repo_description: matplotlib: plotting with Python
repo_topics: data-science data-visualization gtk matplotlib plotting python qt tk wx
code: """
  `matplotlib.figure` implements the following classes:
  
  `Figure`
      Top level `~matplotlib.artist.Artist`, which holds all plot elements.
      Many methods are implemented in `FigureBase`.
  
  `SubFigure`
      A logical figure inside a figure, usually added to a figure (or parent `SubFigure`)
      with `Figure.add_subfigure` or `Figure.subfigures` methods.
  
  Figures are typically created using pyplot methods `~.pyplot.figure`,
  `~.pyplot.subplots`, and `~.pyplot.subplot_mosaic`.
  
  .. plot::
      :include-source:
  
      fig, ax = plt.subplots(figsize=(2, 2), facecolor='lightskyblue',
                             layout='constrained')
      fig.suptitle('Figure')
      ax.set_title('Axes', loc='left', fontstyle='oblique', fontsize='medium')
  
  Some situations call for directly instantiating a `~.figure.Figure` class,
  usually inside an application of some sort (see :ref:`user_interfaces` for a
  list of examples) .  More information about Figures can be found at
  :ref:`figure-intro`.
  """
  
  from contextlib import ExitStack
  import inspect
  import itertools
  import functools
  import logging
  from numbers import Integral
  import threading
  
  import numpy as np
  
  import matplotlib as mpl
  from matplotlib import _blocking_input, backend_bases, _docstring, projections
  from matplotlib.artist import (
      Artist, allow_rasterization, _finalize_rasterization)
  from matplotlib.backend_bases import (
      DrawEvent, FigureCanvasBase, NonGuiException, MouseButton, _get_renderer)
  import matplotlib._api as _api
  import matplotlib.cbook as cbook
  import matplotlib.colorbar as cbar
  import matplotlib.image as mimage
  
  from matplotlib.axes import Axes
  from matplotlib.gridspec import GridSpec, SubplotParams
  from matplotlib.layout_engine import (
      ConstrainedLayoutEngine, TightLayoutEngine, LayoutEngine,
      PlaceHolderLayoutEngine
  )
  import matplotlib.legend as mlegend
  from matplotlib.patches import Rectangle
  from matplotlib.text import Text
  from matplotlib.transforms import (Affine2D, Bbox, BboxTransformTo,
                                     TransformedBbox)
  
  _log = logging.getLogger(__name__)
  
  
  def _stale_figure_callback(self, val):
      if (fig := self.get_figure(root=False)) is not None:
          fig.stale = val
  
  
  class _AxesStack:
      """
      Helper class to track Axes in a figure.
  
      Axes are tracked both in the order in which they have been added
      (``self._axes`` insertion/iteration order) and in the separate "gca" stack
      (which is the index to which they map in the ``self._axes`` dict).
      """
  
      def __init__(self):
          self._axes = {}  # Mapping of Axes to "gca" order.
          self._counter = itertools.count()
  
      def as_list(self):
          """List the Axes that have been added to the figure."""
          return [*self._axes]  # This relies on dict preserving order.
  
      def remove(self, a):
          """Remove the Axes from the stack."""
          self._axes.pop(a)
  
      def bubble(self, a):
          """Move an Axes, which must already exist in the stack, to the top."""
          if a not in self._axes:
              raise ValueError("Axes has not been added yet")
          self._axes[a] = next(self._counter)
  
      def add(self, a):
          """Add an Axes to the stack, ignoring it if already present."""
          if a not in self._axes:
              self._axes[a] = next(self._counter)
  
      def current(self):
          """Return the active Axes, or None if the stack is empty."""
          return max(self._axes, key=self._axes.__getitem__, default=None)
  
      def __getstate__(self):
          return {
              **vars(self),
              "_counter": max(self._axes.values(), default=0)
          }
  
      def __setstate__(self, state):
          next_counter = state.pop('_counter')
          vars(self).update(state)
          self._counter = itertools.count(next_counter)
  
  
  class FigureBase(Artist):
      """
      Base class for `.Figure` and `.SubFigure` containing the methods that add
      artists to the figure or subfigure, create Axes, etc.
      """
      def __init__(self, **kwargs):
          super().__init__()
          # remove the non-figure artist _axes property
          # as it makes no sense for a figure to be _in_ an Axes
          # this is used by the property methods in the artist base class
          # which are over-ridden in this class
          del self._axes
  
          self._suptitle = None
          self._supxlabel = None
          self._supylabel = None
  
          # groupers to keep track of x, y labels and title we want to align.
          # see self.align_xlabels, self.align_ylabels,
          # self.align_titles, and axis._get_tick_boxes_siblings
          self._align_label_groups = {
              "x": cbook.Grouper(),
              "y": cbook.Grouper(),
              "title": cbook.Grouper()
          }
  
          self._localaxes = []  # track all Axes
          self.artists = []
          self.lines = []
          self.patches = []
          self.texts = []
          self.images = []
          self.legends = []
          self.subfigs = []
          self.stale = True
          self.suppressComposite = None
          self.set(**kwargs)
  
      def _get_draw_artists(self, renderer):
          """Also runs apply_aspect"""
          artists = self.get_children()
  
          artists.remove(self.patch)
          artists = sorted(
              (artist for artist in artists if not artist.get_animated()),
              key=lambda artist: artist.get_zorder())
          for ax in self._localaxes:
              locator = ax.get_axes_locator()
              ax.apply_aspect(locator(ax, renderer) if locator else None)
  
              for child in ax.get_children():
                  if hasattr(child, 'apply_aspect'):
                      locator = child.get_axes_locator()
                      child.apply_aspect(
                          locator(child, renderer) if locator else None)
          return artists
  
      def autofmt_xdate(
              self, bottom=0.2, rotation=30, ha='right', which='major'):
          """
          Date ticklabels often overlap, so it is useful to rotate them
          and right align them.  Also, a common use case is a number of
          subplots with shared x-axis where the x-axis is date data.  The
          ticklabels are often long, and it helps to rotate them on the
          bottom subplot and turn them off on other subplots, as well as
          turn off xlabels.
  
          Parameters
          ----------
          bottom : float, default: 0.2
              The bottom of the subplots for `subplots_adjust`.
          rotation : float, default: 30 degrees
              The rotation angle of the xtick labels in degrees.
          ha : {'left', 'center', 'right'}, default: 'right'
              The horizontal alignment of the xticklabels.
          which : {'major', 'minor', 'both'}, default: 'major'
              Selects which ticklabels to rotate.
          """
          _api.check_in_list(['major', 'minor', 'both'], which=which)
          axes = [ax for ax in self.axes if ax._label != '<colorbar>']
          allsubplots = all(ax.get_subplotspec() for ax in axes)
          if len(axes) == 1:
              for label in self.axes[0].get_xticklabels(which=which):
                  label.set_ha(ha)
                  label.set_rotation(rotation)
          else:
              if allsubplots:
                  for ax in axes:
                      if ax.get_subplotspec().is_last_row():
                          for label in ax.get_xticklabels(which=which):
                              label.set_ha(ha)
                              label.set_rotation(rotation)
                      else:
                          for label in ax.get_xticklabels(which=which):
                              label.set_visible(False)
                          ax.set_xlabel('')
  
          engine = self.get_layout_engine()
          if allsubplots and (engine is None or engine.adjust_compatible):
              self.subplots_adjust(bottom=bottom)
          self.stale = True
  
      def get_children(self):
          """Get a list of artists contained in the figure."""
          return [self.patch,
                  *self.artists,
                  *self._localaxes,
                  *self.lines,
                  *self.patches,
                  *self.texts,
                  *self.images,
                  *self.legends,
                  *self.subfigs]
  
      def get_figure(self, root=None):
          """
          Return the `.Figure` or `.SubFigure` instance the (Sub)Figure belongs to.
  
          Parameters
          ----------
          root : bool, default=True
              If False, return the (Sub)Figure this artist is on.  If True,
              return the root Figure for a nested tree of SubFigures.
  
              .. deprecated:: 3.10
  
                  From version 3.12 *root* will default to False.
          """
          if self._root_figure is self:
              # Top level Figure
              return self
  
          if self._parent is self._root_figure:
              # Return early to prevent the deprecation warning when *root* does not
              # matter
              return self._parent
  
          if root is None:
              # When deprecation expires, consider removing the docstring and just
              # inheriting the one from Artist.
              message = ('From Matplotlib 3.12 SubFigure.get_figure will by default '
                         'return the direct parent figure, which may be a SubFigure. '
                         'To suppress this warning, pass the root parameter.  Pass '
                         '`True` to maintain the old behavior and `False` to opt-in to '
                         'the future behavior.')
              _api.warn_deprecated('3.10', message=message)
              root = True
  
          if root:
              return self._root_figure
  
          return self._parent
  
      def set_figure(self, fig):
          """
          .. deprecated:: 3.10
              Currently this method will raise an exception if *fig* is anything other
              than the root `.Figure` this (Sub)Figure is on.  In future it will always
              raise an exception.
          """
          no_switch = ("The parent and root figures of a (Sub)Figure are set at "
                       "instantiation and cannot be changed.")
          if fig is self._root_figure:
              _api.warn_deprecated(
                  "3.10",
                  message=(f"{no_switch} From Matplotlib 3.12 this operation will raise "
                           "an exception."))
              return
  
          raise ValueError(no_switch)
  
      figure = property(functools.partial(get_figure, root=True), set_figure,
                        doc=("The root `Figure`.  To get the parent of a `SubFigure`, "
                             "use the `get_figure` method."))
  
      def contains(self, mouseevent):
          """
          Test whether the mouse event occurred on the figure.
  
          Returns
          -------
              bool, {}
          """
          if self._different_canvas(mouseevent):
              return False, {}
          inside = self.bbox.contains(mouseevent.x, mouseevent.y)
          return inside, {}
  
      def get_window_extent(self, renderer=None):
          # docstring inherited
          return self.bbox
  
      def _suplabels(self, t, info, **kwargs):
          """
          Add a centered %(name)s to the figure.
  
          Parameters
          ----------
          t : str
              The %(name)s text.
          x : float, default: %(x0)s
              The x location of the text in figure coordinates.
          y : float, default: %(y0)s
              The y location of the text in figure coordinates.
          horizontalalignment, ha : {'center', 'left', 'right'}, default: %(ha)s
              The horizontal alignment of the text relative to (*x*, *y*).
          verticalalignment, va : {'top', 'center', 'bottom', 'baseline'}, \
  default: %(va)s
              The vertical alignment of the text relative to (*x*, *y*).
          fontsize, size : default: :rc:`figure.%(rc)ssize`
              The font size of the text. See `.Text.set_size` for possible
              values.
          fontweight, weight : default: :rc:`figure.%(rc)sweight`
              The font weight of the text. See `.Text.set_weight` for possible
              values.
  
          Returns
          -------
          text
              The `.Text` instance of the %(name)s.
  
          Other Parameters
          ----------------
          fontproperties : None or dict, optional
              A dict of font properties. If *fontproperties* is given the
              default values for font size and weight are taken from the
              `.FontProperties` defaults. :rc:`figure.%(rc)ssize` and
              :rc:`figure.%(rc)sweight` are ignored in this case.
  
          **kwargs
              Additional kwargs are `matplotlib.text.Text` properties.
          """
  
          x = kwargs.pop('x', None)
          y = kwargs.pop('y', None)
          if info['name'] in ['_supxlabel', '_suptitle']:
              autopos = y is None
          elif info['name'] == '_supylabel':
              autopos = x is None
          if x is None:
              x = info['x0']
          if y is None:
              y = info['y0']
  
          kwargs = cbook.normalize_kwargs(kwargs, Text)
          kwargs.setdefault('horizontalalignment', info['ha'])
          kwargs.setdefault('verticalalignment', info['va'])
          kwargs.setdefault('rotation', info['rotation'])
  
          if 'fontproperties' not in kwargs:
              kwargs.setdefault('fontsize', mpl.rcParams[info['size']])
              kwargs.setdefault('fontweight', mpl.rcParams[info['weight']])
  
          suplab = getattr(self, info['name'])
          if suplab is not None:
              suplab.set_text(t)
              suplab.set_position((x, y))
              suplab.set(**kwargs)
          else:
              suplab = self.text(x, y, t, **kwargs)
              setattr(self, info['name'], suplab)
              suplab._remove_method = functools.partial(self._remove_suplabel,
                                                        name=info['name'])
  
          suplab._autopos = autopos
          self.stale = True
          return suplab
  
      def _remove_suplabel(self, label, name):
          self.texts.remove(label)
          setattr(self, name, None)
  
      @_docstring.Substitution(x0=0.5, y0=0.98, name='super title', ha='center',
                               va='top', rc='title')
      @_docstring.copy(_suplabels)
      def suptitle(self, t, **kwargs):
          # docstring from _suplabels...
          info = {'name': '_suptitle', 'x0': 0.5, 'y0': 0.98,
                  'ha': 'center', 'va': 'top', 'rotation': 0,
                  'size': 'figure.titlesize', 'weight': 'figure.titleweight'}
          return self._suplabels(t, info, **kwargs)
  
      def get_suptitle(self):
          """Return the suptitle as string or an empty string if not set."""
          text_obj = self._suptitle
          return "" if text_obj is None else text_obj.get_text()
  
      @_docstring.Substitution(x0=0.5, y0=0.01, name='super xlabel', ha='center',
                               va='bottom', rc='label')
      @_docstring.copy(_suplabels)
      def supxlabel(self, t, **kwargs):
          # docstring from _suplabels...
          info = {'name': '_supxlabel', 'x0': 0.5, 'y0': 0.01,
                  'ha': 'center', 'va': 'bottom', 'rotation': 0,
                  'size': 'figure.labelsize', 'weight': 'figure.labelweight'}
          return self._suplabels(t, info, **kwargs)
  
      def get_supxlabel(self):
          """Return the supxlabel as string or an empty string if not set."""
          text_obj = self._supxlabel
          return "" if text_obj is None else text_obj.get_text()
  
      @_docstring.Substitution(x0=0.02, y0=0.5, name='super ylabel', ha='left',
                               va='center', rc='label')
      @_docstring.copy(_suplabels)
      def supylabel(self, t, **kwargs):
          # docstring from _suplabels...
          info = {'name': '_supylabel', 'x0': 0.02, 'y0': 0.5,
                  'ha': 'left', 'va': 'center', 'rotation': 'vertical',
                  'rotation_mode': 'anchor', 'size': 'figure.labelsize',
                  'weight': 'figure.labelweight'}
          return self._suplabels(t, info, **kwargs)
  
      def get_supylabel(self):
          """Return the supylabel as string or an empty string if not set."""
          text_obj = self._supylabel
          return "" if text_obj is None else text_obj.get_text()
  
      def get_edgecolor(self):
          """Get the edge color of the Figure rectangle."""
          return self.patch.get_edgecolor()
  
      def get_facecolor(self):
          """Get the face color of the Figure rectangle."""
          return self.patch.get_facecolor()
  
      def get_frameon(self):
          """
          Return the figure's background patch visibility, i.e.
          whether the figure background will be drawn. Equivalent to
          ``Figure.patch.get_visible()``.
          """
          return self.patch.get_visible()
  
      def set_linewidth(self, linewidth):
          """
          Set the line width of the Figure rectangle.
  
          Parameters
          ----------
          linewidth : number
          """
          self.patch.set_linewidth(linewidth)
  
      def get_linewidth(self):
          """
          Get the line width of the Figure rectangle.
          """
          return self.patch.get_linewidth()
  
      def set_edgecolor(self, color):
          """
          Set the edge color of the Figure rectangle.
  
          Parameters
          ----------
          color : :mpltype:`color`
          """
          self.patch.set_edgecolor(color)
  
      def set_facecolor(self, color):
          """
          Set the face color of the Figure rectangle.
  
          Parameters
          ----------
          color : :mpltype:`color`
          """
          self.patch.set_facecolor(color)
  
      def set_frameon(self, b):
          """
          Set the figure's background patch visibility, i.e.
          whether the figure background will be drawn. Equivalent to
          ``Figure.patch.set_visible()``.
  
          Parameters
          ----------
          b : bool
          """
          self.patch.set_visible(b)
          self.stale = True
  
      frameon = property(get_frameon, set_frameon)
  
      def add_artist(self, artist, clip=False):
          """
          Add an `.Artist` to the figure.
  
          Usually artists are added to `~.axes.Axes` objects using
          `.Axes.add_artist`; this method can be used in the rare cases where
          one needs to add artists directly to the figure instead.
  
          Parameters
          ----------
          artist : `~matplotlib.artist.Artist`
              The artist to add to the figure. If the added artist has no
              transform previously set, its transform will be set to
              ``figure.transSubfigure``.
          clip : bool, default: False
              Whether the added artist should be clipped by the figure patch.
  
          Returns
          -------
          `~matplotlib.artist.Artist`
              The added artist.
          """
          artist.set_figure(self)
          self.artists.append(artist)
          artist._remove_method = self.artists.remove
  
          if not artist.is_transform_set():
              artist.set_transform(self.transSubfigure)
  
          if clip and artist.get_clip_path() is None:
              artist.set_clip_path(self.patch)
  
          self.stale = True
          return artist
  
      @_docstring.interpd
      def add_axes(self, *args, **kwargs):
          """
          Add an `~.axes.Axes` to the figure.
  
          Call signatures::
  
              add_axes(rect, projection=None, polar=False, **kwargs)
              add_axes(ax)
  
          Parameters
          ----------
          rect : tuple (left, bottom, width, height)
              The dimensions (left, bottom, width, height) of the new
              `~.axes.Axes`. All quantities are in fractions of figure width and
              height.
  
          projection : {None, 'aitoff', 'hammer', 'lambert', 'mollweide', \
  'polar', 'rectilinear', str}, optional
              The projection type of the `~.axes.Axes`. *str* is the name of
              a custom projection, see `~matplotlib.projections`. The default
              None results in a 'rectilinear' projection.
  
          polar : bool, default: False
              If True, equivalent to projection='polar'.
  
          axes_class : subclass type of `~.axes.Axes`, optional
              The `.axes.Axes` subclass that is instantiated.  This parameter
              is incompatible with *projection* and *polar*.  See
              :ref:`axisartist_users-guide-index` for examples.
  
          sharex, sharey : `~matplotlib.axes.Axes`, optional
              Share the x or y `~matplotlib.axis` with sharex and/or sharey.
              The axis will have the same limits, ticks, and scale as the axis
              of the shared Axes.
  
          label : str
              A label for the returned Axes.
  
          Returns
          -------
          `~.axes.Axes`, or a subclass of `~.axes.Axes`
              The returned Axes class depends on the projection used. It is
              `~.axes.Axes` if rectilinear projection is used and
              `.projections.polar.PolarAxes` if polar projection is used.
  
          Other Parameters
          ----------------
          **kwargs
              This method also takes the keyword arguments for
              the returned Axes class. The keyword arguments for the
              rectilinear Axes class `~.axes.Axes` can be found in
              the following table but there might also be other keyword
              arguments if another projection is used, see the actual Axes
              class.
  
              %(Axes:kwdoc)s
  
          Notes
          -----
          In rare circumstances, `.add_axes` may be called with a single
          argument, an Axes instance already created in the present figure but
          not in the figure's list of Axes.
  
          See Also
          --------
          .Figure.add_subplot
          .pyplot.subplot
          .pyplot.axes
          .Figure.subplots
          .pyplot.subplots
  
          Examples
          --------
          Some simple examples::
  
              rect = l, b, w, h
              fig = plt.figure()
              fig.add_axes(rect)
              fig.add_axes(rect, frameon=False, facecolor='g')
              fig.add_axes(rect, polar=True)
              ax = fig.add_axes(rect, projection='polar')
              fig.delaxes(ax)
              fig.add_axes(ax)
          """
  
          if not len(args) and 'rect' not in kwargs:
              raise TypeError("add_axes() missing 1 required positional argument: 'rect'")
          elif 'rect' in kwargs:
              if len(args):
                  raise TypeError("add_axes() got multiple values for argument 'rect'")
              args = (kwargs.pop('rect'), )
          if len(args) != 1:
              raise _api.nargs_error("add_axes", 1, len(args))
  
          if isinstance(args[0], Axes):
              a, = args
              key = a._projection_init
              if a.get_figure(root=False) is not self:
                  raise ValueError(
                      "The Axes must have been created in the present figure")
          else:
              rect, = args
              if not np.isfinite(rect).all():
                  raise ValueError(f'all entries in rect must be finite not {rect}')
              projection_class, pkw = self._process_projection_requirements(**kwargs)
  
              # create the new Axes using the Axes class given
              a = projection_class(self, rect, **pkw)
              key = (projection_class, pkw)
  
          return self._add_axes_internal(a, key)
  
      @_docstring.interpd
      def add_subplot(self, *args, **kwargs):
          """
          Add an `~.axes.Axes` to the figure as part of a subplot arrangement.
  
          Call signatures::
  
             add_subplot(nrows, ncols, index, **kwargs)
             add_subplot(pos, **kwargs)
             add_subplot(ax)
             add_subplot()
  
          Parameters
          ----------
          *args : int, (int, int, *index*), or `.SubplotSpec`, default: (1, 1, 1)
              The position of the subplot described by one of
  
              - Three integers (*nrows*, *ncols*, *index*). The subplot will
                take the *index* position on a grid with *nrows* rows and
                *ncols* columns. *index* starts at 1 in the upper left corner
                and increases to the right.  *index* can also be a two-tuple
                specifying the (*first*, *last*) indices (1-based, and including
                *last*) of the subplot, e.g., ``fig.add_subplot(3, 1, (1, 2))``
                makes a subplot that spans the upper 2/3 of the figure.
              - A 3-digit integer. The digits are interpreted as if given
                separately as three single-digit integers, i.e.
                ``fig.add_subplot(235)`` is the same as
                ``fig.add_subplot(2, 3, 5)``. Note that this can only be used
                if there are no more than 9 subplots.
              - A `.SubplotSpec`.
  
              In rare circumstances, `.add_subplot` may be called with a single
              argument, a subplot Axes instance already created in the
              present figure but not in the figure's list of Axes.
  
          projection : {None, 'aitoff', 'hammer', 'lambert', 'mollweide', \
  'polar', 'rectilinear', str}, optional
              The projection type of the subplot (`~.axes.Axes`). *str* is the
              name of a custom projection, see `~matplotlib.projections`. The
              default None results in a 'rectilinear' projection.
  
          polar : bool, default: False
              If True, equivalent to projection='polar'.
  
          axes_class : subclass type of `~.axes.Axes`, optional
              The `.axes.Axes` subclass that is instantiated.  This parameter
              is incompatible with *projection* and *polar*.  See
              :ref:`axisartist_users-guide-index` for examples.
  
          sharex, sharey : `~matplotlib.axes.Axes`, optional
              Share the x or y `~matplotlib.axis` with sharex and/or sharey.
              The axis will have the same limits, ticks, and scale as the axis
              of the shared Axes.
  
          label : str
              A label for the returned Axes.
  
          Returns
          -------
          `~.axes.Axes`
  
              The Axes of the subplot. The returned Axes can actually be an
              instance of a subclass, such as `.projections.polar.PolarAxes` for
              polar projections.
  
          Other Parameters
          ----------------
          **kwargs
              This method also takes the keyword arguments for the returned Axes
              base class; except for the *figure* argument. The keyword arguments
              for the rectilinear base class `~.axes.Axes` can be found in
              the following table but there might also be other keyword
              arguments if another projection is used.
  
              %(Axes:kwdoc)s
  
          See Also
          --------
          .Figure.add_axes
          .pyplot.subplot
          .pyplot.axes
          .Figure.subplots
          .pyplot.subplots
  
          Examples
          --------
          ::
  
              fig = plt.figure()
  
              fig.add_subplot(231)
              ax1 = fig.add_subplot(2, 3, 1)  # equivalent but more general
  
              fig.add_subplot(232, frameon=False)  # subplot with no frame
              fig.add_subplot(233, projection='polar')  # polar subplot
              fig.add_subplot(234, sharex=ax1)  # subplot sharing x-axis with ax1
              fig.add_subplot(235, facecolor="red")  # red subplot
  
              ax1.remove()  # delete ax1 from the figure
              fig.add_subplot(ax1)  # add ax1 back to the figure
          """
          if 'figure' in kwargs:
              # Axes itself allows for a 'figure' kwarg, but since we want to
              # bind the created Axes to self, it is not allowed here.
              raise _api.kwarg_error("add_subplot", "figure")
  
          if (len(args) == 1
                  and isinstance(args[0], mpl.axes._base._AxesBase)
                  and args[0].get_subplotspec()):
              ax = args[0]
              key = ax._projection_init
              if ax.get_figure(root=False) is not self:
                  raise ValueError("The Axes must have been created in "
                                   "the present figure")
          else:
              if not args:
                  args = (1, 1, 1)
              # Normalize correct ijk values to (i, j, k) here so that
              # add_subplot(211) == add_subplot(2, 1, 1).  Invalid values will
              # trigger errors later (via SubplotSpec._from_subplot_args).
              if (len(args) == 1 and isinstance(args[0], Integral)
                      and 100 <= args[0] <= 999):
                  args = tuple(map(int, str(args[0])))
              projection_class, pkw = self._process_projection_requirements(**kwargs)
              ax = projection_class(self, *args, **pkw)
              key = (projection_class, pkw)
          return self._add_axes_internal(ax, key)
  
      def _add_axes_internal(self, ax, key):
          """Private helper for `add_axes` and `add_subplot`."""
          self._axstack.add(ax)
          if ax not in self._localaxes:
              self._localaxes.append(ax)
          self.sca(ax)
          ax._remove_method = self.delaxes
          # this is to support plt.subplot's re-selection logic
          ax._projection_init = key
          self.stale = True
          ax.stale_callback = _stale_figure_callback
          return ax
  
      def subplots(self, nrows=1, ncols=1, *, sharex=False, sharey=False,
                   squeeze=True, width_ratios=None, height_ratios=None,
                   subplot_kw=None, gridspec_kw=None):
          """
          Add a set of subplots to this figure.
  
          This utility wrapper makes it convenient to create common layouts of
          subplots in a single call.
  
          Parameters
          ----------
          nrows, ncols : int, default: 1
              Number of rows/columns of the subplot grid.
  
          sharex, sharey : bool or {'none', 'all', 'row', 'col'}, default: False
              Controls sharing of x-axis (*sharex*) or y-axis (*sharey*):
  
              - True or 'all': x- or y-axis will be shared among all subplots.
              - False or 'none': each subplot x- or y-axis will be independent.
              - 'row': each subplot row will share an x- or y-axis.
              - 'col': each subplot column will share an x- or y-axis.
  
              When subplots have a shared x-axis along a column, only the x tick
              labels of the bottom subplot are created. Similarly, when subplots
              have a shared y-axis along a row, only the y tick labels of the
              first column subplot are created. To later turn other subplots'
              ticklabels on, use `~matplotlib.axes.Axes.tick_params`.
  
              When subplots have a shared axis that has units, calling
              `.Axis.set_units` will update each axis with the new units.
  
              Note that it is not possible to unshare axes.
  
          squeeze : bool, default: True
              - If True, extra dimensions are squeezed out from the returned
                array of Axes:
  
                - if only one subplot is constructed (nrows=ncols=1), the
                  resulting single Axes object is returned as a scalar.
                - for Nx1 or 1xM subplots, the returned object is a 1D numpy
                  object array of Axes objects.
                - for NxM, subplots with N>1 and M>1 are returned as a 2D array.
  
              - If False, no squeezing at all is done: the returned Axes object
                is always a 2D array containing Axes instances, even if it ends
                up being 1x1.
  
          width_ratios : array-like of length *ncols*, optional
              Defines the relative widths of the columns. Each column gets a
              relative width of ``width_ratios[i] / sum(width_ratios)``.
              If not given, all columns will have the same width.  Equivalent
              to ``gridspec_kw={'width_ratios': [...]}``.
  
          height_ratios : array-like of length *nrows*, optional
              Defines the relative heights of the rows. Each row gets a
              relative height of ``height_ratios[i] / sum(height_ratios)``.
              If not given, all rows will have the same height. Equivalent
              to ``gridspec_kw={'height_ratios': [...]}``.
  
          subplot_kw : dict, optional
              Dict with keywords passed to the `.Figure.add_subplot` call used to
              create each subplot.
  
          gridspec_kw : dict, optional
              Dict with keywords passed to the
              `~matplotlib.gridspec.GridSpec` constructor used to create
              the grid the subplots are placed on.
  
          Returns
          -------
          `~.axes.Axes` or array of Axes
              Either a single `~matplotlib.axes.Axes` object or an array of Axes
              objects if more than one subplot was created. The dimensions of the
              resulting array can be controlled with the *squeeze* keyword, see
              above.
  
          See Also
          --------
          .pyplot.subplots
          .Figure.add_subplot
          .pyplot.subplot
  
          Examples
          --------
          ::
  
              # First create some toy data:
              x = np.linspace(0, 2*np.pi, 400)
              y = np.sin(x**2)
  
              # Create a figure
              fig = plt.figure()
  
              # Create a subplot
              ax = fig.subplots()
              ax.plot(x, y)
              ax.set_title('Simple plot')
  
              # Create two subplots and unpack the output array immediately
              ax1, ax2 = fig.subplots(1, 2, sharey=True)
              ax1.plot(x, y)
              ax1.set_title('Sharing Y axis')
              ax2.scatter(x, y)
  
              # Create four polar Axes and access them through the returned array
              axes = fig.subplots(2, 2, subplot_kw=dict(projection='polar'))
              axes[0, 0].plot(x, y)
              axes[1, 1].scatter(x, y)
  
              # Share an X-axis with each column of subplots
              fig.subplots(2, 2, sharex='col')
  
              # Share a Y-axis with each row of subplots
              fig.subplots(2, 2, sharey='row')
  
              # Share both X- and Y-axes with all subplots
              fig.subplots(2, 2, sharex='all', sharey='all')
  
              # Note that this is the same as
              fig.subplots(2, 2, sharex=True, sharey=True)
          """
          gridspec_kw = dict(gridspec_kw or {})
          if height_ratios is not None:
              if 'height_ratios' in gridspec_kw:
                  raise ValueError("'height_ratios' must not be defined both as "
                                   "parameter and as key in 'gridspec_kw'")
              gridspec_kw['height_ratios'] = height_ratios
          if width_ratios is not None:
              if 'width_ratios' in gridspec_kw:
                  raise ValueError("'width_ratios' must not be defined both as "
                                   "parameter and as key in 'gridspec_kw'")
              gridspec_kw['width_ratios'] = width_ratios
  
          gs = self.add_gridspec(nrows, ncols, figure=self, **gridspec_kw)
          axs = gs.subplots(sharex=sharex, sharey=sharey, squeeze=squeeze,
                            subplot_kw=subplot_kw)
          return axs
  
      def delaxes(self, ax):
          """
          Remove the `~.axes.Axes` *ax* from the figure; update the current Axes.
          """
          self._remove_axes(ax, owners=[self._axstack, self._localaxes])
  
      def _remove_axes(self, ax, owners):
          """
          Common helper for removal of standard Axes (via delaxes) and of child Axes.
  
          Parameters
          ----------
          ax : `~.AxesBase`
              The Axes to remove.
          owners
              List of objects (list or _AxesStack) "owning" the Axes, from which the Axes
              will be remove()d.
          """
          for owner in owners:
              owner.remove(ax)
  
          self._axobservers.process("_axes_change_event", self)
          self.stale = True
          self._root_figure.canvas.release_mouse(ax)
  
          for name in ax._axis_names:  # Break link between any shared Axes
              grouper = ax._shared_axes[name]
              siblings = grouper.get_siblings(ax, include_self=False)
              if not siblings:  # Axes was not shared along this axis; we're done.
                  continue
              grouper.remove(ax)
              # Formatters and locators may previously have been associated with the now
              # removed axis.  Update them to point to an axis still there (we can pick
              # any of them, and use the first sibling).
              remaining_axis = siblings[0]._axis_map[name]
              remaining_axis.get_major_formatter().set_axis(remaining_axis)
              remaining_axis.get_major_locator().set_axis(remaining_axis)
              remaining_axis.get_minor_formatter().set_axis(remaining_axis)
              remaining_axis.get_minor_locator().set_axis(remaining_axis)
  
          ax._twinned_axes.remove(ax)  # Break link between any twinned Axes.
  
      def clear(self, keep_observers=False):
          """
          Clear the figure.
  
          Parameters
          ----------
          keep_observers : bool, default: False
              Set *keep_observers* to True if, for example,
              a gui widget is tracking the Axes in the figure.
          """
          self.suppressComposite = None
  
          # first clear the Axes in any subfigures
          for subfig in self.subfigs:
              subfig.clear(keep_observers=keep_observers)
          self.subfigs = []
  
          for ax in tuple(self.axes):  # Iterate over the copy.
              ax.clear()
              self.delaxes(ax)  # Remove ax from self._axstack.
  
          self.artists = []
          self.lines = []
          self.patches = []
          self.texts = []
          self.images = []
          self.legends = []
          self.subplotpars.reset()
          if not keep_observers:
              self._axobservers = cbook.CallbackRegistry()
          self._suptitle = None
          self._supxlabel = None
          self._supylabel = None
  
          self.stale = True
  
      # synonym for `clear`.
      def clf(self, keep_observers=False):
          """
          [*Discouraged*] Alias for the `clear()` method.
  
          .. admonition:: Discouraged
  
              The use of ``clf()`` is discouraged. Use ``clear()`` instead.
  
          Parameters
          ----------
          keep_observers : bool, default: False
              Set *keep_observers* to True if, for example,
              a gui widget is tracking the Axes in the figure.
          """
          return self.clear(keep_observers=keep_observers)
  
      # Note: the docstring below is modified with replace for the pyplot
      # version of this function because the method name differs (plt.figlegend)
      # the replacements are:
      #    " legend(" -> " figlegend(" for the signatures
      #    "fig.legend(" -> "plt.figlegend" for the code examples
      #    "ax.plot" -> "plt.plot" for consistency in using pyplot when able
      @_docstring.interpd
      def legend(self, *args, **kwargs):
          """
          Place a legend on the figure.
  
          Call signatures::
  
              legend()
              legend(handles, labels)
              legend(handles=handles)
              legend(labels)
  
          The call signatures correspond to the following different ways to use
          this method:
  
          **1. Automatic detection of elements to be shown in the legend**
  
          The elements to be added to the legend are automatically determined,
          when you do not pass in any extra arguments.
  
          In this case, the labels are taken from the artist. You can specify
          them either at artist creation or by calling the
          :meth:`~.Artist.set_label` method on the artist::
  
              ax.plot([1, 2, 3], label='Inline label')
              fig.legend()
  
          or::
  
              line, = ax.plot([1, 2, 3])
              line.set_label('Label via method')
              fig.legend()
  
          Specific lines can be excluded from the automatic legend element
          selection by defining a label starting with an underscore.
          This is default for all artists, so calling `.Figure.legend` without
          any arguments and without setting the labels manually will result in
          no legend being drawn.
  
  
          **2. Explicitly listing the artists and labels in the legend**
  
          For full control of which artists have a legend entry, it is possible
          to pass an iterable of legend artists followed by an iterable of
          legend labels respectively::
  
              fig.legend([line1, line2, line3], ['label1', 'label2', 'label3'])
  
  
          **3. Explicitly listing the artists in the legend**
  
          This is similar to 2, but the labels are taken from the artists'
          label properties. Example::
  
              line1, = ax1.plot([1, 2, 3], label='label1')
              line2, = ax2.plot([1, 2, 3], label='label2')
              fig.legend(handles=[line1, line2])
  
  
          **4. Labeling existing plot elements**
  
          .. admonition:: Discouraged
  
              This call signature is discouraged, because the relation between
              plot elements and labels is only implicit by their order and can
              easily be mixed up.
  
          To make a legend for all artists on all Axes, call this function with
          an iterable of strings, one for each legend item. For example::
  
              fig, (ax1, ax2) = plt.subplots(1, 2)
              ax1.plot([1, 3, 5], color='blue')
              ax2.plot([2, 4, 6], color='red')
              fig.legend(['the blues', 'the reds'])
  
  
          Parameters
          ----------
          handles : list of `.Artist`, optional
              A list of Artists (lines, patches) to be added to the legend.
              Use this together with *labels*, if you need full control on what
              is shown in the legend and the automatic mechanism described above
              is not sufficient.
  
              The length of handles and labels should be the same in this
              case. If they are not, they are truncated to the smaller length.
  
          labels : list of str, optional
              A list of labels to show next to the artists.
              Use this together with *handles*, if you need full control on what
              is shown in the legend and the automatic mechanism described above
              is not sufficient.
  
          Returns
          -------
          `~matplotlib.legend.Legend`
  
          Other Parameters
          ----------------
          %(_legend_kw_figure)s
  
          See Also
          --------
          .Axes.legend
  
          Notes
          -----
          Some artists are not supported by this function.  See
          :ref:`legend_guide` for details.
          """
  
          handles, labels, kwargs = mlegend._parse_legend_args(self.axes, *args, **kwargs)
          # explicitly set the bbox transform if the user hasn't.
          kwargs.setdefault("bbox_transform", self.transSubfigure)
          l = mlegend.Legend(self, handles, labels, **kwargs)
          self.legends.append(l)
          l._remove_method = self.legends.remove
          self.stale = True
          return l
  
      @_docstring.interpd
      def text(self, x, y, s, fontdict=None, **kwargs):
          """
          Add text to figure.
  
          Parameters
          ----------
          x, y : float
              The position to place the text. By default, this is in figure
              coordinates, floats in [0, 1]. The coordinate system can be changed
              using the *transform* keyword.
  
          s : str
              The text string.
  
          fontdict : dict, optional
              A dictionary to override the default text properties. If not given,
              the defaults are determined by :rc:`font.*`. Properties passed as
              *kwargs* override the corresponding ones given in *fontdict*.
  
          Returns
          -------
          `~.text.Text`
  
          Other Parameters
          ----------------
          **kwargs : `~matplotlib.text.Text` properties
              Other miscellaneous text parameters.
  
              %(Text:kwdoc)s
  
          See Also
          --------
          .Axes.text
          .pyplot.text
          """
          effective_kwargs = {
              'transform': self.transSubfigure,
              **(fontdict if fontdict is not None else {}),
              **kwargs,
          }
          text = Text(x=x, y=y, text=s, **effective_kwargs)
          text.set_figure(self)
          text.stale_callback = _stale_figure_callback
  
          self.texts.append(text)
          text._remove_method = self.texts.remove
          self.stale = True
          return text
  
      @_docstring.interpd
      def colorbar(
              self, mappable, cax=None, ax=None, use_gridspec=True, **kwargs):
          """
          Add a colorbar to a plot.
  
          Parameters
          ----------
          mappable
              The `matplotlib.colorizer.ColorizingArtist` (i.e., `.AxesImage`,
              `.ContourSet`, etc.) described by this colorbar.  This argument is
              mandatory for the `.Figure.colorbar` method but optional for the
              `.pyplot.colorbar` function, which sets the default to the current
              image.
  
              Note that one can create a `.colorizer.ColorizingArtist` "on-the-fly"
              to generate colorbars not attached to a previously drawn artist, e.g.
              ::
  
                  cr = colorizer.Colorizer(norm=norm, cmap=cmap)
                  fig.colorbar(colorizer.ColorizingArtist(cr), ax=ax)
  
          cax : `~matplotlib.axes.Axes`, optional
              Axes into which the colorbar will be drawn.  If `None`, then a new
              Axes is created and the space for it will be stolen from the Axes(s)
              specified in *ax*.
  
          ax : `~matplotlib.axes.Axes` or iterable or `numpy.ndarray` of Axes, optional
              The one or more parent Axes from which space for a new colorbar Axes
              will be stolen. This parameter is only used if *cax* is not set.
  
              Defaults to the Axes that contains the mappable used to create the
              colorbar.
  
          use_gridspec : bool, optional
              If *cax* is ``None``, a new *cax* is created as an instance of
              Axes.  If *ax* is positioned with a subplotspec and *use_gridspec*
              is ``True``, then *cax* is also positioned with a subplotspec.
  
          Returns
          -------
          colorbar : `~matplotlib.colorbar.Colorbar`
  
          Other Parameters
          ----------------
          %(_make_axes_kw_doc)s
          %(_colormap_kw_doc)s
  
          Notes
          -----
          If *mappable* is a `~.contour.ContourSet`, its *extend* kwarg is
          included automatically.
  
          The *shrink* kwarg provides a simple way to scale the colorbar with
          respect to the Axes. Note that if *cax* is specified, it determines the
          size of the colorbar, and *shrink* and *aspect* are ignored.
  
          For more precise control, you can manually specify the positions of the
          axes objects in which the mappable and the colorbar are drawn.  In this
          case, do not use any of the Axes properties kwargs.
  
          It is known that some vector graphics viewers (svg and pdf) render
          white gaps between segments of the colorbar.  This is due to bugs in
          the viewers, not Matplotlib.  As a workaround, the colorbar can be
          rendered with overlapping segments::
  
              cbar = colorbar()
              cbar.solids.set_edgecolor("face")
              draw()
  
          However, this has negative consequences in other circumstances, e.g.
          with semi-transparent images (alpha < 1) and colorbar extensions;
          therefore, this workaround is not used by default (see issue #1188).
  
          """
  
          if ax is None:
              ax = getattr(mappable, "axes", None)
  
          if cax is None:
              if ax is None:
                  raise ValueError(
                      'Unable to determine Axes to steal space for Colorbar. '
                      'Either provide the *cax* argument to use as the Axes for '
                      'the Colorbar, provide the *ax* argument to steal space '
                      'from it, or add *mappable* to an Axes.')
              fig = (  # Figure of first Axes; logic copied from make_axes.
                  [*ax.flat] if isinstance(ax, np.ndarray)
                  else [*ax] if np.iterable(ax)
                  else [ax])[0].get_figure(root=False)
              current_ax = fig.gca()
              if (fig.get_layout_engine() is not None and
                      not fig.get_layout_engine().colorbar_gridspec):
                  use_gridspec = False
              if (use_gridspec
                      and isinstance(ax, mpl.axes._base._AxesBase)
                      and ax.get_subplotspec()):
                  cax, kwargs = cbar.make_axes_gridspec(ax, **kwargs)
              else:
                  cax, kwargs = cbar.make_axes(ax, **kwargs)
              # make_axes calls add_{axes,subplot} which changes gca; undo that.
              fig.sca(current_ax)
              cax.grid(visible=False, which='both', axis='both')
  
          if (hasattr(mappable, "get_figure") and
                  (mappable_host_fig := mappable.get_figure(root=True)) is not None):
              # Warn in case of mismatch
              if mappable_host_fig is not self._root_figure:
                  _api.warn_external(
                          f'Adding colorbar to a different Figure '
                          f'{repr(mappable_host_fig)} than '
                          f'{repr(self._root_figure)} which '
                          f'fig.colorbar is called on.')
  
          NON_COLORBAR_KEYS = [  # remove kws that cannot be passed to Colorbar
              'fraction', 'pad', 'shrink', 'aspect', 'anchor', 'panchor']
          cb = cbar.Colorbar(cax, mappable, **{
              k: v for k, v in kwargs.items() if k not in NON_COLORBAR_KEYS})
          cax.get_figure(root=False).stale = True
          return cb
  
      def subplots_adjust(self, left=None, bottom=None, right=None, top=None,
                          wspace=None, hspace=None):
          """
          Adjust the subplot layout parameters.
  
          Unset parameters are left unmodified; initial values are given by
          :rc:`figure.subplot.[name]`.
  
          .. plot:: _embedded_plots/figure_subplots_adjust.py
  
          Parameters
          ----------
          left : float, optional
              The position of the left edge of the subplots,
              as a fraction of the figure width.
          right : float, optional
              The position of the right edge of the subplots,
              as a fraction of the figure width.
          bottom : float, optional
              The position of the bottom edge of the subplots,
              as a fraction of the figure height.
          top : float, optional
              The position of the top edge of the subplots,
              as a fraction of the figure height.
          wspace : float, optional
              The width of the padding between subplots,
              as a fraction of the average Axes width.
          hspace : float, optional
              The height of the padding between subplots,
              as a fraction of the average Axes height.
          """
          if (self.get_layout_engine() is not None and
                  not self.get_layout_engine().adjust_compatible):
              _api.warn_external(
                  "This figure was using a layout engine that is "
                  "incompatible with subplots_adjust and/or tight_layout; "
                  "not calling subplots_adjust.")
              return
          self.subplotpars.update(left, bottom, right, top, wspace, hspace)
          for ax in self.axes:
              if ax.get_subplotspec() is not None:
                  ax._set_position(ax.get_subplotspec().get_position(self))
          self.stale = True
  
      def align_xlabels(self, axs=None):
          """
          Align the xlabels of subplots in the same subplot row if label
          alignment is being done automatically (i.e. the label position is
          not manually set).
  
          Alignment persists for draw events after this is called.
  
          If a label is on the bottom, it is aligned with labels on Axes that
          also have their label on the bottom and that have the same
          bottom-most subplot row.  If the label is on the top,
          it is aligned with labels on Axes with the same top-most row.
  
          Parameters
          ----------
          axs : list of `~matplotlib.axes.Axes`
              Optional list of (or `~numpy.ndarray`) `~matplotlib.axes.Axes`
              to align the xlabels.
              Default is to align all Axes on the figure.
  
          See Also
          --------
          matplotlib.figure.Figure.align_ylabels
          matplotlib.figure.Figure.align_titles
          matplotlib.figure.Figure.align_labels
  
          Notes
          -----
          This assumes that all Axes in ``axs`` are from the same `.GridSpec`,
          so that their `.SubplotSpec` positions correspond to figure positions.
  
          Examples
          --------
          Example with rotated xtick labels::
  
              fig, axs = plt.subplots(1, 2)
              axs[0].tick_params(axis='x', rotation=55)
              axs[0].set_xlabel('XLabel 0')
              axs[1].set_xlabel('XLabel 1')
              fig.align_xlabels()
          """
          if axs is None:
              axs = self.axes
          axs = [ax for ax in np.ravel(axs) if ax.get_subplotspec() is not None]
          for ax in axs:
              _log.debug(' Working on: %s', ax.get_xlabel())
              rowspan = ax.get_subplotspec().rowspan
              pos = ax.xaxis.get_label_position()  # top or bottom
              # Search through other Axes for label positions that are same as
              # this one and that share the appropriate row number.
              # Add to a grouper associated with each Axes of siblings.
              # This list is inspected in `axis.draw` by
              # `axis._update_label_position`.
              for axc in axs:
                  if axc.xaxis.get_label_position() == pos:
                      rowspanc = axc.get_subplotspec().rowspan
                      if (pos == 'top' and rowspan.start == rowspanc.start or
                              pos == 'bottom' and rowspan.stop == rowspanc.stop):
                          # grouper for groups of xlabels to align
                          self._align_label_groups['x'].join(ax, axc)
  
      def align_ylabels(self, axs=None):
          """
          Align the ylabels of subplots in the same subplot column if label
          alignment is being done automatically (i.e. the label position is
          not manually set).
  
          Alignment persists for draw events after this is called.
  
          If a label is on the left, it is aligned with labels on Axes that
          also have their label on the left and that have the same
          left-most subplot column.  If the label is on the right,
          it is aligned with labels on Axes with the same right-most column.
  
          Parameters
          ----------
          axs : list of `~matplotlib.axes.Axes`
              Optional list (or `~numpy.ndarray`) of `~matplotlib.axes.Axes`
              to align the ylabels.
              Default is to align all Axes on the figure.
  
          See Also
          --------
          matplotlib.figure.Figure.align_xlabels
          matplotlib.figure.Figure.align_titles
          matplotlib.figure.Figure.align_labels
  
          Notes
          -----
          This assumes that all Axes in ``axs`` are from the same `.GridSpec`,
          so that their `.SubplotSpec` positions correspond to figure positions.
  
          Examples
          --------
          Example with large yticks labels::
  
              fig, axs = plt.subplots(2, 1)
              axs[0].plot(np.arange(0, 1000, 50))
              axs[0].set_ylabel('YLabel 0')
              axs[1].set_ylabel('YLabel 1')
              fig.align_ylabels()
          """
          if axs is None:
              axs = self.axes
          axs = [ax for ax in np.ravel(axs) if ax.get_subplotspec() is not None]
          for ax in axs:
              _log.debug(' Working on: %s', ax.get_ylabel())
              colspan = ax.get_subplotspec().colspan
              pos = ax.yaxis.get_label_position()  # left or right
              # Search through other Axes for label positions that are same as
              # this one and that share the appropriate column number.
              # Add to a list associated with each Axes of siblings.
              # This list is inspected in `axis.draw` by
              # `axis._update_label_position`.
              for axc in axs:
                  if axc.yaxis.get_label_position() == pos:
                      colspanc = axc.get_subplotspec().colspan
                      if (pos == 'left' and colspan.start == colspanc.start or
                              pos == 'right' and colspan.stop == colspanc.stop):
                          # grouper for groups of ylabels to align
                          self._align_label_groups['y'].join(ax, axc)
  
      def align_titles(self, axs=None):
          """
          Align the titles of subplots in the same subplot row if title
          alignment is being done automatically (i.e. the title position is
          not manually set).
  
          Alignment persists for draw events after this is called.
  
          Parameters
          ----------
          axs : list of `~matplotlib.axes.Axes`
              Optional list of (or ndarray) `~matplotlib.axes.Axes`
              to align the titles.
              Default is to align all Axes on the figure.
  
          See Also
          --------
          matplotlib.figure.Figure.align_xlabels
          matplotlib.figure.Figure.align_ylabels
          matplotlib.figure.Figure.align_labels
  
          Notes
          -----
          This assumes that all Axes in ``axs`` are from the same `.GridSpec`,
          so that their `.SubplotSpec` positions correspond to figure positions.
  
          Examples
          --------
          Example with titles::
  
              fig, axs = plt.subplots(1, 2)
              axs[0].set_aspect('equal')
              axs[0].set_title('Title 0')
              axs[1].set_title('Title 1')
              fig.align_titles()
          """
          if axs is None:
              axs = self.axes
          axs = [ax for ax in np.ravel(axs) if ax.get_subplotspec() is not None]
          for ax in axs:
              _log.debug(' Working on: %s', ax.get_title())
              rowspan = ax.get_subplotspec().rowspan
              for axc in axs:
                  rowspanc = axc.get_subplotspec().rowspan
                  if (rowspan.start == rowspanc.start):
                      self._align_label_groups['title'].join(ax, axc)
  
      def align_labels(self, axs=None):
          """
          Align the xlabels and ylabels of subplots with the same subplots
          row or column (respectively) if label alignment is being
          done automatically (i.e. the label position is not manually set).
  
          Alignment persists for draw events after this is called.
  
          Parameters
          ----------
          axs : list of `~matplotlib.axes.Axes`
              Optional list (or `~numpy.ndarray`) of `~matplotlib.axes.Axes`
              to align the labels.
              Default is to align all Axes on the figure.
  
          See Also
          --------
          matplotlib.figure.Figure.align_xlabels
          matplotlib.figure.Figure.align_ylabels
          matplotlib.figure.Figure.align_titles
  
          Notes
          -----
          This assumes that all Axes in ``axs`` are from the same `.GridSpec`,
          so that their `.SubplotSpec` positions correspond to figure positions.
          """
          self.align_xlabels(axs=axs)
          self.align_ylabels(axs=axs)
  
      def add_gridspec(self, nrows=1, ncols=1, **kwargs):
          """
          Low-level API for creating a `.GridSpec` that has this figure as a parent.
  
          This is a low-level API, allowing you to create a gridspec and
          subsequently add subplots based on the gridspec. Most users do
          not need that freedom and should use the higher-level methods
          `~.Figure.subplots` or `~.Figure.subplot_mosaic`.
  
          Parameters
          ----------
          nrows : int, default: 1
              Number of rows in grid.
  
          ncols : int, default: 1
              Number of columns in grid.
  
          Returns
          -------
          `.GridSpec`
  
          Other Parameters
          ----------------
          **kwargs
              Keyword arguments are passed to `.GridSpec`.
  
          See Also
          --------
          matplotlib.pyplot.subplots
  
          Examples
          --------
          Adding a subplot that spans two rows::
  
              fig = plt.figure()
              gs = fig.add_gridspec(2, 2)
              ax1 = fig.add_subplot(gs[0, 0])
              ax2 = fig.add_subplot(gs[1, 0])
              # spans two rows:
              ax3 = fig.add_subplot(gs[:, 1])
  
          """
  
          _ = kwargs.pop('figure', None)  # pop in case user has added this...
          gs = GridSpec(nrows=nrows, ncols=ncols, figure=self, **kwargs)
          return gs
  
      def subfigures(self, nrows=1, ncols=1, squeeze=True,
                     wspace=None, hspace=None,
                     width_ratios=None, height_ratios=None,
                     **kwargs):
          """
          Add a set of subfigures to this figure or subfigure.
  
          A subfigure has the same artist methods as a figure, and is logically
          the same as a figure, but cannot print itself.
          See :doc:`/gallery/subplots_axes_and_figures/subfigures`.
  
          .. versionchanged:: 3.10
              subfigures are now added in row-major order.
  
          Parameters
          ----------
          nrows, ncols : int, default: 1
              Number of rows/columns of the subfigure grid.
  
          squeeze : bool, default: True
              If True, extra dimensions are squeezed out from the returned
              array of subfigures.
  
          wspace, hspace : float, default: None
              The amount of width/height reserved for space between subfigures,
              expressed as a fraction of the average subfigure width/height.
              If not given, the values will be inferred from rcParams if using
              constrained layout (see `~.ConstrainedLayoutEngine`), or zero if
              not using a layout engine.
  
          width_ratios : array-like of length *ncols*, optional
              Defines the relative widths of the columns. Each column gets a
              relative width of ``width_ratios[i] / sum(width_ratios)``.
              If not given, all columns will have the same width.
  
          height_ratios : array-like of length *nrows*, optional
              Defines the relative heights of the rows. Each row gets a
              relative height of ``height_ratios[i] / sum(height_ratios)``.
              If not given, all rows will have the same height.
          """
          gs = GridSpec(nrows=nrows, ncols=ncols, figure=self,
                        wspace=wspace, hspace=hspace,
                        width_ratios=width_ratios,
                        height_ratios=height_ratios,
                        left=0, right=1, bottom=0, top=1)
  
          sfarr = np.empty((nrows, ncols), dtype=object)
          for i in range(nrows):
              for j in range(ncols):
                  sfarr[i, j] = self.add_subfigure(gs[i, j], **kwargs)
  
          if self.get_layout_engine() is None and (wspace is not None or
                                                   hspace is not None):
              # Gridspec wspace and hspace is ignored on subfigure instantiation,
              # and no space is left.  So need to account for it here if required.
              bottoms, tops, lefts, rights = gs.get_grid_positions(self)
              for sfrow, bottom, top in zip(sfarr, bottoms, tops):
                  for sf, left, right in zip(sfrow, lefts, rights):
                      bbox = Bbox.from_extents(left, bottom, right, top)
                      sf._redo_transform_rel_fig(bbox=bbox)
  
          if squeeze:
              # Discarding unneeded dimensions that equal 1.  If we only have one
              # subfigure, just return it instead of a 1-element array.
              return sfarr.item() if sfarr.size == 1 else sfarr.squeeze()
          else:
              # Returned axis array will be always 2-d, even if nrows=ncols=1.
              return sfarr
  
      def add_subfigure(self, subplotspec, **kwargs):
          """
          Add a `.SubFigure` to the figure as part of a subplot arrangement.
  
          Parameters
          ----------
          subplotspec : `.gridspec.SubplotSpec`
              Defines the region in a parent gridspec where the subfigure will
              be placed.
  
          Returns
          -------
          `.SubFigure`
  
          Other Parameters
          ----------------
          **kwargs
              Are passed to the `.SubFigure` object.
  
          See Also
          --------
          .Figure.subfigures
          """
          sf = SubFigure(self, subplotspec, **kwargs)
          self.subfigs += [sf]
          sf._remove_method = self.subfigs.remove
          sf.stale_callback = _stale_figure_callback
          self.stale = True
          return sf
  
      def sca(self, a):
          """Set the current Axes to be *a* and return *a*."""
          self._axstack.bubble(a)
          self._axobservers.process("_axes_change_event", self)
          return a
  
      def gca(self):
          """
          Get the current Axes.
  
          If there is currently no Axes on this Figure, a new one is created
          using `.Figure.add_subplot`.  (To test whether there is currently an
          Axes on a Figure, check whether ``figure.axes`` is empty.  To test
          whether there is currently a Figure on the pyplot figure stack, check
          whether `.pyplot.get_fignums()` is empty.)
          """
          ax = self._axstack.current()
          return ax if ax is not None else self.add_subplot()
  
      def _gci(self):
          # Helper for `~matplotlib.pyplot.gci`.  Do not use elsewhere.
          """
          Get the current colorable artist.
  
          Specifically, returns the current `.ScalarMappable` instance (`.Image`
          created by `imshow` or `figimage`, `.Collection` created by `pcolor` or
          `scatter`, etc.), or *None* if no such instance has been defined.
  
          The current image is an attribute of the current Axes, or the nearest
          earlier Axes in the current figure that contains an image.
  
          Notes
          -----
          Historically, the only colorable artists were images; hence the name
          ``gci`` (get current image).
          """
          # Look first for an image in the current Axes.
          ax = self._axstack.current()
          if ax is None:
              return None
          im = ax._gci()
          if im is not None:
              return im
          # If there is no image in the current Axes, search for
          # one in a previously created Axes.  Whether this makes
          # sense is debatable, but it is the documented behavior.
          for ax in reversed(self.axes):
              im = ax._gci()
              if im is not None:
                  return im
          return None
  
      def _process_projection_requirements(self, *, axes_class=None, polar=False,
                                           projection=None, **kwargs):
          """
          Handle the args/kwargs to add_axes/add_subplot/gca, returning::
  
              (axes_proj_class, proj_class_kwargs)
  
          which can be used for new Axes initialization/identification.
          """
          if axes_class is not None:
              if polar or projection is not None:
                  raise ValueError(
                      "Cannot combine 'axes_class' and 'projection' or 'polar'")
              projection_class = axes_class
          else:
  
              if polar:
                  if projection is not None and projection != 'polar':
                      raise ValueError(
                          f"polar={polar}, yet projection={projection!r}. "
                          "Only one of these arguments should be supplied."
                      )
                  projection = 'polar'
  
              if isinstance(projection, str) or projection is None:
                  projection_class = projections.get_projection_class(projection)
              elif hasattr(projection, '_as_mpl_axes'):
                  projection_class, extra_kwargs = projection._as_mpl_axes()
                  kwargs.update(**extra_kwargs)
              else:
                  raise TypeError(
                      f"projection must be a string, None or implement a "
                      f"_as_mpl_axes method, not {projection!r}")
          return projection_class, kwargs
  
      def get_default_bbox_extra_artists(self):
          """
          Return a list of Artists typically used in `.Figure.get_tightbbox`.
          """
          bbox_artists = [artist for artist in self.get_children()
                          if (artist.get_visible() and artist.get_in_layout())]
          for ax in self.axes:
              if ax.get_visible():
                  bbox_artists.extend(ax.get_default_bbox_extra_artists())
          return bbox_artists
  
      def get_tightbbox(self, renderer=None, *, bbox_extra_artists=None):
          """
          Return a (tight) bounding box of the figure *in inches*.
  
          Note that `.FigureBase` differs from all other artists, which return
          their `.Bbox` in pixels.
  
          Artists that have ``artist.set_in_layout(False)`` are not included
          in the bbox.
  
          Parameters
          ----------
          renderer : `.RendererBase` subclass
              Renderer that will be used to draw the figures (i.e.
              ``fig.canvas.get_renderer()``)
  
          bbox_extra_artists : list of `.Artist` or ``None``
              List of artists to include in the tight bounding box.  If
              ``None`` (default), then all artist children of each Axes are
              included in the tight bounding box.
  
          Returns
          -------
          `.BboxBase`
              containing the bounding box (in figure inches).
          """
  
          if renderer is None:
              renderer = self.get_figure(root=True)._get_renderer()
  
          bb = []
          if bbox_extra_artists is None:
              artists = [artist for artist in self.get_children()
                         if (artist not in self.axes and artist.get_visible()
                             and artist.get_in_layout())]
          else:
              artists = bbox_extra_artists
  
          for a in artists:
              bbox = a.get_tightbbox(renderer)
              if bbox is not None:
                  bb.append(bbox)
  
          for ax in self.axes:
              if ax.get_visible():
                  # some Axes don't take the bbox_extra_artists kwarg so we
                  # need this conditional....
                  try:
                      bbox = ax.get_tightbbox(
                          renderer, bbox_extra_artists=bbox_extra_artists)
                  except TypeError:
                      bbox = ax.get_tightbbox(renderer)
                  bb.append(bbox)
          bb = [b for b in bb
                if (np.isfinite(b.width) and np.isfinite(b.height)
                    and (b.width != 0 or b.height != 0))]
  
          isfigure = hasattr(self, 'bbox_inches')
          if len(bb) == 0:
              if isfigure:
                  return self.bbox_inches
              else:
                  # subfigures do not have bbox_inches, but do have a bbox
                  bb = [self.bbox]
  
          _bbox = Bbox.union(bb)
  
          if isfigure:
              # transform from pixels to inches...
              _bbox = TransformedBbox(_bbox, self.dpi_scale_trans.inverted())
  
          return _bbox
  
      @staticmethod
      def _norm_per_subplot_kw(per_subplot_kw):
          expanded = {}
          for k, v in per_subplot_kw.items():
              if isinstance(k, tuple):
                  for sub_key in k:
                      if sub_key in expanded:
                          raise ValueError(f'The key {sub_key!r} appears multiple times.')
                      expanded[sub_key] = v
              else:
                  if k in expanded:
                      raise ValueError(f'The key {k!r} appears multiple times.')
                  expanded[k] = v
          return expanded
  
      @staticmethod
      def _normalize_grid_string(layout):
          if '\n' not in layout:
              # single-line string
              return [list(ln) for ln in layout.split(';')]
          else:
              # multi-line string
              layout = inspect.cleandoc(layout)
              return [list(ln) for ln in layout.strip('\n').split('\n')]
  
      def subplot_mosaic(self, mosaic, *, sharex=False, sharey=False,
                         width_ratios=None, height_ratios=None,
                         empty_sentinel='.',
                         subplot_kw=None, per_subplot_kw=None, gridspec_kw=None):
          """
          Build a layout of Axes based on ASCII art or nested lists.
  
          This is a helper function to build complex GridSpec layouts visually.
  
          See :ref:`mosaic`
          for an example and full API documentation
  
          Parameters
          ----------
          mosaic : list of list of {hashable or nested} or str
  
              A visual layout of how you want your Axes to be arranged
              labeled as strings.  For example ::
  
                 x = [['A panel', 'A panel', 'edge'],
                      ['C panel', '.',       'edge']]
  
              produces 4 Axes:
  
              - 'A panel' which is 1 row high and spans the first two columns
              - 'edge' which is 2 rows high and is on the right edge
              - 'C panel' which in 1 row and 1 column wide in the bottom left
              - a blank space 1 row and 1 column wide in the bottom center
  
              Any of the entries in the layout can be a list of lists
              of the same form to create nested layouts.
  
              If input is a str, then it can either be a multi-line string of
              the form ::
  
                '''
                AAE
                C.E
                '''
  
              where each character is a column and each line is a row. Or it
              can be a single-line string where rows are separated by ``;``::
  
                'AB;CC'
  
              The string notation allows only single character Axes labels and
              does not support nesting but is very terse.
  
              The Axes identifiers may be `str` or a non-iterable hashable
              object (e.g. `tuple` s may not be used).
  
          sharex, sharey : bool, default: False
              If True, the x-axis (*sharex*) or y-axis (*sharey*) will be shared
              among all subplots.  In that case, tick label visibility and axis
              units behave as for `subplots`.  If False, each subplot's x- or
              y-axis will be independent.
  
          width_ratios : array-like of length *ncols*, optional
              Defines the relative widths of the columns. Each column gets a
              relative width of ``width_ratios[i] / sum(width_ratios)``.
              If not given, all columns will have the same width.  Equivalent
              to ``gridspec_kw={'width_ratios': [...]}``. In the case of nested
              layouts, this argument applies only to the outer layout.
  
          height_ratios : array-like of length *nrows*, optional
              Defines the relative heights of the rows. Each row gets a
              relative height of ``height_ratios[i] / sum(height_ratios)``.
              If not given, all rows will have the same height. Equivalent
              to ``gridspec_kw={'height_ratios': [...]}``. In the case of nested
              layouts, this argument applies only to the outer layout.
  
          subplot_kw : dict, optional
              Dictionary with keywords passed to the `.Figure.add_subplot` call
              used to create each subplot.  These values may be overridden by
              values in *per_subplot_kw*.
  
          per_subplot_kw : dict, optional
              A dictionary mapping the Axes identifiers or tuples of identifiers
              to a dictionary of keyword arguments to be passed to the
              `.Figure.add_subplot` call used to create each subplot.  The values
              in these dictionaries have precedence over the values in
              *subplot_kw*.
  
              If *mosaic* is a string, and thus all keys are single characters,
              it is possible to use a single string instead of a tuple as keys;
              i.e. ``"AB"`` is equivalent to ``("A", "B")``.
  
              .. versionadded:: 3.7
  
          gridspec_kw : dict, optional
              Dictionary with keywords passed to the `.GridSpec` constructor used
              to create the grid the subplots are placed on. In the case of
              nested layouts, this argument applies only to the outer layout.
              For more complex layouts, users should use `.Figure.subfigures`
              to create the nesting.
  
          empty_sentinel : object, optional
              Entry in the layout to mean "leave this space empty".  Defaults
              to ``'.'``. Note, if *layout* is a string, it is processed via
              `inspect.cleandoc` to remove leading white space, which may
              interfere with using white-space as the empty sentinel.
  
          Returns
          -------
          dict[label, Axes]
             A dictionary mapping the labels to the Axes objects.  The order of
             the Axes is left-to-right and top-to-bottom of their position in the
             total layout.
  
          """
          subplot_kw = subplot_kw or {}
          gridspec_kw = dict(gridspec_kw or {})
          per_subplot_kw = per_subplot_kw or {}
  
          if height_ratios is not None:
              if 'height_ratios' in gridspec_kw:
                  raise ValueError("'height_ratios' must not be defined both as "
                                   "parameter and as key in 'gridspec_kw'")
              gridspec_kw['height_ratios'] = height_ratios
          if width_ratios is not None:
              if 'width_ratios' in gridspec_kw:
                  raise ValueError("'width_ratios' must not be defined both as "
                                   "parameter and as key in 'gridspec_kw'")
              gridspec_kw['width_ratios'] = width_ratios
  
          # special-case string input
          if isinstance(mosaic, str):
              mosaic = self._normalize_grid_string(mosaic)
              per_subplot_kw = {
                  tuple(k): v for k, v in per_subplot_kw.items()
              }
  
          per_subplot_kw = self._norm_per_subplot_kw(per_subplot_kw)
  
          # Only accept strict bools to allow a possible future API expansion.
          _api.check_isinstance(bool, sharex=sharex, sharey=sharey)
  
          def _make_array(inp):
              """
              Convert input into 2D array
  
              We need to have this internal function rather than
              ``np.asarray(..., dtype=object)`` so that a list of lists
              of lists does not get converted to an array of dimension > 2.
  
              Returns
              -------
              2D object array
              """
              r0, *rest = inp
              if isinstance(r0, str):
                  raise ValueError('List mosaic specification must be 2D')
              for j, r in enumerate(rest, start=1):
                  if isinstance(r, str):
                      raise ValueError('List mosaic specification must be 2D')
                  if len(r0) != len(r):
                      raise ValueError(
                          "All of the rows must be the same length, however "
                          f"the first row ({r0!r}) has length {len(r0)} "
                          f"and row {j} ({r!r}) has length {len(r)}."
                      )
              out = np.zeros((len(inp), len(r0)), dtype=object)
              for j, r in enumerate(inp):
                  for k, v in enumerate(r):
                      out[j, k] = v
              return out
  
          def _identify_keys_and_nested(mosaic):
              """
              Given a 2D object array, identify unique IDs and nested mosaics
  
              Parameters
              ----------
              mosaic : 2D object array
  
              Returns
              -------
              unique_ids : tuple
                  The unique non-sub mosaic entries in this mosaic
              nested : dict[tuple[int, int], 2D object array]
              """
              # make sure we preserve the user supplied order
              unique_ids = cbook._OrderedSet()
              nested = {}
              for j, row in enumerate(mosaic):
                  for k, v in enumerate(row):
                      if v == empty_sentinel:
                          continue
                      elif not cbook.is_scalar_or_string(v):
                          nested[(j, k)] = _make_array(v)
                      else:
                          unique_ids.add(v)
  
              return tuple(unique_ids), nested
  
          def _do_layout(gs, mosaic, unique_ids, nested):
              """
              Recursively do the mosaic.
  
              Parameters
              ----------
              gs : GridSpec
              mosaic : 2D object array
                  The input converted to a 2D array for this level.
              unique_ids : tuple
                  The identified scalar labels at this level of nesting.
              nested : dict[tuple[int, int]], 2D object array
                  The identified nested mosaics, if any.
  
              Returns
              -------
              dict[label, Axes]
                  A flat dict of all of the Axes created.
              """
              output = dict()
  
              # we need to merge together the Axes at this level and the Axes
              # in the (recursively) nested sub-mosaics so that we can add
              # them to the figure in the "natural" order if you were to
              # ravel in c-order all of the Axes that will be created
              #
              # This will stash the upper left index of each object (axes or
              # nested mosaic) at this level
              this_level = dict()
  
              # go through the unique keys,
              for name in unique_ids:
                  # sort out where each axes starts/ends
                  index = np.argwhere(mosaic == name)
                  start_row, start_col = np.min(index, axis=0)
                  end_row, end_col = np.max(index, axis=0) + 1
                  # and construct the slice object
                  slc = (slice(start_row, end_row), slice(start_col, end_col))
                  # some light error checking
                  if (mosaic[slc] != name).any():
                      raise ValueError(
                          f"While trying to layout\n{mosaic!r}\n"
                          f"we found that the label {name!r} specifies a "
                          "non-rectangular or non-contiguous area.")
                  # and stash this slice for later
                  this_level[(start_row, start_col)] = (name, slc, 'axes')
  
              # do the same thing for the nested mosaics (simpler because these
              # cannot be spans yet!)
              for (j, k), nested_mosaic in nested.items():
                  this_level[(j, k)] = (None, nested_mosaic, 'nested')
  
              # now go through the things in this level and add them
              # in order left-to-right top-to-bottom
              for key in sorted(this_level):
                  name, arg, method = this_level[key]
                  # we are doing some hokey function dispatch here based
                  # on the 'method' string stashed above to sort out if this
                  # element is an Axes or a nested mosaic.
                  if method == 'axes':
                      slc = arg
                      # add a single Axes
                      if name in output:
                          raise ValueError(f"There are duplicate keys {name} "
                                           f"in the layout\n{mosaic!r}")
                      ax = self.add_subplot(
                          gs[slc], **{
                              'label': str(name),
                              **subplot_kw,
                              **per_subplot_kw.get(name, {})
                          }
                      )
                      output[name] = ax
                  elif method == 'nested':
                      nested_mosaic = arg
                      j, k = key
                      # recursively add the nested mosaic
                      rows, cols = nested_mosaic.shape
                      nested_output = _do_layout(
                          gs[j, k].subgridspec(rows, cols),
                          nested_mosaic,
                          *_identify_keys_and_nested(nested_mosaic)
                      )
                      overlap = set(output) & set(nested_output)
                      if overlap:
                          raise ValueError(
                              f"There are duplicate keys {overlap} "
                              f"between the outer layout\n{mosaic!r}\n"
                              f"and the nested layout\n{nested_mosaic}"
                          )
                      output.update(nested_output)
                  else:
                      raise RuntimeError("This should never happen")
              return output
  
          mosaic = _make_array(mosaic)
          rows, cols = mosaic.shape
          gs = self.add_gridspec(rows, cols, **gridspec_kw)
          ret = _do_layout(gs, mosaic, *_identify_keys_and_nested(mosaic))
          ax0 = next(iter(ret.values()))
          for ax in ret.values():
              if sharex:
                  ax.sharex(ax0)
                  ax._label_outer_xaxis(skip_non_rectangular_axes=True)
              if sharey:
                  ax.sharey(ax0)
                  ax._label_outer_yaxis(skip_non_rectangular_axes=True)
          if extra := set(per_subplot_kw) - set(ret):
              raise ValueError(
                  f"The keys {extra} are in *per_subplot_kw* "
                  "but not in the mosaic."
              )
          return ret
  
      def _set_artist_props(self, a):
          if a != self:
              a.set_figure(self)
          a.stale_callback = _stale_figure_callback
          a.set_transform(self.transSubfigure)
  
  
  @_docstring.interpd
  class SubFigure(FigureBase):
      """
      Logical figure that can be placed inside a figure.
  
      See :ref:`figure-api-subfigure` for an index of methods on this class.
      Typically instantiated using `.Figure.add_subfigure` or
      `.SubFigure.add_subfigure`, or `.SubFigure.subfigures`.  A subfigure has
      the same methods as a figure except for those particularly tied to the size
      or dpi of the figure, and is confined to a prescribed region of the figure.
      For example the following puts two subfigures side-by-side::
  
          fig = plt.figure()
          sfigs = fig.subfigures(1, 2)
          axsL = sfigs[0].subplots(1, 2)
          axsR = sfigs[1].subplots(2, 1)
  
      See :doc:`/gallery/subplots_axes_and_figures/subfigures`
      """
  
      def __init__(self, parent, subplotspec, *,
                   facecolor=None,
                   edgecolor=None,
                   linewidth=0.0,
                   frameon=None,
                   **kwargs):
          """
          Parameters
          ----------
          parent : `.Figure` or `.SubFigure`
              Figure or subfigure that contains the SubFigure.  SubFigures
              can be nested.
  
          subplotspec : `.gridspec.SubplotSpec`
              Defines the region in a parent gridspec where the subfigure will
              be placed.
  
          facecolor : default: ``"none"``
              The figure patch face color; transparent by default.
  
          edgecolor : default: :rc:`figure.edgecolor`
              The figure patch edge color.
  
          linewidth : float
              The linewidth of the frame (i.e. the edge linewidth of the figure
              patch).
  
          frameon : bool, default: :rc:`figure.frameon`
              If ``False``, suppress drawing the figure background patch.
  
          Other Parameters
          ----------------
          **kwargs : `.SubFigure` properties, optional
  
              %(SubFigure:kwdoc)s
          """
          super().__init__(**kwargs)
          if facecolor is None:
              facecolor = "none"
          edgecolor = mpl._val_or_rc(edgecolor, 'figure.edgecolor')
          frameon = mpl._val_or_rc(frameon, 'figure.frameon')
  
          self._subplotspec = subplotspec
          self._parent = parent
          self._root_figure = parent._root_figure
  
          # subfigures use the parent axstack
          self._axstack = parent._axstack
          self.subplotpars = parent.subplotpars
          self.dpi_scale_trans = parent.dpi_scale_trans
          self._axobservers = parent._axobservers
          self.transFigure = parent.transFigure
          self.bbox_relative = Bbox.null()
          self._redo_transform_rel_fig()
          self.figbbox = self._parent.figbbox
          self.bbox = TransformedBbox(self.bbox_relative,
                                      self._parent.transSubfigure)
          self.transSubfigure = BboxTransformTo(self.bbox)
  
          self.patch = Rectangle(
              xy=(0, 0), width=1, height=1, visible=frameon,
              facecolor=facecolor, edgecolor=edgecolor, linewidth=linewidth,
              # Don't let the figure patch influence bbox calculation.
              in_layout=False, transform=self.transSubfigure)
          self._set_artist_props(self.patch)
          self.patch.set_antialiased(False)
  
      @property
      def canvas(self):
          return self._parent.canvas
  
      @property
      def dpi(self):
          return self._parent.dpi
  
      @dpi.setter
      def dpi(self, value):
          self._parent.dpi = value
  
      def get_dpi(self):
          """
          Return the resolution of the parent figure in dots-per-inch as a float.
          """
          return self._parent.dpi
  
      def set_dpi(self, val):
          """
          Set the resolution of parent figure in dots-per-inch.
  
          Parameters
          ----------
          val : float
          """
          self._parent.dpi = val
          self.stale = True
  
      def _get_renderer(self):
          return self._parent._get_renderer()
  
      def _redo_transform_rel_fig(self, bbox=None):
          """
          Make the transSubfigure bbox relative to Figure transform.
  
          Parameters
          ----------
          bbox : bbox or None
              If not None, then the bbox is used for relative bounding box.
              Otherwise, it is calculated from the subplotspec.
          """
          if bbox is not None:
              self.bbox_relative.p0 = bbox.p0
              self.bbox_relative.p1 = bbox.p1
              return
          # need to figure out *where* this subplotspec is.
          gs = self._subplotspec.get_gridspec()
          wr = np.asarray(gs.get_width_ratios())
          hr = np.asarray(gs.get_height_ratios())
          dx = wr[self._subplotspec.colspan].sum() / wr.sum()
          dy = hr[self._subplotspec.rowspan].sum() / hr.sum()
          x0 = wr[:self._subplotspec.colspan.start].sum() / wr.sum()
          y0 = 1 - hr[:self._subplotspec.rowspan.stop].sum() / hr.sum()
          self.bbox_relative.p0 = (x0, y0)
          self.bbox_relative.p1 = (x0 + dx, y0 + dy)
  
      def get_constrained_layout(self):
          """
          Return whether constrained layout is being used.
  
          See :ref:`constrainedlayout_guide`.
          """
          return self._parent.get_constrained_layout()
  
      def get_constrained_layout_pads(self, relative=False):
          """
          Get padding for ``constrained_layout``.
  
          Returns a list of ``w_pad, h_pad`` in inches and
          ``wspace`` and ``hspace`` as fractions of the subplot.
  
          See :ref:`constrainedlayout_guide`.
  
          Parameters
          ----------
          relative : bool
              If `True`, then convert from inches to figure relative.
          """
          return self._parent.get_constrained_layout_pads(relative=relative)
  
      def get_layout_engine(self):
          return self._parent.get_layout_engine()
  
      @property
      def axes(self):
          """
          List of Axes in the SubFigure.  You can access and modify the Axes
          in the SubFigure through this list.
  
          Modifying this list has no effect. Instead, use `~.SubFigure.add_axes`,
          `~.SubFigure.add_subplot` or `~.SubFigure.delaxes` to add or remove an
          Axes.
  
          Note: The `.SubFigure.axes` property and `~.SubFigure.get_axes` method
          are equivalent.
          """
          return self._localaxes[:]
  
      get_axes = axes.fget
  
      def draw(self, renderer):
          # docstring inherited
  
          # draw the figure bounding box, perhaps none for white figure
          if not self.get_visible():
              return
  
          artists = self._get_draw_artists(renderer)
  
          try:
              renderer.open_group('subfigure', gid=self.get_gid())
              self.patch.draw(renderer)
              mimage._draw_list_compositing_images(
                  renderer, self, artists, self.get_figure(root=True).suppressComposite)
              renderer.close_group('subfigure')
  
          finally:
              self.stale = False
  
  
  @_docstring.interpd
  class Figure(FigureBase):
      """
      The top level container for all the plot elements.
  
      See `matplotlib.figure` for an index of class methods.
  
      Attributes
      ----------
      patch
          The `.Rectangle` instance representing the figure background patch.
  
      suppressComposite
          For multiple images, the figure will make composite images
          depending on the renderer option_image_nocomposite function.  If
          *suppressComposite* is a boolean, this will override the renderer.
      """
  
      # we want to cache the fonts and mathtext at a global level so that when
      # multiple figures are created we can reuse them.  This helps with a bug on
      # windows where the creation of too many figures leads to too many open
      # file handles and improves the performance of parsing mathtext.  However,
      # these global caches are not thread safe.  The solution here is to let the
      # Figure acquire a shared lock at the start of the draw, and release it when it
      # is done.  This allows multiple renderers to share the cached fonts and
      # parsed text, but only one figure can draw at a time and so the font cache
      # and mathtext cache are used by only one renderer at a time.
  
      _render_lock = threading.RLock()
  
      def __str__(self):
          return "Figure(%gx%g)" % tuple(self.bbox.size)
  
      def __repr__(self):
          return "<{clsname} size {h:g}x{w:g} with {naxes} Axes>".format(
              clsname=self.__class__.__name__,
              h=self.bbox.size[0], w=self.bbox.size[1],
              naxes=len(self.axes),
          )
  
      def __init__(self,
                   figsize=None,
                   dpi=None,
                   *,
                   facecolor=None,
                   edgecolor=None,
                   linewidth=0.0,
                   frameon=None,
                   subplotpars=None,  # rc figure.subplot.*
                   tight_layout=None,  # rc figure.autolayout
                   constrained_layout=None,  # rc figure.constrained_layout.use
                   layout=None,
                   **kwargs
                   ):
          """
          Parameters
          ----------
          figsize : (float, float) or (float, float, str), default: :rc:`figure.figsize`
              The figure dimensions. This can be
  
              - a tuple ``(width, height, unit)``, where *unit* is one of "in" (inch),
                "cm" (centimenter), "px" (pixel).
              - a tuple ``(width, height)``, which is interpreted in inches, i.e. as
                ``(width, height, "in")``.
  
              One of *width* or *height* may be ``None``; the respective value is
              taken from :rc:`figure.figsize`.
  
          dpi : float, default: :rc:`figure.dpi`
              Dots per inch.
  
          facecolor : default: :rc:`figure.facecolor`
              The figure patch facecolor.
  
          edgecolor : default: :rc:`figure.edgecolor`
              The figure patch edge color.
  
          linewidth : float
              The linewidth of the frame (i.e. the edge linewidth of the figure
              patch).
  
          frameon : bool, default: :rc:`figure.frameon`
              If ``False``, suppress drawing the figure background patch.
  
          subplotpars : `~matplotlib.gridspec.SubplotParams`
              Subplot parameters. If not given, the default subplot
              parameters :rc:`figure.subplot.*` are used.
  
          tight_layout : bool or dict, default: :rc:`figure.autolayout`
              Whether to use the tight layout mechanism. See `.set_tight_layout`.
  
              .. admonition:: Discouraged
  
                  The use of this parameter is discouraged. Please use
                  ``layout='tight'`` instead for the common case of
                  ``tight_layout=True`` and use `.set_tight_layout` otherwise.
  
          constrained_layout : bool, default: :rc:`figure.constrained_layout.use`
              This is equal to ``layout='constrained'``.
  
              .. admonition:: Discouraged
  
                  The use of this parameter is discouraged. Please use
                  ``layout='constrained'`` instead.
  
          layout : {'constrained', 'compressed', 'tight', 'none', `.LayoutEngine`, \
  None}, default: None
              The layout mechanism for positioning of plot elements to avoid
              overlapping Axes decorations (labels, ticks, etc). Note that
              layout managers can have significant performance penalties.
  
              - 'constrained': The constrained layout solver adjusts Axes sizes
                to avoid overlapping Axes decorations.  Can handle complex plot
                layouts and colorbars, and is thus recommended.
  
                See :ref:`constrainedlayout_guide` for examples.
  
              - 'compressed': uses the same algorithm as 'constrained', but
                removes extra space between fixed-aspect-ratio Axes.  Best for
                simple grids of Axes.
  
              - 'tight': Use the tight layout mechanism. This is a relatively
                simple algorithm that adjusts the subplot parameters so that
                decorations do not overlap.
  
                See :ref:`tight_layout_guide` for examples.
  
              - 'none': Do not use a layout engine.
  
              - A `.LayoutEngine` instance. Builtin layout classes are
                `.ConstrainedLayoutEngine` and `.TightLayoutEngine`, more easily
                accessible by 'constrained' and 'tight'.  Passing an instance
                allows third parties to provide their own layout engine.
  
              If not given, fall back to using the parameters *tight_layout* and
              *constrained_layout*, including their config defaults
              :rc:`figure.autolayout` and :rc:`figure.constrained_layout.use`.
  
          Other Parameters
          ----------------
          **kwargs : `.Figure` properties, optional
  
              %(Figure:kwdoc)s
          """
          super().__init__(**kwargs)
          self._root_figure = self
          self._layout_engine = None
  
          if layout is not None:
              if (tight_layout is not None):
                  _api.warn_external(
                      "The Figure parameters 'layout' and 'tight_layout' cannot "
                      "be used together. Please use 'layout' only.")
              if (constrained_layout is not None):
                  _api.warn_external(
                      "The Figure parameters 'layout' and 'constrained_layout' "
                      "cannot be used together. Please use 'layout' only.")
              self.set_layout_engine(layout=layout)
          elif tight_layout is not None:
              if constrained_layout is not None:
                  _api.warn_external(
                      "The Figure parameters 'tight_layout' and "
                      "'constrained_layout' cannot be used together. Please use "
                      "'layout' parameter")
              self.set_layout_engine(layout='tight')
              if isinstance(tight_layout, dict):
                  self.get_layout_engine().set(**tight_layout)
          elif constrained_layout is not None:
              if isinstance(constrained_layout, dict):
                  self.set_layout_engine(layout='constrained')
                  self.get_layout_engine().set(**constrained_layout)
              elif constrained_layout:
                  self.set_layout_engine(layout='constrained')
  
          else:
              # everything is None, so use default:
              self.set_layout_engine(layout=layout)
  
          # Callbacks traditionally associated with the canvas (and exposed with
          # a proxy property), but that actually need to be on the figure for
          # pickling.
          self._canvas_callbacks = cbook.CallbackRegistry(
              signals=FigureCanvasBase.events)
          connect = self._canvas_callbacks._connect_picklable
          self._mouse_key_ids = [
              connect('key_press_event', backend_bases._key_handler),
              connect('key_release_event', backend_bases._key_handler),
              connect('key_release_event', backend_bases._key_handler),
              connect('button_press_event', backend_bases._mouse_handler),
              connect('button_release_event', backend_bases._mouse_handler),
              connect('scroll_event', backend_bases._mouse_handler),
              connect('motion_notify_event', backend_bases._mouse_handler),
          ]
          self._button_pick_id = connect('button_press_event', self.pick)
          self._scroll_pick_id = connect('scroll_event', self.pick)
  
          figsize = mpl._val_or_rc(figsize, 'figure.figsize')
          dpi = mpl._val_or_rc(dpi, 'figure.dpi')
          facecolor = mpl._val_or_rc(facecolor, 'figure.facecolor')
          edgecolor = mpl._val_or_rc(edgecolor, 'figure.edgecolor')
          frameon = mpl._val_or_rc(frameon, 'figure.frameon')
  
          figsize = _parse_figsize(figsize, dpi)
  
          if not np.isfinite(figsize).all() or (np.array(figsize) < 0).any():
              raise ValueError('figure size must be positive finite not '
                               f'{figsize}')
          self.bbox_inches = Bbox.from_bounds(0, 0, *figsize)
  
          self.dpi_scale_trans = Affine2D().scale(dpi)
          # do not use property as it will trigger
          self._dpi = dpi
          self.bbox = TransformedBbox(self.bbox_inches, self.dpi_scale_trans)
          self.figbbox = self.bbox
          self.transFigure = BboxTransformTo(self.bbox)
          self.transSubfigure = self.transFigure
  
          self.patch = Rectangle(
              xy=(0, 0), width=1, height=1, visible=frameon,
              facecolor=facecolor, edgecolor=edgecolor, linewidth=linewidth,
              # Don't let the figure patch influence bbox calculation.
              in_layout=False)
          self._set_artist_props(self.patch)
          self.patch.set_antialiased(False)
  
          self._set_base_canvas()
  
          if subplotpars is None:
              subplotpars = SubplotParams()
  
          self.subplotpars = subplotpars
  
          self._axstack = _AxesStack()  # track all figure Axes and current Axes
          self.clear()
  
      def pick(self, mouseevent):
          if not self.canvas.widgetlock.locked():
              super().pick(mouseevent)
  
      def _check_layout_engines_compat(self, old, new):
          """
          Helper for set_layout engine
  
          If the figure has used the old engine and added a colorbar then the
          value of colorbar_gridspec must be the same on the new engine.
          """
          if old is None or new is None:
              return True
          if old.colorbar_gridspec == new.colorbar_gridspec:
              return True
          # colorbar layout different, so check if any colorbars are on the
          # figure...
          for ax in self.axes:
              if hasattr(ax, '_colorbar'):
                  # colorbars list themselves as a colorbar.
                  return False
          return True
  
      def set_layout_engine(self, layout=None, **kwargs):
          """
          Set the layout engine for this figure.
  
          Parameters
          ----------
          layout : {'constrained', 'compressed', 'tight', 'none', `.LayoutEngine`, None}
  
              - 'constrained' will use `~.ConstrainedLayoutEngine`
              - 'compressed' will also use `~.ConstrainedLayoutEngine`, but with
                a correction that attempts to make a good layout for fixed-aspect
                ratio Axes.
              - 'tight' uses `~.TightLayoutEngine`
              - 'none' removes layout engine.
  
              If a `.LayoutEngine` instance, that instance will be used.
  
              If `None`, the behavior is controlled by :rc:`figure.autolayout`
              (which if `True` behaves as if 'tight' was passed) and
              :rc:`figure.constrained_layout.use` (which if `True` behaves as if
              'constrained' was passed).  If both are `True`,
              :rc:`figure.autolayout` takes priority.
  
              Users and libraries can define their own layout engines and pass
              the instance directly as well.
  
          **kwargs
              The keyword arguments are passed to the layout engine to set things
              like padding and margin sizes.  Only used if *layout* is a string.
  
          """
          if layout is None:
              if mpl.rcParams['figure.autolayout']:
                  layout = 'tight'
              elif mpl.rcParams['figure.constrained_layout.use']:
                  layout = 'constrained'
              else:
                  self._layout_engine = None
                  return
          if layout == 'tight':
              new_layout_engine = TightLayoutEngine(**kwargs)
          elif layout == 'constrained':
              new_layout_engine = ConstrainedLayoutEngine(**kwargs)
          elif layout == 'compressed':
              new_layout_engine = ConstrainedLayoutEngine(compress=True,
                                                          **kwargs)
          elif layout == 'none':
              if self._layout_engine is not None:
                  new_layout_engine = PlaceHolderLayoutEngine(
                      self._layout_engine.adjust_compatible,
                      self._layout_engine.colorbar_gridspec
                  )
              else:
                  new_layout_engine = None
          elif isinstance(layout, LayoutEngine):
              new_layout_engine = layout
          else:
              raise ValueError(f"Invalid value for 'layout': {layout!r}")
  
          if self._check_layout_engines_compat(self._layout_engine,
                                               new_layout_engine):
              self._layout_engine = new_layout_engine
          else:
              raise RuntimeError('Colorbar layout of new layout engine not '
                                 'compatible with old engine, and a colorbar '
                                 'has been created.  Engine not changed.')
  
      def get_layout_engine(self):
          return self._layout_engine
  
      # TODO: I'd like to dynamically add the _repr_html_ method
      # to the figure in the right context, but then IPython doesn't
      # use it, for some reason.
  
      def _repr_html_(self):
          # We can't use "isinstance" here, because then we'd end up importing
          # webagg unconditionally.
          if 'WebAgg' in type(self.canvas).__name__:
              from matplotlib.backends import backend_webagg
              return backend_webagg.ipython_inline_display(self)
  
      def show(self, warn=True):
          """
          If using a GUI backend with pyplot, display the figure window.
  
          If the figure was not created using `~.pyplot.figure`, it will lack
          a `~.backend_bases.FigureManagerBase`, and this method will raise an
          AttributeError.
  
          .. warning::
  
              This does not manage a GUI event loop. Consequently, the figure
              may only be shown briefly or not shown at all if you or your
              environment are not managing an event loop.
  
              Use cases for `.Figure.show` include running this from a GUI
              application (where there is persistently an event loop running) or
              from a shell, like IPython, that install an input hook to allow the
              interactive shell to accept input while the figure is also being
              shown and interactive.  Some, but not all, GUI toolkits will
              register an input hook on import.  See :ref:`cp_integration` for
              more details.
  
              If you're in a shell without input hook integration or executing a
              python script, you should use `matplotlib.pyplot.show` with
              ``block=True`` instead, which takes care of starting and running
              the event loop for you.
  
          Parameters
          ----------
          warn : bool, default: True
              If ``True`` and we are not running headless (i.e. on Linux with an
              unset DISPLAY), issue warning when called on a non-GUI backend.
  
          """
          if self.canvas.manager is None:
              raise AttributeError(
                  "Figure.show works only for figures managed by pyplot, "
                  "normally created by pyplot.figure()")
          try:
              self.canvas.manager.show()
          except NonGuiException as exc:
              if warn:
                  _api.warn_external(str(exc))
  
      @property
      def axes(self):
          """
          List of Axes in the Figure. You can access and modify the Axes in the
          Figure through this list.
  
          Do not modify the list itself. Instead, use `~Figure.add_axes`,
          `~.Figure.add_subplot` or `~.Figure.delaxes` to add or remove an Axes.
  
          Note: The `.Figure.axes` property and `~.Figure.get_axes` method are
          equivalent.
          """
          return self._axstack.as_list()
  
      get_axes = axes.fget
  
      @property
      def number(self):
          """The figure id, used to identify figures in `.pyplot`."""
          # Historically, pyplot dynamically added a number attribute to figure.
          # However, this number must stay in sync with the figure manager.
          # AFAICS overwriting the number attribute does not have the desired
          # effect for pyplot. But there are some repos in GitHub that do change
          # number. So let's take it slow and properly migrate away from writing.
          #
          # Making the dynamic attribute private and wrapping it in a property
          # allows to maintain current behavior and deprecate write-access.
          #
          # When the deprecation expires, there's no need for duplicate state
          # anymore and the private _number attribute can be replaced by
          # `self.canvas.manager.num` if that exists and None otherwise.
          if hasattr(self, '_number'):
              return self._number
          else:
              raise AttributeError(
                  "'Figure' object has no attribute 'number'. In the future this"
                  "will change to returning 'None' instead.")
  
      @number.setter
      def number(self, num):
          _api.warn_deprecated(
              "3.10",
              message="Changing 'Figure.number' is deprecated since %(since)s and "
                      "will raise an error starting %(removal)s")
          self._number = num
  
      def _get_renderer(self):
          if hasattr(self.canvas, 'get_renderer'):
              return self.canvas.get_renderer()
          else:
              return _get_renderer(self)
  
      def _get_dpi(self):
          return self._dpi
  
      def _set_dpi(self, dpi, forward=True):
          """
          Parameters
          ----------
          dpi : float
  
          forward : bool
              Passed on to `~.Figure.set_size_inches`
          """
          if dpi == self._dpi:
              # We don't want to cause undue events in backends.
              return
          self._dpi = dpi
          self.dpi_scale_trans.clear().scale(dpi)
          w, h = self.get_size_inches()
          self.set_size_inches(w, h, forward=forward)
  
      dpi = property(_get_dpi, _set_dpi, doc="The resolution in dots per inch.")
  
      def get_tight_layout(self):
          """Return whether `.Figure.tight_layout` is called when drawing."""
          return isinstance(self.get_layout_engine(), TightLayoutEngine)
  
      @_api.deprecated("3.6", alternative="set_layout_engine",
                       pending=True)
      def set_tight_layout(self, tight):
          """
          Set whether and how `.Figure.tight_layout` is called when drawing.
  
          Parameters
          ----------
          tight : bool or dict with keys "pad", "w_pad", "h_pad", "rect" or None
              If a bool, sets whether to call `.Figure.tight_layout` upon drawing.
              If ``None``, use :rc:`figure.autolayout` instead.
              If a dict, pass it as kwargs to `.Figure.tight_layout`, overriding the
              default paddings.
          """
          tight = mpl._val_or_rc(tight, 'figure.autolayout')
          _tight = 'tight' if bool(tight) else 'none'
          _tight_parameters = tight if isinstance(tight, dict) else {}
          self.set_layout_engine(_tight, **_tight_parameters)
          self.stale = True
  
      def get_constrained_layout(self):
          """
          Return whether constrained layout is being used.
  
          See :ref:`constrainedlayout_guide`.
          """
          return isinstance(self.get_layout_engine(), ConstrainedLayoutEngine)
  
      @_api.deprecated("3.6", alternative="set_layout_engine('constrained')",
                       pending=True)
      def set_constrained_layout(self, constrained):
          """
          Set whether ``constrained_layout`` is used upon drawing.
  
          If None, :rc:`figure.constrained_layout.use` value will be used.
  
          When providing a dict containing the keys ``w_pad``, ``h_pad``
          the default ``constrained_layout`` paddings will be
          overridden.  These pads are in inches and default to 3.0/72.0.
          ``w_pad`` is the width padding and ``h_pad`` is the height padding.
  
          Parameters
          ----------
          constrained : bool or dict or None
          """
          constrained = mpl._val_or_rc(constrained, 'figure.constrained_layout.use')
          _constrained = 'constrained' if bool(constrained) else 'none'
          _parameters = constrained if isinstance(constrained, dict) else {}
          self.set_layout_engine(_constrained, **_parameters)
          self.stale = True
  
      @_api.deprecated(
           "3.6", alternative="figure.get_layout_engine().set()",
           pending=True)
      def set_constrained_layout_pads(self, **kwargs):
          """
          Set padding for ``constrained_layout``.
  
          Tip: The parameters can be passed from a dictionary by using
          ``fig.set_constrained_layout(**pad_dict)``.
  
          See :ref:`constrainedlayout_guide`.
  
          Parameters
          ----------
          w_pad : float, default: :rc:`figure.constrained_layout.w_pad`
              Width padding in inches.  This is the pad around Axes
              and is meant to make sure there is enough room for fonts to
              look good.  Defaults to 3 pts = 0.04167 inches
  
          h_pad : float, default: :rc:`figure.constrained_layout.h_pad`
              Height padding in inches. Defaults to 3 pts.
  
          wspace : float, default: :rc:`figure.constrained_layout.wspace`
              Width padding between subplots, expressed as a fraction of the
              subplot width.  The total padding ends up being w_pad + wspace.
  
          hspace : float, default: :rc:`figure.constrained_layout.hspace`
              Height padding between subplots, expressed as a fraction of the
              subplot width. The total padding ends up being h_pad + hspace.
  
          """
          if isinstance(self.get_layout_engine(), ConstrainedLayoutEngine):
              self.get_layout_engine().set(**kwargs)
  
      @_api.deprecated("3.6", alternative="fig.get_layout_engine().get()",
                       pending=True)
      def get_constrained_layout_pads(self, relative=False):
          """
          Get padding for ``constrained_layout``.
  
          Returns a list of ``w_pad, h_pad`` in inches and
          ``wspace`` and ``hspace`` as fractions of the subplot.
          All values are None if ``constrained_layout`` is not used.
  
          See :ref:`constrainedlayout_guide`.
  
          Parameters
          ----------
          relative : bool
              If `True`, then convert from inches to figure relative.
          """
          if not isinstance(self.get_layout_engine(), ConstrainedLayoutEngine):
              return None, None, None, None
          info = self.get_layout_engine().get()
          w_pad = info['w_pad']
          h_pad = info['h_pad']
          wspace = info['wspace']
          hspace = info['hspace']
  
          if relative and (w_pad is not None or h_pad is not None):
              renderer = self._get_renderer()
              dpi = renderer.dpi
              w_pad = w_pad * dpi / renderer.width
              h_pad = h_pad * dpi / renderer.height
  
          return w_pad, h_pad, wspace, hspace
  
      def _set_base_canvas(self):
          """
          Initialize self.canvas with a FigureCanvasBase instance.
  
          This is used upon initialization of the Figure, but also
          to reset the canvas when decoupling from pyplot.
          """
          FigureCanvasBase(self)  # Set self.canvas as a side-effect
          # undo any high-dpi scaling
          if self._dpi != self._original_dpi:
              self.dpi = self._original_dpi
  
      def set_canvas(self, canvas):
          """
          Set the canvas that contains the figure
  
          Parameters
          ----------
          canvas : FigureCanvas
          """
          self.canvas = canvas
  
      @_docstring.interpd
      def figimage(self, X, xo=0, yo=0, alpha=None, norm=None, cmap=None,
                   vmin=None, vmax=None, origin=None, resize=False, *,
                   colorizer=None, **kwargs):
          """
          Add a non-resampled image to the figure.
  
          The image is attached to the lower or upper left corner depending on
          *origin*.
  
          Parameters
          ----------
          X
              The image data. This is an array of one of the following shapes:
  
              - (M, N): an image with scalar data.  Color-mapping is controlled
                by *cmap*, *norm*, *vmin*, and *vmax*.
              - (M, N, 3): an image with RGB values (0-1 float or 0-255 int).
              - (M, N, 4): an image with RGBA values (0-1 float or 0-255 int),
                i.e. including transparency.
  
          xo, yo : int
              The *x*/*y* image offset in pixels.
  
          alpha : None or float
              The alpha blending value.
  
          %(cmap_doc)s
  
              This parameter is ignored if *X* is RGB(A).
  
          %(norm_doc)s
  
              This parameter is ignored if *X* is RGB(A).
  
          %(vmin_vmax_doc)s
  
              This parameter is ignored if *X* is RGB(A).
  
          origin : {'upper', 'lower'}, default: :rc:`image.origin`
              Indicates where the [0, 0] index of the array is in the upper left
              or lower left corner of the Axes.
  
          resize : bool
              If *True*, resize the figure to match the given image size.
  
          %(colorizer_doc)s
  
              This parameter is ignored if *X* is RGB(A).
  
          Returns
          -------
          `matplotlib.image.FigureImage`
  
          Other Parameters
          ----------------
          **kwargs
              Additional kwargs are `.Artist` kwargs passed on to `.FigureImage`.
  
          Notes
          -----
          figimage complements the Axes image (`~matplotlib.axes.Axes.imshow`)
          which will be resampled to fit the current Axes.  If you want
          a resampled image to fill the entire figure, you can define an
          `~matplotlib.axes.Axes` with extent [0, 0, 1, 1].
  
          Examples
          --------
          ::
  
              f = plt.figure()
              nx = int(f.get_figwidth() * f.dpi)
              ny = int(f.get_figheight() * f.dpi)
              data = np.random.random((ny, nx))
              f.figimage(data)
              plt.show()
          """
          if resize:
              dpi = self.get_dpi()
              figsize = [x / dpi for x in (X.shape[1], X.shape[0])]
              self.set_size_inches(figsize, forward=True)
  
          im = mimage.FigureImage(self, cmap=cmap, norm=norm,
                                  colorizer=colorizer,
                                  offsetx=xo, offsety=yo,
                                  origin=origin, **kwargs)
          im.stale_callback = _stale_figure_callback
  
          im.set_array(X)
          im.set_alpha(alpha)
          if norm is None:
              im._check_exclusionary_keywords(colorizer, vmin=vmin, vmax=vmax)
              im.set_clim(vmin, vmax)
          self.images.append(im)
          im._remove_method = self.images.remove
          self.stale = True
          return im
  
      def set_size_inches(self, w, h=None, forward=True):
          """
          Set the figure size in inches.
  
          Call signatures::
  
               fig.set_size_inches(w, h)  # OR
               fig.set_size_inches((w, h))
  
          Parameters
          ----------
          w : (float, float) or float
              Width and height in inches (if height not specified as a separate
              argument) or width.
          h : float
              Height in inches.
          forward : bool, default: True
              If ``True``, the canvas size is automatically updated, e.g.,
              you can resize the figure window from the shell.
  
          See Also
          --------
          matplotlib.figure.Figure.get_size_inches
          matplotlib.figure.Figure.set_figwidth
          matplotlib.figure.Figure.set_figheight
  
          Notes
          -----
          To transform from pixels to inches divide by `Figure.dpi`.
          """
          if h is None:  # Got called with a single pair as argument.
              w, h = w
          if w is None or h is None:
              raise ValueError(
                  "Figure.set_size_inches does not accept None; provide both "
                  "width and height explicitly")
          size = np.array([w, h])
          if not np.isfinite(size).all() or (size < 0).any():
              raise ValueError(f'figure size must be positive finite not {size}')
          self.bbox_inches.p1 = size
          if forward:
              manager = self.canvas.manager
              if manager is not None:
                  manager.resize(*(size * self.dpi).astype(int))
          self.stale = True
  
      def get_size_inches(self):
          """
          Return the current size of the figure in inches.
  
          Returns
          -------
          ndarray
             The size (width, height) of the figure in inches.
  
          See Also
          --------
          matplotlib.figure.Figure.set_size_inches
          matplotlib.figure.Figure.get_figwidth
          matplotlib.figure.Figure.get_figheight
  
          Notes
          -----
          The size in pixels can be obtained by multiplying with `Figure.dpi`.
          """
          return np.array(self.bbox_inches.p1)
  
      def get_figwidth(self):
          """Return the figure width in inches."""
          return self.bbox_inches.width
  
      def get_figheight(self):
          """Return the figure height in inches."""
          return self.bbox_inches.height
  
      def get_dpi(self):
          """Return the resolution in dots per inch as a float."""
          return self.dpi
  
      def set_dpi(self, val):
          """
          Set the resolution of the figure in dots-per-inch.
  
          Parameters
          ----------
          val : float
          """
          self.dpi = val
          self.stale = True
  
      def set_figwidth(self, val, forward=True):
          """
          Set the width of the figure in inches.
  
          Parameters
          ----------
          val : float
          forward : bool
              See `set_size_inches`.
  
          See Also
          --------
          matplotlib.figure.Figure.set_figheight
          matplotlib.figure.Figure.set_size_inches
          """
          self.set_size_inches(val, self.get_figheight(), forward=forward)
  
      def set_figheight(self, val, forward=True):
          """
          Set the height of the figure in inches.
  
          Parameters
          ----------
          val : float
          forward : bool
              See `set_size_inches`.
  
          See Also
          --------
          matplotlib.figure.Figure.set_figwidth
          matplotlib.figure.Figure.set_size_inches
          """
          self.set_size_inches(self.get_figwidth(), val, forward=forward)
  
      def clear(self, keep_observers=False):
          # docstring inherited
          super().clear(keep_observers=keep_observers)
          # FigureBase.clear does not clear toolbars, as
          # only Figure can have toolbars
          toolbar = self.canvas.toolbar
          if toolbar is not None:
              toolbar.update()
  
      @_finalize_rasterization
      @allow_rasterization
      def draw(self, renderer):
          # docstring inherited
          if not self.get_visible():
              return
  
          with self._render_lock:
  
              artists = self._get_draw_artists(renderer)
              try:
                  renderer.open_group('figure', gid=self.get_gid())
                  if self.axes and self.get_layout_engine() is not None:
                      try:
                          self.get_layout_engine().execute(self)
                      except ValueError:
                          pass
                          # ValueError can occur when resizing a window.
  
                  self.patch.draw(renderer)
                  mimage._draw_list_compositing_images(
                      renderer, self, artists, self.suppressComposite)
  
                  renderer.close_group('figure')
              finally:
                  self.stale = False
  
              DrawEvent("draw_event", self.canvas, renderer)._process()
  
      def draw_without_rendering(self):
          """
          Draw the figure with no output.  Useful to get the final size of
          artists that require a draw before their size is known (e.g. text).
          """
          renderer = _get_renderer(self)
          with renderer._draw_disabled():
              self.draw(renderer)
  
      def draw_artist(self, a):
          """
          Draw `.Artist` *a* only.
          """
          a.draw(self.canvas.get_renderer())
  
      def __getstate__(self):
          state = super().__getstate__()
  
          # The canvas cannot currently be pickled, but this has the benefit
          # of meaning that a figure can be detached from one canvas, and
          # re-attached to another.
          state.pop("canvas")
  
          # discard any changes to the dpi due to pixel ratio changes
          state["_dpi"] = state.get('_original_dpi', state['_dpi'])
  
          # add version information to the state
          state['__mpl_version__'] = mpl.__version__
  
          # check whether the figure manager (if any) is registered with pyplot
          from matplotlib import _pylab_helpers
          if self.canvas.manager in _pylab_helpers.Gcf.figs.values():
              state['_restore_to_pylab'] = True
          return state
  
      def __setstate__(self, state):
          version = state.pop('__mpl_version__')
          restore_to_pylab = state.pop('_restore_to_pylab', False)
  
          if version != mpl.__version__:
              _api.warn_external(
                  f"This figure was saved with matplotlib version {version} and "
                  f"loaded with {mpl.__version__} so may not function correctly."
              )
          self.__dict__ = state
  
          # re-initialise some of the unstored state information
          self._set_base_canvas()
          # force the bounding boxes to respect current dpi
          self.dpi_scale_trans.clear().scale(self._dpi)
          if restore_to_pylab:
              # lazy import to avoid circularity
              import matplotlib.pyplot as plt
              import matplotlib._pylab_helpers as pylab_helpers
              allnums = plt.get_fignums()
              num = max(allnums) + 1 if allnums else 1
              backend = plt._get_backend_mod()
              mgr = backend.new_figure_manager_given_figure(num, self)
              pylab_helpers.Gcf._set_new_active_manager(mgr)
              plt.draw_if_interactive()
  
          self.stale = True
  
      def add_axobserver(self, func):
          """Whenever the Axes state change, ``func(self)`` will be called."""
          # Connect a wrapper lambda and not func itself, to avoid it being
          # weakref-collected.
          self._axobservers.connect("_axes_change_event", lambda arg: func(arg))
  
      def savefig(self, fname, *, transparent=None, **kwargs):
          """
          Save the current figure as an image or vector graphic to a file.
  
          Call signature::
  
            savefig(fname, *, transparent=None, dpi='figure', format=None,
                    metadata=None, bbox_inches=None, pad_inches=0.1,
                    facecolor='auto', edgecolor='auto', backend=None,
                    **kwargs
                   )
  
          The available output formats depend on the backend being used.
  
          Parameters
          ----------
          fname : str or path-like or binary file-like
              A path, or a Python file-like object, or
              possibly some backend-dependent object such as
              `matplotlib.backends.backend_pdf.PdfPages`.
  
              If *format* is set, it determines the output format, and the file
              is saved as *fname*.  Note that *fname* is used verbatim, and there
              is no attempt to make the extension, if any, of *fname* match
              *format*, and no extension is appended.
  
              If *format* is not set, then the format is inferred from the
              extension of *fname*, if there is one.  If *format* is not
              set and *fname* has no extension, then the file is saved with
              :rc:`savefig.format` and the appropriate extension is appended to
              *fname*.
  
          Other Parameters
          ----------------
          transparent : bool, default: :rc:`savefig.transparent`
              If *True*, the Axes patches will all be transparent; the
              Figure patch will also be transparent unless *facecolor*
              and/or *edgecolor* are specified via kwargs.
  
              If *False* has no effect and the color of the Axes and
              Figure patches are unchanged (unless the Figure patch
              is specified via the *facecolor* and/or *edgecolor* keyword
              arguments in which case those colors are used).
  
              The transparency of these patches will be restored to their
              original values upon exit of this function.
  
              This is useful, for example, for displaying
              a plot on top of a colored background on a web page.
  
          dpi : float or 'figure', default: :rc:`savefig.dpi`
              The resolution in dots per inch.  If 'figure', use the figure's
              dpi value.
  
          format : str
              The file format, e.g. 'png', 'pdf', 'svg', ... The behavior when
              this is unset is documented under *fname*.
  
          metadata : dict, optional
              Key/value pairs to store in the image metadata. The supported keys
              and defaults depend on the image format and backend:
  
              - 'png' with Agg backend: See the parameter ``metadata`` of
                `~.FigureCanvasAgg.print_png`.
              - 'pdf' with pdf backend: See the parameter ``metadata`` of
                `~.backend_pdf.PdfPages`.
              - 'svg' with svg backend: See the parameter ``metadata`` of
                `~.FigureCanvasSVG.print_svg`.
              - 'eps' and 'ps' with PS backend: Only 'Creator' is supported.
  
              Not supported for 'pgf', 'raw', and 'rgba' as those formats do not support
              embedding metadata.
              Does not currently support 'jpg', 'tiff', or 'webp', but may include
              embedding EXIF metadata in the future.
  
          bbox_inches : str or `.Bbox`, default: :rc:`savefig.bbox`
              Bounding box in inches: only the given portion of the figure is
              saved.  If 'tight', try to figure out the tight bbox of the figure.
  
          pad_inches : float or 'layout', default: :rc:`savefig.pad_inches`
              Amount of padding in inches around the figure when bbox_inches is
              'tight'. If 'layout' use the padding from the constrained or
              compressed layout engine; ignored if one of those engines is not in
              use.
  
          facecolor : :mpltype:`color` or 'auto', default: :rc:`savefig.facecolor`
              The facecolor of the figure.  If 'auto', use the current figure
              facecolor.
  
          edgecolor : :mpltype:`color` or 'auto', default: :rc:`savefig.edgecolor`
              The edgecolor of the figure.  If 'auto', use the current figure
              edgecolor.
  
          backend : str, optional
              Use a non-default backend to render the file, e.g. to render a
              png file with the "cairo" backend rather than the default "agg",
              or a pdf file with the "pgf" backend rather than the default
              "pdf".  Note that the default backend is normally sufficient.  See
              :ref:`the-builtin-backends` for a list of valid backends for each
              file format.  Custom backends can be referenced as "module://...".
  
          orientation : {'landscape', 'portrait'}
              Currently only supported by the postscript backend.
  
          papertype : str
              One of 'letter', 'legal', 'executive', 'ledger', 'a0' through
              'a10', 'b0' through 'b10'. Only supported for postscript
              output.
  
          bbox_extra_artists : list of `~matplotlib.artist.Artist`, optional
              A list of extra artists that will be considered when the
              tight bbox is calculated.
  
          pil_kwargs : dict, optional
              Additional keyword arguments that are passed to
              `PIL.Image.Image.save` when saving the figure.
  
          """
  
          kwargs.setdefault('dpi', mpl.rcParams['savefig.dpi'])
          transparent = mpl._val_or_rc(transparent, 'savefig.transparent')
  
          with ExitStack() as stack:
              if transparent:
                  def _recursively_make_subfig_transparent(exit_stack, subfig):
                      exit_stack.enter_context(
                          subfig.patch._cm_set(
                              facecolor="none", edgecolor="none"))
                      for ax in subfig.axes:
                          exit_stack.enter_context(
                              ax.patch._cm_set(
                                  facecolor="none", edgecolor="none"))
                      for sub_subfig in subfig.subfigs:
                          _recursively_make_subfig_transparent(
                              exit_stack, sub_subfig)
  
                  def _recursively_make_axes_transparent(exit_stack, ax):
                      exit_stack.enter_context(
                          ax.patch._cm_set(facecolor="none", edgecolor="none"))
                      for child_ax in ax.child_axes:
                          exit_stack.enter_context(
                              child_ax.patch._cm_set(
                                  facecolor="none", edgecolor="none"))
                      for child_childax in ax.child_axes:
                          _recursively_make_axes_transparent(
                              exit_stack, child_childax)
  
                  kwargs.setdefault('facecolor', 'none')
                  kwargs.setdefault('edgecolor', 'none')
                  # set subfigure to appear transparent in printed image
                  for subfig in self.subfigs:
                      _recursively_make_subfig_transparent(stack, subfig)
                  # set Axes to be transparent
                  for ax in self.axes:
                      _recursively_make_axes_transparent(stack, ax)
              self.canvas.print_figure(fname, **kwargs)
  
      def ginput(self, n=1, timeout=30, show_clicks=True,
                 mouse_add=MouseButton.LEFT,
                 mouse_pop=MouseButton.RIGHT,
                 mouse_stop=MouseButton.MIDDLE):
          """
          Blocking call to interact with a figure.
  
          Wait until the user clicks *n* times on the figure, and return the
          coordinates of each click in a list.
  
          There are three possible interactions:
  
          - Add a point.
          - Remove the most recently added point.
          - Stop the interaction and return the points added so far.
  
          The actions are assigned to mouse buttons via the arguments
          *mouse_add*, *mouse_pop* and *mouse_stop*.
  
          Parameters
          ----------
          n : int, default: 1
              Number of mouse clicks to accumulate. If negative, accumulate
              clicks until the input is terminated manually.
          timeout : float, default: 30 seconds
              Number of seconds to wait before timing out. If zero or negative
              will never time out.
          show_clicks : bool, default: True
              If True, show a red cross at the location of each click.
          mouse_add : `.MouseButton` or None, default: `.MouseButton.LEFT`
              Mouse button used to add points.
          mouse_pop : `.MouseButton` or None, default: `.MouseButton.RIGHT`
              Mouse button used to remove the most recently added point.
          mouse_stop : `.MouseButton` or None, default: `.MouseButton.MIDDLE`
              Mouse button used to stop input.
  
          Returns
          -------
          list of tuples
              A list of the clicked (x, y) coordinates.
  
          Notes
          -----
          The keyboard can also be used to select points in case your mouse
          does not have one or more of the buttons.  The delete and backspace
          keys act like right-clicking (i.e., remove last point), the enter key
          terminates input and any other key (not already used by the window
          manager) selects a point.
          """
          clicks = []
          marks = []
  
          def handler(event):
              is_button = event.name == "button_press_event"
              is_key = event.name == "key_press_event"
              # Quit (even if not in infinite mode; this is consistent with
              # MATLAB and sometimes quite useful, but will require the user to
              # test how many points were actually returned before using data).
              if (is_button and event.button == mouse_stop
                      or is_key and event.key in ["escape", "enter"]):
                  self.canvas.stop_event_loop()
              # Pop last click.
              elif (is_button and event.button == mouse_pop
                    or is_key and event.key in ["backspace", "delete"]):
                  if clicks:
                      clicks.pop()
                      if show_clicks:
                          marks.pop().remove()
                          self.canvas.draw()
              # Add new click.
              elif (is_button and event.button == mouse_add
                    # On macOS/gtk, some keys return None.
                    or is_key and event.key is not None):
                  if event.inaxes:
                      clicks.append((event.xdata, event.ydata))
                      _log.info("input %i: %f, %f",
                                len(clicks), event.xdata, event.ydata)
                      if show_clicks:
                          line = mpl.lines.Line2D([event.xdata], [event.ydata],
                                                  marker="+", color="r")
                          event.inaxes.add_line(line)
                          marks.append(line)
                          self.canvas.draw()
              if len(clicks) == n and n > 0:
                  self.canvas.stop_event_loop()
  
          _blocking_input.blocking_input_loop(
              self, ["button_press_event", "key_press_event"], timeout, handler)
  
          # Cleanup.
          for mark in marks:
              mark.remove()
          self.canvas.draw()
  
          return clicks
  
      def waitforbuttonpress(self, timeout=-1):
          """
          Blocking call to interact with the figure.
  
          Wait for user input and return True if a key was pressed, False if a
          mouse button was pressed and None if no input was given within
          *timeout* seconds.  Negative values deactivate *timeout*.
          """
          event = None
  
          def handler(ev):
              nonlocal event
              event = ev
              self.canvas.stop_event_loop()
  
          _blocking_input.blocking_input_loop(
              self, ["button_press_event", "key_press_event"], timeout, handler)
  
          return None if event is None else event.name == "key_press_event"
  
      def tight_layout(self, *, pad=1.08, h_pad=None, w_pad=None, rect=None):
          """
          Adjust the padding between and around subplots.
  
          To exclude an artist on the Axes from the bounding box calculation
          that determines the subplot parameters (i.e. legend, or annotation),
          set ``a.set_in_layout(False)`` for that artist.
  
          Parameters
          ----------
          pad : float, default: 1.08
              Padding between the figure edge and the edges of subplots,
              as a fraction of the font size.
          h_pad, w_pad : float, default: *pad*
              Padding (height/width) between edges of adjacent subplots,
              as a fraction of the font size.
          rect : tuple (left, bottom, right, top), default: (0, 0, 1, 1)
              A rectangle in normalized figure coordinates into which the whole
              subplots area (including labels) will fit.
  
          See Also
          --------
          .Figure.set_layout_engine
          .pyplot.tight_layout
          """
          # note that here we do not permanently set the figures engine to
          # tight_layout but rather just perform the layout in place and remove
          # any previous engines.
          engine = TightLayoutEngine(pad=pad, h_pad=h_pad, w_pad=w_pad, rect=rect)
          try:
              previous_engine = self.get_layout_engine()
              self.set_layout_engine(engine)
              engine.execute(self)
              if previous_engine is not None and not isinstance(
                  previous_engine, (TightLayoutEngine, PlaceHolderLayoutEngine)
              ):
                  _api.warn_external('The figure layout has changed to tight')
          finally:
              self.set_layout_engine('none')
  
  
  def figaspect(arg):
      """
      Calculate the width and height for a figure with a specified aspect ratio.
  
      While the height is taken from :rc:`figure.figsize`, the width is
      adjusted to match the desired aspect ratio. Additionally, it is ensured
      that the width is in the range [4., 16.] and the height is in the range
      [2., 16.]. If necessary, the default height is adjusted to ensure this.
  
      Parameters
      ----------
      arg : float or 2D array
          If a float, this defines the aspect ratio (i.e. the ratio height /
          width).
          In case of an array the aspect ratio is number of rows / number of
          columns, so that the array could be fitted in the figure undistorted.
  
      Returns
      -------
      size : (2,) array
          The width and height of the figure in inches.
  
      Notes
      -----
      If you want to create an Axes within the figure, that still preserves the
      aspect ratio, be sure to create it with equal width and height. See
      examples below.
  
      Thanks to Fernando Perez for this function.
  
      Examples
      --------
      Make a figure twice as tall as it is wide::
  
          w, h = figaspect(2.)
          fig = Figure(figsize=(w, h))
          ax = fig.add_axes((0.1, 0.1, 0.8, 0.8))
          ax.imshow(A, **kwargs)
  
      Make a figure with the proper aspect for an array::
  
          A = rand(5, 3)
          w, h = figaspect(A)
          fig = Figure(figsize=(w, h))
          ax = fig.add_axes((0.1, 0.1, 0.8, 0.8))
          ax.imshow(A, **kwargs)
      """
  
      isarray = hasattr(arg, 'shape') and not np.isscalar(arg)
  
      # min/max sizes to respect when autoscaling.  If John likes the idea, they
      # could become rc parameters, for now they're hardwired.
      figsize_min = np.array((4.0, 2.0))  # min length for width/height
      figsize_max = np.array((16.0, 16.0))  # max length for width/height
  
      # Extract the aspect ratio of the array
      if isarray:
          nr, nc = arg.shape[:2]
          arr_ratio = nr / nc
      else:
          arr_ratio = arg
  
      # Height of user figure defaults
      fig_height = mpl.rcParams['figure.figsize'][1]
  
      # New size for the figure, keeping the aspect ratio of the caller
      newsize = np.array((fig_height / arr_ratio, fig_height))
  
      # Sanity checks, don't drop either dimension below figsize_min
      newsize /= min(1.0, *(newsize / figsize_min))
  
      # Avoid humongous windows as well
      newsize /= max(1.0, *(newsize / figsize_max))
  
      # Finally, if we have a really funky aspect ratio, break it but respect
      # the min/max dimensions (we don't want figures 10 feet tall!)
      newsize = np.clip(newsize, figsize_min, figsize_max)
      return newsize
  
  
  def _parse_figsize(figsize, dpi):
      """
      Convert a figsize expression to (width, height) in inches.
  
      Parameters
      ----------
      figsize : (float, float) or (float, float, str)
          This can be
  
          - a tuple ``(width, height, unit)``, where *unit* is one of "in" (inch),
            "cm" (centimenter), "px" (pixel).
          - a tuple ``(width, height)``, which is interpreted in inches, i.e. as
            ``(width, height, "in")``.
  
      dpi : float
          The dots-per-inch; used for converting 'px' to 'in'.
      """
      num_parts = len(figsize)
      if num_parts == 2:
          x, y = figsize
      elif num_parts == 3:
          x, y, unit = figsize
          if unit == 'in':
              pass
          elif unit == 'cm':
              if x is not None:
                  x /= 2.54
              if y is not None:
                  y /= 2.54
          elif unit == 'px':
              if x is not None:
                  x /= dpi
              if y is not None:
                  y /= dpi
          else:
              raise ValueError(
                  f"Invalid unit {unit!r} in 'figsize'; "
                  "supported units are 'in', 'cm', 'px'"
              )
      else:
          raise ValueError(
              "Invalid figsize format, expected (x, y) or (x, y, unit) but got "
              f"{figsize!r}"
          )
  
      if x is None and y is None:
          raise ValueError(
              "figsize=(None, None) is invalid; at least one of width or "
              "height must be provided")
  
      default_width, default_height = mpl.rcParams["figure.figsize"]
      if x is None:
          x = default_width
      if y is None:
          y = default_height
      return x, y
  