flatten=False,
+                 usemask=False, asrecarray=False):
+    """
+    Merge arrays field by field.
+
+    Parameters
+    ----------
+    seqarrays : sequence of ndarrays
+        Sequence of arrays
+    fill_value : {float}, optional
+        Filling value used to pad missing data on the shorter arrays.
+    flatten : {False, True}, optional
+        Whether to collapse nested fields.
+    usemask : {False, True}, optional
+        Whether to return a masked array or not.
+    asrecarray : {False, True}, optional
+        Whether to return a recarray (MaskedRecords) or not.
+
+    Examples
+    --------
+    >>> from numpy.lib import recfunctions as rfn
+    >>> rfn.merge_arrays((np.array([1, 2]), np.array([10., 20., 30.])))
+    array([( 1, 10.), ( 2, 20.), (-1, 30.)],
+          dtype=[('f0', '<i8'), ('f1', '<f8')])
+
+    >>> rfn.merge_arrays((np.array([1, 2], dtype=np.int64),
+    ...         np.array([10., 20., 30.])), usemask=False)
+     array([(1, 10.0), (2, 20.0), (-1, 30.0)],
+             dtype=[('f0', '<i8'), ('f1', '<f8')])
+    >>> rfn.merge_arrays((np.array([1, 2]).view([('a', np.int64)]),
+    ...               np.array([10., 20., 30.])),
+    ...              usemask=False, asrecarray=True)
+    rec.array([( 1, 10.), ( 2, 20.), (-1, 30.)],
+              dtype=[('a', '<i8'), ('f1', '<f8')])
+
+    Notes
+    -----
+    * Without a mask, the missing value will be filled with something,
+      depending on what its corresponding type:
+
+      * ``-1``      for integers
+      * ``-1.0``    for floating point numbers
+      * ``'-'``     for characters
+      * ``'-1'``    for strings
+      * ``True``    for boolean values
+    * XXX: I just obtained these values empirically
+    """
+    # Only one item in the input sequence ?
+    if (len(seqarrays) == 1):
+        seqarrays = np.asanyarray(seqarrays[0])
+    # Do we have a single ndarray as input ?
+    if isinstance(seqarrays, (ndarray, np.void)):
+        seqdtype = seqarrays.dtype
+        # Make sure we have named fields
+        if seqdtype.names is None:
+            seqdtype = np.dtype([('', seqdtype)])
+        if not flatten or _zip_dtype((seqarrays,), flatten=True) == seqdtype:
+            # Minimal processing needed: just make sure everything's a-ok
+            seqarrays = seqarrays.ravel()
+            # Find what type of array we must return
+            if usemask:
+                if asrecarray:
+                    seqtype = MaskedRecords
+                else:
+                    seqtype = MaskedArray
+            elif asrecarray:
+                seqtype = recarray
+            else:
+                seqtype = ndarray
+            return seqarrays.view(dtype=seqdtype, type=seqtype)
+        else:
+            seqarrays = (seqarrays,)
+    else:
+        # Make sure we have arrays in the input sequence
+        seqarrays = [np.asanyarray(_m) for _m in seqarrays]
+    # Find the sizes of the inputs and their maximum
+    sizes = tuple(a.size for a in seqarrays)
+    maxlength = max(sizes)
+    # Get the dtype of the output (flattening if needed)
+    newdtype = _zip_dtype(seqarrays, flatten=flatten)
+    # Initialize the sequences for data and mask
+    seqdata = []
+    seqmask = []
+    # If we expect some kind of MaskedArray, make a special loop.
+    if usemask:
+        for (a, n) in zip(seqarrays, sizes):
+            nbmissing = (maxlength - n)
+            # Get the data and mask
+            data = a.ravel().__array__()
+            mask = ma.getmaskarray(a).ravel()
+            # Get the filling value (if needed)
+            if nbmissing:
+                fval = _check_fill_value(fill_value, a.dtype)
+                if isinstance(fval, (ndarray, np.void)):
+                    if len(fval.dtype) == 1:
+                        fval = fval.item()[0]
+                        fmsk = True
+                    else:
+                        fval = np.array(fval, dtype=a.dtype, ndmin=1)
+                        fmsk = np.ones((1,), dtype=mask.dtype)
+            else:
+                fval = None
+                fmsk = True
+            # Store an iterator padding the input to the expected length
+            seqdata.append(itertools.chain(data, [fval] * nbmissing))
+            seqmask.append(itertools.chain(mask, [fmsk] * nbmissing))
+        # Create an iterator for the data
+        data = tuple(_izip_records(seqdata, flatten=flatten))
+        output = ma.array(np.fromiter(data, dtype=newdtype, count=maxlength),
+                          mask=list(_izip_records(seqmask, flatten=flatten)))
+        if asrecarray:
+            output = output.view(MaskedRecords)
+    else:
+        # Same as before, without the mask we don't need...
+        for (a, n) in zip(seqarrays, sizes):
+            nbmissing = (maxlength - n)
+            data = a.ravel().__array__()
+            if nbmissing:
+                fval = _check_fill_value(fill_value, a.dtype)
+                if isinstance(fval, (ndarray, np.void)):
+                    if len(fval.dtype) == 1:
+                        fval = fval.item()[0]
+                    else:
+                        fval = np.array(fval, dtype=a.dtype, ndmin=1)
+            else:
+                fval = None
+            seqdata.append(itertools.chain(data, [fval] * nbmissing))
+        output = np.fromiter(tuple(_izip_records(seqdata, flatten=flatten)),
+                             dtype=newdtype, count=maxlength)
+        if asrecarray:
+            output = output.view(recarray)
+    # And we're done...
+    return output
+
+
+def _drop_fields_dispatcher(base, drop_names, usemask=None, asrecarray=None):
+    return (base,)
+
+
+@array_function_dispatch(_drop_fields_dispatcher)
+def drop_fields(base, drop_names, usemask=True, asrecarray=False):
+    """
+    Return a new array with fields in `drop_names` dropped.
+
+    Nested fields are supported.
+
+    .. versionchanged:: 1.18.0
+        `drop_fields` returns an array with 0 fields if all fields are dropped,
+        rather than returning ``None`` as it did previously.
+
+    Parameters
+    ----------
+    base : array
+        Input array
+    drop_names : string or sequence
+        String or sequence of strings corresponding to the names of the
+        fields to drop.
+    usemask : {False, True}, optional
+        Whether to return a masked array or not.
+    asrecarray : string or sequence, optional
+        Whether to return a recarray or a mrecarray (`asrecarray=True`) or
+        a plain ndarray or masked array with flexible dtype. The default
+        is False.
+
+    Examples
+    --------
+    >>> from numpy.lib import recfunctions as rfn
+    >>> a = np.array([(1, (2, 3.0)), (4, (5, 6.0))],
+    ...   dtype=[('a', np.int64), ('b', [('ba', np.double), ('bb', np.int64)])])
+    >>> rfn.drop_fields(a, 'a')
+    array([((2., 3),), ((5., 6),)],
+          dtype=[('b', [('ba', '<f8'), ('bb', '<i8')])])
+    >>> rfn.drop_fields(a, 'ba')
+    array([(1, (3,)), (4, (6,))], dtype=[('a', '<i8'), ('b', [('bb', '<i8')])])
+    >>> rfn.drop_fields(a, ['ba', 'bb'])
+    array([(1,), (4,)], dtype=[('a', '<i8')])
+    """
+    if _is_string_like(drop_names):
+        drop_names = [drop_names]
+    else:
+        drop_names = set(drop_names)
+
+    def _drop_descr(ndtype, drop_names):
+        names = ndtype.names
+        newdtype = []
+        for name in names:
+            current = ndtype[name]
+            if name in drop_names:
+                continue
+            if current.names is not None:
+                descr = _drop_descr(current, drop_names)
+                if descr:
+                    newdtype.append((name, descr))
+            else:
+                newdtype.append((name, current))
+        return newdtype
+
+    newdtype = _drop_descr(base.dtype, drop_names)
+
+    output = np.empty(base.shape, dtype=newdtype)
+    output = recursive_fill_fields(base, output)
+    return _fix_output(output, usemask=usemask, asrecarray=asrecarray)
+
+
+def _keep_fields(base, keep_names, usemask=True, asrecarray=False):
+    """
+    Return a new array keeping only the fields in `keep_names`,
+    and preserving the order of those fields.
+
+    Parameters
+    ----------
+    base : array
+        Input array
+    keep_names : string or sequence
+        String or sequence of strings corresponding to the names of the
+        fields to keep. Order of the names will be preserved.
+    usemask : {False, True}, optional
+        Whether to return a masked array or not.
+    asrecarray : string or sequence, optional
+        Whether to return a recarray or a mrecarray (`asrecarray=True`) or
+        a plain ndarray or masked array with flexible dtype. The default
+        is False.
+    """
+    newdtype = [(n, base.dtype[n]) for n in keep_names]
+    output = np.empty(base.shape, dtype=newdtype)
+    output = recursive_fill_fields(base, output)
+    return _fix_output(output, usemask=usemask, asrecarray=asrecarray)
+
+
+def _rec_drop_fields_dispatcher(base, drop_names):
+    return (base,)
+
+
+@array_function_dispatch(_rec_drop_fields_dispatcher)
+def rec_drop_fields(base, drop_names):
+    """
+    Returns a new numpy.recarray with fields in `drop_names` dropped.
+    """
+    return drop_fields(base, drop_names, usemask=False, asrecarray=True)
+
+
+def _rename_fields_dispatcher(base, namemapper):
+    return (base,)
+
+
+@array_function_dispatch(_rename_fields_dispatcher)
+def rename_fields(base, namemapper):
+    """
+    Rename the fields from a flexible-datatype ndarray or recarray.
+
+    Nested fields are supported.
+
+    Parameters
+    ----------
+    base : ndarray
+        Input array whose fields must be modified.
+    namemapper : dictionary
+        Dictionary mapping old field names to their new version.
+
+    Examples
+    --------
+    >>> from numpy.lib import recfunctions as rfn
+    >>> a = np.array([(1, (2, [3.0, 30.])), (4, (5, [6.0, 60.]))],
+    ...   dtype=[('a', int),('b', [('ba', float), ('bb', (float, 2))])])
+    >>> rfn.rename_fields(a, {'a':'A', 'bb':'BB'})
+    array([(1, (2., [ 3., 30.])), (4, (5., [ 6., 60.]))],
+          dtype=[('A', '<i8'), ('b', [('ba', '<f8'), ('BB', '<f8', (2,))])])
+
+    """
+    def _recursive_rename_fields(ndtype, namemapper):
+        newdtype = []
+        for name in ndtype.names:
+            newname = namemapper.get(name, name)
+            current = ndtype[name]
+            if current.names is not None:
+                newdtype.append(
+                    (newname, _recursive_rename_fields(current, namemapper))
+                    )
+            else:
+                newdtype.append((newname, current))
+        return newdtype
+    newdtype = _recursive_rename_fields(base.dtype, namemapper)
+    return base.view(newdtype)
+
+
+def _append_fields_dispatcher(base, names, data, dtypes=None,
+                              fill_value=None, usemask=None, asrecarray=None):
+    yield base
+    yield from data
+
+
+@array_function_dispatch(_append_fields_dispatcher)
+def append_fields(base, names, data, dtypes=None,
+                  fill_value=-1, usemask=True, asrecarray=False):
+    """
+    Add new fields to an existing array.
+
+    The names of the fields are given with the `names` arguments,
+    the corresponding values with the `data` arguments.
+    If a single field is appended, `names`, `data` and `dtypes` do not have
+    to be lists but just values.
+
+    Parameters
+    ----------
+    base : array
+        Input array to extend.
+    names : string, sequence
+        String or sequence of strings corresponding to the names
+        of the new fields.
+    data : array or sequence of arrays
+        Array or sequence of arrays storing the fields to add to the base.
+    dtypes : sequence of datatypes, optional
+        Datatype or sequence of datatypes.
+        If None, the datatypes are estimated from the `data`.
+    fill_value : {float}, optional
+        Filling value used to pad missing data on the shorter arrays.
+    usemask : {False, True}, optional
+        Whether to return a masked array or not.
+    asrecarray : {False, True}, optional
+        Whether to return a recarray (MaskedRecords) or not.
+
+    """
+    # Check the names
+    if isinstance(names, (tuple, list)):
+        if len(names) != len(data):
+            msg = "The number of arrays does not match the number of names"
+            raise ValueError(msg)
+    elif isinstance(names, str):
+        names = [names, ]
+        data = [data, ]
+    #
+    if dtypes is None:
+        data = [np.array(a, copy=False, subok=True) for a in data]
+        data = [a.view([(name, a.dtype)]) for (name, a) in zip(names, data)]
+    else:
+        if not isinstance(dtypes, (tuple, list)):
+            dtypes = [dtypes, ]
+        if len(data) != len(dtypes):
+            if len(dtypes) == 1:
+                dtypes = dtypes * len(data)
+            else:
+                msg = "The dtypes argument must be None, a dtype, or a list."
+                raise ValueError(msg)
+        data = [np.array(a, copy=False, subok=True, dtype=d).view([(n, d)])
+                for (a, n, d) in zip(data, names, dtypes)]
+    #
+    base = merge_arrays(base, usemask=usemask, fill_value=fill_value)
+    if len(data) > 1:
+        data = merge_arrays(data, flatten=True, usemask=usemask,
+                            fill_value=fill_value)
+    else:
+        data = data.pop()
+    #
+    output = ma.masked_all(
+        max(len(base), len(data)),
+        dtype=_get_fieldspec(base.dtype) + _get_fieldspec(data.dtype))
+    output = recursive_fill_fields(base, output)
+    output = recursive_fill_fields(data, output)
+    #
+    return _fix_output(output, usemask=usemask, asrecarray=asrecarray)
+
+
+def _rec_append_fields_dispatcher(base, names, data, dtypes=None):
+    yield base
+    yield from data
+
+
+@array_function_dispatch(_rec_append_fields_dispatcher)
+def rec_append_fields(base, names, data, dtypes=None):
+    """
+    Add new fields to an existing array.
+
+    The names of the fields are given with the `names` arguments,
+    the corresponding values with the `data` arguments.
+    If a single field is appended, `names`, `data` and `dtypes` do not have
+    to be lists but just values.
+
+    Parameters
+    ----------
+    base : array
+        Input array to extend.
+    names : string, sequence
+        String or sequence of strings corresponding to the names
+        of the new fields.
+    data : array or sequence of arrays
+        Array or sequence of arrays storing the fields to add to the base.
+    dtypes : sequence of datatypes, optional
+        Datatype or sequence of datatypes.
+        If None, the datatypes are estimated from the `data`.
+
+    See Also
+    --------
+    append_fields
+
+    Returns
+    -------
+    appended_array : np.recarray
+    """
+    return append_fields(base, names, data=data, dtypes=dtypes,
+                         asrecarray=True, usemask=False)
+
+
+def _repack_fields_dispatcher(a, align=None, recurse=None):
+    return (a,)
+
+
+@array_function_dispatch(_repack_fields_dispatcher)
+def repack_fields(a, align=False, recurse=False):
+    """
+    Re-pack the fields of a structured array or dtype in memory.
+
+    The memory layout of structured datatypes allows fields at arbitrary
+    byte offsets. This means the fields can be separated by padding bytes,
+    their offsets can be non-monotonically increasing, and they can overlap.
+
+    This method removes any overlaps and reorders the fields in memory so they
+    have increasing byte offsets, and adds or removes padding bytes depending
+    on the `align` option, which behaves like the `align` option to
+    `numpy.dtype`.
+
+    If `align=False`, this method produces a "packed" memory layout in which
+    each field starts at the byte the previous field ended, and any padding
+    bytes are removed.
+
+    If `align=True`, this methods produces an "aligned" memory layout in which
+    each field's offset is a multiple of its alignment, and the total itemsize
+    is a multiple of the largest alignment, by adding padding bytes as needed.
+
+    Parameters
+    ----------
+    a : ndarray or dtype
+       array or dtype for which to repack the fields.
+    align : boolean
+       If true, use an "aligned" memory layout, otherwise use a "packed" layout.
+    recurse : boolean
+       If True, also repack nested structures.
+
+    Returns
+    -------
+    repacked : ndarray or dtype
+       Copy of `a` with fields repacked, or `a` itself if no repacking was
+       needed.
+
+    Examples
+    --------
+
+    >>> from numpy.lib import recfunctions as rfn
+    >>> def print_offsets(d):
+    ...     print("offsets:", [d.fields[name][1] for name in d.names])
+    ...     print("itemsize:", d.itemsize)
+    ...
+    >>> dt = np.dtype('u1, <i8, <f8', align=True)
+    >>> dt
+    dtype({'names': ['f0', 'f1', 'f2'], 'formats': ['u1', '<i8', '<f8'], \
+'offsets': [0, 8, 16], 'itemsize': 24}, align=True)
+    >>> print_offsets(dt)
+    offsets: [0, 8, 16]
+    itemsize: 24
+    >>> packed_dt = rfn.repack_fields(dt)
+    >>> packed_dt
+    dtype([('f0', 'u1'), ('f1', '<i8'), ('f2', '<f8')])
+    >>> print_offsets(packed_dt)
+    offsets: [0, 1, 9]
+    itemsize: 17
+
+    """
+    if not isinstance(a, np.dtype):
+        dt = repack_fields(a.dtype, align=align, recurse=recurse)
+        return a.astype(dt, copy=False)
+
+    if a.names is None:
+        return a
+
+    fieldinfo = []
+    for name in a.names:
+        tup = a.fields[name]
+        if recurse:
+            fmt = repack_fields(tup[0], align=align, recurse=True)
+        else:
+            fmt = tup[0]
+
+        if len(tup) == 3:
+            name = (tup[2], name)
+
+        fieldinfo.append((name, fmt))
+
+    dt = np.dtype(fieldinfo, align=align)
+    return np.dtype((a.type, dt))
+
+def _get_fields_and_offsets(dt, offset=0):
+    """
+    Returns a flat list of (dtype, count, offset) tuples of all the
+    scalar fields in the dtype "dt", including nested fields, in left
+    to right order.
+    """
+
+    # counts up elements in subarrays, including nested subarrays, and returns
+    # base dtype and count
+    def count_elem(dt):
+        count = 1
+        while dt.shape != ():
+            for size in dt.shape:
+                count *= size
+            dt = dt.base
+        return dt, count
+
+    fields = []
+    for name in dt.names:
+        field = dt.fields[name]
+        f_dt, f_offset = field[0], field[1]
+        f_dt, n = count_elem(f_dt)
+
+        if f_dt.names is None:
+            fields.append((np.dtype((f_dt, (n,))), n, f_offset + offset))
+        else:
+            subfields = _get_fields_and_offsets(f_dt, f_offset + offset)
+            size = f_dt.itemsize
+
+            for i in range(n):
+                if i == 0:
+                    # optimization: avoid list comprehension if no subarray
+                    fields.extend(subfields)
+                else:
+                    fields.extend([(d, c, o + i*size) for d, c, o in subfields])
+    return fields
+
+def _common_stride(offsets, counts, itemsize):
+    """
+    Returns the stride between the fields, or None if the stride is not
+    constant. The values in "counts" designate the lengths of
+    subarrays. Subarrays are treated as many contiguous fields, with
+    always positive stride.
+    """
+    if len(offsets) <= 1:
+        return itemsize
+
+    negative = offsets[1] < offsets[0]  # negative stride
+    if negative:
+        # reverse, so offsets will be ascending
+        it = zip(reversed(offsets), reversed(counts))
+    else:
+        it = zip(offsets, counts)
+
+    prev_offset = None
+    stride = None
+    for offset, count in it:
+        if count != 1:  # subarray: always c-contiguous
+            if negative:
+                return None  # subarrays can never have a negative stride
+            if stride is None:
+                stride = itemsize
+            if stride != itemsize:
+                return None
+            end_offset = offset + (count - 1) * itemsize
+        else:
+            end_offset = offset
+
+        if prev_offset is not None:
+            new_stride = offset - prev_offset
+            if stride is None:
+                stride = new_stride
+            if stride != new_stride:
+                return None
+
+        prev_offset = end_offset
+
+    if negative:
+        return -stride
+    return stride
+
+
+def _structured_to_unstructured_dispatcher(arr, dtype=None, copy=None,
+                                           casting=None):
+    return (arr,)
+
+@array_function_dispatch(_structured_to_unstructured_dispatcher)
+def structured_to_unstructured(arr, dtype=None, copy=False, casting='unsafe'):
+    """
+    Converts an n-D structured array into an (n+1)-D unstructured array.
+
+    The new array will have a new last dimension equal in size to the
+    number of field-elements of the input array. If not supplied, the output
+    datatype is determined from the numpy type promotion rules applied to all
+    the field datatypes.
+
+    Nested fields, as well as each element of any subarray fields, all count
+    as a single field-elements.
+
+    Parameters
+    ----------
+    arr : ndarray
+       Structured array or dtype to convert. Cannot contain object datatype.
+    dtype : dtype, optional
+       The dtype of the output unstructured array.
+    copy : bool, optional
+        If true, always return a copy. If false, a view is returned if
+        possible, such as when the `dtype` and strides of the fields are
+        suitable and the array subtype is one of `np.ndarray`, `np.recarray`
+        or `np.memmap`.
+
+        .. versionchanged:: 1.25.0
+            A view can now be returned if the fields are separated by a
+            uniform stride.
+
+    casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
+        See casting argument of `numpy.ndarray.astype`. Controls what kind of
+        data casting may occur.
+
+    Returns
+    -------
+    unstructured : ndarray
+       Unstructured array with one more dimension.
+
+    Examples
+    --------
+
+    >>> from numpy.lib import recfunctions as rfn
+    >>> a = np.zeros(4, dtype=[('a', 'i4'), ('b', 'f4,u2'), ('c', 'f4', 2)])
+    >>> a
+    array([(0, (0., 0), [0., 0.]), (0, (0., 0), [0., 0.]),
+           (0, (0., 0), [0., 0.]), (0, (0., 0), [0., 0.])],
+          dtype=[('a', '<i4'), ('b', [('f0', '<f4'), ('f1', '<u2')]), ('c', '<f4', (2,))])
+    >>> rfn.structured_to_unstructured(a)
+    array([[0., 0., 0., 0., 0.],
+           [0., 0., 0., 0., 0.],
+           [0., 0., 0., 0., 0.],
+           [0., 0., 0., 0., 0.]])
+
+    >>> b = np.array([(1, 2, 5), (4, 5, 7), (7, 8 ,11), (10, 11, 12)],
+    ...              dtype=[('x', 'i4'), ('y', 'f4'), ('z', 'f8')])
+    >>> np.mean(rfn.structured_to_unstructured(b[['x', 'z']]), axis=-1)
+    array([ 3. ,  5.5,  9. , 11. ])
+
+    """
+    if arr.dtype.names is None:
+        raise ValueError('arr must be a structured array')
+
+    fields = _get_fields_and_offsets(arr.dtype)
+    n_fields = len(fields)
+    if n_fields == 0 and dtype is None:
+        raise ValueError("arr has no fields. Unable to guess dtype")
+    elif n_fields == 0:
+        # too many bugs elsewhere for this to work now
+        raise NotImplementedError("arr with no fields is not supported")
+
+    dts, counts, offsets = zip(*fields)
+    names = ['f{}'.format(n) for n in range(n_fields)]
+
+    if dtype is None:
+        out_dtype = np.result_type(*[dt.base for dt in dts])
+    else:
+        out_dtype = np.dtype(dtype)
+
+    # Use a series of views and casts to convert to an unstructured array:
+
+    # first view using flattened fields (doesn't work for object arrays)
+    # Note: dts may include a shape for subarrays
+    flattened_fields = np.dtype({'names': names,
+                                 'formats': dts,
+                                 'offsets': offsets,
+                                 'itemsize': arr.dtype.itemsize})
+    arr = arr.view(flattened_fields)
+
+    # we only allow a few types to be unstructured by manipulating the
+    # strides, because we know it won't work with, for example, np.matrix nor
+    # np.ma.MaskedArray.
+    can_view = type(arr) in (np.ndarray, np.recarray, np.memmap)
+    if (not copy) and can_view and all(dt.base == out_dtype for dt in dts):
+        # all elements have the right dtype already; if they have a common
+        # stride, we can just return a view
+        common_stride = _common_stride(offsets, counts, out_dtype.itemsize)
+        if common_stride is not None:
+            wrap = arr.__array_wrap__
+
+            new_shape = arr.shape + (sum(counts), out_dtype.itemsize)
+            new_strides = arr.strides + (abs(common_stride), 1)
+
+            arr = arr[..., np.newaxis].view(np.uint8)  # view as bytes
+            arr = arr[..., min(offsets):]  # remove the leading unused data
+            arr = np.lib.stride_tricks.as_strided(arr,
+                                                  new_shape,
+                                                  new_strides,
+                                                  subok=True)
+
+            # cast and drop the last dimension again
+            arr = arr.view(out_dtype)[..., 0]
+
+            if common_stride < 0:
+                arr = arr[..., ::-1]  # reverse, if the stride was negative
+            if type(arr) is not type(wrap.__self__):
+                # Some types (e.g. recarray) turn into an ndarray along the
+                # way, so we have to wrap it again in order to match the
+                # behavior with copy=True.
+                arr = wrap(arr)
+            return arr
+
+    # next cast to a packed format with all fields converted to new dtype
+    packed_fields = np.dtype({'names': names,
+                              'formats': [(out_dtype, dt.shape) for dt in dts]})
+    arr = arr.astype(packed_fields, copy=copy, casting=casting)
+
+    # finally is it safe to view the packed fields as the unstructured type
+    return arr.view((out_dtype, (sum(counts),)))
+
+
+def _unstructured_to_structured_dispatcher(arr, dtype=None, names=None,
+                                           align=None, copy=None, casting=None):
+    return (arr,)
+
+@array_function_dispatch(_unstructured_to_structured_dispatcher)
+def unstructured_to_structured(arr, dtype=None, names=None, align=False,
+                               copy=False, casting='unsafe'):
+    """
+    Converts an n-D unstructured array into an (n-1)-D structured array.
+
+    The last dimension of the input array is converted into a structure, with
+    number of field-elements equal to the size of the last dimension of the
+    input array. By default all output fields have the input array's dtype, but
+    an output structured dtype with an equal number of fields-elements can be
+    supplied instead.
+
+    Nested fields, as well as each element of any subarray fields, all count
+    towards the number of field-elements.
+
+    Parameters
+    ----------
+    arr : ndarray
+       Unstructured array or dtype to convert.
+    dtype : dtype, optional
+       The structured dtype of the output array
+    names : list of strings, optional
+       If dtype is not supplied, this specifies the field names for the output
+       dtype, in order. The field dtypes will be the same as the input array.
+    align : boolean, optional
+       Whether to create an aligned memory layout.
+    copy : bool, optional
+        See copy argument to `numpy.ndarray.astype`. If true, always return a
+        copy. If false, and `dtype` requirements are satisfied, a view is
+        returned.
+    casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
+        See casting argument of `numpy.ndarray.astype`. Controls what kind of
+        data casting may occur.
+
+    Returns
+    -------
+    structured : ndarray
+       Structured array with fewer dimensions.
+
+    Examples
+    --------
+
+    >>> from numpy.lib import recfunctions as rfn
+    >>> dt = np.dtype([('a', 'i4'), ('b', 'f4,u2'), ('c', 'f4', 2)])
+    >>> a = np.arange(20).reshape((4,5))
+    >>> a
+    array([[ 0,  1,  2,  3,  4],
+           [ 5,  6,  7,  8,  9],
+           [10, 11, 12, 13, 14],
+           [15, 16, 17, 18, 19]])
+    >>> rfn.unstructured_to_structured(a, dt)
+    array([( 0, ( 1.,  2), [ 3.,  4.]), ( 5, ( 6.,  7), [ 8.,  9.]),
+           (10, (11., 12), [13., 14.]), (15, (16., 17), [18., 19.])],
+          dtype=[('a', '<i4'), ('b', [('f0', '<f4'), ('f1', '<u2')]), ('c', '<f4', (2,))])
+
+    """
+    if arr.shape == ():
+        raise ValueError('arr must have at least one dimension')
+    n_elem = arr.shape[-1]
+    if n_elem == 0:
+        # too many bugs elsewhere for this to work now
+        raise NotImplementedError("last axis with size 0 is not supported")
+
+    if dtype is None:
+        if names is None:
+            names = ['f{}'.format(n) for n in range(n_elem)]
+        out_dtype = np.dtype([(n, arr.dtype) for n in names], align=align)
+        fields = _get_fields_and_offsets(out_dtype)
+        dts, counts, offsets = zip(*fields)
+    else:
+        if names is not None:
+            raise ValueError("don't supply both dtype and names")
+        # if dtype is the args of np.dtype, construct it
+        dtype = np.dtype(dtype)
+        # sanity check of the input dtype
+        fields = _get_fields_and_offsets(dtype)
+        if len(fields) == 0:
+            dts, counts, offsets = [], [], []
+        else:
+            dts, counts, offsets = zip(*fields)
+
+        if n_elem != sum(counts):
+            raise ValueError('The length of the last dimension of arr must '
+                             'be equal to the number of fields in dtype')
+        out_dtype = dtype
+        if align and not out_dtype.isalignedstruct:
+            raise ValueError("align was True but dtype is not aligned")
+
+    names = ['f{}'.format(n) for n in range(len(fields))]
+
+    # Use a series of views and casts to convert to a structured array:
+
+    # first view as a packed structured array of one dtype
+    packed_fields = np.dtype({'names': names,
+                              'formats': [(arr.dtype, dt.shape) for dt in dts]})
+    arr = np.ascontiguousarray(arr).view(packed_fields)
+
+    # next cast to an unpacked but flattened format with varied dtypes
+    flattened_fields = np.dtype({'names': names,
+                                 'formats': dts,
+                                 'offsets': offsets,
+                                 'itemsize': out_dtype.itemsize})
+    arr = arr.astype(flattened_fields, copy=copy, casting=casting)
+
+    # finally view as the final nested dtype and remove the last axis
+    return arr.view(out_dtype)[..., 0]
+
+def _apply_along_fields_dispatcher(func, arr):
+    return (arr,)
+
+@array_function_dispatch(_apply_along_fields_dispatcher)
+def apply_along_fields(func, arr):
+    """
+    Apply function 'func' as a reduction across fields of a structured array.
+
+    This is similar to `apply_along_axis`, but treats the fields of a
+    structured array as an extra axis. The fields are all first cast to a
+    common type following the type-promotion rules from `numpy.result_type`
+    applied to the field's dtypes.
+
+    Parameters
+    ----------
+    func : function
+       Function to apply on the "field" dimension. This function must
+       support an `axis` argument, like np.mean, np.sum, etc.
+    arr : ndarray
+       Structured array for which to apply func.
+
+    Returns
+    -------
+    out : ndarray
+       Result of the recution operation
+
+    Examples
+    --------
+
+    >>> from numpy.lib import recfunctions as rfn
+    >>> b = np.array([(1, 2, 5), (4, 5, 7), (7, 8 ,11), (10, 11, 12)],
+    ...              dtype=[('x', 'i4'), ('y', 'f4'), ('z', 'f8')])
+    >>> rfn.apply_along_fields(np.mean, b)
+    array([ 2.66666667,  5.33333333,  8.66666667, 11.        ])
+    >>> rfn.apply_along_fields(np.mean, b[['x', 'z']])
+    array([ 3. ,  5.5,  9. , 11. ])
+
+    """
+    if arr.dtype.names is None:
+        raise ValueError('arr must be a structured array')
+
+    uarr = structured_to_unstructured(arr)
+    return func(uarr, axis=-1)
+    # works and avoids axis requirement, but very, very slow:
+    #return np.apply_along_axis(func, -1, uarr)
+
+def _assign_fields_by_name_dispatcher(dst, src, zero_unassigned=None):
+    return dst, src
+
+@array_function_dispatch(_assign_fields_by_name_dispatcher)
+def assign_fields_by_name(dst, src, zero_unassigned=True):
+    """
+    Assigns values from one structured array to another by field name.
+
+    Normally in numpy >= 1.14, assignment of one structured array to another
+    copies fields "by position", meaning that the first field from the src is
+    copied to the first field of the dst, and so on, regardless of field name.
+
+    This function instead copies "by field name", such that fields in the dst
+    are assigned from the identically named field in the src. This applies
+    recursively for nested structures. This is how structure assignment worked
+    in numpy >= 1.6 to <= 1.13.
+
+    Parameters
+    ----------
+    dst : ndarray
+    src : ndarray
+        The source and destination arrays during assignment.
+    zero_unassigned : bool, optional
+        If True, fields in the dst for which there was no matching
+        field in the src are filled with the value 0 (zero). This
+        was the behavior of numpy <= 1.13. If False, those fields
+        are not modified.
+    """
+
+    if dst.dtype.names is None:
+        dst[...] = src
+        return
+
+    for name in dst.dtype.names:
+        if name not in src.dtype.names:
+            if zero_unassigned:
+                dst[name] = 0
+        else:
+            assign_fields_by_name(dst[name], src[name],
+                                  zero_unassigned)
+
+def _require_fields_dispatcher(array, required_dtype):
+    return (array,)
+
+@array_function_dispatch(_require_fields_dispatcher)
+def require_fields(array, required_dtype):
+    """
+    Casts a structured array to a new dtype using assignment by field-name.
+
+    This function assigns from the old to the new array by name, so the
+    value of a field in the output array is the value of the field with the
+    same name in the source array. This has the effect of creating a new
+    ndarray containing only the fields "required" by the required_dtype.
+
+    If a field name in the required_dtype does not exist in the
+    input array, that field is created and set to 0 in the output array.
+
+    Parameters
+    ----------
+    a : ndarray
+       array to cast
+    required_dtype : dtype
+       datatype for output array
+
+    Returns
+    -------
+    out : ndarray
+        array with the new dtype, with field values copied from the fields in
+        the input array with the same name
+
+    Examples
+    --------
+
+    >>> from numpy.lib import recfunctions as rfn
+    >>> a = np.ones(4, dtype=[('a', 'i4'), ('b', 'f8'), ('c', 'u1')])
+    >>> rfn.require_fields(a, [('b', 'f4'), ('c', 'u1')])
+    array([(1., 1), (1., 1), (1., 1), (1., 1)],
+      dtype=[('b', '<f4'), ('c', 'u1')])
+    >>> rfn.require_fields(a, [('b', 'f4'), ('newf', 'u1')])
+    array([(1., 0), (1., 0), (1., 0), (1., 0)],
+      dtype=[('b', '<f4'), ('newf', 'u1')])
+
+    """
+    out = np.empty(array.shape, dtype=required_dtype)
+    assign_fields_by_name(out, array)
+    return out
+
+
+def _stack_arrays_dispatcher(arrays, defaults=None, usemask=None,
+                             asrecarray=None, autoconvert=None):
+    return arrays
+
+
+@array_function_dispatch(_stack_arrays_dispatcher)
+def stack_arrays(arrays, defaults=None, usemask=True, asrecarray=False,
+                 autoconvert=False):
+    """
+    Superposes arrays fields by fields
+
+    Parameters
+    ----------
+    arrays : array or sequence
+        Sequence of input arrays.
+    defaults : dictionary, optional
+        Dictionary mapping field names to the corresponding default values.
+    usemask : {True, False}, optional
+        Whether to return a MaskedArray (or MaskedRecords is
+        `asrecarray==True`) or a ndarray.
+    asrecarray : {False, True}, optional
+        Whether to return a recarray (or MaskedRecords if `usemask==True`)
+        or just a flexible-type ndarray.
+    autoconvert : {False, True}, optional
+        Whether automatically cast the type of the field to the maximum.
+
+    Examples
+    --------
+    >>> from numpy.lib import recfunctions as rfn
+    >>> x = np.array([1, 2,])
+    >>> rfn.stack_arrays(x) is x
+    True
+    >>> z = np.array([('A', 1), ('B', 2)], dtype=[('A', '|S3'), ('B', float)])
+    >>> zz = np.array([('a', 10., 100.), ('b', 20., 200.), ('c', 30., 300.)],
+    ...   dtype=[('A', '|S3'), ('B', np.double), ('C', np.double)])
+    >>> test = rfn.stack_arrays((z,zz))
+    >>> test
+    masked_array(data=[(b'A', 1.0, --), (b'B', 2.0, --), (b'a', 10.0, 100.0),
+                       (b'b', 20.0, 200.0), (b'c', 30.0, 300.0)],
+                 mask=[(False, False,  True), (False, False,  True),
+                       (False, False, False), (False, False, False),
+                       (False, False, False)],
+           fill_value=(b'N/A', 1.e+20, 1.e+20),
+                dtype=[('A', 'S3'), ('B', '<f8'), ('C', '<f8')])
+
+    """
+    if isinstance(arrays, ndarray):
+        return arrays
+    elif len(arrays) == 1:
+        return arrays[0]
+    seqarrays = [np.asanyarray(a).ravel() for a in arrays]
+    nrecords = [len(a) for a in seqarrays]
+    ndtype = [a.dtype for a in seqarrays]
+    fldnames = [d.names for d in ndtype]
+    #
+    dtype_l = ndtype[0]
+    newdescr = _get_fieldspec(dtype_l)
+    names = [n for n, d in newdescr]
+    for dtype_n in ndtype[1:]:
+        for fname, fdtype in _get_fieldspec(dtype_n):
+            if fname not in names:
+                newdescr.append((fname, fdtype))
+                names.append(fname)
+            else:
+                nameidx = names.index(fname)
+                _, cdtype = newdescr[nameidx]
+                if autoconvert:
+                    newdescr[nameidx] = (fname, max(fdtype, cdtype))
+                elif fdtype != cdtype:
+                    raise TypeError("Incompatible type '%s' <> '%s'" %
+                                    (cdtype, fdtype))
+    # Only one field: use concatenate
+    if len(newdescr) == 1:
+        output = ma.concatenate(seqarrays)
+    else:
+        #
+        output = ma.masked_all((np.sum(nrecords),), newdescr)
+        offset = np.cumsum(np.r_[0, nrecords])
+        seen = []
+        for (a, n, i, j) in zip(seqarrays, fldnames, offset[:-1], offset[1:]):
+            names = a.dtype.names
+            if names is None:
+                output['f%i' % len(seen)][i:j] = a
+            else:
+                for name in n:
+                    output[name][i:j] = a[name]
+                    if name not in seen:
+                        seen.append(name)
+    #
+    return _fix_output(_fix_defaults(output, defaults),
+                       usemask=usemask, asrecarray=asrecarray)
+
+
+def _find_duplicates_dispatcher(
+        a, key=None, ignoremask=None, return_index=None):
+    return (a,)
+
+
+@array_function_dispatch(_find_duplicates_dispatcher)
+def find_duplicates(a, key=None, ignoremask=True, return_index=False):
+    """
+    Find the duplicates in a structured array along a given key
+
+    Parameters
+    ----------
+    a : array-like
+        Input array
+    key : {string, None}, optional
+        Name of the fields along which to check the duplicates.
+        If None, the search is performed by records
+    ignoremask : {True, False}, optional
+        Whether masked data should be discarded or considered as duplicates.
+    return_index : {False, True}, optional
+        Whether to return the indices of the duplicated values.
+
+    Examples
+    --------
+    >>> from numpy.lib import recfunctions as rfn
+    >>> ndtype = [('a', int)]
+    >>> a = np.ma.array([1, 1, 1, 2, 2, 3, 3],
+    ...         mask=[0, 0, 1, 0, 0, 0, 1]).view(ndtype)
+    >>> rfn.find_duplicates(a, ignoremask=True, return_index=True)
+    (masked_array(data=[(1,), (1,), (2,), (2,)],
+                 mask=[(False,), (False,), (False,), (False,)],
+           fill_value=(999999,),
+                dtype=[('a', '<i8')]), array([0, 1, 3, 4]))
+    """
+    a = np.asanyarray(a).ravel()
+    # Get a dictionary of fields
+    fields = get_fieldstructure(a.dtype)
+    # Get the sorting data (by selecting the corresponding field)
+    base = a
+    if key:
+        for f in fields[key]:
+            base = base[f]
+        base = base[key]
+    # Get the sorting indices and the sorted data
+    sortidx = base.argsort()
+    sortedbase = base[sortidx]
+    sorteddata = sortedbase.filled()
+    # Compare the sorting data
+    flag = (sorteddata[:-1] == sorteddata[1:])
+    # If masked data must be ignored, set the flag to false where needed
+    if ignoremask:
+        sortedmask = sortedbase.recordmask
+        flag[sortedmask[1:]] = False
+    flag = np.concatenate(([False], flag))
+    # We need to take the point on the left as well (else we're missing it)
+    flag[:-1] = flag[:-1] + flag[1:]
+    duplicates = a[sortidx][flag]
+    if return_index:
+        return (duplicates, sortidx[flag])
+    else:
+        return duplicates
+
+
+def _join_by_dispatcher(
+        key, r1, r2, jointype=None, r1postfix=None, r2postfix=None,
+        defaults=None, usemask=None, asrecarray=None):
+    return (r1, r2)
+
+
+@array_function_dispatch(_join_by_dispatcher)
+def join_by(key, r1, r2, jointype='inner', r1postfix='1', r2postfix='2',
+            defaults=None, usemask=True, asrecarray=False):
+    """
+    Join arrays `r1` and `r2` on key `key`.
+
+    The key should be either a string or a sequence of string corresponding
+    to the fields used to join the array.  An exception is raised if the
+    `key` field cannot be found in the two input arrays.  Neither `r1` nor
+    `r2` should have any duplicates along `key`: the presence of duplicates
+    will make the output quite unreliable. Note that duplicates are not
+    looked for by the algorithm.
+
+    Parameters
+    ----------
+    key : {string, sequence}
+        A string or a sequence of strings corresponding to the fields used
+        for comparison.
+    r1, r2 : arrays
+        Structured arrays.
+    jointype : {'inner', 'outer', 'leftouter'}, optional
+        If 'inner', returns the elements common to both r1 and r2.
+        If 'outer', returns the common elements as well as the elements of
+        r1 not in r2 and the elements of not in r2.
+        If 'leftouter', returns the common elements and the elements of r1
+        not in r2.
+    r1postfix : string, optional
+        String appended to the names of the fields of r1 that are present
+        in r2 but absent of the key.
+    r2postfix : string, optional
+        String appended to the names of the fields of r2 that are present
+        in r1 but absent of the key.
+    defaults : {dictionary}, optional
+        Dictionary mapping field names to the corresponding default values.
+    usemask : {True, False}, optional
+        Whether to return a MaskedArray (or MaskedRecords is
+        `asrecarray==True`) or a ndarray.
+    asrecarray : {False, True}, optional
+        Whether to return a recarray (or MaskedRecords if `usemask==True`)
+        or just a flexible-type ndarray.
+
+    Notes
+    -----
+    * The output is sorted along the key.
+    * A temporary array is formed by dropping the fields not in the key for
+      the two arrays and concatenating the result. This array is then
+      sorted, and the common entries selected. The output is constructed by
+      filling the fields with the selected entries. Matching is not
+      preserved if there are some duplicates...
+
+    """
+    # Check jointype
+    if jointype not in ('inner', 'outer', 'leftouter'):
+        raise ValueError(
+                "The 'jointype' argument should be in 'inner', "
+                "'outer' or 'leftouter' (got '%s' instead)" % jointype
+                )
+    # If we have a single key, put it in a tuple
+    if isinstance(key, str):
+        key = (key,)
+
+    # Check the keys
+    if len(set(key)) != len(key):
+        dup = next(x for n,x in enumerate(key) if x in key[n+1:])
+        raise ValueError("duplicate join key %r" % dup)
+    for name in key:
+        if name not in r1.dtype.names:
+            raise ValueError('r1 does not have key field %r' % name)
+        if name not in r2.dtype.names:
+            raise ValueError('r2 does not have key field %r' % name)
+
+    # Make sure we work with ravelled arrays
+    r1 = r1.ravel()
+    r2 = r2.ravel()
+    # Fixme: nb2 below is never used. Commenting out for pyflakes.
+    # (nb1, nb2) = (len(r1), len(r2))
+    nb1 = len(r1)
+    (r1names, r2names) = (r1.dtype.names, r2.dtype.names)
+
+    # Check the names for collision
+    collisions = (set(r1names) & set(r2names)) - set(key)
+    if collisions and not (r1postfix or r2postfix):
+        msg = "r1 and r2 contain common names, r1postfix and r2postfix "
+        msg += "can't both be empty"
+        raise ValueError(msg)
+
+    # Make temporary arrays of just the keys
+    #  (use order of keys in `r1` for back-compatibility)
+    key1 = [ n for n in r1names if n in key ]
+    r1k = _keep_fields(r1, key1)
+    r2k = _keep_fields(r2, key1)
+
+    # Concatenate the two arrays for comparison
+    aux = ma.concatenate((r1k, r2k))
+    idx_sort = aux.argsort(order=key)
+    aux = aux[idx_sort]
+    #
+    # Get the common keys
+    flag_in = ma.concatenate(([False], aux[1:] == aux[:-1]))
+    flag_in[:-1] = flag_in[1:] + flag_in[:-1]
+    idx_in = idx_sort[flag_in]
+    idx_1 = idx_in[(idx_in < nb1)]
+    idx_2 = idx_in[(idx_in >= nb1)] - nb1
+    (r1cmn, r2cmn) = (len(idx_1), len(idx_2))
+    if jointype == 'inner':
+        (r1spc, r2spc) = (0, 0)
+    elif jointype == 'outer':
+        idx_out = idx_sort[~flag_in]
+        idx_1 = np.concatenate((idx_1, idx_out[(idx_out < nb1)]))
+        idx_2 = np.concatenate((idx_2, idx_out[(idx_out >= nb1)] - nb1))
+        (r1spc, r2spc) = (len(idx_1) - r1cmn, len(idx_2) - r2cmn)
+    elif jointype == 'leftouter':
+        idx_out = idx_sort[~flag_in]
+        idx_1 = np.concatenate((idx_1, idx_out[(idx_out < nb1)]))
+        (r1spc, r2spc) = (len(idx_1) - r1cmn, 0)
+    # Select the entries from each input
+    (s1, s2) = (r1[idx_1], r2[idx_2])
+    #
+    # Build the new description of the output array .......
+    # Start with the key fields
+    ndtype = _get_fieldspec(r1k.dtype)
+
+    # Add the fields from r1
+    for fname, fdtype in _get_fieldspec(r1.dtype):
+        if fname not in key:
+            ndtype.append((fname, fdtype))
+
+    # Add the fields from r2
+    for fname, fdtype in _get_fieldspec(r2.dtype):
+        # Have we seen the current name already ?
+        # we need to rebuild this list every time
+        names = list(name for name, dtype in ndtype)
+        try:
+            nameidx = names.index(fname)
+        except ValueError:
+            #... we haven't: just add the description to the current list
+            ndtype.append((fname, fdtype))
+        else:
+            # collision
+            _, cdtype = ndtype[nameidx]
+            if fname in key:
+                # The current field is part of the key: take the largest dtype
+                ndtype[nameidx] = (fname, max(fdtype, cdtype))
+            else:
+                # The current field is not part of the key: add the suffixes,
+                # and place the new field adjacent to the old one
+                ndtype[nameidx:nameidx + 1] = [
+                    (fname + r1postfix, cdtype),
+                    (fname + r2postfix, fdtype)
+                ]
+    # Rebuild a dtype from the new fields
+    ndtype = np.dtype(ndtype)
+    # Find the largest nb of common fields :
+    # r1cmn and r2cmn should be equal, but...
+    cmn = max(r1cmn, r2cmn)
+    # Construct an empty array
+    output = ma.masked_all((cmn + r1spc + r2spc,), dtype=ndtype)
+    names = output.dtype.names
+    for f in r1names:
+        selected = s1[f]
+        if f not in names or (f in r2names and not r2postfix and f not in key):
+            f += r1postfix
+        current = output[f]
+        current[:r1cmn] = selected[:r1cmn]
+        if jointype in ('outer', 'leftouter'):
+            current[cmn:cmn + r1spc] = selected[r1cmn:]
+    for f in r2names:
+        selected = s2[f]
+        if f not in names or (f in r1names and not r1postfix and f not in key):
+            f += r2postfix
+        current = output[f]
+        current[:r2cmn] = selected[:r2cmn]
+        if (jointype == 'outer') and r2spc:
+            current[-r2spc:] = selected[r2cmn:]
+    # Sort and finalize the output
+    output.sort(order=key)
+    kwargs = dict(usemask=usemask, asrecarray=asrecarray)
+    return _fix_output(_fix_defaults(output, defaults), **kwargs)
+
+
+def _rec_join_dispatcher(
+        key, r1, r2, jointype=None, r1postfix=None, r2postfix=None,
+        defaults=None):
+    return (r1, r2)
+
+
+@array_function_dispatch(_rec_join_dispatcher)
+def rec_join(key, r1, r2, jointype='inner', r1postfix='1', r2postfix='2',
+             defaults=None):
+    """
+    Join arrays `r1` and `r2` on keys.
+    Alternative to join_by, that always returns a np.recarray.
+
+    See Also
+    --------
+    join_by : equivalent function
+    """
+    kwargs = dict(jointype=jointype, r1postfix=r1postfix, r2postfix=r2postfix,
+                  defaults=defaults, usemask=False, asrecarray=True)
+    return join_by(key, r1, r2, **kwargs)

env-llmeval/lib/python3.10/site-packages/numpy/lib/scimath.py

@@ -0,0 +1,625 @@
+"""
+Wrapper functions to more user-friendly calling of certain math functions
+whose output data-type is different than the input data-type in certain
+domains of the input.
+
+For example, for functions like `log` with branch cuts, the versions in this
+module provide the mathematically valid answers in the complex plane::
+
+  >>> import math
+  >>> np.emath.log(-math.exp(1)) == (1+1j*math.pi)
+  True
+
+Similarly, `sqrt`, other base logarithms, `power` and trig functions are
+correctly handled.  See their respective docstrings for specific examples.
+
+Functions
+---------
+
+.. autosummary::
+   :toctree: generated/
+
+   sqrt
+   log
+   log2
+   logn
+   log10
+   power
+   arccos
+   arcsin
+   arctanh
+
+"""
+import numpy.core.numeric as nx
+import numpy.core.numerictypes as nt
+from numpy.core.numeric import asarray, any
+from numpy.core.overrides import array_function_dispatch
+from numpy.lib.type_check import isreal
+
+
+__all__ = [
+    'sqrt', 'log', 'log2', 'logn', 'log10', 'power', 'arccos', 'arcsin',
+    'arctanh'
+    ]
+
+
+_ln2 = nx.log(2.0)
+
+
+def _tocomplex(arr):
+    """Convert its input `arr` to a complex array.
+
+    The input is returned as a complex array of the smallest type that will fit
+    the original data: types like single, byte, short, etc. become csingle,
+    while others become cdouble.
+
+    A copy of the input is always made.
+
+    Parameters
+    ----------
+    arr : array
+
+    Returns
+    -------
+    array
+        An array with the same input data as the input but in complex form.
+
+    Examples
+    --------
+
+    First, consider an input of type short:
+
+    >>> a = np.array([1,2,3],np.short)
+
+    >>> ac = np.lib.scimath._tocomplex(a); ac
+    array([1.+0.j, 2.+0.j, 3.+0.j], dtype=complex64)
+
+    >>> ac.dtype
+    dtype('complex64')
+
+    If the input is of type double, the output is correspondingly of the
+    complex double type as well:
+
+    >>> b = np.array([1,2,3],np.double)
+
+    >>> bc = np.lib.scimath._tocomplex(b); bc
+    array([1.+0.j, 2.+0.j, 3.+0.j])
+
+    >>> bc.dtype
+    dtype('complex128')
+
+    Note that even if the input was complex to begin with, a copy is still
+    made, since the astype() method always copies:
+
+    >>> c = np.array([1,2,3],np.csingle)
+
+    >>> cc = np.lib.scimath._tocomplex(c); cc
+    array([1.+0.j,  2.+0.j,  3.+0.j], dtype=complex64)
+
+    >>> c *= 2; c
+    array([2.+0.j,  4.+0.j,  6.+0.j], dtype=complex64)
+
+    >>> cc
+    array([1.+0.j,  2.+0.j,  3.+0.j], dtype=complex64)
+    """
+    if issubclass(arr.dtype.type, (nt.single, nt.byte, nt.short, nt.ubyte,
+                                   nt.ushort, nt.csingle)):
+        return arr.astype(nt.csingle)
+    else:
+        return arr.astype(nt.cdouble)
+
+
+def _fix_real_lt_zero(x):
+    """Convert `x` to complex if it has real, negative components.
+
+    Otherwise, output is just the array version of the input (via asarray).
+
+    Parameters
+    ----------
+    x : array_like
+
+    Returns
+    -------
+    array
+
+    Examples
+    --------
+    >>> np.lib.scimath._fix_real_lt_zero([1,2])
+    array([1, 2])
+
+    >>> np.lib.scimath._fix_real_lt_zero([-1,2])
+    array([-1.+0.j,  2.+0.j])
+
+    """
+    x = asarray(x)
+    if any(isreal(x) & (x < 0)):
+        x = _tocomplex(x)
+    return x
+
+
+def _fix_int_lt_zero(x):
+    """Convert `x` to double if it has real, negative components.
+
+    Otherwise, output is just the array version of the input (via asarray).
+
+    Parameters
+    ----------
+    x : array_like
+
+    Returns
+    -------
+    array
+
+    Examples
+    --------
+    >>> np.lib.scimath._fix_int_lt_zero([1,2])
+    array([1, 2])
+
+    >>> np.lib.scimath._fix_int_lt_zero([-1,2])
+    array([-1.,  2.])
+    """
+    x = asarray(x)
+    if any(isreal(x) & (x < 0)):
+        x = x * 1.0
+    return x
+
+
+def _fix_real_abs_gt_1(x):
+    """Convert `x` to complex if it has real components x_i with abs(x_i)>1.
+
+    Otherwise, output is just the array version of the input (via asarray).
+
+    Parameters
+    ----------
+    x : array_like
+
+    Returns
+    -------
+    array
+
+    Examples
+    --------
+    >>> np.lib.scimath._fix_real_abs_gt_1([0,1])
+    array([0, 1])
+
+    >>> np.lib.scimath._fix_real_abs_gt_1([0,2])
+    array([0.+0.j, 2.+0.j])
+    """
+    x = asarray(x)
+    if any(isreal(x) & (abs(x) > 1)):
+        x = _tocomplex(x)
+    return x
+
+
+def _unary_dispatcher(x):
+    return (x,)
+
+
+@array_function_dispatch(_unary_dispatcher)
+def sqrt(x):
+    """
+    Compute the square root of x.
+
+    For negative input elements, a complex value is returned
+    (unlike `numpy.sqrt` which returns NaN).
+
+    Parameters
+    ----------
+    x : array_like
+       The input value(s).
+
+    Returns
+    -------
+    out : ndarray or scalar
+       The square root of `x`. If `x` was a scalar, so is `out`,
+       otherwise an array is returned.
+
+    See Also
+    --------
+    numpy.sqrt
+
+    Examples
+    --------
+    For real, non-negative inputs this works just like `numpy.sqrt`:
+
+    >>> np.emath.sqrt(1)
+    1.0
+    >>> np.emath.sqrt([1, 4])
+    array([1.,  2.])
+
+    But it automatically handles negative inputs:
+
+    >>> np.emath.sqrt(-1)
+    1j
+    >>> np.emath.sqrt([-1,4])
+    array([0.+1.j, 2.+0.j])
+
+    Different results are expected because:
+    floating point 0.0 and -0.0 are distinct.
+
+    For more control, explicitly use complex() as follows:
+
+    >>> np.emath.sqrt(complex(-4.0, 0.0))
+    2j
+    >>> np.emath.sqrt(complex(-4.0, -0.0))
+    -2j
+    """
+    x = _fix_real_lt_zero(x)
+    return nx.sqrt(x)
+
+
+@array_function_dispatch(_unary_dispatcher)
+def log(x):
+    """
+    Compute the natural logarithm of `x`.
+
+    Return the "principal value" (for a description of this, see `numpy.log`)
+    of :math:`log_e(x)`. For real `x > 0`, this is a real number (``log(0)``
+    returns ``-inf`` and ``log(np.inf)`` returns ``inf``). Otherwise, the
+    complex principle value is returned.
+
+    Parameters
+    ----------
+    x : array_like
+       The value(s) whose log is (are) required.
+
+    Returns
+    -------
+    out : ndarray or scalar
+       The log of the `x` value(s). If `x` was a scalar, so is `out`,
+       otherwise an array is returned.
+
+    See Also
+    --------
+    numpy.log
+
+    Notes
+    -----
+    For a log() that returns ``NAN`` when real `x < 0`, use `numpy.log`
+    (note, however, that otherwise `numpy.log` and this `log` are identical,
+    i.e., both return ``-inf`` for `x = 0`, ``inf`` for `x = inf`, and,
+    notably, the complex principle value if ``x.imag != 0``).
+
+    Examples
+    --------
+    >>> np.emath.log(np.exp(1))
+    1.0
+
+    Negative arguments are handled "correctly" (recall that
+    ``exp(log(x)) == x`` does *not* hold for real ``x < 0``):
+
+    >>> np.emath.log(-np.exp(1)) == (1 + np.pi * 1j)
+    True
+
+    """
+    x = _fix_real_lt_zero(x)
+    return nx.log(x)
+
+
+@array_function_dispatch(_unary_dispatcher)
+def log10(x):
+    """
+    Compute the logarithm base 10 of `x`.
+
+    Return the "principal value" (for a description of this, see
+    `numpy.log10`) of :math:`log_{10}(x)`. For real `x > 0`, this
+    is a real number (``log10(0)`` returns ``-inf`` and ``log10(np.inf)``
+    returns ``inf``). Otherwise, the complex principle value is returned.
+
+    Parameters
+    ----------
+    x : array_like or scalar
+       The value(s) whose log base 10 is (are) required.
+
+    Returns
+    -------
+    out : ndarray or scalar
+       The log base 10 of the `x` value(s). If `x` was a scalar, so is `out`,
+       otherwise an array object is returned.
+
+    See Also
+    --------
+    numpy.log10
+
+    Notes
+    -----
+    For a log10() that returns ``NAN`` when real `x < 0`, use `numpy.log10`
+    (note, however, that otherwise `numpy.log10` and this `log10` are
+    identical, i.e., both return ``-inf`` for `x = 0`, ``inf`` for `x = inf`,
+    and, notably, the complex principle value if ``x.imag != 0``).
+
+    Examples
+    --------
+
+    (We set the printing precision so the example can be auto-tested)
+
+    >>> np.set_printoptions(precision=4)
+
+    >>> np.emath.log10(10**1)
+    1.0
+
+    >>> np.emath.log10([-10**1, -10**2, 10**2])
+    array([1.+1.3644j, 2.+1.3644j, 2.+0.j    ])
+
+    """
+    x = _fix_real_lt_zero(x)
+    return nx.log10(x)
+
+
+def _logn_dispatcher(n, x):
+    return (n, x,)
+
+
+@array_function_dispatch(_logn_dispatcher)
+def logn(n, x):
+    """
+    Take log base n of x.
+
+    If `x` contains negative inputs, the answer is computed and returned in the
+    complex domain.
+
+    Parameters
+    ----------
+    n : array_like
+       The integer base(s) in which the log is taken.
+    x : array_like
+       The value(s) whose log base `n` is (are) required.
+
+    Returns
+    -------
+    out : ndarray or scalar
+       The log base `n` of the `x` value(s). If `x` was a scalar, so is
+       `out`, otherwise an array is returned.
+
+    Examples
+    --------
+    >>> np.set_printoptions(precision=4)
+
+    >>> np.emath.logn(2, [4, 8])
+    array([2., 3.])
+    >>> np.emath.logn(2, [-4, -8, 8])
+    array([2.+4.5324j, 3.+4.5324j, 3.+0.j    ])
+
+    """
+    x = _fix_real_lt_zero(x)
+    n = _fix_real_lt_zero(n)
+    return nx.log(x)/nx.log(n)
+
+
+@array_function_dispatch(_unary_dispatcher)
+def log2(x):
+    """
+    Compute the logarithm base 2 of `x`.
+
+    Return the "principal value" (for a description of this, see
+    `numpy.log2`) of :math:`log_2(x)`. For real `x > 0`, this is
+    a real number (``log2(0)`` returns ``-inf`` and ``log2(np.inf)`` returns
+    ``inf``). Otherwise, the complex principle value is returned.
+
+    Parameters
+    ----------
+    x : array_like
+       The value(s) whose log base 2 is (are) required.
+
+    Returns
+    -------
+    out : ndarray or scalar
+       The log base 2 of the `x` value(s). If `x` was a scalar, so is `out`,
+       otherwise an array is returned.
+
+    See Also
+    --------
+    numpy.log2
+
+    Notes
+    -----
+    For a log2() that returns ``NAN`` when real `x < 0`, use `numpy.log2`
+    (note, however, that otherwise `numpy.log2` and this `log2` are
+    identical, i.e., both return ``-inf`` for `x = 0`, ``inf`` for `x = inf`,
+    and, notably, the complex principle value if ``x.imag != 0``).
+
+    Examples
+    --------
+    We set the printing precision so the example can be auto-tested:
+
+    >>> np.set_printoptions(precision=4)
+
+    >>> np.emath.log2(8)
+    3.0
+    >>> np.emath.log2([-4, -8, 8])
+    array([2.+4.5324j, 3.+4.5324j, 3.+0.j    ])
+
+    """
+    x = _fix_real_lt_zero(x)
+    return nx.log2(x)
+
+
+def _power_dispatcher(x, p):
+    return (x, p)
+
+
+@array_function_dispatch(_power_dispatcher)
+def power(x, p):
+    """
+    Return x to the power p, (x**p).
+
+    If `x` contains negative values, the output is converted to the
+    complex domain.
+
+    Parameters
+    ----------
+    x : array_like
+        The input value(s).
+    p : array_like of ints
+        The power(s) to which `x` is raised. If `x` contains multiple values,
+        `p` has to either be a scalar, or contain the same number of values
+        as `x`. In the latter case, the result is
+        ``x[0]**p[0], x[1]**p[1], ...``.
+
+    Returns
+    -------
+    out : ndarray or scalar
+        The result of ``x**p``. If `x` and `p` are scalars, so is `out`,
+        otherwise an array is returned.
+
+    See Also
+    --------
+    numpy.power
+
+    Examples
+    --------
+    >>> np.set_printoptions(precision=4)
+
+    >>> np.emath.power([2, 4], 2)
+    array([ 4, 16])
+    >>> np.emath.power([2, 4], -2)
+    array([0.25  ,  0.0625])
+    >>> np.emath.power([-2, 4], 2)
+    array([ 4.-0.j, 16.+0.j])
+
+    """
+    x = _fix_real_lt_zero(x)
+    p = _fix_int_lt_zero(p)
+    return nx.power(x, p)
+
+
+@array_function_dispatch(_unary_dispatcher)
+def arccos(x):
+    """
+    Compute the inverse cosine of x.
+
+    Return the "principal value" (for a description of this, see
+    `numpy.arccos`) of the inverse cosine of `x`. For real `x` such that
+    `abs(x) <= 1`, this is a real number in the closed interval
+    :math:`[0, \\pi]`.  Otherwise, the complex principle value is returned.
+
+    Parameters
+    ----------
+    x : array_like or scalar
+       The value(s) whose arccos is (are) required.
+
+    Returns
+    -------
+    out : ndarray or scalar
+       The inverse cosine(s) of the `x` value(s). If `x` was a scalar, so
+       is `out`, otherwise an array object is returned.
+
+    See Also
+    --------
+    numpy.arccos
+
+    Notes
+    -----
+    For an arccos() that returns ``NAN`` when real `x` is not in the
+    interval ``[-1,1]``, use `numpy.arccos`.
+
+    Examples
+    --------
+    >>> np.set_printoptions(precision=4)
+
+    >>> np.emath.arccos(1) # a scalar is returned
+    0.0
+
+    >>> np.emath.arccos([1,2])
+    array([0.-0.j   , 0.-1.317j])
+
+    """
+    x = _fix_real_abs_gt_1(x)
+    return nx.arccos(x)
+
+
+@array_function_dispatch(_unary_dispatcher)
+def arcsin(x):
+    """
+    Compute the inverse sine of x.
+
+    Return the "principal value" (for a description of this, see
+    `numpy.arcsin`) of the inverse sine of `x`. For real `x` such that
+    `abs(x) <= 1`, this is a real number in the closed interval
+    :math:`[-\\pi/2, \\pi/2]`.  Otherwise, the complex principle value is
+    returned.
+
+    Parameters
+    ----------
+    x : array_like or scalar
+       The value(s) whose arcsin is (are) required.
+
+    Returns
+    -------
+    out : ndarray or scalar
+       The inverse sine(s) of the `x` value(s). If `x` was a scalar, so
+       is `out`, otherwise an array object is returned.
+
+    See Also
+    --------
+    numpy.arcsin
+
+    Notes
+    -----
+    For an arcsin() that returns ``NAN`` when real `x` is not in the
+    interval ``[-1,1]``, use `numpy.arcsin`.
+
+    Examples
+    --------
+    >>> np.set_printoptions(precision=4)
+
+    >>> np.emath.arcsin(0)
+    0.0
+
+    >>> np.emath.arcsin([0,1])
+    array([0.    , 1.5708])
+
+    """
+    x = _fix_real_abs_gt_1(x)
+    return nx.arcsin(x)
+
+
+@array_function_dispatch(_unary_dispatcher)
+def arctanh(x):
+    """
+    Compute the inverse hyperbolic tangent of `x`.
+
+    Return the "principal value" (for a description of this, see
+    `numpy.arctanh`) of ``arctanh(x)``. For real `x` such that
+    ``abs(x) < 1``, this is a real number.  If `abs(x) > 1`, or if `x` is
+    complex, the result is complex. Finally, `x = 1` returns``inf`` and
+    ``x=-1`` returns ``-inf``.
+
+    Parameters
+    ----------
+    x : array_like
+       The value(s) whose arctanh is (are) required.
+
+    Returns
+    -------
+    out : ndarray or scalar
+       The inverse hyperbolic tangent(s) of the `x` value(s). If `x` was
+       a scalar so is `out`, otherwise an array is returned.
+
+
+    See Also
+    --------
+    numpy.arctanh
+
+    Notes
+    -----
+    For an arctanh() that returns ``NAN`` when real `x` is not in the
+    interval ``(-1,1)``, use `numpy.arctanh` (this latter, however, does
+    return +/-inf for ``x = +/-1``).
+
+    Examples
+    --------
+    >>> np.set_printoptions(precision=4)
+
+    >>> from numpy.testing import suppress_warnings
+    >>> with suppress_warnings() as sup:
+    ...     sup.filter(RuntimeWarning)
+    ...     np.emath.arctanh(np.eye(2))
+    array([[inf,  0.],
+           [ 0., inf]])
+    >>> np.emath.arctanh([1j])
+    array([0.+0.7854j])
+
+    """
+    x = _fix_real_abs_gt_1(x)
+    return nx.arctanh(x)

env-llmeval/lib/python3.10/site-packages/numpy/lib/scimath.pyi

@@ -0,0 +1,94 @@
+from typing import overload, Any
+
+from numpy import complexfloating
+
+from numpy._typing import (
+    NDArray,
+    _ArrayLikeFloat_co,
+    _ArrayLikeComplex_co,
+    _ComplexLike_co,
+    _FloatLike_co,
+)
+
+__all__: list[str]
+
+@overload
+def sqrt(x: _FloatLike_co) -> Any: ...
+@overload
+def sqrt(x: _ComplexLike_co) -> complexfloating[Any, Any]: ...
+@overload
+def sqrt(x: _ArrayLikeFloat_co) -> NDArray[Any]: ...
+@overload
+def sqrt(x: _ArrayLikeComplex_co) -> NDArray[complexfloating[Any, Any]]: ...
+
+@overload
+def log(x: _FloatLike_co) -> Any: ...
+@overload
+def log(x: _ComplexLike_co) -> complexfloating[Any, Any]: ...
+@overload
+def log(x: _ArrayLikeFloat_co) -> NDArray[Any]: ...
+@overload
+def log(x: _ArrayLikeComplex_co) -> NDArray[complexfloating[Any, Any]]: ...
+
+@overload
+def log10(x: _FloatLike_co) -> Any: ...
+@overload
+def log10(x: _ComplexLike_co) -> complexfloating[Any, Any]: ...
+@overload
+def log10(x: _ArrayLikeFloat_co) -> NDArray[Any]: ...
+@overload
+def log10(x: _ArrayLikeComplex_co) -> NDArray[complexfloating[Any, Any]]: ...
+
+@overload
+def log2(x: _FloatLike_co) -> Any: ...
+@overload
+def log2(x: _ComplexLike_co) -> complexfloating[Any, Any]: ...
+@overload
+def log2(x: _ArrayLikeFloat_co) -> NDArray[Any]: ...
+@overload
+def log2(x: _ArrayLikeComplex_co) -> NDArray[complexfloating[Any, Any]]: ...
+
+@overload
+def logn(n: _FloatLike_co, x: _FloatLike_co) -> Any: ...
+@overload
+def logn(n: _ComplexLike_co, x: _ComplexLike_co) -> complexfloating[Any, Any]: ...
+@overload
+def logn(n: _ArrayLikeFloat_co, x: _ArrayLikeFloat_co) -> NDArray[Any]: ...
+@overload
+def logn(n: _ArrayLikeComplex_co, x: _ArrayLikeComplex_co) -> NDArray[complexfloating[Any, Any]]: ...
+
+@overload
+def power(x: _FloatLike_co, p: _FloatLike_co) -> Any: ...
+@overload
+def power(x: _ComplexLike_co, p: _ComplexLike_co) -> complexfloating[Any, Any]: ...
+@overload
+def power(x: _ArrayLikeFloat_co, p: _ArrayLikeFloat_co) -> NDArray[Any]: ...
+@overload
+def power(x: _ArrayLikeComplex_co, p: _ArrayLikeComplex_co) -> NDArray[complexfloating[Any, Any]]: ...
+
+@overload
+def arccos(x: _FloatLike_co) -> Any: ...
+@overload
+def arccos(x: _ComplexLike_co) -> complexfloating[Any, Any]: ...
+@overload
+def arccos(x: _ArrayLikeFloat_co) -> NDArray[Any]: ...
+@overload
+def arccos(x: _ArrayLikeComplex_co) -> NDArray[complexfloating[Any, Any]]: ...
+
+@overload
+def arcsin(x: _FloatLike_co) -> Any: ...
+@overload
+def arcsin(x: _ComplexLike_co) -> complexfloating[Any, Any]: ...
+@overload
+def arcsin(x: _ArrayLikeFloat_co) -> NDArray[Any]: ...
+@overload
+def arcsin(x: _ArrayLikeComplex_co) -> NDArray[complexfloating[Any, Any]]: ...
+
+@overload
+def arctanh(x: _FloatLike_co) -> Any: ...
+@overload
+def arctanh(x: _ComplexLike_co) -> complexfloating[Any, Any]: ...
+@overload
+def arctanh(x: _ArrayLikeFloat_co) -> NDArray[Any]: ...
+@overload
+def arctanh(x: _ArrayLikeComplex_co) -> NDArray[complexfloating[Any, Any]]: ...

env-llmeval/lib/python3.10/site-packages/numpy/lib/shape_base.py

@@ -0,0 +1,1274 @@
+import functools
+
+import numpy.core.numeric as _nx
+from numpy.core.numeric import asarray, zeros, array, asanyarray
+from numpy.core.fromnumeric import reshape, transpose
+from numpy.core.multiarray import normalize_axis_index
+from numpy.core import overrides
+from numpy.core import vstack, atleast_3d
+from numpy.core.numeric import normalize_axis_tuple
+from numpy.core.shape_base import _arrays_for_stack_dispatcher
+from numpy.lib.index_tricks import ndindex
+from numpy.matrixlib.defmatrix import matrix  # this raises all the right alarm bells
+
+
+__all__ = [
+    'column_stack', 'row_stack', 'dstack', 'array_split', 'split',
+    'hsplit', 'vsplit', 'dsplit', 'apply_over_axes', 'expand_dims',
+    'apply_along_axis', 'kron', 'tile', 'get_array_wrap', 'take_along_axis',
+    'put_along_axis'
+    ]
+
+
+array_function_dispatch = functools.partial(
+    overrides.array_function_dispatch, module='numpy')
+
+
+def _make_along_axis_idx(arr_shape, indices, axis):
+    # compute dimensions to iterate over
+    if not _nx.issubdtype(indices.dtype, _nx.integer):
+        raise IndexError('`indices` must be an integer array')
+    if len(arr_shape) != indices.ndim:
+        raise ValueError(
+            "`indices` and `arr` must have the same number of dimensions")
+    shape_ones = (1,) * indices.ndim
+    dest_dims = list(range(axis)) + [None] + list(range(axis+1, indices.ndim))
+
+    # build a fancy index, consisting of orthogonal aranges, with the
+    # requested index inserted at the right location
+    fancy_index = []
+    for dim, n in zip(dest_dims, arr_shape):
+        if dim is None:
+            fancy_index.append(indices)
+        else:
+            ind_shape = shape_ones[:dim] + (-1,) + shape_ones[dim+1:]
+            fancy_index.append(_nx.arange(n).reshape(ind_shape))
+
+    return tuple(fancy_index)
+
+
+def _take_along_axis_dispatcher(arr, indices, axis):
+    return (arr, indices)
+
+
+@array_function_dispatch(_take_along_axis_dispatcher)
+def take_along_axis(arr, indices, 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 maintain the trivial dimension
+    with ``keepdims``:
+
+    >>> np.max(a, axis=1, keepdims=True)
+    array([[30],
+           [60]])
+    >>> ai = np.argmax(a, axis=1, keepdims=True)
+    >>> 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.argmin(a, axis=1, keepdims=True)
+    >>> ai_max = np.argmax(a, axis=1, keepdims=True)
+    >>> 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]])
+    """
+    # normalize inputs
+    if axis is None:
+        arr = arr.flat
+        arr_shape = (len(arr),)  # flatiter has no .shape
+        axis = 0
+    else:
+        axis = normalize_axis_index(axis, arr.ndim)
+        arr_shape = arr.shape
+
+    # use the fancy index
+    return arr[_make_along_axis_idx(arr_shape, indices, axis)]
+
+
+def _put_along_axis_dispatcher(arr, indices, values, axis):
+    return (arr, indices, values)
+
+
+@array_function_dispatch(_put_along_axis_dispatcher)
+def put_along_axis(arr, indices, values, 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.argmax(a, axis=1, keepdims=True)
+    >>> ai
+    array([[1],
+           [0]])
+    >>> np.put_along_axis(a, ai, 99, axis=1)
+    >>> a
+    array([[10, 99, 20],
+           [99, 40, 50]])
+
+    """
+    # normalize inputs
+    if axis is None:
+        arr = arr.flat
+        axis = 0
+        arr_shape = (len(arr),)  # flatiter has no .shape
+    else:
+        axis = normalize_axis_index(axis, arr.ndim)
+        arr_shape = arr.shape
+
+    # use the fancy index
+    arr[_make_along_axis_idx(arr_shape, indices, axis)] = values
+
+
+def _apply_along_axis_dispatcher(func1d, axis, arr, *args, **kwargs):
+    return (arr,)
+
+
+@array_function_dispatch(_apply_along_axis_dispatcher)
+def apply_along_axis(func1d, axis, arr, *args, **kwargs):
+    """
+    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]]])
+    """
+    # handle negative axes
+    arr = asanyarray(arr)
+    nd = arr.ndim
+    axis = normalize_axis_index(axis, nd)
+
+    # arr, with the iteration axis at the end
+    in_dims = list(range(nd))
+    inarr_view = transpose(arr, in_dims[:axis] + in_dims[axis+1:] + [axis])
+
+    # compute indices for the iteration axes, and append a trailing ellipsis to
+    # prevent 0d arrays decaying to scalars, which fixes gh-8642
+    inds = ndindex(inarr_view.shape[:-1])
+    inds = (ind + (Ellipsis,) for ind in inds)
+
+    # invoke the function on the first item
+    try:
+        ind0 = next(inds)
+    except StopIteration:
+        raise ValueError(
+            'Cannot apply_along_axis when any iteration dimensions are 0'
+        ) from None
+    res = asanyarray(func1d(inarr_view[ind0], *args, **kwargs))
+
+    # build a buffer for storing evaluations of func1d.
+    # remove the requested axis, and add the new ones on the end.
+    # laid out so that each write is contiguous.
+    # for a tuple index inds, buff[inds] = func1d(inarr_view[inds])
+    buff = zeros(inarr_view.shape[:-1] + res.shape, res.dtype)
+
+    # permutation of axes such that out = buff.transpose(buff_permute)
+    buff_dims = list(range(buff.ndim))
+    buff_permute = (
+        buff_dims[0 : axis] +
+        buff_dims[buff.ndim-res.ndim : buff.ndim] +
+        buff_dims[axis : buff.ndim-res.ndim]
+    )
+
+    # matrices have a nasty __array_prepare__ and __array_wrap__
+    if not isinstance(res, matrix):
+        buff = res.__array_prepare__(buff)
+
+    # save the first result, then compute and save all remaining results
+    buff[ind0] = res
+    for ind in inds:
+        buff[ind] = asanyarray(func1d(inarr_view[ind], *args, **kwargs))
+
+    if not isinstance(res, matrix):
+        # wrap the array, to preserve subclasses
+        buff = res.__array_wrap__(buff)
+
+        # finally, rotate the inserted axes back to where they belong
+        return transpose(buff, buff_permute)
+
+    else:
+        # matrices have to be transposed first, because they collapse dimensions!
+        out_arr = transpose(buff, buff_permute)
+        return res.__array_wrap__(out_arr)
+
+
+def _apply_over_axes_dispatcher(func, a, axes):
+    return (a,)
+
+
+@array_function_dispatch(_apply_over_axes_dispatcher)
+def apply_over_axes(func, a, 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).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]]])
+
+    """
+    val = asarray(a)
+    N = a.ndim
+    if array(axes).ndim == 0:
+        axes = (axes,)
+    for axis in axes:
+        if axis < 0:
+            axis = N + axis
+        args = (val, axis)
+        res = func(*args)
+        if res.ndim == val.ndim:
+            val = res
+        else:
+            res = expand_dims(res, axis)
+            if res.ndim == val.ndim:
+                val = res
+            else:
+                raise ValueError("function is not returning "
+                                 "an array of the correct shape")
+    return val
+
+
+def _expand_dims_dispatcher(a, axis):
+    return (a,)
+
+
+@array_function_dispatch(_expand_dims_dispatcher)
+def expand_dims(a, axis):
+    """
+    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
+
+    """
+    if isinstance(a, matrix):
+        a = asarray(a)
+    else:
+        a = asanyarray(a)
+
+    if type(axis) not in (tuple, list):
+        axis = (axis,)
+
+    out_ndim = len(axis) + a.ndim
+    axis = normalize_axis_tuple(axis, out_ndim)
+
+    shape_it = iter(a.shape)
+    shape = [1 if ax in axis else next(shape_it) for ax in range(out_ndim)]
+
+    return a.reshape(shape)
+
+
+row_stack = vstack
+
+
+def _column_stack_dispatcher(tup):
+    return _arrays_for_stack_dispatcher(tup)
+
+
+@array_function_dispatch(_column_stack_dispatcher)
+def column_stack(tup):
+    """
+    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]])
+
+    """
+    arrays = []
+    for v in tup:
+        arr = asanyarray(v)
+        if arr.ndim < 2:
+            arr = array(arr, copy=False, subok=True, ndmin=2).T
+        arrays.append(arr)
+    return _nx.concatenate(arrays, 1)
+
+
+def _dstack_dispatcher(tup):
+    return _arrays_for_stack_dispatcher(tup)
+
+
+@array_function_dispatch(_dstack_dispatcher)
+def dstack(tup):
+    """
+    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]]])
+
+    """
+    arrs = atleast_3d(*tup)
+    if not isinstance(arrs, list):
+        arrs = [arrs]
+    return _nx.concatenate(arrs, 2)
+
+
+def _replace_zero_by_x_arrays(sub_arys):
+    for i in range(len(sub_arys)):
+        if _nx.ndim(sub_arys[i]) == 0:
+            sub_arys[i] = _nx.empty(0, dtype=sub_arys[i].dtype)
+        elif _nx.sometrue(_nx.equal(_nx.shape(sub_arys[i]), 0)):
+            sub_arys[i] = _nx.empty(0, dtype=sub_arys[i].dtype)
+    return sub_arys
+
+
+def _array_split_dispatcher(ary, indices_or_sections, axis=None):
+    return (ary, indices_or_sections)
+
+
+@array_function_dispatch(_array_split_dispatcher)
+def array_split(ary, indices_or_sections, axis=0):
+    """
+    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)
+    >>> np.array_split(x, 4)
+    [array([0, 1, 2]), array([3, 4]), array([5, 6]), array([7, 8])]
+
+    """
+    try:
+        Ntotal = ary.shape[axis]
+    except AttributeError:
+        Ntotal = len(ary)
+    try:
+        # handle array case.
+        Nsections = len(indices_or_sections) + 1
+        div_points = [0] + list(indices_or_sections) + [Ntotal]
+    except TypeError:
+        # indices_or_sections is a scalar, not an array.
+        Nsections = int(indices_or_sections)
+        if Nsections <= 0:
+            raise ValueError('number sections must be larger than 0.') from None
+        Neach_section, extras = divmod(Ntotal, Nsections)
+        section_sizes = ([0] +
+                         extras * [Neach_section+1] +
+                         (Nsections-extras) * [Neach_section])
+        div_points = _nx.array(section_sizes, dtype=_nx.intp).cumsum()
+
+    sub_arys = []
+    sary = _nx.swapaxes(ary, axis, 0)
+    for i in range(Nsections):
+        st = div_points[i]
+        end = div_points[i + 1]
+        sub_arys.append(_nx.swapaxes(sary[st:end], axis, 0))
+
+    return sub_arys
+
+
+def _split_dispatcher(ary, indices_or_sections, axis=None):
+    return (ary, indices_or_sections)
+
+
+@array_function_dispatch(_split_dispatcher)
+def split(ary, indices_or_sections, axis=0):
+    """
+    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)]
+
+    """
+    try:
+        len(indices_or_sections)
+    except TypeError:
+        sections = indices_or_sections
+        N = ary.shape[axis]
+        if N % sections:
+            raise ValueError(
+                'array split does not result in an equal division') from None
+    return array_split(ary, indices_or_sections, axis)
+
+
+def _hvdsplit_dispatcher(ary, indices_or_sections):
+    return (ary, indices_or_sections)
+
+
+@array_function_dispatch(_hvdsplit_dispatcher)
+def hsplit(ary, indices_or_sections):
+    """
+    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 except for 1-D arrays, where it is split at ``axis=0``.
+
+    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.]]])]
+
+    With a 1-D array, the split is along axis 0.
+
+    >>> x = np.array([0, 1, 2, 3, 4, 5])
+    >>> np.hsplit(x, 2)
+    [array([0, 1, 2]), array([3, 4, 5])]
+
+    """
+    if _nx.ndim(ary) == 0:
+        raise ValueError('hsplit only works on arrays of 1 or more dimensions')
+    if ary.ndim > 1:
+        return split(ary, indices_or_sections, 1)
+    else:
+        return split(ary, indices_or_sections, 0)
+
+
+@array_function_dispatch(_hvdsplit_dispatcher)
+def vsplit(ary, indices_or_sections):
+    """
+    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.]]])]
+
+    """
+    if _nx.ndim(ary) < 2:
+        raise ValueError('vsplit only works on arrays of 2 or more dimensions')
+    return split(ary, indices_or_sections, 0)
+
+
+@array_function_dispatch(_hvdsplit_dispatcher)
+def dsplit(ary, indices_or_sections):
+    """
+    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)]
+    """
+    if _nx.ndim(ary) < 3:
+        raise ValueError('dsplit only works on arrays of 3 or more dimensions')
+    return split(ary, indices_or_sections, 2)
+
+
+def get_array_prepare(*args):
+    """Find the wrapper for the array with the highest priority.
+
+    In case of ties, leftmost wins. If no wrapper is found, return None
+    """
+    wrappers = sorted((getattr(x, '__array_priority__', 0), -i,
+                 x.__array_prepare__) for i, x in enumerate(args)
+                                   if hasattr(x, '__array_prepare__'))
+    if wrappers:
+        return wrappers[-1][-1]
+    return None
+
+
+def get_array_wrap(*args):
+    """Find the wrapper for the array with the highest priority.
+
+    In case of ties, leftmost wins. If no wrapper is found, return None
+    """
+    wrappers = sorted((getattr(x, '__array_priority__', 0), -i,
+                 x.__array_wrap__) for i, x in enumerate(args)
+                                   if hasattr(x, '__array_wrap__'))
+    if wrappers:
+        return wrappers[-1][-1]
+    return None
+
+
+def _kron_dispatcher(a, b):
+    return (a, b)
+
+
+@array_function_dispatch(_kron_dispatcher)
+def kron(a, b):
+    """
+    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), 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).reshape((2,5,2,5))
+    >>> b = np.arange(24).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
+
+    """
+    # Working:
+    # 1. Equalise the shapes by prepending smaller array with 1s
+    # 2. Expand shapes of both the arrays by adding new axes at
+    #    odd positions for 1st array and even positions for 2nd
+    # 3. Compute the product of the modified array
+    # 4. The inner most array elements now contain the rows of
+    #    the Kronecker product
+    # 5. Reshape the result to kron's shape, which is same as
+    #    product of shapes of the two arrays.
+    b = asanyarray(b)
+    a = array(a, copy=False, subok=True, ndmin=b.ndim)
+    is_any_mat = isinstance(a, matrix) or isinstance(b, matrix)
+    ndb, nda = b.ndim, a.ndim
+    nd = max(ndb, nda)
+
+    if (nda == 0 or ndb == 0):
+        return _nx.multiply(a, b)
+
+    as_ = a.shape
+    bs = b.shape
+    if not a.flags.contiguous:
+        a = reshape(a, as_)
+    if not b.flags.contiguous:
+        b = reshape(b, bs)
+
+    # Equalise the shapes by prepending smaller one with 1s
+    as_ = (1,)*max(0, ndb-nda) + as_
+    bs = (1,)*max(0, nda-ndb) + bs
+
+    # Insert empty dimensions
+    a_arr = expand_dims(a, axis=tuple(range(ndb-nda)))
+    b_arr = expand_dims(b, axis=tuple(range(nda-ndb)))
+
+    # Compute the product
+    a_arr = expand_dims(a_arr, axis=tuple(range(1, nd*2, 2)))
+    b_arr = expand_dims(b_arr, axis=tuple(range(0, nd*2, 2)))
+    # In case of `mat`, convert result to `array`
+    result = _nx.multiply(a_arr, b_arr, subok=(not is_any_mat))
+
+    # Reshape back
+    result = result.reshape(_nx.multiply(as_, bs))
+
+    return result if not is_any_mat else matrix(result, copy=False)
+
+
+def _tile_dispatcher(A, reps):
+    return (A, reps)
+
+
+@array_function_dispatch(_tile_dispatcher)
+def tile(A, reps):
+    """
+    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]])
+    """
+    try:
+        tup = tuple(reps)
+    except TypeError:
+        tup = (reps,)
+    d = len(tup)
+    if all(x == 1 for x in tup) and isinstance(A, _nx.ndarray):
+        # Fixes the problem that the function does not make a copy if A is a
+        # numpy array and the repetitions are 1 in all dimensions
+        return _nx.array(A, copy=True, subok=True, ndmin=d)
+    else:
+        # Note that no copy of zero-sized arrays is made. However since they
+        # have no data there is no risk of an inadvertent overwrite.
+        c = _nx.array(A, copy=False, subok=True, ndmin=d)
+    if (d < c.ndim):
+        tup = (1,)*(c.ndim-d) + tup
+    shape_out = tuple(s*t for s, t in zip(c.shape, tup))
+    n = c.size
+    if n > 0:
+        for dim_in, nrep in zip(c.shape, tup):
+            if nrep != 1:
+                c = c.reshape(-1, n).repeat(nrep, 0)
+            n //= dim_in
+    return c.reshape(shape_out)

env-llmeval/lib/python3.10/site-packages/numpy/lib/twodim_base.py

@@ -0,0 +1,1183 @@
+""" Basic functions for manipulating 2d arrays
+
+"""
+import functools
+import operator
+
+from numpy.core.numeric import (
+    asanyarray, arange, zeros, greater_equal, multiply, ones,
+    asarray, where, int8, int16, int32, int64, intp, empty, promote_types,
+    diagonal, nonzero, indices
+    )
+from numpy.core.overrides import set_array_function_like_doc, set_module
+from numpy.core import overrides
+from numpy.core import iinfo
+from numpy.lib.stride_tricks import broadcast_to
+
+
+__all__ = [
+    'diag', 'diagflat', 'eye', 'fliplr', 'flipud', 'tri', 'triu',
+    'tril', 'vander', 'histogram2d', 'mask_indices', 'tril_indices',
+    'tril_indices_from', 'triu_indices', 'triu_indices_from', ]
+
+
+array_function_dispatch = functools.partial(
+    overrides.array_function_dispatch, module='numpy')
+
+
+i1 = iinfo(int8)
+i2 = iinfo(int16)
+i4 = iinfo(int32)
+
+
+def _min_int(low, high):
+    """ get small int that fits the range """
+    if high <= i1.max and low >= i1.min:
+        return int8
+    if high <= i2.max and low >= i2.min:
+        return int16
+    if high <= i4.max and low >= i4.min:
+        return int32
+    return int64
+
+
+def _flip_dispatcher(m):
+    return (m,)
+
+
+@array_function_dispatch(_flip_dispatcher)
+def fliplr(m):
+    """
+    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)`.
+
+    See Also
+    --------
+    flipud : Flip array in the up/down direction.
+    flip : Flip array in one or more dimensions.
+    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
+
+    """
+    m = asanyarray(m)
+    if m.ndim < 2:
+        raise ValueError("Input must be >= 2-d.")
+    return m[:, ::-1]
+
+
+@array_function_dispatch(_flip_dispatcher)
+def flipud(m):
+    """
+    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)`.
+
+    See Also
+    --------
+    fliplr : Flip array in the left/right direction.
+    flip : Flip array in one or more dimensions.
+    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])
+
+    """
+    m = asanyarray(m)
+    if m.ndim < 1:
+        raise ValueError("Input must be >= 1-d.")
+    return m[::-1, ...]
+
+
+@set_array_function_like_doc
+@set_module('numpy')
+def eye(N, M=None, k=0, dtype=float, order='C', *, like=None):
+    """
+    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
+    ${ARRAY_FUNCTION_LIKE}
+
+        .. 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.]])
+
+    """
+    if like is not None:
+        return _eye_with_like(like, N, M=M, k=k, dtype=dtype, order=order)
+    if M is None:
+        M = N
+    m = zeros((N, M), dtype=dtype, order=order)
+    if k >= M:
+        return m
+    # Ensure M and k are integers, so we don't get any surprise casting
+    # results in the expressions `M-k` and `M+1` used below.  This avoids
+    # a problem with inputs with type (for example) np.uint64.
+    M = operator.index(M)
+    k = operator.index(k)
+    if k >= 0:
+        i = k
+    else:
+        i = (-k) * M
+    m[:M-k].flat[i::M+1] = 1
+    return m
+
+
+_eye_with_like = array_function_dispatch()(eye)
+
+
+def _diag_dispatcher(v, k=None):
+    return (v,)
+
+
+@array_function_dispatch(_diag_dispatcher)
+def diag(v, k=0):
+    """
+    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).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]])
+
+    """
+    v = asanyarray(v)
+    s = v.shape
+    if len(s) == 1:
+        n = s[0]+abs(k)
+        res = zeros((n, n), v.dtype)
+        if k >= 0:
+            i = k
+        else:
+            i = (-k) * n
+        res[:n-k].flat[i::n+1] = v
+        return res
+    elif len(s) == 2:
+        return diagonal(v, k)
+    else:
+        raise ValueError("Input must be 1- or 2-d.")
+
+
+@array_function_dispatch(_diag_dispatcher)
+def diagflat(v, k=0):
+    """
+    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]])
+
+    """
+    try:
+        wrap = v.__array_wrap__
+    except AttributeError:
+        wrap = None
+    v = asarray(v).ravel()
+    s = len(v)
+    n = s + abs(k)
+    res = zeros((n, n), v.dtype)
+    if (k >= 0):
+        i = arange(0, n-k, dtype=intp)
+        fi = i+k+i*n
+    else:
+        i = arange(0, n+k, dtype=intp)
+        fi = i+(i-k)*n
+    res.flat[fi] = v
+    if not wrap:
+        return res
+    return wrap(res)
+
+
+@set_array_function_like_doc
+@set_module('numpy')
+def tri(N, M=None, k=0, dtype=float, *, like=None):
+    """
+    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.
+    ${ARRAY_FUNCTION_LIKE}
+
+        .. 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.]])
+
+    """
+    if like is not None:
+        return _tri_with_like(like, N, M=M, k=k, dtype=dtype)
+
+    if M is None:
+        M = N
+
+    m = greater_equal.outer(arange(N, dtype=_min_int(0, N)),
+                            arange(-k, M-k, dtype=_min_int(-k, M - k)))
+
+    # Avoid making a copy if the requested type is already bool
+    m = m.astype(dtype, copy=False)
+
+    return m
+
+
+_tri_with_like = array_function_dispatch()(tri)
+
+
+def _trilu_dispatcher(m, k=None):
+    return (m,)
+
+
+@array_function_dispatch(_trilu_dispatcher)
+def tril(m, k=0):
+    """
+    Lower triangle of an array.
+
+    Return a copy of an array with elements above the `k`-th diagonal zeroed.
+    For arrays with ``ndim`` exceeding 2, `tril` will apply to the final two
+    axes.
+
+    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]])
+
+    >>> np.tril(np.arange(3*4*5).reshape(3, 4, 5))
+    array([[[ 0,  0,  0,  0,  0],
+            [ 5,  6,  0,  0,  0],
+            [10, 11, 12,  0,  0],
+            [15, 16, 17, 18,  0]],
+           [[20,  0,  0,  0,  0],
+            [25, 26,  0,  0,  0],
+            [30, 31, 32,  0,  0],
+            [35, 36, 37, 38,  0]],
+           [[40,  0,  0,  0,  0],
+            [45, 46,  0,  0,  0],
+            [50, 51, 52,  0,  0],
+            [55, 56, 57, 58,  0]]])
+
+    """
+    m = asanyarray(m)
+    mask = tri(*m.shape[-2:], k=k, dtype=bool)
+
+    return where(mask, m, zeros(1, m.dtype))
+
+
+@array_function_dispatch(_trilu_dispatcher)
+def triu(m, k=0):
+    """
+    Upper triangle of an array.
+
+    Return a copy of an array with the elements below the `k`-th diagonal
+    zeroed. For arrays with ``ndim`` exceeding 2, `triu` will apply to the
+    final two axes.
+
+    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]])
+
+    >>> np.triu(np.arange(3*4*5).reshape(3, 4, 5))
+    array([[[ 0,  1,  2,  3,  4],
+            [ 0,  6,  7,  8,  9],
+            [ 0,  0, 12, 13, 14],
+            [ 0,  0,  0, 18, 19]],
+           [[20, 21, 22, 23, 24],
+            [ 0, 26, 27, 28, 29],
+            [ 0,  0, 32, 33, 34],
+            [ 0,  0,  0, 38, 39]],
+           [[40, 41, 42, 43, 44],
+            [ 0, 46, 47, 48, 49],
+            [ 0,  0, 52, 53, 54],
+            [ 0,  0,  0, 58, 59]]])
+
+    """
+    m = asanyarray(m)
+    mask = tri(*m.shape[-2:], k=k-1, dtype=bool)
+
+    return where(mask, zeros(1, m.dtype), m)
+
+
+def _vander_dispatcher(x, N=None, increasing=None):
+    return (x,)
+
+
+# Originally borrowed from John Hunter and matplotlib
+@array_function_dispatch(_vander_dispatcher)
+def vander(x, N=None, increasing=False):
+    """
+    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
+
+    """
+    x = asarray(x)
+    if x.ndim != 1:
+        raise ValueError("x must be a one-dimensional array or sequence.")
+    if N is None:
+        N = len(x)
+
+    v = empty((len(x), N), dtype=promote_types(x.dtype, int))
+    tmp = v[:, ::-1] if not increasing else v
+
+    if N > 0:
+        tmp[:, 0] = 1
+    if N > 1:
+        tmp[:, 1:] = x[:, None]
+        multiply.accumulate(tmp[:, 1:], out=tmp[:, 1:], axis=1)
+
+    return v
+
+
+def _histogram2d_dispatcher(x, y, bins=None, range=None, density=None,
+                            weights=None):
+    yield x
+    yield y
+
+    # This terrible logic is adapted from the checks in histogram2d
+    try:
+        N = len(bins)
+    except TypeError:
+        N = 1
+    if N == 2:
+        yield from bins  # bins=[x, y]
+    else:
+        yield bins
+
+    yield weights
+
+
+@array_function_dispatch(_histogram2d_dispatcher)
+def histogram2d(x, y, bins=10, range=None, density=None, weights=None):
+    """
+    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``.
+    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 `density` is True. If `density` 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 `density` 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 <matplotlib.pyplot.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]])
+    <matplotlib.image.AxesImage object at 0x...>
+
+    :func:`pcolormesh <matplotlib.pyplot.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)
+    <matplotlib.collections.QuadMesh object at 0x...>
+
+    :class:`NonUniformImage <matplotlib.image.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.add_image(im)
+    >>> plt.show()
+
+    It is also possible to construct a 2-D histogram without specifying bin
+    edges:
+
+    >>> # Generate non-symmetric test data
+    >>> n = 10000
+    >>> x = np.linspace(1, 100, n)
+    >>> y = 2*np.log(x) + np.random.rand(n) - 0.5
+    >>> # Compute 2d histogram. Note the order of x/y and xedges/yedges
+    >>> H, yedges, xedges = np.histogram2d(y, x, bins=20)
+
+    Now we can plot the histogram using
+    :func:`pcolormesh <matplotlib.pyplot.pcolormesh>`, and a
+    :func:`hexbin <matplotlib.pyplot.hexbin>` for comparison.
+
+    >>> # Plot histogram using pcolormesh
+    >>> fig, (ax1, ax2) = plt.subplots(ncols=2, sharey=True)
+    >>> ax1.pcolormesh(xedges, yedges, H, cmap='rainbow')
+    >>> ax1.plot(x, 2*np.log(x), 'k-')
+    >>> ax1.set_xlim(x.min(), x.max())
+    >>> ax1.set_ylim(y.min(), y.max())
+    >>> ax1.set_xlabel('x')
+    >>> ax1.set_ylabel('y')
+    >>> ax1.set_title('histogram2d')
+    >>> ax1.grid()
+
+    >>> # Create hexbin plot for comparison
+    >>> ax2.hexbin(x, y, gridsize=20, cmap='rainbow')
+    >>> ax2.plot(x, 2*np.log(x), 'k-')
+    >>> ax2.set_title('hexbin')
+    >>> ax2.set_xlim(x.min(), x.max())
+    >>> ax2.set_xlabel('x')
+    >>> ax2.grid()
+
+    >>> plt.show()
+    """
+    from numpy import histogramdd
+
+    if len(x) != len(y):
+        raise ValueError('x and y must have the same length.')
+
+    try:
+        N = len(bins)
+    except TypeError:
+        N = 1
+
+    if N != 1 and N != 2:
+        xedges = yedges = asarray(bins)
+        bins = [xedges, yedges]
+    hist, edges = histogramdd([x, y], bins, range, density, weights)
+    return hist, edges[0], edges[1]
+
+
+@set_module('numpy')
+def mask_indices(n, mask_func, k=0):
+    """
+    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).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])
+
+    """
+    m = ones((n, n), int)
+    a = mask_func(m, k)
+    return nonzero(a != 0)
+
+
+@set_module('numpy')
+def tril_indices(n, k=0, m=None):
+    """
+    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)
+    >>> il2 = np.tril_indices(4, 2)
+
+    Here is how they can be used with a sample array:
+
+    >>> a = np.arange(16).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]])
+
+    """
+    tri_ = tri(n, m, k=k, dtype=bool)
+
+    return tuple(broadcast_to(inds, tri_.shape)[tri_]
+                 for inds in indices(tri_.shape, sparse=True))
+
+
+def _trilu_indices_form_dispatcher(arr, k=None):
+    return (arr,)
+
+
+@array_function_dispatch(_trilu_indices_form_dispatcher)
+def tril_indices_from(arr, k=0):
+    """
+    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).
+
+    Examples
+    --------
+
+    Create a 4 by 4 array.
+
+    >>> a = np.arange(16).reshape(4, 4)
+    >>> a
+    array([[ 0,  1,  2,  3],
+           [ 4,  5,  6,  7],
+           [ 8,  9, 10, 11],
+           [12, 13, 14, 15]])
+
+    Pass the array to get the indices of the lower triangular elements.
+
+    >>> trili = np.tril_indices_from(a)
+    >>> trili
+    (array([0, 1, 1, 2, 2, 2, 3, 3, 3, 3]), array([0, 0, 1, 0, 1, 2, 0, 1, 2, 3]))
+
+    >>> a[trili]
+    array([ 0,  4,  5,  8,  9, 10, 12, 13, 14, 15])
+
+    This is syntactic sugar for tril_indices().
+
+    >>> np.tril_indices(a.shape[0])
+    (array([0, 1, 1, 2, 2, 2, 3, 3, 3, 3]), array([0, 0, 1, 0, 1, 2, 0, 1, 2, 3]))
+
+    Use the `k` parameter to return the indices for the lower triangular array
+    up to the k-th diagonal.
+
+    >>> trili1 = np.tril_indices_from(a, k=1)
+    >>> a[trili1]
+    array([ 0,  1,  4,  5,  6,  8,  9, 10, 11, 12, 13, 14, 15])
+
+    See Also
+    --------
+    tril_indices, tril, triu_indices_from
+
+    Notes
+    -----
+    .. versionadded:: 1.4.0
+
+    """
+    if arr.ndim != 2:
+        raise ValueError("input array must be 2-d")
+    return tril_indices(arr.shape[-2], k=k, m=arr.shape[-1])
+
+
+@set_module('numpy')
+def triu_indices(n, k=0, m=None):
+    """
+    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) 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)
+    >>> iu2 = np.triu_indices(4, 2)
+
+    Here is how they can be used with a sample array:
+
+    >>> a = np.arange(16).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]])
+
+    """
+    tri_ = ~tri(n, m, k=k - 1, dtype=bool)
+
+    return tuple(broadcast_to(inds, tri_.shape)[tri_]
+                 for inds in indices(tri_.shape, sparse=True))
+
+
+@array_function_dispatch(_trilu_indices_form_dispatcher)
+def triu_indices_from(arr, k=0):
+    """
+    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) of ndarray, shape(N)
+        Indices for the upper-triangle of `arr`.
+
+    Examples
+    --------
+
+    Create a 4 by 4 array.
+
+    >>> a = np.arange(16).reshape(4, 4)
+    >>> a
+    array([[ 0,  1,  2,  3],
+           [ 4,  5,  6,  7],
+           [ 8,  9, 10, 11],
+           [12, 13, 14, 15]])
+
+    Pass the array to get the indices of the upper triangular elements.
+
+    >>> triui = np.triu_indices_from(a)
+    >>> triui
+    (array([0, 0, 0, 0, 1, 1, 1, 2, 2, 3]), array([0, 1, 2, 3, 1, 2, 3, 2, 3, 3]))
+
+    >>> a[triui]
+    array([ 0,  1,  2,  3,  5,  6,  7, 10, 11, 15])
+
+    This is syntactic sugar for triu_indices().
+
+    >>> np.triu_indices(a.shape[0])
+    (array([0, 0, 0, 0, 1, 1, 1, 2, 2, 3]), array([0, 1, 2, 3, 1, 2, 3, 2, 3, 3]))
+
+    Use the `k` parameter to return the indices for the upper triangular array
+    from the k-th diagonal.
+
+    >>> triuim1 = np.triu_indices_from(a, k=1)
+    >>> a[triuim1]
+    array([ 1,  2,  3,  6,  7, 11])
+
+
+    See Also
+    --------
+    triu_indices, triu, tril_indices_from
+
+    Notes
+    -----
+    .. versionadded:: 1.4.0
+
+    """
+    if arr.ndim != 2:
+        raise ValueError("input array must be 2-d")
+    return triu_indices(arr.shape[-2], k=k, m=arr.shape[-1])

env-llmeval/lib/python3.10/site-packages/numpy/lib/twodim_base.pyi

@@ -0,0 +1,239 @@
+from collections.abc import Callable, Sequence
+from typing import (
+    Any,
+    overload,
+    TypeVar,
+    Union,
+)
+
+from numpy import (
+    generic,
+    number,
+    bool_,
+    timedelta64,
+    datetime64,
+    int_,
+    intp,
+    float64,
+    signedinteger,
+    floating,
+    complexfloating,
+    object_,
+    _OrderCF,
+)
+
+from numpy._typing import (
+    DTypeLike,
+    _DTypeLike,
+    ArrayLike,
+    _ArrayLike,
+    NDArray,
+    _SupportsArrayFunc,
+    _ArrayLikeInt_co,
+    _ArrayLikeFloat_co,
+    _ArrayLikeComplex_co,
+    _ArrayLikeObject_co,
+)
+
+_T = TypeVar("_T")
+_SCT = TypeVar("_SCT", bound=generic)
+
+# The returned arrays dtype must be compatible with `np.equal`
+_MaskFunc = Callable[
+    [NDArray[int_], _T],
+    NDArray[Union[number[Any], bool_, timedelta64, datetime64, object_]],
+]
+
+__all__: list[str]
+
+@overload
+def fliplr(m: _ArrayLike[_SCT]) -> NDArray[_SCT]: ...
+@overload
+def fliplr(m: ArrayLike) -> NDArray[Any]: ...
+
+@overload
+def flipud(m: _ArrayLike[_SCT]) -> NDArray[_SCT]: ...
+@overload
+def flipud(m: ArrayLike) -> NDArray[Any]: ...
+
+@overload
+def eye(
+    N: int,
+    M: None | int = ...,
+    k: int = ...,
+    dtype: None = ...,
+    order: _OrderCF = ...,
+    *,
+    like: None | _SupportsArrayFunc = ...,
+) -> NDArray[float64]: ...
+@overload
+def eye(
+    N: int,
+    M: None | int = ...,
+    k: int = ...,
+    dtype: _DTypeLike[_SCT] = ...,
+    order: _OrderCF = ...,
+    *,
+    like: None | _SupportsArrayFunc = ...,
+) -> NDArray[_SCT]: ...
+@overload
+def eye(
+    N: int,
+    M: None | int = ...,
+    k: int = ...,
+    dtype: DTypeLike = ...,
+    order: _OrderCF = ...,
+    *,
+    like: None | _SupportsArrayFunc = ...,
+) -> NDArray[Any]: ...
+
+@overload
+def diag(v: _ArrayLike[_SCT], k: int = ...) -> NDArray[_SCT]: ...
+@overload
+def diag(v: ArrayLike, k: int = ...) -> NDArray[Any]: ...
+
+@overload
+def diagflat(v: _ArrayLike[_SCT], k: int = ...) -> NDArray[_SCT]: ...
+@overload
+def diagflat(v: ArrayLike, k: int = ...) -> NDArray[Any]: ...
+
+@overload
+def tri(
+    N: int,
+    M: None | int = ...,
+    k: int = ...,
+    dtype: None = ...,
+    *,
+    like: None | _SupportsArrayFunc = ...
+) -> NDArray[float64]: ...
+@overload
+def tri(
+    N: int,
+    M: None | int = ...,
+    k: int = ...,
+    dtype: _DTypeLike[_SCT] = ...,
+    *,
+    like: None | _SupportsArrayFunc = ...
+) -> NDArray[_SCT]: ...
+@overload
+def tri(
+    N: int,
+    M: None | int = ...,
+    k: int = ...,
+    dtype: DTypeLike = ...,
+    *,
+    like: None | _SupportsArrayFunc = ...
+) -> NDArray[Any]: ...
+
+@overload
+def tril(v: _ArrayLike[_SCT], k: int = ...) -> NDArray[_SCT]: ...
+@overload
+def tril(v: ArrayLike, k: int = ...) -> NDArray[Any]: ...
+
+@overload
+def triu(v: _ArrayLike[_SCT], k: int = ...) -> NDArray[_SCT]: ...
+@overload
+def triu(v: ArrayLike, k: int = ...) -> NDArray[Any]: ...
+
+@overload
+def vander(  # type: ignore[misc]
+    x: _ArrayLikeInt_co,
+    N: None | int = ...,
+    increasing: bool = ...,
+) -> NDArray[signedinteger[Any]]: ...
+@overload
+def vander(  # type: ignore[misc]
+    x: _ArrayLikeFloat_co,
+    N: None | int = ...,
+    increasing: bool = ...,
+) -> NDArray[floating[Any]]: ...
+@overload
+def vander(
+    x: _ArrayLikeComplex_co,
+    N: None | int = ...,
+    increasing: bool = ...,
+) -> NDArray[complexfloating[Any, Any]]: ...
+@overload
+def vander(
+    x: _ArrayLikeObject_co,
+    N: None | int = ...,
+    increasing: bool = ...,
+) -> NDArray[object_]: ...
+
+@overload
+def histogram2d(  # type: ignore[misc]
+    x: _ArrayLikeFloat_co,
+    y: _ArrayLikeFloat_co,
+    bins: int | Sequence[int] = ...,
+    range: None | _ArrayLikeFloat_co = ...,
+    density: None | bool = ...,
+    weights: None | _ArrayLikeFloat_co = ...,
+) -> tuple[
+    NDArray[float64],
+    NDArray[floating[Any]],
+    NDArray[floating[Any]],
+]: ...
+@overload
+def histogram2d(
+    x: _ArrayLikeComplex_co,
+    y: _ArrayLikeComplex_co,
+    bins: int | Sequence[int] = ...,
+    range: None | _ArrayLikeFloat_co = ...,
+    density: None | bool = ...,
+    weights: None | _ArrayLikeFloat_co = ...,
+) -> tuple[
+    NDArray[float64],
+    NDArray[complexfloating[Any, Any]],
+    NDArray[complexfloating[Any, Any]],
+]: ...
+@overload  # TODO: Sort out `bins`
+def histogram2d(
+    x: _ArrayLikeComplex_co,
+    y: _ArrayLikeComplex_co,
+    bins: Sequence[_ArrayLikeInt_co],
+    range: None | _ArrayLikeFloat_co = ...,
+    density: None | bool = ...,
+    weights: None | _ArrayLikeFloat_co = ...,
+) -> tuple[
+    NDArray[float64],
+    NDArray[Any],
+    NDArray[Any],
+]: ...
+
+# NOTE: we're assuming/demanding here the `mask_func` returns
+# an ndarray of shape `(n, n)`; otherwise there is the possibility
+# of the output tuple having more or less than 2 elements
+@overload
+def mask_indices(
+    n: int,
+    mask_func: _MaskFunc[int],
+    k: int = ...,
+) -> tuple[NDArray[intp], NDArray[intp]]: ...
+@overload
+def mask_indices(
+    n: int,
+    mask_func: _MaskFunc[_T],
+    k: _T,
+) -> tuple[NDArray[intp], NDArray[intp]]: ...
+
+def tril_indices(
+    n: int,
+    k: int = ...,
+    m: None | int = ...,
+) -> tuple[NDArray[int_], NDArray[int_]]: ...
+
+def tril_indices_from(
+    arr: NDArray[Any],
+    k: int = ...,
+) -> tuple[NDArray[int_], NDArray[int_]]: ...
+
+def triu_indices(
+    n: int,
+    k: int = ...,
+    m: None | int = ...,
+) -> tuple[NDArray[int_], NDArray[int_]]: ...
+
+def triu_indices_from(
+    arr: NDArray[Any],
+    k: int = ...,
+) -> tuple[NDArray[int_], NDArray[int_]]: ...

env-llmeval/lib/python3.10/site-packages/numpy/lib/type_check.py

@@ -0,0 +1,735 @@
+"""Automatically adapted for numpy Sep 19, 2005 by convertcode.py
+
+"""
+import functools
+
+__all__ = ['iscomplexobj', 'isrealobj', 'imag', 'iscomplex',
+           'isreal', 'nan_to_num', 'real', 'real_if_close',
+           'typename', 'asfarray', 'mintypecode',
+           'common_type']
+
+from .._utils import set_module
+import numpy.core.numeric as _nx
+from numpy.core.numeric import asarray, asanyarray, isnan, zeros
+from numpy.core import overrides, getlimits
+from .ufunclike import isneginf, isposinf
+
+
+array_function_dispatch = functools.partial(
+    overrides.array_function_dispatch, module='numpy')
+
+
+_typecodes_by_elsize = 'GDFgdfQqLlIiHhBb?'
+
+
+@set_module('numpy')
+def mintypecode(typechars, typeset='GDFgdf', default='d'):
+    """
+    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'
+
+    """
+    typecodes = ((isinstance(t, str) and t) or asarray(t).dtype.char
+                 for t in typechars)
+    intersection = set(t for t in typecodes if t in typeset)
+    if not intersection:
+        return default
+    if 'F' in intersection and 'd' in intersection:
+        return 'D'
+    return min(intersection, key=_typecodes_by_elsize.index)
+
+
+def _asfarray_dispatcher(a, dtype=None):
+    return (a,)
+
+
+@array_function_dispatch(_asfarray_dispatcher)
+def asfarray(a, dtype=_nx.float_):
+    """
+    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.])
+
+    """
+    if not _nx.issubdtype(dtype, _nx.inexact):
+        dtype = _nx.float_
+    return asarray(a, dtype=dtype)
+
+
+def _real_dispatcher(val):
+    return (val,)
+
+
+@array_function_dispatch(_real_dispatcher)
+def real(val):
+    """
+    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
+
+    """
+    try:
+        return val.real
+    except AttributeError:
+        return asanyarray(val).real
+
+
+def _imag_dispatcher(val):
+    return (val,)
+
+
+@array_function_dispatch(_imag_dispatcher)
+def imag(val):
+    """
+    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
+
+    """
+    try:
+        return val.imag
+    except AttributeError:
+        return asanyarray(val).imag
+
+
+def _is_type_dispatcher(x):
+    return (x,)
+
+
+@array_function_dispatch(_is_type_dispatcher)
+def iscomplex(x):
+    """
+    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])
+
+    """
+    ax = asanyarray(x)
+    if issubclass(ax.dtype.type, _nx.complexfloating):
+        return ax.imag != 0
+    res = zeros(ax.shape, bool)
+    return res[()]   # convert to scalar if needed
+
+
+@array_function_dispatch(_is_type_dispatcher)
+def isreal(x):
+    """
+    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])
+
+    """
+    return imag(x) == 0
+
+
+@array_function_dispatch(_is_type_dispatcher)
+def iscomplexobj(x):
+    """
+    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)
+    False
+    >>> np.iscomplexobj(1+0j)
+    True
+    >>> np.iscomplexobj([3, 1+0j, True])
+    True
+
+    """
+    try:
+        dtype = x.dtype
+        type_ = dtype.type
+    except AttributeError:
+        type_ = asarray(x).dtype.type
+    return issubclass(type_, _nx.complexfloating)
+
+
+@array_function_dispatch(_is_type_dispatcher)
+def isrealobj(x):
+    """
+    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)
+    True
+    >>> np.isrealobj(1+0j)
+    False
+    >>> np.isrealobj([3, 1+0j, True])
+    False
+
+    """
+    return not iscomplexobj(x)
+
+#-----------------------------------------------------------------------------
+
+def _getmaxmin(t):
+    from numpy.core import getlimits
+    f = getlimits.finfo(t)
+    return f.max, f.min
+
+
+def _nan_to_num_dispatcher(x, copy=None, nan=None, posinf=None, neginf=None):
+    return (x,)
+
+
+@array_function_dispatch(_nan_to_num_dispatcher)
+def nan_to_num(x, copy=True, nan=0.0, posinf=None, neginf=None):
+    """
+    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])
+    """
+    x = _nx.array(x, subok=True, copy=copy)
+    xtype = x.dtype.type
+
+    isscalar = (x.ndim == 0)
+
+    if not issubclass(xtype, _nx.inexact):
+        return x[()] if isscalar else x
+
+    iscomplex = issubclass(xtype, _nx.complexfloating)
+
+    dest = (x.real, x.imag) if iscomplex else (x,)
+    maxf, minf = _getmaxmin(x.real.dtype)
+    if posinf is not None:
+        maxf = posinf
+    if neginf is not None:
+        minf = neginf
+    for d in dest:
+        idx_nan = isnan(d)
+        idx_posinf = isposinf(d)
+        idx_neginf = isneginf(d)
+        _nx.copyto(d, nan, where=idx_nan)
+        _nx.copyto(d, maxf, where=idx_posinf)
+        _nx.copyto(d, minf, where=idx_neginf)
+    return x[()] if isscalar else x
+
+#-----------------------------------------------------------------------------
+
+def _real_if_close_dispatcher(a, tol=None):
+    return (a,)
+
+
+@array_function_dispatch(_real_if_close_dispatcher)
+def real_if_close(a, tol=100):
+    """
+    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. If the tolerance is <=1, then the absolute tolerance
+        is used.
+
+    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])
+
+    """
+    a = asanyarray(a)
+    type_ = a.dtype.type
+    if not issubclass(type_, _nx.complexfloating):
+        return a
+    if tol > 1:
+        f = getlimits.finfo(type_)
+        tol = f.eps * tol
+    if _nx.all(_nx.absolute(a.imag) < tol):
+        a = a.real
+    return a
+
+
+#-----------------------------------------------------------------------------
+
+_namefromtype = {'S1': 'character',
+                 '?': 'bool',
+                 'b': 'signed char',
+                 'B': 'unsigned char',
+                 'h': 'short',
+                 'H': 'unsigned short',
+                 'i': 'integer',
+                 'I': 'unsigned integer',
+                 'l': 'long integer',
+                 'L': 'unsigned long integer',
+                 'q': 'long long integer',
+                 'Q': 'unsigned long long integer',
+                 'f': 'single precision',
+                 'd': 'double precision',
+                 'g': 'long precision',
+                 'F': 'complex single precision',
+                 'D': 'complex double precision',
+                 'G': 'complex long double precision',
+                 'S': 'string',
+                 'U': 'unicode',
+                 'V': 'void',
+                 'O': 'object'
+                 }
+
+@set_module('numpy')
+def typename(char):
+    """
+    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
+
+    """
+    return _namefromtype[char]
+
+#-----------------------------------------------------------------------------
+
+#determine the "minimum common type" for a group of arrays.
+array_type = [[_nx.half, _nx.single, _nx.double, _nx.longdouble],
+              [None, _nx.csingle, _nx.cdouble, _nx.clongdouble]]
+array_precision = {_nx.half: 0,
+                   _nx.single: 1,
+                   _nx.double: 2,
+                   _nx.longdouble: 3,
+                   _nx.csingle: 1,
+                   _nx.cdouble: 2,
+                   _nx.clongdouble: 3}
+
+
+def _common_type_dispatcher(*arrays):
+    return arrays
+
+
+@array_function_dispatch(_common_type_dispatcher)
+def common_type(*arrays):
+    """
+    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))
+    <class 'numpy.float32'>
+    >>> np.common_type(np.arange(2, dtype=np.float32), np.arange(2))
+    <class 'numpy.float64'>
+    >>> np.common_type(np.arange(4), np.array([45, 6.j]), np.array([45.0]))
+    <class 'numpy.complex128'>
+
+    """
+    is_complex = False
+    precision = 0
+    for a in arrays:
+        t = a.dtype.type
+        if iscomplexobj(a):
+            is_complex = True
+        if issubclass(t, _nx.integer):
+            p = 2  # array_precision[_nx.double]
+        else:
+            p = array_precision.get(t, None)
+            if p is None:
+                raise TypeError("can't get common type for non-numeric array")
+        precision = max(precision, p)
+    if is_complex:
+        return array_type[1][precision]
+    else:
+        return array_type[0][precision]

env-llmeval/lib/python3.10/site-packages/numpy/lib/ufunclike.pyi

@@ -0,0 +1,66 @@
+from typing import Any, overload, TypeVar
+
+from numpy import floating, bool_, object_, ndarray
+from numpy._typing import (
+    NDArray,
+    _FloatLike_co,
+    _ArrayLikeFloat_co,
+    _ArrayLikeObject_co,
+)
+
+_ArrayType = TypeVar("_ArrayType", bound=ndarray[Any, Any])
+
+__all__: list[str]
+
+@overload
+def fix(  # type: ignore[misc]
+    x: _FloatLike_co,
+    out: None = ...,
+) -> floating[Any]: ...
+@overload
+def fix(
+    x: _ArrayLikeFloat_co,
+    out: None = ...,
+) -> NDArray[floating[Any]]: ...
+@overload
+def fix(
+    x: _ArrayLikeObject_co,
+    out: None = ...,
+) -> NDArray[object_]: ...
+@overload
+def fix(
+    x: _ArrayLikeFloat_co | _ArrayLikeObject_co,
+    out: _ArrayType,
+) -> _ArrayType: ...
+
+@overload
+def isposinf(  # type: ignore[misc]
+    x: _FloatLike_co,
+    out: None = ...,
+) -> bool_: ...
+@overload
+def isposinf(
+    x: _ArrayLikeFloat_co,
+    out: None = ...,
+) -> NDArray[bool_]: ...
+@overload
+def isposinf(
+    x: _ArrayLikeFloat_co,
+    out: _ArrayType,
+) -> _ArrayType: ...
+
+@overload
+def isneginf(  # type: ignore[misc]
+    x: _FloatLike_co,
+    out: None = ...,
+) -> bool_: ...
+@overload
+def isneginf(
+    x: _ArrayLikeFloat_co,
+    out: None = ...,
+) -> NDArray[bool_]: ...
+@overload
+def isneginf(
+    x: _ArrayLikeFloat_co,
+    out: _ArrayType,
+) -> _ArrayType: ...

env-llmeval/lib/python3.10/site-packages/numpy/lib/user_array.py

@@ -0,0 +1,286 @@
+"""
+Standard container-class for easy multiple-inheritance.
+
+Try to inherit from the ndarray instead of using this class as this is not
+complete.
+
+"""
+from numpy.core import (
+    array, asarray, absolute, add, subtract, multiply, divide,
+    remainder, power, left_shift, right_shift, bitwise_and, bitwise_or,
+    bitwise_xor, invert, less, less_equal, not_equal, equal, greater,
+    greater_equal, shape, reshape, arange, sin, sqrt, transpose
+)
+
+
+class container:
+    """
+    container(data, dtype=None, copy=True)
+
+    Standard container-class for easy multiple-inheritance.
+
+    Methods
+    -------
+    copy
+    tostring
+    byteswap
+    astype
+
+    """
+    def __init__(self, data, dtype=None, copy=True):
+        self.array = array(data, dtype, copy=copy)
+
+    def __repr__(self):
+        if self.ndim > 0:
+            return self.__class__.__name__ + repr(self.array)[len("array"):]
+        else:
+            return self.__class__.__name__ + "(" + repr(self.array) + ")"
+
+    def __array__(self, t=None):
+        if t:
+            return self.array.astype(t)
+        return self.array
+
+    # Array as sequence
+    def __len__(self):
+        return len(self.array)
+
+    def __getitem__(self, index):
+        return self._rc(self.array[index])
+
+    def __setitem__(self, index, value):
+        self.array[index] = asarray(value, self.dtype)
+
+    def __abs__(self):
+        return self._rc(absolute(self.array))
+
+    def __neg__(self):
+        return self._rc(-self.array)
+
+    def __add__(self, other):
+        return self._rc(self.array + asarray(other))
+
+    __radd__ = __add__
+
+    def __iadd__(self, other):
+        add(self.array, other, self.array)
+        return self
+
+    def __sub__(self, other):
+        return self._rc(self.array - asarray(other))
+
+    def __rsub__(self, other):
+        return self._rc(asarray(other) - self.array)
+
+    def __isub__(self, other):
+        subtract(self.array, other, self.array)
+        return self
+
+    def __mul__(self, other):
+        return self._rc(multiply(self.array, asarray(other)))
+
+    __rmul__ = __mul__
+
+    def __imul__(self, other):
+        multiply(self.array, other, self.array)
+        return self
+
+    def __div__(self, other):
+        return self._rc(divide(self.array, asarray(other)))
+
+    def __rdiv__(self, other):
+        return self._rc(divide(asarray(other), self.array))
+
+    def __idiv__(self, other):
+        divide(self.array, other, self.array)
+        return self
+
+    def __mod__(self, other):
+        return self._rc(remainder(self.array, other))
+
+    def __rmod__(self, other):
+        return self._rc(remainder(other, self.array))
+
+    def __imod__(self, other):
+        remainder(self.array, other, self.array)
+        return self
+
+    def __divmod__(self, other):
+        return (self._rc(divide(self.array, other)),
+                self._rc(remainder(self.array, other)))
+
+    def __rdivmod__(self, other):
+        return (self._rc(divide(other, self.array)),
+                self._rc(remainder(other, self.array)))
+
+    def __pow__(self, other):
+        return self._rc(power(self.array, asarray(other)))
+
+    def __rpow__(self, other):
+        return self._rc(power(asarray(other), self.array))
+
+    def __ipow__(self, other):
+        power(self.array, other, self.array)
+        return self
+
+    def __lshift__(self, other):
+        return self._rc(left_shift(self.array, other))
+
+    def __rshift__(self, other):
+        return self._rc(right_shift(self.array, other))
+
+    def __rlshift__(self, other):
+        return self._rc(left_shift(other, self.array))
+
+    def __rrshift__(self, other):
+        return self._rc(right_shift(other, self.array))
+
+    def __ilshift__(self, other):
+        left_shift(self.array, other, self.array)
+        return self
+
+    def __irshift__(self, other):
+        right_shift(self.array, other, self.array)
+        return self
+
+    def __and__(self, other):
+        return self._rc(bitwise_and(self.array, other))
+
+    def __rand__(self, other):
+        return self._rc(bitwise_and(other, self.array))
+
+    def __iand__(self, other):
+        bitwise_and(self.array, other, self.array)
+        return self
+
+    def __xor__(self, other):
+        return self._rc(bitwise_xor(self.array, other))
+
+    def __rxor__(self, other):
+        return self._rc(bitwise_xor(other, self.array))
+
+    def __ixor__(self, other):
+        bitwise_xor(self.array, other, self.array)
+        return self
+
+    def __or__(self, other):
+        return self._rc(bitwise_or(self.array, other))
+
+    def __ror__(self, other):
+        return self._rc(bitwise_or(other, self.array))
+
+    def __ior__(self, other):
+        bitwise_or(self.array, other, self.array)
+        return self
+
+    def __pos__(self):
+        return self._rc(self.array)
+
+    def __invert__(self):
+        return self._rc(invert(self.array))
+
+    def _scalarfunc(self, func):
+        if self.ndim == 0:
+            return func(self[0])
+        else:
+            raise TypeError(
+                "only rank-0 arrays can be converted to Python scalars.")
+
+    def __complex__(self):
+        return self._scalarfunc(complex)
+
+    def __float__(self):
+        return self._scalarfunc(float)
+
+    def __int__(self):
+        return self._scalarfunc(int)
+
+    def __hex__(self):
+        return self._scalarfunc(hex)
+
+    def __oct__(self):
+        return self._scalarfunc(oct)
+
+    def __lt__(self, other):
+        return self._rc(less(self.array, other))
+
+    def __le__(self, other):
+        return self._rc(less_equal(self.array, other))
+
+    def __eq__(self, other):
+        return self._rc(equal(self.array, other))
+
+    def __ne__(self, other):
+        return self._rc(not_equal(self.array, other))
+
+    def __gt__(self, other):
+        return self._rc(greater(self.array, other))
+
+    def __ge__(self, other):
+        return self._rc(greater_equal(self.array, other))
+
+    def copy(self):
+        ""
+        return self._rc(self.array.copy())
+
+    def tostring(self):
+        ""
+        return self.array.tostring()
+
+    def tobytes(self):
+        ""
+        return self.array.tobytes()
+
+    def byteswap(self):
+        ""
+        return self._rc(self.array.byteswap())
+
+    def astype(self, typecode):
+        ""
+        return self._rc(self.array.astype(typecode))
+
+    def _rc(self, a):
+        if len(shape(a)) == 0:
+            return a
+        else:
+            return self.__class__(a)
+
+    def __array_wrap__(self, *args):
+        return self.__class__(args[0])
+
+    def __setattr__(self, attr, value):
+        if attr == 'array':
+            object.__setattr__(self, attr, value)
+            return
+        try:
+            self.array.__setattr__(attr, value)
+        except AttributeError:
+            object.__setattr__(self, attr, value)
+
+    # Only called after other approaches fail.
+    def __getattr__(self, attr):
+        if (attr == 'array'):
+            return object.__getattribute__(self, attr)
+        return self.array.__getattribute__(attr)
+
+#############################################################
+# Test of class container
+#############################################################
+if __name__ == '__main__':
+    temp = reshape(arange(10000), (100, 100))
+
+    ua = container(temp)
+    # new object created begin test
+    print(dir(ua))
+    print(shape(ua), ua.shape)  # I have changed Numeric.py
+
+    ua_small = ua[:3, :5]
+    print(ua_small)
+    # this did not change ua[0,0], which is not normal behavior
+    ua_small[0, 0] = 10
+    print(ua_small[0, 0], ua[0, 0])
+    print(sin(ua_small) / 3. * 6. + sqrt(ua_small ** 2))
+    print(less(ua_small, 103), type(less(ua_small, 103)))
+    print(type(ua_small * reshape(arange(15), shape(ua_small))))
+    print(reshape(ua_small, (5, 3)))
+    print(transpose(ua_small))

env-llmeval/lib/python3.10/site-packages/numpy/matrixlib/__init__.py

@@ -0,0 +1,11 @@
+"""Sub-package containing the matrix class and related functions.
+
+"""
+from . import defmatrix
+from .defmatrix import *
+
+__all__ = defmatrix.__all__
+
+from numpy._pytesttester import PytestTester
+test = PytestTester(__name__)
+del PytestTester

env-llmeval/lib/python3.10/site-packages/numpy/matrixlib/__init__.pyi

@@ -0,0 +1,15 @@
+from numpy._pytesttester import PytestTester
+
+from numpy import (
+    matrix as matrix,
+)
+
+from numpy.matrixlib.defmatrix import (
+    bmat as bmat,
+    mat as mat,
+    asmatrix as asmatrix,
+)
+
+__all__: list[str]
+__path__: list[str]
+test: PytestTester

env-llmeval/lib/python3.10/site-packages/numpy/matrixlib/defmatrix.py

@@ -0,0 +1,1114 @@
+__all__ = ['matrix', 'bmat', 'mat', 'asmatrix']
+
+import sys
+import warnings
+import ast
+
+from .._utils import set_module
+import numpy.core.numeric as N
+from numpy.core.numeric import concatenate, isscalar
+# While not in __all__, matrix_power used to be defined here, so we import
+# it for backward compatibility.
+from numpy.linalg import matrix_power
+
+
+def _convert_from_string(data):
+    for char in '[]':
+        data = data.replace(char, '')
+
+    rows = data.split(';')
+    newdata = []
+    count = 0
+    for row in rows:
+        trow = row.split(',')
+        newrow = []
+        for col in trow:
+            temp = col.split()
+            newrow.extend(map(ast.literal_eval, temp))
+        if count == 0:
+            Ncols = len(newrow)
+        elif len(newrow) != Ncols:
+            raise ValueError("Rows not the same size.")
+        count += 1
+        newdata.append(newrow)
+    return newdata
+
+
+@set_module('numpy')
+def 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]])
+
+    """
+    return matrix(data, dtype=dtype, copy=False)
+
+
+@set_module('numpy')
+class matrix(N.ndarray):
+    """
+    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]])
+
+    """
+    __array_priority__ = 10.0
+    def __new__(subtype, data, dtype=None, copy=True):
+        warnings.warn('the matrix subclass is not the recommended way to '
+                      'represent matrices or deal with linear algebra (see '
+                      'https://docs.scipy.org/doc/numpy/user/'
+                      'numpy-for-matlab-users.html). '
+                      'Please adjust your code to use regular ndarray.',
+                      PendingDeprecationWarning, stacklevel=2)
+        if isinstance(data, matrix):
+            dtype2 = data.dtype
+            if (dtype is None):
+                dtype = dtype2
+            if (dtype2 == dtype) and (not copy):
+                return data
+            return data.astype(dtype)
+
+        if isinstance(data, N.ndarray):
+            if dtype is None:
+                intype = data.dtype
+            else:
+                intype = N.dtype(dtype)
+            new = data.view(subtype)
+            if intype != data.dtype:
+                return new.astype(intype)
+            if copy: return new.copy()
+            else: return new
+
+        if isinstance(data, str):
+            data = _convert_from_string(data)
+
+        # now convert data to an array
+        arr = N.array(data, dtype=dtype, copy=copy)
+        ndim = arr.ndim
+        shape = arr.shape
+        if (ndim > 2):
+            raise ValueError("matrix must be 2-dimensional")
+        elif ndim == 0:
+            shape = (1, 1)
+        elif ndim == 1:
+            shape = (1, shape[0])
+
+        order = 'C'
+        if (ndim == 2) and arr.flags.fortran:
+            order = 'F'
+
+        if not (order or arr.flags.contiguous):
+            arr = arr.copy()
+
+        ret = N.ndarray.__new__(subtype, shape, arr.dtype,
+                                buffer=arr,
+                                order=order)
+        return ret
+
+    def __array_finalize__(self, obj):
+        self._getitem = False
+        if (isinstance(obj, matrix) and obj._getitem): return
+        ndim = self.ndim
+        if (ndim == 2):
+            return
+        if (ndim > 2):
+            newshape = tuple([x for x in self.shape if x > 1])
+            ndim = len(newshape)
+            if ndim == 2:
+                self.shape = newshape
+                return
+            elif (ndim > 2):
+                raise ValueError("shape too large to be a matrix.")
+        else:
+            newshape = self.shape
+        if ndim == 0:
+            self.shape = (1, 1)
+        elif ndim == 1:
+            self.shape = (1, newshape[0])
+        return
+
+    def __getitem__(self, index):
+        self._getitem = True
+
+        try:
+            out = N.ndarray.__getitem__(self, index)
+        finally:
+            self._getitem = False
+
+        if not isinstance(out, N.ndarray):
+            return out
+
+        if out.ndim == 0:
+            return out[()]
+        if out.ndim == 1:
+            sh = out.shape[0]
+            # Determine when we should have a column array
+            try:
+                n = len(index)
+            except Exception:
+                n = 0
+            if n > 1 and isscalar(index[1]):
+                out.shape = (sh, 1)
+            else:
+                out.shape = (1, sh)
+        return out
+
+    def __mul__(self, other):
+        if isinstance(other, (N.ndarray, list, tuple)) :
+            # This promotes 1-D vectors to row vectors
+            return N.dot(self, asmatrix(other))
+        if isscalar(other) or not hasattr(other, '__rmul__') :
+            return N.dot(self, other)
+        return NotImplemented
+
+    def __rmul__(self, other):
+        return N.dot(other, self)
+
+    def __imul__(self, other):
+        self[:] = self * other
+        return self
+
+    def __pow__(self, other):
+        return matrix_power(self, other)
+
+    def __ipow__(self, other):
+        self[:] = self ** other
+        return self
+
+    def __rpow__(self, other):
+        return NotImplemented
+
+    def _align(self, axis):
+        """A convenience function for operations that need to preserve axis
+        orientation.
+        """
+        if axis is None:
+            return self[0, 0]
+        elif axis==0:
+            return self
+        elif axis==1:
+            return self.transpose()
+        else:
+            raise ValueError("unsupported axis")
+
+    def _collapse(self, axis):
+        """A convenience function for operations that want to collapse
+        to a scalar like _align, but are using keepdims=True
+        """
+        if axis is None:
+            return self[0, 0]
+        else:
+            return self
+
+    # Necessary because base-class tolist expects dimension
+    #  reduction by x[0]
+    def 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).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]]
+
+        """
+        return self.__array__().tolist()
+
+    # To preserve orientation of result...
+    def 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.]])
+
+        """
+        return N.ndarray.sum(self, axis, dtype, out, keepdims=True)._collapse(axis)
+
+
+    # To update docstring from array to matrix...
+    def 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]])
+
+        """
+        return N.ndarray.squeeze(self, axis=axis)
+
+
+    # To update docstring from array to matrix...
+    def 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]])
+
+        """
+        return N.ndarray.flatten(self, order=order)
+
+    def 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).reshape((3, 4)))
+        >>> x
+        matrix([[ 0,  1,  2,  3],
+                [ 4,  5,  6,  7],
+                [ 8,  9, 10, 11]])
+        >>> x.mean()
+        5.5
+        >>> x.mean(0)
+        matrix([[4., 5., 6., 7.]])
+        >>> x.mean(1)
+        matrix([[ 1.5],
+                [ 5.5],
+                [ 9.5]])
+
+        """
+        return N.ndarray.mean(self, axis, dtype, out, keepdims=True)._collapse(axis)
+
+    def 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).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)
+        matrix([[ 3.26598632,  3.26598632,  3.26598632,  3.26598632]]) # may vary
+        >>> x.std(1)
+        matrix([[ 1.11803399],
+                [ 1.11803399],
+                [ 1.11803399]])
+
+        """
+        return N.ndarray.std(self, axis, dtype, out, ddof, keepdims=True)._collapse(axis)
+
+    def 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).reshape((3, 4)))
+        >>> x
+        matrix([[ 0,  1,  2,  3],
+                [ 4,  5,  6,  7],
+                [ 8,  9, 10, 11]])
+        >>> x.var()
+        11.916666666666666
+        >>> x.var(0)
+        matrix([[ 10.66666667,  10.66666667,  10.66666667,  10.66666667]]) # may vary
+        >>> x.var(1)
+        matrix([[1.25],
+                [1.25],
+                [1.25]])
+
+        """
+        return N.ndarray.var(self, axis, dtype, out, ddof, keepdims=True)._collapse(axis)
+
+    def 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).reshape((3,4))); x
+        matrix([[ 0,  1,  2,  3],
+                [ 4,  5,  6,  7],
+                [ 8,  9, 10, 11]])
+        >>> x.prod()
+        0
+        >>> x.prod(0)
+        matrix([[  0,  45, 120, 231]])
+        >>> x.prod(1)
+        matrix([[   0],
+                [ 840],
+                [7920]])
+
+        """
+        return N.ndarray.prod(self, axis, dtype, out, keepdims=True)._collapse(axis)
+
+    def 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`
+
+        """
+        return N.ndarray.any(self, axis, out, keepdims=True)._collapse(axis)
+
+    def 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).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)
+        matrix([[False, False, False, False]])
+        >>> (x == y).all(1)
+        matrix([[ True],
+                [False],
+                [False]])
+
+        """
+        return N.ndarray.all(self, axis, out, keepdims=True)._collapse(axis)
+
+    def 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).reshape((3,4))); x
+        matrix([[ 0,  1,  2,  3],
+                [ 4,  5,  6,  7],
+                [ 8,  9, 10, 11]])
+        >>> x.max()
+        11
+        >>> x.max(0)
+        matrix([[ 8,  9, 10, 11]])
+        >>> x.max(1)
+        matrix([[ 3],
+                [ 7],
+                [11]])
+
+        """
+        return N.ndarray.max(self, axis, out, keepdims=True)._collapse(axis)
+
+    def 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).reshape((3,4))); x
+        matrix([[ 0,  1,  2,  3],
+                [ 4,  5,  6,  7],
+                [ 8,  9, 10, 11]])
+        >>> x.argmax()
+        11
+        >>> x.argmax(0)
+        matrix([[2, 2, 2, 2]])
+        >>> x.argmax(1)
+        matrix([[3],
+                [3],
+                [3]])
+
+        """
+        return N.ndarray.argmax(self, axis, out)._align(axis)
+
+    def 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).reshape((3,4))); x
+        matrix([[  0,  -1,  -2,  -3],
+                [ -4,  -5,  -6,  -7],
+                [ -8,  -9, -10, -11]])
+        >>> x.min()
+        -11
+        >>> x.min(0)
+        matrix([[ -8,  -9, -10, -11]])
+        >>> x.min(1)
+        matrix([[ -3],
+                [ -7],
+                [-11]])
+
+        """
+        return N.ndarray.min(self, axis, out, keepdims=True)._collapse(axis)
+
+    def 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).reshape((3,4))); x
+        matrix([[  0,  -1,  -2,  -3],
+                [ -4,  -5,  -6,  -7],
+                [ -8,  -9, -10, -11]])
+        >>> x.argmin()
+        11
+        >>> x.argmin(0)
+        matrix([[2, 2, 2, 2]])
+        >>> x.argmin(1)
+        matrix([[3],
+                [3],
+                [3]])
+
+        """
+        return N.ndarray.argmin(self, axis, out)._align(axis)
+
+    def 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).reshape((3,4))); x
+        matrix([[ 0,  1,  2,  3],
+                [ 4,  5,  6,  7],
+                [ 8,  9, 10, 11]])
+        >>> x.ptp()
+        11
+        >>> x.ptp(0)
+        matrix([[8, 8, 8, 8]])
+        >>> x.ptp(1)
+        matrix([[3],
+                [3],
+                [3]])
+
+        """
+        return N.ndarray.ptp(self, axis, out)._align(axis)
+
+    @property
+    def 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.]])
+
+        """
+        M, N = self.shape
+        if M == N:
+            from numpy.linalg import inv as func
+        else:
+            from numpy.linalg import pinv as func
+        return asmatrix(func(self))
+
+    @property
+    def 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).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]])
+
+        """
+        return self.__array__()
+
+    @property
+    def 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).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])
+
+
+        """
+        return self.__array__().ravel()
+
+
+    def 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
+
+        """
+        return N.ndarray.ravel(self, order=order)
+
+    @property
+    def 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]])
+
+        """
+        return self.transpose()
+
+    @property
+    def 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).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]])
+
+        """
+        if issubclass(self.dtype.type, N.complexfloating):
+            return self.transpose().conjugate()
+        else:
+            return self.transpose()
+
+    # kept for compatibility
+    getT = T.fget
+    getA = A.fget
+    getA1 = A1.fget
+    getH = H.fget
+    getI = I.fget
+
+def _from_string(str, gdict, ldict):
+    rows = str.split(';')
+    rowtup = []
+    for row in rows:
+        trow = row.split(',')
+        newrow = []
+        for x in trow:
+            newrow.extend(x.split())
+        trow = newrow
+        coltup = []
+        for col in trow:
+            col = col.strip()
+            try:
+                thismat = ldict[col]
+            except KeyError:
+                try:
+                    thismat = gdict[col]
+                except KeyError as e:
+                    raise NameError(f"name {col!r} is not defined") from None
+
+            coltup.append(thismat)
+        rowtup.append(concatenate(coltup, axis=-1))
+    return concatenate(rowtup, axis=0)
+
+
+@set_module('numpy')
+def bmat(obj, ldict=None, gdict=None):
+    """
+    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]])
+
+    """
+    if isinstance(obj, str):
+        if gdict is None:
+            # get previous frame
+            frame = sys._getframe().f_back
+            glob_dict = frame.f_globals
+            loc_dict = frame.f_locals
+        else:
+            glob_dict = gdict
+            loc_dict = ldict
+
+        return matrix(_from_string(obj, glob_dict, loc_dict))
+
+    if isinstance(obj, (tuple, list)):
+        # [[A,B],[C,D]]
+        arr_rows = []
+        for row in obj:
+            if isinstance(row, N.ndarray):  # not 2-d
+                return matrix(concatenate(obj, axis=-1))
+            else:
+                arr_rows.append(concatenate(row, axis=-1))
+        return matrix(concatenate(arr_rows, axis=0))
+    if isinstance(obj, N.ndarray):
+        return matrix(obj)
+
+mat = asmatrix

env-llmeval/lib/python3.10/site-packages/numpy/matrixlib/defmatrix.pyi

@@ -0,0 +1,16 @@
+from collections.abc import Sequence, Mapping
+from typing import Any
+from numpy import matrix as matrix
+from numpy._typing import ArrayLike, DTypeLike, NDArray
+
+__all__: list[str]
+
+def bmat(
+    obj: str | Sequence[ArrayLike] | NDArray[Any],
+    ldict: None | Mapping[str, Any] = ...,
+    gdict: None | Mapping[str, Any] = ...,
+) -> matrix[Any, Any]: ...
+
+def asmatrix(data: ArrayLike, dtype: DTypeLike = ...) -> matrix[Any, Any]: ...
+
+mat = asmatrix

env-llmeval/lib/python3.10/site-packages/numpy/matrixlib/setup.py

@@ -0,0 +1,12 @@
+#!/usr/bin/env python3
+def configuration(parent_package='', top_path=None):
+    from numpy.distutils.misc_util import Configuration
+    config = Configuration('matrixlib', parent_package, top_path)
+    config.add_subpackage('tests')
+    config.add_data_files('*.pyi')
+    return config
+
+if __name__ == "__main__":
+    from numpy.distutils.core import setup
+    config = configuration(top_path='').todict()
+    setup(**config)

env-llmeval/lib/python3.10/site-packages/numpy/matrixlib/tests/test_defmatrix.py

@@ -0,0 +1,453 @@
+import collections.abc
+
+import numpy as np
+from numpy import matrix, asmatrix, bmat
+from numpy.testing import (
+    assert_, assert_equal, assert_almost_equal, assert_array_equal,
+    assert_array_almost_equal, assert_raises
+    )
+from numpy.linalg import matrix_power
+from numpy.matrixlib import mat
+
+class TestCtor:
+    def test_basic(self):
+        A = np.array([[1, 2], [3, 4]])
+        mA = matrix(A)
+        assert_(np.all(mA.A == A))
+
+        B = bmat("A,A;A,A")
+        C = bmat([[A, A], [A, A]])
+        D = np.array([[1, 2, 1, 2],
+                      [3, 4, 3, 4],
+                      [1, 2, 1, 2],
+                      [3, 4, 3, 4]])
+        assert_(np.all(B.A == D))
+        assert_(np.all(C.A == D))
+
+        E = np.array([[5, 6], [7, 8]])
+        AEresult = matrix([[1, 2, 5, 6], [3, 4, 7, 8]])
+        assert_(np.all(bmat([A, E]) == AEresult))
+
+        vec = np.arange(5)
+        mvec = matrix(vec)
+        assert_(mvec.shape == (1, 5))
+
+    def test_exceptions(self):
+        # Check for ValueError when called with invalid string data.
+        assert_raises(ValueError, matrix, "invalid")
+
+    def test_bmat_nondefault_str(self):
+        A = np.array([[1, 2], [3, 4]])
+        B = np.array([[5, 6], [7, 8]])
+        Aresult = np.array([[1, 2, 1, 2],
+                            [3, 4, 3, 4],
+                            [1, 2, 1, 2],
+                            [3, 4, 3, 4]])
+        mixresult = np.array([[1, 2, 5, 6],
+                              [3, 4, 7, 8],
+                              [5, 6, 1, 2],
+                              [7, 8, 3, 4]])
+        assert_(np.all(bmat("A,A;A,A") == Aresult))
+        assert_(np.all(bmat("A,A;A,A", ldict={'A':B}) == Aresult))
+        assert_raises(TypeError, bmat, "A,A;A,A", gdict={'A':B})
+        assert_(
+            np.all(bmat("A,A;A,A", ldict={'A':A}, gdict={'A':B}) == Aresult))
+        b2 = bmat("A,B;C,D", ldict={'A':A,'B':B}, gdict={'C':B,'D':A})
+        assert_(np.all(b2 == mixresult))
+
+
+class TestProperties:
+    def test_sum(self):
+        """Test whether matrix.sum(axis=1) preserves orientation.
+        Fails in NumPy <= 0.9.6.2127.
+        """
+        M = matrix([[1, 2, 0, 0],
+                   [3, 4, 0, 0],
+                   [1, 2, 1, 2],
+                   [3, 4, 3, 4]])
+        sum0 = matrix([8, 12, 4, 6])
+        sum1 = matrix([3, 7, 6, 14]).T
+        sumall = 30
+        assert_array_equal(sum0, M.sum(axis=0))
+        assert_array_equal(sum1, M.sum(axis=1))
+        assert_equal(sumall, M.sum())
+
+        assert_array_equal(sum0, np.sum(M, axis=0))
+        assert_array_equal(sum1, np.sum(M, axis=1))
+        assert_equal(sumall, np.sum(M))
+
+    def test_prod(self):
+        x = matrix([[1, 2, 3], [4, 5, 6]])
+        assert_equal(x.prod(), 720)
+        assert_equal(x.prod(0), matrix([[4, 10, 18]]))
+        assert_equal(x.prod(1), matrix([[6], [120]]))
+
+        assert_equal(np.prod(x), 720)
+        assert_equal(np.prod(x, axis=0), matrix([[4, 10, 18]]))
+        assert_equal(np.prod(x, axis=1), matrix([[6], [120]]))
+
+        y = matrix([0, 1, 3])
+        assert_(y.prod() == 0)
+
+    def test_max(self):
+        x = matrix([[1, 2, 3], [4, 5, 6]])
+        assert_equal(x.max(), 6)
+        assert_equal(x.max(0), matrix([[4, 5, 6]]))
+        assert_equal(x.max(1), matrix([[3], [6]]))
+
+        assert_equal(np.max(x), 6)
+        assert_equal(np.max(x, axis=0), matrix([[4, 5, 6]]))
+        assert_equal(np.max(x, axis=1), matrix([[3], [6]]))
+
+    def test_min(self):
+        x = matrix([[1, 2, 3], [4, 5, 6]])
+        assert_equal(x.min(), 1)
+        assert_equal(x.min(0), matrix([[1, 2, 3]]))
+        assert_equal(x.min(1), matrix([[1], [4]]))
+
+        assert_equal(np.min(x), 1)
+        assert_equal(np.min(x, axis=0), matrix([[1, 2, 3]]))
+        assert_equal(np.min(x, axis=1), matrix([[1], [4]]))
+
+    def test_ptp(self):
+        x = np.arange(4).reshape((2, 2))
+        assert_(x.ptp() == 3)
+        assert_(np.all(x.ptp(0) == np.array([2, 2])))
+        assert_(np.all(x.ptp(1) == np.array([1, 1])))
+
+    def test_var(self):
+        x = np.arange(9).reshape((3, 3))
+        mx = x.view(np.matrix)
+        assert_equal(x.var(ddof=0), mx.var(ddof=0))
+        assert_equal(x.var(ddof=1), mx.var(ddof=1))
+
+    def test_basic(self):
+        import numpy.linalg as linalg
+
+        A = np.array([[1., 2.],
+                      [3., 4.]])
+        mA = matrix(A)
+        assert_(np.allclose(linalg.inv(A), mA.I))
+        assert_(np.all(np.array(np.transpose(A) == mA.T)))
+        assert_(np.all(np.array(np.transpose(A) == mA.H)))
+        assert_(np.all(A == mA.A))
+
+        B = A + 2j*A
+        mB = matrix(B)
+        assert_(np.allclose(linalg.inv(B), mB.I))
+        assert_(np.all(np.array(np.transpose(B) == mB.T)))
+        assert_(np.all(np.array(np.transpose(B).conj() == mB.H)))
+
+    def test_pinv(self):
+        x = matrix(np.arange(6).reshape(2, 3))
+        xpinv = matrix([[-0.77777778,  0.27777778],
+                        [-0.11111111,  0.11111111],
+                        [ 0.55555556, -0.05555556]])
+        assert_almost_equal(x.I, xpinv)
+
+    def test_comparisons(self):
+        A = np.arange(100).reshape(10, 10)
+        mA = matrix(A)
+        mB = matrix(A) + 0.1
+        assert_(np.all(mB == A+0.1))
+        assert_(np.all(mB == matrix(A+0.1)))
+        assert_(not np.any(mB == matrix(A-0.1)))
+        assert_(np.all(mA < mB))
+        assert_(np.all(mA <= mB))
+        assert_(np.all(mA <= mA))
+        assert_(not np.any(mA < mA))
+
+        assert_(not np.any(mB < mA))
+        assert_(np.all(mB >= mA))
+        assert_(np.all(mB >= mB))
+        assert_(not np.any(mB > mB))
+
+        assert_(np.all(mA == mA))
+        assert_(not np.any(mA == mB))
+        assert_(np.all(mB != mA))
+
+        assert_(not np.all(abs(mA) > 0))
+        assert_(np.all(abs(mB > 0)))
+
+    def test_asmatrix(self):
+        A = np.arange(100).reshape(10, 10)
+        mA = asmatrix(A)
+        A[0, 0] = -10
+        assert_(A[0, 0] == mA[0, 0])
+
+    def test_noaxis(self):
+        A = matrix([[1, 0], [0, 1]])
+        assert_(A.sum() == matrix(2))
+        assert_(A.mean() == matrix(0.5))
+
+    def test_repr(self):
+        A = matrix([[1, 0], [0, 1]])
+        assert_(repr(A) == "matrix([[1, 0],\n        [0, 1]])")
+
+    def test_make_bool_matrix_from_str(self):
+        A = matrix('True; True; False')
+        B = matrix([[True], [True], [False]])
+        assert_array_equal(A, B)
+
+class TestCasting:
+    def test_basic(self):
+        A = np.arange(100).reshape(10, 10)
+        mA = matrix(A)
+
+        mB = mA.copy()
+        O = np.ones((10, 10), np.float64) * 0.1
+        mB = mB + O
+        assert_(mB.dtype.type == np.float64)
+        assert_(np.all(mA != mB))
+        assert_(np.all(mB == mA+0.1))
+
+        mC = mA.copy()
+        O = np.ones((10, 10), np.complex128)
+        mC = mC * O
+        assert_(mC.dtype.type == np.complex128)
+        assert_(np.all(mA != mB))
+
+
+class TestAlgebra:
+    def test_basic(self):
+        import numpy.linalg as linalg
+
+        A = np.array([[1., 2.], [3., 4.]])
+        mA = matrix(A)
+
+        B = np.identity(2)
+        for i in range(6):
+            assert_(np.allclose((mA ** i).A, B))
+            B = np.dot(B, A)
+
+        Ainv = linalg.inv(A)
+        B = np.identity(2)
+        for i in range(6):
+            assert_(np.allclose((mA ** -i).A, B))
+            B = np.dot(B, Ainv)
+
+        assert_(np.allclose((mA * mA).A, np.dot(A, A)))
+        assert_(np.allclose((mA + mA).A, (A + A)))
+        assert_(np.allclose((3*mA).A, (3*A)))
+
+        mA2 = matrix(A)
+        mA2 *= 3
+        assert_(np.allclose(mA2.A, 3*A))
+
+    def test_pow(self):
+        """Test raising a matrix to an integer power works as expected."""
+        m = matrix("1. 2.; 3. 4.")
+        m2 = m.copy()
+        m2 **= 2
+        mi = m.copy()
+        mi **= -1
+        m4 = m2.copy()
+        m4 **= 2
+        assert_array_almost_equal(m2, m**2)
+        assert_array_almost_equal(m4, np.dot(m2, m2))
+        assert_array_almost_equal(np.dot(mi, m), np.eye(2))
+
+    def test_scalar_type_pow(self):
+        m = matrix([[1, 2], [3, 4]])
+        for scalar_t in [np.int8, np.uint8]:
+            two = scalar_t(2)
+            assert_array_almost_equal(m ** 2, m ** two)
+
+    def test_notimplemented(self):
+        '''Check that 'not implemented' operations produce a failure.'''
+        A = matrix([[1., 2.],
+                    [3., 4.]])
+
+        # __rpow__
+        with assert_raises(TypeError):
+            1.0**A
+
+        # __mul__ with something not a list, ndarray, tuple, or scalar
+        with assert_raises(TypeError):
+            A*object()
+
+
+class TestMatrixReturn:
+    def test_instance_methods(self):
+        a = matrix([1.0], dtype='f8')
+        methodargs = {
+            'astype': ('intc',),
+            'clip': (0.0, 1.0),
+            'compress': ([1],),
+            'repeat': (1,),
+            'reshape': (1,),
+            'swapaxes': (0, 0),
+            'dot': np.array([1.0]),
+            }
+        excluded_methods = [
+            'argmin', 'choose', 'dump', 'dumps', 'fill', 'getfield',
+            'getA', 'getA1', 'item', 'nonzero', 'put', 'putmask', 'resize',
+            'searchsorted', 'setflags', 'setfield', 'sort',
+            'partition', 'argpartition',
+            'take', 'tofile', 'tolist', 'tostring', 'tobytes', 'all', 'any',
+            'sum', 'argmax', 'argmin', 'min', 'max', 'mean', 'var', 'ptp',
+            'prod', 'std', 'ctypes', 'itemset',
+            ]
+        for attrib in dir(a):
+            if attrib.startswith('_') or attrib in excluded_methods:
+                continue
+            f = getattr(a, attrib)
+            if isinstance(f, collections.abc.Callable):
+                # reset contents of a
+                a.astype('f8')
+                a.fill(1.0)
+                if attrib in methodargs:
+                    args = methodargs[attrib]
+                else:
+                    args = ()
+                b = f(*args)
+                assert_(type(b) is matrix, "%s" % attrib)
+        assert_(type(a.real) is matrix)
+        assert_(type(a.imag) is matrix)
+        c, d = matrix([0.0]).nonzero()
+        assert_(type(c) is np.ndarray)
+        assert_(type(d) is np.ndarray)
+
+
+class TestIndexing:
+    def test_basic(self):
+        x = asmatrix(np.zeros((3, 2), float))
+        y = np.zeros((3, 1), float)
+        y[:, 0] = [0.8, 0.2, 0.3]
+        x[:, 1] = y > 0.5
+        assert_equal(x, [[0, 1], [0, 0], [0, 0]])
+
+
+class TestNewScalarIndexing:
+    a = matrix([[1, 2], [3, 4]])
+
+    def test_dimesions(self):
+        a = self.a
+        x = a[0]
+        assert_equal(x.ndim, 2)
+
+    def test_array_from_matrix_list(self):
+        a = self.a
+        x = np.array([a, a])
+        assert_equal(x.shape, [2, 2, 2])
+
+    def test_array_to_list(self):
+        a = self.a
+        assert_equal(a.tolist(), [[1, 2], [3, 4]])
+
+    def test_fancy_indexing(self):
+        a = self.a
+        x = a[1, [0, 1, 0]]
+        assert_(isinstance(x, matrix))
+        assert_equal(x, matrix([[3,  4,  3]]))
+        x = a[[1, 0]]
+        assert_(isinstance(x, matrix))
+        assert_equal(x, matrix([[3,  4], [1, 2]]))
+        x = a[[[1], [0]], [[1, 0], [0, 1]]]
+        assert_(isinstance(x, matrix))
+        assert_equal(x, matrix([[4,  3], [1,  2]]))
+
+    def test_matrix_element(self):
+        x = matrix([[1, 2, 3], [4, 5, 6]])
+        assert_equal(x[0][0], matrix([[1, 2, 3]]))
+        assert_equal(x[0][0].shape, (1, 3))
+        assert_equal(x[0].shape, (1, 3))
+        assert_equal(x[:, 0].shape, (2, 1))
+
+        x = matrix(0)
+        assert_equal(x[0, 0], 0)
+        assert_equal(x[0], 0)
+        assert_equal(x[:, 0].shape, x.shape)
+
+    def test_scalar_indexing(self):
+        x = asmatrix(np.zeros((3, 2), float))
+        assert_equal(x[0, 0], x[0][0])
+
+    def test_row_column_indexing(self):
+        x = asmatrix(np.eye(2))
+        assert_array_equal(x[0,:], [[1, 0]])
+        assert_array_equal(x[1,:], [[0, 1]])
+        assert_array_equal(x[:, 0], [[1], [0]])
+        assert_array_equal(x[:, 1], [[0], [1]])
+
+    def test_boolean_indexing(self):
+        A = np.arange(6)
+        A.shape = (3, 2)
+        x = asmatrix(A)
+        assert_array_equal(x[:, np.array([True, False])], x[:, 0])
+        assert_array_equal(x[np.array([True, False, False]),:], x[0,:])
+
+    def test_list_indexing(self):
+        A = np.arange(6)
+        A.shape = (3, 2)
+        x = asmatrix(A)
+        assert_array_equal(x[:, [1, 0]], x[:, ::-1])
+        assert_array_equal(x[[2, 1, 0],:], x[::-1,:])
+
+
+class TestPower:
+    def test_returntype(self):
+        a = np.array([[0, 1], [0, 0]])
+        assert_(type(matrix_power(a, 2)) is np.ndarray)
+        a = mat(a)
+        assert_(type(matrix_power(a, 2)) is matrix)
+
+    def test_list(self):
+        assert_array_equal(matrix_power([[0, 1], [0, 0]], 2), [[0, 0], [0, 0]])
+
+
+class TestShape:
+
+    a = np.array([[1], [2]])
+    m = matrix([[1], [2]])
+
+    def test_shape(self):
+        assert_equal(self.a.shape, (2, 1))
+        assert_equal(self.m.shape, (2, 1))
+
+    def test_numpy_ravel(self):
+        assert_equal(np.ravel(self.a).shape, (2,))
+        assert_equal(np.ravel(self.m).shape, (2,))
+
+    def test_member_ravel(self):
+        assert_equal(self.a.ravel().shape, (2,))
+        assert_equal(self.m.ravel().shape, (1, 2))
+
+    def test_member_flatten(self):
+        assert_equal(self.a.flatten().shape, (2,))
+        assert_equal(self.m.flatten().shape, (1, 2))
+
+    def test_numpy_ravel_order(self):
+        x = np.array([[1, 2, 3], [4, 5, 6]])
+        assert_equal(np.ravel(x), [1, 2, 3, 4, 5, 6])
+        assert_equal(np.ravel(x, order='F'), [1, 4, 2, 5, 3, 6])
+        assert_equal(np.ravel(x.T), [1, 4, 2, 5, 3, 6])
+        assert_equal(np.ravel(x.T, order='A'), [1, 2, 3, 4, 5, 6])
+        x = matrix([[1, 2, 3], [4, 5, 6]])
+        assert_equal(np.ravel(x), [1, 2, 3, 4, 5, 6])
+        assert_equal(np.ravel(x, order='F'), [1, 4, 2, 5, 3, 6])
+        assert_equal(np.ravel(x.T), [1, 4, 2, 5, 3, 6])
+        assert_equal(np.ravel(x.T, order='A'), [1, 2, 3, 4, 5, 6])
+
+    def test_matrix_ravel_order(self):
+        x = matrix([[1, 2, 3], [4, 5, 6]])
+        assert_equal(x.ravel(), [[1, 2, 3, 4, 5, 6]])
+        assert_equal(x.ravel(order='F'), [[1, 4, 2, 5, 3, 6]])
+        assert_equal(x.T.ravel(), [[1, 4, 2, 5, 3, 6]])
+        assert_equal(x.T.ravel(order='A'), [[1, 2, 3, 4, 5, 6]])
+
+    def test_array_memory_sharing(self):
+        assert_(np.may_share_memory(self.a, self.a.ravel()))
+        assert_(not np.may_share_memory(self.a, self.a.flatten()))
+
+    def test_matrix_memory_sharing(self):
+        assert_(np.may_share_memory(self.m, self.m.ravel()))
+        assert_(not np.may_share_memory(self.m, self.m.flatten()))
+
+    def test_expand_dims_matrix(self):
+        # matrices are always 2d - so expand_dims only makes sense when the
+        # type is changed away from matrix.
+        a = np.arange(10).reshape((2, 5)).view(np.matrix)
+        expanded = np.expand_dims(a, axis=1)
+        assert_equal(expanded.ndim, 3)
+        assert_(not isinstance(expanded, np.matrix))

env-llmeval/lib/python3.10/site-packages/numpy/matrixlib/tests/test_interaction.py

@@ -0,0 +1,354 @@
+"""Tests of interaction of matrix with other parts of numpy.
+
+Note that tests with MaskedArray and linalg are done in separate files.
+"""
+import pytest
+
+import textwrap
+import warnings
+
+import numpy as np
+from numpy.testing import (assert_, assert_equal, assert_raises,
+                           assert_raises_regex, assert_array_equal,
+                           assert_almost_equal, assert_array_almost_equal)
+
+
+def test_fancy_indexing():
+    # The matrix class messes with the shape. While this is always
+    # weird (getitem is not used, it does not have setitem nor knows
+    # about fancy indexing), this tests gh-3110
+    # 2018-04-29: moved here from core.tests.test_index.
+    m = np.matrix([[1, 2], [3, 4]])
+
+    assert_(isinstance(m[[0, 1, 0], :], np.matrix))
+
+    # gh-3110. Note the transpose currently because matrices do *not*
+    # support dimension fixing for fancy indexing correctly.
+    x = np.asmatrix(np.arange(50).reshape(5, 10))
+    assert_equal(x[:2, np.array(-1)], x[:2, -1].T)
+
+
+def test_polynomial_mapdomain():
+    # test that polynomial preserved matrix subtype.
+    # 2018-04-29: moved here from polynomial.tests.polyutils.
+    dom1 = [0, 4]
+    dom2 = [1, 3]
+    x = np.matrix([dom1, dom1])
+    res = np.polynomial.polyutils.mapdomain(x, dom1, dom2)
+    assert_(isinstance(res, np.matrix))
+
+
+def test_sort_matrix_none():
+    # 2018-04-29: moved here from core.tests.test_multiarray
+    a = np.matrix([[2, 1, 0]])
+    actual = np.sort(a, axis=None)
+    expected = np.matrix([[0, 1, 2]])
+    assert_equal(actual, expected)
+    assert_(type(expected) is np.matrix)
+
+
+def test_partition_matrix_none():
+    # gh-4301
+    # 2018-04-29: moved here from core.tests.test_multiarray
+    a = np.matrix([[2, 1, 0]])
+    actual = np.partition(a, 1, axis=None)
+    expected = np.matrix([[0, 1, 2]])
+    assert_equal(actual, expected)
+    assert_(type(expected) is np.matrix)
+
+
+def test_dot_scalar_and_matrix_of_objects():
+    # Ticket #2469
+    # 2018-04-29: moved here from core.tests.test_multiarray
+    arr = np.matrix([1, 2], dtype=object)
+    desired = np.matrix([[3, 6]], dtype=object)
+    assert_equal(np.dot(arr, 3), desired)
+    assert_equal(np.dot(3, arr), desired)
+
+
+def test_inner_scalar_and_matrix():
+    # 2018-04-29: moved here from core.tests.test_multiarray
+    for dt in np.typecodes['AllInteger'] + np.typecodes['AllFloat'] + '?':
+        sca = np.array(3, dtype=dt)[()]
+        arr = np.matrix([[1, 2], [3, 4]], dtype=dt)
+        desired = np.matrix([[3, 6], [9, 12]], dtype=dt)
+        assert_equal(np.inner(arr, sca), desired)
+        assert_equal(np.inner(sca, arr), desired)
+
+
+def test_inner_scalar_and_matrix_of_objects():
+    # Ticket #4482
+    # 2018-04-29: moved here from core.tests.test_multiarray
+    arr = np.matrix([1, 2], dtype=object)
+    desired = np.matrix([[3, 6]], dtype=object)
+    assert_equal(np.inner(arr, 3), desired)
+    assert_equal(np.inner(3, arr), desired)
+
+
+def test_iter_allocate_output_subtype():
+    # Make sure that the subtype with priority wins
+    # 2018-04-29: moved here from core.tests.test_nditer, given the
+    # matrix specific shape test.
+
+    # matrix vs ndarray
+    a = np.matrix([[1, 2], [3, 4]])
+    b = np.arange(4).reshape(2, 2).T
+    i = np.nditer([a, b, None], [],
+                  [['readonly'], ['readonly'], ['writeonly', 'allocate']])
+    assert_(type(i.operands[2]) is np.matrix)
+    assert_(type(i.operands[2]) is not np.ndarray)
+    assert_equal(i.operands[2].shape, (2, 2))
+
+    # matrix always wants things to be 2D
+    b = np.arange(4).reshape(1, 2, 2)
+    assert_raises(RuntimeError, np.nditer, [a, b, None], [],
+                  [['readonly'], ['readonly'], ['writeonly', 'allocate']])
+    # but if subtypes are disabled, the result can still work
+    i = np.nditer([a, b, None], [],
+                  [['readonly'], ['readonly'],
+                   ['writeonly', 'allocate', 'no_subtype']])
+    assert_(type(i.operands[2]) is np.ndarray)
+    assert_(type(i.operands[2]) is not np.matrix)
+    assert_equal(i.operands[2].shape, (1, 2, 2))
+
+
+def like_function():
+    # 2018-04-29: moved here from core.tests.test_numeric
+    a = np.matrix([[1, 2], [3, 4]])
+    for like_function in np.zeros_like, np.ones_like, np.empty_like:
+        b = like_function(a)
+        assert_(type(b) is np.matrix)
+
+        c = like_function(a, subok=False)
+        assert_(type(c) is not np.matrix)
+
+
+def test_array_astype():
+    # 2018-04-29: copied here from core.tests.test_api
+    # subok=True passes through a matrix
+    a = np.matrix([[0, 1, 2], [3, 4, 5]], dtype='f4')
+    b = a.astype('f4', subok=True, copy=False)
+    assert_(a is b)
+
+    # subok=True is default, and creates a subtype on a cast
+    b = a.astype('i4', copy=False)
+    assert_equal(a, b)
+    assert_equal(type(b), np.matrix)
+
+    # subok=False never returns a matrix
+    b = a.astype('f4', subok=False, copy=False)
+    assert_equal(a, b)
+    assert_(not (a is b))
+    assert_(type(b) is not np.matrix)
+
+
+def test_stack():
+    # 2018-04-29: copied here from core.tests.test_shape_base
+    # check np.matrix cannot be stacked
+    m = np.matrix([[1, 2], [3, 4]])
+    assert_raises_regex(ValueError, 'shape too large to be a matrix',
+                        np.stack, [m, m])
+
+
+def test_object_scalar_multiply():
+    # Tickets #2469 and #4482
+    # 2018-04-29: moved here from core.tests.test_ufunc
+    arr = np.matrix([1, 2], dtype=object)
+    desired = np.matrix([[3, 6]], dtype=object)
+    assert_equal(np.multiply(arr, 3), desired)
+    assert_equal(np.multiply(3, arr), desired)
+
+
+def test_nanfunctions_matrices():
+    # Check that it works and that type and
+    # shape are preserved
+    # 2018-04-29: moved here from core.tests.test_nanfunctions
+    mat = np.matrix(np.eye(3))
+    for f in [np.nanmin, np.nanmax]:
+        res = f(mat, axis=0)
+        assert_(isinstance(res, np.matrix))
+        assert_(res.shape == (1, 3))
+        res = f(mat, axis=1)
+        assert_(isinstance(res, np.matrix))
+        assert_(res.shape == (3, 1))
+        res = f(mat)
+        assert_(np.isscalar(res))
+    # check that rows of nan are dealt with for subclasses (#4628)
+    mat[1] = np.nan
+    for f in [np.nanmin, np.nanmax]:
+        with warnings.catch_warnings(record=True) as w:
+            warnings.simplefilter('always')
+            res = f(mat, axis=0)
+            assert_(isinstance(res, np.matrix))
+            assert_(not np.any(np.isnan(res)))
+            assert_(len(w) == 0)
+
+        with warnings.catch_warnings(record=True) as w:
+            warnings.simplefilter('always')
+            res = f(mat, axis=1)
+            assert_(isinstance(res, np.matrix))
+            assert_(np.isnan(res[1, 0]) and not np.isnan(res[0, 0])
+                    and not np.isnan(res[2, 0]))
+            assert_(len(w) == 1, 'no warning raised')
+            assert_(issubclass(w[0].category, RuntimeWarning))
+
+        with warnings.catch_warnings(record=True) as w:
+            warnings.simplefilter('always')
+            res = f(mat)
+            assert_(np.isscalar(res))
+            assert_(res != np.nan)
+            assert_(len(w) == 0)
+
+
+def test_nanfunctions_matrices_general():
+    # Check that it works and that type and
+    # shape are preserved
+    # 2018-04-29: moved here from core.tests.test_nanfunctions
+    mat = np.matrix(np.eye(3))
+    for f in (np.nanargmin, np.nanargmax, np.nansum, np.nanprod,
+              np.nanmean, np.nanvar, np.nanstd):
+        res = f(mat, axis=0)
+        assert_(isinstance(res, np.matrix))
+        assert_(res.shape == (1, 3))
+        res = f(mat, axis=1)
+        assert_(isinstance(res, np.matrix))
+        assert_(res.shape == (3, 1))
+        res = f(mat)
+        assert_(np.isscalar(res))
+
+    for f in np.nancumsum, np.nancumprod:
+        res = f(mat, axis=0)
+        assert_(isinstance(res, np.matrix))
+        assert_(res.shape == (3, 3))
+        res = f(mat, axis=1)
+        assert_(isinstance(res, np.matrix))
+        assert_(res.shape == (3, 3))
+        res = f(mat)
+        assert_(isinstance(res, np.matrix))
+        assert_(res.shape == (1, 3*3))
+
+
+def test_average_matrix():
+    # 2018-04-29: moved here from core.tests.test_function_base.
+    y = np.matrix(np.random.rand(5, 5))
+    assert_array_equal(y.mean(0), np.average(y, 0))
+
+    a = np.matrix([[1, 2], [3, 4]])
+    w = np.matrix([[1, 2], [3, 4]])
+
+    r = np.average(a, axis=0, weights=w)
+    assert_equal(type(r), np.matrix)
+    assert_equal(r, [[2.5, 10.0/3]])
+
+
+def test_trapz_matrix():
+    # Test to make sure matrices give the same answer as ndarrays
+    # 2018-04-29: moved here from core.tests.test_function_base.
+    x = np.linspace(0, 5)
+    y = x * x
+    r = np.trapz(y, x)
+    mx = np.matrix(x)
+    my = np.matrix(y)
+    mr = np.trapz(my, mx)
+    assert_almost_equal(mr, r)
+
+
+def test_ediff1d_matrix():
+    # 2018-04-29: moved here from core.tests.test_arraysetops.
+    assert(isinstance(np.ediff1d(np.matrix(1)), np.matrix))
+    assert(isinstance(np.ediff1d(np.matrix(1), to_begin=1), np.matrix))
+
+
+def test_apply_along_axis_matrix():
+    # this test is particularly malicious because matrix
+    # refuses to become 1d
+    # 2018-04-29: moved here from core.tests.test_shape_base.
+    def double(row):
+        return row * 2
+
+    m = np.matrix([[0, 1], [2, 3]])
+    expected = np.matrix([[0, 2], [4, 6]])
+
+    result = np.apply_along_axis(double, 0, m)
+    assert_(isinstance(result, np.matrix))
+    assert_array_equal(result, expected)
+
+    result = np.apply_along_axis(double, 1, m)
+    assert_(isinstance(result, np.matrix))
+    assert_array_equal(result, expected)
+
+
+def test_kron_matrix():
+    # 2018-04-29: moved here from core.tests.test_shape_base.
+    a = np.ones([2, 2])
+    m = np.asmatrix(a)
+    assert_equal(type(np.kron(a, a)), np.ndarray)
+    assert_equal(type(np.kron(m, m)), np.matrix)
+    assert_equal(type(np.kron(a, m)), np.matrix)
+    assert_equal(type(np.kron(m, a)), np.matrix)
+
+
+class TestConcatenatorMatrix:
+    # 2018-04-29: moved here from core.tests.test_index_tricks.
+    def test_matrix(self):
+        a = [1, 2]
+        b = [3, 4]
+
+        ab_r = np.r_['r', a, b]
+        ab_c = np.r_['c', a, b]
+
+        assert_equal(type(ab_r), np.matrix)
+        assert_equal(type(ab_c), np.matrix)
+
+        assert_equal(np.array(ab_r), [[1, 2, 3, 4]])
+        assert_equal(np.array(ab_c), [[1], [2], [3], [4]])
+
+        assert_raises(ValueError, lambda: np.r_['rc', a, b])
+
+    def test_matrix_scalar(self):
+        r = np.r_['r', [1, 2], 3]
+        assert_equal(type(r), np.matrix)
+        assert_equal(np.array(r), [[1, 2, 3]])
+
+    def test_matrix_builder(self):
+        a = np.array([1])
+        b = np.array([2])
+        c = np.array([3])
+        d = np.array([4])
+        actual = np.r_['a, b; c, d']
+        expected = np.bmat([[a, b], [c, d]])
+
+        assert_equal(actual, expected)
+        assert_equal(type(actual), type(expected))
+
+
+def test_array_equal_error_message_matrix():
+    # 2018-04-29: moved here from testing.tests.test_utils.
+    with pytest.raises(AssertionError) as exc_info:
+        assert_equal(np.array([1, 2]), np.matrix([1, 2]))
+    msg = str(exc_info.value)
+    msg_reference = textwrap.dedent("""\
+
+    Arrays are not equal
+
+    (shapes (2,), (1, 2) mismatch)
+     x: array([1, 2])
+     y: matrix([[1, 2]])""")
+    assert_equal(msg, msg_reference)
+
+
+def test_array_almost_equal_matrix():
+    # Matrix slicing keeps things 2-D, while array does not necessarily.
+    # See gh-8452.
+    # 2018-04-29: moved here from testing.tests.test_utils.
+    m1 = np.matrix([[1., 2.]])
+    m2 = np.matrix([[1., np.nan]])
+    m3 = np.matrix([[1., -np.inf]])
+    m4 = np.matrix([[np.nan, np.inf]])
+    m5 = np.matrix([[1., 2.], [np.nan, np.inf]])
+    for assert_func in assert_array_almost_equal, assert_almost_equal:
+        for m in m1, m2, m3, m4, m5:
+            assert_func(m, m)
+            a = np.array(m)
+            assert_func(a, m)
+            assert_func(m, a)

env-llmeval/lib/python3.10/site-packages/numpy/matrixlib/tests/test_masked_matrix.py

@@ -0,0 +1,231 @@
+import numpy as np
+from numpy.testing import assert_warns
+from numpy.ma.testutils import (assert_, assert_equal, assert_raises,
+                                assert_array_equal)
+from numpy.ma.core import (masked_array, masked_values, masked, allequal,
+                           MaskType, getmask, MaskedArray, nomask,
+                           log, add, hypot, divide)
+from numpy.ma.extras import mr_
+from numpy.compat import pickle
+
+
+class MMatrix(MaskedArray, np.matrix,):
+
+    def __new__(cls, data, mask=nomask):
+        mat = np.matrix(data)
+        _data = MaskedArray.__new__(cls, data=mat, mask=mask)
+        return _data
+
+    def __array_finalize__(self, obj):
+        np.matrix.__array_finalize__(self, obj)
+        MaskedArray.__array_finalize__(self, obj)
+        return
+
+    @property
+    def _series(self):
+        _view = self.view(MaskedArray)
+        _view._sharedmask = False
+        return _view
+
+
+class TestMaskedMatrix:
+    def test_matrix_indexing(self):
+        # Tests conversions and indexing
+        x1 = np.matrix([[1, 2, 3], [4, 3, 2]])
+        x2 = masked_array(x1, mask=[[1, 0, 0], [0, 1, 0]])
+        x3 = masked_array(x1, mask=[[0, 1, 0], [1, 0, 0]])
+        x4 = masked_array(x1)
+        # test conversion to strings
+        str(x2)  # raises?
+        repr(x2)  # raises?
+        # tests of indexing
+        assert_(type(x2[1, 0]) is type(x1[1, 0]))
+        assert_(x1[1, 0] == x2[1, 0])
+        assert_(x2[1, 1] is masked)
+        assert_equal(x1[0, 2], x2[0, 2])
+        assert_equal(x1[0, 1:], x2[0, 1:])
+        assert_equal(x1[:, 2], x2[:, 2])
+        assert_equal(x1[:], x2[:])
+        assert_equal(x1[1:], x3[1:])
+        x1[0, 2] = 9
+        x2[0, 2] = 9
+        assert_equal(x1, x2)
+        x1[0, 1:] = 99
+        x2[0, 1:] = 99
+        assert_equal(x1, x2)
+        x2[0, 1] = masked
+        assert_equal(x1, x2)
+        x2[0, 1:] = masked
+        assert_equal(x1, x2)
+        x2[0, :] = x1[0, :]
+        x2[0, 1] = masked
+        assert_(allequal(getmask(x2), np.array([[0, 1, 0], [0, 1, 0]])))
+        x3[1, :] = masked_array([1, 2, 3], [1, 1, 0])
+        assert_(allequal(getmask(x3)[1], masked_array([1, 1, 0])))
+        assert_(allequal(getmask(x3[1]), masked_array([1, 1, 0])))
+        x4[1, :] = masked_array([1, 2, 3], [1, 1, 0])
+        assert_(allequal(getmask(x4[1]), masked_array([1, 1, 0])))
+        assert_(allequal(x4[1], masked_array([1, 2, 3])))
+        x1 = np.matrix(np.arange(5) * 1.0)
+        x2 = masked_values(x1, 3.0)
+        assert_equal(x1, x2)
+        assert_(allequal(masked_array([0, 0, 0, 1, 0], dtype=MaskType),
+                         x2.mask))
+        assert_equal(3.0, x2.fill_value)
+
+    def test_pickling_subbaseclass(self):
+        # Test pickling w/ a subclass of ndarray
+        a = masked_array(np.matrix(list(range(10))), mask=[1, 0, 1, 0, 0] * 2)
+        for proto in range(2, pickle.HIGHEST_PROTOCOL + 1):
+            a_pickled = pickle.loads(pickle.dumps(a, protocol=proto))
+            assert_equal(a_pickled._mask, a._mask)
+            assert_equal(a_pickled, a)
+            assert_(isinstance(a_pickled._data, np.matrix))
+
+    def test_count_mean_with_matrix(self):
+        m = masked_array(np.matrix([[1, 2], [3, 4]]), mask=np.zeros((2, 2)))
+
+        assert_equal(m.count(axis=0).shape, (1, 2))
+        assert_equal(m.count(axis=1).shape, (2, 1))
+
+        # Make sure broadcasting inside mean and var work
+        assert_equal(m.mean(axis=0), [[2., 3.]])
+        assert_equal(m.mean(axis=1), [[1.5], [3.5]])
+
+    def test_flat(self):
+        # Test that flat can return items even for matrices [#4585, #4615]
+        # test simple access
+        test = masked_array(np.matrix([[1, 2, 3]]), mask=[0, 0, 1])
+        assert_equal(test.flat[1], 2)
+        assert_equal(test.flat[2], masked)
+        assert_(np.all(test.flat[0:2] == test[0, 0:2]))
+        # Test flat on masked_matrices
+        test = masked_array(np.matrix([[1, 2, 3]]), mask=[0, 0, 1])
+        test.flat = masked_array([3, 2, 1], mask=[1, 0, 0])
+        control = masked_array(np.matrix([[3, 2, 1]]), mask=[1, 0, 0])
+        assert_equal(test, control)
+        # Test setting
+        test = masked_array(np.matrix([[1, 2, 3]]), mask=[0, 0, 1])
+        testflat = test.flat
+        testflat[:] = testflat[[2, 1, 0]]
+        assert_equal(test, control)
+        testflat[0] = 9
+        # test that matrices keep the correct shape (#4615)
+        a = masked_array(np.matrix(np.eye(2)), mask=0)
+        b = a.flat
+        b01 = b[:2]
+        assert_equal(b01.data, np.array([[1., 0.]]))
+        assert_equal(b01.mask, np.array([[False, False]]))
+
+    def test_allany_onmatrices(self):
+        x = np.array([[0.13, 0.26, 0.90],
+                      [0.28, 0.33, 0.63],
+                      [0.31, 0.87, 0.70]])
+        X = np.matrix(x)
+        m = np.array([[True, False, False],
+                      [False, False, False],
+                      [True, True, False]], dtype=np.bool_)
+        mX = masked_array(X, mask=m)
+        mXbig = (mX > 0.5)
+        mXsmall = (mX < 0.5)
+
+        assert_(not mXbig.all())
+        assert_(mXbig.any())
+        assert_equal(mXbig.all(0), np.matrix([False, False, True]))
+        assert_equal(mXbig.all(1), np.matrix([False, False, True]).T)
+        assert_equal(mXbig.any(0), np.matrix([False, False, True]))
+        assert_equal(mXbig.any(1), np.matrix([True, True, True]).T)
+
+        assert_(not mXsmall.all())
+        assert_(mXsmall.any())
+        assert_equal(mXsmall.all(0), np.matrix([True, True, False]))
+        assert_equal(mXsmall.all(1), np.matrix([False, False, False]).T)
+        assert_equal(mXsmall.any(0), np.matrix([True, True, False]))
+        assert_equal(mXsmall.any(1), np.matrix([True, True, False]).T)
+
+    def test_compressed(self):
+        a = masked_array(np.matrix([1, 2, 3, 4]), mask=[0, 0, 0, 0])
+        b = a.compressed()
+        assert_equal(b, a)
+        assert_(isinstance(b, np.matrix))
+        a[0, 0] = masked
+        b = a.compressed()
+        assert_equal(b, [[2, 3, 4]])
+
+    def test_ravel(self):
+        a = masked_array(np.matrix([1, 2, 3, 4, 5]), mask=[[0, 1, 0, 0, 0]])
+        aravel = a.ravel()
+        assert_equal(aravel.shape, (1, 5))
+        assert_equal(aravel._mask.shape, a.shape)
+
+    def test_view(self):
+        # Test view w/ flexible dtype
+        iterator = list(zip(np.arange(10), np.random.rand(10)))
+        data = np.array(iterator)
+        a = masked_array(iterator, dtype=[('a', float), ('b', float)])
+        a.mask[0] = (1, 0)
+        test = a.view((float, 2), np.matrix)
+        assert_equal(test, data)
+        assert_(isinstance(test, np.matrix))
+        assert_(not isinstance(test, MaskedArray))
+
+
+class TestSubclassing:
+    # Test suite for masked subclasses of ndarray.
+
+    def setup_method(self):
+        x = np.arange(5, dtype='float')
+        mx = MMatrix(x, mask=[0, 1, 0, 0, 0])
+        self.data = (x, mx)
+
+    def test_maskedarray_subclassing(self):
+        # Tests subclassing MaskedArray
+        (x, mx) = self.data
+        assert_(isinstance(mx._data, np.matrix))
+
+    def test_masked_unary_operations(self):
+        # Tests masked_unary_operation
+        (x, mx) = self.data
+        with np.errstate(divide='ignore'):
+            assert_(isinstance(log(mx), MMatrix))
+            assert_equal(log(x), np.log(x))
+
+    def test_masked_binary_operations(self):
+        # Tests masked_binary_operation
+        (x, mx) = self.data
+        # Result should be a MMatrix
+        assert_(isinstance(add(mx, mx), MMatrix))
+        assert_(isinstance(add(mx, x), MMatrix))
+        # Result should work
+        assert_equal(add(mx, x), mx+x)
+        assert_(isinstance(add(mx, mx)._data, np.matrix))
+        with assert_warns(DeprecationWarning):
+            assert_(isinstance(add.outer(mx, mx), MMatrix))
+        assert_(isinstance(hypot(mx, mx), MMatrix))
+        assert_(isinstance(hypot(mx, x), MMatrix))
+
+    def test_masked_binary_operations2(self):
+        # Tests domained_masked_binary_operation
+        (x, mx) = self.data
+        xmx = masked_array(mx.data.__array__(), mask=mx.mask)
+        assert_(isinstance(divide(mx, mx), MMatrix))
+        assert_(isinstance(divide(mx, x), MMatrix))
+        assert_equal(divide(mx, mx), divide(xmx, xmx))
+
+class TestConcatenator:
+    # Tests for mr_, the equivalent of r_ for masked arrays.
+
+    def test_matrix_builder(self):
+        assert_raises(np.ma.MAError, lambda: mr_['1, 2; 3, 4'])
+
+    def test_matrix(self):
+        # Test consistency with unmasked version.  If we ever deprecate
+        # matrix, this test should either still pass, or both actual and
+        # expected should fail to be build.
+        actual = mr_['r', 1, 2, 3]
+        expected = np.ma.array(np.r_['r', 1, 2, 3])
+        assert_array_equal(actual, expected)
+
+        # outer type is masked array, inner type is matrix
+        assert_equal(type(actual), type(expected))
+        assert_equal(type(actual.data), type(expected.data))

env-llmeval/lib/python3.10/site-packages/numpy/matrixlib/tests/test_matrix_linalg.py

@@ -0,0 +1,93 @@
+""" Test functions for linalg module using the matrix class."""
+import numpy as np
+
+from numpy.linalg.tests.test_linalg import (
+    LinalgCase, apply_tag, TestQR as _TestQR, LinalgTestCase,
+    _TestNorm2D, _TestNormDoubleBase, _TestNormSingleBase, _TestNormInt64Base,
+    SolveCases, InvCases, EigvalsCases, EigCases, SVDCases, CondCases,
+    PinvCases, DetCases, LstsqCases)
+
+
+CASES = []
+
+# square test cases
+CASES += apply_tag('square', [
+    LinalgCase("0x0_matrix",
+               np.empty((0, 0), dtype=np.double).view(np.matrix),
+               np.empty((0, 1), dtype=np.double).view(np.matrix),
+               tags={'size-0'}),
+    LinalgCase("matrix_b_only",
+               np.array([[1., 2.], [3., 4.]]),
+               np.matrix([2., 1.]).T),
+    LinalgCase("matrix_a_and_b",
+               np.matrix([[1., 2.], [3., 4.]]),
+               np.matrix([2., 1.]).T),
+])
+
+# hermitian test-cases
+CASES += apply_tag('hermitian', [
+    LinalgCase("hmatrix_a_and_b",
+               np.matrix([[1., 2.], [2., 1.]]),
+               None),
+])
+# No need to make generalized or strided cases for matrices.
+
+
+class MatrixTestCase(LinalgTestCase):
+    TEST_CASES = CASES
+
+
+class TestSolveMatrix(SolveCases, MatrixTestCase):
+    pass
+
+
+class TestInvMatrix(InvCases, MatrixTestCase):
+    pass
+
+
+class TestEigvalsMatrix(EigvalsCases, MatrixTestCase):
+    pass
+
+
+class TestEigMatrix(EigCases, MatrixTestCase):
+    pass
+
+
+class TestSVDMatrix(SVDCases, MatrixTestCase):
+    pass
+
+
+class TestCondMatrix(CondCases, MatrixTestCase):
+    pass
+
+
+class TestPinvMatrix(PinvCases, MatrixTestCase):
+    pass
+
+
+class TestDetMatrix(DetCases, MatrixTestCase):
+    pass
+
+
+class TestLstsqMatrix(LstsqCases, MatrixTestCase):
+    pass
+
+
+class _TestNorm2DMatrix(_TestNorm2D):
+    array = np.matrix
+
+
+class TestNormDoubleMatrix(_TestNorm2DMatrix, _TestNormDoubleBase):
+    pass
+
+
+class TestNormSingleMatrix(_TestNorm2DMatrix, _TestNormSingleBase):
+    pass
+
+
+class TestNormInt64Matrix(_TestNorm2DMatrix, _TestNormInt64Base):
+    pass
+
+
+class TestQRMatrix(_TestQR):
+    array = np.matrix