_base.py

from collections import OrderedDict
import itertools
import logging
import math
from numbers import Real
from operator import attrgetter
import types

import numpy as np

import matplotlib as mpl
from matplotlib import cbook, rcParams
from matplotlib.cbook import _OrderedSet, _check_1d, index_of
from matplotlib import docstring
import matplotlib.colors as mcolors
import matplotlib.lines as mlines
import matplotlib.patches as mpatches
import matplotlib.artist as martist
import matplotlib.transforms as mtransforms
import matplotlib.ticker as mticker
import matplotlib.axis as maxis
import matplotlib.spines as mspines
import matplotlib.font_manager as font_manager
import matplotlib.text as mtext
import matplotlib.image as mimage
from matplotlib.rcsetup import cycler, validate_axisbelow

_log = logging.getLogger(__name__)


def _process_plot_format(fmt):
    """
    Convert a MATLAB style color/line style format string to a (*linestyle*,
    *marker*, *color*) tuple.

    Example format strings include:

    * 'ko': black circles
    * '.b': blue dots
    * 'r--': red dashed lines
    * 'C2--': the third color in the color cycle, dashed lines

    See Also
    --------
    matplotlib.Line2D.lineStyles, matplotlib.colors.cnames
        All possible styles and color format strings.
    """

    linestyle = None
    marker = None
    color = None

    # Is fmt just a colorspec?
    try:
        color = mcolors.to_rgba(fmt)

        # We need to differentiate grayscale '1.0' from tri_down marker '1'
        try:
            fmtint = str(int(fmt))
        except ValueError:
            return linestyle, marker, color  # Yes
        else:
            if fmt != fmtint:
                # user definitely doesn't want tri_down marker
                return linestyle, marker, color  # Yes
            else:
                # ignore converted color
                color = None
    except ValueError:
        pass  # No, not just a color.

    i = 0
    while i < len(fmt):
        c = fmt[i]
        if fmt[i:i+2] in mlines.lineStyles:  # First, the two-char styles.
            if linestyle is not None:
                raise ValueError(
                    'Illegal format string "%s"; two linestyle symbols' % fmt)
            linestyle = fmt[i:i+2]
            i += 2
        elif c in mlines.lineStyles:
            if linestyle is not None:
                raise ValueError(
                    'Illegal format string "%s"; two linestyle symbols' % fmt)
            linestyle = c
            i += 1
        elif c in mlines.lineMarkers:
            if marker is not None:
                raise ValueError(
                    'Illegal format string "%s"; two marker symbols' % fmt)
            marker = c
            i += 1
        elif c in mcolors.get_named_colors_mapping():
            if color is not None:
                raise ValueError(
                    'Illegal format string "%s"; two color symbols' % fmt)
            color = c
            i += 1
        elif c == 'C' and i < len(fmt) - 1:
            color_cycle_number = int(fmt[i + 1])
            color = mcolors.to_rgba("C{}".format(color_cycle_number))
            i += 2
        else:
            raise ValueError(
                'Unrecognized character %c in format string' % c)

    if linestyle is None and marker is None:
        linestyle = rcParams['lines.linestyle']
    if linestyle is None:
        linestyle = 'None'
    if marker is None:
        marker = 'None'

    return linestyle, marker, color


class _process_plot_var_args:
    """
    Process variable length arguments to the plot command, so that
    plot commands like the following are supported::

      plot(t, s)
      plot(t1, s1, t2, s2)
      plot(t1, s1, 'ko', t2, s2)
      plot(t1, s1, 'ko', t2, s2, 'r--', t3, e3)

    an arbitrary number of *x*, *y*, *fmt* are allowed
    """
    def __init__(self, axes, command='plot'):
        self.axes = axes
        self.command = command
        self.set_prop_cycle()

    def __getstate__(self):
        # note: it is not possible to pickle a generator (and thus a cycler).
        return {'axes': self.axes, 'command': self.command}

    def __setstate__(self, state):
        self.__dict__ = state.copy()
        self.set_prop_cycle()

    def set_prop_cycle(self, *args, **kwargs):
        # Can't do `args == (None,)` as that crashes cycler.
        if not (args or kwargs) or (len(args) == 1 and args[0] is None):
            prop_cycler = rcParams['axes.prop_cycle']
        else:
            prop_cycler = cycler(*args, **kwargs)

        self.prop_cycler = itertools.cycle(prop_cycler)
        # This should make a copy
        self._prop_keys = prop_cycler.keys

    def __call__(self, *args, **kwargs):
        self.axes._process_unit_info(kwargs=kwargs)

        for pos_only in "xy":
            if pos_only in kwargs:
                raise TypeError("{} got an unexpected keyword argument {!r}"
                                .format(self.command, pos_only))

        if not args:
            return

        # Process the 'data' kwarg.
        data = kwargs.pop("data", None)
        if data is not None:
            replaced = [mpl._replacer(data, arg) for arg in args]
            if len(args) == 1:
                label_namer_idx = 0
            elif len(args) == 2:  # Can be x, y or y, c.
                # Figure out what the second argument is.
                # 1) If the second argument cannot be a format shorthand, the
                #    second argument is the label_namer.
                # 2) Otherwise (it could have been a format shorthand),
                #    a) if we did perform a substitution, emit a warning, and
                #       use it as label_namer.
                #    b) otherwise, it is indeed a format shorthand; use the
                #       first argument as label_namer.
                try:
                    _process_plot_format(args[1])
                except ValueError:  # case 1)
                    label_namer_idx = 1
                else:
                    if replaced[1] is not args[1]:  # case 2a)
                        cbook._warn_external(
                            f"Second argument {args[1]!r} is ambiguous: could "
                            f"be a format string but is in 'data'; using as "
                            f"data.  If it was intended as data, set the "
                            f"format string to an empty string to suppress "
                            f"this warning.  If it was intended as a format "
                            f"string, explicitly pass the x-values as well.  "
                            f"Alternatively, rename the entry in 'data'.",
                            RuntimeWarning)
                        label_namer_idx = 1
                    else:  # case 2b)
                        label_namer_idx = 0
            elif len(args) == 3:
                label_namer_idx = 1
            else:
                raise ValueError(
                    "Using arbitrary long args with data is not supported due "
                    "to ambiguity of arguments; use multiple plotting calls "
                    "instead")
            if kwargs.get("label") is None:
                kwargs["label"] = mpl._label_from_arg(
                    replaced[label_namer_idx], args[label_namer_idx])
            args = replaced

        # Repeatedly grab (x, y) or (x, y, format) from the front of args and
        # massage them into arguments to plot() or fill().
        while args:
            this, args = args[:2], args[2:]
            if args and isinstance(args[0], str):
                this += args[0],
                args = args[1:]
            yield from self._plot_args(this, kwargs)

    def get_next_color(self):
        """Return the next color in the cycle."""
        if 'color' not in self._prop_keys:
            return 'k'
        return next(self.prop_cycler)['color']

    def _getdefaults(self, ignore, kw):
        """
        If some keys in the property cycle (excluding those in the set
        *ignore*) are absent or set to None in the dict *kw*, return a copy
        of the next entry in the property cycle, excluding keys in *ignore*.
        Otherwise, don't advance the property cycle, and return an empty dict.
        """
        prop_keys = self._prop_keys - ignore
        if any(kw.get(k, None) is None for k in prop_keys):
            # Need to copy this dictionary or else the next time around
            # in the cycle, the dictionary could be missing entries.
            default_dict = next(self.prop_cycler).copy()
            for p in ignore:
                default_dict.pop(p, None)
        else:
            default_dict = {}
        return default_dict

    def _setdefaults(self, defaults, kw):
        """
        Add to the dict *kw* the entries in the dict *default* that are absent
        or set to None in *kw*.
        """
        for k in defaults:
            if kw.get(k, None) is None:
                kw[k] = defaults[k]

    def _makeline(self, x, y, kw, kwargs):
        kw = {**kw, **kwargs}  # Don't modify the original kw.
        default_dict = self._getdefaults(set(), kw)
        self._setdefaults(default_dict, kw)
        seg = mlines.Line2D(x, y, **kw)
        return seg

    def _makefill(self, x, y, kw, kwargs):
        # Polygon doesn't directly support unitized inputs.
        x = self.axes.convert_xunits(x)
        y = self.axes.convert_yunits(y)

        kw = kw.copy()  # Don't modify the original kw.
        kwargs = kwargs.copy()

        # Ignore 'marker'-related properties as they aren't Polygon
        # properties, but they are Line2D properties, and so they are
        # likely to appear in the default cycler construction.
        # This is done here to the defaults dictionary as opposed to the
        # other two dictionaries because we do want to capture when a
        # *user* explicitly specifies a marker which should be an error.
        # We also want to prevent advancing the cycler if there are no
        # defaults needed after ignoring the given properties.
        ignores = {'marker', 'markersize', 'markeredgecolor',
                   'markerfacecolor', 'markeredgewidth'}
        # Also ignore anything provided by *kwargs*.
        for k, v in kwargs.items():
            if v is not None:
                ignores.add(k)

        # Only using the first dictionary to use as basis
        # for getting defaults for back-compat reasons.
        # Doing it with both seems to mess things up in
        # various places (probably due to logic bugs elsewhere).
        default_dict = self._getdefaults(ignores, kw)
        self._setdefaults(default_dict, kw)

        # Looks like we don't want "color" to be interpreted to
        # mean both facecolor and edgecolor for some reason.
        # So the "kw" dictionary is thrown out, and only its
        # 'color' value is kept and translated as a 'facecolor'.
        # This design should probably be revisited as it increases
        # complexity.
        facecolor = kw.get('color', None)

        # Throw out 'color' as it is now handled as a facecolor
        default_dict.pop('color', None)

        # To get other properties set from the cycler
        # modify the kwargs dictionary.
        self._setdefaults(default_dict, kwargs)

        seg = mpatches.Polygon(np.column_stack((x, y)),
                               facecolor=facecolor,
                               fill=kwargs.get('fill', True),
                               closed=kw['closed'])
        seg.set(**kwargs)
        return seg

    def _plot_args(self, tup, kwargs):
        if len(tup) > 1 and isinstance(tup[-1], str):
            linestyle, marker, color = _process_plot_format(tup[-1])
            tup = tup[:-1]
        elif len(tup) == 3:
            raise ValueError('third arg must be a format string')
        else:
            linestyle, marker, color = None, None, None

        # Don't allow any None value; these would be up-converted to one
        # element array of None which causes problems downstream.
        if any(v is None for v in tup):
            raise ValueError("x, y, and format string must not be None")

        kw = {}
        for k, v in zip(('linestyle', 'marker', 'color'),
                        (linestyle, marker, color)):
            if v is not None:
                kw[k] = v

        if len(tup) == 2:
            x = _check_1d(tup[0])
            y = _check_1d(tup[-1])
        else:
            x, y = index_of(tup[-1])

        if self.axes.xaxis is not None:
            self.axes.xaxis.update_units(x)
        if self.axes.yaxis is not None:
            self.axes.yaxis.update_units(y)

        if x.shape[0] != y.shape[0]:
            raise ValueError(f"x and y must have same first dimension, but "
                             f"have shapes {x.shape} and {y.shape}")
        if x.ndim > 2 or y.ndim > 2:
            raise ValueError(f"x and y can be no greater than 2-D, but have "
                             f"shapes {x.shape} and {y.shape}")
        if x.ndim == 1:
            x = x[:, np.newaxis]
        if y.ndim == 1:
            y = y[:, np.newaxis]

        if self.command == 'plot':
            func = self._makeline
        else:
            kw['closed'] = kwargs.get('closed', True)
            func = self._makefill

        ncx, ncy = x.shape[1], y.shape[1]
        if ncx > 1 and ncy > 1 and ncx != ncy:
            cbook.warn_deprecated(
                "2.2", message="cycling among columns of inputs with "
                "non-matching shapes is deprecated.")
        return [func(x[:, j % ncx], y[:, j % ncy], kw, kwargs)
                for j in range(max(ncx, ncy))]


class _AxesBase(martist.Artist):
    name = "rectilinear"

    _shared_x_axes = cbook.Grouper()
    _shared_y_axes = cbook.Grouper()
    _twinned_axes = cbook.Grouper()

    def __str__(self):
        return "{0}({1[0]:g},{1[1]:g};{1[2]:g}x{1[3]:g})".format(
            type(self).__name__, self._position.bounds)

    def __init__(self, fig, rect,
                 facecolor=None,  # defaults to rc axes.facecolor
                 frameon=True,
                 sharex=None,  # use Axes instance's xaxis info
                 sharey=None,  # use Axes instance's yaxis info
                 label='',
                 xscale=None,
                 yscale=None,
                 **kwargs
                 ):
        """
        Build an axes in a figure.

        Parameters
        ----------
        fig : `~matplotlib.figure.Figure`
            The axes is build in the `.Figure` *fig*.

        rect : [left, bottom, width, height]
            The axes is build in the rectangle *rect*. *rect* is in
            `.Figure` coordinates.

        sharex, sharey : `~.axes.Axes`, optional
            The x or y `~.matplotlib.axis` is shared with the x or
            y axis in the input `~.axes.Axes`.

        frameon : bool, optional
            True means that the axes frame is visible.

        **kwargs
            Other optional keyword arguments:

            %(Axes)s

        Returns
        -------
        axes : `~.axes.Axes`
            The new `~.axes.Axes` object.
        """

        martist.Artist.__init__(self)
        if isinstance(rect, mtransforms.Bbox):
            self._position = rect
        else:
            self._position = mtransforms.Bbox.from_bounds(*rect)
        if self._position.width < 0 or self._position.height < 0:
            raise ValueError('Width and height specified must be non-negative')
        self._originalPosition = self._position.frozen()
        self.axes = self
        self._aspect = 'auto'
        self._adjustable = 'box'
        self._anchor = 'C'
        self._stale_viewlim_x = False
        self._stale_viewlim_y = False
        self._sharex = sharex
        self._sharey = sharey
        if sharex is not None:
            self._shared_x_axes.join(self, sharex)
        if sharey is not None:
            self._shared_y_axes.join(self, sharey)
        self.set_label(label)
        self.set_figure(fig)

        self.set_axes_locator(kwargs.get("axes_locator", None))

        self.spines = self._gen_axes_spines()

        # this call may differ for non-sep axes, e.g., polar
        self._init_axis()
        if facecolor is None:
            facecolor = rcParams['axes.facecolor']
        self._facecolor = facecolor
        self._frameon = frameon
        self.set_axisbelow(rcParams['axes.axisbelow'])

        self._rasterization_zorder = None
        self.cla()

        # funcs used to format x and y - fall back on major formatters
        self.fmt_xdata = None
        self.fmt_ydata = None

        self.set_navigate(True)
        self.set_navigate_mode(None)

        if xscale:
            self.set_xscale(xscale)
        if yscale:
            self.set_yscale(yscale)

        self.update(kwargs)

        if self.xaxis is not None:
            self._xcid = self.xaxis.callbacks.connect(
                'units finalize', lambda: self._on_units_changed(scalex=True))

        if self.yaxis is not None:
            self._ycid = self.yaxis.callbacks.connect(
                'units finalize', lambda: self._on_units_changed(scaley=True))

        self.tick_params(
            top=rcParams['xtick.top'] and rcParams['xtick.minor.top'],
            bottom=rcParams['xtick.bottom'] and rcParams['xtick.minor.bottom'],
            labeltop=(rcParams['xtick.labeltop'] and
                      rcParams['xtick.minor.top']),
            labelbottom=(rcParams['xtick.labelbottom'] and
                         rcParams['xtick.minor.bottom']),
            left=rcParams['ytick.left'] and rcParams['ytick.minor.left'],
            right=rcParams['ytick.right'] and rcParams['ytick.minor.right'],
            labelleft=(rcParams['ytick.labelleft'] and
                       rcParams['ytick.minor.left']),
            labelright=(rcParams['ytick.labelright'] and
                        rcParams['ytick.minor.right']),
            which='minor')

        self.tick_params(
            top=rcParams['xtick.top'] and rcParams['xtick.major.top'],
            bottom=rcParams['xtick.bottom'] and rcParams['xtick.major.bottom'],
            labeltop=(rcParams['xtick.labeltop'] and
                      rcParams['xtick.major.top']),
            labelbottom=(rcParams['xtick.labelbottom'] and
                         rcParams['xtick.major.bottom']),
            left=rcParams['ytick.left'] and rcParams['ytick.major.left'],
            right=rcParams['ytick.right'] and rcParams['ytick.major.right'],
            labelleft=(rcParams['ytick.labelleft'] and
                       rcParams['ytick.major.left']),
            labelright=(rcParams['ytick.labelright'] and
                        rcParams['ytick.major.right']),
            which='major')

        self._layoutbox = None
        self._poslayoutbox = None

    def __getstate__(self):
        # The renderer should be re-created by the figure, and then cached at
        # that point.
        state = super().__getstate__()
        for key in ['_layoutbox', '_poslayoutbox']:
            state[key] = None
        # Prune the sharing & twinning info to only contain the current group.
        for grouper_name in [
                '_shared_x_axes', '_shared_y_axes', '_twinned_axes']:
            grouper = getattr(self, grouper_name)
            state[grouper_name] = (grouper.get_siblings(self)
                                   if self in grouper else None)
        return state

    def __setstate__(self, state):
        # Merge the grouping info back into the global groupers.
        for grouper_name in [
                '_shared_x_axes', '_shared_y_axes', '_twinned_axes']:
            siblings = state.pop(grouper_name)
            if siblings:
                getattr(self, grouper_name).join(*siblings)
        self.__dict__ = state
        self._stale = True

    def get_window_extent(self, *args, **kwargs):
        """
        Return the axes bounding box in display space; *args* and *kwargs*
        are empty.

        This bounding box does not include the spines, ticks, ticklables,
        or other labels.  For a bounding box including these elements use
        `~matplotlib.axes.Axes.get_tightbbox`.

        See Also
        --------
        matplotlib.axes.Axes.get_tightbbox
        matplotlib.axis.Axis.get_tightbbox
        matplotlib.spines.get_window_extent

        """
        return self.bbox

    def _init_axis(self):
        "move this out of __init__ because non-separable axes don't use it"
        self.xaxis = maxis.XAxis(self)
        self.spines['bottom'].register_axis(self.xaxis)
        self.spines['top'].register_axis(self.xaxis)
        self.yaxis = maxis.YAxis(self)
        self.spines['left'].register_axis(self.yaxis)
        self.spines['right'].register_axis(self.yaxis)
        self._update_transScale()

    def set_figure(self, fig):
        """
        Set the `.Figure` for this `.Axes`.

        Parameters
        ----------
        fig : `.Figure`
        """
        martist.Artist.set_figure(self, fig)

        self.bbox = mtransforms.TransformedBbox(self._position,
                                                fig.transFigure)
        # these will be updated later as data is added
        self.dataLim = mtransforms.Bbox.null()
        self._viewLim = mtransforms.Bbox.unit()
        self.transScale = mtransforms.TransformWrapper(
            mtransforms.IdentityTransform())

        self._set_lim_and_transforms()

    def _unstale_viewLim(self):
        # We should arrange to store this information once per share-group
        # instead of on every axis.
        scalex = any(ax._stale_viewlim_x
                     for ax in self._shared_x_axes.get_siblings(self))
        scaley = any(ax._stale_viewlim_y
                     for ax in self._shared_y_axes.get_siblings(self))
        if scalex or scaley:
            for ax in self._shared_x_axes.get_siblings(self):
                ax._stale_viewlim_x = False
            for ax in self._shared_y_axes.get_siblings(self):
                ax._stale_viewlim_y = False
            self.autoscale_view(scalex=scalex, scaley=scaley)

    @property
    def viewLim(self):
        self._unstale_viewLim()
        return self._viewLim

    # API could be better, right now this is just to match the old calls to
    # autoscale_view() after each plotting method.
    def _request_autoscale_view(self, tight=None, scalex=True, scaley=True):
        if tight is not None:
            self._tight = tight
        if scalex:
            self._stale_viewlim_x = True  # Else keep old state.
        if scaley:
            self._stale_viewlim_y = True

    def _set_lim_and_transforms(self):
        """
        Set the *_xaxis_transform*, *_yaxis_transform*, *transScale*,
        *transData*, *transLimits* and *transAxes* transformations.

        .. note::

            This method is primarily used by rectilinear projections of the
            `~matplotlib.axes.Axes` class, and is meant to be overridden by
            new kinds of projection axes that need different transformations
            and limits. (See `~matplotlib.projections.polar.PolarAxes` for an
            example.)
        """
        self.transAxes = mtransforms.BboxTransformTo(self.bbox)

        # Transforms the x and y axis separately by a scale factor.
        # It is assumed that this part will have non-linear components
        # (e.g., for a log scale).
        self.transScale = mtransforms.TransformWrapper(
            mtransforms.IdentityTransform())

        # An affine transformation on the data, generally to limit the
        # range of the axes
        self.transLimits = mtransforms.BboxTransformFrom(
            mtransforms.TransformedBbox(self._viewLim, self.transScale))

        # The parentheses are important for efficiency here -- they
        # group the last two (which are usually affines) separately
        # from the first (which, with log-scaling can be non-affine).
        self.transData = self.transScale + (self.transLimits + self.transAxes)

        self._xaxis_transform = mtransforms.blended_transform_factory(
            self.transData, self.transAxes)
        self._yaxis_transform = mtransforms.blended_transform_factory(
            self.transAxes, self.transData)

    def get_xaxis_transform(self, which='grid'):
        """
        Get the transformation used for drawing x-axis labels, ticks
        and gridlines.  The x-direction is in data coordinates and the
        y-direction is in axis coordinates.

        .. note::

            This transformation is primarily used by the
            `~matplotlib.axis.Axis` class, and is meant to be
            overridden by new kinds of projections that may need to
            place axis elements in different locations.
        """
        if which == 'grid':
            return self._xaxis_transform
        elif which == 'tick1':
            # for cartesian projection, this is bottom spine
            return self.spines['bottom'].get_spine_transform()
        elif which == 'tick2':
            # for cartesian projection, this is top spine
            return self.spines['top'].get_spine_transform()
        else:
            raise ValueError('unknown value for which')

    def get_xaxis_text1_transform(self, pad_points):
        """
        Returns
        -------
        transform : Transform
            The transform used for drawing x-axis labels, which will add
            *pad_points* of padding (in points) between the axes and the label.
            The x-direction is in data coordinates and the y-direction is in
            axis corrdinates
        valign : {'center', 'top', 'bottom', 'baseline', 'center_baseline'}
            The text vertical alignment.
        halign : {'center', 'left', 'right'}
            The text horizontal alignment.

        Notes
        -----
        This transformation is primarily used by the `~matplotlib.axis.Axis`
        class, and is meant to be overridden by new kinds of projections that
        may need to place axis elements in different locations.
        """
        labels_align = rcParams["xtick.alignment"]
        return (self.get_xaxis_transform(which='tick1') +
                mtransforms.ScaledTranslation(0, -1 * pad_points / 72,
                                              self.figure.dpi_scale_trans),
                "top", labels_align)

    def get_xaxis_text2_transform(self, pad_points):
        """
        Returns
        -------
        transform : Transform
            The transform used for drawing secondary x-axis labels, which will
            add *pad_points* of padding (in points) between the axes and the
            label.  The x-direction is in data coordinates and the y-direction
            is in axis corrdinates
        valign : {'center', 'top', 'bottom', 'baseline', 'center_baseline'}
            The text vertical alignment.
        halign : {'center', 'left', 'right'}
            The text horizontal alignment.

        Notes
        -----
        This transformation is primarily used by the `~matplotlib.axis.Axis`
        class, and is meant to be overridden by new kinds of projections that
        may need to place axis elements in different locations.
        """
        labels_align = rcParams["xtick.alignment"]
        return (self.get_xaxis_transform(which='tick2') +
                mtransforms.ScaledTranslation(0, pad_points / 72,
                                              self.figure.dpi_scale_trans),
                "bottom", labels_align)

    def get_yaxis_transform(self, which='grid'):
        """
        Get the transformation used for drawing y-axis labels, ticks
        and gridlines.  The x-direction is in axis coordinates and the
        y-direction is in data coordinates.

        .. note::

            This transformation is primarily used by the
            `~matplotlib.axis.Axis` class, and is meant to be
            overridden by new kinds of projections that may need to
            place axis elements in different locations.
        """
        if which == 'grid':
            return self._yaxis_transform
        elif which == 'tick1':
            # for cartesian projection, this is bottom spine
            return self.spines['left'].get_spine_transform()
        elif which == 'tick2':
            # for cartesian projection, this is top spine
            return self.spines['right'].get_spine_transform()
        else:
            raise ValueError('unknown value for which')

    def get_yaxis_text1_transform(self, pad_points):
        """
        Returns
        -------
        transform : Transform
            The transform used for drawing y-axis labels, which will add
            *pad_points* of padding (in points) between the axes and the label.
            The x-direction is in axis coordinates and the y-direction is in
            data corrdinates
        valign : {'center', 'top', 'bottom', 'baseline', 'center_baseline'}
            The text vertical alignment.
        halign : {'center', 'left', 'right'}
            The text horizontal alignment.

        Notes
        -----
        This transformation is primarily used by the `~matplotlib.axis.Axis`
        class, and is meant to be overridden by new kinds of projections that
        may need to place axis elements in different locations.
        """
        labels_align = rcParams["ytick.alignment"]
        return (self.get_yaxis_transform(which='tick1') +
                mtransforms.ScaledTranslation(-1 * pad_points / 72, 0,
                                              self.figure.dpi_scale_trans),
                labels_align, "right")

    def get_yaxis_text2_transform(self, pad_points):
        """
        Returns
        -------
        transform : Transform
            The transform used for drawing secondart y-axis labels, which will
            add *pad_points* of padding (in points) between the axes and the
            label.  The x-direction is in axis coordinates and the y-direction
            is in data corrdinates
        valign : {'center', 'top', 'bottom', 'baseline', 'center_baseline'}
            The text vertical alignment.
        halign : {'center', 'left', 'right'}
            The text horizontal alignment.

        Notes
        -----
        This transformation is primarily used by the `~matplotlib.axis.Axis`
        class, and is meant to be overridden by new kinds of projections that
        may need to place axis elements in different locations.
        """
        labels_align = rcParams["ytick.alignment"]
        return (self.get_yaxis_transform(which='tick2') +
                mtransforms.ScaledTranslation(pad_points / 72, 0,
                                              self.figure.dpi_scale_trans),
                labels_align, "left")

    def _update_transScale(self):
        self.transScale.set(
            mtransforms.blended_transform_factory(
                self.xaxis.get_transform(), self.yaxis.get_transform()))
        for line in getattr(self, "lines", []):  # Not set during init.
            try:
                line._transformed_path.invalidate()
            except AttributeError:
                pass

    def get_position(self, original=False):
        """
        Get a copy of the axes rectangle as a `.Bbox`.

        Parameters
        ----------
        original : bool
            If ``True``, return the original position. Otherwise return the
            active position. For an explanation of the positions see
            `.set_position`.

        Returns
        -------
        pos : `.Bbox`

        """
        if original:
            return self._originalPosition.frozen()
        else:
            locator = self.get_axes_locator()
            if not locator:
                self.apply_aspect()
            return self._position.frozen()

    def set_position(self, pos, which='both'):
        """
        Set the axes position.

        Axes have two position attributes. The 'original' position is the
        position allocated for the Axes. The 'active' position is the
        position the Axes is actually drawn at. These positions are usually
        the same unless a fixed aspect is set to the Axes. See `.set_aspect`
        for details.

        Parameters
        ----------
        pos : [left, bottom, width, height] or `~matplotlib.transforms.Bbox`
            The new position of the in `.Figure` coordinates.

        which : {'both', 'active', 'original'}, optional
            Determines which position variables to change.

        """
        self._set_position(pos, which=which)
        # because this is being called externally to the library we
        # zero the constrained layout parts.
        self._layoutbox = None
        self._poslayoutbox = None

    def _set_position(self, pos, which='both'):
        """
        private version of set_position.  Call this internally
        to get the same functionality of `get_position`, but not
        to take the axis out of the constrained_layout
        hierarchy.
        """
        if not isinstance(pos, mtransforms.BboxBase):
            pos = mtransforms.Bbox.from_bounds(*pos)
        for ax in self._twinned_axes.get_siblings(self):
            if which in ('both', 'active'):
                ax._position.set(pos)
            if which in ('both', 'original'):
                ax._originalPosition.set(pos)
        self.stale = True

    def reset_position(self):
        """
        Reset the active position to the original position.

        This resets the a possible position change due to aspect constraints.
        For an explanation of the positions see `.set_position`.
        """
        for ax in self._twinned_axes.get_siblings(self):
            pos = ax.get_position(original=True)
            ax.set_position(pos, which='active')

    def set_axes_locator(self, locator):
        """
        Set the axes locator.

        Parameters
        ----------
        locator : Callable[[Axes, Renderer], Bbox]
        """
        self._axes_locator = locator
        self.stale = True

    def get_axes_locator(self):
        """
        Return the axes_locator.
        """
        return self._axes_locator

    def _set_artist_props(self, a):
        """set the boilerplate props for artists added to axes"""
        a.set_figure(self.figure)
        if not a.is_transform_set():
            a.set_transform(self.transData)

        a.axes = self
        if a.mouseover:
            self._mouseover_set.add(a)

    def _gen_axes_patch(self):
        """
        Returns
        -------
        Patch
            The patch used to draw the background of the axes.  It is also used
            as the clipping path for any data elements on the axes.

            In the standard axes, this is a rectangle, but in other projections
            it may not be.

        Notes
        -----
        Intended to be overridden by new projection types.
        """
        return mpatches.Rectangle((0.0, 0.0), 1.0, 1.0)

    def _gen_axes_spines(self, locations=None, offset=0.0, units='inches'):
        """
        Returns
        -------
        dict
            Mapping of spine names to `Line2D` or `Patch` instances that are
            used to draw axes spines.

            In the standard axes, spines are single line segments, but in other
            projections they may not be.

        Notes
        -----
        Intended to be overridden by new projection types.
        """
        return OrderedDict((side, mspines.Spine.linear_spine(self, side))
                           for side in ['left', 'right', 'bottom', 'top'])

    def cla(self):
        """Clear the current axes."""
        # Note: this is called by Axes.__init__()

        # stash the current visibility state
        if hasattr(self, 'patch'):
            patch_visible = self.patch.get_visible()
        else:
            patch_visible = True

        xaxis_visible = self.xaxis.get_visible()
        yaxis_visible = self.yaxis.get_visible()

        self.xaxis.cla()
        self.yaxis.cla()

        for name, spine in self.spines.items():
            spine.cla()

        self.ignore_existing_data_limits = True
        self.callbacks = cbook.CallbackRegistry()

        if self._sharex is not None:
            # major and minor are axis.Ticker class instances with
            # locator and formatter attributes
            self.xaxis.major = self._sharex.xaxis.major
            self.xaxis.minor = self._sharex.xaxis.minor
            x0, x1 = self._sharex.get_xlim()
            self.set_xlim(x0, x1, emit=False,
                          auto=self._sharex.get_autoscalex_on())
            self.xaxis._scale = self._sharex.xaxis._scale
        else:
            self.xaxis._set_scale('linear')
            try:
                self.set_xlim(0, 1)
            except TypeError:
                pass

        if self._sharey is not None:
            self.yaxis.major = self._sharey.yaxis.major
            self.yaxis.minor = self._sharey.yaxis.minor
            y0, y1 = self._sharey.get_ylim()
            self.set_ylim(y0, y1, emit=False,
                          auto=self._sharey.get_autoscaley_on())
            self.yaxis._scale = self._sharey.yaxis._scale
        else:
            self.yaxis._set_scale('linear')
            try:
                self.set_ylim(0, 1)
            except TypeError:
                pass
        # update the minor locator for x and y axis based on rcParams
        if rcParams['xtick.minor.visible']:
            self.xaxis.set_minor_locator(mticker.AutoMinorLocator())

        if rcParams['ytick.minor.visible']:
            self.yaxis.set_minor_locator(mticker.AutoMinorLocator())

        if self._sharex is None:
            self._autoscaleXon = True
        if self._sharey is None:
            self._autoscaleYon = True
        self._xmargin = rcParams['axes.xmargin']
        self._ymargin = rcParams['axes.ymargin']
        self._tight = None
        self._use_sticky_edges = True
        self._update_transScale()  # needed?

        self._get_lines = _process_plot_var_args(self)
        self._get_patches_for_fill = _process_plot_var_args(self, 'fill')

        self._gridOn = rcParams['axes.grid']
        self.lines = []
        self.patches = []
        self.texts = []
        self.tables = []
        self.artists = []
        self.images = []
        self._mouseover_set = _OrderedSet()
        self.child_axes = []
        self._current_image = None  # strictly for pyplot via _sci, _gci
        self.legend_ = None
        self.collections = []  # collection.Collection instances
        self.containers = []

        self.grid(False)  # Disable grid on init to use rcParameter
        self.grid(self._gridOn, which=rcParams['axes.grid.which'],
                  axis=rcParams['axes.grid.axis'])
        props = font_manager.FontProperties(
            size=rcParams['axes.titlesize'],
            weight=rcParams['axes.titleweight'])

        self.title = mtext.Text(
            x=0.5, y=1.0, text='',
            fontproperties=props,
            verticalalignment='baseline',
            horizontalalignment='center',
            )
        self._left_title = mtext.Text(
            x=0.0, y=1.0, text='',
            fontproperties=props.copy(),
            verticalalignment='baseline',
            horizontalalignment='left', )
        self._right_title = mtext.Text(
            x=1.0, y=1.0, text='',
            fontproperties=props.copy(),
            verticalalignment='baseline',
            horizontalalignment='right',
            )
        title_offset_points = rcParams['axes.titlepad']
        # refactor this out so it can be called in ax.set_title if
        # pad argument used...
        self._set_title_offset_trans(title_offset_points)
        # determine if the title position has been set manually:
        self._autotitlepos = None

        for _title in (self.title, self._left_title, self._right_title):
            self._set_artist_props(_title)

        # The patch draws the background of the axes.  We want this to be below
        # the other artists.  We use the frame to draw the edges so we are
        # setting the edgecolor to None.
        self.patch = self._gen_axes_patch()
        self.patch.set_figure(self.figure)
        self.patch.set_facecolor(self._facecolor)
        self.patch.set_edgecolor('None')
        self.patch.set_linewidth(0)
        self.patch.set_transform(self.transAxes)

        self.set_axis_on()

        self.xaxis.set_clip_path(self.patch)
        self.yaxis.set_clip_path(self.patch)

        self._shared_x_axes.clean()
        self._shared_y_axes.clean()
        if self._sharex:
            self.xaxis.set_visible(xaxis_visible)
            self.patch.set_visible(patch_visible)

        if self._sharey:
            self.yaxis.set_visible(yaxis_visible)
            self.patch.set_visible(patch_visible)

        self.stale = True

    def clear(self):
        """Clear the axes."""
        self.cla()

    def get_facecolor(self):
        """Get the facecolor of the Axes."""
        return self.patch.get_facecolor()
    get_fc = get_facecolor

    def set_facecolor(self, color):
        """
        Set the facecolor of the Axes.

        Parameters
        ----------
        color : color
        """
        self._facecolor = color
        self.stale = True
        return self.patch.set_facecolor(color)
    set_fc = set_facecolor

    def _set_title_offset_trans(self, title_offset_points):
        """
        Set the offset for the title either from rcParams['axes.titlepad']
        or from set_title kwarg ``pad``.
        """
        self.titleOffsetTrans = mtransforms.ScaledTranslation(
                0.0, title_offset_points / 72,
                self.figure.dpi_scale_trans)
        for _title in (self.title, self._left_title, self._right_title):
            _title.set_transform(self.transAxes + self.titleOffsetTrans)
            _title.set_clip_box(None)

    def set_prop_cycle(self, *args, **kwargs):
        """
        Set the property cycle of the Axes.

        The property cycle controls the style properties such as color,
        marker and linestyle of future plot commands. The style properties
        of data already added to the Axes are not modified.

        Call signatures::

          set_prop_cycle(cycler)
          set_prop_cycle(label=values[, label2=values2[, ...]])
          set_prop_cycle(label, values)

        Form 1 sets given `~cycler.Cycler` object.

        Form 2 creates a `~cycler.Cycler` which cycles over one or more
        properties simultaneously and set it as the property cycle of the
        axes. If multiple properties are given, their value lists must have
        the same length. This is just a shortcut for explicitly creating a
        cycler and passing it to the function, i.e. it's short for
        ``set_prop_cycle(cycler(label=values label2=values2, ...))``.

        Form 3 creates a `~cycler.Cycler` for a single property and set it
        as the property cycle of the axes. This form exists for compatibility
        with the original `cycler.cycler` interface. Its use is discouraged
        in favor of the kwarg form, i.e. ``set_prop_cycle(label=values)``.

        Parameters
        ----------
        cycler : Cycler
            Set the given Cycler. *None* resets to the cycle defined by the
            current style.

        label : str
            The property key. Must be a valid `.Artist` property.
            For example, 'color' or 'linestyle'. Aliases are allowed,
            such as 'c' for 'color' and 'lw' for 'linewidth'.

        values : iterable
            Finite-length iterable of the property values. These values
            are validated and will raise a ValueError if invalid.

        Examples
        --------
        Setting the property cycle for a single property:

        >>> ax.set_prop_cycle(color=['red', 'green', 'blue'])

        Setting the property cycle for simultaneously cycling over multiple
        properties (e.g. red circle, green plus, blue cross):

        >>> ax.set_prop_cycle(color=['red', 'green', 'blue'],
        ...                   marker=['o', '+', 'x'])

        See Also
        --------
        matplotlib.rcsetup.cycler
            Convenience function for creating validated cyclers for properties.
        cycler.cycler
            The original function for creating unvalidated cyclers.

        """
        if args and kwargs:
            raise TypeError("Cannot supply both positional and keyword "
                            "arguments to this method.")
        # Can't do `args == (None,)` as that crashes cycler.
        if len(args) == 1 and args[0] is None:
            prop_cycle = None
        else:
            prop_cycle = cycler(*args, **kwargs)
        self._get_lines.set_prop_cycle(prop_cycle)
        self._get_patches_for_fill.set_prop_cycle(prop_cycle)

    def get_aspect(self):
        return self._aspect

    def set_aspect(self, aspect, adjustable=None, anchor=None, share=False):
        """
        Set the aspect of the axis scaling, i.e. the ratio of y-unit to x-unit.

        Parameters
        ----------
        aspect : {'auto', 'equal'} or num
            Possible values:

            ========   ================================================
            value      description
            ========   ================================================
            'auto'     automatic; fill the position rectangle with data
            'equal'    same scaling from data to plot units for x and y
             num       a circle will be stretched such that the height
                       is num times the width. aspect=1 is the same as
                       aspect='equal'.
            ========   ================================================

        adjustable : None or {'box', 'datalim'}, optional
            If not ``None``, this defines which parameter will be adjusted to
            meet the required aspect. See `.set_adjustable` for further
            details.

        anchor : None or str or 2-tuple of float, optional
            If not ``None``, this defines where the Axes will be drawn if there
            is extra space due to aspect constraints. The most common way to
            to specify the anchor are abbreviations of cardinal directions:

            =====   =====================
            value   description
            =====   =====================
            'C'     centered
            'SW'    lower left corner
            'S'     middle of bottom edge
            'SE'    lower right corner
            etc.
            =====   =====================

            See `.set_anchor` for further details.

        share : bool, optional
            If ``True``, apply the settings to all shared Axes.
            Default is ``False``.

        See Also
        --------
        matplotlib.axes.Axes.set_adjustable
            defining the parameter to adjust in order to meet the required
            aspect.
        matplotlib.axes.Axes.set_anchor
            defining the position in case of extra space.
        """
        if not (cbook._str_equal(aspect, 'equal')
                or cbook._str_equal(aspect, 'auto')):
            aspect = float(aspect)  # raise ValueError if necessary

        if (not cbook._str_equal(aspect, 'auto')) and self.name == '3d':
            raise NotImplementedError(
                'It is not currently possible to manually set the aspect '
                'on 3D axes')

        if share:
            axes = {*self._shared_x_axes.get_siblings(self),
                    *self._shared_y_axes.get_siblings(self)}
        else:
            axes = [self]

        for ax in axes:
            ax._aspect = aspect

        if adjustable is None:
            adjustable = self._adjustable
        self.set_adjustable(adjustable, share=share)  # Handle sharing.

        if anchor is not None:
            self.set_anchor(anchor, share=share)
        self.stale = True

    def get_adjustable(self):
        return self._adjustable

    def set_adjustable(self, adjustable, share=False):
        """
        Define which parameter the Axes will change to achieve a given aspect.

        Parameters
        ----------
        adjustable : {'box', 'datalim'}
            If 'box', change the physical dimensions of the Axes.
            If 'datalim', change the ``x`` or ``y`` data limits.

        share : bool, optional
            If ``True``, apply the settings to all shared Axes.
            Default is ``False``.

        See Also
        --------
        matplotlib.axes.Axes.set_aspect
            for a description of aspect handling.

        Notes
        -----
        Shared Axes (of which twinned Axes are a special case)
        impose restrictions on how aspect ratios can be imposed.
        For twinned Axes, use 'datalim'.  For Axes that share both
        x and y, use 'box'.  Otherwise, either 'datalim' or 'box'
        may be used.  These limitations are partly a requirement
        to avoid over-specification, and partly a result of the
        particular implementation we are currently using, in
        which the adjustments for aspect ratios are done sequentially
        and independently on each Axes as it is drawn.
        """
        cbook._check_in_list(["box", "datalim"], adjustable=adjustable)
        if share:
            axs = {*self._shared_x_axes.get_siblings(self),
                   *self._shared_y_axes.get_siblings(self)}
        else:
            axs = [self]
        if (adjustable == "datalim"
                and any(getattr(ax.get_data_ratio, "__func__", None)
                        != _AxesBase.get_data_ratio
                        for ax in axs)):
            # Limits adjustment by apply_aspect assumes that the axes' aspect
            # ratio can be computed from the data limits and scales.
            raise ValueError("Cannot set axes adjustable to 'datalim' for "
                             "Axes which override 'get_data_ratio'")
        for ax in axs:
            ax._adjustable = adjustable
        self.stale = True

    def get_anchor(self):
        """
        Get the anchor location.

        See Also
        --------
        matplotlib.axes.Axes.set_anchor
            for a description of the anchor.
        matplotlib.axes.Axes.set_aspect
            for a description of aspect handling.
        """
        return self._anchor

    def set_anchor(self, anchor, share=False):
        """
        Define the anchor location.

        The actual drawing area (active position) of the Axes may be smaller
        than the Bbox (original position) when a fixed aspect is required. The
        anchor defines where the drawing area will be located within the
        available space.

        Parameters
        ----------
        anchor : 2-tuple of floats or {'C', 'SW', 'S', 'SE', ...}
            The anchor position may be either:

            - a sequence (*cx*, *cy*). *cx* and *cy* may range from 0
              to 1, where 0 is left or bottom and 1 is right or top.

            - a string using cardinal directions as abbreviation:

              - 'C' for centered
              - 'S' (south) for bottom-center
              - 'SW' (south west) for bottom-left
              - etc.

              Here is an overview of the possible positions:

              +------+------+------+
              | 'NW' | 'N'  | 'NE' |
              +------+------+------+
              | 'W'  | 'C'  | 'E'  |
              +------+------+------+
              | 'SW' | 'S'  | 'SE' |
              +------+------+------+

        share : bool, optional
            If ``True``, apply the settings to all shared Axes.
            Default is ``False``.

        See Also
        --------
        matplotlib.axes.Axes.set_aspect
            for a description of aspect handling.
        """
        if not (anchor in mtransforms.Bbox.coefs or len(anchor) == 2):
            raise ValueError('argument must be among %s' %
                             ', '.join(mtransforms.Bbox.coefs))
        if share:
            axes = {*self._shared_x_axes.get_siblings(self),
                    *self._shared_y_axes.get_siblings(self)}
        else:
            axes = [self]
        for ax in axes:
            ax._anchor = anchor

        self.stale = True

    def get_data_ratio(self):
        """
        Return the aspect ratio of the scaled data.

        Notes
        -----
        This method is intended to be overridden by new projection types.
        """
        txmin, txmax = self.xaxis.get_transform().transform(self.get_xbound())
        tymin, tymax = self.yaxis.get_transform().transform(self.get_ybound())
        xsize = max(abs(txmax - txmin), 1e-30)
        ysize = max(abs(tymax - tymin), 1e-30)
        return ysize / xsize

    @cbook.deprecated("3.2")
    def get_data_ratio_log(self):
        """
        Return the aspect ratio of the raw data in log scale.

        Notes
        -----
        Will be used when both axis are in log scale.
        """
        xmin, xmax = self.get_xbound()
        ymin, ymax = self.get_ybound()

        xsize = max(abs(math.log10(xmax) - math.log10(xmin)), 1e-30)
        ysize = max(abs(math.log10(ymax) - math.log10(ymin)), 1e-30)

        return ysize / xsize

    def apply_aspect(self, position=None):
        """
        Adjust the Axes for a specified data aspect ratio.

        Depending on `.get_adjustable` this will modify either the Axes box
        (position) or the view limits. In the former case, `.get_anchor`
        will affect the position.

        Notes
        -----
        This is called automatically when each Axes is drawn.  You may need
        to call it yourself if you need to update the Axes position and/or
        view limits before the Figure is drawn.

        See Also
        --------
        matplotlib.axes.Axes.set_aspect
            for a description of aspect ratio handling.
        matplotlib.axes.Axes.set_adjustable
            defining the parameter to adjust in order to meet the required
            aspect.
        matplotlib.axes.Axes.set_anchor
            defining the position in case of extra space.
        """
        if position is None:
            position = self.get_position(original=True)

        aspect = self.get_aspect()

        if aspect == 'auto':
            self._set_position(position, which='active')
            return

        if aspect == 'equal':
            aspect = 1

        fig_width, fig_height = self.get_figure().get_size_inches()
        fig_aspect = fig_height / fig_width

        if self._adjustable == 'box':
            if self in self._twinned_axes:
                raise RuntimeError("Adjustable 'box' is not allowed in a "
                                   "twinned Axes; use 'datalim' instead")
            box_aspect = aspect * self.get_data_ratio()
            pb = position.frozen()
            pb1 = pb.shrunk_to_aspect(box_aspect, pb, fig_aspect)
            self._set_position(pb1.anchored(self.get_anchor(), pb), 'active')
            return

        # self._adjustable == 'datalim'

        # reset active to original in case it had been changed by prior use
        # of 'box'
        self._set_position(position, which='active')

        x_trf = self.xaxis.get_transform()
        y_trf = self.yaxis.get_transform()
        xmin, xmax = x_trf.transform(self.get_xbound())
        ymin, ymax = y_trf.transform(self.get_ybound())
        xsize = max(abs(xmax - xmin), 1e-30)
        ysize = max(abs(ymax - ymin), 1e-30)

        l, b, w, h = position.bounds
        box_aspect = fig_aspect * (h / w)
        data_ratio = box_aspect / aspect

        y_expander = data_ratio * xsize / ysize - 1
        # If y_expander > 0, the dy/dx viewLim ratio needs to increase
        if abs(y_expander) < 0.005:
            return

        dL = self.dataLim
        x0, x1 = x_trf.transform(dL.intervalx)
        y0, y1 = y_trf.transform(dL.intervaly)
        xr = 1.05 * (x1 - x0)
        yr = 1.05 * (y1 - y0)

        xmarg = xsize - xr
        ymarg = ysize - yr
        Ysize = data_ratio * xsize
        Xsize = ysize / data_ratio
        Xmarg = Xsize - xr
        Ymarg = Ysize - yr
        # Setting these targets to, e.g., 0.05*xr does not seem to help.
        xm = 0
        ym = 0

        shared_x = self in self._shared_x_axes
        shared_y = self in self._shared_y_axes
        # Not sure whether we need this check:
        if shared_x and shared_y:
            raise RuntimeError("adjustable='datalim' is not allowed when both "
                               "axes are shared")

        # If y is shared, then we are only allowed to change x, etc.
        if shared_y:
            adjust_y = False
        else:
            if xmarg > xm and ymarg > ym:
                adjy = ((Ymarg > 0 and y_expander < 0) or
                        (Xmarg < 0 and y_expander > 0))
            else:
                adjy = y_expander > 0
            adjust_y = shared_x or adjy  # (Ymarg > xmarg)

        if adjust_y:
            yc = 0.5 * (ymin + ymax)
            y0 = yc - Ysize / 2.0
            y1 = yc + Ysize / 2.0
            self.set_ybound(y_trf.inverted().transform([y0, y1]))
        else:
            xc = 0.5 * (xmin + xmax)
            x0 = xc - Xsize / 2.0
            x1 = xc + Xsize / 2.0
            self.set_xbound(x_trf.inverted().transform([x0, x1]))

    def axis(self, *args, emit=True, **kwargs):
        """
        Convenience method to get or set some axis properties.

        Call signatures::

          xmin, xmax, ymin, ymax = axis()
          xmin, xmax, ymin, ymax = axis([xmin, xmax, ymin, ymax])
          xmin, xmax, ymin, ymax = axis(option)
          xmin, xmax, ymin, ymax = axis(**kwargs)

        Parameters
        ----------
        xmin, xmax, ymin, ymax : float, optional
            The axis limits to be set.  This can also be achieved using ::

                ax.set(xlim=(xmin, xmax), ylim=(ymin, ymax))

        option : bool or str
            If a bool, turns axis lines and labels on or off. If a string,
            possible values are:

            ======== ==========================================================
            Value    Description
            ======== ==========================================================
            'on'     Turn on axis lines and labels. Same as ``True``.
            'off'    Turn off axis lines and labels. Same as ``False``.
            'equal'  Set equal scaling (i.e., make circles circular) by
                     changing axis limits. This is the same as
                     ``ax.set_aspect('equal', adjustable='datalim')``.
                     Explicit data limits may not be respected in this case.
            'scaled' Set equal scaling (i.e., make circles circular) by
                     changing dimensions of the plot box. This is the same as
                     ``ax.set_aspect('equal', adjustable='box', anchor='C')``.
                     Additionally, further autoscaling will be disabled.
            'tight'  Set limits just large enough to show all data, then
                     disable further autoscaling.
            'auto'   Automatic scaling (fill plot box with data).
            'normal' Same as 'auto'; deprecated.
            'image'  'scaled' with axis limits equal to data limits.
            'square' Square plot; similar to 'scaled', but initially forcing
                     ``xmax-xmin == ymax-ymin``.
            ======== ==========================================================

        emit : bool, optional, default *True*
            Whether observers are notified of the axis limit change.
            This option is passed on to `~.Axes.set_xlim` and
            `~.Axes.set_ylim`.

        Returns
        -------
        xmin, xmax, ymin, ymax : float
            The axis limits.

        See also
        --------
        matplotlib.axes.Axes.set_xlim
        matplotlib.axes.Axes.set_ylim
        """
        if len(args) == 1 and isinstance(args[0], (str, bool)):
            s = args[0]
            if s is True:
                s = 'on'
            if s is False:
                s = 'off'
            s = s.lower()
            if s == 'on':
                self.set_axis_on()
            elif s == 'off':
                self.set_axis_off()
            elif s in ('equal', 'tight', 'scaled', 'normal',
                       'auto', 'image', 'square'):
                if s == 'normal':
                    cbook.warn_deprecated(
                        "3.1", message="Passing 'normal' to axis() is "
                        "deprecated since %(since)s; use 'auto' instead.")
                self.set_autoscale_on(True)
                self.set_aspect('auto')
                self.autoscale_view(tight=False)
                # self.apply_aspect()
                if s == 'equal':
                    self.set_aspect('equal', adjustable='datalim')
                elif s == 'scaled':
                    self.set_aspect('equal', adjustable='box', anchor='C')
                    self.set_autoscale_on(False)  # Req. by Mark Bakker
                elif s == 'tight':
                    self.autoscale_view(tight=True)
                    self.set_autoscale_on(False)
                elif s == 'image':
                    self.autoscale_view(tight=True)
                    self.set_autoscale_on(False)
                    self.set_aspect('equal', adjustable='box', anchor='C')
                elif s == 'square':
                    self.set_aspect('equal', adjustable='box', anchor='C')
                    self.set_autoscale_on(False)
                    xlim = self.get_xlim()
                    ylim = self.get_ylim()
                    edge_size = max(np.diff(xlim), np.diff(ylim))[0]
                    self.set_xlim([xlim[0], xlim[0] + edge_size],
                                  emit=emit, auto=False)
                    self.set_ylim([ylim[0], ylim[0] + edge_size],
                                  emit=emit, auto=False)
            else:
                raise ValueError('Unrecognized string %s to axis; '
                                 'try on or off' % s)
        else:
            if len(args) >= 1:
                if len(args) != 1:
                    cbook.warn_deprecated(
                        "3.2", message="Passing more than one positional "
                        "argument to axis() is deprecated and will raise a "
                        "TypeError %(removal)s.")
                limits = args[0]
                try:
                    xmin, xmax, ymin, ymax = limits
                except (TypeError, ValueError):
                    raise TypeError('the first argument to axis() must be an '
                                    'interable of the form '
                                    '[xmin, xmax, ymin, ymax]')
            else:
                xmin = kwargs.pop('xmin', None)
                xmax = kwargs.pop('xmax', None)
                ymin = kwargs.pop('ymin', None)
                ymax = kwargs.pop('ymax', None)
            xauto = (None  # Keep autoscale state as is.
                     if xmin is None and xmax is None
                     else False)  # Turn off autoscale.
            yauto = (None
                     if ymin is None and ymax is None
                     else False)
            self.set_xlim(xmin, xmax, emit=emit, auto=xauto)
            self.set_ylim(ymin, ymax, emit=emit, auto=yauto)
        if kwargs:
            cbook.warn_deprecated(
                "3.1", message="Passing unsupported keyword arguments to "
                "axis() will raise a TypeError %(removal)s.")
        return (*self.get_xlim(), *self.get_ylim())

    def get_legend(self):
        """Return the `Legend` instance, or None if no legend is defined."""
        return self.legend_

    def get_images(self):
        """return a list of Axes images contained by the Axes"""
        return cbook.silent_list('AxesImage', self.images)

    def get_lines(self):
        """Return a list of lines contained by the Axes"""
        return cbook.silent_list('Line2D', self.lines)

    def get_xaxis(self):
        """Return the XAxis instance."""
        return self.xaxis

    def get_xgridlines(self):
        """Get the x grid lines as a list of `Line2D` instances."""
        return self.xaxis.get_gridlines()

    def get_xticklines(self):
        """Get the x tick lines as a list of `Line2D` instances."""
        return self.xaxis.get_ticklines()

    def get_yaxis(self):
        """Return the YAxis instance."""
        return self.yaxis

    def get_ygridlines(self):
        """Get the y grid lines as a list of `Line2D` instances."""
        return self.yaxis.get_gridlines()

    def get_yticklines(self):
        """Get the y tick lines as a list of `Line2D` instances."""
        return self.yaxis.get_ticklines()

    # Adding and tracking artists

    def _sci(self, im):
        """Set the current image.

        This image will be the target of colormap functions like
        `~.pyplot.viridis`, and other functions such as `~.pyplot.clim`.  The
        current image is an attribute of the current axes.
        """
        if isinstance(im, mpl.contour.ContourSet):
            if im.collections[0] not in self.collections:
                raise ValueError("ContourSet must be in current Axes")
        elif im not in self.images and im not in self.collections:
            raise ValueError("Argument must be an image, collection, or "
                             "ContourSet in this Axes")
        self._current_image = im

    def _gci(self):
        """
        Helper for :func:`~matplotlib.pyplot.gci`;
        do not use elsewhere.
        """
        return self._current_image

    def has_data(self):
        """
        Return *True* if any artists have been added to axes.

        This should not be used to determine whether the *dataLim*
        need to be updated, and may not actually be useful for
        anything.
        """
        return (
            len(self.collections) +
            len(self.images) +
            len(self.lines) +
            len(self.patches)) > 0

    def add_artist(self, a):
        """
        Add an `~.Artist` to the axes, and return the artist.

        Use `add_artist` only for artists for which there is no dedicated
        "add" method; and if necessary, use a method such as `update_datalim`
        to manually update the dataLim if the artist is to be included in
        autoscaling.

        If no ``transform`` has been specified when creating the artist (e.g.
        ``artist.get_transform() == None``) then the transform is set to
        ``ax.transData``.
        """
        a.axes = self
        self.artists.append(a)
        a._remove_method = self.artists.remove
        self._set_artist_props(a)
        a.set_clip_path(self.patch)
        self.stale = True
        return a

    def add_child_axes(self, ax):
        """
        Add an `~.AxesBase` to the axes' children; return the child axes.

        This is the lowlevel version.  See `.axes.Axes.inset_axes`.
        """

        # normally axes have themselves as the axes, but these need to have
        # their parent...
        # Need to bypass the getter...
        ax._axes = self
        ax.stale_callback = martist._stale_axes_callback

        self.child_axes.append(ax)
        ax._remove_method = self.child_axes.remove
        self.stale = True
        return ax

    def add_collection(self, collection, autolim=True):
        """
        Add a `~.Collection` to the axes' collections; return the collection.
        """
        label = collection.get_label()
        if not label:
            collection.set_label('_collection%d' % len(self.collections))
        self.collections.append(collection)
        collection._remove_method = self.collections.remove
        self._set_artist_props(collection)

        if collection.get_clip_path() is None:
            collection.set_clip_path(self.patch)

        if autolim:
            # Make sure viewLim is not stale (mostly to match
            # pre-lazy-autoscale behavior, which is not really better).
            self._unstale_viewLim()
            self.update_datalim(collection.get_datalim(self.transData))

        self.stale = True
        return collection

    def add_image(self, image):
        """
        Add an `~.AxesImage` to the axes' images; return the image.
        """
        self._set_artist_props(image)
        if not image.get_label():
            image.set_label('_image%d' % len(self.images))
        self.images.append(image)
        image._remove_method = self.images.remove
        self.stale = True
        return image

    def _update_image_limits(self, image):
        xmin, xmax, ymin, ymax = image.get_extent()
        self.axes.update_datalim(((xmin, ymin), (xmax, ymax)))

    def add_line(self, line):
        """
        Add a `.Line2D` to the axes' lines; return the line.
        """
        self._set_artist_props(line)
        if line.get_clip_path() is None:
            line.set_clip_path(self.patch)

        self._update_line_limits(line)
        if not line.get_label():
            line.set_label('_line%d' % len(self.lines))
        self.lines.append(line)
        line._remove_method = self.lines.remove
        self.stale = True
        return line

    def _add_text(self, txt):
        """
        Add a `~.Text` to the axes' texts; return the text.
        """
        self._set_artist_props(txt)
        self.texts.append(txt)
        txt._remove_method = self.texts.remove
        self.stale = True
        return txt

    def _update_line_limits(self, line):
        """
        Figures out the data limit of the given line, updating self.dataLim.
        """
        path = line.get_path()
        if path.vertices.size == 0:
            return

        line_trans = line.get_transform()

        if line_trans == self.transData:
            data_path = path

        elif any(line_trans.contains_branch_seperately(self.transData)):
            # identify the transform to go from line's coordinates
            # to data coordinates
            trans_to_data = line_trans - self.transData

            # if transData is affine we can use the cached non-affine component
            # of line's path. (since the non-affine part of line_trans is
            # entirely encapsulated in trans_to_data).
            if self.transData.is_affine:
                line_trans_path = line._get_transformed_path()
                na_path, _ = line_trans_path.get_transformed_path_and_affine()
                data_path = trans_to_data.transform_path_affine(na_path)
            else:
                data_path = trans_to_data.transform_path(path)
        else:
            # for backwards compatibility we update the dataLim with the
            # coordinate range of the given path, even though the coordinate
            # systems are completely different. This may occur in situations
            # such as when ax.transAxes is passed through for absolute
            # positioning.
            data_path = path

        if data_path.vertices.size > 0:
            updatex, updatey = line_trans.contains_branch_seperately(
                self.transData)
            self.dataLim.update_from_path(data_path,
                                          self.ignore_existing_data_limits,
                                          updatex=updatex,
                                          updatey=updatey)
            self.ignore_existing_data_limits = False

    def add_patch(self, p):
        """
        Add a `~.Patch` to the axes' patches; return the patch.
        """
        self._set_artist_props(p)
        if p.get_clip_path() is None:
            p.set_clip_path(self.patch)
        self._update_patch_limits(p)
        self.patches.append(p)
        p._remove_method = self.patches.remove
        return p

    def _update_patch_limits(self, patch):
        """update the data limits for patch *p*"""
        # hist can add zero height Rectangles, which is useful to keep
        # the bins, counts and patches lined up, but it throws off log
        # scaling.  We'll ignore rects with zero height or width in
        # the auto-scaling

        # cannot check for '==0' since unitized data may not compare to zero
        # issue #2150 - we update the limits if patch has non zero width
        # or height.
        if (isinstance(patch, mpatches.Rectangle) and
                ((not patch.get_width()) and (not patch.get_height()))):
            return
        vertices = patch.get_path().vertices
        if vertices.size > 0:
            xys = patch.get_patch_transform().transform(vertices)
            if patch.get_data_transform() != self.transData:
                patch_to_data = (patch.get_data_transform() -
                                 self.transData)
                xys = patch_to_data.transform(xys)

            updatex, updatey = patch.get_transform().\
                contains_branch_seperately(self.transData)
            self.update_datalim(xys, updatex=updatex,
                                updatey=updatey)

    def add_table(self, tab):
        """
        Add a `~.Table` to the axes' tables; return the table.
        """
        self._set_artist_props(tab)
        self.tables.append(tab)
        tab.set_clip_path(self.patch)
        tab._remove_method = self.tables.remove
        return tab

    def add_container(self, container):
        """
        Add a `~.Container` to the axes' containers; return the container.
        """
        label = container.get_label()
        if not label:
            container.set_label('_container%d' % len(self.containers))
        self.containers.append(container)
        container._remove_method = self.containers.remove
        return container

    def _on_units_changed(self, scalex=False, scaley=False):
        """
        Callback for processing changes to axis units.

        Currently requests updates of data limits and view limits.
        """
        self.relim()
        self._request_autoscale_view(scalex=scalex, scaley=scaley)

    def relim(self, visible_only=False):
        """
        Recompute the data limits based on current artists.

        At present, `~.Collection` instances are not supported.

        Parameters
        ----------
        visible_only : bool
            Whether to exclude invisible artists.  Defaults to False.
        """
        # Collections are deliberately not supported (yet); see
        # the TODO note in artists.py.
        self.dataLim.ignore(True)
        self.dataLim.set_points(mtransforms.Bbox.null().get_points())
        self.ignore_existing_data_limits = True

        for line in self.lines:
            if not visible_only or line.get_visible():
                self._update_line_limits(line)

        for p in self.patches:
            if not visible_only or p.get_visible():
                self._update_patch_limits(p)

        for image in self.images:
            if not visible_only or image.get_visible():
                self._update_image_limits(image)

    def update_datalim(self, xys, updatex=True, updatey=True):
        """
        Extend the `~.Axes.dataLim` Bbox to include the given points.

        If no data is set currently, the Bbox will ignore its limits and set
        the bound to be the bounds of the xydata (*xys*). Otherwise, it will
        compute the bounds of the union of its current data and the data in
        *xys*.

        Parameters
        ----------
        xys : 2D array-like
            The points to include in the data limits Bbox. This can be either
            a list of (x, y) tuples or a Nx2 array.

        updatex, updatey : bool, optional, default *True*
            Whether to update the x/y limits.
        """
        xys = np.asarray(xys)
        if not len(xys):
            return
        self.dataLim.update_from_data_xy(xys, self.ignore_existing_data_limits,
                                         updatex=updatex, updatey=updatey)
        self.ignore_existing_data_limits = False

    def update_datalim_bounds(self, bounds):
        """
        Extend the `~.Axes.datalim` Bbox to include the given
        `~matplotlib.transforms.Bbox`.

        Parameters
        ----------
        bounds : `~matplotlib.transforms.Bbox`
        """
        self.dataLim.set(mtransforms.Bbox.union([self.dataLim, bounds]))

    def _process_unit_info(self, xdata=None, ydata=None, kwargs=None):
        """Look for unit *kwargs* and update the axis instances as necessary"""

        def _process_single_axis(data, axis, unit_name, kwargs):
            # Return if there's no axis set
            if axis is None:
                return kwargs

            if data is not None:
                # We only need to update if there is nothing set yet.
                if not axis.have_units():
                    axis.update_units(data)

            # Check for units in the kwargs, and if present update axis
            if kwargs is not None:
                units = kwargs.pop(unit_name, axis.units)
                if self.name == 'polar':
                    polar_units = {'xunits': 'thetaunits', 'yunits': 'runits'}
                    units = kwargs.pop(polar_units[unit_name], units)

                if units != axis.units:
                    axis.set_units(units)
                    # If the units being set imply a different converter,
                    # we need to update.
                    if data is not None:
                        axis.update_units(data)
            return kwargs

        kwargs = _process_single_axis(xdata, self.xaxis, 'xunits', kwargs)
        kwargs = _process_single_axis(ydata, self.yaxis, 'yunits', kwargs)
        return kwargs

    def in_axes(self, mouseevent):
        """
        Return *True* if the given *mouseevent* (in display coords)
        is in the Axes
        """
        return self.patch.contains(mouseevent)[0]

    def get_autoscale_on(self):
        """
        Get whether autoscaling is applied for both axes on plot commands
        """
        return self._autoscaleXon and self._autoscaleYon

    def get_autoscalex_on(self):
        """
        Get whether autoscaling for the x-axis is applied on plot commands
        """
        return self._autoscaleXon

    def get_autoscaley_on(self):
        """
        Get whether autoscaling for the y-axis is applied on plot commands
        """
        return self._autoscaleYon

    def set_autoscale_on(self, b):
        """
        Set whether autoscaling is applied on plot commands

        Parameters
        ----------
        b : bool
        """
        self._autoscaleXon = b
        self._autoscaleYon = b

    def set_autoscalex_on(self, b):
        """
        Set whether autoscaling for the x-axis is applied on plot commands

        Parameters
        ----------
        b : bool
        """
        self._autoscaleXon = b

    def set_autoscaley_on(self, b):
        """
        Set whether autoscaling for the y-axis is applied on plot commands

        Parameters
        ----------
        b : bool
        """
        self._autoscaleYon = b

    @property
    def use_sticky_edges(self):
        """
        When autoscaling, whether to obey all `Artist.sticky_edges`.

        Default is ``True``.

        Setting this to ``False`` ensures that the specified margins
        will be applied, even if the plot includes an image, for
        example, which would otherwise force a view limit to coincide
        with its data limit.

        The changing this property does not change the plot until
        `autoscale` or `autoscale_view` is called.
        """
        return self._use_sticky_edges

    @use_sticky_edges.setter
    def use_sticky_edges(self, b):
        self._use_sticky_edges = bool(b)
        # No effect until next autoscaling, which will mark the axes as stale.

    def set_xmargin(self, m):
        """
        Set padding of X data limits prior to autoscaling.

        *m* times the data interval will be added to each
        end of that interval before it is used in autoscaling.
        For example, if your data is in the range [0, 2], a factor of
        ``m = 0.1`` will result in a range [-0.2, 2.2].

        Negative values -0.5 < m < 0 will result in clipping of the data range.
        I.e. for a data range [0, 2], a factor of ``m = -0.1`` will result in
        a range [0.2, 1.8].

        Parameters
        ----------
        m : float greater than -0.5
        """
        if m <= -0.5:
            raise ValueError("margin must be greater than -0.5")
        self._xmargin = m
        self.stale = True

    def set_ymargin(self, m):
        """
        Set padding of Y data limits prior to autoscaling.

        *m* times the data interval will be added to each
        end of that interval before it is used in autoscaling.
        For example, if your data is in the range [0, 2], a factor of
        ``m = 0.1`` will result in a range [-0.2, 2.2].

        Negative values -0.5 < m < 0 will result in clipping of the data range.
        I.e. for a data range [0, 2], a factor of ``m = -0.1`` will result in
        a range [0.2, 1.8].

        Parameters
        ----------
        m : float greater than -0.5
        """
        if m <= -0.5:
            raise ValueError("margin must be greater than -0.5")
        self._ymargin = m
        self.stale = True

    def margins(self, *margins, x=None, y=None, tight=True):
        """
        Set or retrieve autoscaling margins.

        The padding added to each limit of the axes is the *margin*
        times the data interval. All input parameters must be floats
        within the range [0, 1]. Passing both positional and keyword
        arguments is invalid and will raise a TypeError. If no
        arguments (positional or otherwise) are provided, the current
        margins will remain in place and simply be returned.

        Specifying any margin changes only the autoscaling; for example,
        if *xmargin* is not None, then *xmargin* times the X data
        interval will be added to each end of that interval before
        it is used in autoscaling.

        Parameters
        ----------
        *margins : float, optional
            If a single positional argument is provided, it specifies
            both margins of the x-axis and y-axis limits. If two
            positional arguments are provided, they will be interpreted
            as *xmargin*, *ymargin*. If setting the margin on a single
            axis is desired, use the keyword arguments described below.

        x, y : float, optional
            Specific margin values for the x-axis and y-axis,
            respectively. These cannot be used with positional
            arguments, but can be used individually to alter on e.g.,
            only the y-axis.

        tight : bool or None, default is True
            The *tight* parameter is passed to :meth:`autoscale_view`,
            which is executed after a margin is changed; the default
            here is *True*, on the assumption that when margins are
            specified, no additional padding to match tick marks is
            usually desired.  Set *tight* to *None* will preserve
            the previous setting.

        Returns
        -------
        xmargin, ymargin : float

        Notes
        -----
        If a previously used Axes method such as :meth:`pcolor` has set
        :attr:`use_sticky_edges` to `True`, only the limits not set by
        the "sticky artists" will be modified. To force all of the
        margins to be set, set :attr:`use_sticky_edges` to `False`
        before calling :meth:`margins`.
        """

        if margins and x is not None and y is not None:
            raise TypeError('Cannot pass both positional and keyword '
                            'arguments for x and/or y.')
        elif len(margins) == 1:
            x = y = margins[0]
        elif len(margins) == 2:
            x, y = margins
        elif margins:
            raise TypeError('Must pass a single positional argument for all '
                            'margins, or one for each margin (x, y).')

        if x is None and y is None:
            if tight is not True:
                cbook._warn_external(f'ignoring tight={tight!r} in get mode')
            return self._xmargin, self._ymargin

        if x is not None:
            self.set_xmargin(x)
        if y is not None:
            self.set_ymargin(y)

        self._request_autoscale_view(
            tight=tight, scalex=(x is not None), scaley=(y is not None)
        )

    def set_rasterization_zorder(self, z):
        """
        Parameters
        ----------
        z : float or None
            zorder below which artists are rasterized.  ``None`` means that
            artists do not get rasterized based on zorder.
        """
        self._rasterization_zorder = z
        self.stale = True

    def get_rasterization_zorder(self):
        """Return the zorder value below which artists will be rasterized."""
        return self._rasterization_zorder

    def autoscale(self, enable=True, axis='both', tight=None):
        """
        Autoscale the axis view to the data (toggle).

        Convenience method for simple axis view autoscaling.
        It turns autoscaling on or off, and then,
        if autoscaling for either axis is on, it performs
        the autoscaling on the specified axis or axes.

        Parameters
        ----------
        enable : bool or None, optional
            True (default) turns autoscaling on, False turns it off.
            None leaves the autoscaling state unchanged.

        axis : {'both', 'x', 'y'}, optional
            Which axis to operate on; default is 'both'.

        tight : bool or None, optional
            If True, first set the margins to zero.  Then, this argument is
            forwarded to `autoscale_view` (regardless of its value); see the
            description of its behavior there.
        """
        if enable is None:
            scalex = True
            scaley = True
        else:
            scalex = False
            scaley = False
            if axis in ['x', 'both']:
                self._autoscaleXon = bool(enable)
                scalex = self._autoscaleXon
            if axis in ['y', 'both']:
                self._autoscaleYon = bool(enable)
                scaley = self._autoscaleYon
        if tight and scalex:
            self._xmargin = 0
        if tight and scaley:
            self._ymargin = 0
        self._request_autoscale_view(tight=tight, scalex=scalex, scaley=scaley)

    def autoscale_view(self, tight=None, scalex=True, scaley=True):
        """
        Autoscale the view limits using the data limits.

        Parameters
        ----------
        tight : bool or None
            If *True*, only expand the axis limits using the margins.  Note
            that unlike for `autoscale`, ``tight=True`` does *not* set the
            margins to zero.

            If *False* and :rc:`axes.autolimit_mode` is 'round_numbers', then
            after expansion by the margins, further expand the axis limits
            using the axis major locator.

            If None (the default), reuse the value set in the previous call to
            `autoscale_view` (the initial value is False, but the default style
            sets :rc:`axes.autolimit_mode` to 'data', in which case this
            behaves like True).

        scalex : bool
            Whether to autoscale the x axis (default is True).

        scaley : bool
            Whether to autoscale the x axis (default is True).

        Notes
        -----
        The autoscaling preserves any preexisting axis direction reversal.

        The data limits are not updated automatically when artist data are
        changed after the artist has been added to an Axes instance.  In that
        case, use :meth:`matplotlib.axes.Axes.relim` prior to calling
        autoscale_view.

        If the views of the axes are fixed, e.g. via `set_xlim`, they will
        not be changed by autoscale_view().
        See :meth:`matplotlib.axes.Axes.autoscale` for an alternative.
        """
        if tight is not None:
            self._tight = bool(tight)

        x_stickies = y_stickies = np.array([])
        if self.use_sticky_edges:
            # Only iterate over axes and artists if needed.  The check for
            # ``hasattr(ax, "lines")`` is necessary because this can be called
            # very early in the axes init process (e.g., for twin axes) when
            # these attributes don't even exist yet, in which case
            # `get_children` would raise an AttributeError.
            if self._xmargin and scalex and self._autoscaleXon:
                x_stickies = np.sort(np.concatenate([
                    artist.sticky_edges.x
                    for ax in self._shared_x_axes.get_siblings(self)
                    if hasattr(ax, "lines")
                    for artist in ax.get_children()]))
            if self._ymargin and scaley and self._autoscaleYon:
                y_stickies = np.sort(np.concatenate([
                    artist.sticky_edges.y
                    for ax in self._shared_y_axes.get_siblings(self)
                    if hasattr(ax, "lines")
                    for artist in ax.get_children()]))
        if self.get_xscale().lower() == 'log':
            x_stickies = x_stickies[x_stickies > 0]
        if self.get_yscale().lower() == 'log':
            y_stickies = y_stickies[y_stickies > 0]

        def handle_single_axis(scale, autoscaleon, shared_axes, interval,
                               minpos, axis, margin, stickies, set_bound):

            if not (scale and autoscaleon):
                return  # nothing to do...

            shared = shared_axes.get_siblings(self)
            dl = [ax.dataLim for ax in shared]
            # ignore non-finite data limits if good limits exist
            finite_dl = [d for d in dl if np.isfinite(d).all()]
            if len(finite_dl):
                # if finite limits exist for atleast one axis (and the
                # other is infinite), restore the finite limits
                x_finite = [d for d in dl
                            if (np.isfinite(d.intervalx).all() and
                                (d not in finite_dl))]
                y_finite = [d for d in dl
                            if (np.isfinite(d.intervaly).all() and
                                (d not in finite_dl))]

                dl = finite_dl
                dl.extend(x_finite)
                dl.extend(y_finite)

            bb = mtransforms.BboxBase.union(dl)
            x0, x1 = getattr(bb, interval)
            # If x0 and x1 are non finite, use the locator to figure out
            # default limits.
            locator = axis.get_major_locator()
            x0, x1 = locator.nonsingular(x0, x1)

            # Prevent margin addition from crossing a sticky value.  Small
            # tolerances (whose values come from isclose()) must be used due to
            # floating point issues with streamplot.
            def tol(x): return 1e-5 * abs(x) + 1e-8
            # Index of largest element < x0 + tol, if any.
            i0 = stickies.searchsorted(x0 + tol(x0)) - 1
            x0bound = stickies[i0] if i0 != -1 else None
            # Index of smallest element > x1 - tol, if any.
            i1 = stickies.searchsorted(x1 - tol(x1))
            x1bound = stickies[i1] if i1 != len(stickies) else None

            # Add the margin in figure space and then transform back, to handle
            # non-linear scales.
            minpos = getattr(bb, minpos)
            transform = axis.get_transform()
            inverse_trans = transform.inverted()
            x0, x1 = axis._scale.limit_range_for_scale(x0, x1, minpos)
            x0t, x1t = transform.transform([x0, x1])
            delta = (x1t - x0t) * margin
            if not np.isfinite(delta):
                delta = 0  # If a bound isn't finite, set margin to zero.
            x0, x1 = inverse_trans.transform([x0t - delta, x1t + delta])

            # Apply sticky bounds.
            if x0bound is not None:
                x0 = max(x0, x0bound)
            if x1bound is not None:
                x1 = min(x1, x1bound)

            if not self._tight:
                x0, x1 = locator.view_limits(x0, x1)
            set_bound(x0, x1)
            # End of definition of internal function 'handle_single_axis'.

        handle_single_axis(
            scalex, self._autoscaleXon, self._shared_x_axes, 'intervalx',
            'minposx', self.xaxis, self._xmargin, x_stickies, self.set_xbound)
        handle_single_axis(
            scaley, self._autoscaleYon, self._shared_y_axes, 'intervaly',
            'minposy', self.yaxis, self._ymargin, y_stickies, self.set_ybound)

    def _get_axis_list(self):
        return (self.xaxis, self.yaxis)

    def _get_axis_map(self):
        """
        Return a mapping of `Axis` "names" to `Axis` instances.

        The `Axis` name is derived from the attribute under which the instance
        is stored, so e.g. for polar axes, the theta-axis is still named "x"
        and the r-axis is still named "y" (for back-compatibility).

        In practice, this means that the entries are typically "x" and "y", and
        additionally "z" for 3D axes.
        """
        d = {}
        axis_list = self._get_axis_list()
        for k, v in vars(self).items():
            if k.endswith("axis") and v in axis_list:
                d[k[:-len("axis")]] = v
        return d

    def _update_title_position(self, renderer):
        """
        Update the title position based on the bounding box enclosing
        all the ticklabels and x-axis spine and xlabel...
        """

        if self._autotitlepos is not None and not self._autotitlepos:
            _log.debug('title position was updated manually, not adjusting')
            return

        titles = (self.title, self._left_title, self._right_title)

        if self._autotitlepos is None:
            for title in titles:
                x, y = title.get_position()
                if not np.isclose(y, 1.0):
                    self._autotitlepos = False
                    _log.debug('not adjusting title pos because a title was'
                             ' already placed manually: %f', y)
                    return
            self._autotitlepos = True

        for title in titles:
            x, _ = title.get_position()
            # need to start again in case of window resizing
            title.set_position((x, 1.0))
            # need to check all our twins too...
            axs = self._twinned_axes.get_siblings(self)
            # and all the children
            for ax in self.child_axes:
                if ax is not None:
                    locator = ax.get_axes_locator()
                    if locator:
                        pos = locator(self, renderer)
                        ax.apply_aspect(pos)
                    else:
                        ax.apply_aspect()
                    axs = axs + [ax]
            top = 0
            for ax in axs:
                if (ax.xaxis.get_ticks_position() in ['top', 'unknown']
                        or ax.xaxis.get_label_position() == 'top'):
                    bb = ax.xaxis.get_tightbbox(renderer)
                else:
                    bb = ax.get_window_extent(renderer)
                if bb is not None:
                    top = max(top, bb.ymax)
            if title.get_window_extent(renderer).ymin < top:
                _, y = self.transAxes.inverted().transform((0, top))
                title.set_position((x, y))
                # empirically, this doesn't always get the min to top,
                # so we need to adjust again.
                if title.get_window_extent(renderer).ymin < top:
                    _, y = self.transAxes.inverted().transform(
                        (0., 2 * top - title.get_window_extent(renderer).ymin))
                    title.set_position((x, y))

        ymax = max(title.get_position()[1] for title in titles)
        for title in titles:
            # now line up all the titles at the highest baseline.
            x, _ = title.get_position()
            title.set_position((x, ymax))

    # Drawing
    @martist.allow_rasterization
    def draw(self, renderer=None, inframe=False):
        """Draw everything (plot lines, axes, labels)"""
        if renderer is None:
            renderer = self.figure._cachedRenderer
        if renderer is None:
            raise RuntimeError('No renderer defined')
        if not self.get_visible():
            return
        self._unstale_viewLim()

        renderer.open_group('axes', gid=self.get_gid())

        # prevent triggering call backs during the draw process
        self._stale = True

        # loop over self and child axes...
        locator = self.get_axes_locator()
        if locator:
            pos = locator(self, renderer)
            self.apply_aspect(pos)
        else:
            self.apply_aspect()

        artists = self.get_children()
        artists.remove(self.patch)

        # the frame draws the edges around the axes patch -- we
        # decouple these so the patch can be in the background and the
        # frame in the foreground. Do this before drawing the axis
        # objects so that the spine has the opportunity to update them.
        if not (self.axison and self._frameon):
            for spine in self.spines.values():
                artists.remove(spine)

        self._update_title_position(renderer)

        if not self.axison or inframe:
            for _axis in self._get_axis_list():
                artists.remove(_axis)

        if inframe:
            artists.remove(self.title)
            artists.remove(self._left_title)
            artists.remove(self._right_title)

        if not self.figure.canvas.is_saving():
            artists = [a for a in artists
                       if not a.get_animated() or a in self.images]
        artists = sorted(artists, key=attrgetter('zorder'))

        # rasterize artists with negative zorder
        # if the minimum zorder is negative, start rasterization
        rasterization_zorder = self._rasterization_zorder

        if (rasterization_zorder is not None and
                artists and artists[0].zorder < rasterization_zorder):
            renderer.start_rasterizing()
            artists_rasterized = [a for a in artists
                                  if a.zorder < rasterization_zorder]
            artists = [a for a in artists
                       if a.zorder >= rasterization_zorder]
        else:
            artists_rasterized = []

        # the patch draws the background rectangle -- the frame below
        # will draw the edges
        if self.axison and self._frameon:
            self.patch.draw(renderer)

        if artists_rasterized:
            for a in artists_rasterized:
                a.draw(renderer)
            renderer.stop_rasterizing()

        mimage._draw_list_compositing_images(renderer, self, artists)

        renderer.close_group('axes')
        self.stale = False

    def draw_artist(self, a):
        """
        This method can only be used after an initial draw which
        caches the renderer.  It is used to efficiently update Axes
        data (axis ticks, labels, etc are not updated)
        """
        if self.figure._cachedRenderer is None:
            raise AttributeError("draw_artist can only be used after an "
                                 "initial draw which caches the renderer")
        a.draw(self.figure._cachedRenderer)

    def redraw_in_frame(self):
        """
        This method can only be used after an initial draw which
        caches the renderer.  It is used to efficiently update Axes
        data (axis ticks, labels, etc are not updated)
        """
        if self.figure._cachedRenderer is None:
            raise AttributeError("redraw_in_frame can only be used after an "
                                 "initial draw which caches the renderer")
        self.draw(self.figure._cachedRenderer, inframe=True)

    def get_renderer_cache(self):
        return self.figure._cachedRenderer

    # Axes rectangle characteristics

    def get_frame_on(self):
        """Get whether the axes rectangle patch is drawn."""
        return self._frameon

    def set_frame_on(self, b):
        """
        Set whether the axes rectangle patch is drawn.

        Parameters
        ----------
        b : bool
        """
        self._frameon = b
        self.stale = True

    def get_axisbelow(self):
        """
        Get whether axis ticks and gridlines are above or below most artists.

        Returns
        -------
        axisbelow : bool or 'line'

        See Also
        --------
        set_axisbelow
        """
        return self._axisbelow

    def set_axisbelow(self, b):
        """
        Set whether axis ticks and gridlines are above or below most artists.

        This controls the zorder of the ticks and gridlines. For more
        information on the zorder see :doc:`/gallery/misc/zorder_demo`.

        Parameters
        ----------
        b : bool or 'line'
            Possible values:

            - *True* (zorder = 0.5): Ticks and gridlines are below all Artists.
            - 'line' (zorder = 1.5): Ticks and gridlines are above patches
              (e.g. rectangles, with default zorder = 1) but still below lines
              and markers (with their default zorder = 2).
            - *False* (zorder = 2.5): Ticks and gridlines are above patches
              and lines / markers.

        See Also
        --------
        get_axisbelow
        """
        self._axisbelow = axisbelow = validate_axisbelow(b)
        if axisbelow is True:
            zorder = 0.5
        elif axisbelow is False:
            zorder = 2.5
        elif axisbelow == "line":
            zorder = 1.5
        else:
            raise ValueError("Unexpected axisbelow value")
        for axis in self._get_axis_list():
            axis.set_zorder(zorder)
        self.stale = True

    @docstring.dedent_interpd
    def grid(self, b=None, which='major', axis='both', **kwargs):
        """
        Configure the grid lines.

        Parameters
        ----------
        b : bool or None, optional
            Whether to show the grid lines. If any *kwargs* are supplied,
            it is assumed you want the grid on and *b* will be set to True.

            If *b* is *None* and there are no *kwargs*, this toggles the
            visibility of the lines.

        which : {'major', 'minor', 'both'}, optional
            The grid lines to apply the changes on.

        axis : {'both', 'x', 'y'}, optional
            The axis to apply the changes on.

        **kwargs : `.Line2D` properties
            Define the line properties of the grid, e.g.::

                grid(color='r', linestyle='-', linewidth=2)

            Valid keyword arguments are:

            %(_Line2D_docstr)s

        Notes
        -----
        The axis is drawn as a unit, so the effective zorder for drawing the
        grid is determined by the zorder of each axis, not by the zorder of the
        `.Line2D` objects comprising the grid.  Therefore, to set grid zorder,
        use `.set_axisbelow` or, for more control, call the
        `~matplotlib.axis.Axis.set_zorder` method of each axis.
        """
        if len(kwargs):
            b = True
        cbook._check_in_list(['x', 'y', 'both'], axis=axis)
        if axis in ['x', 'both']:
            self.xaxis.grid(b, which=which, **kwargs)
        if axis in ['y', 'both']:
            self.yaxis.grid(b, which=which, **kwargs)

    def ticklabel_format(self, *, axis='both', style='', scilimits=None,
                         useOffset=None, useLocale=None, useMathText=None):
        r"""
        Change the `~matplotlib.ticker.ScalarFormatter` used by
        default for linear axes.

        Optional keyword arguments:

          ==============   =========================================
          Keyword          Description
          ==============   =========================================
          *axis*           {'x', 'y', 'both'}
          *style*          {'sci' (or 'scientific'), 'plain'}
                           plain turns off scientific notation
          *scilimits*      (m, n), pair of integers; if *style*
                           is 'sci', scientific notation will
                           be used for numbers outside the range
                           10\ :sup:`m` to 10\ :sup:`n`.
                           Use (0, 0) to include all numbers.
                           Use (m, m) where m != 0 to fix the order
                           of magnitude to 10\ :sup:`m`.
          *useOffset*      bool or float
                           If True, the offset will be calculated as
                           needed; if False, no offset will be used;
                           if a numeric offset is specified, it will
                           be used.
          *useLocale*      If True, format the number according to
                           the current locale.  This affects things
                           such as the character used for the
                           decimal separator.  If False, use
                           C-style (English) formatting.  The
                           default setting is controlled by the
                           axes.formatter.use_locale rcparam.
          *useMathText*    If True, render the offset and scientific
                           notation in mathtext
          ==============   =========================================

        Only the major ticks are affected.
        If the method is called when the `~matplotlib.ticker.ScalarFormatter`
        is not the `~matplotlib.ticker.Formatter` being used, an
        `AttributeError` will be raised.
        """
        style = style.lower()
        axis = axis.lower()
        if scilimits is not None:
            try:
                m, n = scilimits
                m + n + 1  # check that both are numbers
            except (ValueError, TypeError):
                raise ValueError("scilimits must be a sequence of 2 integers")
        STYLES = {'sci': True, 'scientific': True, 'plain': False, '': None}
        is_sci_style = cbook._check_getitem(STYLES, style=style)
        axis_map = {**{k: [v] for k, v in self._get_axis_map().items()},
                    'both': self._get_axis_list()}
        axises = cbook._check_getitem(axis_map, axis=axis)
        try:
            for axis in axises:
                if is_sci_style is not None:
                    axis.major.formatter.set_scientific(is_sci_style)
                if scilimits is not None:
                    axis.major.formatter.set_powerlimits(scilimits)
                if useOffset is not None:
                    axis.major.formatter.set_useOffset(useOffset)
                if useLocale is not None:
                    axis.major.formatter.set_useLocale(useLocale)
                if useMathText is not None:
                    axis.major.formatter.set_useMathText(useMathText)
        except AttributeError:
            raise AttributeError(
                "This method only works with the ScalarFormatter")

    def locator_params(self, axis='both', tight=None, **kwargs):
        """
        Control behavior of major tick locators.

        Because the locator is involved in autoscaling, `~.Axes.autoscale_view`
        is called automatically after the parameters are changed.

        Parameters
        ----------
        axis : {'both', 'x', 'y'}, optional
            The axis on which to operate.

        tight : bool or None, optional
            Parameter passed to `~.Axes.autoscale_view`.
            Default is None, for no change.

        Other Parameters
        ----------------
        **kwargs
            Remaining keyword arguments are passed to directly to the
            ``set_params()`` method of the locator. Supported keywords depend
            on the type of the locator. See for example
            `~.ticker.MaxNLocator.set_params` for the `.ticker.MaxNLocator`
            used by default for linear axes.

        Examples
        --------
        When plotting small subplots, one might want to reduce the maximum
        number of ticks and use tight bounds, for example::

            ax.locator_params(tight=True, nbins=4)

        """
        _x = axis in ['x', 'both']
        _y = axis in ['y', 'both']
        if _x:
            self.xaxis.get_major_locator().set_params(**kwargs)
        if _y:
            self.yaxis.get_major_locator().set_params(**kwargs)
        self._request_autoscale_view(tight=tight, scalex=_x, scaley=_y)

    def tick_params(self, axis='both', **kwargs):
        """Change the appearance of ticks, tick labels, and gridlines.

        Parameters
        ----------
        axis : {'x', 'y', 'both'}, optional
            Which axis to apply the parameters to.

        Other Parameters
        ----------------
        axis : {'x', 'y', 'both'}
            Axis on which to operate; default is 'both'.
        reset : bool, default: False
            If *True*, set all parameters to defaults before processing other
            keyword arguments.
        which : {'major', 'minor', 'both'}
            Default is 'major'; apply arguments to *which* ticks.
        direction : {'in', 'out', 'inout'}
            Puts ticks inside the axes, outside the axes, or both.
        length : float
            Tick length in points.
        width : float
            Tick width in points.
        color : color
            Tick color.
        pad : float
            Distance in points between tick and label.
        labelsize : float or str
            Tick label font size in points or as a string (e.g., 'large').
        labelcolor : color
            Tick label color.
        colors : color
            Tick color and label color.
        zorder : float
            Tick and label zorder.
        bottom, top, left, right : bool
            Whether to draw the respective ticks.
        labelbottom, labeltop, labelleft, labelright : bool
            Whether to draw the respective tick labels.
        labelrotation : float
            Tick label rotation
        grid_color : color
            Gridline color.
        grid_alpha : float
            Transparency of gridlines: 0 (transparent) to 1 (opaque).
        grid_linewidth : float
            Width of gridlines in points.
        grid_linestyle : str
            Any valid `.Line2D` line style spec.

        Examples
        --------
        Usage ::

            ax.tick_params(direction='out', length=6, width=2, colors='r',
                           grid_color='r', grid_alpha=0.5)

        This will make all major ticks be red, pointing out of the box,
        and with dimensions 6 points by 2 points.  Tick labels will
        also be red.  Gridlines will be red and translucent.

        """
        cbook._check_in_list(['x', 'y', 'both'], axis=axis)
        if axis in ['x', 'both']:
            xkw = dict(kwargs)
            xkw.pop('left', None)
            xkw.pop('right', None)
            xkw.pop('labelleft', None)
            xkw.pop('labelright', None)
            self.xaxis.set_tick_params(**xkw)
        if axis in ['y', 'both']:
            ykw = dict(kwargs)
            ykw.pop('top', None)
            ykw.pop('bottom', None)
            ykw.pop('labeltop', None)
            ykw.pop('labelbottom', None)
            self.yaxis.set_tick_params(**ykw)

    def set_axis_off(self):
        """
        Turn the x- and y-axis off.

        This affects the axis lines, ticks, ticklabels, grid and axis labels.
        """
        self.axison = False
        self.stale = True

    def set_axis_on(self):
        """
        Turn the x- and y-axis on.

        This affects the axis lines, ticks, ticklabels, grid and axis labels.
        """
        self.axison = True
        self.stale = True

    # data limits, ticks, tick labels, and formatting

    def invert_xaxis(self):
        """
        Invert the x-axis.

        See Also
        --------
        xaxis_inverted
        get_xlim, set_xlim
        get_xbound, set_xbound
        """
        self.xaxis.set_inverted(not self.xaxis.get_inverted())

    def xaxis_inverted(self):
        """
        Return whether the x-axis is inverted.

        The axis is inverted if the left value is larger than the right value.

        See Also
        --------
        invert_xaxis
        get_xlim, set_xlim
        get_xbound, set_xbound
        """
        return self.xaxis.get_inverted()

    def get_xbound(self):
        """
        Return the lower and upper x-axis bounds, in increasing order.

        See Also
        --------
        set_xbound
        get_xlim, set_xlim
        invert_xaxis, xaxis_inverted
        """
        left, right = self.get_xlim()
        if left < right:
            return left, right
        else:
            return right, left

    def set_xbound(self, lower=None, upper=None):
        """
        Set the lower and upper numerical bounds of the x-axis.

        This method will honor axes inversion regardless of parameter order.
        It will not change the autoscaling setting (``Axes._autoscaleXon``).

        Parameters
        ----------
        lower, upper : float or None
            The lower and upper bounds. If *None*, the respective axis bound
            is not modified.

        See Also
        --------
        get_xbound
        get_xlim, set_xlim
        invert_xaxis, xaxis_inverted
        """
        if upper is None and np.iterable(lower):
            lower, upper = lower

        old_lower, old_upper = self.get_xbound()

        if lower is None:
            lower = old_lower
        if upper is None:
            upper = old_upper

        if self.xaxis_inverted():
            if lower < upper:
                self.set_xlim(upper, lower, auto=None)
            else:
                self.set_xlim(lower, upper, auto=None)
        else:
            if lower < upper:
                self.set_xlim(lower, upper, auto=None)
            else:
                self.set_xlim(upper, lower, auto=None)

    def get_xlim(self):
        """
        Return the x-axis view limits.

        Returns
        -------
        left, right : (float, float)
            The current x-axis limits in data coordinates.

        See Also
        --------
        set_xlim
        set_xbound, get_xbound
        invert_xaxis, xaxis_inverted

        Notes
        -----
        The x-axis may be inverted, in which case the *left* value will
        be greater than the *right* value.

        """
        return tuple(self.viewLim.intervalx)

    def _validate_converted_limits(self, limit, convert):
        """
        Raise ValueError if converted limits are non-finite.

        Note that this function also accepts None as a limit argument.

        Returns
        -------
        The limit value after call to convert(), or None if limit is None.
        """
        if limit is not None:
            converted_limit = convert(limit)
            if (isinstance(converted_limit, Real)
                    and not np.isfinite(converted_limit)):
                raise ValueError("Axis limits cannot be NaN or Inf")
            return converted_limit

    def set_xlim(self, left=None, right=None, emit=True, auto=False,
                 *, xmin=None, xmax=None):
        """
        Set the x-axis view limits.

        Parameters
        ----------
        left : float, optional
            The left xlim in data coordinates. Passing *None* leaves the
            limit unchanged.

            The left and right xlims may also be passed as the tuple
            (*left*, *right*) as the first positional argument (or as
            the *left* keyword argument).

            .. ACCEPTS: (bottom: float, top: float)

        right : float, optional
            The right xlim in data coordinates. Passing *None* leaves the
            limit unchanged.

        emit : bool, optional
            Whether to notify observers of limit change (default: True).

        auto : bool or None, optional
            Whether to turn on autoscaling of the x-axis. True turns on,
            False turns off (default action), None leaves unchanged.

        xmin, xmax : scalar, optional
            They are equivalent to left and right respectively,
            and it is an error to pass both *xmin* and *left* or
            *xmax* and *right*.

        Returns
        -------
        left, right : (float, float)
            The new x-axis limits in data coordinates.

        See Also
        --------
        get_xlim
        set_xbound, get_xbound
        invert_xaxis, xaxis_inverted

        Notes
        -----
        The *left* value may be greater than the *right* value, in which
        case the x-axis values will decrease from left to right.

        Examples
        --------
        >>> set_xlim(left, right)
        >>> set_xlim((left, right))
        >>> left, right = set_xlim(left, right)

        One limit may be left unchanged.

        >>> set_xlim(right=right_lim)

        Limits may be passed in reverse order to flip the direction of
        the x-axis. For example, suppose *x* represents the number of
        years before present. The x-axis limits might be set like the
        following so 5000 years ago is on the left of the plot and the
        present is on the right.

        >>> set_xlim(5000, 0)

        """
        if right is None and np.iterable(left):
            left, right = left
        if xmin is not None:
            if left is not None:
                raise TypeError('Cannot pass both `xmin` and `left`')
            left = xmin
        if xmax is not None:
            if right is not None:
                raise TypeError('Cannot pass both `xmax` and `right`')
            right = xmax

        self._process_unit_info(xdata=(left, right))
        left = self._validate_converted_limits(left, self.convert_xunits)
        right = self._validate_converted_limits(right, self.convert_xunits)

        if left is None or right is None:
            # Axes init calls set_xlim(0, 1) before get_xlim() can be called,
            # so only grab the limits if we really need them.
            old_left, old_right = self.get_xlim()
            if left is None:
                left = old_left
            if right is None:
                right = old_right

        if self.get_xscale() == 'log' and (left <= 0 or right <= 0):
            # Axes init calls set_xlim(0, 1) before get_xlim() can be called,
            # so only grab the limits if we really need them.
            old_left, old_right = self.get_xlim()
            if left <= 0:
                cbook._warn_external(
                    'Attempted to set non-positive left xlim on a '
                    'log-scaled axis.\n'
                    'Invalid limit will be ignored.')
                left = old_left
            if right <= 0:
                cbook._warn_external(
                    'Attempted to set non-positive right xlim on a '
                    'log-scaled axis.\n'
                    'Invalid limit will be ignored.')
                right = old_right
        if left == right:
            cbook._warn_external(
                f"Attempting to set identical left == right == {left} results "
                f"in singular transformations; automatically expanding.")
        reverse = left > right
        left, right = self.xaxis.get_major_locator().nonsingular(left, right)
        left, right = self.xaxis.limit_range_for_scale(left, right)
        # cast to bool to avoid bad interaction between python 3.8 and np.bool_
        left, right = sorted([left, right], reverse=bool(reverse))

        self._viewLim.intervalx = (left, right)
        if auto is not None:
            self._autoscaleXon = bool(auto)

        if emit:
            self.callbacks.process('xlim_changed', self)
            # Call all of the other x-axes that are shared with this one
            for other in self._shared_x_axes.get_siblings(self):
                if other is not self:
                    other.set_xlim(self.viewLim.intervalx,
                                   emit=False, auto=auto)
                    if other.figure != self.figure:
                        other.figure.canvas.draw_idle()
        self.stale = True
        return left, right

    def get_xscale(self):
        """
        Return the x-axis scale as string.

        See Also
        --------
        set_xscale
        """
        return self.xaxis.get_scale()

    def set_xscale(self, value, **kwargs):
        """
        Set the x-axis scale.

        Parameters
        ----------
        value : {"linear", "log", "symlog", "logit", ...}
            The axis scale type to apply.

        **kwargs
            Different keyword arguments are accepted, depending on the scale.
            See the respective class keyword arguments:

            - `matplotlib.scale.LinearScale`
            - `matplotlib.scale.LogScale`
            - `matplotlib.scale.SymmetricalLogScale`
            - `matplotlib.scale.LogitScale`

        Notes
        -----
        By default, Matplotlib supports the above mentioned scales.
        Additionally, custom scales may be registered using
        `matplotlib.scale.register_scale`. These scales can then also
        be used here.
        """
        old_default_lims = (self.xaxis.get_major_locator()
                            .nonsingular(-np.inf, np.inf))
        g = self.get_shared_x_axes()
        for ax in g.get_siblings(self):
            ax.xaxis._set_scale(value, **kwargs)
            ax._update_transScale()
            ax.stale = True
        new_default_lims = (self.xaxis.get_major_locator()
                            .nonsingular(-np.inf, np.inf))
        if old_default_lims != new_default_lims:
            # Force autoscaling now, to take advantage of the scale locator's
            # nonsingular() before it possibly gets swapped out by the user.
            self.autoscale_view(scaley=False)

    @cbook._make_keyword_only("3.2", "minor")
    def get_xticks(self, minor=False):
        """Return the x ticks as a list of locations"""
        return self.xaxis.get_ticklocs(minor=minor)

    @cbook._make_keyword_only("3.2", "minor")
    def set_xticks(self, ticks, minor=False):
        """
        Set the x ticks with list of *ticks*

        Parameters
        ----------
        ticks : list
            List of x-axis tick locations.

        minor : bool, optional
            If ``False`` sets major ticks, if ``True`` sets minor ticks.
            Default is ``False``.
        """
        ret = self.xaxis.set_ticks(ticks, minor=minor)
        self.stale = True
        return ret

    def get_xmajorticklabels(self):
        """
        Get the major x tick labels.

        Returns
        -------
        labels : list
            List of `~matplotlib.text.Text` instances
        """
        return self.xaxis.get_majorticklabels()

    def get_xminorticklabels(self):
        """
        Get the minor x tick labels.

        Returns
        -------
        labels : list
            List of `~matplotlib.text.Text` instances
        """
        return self.xaxis.get_minorticklabels()

    def get_xticklabels(self, minor=False, which=None):
        """
        Get the x tick labels as a list of `~matplotlib.text.Text` instances.

        Parameters
        ----------
        minor : bool, optional
           If True return the minor ticklabels,
           else return the major ticklabels.

        which : None, ('minor', 'major', 'both')
           Overrides *minor*.

           Selects which ticklabels to return

        Returns
        -------
        ret : list
           List of `~matplotlib.text.Text` instances.
        """
        return self.xaxis.get_ticklabels(minor=minor, which=which)

    def set_xticklabels(self, labels, fontdict=None, minor=False, **kwargs):
        """
        Set the x-tick labels with list of string labels.

        Parameters
        ----------
        labels : List[str]
            List of string labels.

        fontdict : dict, optional
            A dictionary controlling the appearance of the ticklabels.
            The default *fontdict* is::

               {'fontsize': rcParams['axes.titlesize'],
                'fontweight': rcParams['axes.titleweight'],
                'verticalalignment': 'baseline',
                'horizontalalignment': loc}

        minor : bool, optional
            Whether to set the minor ticklabels rather than the major ones.

        Returns
        -------
        A list of `~.text.Text` instances.

        Other Parameters
        -----------------
        **kwargs : `~.text.Text` properties.
        """
        if fontdict is not None:
            kwargs.update(fontdict)
        ret = self.xaxis.set_ticklabels(labels,
                                        minor=minor, **kwargs)
        self.stale = True
        return ret

    def invert_yaxis(self):
        """
        Invert the y-axis.

        See Also
        --------
        yaxis_inverted
        get_ylim, set_ylim
        get_ybound, set_ybound
        """
        self.yaxis.set_inverted(not self.yaxis.get_inverted())

    def yaxis_inverted(self):
        """
        Return whether the y-axis is inverted.

        The axis is inverted if the bottom value is larger than the top value.

        See Also
        --------
        invert_yaxis
        get_ylim, set_ylim
        get_ybound, set_ybound
        """
        return self.yaxis.get_inverted()

    def get_ybound(self):
        """
        Return the lower and upper y-axis bounds, in increasing order.

        See Also
        --------
        set_ybound
        get_ylim, set_ylim
        invert_yaxis, yaxis_inverted
        """
        bottom, top = self.get_ylim()
        if bottom < top:
            return bottom, top
        else:
            return top, bottom

    def set_ybound(self, lower=None, upper=None):
        """
        Set the lower and upper numerical bounds of the y-axis.

        This method will honor axes inversion regardless of parameter order.
        It will not change the autoscaling setting (``Axes._autoscaleYon``).

        Parameters
        ----------
        lower, upper : float or None
            The lower and upper bounds. If *None*, the respective axis bound
            is not modified.

        See Also
        --------
        get_ybound
        get_ylim, set_ylim
        invert_yaxis, yaxis_inverted
        """
        if upper is None and np.iterable(lower):
            lower, upper = lower

        old_lower, old_upper = self.get_ybound()

        if lower is None:
            lower = old_lower
        if upper is None:
            upper = old_upper

        if self.yaxis_inverted():
            if lower < upper:
                self.set_ylim(upper, lower, auto=None)
            else:
                self.set_ylim(lower, upper, auto=None)
        else:
            if lower < upper:
                self.set_ylim(lower, upper, auto=None)
            else:
                self.set_ylim(upper, lower, auto=None)

    def get_ylim(self):
        """
        Return the y-axis view limits.

        Returns
        -------
        bottom, top : (float, float)
            The current y-axis limits in data coordinates.

        See Also
        --------
        set_ylim
        set_ybound, get_ybound
        invert_yaxis, yaxis_inverted

        Notes
        -----
        The y-axis may be inverted, in which case the *bottom* value
        will be greater than the *top* value.

        """
        return tuple(self.viewLim.intervaly)

    def set_ylim(self, bottom=None, top=None, emit=True, auto=False,
                 *, ymin=None, ymax=None):
        """
        Set the y-axis view limits.

        Parameters
        ----------
        bottom : float, optional
            The bottom ylim in data coordinates. Passing *None* leaves the
            limit unchanged.

            The bottom and top ylims may also be passed as the tuple
            (*bottom*, *top*) as the first positional argument (or as
            the *bottom* keyword argument).

            .. ACCEPTS: (bottom: float, top: float)

        top : float, optional
            The top ylim in data coordinates. Passing *None* leaves the
            limit unchanged.

        emit : bool, optional
            Whether to notify observers of limit change (default: ``True``).

        auto : bool or None, optional
            Whether to turn on autoscaling of the y-axis. *True* turns on,
            *False* turns off (default action), *None* leaves unchanged.

        ymin, ymax : scalar, optional
            They are equivalent to bottom and top respectively,
            and it is an error to pass both *ymin* and *bottom* or
            *ymax* and *top*.

        Returns
        -------
        bottom, top : (float, float)
            The new y-axis limits in data coordinates.

        See Also
        --------
        get_ylim
        set_ybound, get_ybound
        invert_yaxis, yaxis_inverted

        Notes
        -----
        The *bottom* value may be greater than the *top* value, in which
        case the y-axis values will decrease from *bottom* to *top*.

        Examples
        --------
        >>> set_ylim(bottom, top)
        >>> set_ylim((bottom, top))
        >>> bottom, top = set_ylim(bottom, top)

        One limit may be left unchanged.

        >>> set_ylim(top=top_lim)

        Limits may be passed in reverse order to flip the direction of
        the y-axis. For example, suppose ``y`` represents depth of the
        ocean in m. The y-axis limits might be set like the following
        so 5000 m depth is at the bottom of the plot and the surface,
        0 m, is at the top.

        >>> set_ylim(5000, 0)
        """
        if top is None and np.iterable(bottom):
            bottom, top = bottom
        if ymin is not None:
            if bottom is not None:
                raise TypeError('Cannot pass both `ymin` and `bottom`')
            bottom = ymin
        if ymax is not None:
            if top is not None:
                raise TypeError('Cannot pass both `ymax` and `top`')
            top = ymax

        self._process_unit_info(ydata=(bottom, top))
        bottom = self._validate_converted_limits(bottom, self.convert_yunits)
        top = self._validate_converted_limits(top, self.convert_yunits)

        if bottom is None or top is None:
            # Axes init calls set_ylim(0, 1) before get_ylim() can be called,
            # so only grab the limits if we really need them.
            old_bottom, old_top = self.get_ylim()
            if bottom is None:
                bottom = old_bottom
            if top is None:
                top = old_top

        if self.get_yscale() == 'log' and (bottom <= 0 or top <= 0):
            # Axes init calls set_xlim(0, 1) before get_xlim() can be called,
            # so only grab the limits if we really need them.
            old_bottom, old_top = self.get_ylim()
            if bottom <= 0:
                cbook._warn_external(
                    'Attempted to set non-positive bottom ylim on a '
                    'log-scaled axis.\n'
                    'Invalid limit will be ignored.')
                bottom = old_bottom
            if top <= 0:
                cbook._warn_external(
                    'Attempted to set non-positive top ylim on a '
                    'log-scaled axis.\n'
                    'Invalid limit will be ignored.')
                top = old_top
        if bottom == top:
            cbook._warn_external(
                f"Attempting to set identical bottom == top == {bottom} "
                f"results in singular transformations; automatically "
                f"expanding.")
        reverse = bottom > top
        bottom, top = self.yaxis.get_major_locator().nonsingular(bottom, top)
        bottom, top = self.yaxis.limit_range_for_scale(bottom, top)
        # cast to bool to avoid bad interaction between python 3.8 and np.bool_
        bottom, top = sorted([bottom, top], reverse=bool(reverse))

        self._viewLim.intervaly = (bottom, top)
        if auto is not None:
            self._autoscaleYon = bool(auto)

        if emit:
            self.callbacks.process('ylim_changed', self)
            # Call all of the other y-axes that are shared with this one
            for other in self._shared_y_axes.get_siblings(self):
                if other is not self:
                    other.set_ylim(self.viewLim.intervaly,
                                   emit=False, auto=auto)
                    if other.figure != self.figure:
                        other.figure.canvas.draw_idle()
        self.stale = True
        return bottom, top

    def get_yscale(self):
        """
        Return the y-axis scale as string.

        See Also
        --------
        set_yscale
        """
        return self.yaxis.get_scale()

    def set_yscale(self, value, **kwargs):
        """
        Set the y-axis scale.

        Parameters
        ----------
        value : {"linear", "log", "symlog", "logit", ...}
            The axis scale type to apply.

        **kwargs
            Different keyword arguments are accepted, depending on the scale.
            See the respective class keyword arguments:

            - `matplotlib.scale.LinearScale`
            - `matplotlib.scale.LogScale`
            - `matplotlib.scale.SymmetricalLogScale`
            - `matplotlib.scale.LogitScale`

        Notes
        -----
        By default, Matplotlib supports the above mentioned scales.
        Additionally, custom scales may be registered using
        `matplotlib.scale.register_scale`. These scales can then also
        be used here.
        """
        old_default_lims = (self.yaxis.get_major_locator()
                            .nonsingular(-np.inf, np.inf))
        g = self.get_shared_y_axes()
        for ax in g.get_siblings(self):
            ax.yaxis._set_scale(value, **kwargs)
            ax._update_transScale()
            ax.stale = True
        new_default_lims = (self.yaxis.get_major_locator()
                            .nonsingular(-np.inf, np.inf))
        if old_default_lims != new_default_lims:
            # Force autoscaling now, to take advantage of the scale locator's
            # nonsingular() before it possibly gets swapped out by the user.
            self.autoscale_view(scalex=False)

    @cbook._make_keyword_only("3.2", "minor")
    def get_yticks(self, minor=False):
        """Return the y ticks as a list of locations"""
        return self.yaxis.get_ticklocs(minor=minor)

    @cbook._make_keyword_only("3.2", "minor")
    def set_yticks(self, ticks, minor=False):
        """
        Set the y ticks with list of *ticks*

        Parameters
        ----------
        ticks : list
            List of y-axis tick locations

        minor : bool, optional
            If ``False`` sets major ticks, if ``True`` sets minor ticks.
            Default is ``False``.
        """
        ret = self.yaxis.set_ticks(ticks, minor=minor)
        return ret

    def get_ymajorticklabels(self):
        """
        Get the major y tick labels.

        Returns
        -------
        labels : list
            List of `~matplotlib.text.Text` instances
        """
        return self.yaxis.get_majorticklabels()

    def get_yminorticklabels(self):
        """
        Get the minor y tick labels.

        Returns
        -------
        labels : list
            List of `~matplotlib.text.Text` instances
        """
        return self.yaxis.get_minorticklabels()

    def get_yticklabels(self, minor=False, which=None):
        """
        Get the y tick labels as a list of `~matplotlib.text.Text` instances.

        Parameters
        ----------
        minor : bool
           If True return the minor ticklabels,
           else return the major ticklabels

        which : None, ('minor', 'major', 'both')
           Overrides *minor*.

           Selects which ticklabels to return

        Returns
        -------
        ret : list
           List of `~matplotlib.text.Text` instances.
        """
        return self.yaxis.get_ticklabels(minor=minor, which=which)

    def set_yticklabels(self, labels, fontdict=None, minor=False, **kwargs):
        """
        Set the y-tick labels with list of strings labels.

        Parameters
        ----------
        labels : List[str]
            list of string labels

        fontdict : dict, optional
            A dictionary controlling the appearance of the ticklabels.
            The default *fontdict* is::

               {'fontsize': rcParams['axes.titlesize'],
                'fontweight': rcParams['axes.titleweight'],
                'verticalalignment': 'baseline',
                'horizontalalignment': loc}

        minor : bool, optional
            Whether to set the minor ticklabels rather than the major ones.

        Returns
        -------
        A list of `~.text.Text` instances.

        Other Parameters
        ----------------
        **kwargs : `~.text.Text` properties.
        """
        if fontdict is not None:
            kwargs.update(fontdict)
        return self.yaxis.set_ticklabels(labels,
                                         minor=minor, **kwargs)

    def xaxis_date(self, tz=None):
        """
        Sets up x-axis ticks and labels that treat the x data as dates.

        Parameters
        ----------
        tz : str or `tzinfo` instance, optional
            Timezone.  Defaults to :rc:`timezone`.
        """
        # should be enough to inform the unit conversion interface
        # dates are coming in
        self.xaxis.axis_date(tz)

    def yaxis_date(self, tz=None):
        """
        Sets up y-axis ticks and labels that treat the y data as dates.

        Parameters
        ----------
        tz : str or `tzinfo` instance, optional
            Timezone.  Defaults to :rc:`timezone`.
        """
        self.yaxis.axis_date(tz)

    def format_xdata(self, x):
        """
        Return *x* formatted as an x-value.

        This function will use the `.fmt_xdata` attribute if it is not None,
        else will fall back on the xaxis major formatter.
        """
        return (self.fmt_xdata if self.fmt_xdata is not None
                else self.xaxis.get_major_formatter().format_data_short)(x)

    def format_ydata(self, y):
        """
        Return *y* formatted as an y-value.

        This function will use the `.fmt_ydata` attribute if it is not None,
        else will fall back on the yaxis major formatter.
        """
        return (self.fmt_ydata if self.fmt_ydata is not None
                else self.yaxis.get_major_formatter().format_data_short)(y)

    def format_coord(self, x, y):
        """Return a format string formatting the *x*, *y* coordinates."""
        if x is None:
            xs = '???'
        else:
            xs = self.format_xdata(x)
        if y is None:
            ys = '???'
        else:
            ys = self.format_ydata(y)
        return 'x=%s y=%s' % (xs, ys)

    def minorticks_on(self):
        """
        Display minor ticks on the axes.

        Displaying minor ticks may reduce performance; you may turn them off
        using `minorticks_off()` if drawing speed is a problem.
        """
        for ax in (self.xaxis, self.yaxis):
            scale = ax.get_scale()
            if scale == 'log':
                s = ax._scale
                ax.set_minor_locator(mticker.LogLocator(s.base, s.subs))
            elif scale == 'symlog':
                s = ax._scale
                ax.set_minor_locator(
                    mticker.SymmetricalLogLocator(s._transform, s.subs))
            else:
                ax.set_minor_locator(mticker.AutoMinorLocator())

    def minorticks_off(self):
        """Remove minor ticks from the axes."""
        self.xaxis.set_minor_locator(mticker.NullLocator())
        self.yaxis.set_minor_locator(mticker.NullLocator())

    # Interactive manipulation

    def can_zoom(self):
        """
        Return *True* if this axes supports the zoom box button functionality.
        """
        return True

    def can_pan(self):
        """
        Return *True* if this axes supports any pan/zoom button functionality.
        """
        return True

    def get_navigate(self):
        """
        Get whether the axes responds to navigation commands
        """
        return self._navigate

    def set_navigate(self, b):
        """
        Set whether the axes responds to navigation toolbar commands

        Parameters
        ----------
        b : bool
        """
        self._navigate = b

    def get_navigate_mode(self):
        """
        Get the navigation toolbar button status: 'PAN', 'ZOOM', or None
        """
        return self._navigate_mode

    def set_navigate_mode(self, b):
        """
        Set the navigation toolbar button status;

        .. warning::
            this is not a user-API function.

        """
        self._navigate_mode = b

    def _get_view(self):
        """
        Save information required to reproduce the current view.

        Called before a view is changed, such as during a pan or zoom
        initiated by the user. You may return any information you deem
        necessary to describe the view.

        .. note::

            Intended to be overridden by new projection types, but if not, the
            default implementation saves the view limits. You *must* implement
            :meth:`_set_view` if you implement this method.
        """
        xmin, xmax = self.get_xlim()
        ymin, ymax = self.get_ylim()
        return (xmin, xmax, ymin, ymax)

    def _set_view(self, view):
        """
        Apply a previously saved view.

        Called when restoring a view, such as with the navigation buttons.

        .. note::

            Intended to be overridden by new projection types, but if not, the
            default implementation restores the view limits. You *must*
            implement :meth:`_get_view` if you implement this method.
        """
        xmin, xmax, ymin, ymax = view
        self.set_xlim((xmin, xmax))
        self.set_ylim((ymin, ymax))

    def _set_view_from_bbox(self, bbox, direction='in',
                            mode=None, twinx=False, twiny=False):
        """
        Update view from a selection bbox.

        .. note::

            Intended to be overridden by new projection types, but if not, the
            default implementation sets the view limits to the bbox directly.

        Parameters
        ----------
        bbox : 4-tuple or 3 tuple
            * If bbox is a 4 tuple, it is the selected bounding box limits,
              in *display* coordinates.
            * If bbox is a 3 tuple, it is an (xp, yp, scl) triple, where
              (xp, yp) is the center of zooming and scl the scale factor to
              zoom by.

        direction : str
            The direction to apply the bounding box.
                * `'in'` - The bounding box describes the view directly, i.e.,
                           it zooms in.
                * `'out'` - The bounding box describes the size to make the
                            existing view, i.e., it zooms out.

        mode : str or None
            The selection mode, whether to apply the bounding box in only the
            `'x'` direction, `'y'` direction or both (`None`).

        twinx : bool
            Whether this axis is twinned in the *x*-direction.

        twiny : bool
            Whether this axis is twinned in the *y*-direction.
        """
        Xmin, Xmax = self.get_xlim()
        Ymin, Ymax = self.get_ylim()

        if len(bbox) == 3:
            # Zooming code
            xp, yp, scl = bbox

            # Should not happen
            if scl == 0:
                scl = 1.

            # direction = 'in'
            if scl > 1:
                direction = 'in'
            else:
                direction = 'out'
                scl = 1/scl

            # get the limits of the axes
            tranD2C = self.transData.transform
            xmin, ymin = tranD2C((Xmin, Ymin))
            xmax, ymax = tranD2C((Xmax, Ymax))

            # set the range
            xwidth = xmax - xmin
            ywidth = ymax - ymin
            xcen = (xmax + xmin)*.5
            ycen = (ymax + ymin)*.5
            xzc = (xp*(scl - 1) + xcen)/scl
            yzc = (yp*(scl - 1) + ycen)/scl

            bbox = [xzc - xwidth/2./scl, yzc - ywidth/2./scl,
                    xzc + xwidth/2./scl, yzc + ywidth/2./scl]
        elif len(bbox) != 4:
            # should be len 3 or 4 but nothing else
            cbook._warn_external(
                "Warning in _set_view_from_bbox: bounding box is not a tuple "
                "of length 3 or 4. Ignoring the view change.")
            return

        # Just grab bounding box
        lastx, lasty, x, y = bbox

        # zoom to rect
        inverse = self.transData.inverted()
        (lastx, lasty), (x, y) = inverse.transform([(lastx, lasty), (x, y)])

        if twinx:
            x0, x1 = Xmin, Xmax
        else:
            if Xmin < Xmax:
                if x < lastx:
                    x0, x1 = x, lastx
                else:
                    x0, x1 = lastx, x
                if x0 < Xmin:
                    x0 = Xmin
                if x1 > Xmax:
                    x1 = Xmax
            else:
                if x > lastx:
                    x0, x1 = x, lastx
                else:
                    x0, x1 = lastx, x
                if x0 > Xmin:
                    x0 = Xmin
                if x1 < Xmax:
                    x1 = Xmax

        if twiny:
            y0, y1 = Ymin, Ymax
        else:
            if Ymin < Ymax:
                if y < lasty:
                    y0, y1 = y, lasty
                else:
                    y0, y1 = lasty, y
                if y0 < Ymin:
                    y0 = Ymin
                if y1 > Ymax:
                    y1 = Ymax
            else:
                if y > lasty:
                    y0, y1 = y, lasty
                else:
                    y0, y1 = lasty, y
                if y0 > Ymin:
                    y0 = Ymin
                if y1 < Ymax:
                    y1 = Ymax

        if direction == 'in':
            if mode == 'x':
                self.set_xlim((x0, x1))
            elif mode == 'y':
                self.set_ylim((y0, y1))
            else:
                self.set_xlim((x0, x1))
                self.set_ylim((y0, y1))
        elif direction == 'out':
            if self.get_xscale() == 'log':
                alpha = np.log(Xmax / Xmin) / np.log(x1 / x0)
                rx1 = pow(Xmin / x0, alpha) * Xmin
                rx2 = pow(Xmax / x0, alpha) * Xmin
            else:
                alpha = (Xmax - Xmin) / (x1 - x0)
                rx1 = alpha * (Xmin - x0) + Xmin
                rx2 = alpha * (Xmax - x0) + Xmin
            if self.get_yscale() == 'log':
                alpha = np.log(Ymax / Ymin) / np.log(y1 / y0)
                ry1 = pow(Ymin / y0, alpha) * Ymin
                ry2 = pow(Ymax / y0, alpha) * Ymin
            else:
                alpha = (Ymax - Ymin) / (y1 - y0)
                ry1 = alpha * (Ymin - y0) + Ymin
                ry2 = alpha * (Ymax - y0) + Ymin

            if mode == 'x':
                self.set_xlim((rx1, rx2))
            elif mode == 'y':
                self.set_ylim((ry1, ry2))
            else:
                self.set_xlim((rx1, rx2))
                self.set_ylim((ry1, ry2))

    def start_pan(self, x, y, button):
        """
        Called when a pan operation has started.

        *x*, *y* are the mouse coordinates in display coords.
        button is the mouse button number:

        * 1: LEFT
        * 2: MIDDLE
        * 3: RIGHT

        .. note::

            Intended to be overridden by new projection types.

        """
        self._pan_start = types.SimpleNamespace(
            lim=self.viewLim.frozen(),
            trans=self.transData.frozen(),
            trans_inverse=self.transData.inverted().frozen(),
            bbox=self.bbox.frozen(),
            x=x,
            y=y)

    def end_pan(self):
        """
        Called when a pan operation completes (when the mouse button
        is up.)

        .. note::

            Intended to be overridden by new projection types.

        """
        del self._pan_start

    def drag_pan(self, button, key, x, y):
        """
        Called when the mouse moves during a pan operation.

        *button* is the mouse button number:

        * 1: LEFT
        * 2: MIDDLE
        * 3: RIGHT

        *key* is a "shift" key

        *x*, *y* are the mouse coordinates in display coords.

        .. note::

            Intended to be overridden by new projection types.

        """
        def format_deltas(key, dx, dy):
            if key == 'control':
                if abs(dx) > abs(dy):
                    dy = dx
                else:
                    dx = dy
            elif key == 'x':
                dy = 0
            elif key == 'y':
                dx = 0
            elif key == 'shift':
                if 2 * abs(dx) < abs(dy):
                    dx = 0
                elif 2 * abs(dy) < abs(dx):
                    dy = 0
                elif abs(dx) > abs(dy):
                    dy = dy / abs(dy) * abs(dx)
                else:
                    dx = dx / abs(dx) * abs(dy)
            return dx, dy

        p = self._pan_start
        dx = x - p.x
        dy = y - p.y
        if dx == dy == 0:
            return
        if button == 1:
            dx, dy = format_deltas(key, dx, dy)
            result = p.bbox.translated(-dx, -dy).transformed(p.trans_inverse)
        elif button == 3:
            try:
                dx = -dx / self.bbox.width
                dy = -dy / self.bbox.height
                dx, dy = format_deltas(key, dx, dy)
                if self.get_aspect() != 'auto':
                    dx = dy = 0.5 * (dx + dy)
                alpha = np.power(10.0, (dx, dy))
                start = np.array([p.x, p.y])
                oldpoints = p.lim.transformed(p.trans)
                newpoints = start + alpha * (oldpoints - start)
                result = (mtransforms.Bbox(newpoints)
                          .transformed(p.trans_inverse))
            except OverflowError:
                cbook._warn_external('Overflow while panning')
                return
        else:
            return

        valid = np.isfinite(result.transformed(p.trans))
        points = result.get_points().astype(object)
        # Just ignore invalid limits (typically, underflow in log-scale).
        points[~valid] = None
        self.set_xlim(points[:, 0])
        self.set_ylim(points[:, 1])

    def get_children(self):
        # docstring inherited.
        return [
            *self.collections,
            *self.patches,
            *self.lines,
            *self.texts,
            *self.artists,
            *self.spines.values(),
            *self._get_axis_list(),
            self.title, self._left_title, self._right_title,
            *self.tables,
            *self.images,
            *self.child_axes,
            *([self.legend_] if self.legend_ is not None else []),
            self.patch,
        ]

    def contains(self, mouseevent):
        # docstring inherited.
        inside, info = self._default_contains(mouseevent)
        if inside is not None:
            return inside, info
        return self.patch.contains(mouseevent)

    def contains_point(self, point):
        """
        Return whether *point* (pair of pixel coordinates) is inside the axes
        patch.
        """
        return self.patch.contains_point(point, radius=1.0)

    def get_default_bbox_extra_artists(self):
        """
        Return a default list of artists that are used for the bounding box
        calculation.

        Artists are excluded either by not being visible or
        ``artist.set_in_layout(False)``.
        """

        artists = self.get_children()

        if not (self.axison and self._frameon):
            # don't do bbox on spines if frame not on.
            for spine in self.spines.values():
                artists.remove(spine)

        if not self.axison:
            for _axis in self._get_axis_list():
                artists.remove(_axis)

        return [artist for artist in artists
                if (artist.get_visible() and artist.get_in_layout())]

    def get_tightbbox(self, renderer, call_axes_locator=True,
                      bbox_extra_artists=None):
        """
        Return the tight bounding box of the axes, including axis and their
        decorators (xlabel, title, etc).

        Artists that have ``artist.set_in_layout(False)`` are not included
        in the bbox.

        Parameters
        ----------
        renderer : `.RendererBase` instance
            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 the axes are
            included in the tight bounding box.

        call_axes_locator : boolean (default ``True``)
            If *call_axes_locator* is ``False``, it does not call the
            ``_axes_locator`` attribute, which is necessary to get the correct
            bounding box. ``call_axes_locator=False`` can be used if the
            caller is only interested in the relative size of the tightbbox
            compared to the axes bbox.

        Returns
        -------
        bbox : `.BboxBase`
            bounding box in figure pixel coordinates.

        See Also
        --------
        matplotlib.axes.Axes.get_window_extent
        matplotlib.axis.Axis.get_tightbbox
        matplotlib.spines.Spine.get_window_extent

        """

        bb = []

        if not self.get_visible():
            return None

        locator = self.get_axes_locator()
        if locator and call_axes_locator:
            pos = locator(self, renderer)
            self.apply_aspect(pos)
        else:
            self.apply_aspect()

        if self.axison:
            bb_xaxis = self.xaxis.get_tightbbox(renderer)
            if bb_xaxis:
                bb.append(bb_xaxis)

            bb_yaxis = self.yaxis.get_tightbbox(renderer)
            if bb_yaxis:
                bb.append(bb_yaxis)

        self._update_title_position(renderer)
        axbbox = self.get_window_extent(renderer)
        bb.append(axbbox)

        self._update_title_position(renderer)
        if self.title.get_visible():
            bb.append(self.title.get_window_extent(renderer))
        if self._left_title.get_visible():
            bb.append(self._left_title.get_window_extent(renderer))
        if self._right_title.get_visible():
            bb.append(self._right_title.get_window_extent(renderer))

        bb.append(self.get_window_extent(renderer))

        bbox_artists = bbox_extra_artists
        if bbox_artists is None:
            bbox_artists = self.get_default_bbox_extra_artists()

        for a in bbox_artists:
            # Extra check here to quickly see if clipping is on and
            # contained in the axes.  If it is, don't get the tightbbox for
            # this artist because this can be expensive:
            clip_extent = a._get_clipping_extent_bbox()
            if clip_extent is not None:
                clip_extent = mtransforms.Bbox.intersection(clip_extent,
                    axbbox)
                if np.all(clip_extent.extents == axbbox.extents):
                    # clip extent is inside the axes bbox so don't check
                    # this artist
                    continue
            bbox = a.get_tightbbox(renderer)
            if (bbox is not None
                    and 0 < bbox.width < np.inf
                    and 0 < bbox.height < np.inf):
                bb.append(bbox)
        _bbox = mtransforms.Bbox.union(
            [b for b in bb if b.width != 0 or b.height != 0])

        return _bbox

    def _make_twin_axes(self, *args, **kwargs):
        """Make a twinx axes of self. This is used for twinx and twiny."""
        # Typically, SubplotBase._make_twin_axes is called instead of this.
        if 'sharex' in kwargs and 'sharey' in kwargs:
            raise ValueError("Twinned Axes may share only one axis")
        ax2 = self.figure.add_axes(self.get_position(True), *args, **kwargs)
        self.set_adjustable('datalim')
        ax2.set_adjustable('datalim')
        self._twinned_axes.join(self, ax2)
        return ax2

    def twinx(self):
        """
        Create a twin Axes sharing the xaxis.

        Create a new Axes with an invisible x-axis and an independent
        y-axis positioned opposite to the original one (i.e. at right). The
        x-axis autoscale setting will be inherited from the original
        Axes.  To ensure that the tick marks of both y-axes align, see
        `~matplotlib.ticker.LinearLocator`.

        Returns
        -------
        ax_twin : Axes
            The newly created Axes instance

        Notes
        -----
        For those who are 'picking' artists while using twinx, pick
        events are only called for the artists in the top-most axes.
        """
        ax2 = self._make_twin_axes(sharex=self)
        ax2.yaxis.tick_right()
        ax2.yaxis.set_label_position('right')
        ax2.yaxis.set_offset_position('right')
        ax2.set_autoscalex_on(self.get_autoscalex_on())
        self.yaxis.tick_left()
        ax2.xaxis.set_visible(False)
        ax2.patch.set_visible(False)
        return ax2

    def twiny(self):
        """
        Create a twin Axes sharing the yaxis.

        Create a new Axes with an invisible y-axis and an independent
        x-axis positioned opposite to the original one (i.e. at top). The
        y-axis autoscale setting will be inherited from the original Axes.
        To ensure that the tick marks of both x-axes align, see
        `~matplotlib.ticker.LinearLocator`.

        Returns
        -------
        ax_twin : Axes
            The newly created Axes instance

        Notes
        -----
        For those who are 'picking' artists while using twiny, pick
        events are only called for the artists in the top-most axes.
        """
        ax2 = self._make_twin_axes(sharey=self)
        ax2.xaxis.tick_top()
        ax2.xaxis.set_label_position('top')
        ax2.set_autoscaley_on(self.get_autoscaley_on())
        self.xaxis.tick_bottom()
        ax2.yaxis.set_visible(False)
        ax2.patch.set_visible(False)
        return ax2

    def get_shared_x_axes(self):
        """Return a reference to the shared axes Grouper object for x axes."""
        return self._shared_x_axes

    def get_shared_y_axes(self):
        """Return a reference to the shared axes Grouper object for y axes."""
        return self._shared_y_axes