text: """
  A collection of utility functions and classes.  Originally, many
  (but not all) were from the Python Cookbook -- hence the name cbook.
  
  This module is safe to import from anywhere within Matplotlib;
  it imports Matplotlib only at runtime.
  """
  
  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 warnings
  import weakref
  
  import numpy as np
  
  import matplotlib
  from matplotlib import _api, _c_internal_utils
  from matplotlib._api.deprecation import (
      MatplotlibDeprecationWarning, mplDeprecation)
  
  
  @_api.deprecated("3.4")
  def deprecated(*args, **kwargs):
      return _api.deprecated(*args, **kwargs)
  
  
  @_api.deprecated("3.4")
  def warn_deprecated(*args, **kwargs):
      _api.warn_deprecated(*args, **kwargs)
  
  
  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
      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 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.
      """
  
      # 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):
          self.exception_handler = exception_handler
          self.callbacks = {}
          self._cid_gen = itertools.count()
          self._func_cid_map = {}
          # 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,
          }
  
      def __setstate__(self, state):
          vars(self).update(state)
          self.callbacks = {
              s: {cid: _weak_or_strong_ref(func, self._remove_proxy)
                  for cid, func in d.items()}
              for s, d in self.callbacks.items()}
          self._func_cid_map = {
              s: {proxy: cid for cid, proxy in d.items()}
              for s, d in self.callbacks.items()}
  
      @_api.rename_parameter("3.4", "s", "signal")
      def connect(self, signal, func):
          """Register *func* to be called when signal *signal* is generated."""
          if signal == "units finalize":
              _api.warn_deprecated(
                  "3.5", name=signal, obj_type="signal", alternative="units")
          self._func_cid_map.setdefault(signal, {})
          proxy = _weak_or_strong_ref(func, self._remove_proxy)
          if proxy in self._func_cid_map[signal]:
              return self._func_cid_map[signal][proxy]
          cid = next(self._cid_gen)
          self._func_cid_map[signal][proxy] = cid
          self.callbacks.setdefault(signal, {})
          self.callbacks[signal][cid] = proxy
          return cid
  
      # Keep a reference to sys.is_finalizing, as sys may have been cleared out
      # at that point.
      def _remove_proxy(self, proxy, *, _is_finalizing=sys.is_finalizing):
          if _is_finalizing():
              # Weakrefs can't be properly torn down at that point anymore.
              return
          for signal, proxy_to_cid in list(self._func_cid_map.items()):
              cid = proxy_to_cid.pop(proxy, None)
              if cid is not None:
                  del self.callbacks[signal][cid]
                  self._pickled_cids.discard(cid)
                  break
          else:
              # Not found
              return
          # Clean up empty dicts
          if len(self.callbacks[signal]) == 0:
              del self.callbacks[signal]
              del self._func_cid_map[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)
          # Clean up callbacks
          for signal, cid_to_proxy in list(self.callbacks.items()):
              proxy = cid_to_proxy.pop(cid, None)
              if proxy is not None:
                  break
          else:
              # Not found
              return
  
          proxy_to_cid = self._func_cid_map[signal]
          for current_proxy, current_cid in list(proxy_to_cid.items()):
              if current_cid == cid:
                  assert proxy is current_proxy
                  del proxy_to_cid[current_proxy]
          # Clean up empty dicts
          if len(self.callbacks[signal]) == 0:
              del self.callbacks[signal]
              del self._func_cid_map[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``.
          """
          for cid, ref in list(self.callbacks.get(s, {}).items()):
              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=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 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, *, np_load=False):
      """
      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, *asfileobj* is True, and *np_load* is
      True, the file is loaded with `numpy.load`.  *np_load* currently defaults
      to False but will default to True in a future release.
      """
      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']:
              if np_load:
                  return np.load(path)
              else:
                  _api.warn_deprecated(
                      "3.3", message="In a future release, get_sample_data "
                      "will automatically load numpy arrays.  Set np_load to "
                      "True to get the array and suppress this warning.  Set "
                      "asfileobj to False to get the path to the data file and "
                      "suppress this warning.")
                  return path.open('rb')
          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/
      and Recipe 1.12 in cookbook
      """
      for item in seq:
          if scalarp(item) or item is None:
              yield item
          else:
              yield from flatten(item, scalarp)
  
  
  class maxdict(dict):
      """
      A dictionary with a maximum size.
  
      Notes
      -----
      This doesn't override all the relevant methods to constrain the size,
      just ``__setitem__``, so use with caution.
      """
  
      def __init__(self, maxsize):
          super().__init__()
          self.maxsize = maxsize
  
      def __setitem__(self, k, v):
          super().__setitem__(k, v)
          while len(self) >= self.maxsize:
              del self[next(iter(self))]
  
  
  class Stack:
      """
      Stack of elements with a movable cursor.
  
      Mimics home/back/forward in a web browser.
      """
  
      def __init__(self, default=None):
          self.clear()
          self._default = default
  
      def __call__(self):
          """Return the current element, or None."""
          if not self._elements:
              return self._default
          else:
              return self._elements[self._pos]
  
      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."""
          if self._pos > 0:
              self._pos -= 1
          return self()
  
      def push(self, o):
          """
          Push *o* to the stack at current position.  Discard all later elements.
  
          *o* is returned.
          """
          self._elements = self._elements[:self._pos + 1] + [o]
          self._pos = len(self._elements) - 1
          return self()
  
      def home(self):
          """
          Push the first element onto the top of the stack.
  
          The first element is returned.
          """
          if not self._elements:
              return
          self.push(self._elements[0])
          return self()
  
      def empty(self):
          """Return whether the stack is empty."""
          return len(self._elements) == 0
  
      def clear(self):
          """Empty the stack."""
          self._pos = -1
          self._elements = []
  
      def bubble(self, o):
          """
          Raise all references of *o* to the top of the stack, and return it.
  
          Raises
          ------
          ValueError
              If *o* is not in the stack.
          """
          if o not in self._elements:
              raise ValueError('Given element not contained in the stack')
          old_elements = self._elements.copy()
          self.clear()
          top_elements = []
          for elem in old_elements:
              if elem == o:
                  top_elements.append(elem)
              else:
                  self.push(elem)
          for _ in top_elements:
              self.push(o)
          return o
  
      def remove(self, o):
          """
          Remove *o* from the stack.
  
          Raises
          ------
          ValueError
              If *o* is not in the stack.
          """
          if o not in self._elements:
              raise ValueError('Given element not contained in the stack')
          old_elements = self._elements.copy()
          self.clear()
          for elem in old_elements:
              if elem != o:
                  self.push(elem)
  
  
  @_api.deprecated("3.5", alternative="psutil.virtual_memory")
  def report_memory(i=0):  # argument may go away
      """Return the memory consumed by the process."""
      def call(command, os_name):
          try:
              return subprocess.check_output(command)
          except subprocess.CalledProcessError as err:
              raise NotImplementedError(
                  "report_memory works on %s only if "
                  "the '%s' program is found" % (os_name, command[0])
              ) from err
  
      pid = os.getpid()
      if sys.platform == 'sunos5':
          lines = call(['ps', '-p', '%d' % pid, '-o', 'osz'], 'Sun OS')
          mem = int(lines[-1].strip())
      elif sys.platform == 'linux':
          lines = call(['ps', '-p', '%d' % pid, '-o', 'rss,sz'], 'Linux')
          mem = int(lines[1].split()[1])
      elif sys.platform == 'darwin':
          lines = call(['ps', '-p', '%d' % pid, '-o', 'rss,vsz'], 'Mac OS')
          mem = int(lines[1].split()[0])
      elif sys.platform == 'win32':
          lines = call(["tasklist", "/nh", "/fi", "pid eq %d" % pid], 'Windows')
          mem = int(lines.strip().split()[-2].replace(',', ''))
      else:
          raise NotImplementedError(
              "We don't have a memory monitor for %s" % sys.platform)
      return mem
  
  
  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.
          x = x.byteswap(inplace=copy).newbyteorder('N')  # Swap to native order.
      try:
          xm = np.ma.masked_invalid(x, copy=False)
          xm.shrink_mask()
      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("[{!r}]".format(key))
                          break
                      if key is next:
                          outstream.write("[key] = {!r}".format(val))
                          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.ref(x): [weakref.ref(x)] for x in init}
  
      def __contains__(self, item):
          return weakref.ref(item) in self._mapping
  
      def clean(self):
          """Clean dead weak references from the dictionary."""
          mapping = self._mapping
          to_drop = [key for key in mapping if key() is None]
          for key in to_drop:
              val = mapping.pop(key)
              val.remove(key)
  
      def join(self, a, *args):
          """
          Join given arguments into the same set.  Accepts one or more arguments.
          """
          mapping = self._mapping
          set_a = mapping.setdefault(weakref.ref(a), [weakref.ref(a)])
  
          for arg in args:
              set_b = mapping.get(weakref.ref(arg), [weakref.ref(arg)])
              if set_b is not set_a:
                  if len(set_b) > len(set_a):
                      set_a, set_b = set_b, set_a
                  set_a.extend(set_b)
                  for elem in set_b:
                      mapping[elem] = set_a
  
          self.clean()
  
      def joined(self, a, b):
          """Return whether *a* and *b* are members of the same set."""
          self.clean()
          return (self._mapping.get(weakref.ref(a), object())
                  is self._mapping.get(weakref.ref(b)))
  
      def remove(self, a):
          self.clean()
          set_a = self._mapping.pop(weakref.ref(a), None)
          if set_a:
              set_a.remove(weakref.ref(a))
  
      def __iter__(self):
          """
          Iterate over each of the disjoint sets as a list.
  
          The iterator is invalid if interleaved with calls to join().
          """
          self.clean()
          unique_groups = {id(group): group for group in self._mapping.values()}
          for group in unique_groups.values():
              yield [x() for x in group]
  
      def get_siblings(self, a):
          """Return all of the items joined with *a*, including itself."""
          self.clean()
          siblings = self._mapping.get(weakref.ref(a), [weakref.ref(a)])
          return [x() for x in siblings]
  
  
  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 (np.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 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 : array-like, 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)
          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['cilo'] = np.nan
              stats['cihi'] = np.nan
              stats['whislo'] = np.nan
              stats['whishi'] = np.nan
              stats['med'] = np.nan
              continue
  
          # up-convert to an array, just to be safe
          x = np.asarray(x)
  
          # 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."""
      if not hasattr(x, 'shape') or len(x.shape) < 1:
          return np.atleast_1d(x)
      else:
          try:
              # work around
              # https://github.com/pandas-dev/pandas/issues/27775 which
              # means the shape of multi-dimensional slicing is not as
              # expected.  That this ever worked was an unintentional
              # quirk of pandas and will raise an exception in the
              # future.  This slicing warns in pandas >= 1.0rc0 via
              # https://github.com/pandas-dev/pandas/pull/30588
              #
              # < 1.0rc0 : x[:, None].ndim == 1, no warning, custom type
              # >= 1.0rc1 : x[:, None].ndim == 2, warns, numpy array
              # future : x[:, None] -> raises
              #
              # This code should correctly identify and coerce to a
              # numpy array all pandas versions.
              with warnings.catch_warnings(record=True) as w:
                  warnings.filterwarnings(
                      "always",
                      category=Warning,
                      message='Support for multi-dimensional indexing')
  
                  ndim = x[:, None].ndim
                  # we have definitely hit a pandas index or series object
                  # cast to a numpy array.
                  if len(w) > 0:
                      return np.asanyarray(x)
              # We have likely hit a pandas object, or at least
              # something where 2D slicing does not result in a 2D
              # object.
              if ndim < 2:
                  return np.atleast_1d(x)
              return x
          # In pandas 1.1.0, multidimensional indexing leads to an
          # AssertionError for some Series objects, but should be
          # IndexError as described in
          # https://github.com/pandas-dev/pandas/issues/35527
          except (AssertionError, IndexError, TypeError):
              return np.atleast_1d(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 if we have a values or to_numpy method.
      try:
          X = X.to_numpy()
      except AttributeError:
          try:
              if isinstance(X.values, np.ndarray):
                  X = X.values
          except AttributeError:
              pass
  
      # Iterate over columns for ndarrays.
      if isinstance(X, np.ndarray):
          X = X.T
  
          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 (isinstance(xi, collections.abc.Iterable) and
                  not isinstance(xi, str)):
              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 has 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.values, y.values
      except AttributeError:
          pass
      try:
          y = _check_1d(y)
      except (np.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 an 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 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 = dict()
      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 _define_aliases(alias_d, cls=None):
      """
      Class decorator for defining property aliases.
  
      Use as ::
  
          @cbook._define_aliases({"property": ["alias", ...], ...})
          class C: ...
  
      For each property, if the corresponding ``get_property`` is defined in the
      class so far, an alias named ``get_alias`` will be defined; the same will
      be done for setters.  If neither the getter nor the setter exists, an
      exception will be raised.
  
      The alias map is stored as the ``_alias_map`` attribute on the class and
      can be used by `.normalize_kwargs` (which assumes that higher priority
      aliases come last).
      """
      if cls is None:  # Return the actual class decorator.
          return functools.partial(_define_aliases, alias_d)
  
      def make_alias(name):  # Enforce a closure over *name*.
          @functools.wraps(getattr(cls, name))
          def method(self, *args, **kwargs):
              return getattr(self, name)(*args, **kwargs)
          return method
  
      for prop, aliases in alias_d.items():
          exists = False
          for prefix in ["get_", "set_"]:
              if prefix + prop in vars(cls):
                  exists = True
                  for alias in aliases:
                      method = make_alias(prefix + prop)
                      method.__name__ = prefix + alias
                      method.__doc__ = "Alias for `{}`.".format(prefix + prop)
                      setattr(cls, prefix + alias, method)
          if not exists:
              raise ValueError(
                  "Neither getter nor setter exists for {!r}".format(prop))
  
      def get_aliased_and_aliases(d):
          return {*d, *(alias for aliases in d.values() for alias in aliases)}
  
      preexisting_aliases = getattr(cls, "_alias_map", {})
      conflicting = (get_aliased_and_aliases(preexisting_aliases)
                     & get_aliased_and_aliases(alias_d))
      if conflicting:
          # Need to decide on conflict resolution policy.
          raise NotImplementedError(
              f"Parent class already defines conflicting aliases: {conflicting}")
      cls._alias_map = {**preexisting_aliases, **alias_d}
      return cls
  
  
  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 PyQt5 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, stdout=subprocess.PIPE, stderr=subprocess.PIPE, **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 _backend_module_name(name):
      """
      Convert a backend name (either a standard backend -- "Agg", "TkAgg", ... --
      or a custom backend -- "module://...") to the corresponding module name).
      """
      return (name[9:] if name.startswith("module://")
              else "matplotlib.backends.backend_{}".format(name.lower()))
  
  
  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*.
      """
      if delta == 0:
          # 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 = 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.
      # For inf or nan, the precision doesn't matter.
      return max(
          0,
          (math.floor(math.log10(abs(value))) + 1 if value else 1)
          - math.floor(math.log10(delta))) if math.isfinite(value) else 0
  
  
  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]
      key = {
          "return": "enter",
          "prior": "pageup",  # Used by tk.
          "next": "pagedown",  # Used by tk.
      }.get(key, key)
      return key
  
  
  @functools.lru_cache(None)
  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.lru_cache(None)
      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)
  