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Please use the +functions as ``np.`` 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)) + diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/lib/__init__.pyi b/env-llmeval/lib/python3.10/site-packages/numpy/lib/__init__.pyi new file mode 100644 index 0000000000000000000000000000000000000000..d3553bbcca7ba16703f7229c051aadfbe3a34b4d --- /dev/null +++ b/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 diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/lib/_datasource.py b/env-llmeval/lib/python3.10/site-packages/numpy/lib/_datasource.py new file mode 100644 index 0000000000000000000000000000000000000000..613733fa51675360caf33fd97b0b038c6fb6dfa2 --- /dev/null +++ b/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') + + >>> 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) diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/lib/_iotools.py b/env-llmeval/lib/python3.10/site-packages/numpy/lib/_iotools.py new file mode 100644 index 0000000000000000000000000000000000000000..534d1b3eea636d4f68151531945ea9132d304872 --- /dev/null +++ b/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', '>> np.lib._iotools.easy_dtype("i4, f8", defaultfmt="field_%03i") + dtype([('field_000', '>> np.lib._iotools.easy_dtype((int, float, float), names="a,b,c") + dtype([('a', '>> np.lib._iotools.easy_dtype(float, names="a,b,c") + dtype([('a', ' 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 diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/lib/_version.pyi b/env-llmeval/lib/python3.10/site-packages/numpy/lib/_version.pyi new file mode 100644 index 0000000000000000000000000000000000000000..1c82c99b686e2be8e34a1b6bc45dacce15532082 --- /dev/null +++ b/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: ... diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/lib/arraypad.py b/env-llmeval/lib/python3.10/site-packages/numpy/lib/arraypad.py new file mode 100644 index 0000000000000000000000000000000000000000..b06a645d836c5e0c4e445a138ca0af905236932f --- /dev/null +++ b/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 + + + 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 diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/lib/arraypad.pyi b/env-llmeval/lib/python3.10/site-packages/numpy/lib/arraypad.pyi new file mode 100644 index 0000000000000000000000000000000000000000..1ac6fc7d91c868ba077235b8229cd00869386660 --- /dev/null +++ b/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]: ... diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/lib/arraysetops.py b/env-llmeval/lib/python3.10/site-packages/numpy/lib/arraysetops.py new file mode 100644 index 0000000000000000000000000000000000000000..300bbda26ceb547752857e26a5871fa802ca6a6d --- /dev/null +++ b/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='>> indices + array([0, 1, 3]) + >>> a[indices] + array(['a', 'b', 'c'], dtype='>> a = np.array([1, 2, 6, 4, 2, 3, 2]) + >>> u, indices = np.unique(a, return_inverse=True) + >>> u + array([1, 2, 3, 4, 6]) + >>> indices + array([0, 1, 4, 3, 1, 2, 1]) + >>> u[indices] + array([1, 2, 6, 4, 2, 3, 2]) + + Reconstruct the input values from the unique values and counts: + + >>> a = np.array([1, 2, 6, 4, 2, 3, 2]) + >>> values, counts = np.unique(a, return_counts=True) + >>> values + array([1, 2, 3, 4, 6]) + >>> counts + array([1, 3, 1, 1, 1]) + >>> np.repeat(values, counts) + array([1, 2, 2, 2, 3, 4, 6]) # original order not preserved + + """ + 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)] diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/lib/arraysetops.pyi b/env-llmeval/lib/python3.10/site-packages/numpy/lib/arraysetops.pyi new file mode 100644 index 0000000000000000000000000000000000000000..7075c334ea7dbcffa435bb1e271e721990132933 --- /dev/null +++ b/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]: ... diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/lib/arrayterator.py b/env-llmeval/lib/python3.10/site-packages/numpy/lib/arrayterator.py new file mode 100644 index 0000000000000000000000000000000000000000..b9ea21f8e49f60461416962fc6e2a2ca625c04cd --- /dev/null +++ b/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 + + """ + 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 diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/lib/format.py b/env-llmeval/lib/python3.10/site-packages/numpy/lib/format.py new file mode 100644 index 0000000000000000000000000000000000000000..d5b3fbac23ab6e680510cbc3d47387cdee2c6048 --- /dev/null +++ b/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 `, 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): (' 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 diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/lib/format.pyi b/env-llmeval/lib/python3.10/site-packages/numpy/lib/format.pyi new file mode 100644 index 0000000000000000000000000000000000000000..a4468f52f4646b8b9413f279b09f85cd201aaf51 --- /dev/null +++ b/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=...): ... diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/lib/function_base.py b/env-llmeval/lib/python3.10/site-packages/numpy/lib/function_base.py new file mode 100644 index 0000000000000000000000000000000000000000..a3dab04d3331132f75787a81b0237aab73169eb4 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/numpy/lib/function_base.py @@ -0,0 +1,5733 @@ +import collections.abc +import functools +import re +import sys +import warnings + +from .._utils import set_module +import numpy as np +import numpy.core.numeric as _nx +from numpy.core import transpose +from numpy.core.numeric import ( + ones, zeros_like, arange, concatenate, array, asarray, asanyarray, empty, + ndarray, take, dot, where, intp, integer, isscalar, absolute + ) +from numpy.core.umath import ( + pi, add, arctan2, frompyfunc, cos, less_equal, sqrt, sin, + mod, exp, not_equal, subtract + ) +from numpy.core.fromnumeric import ( + ravel, nonzero, partition, mean, any, sum + ) +from numpy.core.numerictypes import typecodes +from numpy.core import overrides +from numpy.core.function_base import add_newdoc +from numpy.lib.twodim_base import diag +from numpy.core.multiarray import ( + _place, add_docstring, bincount, normalize_axis_index, _monotonicity, + interp as compiled_interp, interp_complex as compiled_interp_complex + ) +from numpy.core.umath import _add_newdoc_ufunc as add_newdoc_ufunc + +import builtins + +# needed in this module for compatibility +from numpy.lib.histograms import histogram, histogramdd # noqa: F401 + + +array_function_dispatch = functools.partial( + overrides.array_function_dispatch, module='numpy') + + +__all__ = [ + 'select', 'piecewise', 'trim_zeros', 'copy', 'iterable', 'percentile', + 'diff', 'gradient', 'angle', 'unwrap', 'sort_complex', 'disp', 'flip', + 'rot90', 'extract', 'place', 'vectorize', 'asarray_chkfinite', 'average', + 'bincount', 'digitize', 'cov', 'corrcoef', + 'msort', 'median', 'sinc', 'hamming', 'hanning', 'bartlett', + 'blackman', 'kaiser', 'trapz', 'i0', 'add_newdoc', 'add_docstring', + 'meshgrid', 'delete', 'insert', 'append', 'interp', 'add_newdoc_ufunc', + 'quantile' + ] + +# _QuantileMethods is a dictionary listing all the supported methods to +# compute quantile/percentile. +# +# Below virtual_index refer to the index of the element where the percentile +# would be found in the sorted sample. +# When the sample contains exactly the percentile wanted, the virtual_index is +# an integer to the index of this element. +# When the percentile wanted is in between two elements, the virtual_index +# is made of a integer part (a.k.a 'i' or 'left') and a fractional part +# (a.k.a 'g' or 'gamma') +# +# Each method in _QuantileMethods has two properties +# get_virtual_index : Callable +# The function used to compute the virtual_index. +# fix_gamma : Callable +# A function used for discret methods to force the index to a specific value. +_QuantileMethods = dict( + # --- HYNDMAN and FAN METHODS + # Discrete methods + inverted_cdf=dict( + get_virtual_index=lambda n, quantiles: _inverted_cdf(n, quantiles), + fix_gamma=lambda gamma, _: gamma, # should never be called + ), + averaged_inverted_cdf=dict( + get_virtual_index=lambda n, quantiles: (n * quantiles) - 1, + fix_gamma=lambda gamma, _: _get_gamma_mask( + shape=gamma.shape, + default_value=1., + conditioned_value=0.5, + where=gamma == 0), + ), + closest_observation=dict( + get_virtual_index=lambda n, quantiles: _closest_observation(n, + quantiles), + fix_gamma=lambda gamma, _: gamma, # should never be called + ), + # Continuous methods + interpolated_inverted_cdf=dict( + get_virtual_index=lambda n, quantiles: + _compute_virtual_index(n, quantiles, 0, 1), + fix_gamma=lambda gamma, _: gamma, + ), + hazen=dict( + get_virtual_index=lambda n, quantiles: + _compute_virtual_index(n, quantiles, 0.5, 0.5), + fix_gamma=lambda gamma, _: gamma, + ), + weibull=dict( + get_virtual_index=lambda n, quantiles: + _compute_virtual_index(n, quantiles, 0, 0), + fix_gamma=lambda gamma, _: gamma, + ), + # Default method. + # To avoid some rounding issues, `(n-1) * quantiles` is preferred to + # `_compute_virtual_index(n, quantiles, 1, 1)`. + # They are mathematically equivalent. + linear=dict( + get_virtual_index=lambda n, quantiles: (n - 1) * quantiles, + fix_gamma=lambda gamma, _: gamma, + ), + median_unbiased=dict( + get_virtual_index=lambda n, quantiles: + _compute_virtual_index(n, quantiles, 1 / 3.0, 1 / 3.0), + fix_gamma=lambda gamma, _: gamma, + ), + normal_unbiased=dict( + get_virtual_index=lambda n, quantiles: + _compute_virtual_index(n, quantiles, 3 / 8.0, 3 / 8.0), + fix_gamma=lambda gamma, _: gamma, + ), + # --- OTHER METHODS + lower=dict( + get_virtual_index=lambda n, quantiles: np.floor( + (n - 1) * quantiles).astype(np.intp), + fix_gamma=lambda gamma, _: gamma, + # should never be called, index dtype is int + ), + higher=dict( + get_virtual_index=lambda n, quantiles: np.ceil( + (n - 1) * quantiles).astype(np.intp), + fix_gamma=lambda gamma, _: gamma, + # should never be called, index dtype is int + ), + midpoint=dict( + get_virtual_index=lambda n, quantiles: 0.5 * ( + np.floor((n - 1) * quantiles) + + np.ceil((n - 1) * quantiles)), + fix_gamma=lambda gamma, index: _get_gamma_mask( + shape=gamma.shape, + default_value=0.5, + conditioned_value=0., + where=index % 1 == 0), + ), + nearest=dict( + get_virtual_index=lambda n, quantiles: np.around( + (n - 1) * quantiles).astype(np.intp), + fix_gamma=lambda gamma, _: gamma, + # should never be called, index dtype is int + )) + + +def _rot90_dispatcher(m, k=None, axes=None): + return (m,) + + +@array_function_dispatch(_rot90_dispatcher) +def rot90(m, k=1, axes=(0, 1)): + """ + Rotate an array by 90 degrees in the plane specified by axes. + + Rotation direction is from the first towards the second axis. + This means for a 2D array with the default `k` and `axes`, the + rotation will be counterclockwise. + + Parameters + ---------- + m : array_like + Array of two or more dimensions. + k : integer + Number of times the array is rotated by 90 degrees. + axes : (2,) array_like + The array is rotated in the plane defined by the axes. + Axes must be different. + + .. versionadded:: 1.12.0 + + Returns + ------- + y : ndarray + A rotated view of `m`. + + See Also + -------- + flip : Reverse the order of elements in an array along the given axis. + fliplr : Flip an array horizontally. + flipud : Flip an array vertically. + + Notes + ----- + ``rot90(m, k=1, axes=(1,0))`` is the reverse of + ``rot90(m, k=1, axes=(0,1))`` + + ``rot90(m, k=1, axes=(1,0))`` is equivalent to + ``rot90(m, k=-1, axes=(0,1))`` + + Examples + -------- + >>> m = np.array([[1,2],[3,4]], int) + >>> m + array([[1, 2], + [3, 4]]) + >>> np.rot90(m) + array([[2, 4], + [1, 3]]) + >>> np.rot90(m, 2) + array([[4, 3], + [2, 1]]) + >>> m = np.arange(8).reshape((2,2,2)) + >>> np.rot90(m, 1, (1,2)) + array([[[1, 3], + [0, 2]], + [[5, 7], + [4, 6]]]) + + """ + axes = tuple(axes) + if len(axes) != 2: + raise ValueError("len(axes) must be 2.") + + m = asanyarray(m) + + if axes[0] == axes[1] or absolute(axes[0] - axes[1]) == m.ndim: + raise ValueError("Axes must be different.") + + if (axes[0] >= m.ndim or axes[0] < -m.ndim + or axes[1] >= m.ndim or axes[1] < -m.ndim): + raise ValueError("Axes={} out of range for array of ndim={}." + .format(axes, m.ndim)) + + k %= 4 + + if k == 0: + return m[:] + if k == 2: + return flip(flip(m, axes[0]), axes[1]) + + axes_list = arange(0, m.ndim) + (axes_list[axes[0]], axes_list[axes[1]]) = (axes_list[axes[1]], + axes_list[axes[0]]) + + if k == 1: + return transpose(flip(m, axes[1]), axes_list) + else: + # k == 3 + return flip(transpose(m, axes_list), axes[1]) + + +def _flip_dispatcher(m, axis=None): + return (m,) + + +@array_function_dispatch(_flip_dispatcher) +def flip(m, axis=None): + """ + Reverse the order of elements in an array along the given axis. + + The shape of the array is preserved, but the elements are reordered. + + .. versionadded:: 1.12.0 + + Parameters + ---------- + m : array_like + Input array. + axis : None or int or tuple of ints, optional + Axis or axes along which to flip over. The default, + axis=None, will flip over all of the axes of the input array. + If axis is negative it counts from the last to the first axis. + + If axis is a tuple of ints, flipping is performed on all of the axes + specified in the tuple. + + .. versionchanged:: 1.15.0 + None and tuples of axes are supported + + Returns + ------- + out : array_like + A view of `m` with the entries of axis reversed. Since a view is + returned, this operation is done in constant time. + + See Also + -------- + flipud : Flip an array vertically (axis=0). + fliplr : Flip an array horizontally (axis=1). + + Notes + ----- + flip(m, 0) is equivalent to flipud(m). + + flip(m, 1) is equivalent to fliplr(m). + + flip(m, n) corresponds to ``m[...,::-1,...]`` with ``::-1`` at position n. + + flip(m) corresponds to ``m[::-1,::-1,...,::-1]`` with ``::-1`` at all + positions. + + flip(m, (0, 1)) corresponds to ``m[::-1,::-1,...]`` with ``::-1`` at + position 0 and position 1. + + Examples + -------- + >>> A = np.arange(8).reshape((2,2,2)) + >>> A + array([[[0, 1], + [2, 3]], + [[4, 5], + [6, 7]]]) + >>> np.flip(A, 0) + array([[[4, 5], + [6, 7]], + [[0, 1], + [2, 3]]]) + >>> np.flip(A, 1) + array([[[2, 3], + [0, 1]], + [[6, 7], + [4, 5]]]) + >>> np.flip(A) + array([[[7, 6], + [5, 4]], + [[3, 2], + [1, 0]]]) + >>> np.flip(A, (0, 2)) + array([[[5, 4], + [7, 6]], + [[1, 0], + [3, 2]]]) + >>> A = np.random.randn(3,4,5) + >>> np.all(np.flip(A,2) == A[:,:,::-1,...]) + True + """ + if not hasattr(m, 'ndim'): + m = asarray(m) + if axis is None: + indexer = (np.s_[::-1],) * m.ndim + else: + axis = _nx.normalize_axis_tuple(axis, m.ndim) + indexer = [np.s_[:]] * m.ndim + for ax in axis: + indexer[ax] = np.s_[::-1] + indexer = tuple(indexer) + return m[indexer] + + +@set_module('numpy') +def iterable(y): + """ + Check whether or not an object can be iterated over. + + Parameters + ---------- + y : object + Input object. + + Returns + ------- + b : bool + Return ``True`` if the object has an iterator method or is a + sequence and ``False`` otherwise. + + + Examples + -------- + >>> np.iterable([1, 2, 3]) + True + >>> np.iterable(2) + False + + Notes + ----- + In most cases, the results of ``np.iterable(obj)`` are consistent with + ``isinstance(obj, collections.abc.Iterable)``. One notable exception is + the treatment of 0-dimensional arrays:: + + >>> from collections.abc import Iterable + >>> a = np.array(1.0) # 0-dimensional numpy array + >>> isinstance(a, Iterable) + True + >>> np.iterable(a) + False + + """ + try: + iter(y) + except TypeError: + return False + return True + + +def _average_dispatcher(a, axis=None, weights=None, returned=None, *, + keepdims=None): + return (a, weights) + + +@array_function_dispatch(_average_dispatcher) +def average(a, axis=None, weights=None, returned=False, *, + keepdims=np._NoValue): + """ + Compute the weighted average along the specified axis. + + Parameters + ---------- + a : array_like + Array containing data to be averaged. If `a` is not an array, a + conversion is attempted. + axis : None or int or tuple of ints, optional + Axis or axes along which to average `a`. The default, + axis=None, will average over all of the elements of the input array. + If axis is negative it counts from the last to the first axis. + + .. versionadded:: 1.7.0 + + If axis is a tuple of ints, averaging is performed on all of the axes + specified in the tuple instead of a single axis or all the axes as + before. + weights : array_like, optional + An array of weights associated with the values in `a`. Each value in + `a` contributes to the average according to its associated weight. + The weights array can either be 1-D (in which case its length must be + the size of `a` along the given axis) or of the same shape as `a`. + If `weights=None`, then all data in `a` are assumed to have a + weight equal to one. The 1-D calculation is:: + + avg = sum(a * weights) / sum(weights) + + The only constraint on `weights` is that `sum(weights)` must not be 0. + returned : bool, optional + Default is `False`. If `True`, the tuple (`average`, `sum_of_weights`) + is returned, otherwise only the average is returned. + If `weights=None`, `sum_of_weights` is equivalent to the number of + elements over which the average is taken. + 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`. + *Note:* `keepdims` will not work with instances of `numpy.matrix` + or other classes whose methods do not support `keepdims`. + + .. versionadded:: 1.23.0 + + Returns + ------- + retval, [sum_of_weights] : array_type or double + Return the average along the specified axis. When `returned` is `True`, + return a tuple with the average as the first element and the sum + of the weights as the second element. `sum_of_weights` is of the + same type as `retval`. The result dtype follows a genereal pattern. + If `weights` is None, the result dtype will be that of `a` , or ``float64`` + if `a` is integral. Otherwise, if `weights` is not None and `a` is non- + integral, the result type will be the type of lowest precision capable of + representing values of both `a` and `weights`. If `a` happens to be + integral, the previous rules still applies but the result dtype will + at least be ``float64``. + + Raises + ------ + ZeroDivisionError + When all weights along axis are zero. See `numpy.ma.average` for a + version robust to this type of error. + TypeError + When the length of 1D `weights` is not the same as the shape of `a` + along axis. + + See Also + -------- + mean + + ma.average : average for masked arrays -- useful if your data contains + "missing" values + numpy.result_type : Returns the type that results from applying the + numpy type promotion rules to the arguments. + + Examples + -------- + >>> data = np.arange(1, 5) + >>> data + array([1, 2, 3, 4]) + >>> np.average(data) + 2.5 + >>> np.average(np.arange(1, 11), weights=np.arange(10, 0, -1)) + 4.0 + + >>> data = np.arange(6).reshape((3, 2)) + >>> data + array([[0, 1], + [2, 3], + [4, 5]]) + >>> np.average(data, axis=1, weights=[1./4, 3./4]) + array([0.75, 2.75, 4.75]) + >>> np.average(data, weights=[1./4, 3./4]) + Traceback (most recent call last): + ... + TypeError: Axis must be specified when shapes of a and weights differ. + + >>> a = np.ones(5, dtype=np.float128) + >>> w = np.ones(5, dtype=np.complex64) + >>> avg = np.average(a, weights=w) + >>> print(avg.dtype) + complex256 + + With ``keepdims=True``, the following result has shape (3, 1). + + >>> np.average(data, axis=1, keepdims=True) + array([[0.5], + [2.5], + [4.5]]) + """ + a = np.asanyarray(a) + + if keepdims is np._NoValue: + # Don't pass on the keepdims argument if one wasn't given. + keepdims_kw = {} + else: + keepdims_kw = {'keepdims': keepdims} + + if weights is None: + avg = a.mean(axis, **keepdims_kw) + avg_as_array = np.asanyarray(avg) + scl = avg_as_array.dtype.type(a.size/avg_as_array.size) + else: + wgt = np.asanyarray(weights) + + if issubclass(a.dtype.type, (np.integer, np.bool_)): + result_dtype = np.result_type(a.dtype, wgt.dtype, 'f8') + else: + result_dtype = np.result_type(a.dtype, wgt.dtype) + + # Sanity checks + if a.shape != wgt.shape: + if axis is None: + raise TypeError( + "Axis must be specified when shapes of a and weights " + "differ.") + if wgt.ndim != 1: + raise TypeError( + "1D weights expected when shapes of a and weights differ.") + if wgt.shape[0] != a.shape[axis]: + raise ValueError( + "Length of weights not compatible with specified axis.") + + # setup wgt to broadcast along axis + wgt = np.broadcast_to(wgt, (a.ndim-1)*(1,) + wgt.shape) + wgt = wgt.swapaxes(-1, axis) + + scl = wgt.sum(axis=axis, dtype=result_dtype, **keepdims_kw) + if np.any(scl == 0.0): + raise ZeroDivisionError( + "Weights sum to zero, can't be normalized") + + avg = avg_as_array = np.multiply(a, wgt, + dtype=result_dtype).sum(axis, **keepdims_kw) / scl + + if returned: + if scl.shape != avg_as_array.shape: + scl = np.broadcast_to(scl, avg_as_array.shape).copy() + return avg, scl + else: + return avg + + +@set_module('numpy') +def asarray_chkfinite(a, dtype=None, order=None): + """Convert the input to an array, checking for NaNs or Infs. + + Parameters + ---------- + a : array_like + Input data, in any form that can be converted to an array. This + includes lists, lists of tuples, tuples, tuples of tuples, tuples + of lists and ndarrays. Success requires no NaNs or Infs. + dtype : data-type, optional + By default, the data-type is inferred from the input data. + order : {'C', 'F', 'A', 'K'}, optional + Memory layout. 'A' and 'K' depend on the order of input array a. + 'C' row-major (C-style), + 'F' column-major (Fortran-style) memory representation. + 'A' (any) means 'F' if `a` is Fortran contiguous, 'C' otherwise + 'K' (keep) preserve input order + Defaults to 'C'. + + Returns + ------- + out : ndarray + Array interpretation of `a`. No copy is performed if the input + is already an ndarray. If `a` is a subclass of ndarray, a base + class ndarray is returned. + + Raises + ------ + ValueError + Raises ValueError if `a` contains NaN (Not a Number) or Inf (Infinity). + + See Also + -------- + asarray : Create and array. + asanyarray : Similar function which passes through subclasses. + ascontiguousarray : Convert input to a contiguous array. + asfarray : Convert input to a floating point ndarray. + asfortranarray : Convert input to an ndarray with column-major + memory order. + fromiter : Create an array from an iterator. + fromfunction : Construct an array by executing a function on grid + positions. + + Examples + -------- + Convert a list into an array. If all elements are finite + ``asarray_chkfinite`` is identical to ``asarray``. + + >>> a = [1, 2] + >>> np.asarray_chkfinite(a, dtype=float) + array([1., 2.]) + + Raises ValueError if array_like contains Nans or Infs. + + >>> a = [1, 2, np.inf] + >>> try: + ... np.asarray_chkfinite(a) + ... except ValueError: + ... print('ValueError') + ... + ValueError + + """ + a = asarray(a, dtype=dtype, order=order) + if a.dtype.char in typecodes['AllFloat'] and not np.isfinite(a).all(): + raise ValueError( + "array must not contain infs or NaNs") + return a + + +def _piecewise_dispatcher(x, condlist, funclist, *args, **kw): + yield x + # support the undocumented behavior of allowing scalars + if np.iterable(condlist): + yield from condlist + + +@array_function_dispatch(_piecewise_dispatcher) +def piecewise(x, condlist, funclist, *args, **kw): + """ + Evaluate a piecewise-defined function. + + Given a set of conditions and corresponding functions, evaluate each + function on the input data wherever its condition is true. + + Parameters + ---------- + x : ndarray or scalar + The input domain. + condlist : list of bool arrays or bool scalars + Each boolean array corresponds to a function in `funclist`. Wherever + `condlist[i]` is True, `funclist[i](x)` is used as the output value. + + Each boolean array in `condlist` selects a piece of `x`, + and should therefore be of the same shape as `x`. + + The length of `condlist` must correspond to that of `funclist`. + If one extra function is given, i.e. if + ``len(funclist) == len(condlist) + 1``, then that extra function + is the default value, used wherever all conditions are false. + funclist : list of callables, f(x,*args,**kw), or scalars + Each function is evaluated over `x` wherever its corresponding + condition is True. It should take a 1d array as input and give an 1d + array or a scalar value as output. If, instead of a callable, + a scalar is provided then a constant function (``lambda x: scalar``) is + assumed. + args : tuple, optional + Any further arguments given to `piecewise` are passed to the functions + upon execution, i.e., if called ``piecewise(..., ..., 1, 'a')``, then + each function is called as ``f(x, 1, 'a')``. + kw : dict, optional + Keyword arguments used in calling `piecewise` are passed to the + functions upon execution, i.e., if called + ``piecewise(..., ..., alpha=1)``, then each function is called as + ``f(x, alpha=1)``. + + Returns + ------- + out : ndarray + The output is the same shape and type as x and is found by + calling the functions in `funclist` on the appropriate portions of `x`, + as defined by the boolean arrays in `condlist`. Portions not covered + by any condition have a default value of 0. + + + See Also + -------- + choose, select, where + + Notes + ----- + This is similar to choose or select, except that functions are + evaluated on elements of `x` that satisfy the corresponding condition from + `condlist`. + + The result is:: + + |-- + |funclist[0](x[condlist[0]]) + out = |funclist[1](x[condlist[1]]) + |... + |funclist[n2](x[condlist[n2]]) + |-- + + Examples + -------- + Define the sigma function, which is -1 for ``x < 0`` and +1 for ``x >= 0``. + + >>> x = np.linspace(-2.5, 2.5, 6) + >>> np.piecewise(x, [x < 0, x >= 0], [-1, 1]) + array([-1., -1., -1., 1., 1., 1.]) + + Define the absolute value, which is ``-x`` for ``x <0`` and ``x`` for + ``x >= 0``. + + >>> np.piecewise(x, [x < 0, x >= 0], [lambda x: -x, lambda x: x]) + array([2.5, 1.5, 0.5, 0.5, 1.5, 2.5]) + + Apply the same function to a scalar value. + + >>> y = -2 + >>> np.piecewise(y, [y < 0, y >= 0], [lambda x: -x, lambda x: x]) + array(2) + + """ + x = asanyarray(x) + n2 = len(funclist) + + # undocumented: single condition is promoted to a list of one condition + if isscalar(condlist) or ( + not isinstance(condlist[0], (list, ndarray)) and x.ndim != 0): + condlist = [condlist] + + condlist = asarray(condlist, dtype=bool) + n = len(condlist) + + if n == n2 - 1: # compute the "otherwise" condition. + condelse = ~np.any(condlist, axis=0, keepdims=True) + condlist = np.concatenate([condlist, condelse], axis=0) + n += 1 + elif n != n2: + raise ValueError( + "with {} condition(s), either {} or {} functions are expected" + .format(n, n, n+1) + ) + + y = zeros_like(x) + for cond, func in zip(condlist, funclist): + if not isinstance(func, collections.abc.Callable): + y[cond] = func + else: + vals = x[cond] + if vals.size > 0: + y[cond] = func(vals, *args, **kw) + + return y + + +def _select_dispatcher(condlist, choicelist, default=None): + yield from condlist + yield from choicelist + + +@array_function_dispatch(_select_dispatcher) +def select(condlist, choicelist, default=0): + """ + Return an array drawn from elements in choicelist, depending on conditions. + + Parameters + ---------- + condlist : list of bool ndarrays + The list of conditions which determine from which array in `choicelist` + the output elements are taken. When multiple conditions are satisfied, + the first one encountered in `condlist` is used. + choicelist : list of ndarrays + The list of arrays from which the output elements are taken. It has + to be of the same length as `condlist`. + default : scalar, optional + The element inserted in `output` when all conditions evaluate to False. + + Returns + ------- + output : ndarray + The output at position m is the m-th element of the array in + `choicelist` where the m-th element of the corresponding array in + `condlist` is True. + + See Also + -------- + where : Return elements from one of two arrays depending on condition. + take, choose, compress, diag, diagonal + + Examples + -------- + >>> x = np.arange(6) + >>> condlist = [x<3, x>3] + >>> choicelist = [x, x**2] + >>> np.select(condlist, choicelist, 42) + array([ 0, 1, 2, 42, 16, 25]) + + >>> condlist = [x<=4, x>3] + >>> choicelist = [x, x**2] + >>> np.select(condlist, choicelist, 55) + array([ 0, 1, 2, 3, 4, 25]) + + """ + # Check the size of condlist and choicelist are the same, or abort. + if len(condlist) != len(choicelist): + raise ValueError( + 'list of cases must be same length as list of conditions') + + # Now that the dtype is known, handle the deprecated select([], []) case + if len(condlist) == 0: + raise ValueError("select with an empty condition list is not possible") + + choicelist = [np.asarray(choice) for choice in choicelist] + + try: + intermediate_dtype = np.result_type(*choicelist) + except TypeError as e: + msg = f'Choicelist elements do not have a common dtype: {e}' + raise TypeError(msg) from None + default_array = np.asarray(default) + choicelist.append(default_array) + + # need to get the result type before broadcasting for correct scalar + # behaviour + try: + dtype = np.result_type(intermediate_dtype, default_array) + except TypeError as e: + msg = f'Choicelists and default value do not have a common dtype: {e}' + raise TypeError(msg) from None + + # Convert conditions to arrays and broadcast conditions and choices + # as the shape is needed for the result. Doing it separately optimizes + # for example when all choices are scalars. + condlist = np.broadcast_arrays(*condlist) + choicelist = np.broadcast_arrays(*choicelist) + + # If cond array is not an ndarray in boolean format or scalar bool, abort. + for i, cond in enumerate(condlist): + if cond.dtype.type is not np.bool_: + raise TypeError( + 'invalid entry {} in condlist: should be boolean ndarray'.format(i)) + + if choicelist[0].ndim == 0: + # This may be common, so avoid the call. + result_shape = condlist[0].shape + else: + result_shape = np.broadcast_arrays(condlist[0], choicelist[0])[0].shape + + result = np.full(result_shape, choicelist[-1], dtype) + + # Use np.copyto to burn each choicelist array onto result, using the + # corresponding condlist as a boolean mask. This is done in reverse + # order since the first choice should take precedence. + choicelist = choicelist[-2::-1] + condlist = condlist[::-1] + for choice, cond in zip(choicelist, condlist): + np.copyto(result, choice, where=cond) + + return result + + +def _copy_dispatcher(a, order=None, subok=None): + return (a,) + + +@array_function_dispatch(_copy_dispatcher) +def copy(a, order='K', subok=False): + """ + Return an array copy of the given object. + + Parameters + ---------- + a : array_like + Input data. + order : {'C', 'F', 'A', 'K'}, optional + Controls the memory layout of the copy. 'C' means C-order, + 'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous, + 'C' otherwise. 'K' means match the layout of `a` as closely + as possible. (Note that this function and :meth:`ndarray.copy` are very + similar, but have different default values for their order= + arguments.) + subok : bool, optional + If True, then sub-classes will be passed-through, otherwise the + returned array will be forced to be a base-class array (defaults to False). + + .. versionadded:: 1.19.0 + + Returns + ------- + arr : ndarray + Array interpretation of `a`. + + See Also + -------- + ndarray.copy : Preferred method for creating an array copy + + Notes + ----- + This is equivalent to: + + >>> np.array(a, copy=True) #doctest: +SKIP + + Examples + -------- + Create an array x, with a reference y and a copy z: + + >>> x = np.array([1, 2, 3]) + >>> y = x + >>> z = np.copy(x) + + Note that, when we modify x, y changes, but not z: + + >>> x[0] = 10 + >>> x[0] == y[0] + True + >>> x[0] == z[0] + False + + Note that, np.copy clears previously set WRITEABLE=False flag. + + >>> a = np.array([1, 2, 3]) + >>> a.flags["WRITEABLE"] = False + >>> b = np.copy(a) + >>> b.flags["WRITEABLE"] + True + >>> b[0] = 3 + >>> b + array([3, 2, 3]) + + Note that np.copy is a shallow copy and will not copy object + elements within arrays. This is mainly important for arrays + containing Python objects. The new array will contain the + same object which may lead to surprises if that object can + be modified (is mutable): + + >>> a = np.array([1, 'm', [2, 3, 4]], dtype=object) + >>> b = np.copy(a) + >>> b[2][0] = 10 + >>> a + array([1, 'm', list([10, 3, 4])], dtype=object) + + To ensure all elements within an ``object`` array are copied, + use `copy.deepcopy`: + + >>> import copy + >>> a = np.array([1, 'm', [2, 3, 4]], dtype=object) + >>> c = copy.deepcopy(a) + >>> c[2][0] = 10 + >>> c + array([1, 'm', list([10, 3, 4])], dtype=object) + >>> a + array([1, 'm', list([2, 3, 4])], dtype=object) + + """ + return array(a, order=order, subok=subok, copy=True) + +# Basic operations + + +def _gradient_dispatcher(f, *varargs, axis=None, edge_order=None): + yield f + yield from varargs + + +@array_function_dispatch(_gradient_dispatcher) +def gradient(f, *varargs, axis=None, edge_order=1): + """ + Return the gradient of an N-dimensional array. + + The gradient is computed using second order accurate central differences + in the interior points and either first or second order accurate one-sides + (forward or backwards) differences at the boundaries. + The returned gradient hence has the same shape as the input array. + + Parameters + ---------- + f : array_like + An N-dimensional array containing samples of a scalar function. + varargs : list of scalar or array, optional + Spacing between f values. Default unitary spacing for all dimensions. + Spacing can be specified using: + + 1. single scalar to specify a sample distance for all dimensions. + 2. N scalars to specify a constant sample distance for each dimension. + i.e. `dx`, `dy`, `dz`, ... + 3. N arrays to specify the coordinates of the values along each + dimension of F. The length of the array must match the size of + the corresponding dimension + 4. Any combination of N scalars/arrays with the meaning of 2. and 3. + + If `axis` is given, the number of varargs must equal the number of axes. + Default: 1. + + edge_order : {1, 2}, optional + Gradient is calculated using N-th order accurate differences + at the boundaries. Default: 1. + + .. versionadded:: 1.9.1 + + axis : None or int or tuple of ints, optional + Gradient is calculated only along the given axis or axes + The default (axis = None) is to calculate the gradient for all the axes + of the input array. axis may be negative, in which case it counts from + the last to the first axis. + + .. versionadded:: 1.11.0 + + Returns + ------- + gradient : ndarray or list of ndarray + A list of ndarrays (or a single ndarray if there is only one dimension) + corresponding to the derivatives of f with respect to each dimension. + Each derivative has the same shape as f. + + Examples + -------- + >>> f = np.array([1, 2, 4, 7, 11, 16], dtype=float) + >>> np.gradient(f) + array([1. , 1.5, 2.5, 3.5, 4.5, 5. ]) + >>> np.gradient(f, 2) + array([0.5 , 0.75, 1.25, 1.75, 2.25, 2.5 ]) + + Spacing can be also specified with an array that represents the coordinates + of the values F along the dimensions. + For instance a uniform spacing: + + >>> x = np.arange(f.size) + >>> np.gradient(f, x) + array([1. , 1.5, 2.5, 3.5, 4.5, 5. ]) + + Or a non uniform one: + + >>> x = np.array([0., 1., 1.5, 3.5, 4., 6.], dtype=float) + >>> np.gradient(f, x) + array([1. , 3. , 3.5, 6.7, 6.9, 2.5]) + + For two dimensional arrays, the return will be two arrays ordered by + axis. In this example the first array stands for the gradient in + rows and the second one in columns direction: + + >>> np.gradient(np.array([[1, 2, 6], [3, 4, 5]], dtype=float)) + [array([[ 2., 2., -1.], + [ 2., 2., -1.]]), array([[1. , 2.5, 4. ], + [1. , 1. , 1. ]])] + + In this example the spacing is also specified: + uniform for axis=0 and non uniform for axis=1 + + >>> dx = 2. + >>> y = [1., 1.5, 3.5] + >>> np.gradient(np.array([[1, 2, 6], [3, 4, 5]], dtype=float), dx, y) + [array([[ 1. , 1. , -0.5], + [ 1. , 1. , -0.5]]), array([[2. , 2. , 2. ], + [2. , 1.7, 0.5]])] + + It is possible to specify how boundaries are treated using `edge_order` + + >>> x = np.array([0, 1, 2, 3, 4]) + >>> f = x**2 + >>> np.gradient(f, edge_order=1) + array([1., 2., 4., 6., 7.]) + >>> np.gradient(f, edge_order=2) + array([0., 2., 4., 6., 8.]) + + The `axis` keyword can be used to specify a subset of axes of which the + gradient is calculated + + >>> np.gradient(np.array([[1, 2, 6], [3, 4, 5]], dtype=float), axis=0) + array([[ 2., 2., -1.], + [ 2., 2., -1.]]) + + Notes + ----- + Assuming that :math:`f\\in C^{3}` (i.e., :math:`f` has at least 3 continuous + derivatives) and let :math:`h_{*}` be a non-homogeneous stepsize, we + minimize the "consistency error" :math:`\\eta_{i}` between the true gradient + and its estimate from a linear combination of the neighboring grid-points: + + .. math:: + + \\eta_{i} = f_{i}^{\\left(1\\right)} - + \\left[ \\alpha f\\left(x_{i}\\right) + + \\beta f\\left(x_{i} + h_{d}\\right) + + \\gamma f\\left(x_{i}-h_{s}\\right) + \\right] + + By substituting :math:`f(x_{i} + h_{d})` and :math:`f(x_{i} - h_{s})` + with their Taylor series expansion, this translates into solving + the following the linear system: + + .. math:: + + \\left\\{ + \\begin{array}{r} + \\alpha+\\beta+\\gamma=0 \\\\ + \\beta h_{d}-\\gamma h_{s}=1 \\\\ + \\beta h_{d}^{2}+\\gamma h_{s}^{2}=0 + \\end{array} + \\right. + + The resulting approximation of :math:`f_{i}^{(1)}` is the following: + + .. math:: + + \\hat f_{i}^{(1)} = + \\frac{ + h_{s}^{2}f\\left(x_{i} + h_{d}\\right) + + \\left(h_{d}^{2} - h_{s}^{2}\\right)f\\left(x_{i}\\right) + - h_{d}^{2}f\\left(x_{i}-h_{s}\\right)} + { h_{s}h_{d}\\left(h_{d} + h_{s}\\right)} + + \\mathcal{O}\\left(\\frac{h_{d}h_{s}^{2} + + h_{s}h_{d}^{2}}{h_{d} + + h_{s}}\\right) + + It is worth noting that if :math:`h_{s}=h_{d}` + (i.e., data are evenly spaced) + we find the standard second order approximation: + + .. math:: + + \\hat f_{i}^{(1)}= + \\frac{f\\left(x_{i+1}\\right) - f\\left(x_{i-1}\\right)}{2h} + + \\mathcal{O}\\left(h^{2}\\right) + + With a similar procedure the forward/backward approximations used for + boundaries can be derived. + + References + ---------- + .. [1] Quarteroni A., Sacco R., Saleri F. (2007) Numerical Mathematics + (Texts in Applied Mathematics). New York: Springer. + .. [2] Durran D. R. (1999) Numerical Methods for Wave Equations + in Geophysical Fluid Dynamics. New York: Springer. + .. [3] Fornberg B. (1988) Generation of Finite Difference Formulas on + Arbitrarily Spaced Grids, + Mathematics of Computation 51, no. 184 : 699-706. + `PDF `_. + """ + f = np.asanyarray(f) + N = f.ndim # number of dimensions + + if axis is None: + axes = tuple(range(N)) + else: + axes = _nx.normalize_axis_tuple(axis, N) + + len_axes = len(axes) + n = len(varargs) + if n == 0: + # no spacing argument - use 1 in all axes + dx = [1.0] * len_axes + elif n == 1 and np.ndim(varargs[0]) == 0: + # single scalar for all axes + dx = varargs * len_axes + elif n == len_axes: + # scalar or 1d array for each axis + dx = list(varargs) + for i, distances in enumerate(dx): + distances = np.asanyarray(distances) + if distances.ndim == 0: + continue + elif distances.ndim != 1: + raise ValueError("distances must be either scalars or 1d") + if len(distances) != f.shape[axes[i]]: + raise ValueError("when 1d, distances must match " + "the length of the corresponding dimension") + if np.issubdtype(distances.dtype, np.integer): + # Convert numpy integer types to float64 to avoid modular + # arithmetic in np.diff(distances). + distances = distances.astype(np.float64) + diffx = np.diff(distances) + # if distances are constant reduce to the scalar case + # since it brings a consistent speedup + if (diffx == diffx[0]).all(): + diffx = diffx[0] + dx[i] = diffx + else: + raise TypeError("invalid number of arguments") + + if edge_order > 2: + raise ValueError("'edge_order' greater than 2 not supported") + + # use central differences on interior and one-sided differences on the + # endpoints. This preserves second order-accuracy over the full domain. + + outvals = [] + + # create slice objects --- initially all are [:, :, ..., :] + slice1 = [slice(None)]*N + slice2 = [slice(None)]*N + slice3 = [slice(None)]*N + slice4 = [slice(None)]*N + + otype = f.dtype + if otype.type is np.datetime64: + # the timedelta dtype with the same unit information + otype = np.dtype(otype.name.replace('datetime', 'timedelta')) + # view as timedelta to allow addition + f = f.view(otype) + elif otype.type is np.timedelta64: + pass + elif np.issubdtype(otype, np.inexact): + pass + else: + # All other types convert to floating point. + # First check if f is a numpy integer type; if so, convert f to float64 + # to avoid modular arithmetic when computing the changes in f. + if np.issubdtype(otype, np.integer): + f = f.astype(np.float64) + otype = np.float64 + + for axis, ax_dx in zip(axes, dx): + if f.shape[axis] < edge_order + 1: + raise ValueError( + "Shape of array too small to calculate a numerical gradient, " + "at least (edge_order + 1) elements are required.") + # result allocation + out = np.empty_like(f, dtype=otype) + + # spacing for the current axis + uniform_spacing = np.ndim(ax_dx) == 0 + + # Numerical differentiation: 2nd order interior + slice1[axis] = slice(1, -1) + slice2[axis] = slice(None, -2) + slice3[axis] = slice(1, -1) + slice4[axis] = slice(2, None) + + if uniform_spacing: + out[tuple(slice1)] = (f[tuple(slice4)] - f[tuple(slice2)]) / (2. * ax_dx) + else: + dx1 = ax_dx[0:-1] + dx2 = ax_dx[1:] + a = -(dx2)/(dx1 * (dx1 + dx2)) + b = (dx2 - dx1) / (dx1 * dx2) + c = dx1 / (dx2 * (dx1 + dx2)) + # fix the shape for broadcasting + shape = np.ones(N, dtype=int) + shape[axis] = -1 + a.shape = b.shape = c.shape = shape + # 1D equivalent -- out[1:-1] = a * f[:-2] + b * f[1:-1] + c * f[2:] + out[tuple(slice1)] = a * f[tuple(slice2)] + b * f[tuple(slice3)] + c * f[tuple(slice4)] + + # Numerical differentiation: 1st order edges + if edge_order == 1: + slice1[axis] = 0 + slice2[axis] = 1 + slice3[axis] = 0 + dx_0 = ax_dx if uniform_spacing else ax_dx[0] + # 1D equivalent -- out[0] = (f[1] - f[0]) / (x[1] - x[0]) + out[tuple(slice1)] = (f[tuple(slice2)] - f[tuple(slice3)]) / dx_0 + + slice1[axis] = -1 + slice2[axis] = -1 + slice3[axis] = -2 + dx_n = ax_dx if uniform_spacing else ax_dx[-1] + # 1D equivalent -- out[-1] = (f[-1] - f[-2]) / (x[-1] - x[-2]) + out[tuple(slice1)] = (f[tuple(slice2)] - f[tuple(slice3)]) / dx_n + + # Numerical differentiation: 2nd order edges + else: + slice1[axis] = 0 + slice2[axis] = 0 + slice3[axis] = 1 + slice4[axis] = 2 + if uniform_spacing: + a = -1.5 / ax_dx + b = 2. / ax_dx + c = -0.5 / ax_dx + else: + dx1 = ax_dx[0] + dx2 = ax_dx[1] + a = -(2. * dx1 + dx2)/(dx1 * (dx1 + dx2)) + b = (dx1 + dx2) / (dx1 * dx2) + c = - dx1 / (dx2 * (dx1 + dx2)) + # 1D equivalent -- out[0] = a * f[0] + b * f[1] + c * f[2] + out[tuple(slice1)] = a * f[tuple(slice2)] + b * f[tuple(slice3)] + c * f[tuple(slice4)] + + slice1[axis] = -1 + slice2[axis] = -3 + slice3[axis] = -2 + slice4[axis] = -1 + if uniform_spacing: + a = 0.5 / ax_dx + b = -2. / ax_dx + c = 1.5 / ax_dx + else: + dx1 = ax_dx[-2] + dx2 = ax_dx[-1] + a = (dx2) / (dx1 * (dx1 + dx2)) + b = - (dx2 + dx1) / (dx1 * dx2) + c = (2. * dx2 + dx1) / (dx2 * (dx1 + dx2)) + # 1D equivalent -- out[-1] = a * f[-3] + b * f[-2] + c * f[-1] + out[tuple(slice1)] = a * f[tuple(slice2)] + b * f[tuple(slice3)] + c * f[tuple(slice4)] + + outvals.append(out) + + # reset the slice object in this dimension to ":" + slice1[axis] = slice(None) + slice2[axis] = slice(None) + slice3[axis] = slice(None) + slice4[axis] = slice(None) + + if len_axes == 1: + return outvals[0] + elif np._using_numpy2_behavior(): + return tuple(outvals) + else: + return outvals + + +def _diff_dispatcher(a, n=None, axis=None, prepend=None, append=None): + return (a, prepend, append) + + +@array_function_dispatch(_diff_dispatcher) +def diff(a, n=1, axis=-1, prepend=np._NoValue, append=np._NoValue): + """ + Calculate the n-th discrete difference along the given axis. + + The first difference is given by ``out[i] = a[i+1] - a[i]`` along + the given axis, higher differences are calculated by using `diff` + recursively. + + Parameters + ---------- + a : array_like + Input array + n : int, optional + The number of times values are differenced. If zero, the input + is returned as-is. + axis : int, optional + The axis along which the difference is taken, default is the + last axis. + prepend, append : array_like, optional + Values to prepend or append to `a` along axis prior to + performing the difference. Scalar values are expanded to + arrays with length 1 in the direction of axis and the shape + of the input array in along all other axes. Otherwise the + dimension and shape must match `a` except along axis. + + .. versionadded:: 1.16.0 + + Returns + ------- + diff : ndarray + The n-th differences. The shape of the output is the same as `a` + except along `axis` where the dimension is smaller by `n`. The + type of the output is the same as the type of the difference + between any two elements of `a`. This is the same as the type of + `a` in most cases. A notable exception is `datetime64`, which + results in a `timedelta64` output array. + + See Also + -------- + gradient, ediff1d, cumsum + + Notes + ----- + Type is preserved for boolean arrays, so the result will contain + `False` when consecutive elements are the same and `True` when they + differ. + + For unsigned integer arrays, the results will also be unsigned. This + should not be surprising, as the result is consistent with + calculating the difference directly: + + >>> u8_arr = np.array([1, 0], dtype=np.uint8) + >>> np.diff(u8_arr) + array([255], dtype=uint8) + >>> u8_arr[1,...] - u8_arr[0,...] + 255 + + If this is not desirable, then the array should be cast to a larger + integer type first: + + >>> i16_arr = u8_arr.astype(np.int16) + >>> np.diff(i16_arr) + array([-1], dtype=int16) + + Examples + -------- + >>> x = np.array([1, 2, 4, 7, 0]) + >>> np.diff(x) + array([ 1, 2, 3, -7]) + >>> np.diff(x, n=2) + array([ 1, 1, -10]) + + >>> x = np.array([[1, 3, 6, 10], [0, 5, 6, 8]]) + >>> np.diff(x) + array([[2, 3, 4], + [5, 1, 2]]) + >>> np.diff(x, axis=0) + array([[-1, 2, 0, -2]]) + + >>> x = np.arange('1066-10-13', '1066-10-16', dtype=np.datetime64) + >>> np.diff(x) + array([1, 1], dtype='timedelta64[D]') + + """ + if n == 0: + return a + if n < 0: + raise ValueError( + "order must be non-negative but got " + repr(n)) + + a = asanyarray(a) + nd = a.ndim + if nd == 0: + raise ValueError("diff requires input that is at least one dimensional") + axis = normalize_axis_index(axis, nd) + + combined = [] + if prepend is not np._NoValue: + prepend = np.asanyarray(prepend) + if prepend.ndim == 0: + shape = list(a.shape) + shape[axis] = 1 + prepend = np.broadcast_to(prepend, tuple(shape)) + combined.append(prepend) + + combined.append(a) + + if append is not np._NoValue: + append = np.asanyarray(append) + if append.ndim == 0: + shape = list(a.shape) + shape[axis] = 1 + append = np.broadcast_to(append, tuple(shape)) + combined.append(append) + + if len(combined) > 1: + a = np.concatenate(combined, axis) + + slice1 = [slice(None)] * nd + slice2 = [slice(None)] * nd + slice1[axis] = slice(1, None) + slice2[axis] = slice(None, -1) + slice1 = tuple(slice1) + slice2 = tuple(slice2) + + op = not_equal if a.dtype == np.bool_ else subtract + for _ in range(n): + a = op(a[slice1], a[slice2]) + + return a + + +def _interp_dispatcher(x, xp, fp, left=None, right=None, period=None): + return (x, xp, fp) + + +@array_function_dispatch(_interp_dispatcher) +def interp(x, xp, fp, left=None, right=None, period=None): + """ + One-dimensional linear interpolation for monotonically increasing sample points. + + Returns the one-dimensional piecewise linear interpolant to a function + with given discrete data points (`xp`, `fp`), evaluated at `x`. + + Parameters + ---------- + x : array_like + The x-coordinates at which to evaluate the interpolated values. + + xp : 1-D sequence of floats + The x-coordinates of the data points, must be increasing if argument + `period` is not specified. Otherwise, `xp` is internally sorted after + normalizing the periodic boundaries with ``xp = xp % period``. + + fp : 1-D sequence of float or complex + The y-coordinates of the data points, same length as `xp`. + + left : optional float or complex corresponding to fp + Value to return for `x < xp[0]`, default is `fp[0]`. + + right : optional float or complex corresponding to fp + Value to return for `x > xp[-1]`, default is `fp[-1]`. + + period : None or float, optional + A period for the x-coordinates. This parameter allows the proper + interpolation of angular x-coordinates. Parameters `left` and `right` + are ignored if `period` is specified. + + .. versionadded:: 1.10.0 + + Returns + ------- + y : float or complex (corresponding to fp) or ndarray + The interpolated values, same shape as `x`. + + Raises + ------ + ValueError + If `xp` and `fp` have different length + If `xp` or `fp` are not 1-D sequences + If `period == 0` + + See Also + -------- + scipy.interpolate + + Warnings + -------- + The x-coordinate sequence is expected to be increasing, but this is not + explicitly enforced. However, if the sequence `xp` is non-increasing, + interpolation results are meaningless. + + Note that, since NaN is unsortable, `xp` also cannot contain NaNs. + + A simple check for `xp` being strictly increasing is:: + + np.all(np.diff(xp) > 0) + + Examples + -------- + >>> xp = [1, 2, 3] + >>> fp = [3, 2, 0] + >>> np.interp(2.5, xp, fp) + 1.0 + >>> np.interp([0, 1, 1.5, 2.72, 3.14], xp, fp) + array([3. , 3. , 2.5 , 0.56, 0. ]) + >>> UNDEF = -99.0 + >>> np.interp(3.14, xp, fp, right=UNDEF) + -99.0 + + Plot an interpolant to the sine function: + + >>> x = np.linspace(0, 2*np.pi, 10) + >>> y = np.sin(x) + >>> xvals = np.linspace(0, 2*np.pi, 50) + >>> yinterp = np.interp(xvals, x, y) + >>> import matplotlib.pyplot as plt + >>> plt.plot(x, y, 'o') + [] + >>> plt.plot(xvals, yinterp, '-x') + [] + >>> plt.show() + + Interpolation with periodic x-coordinates: + + >>> x = [-180, -170, -185, 185, -10, -5, 0, 365] + >>> xp = [190, -190, 350, -350] + >>> fp = [5, 10, 3, 4] + >>> np.interp(x, xp, fp, period=360) + array([7.5 , 5. , 8.75, 6.25, 3. , 3.25, 3.5 , 3.75]) + + Complex interpolation: + + >>> x = [1.5, 4.0] + >>> xp = [2,3,5] + >>> fp = [1.0j, 0, 2+3j] + >>> np.interp(x, xp, fp) + array([0.+1.j , 1.+1.5j]) + + """ + + fp = np.asarray(fp) + + if np.iscomplexobj(fp): + interp_func = compiled_interp_complex + input_dtype = np.complex128 + else: + interp_func = compiled_interp + input_dtype = np.float64 + + if period is not None: + if period == 0: + raise ValueError("period must be a non-zero value") + period = abs(period) + left = None + right = None + + x = np.asarray(x, dtype=np.float64) + xp = np.asarray(xp, dtype=np.float64) + fp = np.asarray(fp, dtype=input_dtype) + + if xp.ndim != 1 or fp.ndim != 1: + raise ValueError("Data points must be 1-D sequences") + if xp.shape[0] != fp.shape[0]: + raise ValueError("fp and xp are not of the same length") + # normalizing periodic boundaries + x = x % period + xp = xp % period + asort_xp = np.argsort(xp) + xp = xp[asort_xp] + fp = fp[asort_xp] + xp = np.concatenate((xp[-1:]-period, xp, xp[0:1]+period)) + fp = np.concatenate((fp[-1:], fp, fp[0:1])) + + return interp_func(x, xp, fp, left, right) + + +def _angle_dispatcher(z, deg=None): + return (z,) + + +@array_function_dispatch(_angle_dispatcher) +def angle(z, deg=False): + """ + Return the angle of the complex argument. + + Parameters + ---------- + z : array_like + A complex number or sequence of complex numbers. + deg : bool, optional + Return angle in degrees if True, radians if False (default). + + Returns + ------- + angle : ndarray or scalar + The counterclockwise angle from the positive real axis on the complex + plane in the range ``(-pi, pi]``, with dtype as numpy.float64. + + .. versionchanged:: 1.16.0 + This function works on subclasses of ndarray like `ma.array`. + + See Also + -------- + arctan2 + absolute + + Notes + ----- + Although the angle of the complex number 0 is undefined, ``numpy.angle(0)`` + returns the value 0. + + Examples + -------- + >>> np.angle([1.0, 1.0j, 1+1j]) # in radians + array([ 0. , 1.57079633, 0.78539816]) # may vary + >>> np.angle(1+1j, deg=True) # in degrees + 45.0 + + """ + z = asanyarray(z) + if issubclass(z.dtype.type, _nx.complexfloating): + zimag = z.imag + zreal = z.real + else: + zimag = 0 + zreal = z + + a = arctan2(zimag, zreal) + if deg: + a *= 180/pi + return a + + +def _unwrap_dispatcher(p, discont=None, axis=None, *, period=None): + return (p,) + + +@array_function_dispatch(_unwrap_dispatcher) +def unwrap(p, discont=None, axis=-1, *, period=2*pi): + r""" + Unwrap by taking the complement of large deltas with respect to the period. + + This unwraps a signal `p` by changing elements which have an absolute + difference from their predecessor of more than ``max(discont, period/2)`` + to their `period`-complementary values. + + For the default case where `period` is :math:`2\pi` and `discont` is + :math:`\pi`, this unwraps a radian phase `p` such that adjacent differences + are never greater than :math:`\pi` by adding :math:`2k\pi` for some + integer :math:`k`. + + Parameters + ---------- + p : array_like + Input array. + discont : float, optional + Maximum discontinuity between values, default is ``period/2``. + Values below ``period/2`` are treated as if they were ``period/2``. + To have an effect different from the default, `discont` should be + larger than ``period/2``. + axis : int, optional + Axis along which unwrap will operate, default is the last axis. + period : float, optional + Size of the range over which the input wraps. By default, it is + ``2 pi``. + + .. versionadded:: 1.21.0 + + Returns + ------- + out : ndarray + Output array. + + See Also + -------- + rad2deg, deg2rad + + Notes + ----- + If the discontinuity in `p` is smaller than ``period/2``, + but larger than `discont`, no unwrapping is done because taking + the complement would only make the discontinuity larger. + + Examples + -------- + >>> phase = np.linspace(0, np.pi, num=5) + >>> phase[3:] += np.pi + >>> phase + array([ 0. , 0.78539816, 1.57079633, 5.49778714, 6.28318531]) # may vary + >>> np.unwrap(phase) + array([ 0. , 0.78539816, 1.57079633, -0.78539816, 0. ]) # may vary + >>> np.unwrap([0, 1, 2, -1, 0], period=4) + array([0, 1, 2, 3, 4]) + >>> np.unwrap([ 1, 2, 3, 4, 5, 6, 1, 2, 3], period=6) + array([1, 2, 3, 4, 5, 6, 7, 8, 9]) + >>> np.unwrap([2, 3, 4, 5, 2, 3, 4, 5], period=4) + array([2, 3, 4, 5, 6, 7, 8, 9]) + >>> phase_deg = np.mod(np.linspace(0 ,720, 19), 360) - 180 + >>> np.unwrap(phase_deg, period=360) + array([-180., -140., -100., -60., -20., 20., 60., 100., 140., + 180., 220., 260., 300., 340., 380., 420., 460., 500., + 540.]) + """ + p = asarray(p) + nd = p.ndim + dd = diff(p, axis=axis) + if discont is None: + discont = period/2 + slice1 = [slice(None, None)]*nd # full slices + slice1[axis] = slice(1, None) + slice1 = tuple(slice1) + dtype = np.result_type(dd, period) + if _nx.issubdtype(dtype, _nx.integer): + interval_high, rem = divmod(period, 2) + boundary_ambiguous = rem == 0 + else: + interval_high = period / 2 + boundary_ambiguous = True + interval_low = -interval_high + ddmod = mod(dd - interval_low, period) + interval_low + if boundary_ambiguous: + # for `mask = (abs(dd) == period/2)`, the above line made + # `ddmod[mask] == -period/2`. correct these such that + # `ddmod[mask] == sign(dd[mask])*period/2`. + _nx.copyto(ddmod, interval_high, + where=(ddmod == interval_low) & (dd > 0)) + ph_correct = ddmod - dd + _nx.copyto(ph_correct, 0, where=abs(dd) < discont) + up = array(p, copy=True, dtype=dtype) + up[slice1] = p[slice1] + ph_correct.cumsum(axis) + return up + + +def _sort_complex(a): + return (a,) + + +@array_function_dispatch(_sort_complex) +def sort_complex(a): + """ + Sort a complex array using the real part first, then the imaginary part. + + Parameters + ---------- + a : array_like + Input array + + Returns + ------- + out : complex ndarray + Always returns a sorted complex array. + + Examples + -------- + >>> np.sort_complex([5, 3, 6, 2, 1]) + array([1.+0.j, 2.+0.j, 3.+0.j, 5.+0.j, 6.+0.j]) + + >>> np.sort_complex([1 + 2j, 2 - 1j, 3 - 2j, 3 - 3j, 3 + 5j]) + array([1.+2.j, 2.-1.j, 3.-3.j, 3.-2.j, 3.+5.j]) + + """ + b = array(a, copy=True) + b.sort() + if not issubclass(b.dtype.type, _nx.complexfloating): + if b.dtype.char in 'bhBH': + return b.astype('F') + elif b.dtype.char == 'g': + return b.astype('G') + else: + return b.astype('D') + else: + return b + + +def _trim_zeros(filt, trim=None): + return (filt,) + + +@array_function_dispatch(_trim_zeros) +def trim_zeros(filt, trim='fb'): + """ + Trim the leading and/or trailing zeros from a 1-D array or sequence. + + Parameters + ---------- + filt : 1-D array or sequence + Input array. + trim : str, optional + A string with 'f' representing trim from front and 'b' to trim from + back. Default is 'fb', trim zeros from both front and back of the + array. + + Returns + ------- + trimmed : 1-D array or sequence + The result of trimming the input. The input data type is preserved. + + Examples + -------- + >>> a = np.array((0, 0, 0, 1, 2, 3, 0, 2, 1, 0)) + >>> np.trim_zeros(a) + array([1, 2, 3, 0, 2, 1]) + + >>> np.trim_zeros(a, 'b') + array([0, 0, 0, ..., 0, 2, 1]) + + The input data type is preserved, list/tuple in means list/tuple out. + + >>> np.trim_zeros([0, 1, 2, 0]) + [1, 2] + + """ + + first = 0 + trim = trim.upper() + if 'F' in trim: + for i in filt: + if i != 0.: + break + else: + first = first + 1 + last = len(filt) + if 'B' in trim: + for i in filt[::-1]: + if i != 0.: + break + else: + last = last - 1 + return filt[first:last] + + +def _extract_dispatcher(condition, arr): + return (condition, arr) + + +@array_function_dispatch(_extract_dispatcher) +def extract(condition, arr): + """ + Return the elements of an array that satisfy some condition. + + This is equivalent to ``np.compress(ravel(condition), ravel(arr))``. If + `condition` is boolean ``np.extract`` is equivalent to ``arr[condition]``. + + Note that `place` does the exact opposite of `extract`. + + Parameters + ---------- + condition : array_like + An array whose nonzero or True entries indicate the elements of `arr` + to extract. + arr : array_like + Input array of the same size as `condition`. + + Returns + ------- + extract : ndarray + Rank 1 array of values from `arr` where `condition` is True. + + See Also + -------- + take, put, copyto, compress, place + + Examples + -------- + >>> arr = np.arange(12).reshape((3, 4)) + >>> arr + array([[ 0, 1, 2, 3], + [ 4, 5, 6, 7], + [ 8, 9, 10, 11]]) + >>> condition = np.mod(arr, 3)==0 + >>> condition + array([[ True, False, False, True], + [False, False, True, False], + [False, True, False, False]]) + >>> np.extract(condition, arr) + array([0, 3, 6, 9]) + + + If `condition` is boolean: + + >>> arr[condition] + array([0, 3, 6, 9]) + + """ + return _nx.take(ravel(arr), nonzero(ravel(condition))[0]) + + +def _place_dispatcher(arr, mask, vals): + return (arr, mask, vals) + + +@array_function_dispatch(_place_dispatcher) +def place(arr, mask, vals): + """ + Change elements of an array based on conditional and input values. + + Similar to ``np.copyto(arr, vals, where=mask)``, the difference is that + `place` uses the first N elements of `vals`, where N is the number of + True values in `mask`, while `copyto` uses the elements where `mask` + is True. + + Note that `extract` does the exact opposite of `place`. + + Parameters + ---------- + arr : ndarray + Array to put data into. + mask : array_like + Boolean mask array. Must have the same size as `a`. + vals : 1-D sequence + Values to put into `a`. Only the first N elements are used, where + N is the number of True values in `mask`. If `vals` is smaller + than N, it will be repeated, and if elements of `a` are to be masked, + this sequence must be non-empty. + + See Also + -------- + copyto, put, take, extract + + Examples + -------- + >>> arr = np.arange(6).reshape(2, 3) + >>> np.place(arr, arr>2, [44, 55]) + >>> arr + array([[ 0, 1, 2], + [44, 55, 44]]) + + """ + return _place(arr, mask, vals) + + +def disp(mesg, device=None, linefeed=True): + """ + Display a message on a device. + + Parameters + ---------- + mesg : str + Message to display. + device : object + Device to write message. If None, defaults to ``sys.stdout`` which is + very similar to ``print``. `device` needs to have ``write()`` and + ``flush()`` methods. + linefeed : bool, optional + Option whether to print a line feed or not. Defaults to True. + + Raises + ------ + AttributeError + If `device` does not have a ``write()`` or ``flush()`` method. + + Examples + -------- + Besides ``sys.stdout``, a file-like object can also be used as it has + both required methods: + + >>> from io import StringIO + >>> buf = StringIO() + >>> np.disp(u'"Display" in a file', device=buf) + >>> buf.getvalue() + '"Display" in a file\\n' + + """ + if device is None: + device = sys.stdout + if linefeed: + device.write('%s\n' % mesg) + else: + device.write('%s' % mesg) + device.flush() + return + + +# See https://docs.scipy.org/doc/numpy/reference/c-api.generalized-ufuncs.html +_DIMENSION_NAME = r'\w+' +_CORE_DIMENSION_LIST = '(?:{0:}(?:,{0:})*)?'.format(_DIMENSION_NAME) +_ARGUMENT = r'\({}\)'.format(_CORE_DIMENSION_LIST) +_ARGUMENT_LIST = '{0:}(?:,{0:})*'.format(_ARGUMENT) +_SIGNATURE = '^{0:}->{0:}$'.format(_ARGUMENT_LIST) + + +def _parse_gufunc_signature(signature): + """ + Parse string signatures for a generalized universal function. + + Arguments + --------- + signature : string + Generalized universal function signature, e.g., ``(m,n),(n,p)->(m,p)`` + for ``np.matmul``. + + Returns + ------- + Tuple of input and output core dimensions parsed from the signature, each + of the form List[Tuple[str, ...]]. + """ + signature = re.sub(r'\s+', '', signature) + + if not re.match(_SIGNATURE, signature): + raise ValueError( + 'not a valid gufunc signature: {}'.format(signature)) + return tuple([tuple(re.findall(_DIMENSION_NAME, arg)) + for arg in re.findall(_ARGUMENT, arg_list)] + for arg_list in signature.split('->')) + + +def _update_dim_sizes(dim_sizes, arg, core_dims): + """ + Incrementally check and update core dimension sizes for a single argument. + + Arguments + --------- + dim_sizes : Dict[str, int] + Sizes of existing core dimensions. Will be updated in-place. + arg : ndarray + Argument to examine. + core_dims : Tuple[str, ...] + Core dimensions for this argument. + """ + if not core_dims: + return + + num_core_dims = len(core_dims) + if arg.ndim < num_core_dims: + raise ValueError( + '%d-dimensional argument does not have enough ' + 'dimensions for all core dimensions %r' + % (arg.ndim, core_dims)) + + core_shape = arg.shape[-num_core_dims:] + for dim, size in zip(core_dims, core_shape): + if dim in dim_sizes: + if size != dim_sizes[dim]: + raise ValueError( + 'inconsistent size for core dimension %r: %r vs %r' + % (dim, size, dim_sizes[dim])) + else: + dim_sizes[dim] = size + + +def _parse_input_dimensions(args, input_core_dims): + """ + Parse broadcast and core dimensions for vectorize with a signature. + + Arguments + --------- + args : Tuple[ndarray, ...] + Tuple of input arguments to examine. + input_core_dims : List[Tuple[str, ...]] + List of core dimensions corresponding to each input. + + Returns + ------- + broadcast_shape : Tuple[int, ...] + Common shape to broadcast all non-core dimensions to. + dim_sizes : Dict[str, int] + Common sizes for named core dimensions. + """ + broadcast_args = [] + dim_sizes = {} + for arg, core_dims in zip(args, input_core_dims): + _update_dim_sizes(dim_sizes, arg, core_dims) + ndim = arg.ndim - len(core_dims) + dummy_array = np.lib.stride_tricks.as_strided(0, arg.shape[:ndim]) + broadcast_args.append(dummy_array) + broadcast_shape = np.lib.stride_tricks._broadcast_shape(*broadcast_args) + return broadcast_shape, dim_sizes + + +def _calculate_shapes(broadcast_shape, dim_sizes, list_of_core_dims): + """Helper for calculating broadcast shapes with core dimensions.""" + return [broadcast_shape + tuple(dim_sizes[dim] for dim in core_dims) + for core_dims in list_of_core_dims] + + +def _create_arrays(broadcast_shape, dim_sizes, list_of_core_dims, dtypes, + results=None): + """Helper for creating output arrays in vectorize.""" + shapes = _calculate_shapes(broadcast_shape, dim_sizes, list_of_core_dims) + if dtypes is None: + dtypes = [None] * len(shapes) + if results is None: + arrays = tuple(np.empty(shape=shape, dtype=dtype) + for shape, dtype in zip(shapes, dtypes)) + else: + arrays = tuple(np.empty_like(result, shape=shape, dtype=dtype) + for result, shape, dtype + in zip(results, shapes, dtypes)) + return arrays + + +@set_module('numpy') +class vectorize: + """ + vectorize(pyfunc=np._NoValue, otypes=None, doc=None, excluded=None, + cache=False, signature=None) + + Returns an object that acts like pyfunc, but takes arrays as input. + + Define a vectorized function which takes a nested sequence of objects or + numpy arrays as inputs and returns a single numpy array or a tuple of numpy + arrays. The vectorized function evaluates `pyfunc` over successive tuples + of the input arrays like the python map function, except it uses the + broadcasting rules of numpy. + + The data type of the output of `vectorized` is determined by calling + the function with the first element of the input. This can be avoided + by specifying the `otypes` argument. + + Parameters + ---------- + pyfunc : callable, optional + A python function or method. + Can be omitted to produce a decorator with keyword arguments. + otypes : str or list of dtypes, optional + The output data type. It must be specified as either a string of + typecode characters or a list of data type specifiers. There should + be one data type specifier for each output. + doc : str, optional + The docstring for the function. If None, the docstring will be the + ``pyfunc.__doc__``. + excluded : set, optional + Set of strings or integers representing the positional or keyword + arguments for which the function will not be vectorized. These will be + passed directly to `pyfunc` unmodified. + + .. versionadded:: 1.7.0 + + cache : bool, optional + If `True`, then cache the first function call that determines the number + of outputs if `otypes` is not provided. + + .. versionadded:: 1.7.0 + + signature : string, optional + Generalized universal function signature, e.g., ``(m,n),(n)->(m)`` for + vectorized matrix-vector multiplication. If provided, ``pyfunc`` will + be called with (and expected to return) arrays with shapes given by the + size of corresponding core dimensions. By default, ``pyfunc`` is + assumed to take scalars as input and output. + + .. versionadded:: 1.12.0 + + Returns + ------- + out : callable + A vectorized function if ``pyfunc`` was provided, + a decorator otherwise. + + See Also + -------- + frompyfunc : Takes an arbitrary Python function and returns a ufunc + + Notes + ----- + The `vectorize` function is provided primarily for convenience, not for + performance. The implementation is essentially a for loop. + + If `otypes` is not specified, then a call to the function with the + first argument will be used to determine the number of outputs. The + results of this call will be cached if `cache` is `True` to prevent + calling the function twice. However, to implement the cache, the + original function must be wrapped which will slow down subsequent + calls, so only do this if your function is expensive. + + The new keyword argument interface and `excluded` argument support + further degrades performance. + + References + ---------- + .. [1] :doc:`/reference/c-api/generalized-ufuncs` + + Examples + -------- + >>> def myfunc(a, b): + ... "Return a-b if a>b, otherwise return a+b" + ... if a > b: + ... return a - b + ... else: + ... return a + b + + >>> vfunc = np.vectorize(myfunc) + >>> vfunc([1, 2, 3, 4], 2) + array([3, 4, 1, 2]) + + The docstring is taken from the input function to `vectorize` unless it + is specified: + + >>> vfunc.__doc__ + 'Return a-b if a>b, otherwise return a+b' + >>> vfunc = np.vectorize(myfunc, doc='Vectorized `myfunc`') + >>> vfunc.__doc__ + 'Vectorized `myfunc`' + + The output type is determined by evaluating the first element of the input, + unless it is specified: + + >>> out = vfunc([1, 2, 3, 4], 2) + >>> type(out[0]) + + >>> vfunc = np.vectorize(myfunc, otypes=[float]) + >>> out = vfunc([1, 2, 3, 4], 2) + >>> type(out[0]) + + + The `excluded` argument can be used to prevent vectorizing over certain + arguments. This can be useful for array-like arguments of a fixed length + such as the coefficients for a polynomial as in `polyval`: + + >>> def mypolyval(p, x): + ... _p = list(p) + ... res = _p.pop(0) + ... while _p: + ... res = res*x + _p.pop(0) + ... return res + >>> vpolyval = np.vectorize(mypolyval, excluded=['p']) + >>> vpolyval(p=[1, 2, 3], x=[0, 1]) + array([3, 6]) + + Positional arguments may also be excluded by specifying their position: + + >>> vpolyval.excluded.add(0) + >>> vpolyval([1, 2, 3], x=[0, 1]) + array([3, 6]) + + The `signature` argument allows for vectorizing functions that act on + non-scalar arrays of fixed length. For example, you can use it for a + vectorized calculation of Pearson correlation coefficient and its p-value: + + >>> import scipy.stats + >>> pearsonr = np.vectorize(scipy.stats.pearsonr, + ... signature='(n),(n)->(),()') + >>> pearsonr([[0, 1, 2, 3]], [[1, 2, 3, 4], [4, 3, 2, 1]]) + (array([ 1., -1.]), array([ 0., 0.])) + + Or for a vectorized convolution: + + >>> convolve = np.vectorize(np.convolve, signature='(n),(m)->(k)') + >>> convolve(np.eye(4), [1, 2, 1]) + array([[1., 2., 1., 0., 0., 0.], + [0., 1., 2., 1., 0., 0.], + [0., 0., 1., 2., 1., 0.], + [0., 0., 0., 1., 2., 1.]]) + + Decorator syntax is supported. The decorator can be called as + a function to provide keyword arguments. + >>>@np.vectorize + ...def identity(x): + ... return x + ... + >>>identity([0, 1, 2]) + array([0, 1, 2]) + >>>@np.vectorize(otypes=[float]) + ...def as_float(x): + ... return x + ... + >>>as_float([0, 1, 2]) + array([0., 1., 2.]) + """ + def __init__(self, pyfunc=np._NoValue, otypes=None, doc=None, + excluded=None, cache=False, signature=None): + + if (pyfunc != np._NoValue) and (not callable(pyfunc)): + #Splitting the error message to keep + #the length below 79 characters. + part1 = "When used as a decorator, " + part2 = "only accepts keyword arguments." + raise TypeError(part1 + part2) + + self.pyfunc = pyfunc + self.cache = cache + self.signature = signature + if pyfunc != np._NoValue and hasattr(pyfunc, '__name__'): + self.__name__ = pyfunc.__name__ + + self._ufunc = {} # Caching to improve default performance + self._doc = None + self.__doc__ = doc + if doc is None and hasattr(pyfunc, '__doc__'): + self.__doc__ = pyfunc.__doc__ + else: + self._doc = doc + + if isinstance(otypes, str): + for char in otypes: + if char not in typecodes['All']: + raise ValueError("Invalid otype specified: %s" % (char,)) + elif iterable(otypes): + otypes = ''.join([_nx.dtype(x).char for x in otypes]) + elif otypes is not None: + raise ValueError("Invalid otype specification") + self.otypes = otypes + + # Excluded variable support + if excluded is None: + excluded = set() + self.excluded = set(excluded) + + if signature is not None: + self._in_and_out_core_dims = _parse_gufunc_signature(signature) + else: + self._in_and_out_core_dims = None + + def _init_stage_2(self, pyfunc, *args, **kwargs): + self.__name__ = pyfunc.__name__ + self.pyfunc = pyfunc + if self._doc is None: + self.__doc__ = pyfunc.__doc__ + else: + self.__doc__ = self._doc + + def _call_as_normal(self, *args, **kwargs): + """ + Return arrays with the results of `pyfunc` broadcast (vectorized) over + `args` and `kwargs` not in `excluded`. + """ + excluded = self.excluded + if not kwargs and not excluded: + func = self.pyfunc + vargs = args + else: + # The wrapper accepts only positional arguments: we use `names` and + # `inds` to mutate `the_args` and `kwargs` to pass to the original + # function. + nargs = len(args) + + names = [_n for _n in kwargs if _n not in excluded] + inds = [_i for _i in range(nargs) if _i not in excluded] + the_args = list(args) + + def func(*vargs): + for _n, _i in enumerate(inds): + the_args[_i] = vargs[_n] + kwargs.update(zip(names, vargs[len(inds):])) + return self.pyfunc(*the_args, **kwargs) + + vargs = [args[_i] for _i in inds] + vargs.extend([kwargs[_n] for _n in names]) + + return self._vectorize_call(func=func, args=vargs) + + def __call__(self, *args, **kwargs): + if self.pyfunc is np._NoValue: + self._init_stage_2(*args, **kwargs) + return self + + return self._call_as_normal(*args, **kwargs) + + def _get_ufunc_and_otypes(self, func, args): + """Return (ufunc, otypes).""" + # frompyfunc will fail if args is empty + if not args: + raise ValueError('args can not be empty') + + if self.otypes is not None: + otypes = self.otypes + + # self._ufunc is a dictionary whose keys are the number of + # arguments (i.e. len(args)) and whose values are ufuncs created + # by frompyfunc. len(args) can be different for different calls if + # self.pyfunc has parameters with default values. We only use the + # cache when func is self.pyfunc, which occurs when the call uses + # only positional arguments and no arguments are excluded. + + nin = len(args) + nout = len(self.otypes) + if func is not self.pyfunc or nin not in self._ufunc: + ufunc = frompyfunc(func, nin, nout) + else: + ufunc = None # We'll get it from self._ufunc + if func is self.pyfunc: + ufunc = self._ufunc.setdefault(nin, ufunc) + else: + # Get number of outputs and output types by calling the function on + # the first entries of args. We also cache the result to prevent + # the subsequent call when the ufunc is evaluated. + # Assumes that ufunc first evaluates the 0th elements in the input + # arrays (the input values are not checked to ensure this) + args = [asarray(arg) for arg in args] + if builtins.any(arg.size == 0 for arg in args): + raise ValueError('cannot call `vectorize` on size 0 inputs ' + 'unless `otypes` is set') + + inputs = [arg.flat[0] for arg in args] + outputs = func(*inputs) + + # Performance note: profiling indicates that -- for simple + # functions at least -- this wrapping can almost double the + # execution time. + # Hence we make it optional. + if self.cache: + _cache = [outputs] + + def _func(*vargs): + if _cache: + return _cache.pop() + else: + return func(*vargs) + else: + _func = func + + if isinstance(outputs, tuple): + nout = len(outputs) + else: + nout = 1 + outputs = (outputs,) + + otypes = ''.join([asarray(outputs[_k]).dtype.char + for _k in range(nout)]) + + # Performance note: profiling indicates that creating the ufunc is + # not a significant cost compared with wrapping so it seems not + # worth trying to cache this. + ufunc = frompyfunc(_func, len(args), nout) + + return ufunc, otypes + + def _vectorize_call(self, func, args): + """Vectorized call to `func` over positional `args`.""" + if self.signature is not None: + res = self._vectorize_call_with_signature(func, args) + elif not args: + res = func() + else: + ufunc, otypes = self._get_ufunc_and_otypes(func=func, args=args) + + # Convert args to object arrays first + inputs = [asanyarray(a, dtype=object) for a in args] + + outputs = ufunc(*inputs) + + if ufunc.nout == 1: + res = asanyarray(outputs, dtype=otypes[0]) + else: + res = tuple([asanyarray(x, dtype=t) + for x, t in zip(outputs, otypes)]) + return res + + def _vectorize_call_with_signature(self, func, args): + """Vectorized call over positional arguments with a signature.""" + input_core_dims, output_core_dims = self._in_and_out_core_dims + + if len(args) != len(input_core_dims): + raise TypeError('wrong number of positional arguments: ' + 'expected %r, got %r' + % (len(input_core_dims), len(args))) + args = tuple(asanyarray(arg) for arg in args) + + broadcast_shape, dim_sizes = _parse_input_dimensions( + args, input_core_dims) + input_shapes = _calculate_shapes(broadcast_shape, dim_sizes, + input_core_dims) + args = [np.broadcast_to(arg, shape, subok=True) + for arg, shape in zip(args, input_shapes)] + + outputs = None + otypes = self.otypes + nout = len(output_core_dims) + + for index in np.ndindex(*broadcast_shape): + results = func(*(arg[index] for arg in args)) + + n_results = len(results) if isinstance(results, tuple) else 1 + + if nout != n_results: + raise ValueError( + 'wrong number of outputs from pyfunc: expected %r, got %r' + % (nout, n_results)) + + if nout == 1: + results = (results,) + + if outputs is None: + for result, core_dims in zip(results, output_core_dims): + _update_dim_sizes(dim_sizes, result, core_dims) + + outputs = _create_arrays(broadcast_shape, dim_sizes, + output_core_dims, otypes, results) + + for output, result in zip(outputs, results): + output[index] = result + + if outputs is None: + # did not call the function even once + if otypes is None: + raise ValueError('cannot call `vectorize` on size 0 inputs ' + 'unless `otypes` is set') + if builtins.any(dim not in dim_sizes + for dims in output_core_dims + for dim in dims): + raise ValueError('cannot call `vectorize` with a signature ' + 'including new output dimensions on size 0 ' + 'inputs') + outputs = _create_arrays(broadcast_shape, dim_sizes, + output_core_dims, otypes) + + return outputs[0] if nout == 1 else outputs + + +def _cov_dispatcher(m, y=None, rowvar=None, bias=None, ddof=None, + fweights=None, aweights=None, *, dtype=None): + return (m, y, fweights, aweights) + + +@array_function_dispatch(_cov_dispatcher) +def cov(m, y=None, rowvar=True, bias=False, ddof=None, fweights=None, + aweights=None, *, dtype=None): + """ + Estimate a covariance matrix, given data and weights. + + Covariance indicates the level to which two variables vary together. + If we examine N-dimensional samples, :math:`X = [x_1, x_2, ... x_N]^T`, + then the covariance matrix element :math:`C_{ij}` is the covariance of + :math:`x_i` and :math:`x_j`. The element :math:`C_{ii}` is the variance + of :math:`x_i`. + + See the notes for an outline of the algorithm. + + Parameters + ---------- + m : array_like + A 1-D or 2-D array containing multiple variables and observations. + Each row of `m` represents a variable, and each column a single + observation of all those variables. Also see `rowvar` below. + y : array_like, optional + An additional set of variables and observations. `y` has the same form + as that of `m`. + rowvar : bool, optional + If `rowvar` is True (default), then each row represents a + variable, with observations in the columns. Otherwise, the relationship + is transposed: each column represents a variable, while the rows + contain observations. + bias : bool, optional + Default normalization (False) is by ``(N - 1)``, where ``N`` is the + number of observations given (unbiased estimate). If `bias` is True, + then normalization is by ``N``. These values can be overridden by using + the keyword ``ddof`` in numpy versions >= 1.5. + ddof : int, optional + If not ``None`` the default value implied by `bias` is overridden. + Note that ``ddof=1`` will return the unbiased estimate, even if both + `fweights` and `aweights` are specified, and ``ddof=0`` will return + the simple average. See the notes for the details. The default value + is ``None``. + + .. versionadded:: 1.5 + fweights : array_like, int, optional + 1-D array of integer frequency weights; the number of times each + observation vector should be repeated. + + .. versionadded:: 1.10 + aweights : array_like, optional + 1-D array of observation vector weights. These relative weights are + typically large for observations considered "important" and smaller for + observations considered less "important". If ``ddof=0`` the array of + weights can be used to assign probabilities to observation vectors. + + .. versionadded:: 1.10 + dtype : data-type, optional + Data-type of the result. By default, the return data-type will have + at least `numpy.float64` precision. + + .. versionadded:: 1.20 + + Returns + ------- + out : ndarray + The covariance matrix of the variables. + + See Also + -------- + corrcoef : Normalized covariance matrix + + Notes + ----- + Assume that the observations are in the columns of the observation + array `m` and let ``f = fweights`` and ``a = aweights`` for brevity. The + steps to compute the weighted covariance are as follows:: + + >>> m = np.arange(10, dtype=np.float64) + >>> f = np.arange(10) * 2 + >>> a = np.arange(10) ** 2. + >>> ddof = 1 + >>> w = f * a + >>> v1 = np.sum(w) + >>> v2 = np.sum(w * a) + >>> m -= np.sum(m * w, axis=None, keepdims=True) / v1 + >>> cov = np.dot(m * w, m.T) * v1 / (v1**2 - ddof * v2) + + Note that when ``a == 1``, the normalization factor + ``v1 / (v1**2 - ddof * v2)`` goes over to ``1 / (np.sum(f) - ddof)`` + as it should. + + Examples + -------- + Consider two variables, :math:`x_0` and :math:`x_1`, which + correlate perfectly, but in opposite directions: + + >>> x = np.array([[0, 2], [1, 1], [2, 0]]).T + >>> x + array([[0, 1, 2], + [2, 1, 0]]) + + Note how :math:`x_0` increases while :math:`x_1` decreases. The covariance + matrix shows this clearly: + + >>> np.cov(x) + array([[ 1., -1.], + [-1., 1.]]) + + Note that element :math:`C_{0,1}`, which shows the correlation between + :math:`x_0` and :math:`x_1`, is negative. + + Further, note how `x` and `y` are combined: + + >>> x = [-2.1, -1, 4.3] + >>> y = [3, 1.1, 0.12] + >>> X = np.stack((x, y), axis=0) + >>> np.cov(X) + array([[11.71 , -4.286 ], # may vary + [-4.286 , 2.144133]]) + >>> np.cov(x, y) + array([[11.71 , -4.286 ], # may vary + [-4.286 , 2.144133]]) + >>> np.cov(x) + array(11.71) + + """ + # Check inputs + if ddof is not None and ddof != int(ddof): + raise ValueError( + "ddof must be integer") + + # Handles complex arrays too + m = np.asarray(m) + if m.ndim > 2: + raise ValueError("m has more than 2 dimensions") + + if y is not None: + y = np.asarray(y) + if y.ndim > 2: + raise ValueError("y has more than 2 dimensions") + + if dtype is None: + if y is None: + dtype = np.result_type(m, np.float64) + else: + dtype = np.result_type(m, y, np.float64) + + X = array(m, ndmin=2, dtype=dtype) + if not rowvar and X.shape[0] != 1: + X = X.T + if X.shape[0] == 0: + return np.array([]).reshape(0, 0) + if y is not None: + y = array(y, copy=False, ndmin=2, dtype=dtype) + if not rowvar and y.shape[0] != 1: + y = y.T + X = np.concatenate((X, y), axis=0) + + if ddof is None: + if bias == 0: + ddof = 1 + else: + ddof = 0 + + # Get the product of frequencies and weights + w = None + if fweights is not None: + fweights = np.asarray(fweights, dtype=float) + if not np.all(fweights == np.around(fweights)): + raise TypeError( + "fweights must be integer") + if fweights.ndim > 1: + raise RuntimeError( + "cannot handle multidimensional fweights") + if fweights.shape[0] != X.shape[1]: + raise RuntimeError( + "incompatible numbers of samples and fweights") + if any(fweights < 0): + raise ValueError( + "fweights cannot be negative") + w = fweights + if aweights is not None: + aweights = np.asarray(aweights, dtype=float) + if aweights.ndim > 1: + raise RuntimeError( + "cannot handle multidimensional aweights") + if aweights.shape[0] != X.shape[1]: + raise RuntimeError( + "incompatible numbers of samples and aweights") + if any(aweights < 0): + raise ValueError( + "aweights cannot be negative") + if w is None: + w = aweights + else: + w *= aweights + + avg, w_sum = average(X, axis=1, weights=w, returned=True) + w_sum = w_sum[0] + + # Determine the normalization + if w is None: + fact = X.shape[1] - ddof + elif ddof == 0: + fact = w_sum + elif aweights is None: + fact = w_sum - ddof + else: + fact = w_sum - ddof*sum(w*aweights)/w_sum + + if fact <= 0: + warnings.warn("Degrees of freedom <= 0 for slice", + RuntimeWarning, stacklevel=2) + fact = 0.0 + + X -= avg[:, None] + if w is None: + X_T = X.T + else: + X_T = (X*w).T + c = dot(X, X_T.conj()) + c *= np.true_divide(1, fact) + return c.squeeze() + + +def _corrcoef_dispatcher(x, y=None, rowvar=None, bias=None, ddof=None, *, + dtype=None): + return (x, y) + + +@array_function_dispatch(_corrcoef_dispatcher) +def corrcoef(x, y=None, rowvar=True, bias=np._NoValue, ddof=np._NoValue, *, + dtype=None): + """ + Return Pearson product-moment correlation coefficients. + + Please refer to the documentation for `cov` for more detail. The + relationship between the correlation coefficient matrix, `R`, and the + covariance matrix, `C`, is + + .. math:: R_{ij} = \\frac{ C_{ij} } { \\sqrt{ C_{ii} C_{jj} } } + + The values of `R` are between -1 and 1, inclusive. + + Parameters + ---------- + x : array_like + A 1-D or 2-D array containing multiple variables and observations. + Each row of `x` represents a variable, and each column a single + observation of all those variables. Also see `rowvar` below. + y : array_like, optional + An additional set of variables and observations. `y` has the same + shape as `x`. + rowvar : bool, optional + If `rowvar` is True (default), then each row represents a + variable, with observations in the columns. Otherwise, the relationship + is transposed: each column represents a variable, while the rows + contain observations. + bias : _NoValue, optional + Has no effect, do not use. + + .. deprecated:: 1.10.0 + ddof : _NoValue, optional + Has no effect, do not use. + + .. deprecated:: 1.10.0 + dtype : data-type, optional + Data-type of the result. By default, the return data-type will have + at least `numpy.float64` precision. + + .. versionadded:: 1.20 + + Returns + ------- + R : ndarray + The correlation coefficient matrix of the variables. + + See Also + -------- + cov : Covariance matrix + + Notes + ----- + Due to floating point rounding the resulting array may not be Hermitian, + the diagonal elements may not be 1, and the elements may not satisfy the + inequality abs(a) <= 1. The real and imaginary parts are clipped to the + interval [-1, 1] in an attempt to improve on that situation but is not + much help in the complex case. + + This function accepts but discards arguments `bias` and `ddof`. This is + for backwards compatibility with previous versions of this function. These + arguments had no effect on the return values of the function and can be + safely ignored in this and previous versions of numpy. + + Examples + -------- + In this example we generate two random arrays, ``xarr`` and ``yarr``, and + compute the row-wise and column-wise Pearson correlation coefficients, + ``R``. Since ``rowvar`` is true by default, we first find the row-wise + Pearson correlation coefficients between the variables of ``xarr``. + + >>> import numpy as np + >>> rng = np.random.default_rng(seed=42) + >>> xarr = rng.random((3, 3)) + >>> xarr + array([[0.77395605, 0.43887844, 0.85859792], + [0.69736803, 0.09417735, 0.97562235], + [0.7611397 , 0.78606431, 0.12811363]]) + >>> R1 = np.corrcoef(xarr) + >>> R1 + array([[ 1. , 0.99256089, -0.68080986], + [ 0.99256089, 1. , -0.76492172], + [-0.68080986, -0.76492172, 1. ]]) + + If we add another set of variables and observations ``yarr``, we can + compute the row-wise Pearson correlation coefficients between the + variables in ``xarr`` and ``yarr``. + + >>> yarr = rng.random((3, 3)) + >>> yarr + array([[0.45038594, 0.37079802, 0.92676499], + [0.64386512, 0.82276161, 0.4434142 ], + [0.22723872, 0.55458479, 0.06381726]]) + >>> R2 = np.corrcoef(xarr, yarr) + >>> R2 + array([[ 1. , 0.99256089, -0.68080986, 0.75008178, -0.934284 , + -0.99004057], + [ 0.99256089, 1. , -0.76492172, 0.82502011, -0.97074098, + -0.99981569], + [-0.68080986, -0.76492172, 1. , -0.99507202, 0.89721355, + 0.77714685], + [ 0.75008178, 0.82502011, -0.99507202, 1. , -0.93657855, + -0.83571711], + [-0.934284 , -0.97074098, 0.89721355, -0.93657855, 1. , + 0.97517215], + [-0.99004057, -0.99981569, 0.77714685, -0.83571711, 0.97517215, + 1. ]]) + + Finally if we use the option ``rowvar=False``, the columns are now + being treated as the variables and we will find the column-wise Pearson + correlation coefficients between variables in ``xarr`` and ``yarr``. + + >>> R3 = np.corrcoef(xarr, yarr, rowvar=False) + >>> R3 + array([[ 1. , 0.77598074, -0.47458546, -0.75078643, -0.9665554 , + 0.22423734], + [ 0.77598074, 1. , -0.92346708, -0.99923895, -0.58826587, + -0.44069024], + [-0.47458546, -0.92346708, 1. , 0.93773029, 0.23297648, + 0.75137473], + [-0.75078643, -0.99923895, 0.93773029, 1. , 0.55627469, + 0.47536961], + [-0.9665554 , -0.58826587, 0.23297648, 0.55627469, 1. , + -0.46666491], + [ 0.22423734, -0.44069024, 0.75137473, 0.47536961, -0.46666491, + 1. ]]) + + """ + if bias is not np._NoValue or ddof is not np._NoValue: + # 2015-03-15, 1.10 + warnings.warn('bias and ddof have no effect and are deprecated', + DeprecationWarning, stacklevel=2) + c = cov(x, y, rowvar, dtype=dtype) + try: + d = diag(c) + except ValueError: + # scalar covariance + # nan if incorrect value (nan, inf, 0), 1 otherwise + return c / c + stddev = sqrt(d.real) + c /= stddev[:, None] + c /= stddev[None, :] + + # Clip real and imaginary parts to [-1, 1]. This does not guarantee + # abs(a[i,j]) <= 1 for complex arrays, but is the best we can do without + # excessive work. + np.clip(c.real, -1, 1, out=c.real) + if np.iscomplexobj(c): + np.clip(c.imag, -1, 1, out=c.imag) + + return c + + +@set_module('numpy') +def blackman(M): + """ + Return the Blackman window. + + The Blackman window is a taper formed by using the first three + terms of a summation of cosines. It was designed to have close to the + minimal leakage possible. It is close to optimal, only slightly worse + than a Kaiser window. + + Parameters + ---------- + M : int + Number of points in the output window. If zero or less, an empty + array is returned. + + Returns + ------- + out : ndarray + The window, with the maximum value normalized to one (the value one + appears only if the number of samples is odd). + + See Also + -------- + bartlett, hamming, hanning, kaiser + + Notes + ----- + The Blackman window is defined as + + .. math:: w(n) = 0.42 - 0.5 \\cos(2\\pi n/M) + 0.08 \\cos(4\\pi n/M) + + Most references to the Blackman window come from the signal processing + literature, where it is used as one of many windowing functions for + smoothing values. It is also known as an apodization (which means + "removing the foot", i.e. smoothing discontinuities at the beginning + and end of the sampled signal) or tapering function. It is known as a + "near optimal" tapering function, almost as good (by some measures) + as the kaiser window. + + References + ---------- + Blackman, R.B. and Tukey, J.W., (1958) The measurement of power spectra, + Dover Publications, New York. + + Oppenheim, A.V., and R.W. Schafer. Discrete-Time Signal Processing. + Upper Saddle River, NJ: Prentice-Hall, 1999, pp. 468-471. + + Examples + -------- + >>> import matplotlib.pyplot as plt + >>> np.blackman(12) + array([-1.38777878e-17, 3.26064346e-02, 1.59903635e-01, # may vary + 4.14397981e-01, 7.36045180e-01, 9.67046769e-01, + 9.67046769e-01, 7.36045180e-01, 4.14397981e-01, + 1.59903635e-01, 3.26064346e-02, -1.38777878e-17]) + + Plot the window and the frequency response: + + >>> from numpy.fft import fft, fftshift + >>> window = np.blackman(51) + >>> plt.plot(window) + [] + >>> plt.title("Blackman window") + Text(0.5, 1.0, 'Blackman window') + >>> plt.ylabel("Amplitude") + Text(0, 0.5, 'Amplitude') + >>> plt.xlabel("Sample") + Text(0.5, 0, 'Sample') + >>> plt.show() + + >>> plt.figure() +
+ >>> A = fft(window, 2048) / 25.5 + >>> mag = np.abs(fftshift(A)) + >>> freq = np.linspace(-0.5, 0.5, len(A)) + >>> with np.errstate(divide='ignore', invalid='ignore'): + ... response = 20 * np.log10(mag) + ... + >>> response = np.clip(response, -100, 100) + >>> plt.plot(freq, response) + [] + >>> plt.title("Frequency response of Blackman window") + Text(0.5, 1.0, 'Frequency response of Blackman window') + >>> plt.ylabel("Magnitude [dB]") + Text(0, 0.5, 'Magnitude [dB]') + >>> plt.xlabel("Normalized frequency [cycles per sample]") + Text(0.5, 0, 'Normalized frequency [cycles per sample]') + >>> _ = plt.axis('tight') + >>> plt.show() + + """ + # Ensures at least float64 via 0.0. M should be an integer, but conversion + # to double is safe for a range. + values = np.array([0.0, M]) + M = values[1] + + if M < 1: + return array([], dtype=values.dtype) + if M == 1: + return ones(1, dtype=values.dtype) + n = arange(1-M, M, 2) + return 0.42 + 0.5*cos(pi*n/(M-1)) + 0.08*cos(2.0*pi*n/(M-1)) + + +@set_module('numpy') +def bartlett(M): + """ + Return the Bartlett window. + + The Bartlett window is very similar to a triangular window, except + that the end points are at zero. It is often used in signal + processing for tapering a signal, without generating too much + ripple in the frequency domain. + + Parameters + ---------- + M : int + Number of points in the output window. If zero or less, an + empty array is returned. + + Returns + ------- + out : array + The triangular window, with the maximum value normalized to one + (the value one appears only if the number of samples is odd), with + the first and last samples equal to zero. + + See Also + -------- + blackman, hamming, hanning, kaiser + + Notes + ----- + The Bartlett window is defined as + + .. math:: w(n) = \\frac{2}{M-1} \\left( + \\frac{M-1}{2} - \\left|n - \\frac{M-1}{2}\\right| + \\right) + + Most references to the Bartlett window come from the signal processing + literature, where it is used as one of many windowing functions for + smoothing values. Note that convolution with this window produces linear + interpolation. It is also known as an apodization (which means "removing + the foot", i.e. smoothing discontinuities at the beginning and end of the + sampled signal) or tapering function. The Fourier transform of the + Bartlett window is the product of two sinc functions. Note the excellent + discussion in Kanasewich [2]_. + + References + ---------- + .. [1] M.S. Bartlett, "Periodogram Analysis and Continuous Spectra", + Biometrika 37, 1-16, 1950. + .. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics", + The University of Alberta Press, 1975, pp. 109-110. + .. [3] A.V. Oppenheim and R.W. Schafer, "Discrete-Time Signal + Processing", Prentice-Hall, 1999, pp. 468-471. + .. [4] Wikipedia, "Window function", + https://en.wikipedia.org/wiki/Window_function + .. [5] W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling, + "Numerical Recipes", Cambridge University Press, 1986, page 429. + + Examples + -------- + >>> import matplotlib.pyplot as plt + >>> np.bartlett(12) + array([ 0. , 0.18181818, 0.36363636, 0.54545455, 0.72727273, # may vary + 0.90909091, 0.90909091, 0.72727273, 0.54545455, 0.36363636, + 0.18181818, 0. ]) + + Plot the window and its frequency response (requires SciPy and matplotlib): + + >>> from numpy.fft import fft, fftshift + >>> window = np.bartlett(51) + >>> plt.plot(window) + [] + >>> plt.title("Bartlett window") + Text(0.5, 1.0, 'Bartlett window') + >>> plt.ylabel("Amplitude") + Text(0, 0.5, 'Amplitude') + >>> plt.xlabel("Sample") + Text(0.5, 0, 'Sample') + >>> plt.show() + + >>> plt.figure() +
+ >>> A = fft(window, 2048) / 25.5 + >>> mag = np.abs(fftshift(A)) + >>> freq = np.linspace(-0.5, 0.5, len(A)) + >>> with np.errstate(divide='ignore', invalid='ignore'): + ... response = 20 * np.log10(mag) + ... + >>> response = np.clip(response, -100, 100) + >>> plt.plot(freq, response) + [] + >>> plt.title("Frequency response of Bartlett window") + Text(0.5, 1.0, 'Frequency response of Bartlett window') + >>> plt.ylabel("Magnitude [dB]") + Text(0, 0.5, 'Magnitude [dB]') + >>> plt.xlabel("Normalized frequency [cycles per sample]") + Text(0.5, 0, 'Normalized frequency [cycles per sample]') + >>> _ = plt.axis('tight') + >>> plt.show() + + """ + # Ensures at least float64 via 0.0. M should be an integer, but conversion + # to double is safe for a range. + values = np.array([0.0, M]) + M = values[1] + + if M < 1: + return array([], dtype=values.dtype) + if M == 1: + return ones(1, dtype=values.dtype) + n = arange(1-M, M, 2) + return where(less_equal(n, 0), 1 + n/(M-1), 1 - n/(M-1)) + + +@set_module('numpy') +def hanning(M): + """ + Return the Hanning window. + + The Hanning window is a taper formed by using a weighted cosine. + + Parameters + ---------- + M : int + Number of points in the output window. If zero or less, an + empty array is returned. + + Returns + ------- + out : ndarray, shape(M,) + The window, with the maximum value normalized to one (the value + one appears only if `M` is odd). + + See Also + -------- + bartlett, blackman, hamming, kaiser + + Notes + ----- + The Hanning window is defined as + + .. math:: w(n) = 0.5 - 0.5\\cos\\left(\\frac{2\\pi{n}}{M-1}\\right) + \\qquad 0 \\leq n \\leq M-1 + + The Hanning was named for Julius von Hann, an Austrian meteorologist. + It is also known as the Cosine Bell. Some authors prefer that it be + called a Hann window, to help avoid confusion with the very similar + Hamming window. + + Most references to the Hanning window come from the signal processing + literature, where it is used as one of many windowing functions for + smoothing values. It is also known as an apodization (which means + "removing the foot", i.e. smoothing discontinuities at the beginning + and end of the sampled signal) or tapering function. + + References + ---------- + .. [1] Blackman, R.B. and Tukey, J.W., (1958) The measurement of power + spectra, Dover Publications, New York. + .. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics", + The University of Alberta Press, 1975, pp. 106-108. + .. [3] Wikipedia, "Window function", + https://en.wikipedia.org/wiki/Window_function + .. [4] W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling, + "Numerical Recipes", Cambridge University Press, 1986, page 425. + + Examples + -------- + >>> np.hanning(12) + array([0. , 0.07937323, 0.29229249, 0.57115742, 0.82743037, + 0.97974649, 0.97974649, 0.82743037, 0.57115742, 0.29229249, + 0.07937323, 0. ]) + + Plot the window and its frequency response: + + >>> import matplotlib.pyplot as plt + >>> from numpy.fft import fft, fftshift + >>> window = np.hanning(51) + >>> plt.plot(window) + [] + >>> plt.title("Hann window") + Text(0.5, 1.0, 'Hann window') + >>> plt.ylabel("Amplitude") + Text(0, 0.5, 'Amplitude') + >>> plt.xlabel("Sample") + Text(0.5, 0, 'Sample') + >>> plt.show() + + >>> plt.figure() +
+ >>> A = fft(window, 2048) / 25.5 + >>> mag = np.abs(fftshift(A)) + >>> freq = np.linspace(-0.5, 0.5, len(A)) + >>> with np.errstate(divide='ignore', invalid='ignore'): + ... response = 20 * np.log10(mag) + ... + >>> response = np.clip(response, -100, 100) + >>> plt.plot(freq, response) + [] + >>> plt.title("Frequency response of the Hann window") + Text(0.5, 1.0, 'Frequency response of the Hann window') + >>> plt.ylabel("Magnitude [dB]") + Text(0, 0.5, 'Magnitude [dB]') + >>> plt.xlabel("Normalized frequency [cycles per sample]") + Text(0.5, 0, 'Normalized frequency [cycles per sample]') + >>> plt.axis('tight') + ... + >>> plt.show() + + """ + # Ensures at least float64 via 0.0. M should be an integer, but conversion + # to double is safe for a range. + values = np.array([0.0, M]) + M = values[1] + + if M < 1: + return array([], dtype=values.dtype) + if M == 1: + return ones(1, dtype=values.dtype) + n = arange(1-M, M, 2) + return 0.5 + 0.5*cos(pi*n/(M-1)) + + +@set_module('numpy') +def hamming(M): + """ + Return the Hamming window. + + The Hamming window is a taper formed by using a weighted cosine. + + Parameters + ---------- + M : int + Number of points in the output window. If zero or less, an + empty array is returned. + + Returns + ------- + out : ndarray + The window, with the maximum value normalized to one (the value + one appears only if the number of samples is odd). + + See Also + -------- + bartlett, blackman, hanning, kaiser + + Notes + ----- + The Hamming window is defined as + + .. math:: w(n) = 0.54 - 0.46\\cos\\left(\\frac{2\\pi{n}}{M-1}\\right) + \\qquad 0 \\leq n \\leq M-1 + + The Hamming was named for R. W. Hamming, an associate of J. W. Tukey + and is described in Blackman and Tukey. It was recommended for + smoothing the truncated autocovariance function in the time domain. + Most references to the Hamming window come from the signal processing + literature, where it is used as one of many windowing functions for + smoothing values. It is also known as an apodization (which means + "removing the foot", i.e. smoothing discontinuities at the beginning + and end of the sampled signal) or tapering function. + + References + ---------- + .. [1] Blackman, R.B. and Tukey, J.W., (1958) The measurement of power + spectra, Dover Publications, New York. + .. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics", The + University of Alberta Press, 1975, pp. 109-110. + .. [3] Wikipedia, "Window function", + https://en.wikipedia.org/wiki/Window_function + .. [4] W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling, + "Numerical Recipes", Cambridge University Press, 1986, page 425. + + Examples + -------- + >>> np.hamming(12) + array([ 0.08 , 0.15302337, 0.34890909, 0.60546483, 0.84123594, # may vary + 0.98136677, 0.98136677, 0.84123594, 0.60546483, 0.34890909, + 0.15302337, 0.08 ]) + + Plot the window and the frequency response: + + >>> import matplotlib.pyplot as plt + >>> from numpy.fft import fft, fftshift + >>> window = np.hamming(51) + >>> plt.plot(window) + [] + >>> plt.title("Hamming window") + Text(0.5, 1.0, 'Hamming window') + >>> plt.ylabel("Amplitude") + Text(0, 0.5, 'Amplitude') + >>> plt.xlabel("Sample") + Text(0.5, 0, 'Sample') + >>> plt.show() + + >>> plt.figure() +
+ >>> A = fft(window, 2048) / 25.5 + >>> mag = np.abs(fftshift(A)) + >>> freq = np.linspace(-0.5, 0.5, len(A)) + >>> response = 20 * np.log10(mag) + >>> response = np.clip(response, -100, 100) + >>> plt.plot(freq, response) + [] + >>> plt.title("Frequency response of Hamming window") + Text(0.5, 1.0, 'Frequency response of Hamming window') + >>> plt.ylabel("Magnitude [dB]") + Text(0, 0.5, 'Magnitude [dB]') + >>> plt.xlabel("Normalized frequency [cycles per sample]") + Text(0.5, 0, 'Normalized frequency [cycles per sample]') + >>> plt.axis('tight') + ... + >>> plt.show() + + """ + # Ensures at least float64 via 0.0. M should be an integer, but conversion + # to double is safe for a range. + values = np.array([0.0, M]) + M = values[1] + + if M < 1: + return array([], dtype=values.dtype) + if M == 1: + return ones(1, dtype=values.dtype) + n = arange(1-M, M, 2) + return 0.54 + 0.46*cos(pi*n/(M-1)) + + +## Code from cephes for i0 + +_i0A = [ + -4.41534164647933937950E-18, + 3.33079451882223809783E-17, + -2.43127984654795469359E-16, + 1.71539128555513303061E-15, + -1.16853328779934516808E-14, + 7.67618549860493561688E-14, + -4.85644678311192946090E-13, + 2.95505266312963983461E-12, + -1.72682629144155570723E-11, + 9.67580903537323691224E-11, + -5.18979560163526290666E-10, + 2.65982372468238665035E-9, + -1.30002500998624804212E-8, + 6.04699502254191894932E-8, + -2.67079385394061173391E-7, + 1.11738753912010371815E-6, + -4.41673835845875056359E-6, + 1.64484480707288970893E-5, + -5.75419501008210370398E-5, + 1.88502885095841655729E-4, + -5.76375574538582365885E-4, + 1.63947561694133579842E-3, + -4.32430999505057594430E-3, + 1.05464603945949983183E-2, + -2.37374148058994688156E-2, + 4.93052842396707084878E-2, + -9.49010970480476444210E-2, + 1.71620901522208775349E-1, + -3.04682672343198398683E-1, + 6.76795274409476084995E-1 + ] + +_i0B = [ + -7.23318048787475395456E-18, + -4.83050448594418207126E-18, + 4.46562142029675999901E-17, + 3.46122286769746109310E-17, + -2.82762398051658348494E-16, + -3.42548561967721913462E-16, + 1.77256013305652638360E-15, + 3.81168066935262242075E-15, + -9.55484669882830764870E-15, + -4.15056934728722208663E-14, + 1.54008621752140982691E-14, + 3.85277838274214270114E-13, + 7.18012445138366623367E-13, + -1.79417853150680611778E-12, + -1.32158118404477131188E-11, + -3.14991652796324136454E-11, + 1.18891471078464383424E-11, + 4.94060238822496958910E-10, + 3.39623202570838634515E-9, + 2.26666899049817806459E-8, + 2.04891858946906374183E-7, + 2.89137052083475648297E-6, + 6.88975834691682398426E-5, + 3.36911647825569408990E-3, + 8.04490411014108831608E-1 + ] + + +def _chbevl(x, vals): + b0 = vals[0] + b1 = 0.0 + + for i in range(1, len(vals)): + b2 = b1 + b1 = b0 + b0 = x*b1 - b2 + vals[i] + + return 0.5*(b0 - b2) + + +def _i0_1(x): + return exp(x) * _chbevl(x/2.0-2, _i0A) + + +def _i0_2(x): + return exp(x) * _chbevl(32.0/x - 2.0, _i0B) / sqrt(x) + + +def _i0_dispatcher(x): + return (x,) + + +@array_function_dispatch(_i0_dispatcher) +def i0(x): + """ + Modified Bessel function of the first kind, order 0. + + Usually denoted :math:`I_0`. + + Parameters + ---------- + x : array_like of float + Argument of the Bessel function. + + Returns + ------- + out : ndarray, shape = x.shape, dtype = float + The modified Bessel function evaluated at each of the elements of `x`. + + See Also + -------- + scipy.special.i0, scipy.special.iv, scipy.special.ive + + Notes + ----- + The scipy implementation is recommended over this function: it is a + proper ufunc written in C, and more than an order of magnitude faster. + + We use the algorithm published by Clenshaw [1]_ and referenced by + Abramowitz and Stegun [2]_, for which the function domain is + partitioned into the two intervals [0,8] and (8,inf), and Chebyshev + polynomial expansions are employed in each interval. Relative error on + the domain [0,30] using IEEE arithmetic is documented [3]_ as having a + peak of 5.8e-16 with an rms of 1.4e-16 (n = 30000). + + References + ---------- + .. [1] C. W. Clenshaw, "Chebyshev series for mathematical functions", in + *National Physical Laboratory Mathematical Tables*, vol. 5, London: + Her Majesty's Stationery Office, 1962. + .. [2] M. Abramowitz and I. A. Stegun, *Handbook of Mathematical + Functions*, 10th printing, New York: Dover, 1964, pp. 379. + https://personal.math.ubc.ca/~cbm/aands/page_379.htm + .. [3] https://metacpan.org/pod/distribution/Math-Cephes/lib/Math/Cephes.pod#i0:-Modified-Bessel-function-of-order-zero + + Examples + -------- + >>> np.i0(0.) + array(1.0) + >>> np.i0([0, 1, 2, 3]) + array([1. , 1.26606588, 2.2795853 , 4.88079259]) + + """ + x = np.asanyarray(x) + if x.dtype.kind == 'c': + raise TypeError("i0 not supported for complex values") + if x.dtype.kind != 'f': + x = x.astype(float) + x = np.abs(x) + return piecewise(x, [x <= 8.0], [_i0_1, _i0_2]) + +## End of cephes code for i0 + + +@set_module('numpy') +def kaiser(M, beta): + """ + Return the Kaiser window. + + The Kaiser window is a taper formed by using a Bessel function. + + Parameters + ---------- + M : int + Number of points in the output window. If zero or less, an + empty array is returned. + beta : float + Shape parameter for window. + + Returns + ------- + out : array + The window, with the maximum value normalized to one (the value + one appears only if the number of samples is odd). + + See Also + -------- + bartlett, blackman, hamming, hanning + + Notes + ----- + The Kaiser window is defined as + + .. math:: w(n) = I_0\\left( \\beta \\sqrt{1-\\frac{4n^2}{(M-1)^2}} + \\right)/I_0(\\beta) + + with + + .. math:: \\quad -\\frac{M-1}{2} \\leq n \\leq \\frac{M-1}{2}, + + where :math:`I_0` is the modified zeroth-order Bessel function. + + The Kaiser was named for Jim Kaiser, who discovered a simple + approximation to the DPSS window based on Bessel functions. The Kaiser + window is a very good approximation to the Digital Prolate Spheroidal + Sequence, or Slepian window, which is the transform which maximizes the + energy in the main lobe of the window relative to total energy. + + The Kaiser can approximate many other windows by varying the beta + parameter. + + ==== ======================= + beta Window shape + ==== ======================= + 0 Rectangular + 5 Similar to a Hamming + 6 Similar to a Hanning + 8.6 Similar to a Blackman + ==== ======================= + + A beta value of 14 is probably a good starting point. Note that as beta + gets large, the window narrows, and so the number of samples needs to be + large enough to sample the increasingly narrow spike, otherwise NaNs will + get returned. + + Most references to the Kaiser window come from the signal processing + literature, where it is used as one of many windowing functions for + smoothing values. It is also known as an apodization (which means + "removing the foot", i.e. smoothing discontinuities at the beginning + and end of the sampled signal) or tapering function. + + References + ---------- + .. [1] J. F. Kaiser, "Digital Filters" - Ch 7 in "Systems analysis by + digital computer", Editors: F.F. Kuo and J.F. Kaiser, p 218-285. + John Wiley and Sons, New York, (1966). + .. [2] E.R. Kanasewich, "Time Sequence Analysis in Geophysics", The + University of Alberta Press, 1975, pp. 177-178. + .. [3] Wikipedia, "Window function", + https://en.wikipedia.org/wiki/Window_function + + Examples + -------- + >>> import matplotlib.pyplot as plt + >>> np.kaiser(12, 14) + array([7.72686684e-06, 3.46009194e-03, 4.65200189e-02, # may vary + 2.29737120e-01, 5.99885316e-01, 9.45674898e-01, + 9.45674898e-01, 5.99885316e-01, 2.29737120e-01, + 4.65200189e-02, 3.46009194e-03, 7.72686684e-06]) + + + Plot the window and the frequency response: + + >>> from numpy.fft import fft, fftshift + >>> window = np.kaiser(51, 14) + >>> plt.plot(window) + [] + >>> plt.title("Kaiser window") + Text(0.5, 1.0, 'Kaiser window') + >>> plt.ylabel("Amplitude") + Text(0, 0.5, 'Amplitude') + >>> plt.xlabel("Sample") + Text(0.5, 0, 'Sample') + >>> plt.show() + + >>> plt.figure() +
+ >>> A = fft(window, 2048) / 25.5 + >>> mag = np.abs(fftshift(A)) + >>> freq = np.linspace(-0.5, 0.5, len(A)) + >>> response = 20 * np.log10(mag) + >>> response = np.clip(response, -100, 100) + >>> plt.plot(freq, response) + [] + >>> plt.title("Frequency response of Kaiser window") + Text(0.5, 1.0, 'Frequency response of Kaiser window') + >>> plt.ylabel("Magnitude [dB]") + Text(0, 0.5, 'Magnitude [dB]') + >>> plt.xlabel("Normalized frequency [cycles per sample]") + Text(0.5, 0, 'Normalized frequency [cycles per sample]') + >>> plt.axis('tight') + (-0.5, 0.5, -100.0, ...) # may vary + >>> plt.show() + + """ + # Ensures at least float64 via 0.0. M should be an integer, but conversion + # to double is safe for a range. (Simplified result_type with 0.0 + # strongly typed. result-type is not/less order sensitive, but that mainly + # matters for integers anyway.) + values = np.array([0.0, M, beta]) + M = values[1] + beta = values[2] + + if M == 1: + return np.ones(1, dtype=values.dtype) + n = arange(0, M) + alpha = (M-1)/2.0 + return i0(beta * sqrt(1-((n-alpha)/alpha)**2.0))/i0(beta) + + +def _sinc_dispatcher(x): + return (x,) + + +@array_function_dispatch(_sinc_dispatcher) +def sinc(x): + r""" + Return the normalized sinc function. + + The sinc function is equal to :math:`\sin(\pi x)/(\pi x)` for any argument + :math:`x\ne 0`. ``sinc(0)`` takes the limit value 1, making ``sinc`` not + only everywhere continuous but also infinitely differentiable. + + .. note:: + + Note the normalization factor of ``pi`` used in the definition. + This is the most commonly used definition in signal processing. + Use ``sinc(x / np.pi)`` to obtain the unnormalized sinc function + :math:`\sin(x)/x` that is more common in mathematics. + + Parameters + ---------- + x : ndarray + Array (possibly multi-dimensional) of values for which to calculate + ``sinc(x)``. + + Returns + ------- + out : ndarray + ``sinc(x)``, which has the same shape as the input. + + Notes + ----- + The name sinc is short for "sine cardinal" or "sinus cardinalis". + + The sinc function is used in various signal processing applications, + including in anti-aliasing, in the construction of a Lanczos resampling + filter, and in interpolation. + + For bandlimited interpolation of discrete-time signals, the ideal + interpolation kernel is proportional to the sinc function. + + References + ---------- + .. [1] Weisstein, Eric W. "Sinc Function." From MathWorld--A Wolfram Web + Resource. http://mathworld.wolfram.com/SincFunction.html + .. [2] Wikipedia, "Sinc function", + https://en.wikipedia.org/wiki/Sinc_function + + Examples + -------- + >>> import matplotlib.pyplot as plt + >>> x = np.linspace(-4, 4, 41) + >>> np.sinc(x) + array([-3.89804309e-17, -4.92362781e-02, -8.40918587e-02, # may vary + -8.90384387e-02, -5.84680802e-02, 3.89804309e-17, + 6.68206631e-02, 1.16434881e-01, 1.26137788e-01, + 8.50444803e-02, -3.89804309e-17, -1.03943254e-01, + -1.89206682e-01, -2.16236208e-01, -1.55914881e-01, + 3.89804309e-17, 2.33872321e-01, 5.04551152e-01, + 7.56826729e-01, 9.35489284e-01, 1.00000000e+00, + 9.35489284e-01, 7.56826729e-01, 5.04551152e-01, + 2.33872321e-01, 3.89804309e-17, -1.55914881e-01, + -2.16236208e-01, -1.89206682e-01, -1.03943254e-01, + -3.89804309e-17, 8.50444803e-02, 1.26137788e-01, + 1.16434881e-01, 6.68206631e-02, 3.89804309e-17, + -5.84680802e-02, -8.90384387e-02, -8.40918587e-02, + -4.92362781e-02, -3.89804309e-17]) + + >>> plt.plot(x, np.sinc(x)) + [] + >>> plt.title("Sinc Function") + Text(0.5, 1.0, 'Sinc Function') + >>> plt.ylabel("Amplitude") + Text(0, 0.5, 'Amplitude') + >>> plt.xlabel("X") + Text(0.5, 0, 'X') + >>> plt.show() + + """ + x = np.asanyarray(x) + y = pi * where(x == 0, 1.0e-20, x) + return sin(y)/y + + +def _msort_dispatcher(a): + return (a,) + + +@array_function_dispatch(_msort_dispatcher) +def msort(a): + """ + Return a copy of an array sorted along the first axis. + + .. deprecated:: 1.24 + + msort is deprecated, use ``np.sort(a, axis=0)`` instead. + + Parameters + ---------- + a : array_like + Array to be sorted. + + Returns + ------- + sorted_array : ndarray + Array of the same type and shape as `a`. + + See Also + -------- + sort + + Notes + ----- + ``np.msort(a)`` is equivalent to ``np.sort(a, axis=0)``. + + Examples + -------- + >>> a = np.array([[1, 4], [3, 1]]) + >>> np.msort(a) # sort along the first axis + array([[1, 1], + [3, 4]]) + + """ + # 2022-10-20 1.24 + warnings.warn( + "msort is deprecated, use np.sort(a, axis=0) instead", + DeprecationWarning, + stacklevel=2, + ) + b = array(a, subok=True, copy=True) + b.sort(0) + return b + + +def _ureduce(a, func, keepdims=False, **kwargs): + """ + Internal Function. + Call `func` with `a` as first argument swapping the axes to use extended + axis on functions that don't support it natively. + + Returns result and a.shape with axis dims set to 1. + + Parameters + ---------- + a : array_like + Input array or object that can be converted to an array. + func : callable + Reduction function capable of receiving a single axis argument. + It is called with `a` as first argument followed by `kwargs`. + kwargs : keyword arguments + additional keyword arguments to pass to `func`. + + Returns + ------- + result : tuple + Result of func(a, **kwargs) and a.shape with axis dims set to 1 + which can be used to reshape the result to the same shape a ufunc with + keepdims=True would produce. + + """ + a = np.asanyarray(a) + axis = kwargs.get('axis', None) + out = kwargs.get('out', None) + + if keepdims is np._NoValue: + keepdims = False + + nd = a.ndim + if axis is not None: + axis = _nx.normalize_axis_tuple(axis, nd) + + if keepdims: + if out is not None: + index_out = tuple( + 0 if i in axis else slice(None) for i in range(nd)) + kwargs['out'] = out[(Ellipsis, ) + index_out] + + if len(axis) == 1: + kwargs['axis'] = axis[0] + else: + keep = set(range(nd)) - set(axis) + nkeep = len(keep) + # swap axis that should not be reduced to front + for i, s in enumerate(sorted(keep)): + a = a.swapaxes(i, s) + # merge reduced axis + a = a.reshape(a.shape[:nkeep] + (-1,)) + kwargs['axis'] = -1 + else: + if keepdims: + if out is not None: + index_out = (0, ) * nd + kwargs['out'] = out[(Ellipsis, ) + index_out] + + r = func(a, **kwargs) + + if out is not None: + return out + + if keepdims: + if axis is None: + index_r = (np.newaxis, ) * nd + else: + index_r = tuple( + np.newaxis if i in axis else slice(None) + for i in range(nd)) + r = r[(Ellipsis, ) + index_r] + + return r + + +def _median_dispatcher( + a, axis=None, out=None, overwrite_input=None, keepdims=None): + return (a, out) + + +@array_function_dispatch(_median_dispatcher) +def median(a, axis=None, out=None, overwrite_input=False, keepdims=False): + """ + Compute the median along the specified axis. + + Returns the median of the array elements. + + Parameters + ---------- + a : array_like + Input array or object that can be converted to an array. + axis : {int, sequence of int, None}, optional + Axis or axes along which the medians are computed. The default + is to compute the median along a flattened version of the array. + A sequence of axes is supported since version 1.9.0. + out : ndarray, optional + Alternative output array in which to place the result. It must + have the same shape and buffer length as the expected output, + but the type (of the output) will be cast if necessary. + overwrite_input : bool, optional + If True, then allow use of memory of input array `a` for + calculations. The input array will be modified by the call to + `median`. This will save memory when you do not need to preserve + the contents of the input array. Treat the input as undefined, + but it will probably be fully or partially sorted. Default is + False. If `overwrite_input` is ``True`` and `a` is not already an + `ndarray`, an error will be raised. + keepdims : bool, optional + If this is set to True, the axes which are reduced are left + in the result as dimensions with size one. With this option, + the result will broadcast correctly against the original `arr`. + + .. versionadded:: 1.9.0 + + Returns + ------- + median : ndarray + A new array holding the result. If the input contains integers + or floats smaller than ``float64``, then the output data-type is + ``np.float64``. Otherwise, the data-type of the output is the + same as that of the input. If `out` is specified, that array is + returned instead. + + See Also + -------- + mean, percentile + + Notes + ----- + Given a vector ``V`` of length ``N``, the median of ``V`` is the + middle value of a sorted copy of ``V``, ``V_sorted`` - i + e., ``V_sorted[(N-1)/2]``, when ``N`` is odd, and the average of the + two middle values of ``V_sorted`` when ``N`` is even. + + Examples + -------- + >>> a = np.array([[10, 7, 4], [3, 2, 1]]) + >>> a + array([[10, 7, 4], + [ 3, 2, 1]]) + >>> np.median(a) + 3.5 + >>> np.median(a, axis=0) + array([6.5, 4.5, 2.5]) + >>> np.median(a, axis=1) + array([7., 2.]) + >>> m = np.median(a, axis=0) + >>> out = np.zeros_like(m) + >>> np.median(a, axis=0, out=m) + array([6.5, 4.5, 2.5]) + >>> m + array([6.5, 4.5, 2.5]) + >>> b = a.copy() + >>> np.median(b, axis=1, overwrite_input=True) + array([7., 2.]) + >>> assert not np.all(a==b) + >>> b = a.copy() + >>> np.median(b, axis=None, overwrite_input=True) + 3.5 + >>> assert not np.all(a==b) + + """ + return _ureduce(a, func=_median, keepdims=keepdims, axis=axis, out=out, + overwrite_input=overwrite_input) + + +def _median(a, axis=None, out=None, overwrite_input=False): + # can't be reasonably be implemented in terms of percentile as we have to + # call mean to not break astropy + a = np.asanyarray(a) + + # Set the partition indexes + if axis is None: + sz = a.size + else: + sz = a.shape[axis] + if sz % 2 == 0: + szh = sz // 2 + kth = [szh - 1, szh] + else: + kth = [(sz - 1) // 2] + + # We have to check for NaNs (as of writing 'M' doesn't actually work). + supports_nans = np.issubdtype(a.dtype, np.inexact) or a.dtype.kind in 'Mm' + if supports_nans: + kth.append(-1) + + if overwrite_input: + if axis is None: + part = a.ravel() + part.partition(kth) + else: + a.partition(kth, axis=axis) + part = a + else: + part = partition(a, kth, axis=axis) + + if part.shape == (): + # make 0-D arrays work + return part.item() + if axis is None: + axis = 0 + + indexer = [slice(None)] * part.ndim + index = part.shape[axis] // 2 + if part.shape[axis] % 2 == 1: + # index with slice to allow mean (below) to work + indexer[axis] = slice(index, index+1) + else: + indexer[axis] = slice(index-1, index+1) + indexer = tuple(indexer) + + # Use mean in both odd and even case to coerce data type, + # using out array if needed. + rout = mean(part[indexer], axis=axis, out=out) + if supports_nans and sz > 0: + # If nans are possible, warn and replace by nans like mean would. + rout = np.lib.utils._median_nancheck(part, rout, axis) + + return rout + + +def _percentile_dispatcher(a, q, axis=None, out=None, overwrite_input=None, + method=None, keepdims=None, *, interpolation=None): + return (a, q, out) + + +@array_function_dispatch(_percentile_dispatcher) +def percentile(a, + q, + axis=None, + out=None, + overwrite_input=False, + method="linear", + keepdims=False, + *, + interpolation=None): + """ + Compute the q-th percentile of the data along the specified axis. + + Returns the q-th percentile(s) of the array elements. + + Parameters + ---------- + a : array_like of real numbers + Input array or object that can be converted to an array. + q : array_like of float + Percentage or sequence of percentages for the percentiles to compute. + Values must be between 0 and 100 inclusive. + axis : {int, tuple of int, None}, optional + Axis or axes along which the percentiles are computed. The + default is to compute the percentile(s) along a flattened + version of the array. + + .. versionchanged:: 1.9.0 + A tuple of axes is supported + out : ndarray, optional + Alternative output array in which to place the result. It must + have the same shape and buffer length as the expected output, + but the type (of the output) will be cast if necessary. + overwrite_input : bool, optional + If True, then allow the input array `a` to be modified by intermediate + calculations, to save memory. In this case, the contents of the input + `a` after this function completes is undefined. + 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`. + + .. versionadded:: 1.9.0 + + 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 + -------- + mean + median : equivalent to ``percentile(..., 50)`` + nanpercentile + quantile : equivalent to percentile, except q in the range [0, 1]. + + Notes + ----- + Given a vector ``V`` of length ``n``, the q-th percentile of ``V`` is + the value ``q/100`` of the way from the minimum to the maximum in a + sorted copy of ``V``. The values and distances of the two nearest + neighbors as well as the `method` parameter will determine the + percentile if the normalized ranking does not match the location of + ``q`` exactly. This function is the same as the median if ``q=50``, the + same as the minimum if ``q=0`` and the same as the maximum if + ``q=100``. + + The optional `method` parameter specifies the method to use when the + desired percentile lies between two indexes ``i`` and ``j = i + 1``. + In that case, we first determine ``i + g``, a virtual index that lies + between ``i`` and ``j``, where ``i`` is the floor and ``g`` is the + fractional part of the index. The final result is, then, an interpolation + of ``a[i]`` and ``a[j]`` based on ``g``. During the computation of ``g``, + ``i`` and ``j`` are modified using correction constants ``alpha`` and + ``beta`` whose choices depend on the ``method`` used. Finally, note that + since Python uses 0-based indexing, the code subtracts another 1 from the + index internally. + + The following formula determines the virtual index ``i + g``, the location + of the percentile in the sorted sample: + + .. math:: + i + g = (q / 100) * ( n - alpha - beta + 1 ) + alpha + + The different methods then work as follows + + inverted_cdf: + method 1 of H&F [1]_. + This method gives discontinuous results: + + * if g > 0 ; then take j + * if g = 0 ; then take i + + averaged_inverted_cdf: + method 2 of H&F [1]_. + This method give discontinuous results: + + * if g > 0 ; then take j + * if g = 0 ; then average between bounds + + closest_observation: + method 3 of H&F [1]_. + This method give discontinuous results: + + * if g > 0 ; then take j + * if g = 0 and index is odd ; then take j + * if g = 0 and index is even ; then take i + + interpolated_inverted_cdf: + method 4 of H&F [1]_. + This method give continuous results using: + + * alpha = 0 + * beta = 1 + + hazen: + method 5 of H&F [1]_. + This method give continuous results using: + + * alpha = 1/2 + * beta = 1/2 + + weibull: + method 6 of H&F [1]_. + This method give continuous results using: + + * alpha = 0 + * beta = 0 + + linear: + method 7 of H&F [1]_. + This method give continuous results using: + + * alpha = 1 + * beta = 1 + + median_unbiased: + method 8 of H&F [1]_. + This method is probably the best method if the sample + distribution function is unknown (see reference). + This method give continuous results using: + + * alpha = 1/3 + * beta = 1/3 + + normal_unbiased: + method 9 of H&F [1]_. + This method is probably the best method if the sample + distribution function is known to be normal. + This method give continuous results using: + + * alpha = 3/8 + * beta = 3/8 + + lower: + NumPy method kept for backwards compatibility. + Takes ``i`` as the interpolation point. + + higher: + NumPy method kept for backwards compatibility. + Takes ``j`` as the interpolation point. + + nearest: + NumPy method kept for backwards compatibility. + Takes ``i`` or ``j``, whichever is nearest. + + midpoint: + NumPy method kept for backwards compatibility. + Uses ``(i + j) / 2``. + + Examples + -------- + >>> a = np.array([[10, 7, 4], [3, 2, 1]]) + >>> a + array([[10, 7, 4], + [ 3, 2, 1]]) + >>> np.percentile(a, 50) + 3.5 + >>> np.percentile(a, 50, axis=0) + array([6.5, 4.5, 2.5]) + >>> np.percentile(a, 50, axis=1) + array([7., 2.]) + >>> np.percentile(a, 50, axis=1, keepdims=True) + array([[7.], + [2.]]) + + >>> m = np.percentile(a, 50, axis=0) + >>> out = np.zeros_like(m) + >>> np.percentile(a, 50, axis=0, out=out) + array([6.5, 4.5, 2.5]) + >>> m + array([6.5, 4.5, 2.5]) + + >>> b = a.copy() + >>> np.percentile(b, 50, axis=1, overwrite_input=True) + array([7., 2.]) + >>> assert not np.all(a == b) + + The different methods can be visualized graphically: + + .. plot:: + + import matplotlib.pyplot as plt + + a = np.arange(4) + p = np.linspace(0, 100, 6001) + ax = plt.gca() + lines = [ + ('linear', '-', 'C0'), + ('inverted_cdf', ':', 'C1'), + # Almost the same as `inverted_cdf`: + ('averaged_inverted_cdf', '-.', 'C1'), + ('closest_observation', ':', 'C2'), + ('interpolated_inverted_cdf', '--', 'C1'), + ('hazen', '--', 'C3'), + ('weibull', '-.', 'C4'), + ('median_unbiased', '--', 'C5'), + ('normal_unbiased', '-.', 'C6'), + ] + for method, style, color in lines: + ax.plot( + p, np.percentile(a, p, method=method), + label=method, linestyle=style, color=color) + ax.set( + title='Percentiles for different methods and data: ' + str(a), + xlabel='Percentile', + ylabel='Estimated percentile value', + yticks=a) + ax.legend(bbox_to_anchor=(1.03, 1)) + plt.tight_layout() + plt.show() + + 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 = _check_interpolation_as_method( + method, interpolation, "percentile") + + 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) + q = asanyarray(q) # undo any decay that the ufunc performed (see gh-13105) + if not _quantile_is_valid(q): + raise ValueError("Percentiles must be in the range [0, 100]") + return _quantile_unchecked( + a, q, axis, out, overwrite_input, method, keepdims) + + +def _quantile_dispatcher(a, q, axis=None, out=None, overwrite_input=None, + method=None, keepdims=None, *, interpolation=None): + return (a, q, out) + + +@array_function_dispatch(_quantile_dispatcher) +def quantile(a, + q, + axis=None, + out=None, + overwrite_input=False, + method="linear", + keepdims=False, + *, + interpolation=None): + """ + Compute the q-th quantile of the data along the specified axis. + + .. versionadded:: 1.15.0 + + Parameters + ---------- + a : array_like of real numbers + Input array or object that can be converted to an array. + 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`. + + 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 probabilies 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 + -------- + mean + percentile : equivalent to quantile, but with q in the range [0, 100]. + median : equivalent to ``quantile(..., 0.5)`` + nanquantile + + Notes + ----- + Given a vector ``V`` of length ``n``, the q-th quantile of ``V`` is + the value ``q`` of the way from the minimum to the maximum in a + sorted copy of ``V``. The values and distances of the two nearest + neighbors as well as the `method` parameter will determine the + quantile if the normalized ranking does not match the location of + ``q`` exactly. This function is the same as the median if ``q=0.5``, the + same as the minimum if ``q=0.0`` and the same as the maximum if + ``q=1.0``. + + The optional `method` parameter specifies the method to use when the + desired quantile lies between two indexes ``i`` and ``j = i + 1``. + In that case, we first determine ``i + g``, a virtual index that lies + between ``i`` and ``j``, where ``i`` is the floor and ``g`` is the + fractional part of the index. The final result is, then, an interpolation + of ``a[i]`` and ``a[j]`` based on ``g``. During the computation of ``g``, + ``i`` and ``j`` are modified using correction constants ``alpha`` and + ``beta`` whose choices depend on the ``method`` used. Finally, note that + since Python uses 0-based indexing, the code subtracts another 1 from the + index internally. + + The following formula determines the virtual index ``i + g``, the location + of the quantile in the sorted sample: + + .. math:: + i + g = q * ( n - alpha - beta + 1 ) + alpha + + The different methods then work as follows + + inverted_cdf: + method 1 of H&F [1]_. + This method gives discontinuous results: + + * if g > 0 ; then take j + * if g = 0 ; then take i + + averaged_inverted_cdf: + method 2 of H&F [1]_. + This method gives discontinuous results: + + * if g > 0 ; then take j + * if g = 0 ; then average between bounds + + closest_observation: + method 3 of H&F [1]_. + This method gives discontinuous results: + + * if g > 0 ; then take j + * if g = 0 and index is odd ; then take j + * if g = 0 and index is even ; then take i + + interpolated_inverted_cdf: + method 4 of H&F [1]_. + This method gives continuous results using: + + * alpha = 0 + * beta = 1 + + hazen: + method 5 of H&F [1]_. + This method gives continuous results using: + + * alpha = 1/2 + * beta = 1/2 + + weibull: + method 6 of H&F [1]_. + This method gives continuous results using: + + * alpha = 0 + * beta = 0 + + linear: + method 7 of H&F [1]_. + This method gives continuous results using: + + * alpha = 1 + * beta = 1 + + median_unbiased: + method 8 of H&F [1]_. + This method is probably the best method if the sample + distribution function is unknown (see reference). + This method gives continuous results using: + + * alpha = 1/3 + * beta = 1/3 + + normal_unbiased: + method 9 of H&F [1]_. + This method is probably the best method if the sample + distribution function is known to be normal. + This method gives continuous results using: + + * alpha = 3/8 + * beta = 3/8 + + lower: + NumPy method kept for backwards compatibility. + Takes ``i`` as the interpolation point. + + higher: + NumPy method kept for backwards compatibility. + Takes ``j`` as the interpolation point. + + nearest: + NumPy method kept for backwards compatibility. + Takes ``i`` or ``j``, whichever is nearest. + + midpoint: + NumPy method kept for backwards compatibility. + Uses ``(i + j) / 2``. + + Examples + -------- + >>> a = np.array([[10, 7, 4], [3, 2, 1]]) + >>> a + array([[10, 7, 4], + [ 3, 2, 1]]) + >>> np.quantile(a, 0.5) + 3.5 + >>> np.quantile(a, 0.5, axis=0) + array([6.5, 4.5, 2.5]) + >>> np.quantile(a, 0.5, axis=1) + array([7., 2.]) + >>> np.quantile(a, 0.5, axis=1, keepdims=True) + array([[7.], + [2.]]) + >>> m = np.quantile(a, 0.5, axis=0) + >>> out = np.zeros_like(m) + >>> np.quantile(a, 0.5, axis=0, out=out) + array([6.5, 4.5, 2.5]) + >>> m + array([6.5, 4.5, 2.5]) + >>> b = a.copy() + >>> np.quantile(b, 0.5, axis=1, overwrite_input=True) + array([7., 2.]) + >>> assert not np.all(a == b) + + See also `numpy.percentile` for a visualization of most methods. + + 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 = _check_interpolation_as_method( + method, interpolation, "quantile") + + 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 _quantile_is_valid(q): + raise ValueError("Quantiles must be in the range [0, 1]") + return _quantile_unchecked( + a, q, axis, out, overwrite_input, method, keepdims) + + +def _quantile_unchecked(a, + q, + axis=None, + out=None, + overwrite_input=False, + method="linear", + keepdims=False): + """Assumes that q is in [0, 1], and is an ndarray""" + return _ureduce(a, + func=_quantile_ureduce_func, + q=q, + keepdims=keepdims, + axis=axis, + out=out, + overwrite_input=overwrite_input, + method=method) + + +def _quantile_is_valid(q): + # avoid expensive reductions, relevant for arrays with < O(1000) elements + if q.ndim == 1 and q.size < 10: + for i in range(q.size): + if not (0.0 <= q[i] <= 1.0): + return False + else: + if not (np.all(0 <= q) and np.all(q <= 1)): + return False + return True + + +def _check_interpolation_as_method(method, interpolation, fname): + # Deprecated NumPy 1.22, 2021-11-08 + warnings.warn( + f"the `interpolation=` argument to {fname} was renamed to " + "`method=`, which has additional options.\n" + "Users of the modes 'nearest', 'lower', 'higher', or " + "'midpoint' are encouraged to review the method they used. " + "(Deprecated NumPy 1.22)", + DeprecationWarning, stacklevel=4) + if method != "linear": + # sanity check, we assume this basically never happens + raise TypeError( + "You shall not pass both `method` and `interpolation`!\n" + "(`interpolation` is Deprecated in favor of `method`)") + return interpolation + + +def _compute_virtual_index(n, quantiles, alpha: float, beta: float): + """ + Compute the floating point indexes of an array for the linear + interpolation of quantiles. + n : array_like + The sample sizes. + quantiles : array_like + The quantiles values. + alpha : float + A constant used to correct the index computed. + beta : float + A constant used to correct the index computed. + + alpha and beta values depend on the chosen method + (see quantile documentation) + + Reference: + Hyndman&Fan paper "Sample Quantiles in Statistical Packages", + DOI: 10.1080/00031305.1996.10473566 + """ + return n * quantiles + ( + alpha + quantiles * (1 - alpha - beta) + ) - 1 + + +def _get_gamma(virtual_indexes, previous_indexes, method): + """ + Compute gamma (a.k.a 'm' or 'weight') for the linear interpolation + of quantiles. + + virtual_indexes : array_like + The indexes where the percentile is supposed to be found in the sorted + sample. + previous_indexes : array_like + The floor values of virtual_indexes. + interpolation : dict + The interpolation method chosen, which may have a specific rule + modifying gamma. + + gamma is usually the fractional part of virtual_indexes but can be modified + by the interpolation method. + """ + gamma = np.asanyarray(virtual_indexes - previous_indexes) + gamma = method["fix_gamma"](gamma, virtual_indexes) + return np.asanyarray(gamma) + + +def _lerp(a, b, t, out=None): + """ + Compute the linear interpolation weighted by gamma on each point of + two same shape array. + + a : array_like + Left bound. + b : array_like + Right bound. + t : array_like + The interpolation weight. + out : array_like + Output array. + """ + diff_b_a = subtract(b, a) + # asanyarray is a stop-gap until gh-13105 + lerp_interpolation = asanyarray(add(a, diff_b_a * t, out=out)) + subtract(b, diff_b_a * (1 - t), out=lerp_interpolation, where=t >= 0.5, + casting='unsafe', dtype=type(lerp_interpolation.dtype)) + if lerp_interpolation.ndim == 0 and out is None: + lerp_interpolation = lerp_interpolation[()] # unpack 0d arrays + return lerp_interpolation + + +def _get_gamma_mask(shape, default_value, conditioned_value, where): + out = np.full(shape, default_value) + np.copyto(out, conditioned_value, where=where, casting="unsafe") + return out + + +def _discret_interpolation_to_boundaries(index, gamma_condition_fun): + previous = np.floor(index) + next = previous + 1 + gamma = index - previous + res = _get_gamma_mask(shape=index.shape, + default_value=next, + conditioned_value=previous, + where=gamma_condition_fun(gamma, index) + ).astype(np.intp) + # Some methods can lead to out-of-bound integers, clip them: + res[res < 0] = 0 + return res + + +def _closest_observation(n, quantiles): + gamma_fun = lambda gamma, index: (gamma == 0) & (np.floor(index) % 2 == 0) + return _discret_interpolation_to_boundaries((n * quantiles) - 1 - 0.5, + gamma_fun) + + +def _inverted_cdf(n, quantiles): + gamma_fun = lambda gamma, _: (gamma == 0) + return _discret_interpolation_to_boundaries((n * quantiles) - 1, + gamma_fun) + + +def _quantile_ureduce_func( + a: np.array, + q: np.array, + axis: int = None, + out=None, + overwrite_input: bool = False, + method="linear", +) -> np.array: + if q.ndim > 2: + # The code below works fine for nd, but it might not have useful + # semantics. For now, keep the supported dimensions the same as it was + # before. + raise ValueError("q must be a scalar or 1d") + if overwrite_input: + if axis is None: + axis = 0 + arr = a.ravel() + else: + arr = a + else: + if axis is None: + axis = 0 + arr = a.flatten() + else: + arr = a.copy() + result = _quantile(arr, + quantiles=q, + axis=axis, + method=method, + out=out) + return result + + +def _get_indexes(arr, virtual_indexes, valid_values_count): + """ + Get the valid indexes of arr neighbouring virtual_indexes. + Note + This is a companion function to linear interpolation of + Quantiles + + Returns + ------- + (previous_indexes, next_indexes): Tuple + A Tuple of virtual_indexes neighbouring indexes + """ + previous_indexes = np.asanyarray(np.floor(virtual_indexes)) + next_indexes = np.asanyarray(previous_indexes + 1) + indexes_above_bounds = virtual_indexes >= valid_values_count - 1 + # When indexes is above max index, take the max value of the array + if indexes_above_bounds.any(): + previous_indexes[indexes_above_bounds] = -1 + next_indexes[indexes_above_bounds] = -1 + # When indexes is below min index, take the min value of the array + indexes_below_bounds = virtual_indexes < 0 + if indexes_below_bounds.any(): + previous_indexes[indexes_below_bounds] = 0 + next_indexes[indexes_below_bounds] = 0 + if np.issubdtype(arr.dtype, np.inexact): + # After the sort, slices having NaNs will have for last element a NaN + virtual_indexes_nans = np.isnan(virtual_indexes) + if virtual_indexes_nans.any(): + previous_indexes[virtual_indexes_nans] = -1 + next_indexes[virtual_indexes_nans] = -1 + previous_indexes = previous_indexes.astype(np.intp) + next_indexes = next_indexes.astype(np.intp) + return previous_indexes, next_indexes + + +def _quantile( + arr: np.array, + quantiles: np.array, + axis: int = -1, + method="linear", + out=None, +): + """ + Private function that doesn't support extended axis or keepdims. + These methods are extended to this function using _ureduce + See nanpercentile for parameter usage + It computes the quantiles of the array for the given axis. + A linear interpolation is performed based on the `interpolation`. + + By default, the method is "linear" where alpha == beta == 1 which + performs the 7th method of Hyndman&Fan. + With "median_unbiased" we get alpha == beta == 1/3 + thus the 8th method of Hyndman&Fan. + """ + # --- Setup + arr = np.asanyarray(arr) + values_count = arr.shape[axis] + # The dimensions of `q` are prepended to the output shape, so we need the + # axis being sampled from `arr` to be last. + + if axis != 0: # But moveaxis is slow, so only call it if necessary. + arr = np.moveaxis(arr, axis, destination=0) + # --- Computation of indexes + # Index where to find the value in the sorted array. + # Virtual because it is a floating point value, not an valid index. + # The nearest neighbours are used for interpolation + try: + method = _QuantileMethods[method] + except KeyError: + raise ValueError( + f"{method!r} is not a valid method. Use one of: " + f"{_QuantileMethods.keys()}") from None + virtual_indexes = method["get_virtual_index"](values_count, quantiles) + virtual_indexes = np.asanyarray(virtual_indexes) + + supports_nans = ( + np.issubdtype(arr.dtype, np.inexact) or arr.dtype.kind in 'Mm') + + if np.issubdtype(virtual_indexes.dtype, np.integer): + # No interpolation needed, take the points along axis + if supports_nans: + # may contain nan, which would sort to the end + arr.partition(concatenate((virtual_indexes.ravel(), [-1])), axis=0) + slices_having_nans = np.isnan(arr[-1, ...]) + else: + # cannot contain nan + arr.partition(virtual_indexes.ravel(), axis=0) + slices_having_nans = np.array(False, dtype=bool) + result = take(arr, virtual_indexes, axis=0, out=out) + else: + previous_indexes, next_indexes = _get_indexes(arr, + virtual_indexes, + values_count) + # --- Sorting + arr.partition( + np.unique(np.concatenate(([0, -1], + previous_indexes.ravel(), + next_indexes.ravel(), + ))), + axis=0) + if supports_nans: + slices_having_nans = np.isnan(arr[-1, ...]) + else: + slices_having_nans = None + # --- Get values from indexes + previous = arr[previous_indexes] + next = arr[next_indexes] + # --- Linear interpolation + gamma = _get_gamma(virtual_indexes, previous_indexes, method) + result_shape = virtual_indexes.shape + (1,) * (arr.ndim - 1) + gamma = gamma.reshape(result_shape) + result = _lerp(previous, + next, + gamma, + out=out) + if np.any(slices_having_nans): + if result.ndim == 0 and out is None: + # can't write to a scalar, but indexing will be correct + result = arr[-1] + else: + np.copyto(result, arr[-1, ...], where=slices_having_nans) + return result + + +def _trapz_dispatcher(y, x=None, dx=None, axis=None): + return (y, x) + + +@array_function_dispatch(_trapz_dispatcher) +def trapz(y, x=None, dx=1.0, axis=-1): + r""" + Integrate along the given axis using the composite trapezoidal rule. + + If `x` is provided, the integration happens in sequence along its + elements - they are not sorted. + + Integrate `y` (`x`) along each 1d slice on the given axis, compute + :math:`\int y(x) dx`. + When `x` is specified, this integrates along the parametric curve, + computing :math:`\int_t y(t) dt = + \int_t y(t) \left.\frac{dx}{dt}\right|_{x=x(t)} dt`. + + Parameters + ---------- + y : array_like + Input array to integrate. + x : array_like, optional + The sample points corresponding to the `y` values. If `x` is None, + the sample points are assumed to be evenly spaced `dx` apart. The + default is None. + dx : scalar, optional + The spacing between sample points when `x` is None. The default is 1. + axis : int, optional + The axis along which to integrate. + + Returns + ------- + trapz : float or ndarray + Definite integral of `y` = n-dimensional array as approximated along + a single axis by the trapezoidal rule. If `y` is a 1-dimensional array, + then the result is a float. If `n` is greater than 1, then the result + is an `n`-1 dimensional array. + + See Also + -------- + sum, cumsum + + Notes + ----- + Image [2]_ illustrates trapezoidal rule -- y-axis locations of points + will be taken from `y` array, by default x-axis distances between + points will be 1.0, alternatively they can be provided with `x` array + or with `dx` scalar. Return value will be equal to combined area under + the red lines. + + + References + ---------- + .. [1] Wikipedia page: https://en.wikipedia.org/wiki/Trapezoidal_rule + + .. [2] Illustration image: + https://en.wikipedia.org/wiki/File:Composite_trapezoidal_rule_illustration.png + + Examples + -------- + Use the trapezoidal rule on evenly spaced points: + + >>> np.trapz([1, 2, 3]) + 4.0 + + The spacing between sample points can be selected by either the + ``x`` or ``dx`` arguments: + + >>> np.trapz([1, 2, 3], x=[4, 6, 8]) + 8.0 + >>> np.trapz([1, 2, 3], dx=2) + 8.0 + + Using a decreasing ``x`` corresponds to integrating in reverse: + + >>> np.trapz([1, 2, 3], x=[8, 6, 4]) + -8.0 + + More generally ``x`` is used to integrate along a parametric curve. We can + estimate the integral :math:`\int_0^1 x^2 = 1/3` using: + + >>> x = np.linspace(0, 1, num=50) + >>> y = x**2 + >>> np.trapz(y, x) + 0.33340274885464394 + + Or estimate the area of a circle, noting we repeat the sample which closes + the curve: + + >>> theta = np.linspace(0, 2 * np.pi, num=1000, endpoint=True) + >>> np.trapz(np.cos(theta), x=np.sin(theta)) + 3.141571941375841 + + ``np.trapz`` can be applied along a specified axis to do multiple + computations in one call: + + >>> a = np.arange(6).reshape(2, 3) + >>> a + array([[0, 1, 2], + [3, 4, 5]]) + >>> np.trapz(a, axis=0) + array([1.5, 2.5, 3.5]) + >>> np.trapz(a, axis=1) + array([2., 8.]) + """ + y = asanyarray(y) + if x is None: + d = dx + else: + x = asanyarray(x) + if x.ndim == 1: + d = diff(x) + # reshape to correct shape + shape = [1]*y.ndim + shape[axis] = d.shape[0] + d = d.reshape(shape) + else: + d = diff(x, axis=axis) + nd = y.ndim + slice1 = [slice(None)]*nd + slice2 = [slice(None)]*nd + slice1[axis] = slice(1, None) + slice2[axis] = slice(None, -1) + try: + ret = (d * (y[tuple(slice1)] + y[tuple(slice2)]) / 2.0).sum(axis) + except ValueError: + # Operations didn't work, cast to ndarray + d = np.asarray(d) + y = np.asarray(y) + ret = add.reduce(d * (y[tuple(slice1)]+y[tuple(slice2)])/2.0, axis) + return ret + + +# __array_function__ has no __code__ or other attributes normal Python funcs we +# wrap everything into a C callable. SciPy however, tries to "clone" `trapz` +# into a new Python function which requires `__code__` and a few other +# attributes. So we create a dummy clone and copy over its attributes allowing +# SciPy <= 1.10 to work: https://github.com/scipy/scipy/issues/17811 +assert not hasattr(trapz, "__code__") + +def _fake_trapz(y, x=None, dx=1.0, axis=-1): + return trapz(y, x=x, dx=dx, axis=axis) + + +trapz.__code__ = _fake_trapz.__code__ +trapz.__globals__ = _fake_trapz.__globals__ +trapz.__defaults__ = _fake_trapz.__defaults__ +trapz.__closure__ = _fake_trapz.__closure__ +trapz.__kwdefaults__ = _fake_trapz.__kwdefaults__ + + +def _meshgrid_dispatcher(*xi, copy=None, sparse=None, indexing=None): + return xi + + +# Based on scitools meshgrid +@array_function_dispatch(_meshgrid_dispatcher) +def meshgrid(*xi, copy=True, sparse=False, indexing='xy'): + """ + Return a list of coordinate matrices from coordinate vectors. + + Make N-D coordinate arrays for vectorized evaluations of + N-D scalar/vector fields over N-D grids, given + one-dimensional coordinate arrays x1, x2,..., xn. + + .. versionchanged:: 1.9 + 1-D and 0-D cases are allowed. + + Parameters + ---------- + x1, x2,..., xn : array_like + 1-D arrays representing the coordinates of a grid. + indexing : {'xy', 'ij'}, optional + Cartesian ('xy', default) or matrix ('ij') indexing of output. + See Notes for more details. + + .. versionadded:: 1.7.0 + sparse : bool, optional + If True the shape of the returned coordinate array for dimension *i* + is reduced from ``(N1, ..., Ni, ... Nn)`` to + ``(1, ..., 1, Ni, 1, ..., 1)``. These sparse coordinate grids are + intended to be use with :ref:`basics.broadcasting`. When all + coordinates are used in an expression, broadcasting still leads to a + fully-dimensonal result array. + + Default is False. + + .. versionadded:: 1.7.0 + copy : bool, optional + If False, a view into the original arrays are returned in order to + conserve memory. Default is True. Please note that + ``sparse=False, copy=False`` will likely return non-contiguous + arrays. Furthermore, more than one element of a broadcast array + may refer to a single memory location. If you need to write to the + arrays, make copies first. + + .. versionadded:: 1.7.0 + + Returns + ------- + X1, X2,..., XN : list of ndarrays + For vectors `x1`, `x2`,..., `xn` with lengths ``Ni=len(xi)``, + returns ``(N1, N2, N3,..., Nn)`` shaped arrays if indexing='ij' + or ``(N2, N1, N3,..., Nn)`` shaped arrays if indexing='xy' + with the elements of `xi` repeated to fill the matrix along + the first dimension for `x1`, the second for `x2` and so on. + + Notes + ----- + This function supports both indexing conventions through the indexing + keyword argument. Giving the string 'ij' returns a meshgrid with + matrix indexing, while 'xy' returns a meshgrid with Cartesian indexing. + In the 2-D case with inputs of length M and N, the outputs are of shape + (N, M) for 'xy' indexing and (M, N) for 'ij' indexing. In the 3-D case + with inputs of length M, N and P, outputs are of shape (N, M, P) for + 'xy' indexing and (M, N, P) for 'ij' indexing. The difference is + illustrated by the following code snippet:: + + xv, yv = np.meshgrid(x, y, indexing='ij') + for i in range(nx): + for j in range(ny): + # treat xv[i,j], yv[i,j] + + xv, yv = np.meshgrid(x, y, indexing='xy') + for i in range(nx): + for j in range(ny): + # treat xv[j,i], yv[j,i] + + In the 1-D and 0-D case, the indexing and sparse keywords have no effect. + + See Also + -------- + mgrid : Construct a multi-dimensional "meshgrid" using indexing notation. + ogrid : Construct an open multi-dimensional "meshgrid" using indexing + notation. + how-to-index + + Examples + -------- + >>> nx, ny = (3, 2) + >>> x = np.linspace(0, 1, nx) + >>> y = np.linspace(0, 1, ny) + >>> xv, yv = np.meshgrid(x, y) + >>> xv + array([[0. , 0.5, 1. ], + [0. , 0.5, 1. ]]) + >>> yv + array([[0., 0., 0.], + [1., 1., 1.]]) + + The result of `meshgrid` is a coordinate grid: + + >>> import matplotlib.pyplot as plt + >>> plt.plot(xv, yv, marker='o', color='k', linestyle='none') + >>> plt.show() + + You can create sparse output arrays to save memory and computation time. + + >>> xv, yv = np.meshgrid(x, y, sparse=True) + >>> xv + array([[0. , 0.5, 1. ]]) + >>> yv + array([[0.], + [1.]]) + + `meshgrid` is very useful to evaluate functions on a grid. If the + function depends on all coordinates, both dense and sparse outputs can be + used. + + >>> x = np.linspace(-5, 5, 101) + >>> y = np.linspace(-5, 5, 101) + >>> # full coordinate arrays + >>> xx, yy = np.meshgrid(x, y) + >>> zz = np.sqrt(xx**2 + yy**2) + >>> xx.shape, yy.shape, zz.shape + ((101, 101), (101, 101), (101, 101)) + >>> # sparse coordinate arrays + >>> xs, ys = np.meshgrid(x, y, sparse=True) + >>> zs = np.sqrt(xs**2 + ys**2) + >>> xs.shape, ys.shape, zs.shape + ((1, 101), (101, 1), (101, 101)) + >>> np.array_equal(zz, zs) + True + + >>> h = plt.contourf(x, y, zs) + >>> plt.axis('scaled') + >>> plt.colorbar() + >>> plt.show() + """ + ndim = len(xi) + + if indexing not in ['xy', 'ij']: + raise ValueError( + "Valid values for `indexing` are 'xy' and 'ij'.") + + s0 = (1,) * ndim + output = [np.asanyarray(x).reshape(s0[:i] + (-1,) + s0[i + 1:]) + for i, x in enumerate(xi)] + + if indexing == 'xy' and ndim > 1: + # switch first and second axis + output[0].shape = (1, -1) + s0[2:] + output[1].shape = (-1, 1) + s0[2:] + + if not sparse: + # Return the full N-D matrix (not only the 1-D vector) + output = np.broadcast_arrays(*output, subok=True) + + if copy: + output = [x.copy() for x in output] + + return output + + +def _delete_dispatcher(arr, obj, axis=None): + return (arr, obj) + + +@array_function_dispatch(_delete_dispatcher) +def delete(arr, obj, axis=None): + """ + Return a new array with sub-arrays along an axis deleted. For a one + dimensional array, this returns those entries not returned by + `arr[obj]`. + + Parameters + ---------- + arr : array_like + Input array. + obj : slice, int or array of ints + Indicate indices of sub-arrays to remove along the specified axis. + + .. versionchanged:: 1.19.0 + Boolean indices are now treated as a mask of elements to remove, + rather than being cast to the integers 0 and 1. + + axis : int, optional + The axis along which to delete the subarray defined by `obj`. + If `axis` is None, `obj` is applied to the flattened array. + + Returns + ------- + out : ndarray + A copy of `arr` with the elements specified by `obj` removed. Note + that `delete` does not occur in-place. If `axis` is None, `out` is + a flattened array. + + See Also + -------- + insert : Insert elements into an array. + append : Append elements at the end of an array. + + Notes + ----- + Often it is preferable to use a boolean mask. For example: + + >>> arr = np.arange(12) + 1 + >>> mask = np.ones(len(arr), dtype=bool) + >>> mask[[0,2,4]] = False + >>> result = arr[mask,...] + + Is equivalent to ``np.delete(arr, [0,2,4], axis=0)``, but allows further + use of `mask`. + + Examples + -------- + >>> arr = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]]) + >>> arr + array([[ 1, 2, 3, 4], + [ 5, 6, 7, 8], + [ 9, 10, 11, 12]]) + >>> np.delete(arr, 1, 0) + array([[ 1, 2, 3, 4], + [ 9, 10, 11, 12]]) + + >>> np.delete(arr, np.s_[::2], 1) + array([[ 2, 4], + [ 6, 8], + [10, 12]]) + >>> np.delete(arr, [1,3,5], None) + array([ 1, 3, 5, 7, 8, 9, 10, 11, 12]) + + """ + wrap = None + if type(arr) is not ndarray: + try: + wrap = arr.__array_wrap__ + except AttributeError: + pass + + arr = asarray(arr) + ndim = arr.ndim + arrorder = 'F' if arr.flags.fnc else 'C' + if axis is None: + if ndim != 1: + arr = arr.ravel() + # needed for np.matrix, which is still not 1d after being ravelled + ndim = arr.ndim + axis = ndim - 1 + else: + axis = normalize_axis_index(axis, ndim) + + slobj = [slice(None)]*ndim + N = arr.shape[axis] + newshape = list(arr.shape) + + if isinstance(obj, slice): + start, stop, step = obj.indices(N) + xr = range(start, stop, step) + numtodel = len(xr) + + if numtodel <= 0: + if wrap: + return wrap(arr.copy(order=arrorder)) + else: + return arr.copy(order=arrorder) + + # Invert if step is negative: + if step < 0: + step = -step + start = xr[-1] + stop = xr[0] + 1 + + newshape[axis] -= numtodel + new = empty(newshape, arr.dtype, arrorder) + # copy initial chunk + if start == 0: + pass + else: + slobj[axis] = slice(None, start) + new[tuple(slobj)] = arr[tuple(slobj)] + # copy end chunk + if stop == N: + pass + else: + slobj[axis] = slice(stop-numtodel, None) + slobj2 = [slice(None)]*ndim + slobj2[axis] = slice(stop, None) + new[tuple(slobj)] = arr[tuple(slobj2)] + # copy middle pieces + if step == 1: + pass + else: # use array indexing. + keep = ones(stop-start, dtype=bool) + keep[:stop-start:step] = False + slobj[axis] = slice(start, stop-numtodel) + slobj2 = [slice(None)]*ndim + slobj2[axis] = slice(start, stop) + arr = arr[tuple(slobj2)] + slobj2[axis] = keep + new[tuple(slobj)] = arr[tuple(slobj2)] + if wrap: + return wrap(new) + else: + return new + + if isinstance(obj, (int, integer)) and not isinstance(obj, bool): + single_value = True + else: + single_value = False + _obj = obj + obj = np.asarray(obj) + # `size == 0` to allow empty lists similar to indexing, but (as there) + # is really too generic: + if obj.size == 0 and not isinstance(_obj, np.ndarray): + obj = obj.astype(intp) + elif obj.size == 1 and obj.dtype.kind in "ui": + # For a size 1 integer array we can use the single-value path + # (most dtypes, except boolean, should just fail later). + obj = obj.item() + single_value = True + + if single_value: + # optimization for a single value + if (obj < -N or obj >= N): + raise IndexError( + "index %i is out of bounds for axis %i with " + "size %i" % (obj, axis, N)) + if (obj < 0): + obj += N + newshape[axis] -= 1 + new = empty(newshape, arr.dtype, arrorder) + slobj[axis] = slice(None, obj) + new[tuple(slobj)] = arr[tuple(slobj)] + slobj[axis] = slice(obj, None) + slobj2 = [slice(None)]*ndim + slobj2[axis] = slice(obj+1, None) + new[tuple(slobj)] = arr[tuple(slobj2)] + else: + if obj.dtype == bool: + if obj.shape != (N,): + raise ValueError('boolean array argument obj to delete ' + 'must be one dimensional and match the axis ' + 'length of {}'.format(N)) + + # optimization, the other branch is slower + keep = ~obj + else: + keep = ones(N, dtype=bool) + keep[obj,] = False + + slobj[axis] = keep + new = arr[tuple(slobj)] + + if wrap: + return wrap(new) + else: + return new + + +def _insert_dispatcher(arr, obj, values, axis=None): + return (arr, obj, values) + + +@array_function_dispatch(_insert_dispatcher) +def insert(arr, obj, values, axis=None): + """ + Insert values along the given axis before the given indices. + + Parameters + ---------- + arr : array_like + Input array. + obj : int, slice or sequence of ints + Object that defines the index or indices before which `values` is + inserted. + + .. versionadded:: 1.8.0 + + Support for multiple insertions when `obj` is a single scalar or a + sequence with one element (similar to calling insert multiple + times). + values : array_like + Values to insert into `arr`. If the type of `values` is different + from that of `arr`, `values` is converted to the type of `arr`. + `values` should be shaped so that ``arr[...,obj,...] = values`` + is legal. + axis : int, optional + Axis along which to insert `values`. If `axis` is None then `arr` + is flattened first. + + Returns + ------- + out : ndarray + A copy of `arr` with `values` inserted. Note that `insert` + does not occur in-place: a new array is returned. If + `axis` is None, `out` is a flattened array. + + See Also + -------- + append : Append elements at the end of an array. + concatenate : Join a sequence of arrays along an existing axis. + delete : Delete elements from an array. + + Notes + ----- + Note that for higher dimensional inserts ``obj=0`` behaves very different + from ``obj=[0]`` just like ``arr[:,0,:] = values`` is different from + ``arr[:,[0],:] = values``. + + Examples + -------- + >>> a = np.array([[1, 1], [2, 2], [3, 3]]) + >>> a + array([[1, 1], + [2, 2], + [3, 3]]) + >>> np.insert(a, 1, 5) + array([1, 5, 1, ..., 2, 3, 3]) + >>> np.insert(a, 1, 5, axis=1) + array([[1, 5, 1], + [2, 5, 2], + [3, 5, 3]]) + + Difference between sequence and scalars: + + >>> np.insert(a, [1], [[1],[2],[3]], axis=1) + array([[1, 1, 1], + [2, 2, 2], + [3, 3, 3]]) + >>> np.array_equal(np.insert(a, 1, [1, 2, 3], axis=1), + ... np.insert(a, [1], [[1],[2],[3]], axis=1)) + True + + >>> b = a.flatten() + >>> b + array([1, 1, 2, 2, 3, 3]) + >>> np.insert(b, [2, 2], [5, 6]) + array([1, 1, 5, ..., 2, 3, 3]) + + >>> np.insert(b, slice(2, 4), [5, 6]) + array([1, 1, 5, ..., 2, 3, 3]) + + >>> np.insert(b, [2, 2], [7.13, False]) # type casting + array([1, 1, 7, ..., 2, 3, 3]) + + >>> x = np.arange(8).reshape(2, 4) + >>> idx = (1, 3) + >>> np.insert(x, idx, 999, axis=1) + array([[ 0, 999, 1, 2, 999, 3], + [ 4, 999, 5, 6, 999, 7]]) + + """ + wrap = None + if type(arr) is not ndarray: + try: + wrap = arr.__array_wrap__ + except AttributeError: + pass + + arr = asarray(arr) + ndim = arr.ndim + arrorder = 'F' if arr.flags.fnc else 'C' + if axis is None: + if ndim != 1: + arr = arr.ravel() + # needed for np.matrix, which is still not 1d after being ravelled + ndim = arr.ndim + axis = ndim - 1 + else: + axis = normalize_axis_index(axis, ndim) + slobj = [slice(None)]*ndim + N = arr.shape[axis] + newshape = list(arr.shape) + + if isinstance(obj, slice): + # turn it into a range object + indices = arange(*obj.indices(N), dtype=intp) + else: + # need to copy obj, because indices will be changed in-place + indices = np.array(obj) + if indices.dtype == bool: + # See also delete + # 2012-10-11, NumPy 1.8 + warnings.warn( + "in the future insert will treat boolean arrays and " + "array-likes as a boolean index instead of casting it to " + "integer", FutureWarning, stacklevel=2) + indices = indices.astype(intp) + # Code after warning period: + #if obj.ndim != 1: + # raise ValueError('boolean array argument obj to insert ' + # 'must be one dimensional') + #indices = np.flatnonzero(obj) + elif indices.ndim > 1: + raise ValueError( + "index array argument obj to insert must be one dimensional " + "or scalar") + if indices.size == 1: + index = indices.item() + if index < -N or index > N: + raise IndexError(f"index {obj} is out of bounds for axis {axis} " + f"with size {N}") + if (index < 0): + index += N + + # There are some object array corner cases here, but we cannot avoid + # that: + values = array(values, copy=False, ndmin=arr.ndim, dtype=arr.dtype) + if indices.ndim == 0: + # broadcasting is very different here, since a[:,0,:] = ... behaves + # very different from a[:,[0],:] = ...! This changes values so that + # it works likes the second case. (here a[:,0:1,:]) + values = np.moveaxis(values, 0, axis) + numnew = values.shape[axis] + newshape[axis] += numnew + new = empty(newshape, arr.dtype, arrorder) + slobj[axis] = slice(None, index) + new[tuple(slobj)] = arr[tuple(slobj)] + slobj[axis] = slice(index, index+numnew) + new[tuple(slobj)] = values + slobj[axis] = slice(index+numnew, None) + slobj2 = [slice(None)] * ndim + slobj2[axis] = slice(index, None) + new[tuple(slobj)] = arr[tuple(slobj2)] + if wrap: + return wrap(new) + return new + elif indices.size == 0 and not isinstance(obj, np.ndarray): + # Can safely cast the empty list to intp + indices = indices.astype(intp) + + indices[indices < 0] += N + + numnew = len(indices) + order = indices.argsort(kind='mergesort') # stable sort + indices[order] += np.arange(numnew) + + newshape[axis] += numnew + old_mask = ones(newshape[axis], dtype=bool) + old_mask[indices] = False + + new = empty(newshape, arr.dtype, arrorder) + slobj2 = [slice(None)]*ndim + slobj[axis] = indices + slobj2[axis] = old_mask + new[tuple(slobj)] = values + new[tuple(slobj2)] = arr + + if wrap: + return wrap(new) + return new + + +def _append_dispatcher(arr, values, axis=None): + return (arr, values) + + +@array_function_dispatch(_append_dispatcher) +def append(arr, values, axis=None): + """ + Append values to the end of an array. + + Parameters + ---------- + arr : array_like + Values are appended to a copy of this array. + values : array_like + These values are appended to a copy of `arr`. It must be of the + correct shape (the same shape as `arr`, excluding `axis`). If + `axis` is not specified, `values` can be any shape and will be + flattened before use. + axis : int, optional + The axis along which `values` are appended. If `axis` is not + given, both `arr` and `values` are flattened before use. + + Returns + ------- + append : ndarray + A copy of `arr` with `values` appended to `axis`. Note that + `append` does not occur in-place: a new array is allocated and + filled. If `axis` is None, `out` is a flattened array. + + See Also + -------- + insert : Insert elements into an array. + delete : Delete elements from an array. + + Examples + -------- + >>> np.append([1, 2, 3], [[4, 5, 6], [7, 8, 9]]) + array([1, 2, 3, ..., 7, 8, 9]) + + When `axis` is specified, `values` must have the correct shape. + + >>> np.append([[1, 2, 3], [4, 5, 6]], [[7, 8, 9]], axis=0) + array([[1, 2, 3], + [4, 5, 6], + [7, 8, 9]]) + >>> np.append([[1, 2, 3], [4, 5, 6]], [7, 8, 9], axis=0) + Traceback (most recent call last): + ... + ValueError: all the input arrays must have same number of dimensions, but + the array at index 0 has 2 dimension(s) and the array at index 1 has 1 + dimension(s) + + """ + arr = asanyarray(arr) + if axis is None: + if arr.ndim != 1: + arr = arr.ravel() + values = ravel(values) + axis = arr.ndim-1 + return concatenate((arr, values), axis=axis) + + +def _digitize_dispatcher(x, bins, right=None): + return (x, bins) + + +@array_function_dispatch(_digitize_dispatcher) +def digitize(x, bins, right=False): + """ + Return the indices of the bins to which each value in input array belongs. + + ========= ============= ============================ + `right` order of bins returned index `i` satisfies + ========= ============= ============================ + ``False`` increasing ``bins[i-1] <= x < bins[i]`` + ``True`` increasing ``bins[i-1] < x <= bins[i]`` + ``False`` decreasing ``bins[i-1] > x >= bins[i]`` + ``True`` decreasing ``bins[i-1] >= x > bins[i]`` + ========= ============= ============================ + + If values in `x` are beyond the bounds of `bins`, 0 or ``len(bins)`` is + returned as appropriate. + + Parameters + ---------- + x : array_like + Input array to be binned. Prior to NumPy 1.10.0, this array had to + be 1-dimensional, but can now have any shape. + bins : array_like + Array of bins. It has to be 1-dimensional and monotonic. + right : bool, optional + Indicating whether the intervals include the right or the left bin + edge. Default behavior is (right==False) indicating that the interval + does not include the right edge. The left bin end is open in this + case, i.e., bins[i-1] <= x < bins[i] is the default behavior for + monotonically increasing bins. + + Returns + ------- + indices : ndarray of ints + Output array of indices, of same shape as `x`. + + Raises + ------ + ValueError + If `bins` is not monotonic. + TypeError + If the type of the input is complex. + + See Also + -------- + bincount, histogram, unique, searchsorted + + Notes + ----- + If values in `x` are such that they fall outside the bin range, + attempting to index `bins` with the indices that `digitize` returns + will result in an IndexError. + + .. versionadded:: 1.10.0 + + `np.digitize` is implemented in terms of `np.searchsorted`. This means + that a binary search is used to bin the values, which scales much better + for larger number of bins than the previous linear search. It also removes + the requirement for the input array to be 1-dimensional. + + For monotonically _increasing_ `bins`, the following are equivalent:: + + np.digitize(x, bins, right=True) + np.searchsorted(bins, x, side='left') + + Note that as the order of the arguments are reversed, the side must be too. + The `searchsorted` call is marginally faster, as it does not do any + monotonicity checks. Perhaps more importantly, it supports all dtypes. + + Examples + -------- + >>> x = np.array([0.2, 6.4, 3.0, 1.6]) + >>> bins = np.array([0.0, 1.0, 2.5, 4.0, 10.0]) + >>> inds = np.digitize(x, bins) + >>> inds + array([1, 4, 3, 2]) + >>> for n in range(x.size): + ... print(bins[inds[n]-1], "<=", x[n], "<", bins[inds[n]]) + ... + 0.0 <= 0.2 < 1.0 + 4.0 <= 6.4 < 10.0 + 2.5 <= 3.0 < 4.0 + 1.0 <= 1.6 < 2.5 + + >>> x = np.array([1.2, 10.0, 12.4, 15.5, 20.]) + >>> bins = np.array([0, 5, 10, 15, 20]) + >>> np.digitize(x,bins,right=True) + array([1, 2, 3, 4, 4]) + >>> np.digitize(x,bins,right=False) + array([1, 3, 3, 4, 5]) + """ + x = _nx.asarray(x) + bins = _nx.asarray(bins) + + # here for compatibility, searchsorted below is happy to take this + if np.issubdtype(x.dtype, _nx.complexfloating): + raise TypeError("x may not be complex") + + mono = _monotonicity(bins) + if mono == 0: + raise ValueError("bins must be monotonically increasing or decreasing") + + # this is backwards because the arguments below are swapped + side = 'left' if right else 'right' + if mono == -1: + # reverse the bins, and invert the results + return len(bins) - _nx.searchsorted(bins[::-1], x, side=side) + else: + return _nx.searchsorted(bins, x, side=side) diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/lib/function_base.pyi b/env-llmeval/lib/python3.10/site-packages/numpy/lib/function_base.pyi new file mode 100644 index 0000000000000000000000000000000000000000..687e4ab1708bf2667f1ff4fc8344bab9786cefc9 --- /dev/null +++ b/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]: ... diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/lib/histograms.py b/env-llmeval/lib/python3.10/site-packages/numpy/lib/histograms.py new file mode 100644 index 0000000000000000000000000000000000000000..6ac65b726928bb21432a7a6edcbf73fbeaedb137 --- /dev/null +++ b/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 diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/lib/index_tricks.py b/env-llmeval/lib/python3.10/site-packages/numpy/lib/index_tricks.py new file mode 100644 index 0000000000000000000000000000000000000000..6913d2b95b76521f9f9d532b2762400e1bd68f43 --- /dev/null +++ b/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 +# 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) diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/lib/index_tricks.pyi b/env-llmeval/lib/python3.10/site-packages/numpy/lib/index_tricks.pyi new file mode 100644 index 0000000000000000000000000000000000000000..29a6b9e2b9f95c260b5123cef75c9a1d0b34833b --- /dev/null +++ b/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` diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/lib/mixins.py b/env-llmeval/lib/python3.10/site-packages/numpy/lib/mixins.py new file mode 100644 index 0000000000000000000000000000000000000000..117cc785187be45e8597af48d26f723eb0024d23 --- /dev/null +++ b/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 + `_. + + 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') diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/lib/mixins.pyi b/env-llmeval/lib/python3.10/site-packages/numpy/lib/mixins.pyi new file mode 100644 index 0000000000000000000000000000000000000000..c5744213372cf746fcba3a3b711b49730629e28c --- /dev/null +++ b/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: ... diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/lib/nanfunctions.py b/env-llmeval/lib/python3.10/site-packages/numpy/lib/nanfunctions.py new file mode 100644 index 0000000000000000000000000000000000000000..b3b570860ff87521f103776c42b4f2462f778dae --- /dev/null +++ b/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 diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/lib/nanfunctions.pyi b/env-llmeval/lib/python3.10/site-packages/numpy/lib/nanfunctions.pyi new file mode 100644 index 0000000000000000000000000000000000000000..8642055fedd2e5b851c656efd563453e8bd94bd6 --- /dev/null +++ b/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 diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/lib/npyio.py b/env-llmeval/lib/python3.10/site-packages/numpy/lib/npyio.py new file mode 100644 index 0000000000000000000000000000000000000000..339b1dc6211377442f7c01b78c8b3c65c65be2b7 --- /dev/null +++ b/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', '= 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', '>> 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', '>> 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', '>> s = StringIO('"Hello, my name is ""Monty""!"') + >>> np.loadtxt(s, dtype="U", delimiter=",", quotechar='"') + array('Hello, my name is "Monty"!', dtype='>> 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 + `_, + 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', '>> 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 + `_. + + Examples + -------- + >>> from io import StringIO + >>> import numpy as np + + Comma delimited file with mixed dtype + + >>> s = StringIO(u"1,1.3,abcde") + >>> data = np.genfromtxt(s, dtype=[('myint','i8'),('myfloat','f8'), + ... ('mystring','S5')], delimiter=",") + >>> data + array((1, 1.3, b'abcde'), + dtype=[('myint', '>> _ = s.seek(0) # needed for StringIO example only + >>> data = np.genfromtxt(s, dtype=None, + ... names = ['myint','myfloat','mystring'], delimiter=",") + >>> data + array((1, 1.3, b'abcde'), + dtype=[('myint', '>> _ = s.seek(0) + >>> data = np.genfromtxt(s, dtype="i8,f8,S5", + ... names=['myint','myfloat','mystring'], delimiter=",") + >>> data + array((1, 1.3, b'abcde'), + dtype=[('myint', '>> s = StringIO(u"11.3abcde") + >>> data = np.genfromtxt(s, dtype=None, names=['intvar','fltvar','strvar'], + ... delimiter=[1,3,5]) + >>> data + array((1, 1.3, b'abcde'), + dtype=[('intvar', '>> f = StringIO(''' + ... text,# of chars + ... hello world,11 + ... numpy,5''') + >>> np.genfromtxt(f, dtype='S12,S12', delimiter=',') + array([(b'text', b''), (b'hello world', b'11'), (b'numpy', b'5')], + dtype=[('f0', 'S12'), ('f1', 'S12')]) + + """ + + 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 diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/lib/polynomial.py b/env-llmeval/lib/python3.10/site-packages/numpy/lib/polynomial.py new file mode 100644 index 0000000000000000000000000000000000000000..3b8db2a9512694c8148cd6e3538c70087e3cd1a8 --- /dev/null +++ b/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 `. + + 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 `. + + 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 `. + + 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 `. + + 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 `. + + Fit a polynomial ``p(x) = p[0] * x**deg + ... + p[deg]`` of degree `deg` + to points `(x, y)`. Returns a vector of coefficients `p` that minimises + the squared error in the order `deg`, `deg-1`, ... `0`. + + The `Polynomial.fit ` class + method is recommended for new code as it is more stable numerically. See + the documentation of the method for more information. + + Parameters + ---------- + x : array_like, shape (M,) + x-coordinates of the M sample points ``(x[i], y[i])``. + y : array_like, shape (M,) or (M, K) + y-coordinates of the sample points. Several data sets of sample + points sharing the same x-coordinates can be fitted at once by + passing in a 2D-array that contains one dataset per column. + deg : int + Degree of the fitting polynomial + rcond : float, optional + Relative condition number of the fit. Singular values smaller than + this relative to the largest singular value will be ignored. The + default value is len(x)*eps, where eps is the relative precision of + the float type, about 2e-16 in most cases. + full : bool, optional + Switch determining nature of return value. When it is False (the + default) just the coefficients are returned, when True diagnostic + information from the singular value decomposition is also returned. + w : array_like, shape (M,), optional + Weights. 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 `. + + 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 `. + + 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 `. + + 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 `. + + 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 `. + + 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 `. + + 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) diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/lib/polynomial.pyi b/env-llmeval/lib/python3.10/site-packages/numpy/lib/polynomial.pyi new file mode 100644 index 0000000000000000000000000000000000000000..14bbaf39d24944fb565cf543002ce1a8ba06ffe0 --- /dev/null +++ b/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]]: ... diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/lib/recfunctions.py b/env-llmeval/lib/python3.10/site-packages/numpy/lib/recfunctions.py new file mode 100644 index 0000000000000000000000000000000000000000..83ae413c6032bceec05c7e4dce17e16113f7625c --- /dev/null +++ b/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', '>> dt = np.dtype([(('a', 'A'), np.int64), ('b', np.double, 3)]) + >>> dt.descr + [(('a', 'A'), '>> _get_fieldspec(dt) + [(('a', 'A'), dtype('int64')), ('b', dtype(('>> 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', '>> 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', '>> 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', '>> 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', '>> 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', '>> rfn.drop_fields(a, 'ba') + array([(1, (3,)), (4, (6,))], dtype=[('a', '>> rfn.drop_fields(a, ['ba', 'bb']) + array([(1,), (4,)], dtype=[('a', '>> 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', ' 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, >> dt + dtype({'names': ['f0', 'f1', 'f2'], 'formats': ['u1', '>> print_offsets(dt) + offsets: [0, 8, 16] + itemsize: 24 + >>> packed_dt = rfn.repack_fields(dt) + >>> packed_dt + dtype([('f0', 'u1'), ('f1', '>> 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', '>> 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', '>> 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', '>> rfn.require_fields(a, [('b', 'f4'), ('newf', 'u1')]) + array([(1., 0), (1., 0), (1., 0), (1., 0)], + dtype=[('b', '>> 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', ' '%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', '= 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) diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/lib/scimath.py b/env-llmeval/lib/python3.10/site-packages/numpy/lib/scimath.py new file mode 100644 index 0000000000000000000000000000000000000000..b7ef0d7109c63cffc7c30f59d97389a4a4a230f7 --- /dev/null +++ b/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) diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/lib/scimath.pyi b/env-llmeval/lib/python3.10/site-packages/numpy/lib/scimath.pyi new file mode 100644 index 0000000000000000000000000000000000000000..589feb15f8ff38bc5003928f6d934454c8e2a94d --- /dev/null +++ b/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]]: ... diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/lib/shape_base.py b/env-llmeval/lib/python3.10/site-packages/numpy/lib/shape_base.py new file mode 100644 index 0000000000000000000000000000000000000000..5d8a41bfe4a9c6d0c5666968a31c78b7c27497dd --- /dev/null +++ b/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) diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/lib/twodim_base.py b/env-llmeval/lib/python3.10/site-packages/numpy/lib/twodim_base.py new file mode 100644 index 0000000000000000000000000000000000000000..6dcb656519342e516a6f1be0bf283bb1f326214f --- /dev/null +++ b/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 ` can only display square bins: + + >>> fig = plt.figure(figsize=(7, 3)) + >>> ax = fig.add_subplot(131, title='imshow: square bins') + >>> plt.imshow(H, interpolation='nearest', origin='lower', + ... extent=[xedges[0], xedges[-1], yedges[0], yedges[-1]]) + + + :func:`pcolormesh ` can display actual edges: + + >>> ax = fig.add_subplot(132, title='pcolormesh: actual edges', + ... aspect='equal') + >>> X, Y = np.meshgrid(xedges, yedges) + >>> ax.pcolormesh(X, Y, H) + + + :class:`NonUniformImage ` can be used to + display actual bin edges with interpolation: + + >>> ax = fig.add_subplot(133, title='NonUniformImage: interpolated', + ... aspect='equal', xlim=xedges[[0, -1]], ylim=yedges[[0, -1]]) + >>> im = NonUniformImage(ax, interpolation='bilinear') + >>> xcenters = (xedges[:-1] + xedges[1:]) / 2 + >>> ycenters = (yedges[:-1] + yedges[1:]) / 2 + >>> im.set_data(xcenters, ycenters, H) + >>> ax.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 `, and a + :func:`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]) diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/lib/twodim_base.pyi b/env-llmeval/lib/python3.10/site-packages/numpy/lib/twodim_base.pyi new file mode 100644 index 0000000000000000000000000000000000000000..1b3b94bd5cba589f3d16c7e9a66ab261f0bd97cf --- /dev/null +++ b/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_]]: ... diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/lib/type_check.py b/env-llmeval/lib/python3.10/site-packages/numpy/lib/type_check.py new file mode 100644 index 0000000000000000000000000000000000000000..3f84b80e5860c5bbd9e73790f8a5d21715ab9b6d --- /dev/null +++ b/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)) + + >>> np.common_type(np.arange(2, dtype=np.float32), np.arange(2)) + + >>> np.common_type(np.arange(4), np.array([45, 6.j]), np.array([45.0])) + + + """ + 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] diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/lib/ufunclike.pyi b/env-llmeval/lib/python3.10/site-packages/numpy/lib/ufunclike.pyi new file mode 100644 index 0000000000000000000000000000000000000000..82537e2acd953e3ce82541b04cdca0dfba1963b4 --- /dev/null +++ b/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: ... diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/lib/user_array.py b/env-llmeval/lib/python3.10/site-packages/numpy/lib/user_array.py new file mode 100644 index 0000000000000000000000000000000000000000..0e96b477ef7456e5ce575b17698323b7ff479dcd --- /dev/null +++ b/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)) diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/matrixlib/__init__.py b/env-llmeval/lib/python3.10/site-packages/numpy/matrixlib/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..8a7597d30387c98c0e7e66a0bfc82f5e64823d95 --- /dev/null +++ b/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 diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/matrixlib/__init__.pyi b/env-llmeval/lib/python3.10/site-packages/numpy/matrixlib/__init__.pyi new file mode 100644 index 0000000000000000000000000000000000000000..b0ca8c9ca03d39efa03bede061f2a4f8ef90523a --- /dev/null +++ b/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 diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/matrixlib/defmatrix.py b/env-llmeval/lib/python3.10/site-packages/numpy/matrixlib/defmatrix.py new file mode 100644 index 0000000000000000000000000000000000000000..d029b13fb8b561247fb031e44a14de285a1d9d4a --- /dev/null +++ b/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 diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/matrixlib/defmatrix.pyi b/env-llmeval/lib/python3.10/site-packages/numpy/matrixlib/defmatrix.pyi new file mode 100644 index 0000000000000000000000000000000000000000..9d0d1ee50b6600bce80f1f5b1363e5ee3102a02a --- /dev/null +++ b/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 diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/matrixlib/setup.py b/env-llmeval/lib/python3.10/site-packages/numpy/matrixlib/setup.py new file mode 100644 index 0000000000000000000000000000000000000000..4fed75de1cbc22357c675fd8ce2d52cbb6829b50 --- /dev/null +++ b/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) diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/matrixlib/tests/__init__.py b/env-llmeval/lib/python3.10/site-packages/numpy/matrixlib/tests/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/matrixlib/tests/__pycache__/test_numeric.cpython-310.pyc b/env-llmeval/lib/python3.10/site-packages/numpy/matrixlib/tests/__pycache__/test_numeric.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..fe714235415f386d8d71c4a11add41fb16c74472 Binary files /dev/null and b/env-llmeval/lib/python3.10/site-packages/numpy/matrixlib/tests/__pycache__/test_numeric.cpython-310.pyc differ diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/matrixlib/tests/test_defmatrix.py b/env-llmeval/lib/python3.10/site-packages/numpy/matrixlib/tests/test_defmatrix.py new file mode 100644 index 0000000000000000000000000000000000000000..4cb5f3a375e933fbc63b3aaab12527e60423de0c --- /dev/null +++ b/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)) diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/matrixlib/tests/test_interaction.py b/env-llmeval/lib/python3.10/site-packages/numpy/matrixlib/tests/test_interaction.py new file mode 100644 index 0000000000000000000000000000000000000000..5154bd621c61d7c081630c4659f74d70059e1746 --- /dev/null +++ b/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) diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/matrixlib/tests/test_masked_matrix.py b/env-llmeval/lib/python3.10/site-packages/numpy/matrixlib/tests/test_masked_matrix.py new file mode 100644 index 0000000000000000000000000000000000000000..d0ce357aef2765ad72cd3a5f4d0ed48fc07463c1 --- /dev/null +++ b/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)) diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/matrixlib/tests/test_matrix_linalg.py b/env-llmeval/lib/python3.10/site-packages/numpy/matrixlib/tests/test_matrix_linalg.py new file mode 100644 index 0000000000000000000000000000000000000000..106c2e38217a633829329a94df077c097fbcbf7a --- /dev/null +++ b/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 diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/matrixlib/tests/test_multiarray.py b/env-llmeval/lib/python3.10/site-packages/numpy/matrixlib/tests/test_multiarray.py new file mode 100644 index 0000000000000000000000000000000000000000..638d0d1534deba060140ffda3b61950a0b4f815d --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/numpy/matrixlib/tests/test_multiarray.py @@ -0,0 +1,16 @@ +import numpy as np +from numpy.testing import assert_, assert_equal, assert_array_equal + +class TestView: + def test_type(self): + x = np.array([1, 2, 3]) + assert_(isinstance(x.view(np.matrix), np.matrix)) + + def test_keywords(self): + x = np.array([(1, 2)], dtype=[('a', np.int8), ('b', np.int8)]) + # We must be specific about the endianness here: + y = x.view(dtype='>> from numpy.polynomial.laguerre import poly2lag + >>> poly2lag(np.arange(4)) + array([ 23., -63., 58., -18.]) + + """ + [pol] = pu.as_series([pol]) + res = 0 + for p in pol[::-1]: + res = lagadd(lagmulx(res), p) + return res + + +def lag2poly(c): + """ + Convert a Laguerre series to a polynomial. + + Convert an array representing the coefficients of a Laguerre series, + ordered from lowest degree to highest, to an array of the coefficients + of the equivalent polynomial (relative to the "standard" basis) ordered + from lowest to highest degree. + + Parameters + ---------- + c : array_like + 1-D array containing the Laguerre series coefficients, ordered + from lowest order term to highest. + + Returns + ------- + pol : ndarray + 1-D array containing the coefficients of the equivalent polynomial + (relative to the "standard" basis) ordered from lowest order term + to highest. + + See Also + -------- + poly2lag + + Notes + ----- + The easy way to do conversions between polynomial basis sets + is to use the convert method of a class instance. + + Examples + -------- + >>> from numpy.polynomial.laguerre import lag2poly + >>> lag2poly([ 23., -63., 58., -18.]) + array([0., 1., 2., 3.]) + + """ + from .polynomial import polyadd, polysub, polymulx + + [c] = pu.as_series([c]) + n = len(c) + if n == 1: + return c + else: + c0 = c[-2] + c1 = c[-1] + # i is the current degree of c1 + for i in range(n - 1, 1, -1): + tmp = c0 + c0 = polysub(c[i - 2], (c1*(i - 1))/i) + c1 = polyadd(tmp, polysub((2*i - 1)*c1, polymulx(c1))/i) + return polyadd(c0, polysub(c1, polymulx(c1))) + +# +# These are constant arrays are of integer type so as to be compatible +# with the widest range of other types, such as Decimal. +# + +# Laguerre +lagdomain = np.array([0, 1]) + +# Laguerre coefficients representing zero. +lagzero = np.array([0]) + +# Laguerre coefficients representing one. +lagone = np.array([1]) + +# Laguerre coefficients representing the identity x. +lagx = np.array([1, -1]) + + +def lagline(off, scl): + """ + Laguerre series whose graph is a straight line. + + Parameters + ---------- + off, scl : scalars + The specified line is given by ``off + scl*x``. + + Returns + ------- + y : ndarray + This module's representation of the Laguerre series for + ``off + scl*x``. + + See Also + -------- + numpy.polynomial.polynomial.polyline + numpy.polynomial.chebyshev.chebline + numpy.polynomial.legendre.legline + numpy.polynomial.hermite.hermline + numpy.polynomial.hermite_e.hermeline + + Examples + -------- + >>> from numpy.polynomial.laguerre import lagline, lagval + >>> lagval(0,lagline(3, 2)) + 3.0 + >>> lagval(1,lagline(3, 2)) + 5.0 + + """ + if scl != 0: + return np.array([off + scl, -scl]) + else: + return np.array([off]) + + +def lagfromroots(roots): + """ + Generate a Laguerre series with given roots. + + The function returns the coefficients of the polynomial + + .. math:: p(x) = (x - r_0) * (x - r_1) * ... * (x - r_n), + + in Laguerre form, where the `r_n` are the roots specified in `roots`. + If a zero has multiplicity n, then it must appear in `roots` n times. + For instance, if 2 is a root of multiplicity three and 3 is a root of + multiplicity 2, then `roots` looks something like [2, 2, 2, 3, 3]. The + roots can appear in any order. + + If the returned coefficients are `c`, then + + .. math:: p(x) = c_0 + c_1 * L_1(x) + ... + c_n * L_n(x) + + The coefficient of the last term is not generally 1 for monic + polynomials in Laguerre form. + + Parameters + ---------- + roots : array_like + Sequence containing the roots. + + Returns + ------- + out : ndarray + 1-D array of coefficients. If all roots are real then `out` is a + real array, if some of the roots are complex, then `out` is complex + even if all the coefficients in the result are real (see Examples + below). + + See Also + -------- + numpy.polynomial.polynomial.polyfromroots + numpy.polynomial.legendre.legfromroots + numpy.polynomial.chebyshev.chebfromroots + numpy.polynomial.hermite.hermfromroots + numpy.polynomial.hermite_e.hermefromroots + + Examples + -------- + >>> from numpy.polynomial.laguerre import lagfromroots, lagval + >>> coef = lagfromroots((-1, 0, 1)) + >>> lagval((-1, 0, 1), coef) + array([0., 0., 0.]) + >>> coef = lagfromroots((-1j, 1j)) + >>> lagval((-1j, 1j), coef) + array([0.+0.j, 0.+0.j]) + + """ + return pu._fromroots(lagline, lagmul, roots) + + +def lagadd(c1, c2): + """ + Add one Laguerre series to another. + + Returns the sum of two Laguerre series `c1` + `c2`. The arguments + are sequences of coefficients ordered from lowest order term to + highest, i.e., [1,2,3] represents the series ``P_0 + 2*P_1 + 3*P_2``. + + Parameters + ---------- + c1, c2 : array_like + 1-D arrays of Laguerre series coefficients ordered from low to + high. + + Returns + ------- + out : ndarray + Array representing the Laguerre series of their sum. + + See Also + -------- + lagsub, lagmulx, lagmul, lagdiv, lagpow + + Notes + ----- + Unlike multiplication, division, etc., the sum of two Laguerre series + is a Laguerre series (without having to "reproject" the result onto + the basis set) so addition, just like that of "standard" polynomials, + is simply "component-wise." + + Examples + -------- + >>> from numpy.polynomial.laguerre import lagadd + >>> lagadd([1, 2, 3], [1, 2, 3, 4]) + array([2., 4., 6., 4.]) + + + """ + return pu._add(c1, c2) + + +def lagsub(c1, c2): + """ + Subtract one Laguerre series from another. + + Returns the difference of two Laguerre series `c1` - `c2`. The + sequences of coefficients are from lowest order term to highest, i.e., + [1,2,3] represents the series ``P_0 + 2*P_1 + 3*P_2``. + + Parameters + ---------- + c1, c2 : array_like + 1-D arrays of Laguerre series coefficients ordered from low to + high. + + Returns + ------- + out : ndarray + Of Laguerre series coefficients representing their difference. + + See Also + -------- + lagadd, lagmulx, lagmul, lagdiv, lagpow + + Notes + ----- + Unlike multiplication, division, etc., the difference of two Laguerre + series is a Laguerre series (without having to "reproject" the result + onto the basis set) so subtraction, just like that of "standard" + polynomials, is simply "component-wise." + + Examples + -------- + >>> from numpy.polynomial.laguerre import lagsub + >>> lagsub([1, 2, 3, 4], [1, 2, 3]) + array([0., 0., 0., 4.]) + + """ + return pu._sub(c1, c2) + + +def lagmulx(c): + """Multiply a Laguerre series by x. + + Multiply the Laguerre series `c` by x, where x is the independent + variable. + + + Parameters + ---------- + c : array_like + 1-D array of Laguerre series coefficients ordered from low to + high. + + Returns + ------- + out : ndarray + Array representing the result of the multiplication. + + See Also + -------- + lagadd, lagsub, lagmul, lagdiv, lagpow + + Notes + ----- + The multiplication uses the recursion relationship for Laguerre + polynomials in the form + + .. math:: + + xP_i(x) = (-(i + 1)*P_{i + 1}(x) + (2i + 1)P_{i}(x) - iP_{i - 1}(x)) + + Examples + -------- + >>> from numpy.polynomial.laguerre import lagmulx + >>> lagmulx([1, 2, 3]) + array([-1., -1., 11., -9.]) + + """ + # c is a trimmed copy + [c] = pu.as_series([c]) + # The zero series needs special treatment + if len(c) == 1 and c[0] == 0: + return c + + prd = np.empty(len(c) + 1, dtype=c.dtype) + prd[0] = c[0] + prd[1] = -c[0] + for i in range(1, len(c)): + prd[i + 1] = -c[i]*(i + 1) + prd[i] += c[i]*(2*i + 1) + prd[i - 1] -= c[i]*i + return prd + + +def lagmul(c1, c2): + """ + Multiply one Laguerre series by another. + + Returns the product of two Laguerre series `c1` * `c2`. The arguments + are sequences of coefficients, from lowest order "term" to highest, + e.g., [1,2,3] represents the series ``P_0 + 2*P_1 + 3*P_2``. + + Parameters + ---------- + c1, c2 : array_like + 1-D arrays of Laguerre series coefficients ordered from low to + high. + + Returns + ------- + out : ndarray + Of Laguerre series coefficients representing their product. + + See Also + -------- + lagadd, lagsub, lagmulx, lagdiv, lagpow + + Notes + ----- + In general, the (polynomial) product of two C-series results in terms + that are not in the Laguerre polynomial basis set. Thus, to express + the product as a Laguerre series, it is necessary to "reproject" the + product onto said basis set, which may produce "unintuitive" (but + correct) results; see Examples section below. + + Examples + -------- + >>> from numpy.polynomial.laguerre import lagmul + >>> lagmul([1, 2, 3], [0, 1, 2]) + array([ 8., -13., 38., -51., 36.]) + + """ + # s1, s2 are trimmed copies + [c1, c2] = pu.as_series([c1, c2]) + + if len(c1) > len(c2): + c = c2 + xs = c1 + else: + c = c1 + xs = c2 + + if len(c) == 1: + c0 = c[0]*xs + c1 = 0 + elif len(c) == 2: + c0 = c[0]*xs + c1 = c[1]*xs + else: + nd = len(c) + c0 = c[-2]*xs + c1 = c[-1]*xs + for i in range(3, len(c) + 1): + tmp = c0 + nd = nd - 1 + c0 = lagsub(c[-i]*xs, (c1*(nd - 1))/nd) + c1 = lagadd(tmp, lagsub((2*nd - 1)*c1, lagmulx(c1))/nd) + return lagadd(c0, lagsub(c1, lagmulx(c1))) + + +def lagdiv(c1, c2): + """ + Divide one Laguerre series by another. + + Returns the quotient-with-remainder of two Laguerre series + `c1` / `c2`. The arguments are sequences of coefficients from lowest + order "term" to highest, e.g., [1,2,3] represents the series + ``P_0 + 2*P_1 + 3*P_2``. + + Parameters + ---------- + c1, c2 : array_like + 1-D arrays of Laguerre series coefficients ordered from low to + high. + + Returns + ------- + [quo, rem] : ndarrays + Of Laguerre series coefficients representing the quotient and + remainder. + + See Also + -------- + lagadd, lagsub, lagmulx, lagmul, lagpow + + Notes + ----- + In general, the (polynomial) division of one Laguerre series by another + results in quotient and remainder terms that are not in the Laguerre + polynomial basis set. Thus, to express these results as a Laguerre + series, it is necessary to "reproject" the results onto the Laguerre + basis set, which may produce "unintuitive" (but correct) results; see + Examples section below. + + Examples + -------- + >>> from numpy.polynomial.laguerre import lagdiv + >>> lagdiv([ 8., -13., 38., -51., 36.], [0, 1, 2]) + (array([1., 2., 3.]), array([0.])) + >>> lagdiv([ 9., -12., 38., -51., 36.], [0, 1, 2]) + (array([1., 2., 3.]), array([1., 1.])) + + """ + return pu._div(lagmul, c1, c2) + + +def lagpow(c, pow, maxpower=16): + """Raise a Laguerre series to a power. + + Returns the Laguerre series `c` raised to the power `pow`. The + argument `c` is a sequence of coefficients ordered from low to high. + i.e., [1,2,3] is the series ``P_0 + 2*P_1 + 3*P_2.`` + + Parameters + ---------- + c : array_like + 1-D array of Laguerre series coefficients ordered from low to + high. + pow : integer + Power to which the series will be raised + maxpower : integer, optional + Maximum power allowed. This is mainly to limit growth of the series + to unmanageable size. Default is 16 + + Returns + ------- + coef : ndarray + Laguerre series of power. + + See Also + -------- + lagadd, lagsub, lagmulx, lagmul, lagdiv + + Examples + -------- + >>> from numpy.polynomial.laguerre import lagpow + >>> lagpow([1, 2, 3], 2) + array([ 14., -16., 56., -72., 54.]) + + """ + return pu._pow(lagmul, c, pow, maxpower) + + +def lagder(c, m=1, scl=1, axis=0): + """ + Differentiate a Laguerre series. + + Returns the Laguerre series coefficients `c` differentiated `m` times + along `axis`. At each iteration the result is multiplied by `scl` (the + scaling factor is for use in a linear change of variable). The argument + `c` is an array of coefficients from low to high degree along each + axis, e.g., [1,2,3] represents the series ``1*L_0 + 2*L_1 + 3*L_2`` + while [[1,2],[1,2]] represents ``1*L_0(x)*L_0(y) + 1*L_1(x)*L_0(y) + + 2*L_0(x)*L_1(y) + 2*L_1(x)*L_1(y)`` if axis=0 is ``x`` and axis=1 is + ``y``. + + Parameters + ---------- + c : array_like + Array of Laguerre series coefficients. If `c` is multidimensional + the different axis correspond to different variables with the + degree in each axis given by the corresponding index. + m : int, optional + Number of derivatives taken, must be non-negative. (Default: 1) + scl : scalar, optional + Each differentiation is multiplied by `scl`. The end result is + multiplication by ``scl**m``. This is for use in a linear change of + variable. (Default: 1) + axis : int, optional + Axis over which the derivative is taken. (Default: 0). + + .. versionadded:: 1.7.0 + + Returns + ------- + der : ndarray + Laguerre series of the derivative. + + See Also + -------- + lagint + + Notes + ----- + In general, the result of differentiating a Laguerre series does not + resemble the same operation on a power series. Thus the result of this + function may be "unintuitive," albeit correct; see Examples section + below. + + Examples + -------- + >>> from numpy.polynomial.laguerre import lagder + >>> lagder([ 1., 1., 1., -3.]) + array([1., 2., 3.]) + >>> lagder([ 1., 0., 0., -4., 3.], m=2) + array([1., 2., 3.]) + + """ + c = np.array(c, ndmin=1, copy=True) + if c.dtype.char in '?bBhHiIlLqQpP': + c = c.astype(np.double) + + cnt = pu._deprecate_as_int(m, "the order of derivation") + iaxis = pu._deprecate_as_int(axis, "the axis") + if cnt < 0: + raise ValueError("The order of derivation must be non-negative") + iaxis = normalize_axis_index(iaxis, c.ndim) + + if cnt == 0: + return c + + c = np.moveaxis(c, iaxis, 0) + n = len(c) + if cnt >= n: + c = c[:1]*0 + else: + for i in range(cnt): + n = n - 1 + c *= scl + der = np.empty((n,) + c.shape[1:], dtype=c.dtype) + for j in range(n, 1, -1): + der[j - 1] = -c[j] + c[j - 1] += c[j] + der[0] = -c[1] + c = der + c = np.moveaxis(c, 0, iaxis) + return c + + +def lagint(c, m=1, k=[], lbnd=0, scl=1, axis=0): + """ + Integrate a Laguerre series. + + Returns the Laguerre series coefficients `c` integrated `m` times from + `lbnd` along `axis`. At each iteration the resulting series is + **multiplied** by `scl` and an integration constant, `k`, is added. + The scaling factor is for use in a linear change of variable. ("Buyer + beware": note that, depending on what one is doing, one may want `scl` + to be the reciprocal of what one might expect; for more information, + see the Notes section below.) The argument `c` is an array of + coefficients from low to high degree along each axis, e.g., [1,2,3] + represents the series ``L_0 + 2*L_1 + 3*L_2`` while [[1,2],[1,2]] + represents ``1*L_0(x)*L_0(y) + 1*L_1(x)*L_0(y) + 2*L_0(x)*L_1(y) + + 2*L_1(x)*L_1(y)`` if axis=0 is ``x`` and axis=1 is ``y``. + + + Parameters + ---------- + c : array_like + Array of Laguerre series coefficients. If `c` is multidimensional + the different axis correspond to different variables with the + degree in each axis given by the corresponding index. + m : int, optional + Order of integration, must be positive. (Default: 1) + k : {[], list, scalar}, optional + Integration constant(s). The value of the first integral at + ``lbnd`` is the first value in the list, the value of the second + integral at ``lbnd`` is the second value, etc. If ``k == []`` (the + default), all constants are set to zero. If ``m == 1``, a single + scalar can be given instead of a list. + lbnd : scalar, optional + The lower bound of the integral. (Default: 0) + scl : scalar, optional + Following each integration the result is *multiplied* by `scl` + before the integration constant is added. (Default: 1) + axis : int, optional + Axis over which the integral is taken. (Default: 0). + + .. versionadded:: 1.7.0 + + Returns + ------- + S : ndarray + Laguerre series coefficients of the integral. + + Raises + ------ + ValueError + If ``m < 0``, ``len(k) > m``, ``np.ndim(lbnd) != 0``, or + ``np.ndim(scl) != 0``. + + See Also + -------- + lagder + + Notes + ----- + Note that the result of each integration is *multiplied* by `scl`. + Why is this important to note? Say one is making a linear change of + variable :math:`u = ax + b` in an integral relative to `x`. Then + :math:`dx = du/a`, so one will need to set `scl` equal to + :math:`1/a` - perhaps not what one would have first thought. + + Also note that, in general, the result of integrating a C-series needs + to be "reprojected" onto the C-series basis set. Thus, typically, + the result of this function is "unintuitive," albeit correct; see + Examples section below. + + Examples + -------- + >>> from numpy.polynomial.laguerre import lagint + >>> lagint([1,2,3]) + array([ 1., 1., 1., -3.]) + >>> lagint([1,2,3], m=2) + array([ 1., 0., 0., -4., 3.]) + >>> lagint([1,2,3], k=1) + array([ 2., 1., 1., -3.]) + >>> lagint([1,2,3], lbnd=-1) + array([11.5, 1. , 1. , -3. ]) + >>> lagint([1,2], m=2, k=[1,2], lbnd=-1) + array([ 11.16666667, -5. , -3. , 2. ]) # may vary + + """ + c = np.array(c, ndmin=1, copy=True) + if c.dtype.char in '?bBhHiIlLqQpP': + c = c.astype(np.double) + if not np.iterable(k): + k = [k] + cnt = pu._deprecate_as_int(m, "the order of integration") + iaxis = pu._deprecate_as_int(axis, "the axis") + if cnt < 0: + raise ValueError("The order of integration must be non-negative") + if len(k) > cnt: + raise ValueError("Too many integration constants") + if np.ndim(lbnd) != 0: + raise ValueError("lbnd must be a scalar.") + if np.ndim(scl) != 0: + raise ValueError("scl must be a scalar.") + iaxis = normalize_axis_index(iaxis, c.ndim) + + if cnt == 0: + return c + + c = np.moveaxis(c, iaxis, 0) + k = list(k) + [0]*(cnt - len(k)) + for i in range(cnt): + n = len(c) + c *= scl + if n == 1 and np.all(c[0] == 0): + c[0] += k[i] + else: + tmp = np.empty((n + 1,) + c.shape[1:], dtype=c.dtype) + tmp[0] = c[0] + tmp[1] = -c[0] + for j in range(1, n): + tmp[j] += c[j] + tmp[j + 1] = -c[j] + tmp[0] += k[i] - lagval(lbnd, tmp) + c = tmp + c = np.moveaxis(c, 0, iaxis) + return c + + +def lagval(x, c, tensor=True): + """ + Evaluate a Laguerre series at points x. + + If `c` is of length `n + 1`, this function returns the value: + + .. math:: p(x) = c_0 * L_0(x) + c_1 * L_1(x) + ... + c_n * L_n(x) + + The parameter `x` is converted to an array only if it is a tuple or a + list, otherwise it is treated as a scalar. In either case, either `x` + or its elements must support multiplication and addition both with + themselves and with the elements of `c`. + + If `c` is a 1-D array, then `p(x)` will have the same shape as `x`. If + `c` is multidimensional, then the shape of the result depends on the + value of `tensor`. If `tensor` is true the shape will be c.shape[1:] + + x.shape. If `tensor` is false the shape will be c.shape[1:]. Note that + scalars have shape (,). + + Trailing zeros in the coefficients will be used in the evaluation, so + they should be avoided if efficiency is a concern. + + Parameters + ---------- + x : array_like, compatible object + If `x` is a list or tuple, it is converted to an ndarray, otherwise + it is left unchanged and treated as a scalar. In either case, `x` + or its elements must support addition and multiplication with + themselves and with the elements of `c`. + c : array_like + Array of coefficients ordered so that the coefficients for terms of + degree n are contained in c[n]. If `c` is multidimensional the + remaining indices enumerate multiple polynomials. In the two + dimensional case the coefficients may be thought of as stored in + the columns of `c`. + tensor : boolean, optional + If True, the shape of the coefficient array is extended with ones + on the right, one for each dimension of `x`. Scalars have dimension 0 + for this action. The result is that every column of coefficients in + `c` is evaluated for every element of `x`. If False, `x` is broadcast + over the columns of `c` for the evaluation. This keyword is useful + when `c` is multidimensional. The default value is True. + + .. versionadded:: 1.7.0 + + Returns + ------- + values : ndarray, algebra_like + The shape of the return value is described above. + + See Also + -------- + lagval2d, laggrid2d, lagval3d, laggrid3d + + Notes + ----- + The evaluation uses Clenshaw recursion, aka synthetic division. + + Examples + -------- + >>> from numpy.polynomial.laguerre import lagval + >>> coef = [1,2,3] + >>> lagval(1, coef) + -0.5 + >>> lagval([[1,2],[3,4]], coef) + array([[-0.5, -4. ], + [-4.5, -2. ]]) + + """ + c = np.array(c, ndmin=1, copy=False) + if c.dtype.char in '?bBhHiIlLqQpP': + c = c.astype(np.double) + if isinstance(x, (tuple, list)): + x = np.asarray(x) + if isinstance(x, np.ndarray) and tensor: + c = c.reshape(c.shape + (1,)*x.ndim) + + if len(c) == 1: + c0 = c[0] + c1 = 0 + elif len(c) == 2: + c0 = c[0] + c1 = c[1] + else: + nd = len(c) + c0 = c[-2] + c1 = c[-1] + for i in range(3, len(c) + 1): + tmp = c0 + nd = nd - 1 + c0 = c[-i] - (c1*(nd - 1))/nd + c1 = tmp + (c1*((2*nd - 1) - x))/nd + return c0 + c1*(1 - x) + + +def lagval2d(x, y, c): + """ + Evaluate a 2-D Laguerre series at points (x, y). + + This function returns the values: + + .. math:: p(x,y) = \\sum_{i,j} c_{i,j} * L_i(x) * L_j(y) + + The parameters `x` and `y` are converted to arrays only if they are + tuples or a lists, otherwise they are treated as a scalars and they + must have the same shape after conversion. In either case, either `x` + and `y` or their elements must support multiplication and addition both + with themselves and with the elements of `c`. + + If `c` is a 1-D array a one is implicitly appended to its shape to make + it 2-D. The shape of the result will be c.shape[2:] + x.shape. + + Parameters + ---------- + x, y : array_like, compatible objects + The two dimensional series is evaluated at the points `(x, y)`, + where `x` and `y` must have the same shape. If `x` or `y` is a list + or tuple, it is first converted to an ndarray, otherwise it is left + unchanged and if it isn't an ndarray it is treated as a scalar. + c : array_like + Array of coefficients ordered so that the coefficient of the term + of multi-degree i,j is contained in ``c[i,j]``. If `c` has + dimension greater than two the remaining indices enumerate multiple + sets of coefficients. + + Returns + ------- + values : ndarray, compatible object + The values of the two dimensional polynomial at points formed with + pairs of corresponding values from `x` and `y`. + + See Also + -------- + lagval, laggrid2d, lagval3d, laggrid3d + + Notes + ----- + + .. versionadded:: 1.7.0 + + """ + return pu._valnd(lagval, c, x, y) + + +def laggrid2d(x, y, c): + """ + Evaluate a 2-D Laguerre series on the Cartesian product of x and y. + + This function returns the values: + + .. math:: p(a,b) = \\sum_{i,j} c_{i,j} * L_i(a) * L_j(b) + + where the points `(a, b)` consist of all pairs formed by taking + `a` from `x` and `b` from `y`. The resulting points form a grid with + `x` in the first dimension and `y` in the second. + + The parameters `x` and `y` are converted to arrays only if they are + tuples or a lists, otherwise they are treated as a scalars. In either + case, either `x` and `y` or their elements must support multiplication + and addition both with themselves and with the elements of `c`. + + If `c` has fewer than two dimensions, ones are implicitly appended to + its shape to make it 2-D. The shape of the result will be c.shape[2:] + + x.shape + y.shape. + + Parameters + ---------- + x, y : array_like, compatible objects + The two dimensional series is evaluated at the points in the + Cartesian product of `x` and `y`. If `x` or `y` is a list or + tuple, it is first converted to an ndarray, otherwise it is left + unchanged and, if it isn't an ndarray, it is treated as a scalar. + c : array_like + Array of coefficients ordered so that the coefficient of the term of + multi-degree i,j is contained in `c[i,j]`. If `c` has dimension + greater than two the remaining indices enumerate multiple sets of + coefficients. + + Returns + ------- + values : ndarray, compatible object + The values of the two dimensional Chebyshev series at points in the + Cartesian product of `x` and `y`. + + See Also + -------- + lagval, lagval2d, lagval3d, laggrid3d + + Notes + ----- + + .. versionadded:: 1.7.0 + + """ + return pu._gridnd(lagval, c, x, y) + + +def lagval3d(x, y, z, c): + """ + Evaluate a 3-D Laguerre series at points (x, y, z). + + This function returns the values: + + .. math:: p(x,y,z) = \\sum_{i,j,k} c_{i,j,k} * L_i(x) * L_j(y) * L_k(z) + + The parameters `x`, `y`, and `z` are converted to arrays only if + they are tuples or a lists, otherwise they are treated as a scalars and + they must have the same shape after conversion. In either case, either + `x`, `y`, and `z` or their elements must support multiplication and + addition both with themselves and with the elements of `c`. + + If `c` has fewer than 3 dimensions, ones are implicitly appended to its + shape to make it 3-D. The shape of the result will be c.shape[3:] + + x.shape. + + Parameters + ---------- + x, y, z : array_like, compatible object + The three dimensional series is evaluated at the points + `(x, y, z)`, where `x`, `y`, and `z` must have the same shape. If + any of `x`, `y`, or `z` is a list or tuple, it is first converted + to an ndarray, otherwise it is left unchanged and if it isn't an + ndarray it is treated as a scalar. + c : array_like + Array of coefficients ordered so that the coefficient of the term of + multi-degree i,j,k is contained in ``c[i,j,k]``. If `c` has dimension + greater than 3 the remaining indices enumerate multiple sets of + coefficients. + + Returns + ------- + values : ndarray, compatible object + The values of the multidimensional polynomial on points formed with + triples of corresponding values from `x`, `y`, and `z`. + + See Also + -------- + lagval, lagval2d, laggrid2d, laggrid3d + + Notes + ----- + + .. versionadded:: 1.7.0 + + """ + return pu._valnd(lagval, c, x, y, z) + + +def laggrid3d(x, y, z, c): + """ + Evaluate a 3-D Laguerre series on the Cartesian product of x, y, and z. + + This function returns the values: + + .. math:: p(a,b,c) = \\sum_{i,j,k} c_{i,j,k} * L_i(a) * L_j(b) * L_k(c) + + where the points `(a, b, c)` consist of all triples formed by taking + `a` from `x`, `b` from `y`, and `c` from `z`. The resulting points form + a grid with `x` in the first dimension, `y` in the second, and `z` in + the third. + + The parameters `x`, `y`, and `z` are converted to arrays only if they + are tuples or a lists, otherwise they are treated as a scalars. In + either case, either `x`, `y`, and `z` or their elements must support + multiplication and addition both with themselves and with the elements + of `c`. + + If `c` has fewer than three dimensions, ones are implicitly appended to + its shape to make it 3-D. The shape of the result will be c.shape[3:] + + x.shape + y.shape + z.shape. + + Parameters + ---------- + x, y, z : array_like, compatible objects + The three dimensional series is evaluated at the points in the + Cartesian product of `x`, `y`, and `z`. If `x`,`y`, or `z` is a + list or tuple, it is first converted to an ndarray, otherwise it is + left unchanged and, if it isn't an ndarray, it is treated as a + scalar. + c : array_like + Array of coefficients ordered so that the coefficients for terms of + degree i,j are contained in ``c[i,j]``. If `c` has dimension + greater than two the remaining indices enumerate multiple sets of + coefficients. + + Returns + ------- + values : ndarray, compatible object + The values of the two dimensional polynomial at points in the Cartesian + product of `x` and `y`. + + See Also + -------- + lagval, lagval2d, laggrid2d, lagval3d + + Notes + ----- + + .. versionadded:: 1.7.0 + + """ + return pu._gridnd(lagval, c, x, y, z) + + +def lagvander(x, deg): + """Pseudo-Vandermonde matrix of given degree. + + Returns the pseudo-Vandermonde matrix of degree `deg` and sample points + `x`. The pseudo-Vandermonde matrix is defined by + + .. math:: V[..., i] = L_i(x) + + where `0 <= i <= deg`. The leading indices of `V` index the elements of + `x` and the last index is the degree of the Laguerre polynomial. + + If `c` is a 1-D array of coefficients of length `n + 1` and `V` is the + array ``V = lagvander(x, n)``, then ``np.dot(V, c)`` and + ``lagval(x, c)`` are the same up to roundoff. This equivalence is + useful both for least squares fitting and for the evaluation of a large + number of Laguerre series of the same degree and sample points. + + Parameters + ---------- + x : array_like + Array of points. The dtype is converted to float64 or complex128 + depending on whether any of the elements are complex. If `x` is + scalar it is converted to a 1-D array. + deg : int + Degree of the resulting matrix. + + Returns + ------- + vander : ndarray + The pseudo-Vandermonde matrix. The shape of the returned matrix is + ``x.shape + (deg + 1,)``, where The last index is the degree of the + corresponding Laguerre polynomial. The dtype will be the same as + the converted `x`. + + Examples + -------- + >>> from numpy.polynomial.laguerre import lagvander + >>> x = np.array([0, 1, 2]) + >>> lagvander(x, 3) + array([[ 1. , 1. , 1. , 1. ], + [ 1. , 0. , -0.5 , -0.66666667], + [ 1. , -1. , -1. , -0.33333333]]) + + """ + ideg = pu._deprecate_as_int(deg, "deg") + if ideg < 0: + raise ValueError("deg must be non-negative") + + x = np.array(x, copy=False, ndmin=1) + 0.0 + dims = (ideg + 1,) + x.shape + dtyp = x.dtype + v = np.empty(dims, dtype=dtyp) + v[0] = x*0 + 1 + if ideg > 0: + v[1] = 1 - x + for i in range(2, ideg + 1): + v[i] = (v[i-1]*(2*i - 1 - x) - v[i-2]*(i - 1))/i + return np.moveaxis(v, 0, -1) + + +def lagvander2d(x, y, deg): + """Pseudo-Vandermonde matrix of given degrees. + + Returns the pseudo-Vandermonde matrix of degrees `deg` and sample + points `(x, y)`. The pseudo-Vandermonde matrix is defined by + + .. math:: V[..., (deg[1] + 1)*i + j] = L_i(x) * L_j(y), + + where `0 <= i <= deg[0]` and `0 <= j <= deg[1]`. The leading indices of + `V` index the points `(x, y)` and the last index encodes the degrees of + the Laguerre polynomials. + + If ``V = lagvander2d(x, y, [xdeg, ydeg])``, then the columns of `V` + correspond to the elements of a 2-D coefficient array `c` of shape + (xdeg + 1, ydeg + 1) in the order + + .. math:: c_{00}, c_{01}, c_{02} ... , c_{10}, c_{11}, c_{12} ... + + and ``np.dot(V, c.flat)`` and ``lagval2d(x, y, c)`` will be the same + up to roundoff. This equivalence is useful both for least squares + fitting and for the evaluation of a large number of 2-D Laguerre + series of the same degrees and sample points. + + Parameters + ---------- + x, y : array_like + Arrays of point coordinates, all of the same shape. The dtypes + will be converted to either float64 or complex128 depending on + whether any of the elements are complex. Scalars are converted to + 1-D arrays. + deg : list of ints + List of maximum degrees of the form [x_deg, y_deg]. + + Returns + ------- + vander2d : ndarray + The shape of the returned matrix is ``x.shape + (order,)``, where + :math:`order = (deg[0]+1)*(deg[1]+1)`. The dtype will be the same + as the converted `x` and `y`. + + See Also + -------- + lagvander, lagvander3d, lagval2d, lagval3d + + Notes + ----- + + .. versionadded:: 1.7.0 + + """ + return pu._vander_nd_flat((lagvander, lagvander), (x, y), deg) + + +def lagvander3d(x, y, z, deg): + """Pseudo-Vandermonde matrix of given degrees. + + Returns the pseudo-Vandermonde matrix of degrees `deg` and sample + points `(x, y, z)`. If `l, m, n` are the given degrees in `x, y, z`, + then The pseudo-Vandermonde matrix is defined by + + .. math:: V[..., (m+1)(n+1)i + (n+1)j + k] = L_i(x)*L_j(y)*L_k(z), + + where `0 <= i <= l`, `0 <= j <= m`, and `0 <= j <= n`. The leading + indices of `V` index the points `(x, y, z)` and the last index encodes + the degrees of the Laguerre polynomials. + + If ``V = lagvander3d(x, y, z, [xdeg, ydeg, zdeg])``, then the columns + of `V` correspond to the elements of a 3-D coefficient array `c` of + shape (xdeg + 1, ydeg + 1, zdeg + 1) in the order + + .. math:: c_{000}, c_{001}, c_{002},... , c_{010}, c_{011}, c_{012},... + + and ``np.dot(V, c.flat)`` and ``lagval3d(x, y, z, c)`` will be the + same up to roundoff. This equivalence is useful both for least squares + fitting and for the evaluation of a large number of 3-D Laguerre + series of the same degrees and sample points. + + Parameters + ---------- + x, y, z : array_like + Arrays of point coordinates, all of the same shape. The dtypes will + be converted to either float64 or complex128 depending on whether + any of the elements are complex. Scalars are converted to 1-D + arrays. + deg : list of ints + List of maximum degrees of the form [x_deg, y_deg, z_deg]. + + Returns + ------- + vander3d : ndarray + The shape of the returned matrix is ``x.shape + (order,)``, where + :math:`order = (deg[0]+1)*(deg[1]+1)*(deg[2]+1)`. The dtype will + be the same as the converted `x`, `y`, and `z`. + + See Also + -------- + lagvander, lagvander3d, lagval2d, lagval3d + + Notes + ----- + + .. versionadded:: 1.7.0 + + """ + return pu._vander_nd_flat((lagvander, lagvander, lagvander), (x, y, z), deg) + + +def lagfit(x, y, deg, rcond=None, full=False, w=None): + """ + Least squares fit of Laguerre series to data. + + Return the coefficients of a Laguerre series of degree `deg` that is the + least squares fit to the data values `y` given at points `x`. If `y` is + 1-D the returned coefficients will also be 1-D. If `y` is 2-D multiple + fits are done, one for each column of `y`, and the resulting + coefficients are stored in the corresponding columns of a 2-D return. + The fitted polynomial(s) are in the form + + .. math:: p(x) = c_0 + c_1 * L_1(x) + ... + c_n * L_n(x), + + where ``n`` is `deg`. + + 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 or 1-D array_like + Degree(s) of the fitting polynomials. If `deg` is a single integer + all terms up to and including the `deg`'th term are included in the + fit. For NumPy versions >= 1.11.0 a list of integers specifying the + degrees of the terms to include may be used instead. + 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. + + Returns + ------- + coef : ndarray, shape (M,) or (M, K) + Laguerre coefficients ordered from low to high. If `y` was 2-D, + the coefficients for the data in column *k* of `y` are in column + *k*. + + [residuals, rank, singular_values, rcond] : list + These values are only returned if ``full == True`` + + - residuals -- sum of squared residuals of the least squares fit + - rank -- the numerical rank of the scaled Vandermonde matrix + - singular_values -- singular values of the scaled Vandermonde matrix + - rcond -- value of `rcond`. + + For more details, see `numpy.linalg.lstsq`. + + 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 + -------- + numpy.polynomial.polynomial.polyfit + numpy.polynomial.legendre.legfit + numpy.polynomial.chebyshev.chebfit + numpy.polynomial.hermite.hermfit + numpy.polynomial.hermite_e.hermefit + lagval : Evaluates a Laguerre series. + lagvander : pseudo Vandermonde matrix of Laguerre series. + lagweight : Laguerre weight function. + numpy.linalg.lstsq : Computes a least-squares fit from the matrix. + scipy.interpolate.UnivariateSpline : Computes spline fits. + + Notes + ----- + The solution is the coefficients of the Laguerre series ``p`` that + minimizes the sum of the weighted squared errors + + .. math:: E = \\sum_j w_j^2 * |y_j - p(x_j)|^2, + + where the :math:`w_j` are the weights. This problem is solved by + setting up as the (typically) overdetermined matrix equation + + .. math:: V(x) * c = w * y, + + where ``V`` is the weighted pseudo Vandermonde matrix of `x`, ``c`` are the + coefficients to be solved for, `w` are the weights, and `y` are the + observed values. This equation is then solved using the singular value + decomposition of ``V``. + + If some of the singular values of `V` are so small that they are + neglected, then a `RankWarning` will be issued. This means that the + coefficient values may be poorly determined. Using a lower order fit + will usually get rid of the warning. The `rcond` parameter can also be + set to a value smaller than its default, but the resulting fit may be + spurious and have large contributions from roundoff error. + + Fits using Laguerre series are probably most useful when the data can + be approximated by ``sqrt(w(x)) * p(x)``, where ``w(x)`` is the Laguerre + weight. In that case the weight ``sqrt(w(x[i]))`` should be used + together with data values ``y[i]/sqrt(w(x[i]))``. The weight function is + available as `lagweight`. + + References + ---------- + .. [1] Wikipedia, "Curve fitting", + https://en.wikipedia.org/wiki/Curve_fitting + + Examples + -------- + >>> from numpy.polynomial.laguerre import lagfit, lagval + >>> x = np.linspace(0, 10) + >>> err = np.random.randn(len(x))/10 + >>> y = lagval(x, [1, 2, 3]) + err + >>> lagfit(x, y, 2) + array([ 0.96971004, 2.00193749, 3.00288744]) # may vary + + """ + return pu._fit(lagvander, x, y, deg, rcond, full, w) + + +def lagcompanion(c): + """ + Return the companion matrix of c. + + The usual companion matrix of the Laguerre polynomials is already + symmetric when `c` is a basis Laguerre polynomial, so no scaling is + applied. + + Parameters + ---------- + c : array_like + 1-D array of Laguerre series coefficients ordered from low to high + degree. + + Returns + ------- + mat : ndarray + Companion matrix of dimensions (deg, deg). + + Notes + ----- + + .. versionadded:: 1.7.0 + + """ + # c is a trimmed copy + [c] = pu.as_series([c]) + if len(c) < 2: + raise ValueError('Series must have maximum degree of at least 1.') + if len(c) == 2: + return np.array([[1 + c[0]/c[1]]]) + + n = len(c) - 1 + mat = np.zeros((n, n), dtype=c.dtype) + top = mat.reshape(-1)[1::n+1] + mid = mat.reshape(-1)[0::n+1] + bot = mat.reshape(-1)[n::n+1] + top[...] = -np.arange(1, n) + mid[...] = 2.*np.arange(n) + 1. + bot[...] = top + mat[:, -1] += (c[:-1]/c[-1])*n + return mat + + +def lagroots(c): + """ + Compute the roots of a Laguerre series. + + Return the roots (a.k.a. "zeros") of the polynomial + + .. math:: p(x) = \\sum_i c[i] * L_i(x). + + Parameters + ---------- + c : 1-D array_like + 1-D array of coefficients. + + Returns + ------- + out : ndarray + Array of the roots of the series. If all the roots are real, + then `out` is also real, otherwise it is complex. + + See Also + -------- + numpy.polynomial.polynomial.polyroots + numpy.polynomial.legendre.legroots + numpy.polynomial.chebyshev.chebroots + numpy.polynomial.hermite.hermroots + numpy.polynomial.hermite_e.hermeroots + + Notes + ----- + The root estimates are obtained as the eigenvalues of the companion + matrix, Roots far from the origin of the complex plane may have large + errors due to the numerical instability of the series for such + values. Roots with multiplicity greater than 1 will also show larger + errors as the value of the series near such points is relatively + insensitive to errors in the roots. Isolated roots near the origin can + be improved by a few iterations of Newton's method. + + The Laguerre series basis polynomials aren't powers of `x` so the + results of this function may seem unintuitive. + + Examples + -------- + >>> from numpy.polynomial.laguerre import lagroots, lagfromroots + >>> coef = lagfromroots([0, 1, 2]) + >>> coef + array([ 2., -8., 12., -6.]) + >>> lagroots(coef) + array([-4.4408921e-16, 1.0000000e+00, 2.0000000e+00]) + + """ + # c is a trimmed copy + [c] = pu.as_series([c]) + if len(c) <= 1: + return np.array([], dtype=c.dtype) + if len(c) == 2: + return np.array([1 + c[0]/c[1]]) + + # rotated companion matrix reduces error + m = lagcompanion(c)[::-1,::-1] + r = la.eigvals(m) + r.sort() + return r + + +def laggauss(deg): + """ + Gauss-Laguerre quadrature. + + Computes the sample points and weights for Gauss-Laguerre quadrature. + These sample points and weights will correctly integrate polynomials of + degree :math:`2*deg - 1` or less over the interval :math:`[0, \\inf]` + with the weight function :math:`f(x) = \\exp(-x)`. + + Parameters + ---------- + deg : int + Number of sample points and weights. It must be >= 1. + + Returns + ------- + x : ndarray + 1-D ndarray containing the sample points. + y : ndarray + 1-D ndarray containing the weights. + + Notes + ----- + + .. versionadded:: 1.7.0 + + The results have only been tested up to degree 100 higher degrees may + be problematic. The weights are determined by using the fact that + + .. math:: w_k = c / (L'_n(x_k) * L_{n-1}(x_k)) + + where :math:`c` is a constant independent of :math:`k` and :math:`x_k` + is the k'th root of :math:`L_n`, and then scaling the results to get + the right value when integrating 1. + + """ + ideg = pu._deprecate_as_int(deg, "deg") + if ideg <= 0: + raise ValueError("deg must be a positive integer") + + # first approximation of roots. We use the fact that the companion + # matrix is symmetric in this case in order to obtain better zeros. + c = np.array([0]*deg + [1]) + m = lagcompanion(c) + x = la.eigvalsh(m) + + # improve roots by one application of Newton + dy = lagval(x, c) + df = lagval(x, lagder(c)) + x -= dy/df + + # compute the weights. We scale the factor to avoid possible numerical + # overflow. + fm = lagval(x, c[1:]) + fm /= np.abs(fm).max() + df /= np.abs(df).max() + w = 1/(fm * df) + + # scale w to get the right value, 1 in this case + w /= w.sum() + + return x, w + + +def lagweight(x): + """Weight function of the Laguerre polynomials. + + The weight function is :math:`exp(-x)` and the interval of integration + is :math:`[0, \\inf]`. The Laguerre polynomials are orthogonal, but not + normalized, with respect to this weight function. + + Parameters + ---------- + x : array_like + Values at which the weight function will be computed. + + Returns + ------- + w : ndarray + The weight function at `x`. + + Notes + ----- + + .. versionadded:: 1.7.0 + + """ + w = np.exp(-x) + return w + +# +# Laguerre series class +# + +class Laguerre(ABCPolyBase): + """A Laguerre series class. + + The Laguerre class provides the standard Python numerical methods + '+', '-', '*', '//', '%', 'divmod', '**', and '()' as well as the + attributes and methods listed in the `ABCPolyBase` documentation. + + Parameters + ---------- + coef : array_like + Laguerre coefficients in order of increasing degree, i.e, + ``(1, 2, 3)`` gives ``1*L_0(x) + 2*L_1(X) + 3*L_2(x)``. + domain : (2,) array_like, optional + Domain to use. The interval ``[domain[0], domain[1]]`` is mapped + to the interval ``[window[0], window[1]]`` by shifting and scaling. + The default value is [0, 1]. + window : (2,) array_like, optional + Window, see `domain` for its use. The default value is [0, 1]. + + .. versionadded:: 1.6.0 + symbol : str, optional + Symbol used to represent the independent variable in string + representations of the polynomial expression, e.g. for printing. + The symbol must be a valid Python identifier. Default value is 'x'. + + .. versionadded:: 1.24 + + """ + # Virtual Functions + _add = staticmethod(lagadd) + _sub = staticmethod(lagsub) + _mul = staticmethod(lagmul) + _div = staticmethod(lagdiv) + _pow = staticmethod(lagpow) + _val = staticmethod(lagval) + _int = staticmethod(lagint) + _der = staticmethod(lagder) + _fit = staticmethod(lagfit) + _line = staticmethod(lagline) + _roots = staticmethod(lagroots) + _fromroots = staticmethod(lagfromroots) + + # Virtual properties + domain = np.array(lagdomain) + window = np.array(lagdomain) + basis_name = 'L' diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/polynomial/legendre.pyi b/env-llmeval/lib/python3.10/site-packages/numpy/polynomial/legendre.pyi new file mode 100644 index 0000000000000000000000000000000000000000..63a1c3f3a1f89c2c2da61e385f7dba1e7be16c06 --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/numpy/polynomial/legendre.pyi @@ -0,0 +1,46 @@ +from typing import Any + +from numpy import ndarray, dtype, int_ +from numpy.polynomial._polybase import ABCPolyBase +from numpy.polynomial.polyutils import trimcoef + +__all__: list[str] + +legtrim = trimcoef + +def poly2leg(pol): ... +def leg2poly(c): ... + +legdomain: ndarray[Any, dtype[int_]] +legzero: ndarray[Any, dtype[int_]] +legone: ndarray[Any, dtype[int_]] +legx: ndarray[Any, dtype[int_]] + +def legline(off, scl): ... +def legfromroots(roots): ... +def legadd(c1, c2): ... +def legsub(c1, c2): ... +def legmulx(c): ... +def legmul(c1, c2): ... +def legdiv(c1, c2): ... +def legpow(c, pow, maxpower=...): ... +def legder(c, m=..., scl=..., axis=...): ... +def legint(c, m=..., k = ..., lbnd=..., scl=..., axis=...): ... +def legval(x, c, tensor=...): ... +def legval2d(x, y, c): ... +def leggrid2d(x, y, c): ... +def legval3d(x, y, z, c): ... +def leggrid3d(x, y, z, c): ... +def legvander(x, deg): ... +def legvander2d(x, y, deg): ... +def legvander3d(x, y, z, deg): ... +def legfit(x, y, deg, rcond=..., full=..., w=...): ... +def legcompanion(c): ... +def legroots(c): ... +def leggauss(deg): ... +def legweight(x): ... + +class Legendre(ABCPolyBase): + domain: Any + window: Any + basis_name: Any diff --git a/env-llmeval/lib/python3.10/site-packages/numpy/polynomial/polyutils.py b/env-llmeval/lib/python3.10/site-packages/numpy/polynomial/polyutils.py new file mode 100644 index 0000000000000000000000000000000000000000..4829138920169efc5b18b20be4a7d7c9509ba7fb --- /dev/null +++ b/env-llmeval/lib/python3.10/site-packages/numpy/polynomial/polyutils.py @@ -0,0 +1,789 @@ +""" +Utility classes and functions for the polynomial modules. + +This module provides: error and warning objects; a polynomial base class; +and some routines used in both the `polynomial` and `chebyshev` modules. + +Warning objects +--------------- + +.. autosummary:: + :toctree: generated/ + + RankWarning raised in least-squares fit for rank-deficient matrix. + +Functions +--------- + +.. autosummary:: + :toctree: generated/ + + as_series convert list of array_likes into 1-D arrays of common type. + trimseq remove trailing zeros. + trimcoef remove small trailing coefficients. + getdomain return the domain appropriate for a given set of abscissae. + mapdomain maps points between domains. + mapparms parameters of the linear map between domains. + +""" +import operator +import functools +import warnings + +import numpy as np + +from numpy.core.multiarray import dragon4_positional, dragon4_scientific +from numpy.core.umath import absolute + +__all__ = [ + 'RankWarning', 'as_series', 'trimseq', + 'trimcoef', 'getdomain', 'mapdomain', 'mapparms', + 'format_float'] + +# +# Warnings and Exceptions +# + +class RankWarning(UserWarning): + """Issued by chebfit when the design matrix is rank deficient.""" + pass + +# +# Helper functions to convert inputs to 1-D arrays +# +def trimseq(seq): + """Remove small Poly series coefficients. + + Parameters + ---------- + seq : sequence + Sequence of Poly series coefficients. This routine fails for + empty sequences. + + Returns + ------- + series : sequence + Subsequence with trailing zeros removed. If the resulting sequence + would be empty, return the first element. The returned sequence may + or may not be a view. + + Notes + ----- + Do not lose the type info if the sequence contains unknown objects. + + """ + if len(seq) == 0: + return seq + else: + for i in range(len(seq) - 1, -1, -1): + if seq[i] != 0: + break + return seq[:i+1] + + +def as_series(alist, trim=True): + """ + Return argument as a list of 1-d arrays. + + The returned list contains array(s) of dtype double, complex double, or + object. A 1-d argument of shape ``(N,)`` is parsed into ``N`` arrays of + size one; a 2-d argument of shape ``(M,N)`` is parsed into ``M`` arrays + of size ``N`` (i.e., is "parsed by row"); and a higher dimensional array + raises a Value Error if it is not first reshaped into either a 1-d or 2-d + array. + + Parameters + ---------- + alist : array_like + A 1- or 2-d array_like + trim : boolean, optional + When True, trailing zeros are removed from the inputs. + When False, the inputs are passed through intact. + + Returns + ------- + [a1, a2,...] : list of 1-D arrays + A copy of the input data as a list of 1-d arrays. + + Raises + ------ + ValueError + Raised when `as_series` cannot convert its input to 1-d arrays, or at + least one of the resulting arrays is empty. + + Examples + -------- + >>> from numpy.polynomial import polyutils as pu + >>> a = np.arange(4) + >>> pu.as_series(a) + [array([0.]), array([1.]), array([2.]), array([3.])] + >>> b = np.arange(6).reshape((2,3)) + >>> pu.as_series(b) + [array([0., 1., 2.]), array([3., 4., 5.])] + + >>> pu.as_series((1, np.arange(3), np.arange(2, dtype=np.float16))) + [array([1.]), array([0., 1., 2.]), array([0., 1.])] + + >>> pu.as_series([2, [1.1, 0.]]) + [array([2.]), array([1.1])] + + >>> pu.as_series([2, [1.1, 0.]], trim=False) + [array([2.]), array([1.1, 0. ])] + + """ + arrays = [np.array(a, ndmin=1, copy=False) for a in alist] + if min([a.size for a in arrays]) == 0: + raise ValueError("Coefficient array is empty") + if any(a.ndim != 1 for a in arrays): + raise ValueError("Coefficient array is not 1-d") + if trim: + arrays = [trimseq(a) for a in arrays] + + if any(a.dtype == np.dtype(object) for a in arrays): + ret = [] + for a in arrays: + if a.dtype != np.dtype(object): + tmp = np.empty(len(a), dtype=np.dtype(object)) + tmp[:] = a[:] + ret.append(tmp) + else: + ret.append(a.copy()) + else: + try: + dtype = np.common_type(*arrays) + except Exception as e: + raise ValueError("Coefficient arrays have no common type") from e + ret = [np.array(a, copy=True, dtype=dtype) for a in arrays] + return ret + + +def trimcoef(c, tol=0): + """ + Remove "small" "trailing" coefficients from a polynomial. + + "Small" means "small in absolute value" and is controlled by the + parameter `tol`; "trailing" means highest order coefficient(s), e.g., in + ``[0, 1, 1, 0, 0]`` (which represents ``0 + x + x**2 + 0*x**3 + 0*x**4``) + both the 3-rd and 4-th order coefficients would be "trimmed." + + Parameters + ---------- + c : array_like + 1-d array of coefficients, ordered from lowest order to highest. + tol : number, optional + Trailing (i.e., highest order) elements with absolute value less + than or equal to `tol` (default value is zero) are removed. + + Returns + ------- + trimmed : ndarray + 1-d array with trailing zeros removed. If the resulting series + would be empty, a series containing a single zero is returned. + + Raises + ------ + ValueError + If `tol` < 0 + + See Also + -------- + trimseq + + Examples + -------- + >>> from numpy.polynomial import polyutils as pu + >>> pu.trimcoef((0,0,3,0,5,0,0)) + array([0., 0., 3., 0., 5.]) + >>> pu.trimcoef((0,0,1e-3,0,1e-5,0,0),1e-3) # item == tol is trimmed + array([0.]) + >>> i = complex(0,1) # works for complex + >>> pu.trimcoef((3e-4,1e-3*(1-i),5e-4,2e-5*(1+i)), 1e-3) + array([0.0003+0.j , 0.001 -0.001j]) + + """ + if tol < 0: + raise ValueError("tol must be non-negative") + + [c] = as_series([c]) + [ind] = np.nonzero(np.abs(c) > tol) + if len(ind) == 0: + return c[:1]*0 + else: + return c[:ind[-1] + 1].copy() + +def getdomain(x): + """ + Return a domain suitable for given abscissae. + + Find a domain suitable for a polynomial or Chebyshev series + defined at the values supplied. + + Parameters + ---------- + x : array_like + 1-d array of abscissae whose domain will be determined. + + Returns + ------- + domain : ndarray + 1-d array containing two values. If the inputs are complex, then + the two returned points are the lower left and upper right corners + of the smallest rectangle (aligned with the axes) in the complex + plane containing the points `x`. If the inputs are real, then the + two points are the ends of the smallest interval containing the + points `x`. + + See Also + -------- + mapparms, mapdomain + + Examples + -------- + >>> from numpy.polynomial import polyutils as pu + >>> points = np.arange(4)**2 - 5; points + array([-5, -4, -1, 4]) + >>> pu.getdomain(points) + array([-5., 4.]) + >>> c = np.exp(complex(0,1)*np.pi*np.arange(12)/6) # unit circle + >>> pu.getdomain(c) + array([-1.-1.j, 1.+1.j]) + + """ + [x] = as_series([x], trim=False) + if x.dtype.char in np.typecodes['Complex']: + rmin, rmax = x.real.min(), x.real.max() + imin, imax = x.imag.min(), x.imag.max() + return np.array((complex(rmin, imin), complex(rmax, imax))) + else: + return np.array((x.min(), x.max())) + +def mapparms(old, new): + """ + Linear map parameters between domains. + + Return the parameters of the linear map ``offset + scale*x`` that maps + `old` to `new` such that ``old[i] -> new[i]``, ``i = 0, 1``. + + Parameters + ---------- + old, new : array_like + Domains. Each domain must (successfully) convert to a 1-d array + containing precisely two values. + + Returns + ------- + offset, scale : scalars + The map ``L(x) = offset + scale*x`` maps the first domain to the + second. + + See Also + -------- + getdomain, mapdomain + + Notes + ----- + Also works for complex numbers, and thus can be used to calculate the + parameters required to map any line in the complex plane to any other + line therein. + + Examples + -------- + >>> from numpy.polynomial import polyutils as pu + >>> pu.mapparms((-1,1),(-1,1)) + (0.0, 1.0) + >>> pu.mapparms((1,-1),(-1,1)) + (-0.0, -1.0) + >>> i = complex(0,1) + >>> pu.mapparms((-i,-1),(1,i)) + ((1+1j), (1-0j)) + + """ + oldlen = old[1] - old[0] + newlen = new[1] - new[0] + off = (old[1]*new[0] - old[0]*new[1])/oldlen + scl = newlen/oldlen + return off, scl + +def mapdomain(x, old, new): + """ + Apply linear map to input points. + + The linear map ``offset + scale*x`` that maps the domain `old` to + the domain `new` is applied to the points `x`. + + Parameters + ---------- + x : array_like + Points to be mapped. If `x` is a subtype of ndarray the subtype + will be preserved. + old, new : array_like + The two domains that determine the map. Each must (successfully) + convert to 1-d arrays containing precisely two values. + + Returns + ------- + x_out : ndarray + Array of points of the same shape as `x`, after application of the + linear map between the two domains. + + See Also + -------- + getdomain, mapparms + + Notes + ----- + Effectively, this implements: + + .. math:: + x\\_out = new[0] + m(x - old[0]) + + where + + .. math:: + m = \\frac{new[1]-new[0]}{old[1]-old[0]} + + Examples + -------- + >>> from numpy.polynomial import polyutils as pu + >>> old_domain = (-1,1) + >>> new_domain = (0,2*np.pi) + >>> x = np.linspace(-1,1,6); x + array([-1. , -0.6, -0.2, 0.2, 0.6, 1. ]) + >>> x_out = pu.mapdomain(x, old_domain, new_domain); x_out + array([ 0. , 1.25663706, 2.51327412, 3.76991118, 5.02654825, # may vary + 6.28318531]) + >>> x - pu.mapdomain(x_out, new_domain, old_domain) + array([0., 0., 0., 0., 0., 0.]) + + Also works for complex numbers (and thus can be used to map any line in + the complex plane to any other line therein). + + >>> i = complex(0,1) + >>> old = (-1 - i, 1 + i) + >>> new = (-1 + i, 1 - i) + >>> z = np.linspace(old[0], old[1], 6); z + array([-1. -1.j , -0.6-0.6j, -0.2-0.2j, 0.2+0.2j, 0.6+0.6j, 1. +1.j ]) + >>> new_z = pu.mapdomain(z, old, new); new_z + array([-1.0+1.j , -0.6+0.6j, -0.2+0.2j, 0.2-0.2j, 0.6-0.6j, 1.0-1.j ]) # may vary + + """ + x = np.asanyarray(x) + off, scl = mapparms(old, new) + return off + scl*x + + +def _nth_slice(i, ndim): + sl = [np.newaxis] * ndim + sl[i] = slice(None) + return tuple(sl) + + +def _vander_nd(vander_fs, points, degrees): + r""" + A generalization of the Vandermonde matrix for N dimensions + + The result is built by combining the results of 1d Vandermonde matrices, + + .. math:: + W[i_0, \ldots, i_M, j_0, \ldots, j_N] = \prod_{k=0}^N{V_k(x_k)[i_0, \ldots, i_M, j_k]} + + where + + .. math:: + N &= \texttt{len(points)} = \texttt{len(degrees)} = \texttt{len(vander\_fs)} \\ + M &= \texttt{points[k].ndim} \\ + V_k &= \texttt{vander\_fs[k]} \\ + x_k &= \texttt{points[k]} \\ + 0 \le j_k &\le \texttt{degrees[k]} + + Expanding the one-dimensional :math:`V_k` functions gives: + + .. math:: + W[i_0, \ldots, i_M, j_0, \ldots, j_N] = \prod_{k=0}^N{B_{k, j_k}(x_k[i_0, \ldots, i_M])} + + where :math:`B_{k,m}` is the m'th basis of the polynomial construction used along + dimension :math:`k`. For a regular polynomial, :math:`B_{k, m}(x) = P_m(x) = x^m`. + + Parameters + ---------- + vander_fs : Sequence[function(array_like, int) -> ndarray] + The 1d vander function to use for each axis, such as ``polyvander`` + points : Sequence[array_like] + Arrays of point coordinates, all of the same shape. The dtypes + will be converted to either float64 or complex128 depending on + whether any of the elements are complex. Scalars are converted to + 1-D arrays. + This must be the same length as `vander_fs`. + degrees : Sequence[int] + The maximum degree (inclusive) to use for each axis. + This must be the same length as `vander_fs`. + + Returns + ------- + vander_nd : ndarray + An array of shape ``points[0].shape + tuple(d + 1 for d in degrees)``. + """ + n_dims = len(vander_fs) + if n_dims != len(points): + raise ValueError( + f"Expected {n_dims} dimensions of sample points, got {len(points)}") + if n_dims != len(degrees): + raise ValueError( + f"Expected {n_dims} dimensions of degrees, got {len(degrees)}") + if n_dims == 0: + raise ValueError("Unable to guess a dtype or shape when no points are given") + + # convert to the same shape and type + points = tuple(np.array(tuple(points), copy=False) + 0.0) + + # produce the vandermonde matrix for each dimension, placing the last + # axis of each in an independent trailing axis of the output + vander_arrays = ( + vander_fs[i](points[i], degrees[i])[(...,) + _nth_slice(i, n_dims)] + for i in range(n_dims) + ) + + # we checked this wasn't empty already, so no `initial` needed + return functools.reduce(operator.mul, vander_arrays) + + +def _vander_nd_flat(vander_fs, points, degrees): + """ + Like `_vander_nd`, but flattens the last ``len(degrees)`` axes into a single axis + + Used to implement the public ``vanderd`` functions. + """ + v = _vander_nd(vander_fs, points, degrees) + return v.reshape(v.shape[:-len(degrees)] + (-1,)) + + +def _fromroots(line_f, mul_f, roots): + """ + Helper function used to implement the ``fromroots`` functions. + + Parameters + ---------- + line_f : function(float, float) -> ndarray + The ``line`` function, such as ``polyline`` + mul_f : function(array_like, array_like) -> ndarray + The ``mul`` function, such as ``polymul`` + roots + See the ``fromroots`` functions for more detail + """ + if len(roots) == 0: + return np.ones(1) + else: + [roots] = as_series([roots], trim=False) + roots.sort() + p = [line_f(-r, 1) for r in roots] + n = len(p) + while n > 1: + m, r = divmod(n, 2) + tmp = [mul_f(p[i], p[i+m]) for i in range(m)] + if r: + tmp[0] = mul_f(tmp[0], p[-1]) + p = tmp + n = m + return p[0] + + +def _valnd(val_f, c, *args): + """ + Helper function used to implement the ``vald`` functions. + + Parameters + ---------- + val_f : function(array_like, array_like, tensor: bool) -> array_like + The ``val`` function, such as ``polyval`` + c, args + See the ``vald`` functions for more detail + """ + args = [np.asanyarray(a) for a in args] + shape0 = args[0].shape + if not all((a.shape == shape0 for a in args[1:])): + if len(args) == 3: + raise ValueError('x, y, z are incompatible') + elif len(args) == 2: + raise ValueError('x, y are incompatible') + else: + raise ValueError('ordinates are incompatible') + it = iter(args) + x0 = next(it) + + # use tensor on only the first + c = val_f(x0, c) + for xi in it: + c = val_f(xi, c, tensor=False) + return c + + +def _gridnd(val_f, c, *args): + """ + Helper function used to implement the ``gridd`` functions. + + Parameters + ---------- + val_f : function(array_like, array_like, tensor: bool) -> array_like + The ``val`` function, such as ``polyval`` + c, args + See the ``gridd`` functions for more detail + """ + for xi in args: + c = val_f(xi, c) + return c + + +def _div(mul_f, c1, c2): + """ + Helper function used to implement the ``div`` functions. + + Implementation uses repeated subtraction of c2 multiplied by the nth basis. + For some polynomial types, a more efficient approach may be possible. + + Parameters + ---------- + mul_f : function(array_like, array_like) -> array_like + The ``mul`` function, such as ``polymul`` + c1, c2 + See the ``div`` functions for more detail + """ + # c1, c2 are trimmed copies + [c1, c2] = as_series([c1, c2]) + if c2[-1] == 0: + raise ZeroDivisionError() + + lc1 = len(c1) + lc2 = len(c2) + if lc1 < lc2: + return c1[:1]*0, c1 + elif lc2 == 1: + return c1/c2[-1], c1[:1]*0 + else: + quo = np.empty(lc1 - lc2 + 1, dtype=c1.dtype) + rem = c1 + for i in range(lc1 - lc2, - 1, -1): + p = mul_f([0]*i + [1], c2) + q = rem[-1]/p[-1] + rem = rem[:-1] - q*p[:-1] + quo[i] = q + return quo, trimseq(rem) + + +def _add(c1, c2): + """ Helper function used to implement the ``add`` functions. """ + # c1, c2 are trimmed copies + [c1, c2] = as_series([c1, c2]) + if len(c1) > len(c2): + c1[:c2.size] += c2 + ret = c1 + else: + c2[:c1.size] += c1 + ret = c2 + return trimseq(ret) + + +def _sub(c1, c2): + """ Helper function used to implement the ``sub`` functions. """ + # c1, c2 are trimmed copies + [c1, c2] = as_series([c1, c2]) + if len(c1) > len(c2): + c1[:c2.size] -= c2 + ret = c1 + else: + c2 = -c2 + c2[:c1.size] += c1 + ret = c2 + return trimseq(ret) + + +def _fit(vander_f, x, y, deg, rcond=None, full=False, w=None): + """ + Helper function used to implement the ``fit`` functions. + + Parameters + ---------- + vander_f : function(array_like, int) -> ndarray + The 1d vander function, such as ``polyvander`` + c1, c2 + See the ``fit`` functions for more detail + """ + x = np.asarray(x) + 0.0 + y = np.asarray(y) + 0.0 + deg = np.asarray(deg) + + # check arguments. + if deg.ndim > 1 or deg.dtype.kind not in 'iu' or deg.size == 0: + raise TypeError("deg must be an int or non-empty 1-D array of int") + if deg.min() < 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 len(x) != len(y): + raise TypeError("expected x and y to have same length") + + if deg.ndim == 0: + lmax = deg + order = lmax + 1 + van = vander_f(x, lmax) + else: + deg = np.sort(deg) + lmax = deg[-1] + order = len(deg) + van = vander_f(x, lmax)[:, deg] + + # set up the least squares matrices in transposed form + lhs = van.T + rhs = y.T + if w is not None: + w = np.asarray(w) + 0.0 + if w.ndim != 1: + raise TypeError("expected 1D vector for w") + if len(x) != len(w): + raise TypeError("expected x and w to have same length") + # apply weights. Don't use inplace operations as they + # can cause problems with NA. + lhs = lhs * w + rhs = rhs * w + + # set rcond + if rcond is None: + rcond = len(x)*np.finfo(x.dtype).eps + + # Determine the norms of the design matrix columns. + if issubclass(lhs.dtype.type, np.complexfloating): + scl = np.sqrt((np.square(lhs.real) + np.square(lhs.imag)).sum(1)) + else: + scl = np.sqrt(np.square(lhs).sum(1)) + scl[scl == 0] = 1 + + # Solve the least squares problem. + c, resids, rank, s = np.linalg.lstsq(lhs.T/scl, rhs.T, rcond) + c = (c.T/scl).T + + # Expand c to include non-fitted coefficients which are set to zero + if deg.ndim > 0: + if c.ndim == 2: + cc = np.zeros((lmax+1, c.shape[1]), dtype=c.dtype) + else: + cc = np.zeros(lmax+1, dtype=c.dtype) + cc[deg] = c + c = cc + + # warn on rank reduction + if rank != order and not full: + msg = "The fit may be poorly conditioned" + warnings.warn(msg, RankWarning, stacklevel=2) + + if full: + return c, [resids, rank, s, rcond] + else: + return c + + +def _pow(mul_f, c, pow, maxpower): + """ + Helper function used to implement the ``pow`` functions. + + Parameters + ---------- + mul_f : function(array_like, array_like) -> ndarray + The ``mul`` function, such as ``polymul`` + c : array_like + 1-D array of array of series coefficients + pow, maxpower + See the ``pow`` functions for more detail + """ + # c is a trimmed copy + [c] = as_series([c]) + power = int(pow) + if power != pow or power < 0: + raise ValueError("Power must be a non-negative integer.") + elif maxpower is not None and power > maxpower: + raise ValueError("Power is too large") + elif power == 0: + return np.array([1], dtype=c.dtype) + elif power == 1: + return c + else: + # This can be made more efficient by using powers of two + # in the usual way. + prd = c + for i in range(2, power + 1): + prd = mul_f(prd, c) + return prd + + +def _deprecate_as_int(x, desc): + """ + Like `operator.index`, but emits a deprecation warning when passed a float + + Parameters + ---------- + x : int-like, or float with integral value + Value to interpret as an integer + desc : str + description to include in any error message + + Raises + ------ + TypeError : if x is a non-integral float or non-numeric + DeprecationWarning : if x is an integral float + """ + try: + return operator.index(x) + except TypeError as e: + # Numpy 1.17.0, 2019-03-11 + try: + ix = int(x) + except TypeError: + pass + else: + if ix == x: + warnings.warn( + f"In future, this will raise TypeError, as {desc} will " + "need to be an integer not just an integral float.", + DeprecationWarning, + stacklevel=3 + ) + return ix + + raise TypeError(f"{desc} must be an integer") from e + + +def format_float(x, parens=False): + if not np.issubdtype(type(x), np.floating): + return str(x) + + opts = np.get_printoptions() + + if np.isnan(x): + return opts['nanstr'] + elif np.isinf(x): + return opts['infstr'] + + exp_format = False + if x != 0: + a = absolute(x) + if a >= 1.e8 or a < 10**min(0, 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