image-match/python/py/Lib/site-packages/matplotlib/axis.py

"""
Classes for the ticks and x- and y-axis.
"""

import datetime
import functools
import logging
from numbers import Real
import warnings

import numpy as np

import matplotlib as mpl
from matplotlib import _api, cbook
import matplotlib.artist as martist
import matplotlib.colors as mcolors
import matplotlib.lines as mlines
import matplotlib.scale as mscale
import matplotlib.text as mtext
import matplotlib.ticker as mticker
import matplotlib.transforms as mtransforms
import matplotlib.units as munits

_log = logging.getLogger(__name__)

GRIDLINE_INTERPOLATION_STEPS = 180

# This list is being used for compatibility with Axes.grid, which
# allows all Line2D kwargs.
_line_inspector = martist.ArtistInspector(mlines.Line2D)
_line_param_names = _line_inspector.get_setters()
_line_param_aliases = [next(iter(d)) for d in _line_inspector.aliasd.values()]
_gridline_param_names = ['grid_' + name
                         for name in _line_param_names + _line_param_aliases]


class Tick(martist.Artist):
    """
    Abstract base class for the axis ticks, grid lines and labels.

    Ticks mark a position on an Axis. They contain two lines as markers and
    two labels; one each for the bottom and top positions (in case of an
    `.XAxis`) or for the left and right positions (in case of a `.YAxis`).

    Attributes
    ----------
    tick1line : `~matplotlib.lines.Line2D`
        The left/bottom tick marker.
    tick2line : `~matplotlib.lines.Line2D`
        The right/top tick marker.
    gridline : `~matplotlib.lines.Line2D`
        The grid line associated with the label position.
    label1 : `~matplotlib.text.Text`
        The left/bottom tick label.
    label2 : `~matplotlib.text.Text`
        The right/top tick label.

    """
    def __init__(
        self, axes, loc, *,
        size=None,  # points
        width=None,
        color=None,
        tickdir=None,
        pad=None,
        labelsize=None,
        labelcolor=None,
        labelfontfamily=None,
        zorder=None,
        gridOn=None,  # defaults to axes.grid depending on axes.grid.which
        tick1On=True,
        tick2On=True,
        label1On=True,
        label2On=False,
        major=True,
        labelrotation=0,
        grid_color=None,
        grid_linestyle=None,
        grid_linewidth=None,
        grid_alpha=None,
        **kwargs,  # Other Line2D kwargs applied to gridlines.
    ):
        """
        bbox is the Bound2D bounding box in display coords of the Axes
        loc is the tick location in data coords
        size is the tick size in points
        """
        super().__init__()

        if gridOn is None:
            which = mpl.rcParams['axes.grid.which']
            if major and (which in ('both', 'major')):
                gridOn = mpl.rcParams['axes.grid']
            elif (not major) and (which in ('both', 'minor')):
                gridOn = mpl.rcParams['axes.grid']
            else:
                gridOn = False

        self.set_figure(axes.get_figure(root=False))
        self.axes = axes

        self._loc = loc
        self._major = major

        name = self.__name__
        major_minor = "major" if major else "minor"

        if size is None:
            size = mpl.rcParams[f"{name}.{major_minor}.size"]
        self._size = size

        if width is None:
            width = mpl.rcParams[f"{name}.{major_minor}.width"]
        self._width = width

        if color is None:
            color = mpl.rcParams[f"{name}.color"]

        if pad is None:
            pad = mpl.rcParams[f"{name}.{major_minor}.pad"]
        self._base_pad = pad

        if labelcolor is None:
            labelcolor = mpl.rcParams[f"{name}.labelcolor"]

        if cbook._str_equal(labelcolor, 'inherit'):
            # inherit from tick color
            labelcolor = mpl.rcParams[f"{name}.color"]

        if labelsize is None:
            labelsize = mpl.rcParams[f"{name}.labelsize"]

        self._set_labelrotation(labelrotation)

        if zorder is None:
            if major:
                zorder = mlines.Line2D.zorder + 0.01
            else:
                zorder = mlines.Line2D.zorder
        self._zorder = zorder

        grid_color = mpl._val_or_rc(grid_color, "grid.color")
        grid_linestyle = mpl._val_or_rc(grid_linestyle, "grid.linestyle")
        grid_linewidth = mpl._val_or_rc(grid_linewidth, "grid.linewidth")
        if grid_alpha is None and not mcolors._has_alpha_channel(grid_color):
            # alpha precedence: kwarg > color alpha > rcParams['grid.alpha']
            # Note: only resolve to rcParams if the color does not have alpha
            # otherwise `grid(color=(1, 1, 1, 0.5))` would work like
            #   grid(color=(1, 1, 1, 0.5), alpha=rcParams['grid.alpha'])
            # so the that the rcParams default would override color alpha.
            grid_alpha = mpl.rcParams["grid.alpha"]
        grid_kw = {k[5:]: v for k, v in kwargs.items()}

        self.tick1line = mlines.Line2D(
            [], [],
            color=color, linestyle="none", zorder=zorder, visible=tick1On,
            markeredgecolor=color, markersize=size, markeredgewidth=width,
        )
        self.tick2line = mlines.Line2D(
            [], [],
            color=color, linestyle="none", zorder=zorder, visible=tick2On,
            markeredgecolor=color, markersize=size, markeredgewidth=width,
        )
        self.gridline = mlines.Line2D(
            [], [],
            color=grid_color, alpha=grid_alpha, visible=gridOn,
            linestyle=grid_linestyle, linewidth=grid_linewidth, marker="",
            **grid_kw,
        )
        self.gridline.get_path()._interpolation_steps = \
            GRIDLINE_INTERPOLATION_STEPS
        self.label1 = mtext.Text(
            np.nan, np.nan,
            fontsize=labelsize, color=labelcolor, visible=label1On,
            fontfamily=labelfontfamily, rotation=self._labelrotation[1])
        self.label2 = mtext.Text(
            np.nan, np.nan,
            fontsize=labelsize, color=labelcolor, visible=label2On,
            fontfamily=labelfontfamily, rotation=self._labelrotation[1])

        self._apply_tickdir(tickdir)

        for artist in [self.tick1line, self.tick2line, self.gridline,
                       self.label1, self.label2]:
            self._set_artist_props(artist)

        self.update_position(loc)

    def _set_labelrotation(self, labelrotation):
        if isinstance(labelrotation, str):
            mode = labelrotation
            angle = 0
        elif isinstance(labelrotation, (tuple, list)):
            mode, angle = labelrotation
        else:
            mode = 'default'
            angle = labelrotation
        _api.check_in_list(['auto', 'default'], labelrotation=mode)
        self._labelrotation = (mode, angle)

    @property
    def _pad(self):
        return self._base_pad + self.get_tick_padding()

    def _apply_tickdir(self, tickdir):
        """Set tick direction.  Valid values are 'out', 'in', 'inout'."""
        # This method is responsible for verifying input and, in subclasses, for setting
        # the tick{1,2}line markers.  From the user perspective this should always be
        # called through _apply_params, which further updates ticklabel positions using
        # the new pads.
        if tickdir is None:
            tickdir = mpl.rcParams[f'{self.__name__}.direction']
        else:
            _api.check_in_list(['in', 'out', 'inout'], tickdir=tickdir)
        self._tickdir = tickdir

    def get_tickdir(self):
        return self._tickdir

    def get_tick_padding(self):
        """Get the length of the tick outside of the Axes."""
        padding = {
            'in': 0.0,
            'inout': 0.5,
            'out': 1.0
        }
        return self._size * padding[self._tickdir]

    def get_children(self):
        children = [self.tick1line, self.tick2line,
                    self.gridline, self.label1, self.label2]
        return children

    def set_clip_path(self, path, transform=None):
        # docstring inherited
        super().set_clip_path(path, transform)
        self.gridline.set_clip_path(path, transform)
        self.stale = True

    def contains(self, mouseevent):
        """
        Test whether the mouse event occurred in the Tick marks.

        This function always returns false.  It is more useful to test if the
        axis as a whole contains the mouse rather than the set of tick marks.
        """
        return False, {}

    def set_pad(self, val):
        """
        Set the tick label pad in points

        Parameters
        ----------
        val : float
        """
        self._apply_params(pad=val)
        self.stale = True

    def get_pad(self):
        """Get the value of the tick label pad in points."""
        return self._base_pad

    def get_loc(self):
        """Return the tick location (data coords) as a scalar."""
        return self._loc

    @martist.allow_rasterization
    def draw(self, renderer):
        if not self.get_visible():
            self.stale = False
            return
        renderer.open_group(self.__name__, gid=self.get_gid())
        for artist in [self.gridline, self.tick1line, self.tick2line,
                       self.label1, self.label2]:
            artist.draw(renderer)
        renderer.close_group(self.__name__)
        self.stale = False

    def set_url(self, url):
        """
        Set the url of label1 and label2.

        Parameters
        ----------
        url : str
        """
        super().set_url(url)
        self.label1.set_url(url)
        self.label2.set_url(url)
        self.stale = True

    def _set_artist_props(self, a):
        a.set_figure(self.get_figure(root=False))

    def get_view_interval(self):
        """
        Return the view limits ``(min, max)`` of the axis the tick belongs to.
        """
        raise NotImplementedError('Derived must override')

    def _apply_params(self, **kwargs):
        for name, target in [("gridOn", self.gridline),
                             ("tick1On", self.tick1line),
                             ("tick2On", self.tick2line),
                             ("label1On", self.label1),
                             ("label2On", self.label2)]:
            if name in kwargs:
                target.set_visible(kwargs.pop(name))
        if any(k in kwargs for k in ['size', 'width', 'pad', 'tickdir']):
            self._size = kwargs.pop('size', self._size)
            # Width could be handled outside this block, but it is
            # convenient to leave it here.
            self._width = kwargs.pop('width', self._width)
            self._base_pad = kwargs.pop('pad', self._base_pad)
            # _apply_tickdir uses _size and _base_pad to make _pad, and also
            # sets the ticklines markers.
            self._apply_tickdir(kwargs.pop('tickdir', self._tickdir))
            for line in (self.tick1line, self.tick2line):
                line.set_markersize(self._size)
                line.set_markeredgewidth(self._width)
            # _get_text1_transform uses _pad from _apply_tickdir.
            trans = self._get_text1_transform()[0]
            self.label1.set_transform(trans)
            trans = self._get_text2_transform()[0]
            self.label2.set_transform(trans)
        tick_kw = {k: v for k, v in kwargs.items() if k in ['color', 'zorder']}
        if 'color' in kwargs:
            tick_kw['markeredgecolor'] = kwargs['color']
        self.tick1line.set(**tick_kw)
        self.tick2line.set(**tick_kw)
        for k, v in tick_kw.items():
            setattr(self, '_' + k, v)

        if 'labelrotation' in kwargs:
            self._set_labelrotation(kwargs.pop('labelrotation'))
            self.label1.set(rotation=self._labelrotation[1])
            self.label2.set(rotation=self._labelrotation[1])

        label_kw = {k[5:]: v for k, v in kwargs.items()
                    if k in ['labelsize', 'labelcolor', 'labelfontfamily']}
        self.label1.set(**label_kw)
        self.label2.set(**label_kw)

        grid_kw = {k[5:]: v for k, v in kwargs.items()
                   if k in _gridline_param_names}
        self.gridline.set(**grid_kw)

    def update_position(self, loc):
        """Set the location of tick in data coords with scalar *loc*."""
        raise NotImplementedError('Derived must override')

    def _get_text1_transform(self):
        raise NotImplementedError('Derived must override')

    def _get_text2_transform(self):
        raise NotImplementedError('Derived must override')


class XTick(Tick):
    """
    Contains all the Artists needed to make an x tick - the tick line,
    the label text and the grid line
    """
    __name__ = 'xtick'

    def __init__(self, *args, **kwargs):
        super().__init__(*args, **kwargs)
        # x in data coords, y in axes coords
        ax = self.axes
        self.tick1line.set(
            data=([0], [0]), transform=ax.get_xaxis_transform("tick1"))
        self.tick2line.set(
            data=([0], [1]), transform=ax.get_xaxis_transform("tick2"))
        self.gridline.set(
            data=([0, 0], [0, 1]), transform=ax.get_xaxis_transform("grid"))
        # the y loc is 3 points below the min of y axis
        trans, va, ha = self._get_text1_transform()
        self.label1.set(
            x=0, y=0,
            verticalalignment=va, horizontalalignment=ha, transform=trans,
        )
        trans, va, ha = self._get_text2_transform()
        self.label2.set(
            x=0, y=1,
            verticalalignment=va, horizontalalignment=ha, transform=trans,
        )

    def _get_text1_transform(self):
        return self.axes.get_xaxis_text1_transform(self._pad)

    def _get_text2_transform(self):
        return self.axes.get_xaxis_text2_transform(self._pad)

    def _apply_tickdir(self, tickdir):
        # docstring inherited
        super()._apply_tickdir(tickdir)
        mark1, mark2 = {
            'out': (mlines.TICKDOWN, mlines.TICKUP),
            'in': (mlines.TICKUP, mlines.TICKDOWN),
            'inout': ('|', '|'),
        }[self._tickdir]
        self.tick1line.set_marker(mark1)
        self.tick2line.set_marker(mark2)

    def update_position(self, loc):
        """Set the location of tick in data coords with scalar *loc*."""
        self.tick1line.set_xdata((loc,))
        self.tick2line.set_xdata((loc,))
        self.gridline.set_xdata((loc,))
        self.label1.set_x(loc)
        self.label2.set_x(loc)
        self._loc = loc
        self.stale = True

    def get_view_interval(self):
        # docstring inherited
        return self.axes.viewLim.intervalx


class YTick(Tick):
    """
    Contains all the Artists needed to make a Y tick - the tick line,
    the label text and the grid line
    """
    __name__ = 'ytick'

    def __init__(self, *args, **kwargs):
        super().__init__(*args, **kwargs)
        # x in axes coords, y in data coords
        ax = self.axes
        self.tick1line.set(
            data=([0], [0]), transform=ax.get_yaxis_transform("tick1"))
        self.tick2line.set(
            data=([1], [0]), transform=ax.get_yaxis_transform("tick2"))
        self.gridline.set(
            data=([0, 1], [0, 0]), transform=ax.get_yaxis_transform("grid"))
        # the y loc is 3 points below the min of y axis
        trans, va, ha = self._get_text1_transform()
        self.label1.set(
            x=0, y=0,
            verticalalignment=va, horizontalalignment=ha, transform=trans,
        )
        trans, va, ha = self._get_text2_transform()
        self.label2.set(
            x=1, y=0,
            verticalalignment=va, horizontalalignment=ha, transform=trans,
        )

    def _get_text1_transform(self):
        return self.axes.get_yaxis_text1_transform(self._pad)

    def _get_text2_transform(self):
        return self.axes.get_yaxis_text2_transform(self._pad)

    def _apply_tickdir(self, tickdir):
        # docstring inherited
        super()._apply_tickdir(tickdir)
        mark1, mark2 = {
            'out': (mlines.TICKLEFT, mlines.TICKRIGHT),
            'in': (mlines.TICKRIGHT, mlines.TICKLEFT),
            'inout': ('_', '_'),
        }[self._tickdir]
        self.tick1line.set_marker(mark1)
        self.tick2line.set_marker(mark2)

    def update_position(self, loc):
        """Set the location of tick in data coords with scalar *loc*."""
        self.tick1line.set_ydata((loc,))
        self.tick2line.set_ydata((loc,))
        self.gridline.set_ydata((loc,))
        self.label1.set_y(loc)
        self.label2.set_y(loc)
        self._loc = loc
        self.stale = True

    def get_view_interval(self):
        # docstring inherited
        return self.axes.viewLim.intervaly


class Ticker:
    """
    A container for the objects defining tick position and format.

    Attributes
    ----------
    locator : `~matplotlib.ticker.Locator` subclass
        Determines the positions of the ticks.
    formatter : `~matplotlib.ticker.Formatter` subclass
        Determines the format of the tick labels.
    """

    def __init__(self):
        self._locator = None
        self._formatter = None
        self._locator_is_default = True
        self._formatter_is_default = True

    @property
    def locator(self):
        return self._locator

    @locator.setter
    def locator(self, locator):
        if not isinstance(locator, mticker.Locator):
            raise TypeError('locator must be a subclass of '
                            'matplotlib.ticker.Locator')
        self._locator = locator

    @property
    def formatter(self):
        return self._formatter

    @formatter.setter
    def formatter(self, formatter):
        if not isinstance(formatter, mticker.Formatter):
            raise TypeError('formatter must be a subclass of '
                            'matplotlib.ticker.Formatter')
        self._formatter = formatter


class _LazyTickList:
    """
    A descriptor for lazy instantiation of tick lists.

    See comment above definition of the ``majorTicks`` and ``minorTicks``
    attributes.
    """

    def __init__(self, major):
        self._major = major

    def __get__(self, instance, owner):
        if instance is None:
            return self
        else:
            # instance._get_tick() can itself try to access the majorTicks
            # attribute (e.g. in certain projection classes which override
            # e.g. get_xaxis_text1_transform).  In order to avoid infinite
            # recursion, first set the majorTicks on the instance temporarily
            # to an empty lis. Then create the tick; note that _get_tick()
            # may call reset_ticks(). Therefore, the final tick list is
            # created and assigned afterwards.
            if self._major:
                instance.majorTicks = []
                tick = instance._get_tick(major=True)
                instance.majorTicks = [tick]
                return instance.majorTicks
            else:
                instance.minorTicks = []
                tick = instance._get_tick(major=False)
                instance.minorTicks = [tick]
                return instance.minorTicks


class Axis(martist.Artist):
    """
    Base class for `.XAxis` and `.YAxis`.

    Attributes
    ----------
    isDefault_label : bool

    axes : `~matplotlib.axes.Axes`
        The `~.axes.Axes` to which the Axis belongs.
    major : `~matplotlib.axis.Ticker`
        Determines the major tick positions and their label format.
    minor : `~matplotlib.axis.Ticker`
        Determines the minor tick positions and their label format.
    callbacks : `~matplotlib.cbook.CallbackRegistry`

    label : `~matplotlib.text.Text`
        The axis label.
    labelpad : float
        The distance between the axis label and the tick labels.
        Defaults to :rc:`axes.labelpad`.
    offsetText : `~matplotlib.text.Text`
        A `.Text` object containing the data offset of the ticks (if any).
    pickradius : float
        The acceptance radius for containment tests. See also `.Axis.contains`.
    majorTicks : list of `.Tick`
        The major ticks.

        .. warning::

            Ticks are not guaranteed to be persistent. Various operations
            can create, delete and modify the Tick instances. There is an
            imminent risk that changes to individual ticks will not
            survive if you work on the figure further (including also
            panning/zooming on a displayed figure).

            Working on the individual ticks is a method of last resort.
            Use `.set_tick_params` instead if possible.

    minorTicks : list of `.Tick`
        The minor ticks.
    """
    OFFSETTEXTPAD = 3
    # The class used in _get_tick() to create tick instances. Must either be
    # overwritten in subclasses, or subclasses must reimplement _get_tick().
    _tick_class = None
    converter = _api.deprecate_privatize_attribute(
                    "3.10",
                    alternative="get_converter and set_converter methods"
                )

    def __str__(self):
        return "{}({},{})".format(
            type(self).__name__, *self.axes.transAxes.transform((0, 0)))

    def __init__(self, axes, *, pickradius=15, clear=True):
        """
        Parameters
        ----------
        axes : `~matplotlib.axes.Axes`
            The `~.axes.Axes` to which the created Axis belongs.
        pickradius : float
            The acceptance radius for containment tests. See also
            `.Axis.contains`.
        clear : bool, default: True
            Whether to clear the Axis on creation. This is not required, e.g.,  when
            creating an Axis as part of an Axes, as ``Axes.clear`` will call
            ``Axis.clear``.
            .. versionadded:: 3.8
        """
        super().__init__()
        self._remove_overlapping_locs = True

        self.set_figure(axes.get_figure(root=False))

        self.isDefault_label = True

        self.axes = axes
        self.major = Ticker()
        self.minor = Ticker()
        self.callbacks = cbook.CallbackRegistry(signals=["units"])

        self._autolabelpos = True

        self.label = mtext.Text(
            np.nan, np.nan,
            fontsize=mpl.rcParams['axes.labelsize'],
            fontweight=mpl.rcParams['axes.labelweight'],
            color=mpl.rcParams['axes.labelcolor'],
        )  #: The `.Text` object of the axis label.

        self._set_artist_props(self.label)
        self.offsetText = mtext.Text(np.nan, np.nan)
        self._set_artist_props(self.offsetText)

        self.labelpad = mpl.rcParams['axes.labelpad']

        self.pickradius = pickradius

        # Initialize here for testing; later add API
        self._major_tick_kw = dict()
        self._minor_tick_kw = dict()

        if clear:
            self.clear()
        else:
            self._converter = None
            self._converter_is_explicit = False
            self.units = None

        self._autoscale_on = True

    @property
    def isDefault_majloc(self):
        return self.major._locator_is_default

    @isDefault_majloc.setter
    def isDefault_majloc(self, value):
        self.major._locator_is_default = value

    @property
    def isDefault_majfmt(self):
        return self.major._formatter_is_default

    @isDefault_majfmt.setter
    def isDefault_majfmt(self, value):
        self.major._formatter_is_default = value

    @property
    def isDefault_minloc(self):
        return self.minor._locator_is_default

    @isDefault_minloc.setter
    def isDefault_minloc(self, value):
        self.minor._locator_is_default = value

    @property
    def isDefault_minfmt(self):
        return self.minor._formatter_is_default

    @isDefault_minfmt.setter
    def isDefault_minfmt(self, value):
        self.minor._formatter_is_default = value

    def _get_shared_axes(self):
        """Return Grouper of shared Axes for current axis."""
        return self.axes._shared_axes[
            self._get_axis_name()].get_siblings(self.axes)

    def _get_shared_axis(self):
        """Return list of shared axis for current axis."""
        name = self._get_axis_name()
        return [ax._axis_map[name] for ax in self._get_shared_axes()]

    def _get_axis_name(self):
        """Return the axis name."""
        return next(name for name, axis in self.axes._axis_map.items()
                    if axis is self)

    # During initialization, Axis objects often create ticks that are later
    # unused; this turns out to be a very slow step.  Instead, use a custom
    # descriptor to make the tick lists lazy and instantiate them as needed.
    majorTicks = _LazyTickList(major=True)
    minorTicks = _LazyTickList(major=False)

    def get_remove_overlapping_locs(self):
        return self._remove_overlapping_locs

    def set_remove_overlapping_locs(self, val):
        self._remove_overlapping_locs = bool(val)

    remove_overlapping_locs = property(
        get_remove_overlapping_locs, set_remove_overlapping_locs,
        doc=('If minor ticker locations that overlap with major '
             'ticker locations should be trimmed.'))

    def set_label_coords(self, x, y, transform=None):
        """
        Set the coordinates of the label.

        By default, the x coordinate of the y label and the y coordinate of the
        x label are determined by the tick label bounding boxes, but this can
        lead to poor alignment of multiple labels if there are multiple Axes.

        You can also specify the coordinate system of the label with the
        transform.  If None, the default coordinate system will be the axes
        coordinate system: (0, 0) is bottom left, (0.5, 0.5) is center, etc.
        """
        self._autolabelpos = False
        if transform is None:
            transform = self.axes.transAxes

        self.label.set_transform(transform)
        self.label.set_position((x, y))
        self.stale = True

    def get_transform(self):
        """Return the transform used in the Axis' scale"""
        return self._scale.get_transform()

    def get_scale(self):
        """Return this Axis' scale (as a str)."""
        return self._scale.name

    def _set_scale(self, value, **kwargs):
        if not isinstance(value, mscale.ScaleBase):
            self._scale = mscale.scale_factory(value, self, **kwargs)
        else:
            self._scale = value
        self._scale.set_default_locators_and_formatters(self)

        self.isDefault_majloc = True
        self.isDefault_minloc = True
        self.isDefault_majfmt = True
        self.isDefault_minfmt = True

    # This method is directly wrapped by Axes.set_{x,y}scale.
    def _set_axes_scale(self, value, **kwargs):
        """
        Set this Axis' scale.

        Parameters
        ----------
        value : str or `.ScaleBase`
            The axis scale type to apply.  Valid string values are the names of scale
            classes ("linear", "log", "function",...).  These may be the names of any
            of the :ref:`built-in scales<builtin_scales>` or of any custom scales
            registered using `matplotlib.scale.register_scale`.

        **kwargs
            If *value* is a string, keywords are passed to the instantiation method of
            the respective class.
        """
        name = self._get_axis_name()
        old_default_lims = (self.get_major_locator()
                            .nonsingular(-np.inf, np.inf))
        for ax in self._get_shared_axes():
            ax._axis_map[name]._set_scale(value, **kwargs)
            ax._update_transScale()
            ax.stale = True
        new_default_lims = (self.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.axes.autoscale_view(
                **{f"scale{k}": k == name for k in self.axes._axis_names})

    def limit_range_for_scale(self, vmin, vmax):
        """
        Return the range *vmin*, *vmax*, restricted to the domain supported by the
        current scale.
        """
        return self._scale.limit_range_for_scale(vmin, vmax, self.get_minpos())

    def _get_autoscale_on(self):
        """Return whether this Axis is autoscaled."""
        return self._autoscale_on

    def _set_autoscale_on(self, b):
        """
        Set whether this Axis is autoscaled when drawing or by `.Axes.autoscale_view`.

        If b is None, then the value is not changed.

        Parameters
        ----------
        b : bool
        """
        if b is not None:
            self._autoscale_on = b

    def get_children(self):
        return [self.label, self.offsetText,
                *self.get_major_ticks(), *self.get_minor_ticks()]

    def _reset_major_tick_kw(self):
        self._major_tick_kw.clear()
        self._major_tick_kw['gridOn'] = (
                mpl.rcParams['axes.grid'] and
                mpl.rcParams['axes.grid.which'] in ('both', 'major'))

    def _reset_minor_tick_kw(self):
        self._minor_tick_kw.clear()
        self._minor_tick_kw['gridOn'] = (
                mpl.rcParams['axes.grid'] and
                mpl.rcParams['axes.grid.which'] in ('both', 'minor'))

    def clear(self):
        """
        Clear the axis.

        This resets axis properties to their default values:

        - the label
        - the scale
        - locators, formatters and ticks
        - major and minor grid
        - units
        - registered callbacks
        """
        self.label._reset_visual_defaults()
        # The above resets the label formatting using text rcParams,
        # so we then update the formatting using axes rcParams
        self.label.set_color(mpl.rcParams['axes.labelcolor'])
        self.label.set_fontsize(mpl.rcParams['axes.labelsize'])
        self.label.set_fontweight(mpl.rcParams['axes.labelweight'])
        self.offsetText._reset_visual_defaults()
        self.labelpad = mpl.rcParams['axes.labelpad']

        self._init()

        self._set_scale('linear')

        # Clear the callback registry for this axis, or it may "leak"
        self.callbacks = cbook.CallbackRegistry(signals=["units"])

        # whether the grids are on
        self._major_tick_kw['gridOn'] = (
                mpl.rcParams['axes.grid'] and
                mpl.rcParams['axes.grid.which'] in ('both', 'major'))
        self._minor_tick_kw['gridOn'] = (
                mpl.rcParams['axes.grid'] and
                mpl.rcParams['axes.grid.which'] in ('both', 'minor'))
        self.reset_ticks()

        self._converter = None
        self._converter_is_explicit = False
        self.units = None
        self.stale = True

    def reset_ticks(self):
        """
        Re-initialize the major and minor Tick lists.

        Each list starts with a single fresh Tick.
        """
        # Restore the lazy tick lists.
        try:
            del self.majorTicks
        except AttributeError:
            pass
        try:
            del self.minorTicks
        except AttributeError:
            pass
        try:
            self.set_clip_path(self.axes.patch)
        except AttributeError:
            pass

    def minorticks_on(self):
        """
        Display default minor ticks on the Axis, depending on the scale
        (`~.axis.Axis.get_scale`).

        Scales use specific minor locators:

        - log: `~.LogLocator`
        - symlog: `~.SymmetricalLogLocator`
        - asinh: `~.AsinhLocator`
        - logit: `~.LogitLocator`
        - default: `~.AutoMinorLocator`

        Displaying minor ticks may reduce performance; you may turn them off
        using `minorticks_off()` if drawing speed is a problem.
        """
        scale = self.get_scale()
        if scale == 'log':
            s = self._scale
            self.set_minor_locator(mticker.LogLocator(s.base, s.subs))
        elif scale == 'symlog':
            s = self._scale
            self.set_minor_locator(
                mticker.SymmetricalLogLocator(s._transform, s.subs))
        elif scale == 'asinh':
            s = self._scale
            self.set_minor_locator(
                    mticker.AsinhLocator(s.linear_width, base=s._base,
                                         subs=s._subs))
        elif scale == 'logit':
            self.set_minor_locator(mticker.LogitLocator(minor=True))
        else:
            self.set_minor_locator(mticker.AutoMinorLocator())

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

    def set_tick_params(self, which='major', reset=False, **kwargs):
        """
        Set appearance parameters for ticks, ticklabels, and gridlines.

        For documentation of keyword arguments, see
        :meth:`matplotlib.axes.Axes.tick_params`.

        See Also
        --------
        .Axis.get_tick_params
            View the current style settings for ticks, ticklabels, and
            gridlines.
        """
        _api.check_in_list(['major', 'minor', 'both'], which=which)
        kwtrans = self._translate_tick_params(kwargs)

        # the kwargs are stored in self._major/minor_tick_kw so that any
        # future new ticks will automatically get them
        if reset:
            if which in ['major', 'both']:
                self._reset_major_tick_kw()
                self._major_tick_kw.update(kwtrans)
            if which in ['minor', 'both']:
                self._reset_minor_tick_kw()
                self._minor_tick_kw.update(kwtrans)
            self.reset_ticks()
        else:
            if which in ['major', 'both']:
                self._major_tick_kw.update(kwtrans)
                for tick in self.majorTicks:
                    tick._apply_params(**kwtrans)
            if which in ['minor', 'both']:
                self._minor_tick_kw.update(kwtrans)
                for tick in self.minorTicks:
                    tick._apply_params(**kwtrans)
            # labelOn and labelcolor also apply to the offset text.
            if 'label1On' in kwtrans or 'label2On' in kwtrans:
                self.offsetText.set_visible(
                    self._major_tick_kw.get('label1On', False)
                    or self._major_tick_kw.get('label2On', False))
            if 'labelcolor' in kwtrans:
                self.offsetText.set_color(kwtrans['labelcolor'])

        self.stale = True

    def get_tick_params(self, which='major'):
        """
        Get appearance parameters for ticks, ticklabels, and gridlines.

        .. versionadded:: 3.7

        Parameters
        ----------
        which : {'major', 'minor'}, default: 'major'
            The group of ticks for which the parameters are retrieved.

        Returns
        -------
        dict
            Properties for styling tick elements added to the axis.

        Notes
        -----
        This method returns the appearance parameters for styling *new*
        elements added to this axis and may be different from the values
        on current elements if they were modified directly by the user
        (e.g., via ``set_*`` methods on individual tick objects).

        Examples
        --------
        ::

            >>> ax.yaxis.set_tick_params(labelsize=30, labelcolor='red',
            ...                          direction='out', which='major')
            >>> ax.yaxis.get_tick_params(which='major')
            {'direction': 'out',
            'left': True,
            'right': False,
            'labelleft': True,
            'labelright': False,
            'gridOn': False,
            'labelsize': 30,
            'labelcolor': 'red'}
            >>> ax.yaxis.get_tick_params(which='minor')
            {'left': True,
            'right': False,
            'labelleft': True,
            'labelright': False,
            'gridOn': False}


        """
        _api.check_in_list(['major', 'minor'], which=which)
        if which == 'major':
            return self._translate_tick_params(
                self._major_tick_kw, reverse=True
            )
        return self._translate_tick_params(self._minor_tick_kw, reverse=True)

    @classmethod
    def _translate_tick_params(cls, kw, reverse=False):
        """
        Translate the kwargs supported by `.Axis.set_tick_params` to kwargs
        supported by `.Tick._apply_params`.

        In particular, this maps axis specific names like 'top', 'left'
        to the generic tick1, tick2 logic of the axis. Additionally, there
        are some other name translations.

        Returns a new dict of translated kwargs.

        Note: Use reverse=True to translate from those supported by
        `.Tick._apply_params` back to those supported by
        `.Axis.set_tick_params`.
        """
        kw_ = {**kw}

        # The following lists may be moved to a more accessible location.
        allowed_keys = [
            'size', 'width', 'color', 'tickdir', 'pad',
            'labelsize', 'labelcolor', 'labelfontfamily', 'zorder', 'gridOn',
            'tick1On', 'tick2On', 'label1On', 'label2On',
            'length', 'direction', 'left', 'bottom', 'right', 'top',
            'labelleft', 'labelbottom', 'labelright', 'labeltop',
            'labelrotation',
            *_gridline_param_names]

        keymap = {
            # tick_params key -> axis key
            'length': 'size',
            'direction': 'tickdir',
            'rotation': 'labelrotation',
            'left': 'tick1On',
            'bottom': 'tick1On',
            'right': 'tick2On',
            'top': 'tick2On',
            'labelleft': 'label1On',
            'labelbottom': 'label1On',
            'labelright': 'label2On',
            'labeltop': 'label2On',
        }
        if reverse:
            kwtrans = {}
            is_x_axis = cls.axis_name == 'x'
            y_axis_keys = ['left', 'right', 'labelleft', 'labelright']
            for oldkey, newkey in keymap.items():
                if newkey in kw_:
                    if is_x_axis and oldkey in y_axis_keys:
                        continue
                    else:
                        kwtrans[oldkey] = kw_.pop(newkey)
        else:
            kwtrans = {
                newkey: kw_.pop(oldkey)
                for oldkey, newkey in keymap.items() if oldkey in kw_
            }
        if 'colors' in kw_:
            c = kw_.pop('colors')
            kwtrans['color'] = c
            kwtrans['labelcolor'] = c
        # Maybe move the checking up to the caller of this method.
        for key in kw_:
            if key not in allowed_keys:
                raise ValueError(
                    "keyword %s is not recognized; valid keywords are %s"
                    % (key, allowed_keys))
        kwtrans.update(kw_)
        return kwtrans

    def set_clip_path(self, path, transform=None):
        super().set_clip_path(path, transform)
        for child in self.majorTicks + self.minorTicks:
            child.set_clip_path(path, transform)
        self.stale = True

    def get_view_interval(self):
        """Return the ``(min, max)`` view limits of this axis."""
        raise NotImplementedError('Derived must override')

    def set_view_interval(self, vmin, vmax, ignore=False):
        """
        Set the axis view limits.  This method is for internal use; Matplotlib
        users should typically use e.g. `~.Axes.set_xlim` or `~.Axes.set_ylim`.

        If *ignore* is False (the default), this method will never reduce the
        preexisting view limits, only expand them if *vmin* or *vmax* are not
        within them.  Moreover, the order of *vmin* and *vmax* does not matter;
        the orientation of the axis will not change.

        If *ignore* is True, the view limits will be set exactly to ``(vmin,
        vmax)`` in that order.
        """
        raise NotImplementedError('Derived must override')

    def get_data_interval(self):
        """Return the ``(min, max)`` data limits of this axis."""
        raise NotImplementedError('Derived must override')

    def set_data_interval(self, vmin, vmax, ignore=False):
        """
        Set the axis data limits.  This method is for internal use.

        If *ignore* is False (the default), this method will never reduce the
        preexisting data limits, only expand them if *vmin* or *vmax* are not
        within them.  Moreover, the order of *vmin* and *vmax* does not matter;
        the orientation of the axis will not change.

        If *ignore* is True, the data limits will be set exactly to ``(vmin,
        vmax)`` in that order.
        """
        raise NotImplementedError('Derived must override')

    def get_inverted(self):
        """
        Return whether this Axis is oriented in the "inverse" direction.

        The "normal" direction is increasing to the right for the x-axis and to
        the top for the y-axis; the "inverse" direction is increasing to the
        left for the x-axis and to the bottom for the y-axis.
        """
        low, high = self.get_view_interval()
        return high < low

    def set_inverted(self, inverted):
        """
        Set whether this Axis is oriented in the "inverse" direction.

        The "normal" direction is increasing to the right for the x-axis and to
        the top for the y-axis; the "inverse" direction is increasing to the
        left for the x-axis and to the bottom for the y-axis.
        """
        a, b = self.get_view_interval()
        # cast to bool to avoid bad interaction between python 3.8 and np.bool_
        self._set_lim(*sorted((a, b), reverse=bool(inverted)), auto=None)

    def set_default_intervals(self):
        """
        Set the default limits for the axis data and view interval if they
        have not been not mutated yet.
        """
        # this is mainly in support of custom object plotting.  For
        # example, if someone passes in a datetime object, we do not
        # know automagically how to set the default min/max of the
        # data and view limits.  The unit conversion AxisInfo
        # interface provides a hook for custom types to register
        # default limits through the AxisInfo.default_limits
        # attribute, and the derived code below will check for that
        # and use it if it's available (else just use 0..1)

    def _set_lim(self, v0, v1, *, emit=True, auto):
        """
        Set view limits.

        This method is a helper for the Axes ``set_xlim``, ``set_ylim``, and
        ``set_zlim`` methods.

        Parameters
        ----------
        v0, v1 : float
            The view limits.  (Passing *v0* as a (low, high) pair is not
            supported; normalization must occur in the Axes setters.)
        emit : bool, default: True
            Whether to notify observers of limit change.
        auto : bool or None, default: False
            Whether to turn on autoscaling of the x-axis. True turns on, False
            turns off, None leaves unchanged.
        """
        name = self._get_axis_name()

        self.axes._process_unit_info([(name, (v0, v1))], convert=False)
        v0 = self.axes._validate_converted_limits(v0, self.convert_units)
        v1 = self.axes._validate_converted_limits(v1, self.convert_units)

        if v0 is None or v1 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.
            old0, old1 = self.get_view_interval()
            if v0 is None:
                v0 = old0
            if v1 is None:
                v1 = old1

        if self.get_scale() == 'log' and (v0 <= 0 or v1 <= 0):
            # Axes init calls set_xlim(0, 1) before get_xlim() can be called,
            # so only grab the limits if we really need them.
            old0, old1 = self.get_view_interval()
            if v0 <= 0:
                _api.warn_external(f"Attempt to set non-positive {name}lim on "
                                   f"a log-scaled axis will be ignored.")
                v0 = old0
            if v1 <= 0:
                _api.warn_external(f"Attempt to set non-positive {name}lim on "
                                   f"a log-scaled axis will be ignored.")
                v1 = old1
        if v0 == v1:
            _api.warn_external(
                f"Attempting to set identical low and high {name}lims "
                f"makes transformation singular; automatically expanding.")
        reverse = bool(v0 > v1)  # explicit cast needed for python3.8+np.bool_.
        v0, v1 = self.get_major_locator().nonsingular(v0, v1)
        v0, v1 = self.limit_range_for_scale(v0, v1)
        v0, v1 = sorted([v0, v1], reverse=bool(reverse))

        self.set_view_interval(v0, v1, ignore=True)
        # Mark viewlims as no longer stale without triggering an autoscale.
        for ax in self._get_shared_axes():
            ax._stale_viewlims[name] = False
        self._set_autoscale_on(auto)

        if emit:
            self.axes.callbacks.process(f"{name}lim_changed", self.axes)
            # Call all of the other Axes that are shared with this one
            for other in self._get_shared_axes():
                if other is self.axes:
                    continue
                other._axis_map[name]._set_lim(v0, v1, emit=False, auto=auto)
                if emit:
                    other.callbacks.process(f"{name}lim_changed", other)
                if ((other_fig := other.get_figure(root=False)) !=
                        self.get_figure(root=False)):
                    other_fig.canvas.draw_idle()

        self.stale = True
        return v0, v1

    def _set_artist_props(self, a):
        if a is None:
            return
        a.set_figure(self.get_figure(root=False))

    def _update_ticks(self):
        """
        Update ticks (position and labels) using the current data interval of
        the axes.  Return the list of ticks that will be drawn.
        """
        major_locs = self.get_majorticklocs()
        major_labels = self.major.formatter.format_ticks(major_locs)
        major_ticks = self.get_major_ticks(len(major_locs))
        for tick, loc, label in zip(major_ticks, major_locs, major_labels):
            tick.update_position(loc)
            tick.label1.set_text(label)
            tick.label2.set_text(label)
        minor_locs = self.get_minorticklocs()
        minor_labels = self.minor.formatter.format_ticks(minor_locs)
        minor_ticks = self.get_minor_ticks(len(minor_locs))
        for tick, loc, label in zip(minor_ticks, minor_locs, minor_labels):
            tick.update_position(loc)
            tick.label1.set_text(label)
            tick.label2.set_text(label)
        ticks = [*major_ticks, *minor_ticks]

        view_low, view_high = self.get_view_interval()
        if view_low > view_high:
            view_low, view_high = view_high, view_low

        if (hasattr(self, "axes") and self.axes.name == '3d'
                and mpl.rcParams['axes3d.automargin']):
            # In mpl3.8, the margin was 1/48. Due to the change in automargin
            # behavior in mpl3.9, we need to adjust this to compensate for a
            # zoom factor of 2/48, giving us a 23/24 modifier. So the new
            # margin is 0.019965277777777776 = 1/48*23/24.
            margin = 0.019965277777777776
            delta = view_high - view_low
            view_high = view_high - delta * margin
            view_low = view_low + delta * margin

        interval_t = self.get_transform().transform([view_low, view_high])

        ticks_to_draw = []
        for tick in ticks:
            try:
                loc_t = self.get_transform().transform(tick.get_loc())
            except AssertionError:
                # transforms.transform doesn't allow masked values but
                # some scales might make them, so we need this try/except.
                pass
            else:
                if mtransforms._interval_contains_close(interval_t, loc_t):
                    ticks_to_draw.append(tick)

        return ticks_to_draw

    def _get_ticklabel_bboxes(self, ticks, renderer=None):
        """Return lists of bboxes for ticks' label1's and label2's."""
        if renderer is None:
            renderer = self.get_figure(root=True)._get_renderer()
        return ([tick.label1.get_window_extent(renderer)
                 for tick in ticks if tick.label1.get_visible()],
                [tick.label2.get_window_extent(renderer)
                 for tick in ticks if tick.label2.get_visible()])

    def get_tightbbox(self, renderer=None, *, for_layout_only=False):
        """
        Return a bounding box that encloses the axis. It only accounts
        tick labels, axis label, and offsetText.

        If *for_layout_only* is True, then the width of the label (if this
        is an x-axis) or the height of the label (if this is a y-axis) is
        collapsed to near zero.  This allows tight/constrained_layout to ignore
        too-long labels when doing their layout.
        """
        if not self.get_visible() or for_layout_only and not self.get_in_layout():
            return
        if renderer is None:
            renderer = self.get_figure(root=True)._get_renderer()
        ticks_to_draw = self._update_ticks()

        self._update_label_position(renderer)

        # go back to just this axis's tick labels
        tlb1, tlb2 = self._get_ticklabel_bboxes(ticks_to_draw, renderer)

        self._update_offset_text_position(tlb1, tlb2)
        self.offsetText.set_text(self.major.formatter.get_offset())

        bboxes = [
            *(a.get_window_extent(renderer)
              for a in [self.offsetText]
              if a.get_visible()),
            *tlb1, *tlb2,
        ]
        # take care of label
        if self.label.get_visible():
            bb = self.label.get_window_extent(renderer)
            # for constrained/tight_layout, we want to ignore the label's
            # width/height because the adjustments they make can't be improved.
            # this code collapses the relevant direction
            if for_layout_only:
                if self.axis_name == "x" and bb.width > 0:
                    bb.x0 = (bb.x0 + bb.x1) / 2 - 0.5
                    bb.x1 = bb.x0 + 1.0
                if self.axis_name == "y" and bb.height > 0:
                    bb.y0 = (bb.y0 + bb.y1) / 2 - 0.5
                    bb.y1 = bb.y0 + 1.0
            bboxes.append(bb)
        bboxes = [b for b in bboxes
                  if 0 < b.width < np.inf and 0 < b.height < np.inf]
        if bboxes:
            return mtransforms.Bbox.union(bboxes)
        else:
            return None

    def get_tick_padding(self):
        values = []
        if len(self.majorTicks):
            values.append(self.majorTicks[0].get_tick_padding())
        if len(self.minorTicks):
            values.append(self.minorTicks[0].get_tick_padding())
        return max(values, default=0)

    @martist.allow_rasterization
    def draw(self, renderer):
        # docstring inherited

        if not self.get_visible():
            return
        renderer.open_group(__name__, gid=self.get_gid())

        ticks_to_draw = self._update_ticks()
        tlb1, tlb2 = self._get_ticklabel_bboxes(ticks_to_draw, renderer)

        for tick in ticks_to_draw:
            tick.draw(renderer)

        # Shift label away from axes to avoid overlapping ticklabels.
        self._update_label_position(renderer)
        self.label.draw(renderer)

        self._update_offset_text_position(tlb1, tlb2)
        self.offsetText.set_text(self.major.formatter.get_offset())
        self.offsetText.draw(renderer)

        renderer.close_group(__name__)
        self.stale = False

    def get_gridlines(self):
        r"""Return this Axis' grid lines as a list of `.Line2D`\s."""
        ticks = self.get_major_ticks()
        return cbook.silent_list('Line2D gridline',
                                 [tick.gridline for tick in ticks])

    def set_label(self, s):
        """Assigning legend labels is not supported. Raises RuntimeError."""
        raise RuntimeError(
            "A legend label cannot be assigned to an Axis. Did you mean to "
            "set the axis label via set_label_text()?")

    def get_label(self):
        """
        Return the axis label as a Text instance.

        .. admonition:: Discouraged

           This overrides `.Artist.get_label`, which is for legend labels, with a new
           semantic. It is recommended to use the attribute ``Axis.label`` instead.
        """
        return self.label

    def get_offset_text(self):
        """Return the axis offsetText as a Text instance."""
        return self.offsetText

    def get_pickradius(self):
        """Return the depth of the axis used by the picker."""
        return self._pickradius

    def get_majorticklabels(self):
        """Return this Axis' major tick labels, as a list of `~.text.Text`."""
        self._update_ticks()
        ticks = self.get_major_ticks()
        labels1 = [tick.label1 for tick in ticks if tick.label1.get_visible()]
        labels2 = [tick.label2 for tick in ticks if tick.label2.get_visible()]
        return labels1 + labels2

    def get_minorticklabels(self):
        """Return this Axis' minor tick labels, as a list of `~.text.Text`."""
        self._update_ticks()
        ticks = self.get_minor_ticks()
        labels1 = [tick.label1 for tick in ticks if tick.label1.get_visible()]
        labels2 = [tick.label2 for tick in ticks if tick.label2.get_visible()]
        return labels1 + labels2

    def get_ticklabels(self, minor=False, which=None):
        """
        Get this Axis' tick labels.

        Parameters
        ----------
        minor : bool
           Whether to return the minor or the major ticklabels.

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

           Selects which ticklabels to return

        Returns
        -------
        list of `~matplotlib.text.Text`
        """
        if which is not None:
            if which == 'minor':
                return self.get_minorticklabels()
            elif which == 'major':
                return self.get_majorticklabels()
            elif which == 'both':
                return self.get_majorticklabels() + self.get_minorticklabels()
            else:
                _api.check_in_list(['major', 'minor', 'both'], which=which)
        if minor:
            return self.get_minorticklabels()
        return self.get_majorticklabels()

    def get_majorticklines(self):
        r"""Return this Axis' major tick lines as a list of `.Line2D`\s."""
        lines = []
        ticks = self.get_major_ticks()
        for tick in ticks:
            lines.append(tick.tick1line)
            lines.append(tick.tick2line)
        return cbook.silent_list('Line2D ticklines', lines)

    def get_minorticklines(self):
        r"""Return this Axis' minor tick lines as a list of `.Line2D`\s."""
        lines = []
        ticks = self.get_minor_ticks()
        for tick in ticks:
            lines.append(tick.tick1line)
            lines.append(tick.tick2line)
        return cbook.silent_list('Line2D ticklines', lines)

    def get_ticklines(self, minor=False):
        r"""Return this Axis' tick lines as a list of `.Line2D`\s."""
        if minor:
            return self.get_minorticklines()
        return self.get_majorticklines()

    def get_majorticklocs(self):
        """Return this Axis' major tick locations in data coordinates."""
        return self.major.locator()

    def get_minorticklocs(self):
        """Return this Axis' minor tick locations in data coordinates."""
        # Remove minor ticks duplicating major ticks.
        minor_locs = np.asarray(self.minor.locator())
        if self.remove_overlapping_locs:
            major_locs = self.major.locator()
            transform = self._scale.get_transform()
            tr_minor_locs = transform.transform(minor_locs)
            tr_major_locs = transform.transform(major_locs)
            lo, hi = sorted(transform.transform(self.get_view_interval()))
            # Use the transformed view limits as scale.  1e-5 is the default
            # rtol for np.isclose.
            tol = (hi - lo) * 1e-5
            mask = np.isclose(tr_minor_locs[:, None], tr_major_locs[None, :],
                              atol=tol, rtol=0).any(axis=1)
            minor_locs = minor_locs[~mask]
        return minor_locs

    def get_ticklocs(self, *, minor=False):
        """
        Return this Axis' tick locations in data coordinates.

        The locations are not clipped to the current axis limits and hence
        may contain locations that are not visible in the output.

        Parameters
        ----------
        minor : bool, default: False
            True to return the minor tick directions,
            False to return the major tick directions.

        Returns
        -------
        array of tick locations
        """
        return self.get_minorticklocs() if minor else self.get_majorticklocs()

    def get_ticks_direction(self, minor=False):
        """
        Return an array of this Axis' tick directions.

        Parameters
        ----------
        minor : bool, default: False
            True to return the minor tick directions,
            False to return the major tick directions.

        Returns
        -------
        array of tick directions
        """
        if minor:
            return np.array(
                [tick._tickdir for tick in self.get_minor_ticks()])
        else:
            return np.array(
                [tick._tickdir for tick in self.get_major_ticks()])

    def _get_tick(self, major):
        """Return the default tick instance."""
        if self._tick_class is None:
            raise NotImplementedError(
                f"The Axis subclass {self.__class__.__name__} must define "
                "_tick_class or reimplement _get_tick()")
        tick_kw = self._major_tick_kw if major else self._minor_tick_kw
        return self._tick_class(self.axes, 0, major=major, **tick_kw)

    def _get_tick_label_size(self, axis_name):
        """
        Return the text size of tick labels for this Axis.

        This is a convenience function to avoid having to create a `Tick` in
        `.get_tick_space`, since it is expensive.
        """
        tick_kw = self._major_tick_kw
        size = tick_kw.get('labelsize',
                           mpl.rcParams[f'{axis_name}tick.labelsize'])
        return mtext.FontProperties(size=size).get_size_in_points()

    def _copy_tick_props(self, src, dest):
        """Copy the properties from *src* tick to *dest* tick."""
        if src is None or dest is None:
            return
        dest.label1.update_from(src.label1)
        dest.label2.update_from(src.label2)
        dest.tick1line.update_from(src.tick1line)
        dest.tick2line.update_from(src.tick2line)
        dest.gridline.update_from(src.gridline)
        dest.update_from(src)
        dest._loc = src._loc
        dest._size = src._size
        dest._width = src._width
        dest._base_pad = src._base_pad
        dest._labelrotation = src._labelrotation
        dest._zorder = src._zorder
        dest._tickdir = src._tickdir

    def get_label_text(self):
        """Get the text of the label."""
        return self.label.get_text()

    def get_major_locator(self):
        """Get the locator of the major ticker."""
        return self.major.locator

    def get_minor_locator(self):
        """Get the locator of the minor ticker."""
        return self.minor.locator

    def get_major_formatter(self):
        """Get the formatter of the major ticker."""
        return self.major.formatter

    def get_minor_formatter(self):
        """Get the formatter of the minor ticker."""
        return self.minor.formatter

    def get_major_ticks(self, numticks=None):
        r"""
        Return the list of major `.Tick`\s.

        .. warning::

            Ticks are not guaranteed to be persistent. Various operations
            can create, delete and modify the Tick instances. There is an
            imminent risk that changes to individual ticks will not
            survive if you work on the figure further (including also
            panning/zooming on a displayed figure).

            Working on the individual ticks is a method of last resort.
            Use `.set_tick_params` instead if possible.
        """
        if numticks is None:
            numticks = len(self.get_majorticklocs())

        while len(self.majorTicks) < numticks:
            # Update the new tick label properties from the old.
            tick = self._get_tick(major=True)
            self.majorTicks.append(tick)
            self._copy_tick_props(self.majorTicks[0], tick)

        return self.majorTicks[:numticks]

    def get_minor_ticks(self, numticks=None):
        r"""
        Return the list of minor `.Tick`\s.

        .. warning::

            Ticks are not guaranteed to be persistent. Various operations
            can create, delete and modify the Tick instances. There is an
            imminent risk that changes to individual ticks will not
            survive if you work on the figure further (including also
            panning/zooming on a displayed figure).

            Working on the individual ticks is a method of last resort.
            Use `.set_tick_params` instead if possible.
        """
        if numticks is None:
            numticks = len(self.get_minorticklocs())

        while len(self.minorTicks) < numticks:
            # Update the new tick label properties from the old.
            tick = self._get_tick(major=False)
            self.minorTicks.append(tick)
            self._copy_tick_props(self.minorTicks[0], tick)

        return self.minorTicks[:numticks]

    def grid(self, visible=None, which='major', **kwargs):
        """
        Configure the grid lines.

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

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

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

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

                grid(color='r', linestyle='-', linewidth=2)
        """
        if kwargs:
            if visible is None:
                visible = True
            elif not visible:  # something false-like but not None
                _api.warn_external('First parameter to grid() is false, '
                                   'but line properties are supplied. The '
                                   'grid will be enabled.')
                visible = True
        which = which.lower()
        _api.check_in_list(['major', 'minor', 'both'], which=which)
        gridkw = {f'grid_{name}': value for name, value in kwargs.items()}
        if which in ['minor', 'both']:
            gridkw['gridOn'] = (not self._minor_tick_kw['gridOn']
                                if visible is None else visible)
            self.set_tick_params(which='minor', **gridkw)
        if which in ['major', 'both']:
            gridkw['gridOn'] = (not self._major_tick_kw['gridOn']
                                if visible is None else visible)
            self.set_tick_params(which='major', **gridkw)
        self.stale = True

    def update_units(self, data):
        """
        Introspect *data* for units converter and update the
        ``axis.get_converter`` instance if necessary. Return *True*
        if *data* is registered for unit conversion.
        """
        if not self._converter_is_explicit:
            converter = munits.registry.get_converter(data)
        else:
            converter = self._converter

        if converter is None:
            return False

        neednew = self._converter != converter
        self._set_converter(converter)
        default = self._converter.default_units(data, self)
        if default is not None and self.units is None:
            self.set_units(default)

        elif neednew:
            self._update_axisinfo()
        self.stale = True
        return True

    def _update_axisinfo(self):
        """
        Check the axis converter for the stored units to see if the
        axis info needs to be updated.
        """
        if self._converter is None:
            return

        info = self._converter.axisinfo(self.units, self)

        if info is None:
            return
        if info.majloc is not None and \
           self.major.locator != info.majloc and self.isDefault_majloc:
            self.set_major_locator(info.majloc)
            self.isDefault_majloc = True
        if info.minloc is not None and \
           self.minor.locator != info.minloc and self.isDefault_minloc:
            self.set_minor_locator(info.minloc)
            self.isDefault_minloc = True
        if info.majfmt is not None and \
           self.major.formatter != info.majfmt and self.isDefault_majfmt:
            self.set_major_formatter(info.majfmt)
            self.isDefault_majfmt = True
        if info.minfmt is not None and \
           self.minor.formatter != info.minfmt and self.isDefault_minfmt:
            self.set_minor_formatter(info.minfmt)
            self.isDefault_minfmt = True
        if info.label is not None and self.isDefault_label:
            self.set_label_text(info.label)
            self.isDefault_label = True

        self.set_default_intervals()

    def have_units(self):
        return self._converter is not None or self.units is not None

    def convert_units(self, x):
        # If x is natively supported by Matplotlib, doesn't need converting
        if munits._is_natively_supported(x):
            return x

        if self._converter is None:
            self._set_converter(munits.registry.get_converter(x))

        if self._converter is None:
            return x
        try:
            ret = self._converter.convert(x, self.units, self)
        except Exception as e:
            raise munits.ConversionError('Failed to convert value(s) to axis '
                                         f'units: {x!r}') from e
        return ret

    def get_converter(self):
        """
        Get the unit converter for axis.

        Returns
        -------
        `~matplotlib.units.ConversionInterface` or None
        """
        return self._converter

    def set_converter(self, converter):
        """
        Set the unit converter for axis.

        Parameters
        ----------
        converter : `~matplotlib.units.ConversionInterface`
        """
        self._set_converter(converter)
        self._converter_is_explicit = True

    def _set_converter(self, converter):
        if self._converter is converter or self._converter == converter:
            return
        if self._converter_is_explicit:
            raise RuntimeError("Axis already has an explicit converter set")
        elif (
            self._converter is not None and
            not isinstance(converter, type(self._converter)) and
            not isinstance(self._converter, type(converter))
        ):
            _api.warn_external(
                "This axis already has a converter set and "
                "is updating to a potentially incompatible converter"
            )
        self._converter = converter

    def set_units(self, u):
        """
        Set the units for axis.

        Parameters
        ----------
        u : units tag

        Notes
        -----
        The units of any shared axis will also be updated.
        """
        if u == self.units:
            return
        for axis in self._get_shared_axis():
            axis.units = u
            axis._update_axisinfo()
            axis.callbacks.process('units')
            axis.stale = True

    def get_units(self):
        """Return the units for axis."""
        return self.units

    def set_label_text(self, label, fontdict=None, **kwargs):
        """
        Set the text value of the axis label.

        Parameters
        ----------
        label : str
            Text string.
        fontdict : dict
            Text properties.

            .. admonition:: Discouraged

               The use of *fontdict* is discouraged. Parameters should be passed as
               individual keyword arguments or using dictionary-unpacking
               ``set_label_text(..., **fontdict)``.

        **kwargs
            Merged into fontdict.
        """
        self.isDefault_label = False
        self.label.set_text(label)
        if fontdict is not None:
            self.label.update(fontdict)
        self.label.update(kwargs)
        self.stale = True
        return self.label

    def set_major_formatter(self, formatter):
        """
        Set the formatter of the major ticker.

        In addition to a `~matplotlib.ticker.Formatter` instance,
        this also accepts a ``str`` or function.

        For a ``str`` a `~matplotlib.ticker.StrMethodFormatter` is used.
        The field used for the value must be labeled ``'x'`` and the field used
        for the position must be labeled ``'pos'``.
        See the  `~matplotlib.ticker.StrMethodFormatter` documentation for
        more information.

        For a function, a `~matplotlib.ticker.FuncFormatter` is used.
        The function must take two inputs (a tick value ``x`` and a
        position ``pos``), and return a string containing the corresponding
        tick label.
        See the  `~matplotlib.ticker.FuncFormatter` documentation for
        more information.

        Parameters
        ----------
        formatter : `~matplotlib.ticker.Formatter`, ``str``, or function
        """
        self._set_formatter(formatter, self.major)

    def set_minor_formatter(self, formatter):
        """
        Set the formatter of the minor ticker.

        In addition to a `~matplotlib.ticker.Formatter` instance,
        this also accepts a ``str`` or function.
        See `.Axis.set_major_formatter` for more information.

        Parameters
        ----------
        formatter : `~matplotlib.ticker.Formatter`, ``str``, or function
        """
        self._set_formatter(formatter, self.minor)

    def _set_formatter(self, formatter, level):
        if isinstance(formatter, str):
            formatter = mticker.StrMethodFormatter(formatter)
        # Don't allow any other TickHelper to avoid easy-to-make errors,
        # like using a Locator instead of a Formatter.
        elif (callable(formatter) and
              not isinstance(formatter, mticker.TickHelper)):
            formatter = mticker.FuncFormatter(formatter)
        else:
            _api.check_isinstance(mticker.Formatter, formatter=formatter)

        if (isinstance(formatter, mticker.FixedFormatter)
                and len(formatter.seq) > 0
                and not isinstance(level.locator, mticker.FixedLocator)):
            _api.warn_external('FixedFormatter should only be used together '
                               'with FixedLocator')

        if level == self.major:
            self.isDefault_majfmt = False
        else:
            self.isDefault_minfmt = False

        level.formatter = formatter
        formatter.set_axis(self)
        self.stale = True

    def set_major_locator(self, locator):
        """
        Set the locator of the major ticker.

        Parameters
        ----------
        locator : `~matplotlib.ticker.Locator`
        """
        _api.check_isinstance(mticker.Locator, locator=locator)
        self.isDefault_majloc = False
        self.major.locator = locator
        if self.major.formatter:
            self.major.formatter._set_locator(locator)
        locator.set_axis(self)
        self.stale = True

    def set_minor_locator(self, locator):
        """
        Set the locator of the minor ticker.

        Parameters
        ----------
        locator : `~matplotlib.ticker.Locator`
        """
        _api.check_isinstance(mticker.Locator, locator=locator)
        self.isDefault_minloc = False
        self.minor.locator = locator
        if self.minor.formatter:
            self.minor.formatter._set_locator(locator)
        locator.set_axis(self)
        self.stale = True

    def set_pickradius(self, pickradius):
        """
        Set the depth of the axis used by the picker.

        Parameters
        ----------
        pickradius : float
            The acceptance radius for containment tests.
            See also `.Axis.contains`.
        """
        if not isinstance(pickradius, Real) or pickradius < 0:
            raise ValueError("pick radius should be a distance")
        self._pickradius = pickradius

    pickradius = property(
        get_pickradius, set_pickradius, doc="The acceptance radius for "
        "containment tests. See also `.Axis.contains`.")

    # Helper for set_ticklabels. Defining it here makes it picklable.
    @staticmethod
    def _format_with_dict(tickd, x, pos):
        return tickd.get(x, "")

    def set_ticklabels(self, labels, *, minor=False, fontdict=None, **kwargs):
        r"""
        [*Discouraged*] Set this Axis' tick labels with list of string labels.

        .. admonition:: Discouraged

            The use of this method is discouraged, because of the dependency on
            tick positions. In most cases, you'll want to use
            ``Axes.set_[x/y/z]ticks(positions, labels)`` or ``Axis.set_ticks``
            instead.

            If you are using this method, you should always fix the tick
            positions before, e.g. by using `.Axis.set_ticks` or by explicitly
            setting a `~.ticker.FixedLocator`. Otherwise, ticks are free to
            move and the labels may end up in unexpected positions.

        Parameters
        ----------
        labels : sequence of str or of `.Text`\s
            Texts for labeling each tick location in the sequence set by
            `.Axis.set_ticks`; the number of labels must match the number of locations.
            The labels are used as is, via a `.FixedFormatter` (without further
            formatting).

        minor : bool
            If True, set minor ticks instead of major ticks.

        fontdict : dict, optional

            .. admonition:: Discouraged

               The use of *fontdict* is discouraged. Parameters should be passed as
               individual keyword arguments or using dictionary-unpacking
               ``set_ticklabels(..., **fontdict)``.

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

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

        **kwargs
            Text properties.

            .. warning::

                This only sets the properties of the current ticks, which is
                only sufficient for static plots.

                Ticks are not guaranteed to be persistent. Various operations
                can create, delete and modify the Tick instances. There is an
                imminent risk that these settings can get lost if you work on
                the figure further (including also panning/zooming on a
                displayed figure).

                Use `.set_tick_params` instead if possible.

        Returns
        -------
        list of `.Text`\s
            For each tick, includes ``tick.label1`` if it is visible, then
            ``tick.label2`` if it is visible, in that order.
        """
        try:
            labels = [t.get_text() if hasattr(t, 'get_text') else t
                      for t in labels]
        except TypeError:
            raise TypeError(f"{labels:=} must be a sequence") from None
        locator = (self.get_minor_locator() if minor
                   else self.get_major_locator())
        if not labels:
            # eg labels=[]:
            formatter = mticker.NullFormatter()
        elif isinstance(locator, mticker.FixedLocator):
            # Passing [] as a list of labels is often used as a way to
            # remove all tick labels, so only error for > 0 labels
            if len(locator.locs) != len(labels) and len(labels) != 0:
                raise ValueError(
                    "The number of FixedLocator locations"
                    f" ({len(locator.locs)}), usually from a call to"
                    " set_ticks, does not match"
                    f" the number of labels ({len(labels)}).")
            tickd = {loc: lab for loc, lab in zip(locator.locs, labels)}
            func = functools.partial(self._format_with_dict, tickd)
            formatter = mticker.FuncFormatter(func)
        else:
            _api.warn_external(
                 "set_ticklabels() should only be used with a fixed number of "
                 "ticks, i.e. after set_ticks() or using a FixedLocator.")
            formatter = mticker.FixedFormatter(labels)

        with warnings.catch_warnings():
            warnings.filterwarnings(
                "ignore",
                message="FixedFormatter should only be used together with FixedLocator")
            if minor:
                self.set_minor_formatter(formatter)
                locs = self.get_minorticklocs()
                ticks = self.get_minor_ticks(len(locs))
            else:
                self.set_major_formatter(formatter)
                locs = self.get_majorticklocs()
                ticks = self.get_major_ticks(len(locs))

        ret = []
        if fontdict is not None:
            kwargs.update(fontdict)
        for pos, (loc, tick) in enumerate(zip(locs, ticks)):
            tick.update_position(loc)
            tick_label = formatter(loc, pos)
            # deal with label1
            tick.label1.set_text(tick_label)
            tick.label1._internal_update(kwargs)
            # deal with label2
            tick.label2.set_text(tick_label)
            tick.label2._internal_update(kwargs)
            # only return visible tick labels
            if tick.label1.get_visible():
                ret.append(tick.label1)
            if tick.label2.get_visible():
                ret.append(tick.label2)

        self.stale = True
        return ret

    def _set_tick_locations(self, ticks, *, minor=False):
        # see docstring of set_ticks

        # XXX if the user changes units, the information will be lost here
        ticks = self.convert_units(ticks)
        locator = mticker.FixedLocator(ticks)  # validate ticks early.
        if len(ticks):
            for axis in self._get_shared_axis():
                # set_view_interval maintains any preexisting inversion.
                axis.set_view_interval(min(ticks), max(ticks))
        self.axes.stale = True
        if minor:
            self.set_minor_locator(locator)
            return self.get_minor_ticks(len(ticks))
        else:
            self.set_major_locator(locator)
            return self.get_major_ticks(len(ticks))

    def set_ticks(self, ticks, labels=None, *, minor=False, **kwargs):
        """
        Set this Axis' tick locations and optionally tick labels.

        If necessary, the view limits of the Axis are expanded so that all
        given ticks are visible.

        Parameters
        ----------
        ticks : 1D array-like
            Array of tick locations (either floats or in axis units). The axis
            `.Locator` is replaced by a `~.ticker.FixedLocator`.

            Pass an empty list (``set_ticks([])``) to remove all ticks.

            Some tick formatters will not label arbitrary tick positions;
            e.g. log formatters only label decade ticks by default. In
            such a case you can set a formatter explicitly on the axis
            using `.Axis.set_major_formatter` or provide formatted
            *labels* yourself.

        labels : list of str, optional
            Tick labels for each location in *ticks*; must have the same length as
            *ticks*. If set, the labels are used as is, via a `.FixedFormatter`.
            If not set, the labels are generated using the axis tick `.Formatter`.

        minor : bool, default: False
            If ``False``, set only the major ticks; if ``True``, only the minor ticks.

        **kwargs
            `.Text` properties for the labels. Using these is only allowed if
            you pass *labels*. In other cases, please use `~.Axes.tick_params`.

        Notes
        -----
        The mandatory expansion of the view limits is an intentional design
        choice to prevent the surprise of a non-visible tick. If you need
        other limits, you should set the limits explicitly after setting the
        ticks.
        """
        if labels is None and kwargs:
            first_key = next(iter(kwargs))
            raise ValueError(
                f"Incorrect use of keyword argument {first_key!r}. Keyword arguments "
                "other than 'minor' modify the text labels and can only be used if "
                "'labels' are passed as well.")
        result = self._set_tick_locations(ticks, minor=minor)
        if labels is not None:
            self.set_ticklabels(labels, minor=minor, **kwargs)
        return result

    def _get_tick_boxes_siblings(self, renderer):
        """
        Get the bounding boxes for this `.axis` and its siblings
        as set by `.Figure.align_xlabels` or  `.Figure.align_ylabels`.

        By default, it just gets bboxes for *self*.
        """
        # Get the Grouper keeping track of x or y label groups for this figure.
        name = self._get_axis_name()
        if name not in self.get_figure(root=False)._align_label_groups:
            return [], []
        grouper = self.get_figure(root=False)._align_label_groups[name]
        bboxes = []
        bboxes2 = []
        # If we want to align labels from other Axes:
        for ax in grouper.get_siblings(self.axes):
            axis = ax._axis_map[name]
            ticks_to_draw = axis._update_ticks()
            tlb, tlb2 = axis._get_ticklabel_bboxes(ticks_to_draw, renderer)
            bboxes.extend(tlb)
            bboxes2.extend(tlb2)
        return bboxes, bboxes2

    def _update_label_position(self, renderer):
        """
        Update the label position based on the bounding box enclosing
        all the ticklabels and axis spine.
        """
        raise NotImplementedError('Derived must override')

    def _update_offset_text_position(self, bboxes, bboxes2):
        """
        Update the offset text position based on the sequence of bounding
        boxes of all the ticklabels.
        """
        raise NotImplementedError('Derived must override')

    def axis_date(self, tz=None):
        """
        Set up axis ticks and labels to treat data along this Axis as dates.

        Parameters
        ----------
        tz : str or `datetime.tzinfo`, default: :rc:`timezone`
            The timezone used to create date labels.
        """
        # By providing a sample datetime instance with the desired timezone,
        # the registered converter can be selected, and the "units" attribute,
        # which is the timezone, can be set.
        if isinstance(tz, str):
            import dateutil.tz
            tz = dateutil.tz.gettz(tz)
        self.update_units(datetime.datetime(2009, 1, 1, 0, 0, 0, 0, tz))

    def get_tick_space(self):
        """Return the estimated number of ticks that can fit on the axis."""
        # Must be overridden in the subclass
        raise NotImplementedError()

    def _get_ticks_position(self):
        """
        Helper for `XAxis.get_ticks_position` and `YAxis.get_ticks_position`.

        Check the visibility of tick1line, label1, tick2line, and label2 on
        the first major and the first minor ticks, and return

        - 1 if only tick1line and label1 are visible (which corresponds to
          "bottom" for the x-axis and "left" for the y-axis);
        - 2 if only tick2line and label2 are visible (which corresponds to
          "top" for the x-axis and "right" for the y-axis);
        - "default" if only tick1line, tick2line and label1 are visible;
        - "unknown" otherwise.
        """
        major = self.majorTicks[0]
        minor = self.minorTicks[0]
        if all(tick.tick1line.get_visible()
               and not tick.tick2line.get_visible()
               and tick.label1.get_visible()
               and not tick.label2.get_visible()
               for tick in [major, minor]):
            return 1
        elif all(tick.tick2line.get_visible()
                 and not tick.tick1line.get_visible()
                 and tick.label2.get_visible()
                 and not tick.label1.get_visible()
                 for tick in [major, minor]):
            return 2
        elif all(tick.tick1line.get_visible()
                 and tick.tick2line.get_visible()
                 and tick.label1.get_visible()
                 and not tick.label2.get_visible()
                 for tick in [major, minor]):
            return "default"
        else:
            return "unknown"

    def get_label_position(self):
        """
        Return the label position (top or bottom)
        """
        return self.label_position

    def set_label_position(self, position):
        """
        Set the label position (top or bottom)

        Parameters
        ----------
        position : {'top', 'bottom'}
        """
        raise NotImplementedError()

    def get_minpos(self):
        raise NotImplementedError()


def _make_getset_interval(method_name, lim_name, attr_name):
    """
    Helper to generate ``get_{data,view}_interval`` and
    ``set_{data,view}_interval`` implementations.
    """

    def getter(self):
        # docstring inherited.
        return getattr(getattr(self.axes, lim_name), attr_name)

    def setter(self, vmin, vmax, ignore=False):
        # docstring inherited.
        if ignore:
            setattr(getattr(self.axes, lim_name), attr_name, (vmin, vmax))
        else:
            oldmin, oldmax = getter(self)
            if oldmin < oldmax:
                setter(self, min(vmin, vmax, oldmin), max(vmin, vmax, oldmax),
                       ignore=True)
            else:
                setter(self, max(vmin, vmax, oldmin), min(vmin, vmax, oldmax),
                       ignore=True)
        self.stale = True

    getter.__name__ = f"get_{method_name}_interval"
    setter.__name__ = f"set_{method_name}_interval"

    return getter, setter


class XAxis(Axis):
    __name__ = 'xaxis'
    axis_name = 'x'  #: Read-only name identifying the axis.
    _tick_class = XTick

    def __init__(self, *args, **kwargs):
        super().__init__(*args, **kwargs)
        self._init()

    def _init(self):
        """
        Initialize the label and offsetText instance values and
        `label_position` / `offset_text_position`.
        """
        # x in axes coords, y in display coords (to be updated at draw time by
        # _update_label_positions and _update_offset_text_position).
        self.label.set(
            x=0.5, y=0,
            verticalalignment='top', horizontalalignment='center',
            transform=mtransforms.blended_transform_factory(
                self.axes.transAxes, mtransforms.IdentityTransform()),
        )
        self.label_position = 'bottom'

        if mpl.rcParams['xtick.labelcolor'] == 'inherit':
            tick_color = mpl.rcParams['xtick.color']
        else:
            tick_color = mpl.rcParams['xtick.labelcolor']

        self.offsetText.set(
            x=1, y=0,
            verticalalignment='top', horizontalalignment='right',
            transform=mtransforms.blended_transform_factory(
                self.axes.transAxes, mtransforms.IdentityTransform()),
            fontsize=mpl.rcParams['xtick.labelsize'],
            color=tick_color
        )
        self.offset_text_position = 'bottom'

    def contains(self, mouseevent):
        """Test whether the mouse event occurred in the x-axis."""
        if self._different_canvas(mouseevent):
            return False, {}
        x, y = mouseevent.x, mouseevent.y
        try:
            trans = self.axes.transAxes.inverted()
            xaxes, yaxes = trans.transform((x, y))
        except ValueError:
            return False, {}
        (l, b), (r, t) = self.axes.transAxes.transform([(0, 0), (1, 1)])
        inaxis = 0 <= xaxes <= 1 and (
            b - self._pickradius < y < b or
            t < y < t + self._pickradius)
        return inaxis, {}

    def set_label_position(self, position):
        """
        Set the label position (top or bottom)

        Parameters
        ----------
        position : {'top', 'bottom'}
        """
        self.label.set_verticalalignment(_api.check_getitem({
            'top': 'baseline', 'bottom': 'top',
        }, position=position))
        self.label_position = position
        self.stale = True

    def _update_label_position(self, renderer):
        """
        Update the label position based on the bounding box enclosing
        all the ticklabels and axis spine
        """
        if not self._autolabelpos:
            return

        # get bounding boxes for this axis and any siblings
        # that have been set by `fig.align_xlabels()`
        bboxes, bboxes2 = self._get_tick_boxes_siblings(renderer=renderer)
        x, y = self.label.get_position()

        if self.label_position == 'bottom':
            # Union with extents of the bottom spine if present, of the axes otherwise.
            bbox = mtransforms.Bbox.union([
                *bboxes, self.axes.spines.get("bottom", self.axes).get_window_extent()])
            self.label.set_position(
                (x, bbox.y0 - self.labelpad * self.get_figure(root=True).dpi / 72))
        else:
            # Union with extents of the top spine if present, of the axes otherwise.
            bbox = mtransforms.Bbox.union([
                *bboxes2, self.axes.spines.get("top", self.axes).get_window_extent()])
            self.label.set_position(
                (x, bbox.y1 + self.labelpad * self.get_figure(root=True).dpi / 72))

    def _update_offset_text_position(self, bboxes, bboxes2):
        """
        Update the offset_text position based on the sequence of bounding
        boxes of all the ticklabels
        """
        x, y = self.offsetText.get_position()
        if not hasattr(self, '_tick_position'):
            self._tick_position = 'bottom'
        if self._tick_position == 'bottom':
            if not len(bboxes):
                bottom = self.axes.bbox.ymin
            else:
                bbox = mtransforms.Bbox.union(bboxes)
                bottom = bbox.y0
            y = bottom - self.OFFSETTEXTPAD * self.get_figure(root=True).dpi / 72
        else:
            if not len(bboxes2):
                top = self.axes.bbox.ymax
            else:
                bbox = mtransforms.Bbox.union(bboxes2)
                top = bbox.y1
            y = top + self.OFFSETTEXTPAD * self.get_figure(root=True).dpi / 72
        self.offsetText.set_position((x, y))

    def set_ticks_position(self, position):
        """
        Set the ticks position.

        Parameters
        ----------
        position : {'top', 'bottom', 'both', 'default', 'none'}
            'both' sets the ticks to appear on both positions, but does not
            change the tick labels.  'default' resets the tick positions to
            the default: ticks on both positions, labels at bottom.  'none'
            can be used if you don't want any ticks. 'none' and 'both'
            affect only the ticks, not the labels.
        """
        if position == 'top':
            self.set_tick_params(which='both', top=True, labeltop=True,
                                 bottom=False, labelbottom=False)
            self._tick_position = 'top'
            self.offsetText.set_verticalalignment('bottom')
        elif position == 'bottom':
            self.set_tick_params(which='both', top=False, labeltop=False,
                                 bottom=True, labelbottom=True)
            self._tick_position = 'bottom'
            self.offsetText.set_verticalalignment('top')
        elif position == 'both':
            self.set_tick_params(which='both', top=True,
                                 bottom=True)
        elif position == 'none':
            self.set_tick_params(which='both', top=False,
                                 bottom=False)
        elif position == 'default':
            self.set_tick_params(which='both', top=True, labeltop=False,
                                 bottom=True, labelbottom=True)
            self._tick_position = 'bottom'
            self.offsetText.set_verticalalignment('top')
        else:
            _api.check_in_list(['top', 'bottom', 'both', 'default', 'none'],
                               position=position)
        self.stale = True

    def tick_top(self):
        """
        Move ticks and ticklabels (if present) to the top of the Axes.
        """
        label = True
        if 'label1On' in self._major_tick_kw:
            label = (self._major_tick_kw['label1On']
                     or self._major_tick_kw['label2On'])
        self.set_ticks_position('top')
        # If labels were turned off before this was called, leave them off.
        self.set_tick_params(which='both', labeltop=label)

    def tick_bottom(self):
        """
        Move ticks and ticklabels (if present) to the bottom of the Axes.
        """
        label = True
        if 'label1On' in self._major_tick_kw:
            label = (self._major_tick_kw['label1On']
                     or self._major_tick_kw['label2On'])
        self.set_ticks_position('bottom')
        # If labels were turned off before this was called, leave them off.
        self.set_tick_params(which='both', labelbottom=label)

    def get_ticks_position(self):
        """
        Return the ticks position ("top", "bottom", "default", or "unknown").
        """
        return {1: "bottom", 2: "top",
                "default": "default", "unknown": "unknown"}[
                    self._get_ticks_position()]

    get_view_interval, set_view_interval = _make_getset_interval(
        "view", "viewLim", "intervalx")
    get_data_interval, set_data_interval = _make_getset_interval(
        "data", "dataLim", "intervalx")

    def get_minpos(self):
        return self.axes.dataLim.minposx

    def set_default_intervals(self):
        # docstring inherited
        # only change view if dataLim has not changed and user has
        # not changed the view:
        if (not self.axes.dataLim.mutatedx() and
                not self.axes.viewLim.mutatedx()):
            if self._converter is not None:
                info = self._converter.axisinfo(self.units, self)
                if info.default_limits is not None:
                    xmin, xmax = self.convert_units(info.default_limits)
                    self.axes.viewLim.intervalx = xmin, xmax
        self.stale = True

    def get_tick_space(self):
        ends = mtransforms.Bbox.unit().transformed(
            self.axes.transAxes - self.get_figure(root=False).dpi_scale_trans)
        length = ends.width * 72
        # There is a heuristic here that the aspect ratio of tick text
        # is no more than 3:1
        size = self._get_tick_label_size('x') * 3
        if size > 0:
            return int(np.floor(length / size))
        else:
            return 2**31 - 1


class YAxis(Axis):
    __name__ = 'yaxis'
    axis_name = 'y'  #: Read-only name identifying the axis.
    _tick_class = YTick

    def __init__(self, *args, **kwargs):
        super().__init__(*args, **kwargs)
        self._init()

    def _init(self):
        """
        Initialize the label and offsetText instance values and
        `label_position` / `offset_text_position`.
        """
        # x in display coords, y in axes coords (to be updated at draw time by
        # _update_label_positions and _update_offset_text_position).
        self.label.set(
            x=0, y=0.5,
            verticalalignment='bottom', horizontalalignment='center',
            rotation='vertical', rotation_mode='anchor',
            transform=mtransforms.blended_transform_factory(
                mtransforms.IdentityTransform(), self.axes.transAxes),
        )
        self.label_position = 'left'

        if mpl.rcParams['ytick.labelcolor'] == 'inherit':
            tick_color = mpl.rcParams['ytick.color']
        else:
            tick_color = mpl.rcParams['ytick.labelcolor']

        # x in axes coords, y in display coords(!).
        self.offsetText.set(
            x=0, y=0.5,
            verticalalignment='baseline', horizontalalignment='left',
            transform=mtransforms.blended_transform_factory(
                self.axes.transAxes, mtransforms.IdentityTransform()),
            fontsize=mpl.rcParams['ytick.labelsize'],
            color=tick_color
        )
        self.offset_text_position = 'left'

    def contains(self, mouseevent):
        # docstring inherited
        if self._different_canvas(mouseevent):
            return False, {}
        x, y = mouseevent.x, mouseevent.y
        try:
            trans = self.axes.transAxes.inverted()
            xaxes, yaxes = trans.transform((x, y))
        except ValueError:
            return False, {}
        (l, b), (r, t) = self.axes.transAxes.transform([(0, 0), (1, 1)])
        inaxis = 0 <= yaxes <= 1 and (
            l - self._pickradius < x < l or
            r < x < r + self._pickradius)
        return inaxis, {}

    def set_label_position(self, position):
        """
        Set the label position (left or right)

        Parameters
        ----------
        position : {'left', 'right'}
        """
        self.label.set_rotation_mode('anchor')
        self.label.set_verticalalignment(_api.check_getitem({
            'left': 'bottom', 'right': 'top',
        }, position=position))
        self.label_position = position
        self.stale = True

    def _update_label_position(self, renderer):
        """
        Update the label position based on the bounding box enclosing
        all the ticklabels and axis spine
        """
        if not self._autolabelpos:
            return

        # get bounding boxes for this axis and any siblings
        # that have been set by `fig.align_ylabels()`
        bboxes, bboxes2 = self._get_tick_boxes_siblings(renderer=renderer)
        x, y = self.label.get_position()

        if self.label_position == 'left':
            # Union with extents of the left spine if present, of the axes otherwise.
            bbox = mtransforms.Bbox.union([
                *bboxes, self.axes.spines.get("left", self.axes).get_window_extent()])
            self.label.set_position(
                (bbox.x0 - self.labelpad * self.get_figure(root=True).dpi / 72, y))
        else:
            # Union with extents of the right spine if present, of the axes otherwise.
            bbox = mtransforms.Bbox.union([
                *bboxes2, self.axes.spines.get("right", self.axes).get_window_extent()])
            self.label.set_position(
                (bbox.x1 + self.labelpad * self.get_figure(root=True).dpi / 72, y))

    def _update_offset_text_position(self, bboxes, bboxes2):
        """
        Update the offset_text position based on the sequence of bounding
        boxes of all the ticklabels
        """
        x, _ = self.offsetText.get_position()
        if 'outline' in self.axes.spines:
            # Special case for colorbars:
            bbox = self.axes.spines['outline'].get_window_extent()
        else:
            bbox = self.axes.bbox
        top = bbox.ymax
        self.offsetText.set_position(
            (x, top + self.OFFSETTEXTPAD * self.get_figure(root=True).dpi / 72)
        )

    def set_offset_position(self, position):
        """
        Parameters
        ----------
        position : {'left', 'right'}
        """
        x, y = self.offsetText.get_position()
        x = _api.check_getitem({'left': 0, 'right': 1}, position=position)

        self.offsetText.set_ha(position)
        self.offsetText.set_position((x, y))
        self.stale = True

    def set_ticks_position(self, position):
        """
        Set the ticks position.

        Parameters
        ----------
        position : {'left', 'right', 'both', 'default', 'none'}
            'both' sets the ticks to appear on both positions, but does not
            change the tick labels.  'default' resets the tick positions to
            the default: ticks on both positions, labels at left.  'none'
            can be used if you don't want any ticks. 'none' and 'both'
            affect only the ticks, not the labels.
        """
        if position == 'right':
            self.set_tick_params(which='both', right=True, labelright=True,
                                 left=False, labelleft=False)
            self.set_offset_position(position)
        elif position == 'left':
            self.set_tick_params(which='both', right=False, labelright=False,
                                 left=True, labelleft=True)
            self.set_offset_position(position)
        elif position == 'both':
            self.set_tick_params(which='both', right=True,
                                 left=True)
        elif position == 'none':
            self.set_tick_params(which='both', right=False,
                                 left=False)
        elif position == 'default':
            self.set_tick_params(which='both', right=True, labelright=False,
                                 left=True, labelleft=True)
        else:
            _api.check_in_list(['left', 'right', 'both', 'default', 'none'],
                               position=position)
        self.stale = True

    def tick_right(self):
        """
        Move ticks and ticklabels (if present) to the right of the Axes.
        """
        label = True
        if 'label1On' in self._major_tick_kw:
            label = (self._major_tick_kw['label1On']
                     or self._major_tick_kw['label2On'])
        self.set_ticks_position('right')
        # if labels were turned off before this was called
        # leave them off
        self.set_tick_params(which='both', labelright=label)

    def tick_left(self):
        """
        Move ticks and ticklabels (if present) to the left of the Axes.
        """
        label = True
        if 'label1On' in self._major_tick_kw:
            label = (self._major_tick_kw['label1On']
                     or self._major_tick_kw['label2On'])
        self.set_ticks_position('left')
        # if labels were turned off before this was called
        # leave them off
        self.set_tick_params(which='both', labelleft=label)

    def get_ticks_position(self):
        """
        Return the ticks position ("left", "right", "default", or "unknown").
        """
        return {1: "left", 2: "right",
                "default": "default", "unknown": "unknown"}[
                    self._get_ticks_position()]

    get_view_interval, set_view_interval = _make_getset_interval(
        "view", "viewLim", "intervaly")
    get_data_interval, set_data_interval = _make_getset_interval(
        "data", "dataLim", "intervaly")

    def get_minpos(self):
        return self.axes.dataLim.minposy

    def set_default_intervals(self):
        # docstring inherited
        # only change view if dataLim has not changed and user has
        # not changed the view:
        if (not self.axes.dataLim.mutatedy() and
                not self.axes.viewLim.mutatedy()):
            if self._converter is not None:
                info = self._converter.axisinfo(self.units, self)
                if info.default_limits is not None:
                    ymin, ymax = self.convert_units(info.default_limits)
                    self.axes.viewLim.intervaly = ymin, ymax
        self.stale = True

    def get_tick_space(self):
        ends = mtransforms.Bbox.unit().transformed(
            self.axes.transAxes - self.get_figure(root=False).dpi_scale_trans)
        length = ends.height * 72
        # Having a spacing of at least 2 just looks good.
        size = self._get_tick_label_size('y') * 2
        if size > 0:
            return int(np.floor(length / size))
        else:
            return 2**31 - 1