80 kB

	"""
	A collection of utility functions and classes. Originally, many
	(but not all) were from the Python Cookbook -- hence the name cbook.
	"""

	import collections
	import collections.abc
	import contextlib
	import functools
	import gzip
	import itertools
	import math
	import operator
	import os
	from pathlib import Path
	import shlex
	import subprocess
	import sys
	import time
	import traceback
	import types
	import weakref

	import numpy as np

	try:
	from numpy.exceptions import VisibleDeprecationWarning # numpy >= 1.25
	except ImportError:
	from numpy import VisibleDeprecationWarning

	import matplotlib
	from matplotlib import _api, _c_internal_utils


	class _ExceptionInfo:
	"""
	A class to carry exception information around.

	This is used to store and later raise exceptions. It's an alternative to
	directly storing Exception instances that circumvents traceback-related
	issues: caching tracebacks can keep user's objects in local namespaces
	alive indefinitely, which can lead to very surprising memory issues for
	users and result in incorrect tracebacks.
	"""

	def __init__(self, cls, *args):
	self._cls = cls
	self._args = args

	@classmethod
	def from_exception(cls, exc):
	return cls(type(exc), *exc.args)

	def to_exception(self):
	return self._cls(*self._args)


	def _get_running_interactive_framework():
	"""
	Return the interactive framework whose event loop is currently running, if
	any, or "headless" if no event loop can be started, or None.

	Returns
	-------
	Optional[str]
	One of the following values: "qt", "gtk3", "gtk4", "wx", "tk",
	"macosx", "headless", ``None``.
	"""
	# Use ``sys.modules.get(name)`` rather than ``name in sys.modules`` as
	# entries can also have been explicitly set to None.
	QtWidgets = (
	sys.modules.get("PyQt6.QtWidgets")
	or sys.modules.get("PySide6.QtWidgets")
	or sys.modules.get("PyQt5.QtWidgets")
	or sys.modules.get("PySide2.QtWidgets")
	)
	if QtWidgets and QtWidgets.QApplication.instance():
	return "qt"
	Gtk = sys.modules.get("gi.repository.Gtk")
	if Gtk:
	if Gtk.MAJOR_VERSION == 4:
	from gi.repository import GLib
	if GLib.main_depth():
	return "gtk4"
	if Gtk.MAJOR_VERSION == 3 and Gtk.main_level():
	return "gtk3"
	wx = sys.modules.get("wx")
	if wx and wx.GetApp():
	return "wx"
	tkinter = sys.modules.get("tkinter")
	if tkinter:
	codes = {tkinter.mainloop.__code__, tkinter.Misc.mainloop.__code__}
	for frame in sys._current_frames().values():
	while frame:
	if frame.f_code in codes:
	return "tk"
	frame = frame.f_back
	# Preemptively break reference cycle between locals and the frame.
	del frame
	macosx = sys.modules.get("matplotlib.backends._macosx")
	if macosx and macosx.event_loop_is_running():
	return "macosx"
	if not _c_internal_utils.display_is_valid():
	return "headless"
	return None


	def _exception_printer(exc):
	if _get_running_interactive_framework() in ["headless", None]:
	raise exc
	else:
	traceback.print_exc()


	class _StrongRef:
	"""
	Wrapper similar to a weakref, but keeping a strong reference to the object.
	"""

	def __init__(self, obj):
	self._obj = obj

	def __call__(self):
	return self._obj

	def __eq__(self, other):
	return isinstance(other, _StrongRef) and self._obj == other._obj

	def __hash__(self):
	return hash(self._obj)


	def _weak_or_strong_ref(func, callback):
	"""
	Return a `WeakMethod` wrapping func if possible, else a `_StrongRef`.
	"""
	try:
	return weakref.WeakMethod(func, callback)
	except TypeError:
	return _StrongRef(func)


	class _UnhashDict:
	"""
	A minimal dict-like class that also supports unhashable keys, storing them
	in a list of key-value pairs.

	This class only implements the interface needed for `CallbackRegistry`, and
	tries to minimize the overhead for the hashable case.
	"""

	def __init__(self, pairs):
	self._dict = {}
	self._pairs = []
	for k, v in pairs:
	self[k] = v

	def __setitem__(self, key, value):
	try:
	self._dict[key] = value
	except TypeError:
	for i, (k, v) in enumerate(self._pairs):
	if k == key:
	self._pairs[i] = (key, value)
	break
	else:
	self._pairs.append((key, value))

	def __getitem__(self, key):
	try:
	return self._dict[key]
	except TypeError:
	pass
	for k, v in self._pairs:
	if k == key:
	return v
	raise KeyError(key)

	def pop(self, key, *args):
	try:
	if key in self._dict:
	return self._dict.pop(key)
	except TypeError:
	for i, (k, v) in enumerate(self._pairs):
	if k == key:
	del self._pairs[i]
	return v
	if args:
	return args[0]
	raise KeyError(key)

	def __iter__(self):
	yield from self._dict
	for k, v in self._pairs:
	yield k


	class CallbackRegistry:
	"""
	Handle registering, processing, blocking, and disconnecting
	for a set of signals and callbacks:

	>>> def oneat(x):
	... print('eat', x)
	>>> def ondrink(x):
	... print('drink', x)

	>>> from matplotlib.cbook import CallbackRegistry
	>>> callbacks = CallbackRegistry()

	>>> id_eat = callbacks.connect('eat', oneat)
	>>> id_drink = callbacks.connect('drink', ondrink)

	>>> callbacks.process('drink', 123)
	drink 123
	>>> callbacks.process('eat', 456)
	eat 456
	>>> callbacks.process('be merry', 456) # nothing will be called

	>>> callbacks.disconnect(id_eat)
	>>> callbacks.process('eat', 456) # nothing will be called

	>>> with callbacks.blocked(signal='drink'):
	... callbacks.process('drink', 123) # nothing will be called
	>>> callbacks.process('drink', 123)
	drink 123

	In practice, one should always disconnect all callbacks when they are
	no longer needed to avoid dangling references (and thus memory leaks).
	However, real code in Matplotlib rarely does so, and due to its design,
	it is rather difficult to place this kind of code. To get around this,
	and prevent this class of memory leaks, we instead store weak references
	to bound methods only, so when the destination object needs to die, the
	CallbackRegistry won't keep it alive.

	Parameters
	----------
	exception_handler : callable, optional
	If not None, exception_handler must be a function that takes an
	`Exception` as single parameter. It gets called with any `Exception`
	raised by the callbacks during `CallbackRegistry.process`, and may
	either re-raise the exception or handle it in another manner.

	The default handler prints the exception (with `traceback.print_exc`) if
	an interactive event loop is running; it re-raises the exception if no
	interactive event loop is running.

	signals : list, optional
	If not None, signals is a list of signals that this registry handles:
	attempting to `process` or to `connect` to a signal not in the list
	throws a `ValueError`. The default, None, does not restrict the
	handled signals.
	"""

	# We maintain two mappings:
	# callbacks: signal -> {cid -> weakref-to-callback}
	# _func_cid_map: {(signal, weakref-to-callback) -> cid}

	def __init__(self, exception_handler=_exception_printer, *, signals=None):
	self._signals = None if signals is None else list(signals) # Copy it.
	self.exception_handler = exception_handler
	self.callbacks = {}
	self._cid_gen = itertools.count()
	self._func_cid_map = _UnhashDict([])
	# A hidden variable that marks cids that need to be pickled.
	self._pickled_cids = set()

	def __getstate__(self):
	return {
	**vars(self),
	# In general, callbacks may not be pickled, so we just drop them,
	# unless directed otherwise by self._pickled_cids.
	"callbacks": {s: {cid: proxy() for cid, proxy in d.items()
	if cid in self._pickled_cids}
	for s, d in self.callbacks.items()},
	# It is simpler to reconstruct this from callbacks in __setstate__.
	"_func_cid_map": None,
	"_cid_gen": next(self._cid_gen)
	}

	def __setstate__(self, state):
	cid_count = state.pop('_cid_gen')
	vars(self).update(state)
	self.callbacks = {
	s: {cid: _weak_or_strong_ref(func, functools.partial(self._remove_proxy, s))
	for cid, func in d.items()}
	for s, d in self.callbacks.items()}
	self._func_cid_map = _UnhashDict(
	((s, proxy), cid)
	for s, d in self.callbacks.items() for cid, proxy in d.items())
	self._cid_gen = itertools.count(cid_count)

	def connect(self, signal, func):
	"""Register func to be called when signal signal is generated."""
	if self._signals is not None:
	_api.check_in_list(self._signals, signal=signal)
	proxy = _weak_or_strong_ref(func, functools.partial(self._remove_proxy, signal))
	try:
	return self._func_cid_map[signal, proxy]
	except KeyError:
	cid = self._func_cid_map[signal, proxy] = next(self._cid_gen)
	self.callbacks.setdefault(signal, {})[cid] = proxy
	return cid

	def _connect_picklable(self, signal, func):
	"""
	Like `.connect`, but the callback is kept when pickling/unpickling.

	Currently internal-use only.
	"""
	cid = self.connect(signal, func)
	self._pickled_cids.add(cid)
	return cid

	# Keep a reference to sys.is_finalizing, as sys may have been cleared out
	# at that point.
	def _remove_proxy(self, signal, proxy, *, _is_finalizing=sys.is_finalizing):
	if _is_finalizing():
	# Weakrefs can't be properly torn down at that point anymore.
	return
	cid = self._func_cid_map.pop((signal, proxy), None)
	if cid is not None:
	del self.callbacks[signal][cid]
	self._pickled_cids.discard(cid)
	else: # Not found
	return
	if len(self.callbacks[signal]) == 0: # Clean up empty dicts
	del self.callbacks[signal]

	def disconnect(self, cid):
	"""
	Disconnect the callback registered with callback id cid.

	No error is raised if such a callback does not exist.
	"""
	self._pickled_cids.discard(cid)
	for signal, proxy in self._func_cid_map:
	if self._func_cid_map[signal, proxy] == cid:
	break
	else: # Not found
	return
	assert self.callbacks[signal][cid] == proxy
	del self.callbacks[signal][cid]
	self._func_cid_map.pop((signal, proxy))
	if len(self.callbacks[signal]) == 0: # Clean up empty dicts
	del self.callbacks[signal]

	def process(self, s, args, *kwargs):
	"""
	Process signal s.

	All of the functions registered to receive callbacks on s will be
	called with ``args`` and ``*kwargs``.
	"""
	if self._signals is not None:
	_api.check_in_list(self._signals, signal=s)
	for ref in list(self.callbacks.get(s, {}).values()):
	func = ref()
	if func is not None:
	try:
	func(args, *kwargs)
	# this does not capture KeyboardInterrupt, SystemExit,
	# and GeneratorExit
	except Exception as exc:
	if self.exception_handler is not None:
	self.exception_handler(exc)
	else:
	raise

	@contextlib.contextmanager
	def blocked(self, *, signal=None):
	"""
	Block callback signals from being processed.

	A context manager to temporarily block/disable callback signals
	from being processed by the registered listeners.

	Parameters
	----------
	signal : str, optional
	The callback signal to block. The default is to block all signals.
	"""
	orig = self.callbacks
	try:
	if signal is None:
	# Empty out the callbacks
	self.callbacks = {}
	else:
	# Only remove the specific signal
	self.callbacks = {k: orig[k] for k in orig if k != signal}
	yield
	finally:
	self.callbacks = orig


	class silent_list(list):
	"""
	A list with a short ``repr()``.

	This is meant to be used for a homogeneous list of artists, so that they
	don't cause long, meaningless output.

	Instead of ::

	[<matplotlib.lines.Line2D object at 0x7f5749fed3c8>,
	<matplotlib.lines.Line2D object at 0x7f5749fed4e0>,
	<matplotlib.lines.Line2D object at 0x7f5758016550>]

	one will get ::

	<a list of 3 Line2D objects>

	If ``self.type`` is None, the type name is obtained from the first item in
	the list (if any).
	"""

	def __init__(self, type, seq=None):
	self.type = type
	if seq is not None:
	self.extend(seq)

	def __repr__(self):
	if self.type is not None or len(self) != 0:
	tp = self.type if self.type is not None else type(self[0]).__name__
	return f"<a list of {len(self)} {tp} objects>"
	else:
	return "<an empty list>"


	def _local_over_kwdict(
	local_var, kwargs, *keys,
	warning_cls=_api.MatplotlibDeprecationWarning):
	out = local_var
	for key in keys:
	kwarg_val = kwargs.pop(key, None)
	if kwarg_val is not None:
	if out is None:
	out = kwarg_val
	else:
	_api.warn_external(f'"{key}" keyword argument will be ignored',
	warning_cls)
	return out


	def strip_math(s):
	"""
	Remove latex formatting from mathtext.

	Only handles fully math and fully non-math strings.
	"""
	if len(s) >= 2 and s[0] == s[-1] == "$":
	s = s[1:-1]
	for tex, plain in [
	(r"\times", "x"), # Specifically for Formatter support.
	(r"\mathdefault", ""),
	(r"\rm", ""),
	(r"\cal", ""),
	(r"\tt", ""),
	(r"\it", ""),
	("\\", ""),
	("{", ""),
	("}", ""),
	]:
	s = s.replace(tex, plain)
	return s


	def _strip_comment(s):
	"""Strip everything from the first unquoted #."""
	pos = 0
	while True:
	quote_pos = s.find('"', pos)
	hash_pos = s.find('#', pos)
	if quote_pos < 0:
	without_comment = s if hash_pos < 0 else s[:hash_pos]
	return without_comment.strip()
	elif 0 <= hash_pos < quote_pos:
	return s[:hash_pos].strip()
	else:
	closing_quote_pos = s.find('"', quote_pos + 1)
	if closing_quote_pos < 0:
	raise ValueError(
	f"Missing closing quote in: {s!r}. If you need a double-"
	'quote inside a string, use escaping: e.g. "the \" char"')
	pos = closing_quote_pos + 1 # behind closing quote


	def is_writable_file_like(obj):
	"""Return whether obj looks like a file object with a write method."""
	return callable(getattr(obj, 'write', None))


	def file_requires_unicode(x):
	"""
	Return whether the given writable file-like object requires Unicode to be
	written to it.
	"""
	try:
	x.write(b'')
	except TypeError:
	return True
	else:
	return False


	def to_filehandle(fname, flag='r', return_opened=False, encoding=None):
	"""
	Convert a path to an open file handle or pass-through a file-like object.

	Consider using `open_file_cm` instead, as it allows one to properly close
	newly created file objects more easily.

	Parameters
	----------
	fname : str or path-like or file-like
	If `str` or `os.PathLike`, the file is opened using the flags specified
	by flag and encoding. If a file-like object, it is passed through.
	flag : str, default: 'r'
	Passed as the mode argument to `open` when fname is `str` or
	`os.PathLike`; ignored if fname is file-like.
	return_opened : bool, default: False
	If True, return both the file object and a boolean indicating whether
	this was a new file (that the caller needs to close). If False, return
	only the new file.
	encoding : str or None, default: None
	Passed as the mode argument to `open` when fname is `str` or
	`os.PathLike`; ignored if fname is file-like.

	Returns
	-------
	fh : file-like
	opened : bool
	opened is only returned if return_opened is True.
	"""
	if isinstance(fname, os.PathLike):
	fname = os.fspath(fname)
	if isinstance(fname, str):
	if fname.endswith('.gz'):
	fh = gzip.open(fname, flag)
	elif fname.endswith('.bz2'):
	# python may not be compiled with bz2 support,
	# bury import until we need it
	import bz2
	fh = bz2.BZ2File(fname, flag)
	else:
	fh = open(fname, flag, encoding=encoding)
	opened = True
	elif hasattr(fname, 'seek'):
	fh = fname
	opened = False
	else:
	raise ValueError('fname must be a PathLike or file handle')
	if return_opened:
	return fh, opened
	return fh


	def open_file_cm(path_or_file, mode="r", encoding=None):
	r"""Pass through file objects and context-manage path-likes."""
	fh, opened = to_filehandle(path_or_file, mode, True, encoding)
	return fh if opened else contextlib.nullcontext(fh)


	def is_scalar_or_string(val):
	"""Return whether the given object is a scalar or string like."""
	return isinstance(val, str) or not np.iterable(val)


	def get_sample_data(fname, asfileobj=True):
	"""
	Return a sample data file. fname is a path relative to the
	:file:`mpl-data/sample_data` directory. If asfileobj is `True`
	return a file object, otherwise just a file path.

	Sample data files are stored in the 'mpl-data/sample_data' directory within
	the Matplotlib package.

	If the filename ends in .gz, the file is implicitly ungzipped. If the
	filename ends with .npy or .npz, and asfileobj is `True`, the file is
	loaded with `numpy.load`.
	"""
	path = _get_data_path('sample_data', fname)
	if asfileobj:
	suffix = path.suffix.lower()
	if suffix == '.gz':
	return gzip.open(path)
	elif suffix in ['.npy', '.npz']:
	return np.load(path)
	elif suffix in ['.csv', '.xrc', '.txt']:
	return path.open('r')
	else:
	return path.open('rb')
	else:
	return str(path)


	def _get_data_path(*args):
	"""
	Return the `pathlib.Path` to a resource file provided by Matplotlib.

	``*args`` specify a path relative to the base data path.
	"""
	return Path(matplotlib.get_data_path(), *args)


	def flatten(seq, scalarp=is_scalar_or_string):
	"""
	Return a generator of flattened nested containers.

	For example:

	>>> from matplotlib.cbook import flatten
	>>> l = (('John', ['Hunter']), (1, 23), [[([42, (5, 23)], )]])
	>>> print(list(flatten(l)))
	['John', 'Hunter', 1, 23, 42, 5, 23]

	By: Composite of Holger Krekel and Luther Blissett
	From: https://code.activestate.com/recipes/121294-simple-generator-for-flattening-nested-containers/
	and Recipe 1.12 in cookbook
	""" # noqa: E501
	for item in seq:
	if scalarp(item) or item is None:
	yield item
	else:
	yield from flatten(item, scalarp)


	class _Stack:
	"""
	Stack of elements with a movable cursor.

	Mimics home/back/forward in a web browser.
	"""

	def __init__(self):
	self._pos = -1
	self._elements = []

	def clear(self):
	"""Empty the stack."""
	self._pos = -1
	self._elements = []

	def __call__(self):
	"""Return the current element, or None."""
	return self._elements[self._pos] if self._elements else None

	def __len__(self):
	return len(self._elements)

	def __getitem__(self, ind):
	return self._elements[ind]

	def forward(self):
	"""Move the position forward and return the current element."""
	self._pos = min(self._pos + 1, len(self._elements) - 1)
	return self()

	def back(self):
	"""Move the position back and return the current element."""
	self._pos = max(self._pos - 1, 0)
	return self()

	def push(self, o):
	"""
	Push o to the stack after the current position, and return o.

	Discard all later elements.
	"""
	self._elements[self._pos + 1:] = [o]
	self._pos = len(self._elements) - 1
	return o

	def home(self):
	"""
	Push the first element onto the top of the stack.

	The first element is returned.
	"""
	return self.push(self._elements[0]) if self._elements else None


	def safe_masked_invalid(x, copy=False):
	x = np.array(x, subok=True, copy=copy)
	if not x.dtype.isnative:
	# If we have already made a copy, do the byteswap in place, else make a
	# copy with the byte order swapped.
	# Swap to native order.
	x = x.byteswap(inplace=copy).view(x.dtype.newbyteorder('N'))
	try:
	xm = np.ma.masked_where(~(np.isfinite(x)), x, copy=False)
	except TypeError:
	return x
	return xm


	def print_cycles(objects, outstream=sys.stdout, show_progress=False):
	"""
	Print loops of cyclic references in the given objects.

	It is often useful to pass in ``gc.garbage`` to find the cycles that are
	preventing some objects from being garbage collected.

	Parameters
	----------
	objects
	A list of objects to find cycles in.
	outstream
	The stream for output.
	show_progress : bool
	If True, print the number of objects reached as they are found.
	"""
	import gc

	def print_path(path):
	for i, step in enumerate(path):
	# next "wraps around"
	next = path[(i + 1) % len(path)]

	outstream.write(" %s -- " % type(step))
	if isinstance(step, dict):
	for key, val in step.items():
	if val is next:
	outstream.write(f"[{key!r}]")
	break
	if key is next:
	outstream.write(f"[key] = {val!r}")
	break
	elif isinstance(step, list):
	outstream.write("[%d]" % step.index(next))
	elif isinstance(step, tuple):
	outstream.write("( tuple )")
	else:
	outstream.write(repr(step))
	outstream.write(" ->\n")
	outstream.write("\n")

	def recurse(obj, start, all, current_path):
	if show_progress:
	outstream.write("%d\r" % len(all))

	all[id(obj)] = None

	referents = gc.get_referents(obj)
	for referent in referents:
	# If we've found our way back to the start, this is
	# a cycle, so print it out
	if referent is start:
	print_path(current_path)

	# Don't go back through the original list of objects, or
	# through temporary references to the object, since those
	# are just an artifact of the cycle detector itself.
	elif referent is objects or isinstance(referent, types.FrameType):
	continue

	# We haven't seen this object before, so recurse
	elif id(referent) not in all:
	recurse(referent, start, all, current_path + [obj])

	for obj in objects:
	outstream.write(f"Examining: {obj!r}\n")
	recurse(obj, obj, {}, [])


	class Grouper:
	"""
	A disjoint-set data structure.

	Objects can be joined using :meth:`join`, tested for connectedness
	using :meth:`joined`, and all disjoint sets can be retrieved by
	using the object as an iterator.

	The objects being joined must be hashable and weak-referenceable.

	Examples
	--------
	>>> from matplotlib.cbook import Grouper
	>>> class Foo:
	... def __init__(self, s):
	... self.s = s
	... def __repr__(self):
	... return self.s
	...
	>>> a, b, c, d, e, f = [Foo(x) for x in 'abcdef']
	>>> grp = Grouper()
	>>> grp.join(a, b)
	>>> grp.join(b, c)
	>>> grp.join(d, e)
	>>> list(grp)
	[[a, b, c], [d, e]]
	>>> grp.joined(a, b)
	True
	>>> grp.joined(a, c)
	True
	>>> grp.joined(a, d)
	False
	"""

	def __init__(self, init=()):
	self._mapping = weakref.WeakKeyDictionary(
	{x: weakref.WeakSet([x]) for x in init})
	self._ordering = weakref.WeakKeyDictionary()
	for x in init:
	if x not in self._ordering:
	self._ordering[x] = len(self._ordering)
	self._next_order = len(self._ordering) # Plain int to simplify pickling.

	def __getstate__(self):
	return {
	**vars(self),
	# Convert weak refs to strong ones.
	"_mapping": {k: set(v) for k, v in self._mapping.items()},
	"_ordering": {**self._ordering},
	}

	def __setstate__(self, state):
	vars(self).update(state)
	# Convert strong refs to weak ones.
	self._mapping = weakref.WeakKeyDictionary(
	{k: weakref.WeakSet(v) for k, v in self._mapping.items()})
	self._ordering = weakref.WeakKeyDictionary(self._ordering)

	def __contains__(self, item):
	return item in self._mapping

	def join(self, a, *args):
	"""
	Join given arguments into the same set. Accepts one or more arguments.
	"""
	mapping = self._mapping
	try:
	set_a = mapping[a]
	except KeyError:
	set_a = mapping[a] = weakref.WeakSet([a])
	self._ordering[a] = self._next_order
	self._next_order += 1
	for arg in args:
	try:
	set_b = mapping[arg]
	except KeyError:
	set_b = mapping[arg] = weakref.WeakSet([arg])
	self._ordering[arg] = self._next_order
	self._next_order += 1
	if set_b is not set_a:
	if len(set_b) > len(set_a):
	set_a, set_b = set_b, set_a
	set_a.update(set_b)
	for elem in set_b:
	mapping[elem] = set_a

	def joined(self, a, b):
	"""Return whether a and b are members of the same set."""
	return (self._mapping.get(a, object()) is self._mapping.get(b))

	def remove(self, a):
	"""Remove a from the grouper, doing nothing if it is not there."""
	self._mapping.pop(a, {a}).remove(a)
	self._ordering.pop(a, None)

	def __iter__(self):
	"""
	Iterate over each of the disjoint sets as a list.

	The iterator is invalid if interleaved with calls to join().
	"""
	unique_groups = {id(group): group for group in self._mapping.values()}
	for group in unique_groups.values():
	yield sorted(group, key=self._ordering.__getitem__)

	def get_siblings(self, a):
	"""Return all of the items joined with a, including itself."""
	siblings = self._mapping.get(a, [a])
	return sorted(siblings, key=self._ordering.get)


	class GrouperView:
	"""Immutable view over a `.Grouper`."""

	def __init__(self, grouper): self._grouper = grouper
	def __contains__(self, item): return item in self._grouper
	def __iter__(self): return iter(self._grouper)

	def joined(self, a, b):
	"""
	Return whether a and b are members of the same set.
	"""
	return self._grouper.joined(a, b)

	def get_siblings(self, a):
	"""
	Return all of the items joined with a, including itself.
	"""
	return self._grouper.get_siblings(a)


	def simple_linear_interpolation(a, steps):
	"""
	Resample an array with ``steps - 1`` points between original point pairs.

	Along each column of a, ``(steps - 1)`` points are introduced between
	each original values; the values are linearly interpolated.

	Parameters
	----------
	a : array, shape (n, ...)
	steps : int

	Returns
	-------
	array
	shape ``((n - 1) * steps + 1, ...)``
	"""
	fps = a.reshape((len(a), -1))
	xp = np.arange(len(a)) * steps
	x = np.arange((len(a) - 1) * steps + 1)
	return (np.column_stack([np.interp(x, xp, fp) for fp in fps.T])
	.reshape((len(x),) + a.shape[1:]))


	def delete_masked_points(*args):
	"""
	Find all masked and/or non-finite points in a set of arguments,
	and return the arguments with only the unmasked points remaining.

	Arguments can be in any of 5 categories:

	1) 1-D masked arrays
	2) 1-D ndarrays
	3) ndarrays with more than one dimension
	4) other non-string iterables
	5) anything else

	The first argument must be in one of the first four categories;
	any argument with a length differing from that of the first
	argument (and hence anything in category 5) then will be
	passed through unchanged.

	Masks are obtained from all arguments of the correct length
	in categories 1, 2, and 4; a point is bad if masked in a masked
	array or if it is a nan or inf. No attempt is made to
	extract a mask from categories 2, 3, and 4 if `numpy.isfinite`
	does not yield a Boolean array.

	All input arguments that are not passed unchanged are returned
	as ndarrays after removing the points or rows corresponding to
	masks in any of the arguments.

	A vastly simpler version of this function was originally
	written as a helper for Axes.scatter().

	"""
	if not len(args):
	return ()
	if is_scalar_or_string(args[0]):
	raise ValueError("First argument must be a sequence")
	nrecs = len(args[0])
	margs = []
	seqlist = [False] * len(args)
	for i, x in enumerate(args):
	if not isinstance(x, str) and np.iterable(x) and len(x) == nrecs:
	seqlist[i] = True
	if isinstance(x, np.ma.MaskedArray):
	if x.ndim > 1:
	raise ValueError("Masked arrays must be 1-D")
	else:
	x = np.asarray(x)
	margs.append(x)
	masks = [] # List of masks that are True where good.
	for i, x in enumerate(margs):
	if seqlist[i]:
	if x.ndim > 1:
	continue # Don't try to get nan locations unless 1-D.
	if isinstance(x, np.ma.MaskedArray):
	masks.append(~np.ma.getmaskarray(x)) # invert the mask
	xd = x.data
	else:
	xd = x
	try:
	mask = np.isfinite(xd)
	if isinstance(mask, np.ndarray):
	masks.append(mask)
	except Exception: # Fixme: put in tuple of possible exceptions?
	pass
	if len(masks):
	mask = np.logical_and.reduce(masks)
	igood = mask.nonzero()[0]
	if len(igood) < nrecs:
	for i, x in enumerate(margs):
	if seqlist[i]:
	margs[i] = x[igood]
	for i, x in enumerate(margs):
	if seqlist[i] and isinstance(x, np.ma.MaskedArray):
	margs[i] = x.filled()
	return margs


	def _combine_masks(*args):
	"""
	Find all masked and/or non-finite points in a set of arguments,
	and return the arguments as masked arrays with a common mask.

	Arguments can be in any of 5 categories:

	1) 1-D masked arrays
	2) 1-D ndarrays
	3) ndarrays with more than one dimension
	4) other non-string iterables
	5) anything else

	The first argument must be in one of the first four categories;
	any argument with a length differing from that of the first
	argument (and hence anything in category 5) then will be
	passed through unchanged.

	Masks are obtained from all arguments of the correct length
	in categories 1, 2, and 4; a point is bad if masked in a masked
	array or if it is a nan or inf. No attempt is made to
	extract a mask from categories 2 and 4 if `numpy.isfinite`
	does not yield a Boolean array. Category 3 is included to
	support RGB or RGBA ndarrays, which are assumed to have only
	valid values and which are passed through unchanged.

	All input arguments that are not passed unchanged are returned
	as masked arrays if any masked points are found, otherwise as
	ndarrays.

	"""
	if not len(args):
	return ()
	if is_scalar_or_string(args[0]):
	raise ValueError("First argument must be a sequence")
	nrecs = len(args[0])
	margs = [] # Output args; some may be modified.
	seqlist = [False] * len(args) # Flags: True if output will be masked.
	masks = [] # List of masks.
	for i, x in enumerate(args):
	if is_scalar_or_string(x) or len(x) != nrecs:
	margs.append(x) # Leave it unmodified.
	else:
	if isinstance(x, np.ma.MaskedArray) and x.ndim > 1:
	raise ValueError("Masked arrays must be 1-D")
	try:
	x = np.asanyarray(x)
	except (VisibleDeprecationWarning, ValueError):
	# NumPy 1.19 raises a warning about ragged arrays, but we want
	# to accept basically anything here.
	x = np.asanyarray(x, dtype=object)
	if x.ndim == 1:
	x = safe_masked_invalid(x)
	seqlist[i] = True
	if np.ma.is_masked(x):
	masks.append(np.ma.getmaskarray(x))
	margs.append(x) # Possibly modified.
	if len(masks):
	mask = np.logical_or.reduce(masks)
	for i, x in enumerate(margs):
	if seqlist[i]:
	margs[i] = np.ma.array(x, mask=mask)
	return margs


	def _broadcast_with_masks(*args, compress=False):
	"""
	Broadcast inputs, combining all masked arrays.

	Parameters
	----------
	*args : array-like
	The inputs to broadcast.
	compress : bool, default: False
	Whether to compress the masked arrays. If False, the masked values
	are replaced by NaNs.

	Returns
	-------
	list of array-like
	The broadcasted and masked inputs.
	"""
	# extract the masks, if any
	masks = [k.mask for k in args if isinstance(k, np.ma.MaskedArray)]
	# broadcast to match the shape
	bcast = np.broadcast_arrays(args, masks)
	inputs = bcast[:len(args)]
	masks = bcast[len(args):]
	if masks:
	# combine the masks into one
	mask = np.logical_or.reduce(masks)
	# put mask on and compress
	if compress:
	inputs = [np.ma.array(k, mask=mask).compressed()
	for k in inputs]
	else:
	inputs = [np.ma.array(k, mask=mask, dtype=float).filled(np.nan).ravel()
	for k in inputs]
	else:
	inputs = [np.ravel(k) for k in inputs]
	return inputs


	def boxplot_stats(X, whis=1.5, bootstrap=None, labels=None, autorange=False):
	r"""
	Return a list of dictionaries of statistics used to draw a series of box
	and whisker plots using `~.Axes.bxp`.

	Parameters
	----------
	X : array-like
	Data that will be represented in the boxplots. Should have 2 or
	fewer dimensions.

	whis : float or (float, float), default: 1.5
	The position of the whiskers.

	If a float, the lower whisker is at the lowest datum above
	``Q1 - whis*(Q3-Q1)``, and the upper whisker at the highest datum below
	``Q3 + whis*(Q3-Q1)``, where Q1 and Q3 are the first and third
	quartiles. The default value of ``whis = 1.5`` corresponds to Tukey's
	original definition of boxplots.

	If a pair of floats, they indicate the percentiles at which to draw the
	whiskers (e.g., (5, 95)). In particular, setting this to (0, 100)
	results in whiskers covering the whole range of the data.

	In the edge case where ``Q1 == Q3``, whis is automatically set to
	(0, 100) (cover the whole range of the data) if autorange is True.

	Beyond the whiskers, data are considered outliers and are plotted as
	individual points.

	bootstrap : int, optional
	Number of times the confidence intervals around the median
	should be bootstrapped (percentile method).

	labels : list of str, optional
	Labels for each dataset. Length must be compatible with
	dimensions of X.

	autorange : bool, optional (False)
	When `True` and the data are distributed such that the 25th and 75th
	percentiles are equal, ``whis`` is set to (0, 100) such that the
	whisker ends are at the minimum and maximum of the data.

	Returns
	-------
	list of dict
	A list of dictionaries containing the results for each column
	of data. Keys of each dictionary are the following:

	======== ===================================
	Key Value Description
	======== ===================================
	label tick label for the boxplot
	mean arithmetic mean value
	med 50th percentile
	q1 first quartile (25th percentile)
	q3 third quartile (75th percentile)
	iqr interquartile range
	cilo lower notch around the median
	cihi upper notch around the median
	whislo end of the lower whisker
	whishi end of the upper whisker
	fliers outliers
	======== ===================================

	Notes
	-----
	Non-bootstrapping approach to confidence interval uses Gaussian-based
	asymptotic approximation:

	.. math::

	\mathrm{med} \pm 1.57 \times \frac{\mathrm{iqr}}{\sqrt{N}}

	General approach from:
	McGill, R., Tukey, J.W., and Larsen, W.A. (1978) "Variations of
	Boxplots", The American Statistician, 32:12-16.
	"""

	def _bootstrap_median(data, N=5000):
	# determine 95% confidence intervals of the median
	M = len(data)
	percentiles = [2.5, 97.5]

	bs_index = np.random.randint(M, size=(N, M))
	bsData = data[bs_index]
	estimate = np.median(bsData, axis=1, overwrite_input=True)

	CI = np.percentile(estimate, percentiles)
	return CI

	def _compute_conf_interval(data, med, iqr, bootstrap):
	if bootstrap is not None:
	# Do a bootstrap estimate of notch locations.
	# get conf. intervals around median
	CI = _bootstrap_median(data, N=bootstrap)
	notch_min = CI[0]
	notch_max = CI[1]
	else:

	N = len(data)
	notch_min = med - 1.57 * iqr / np.sqrt(N)
	notch_max = med + 1.57 * iqr / np.sqrt(N)

	return notch_min, notch_max

	# output is a list of dicts
	bxpstats = []

	# convert X to a list of lists
	X = _reshape_2D(X, "X")

	ncols = len(X)
	if labels is None:
	labels = itertools.repeat(None)
	elif len(labels) != ncols:
	raise ValueError("Dimensions of labels and X must be compatible")

	input_whis = whis
	for ii, (x, label) in enumerate(zip(X, labels)):

	# empty dict
	stats = {}
	if label is not None:
	stats['label'] = label

	# restore whis to the input values in case it got changed in the loop
	whis = input_whis

	# note tricksiness, append up here and then mutate below
	bxpstats.append(stats)

	# if empty, bail
	if len(x) == 0:
	stats['fliers'] = np.array([])
	stats['mean'] = np.nan
	stats['med'] = np.nan
	stats['q1'] = np.nan
	stats['q3'] = np.nan
	stats['iqr'] = np.nan
	stats['cilo'] = np.nan
	stats['cihi'] = np.nan
	stats['whislo'] = np.nan
	stats['whishi'] = np.nan
	continue

	# up-convert to an array, just to be safe
	x = np.ma.asarray(x)
	x = x.data[~x.mask].ravel()

	# arithmetic mean
	stats['mean'] = np.mean(x)

	# medians and quartiles
	q1, med, q3 = np.percentile(x, [25, 50, 75])

	# interquartile range
	stats['iqr'] = q3 - q1
	if stats['iqr'] == 0 and autorange:
	whis = (0, 100)

	# conf. interval around median
	stats['cilo'], stats['cihi'] = _compute_conf_interval(
	x, med, stats['iqr'], bootstrap
	)

	# lowest/highest non-outliers
	if np.iterable(whis) and not isinstance(whis, str):
	loval, hival = np.percentile(x, whis)
	elif np.isreal(whis):
	loval = q1 - whis * stats['iqr']
	hival = q3 + whis * stats['iqr']
	else:
	raise ValueError('whis must be a float or list of percentiles')

	# get high extreme
	wiskhi = x[x <= hival]
	if len(wiskhi) == 0 or np.max(wiskhi) < q3:
	stats['whishi'] = q3
	else:
	stats['whishi'] = np.max(wiskhi)

	# get low extreme
	wisklo = x[x >= loval]
	if len(wisklo) == 0 or np.min(wisklo) > q1:
	stats['whislo'] = q1
	else:
	stats['whislo'] = np.min(wisklo)

	# compute a single array of outliers
	stats['fliers'] = np.concatenate([
	x[x < stats['whislo']],
	x[x > stats['whishi']],
	])

	# add in the remaining stats
	stats['q1'], stats['med'], stats['q3'] = q1, med, q3

	return bxpstats


	#: Maps short codes for line style to their full name used by backends.
	ls_mapper = {'-': 'solid', '--': 'dashed', '-.': 'dashdot', ':': 'dotted'}
	#: Maps full names for line styles used by backends to their short codes.
	ls_mapper_r = {v: k for k, v in ls_mapper.items()}


	def contiguous_regions(mask):
	"""
	Return a list of (ind0, ind1) such that ``mask[ind0:ind1].all()`` is
	True and we cover all such regions.
	"""
	mask = np.asarray(mask, dtype=bool)

	if not mask.size:
	return []

	# Find the indices of region changes, and correct offset
	idx, = np.nonzero(mask[:-1] != mask[1:])
	idx += 1

	# List operations are faster for moderately sized arrays
	idx = idx.tolist()

	# Add first and/or last index if needed
	if mask[0]:
	idx = [0] + idx
	if mask[-1]:
	idx.append(len(mask))

	return list(zip(idx[::2], idx[1::2]))


	def is_math_text(s):
	"""
	Return whether the string s contains math expressions.

	This is done by checking whether s contains an even number of
	non-escaped dollar signs.
	"""
	s = str(s)
	dollar_count = s.count(r'$') - s.count(r'\$')
	even_dollars = (dollar_count > 0 and dollar_count % 2 == 0)
	return even_dollars


	def _to_unmasked_float_array(x):
	"""
	Convert a sequence to a float array; if input was a masked array, masked
	values are converted to nans.
	"""
	if hasattr(x, 'mask'):
	return np.ma.asarray(x, float).filled(np.nan)
	else:
	return np.asarray(x, float)


	def _check_1d(x):
	"""Convert scalars to 1D arrays; pass-through arrays as is."""
	# Unpack in case of e.g. Pandas or xarray object
	x = _unpack_to_numpy(x)
	# plot requires `shape` and `ndim`. If passed an
	# object that doesn't provide them, then force to numpy array.
	# Note this will strip unit information.
	if (not hasattr(x, 'shape') or
	not hasattr(x, 'ndim') or
	len(x.shape) < 1):
	return np.atleast_1d(x)
	else:
	return x


	def _reshape_2D(X, name):
	"""
	Use Fortran ordering to convert ndarrays and lists of iterables to lists of
	1D arrays.

	Lists of iterables are converted by applying `numpy.asanyarray` to each of
	their elements. 1D ndarrays are returned in a singleton list containing
	them. 2D ndarrays are converted to the list of their columns.

	name is used to generate the error message for invalid inputs.
	"""

	# Unpack in case of e.g. Pandas or xarray object
	X = _unpack_to_numpy(X)

	# Iterate over columns for ndarrays.
	if isinstance(X, np.ndarray):
	X = X.transpose()

	if len(X) == 0:
	return [[]]
	elif X.ndim == 1 and np.ndim(X[0]) == 0:
	# 1D array of scalars: directly return it.
	return [X]
	elif X.ndim in [1, 2]:
	# 2D array, or 1D array of iterables: flatten them first.
	return [np.reshape(x, -1) for x in X]
	else:
	raise ValueError(f'{name} must have 2 or fewer dimensions')

	# Iterate over list of iterables.
	if len(X) == 0:
	return [[]]

	result = []
	is_1d = True
	for xi in X:
	# check if this is iterable, except for strings which we
	# treat as singletons.
	if not isinstance(xi, str):
	try:
	iter(xi)
	except TypeError:
	pass
	else:
	is_1d = False
	xi = np.asanyarray(xi)
	nd = np.ndim(xi)
	if nd > 1:
	raise ValueError(f'{name} must have 2 or fewer dimensions')
	result.append(xi.reshape(-1))

	if is_1d:
	# 1D array of scalars: directly return it.
	return [np.reshape(result, -1)]
	else:
	# 2D array, or 1D array of iterables: use flattened version.
	return result


	def violin_stats(X, method, points=100, quantiles=None):
	"""
	Return a list of dictionaries of data which can be used to draw a series
	of violin plots.

	See the ``Returns`` section below to view the required keys of the
	dictionary.

	Users can skip this function and pass a user-defined set of dictionaries
	with the same keys to `~.axes.Axes.violinplot` instead of using Matplotlib
	to do the calculations. See the Returns section below for the keys
	that must be present in the dictionaries.

	Parameters
	----------
	X : array-like
	Sample data that will be used to produce the gaussian kernel density
	estimates. Must have 2 or fewer dimensions.

	method : callable
	The method used to calculate the kernel density estimate for each
	column of data. When called via ``method(v, coords)``, it should
	return a vector of the values of the KDE evaluated at the values
	specified in coords.

	points : int, default: 100
	Defines the number of points to evaluate each of the gaussian kernel
	density estimates at.

	quantiles : array-like, default: None
	Defines (if not None) a list of floats in interval [0, 1] for each
	column of data, which represents the quantiles that will be rendered
	for that column of data. Must have 2 or fewer dimensions. 1D array will
	be treated as a singleton list containing them.

	Returns
	-------
	list of dict
	A list of dictionaries containing the results for each column of data.
	The dictionaries contain at least the following:

	- coords: A list of scalars containing the coordinates this particular
	kernel density estimate was evaluated at.
	- vals: A list of scalars containing the values of the kernel density
	estimate at each of the coordinates given in coords.
	- mean: The mean value for this column of data.
	- median: The median value for this column of data.
	- min: The minimum value for this column of data.
	- max: The maximum value for this column of data.
	- quantiles: The quantile values for this column of data.
	"""

	# List of dictionaries describing each of the violins.
	vpstats = []

	# Want X to be a list of data sequences
	X = _reshape_2D(X, "X")

	# Want quantiles to be as the same shape as data sequences
	if quantiles is not None and len(quantiles) != 0:
	quantiles = _reshape_2D(quantiles, "quantiles")
	# Else, mock quantiles if it's none or empty
	else:
	quantiles = [[]] * len(X)

	# quantiles should have the same size as dataset
	if len(X) != len(quantiles):
	raise ValueError("List of violinplot statistics and quantiles values"
	" must have the same length")

	# Zip x and quantiles
	for (x, q) in zip(X, quantiles):
	# Dictionary of results for this distribution
	stats = {}

	# Calculate basic stats for the distribution
	min_val = np.min(x)
	max_val = np.max(x)
	quantile_val = np.percentile(x, 100 * q)

	# Evaluate the kernel density estimate
	coords = np.linspace(min_val, max_val, points)
	stats['vals'] = method(x, coords)
	stats['coords'] = coords

	# Store additional statistics for this distribution
	stats['mean'] = np.mean(x)
	stats['median'] = np.median(x)
	stats['min'] = min_val
	stats['max'] = max_val
	stats['quantiles'] = np.atleast_1d(quantile_val)

	# Append to output
	vpstats.append(stats)

	return vpstats


	def pts_to_prestep(x, *args):
	"""
	Convert continuous line to pre-steps.

	Given a set of ``N`` points, convert to ``2N - 1`` points, which when
	connected linearly give a step function which changes values at the
	beginning of the intervals.

	Parameters
	----------
	x : array
	The x location of the steps. May be empty.

	y1, ..., yp : array
	y arrays to be turned into steps; all must be the same length as ``x``.

	Returns
	-------
	array
	The x and y values converted to steps in the same order as the input;
	can be unpacked as ``x_out, y1_out, ..., yp_out``. If the input is
	length ``N``, each of these arrays will be length ``2N + 1``. For
	``N=0``, the length will be 0.

	Examples
	--------
	>>> x_s, y1_s, y2_s = pts_to_prestep(x, y1, y2)
	"""
	steps = np.zeros((1 + len(args), max(2 * len(x) - 1, 0)))
	# In all `pts_to_step` functions, only assign once using x* and args,
	# as converting to an array may be expensive.
	steps[0, 0::2] = x
	steps[0, 1::2] = steps[0, 0:-2:2]
	steps[1:, 0::2] = args
	steps[1:, 1::2] = steps[1:, 2::2]
	return steps


	def pts_to_poststep(x, *args):
	"""
	Convert continuous line to post-steps.

	Given a set of ``N`` points convert to ``2N + 1`` points, which when
	connected linearly give a step function which changes values at the end of
	the intervals.

	Parameters
	----------
	x : array
	The x location of the steps. May be empty.

	y1, ..., yp : array
	y arrays to be turned into steps; all must be the same length as ``x``.

	Returns
	-------
	array
	The x and y values converted to steps in the same order as the input;
	can be unpacked as ``x_out, y1_out, ..., yp_out``. If the input is
	length ``N``, each of these arrays will be length ``2N + 1``. For
	``N=0``, the length will be 0.

	Examples
	--------
	>>> x_s, y1_s, y2_s = pts_to_poststep(x, y1, y2)
	"""
	steps = np.zeros((1 + len(args), max(2 * len(x) - 1, 0)))
	steps[0, 0::2] = x
	steps[0, 1::2] = steps[0, 2::2]
	steps[1:, 0::2] = args
	steps[1:, 1::2] = steps[1:, 0:-2:2]
	return steps


	def pts_to_midstep(x, *args):
	"""
	Convert continuous line to mid-steps.

	Given a set of ``N`` points convert to ``2N`` points which when connected
	linearly give a step function which changes values at the middle of the
	intervals.

	Parameters
	----------
	x : array
	The x location of the steps. May be empty.

	y1, ..., yp : array
	y arrays to be turned into steps; all must be the same length as
	``x``.

	Returns
	-------
	array
	The x and y values converted to steps in the same order as the input;
	can be unpacked as ``x_out, y1_out, ..., yp_out``. If the input is
	length ``N``, each of these arrays will be length ``2N``.

	Examples
	--------
	>>> x_s, y1_s, y2_s = pts_to_midstep(x, y1, y2)
	"""
	steps = np.zeros((1 + len(args), 2 * len(x)))
	x = np.asanyarray(x)
	steps[0, 1:-1:2] = steps[0, 2::2] = (x[:-1] + x[1:]) / 2
	steps[0, :1] = x[:1] # Also works for zero-sized input.
	steps[0, -1:] = x[-1:]
	steps[1:, 0::2] = args
	steps[1:, 1::2] = steps[1:, 0::2]
	return steps


	STEP_LOOKUP_MAP = {'default': lambda x, y: (x, y),
	'steps': pts_to_prestep,
	'steps-pre': pts_to_prestep,
	'steps-post': pts_to_poststep,
	'steps-mid': pts_to_midstep}


	def index_of(y):
	"""
	A helper function to create reasonable x values for the given y.

	This is used for plotting (x, y) if x values are not explicitly given.

	First try ``y.index`` (assuming y is a `pandas.Series`), if that
	fails, use ``range(len(y))``.

	This will be extended in the future to deal with more types of
	labeled data.

	Parameters
	----------
	y : float or array-like

	Returns
	-------
	x, y : ndarray
	The x and y values to plot.
	"""
	try:
	return y.index.to_numpy(), y.to_numpy()
	except AttributeError:
	pass
	try:
	y = _check_1d(y)
	except (VisibleDeprecationWarning, ValueError):
	# NumPy 1.19 will warn on ragged input, and we can't actually use it.
	pass
	else:
	return np.arange(y.shape[0], dtype=float), y
	raise ValueError('Input could not be cast to an at-least-1D NumPy array')


	def safe_first_element(obj):
	"""
	Return the first element in obj.

	This is a type-independent way of obtaining the first element,
	supporting both index access and the iterator protocol.
	"""
	if isinstance(obj, collections.abc.Iterator):
	# needed to accept `array.flat` as input.
	# np.flatiter reports as an instance of collections.Iterator but can still be
	# indexed via []. This has the side effect of re-setting the iterator, but
	# that is acceptable.
	try:
	return obj[0]
	except TypeError:
	pass
	raise RuntimeError("matplotlib does not support generators as input")
	return next(iter(obj))


	def _safe_first_finite(obj):
	"""
	Return the first finite element in obj if one is available and skip_nonfinite is
	True. Otherwise, return the first element.

	This is a method for internal use.

	This is a type-independent way of obtaining the first finite element, supporting
	both index access and the iterator protocol.
	"""
	def safe_isfinite(val):
	if val is None:
	return False
	try:
	return math.isfinite(val)
	except (TypeError, ValueError):
	# if the outer object is 2d, then val is a 1d array, and
	# - math.isfinite(numpy.zeros(3)) raises TypeError
	# - math.isfinite(torch.zeros(3)) raises ValueError
	pass
	try:
	return np.isfinite(val) if np.isscalar(val) else True
	except TypeError:
	# This is something that NumPy cannot make heads or tails of,
	# assume "finite"
	return True

	if isinstance(obj, np.flatiter):
	# TODO do the finite filtering on this
	return obj[0]
	elif isinstance(obj, collections.abc.Iterator):
	raise RuntimeError("matplotlib does not support generators as input")
	else:
	for val in obj:
	if safe_isfinite(val):
	return val
	return safe_first_element(obj)


	def sanitize_sequence(data):
	"""
	Convert dictview objects to list. Other inputs are returned unchanged.
	"""
	return (list(data) if isinstance(data, collections.abc.MappingView)
	else data)


	def normalize_kwargs(kw, alias_mapping=None):
	"""
	Helper function to normalize kwarg inputs.

	Parameters
	----------
	kw : dict or None
	A dict of keyword arguments. None is explicitly supported and treated
	as an empty dict, to support functions with an optional parameter of
	the form ``props=None``.

	alias_mapping : dict or Artist subclass or Artist instance, optional
	A mapping between a canonical name to a list of aliases, in order of
	precedence from lowest to highest.

	If the canonical value is not in the list it is assumed to have the
	highest priority.

	If an Artist subclass or instance is passed, use its properties alias
	mapping.

	Raises
	------
	TypeError
	To match what Python raises if invalid arguments/keyword arguments are
	passed to a callable.
	"""
	from matplotlib.artist import Artist

	if kw is None:
	return {}

	# deal with default value of alias_mapping
	if alias_mapping is None:
	alias_mapping = {}
	elif (isinstance(alias_mapping, type) and issubclass(alias_mapping, Artist)
	or isinstance(alias_mapping, Artist)):
	alias_mapping = getattr(alias_mapping, "_alias_map", {})

	to_canonical = {alias: canonical
	for canonical, alias_list in alias_mapping.items()
	for alias in alias_list}
	canonical_to_seen = {}
	ret = {} # output dictionary

	for k, v in kw.items():
	canonical = to_canonical.get(k, k)
	if canonical in canonical_to_seen:
	raise TypeError(f"Got both {canonical_to_seen[canonical]!r} and "
	f"{k!r}, which are aliases of one another")
	canonical_to_seen[canonical] = k
	ret[canonical] = v

	return ret


	@contextlib.contextmanager
	def _lock_path(path):
	"""
	Context manager for locking a path.

	Usage::

	with _lock_path(path):
	...

	Another thread or process that attempts to lock the same path will wait
	until this context manager is exited.

	The lock is implemented by creating a temporary file in the parent
	directory, so that directory must exist and be writable.
	"""
	path = Path(path)
	lock_path = path.with_name(path.name + ".matplotlib-lock")
	retries = 50
	sleeptime = 0.1
	for _ in range(retries):
	try:
	with lock_path.open("xb"):
	break
	except FileExistsError:
	time.sleep(sleeptime)
	else:
	raise TimeoutError("""\
	Lock error: Matplotlib failed to acquire the following lock file:
	{}
	This maybe due to another process holding this lock file. If you are sure no
	other Matplotlib process is running, remove this file and try again.""".format(
	lock_path))
	try:
	yield
	finally:
	lock_path.unlink()


	def _topmost_artist(
	artists,
	_cached_max=functools.partial(max, key=operator.attrgetter("zorder"))):
	"""
	Get the topmost artist of a list.

	In case of a tie, return the last of the tied artists, as it will be
	drawn on top of the others. `max` returns the first maximum in case of
	ties, so we need to iterate over the list in reverse order.
	"""
	return _cached_max(reversed(artists))


	def _str_equal(obj, s):
	"""
	Return whether obj is a string equal to string s.

	This helper solely exists to handle the case where obj is a numpy array,
	because in such cases, a naive ``obj == s`` would yield an array, which
	cannot be used in a boolean context.
	"""
	return isinstance(obj, str) and obj == s


	def _str_lower_equal(obj, s):
	"""
	Return whether obj is a string equal, when lowercased, to string s.

	This helper solely exists to handle the case where obj is a numpy array,
	because in such cases, a naive ``obj == s`` would yield an array, which
	cannot be used in a boolean context.
	"""
	return isinstance(obj, str) and obj.lower() == s


	def _array_perimeter(arr):
	"""
	Get the elements on the perimeter of arr.

	Parameters
	----------
	arr : ndarray, shape (M, N)
	The input array.

	Returns
	-------
	ndarray, shape (2(M - 1) + 2(N - 1),)
	The elements on the perimeter of the array::

	[arr[0, 0], ..., arr[0, -1], ..., arr[-1, -1], ..., arr[-1, 0], ...]

	Examples
	--------
	>>> i, j = np.ogrid[:3, :4]
	>>> a = i*10 + j
	>>> a
	array([[ 0, 1, 2, 3],
	[10, 11, 12, 13],
	[20, 21, 22, 23]])
	>>> _array_perimeter(a)
	array([ 0, 1, 2, 3, 13, 23, 22, 21, 20, 10])
	"""
	# note we use Python's half-open ranges to avoid repeating
	# the corners
	forward = np.s_[0:-1] # [0 ... -1)
	backward = np.s_[-1:0:-1] # [-1 ... 0)
	return np.concatenate((
	arr[0, forward],
	arr[forward, -1],
	arr[-1, backward],
	arr[backward, 0],
	))


	def _unfold(arr, axis, size, step):
	"""
	Append an extra dimension containing sliding windows along axis.

	All windows are of size size and begin with every step elements.

	Parameters
	----------
	arr : ndarray, shape (N_1, ..., N_k)
	The input array
	axis : int
	Axis along which the windows are extracted
	size : int
	Size of the windows
	step : int
	Stride between first elements of subsequent windows.

	Returns
	-------
	ndarray, shape (N_1, ..., 1 + (N_axis-size)/step, ..., N_k, size)

	Examples
	--------
	>>> i, j = np.ogrid[:3, :7]
	>>> a = i*10 + j
	>>> a
	array([[ 0, 1, 2, 3, 4, 5, 6],
	[10, 11, 12, 13, 14, 15, 16],
	[20, 21, 22, 23, 24, 25, 26]])
	>>> _unfold(a, axis=1, size=3, step=2)
	array([[[ 0, 1, 2],
	[ 2, 3, 4],
	[ 4, 5, 6]],
	[[10, 11, 12],
	[12, 13, 14],
	[14, 15, 16]],
	[[20, 21, 22],
	[22, 23, 24],
	[24, 25, 26]]])
	"""
	new_shape = [*arr.shape, size]
	new_strides = [*arr.strides, arr.strides[axis]]
	new_shape[axis] = (new_shape[axis] - size) // step + 1
	new_strides[axis] = new_strides[axis] * step
	return np.lib.stride_tricks.as_strided(arr,
	shape=new_shape,
	strides=new_strides,
	writeable=False)


	def _array_patch_perimeters(x, rstride, cstride):
	"""
	Extract perimeters of patches from arr.

	Extracted patches are of size (rstride + 1) x (cstride + 1) and
	share perimeters with their neighbors. The ordering of the vertices matches
	that returned by ``_array_perimeter``.

	Parameters
	----------
	x : ndarray, shape (N, M)
	Input array
	rstride : int
	Vertical (row) stride between corresponding elements of each patch
	cstride : int
	Horizontal (column) stride between corresponding elements of each patch

	Returns
	-------
	ndarray, shape (N/rstride * M/cstride, 2 * (rstride + cstride))
	"""
	assert rstride > 0 and cstride > 0
	assert (x.shape[0] - 1) % rstride == 0
	assert (x.shape[1] - 1) % cstride == 0
	# We build up each perimeter from four half-open intervals. Here is an
	# illustrated explanation for rstride == cstride == 3
	#
	# T T T R
	# L R
	# L R
	# L B B B
	#
	# where T means that this element will be in the top array, R for right,
	# B for bottom and L for left. Each of the arrays below has a shape of:
	#
	# (number of perimeters that can be extracted vertically,
	# number of perimeters that can be extracted horizontally,
	# cstride for top and bottom and rstride for left and right)
	#
	# Note that _unfold doesn't incur any memory copies, so the only costly
	# operation here is the np.concatenate.
	top = _unfold(x[:-1:rstride, :-1], 1, cstride, cstride)
	bottom = _unfold(x[rstride::rstride, 1:], 1, cstride, cstride)[..., ::-1]
	right = _unfold(x[:-1, cstride::cstride], 0, rstride, rstride)
	left = _unfold(x[1:, :-1:cstride], 0, rstride, rstride)[..., ::-1]
	return (np.concatenate((top, right, bottom, left), axis=2)
	.reshape(-1, 2 * (rstride + cstride)))


	@contextlib.contextmanager
	def _setattr_cm(obj, **kwargs):
	"""
	Temporarily set some attributes; restore original state at context exit.
	"""
	sentinel = object()
	origs = {}
	for attr in kwargs:
	orig = getattr(obj, attr, sentinel)
	if attr in obj.__dict__ or orig is sentinel:
	# if we are pulling from the instance dict or the object
	# does not have this attribute we can trust the above
	origs[attr] = orig
	else:
	# if the attribute is not in the instance dict it must be
	# from the class level
	cls_orig = getattr(type(obj), attr)
	# if we are dealing with a property (but not a general descriptor)
	# we want to set the original value back.
	if isinstance(cls_orig, property):
	origs[attr] = orig
	# otherwise this is _something_ we are going to shadow at
	# the instance dict level from higher up in the MRO. We
	# are going to assume we can delattr(obj, attr) to clean
	# up after ourselves. It is possible that this code will
	# fail if used with a non-property custom descriptor which
	# implements __set__ (and __delete__ does not act like a
	# stack). However, this is an internal tool and we do not
	# currently have any custom descriptors.
	else:
	origs[attr] = sentinel

	try:
	for attr, val in kwargs.items():
	setattr(obj, attr, val)
	yield
	finally:
	for attr, orig in origs.items():
	if orig is sentinel:
	delattr(obj, attr)
	else:
	setattr(obj, attr, orig)


	class _OrderedSet(collections.abc.MutableSet):
	def __init__(self):
	self._od = collections.OrderedDict()

	def __contains__(self, key):
	return key in self._od

	def __iter__(self):
	return iter(self._od)

	def __len__(self):
	return len(self._od)

	def add(self, key):
	self._od.pop(key, None)
	self._od[key] = None

	def discard(self, key):
	self._od.pop(key, None)


	# Agg's buffers are unmultiplied RGBA8888, which neither PyQt<=5.1 nor cairo
	# support; however, both do support premultiplied ARGB32.


	def _premultiplied_argb32_to_unmultiplied_rgba8888(buf):
	"""
	Convert a premultiplied ARGB32 buffer to an unmultiplied RGBA8888 buffer.
	"""
	rgba = np.take( # .take() ensures C-contiguity of the result.
	buf,
	[2, 1, 0, 3] if sys.byteorder == "little" else [1, 2, 3, 0], axis=2)
	rgb = rgba[..., :-1]
	alpha = rgba[..., -1]
	# Un-premultiply alpha. The formula is the same as in cairo-png.c.
	mask = alpha != 0
	for channel in np.rollaxis(rgb, -1):
	channel[mask] = (
	(channel[mask].astype(int) * 255 + alpha[mask] // 2)
	// alpha[mask])
	return rgba


	def _unmultiplied_rgba8888_to_premultiplied_argb32(rgba8888):
	"""
	Convert an unmultiplied RGBA8888 buffer to a premultiplied ARGB32 buffer.
	"""
	if sys.byteorder == "little":
	argb32 = np.take(rgba8888, [2, 1, 0, 3], axis=2)
	rgb24 = argb32[..., :-1]
	alpha8 = argb32[..., -1:]
	else:
	argb32 = np.take(rgba8888, [3, 0, 1, 2], axis=2)
	alpha8 = argb32[..., :1]
	rgb24 = argb32[..., 1:]
	# Only bother premultiplying when the alpha channel is not fully opaque,
	# as the cost is not negligible. The unsafe cast is needed to do the
	# multiplication in-place in an integer buffer.
	if alpha8.min() != 0xff:
	np.multiply(rgb24, alpha8 / 0xff, out=rgb24, casting="unsafe")
	return argb32


	def _get_nonzero_slices(buf):
	"""
	Return the bounds of the nonzero region of a 2D array as a pair of slices.

	``buf[_get_nonzero_slices(buf)]`` is the smallest sub-rectangle in buf
	that encloses all non-zero entries in buf. If buf is fully zero, then
	``(slice(0, 0), slice(0, 0))`` is returned.
	"""
	x_nz, = buf.any(axis=0).nonzero()
	y_nz, = buf.any(axis=1).nonzero()
	if len(x_nz) and len(y_nz):
	l, r = x_nz[[0, -1]]
	b, t = y_nz[[0, -1]]
	return slice(b, t + 1), slice(l, r + 1)
	else:
	return slice(0, 0), slice(0, 0)


	def _pformat_subprocess(command):
	"""Pretty-format a subprocess command for printing/logging purposes."""
	return (command if isinstance(command, str)
	else " ".join(shlex.quote(os.fspath(arg)) for arg in command))


	def _check_and_log_subprocess(command, logger, **kwargs):
	"""
	Run command, returning its stdout output if it succeeds.

	If it fails (exits with nonzero return code), raise an exception whose text
	includes the failed command and captured stdout and stderr output.

	Regardless of the return code, the command is logged at DEBUG level on
	logger. In case of success, the output is likewise logged.
	"""
	logger.debug('%s', _pformat_subprocess(command))
	proc = subprocess.run(command, capture_output=True, **kwargs)
	if proc.returncode:
	stdout = proc.stdout
	if isinstance(stdout, bytes):
	stdout = stdout.decode()
	stderr = proc.stderr
	if isinstance(stderr, bytes):
	stderr = stderr.decode()
	raise RuntimeError(
	f"The command\n"
	f" {_pformat_subprocess(command)}\n"
	f"failed and generated the following output:\n"
	f"{stdout}\n"
	f"and the following error:\n"
	f"{stderr}")
	if proc.stdout:
	logger.debug("stdout:\n%s", proc.stdout)
	if proc.stderr:
	logger.debug("stderr:\n%s", proc.stderr)
	return proc.stdout


	def _setup_new_guiapp():
	"""
	Perform OS-dependent setup when Matplotlib creates a new GUI application.
	"""
	# Windows: If not explicit app user model id has been set yet (so we're not
	# already embedded), then set it to "matplotlib", so that taskbar icons are
	# correct.
	try:
	_c_internal_utils.Win32_GetCurrentProcessExplicitAppUserModelID()
	except OSError:
	_c_internal_utils.Win32_SetCurrentProcessExplicitAppUserModelID(
	"matplotlib")


	def _format_approx(number, precision):
	"""
	Format the number with at most the number of decimals given as precision.
	Remove trailing zeros and possibly the decimal point.
	"""
	return f'{number:.{precision}f}'.rstrip('0').rstrip('.') or '0'


	def _g_sig_digits(value, delta):
	"""
	Return the number of significant digits to %g-format value, assuming that
	it is known with an error of delta.
	"""
	# For inf or nan, the precision doesn't matter.
	if not math.isfinite(value):
	return 0
	if delta == 0:
	if value == 0:
	# if both value and delta are 0, np.spacing below returns 5e-324
	# which results in rather silly results
	return 3
	# delta = 0 may occur when trying to format values over a tiny range;
	# in that case, replace it by the distance to the closest float.
	delta = abs(np.spacing(value))
	# If e.g. value = 45.67 and delta = 0.02, then we want to round to 2 digits
	# after the decimal point (floor(log10(0.02)) = -2); 45.67 contributes 2
	# digits before the decimal point (floor(log10(45.67)) + 1 = 2): the total
	# is 4 significant digits. A value of 0 contributes 1 "digit" before the
	# decimal point.
	return max(
	0,
	(math.floor(math.log10(abs(value))) + 1 if value else 1)
	- math.floor(math.log10(delta)))


	def _unikey_or_keysym_to_mplkey(unikey, keysym):
	"""
	Convert a Unicode key or X keysym to a Matplotlib key name.

	The Unicode key is checked first; this avoids having to list most printable
	keysyms such as ``EuroSign``.
	"""
	# For non-printable characters, gtk3 passes "\0" whereas tk passes an "".
	if unikey and unikey.isprintable():
	return unikey
	key = keysym.lower()
	if key.startswith("kp_"): # keypad_x (including kp_enter).
	key = key[3:]
	if key.startswith("page_"): # page_{up,down}
	key = key.replace("page_", "page")
	if key.endswith(("_l", "_r")): # alt_l, ctrl_l, shift_l.
	key = key[:-2]
	if sys.platform == "darwin" and key == "meta":
	# meta should be reported as command on mac
	key = "cmd"
	key = {
	"return": "enter",
	"prior": "pageup", # Used by tk.
	"next": "pagedown", # Used by tk.
	}.get(key, key)
	return key


	@functools.cache
	def _make_class_factory(mixin_class, fmt, attr_name=None):
	"""
	Return a function that creates picklable classes inheriting from a mixin.

	After ::

	factory = _make_class_factory(FooMixin, fmt, attr_name)
	FooAxes = factory(Axes)

	``Foo`` is a class that inherits from ``FooMixin`` and ``Axes`` and **is
	picklable** (picklability is what differentiates this from a plain call to
	`type`). Its ``__name__`` is set to ``fmt.format(Axes.__name__)`` and the
	base class is stored in the ``attr_name`` attribute, if not None.

	Moreover, the return value of ``factory`` is memoized: calls with the same
	``Axes`` class always return the same subclass.
	"""

	@functools.cache
	def class_factory(axes_class):
	# if we have already wrapped this class, declare victory!
	if issubclass(axes_class, mixin_class):
	return axes_class

	# The parameter is named "axes_class" for backcompat but is really just
	# a base class; no axes semantics are used.
	base_class = axes_class

	class subcls(mixin_class, base_class):
	# Better approximation than __module__ = "matplotlib.cbook".
	__module__ = mixin_class.__module__

	def __reduce__(self):
	return (_picklable_class_constructor,
	(mixin_class, fmt, attr_name, base_class),
	self.__getstate__())

	subcls.__name__ = subcls.__qualname__ = fmt.format(base_class.__name__)
	if attr_name is not None:
	setattr(subcls, attr_name, base_class)
	return subcls

	class_factory.__module__ = mixin_class.__module__
	return class_factory


	def _picklable_class_constructor(mixin_class, fmt, attr_name, base_class):
	"""Internal helper for _make_class_factory."""
	factory = _make_class_factory(mixin_class, fmt, attr_name)
	cls = factory(base_class)
	return cls.__new__(cls)


	def _is_torch_array(x):
	"""Return whether x is a PyTorch Tensor."""
	try:
	# We're intentionally not attempting to import torch. If somebody
	# has created a torch array, torch should already be in sys.modules.
	tp = sys.modules.get("torch").Tensor
	except AttributeError:
	return False # Module not imported or a nonstandard module with no Tensor attr.
	return (isinstance(tp, type) # Just in case it's a very nonstandard module.
	and isinstance(x, tp))


	def _is_jax_array(x):
	"""Return whether x is a JAX Array."""
	try:
	# We're intentionally not attempting to import jax. If somebody
	# has created a jax array, jax should already be in sys.modules.
	tp = sys.modules.get("jax").Array
	except AttributeError:
	return False # Module not imported or a nonstandard module with no Array attr.
	return (isinstance(tp, type) # Just in case it's a very nonstandard module.
	and isinstance(x, tp))


	def _is_pandas_dataframe(x):
	"""Check if x is a Pandas DataFrame."""
	try:
	# We're intentionally not attempting to import Pandas. If somebody
	# has created a Pandas DataFrame, Pandas should already be in sys.modules.
	tp = sys.modules.get("pandas").DataFrame
	except AttributeError:
	return False # Module not imported or a nonstandard module with no Array attr.
	return (isinstance(tp, type) # Just in case it's a very nonstandard module.
	and isinstance(x, tp))


	def _is_tensorflow_array(x):
	"""Return whether x is a TensorFlow Tensor or Variable."""
	try:
	# We're intentionally not attempting to import TensorFlow. If somebody
	# has created a TensorFlow array, TensorFlow should already be in
	# sys.modules we use `is_tensor` to not depend on the class structure
	# of TensorFlow arrays, as `tf.Variables` are not instances of
	# `tf.Tensor` (they both convert the same way).
	is_tensor = sys.modules.get("tensorflow").is_tensor
	except AttributeError:
	return False
	try:
	return is_tensor(x)
	except Exception:
	return False # Just in case it's a very nonstandard module.


	def _unpack_to_numpy(x):
	"""Internal helper to extract data from e.g. pandas and xarray objects."""
	if isinstance(x, np.ndarray):
	# If numpy, return directly
	return x
	if hasattr(x, 'to_numpy'):
	# Assume that any to_numpy() method actually returns a numpy array
	return x.to_numpy()
	if hasattr(x, 'values'):
	xtmp = x.values
	# For example a dict has a 'values' attribute, but it is not a property
	# so in this case we do not want to return a function
	if isinstance(xtmp, np.ndarray):
	return xtmp
	if _is_torch_array(x) or _is_jax_array(x) or _is_tensorflow_array(x):
	# using np.asarray() instead of explicitly __array__(), as the latter is
	# only _one_ of many methods, and it's the last resort, see also
	# https://numpy.org/devdocs/user/basics.interoperability.html#using-arbitrary-objects-in-numpy
	# therefore, let arrays do better if they can
	xtmp = np.asarray(x)

	# In case np.asarray method does not return a numpy array in future
	if isinstance(xtmp, np.ndarray):
	return xtmp
	return x


	def _auto_format_str(fmt, value):
	"""
	Apply value to the format string fmt.

	This works both with unnamed %-style formatting and
	unnamed {}-style formatting. %-style formatting has priority.
	If fmt is %-style formattable that will be used. Otherwise,
	{}-formatting is applied. Strings without formatting placeholders
	are passed through as is.

	Examples
	--------
	>>> _auto_format_str('%.2f m', 0.2)
	'0.20 m'
	>>> _auto_format_str('{} m', 0.2)
	'0.2 m'
	>>> _auto_format_str('const', 0.2)
	'const'
	>>> _auto_format_str('%d or {}', 0.2)
	'0 or {}'
	"""
	try:
	return fmt % (value,)
	except (TypeError, ValueError):
	return fmt.format(value)

Xet Storage Details

Size:: 80 kB
Xet hash:: 59224676e89b9518c440b85127a906fdb7c05b46aad4350d59c09e9e3d459ae5

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