base.py

#!/usr/bin/env python3
"""
The first-level axes subclass used for all ultraplot figures.
Implements basic shared functionality.
"""
import copy
import inspect
import re
import sys
import types
from collections.abc import Iterable as IterableType
from numbers import Integral, Number
from typing import Iterable, MutableMapping, Optional, Tuple, Union

try:
    # From python 3.12
    from typing import override
except ImportError:
    # From Python 3.5
    from typing_extensions import override

import matplotlib.axes as maxes
import matplotlib.axis as maxis
import matplotlib.cm as mcm
import matplotlib.colors as mcolors
import matplotlib.container as mcontainer
import matplotlib.contour as mcontour
import matplotlib.offsetbox as moffsetbox
import matplotlib.patches as mpatches
import matplotlib.projections as mproj
import matplotlib.text as mtext
import matplotlib.ticker as mticker
import matplotlib.transforms as mtransforms
import numpy as np
from matplotlib import cbook
from packaging import version

from .. import colors as pcolors
from .. import constructor
from .. import legend as plegend
from .. import ticker as pticker
from ..config import rc
from ..internals import (
    _kwargs_to_args,
    _not_none,
    _pop_kwargs,
    _pop_params,
    _pop_props,
    _pop_rc,
    _translate_loc,
    _version_mpl,
    docstring,
    guides,
    ic,  # noqa: F401
    labels,
    rcsetup,
    warnings,
)
from ..utils import _fontsize_to_pt, edges, units

try:
    from cartopy.crs import CRS, PlateCarree
except Exception:
    CRS = PlateCarree = object

__all__ = ["Axes"]


# A-b-c label string
ABC_STRING = "abcdefghijklmnopqrstuvwxyz"

# Legend align options
ALIGN_OPTS = {
    None: {
        "center": "center",
        "left": "center left",
        "right": "center right",
        "top": "upper center",
        "bottom": "lower center",
    },
    "left": {
        "top": "upper right",
        "center": "center right",
        "bottom": "lower right",
    },
    "right": {
        "top": "upper left",
        "center": "center left",
        "bottom": "lower left",
    },
    "top": {"left": "lower left", "center": "lower center", "right": "lower right"},
    "bottom": {"left": "upper left", "center": "upper center", "right": "upper right"},
}


# Projection docstring
_proj_docstring = """
proj, projection : \\
str, `cartopy.crs.Projection`, or `~mpl_toolkits.basemap.Basemap`, optional
    The map projection specification(s). If ``'cart'`` or ``'cartesian'``
    (the default), a `~ultraplot.axes.CartesianAxes` is created. If ``'polar'``,
    a :class:`~ultraplot.axes.PolarAxes` is created. Otherwise, the argument is
    interpreted by `~ultraplot.constructor.Proj`, and the result is used
    to make a `~ultraplot.axes.GeoAxes` (in this case the argument can be
    a `cartopy.crs.Projection` instance, a `~mpl_toolkits.basemap.Basemap`
    instance, or a projection name listed in :ref:`this table <proj_table>`).
"""
_proj_kw_docstring = """
proj_kw, projection_kw : dict-like, optional
    Keyword arguments passed to `~mpl_toolkits.basemap.Basemap` or
    cartopy `~cartopy.crs.Projection` classes on instantiation.
"""
_backend_docstring = """
backend : {'cartopy', 'basemap'}, default: :rc:`geo.backend`
    Whether to use `~mpl_toolkits.basemap.Basemap` or
    `~cartopy.crs.Projection` for map projections.
"""
docstring._snippet_manager["axes.proj"] = _proj_docstring
docstring._snippet_manager["axes.proj_kw"] = _proj_kw_docstring
docstring._snippet_manager["axes.backend"] = _backend_docstring


# Colorbar and legend space
_space_docstring = """
queue : bool, optional
    If ``True`` and `loc` is the same as an existing {name}, the input
    arguments are added to a queue and this function returns ``None``.
    This is used to "update" the same {name} with successive ``ax.{name}(...)``
    calls. If ``False`` (the default) and `loc` is the same as an existing
    *inset* {name}, the old {name} is removed. If ``False`` and `loc` is an
    *outer* {name}, the {name}s are "stacked".
space : unit-spec, default: None
    For outer {name}s only. The fixed space between the {name} and the subplot
    edge. %(units.em)s
    When the :ref:`tight layout algorithm <ug_tight>` is active for the figure,
    `space` is computed automatically (see `pad`). Otherwise, `space` is set to
    a suitable default.
pad : unit-spec, default: :rc:`subplots.panelpad` or :rc:`{default}`
    For outer {name}s, this is the :ref:`tight layout padding <ug_tight>`
    between the {name} and the subplot (default is :rcraw:`subplots.panelpad`).
    For inset {name}s, this is the fixed space between the axes
    edge and the {name} (default is :rcraw:`{default}`).
    %(units.em)s
align : {{'center', 'top', 'bottom', 'left', 'right', 't', 'b', 'l', 'r'}}, optional
    For outer {name}s only. How to align the {name} against the subplot edge.
    The values ``'top'`` and ``'bottom'`` are valid for left and right {name}s
    and ``'left'`` and ``'right'`` are valid for top and bottom {name}s.
    The default is always ``'center'``.
"""
docstring._snippet_manager["axes.legend_space"] = _space_docstring.format(
    name="legend", default="legend.borderaxespad"
)
docstring._snippet_manager["axes.colorbar_space"] = _space_docstring.format(
    name="colorbar", default="colorbar.insetpad"
)


# Transform docstring
# Used for text and add_axes
_transform_docstring = """
transform : {'data', 'axes', 'figure', 'subfigure'} \\
or `~matplotlib.transforms.Transform`, optional
    The transform used to interpret the bounds. Can be a
    `~matplotlib.transforms.Transform` instance or a string representing
    the `~matplotlib.axes.Axes.transData`, `~matplotlib.axes.Axes.transAxes`,
    `~matplotlib.figure.Figure.transFigure`, or
    `~matplotlib.figure.Figure.transSubfigure`, transforms.
"""
docstring._snippet_manager["axes.transform"] = _transform_docstring


# Inset docstring
# NOTE: Used by SubplotGrid.inset_axes
_inset_docstring = """
Add an inset axes.
This is similar to `matplotlib.axes.Axes.inset_axes`.

Parameters
-----------
bounds : 4-tuple of float
    The (left, bottom, width, height) coordinates for the axes.
%(axes.transform)s
    Default is to use the same projection as the current axes.
%(axes.proj)s
%(axes.proj_kw)s
%(axes.backend)s
zorder : float, default: 4
    The `zorder <https://matplotlib.org/stable/gallery/misc/zorder_demo.html>`__
    of the axes. Should be greater than the zorder of elements in the parent axes.
zoom : bool, default: True or False
    Whether to draw lines indicating the inset zoom using `~Axes.indicate_inset_zoom`.
    The line positions will automatically adjust when the parent or inset axes limits
    change. Default is ``True`` only if both axes are `~ultraplot.axes.CartesianAxes`.
zoom_kw : dict, optional
    Passed to `~Axes.indicate_inset_zoom`.

Other parameters
-----------------
**kwargs
    Passed to `ultraplot.axes.Axes`.

Returns
--------
ultraplot.axes.Axes
    The inset axes.

See also
---------
Axes.indicate_inset_zoom
matplotlib.axes.Axes.inset_axes
matplotlib.axes.Axes.indicate_inset
matplotlib.axes.Axes.indicate_inset_zoom
"""
_indicate_inset_docstring = """
Add indicators denoting the zoom range of the inset axes.
This will replace previously drawn zoom indicators.

Parameters
-----------
%(artist.patch)s
zorder : float, default: 3.5
    The `zorder <https://matplotlib.org/stable/gallery/misc/zorder_demo.html>`__ of
    the indicators. Should be greater than the zorder of elements in the parent axes.

Other parameters
-----------------
**kwargs
    Passed to `~matplotlib.patches.Patch`.

Note
-----
This command must be called from the inset axes rather than the parent axes.
It is called automatically when ``zoom=True`` is passed to `~Axes.inset_axes`
and whenever the axes are drawn (so the line positions always track the axis
limits even if they are later changed).

See also
---------
matplotlib.axes.Axes.indicate_inset
matplotlib.axes.Axes.indicate_inset_zoom
"""
docstring._snippet_manager["axes.inset"] = _inset_docstring
docstring._snippet_manager["axes.indicate_inset"] = _indicate_inset_docstring


# Panel docstring
# NOTE: Used by SubplotGrid.panel_axes
_panel_loc_docstring = """
    ==========  =====================
    Location    Valid keys
    ==========  =====================
    left        ``'left'``, ``'l'``
    right       ``'right'``, ``'r'``
    bottom      ``'bottom'``, ``'b'``
    top         ``'top'``, ``'t'``
    ==========  =====================
"""
_panel_docstring = """
Add a panel axes.

Parameters
-----------
side : str, optional
    The panel location. Valid location keys are as follows.

%(axes.panel_loc)s

width : unit-spec, default: :rc:`subplots.panelwidth`
    The panel width.
    %(units.in)s
space : unit-spec, default: None
    The fixed space between the panel and the subplot edge.
    %(units.em)s
    When the :ref:`tight layout algorithm <ug_tight>` is active for the figure,
    `space` is computed automatically (see `pad`). Otherwise, `space` is set to
    a suitable default.
pad : unit-spec, default: :rc:`subplots.panelpad`
    The :ref:`tight layout padding <ug_tight>` between the panel and the subplot.
    %(units.em)s
row, rows
    Aliases for `span` for panels on the left or right side (vertical panels).
col, cols
    Aliases for `span` for panels on the top or bottom side (horizontal panels).
span : int or 2-tuple of int, default: None
    Integer(s) indicating the span of the panel across rows and columns of
    subplots. For panels on the left or right side, use `rows` or `row` to
    specify which rows the panel should span. For panels on the top or bottom
    side, use `cols` or `col` to specify which columns the panel should span.
    For example, ``ax.panel('b', col=1)`` draws a panel beneath only the
    leftmost column, and ``ax.panel('b', cols=(1, 2))`` draws a panel beneath
    the left two columns. By default the panel will span all rows or columns
    aligned with the parent axes.
share : bool, default: True
    Whether to enable axis sharing between the *x* and *y* axes of the
    main subplot and the panel long axes for each panel in the "stack".
    Sharing between the panel short axis and other panel short axes
    is determined by figure-wide `sharex` and `sharey` settings.

Other parameters
-----------------
**kwargs
    Passed to `ultraplot.axes.CartesianAxes`. Supports all valid
    `~ultraplot.axes.CartesianAxes.format` keywords.

Returns
--------
ultraplot.axes.CartesianAxes
    The panel axes.
"""
docstring._snippet_manager["axes.panel_loc"] = _panel_loc_docstring
docstring._snippet_manager["axes.panel"] = _panel_docstring


# Format docstrings
_axes_format_docstring = """
title : str or sequence, optional
    The axes title. Can optionally be a sequence strings, in which case
    the title will be selected from the sequence according to `~Axes.number`.
abc : bool or str or sequence, default: :rc:`abc`
    The "a-b-c" subplot label style. Must contain the character `a` or `A`,
    for example ``'a.'``, or ``'A'``. If ``True`` then the default style of
    ``'a'`` is used. The `a` or ``A`` is replaced with the alphabetic character
    matching the `~Axes.number`. If `~Axes.number` is greater than 26, the
    characters loop around to a, ..., z, aa, ..., zz, aaa, ..., zzz, etc.
    Can also be a sequence of strings, in which case the "a-b-c" label will be selected sequentially from the list. For example `axs.format(abc = ["X", "Y"])` for a two-panel figure, and `axes[3:5].format(abc = ["X", "Y"])` for a two-panel subset of a larger figure.
abcloc, titleloc : str, default: :rc:`abc.loc`, :rc:`title.loc`
    Strings indicating the location for the a-b-c label and main title.
    The following locations are valid:

    .. _title_table:

    ========================  ============================
    Location                  Valid keys
    ========================  ============================
    center above axes         ``'center'``, ``'c'``
    left above axes           ``'left'``, ``'l'``
    right above axes          ``'right'``, ``'r'``
    lower center inside axes  ``'lower center'``, ``'lc'``
    upper center inside axes  ``'upper center'``, ``'uc'``
    upper right inside axes   ``'upper right'``, ``'ur'``
    upper left inside axes    ``'upper left'``, ``'ul'``
    lower left inside axes    ``'lower left'``, ``'ll'``
    lower right inside axes   ``'lower right'``, ``'lr'``
    left of y axis            ``'outer left'``, ``'ol'``
    right of y axis           ``'outer right'``, ``'or'``
    ========================  ============================

abcborder, titleborder : bool, default: :rc:`abc.border` and :rc:`title.border`
    Whether to draw a white border around titles and a-b-c labels positioned
    inside the axes. This can help them stand out on top of artists
    plotted inside the axes.
abcbbox, titlebbox : bool, default: :rc:`abc.bbox` and :rc:`title.bbox`
    Whether to draw a white bbox around titles and a-b-c labels positioned
    inside the axes. This can help them stand out on top of artists plotted
    inside the axes.
abcpad : float or unit-spec, default: :rc:`abc.pad`
    Horizontal offset to shift the a-b-c label position. Positive values move
    the label right, negative values move it left. This is separate from
    `abctitlepad`, which controls spacing between abc and title when co-located.
    %(units.pt)s
abc_kw, title_kw : dict-like, optional
    Additional settings used to update the a-b-c label and title
    with ``text.update()``.
titlepad : float, default: :rc:`title.pad`
    The padding for the inner and outer titles and a-b-c labels.
    %(units.pt)s
titleabove : bool, default: :rc:`title.above`
    Whether to try to put outer titles and a-b-c labels above panels,
    colorbars, or legends that are above the axes.
abctitlepad : float, default: :rc:`abc.titlepad`
    The horizontal padding between a-b-c labels and titles in the same location.
    %(units.pt)s
ltitle, ctitle, rtitle, ultitle, uctitle, urtitle, lltitle, lctitle, lrtitle : str or sequence, optional \\
    Shorthands for the below keywords.
    lefttitle, centertitle, righttitle, upperlefttitle, uppercentertitle, upperrighttitle : str or sequence, optional
lowerlefttitle, lowercentertitle, lowerrighttitle : str or sequence, optional
    Additional titles in specific positions (see `title` for details). This works as
    an alternative to the ``ax.format(title='Title', titleloc=loc)`` workflow and
    permits adding more than one title-like label for a single axes.
a, alpha, fc, facecolor, ec, edgecolor, lw, linewidth, ls, linestyle : default:
    :rc:`axes.alpha` (default: 1.0), :rc:`axes.facecolor` (default: white), :rc:`axes.edgecolor` (default: black), :rc:`axes.linewidth` (default: 0.6), -
    Additional settings applied to the background patch, and their
    shorthands. Their defaults values are the ``'axes'`` properties.
"""
_figure_format_docstring = """
rowlabels, collabels, llabels, tlabels, rlabels, blabels
    Aliases for `leftlabels` and `toplabels`, and for `leftlabels`,
    `toplabels`, `rightlabels`, and `bottomlabels`, respectively.
leftlabels, toplabels, rightlabels, bottomlabels : sequence of str, optional
    Labels for the subplots lying along the left, top, right, and
    bottom edges of the figure. The length of each list must match
    the number of subplots along the corresponding edge.
leftlabelpad, toplabelpad, rightlabelpad, bottomlabelpad : float or unit-spec, default\\
: :rc:`leftlabel.pad`, :rc:`toplabel.pad`, :rc:`rightlabel.pad`, :rc:`bottomlabel.pad`
    The padding between the labels and the axes content.
    %(units.pt)s
leftlabels_kw, toplabels_kw, rightlabels_kw, bottomlabels_kw : dict-like, optional
    Additional settings used to update the labels with ``text.update()``.
figtitle
    Alias for `suptitle`.
suptitle : str, optional
    The figure "super" title, centered between the left edge of the leftmost
    subplot and the right edge of the rightmost subplot.
suptitlepad : float, default: :rc:`suptitle.pad`
    The padding between the super title and the axes content.
    %(units.pt)s
suptitle_kw : optional
    Additional settings used to update the super title with ``text.update()``.
includepanels : bool, default: False
    Whether to include panels when aligning figure "super titles" along the top
    of the subplot grid and when aligning the `spanx` *x* axis labels and
    `spany` *y* axis labels along the sides of the subplot grid.
"""
_rc_init_docstring = """
"""
_rc_format_docstring = """
rc_mode : int, optional
    The context mode passed to `~ultraplot.config.Configurator.context`.
rc_kw : dict-like, optional
    An alternative to passing extra keyword arguments. See below.
**kwargs
    {}Keyword arguments that match the name of an `~ultraplot.config.rc` setting are
    passed to `ultraplot.config.Configurator.context` and used to update the axes.
    If the setting name has "dots" you can simply omit the dots. For example,
    ``abc='A.'`` modifies the :rcraw:`abc` setting, ``titleloc='left'`` modifies the
    :rcraw:`title.loc` setting, ``gridminor=True`` modifies the :rcraw:`gridminor`
    setting, and ``gridbelow=True`` modifies the :rcraw:`grid.below` setting. Many
    of the keyword arguments documented above are internally applied by retrieving
    settings passed to `~ultraplot.config.Configurator.context`.
"""
docstring._snippet_manager["rc.init"] = _rc_format_docstring.format(
    "Remaining keyword arguments are passed to `matplotlib.axes.Axes`.\\n    "
)
docstring._snippet_manager["rc.format"] = _rc_format_docstring.format("")
docstring._snippet_manager["axes.format"] = _axes_format_docstring
docstring._snippet_manager["figure.format"] = _figure_format_docstring


# Colorbar docstrings
_colorbar_args_docstring = """
mappable : mappable, colormap-spec, sequence of color-spec, \\
or sequence of `~matplotlib.artist.Artist`
    There are four options here:

    1. A `~matplotlib.cm.ScalarMappable` (e.g., an object returned by
       `~ultraplot.axes.PlotAxes.contourf` or `~ultraplot.axes.PlotAxes.pcolormesh`).
    2. A `~matplotlib.colors.Colormap` or registered colormap name used to build a
       `~matplotlib.cm.ScalarMappable` on-the-fly. The colorbar range and ticks depend
       on the arguments `values`, `vmin`, `vmax`, and `norm`. The default for a
       :class:`~ultraplot.colors.ContinuousColormap` is ``vmin=0`` and ``vmax=1`` (note that
       passing `values` will "discretize" the colormap). The default for a
       :class:`~ultraplot.colors.DiscreteColormap` is ``values=np.arange(0, cmap.N)``.
    3. A sequence of hex strings, color names, or RGB[A] tuples. A
       :class:`~ultraplot.colors.DiscreteColormap` will be generated from these colors and
       used to build a `~matplotlib.cm.ScalarMappable` on-the-fly. The colorbar
       range and ticks depend on the arguments `values`, `norm`, and
       `norm_kw`. The default is ``values=np.arange(0, len(mappable))``.
    4. A sequence of `matplotlib.artist.Artist` instances (e.g., a list of
       `~matplotlib.lines.Line2D` instances returned by `~ultraplot.axes.PlotAxes.plot`).
       A colormap will be generated from the colors of these objects (where the
       color is determined by ``get_color``, if available, or ``get_facecolor``).
       The colorbar range and ticks depend on the arguments `values`, `norm`, and
       `norm_kw`. The default is to infer colorbar ticks and tick labels
       by calling `~matplotlib.artist.Artist.get_label` on each artist.

values : sequence of float or str, optional
    Ignored if `mappable` is a `~matplotlib.cm.ScalarMappable`. This maps the colormap
    colors to numeric values using `~ultraplot.colors.DiscreteNorm`. If the colormap is
    a :class:`~ultraplot.colors.ContinuousColormap` then its colors will be "discretized".
    These These can also be strings, in which case the list indices are used for
    tick locations and the strings are applied as tick labels.
"""
_colorbar_kwargs_docstring = """
orientation : {None, 'horizontal', 'vertical'}, optional
    The colorbar orientation. By default this depends on the "side" of the subplot
    or figure where the colorbar is drawn. Inset colorbars are always horizontal.
norm : norm-spec, optional
    Ignored if `mappable` is a `~matplotlib.cm.ScalarMappable`. This is the continuous
    normalizer used to scale the :class:`~ultraplot.colors.ContinuousColormap` (or passed
    to `~ultraplot.colors.DiscreteNorm` if `values` was passed). Passed to the
    `~ultraplot.constructor.Norm` constructor function.
norm_kw : dict-like, optional
    Ignored if `mappable` is a `~matplotlib.cm.ScalarMappable`. These are the
    normalizer keyword arguments. Passed to `~ultraplot.constructor.Norm`.
vmin, vmax : float, optional
    Ignored if `mappable` is a `~matplotlib.cm.ScalarMappable`. These are the minimum
    and maximum colorbar values. Passed to `~ultraplot.constructor.Norm`.
label, title : str, optional
    The colorbar label. The `title` keyword is also accepted for
    consistency with `~matplotlib.axes.Axes.legend`.
reverse : bool, optional
    Whether to reverse the direction of the colorbar. This is done automatically
    when descending levels are used with `~ultraplot.colors.DiscreteNorm`.
rotation : float, default: 0
    The tick label rotation.
grid, edges, drawedges : bool, default: :rc:`colorbar.grid`
    Whether to draw "grid" dividers between each distinct color.
extend : {'neither', 'both', 'min', 'max'}, optional
    Direction for drawing colorbar "extensions" (i.e. color keys for out-of-bounds
    data on the end of the colorbar). Default behavior is to use the value of `extend`
    passed to the plotting command or use ``'neither'`` if the value is unknown.
extendfrac : float, optional
    The length of the colorbar "extensions" relative to the length of the colorbar.
    This is a native matplotlib `~matplotlib.figure.Figure.colorbar` keyword.
extendsize : unit-spec, default: :rc:`colorbar.extend` or :rc:`colorbar.insetextend`
    The length of the colorbar "extensions" in physical units. Default is
    :rcraw:`colorbar.extend` for outer colorbars and :rcraw:`colorbar.insetextend`
    for inset colorbars. %(units.em)s
extendrect : bool, default: False
    Whether to draw colorbar "extensions" as rectangles. If ``False`` then
    the extensions are drawn as triangles.
locator, ticks : locator-spec, optional
    Used to determine the colorbar tick positions. Passed to the
    `~ultraplot.constructor.Locator` constructor function. By default
    `~matplotlib.ticker.AutoLocator` is used for continuous color levels
    and `~ultraplot.ticker.DiscreteLocator` is used for discrete color levels.
locator_kw : dict-like, optional
    Keyword arguments passed to `matplotlib.ticker.Locator` class.
minorlocator, minorticks
    As with `locator`, `ticks` but for the minor ticks. By default
    `~matplotlib.ticker.AutoMinorLocator` is used for continuous color levels
    and `~ultraplot.ticker.DiscreteLocator` is used for discrete color levels.
minorlocator_kw
    As with `locator_kw`, but for the minor ticks.
format, formatter, ticklabels : formatter-spec, optional
    The tick label format. Passed to the `~ultraplot.constructor.Formatter`
    constructor function.
formatter_kw : dict-like, optional
    Keyword arguments passed to `matplotlib.ticker.Formatter` class.
frame, frameon : bool, default: :rc:`colorbar.frameon`
    For inset colorbars only. Indicates whether to draw a "frame",
    just like `~matplotlib.axes.Axes.legend`.
tickminor : bool, optional
    Whether to add minor ticks using `~matplotlib.colorbar.ColorbarBase.minorticks_on`.
tickloc, ticklocation : {'bottom', 'top', 'left', 'right'}, optional
    Where to draw tick marks on the colorbar. Default is toward the outside
    of the subplot for outer colorbars and ``'bottom'`` for inset colorbars.
tickdir, tickdirection : {'out', 'in', 'inout'}, default: :rc:`tick.dir`
    Direction of major and minor colorbar ticks.
ticklen : unit-spec, default: :rc:`tick.len`
    Major tick lengths for the colorbar ticks.
ticklenratio : float, default: :rc:`tick.lenratio`
    Relative scaling of `ticklen` used to determine minor tick lengths.
tickwidth : unit-spec, default: `linewidth`
    Major tick widths for the colorbar ticks.
    or :rc:`tick.width` if `linewidth` was not passed.
tickwidthratio : float, default: :rc:`tick.widthratio`
    Relative scaling of `tickwidth` used to determine minor tick widths.
ticklabelcolor, ticklabelsize, ticklabelweight \\
: default: :rc:`tick.labelcolor`, :rc:`tick.labelsize`, :rc:`tick.labelweight`.
    The font color, size, and weight for colorbar tick labels
labelloc, labellocation : {'bottom', 'top', 'left', 'right'}
    The colorbar label location. Inherits from `tickloc` by default. Default is toward
    the outside of the subplot for outer colorbars and ``'bottom'`` for inset colorbars.
labelcolor, labelsize, labelweight \\
: default: :rc:`label.color`, :rc:`label.size`, and :rc:`label.weight`.
    The font color, size, and weight for the colorbar label.
a, alpha, framealpha, fc, facecolor, framecolor, ec, edgecolor, ew, edgewidth : default\\
: :rc:`colorbar.framealpha`, :rc:`colorbar.framecolor`
    For inset colorbars only. Controls the transparency and color of
    the background frame.
lw, linewidth, c, color : optional
    Controls the line width and edge color for both the colorbar
    outline and the level dividers.
%(axes.edgefix)s
rasterize : bool, default: :rc:`colorbar.rasterized`
    Whether to rasterize the colorbar solids. The matplotlib default was ``True``
    but ultraplot changes this to ``False`` since rasterization can cause misalignment
    between the color patches and the colorbar outline.
outline : bool, None default : None
    Controls the visibility of the frame. When set to False, the spines of the colorbar are hidden. If set to `None` it uses the `rc['colorbar.outline']` value.
labelrotation : str, float, default: None
    Controls the rotation of the colorbar label. When set to None it takes on the value of `rc["colorbar.labelrotation"]`. When set to auto it produces a sensible default where the rotation is adjusted to where the colorbar is located. For example, a horizontal colorbar with a label to the left or right will match the horizontal alignment and rotate the label to 0 degrees. Users can provide a float to rotate to any arbitrary angle.



**kwargs
    Passed to `~matplotlib.figure.Figure.colorbar`.
"""
_edgefix_docstring = """
edgefix : bool or float, default: :rc:`edgefix`
    Whether to fix the common issue where white lines appear between adjacent
    patches in saved vector graphics (this can slow down figure rendering).
    See this `github repo <https://github.com/jklymak/contourfIssues>`__ for a
    demonstration of the problem. If ``True``, a small default linewidth of
    ``0.3`` is used to cover up the white lines. If float (e.g. ``edgefix=0.5``),
    this specific linewidth is used to cover up the white lines. This feature is
    automatically disabled when the patches have transparency.
"""
docstring._snippet_manager["axes.edgefix"] = _edgefix_docstring
docstring._snippet_manager["axes.colorbar_args"] = _colorbar_args_docstring
docstring._snippet_manager["axes.colorbar_kwargs"] = _colorbar_kwargs_docstring


# Legend docstrings
_legend_args_docstring = """
handles : list of artist, optional
    List of matplotlib artists, or a list of lists of artist instances (see the `center`
    keyword). If not passed, artists with valid labels (applied by passing `label` or
    `labels` to a plotting command or calling `~matplotlib.artist.Artist.set_label`)
    are retrieved automatically. If the object is a `~matplotlib.contour.ContourSet`,
    `~matplotlib.contour.ContourSet.legend_elements` is used to select the central
    artist in the list (generally useful for single-color contour plots). Note that
    ultraplot's `~ultraplot.axes.PlotAxes.contour` and `~ultraplot.axes.PlotAxes.contourf`
    accept a legend `label` keyword argument.
labels : list of str, optional
    A matching list of string labels or ``None`` placeholders, or a matching list of
    lists (see the `center` keyword). Wherever ``None`` appears in the list (or
    if no labels were passed at all), labels are retrieved by calling
    `~matplotlib.artist.Artist.get_label` on each `~matplotlib.artist.Artist` in the
    handle list. If a handle consists of a tuple group of artists, labels are inferred
    from the artists in the tuple (if there are multiple unique labels in the tuple
    group of artists, the tuple group is expanded into unique legend entries --
    otherwise, the tuple group elements are drawn on top of eachother). For details
    on matplotlib legend handlers and tuple groups, see the matplotlib `legend guide \\
-<https://matplotlib.org/stable/tutorials/intermediate/legend_guide.html>`__.
"""
_legend_kwargs_docstring = """
frame, frameon : bool, optional
    Toggles the legend frame. For centered-row legends, a frame
    independent from matplotlib's built-in legend frame is created.
ncol, ncols : int, optional
    The number of columns. `ncols` is an alias, added
    for consistency with `~matplotlib.pyplot.subplots`.
order : {'C', 'F'}, optional
    Whether legend handles are drawn in row-major (``'C'``) or column-major
    (``'F'``) order. Analagous to `numpy.array` ordering. The matplotlib
    default was ``'F'`` but ultraplot changes this to ``'C'``.
center : bool, optional
    Whether to center each legend row individually. If ``True``, we draw
    successive single-row legends "stacked" on top of each other. If ``None``,
    we infer this setting from `handles`. By default, `center` is set to ``True``
    if `handles` is a list of lists (each sublist is used as a row in the legend).
alphabetize : bool, default: False
    Whether to alphabetize the legend entries according to
    the legend labels.
title, label : str, optional
    The legend title. The `label` keyword is also accepted, for consistency
    with `~matplotlib.figure.Figure.colorbar`.
fontsize, fontweight, fontcolor : optional
    The font size, weight, and color for the legend text. Font size is interpreted
    by `~ultraplot.utils.units`. The default font size is :rcraw:`legend.fontsize`.
titlefontsize, titlefontweight, titlefontcolor : optional
    The font size, weight, and color for the legend title. Font size is interpreted
    by `~ultraplot.utils.units`. The default size is `fontsize`.
borderpad, borderaxespad, handlelength, handleheight, handletextpad, \\
labelspacing, columnspacing : unit-spec, optional
    Various matplotlib `~matplotlib.axes.Axes.legend` spacing arguments.
    %(units.em)s
a, alpha, framealpha, fc, facecolor, framecolor, ec, edgecolor, ew, edgewidth \\
: default: :rc:`legend.framealpha`, :rc:`legend.facecolor`, :rc:`legend.edgecolor`, \\
:rc:`axes.linewidth`
    The opacity, face color, edge color, and edge width for the legend frame.
c, color, lw, linewidth, m, marker, ls, linestyle, dashes, ms, markersize : optional
    Properties used to override the legend handles. For example, for a
    legend describing variations in line style ignoring variations
    in color, you might want to use ``color='black'``.
handle_kw : dict-like, optional
    Additional properties used to override legend handles, e.g.
    ``handle_kw={'edgecolor': 'black'}``. Only line properties
    can be passed as keyword arguments.
handler_map : dict-like, optional
    A dictionary mapping instances or types to a legend handler.
    This `handler_map` updates the default handler map found at
    `matplotlib.legend.Legend.get_legend_handler_map`.
**kwargs
    Passed to `~matplotlib.axes.Axes.legend`.
"""
docstring._snippet_manager["axes.legend_args"] = _legend_args_docstring
docstring._snippet_manager["axes.legend_kwargs"] = _legend_kwargs_docstring


def _align_bbox(align, length):
    """
    Return a simple alignment bounding box for intersection calculations.
    """
    if align in ("left", "bottom"):
        bounds = [[0, 0], [length, 0]]
    elif align in ("top", "right"):
        bounds = [[1 - length, 0], [1, 0]]
    elif align == "center":
        bounds = [[0.5 * (1 - length), 0], [0.5 * (1 + length), 0]]
    else:
        raise ValueError(f"Invalid align {align!r}.")
    return mtransforms.Bbox(bounds)


class _TransformedBoundsLocator:
    """
    Axes locator for `~Axes.inset_axes` and other axes.
    """

    def __init__(self, bounds, transform):
        self._bounds = bounds
        self._transform = transform

    def __call__(self, ax, renderer):  # noqa: U100
        transfig = getattr(ax.figure, "transSubfigure", ax.figure.transFigure)
        bbox = mtransforms.Bbox.from_bounds(*self._bounds)
        bbox = mtransforms.TransformedBbox(bbox, self._transform)
        bbox = mtransforms.TransformedBbox(bbox, transfig.inverted())
        return bbox


class _ExternalModeMixin:
    """
    Mixin providing explicit external-mode control and a context manager.
    """

    def set_external(self, value=True):
        """
        Set explicit external-mode override for this axes.

        value:
          - True: force external behavior (defer on-the-fly guides, etc.)
          - False: force UltraPlot behavior
        """
        if value not in (True, False):
            raise ValueError("set_external expects True or False")
        setattr(self, "_integration_external", value)
        return self

    class _ExternalContext:
        def __init__(self, ax, value=True):
            self._ax = ax
            self._value = True if value is None else value
            self._prev = getattr(ax, "_integration_external", None)

        def __enter__(self):
            self._ax._integration_external = self._value
            return self._ax

        def __exit__(self, exc_type, exc, tb):
            self._ax._integration_external = self._prev

    def external(self, value=True):
        """
        Context manager toggling external mode during the block.
        """
        return _ExternalModeMixin._ExternalContext(self, value)

    def _in_external_context(self):
        """
        Return True if UltraPlot helper behaviors should be suppressed.
        """
        mode = getattr(self, "_integration_external", None)
        return mode is True


class Axes(_ExternalModeMixin, maxes.Axes):
    """
    The lowest-level `~matplotlib.axes.Axes` subclass used by ultraplot.
    Implements basic universal features.
    """

    _name = None  # derived must override
    _name_aliases = ()
    _make_inset_locator = _TransformedBoundsLocator

    def __repr__(self):
        # Show the position in the geometry excluding panels. Panels are
        # indicated by showing their parent geometry plus a 'side' argument.
        # WARNING: This will not be used in matplotlib 3.3.0 (and probably next
        # minor releases) because native __repr__ is defined in SubplotBase.
        ax = self._get_topmost_axes()
        name = type(self).__name__
        prefix = "" if ax is self else "parent_"
        params = {}
        if self._name in ("cartopy", "basemap"):
            name = name.replace("_" + self._name.title(), "Geo")
            params["backend"] = self._name
        if self._inset_parent:
            name = re.sub("Axes(Subplot)?", "AxesInset", name)
            params["bounds"] = tuple(np.round(self._inset_bounds, 2))
        if self._altx_parent or self._alty_parent:
            name = re.sub("Axes(Subplot)?", "AxesTwin", name)
            params["axis"] = "x" if self._altx_parent else "y"
        if self._colorbar_fill:
            name = re.sub("Axes(Subplot)?", "AxesFill", name)
            params["side"] = self._axes._panel_side
        if self._panel_side:
            name = re.sub("Axes(Subplot)?", "AxesPanel", name)
            params["side"] = self._panel_side
        try:
            nrows, ncols, num1, num2 = (
                ax.get_subplotspec().get_topmost_subplotspec()._get_geometry()
            )  # noqa: E501
            params[prefix + "index"] = (num1, num2)
        except (IndexError, ValueError, AttributeError):  # e.g. a loose axes
            left, bottom, width, height = np.round(self._position.bounds, 2)
            params["left"], params["bottom"], params["size"] = (
                left,
                bottom,
                (width, bottom),
            )  # noqa: E501
        if ax.number:
            params[prefix + "number"] = ax.number
        params = ", ".join(f"{key}={value!r}" for key, value in params.items())
        return f"{name}({params})"

    def __str__(self):
        return self.__repr__()

    @docstring._snippet_manager
    def __init__(self, *args, **kwargs):
        """
        Parameters
        ----------
        *args
            Passed to `matplotlib.axes.Axes`.
        %(axes.format)s

        Other parameters
        ----------------
        %(rc.init)s

        See also
        --------
        Axes.format
        matplotlib.axes.Axes
        ultraplot.axes.PlotAxes
        ultraplot.axes.CartesianAxes
        ultraplot.axes.PolarAxes
        ultraplot.axes.GeoAxes
        ultraplot.figure.Figure.subplot
        ultraplot.figure.Figure.add_subplot
        """
        # Remove subplot-related args
        # NOTE: These are documented on add_subplot()
        ss = kwargs.pop("_subplot_spec", None)  # see below
        number = kwargs.pop("number", None)
        autoshare = kwargs.pop("autoshare", None)
        autoshare = _not_none(autoshare, True)

        # Remove format-related args and initialize
        rc_kw, rc_mode = _pop_rc(kwargs)
        kw_format = _pop_props(kwargs, "patch")  # background properties
        if "zorder" in kw_format:  # special case: refers to the entire axes
            kwargs["zorder"] = kw_format.pop("zorder")
        for cls, sig in self._format_signatures.items():
            if isinstance(self, cls):
                kw_format.update(_pop_params(kwargs, sig))
        super().__init__(*args, **kwargs)

        # Varous scalar properties
        self._active_cycle = rc["axes.prop_cycle"]
        self._auto_format = None  # manipulated by wrapper functions
        self._abc_border_kwargs = {}
        self._abc_loc = None
        self._abc_pad = 0  # User's horizontal offset for abc label (in points)
        self._abc_title_pad = rc[
            "abc.titlepad"
        ]  # Spacing between abc and title when co-located
        self._title_above = rc["title.above"]
        self._title_border_kwargs = {}  # title border properties
        self._title_loc = None
        self._title_pad = rc["title.pad"]
        self._title_pad_current = None
        self._altx_parent = None  # for cartesian axes only
        self._alty_parent = None
        self._colorbar_fill = None
        self._inset_parent = None
        self._inset_bounds = None  # for introspection ony
        self._inset_zoom = False
        self._inset_zoom_artists = None
        self._panel_hidden = False  # True when "filled" with cbar/legend
        self._panel_align = {}  # store 'align' and 'length' for "filled" cbar/legend
        self._panel_parent = None
        self._panel_share = False
        self._panel_sharex_group = False  # see _apply_auto_share
        self._panel_sharey_group = False  # see _apply_auto_share
        self._panel_side = None
        self._tight_bbox = None  # bounding boxes are saved
        self._integration_external = None  # explicit external-mode override (None=auto)
        self.xaxis.isDefault_minloc = True  # ensure enabled at start (needed for dual)
        self.yaxis.isDefault_minloc = True

        # Various dictionary properties
        # NOTE: Critical to use self.text() so they are patched with _update_label
        self._legend_dict = {}
        self._colorbar_dict = {}
        d = self._panel_dict = {}
        d["left"] = []  # NOTE: panels will be sorted inside-to-outside
        d["right"] = []
        d["bottom"] = []
        d["top"] = []
        d = self._title_dict = {}
        kw = {"zorder": 3.5, "transform": self.transAxes}
        d["abc"] = self.text(0, 0, "", **kw)
        d["left"] = self._left_title  # WARNING: track in case mpl changes this
        d["center"] = self.title
        d["right"] = self._right_title
        d["upper left"] = self.text(0, 0, "", va="top", ha="left", **kw)
        d["upper center"] = self.text(0, 0.5, "", va="top", ha="center", **kw)
        d["upper right"] = self.text(0, 1, "", va="top", ha="right", **kw)
        d["lower left"] = self.text(0, 0, "", va="bottom", ha="left", **kw)
        d["lower center"] = self.text(0, 0.5, "", va="bottom", ha="center", **kw)
        d["lower right"] = self.text(0, 1, "", va="bottom", ha="right", **kw)
        d["outer left"] = self.text(0, 1, "", va="bottom", ha="right", **kw)
        d["outer right"] = self.text(1, 1, "", va="bottom", ha="left", **kw)

        # Subplot-specific settings
        # NOTE: Default number for any axes is None (i.e., no a-b-c labels allowed)
        # and for subplots added with add_subplot is incremented automatically
        # WARNING: For mpl>=3.4.0 subplotspec assigned *after* initialization using
        # set_subplotspec. Tried to defer to setter but really messes up both format()
        # and _apply_auto_share(). Instead use workaround: Have Figure.add_subplot pass
        # subplotspec as a hidden keyword arg. Non-subplots don't need this arg.
        # See: https://github.com/matplotlib/matplotlib/pull/18564
        self._number = None
        if number:  # not None or False
            self.number = number
        if ss is not None:  # always passed from add_subplot
            self.set_subplotspec(ss)
        if autoshare:
            self._apply_auto_share()

        # Default formatting
        # NOTE: This ignores user-input rc_mode. Mode '1' applies ultraplot
        # features which is necessary on first run. Default otherwise is mode '2'
        self.format(rc_kw=rc_kw, rc_mode=1, skip_figure=True, **kw_format)

    def _add_inset_axes(
        self,
        bounds,
        transform=None,
        *,
        proj=None,
        projection=None,
        zoom=None,
        zoom_kw=None,
        zorder=None,
        **kwargs,
    ):
        """
        Add an inset axes using arbitrary projection.
        """
        # Converting transform to figure-relative coordinates
        transform = self._get_transform(transform, "axes")
        locator = self._make_inset_locator(bounds, transform)
        bounds = locator(self, None).bounds
        label = kwargs.pop("label", "inset_axes")
        zorder = _not_none(zorder, 4)

        # Parse projection and inherit from the current axes by default
        # NOTE: The _parse_proj method also accepts axes classes.
        proj = _not_none(proj=proj, projection=projection)
        if proj is None:
            if self._name in ("cartopy", "basemap"):
                proj = copy.copy(self.projection)
            else:
                proj = self._name
        kwargs = self.figure._parse_proj(proj, **kwargs)

        # Create axes and apply locator. The locator lets the axes adjust
        # automatically if we used data coords. Called by ax.apply_aspect()
        cls = mproj.get_projection_class(kwargs.pop("projection"))
        ax = cls(self.figure, bounds, zorder=zorder, label=label, **kwargs)
        ax.set_axes_locator(locator)
        ax._inset_parent = self
        ax._inset_bounds = bounds
        self.add_child_axes(ax)

        # Add zoom indicator (NOTE: requires matplotlib >= 3.0)
        zoom_default = self._name == "cartesian" and ax._name == "cartesian"
        zoom = ax._inset_zoom = _not_none(zoom, zoom_default)
        if zoom:
            zoom_kw = zoom_kw or {}
            ax.indicate_inset_zoom(**zoom_kw)
        return ax

    def _add_queued_guides(self):
        """
        Draw the queued-up legends and colorbars. Wrapper funcs and legend func let
        user add handles to location lists with successive calls.
        """
        # Draw queued colorbars
        for (loc, align), colorbar in tuple(self._colorbar_dict.items()):
            if not isinstance(colorbar, tuple):
                continue
            handles, labels, kwargs = colorbar
            cb = self._add_colorbar(handles, labels, loc=loc, align=align, **kwargs)
            self._colorbar_dict[(loc, align)] = cb

        # Draw queued legends
        # WARNING: Passing empty list labels=[] to legend causes matplotlib
        # _parse_legend_args to search for everything. Ensure None if empty.
        for (loc, align), legend in tuple(self._legend_dict.items()):
            if not isinstance(legend, tuple) or any(
                isinstance(_, plegend.Legend) for _ in legend
            ):  # noqa: E501
                continue
            handles, labels, kwargs = legend
            leg = self._add_legend(handles, labels, loc=loc, align=align, **kwargs)
            self._legend_dict[(loc, align)] = leg

    def _add_guide_frame(
        self, xmin, ymin, width, height, *, fontsize, fancybox=None, **kwargs
    ):
        """
        Add a colorbar or multilegend frame.
        """
        # TODO: Shadow patch does not seem to work. Unsure why.
        # TODO: Add basic 'colorbar' and 'legend' artists with
        # shared control over background frame.
        shadow = kwargs.pop("shadow", None)  # noqa: F841
        renderer = self.figure._get_renderer()
        fontsize = _fontsize_to_pt(fontsize)
        fontsize = (fontsize / 72) / self._get_size_inches()[0]  # axes relative units
        fontsize = renderer.points_to_pixels(fontsize)
        patch = mpatches.FancyBboxPatch(
            (xmin, ymin),
            width,
            height,
            snap=True,
            zorder=4.5,
            mutation_scale=fontsize,
            transform=self.transAxes,
        )
        patch.set_clip_on(False)
        if fancybox:
            patch.set_boxstyle("round", pad=0, rounding_size=0.2)
        else:
            patch.set_boxstyle("square", pad=0)
        patch.update(kwargs)
        self.add_artist(patch)
        return patch

    def _add_guide_panel(
        self,
        loc: str = "fill",
        align: str = "center",
        length: Union[float, str] = 0,
        span: Optional[Union[int, Tuple[int, int]]] = None,
        row: Optional[int] = None,
        col: Optional[int] = None,
        rows: Optional[Union[int, Tuple[int, int]]] = None,
        cols: Optional[Union[int, Tuple[int, int]]] = None,
        **kwargs,
    ) -> "Axes":
        """
        Add a panel to be filled by an "outer" colorbar or legend.
        """
        # NOTE: For colorbars we include 'length' when determining whether to allocate
        # new panel but for legend just test whether that 'align' position was filled.
        # WARNING: Hide content but 1) do not use ax.set_visible(False) so that
        # tight layout will include legend and colorbar and 2) do not use
        # ax.clear() so that top panel title and a-b-c label can remain.
        bbox = _align_bbox(align, length)
        if loc == "fill":
            ax = self
        elif loc in ("left", "right", "top", "bottom"):
            ax = None
            for pax in self._panel_dict[loc]:
                if not pax._panel_hidden or align in pax._panel_align:
                    continue
                if not any(bbox.overlaps(b) for b in pax._panel_align.values()):
                    ax = pax
                    break
            if ax is None:
                ax = self.panel_axes(
                    loc,
                    filled=True,
                    span=span,
                    row=row,
                    col=col,
                    rows=rows,
                    cols=cols,
                    **kwargs,
                )
        else:
            raise ValueError(f"Invalid filled panel location {loc!r}.")
        for s in ax.spines.values():
            s.set_visible(False)
        ax.xaxis.set_visible(False)
        ax.yaxis.set_visible(False)
        ax.patch.set_facecolor("none")  # ignore axes.alpha application
        ax._panel_hidden = True
        ax._panel_align[align] = bbox
        return ax

    @warnings._rename_kwargs("0.10", rasterize="rasterized")
    def _add_colorbar(
        self,
        mappable,
        values=None,
        *,
        loc: Optional[str] = None,
        align: Optional[str] = None,
        space: Optional[Union[float, str]] = None,
        pad: Optional[Union[float, str]] = None,
        width: Optional[Union[float, str]] = None,
        length: Optional[Union[float, str]] = None,
        span: Optional[Union[int, Tuple[int, int]]] = None,
        row: Optional[int] = None,
        col: Optional[int] = None,
        rows: Optional[Union[int, Tuple[int, int]]] = None,
        cols: Optional[Union[int, Tuple[int, int]]] = None,
        shrink: Optional[Union[float, str]] = None,
        label=None,
        title=None,
        reverse=False,
        rotation=None,
        grid=None,
        edges=None,
        drawedges=None,
        extend=None,
        extendsize=None,
        extendfrac=None,
        ticks=None,
        locator=None,
        locator_kw=None,
        format=None,
        formatter=None,
        ticklabels=None,
        formatter_kw=None,
        minorticks=None,
        minorlocator=None,
        minorlocator_kw=None,
        tickminor=None,
        ticklen=None,
        ticklenratio=None,
        tickdir=None,
        tickdirection=None,
        tickwidth=None,
        tickwidthratio=None,
        ticklabelsize=None,
        ticklabelweight=None,
        ticklabelcolor=None,
        labelloc=None,
        labellocation=None,
        labelsize=None,
        labelweight=None,
        labelcolor=None,
        c=None,
        color=None,
        lw=None,
        linewidth=None,
        edgefix=None,
        rasterized=None,
        outline: Union[bool, None] = None,
        labelrotation: Union[str, float] = None,
        center_levels=None,
        **kwargs,
    ):
        """
        The driver function for adding axes colorbars.
        """
        # Parse input arguments and apply defaults
        # TODO: Get the 'best' inset colorbar location using the legend algorithm
        # and implement inset colorbars the same as inset legends.
        grid = _not_none(
            grid=grid, edges=edges, drawedges=drawedges, default=rc["colorbar.grid"]
        )  # noqa: E501
        length = _not_none(length=length, shrink=shrink)
        label = _not_none(title=title, label=label)
        labelloc = _not_none(labelloc=labelloc, labellocation=labellocation)
        locator = _not_none(ticks=ticks, locator=locator)
        formatter = _not_none(ticklabels=ticklabels, formatter=formatter, format=format)
        minorlocator = _not_none(minorticks=minorticks, minorlocator=minorlocator)
        color = _not_none(c=c, color=color, default=rc["axes.edgecolor"])
        linewidth = _not_none(lw=lw, linewidth=linewidth)
        ticklen = units(_not_none(ticklen, rc["tick.len"]), "pt")
        tickdir = _not_none(tickdir=tickdir, tickdirection=tickdirection)
        tickwidth = units(_not_none(tickwidth, linewidth, rc["tick.width"]), "pt")
        linewidth = units(_not_none(linewidth, default=rc["axes.linewidth"]), "pt")
        ticklenratio = _not_none(ticklenratio, rc["tick.lenratio"])
        tickwidthratio = _not_none(tickwidthratio, rc["tick.widthratio"])
        rasterized = _not_none(rasterized, rc["colorbar.rasterized"])
        center_levels = _not_none(center_levels, rc["colorbar.center_levels"])

        # Build label and locator keyword argument dicts
        # NOTE: This carefully handles the 'maxn' and 'maxn_minor' deprecations
        kw_label = {}
        locator_kw = locator_kw or {}
        formatter_kw = formatter_kw or {}
        minorlocator_kw = minorlocator_kw or {}
        for key, value in (
            ("size", labelsize),
            ("weight", labelweight),
            ("color", labelcolor),
        ):
            if value is not None:
                kw_label[key] = value
        kw_ticklabels = {}
        for key, value in (
            ("size", ticklabelsize),
            ("weight", ticklabelweight),
            ("color", ticklabelcolor),
            ("rotation", rotation),
        ):
            if value is not None:
                kw_ticklabels[key] = value
        for b, kw in enumerate((locator_kw, minorlocator_kw)):
            key = "maxn_minor" if b else "maxn"
            name = "minorlocator" if b else "locator"
            nbins = kwargs.pop("maxn_minor" if b else "maxn", None)
            if nbins is not None:
                kw["nbins"] = nbins
                warnings._warn_ultraplot(
                    f"The colorbar() keyword {key!r} was deprecated in v0.10. To "
                    "achieve the same effect, you can pass 'nbins' to the new default "
                    f"locator DiscreteLocator using {name}_kw={{'nbins': {nbins}}}. "
                )

        # Generate and prepare the colorbar axes
        # NOTE: The inset axes function needs 'label' to know how to pad the box
        # TODO: Use seperate keywords for frame properties vs. colorbar edge properties?
        if loc in ("fill", "left", "right", "top", "bottom"):
            length = _not_none(length, rc["colorbar.length"])  # for _add_guide_panel
            kwargs.update({"align": align, "length": length})
            extendsize = _not_none(extendsize, rc["colorbar.extend"])
            ax = self._add_guide_panel(
                loc,
                align,
                length=length,
                width=width,
                space=space,
                pad=pad,
                span=span,
                row=row,
                col=col,
                rows=rows,
                cols=cols,
            )  # noqa: E501
            cax, kwargs = ax._parse_colorbar_filled(**kwargs)
        else:
            kwargs.update({"label": label, "length": length, "width": width})
            extendsize = _not_none(extendsize, rc["colorbar.insetextend"])
            cax, kwargs = self._parse_colorbar_inset(
                loc=loc,
                labelloc=labelloc,
                labelrotation=labelrotation,
                pad=pad,
                **kwargs,
            )  # noqa: E501

        # Parse the colorbar mappable
        # NOTE: Account for special case where auto colorbar is generated from 1D
        # methods that construct an 'artist list' (i.e. colormap scatter object)
        if (
            np.iterable(mappable)
            and len(mappable) == 1
            and isinstance(mappable[0], mcm.ScalarMappable)
        ):  # noqa: E501
            mappable = mappable[0]
        if not isinstance(mappable, mcm.ScalarMappable):
            mappable, kwargs = cax._parse_colorbar_arg(mappable, values, **kwargs)
        else:
            pop = _pop_params(kwargs, cax._parse_colorbar_arg, ignore_internal=True)
            if pop:
                warnings._warn_ultraplot(
                    f"Input is already a ScalarMappable. "
                    f"Ignoring unused keyword arg(s): {pop}"
                )

        # Parse 'extendsize' and 'extendfrac' keywords
        # TODO: Make this auto-adjust to the subplot size
        vert = kwargs["orientation"] == "vertical"
        if extendsize is not None and extendfrac is not None:
            warnings._warn_ultraplot(
                f"You cannot specify both an absolute extendsize={extendsize!r} "
                f"and a relative extendfrac={extendfrac!r}. Ignoring 'extendfrac'."
            )
            extendfrac = None
        if extendfrac is None:
            width, height = cax._get_size_inches()
            scale = height if vert else width
            extendsize = units(extendsize, "em", "in")
            extendfrac = extendsize / max(scale - 2 * extendsize, units(1, "em", "in"))

        # Parse the tick locators and formatters
        # NOTE: In presence of BoundaryNorm or similar handle ticks with special
        # DiscreteLocator or else get issues (see mpl #22233).
        norm = mappable.norm
        formatter = _not_none(formatter, getattr(norm, "_labels", None), "auto")
        formatter_kw.setdefault("tickrange", (norm.vmin, norm.vmax))
        formatter = constructor.Formatter(formatter, **formatter_kw)
        categorical = isinstance(formatter, mticker.FixedFormatter)
        if locator is not None:
            locator = constructor.Locator(locator, **locator_kw)
        if minorlocator is not None:  # overrides tickminor
            minorlocator = constructor.Locator(minorlocator, **minorlocator_kw)
        elif tickminor is None:
            tickminor = False if categorical else rc["xy"[vert] + "tick.minor.visible"]
        if isinstance(norm, mcolors.BoundaryNorm):  # DiscreteNorm or BoundaryNorm
            ticks = getattr(norm, "_ticks", norm.boundaries)
            segmented = isinstance(getattr(norm, "_norm", None), pcolors.SegmentedNorm)
            if locator is None:
                if categorical or segmented:
                    locator = mticker.FixedLocator(ticks)
                else:
                    locator = pticker.DiscreteLocator(ticks)

            if tickminor and minorlocator is None:
                minorlocator = pticker.DiscreteLocator(ticks, minor=True)

        # Special handling for colorbar keyword arguments
        # WARNING: Critical to not pass empty major locators in matplotlib < 3.5
        # See this issue: https://github.com/ultraplot-dev/ultraplot/issues/301
        # WARNING: ultraplot 'supports' passing one extend to a mappable function
        # then overwriting by passing another 'extend' to colobar. But contour
        # colorbars break when you try to change its 'extend'. Matplotlib gets
        # around this by just silently ignoring 'extend' passed to colorbar() but
        # we issue warning. Also note ContourSet.extend existed in matplotlib 3.0.
        # WARNING: Confusingly the only default way to have auto-adjusting
        # colorbar ticks is to specify no locator. Then _get_ticker_locator_formatter
        # uses the default ScalarFormatter on the axis that already has a set axis.
        # Otherwise it sets a default axis with locator.create_dummy_axis() in
        # update_ticks() which does not track axis size. Workaround is to manually
        # set the locator and formatter axis... however this messes up colorbar lengths
        # in matplotlib < 3.2. So we only apply this conditionally and in earlier
        # verisons recognize that DiscreteLocator will behave like FixedLocator.
        axis = cax.yaxis if vert else cax.xaxis
        if not isinstance(mappable, mcontour.ContourSet):
            extend = _not_none(extend, "neither")
            kwargs["extend"] = extend
        elif extend is not None and extend != mappable.extend:
            warnings._warn_ultraplot(
                "Ignoring extend={extend!r}. ContourSet extend cannot be changed."
            )
        if (
            isinstance(locator, mticker.NullLocator)
            or hasattr(locator, "locs")
            and len(locator.locs) == 0
        ):
            minorlocator, tickminor = None, False  # attempted fix
        for ticker in (locator, formatter, minorlocator):
            if version.parse(str(_version_mpl)) < version.parse("3.2"):
                pass  # see notes above
            elif isinstance(ticker, mticker.TickHelper):
                ticker.set_axis(axis)

        # Create colorbar and update ticks and axis direction
        # NOTE: This also adds the guides._update_ticks() monkey patch that triggers
        # updates to DiscreteLocator when parent axes is drawn.
        orientation = _not_none(
            kwargs.pop("orientation", None), kwargs.pop("vert", None)
        )

        obj = cax._colorbar_fill = cax.figure.colorbar(
            mappable,
            cax=cax,
            ticks=locator,
            format=formatter,
            drawedges=grid,
            extendfrac=extendfrac,
            orientation=orientation,
            **kwargs,
        )
        outline = _not_none(outline, rc["colorbar.outline"])
        obj.outline.set_visible(outline)
        obj.ax.grid(False)
        # obj.minorlocator = minorlocator  # backwards compatibility
        obj.update_ticks = guides._update_ticks.__get__(obj)  # backwards compatible
        if minorlocator is not None:
            # Note we make use of mpl's setters and getters
            current = obj.minorlocator
            if current != minorlocator:
                obj.minorlocator = minorlocator
            obj.update_ticks()
        elif tickminor:
            obj.minorticks_on()
        else:
            obj.minorticks_off()
        if getattr(norm, "descending", None):
            axis.set_inverted(True)
        if reverse:  # potentially double reverse, although that would be weird...
            axis.set_inverted(True)

        # Update other colorbar settings
        # WARNING: Must use the colorbar set_label to set text. Calling set_label
        # on the actual axis will do nothing!
        if center_levels:
            # Center the ticks to the center of the colorbar
            # rather than showing them on  the edges
            if hasattr(obj.norm, "boundaries"):
                # Only apply to discrete norms
                bounds = obj.norm.boundaries
                centers = 0.5 * (bounds[:-1] + bounds[1:])
                axis.set_ticks(centers)
                ticklenratio = 0
                tickwidthratio = 0
        axis.set_tick_params(which="both", color=color, direction=tickdir)
        axis.set_tick_params(which="major", length=ticklen, width=tickwidth)
        axis.set_tick_params(
            which="minor",
            length=ticklen * ticklenratio,
            width=tickwidth * tickwidthratio,
        )  # noqa: E501

        # Set label and label location
        long_or_short_axis = _get_axis_for(
            labelloc, loc, orientation=orientation, ax=obj
        )
        if labelloc is None:
            labelloc = long_or_short_axis.get_ticks_position()
        long_or_short_axis.set_label_text(label)
        long_or_short_axis.set_label_position(labelloc)

        labelrotation = _not_none(labelrotation, rc["colorbar.labelrotation"])
        # Note kw_label is updated in place
        _determine_label_rotation(
            labelrotation,
            labelloc=labelloc,
            orientation=orientation,
            kw_label=kw_label,
        )

        long_or_short_axis.label.update(kw_label)
        # Assume ticks are set on the long axis(!))
        if hasattr(obj, "_long_axis"):
            # mpl <=3.9
            longaxis = obj._long_axis()
        else:
            # mpl >=3.10
            longaxis = obj.long_axis
        for label in longaxis.get_ticklabels():
            label.update(kw_ticklabels)
        kw_outline = {"edgecolor": color, "linewidth": linewidth}
        if obj.outline is not None:
            obj.outline.update(kw_outline)
        if obj.dividers is not None:
            obj.dividers.update(kw_outline)
        if obj.solids:
            from . import PlotAxes

            obj.solids.set_rasterized(rasterized)
            PlotAxes._fix_patch_edges(obj.solids, edgefix=edgefix)

        # Register location and return
        self._register_guide("colorbar", obj, (loc, align))  # possibly replace another
        return obj

    def _add_legend(
        self,
        handles=None,
        labels=None,
        *,
        loc=None,
        align=None,
        width=None,
        pad=None,
        space=None,
        frame=None,
        frameon=None,
        ncol=None,
        ncols=None,
        alphabetize=False,
        center=None,
        order=None,
        label=None,
        title=None,
        fontsize=None,
        fontweight=None,
        fontcolor=None,
        titlefontsize=None,
        titlefontweight=None,
        titlefontcolor=None,
        handle_kw=None,
        handler_map=None,
        span: Optional[Union[int, Tuple[int, int]]] = None,
        row: Optional[int] = None,
        col: Optional[int] = None,
        rows: Optional[Union[int, Tuple[int, int]]] = None,
        cols: Optional[Union[int, Tuple[int, int]]] = None,
        **kwargs,
    ):
        """
        The driver function for adding axes legends.
        """
        # Parse input argument units
        ncol = _not_none(ncols=ncols, ncol=ncol)
        order = _not_none(order, "C")
        frameon = _not_none(frame=frame, frameon=frameon, default=rc["legend.frameon"])
        fontsize = _not_none(fontsize, rc["legend.fontsize"])
        titlefontsize = _not_none(
            title_fontsize=kwargs.pop("title_fontsize", None),
            titlefontsize=titlefontsize,
            default=rc["legend.title_fontsize"],
        )
        fontsize = _fontsize_to_pt(fontsize)
        titlefontsize = _fontsize_to_pt(titlefontsize)
        if order not in ("F", "C"):
            raise ValueError(
                f"Invalid order {order!r}. Please choose from "
                "'C' (row-major, default) or 'F' (column-major)."
            )

        # Convert relevant keys to em-widths
        for setting in rcsetup.EM_KEYS:  # em-width keys
            pair = setting.split("legend.", 1)
            if len(pair) == 1:
                continue
            _, key = pair
            value = kwargs.pop(key, None)
            if isinstance(value, str):
                value = units(value, "em", fontsize=fontsize)
            if value is not None:
                kwargs[key] = value

        # Generate and prepare the legend axes
        if loc in ("fill", "left", "right", "top", "bottom"):
            lax = self._add_guide_panel(
                loc,
                align,
                width=width,
                space=space,
                pad=pad,
                span=span,
                row=row,
                col=col,
                rows=rows,
                cols=cols,
            )
            kwargs.setdefault("borderaxespad", 0)
            if not frameon:
                kwargs.setdefault("borderpad", 0)
            try:
                kwargs["loc"] = ALIGN_OPTS[lax._panel_side][align]
            except KeyError:
                raise ValueError(f"Invalid align={align!r} for legend loc={loc!r}.")
        else:
            lax = self
            pad = kwargs.pop("borderaxespad", pad)
            kwargs["loc"] = loc  # simply pass to legend
            kwargs["borderaxespad"] = units(pad, "em", fontsize=fontsize)

        # Handle and text properties that are applied after-the-fact
        # NOTE: Set solid_capstyle to 'butt' so line does not extend past error bounds
        # shading in legend entry. This change is not noticable in other situations.
        kw_frame, kwargs = lax._parse_frame("legend", **kwargs)
        kw_text = {}
        if fontcolor is not None:
            kw_text["color"] = fontcolor
        if fontweight is not None:
            kw_text["weight"] = fontweight
        kw_title = {}
        if titlefontcolor is not None:
            kw_title["color"] = titlefontcolor
        if titlefontweight is not None:
            kw_title["weight"] = titlefontweight
        kw_handle = _pop_props(kwargs, "line")
        kw_handle.setdefault("solid_capstyle", "butt")
        kw_handle.update(handle_kw or {})

        # Parse the legend arguments using axes for auto-handle detection
        # TODO: Update this when we no longer use "filled panels" for outer legends
        pairs, multi = lax._parse_legend_handles(
            handles,
            labels,
            ncol=ncol,
            order=order,
            center=center,
            alphabetize=alphabetize,
            handler_map=handler_map,
        )
        title = _not_none(label=label, title=title)
        kwargs.update(
            {
                "title": title,
                "frameon": frameon,
                "fontsize": fontsize,
                "handler_map": handler_map,
                "title_fontsize": titlefontsize,
            }
        )

        # Add the legend and update patch properties
        # TODO: Add capacity for categorical labels in a single legend like seaborn
        # rather than manual handle overrides with multiple legends.
        if multi:
            objs = lax._parse_legend_centered(pairs, kw_frame=kw_frame, **kwargs)
        else:
            kwargs.update({key: kw_frame.pop(key) for key in ("shadow", "fancybox")})
            objs = [lax._parse_legend_aligned(pairs, ncol=ncol, order=order, **kwargs)]
            objs[0].legendPatch.update(kw_frame)
        for obj in objs:
            if hasattr(lax, "legend_") and lax.legend_ is None:
                lax.legend_ = obj  # make first legend accessible with get_legend()
            else:
                lax.add_artist(obj)

        # Update legend patch and elements
        # WARNING: legendHandles only contains the *first* artist per legend because
        # HandlerBase.legend_artist() called in Legend._init_legend_box() only
        # returns the first artist. Instead we try to iterate through offset boxes.
        for obj in objs:
            obj.set_clip_on(False)  # needed for tight bounding box calculations
            box = getattr(obj, "_legend_handle_box", None)
            for obj in guides._iter_children(box):
                if isinstance(obj, mtext.Text):
                    kw = kw_text
                else:
                    kw = {
                        key: val
                        for key, val in kw_handle.items()
                        if hasattr(obj, "set_" + key)
                    }  # noqa: E501
                    if hasattr(obj, "set_sizes") and "markersize" in kw_handle:
                        kw["sizes"] = np.atleast_1d(kw_handle["markersize"])
                obj.update(kw)

        # Register location and return
        if isinstance(objs[0], mpatches.FancyBboxPatch):
            objs = objs[1:]
        obj = objs[0] if len(objs) == 1 else tuple(objs)
        self._register_guide("legend", obj, (loc, align))  # possibly replace another

        return obj

    def _apply_title_above(self):
        """
        Change assignment of outer titles between main subplot and upper panels.
        This is called when a panel is created or `_update_title` is called.
        """
        # NOTE: Similar to how _apply_axis_sharing() is called in _align_axis_labels()
        # this is called in _align_super_labels() so we get the correct offset.
        paxs = self._panel_dict["top"]
        if not paxs:
            return
        pax = paxs[-1]
        names = ("left", "center", "right")
        if self._abc_loc in names:
            names += ("abc",)
        if not self._title_above:
            return
        if pax._panel_hidden and self._title_above == "panels":
            return
        pax._title_pad = self._title_pad
        pax._abc_title_pad = self._abc_title_pad
        for name in names:
            labels._transfer_label(self._title_dict[name], pax._title_dict[name])

    def _apply_auto_share(self):
        """
        Automatically configure axis sharing based on the horizontal and
        vertical extent of subplots in the figure gridspec.
        """

        # Panel axes sharing, between main subplot and its panels
        # NOTE: _panel_share means "include this panel in the axis sharing group" while
        # _panel_sharex_group indicates the group itself and may include main axes
        def shared(paxs):
            return [pax for pax in paxs if not pax._panel_hidden and pax._panel_share]

        # Internal axis sharing, share stacks of panels and main axes with each other
        # NOTE: This is called on the main axes whenever a panel is created.
        # NOTE: This block is why, even though we have figure-wide share[xy], we
        # still need the axes-specific _share[xy]_override attribute.
        if not self._panel_side:  # this is a main axes
            # Top and bottom
            bottom = self
            paxs = shared(self._panel_dict["bottom"])
            if paxs:
                bottom = paxs[-1]
                bottom._panel_sharex_group = False
                for iax in (self, *paxs[:-1]):
                    iax._panel_sharex_group = True
                    iax._sharex_setup(bottom)  # parent is bottom-most
            paxs = shared(self._panel_dict["top"])
            if paxs and self.figure._sharex > 0:
                self._panel_sharex_group = True
            for iax in paxs:
                iax._panel_sharex_group = True
                iax._sharex_setup(bottom)
            # Left and right
            # NOTE: Order of panel lists is always inside-to-outside
            left = self
            paxs = shared(self._panel_dict["left"])
            if paxs:
                left = paxs[-1]
                left._panel_sharey_group = False
                for iax in (self, *paxs[:-1]):
                    iax._panel_sharey_group = True
                    iax._sharey_setup(left)  # parent is left-most
            paxs = shared(self._panel_dict["right"])
            if paxs and self.figure._sharey > 0:
                self._panel_sharey_group = True
            for iax in paxs:
                iax._panel_sharey_group = True
                iax._sharey_setup(left)

        # External axes sharing, sometimes overrides panel axes sharing
        # Share x axes
        parent, *children = self._get_share_axes("x")
        for child in children:
            child._sharex_setup(parent)
        # Share y axes
        parent, *children = self._get_share_axes("y")
        for child in children:
            child._sharey_setup(parent)
        # Global sharing, use the reference subplot because why not
        ref = self.figure._subplot_dict.get(self.figure._refnum, None)
        if self is not ref:
            if self.figure._sharex > 3:
                self._sharex_setup(ref, labels=False)
            if self.figure._sharey > 3:
                self._sharey_setup(ref, labels=False)

    def _artist_fully_clipped(self, artist):
        """
        Return a boolean flag, ``True`` if the artist is clipped to the axes
        and can thus be skipped in layout calculations.
        """
        clip_box = artist.get_clip_box()
        clip_path = artist.get_clip_path()
        types_noclip = (
            maxes.Axes,
            maxis.Axis,
            moffsetbox.AnnotationBbox,
            moffsetbox.OffsetBox,
        )
        return not isinstance(artist, types_noclip) and (
            artist.get_clip_on()
            and (clip_box is not None or clip_path is not None)
            and (clip_box is None or np.all(clip_box.extents == self.bbox.extents))
            and (
                clip_path is None
                or isinstance(clip_path, mtransforms.TransformedPatchPath)
                and clip_path._patch is self.patch
            )
        )

    def _format_inset(
        self,
        bounds: tuple[float, float, float, float],
        parent: "Axes",
        **kwargs,
    ) -> "tuple | InsetIndicator":

        if version.parse(str(_version_mpl)) >= version.parse("3.10.0"):
            return self.__format_inset(bounds, parent, **kwargs)
        return self.__format_inset_legacy(bounds, parent, **kwargs)

    def __format_inset(
        self,
        bounds: tuple[float, float, float, float],
        parent: "Axes",
        **kwargs,
    ) -> "InsetIndicator":
        # Implementation for matplotlib >= 3.10
        # NOTE: if the api changes we need to deprecate the old
        # one. At the time of writing the IndicateInset is
        # experimental and may change in the future. This would
        # require us to change potentially the return signature
        # of this function.
        kwargs.setdefault("label", "_indicate_inset")

        # If we already have a zoom indicator we need to update
        # the properties or add them
        # Note the first time we enter this function, we create
        #  the object. Afterwards the function is accessed again but with different updates
        if self._inset_zoom_artists:
            indicator = self._inset_zoom_artists
            indicator.rectangle.update(kwargs)
            indicator.rectangle.set_bounds(bounds)  # otherwise the patch is not updated
            indicator.rectangle.set_zorder(
                self.get_zorder() + 1
            )  # Ensure rectangle appears above axes
            z = self.get_zorder() + 1
            for connector in indicator.connectors:
                connector.set_zorder(z)
                connector.update(kwargs)
        else:
            indicator = parent.indicate_inset(bounds, self, **kwargs)
            self._inset_zoom_artists = indicator
        return indicator

    def __format_inset_legacy(
        self, bounds: tuple[float, float, float, float], parent: "Axes", **kwargs
    ) -> tuple[mpatches.Rectangle, list[mpatches.ConnectionPatch]]:
        # Implementation for matplotlib < 3.10
        rectpatch, connects = parent.indicate_inset(bounds, self)

        # Update indicator properties
        if self._inset_zoom_artists:
            rectpatch_prev, connects_prev = self._inset_zoom_artists
            rectpatch.update_from(rectpatch_prev)
            rectpatch.set_zorder(rectpatch_prev.get_zorder())
            rectpatch_prev.remove()
            for line, line_prev in zip(connects, connects_prev):
                line.update_from(line_prev)
                line.set_zorder(line_prev.get_zorder())  # not included in update_from
                line_prev.remove()

        rectpatch.update(kwargs)
        for line in connects:
            line.update(kwargs)

        self._inset_zoom_artists = (rectpatch, connects)
        return rectpatch, connects

    def _get_legend_handles(self, handler_map=None):
        """
        Internal implementation of matplotlib's ``get_legend_handles_labels``.
        """
        if not self._panel_hidden:  # this is a normal axes
            axs = [self]
        elif self._panel_parent:  # this is an axes-wide legend
            axs = list(self._panel_parent._iter_axes(hidden=False, children=True))
        else:  # this is a figure-wide legend
            axs = list(self.figure._iter_axes(hidden=False, children=True))
        handles = []
        handler_map_full = plegend.Legend.get_default_handler_map()
        handler_map_full = handler_map_full.copy()
        handler_map_full.update(handler_map or {})
        # Prefer synthetic tagging to exclude helper artists; see _ultraplot_synthetic flag on artists.
        for ax in axs:
            for attr in ("lines", "patches", "collections", "containers"):
                for handle in getattr(ax, attr, []):  # guard against API changes
                    label = handle.get_label()
                    handler = plegend.Legend.get_legend_handler(
                        handler_map_full, handle
                    )  # noqa: E501
                    if (
                        handler
                        and label
                        and label[0] != "_"
                        and not getattr(handle, "_ultraplot_synthetic", False)
                    ):
                        handles.append(handle)
        return handles

    def _get_share_axes(self, sx, panels=False):
        """
        Return the axes whose horizontal or vertical extent in the main gridspec
        matches the horizontal or vertical extent of this axes.
        """
        # NOTE: The lefmost or bottommost axes are at the start of the list.
        if not isinstance(self, maxes.SubplotBase):
            return [self]
        i = 0 if sx == "x" else 1
        sy = "y" if sx == "x" else "x"
        argfunc = np.argmax if sx == "x" else np.argmin
        irange = self._range_subplotspec(sx)
        axs = self.figure._iter_axes(hidden=False, children=False, panels=panels)
        axs = [ax for ax in axs if ax._range_subplotspec(sx) == irange]
        axs = list({self, *axs})  # self may be missing during initialization
        pax = axs.pop(argfunc([ax._range_subplotspec(sy)[i] for ax in axs]))
        return [pax, *axs]  # return with leftmost or bottommost first

    def _get_span_axes(self, side, panels=False):
        """
        Return the axes whose left, right, top, or bottom sides abutt against
        the same row or column as this axes. Deflect to shared panels.
        """
        if side not in ("left", "right", "bottom", "top"):
            raise ValueError(f"Invalid side {side!r}.")
        if not isinstance(self, maxes.SubplotBase):
            return [self]
        x, y = "xy" if side in ("left", "right") else "yx"
        idx = 0 if side in ("left", "top") else 1  # which side to test
        coord = self._range_subplotspec(x)[idx]  # side for a particular axes
        axs = self.figure._iter_axes(hidden=False, children=False, panels=panels)
        axs = [ax for ax in axs if ax._range_subplotspec(x)[idx] == coord] or [self]
        out = []
        for ax in axs:
            other = getattr(ax, "_share" + y)
            if other and other._panel_parent:  # this is a shared panel
                ax = other
            out.append(ax)
        return out

    def _get_size_inches(self):
        """
        Return the width and height of the axes in inches.
        """
        width, height = self.figure.get_size_inches()
        bbox = self.get_position()
        width = width * abs(bbox.width)
        height = height * abs(bbox.height)
        return np.array([width, height])

    def _get_topmost_axes(self):
        """
        Return the topmost axes including panels and parents.
        """
        for _ in range(5):
            self = self._axes or self
            self = self._panel_parent or self
        return self

    def _get_transform(self, transform, default="data"):
        """
        Translates user input transform. Also used in an axes method.
        """
        # TODO: Can this support cartopy transforms? Seems not when this
        # is used for inset axes bounds but maybe in other places?
        transform = _not_none(transform, default)
        if isinstance(transform, mtransforms.Transform):
            return transform
        elif CRS is not object and isinstance(transform, CRS):
            return transform
        elif PlateCarree is not object and transform == "map":
            return PlateCarree()
        elif transform == "data":
            return self.transData
        elif transform == "axes":
            return self.transAxes
        elif transform == "figure":
            return self.figure.transFigure
        elif transform == "subfigure":
            return self.figure.transSubfigure
        else:
            raise ValueError(f"Unknown transform {transform!r}.")

    def _register_guide(self, guide, obj, key, **kwargs):
        """
        Queue up or replace objects for legends and list-of-artist style colorbars.
        """
        # Initial stuff
        if guide not in ("legend", "colorbar"):
            raise TypeError(f"Invalid type {guide!r}.")
        dict_ = self._legend_dict if guide == "legend" else self._colorbar_dict

        # Remove previous instances
        # NOTE: No good way to remove inset colorbars right now until the bounding
        # box and axes are merged into some kind of subclass. Just fine for now.
        if key in dict_ and not isinstance(dict_[key], tuple):
            prev = dict_.pop(key)  # possibly pop a queued object
            if guide == "colorbar":
                pass
            elif hasattr(self, "legend_") and prev.axes.legend_ is prev:
                self.legend_ = None  # was never added as artist
            else:
                prev.remove()  # remove legends and inner colorbars

        # Replace with instance or update the queue
        # NOTE: This is valid for both mappable-values pairs and handles-labels pairs
        if not isinstance(obj, tuple) or any(
            isinstance(_, plegend.Legend) for _ in obj
        ):  # noqa: E501
            dict_[key] = obj
        else:
            handles, labels = obj
            if not np.iterable(handles) or type(handles) is tuple:
                handles = [handles]
            if not np.iterable(labels) or isinstance(labels, str):
                labels = [labels] * len(handles)
            length = min(len(handles), len(labels))  # mimics 'zip' behavior
            handles_full, labels_full, kwargs_full = dict_.setdefault(key, ([], [], {}))
            handles_full.extend(handles[:length])
            labels_full.extend(labels[:length])
            kwargs_full.update(kwargs)

    def _update_guide(
        self,
        objs,
        legend=None,
        legend_kw=None,
        queue_legend=True,
        colorbar=None,
        colorbar_kw=None,
        queue_colorbar=True,
    ):
        """
        Update queues for on-the-fly legends and colorbars or track keyword arguments.
        """
        # WARNING: Important to always cache the keyword arguments so e.g.
        # duplicate subsequent calls still enforce user and default behavior.
        # WARNING: This should generally be last in the pipeline before calling
        # the plot function or looping over data columns. The colormap parser
        # and standardize functions both modify colorbar_kw and legend_kw.
        legend_kw = legend_kw or {}
        colorbar_kw = colorbar_kw or {}
        guides._cache_guide_kw(objs, "legend", legend_kw)
        guides._cache_guide_kw(objs, "colorbar", colorbar_kw)
        if legend:
            align = legend_kw.pop("align", None)
            queue = legend_kw.pop("queue", queue_legend)
            # Avoid immediate legend creation in external context
            if not self._in_external_context():
                self.legend(objs, loc=legend, align=align, queue=queue, **legend_kw)
        if colorbar:
            align = colorbar_kw.pop("align", None)
            queue = colorbar_kw.pop("queue", queue_colorbar)
            # Avoid immediate colorbar creation in external context
            if not self._in_external_context():
                self.colorbar(
                    objs, loc=colorbar, align=align, queue=queue, **colorbar_kw
                )

    @staticmethod
    def _parse_frame(guide, fancybox=None, shadow=None, **kwargs):
        """
        Parse frame arguments.
        """
        # NOTE: Here we permit only 'edgewidth' to avoid conflict with
        # 'linewidth' used for legend handles and colorbar edge.
        kw_frame = _pop_kwargs(
            kwargs,
            alpha=("a", "framealpha", "facealpha"),
            facecolor=("fc", "framecolor", "facecolor"),
            edgecolor=("ec",),
            edgewidth=("ew",),
        )
        _kw_frame_default = {
            "alpha": f"{guide}.framealpha",
            "facecolor": f"{guide}.facecolor",
            "edgecolor": f"{guide}.edgecolor",
            "edgewidth": "axes.linewidth",
        }
        for key, name in _kw_frame_default.items():
            kw_frame.setdefault(key, rc[name])
        for key in ("facecolor", "edgecolor"):
            if kw_frame[key] == "inherit":
                kw_frame[key] = rc["axes." + key]
        kw_frame["linewidth"] = kw_frame.pop("edgewidth")
        kw_frame["fancybox"] = _not_none(fancybox, rc[f"{guide}.fancybox"])
        kw_frame["shadow"] = _not_none(shadow, rc[f"{guide}.shadow"])
        return kw_frame, kwargs

    @staticmethod
    def _parse_colorbar_arg(
        mappable, values=None, norm=None, norm_kw=None, vmin=None, vmax=None, **kwargs
    ):
        """
        Generate a mappable from flexible non-mappable input. Useful in bridging
        the gap between legends and colorbars (e.g., creating colorbars from line
        objects whose data values span a natural colormap range).
        """
        # For container objects, we just assume color is the same for every item.
        # Works for ErrorbarContainer, StemContainer, BarContainer.
        if (
            np.iterable(mappable)
            and len(mappable) > 0
            and all(isinstance(obj, mcontainer.Container) for obj in mappable)
        ):
            mappable = [obj[0] for obj in mappable]

        # Colormap instance
        if isinstance(mappable, mcolors.Colormap) or isinstance(mappable, str):
            cmap = constructor.Colormap(mappable)
            if values is None and isinstance(cmap, pcolors.DiscreteColormap):
                values = [None] * cmap.N  # sometimes use discrete norm

        # List of colors
        elif np.iterable(mappable) and all(map(mcolors.is_color_like, mappable)):
            cmap = pcolors.DiscreteColormap(list(mappable), "_no_name")
            if values is None:
                values = [None] * len(mappable)  # always use discrete norm

        # List of artists
        # NOTE: Do not check for isinstance(Artist) in case it is an mpl collection
        elif np.iterable(mappable) and all(
            hasattr(obj, "get_color") or hasattr(obj, "get_facecolor")
            for obj in mappable  # noqa: E501
        ):
            # Generate colormap from colors and infer tick labels
            colors = []
            for obj in mappable:
                if hasattr(obj, "update_scalarmappable"):  # for e.g. pcolor
                    obj.update_scalarmappable()
                color = (
                    obj.get_color()
                    if hasattr(obj, "get_color")
                    else obj.get_facecolor()
                )  # noqa: E501
                if isinstance(color, np.ndarray):
                    color = color.squeeze()  # e.g. single color scatter plot
                if not mcolors.is_color_like(color):
                    raise ValueError(
                        "Cannot make colorbar from artists with more than one color."
                    )  # noqa: E501
                colors.append(color)
            # Try to infer tick values and tick labels from Artist labels
            cmap = pcolors.DiscreteColormap(colors, "_no_name")
            if values is None:
                values = [None] * len(mappable)
            else:
                values = list(values)
            for i, (obj, val) in enumerate(zip(mappable, values)):
                if val is not None:
                    continue
                val = obj.get_label()
                if val and val[0] == "_":
                    continue
                values[i] = val

        else:
            raise ValueError(
                "Input colorbar() argument must be a scalar mappable, colormap name "
                f"or object, list of colors, or list of artists. Got {mappable!r}."
            )

        # Generate continuous normalizer, and possibly discrete normalizer. Update
        # the outgoing locator and formatter if user does not override.
        norm_kw = norm_kw or {}
        norm = norm or "linear"
        vmin = _not_none(vmin=vmin, norm_kw_vmin=norm_kw.pop("vmin", None), default=0)
        vmax = _not_none(vmax=vmax, norm_kw_vmax=norm_kw.pop("vmax", None), default=1)
        norm = constructor.Norm(norm, vmin=vmin, vmax=vmax, **norm_kw)
        if values is not None:
            ticks = []
            labels = None
            for i, val in enumerate(values):
                try:
                    val = float(val)
                except (TypeError, ValueError):
                    pass
                if val is None:
                    val = i
                ticks.append(val)
            if any(isinstance(_, str) for _ in ticks):
                labels = list(map(str, ticks))
                ticks = np.arange(len(ticks))
            if len(ticks) == 1:
                levels = [ticks[0] - 1, ticks[0] + 1]
            else:
                levels = edges(ticks)
            from . import PlotAxes

            norm, cmap, _ = PlotAxes._parse_level_norm(
                levels, norm, cmap, discrete_ticks=ticks, discrete_labels=labels
            )

        # Return ad hoc ScalarMappable and update locator and formatter
        # NOTE: If value list doesn't match this may cycle over colors.
        mappable = mcm.ScalarMappable(norm, cmap)
        return mappable, kwargs

    def _parse_colorbar_filled(
        self,
        length=None,
        align=None,
        tickloc=None,
        ticklocation=None,
        orientation=None,
        **kwargs,
    ):
        """
        Return the axes and adjusted keyword args for a panel-filling colorbar.
        """
        # Parse input arguments
        side = self._panel_side
        side = _not_none(side, "left" if orientation == "vertical" else "bottom")
        align = _not_none(align, "center")
        length = _not_none(length=length, default=rc["colorbar.length"])
        ticklocation = _not_none(tickloc=tickloc, ticklocation=ticklocation)

        # Calculate inset bounds for the colorbar
        delta = 0.5 * (1 - length)
        if side in ("bottom", "top"):
            if align == "left":
                bounds = (0, 0, length, 1)
            elif align == "center":
                bounds = (delta, 0, length, 1)
            elif align == "right":
                bounds = (2 * delta, 0, length, 1)
            else:
                raise ValueError(f"Invalid align={align!r} for colorbar loc={side!r}.")
        else:
            if align == "bottom":
                bounds = (0, 0, 1, length)
            elif align == "center":
                bounds = (0, delta, 1, length)
            elif align == "top":
                bounds = (0, 2 * delta, 1, length)
            else:
                raise ValueError(f"Invalid align={align!r} for colorbar loc={side!r}.")

        # Add the axes as a child of the original axes
        cls = mproj.get_projection_class("ultraplot_cartesian")
        locator = self._make_inset_locator(bounds, self.transAxes)
        ax = cls(self.figure, locator(self, None).bounds, zorder=5)
        ax.set_axes_locator(locator)
        self.add_child_axes(ax)
        ax.patch.set_facecolor("none")  # ignore axes.alpha application

        # Handle default keyword args
        if orientation is None:
            orientation = "horizontal" if side in ("bottom", "top") else "vertical"
        if orientation == "horizontal":
            outside, inside = "bottom", "top"
            if side == "top":
                outside, inside = inside, outside
            ticklocation = _not_none(ticklocation, outside)
        else:
            outside, inside = "left", "right"
            if side == "right":
                outside, inside = inside, outside
            ticklocation = _not_none(ticklocation, outside)
        kwargs.update({"orientation": orientation, "ticklocation": ticklocation})
        return ax, kwargs

    def _parse_colorbar_inset(
        self,
        loc=None,
        width=None,
        length=None,
        shrink=None,
        frame=None,
        frameon=None,
        label=None,
        pad=None,
        tickloc=None,
        ticklocation=None,
        orientation=None,
        labelloc=None,
        labelrotation=None,
        **kwargs,
    ):
        """
        Return the axes and adjusted keyword args for an inset colorbar.
        """
        # Basic colorbar properties
        frame = _not_none(frame=frame, frameon=frameon, default=rc["colorbar.frameon"])
        length = _not_none(
            length=length, shrink=shrink, default=rc["colorbar.insetlength"]
        )  # noqa: E501
        width = _not_none(width, rc["colorbar.insetwidth"])
        pad = _not_none(pad, rc["colorbar.insetpad"])
        orientation = _not_none(orientation, "horizontal")
        ticklocation = _not_none(
            tickloc, ticklocation, "bottom" if orientation == "horizontal" else "right"
        )
        length = units(length, "em", "ax", axes=self, width=True)  # x direction
        width = units(width, "em", "ax", axes=self, width=False)  # y direction
        xpad = units(pad, "em", "ax", axes=self, width=True)
        ypad = units(pad, "em", "ax", axes=self, width=False)

        # Calculate space requirements for labels and ticks
        labspace = rc["xtick.major.size"] / 72
        fontsize = rc["xtick.labelsize"]
        fontsize = _fontsize_to_pt(fontsize)
        scale = 1.2
        if orientation == "vertical" and labelloc in ("left", "right"):
            scale = 2  # we need a little more room
        if label is not None:
            labspace += 2 * scale * fontsize / 72
        else:
            labspace += scale * fontsize / 72

        # Convert to axes-relative coordinates
        if orientation == "horizontal":
            labspace /= self._get_size_inches()[1]
        else:
            labspace /= self._get_size_inches()[0]

        # Initial frame dimensions (will be adjusted based on label position)
        if orientation == "horizontal":
            frame_width = 2 * xpad + length
            frame_height = 2 * ypad + width + labspace
        else:  # vertical
            frame_width = 2 * xpad + width + labspace
            frame_height = 2 * ypad + length

        # Initialize frame position and colorbar position
        xframe = yframe = 0  # frame lower left corner
        if loc == "upper right":
            xframe = 1 - frame_width
            yframe = 1 - frame_height
            cb_x = xframe + xpad
            cb_y = yframe + ypad
        elif loc == "upper left":
            yframe = 1 - frame_height
            cb_x = xpad
            cb_y = yframe + ypad
        elif loc == "lower left":
            cb_x = xpad
            cb_y = ypad
        else:  # lower right
            xframe = 1 - frame_width
            cb_x = xframe + xpad
            cb_y = ypad

        # Adjust frame and colorbar position based on label location
        label_offset = 0.5 * labspace

        # Account for label rotation if specified
        labelrotation = _not_none(labelrotation, 0)  # default to 0 degrees
        if labelrotation != 0 and label is not None:
            # Estimate label text dimensions
            import math

            # Rough estimate of text width (characters * font size * 0.6)
            estimated_text_width = len(str(label)) * fontsize * 0.6 / 72
            text_height = fontsize / 72

            # Convert rotation to radians
            angle_rad = math.radians(abs(labelrotation))

            # Calculate rotated dimensions
            rotated_width = estimated_text_width * math.cos(
                angle_rad
            ) + text_height * math.sin(angle_rad)
            rotated_height = estimated_text_width * math.sin(
                angle_rad
            ) + text_height * math.cos(angle_rad)

            # Convert back to axes-relative coordinates
            if orientation == "horizontal":
                # For horizontal colorbars, rotation affects vertical space
                rotation_offset = rotated_height / self._get_size_inches()[1]
            else:
                # For vertical colorbars, rotation affects horizontal space
                rotation_offset = rotated_width / self._get_size_inches()[0]

            # Use the larger of the original offset or rotation-adjusted offset
            label_offset = max(label_offset, rotation_offset)

        if orientation == "vertical":
            if labelloc == "left":
                # Move colorbar right to make room for left labels
                cb_x += label_offset

            elif labelloc == "top":
                # Center colorbar horizontally and extend frame for top labels
                cb_x += label_offset
                if "upper" in loc:
                    # Upper positions: extend frame downward
                    cb_y -= label_offset
                    yframe -= label_offset
                    frame_height += label_offset
                    frame_width += label_offset
                    if "right" in loc:
                        xframe -= label_offset
                        cb_x -= label_offset
                elif "lower" in loc:
                    # Lower positions: extend frame upward
                    frame_height += label_offset
                    frame_width += label_offset
                    if "right" in loc:
                        xframe -= label_offset
                        cb_x -= label_offset

            elif labelloc == "bottom":
                # Extend frame for bottom labels
                if "left" in loc:
                    cb_x += label_offset
                    frame_width += label_offset
                else:  # right
                    xframe -= label_offset
                    frame_width += label_offset

                if "lower" in loc:
                    cb_y += label_offset
                    frame_height += label_offset
                elif "upper" in loc:
                    yframe -= label_offset
                    frame_height += label_offset

        elif orientation == "horizontal":
            # Base vertical adjustment for horizontal colorbars
            cb_y += 2 * label_offset

            if labelloc == "bottom":
                if "upper" in loc:
                    yframe -= label_offset
                    frame_height += label_offset
                elif "lower" in loc:
                    frame_height += label_offset
                    cb_y += 0.5 * label_offset

            elif labelloc == "top":
                if "upper" in loc:
                    cb_y -= 1.5 * label_offset
                    yframe -= label_offset
                    frame_height += label_offset
                elif "lower" in loc:
                    frame_height += label_offset
                    cb_y -= 0.5 * label_offset

        # Set final bounds
        bounds_inset = [cb_x, cb_y]
        bounds_frame = [xframe, yframe]

        if orientation == "horizontal":
            bounds_inset.extend((length, width))
        else:  # vertical
            bounds_inset.extend((width, length))

        bounds_frame.extend((frame_width, frame_height))

        # Create axes and frame
        cls = mproj.get_projection_class("ultraplot_cartesian")
        locator = self._make_inset_locator(bounds_inset, self.transAxes)
        ax = cls(self.figure, locator(self, None).bounds, zorder=5)
        ax.patch.set_facecolor("none")
        ax.set_axes_locator(locator)
        self.add_child_axes(ax)
        kw_frame, kwargs = self._parse_frame("colorbar", **kwargs)
        if frame:
            frame = self._add_guide_frame(*bounds_frame, fontsize=fontsize, **kw_frame)

        kwargs.update({"orientation": orientation, "ticklocation": ticklocation})
        return ax, kwargs

    def _parse_legend_aligned(self, pairs, ncol=None, order=None, **kwargs):
        """
        Draw an individual legend with aligned columns. Includes support
        for switching legend-entries between column-major and row-major.
        """
        # Potentially change the order of handles to column-major
        npairs = len(pairs)
        ncol = _not_none(ncol, 3)
        nrow = npairs // ncol + 1
        array = np.empty((nrow, ncol), dtype=object)
        for i, pair in enumerate(pairs):
            array.flat[i] = pair  # must be assigned individually
        if order == "C":
            array = array.T

        # Return a legend
        # NOTE: Permit drawing empty legend to catch edge cases
        pairs = [pair for pair in array.flat if isinstance(pair, tuple)]
        args = tuple(zip(*pairs)) or ([], [])
        return plegend.Legend(self, *args, ncol=ncol, **kwargs)

    def _parse_legend_centered(
        self,
        pairs,
        *,
        fontsize,
        loc=None,
        title=None,
        frameon=None,
        kw_frame=None,
        **kwargs,
    ):
        """
        Draw "legend" with centered rows by creating separate legends for
        each row. The label spacing/border spacing will be exactly replicated.
        """
        # Parse input args
        # NOTE: Main legend() function applies default 'legend.loc' of 'best' when
        # users pass legend=True or call legend without 'loc'. Cannot issue warning.
        kw_frame = kw_frame or {}
        kw_frame["fontsize"] = fontsize
        if loc is None or loc == "best":  # white lie
            loc = "upper center"
        if not isinstance(loc, str):
            raise ValueError(
                f"Invalid loc={loc!r} for centered-row legend. Must be string."
            )
        keys = ("bbox_transform", "bbox_to_anchor")
        kw_ignore = {key: kwargs.pop(key) for key in keys if key in kwargs}
        if kw_ignore:
            warnings._warn_ultraplot(
                f"Ignoring invalid centered-row legend keyword args: {kw_ignore!r}"
            )

        # Iterate and draw
        # NOTE: Empirical testing shows spacing fudge factor necessary to
        # exactly replicate the spacing of standard aligned legends.
        # NOTE: We confine possible bounding box in *y*-direction, but do not
        # confine it in *x*-direction. Matplotlib will automatically move
        # left-to-right if you request this.
        legs = []
        kwargs.update({"loc": loc, "frameon": False})
        space = kwargs.get("labelspacing", None) or rc["legend.labelspacing"]
        height = (((1 + space * 0.85) * fontsize) / 72) / self._get_size_inches()[1]
        for i, ipairs in enumerate(pairs):
            extra = int(i > 0 and title is not None)
            if "upper" in loc:
                base, offset = 1, -extra
            elif "lower" in loc:
                base, offset = 0, len(pairs)
            else:  # center
                base, offset = 0.5, 0.5 * (len(pairs) - extra)
            y0, y1 = base + (offset - np.array([i + 1, i])) * height
            bb = mtransforms.Bbox([[0, y0], [1, y1]])
            leg = plegend.Legend(
                self,
                *zip(*ipairs),
                bbox_to_anchor=bb,
                bbox_transform=self.transAxes,
                ncol=len(ipairs),
                title=title if i == 0 else None,
                **kwargs,
            )
            legs.append(leg)

        # Draw manual fancy bounding box for un-aligned legend
        # WARNING: legendPatch uses the default transform, i.e. universal coordinates
        # in points. Means we have to transform mutation scale into transAxes sizes.
        # WARNING: Tempting to use legendPatch for everything but for some reason
        # coordinates are messed up. In some tests all coordinates were just result
        # of get window extent multiplied by 2 (???). Anyway actual box is found in
        # _legend_box attribute, which is accessed by get_window_extent.
        objs = tuple(legs)
        if frameon and legs:
            rend = self.figure._get_renderer()  # arbitrary renderer
            trans = self.transAxes.inverted()
            bboxes = [leg.get_window_extent(rend).transformed(trans) for leg in legs]
            bb = mtransforms.Bbox.union(bboxes)
            bounds = (bb.xmin, bb.ymin, bb.xmax - bb.xmin, bb.ymax - bb.ymin)
            self._add_guide_frame(*bounds, **kw_frame)
        return objs

    @staticmethod
    def _parse_legend_group(handles, labels=None):
        """
        Parse possibly tuple-grouped input handles.
        """

        # Helper function. Retrieve labels from a tuple group or from objects
        # in a container. Multiple labels lead to multiple legend entries.
        def _legend_label(*objs):  # noqa: E301
            labs = []
            for obj in objs:
                if hasattr(obj, "get_label"):  # e.g. silent list
                    if getattr(obj, "_ultraplot_synthetic", False):
                        continue
                    lab = obj.get_label()
                    if lab is not None and not str(lab).startswith("_"):
                        labs.append(lab)
            return tuple(labs)

        # Helper function. Translate handles in the input tuple group. Extracts
        # legend handles from contour sets and extracts labeled elements from
        # matplotlib containers (important for histogram plots).
        ignore = (mcontainer.ErrorbarContainer,)
        containers = (cbook.silent_list, mcontainer.Container)

        def _legend_tuple(*objs):  # noqa: E306
            handles = []
            for obj in objs:
                if isinstance(obj, ignore) and not _legend_label(obj):
                    continue
                if hasattr(obj, "update_scalarmappable"):  # for e.g. pcolor
                    obj.update_scalarmappable()
                if isinstance(obj, mcontour.ContourSet):  # extract single element
                    hs, _ = obj.legend_elements()
                    label = getattr(obj, "_legend_label", "_no_label")
                    if hs:  # non-empty
                        obj = hs[len(hs) // 2]
                        obj.set_label(label)
                if isinstance(obj, containers):  # extract labeled elements
                    hs = (obj, *guides._iter_iterables(obj))
                    hs = tuple(filter(_legend_label, hs))
                    if hs:
                        handles.extend(hs)
                    elif obj:  # fallback to first element
                        # Skip synthetic helpers and fill_between collections
                        if not getattr(obj[0], "_ultraplot_synthetic", False):
                            handles.append(obj[0])
                    else:
                        handles.append(obj)
                elif hasattr(obj, "get_label"):
                    # Skip synthetic helpers and fill_between collections
                    if getattr(obj, "_ultraplot_synthetic", False):
                        continue
                    handles.append(obj)
                else:
                    warnings._warn_ultraplot(f"Ignoring invalid legend handle {obj!r}.")
            return tuple(handles)

        # Sanitize labels. Ignore e.g. extra hist() or hist2d() return values,
        # auto-detect labels in tuple group, auto-expand tuples with diff labels
        # NOTE: Allow handles and labels of different length like
        # native matplotlib. Just truncate extra values with zip().
        if labels is None:
            labels = [None] * len(handles)
        ihandles, ilabels = [], []
        for hs, label in zip(handles, labels):
            # Filter objects
            if type(hs) is not tuple:  # ignore Containers (tuple subclasses)
                hs = (hs,)
            hs = _legend_tuple(*hs)
            labs = _legend_label(*hs)
            if not hs:
                continue
            # Unfurl tuple of handles
            if label is None and len(labs) > 1:
                hs = tuple(filter(_legend_label, hs))
                ihandles.extend(hs)
                ilabels.extend(_.get_label() for _ in hs)
            # Append this handle with some name
            else:
                hs = hs[0] if len(hs) == 1 else hs  # unfurl for better error messages
                label = label if label is not None else labs[0] if labs else "_no_label"
                ihandles.append(hs)
                ilabels.append(label)
        return ihandles, ilabels

    def _parse_legend_handles(
        self,
        handles,
        labels,
        ncol=None,
        order=None,
        center=None,
        alphabetize=None,
        handler_map=None,
    ):
        """
        Parse input handles and labels.
        """
        # Handle lists of lists
        # TODO: Often desirable to label a "mappable" with one data value. Maybe add a
        # legend option for the *number of samples* or *sample points* when drawing
        # legends for mappables. Look into "legend handlers", might just want to add
        # handlers by passing handler_map to legend() and get_legend_handles_labels().
        is_list = lambda obj: (  # noqa: E731
            np.iterable(obj) and not isinstance(obj, (str, tuple))
        )
        to_list = lambda obj: (  # noqa: E731
            obj.tolist()
            if isinstance(obj, np.ndarray)
            else obj if obj is None or is_list(obj) else [obj]
        )
        handles, labels = to_list(handles), to_list(labels)
        if handles and not labels and all(isinstance(h, str) for h in handles):
            handles, labels = labels, handles
        multi = any(is_list(h) and len(h) > 1 for h in (handles or ()))
        if multi and order == "F":
            warnings._warn_ultraplot(
                "Column-major ordering of legend handles is not supported "
                "for horizontally-centered legends."
            )
        if multi and ncol is not None:
            warnings._warn_ultraplot(
                "Detected list of *lists* of legend handles. Ignoring "
                'the user input property "ncol".'
            )
        if labels and not handles:
            warnings._warn_ultraplot(
                "Passing labels without handles is unsupported in ultraplot. "
                "Please explicitly pass the handles to legend() or pass labels "
                "to plotting commands with e.g. plot(data_1d, label='label') or "
                "plot(data_2d, labels=['label1', 'label2', ...]). After passing "
                "labels to plotting commands you can call legend() without any "
                "arguments or with the handles as a sole positional argument."
            )
        ncol = _not_none(ncol, 3)
        center = _not_none(center, multi)

        # Iterate over each sublist and parse independently
        pairs = []
        if not multi:  # temporary
            handles, labels = [handles], [labels]
        elif labels is None:
            labels = [labels] * len(handles)
        for ihandles, ilabels in zip(handles, labels):
            ihandles, ilabels = to_list(ihandles), to_list(ilabels)
            if ihandles is None:
                ihandles = self._get_legend_handles(handler_map)
            ihandles, ilabels = self._parse_legend_group(ihandles, ilabels)
            ipairs = list(zip(ihandles, ilabels))
            if alphabetize:
                ipairs = sorted(ipairs, key=lambda pair: pair[1])
            pairs.append(ipairs)

        # Manage (handle, label) pairs in context of the 'center' option
        if not multi:
            pairs = pairs[0]
            if center:
                multi = True
                pairs = [pairs[i * ncol : (i + 1) * ncol] for i in range(len(pairs))]
        else:
            if not center:  # standardize format based on input
                multi = False  # no longer is list of lists
                pairs = [pair for ipairs in pairs for pair in ipairs]

        if multi:
            pairs = [ipairs for ipairs in pairs if ipairs]
        return pairs, multi

    def _range_subplotspec(self, s):
        """
        Return the column or row range for the subplotspec.
        """
        if not isinstance(self, maxes.SubplotBase):
            raise RuntimeError("Axes must be a subplot.")
        ss = self.get_subplotspec().get_topmost_subplotspec()
        row1, row2, col1, col2 = ss._get_rows_columns()
        if s == "x":
            return (col1, col2)
        else:
            return (row1, row2)

    def _range_tightbbox(self, s):
        """
        Return the tight bounding box span from the cached bounding box.
        """
        # TODO: Better testing for axes visibility
        bbox = self._tight_bbox
        if bbox is None:
            return np.nan, np.nan
        if s == "x":
            return bbox.xmin, bbox.xmax
        else:
            return bbox.ymin, bbox.ymax

    def _unshare(self, *, which: str):
        """
        Remove this Axes from the shared Grouper for the given axis ('x', 'y', 'z', or 'view').
        Note this isolates the axis and does not preserve the transitivity of sharing.
        """
        if which not in self._shared_axes:
            warnings._warn_ultraplot(f"Axis {which} is not shared")
            return
        if which in "xy":
            setattr(self, f"_share{which}", None)  # essential
        # Note _scale is also set when calling sharex or y.
        # I think it is fine to leave it as otherwise we would
        # need to determine the scale, which may get messy.

        grouper = self._shared_axes[which]
        siblings = list(grouper.get_siblings(self))
        for sibling in siblings:
            if sibling is not self:
                # Unshare by removing them from the grouper
                grouper.remove(sibling)
                sibling._shared_axes[which].remove(self)
                # To be safe let's remove this
                self._shared_axes[which].remove(sibling)
                if which in "xy":
                    setattr(sibling, f"_share{which}", None)
                this_ax = getattr(self, f"{which}axis")
                sib_ax = getattr(sibling, f"{which}axis")
                # Reset formatters by creating new Ticker objects.
                # A deepcopy can trigger redraws.
                new_major = maxis.Ticker()
                if this_ax.major:
                    new_major.locator = copy.copy(this_ax.major.locator)
                    new_major.formatter = copy.copy(this_ax.major.formatter)
                this_ax.major = new_major

                new_minor = maxis.Ticker()
                if this_ax.minor:
                    new_minor.locator = copy.copy(this_ax.minor.locator)
                    new_minor.formatter = copy.copy(this_ax.minor.formatter)
                this_ax.minor = new_minor

    def _sharex_setup(self, sharex, **kwargs):
        """
        Configure x-axis sharing for panels. See also `~CartesianAxes._sharex_setup`.
        """
        self._share_short_axis(sharex, "left", **kwargs)  # x axis of left panels
        self._share_short_axis(sharex, "right", **kwargs)
        self._share_long_axis(sharex, "bottom", **kwargs)  # x axis of bottom panels
        self._share_long_axis(sharex, "top", **kwargs)

    def _sharey_setup(self, sharey, **kwargs):
        """
        Configure y-axis sharing for panels. See also `~CartesianAxes._sharey_setup`.
        """
        self._share_short_axis(sharey, "bottom", **kwargs)  # y axis of bottom panels
        self._share_short_axis(sharey, "top", **kwargs)
        self._share_long_axis(sharey, "left", **kwargs)  # y axis of left panels
        self._share_long_axis(sharey, "right", **kwargs)

    def _share_short_axis(self, share, side, **kwargs):
        """
        Share the "short" axes of panels in this subplot with other panels.
        """
        if share is None or self._panel_side:
            return  # if this is a panel
        s = "x" if side in ("left", "right") else "y"
        caxs = self._panel_dict[side]
        paxs = share._panel_dict[side]
        caxs = [pax for pax in caxs if not pax._panel_hidden]
        paxs = [pax for pax in paxs if not pax._panel_hidden]
        for cax, pax in zip(caxs, paxs):  # may be uneven
            getattr(cax, f"_share{s}_setup")(pax, **kwargs)

    def _share_long_axis(self, share, side, **kwargs):
        """
        Share the "long" axes of panels in this subplot with other panels.
        """
        # NOTE: We do not check _panel_share because that only controls
        # sharing with main subplot, not other subplots
        if share is None or self._panel_side:
            return  # if this is a panel
        s = "x" if side in ("top", "bottom") else "y"
        paxs = self._panel_dict[side]
        paxs = [pax for pax in paxs if not pax._panel_hidden]
        for pax in paxs:
            getattr(pax, f"_share{s}_setup")(share, **kwargs)

    def _reposition_subplot(self):
        """
        Reposition the subplot axes.
        """
        # WARNING: In later versions self.numRows, self.numCols, and self.figbox
        # are @property definitions that never go stale but in mpl < 3.4 they are
        # attributes that must be updated explicitly with update_params().
        # WARNING: In early versions matplotlib only removes '_layoutbox' and
        # '_poslayoutbox' when calling public set_position but in later versions it
        # calls set_in_layout(False) which removes children from get_tightbbox().
        # Therefore try to use _set_position() even though it is private
        if not isinstance(self, maxes.SubplotBase):
            raise RuntimeError("Axes must be a subplot.")
        setter = getattr(self, "_set_position", self.set_position)
        if version.parse(str(_version_mpl)) >= version.parse("3.4"):
            setter(self.get_subplotspec().get_position(self.figure))
        else:
            self.update_params()
            setter(self.figbox)  # equivalent to above

    def _update_abc(self, **kwargs):
        """
        Update the a-b-c label.
        """
        # Properties
        # NOTE: Border props only apply for "inner" title locations so we need to
        # store on the axes whenever they are modified in case the current location
        # is an 'outer' location then re-apply in case 'loc' is subsequently changed
        kw = rc.fill(
            {
                "size": "abc.size",
                "weight": "abc.weight",
                "color": "abc.color",
                "family": "font.family",
            },
            context=True,
        )
        kwb = rc.fill(
            {
                "border": "abc.border",
                "borderwidth": "abc.borderwidth",
                "bbox": "abc.bbox",
                "bboxpad": "abc.bboxpad",
                "bboxcolor": "abc.bboxcolor",
                "bboxstyle": "abc.bboxstyle",
                "bboxalpha": "abc.bboxalpha",
            },
            context=True,
        )
        self._abc_border_kwargs.update(kwb)

        # A-b-c labels. Build as a...z...aa...zz...aaa...zzz
        # NOTE: The abc string should already be validated here
        abc = rc.find("abc", context=True)  # 1st run, or changed
        if abc is True:
            abc = "a"
        if abc is False:
            abc = ""
        if abc is None or self.number is None:
            pass
        elif isinstance(abc, str):
            nabc, iabc = divmod(self.number - 1, 26)
            if abc:  # should have been validated to contain 'a' or 'A'
                old = re.search("[aA]", abc).group()  # return first occurrence
                new = (nabc + 1) * ABC_STRING[iabc]
                new = new.upper() if old == "A" else new
                abc = abc.replace(old, new, 1)  # replace first occurrence
            kw["text"] = abc
        else:
            if self.number > len(abc):
                raise ValueError(
                    f"Invalid abc list length {len(abc)} "
                    f"for axes with number {self.number}."
                )
            else:
                kw["text"] = abc[self._number - 1]

        # Update a-b-c label
        loc = rc.find("abc.loc", context=True)
        loc = self._abc_loc = _translate_loc(loc or self._abc_loc, "text")
        if loc not in ("left", "right", "center"):
            kw.update(self._abc_border_kwargs)
        kw.update(kwargs)
        self._update_outer_abc_loc(loc)
        self._title_dict["abc"].update(kw)

    def _update_outer_abc_loc(self, loc):
        """
        For the outer labels, we need to align them vertically and create the
        offset based on the tick length and the tick label. This function loops
        through all axes in the figure to find maximum tick length and label size
        and transforms the position accordingly.
        """
        if loc not in ["outer left", "outer right"]:
            return
        # Find the largest offset by considering the tick and label size
        tick_length = label_size = 0
        ha = "right" if loc == "outer left" else "left"
        side = 0 if loc == "outer left" else -1

        # Loop through all axes in the figure to find maximum tick length and label size
        for axi in self.figure.axes:
            axis = axi.yaxis
            # Determine if ticks are visible and get their size
            has_ticks = (
                axis.get_major_ticks() and axis.get_major_ticks()[side].get_visible()
            )
            if has_ticks:
                # Ignore if tick direction is not outwards
                tickdir = axis._major_tick_kw.get("tickdir", "out")
                if tickdir and tickdir != "in":
                    tick_length = max(
                        axis.majorTicks[0].tick1line.get_markersize(), tick_length
                    )

            # Get the size of tick labels if they exist
            has_labels = True if axis.get_ticklabels() else False
            # Estimate label size; note it uses the raw text representation which can be misleading due to the latex processing
            if has_labels and axis.get_ticklabels():
                _offset = max(
                    [
                        len(l.get_text()) * l.get_fontsize() * 0.6
                        for l in axis.get_ticklabels()
                    ]
                )
                label_size = max(_offset, label_size)
        # Calculate symmetrical offset based on tick length and label size
        base_offset = (tick_length / 72) + (label_size / 72)
        offset = -base_offset if ha == "right" else base_offset

        # Create text with appropriate position and transform
        aobj = self._title_dict[loc]
        aobj.set_transform(
            self.transAxes
            + mtransforms.ScaledTranslation(offset, 0, self.figure.dpi_scale_trans)
        )
        p = aobj.get_position()
        aobj.set_position((p[0] + offset, p[1]))

    def _update_title(self, loc, title=None, **kwargs):
        """
        Update the title at the specified location.
        """
        # Titles, with two workflows here:
        # 1. title='name' and titleloc='position'
        # 2. ltitle='name', rtitle='name', etc., arbitrarily many titles
        # NOTE: This always updates the *current* title and deflection to panels
        # is handled later so that titles set with set_title() are deflected too.
        # See notes in _update_super_labels() and _apply_title_above().
        # NOTE: Matplotlib added axes.titlecolor in version 3.2 but we still use
        # custom title.size, title.weight, title.color properties for retroactive
        # support in older matplotlib versions. First get params and update kwargs.
        kw = rc.fill(
            {
                "size": "title.size",
                "weight": "title.weight",
                "color": "title.color",
                "family": "font.family",
            },
            context=True,
        )
        if "color" in kw and kw["color"] == "auto":
            del kw["color"]  # WARNING: matplotlib permits invalid color here
        kwb = rc.fill(
            {
                "border": "title.border",
                "borderwidth": "title.borderwidth",
                "bbox": "title.bbox",
                "bboxpad": "title.bboxpad",
                "bboxcolor": "title.bboxcolor",
                "bboxstyle": "title.bboxstyle",
                "bboxalpha": "title.bboxalpha",
            },
            context=True,
        )
        self._title_border_kwargs.update(kwb)

        # Update the padding settings read at drawtime. Make sure to
        # update them on the panel axes if 'title.above' is active.
        pad = rc.find("abc.titlepad", context=True)
        if pad is not None:
            self._abc_title_pad = pad
        pad = rc.find("title.pad", context=True)  # title
        if pad is not None:
            self._title_pad = pad
            self._set_title_offset_trans(pad)

        # Get the title location. If 'titleloc' was used then transfer text
        # from the old location to the new location.
        if loc is not None:
            loc = _translate_loc(loc, "text")
        else:
            old = self._title_loc
            loc = rc.find("title.loc", context=True)
            loc = self._title_loc = _translate_loc(loc or self._title_loc, "text")
            if loc != old and old is not None:
                labels._transfer_label(self._title_dict[old], self._title_dict[loc])

        # Update the title text. For outer panels, add text to the panel if
        # necesssary. For inner panels, use the border and bbox settings.
        if loc not in ("left", "right", "center"):
            kw.update(self._title_border_kwargs)
        if title is None:
            pass
        elif isinstance(title, str):
            kw["text"] = title
        elif np.iterable(title) and all(isinstance(_, str) for _ in title):
            if self.number is None:
                pass
            elif self.number > len(title):
                raise ValueError(
                    f"Invalid title list length {len(title)} "
                    f"for axes with number {self.number}."
                )
            else:
                kw["text"] = title[self.number - 1]
        else:
            raise ValueError(f"Invalid title {title!r}. Must be string(s).")
        if any(key in kwargs for key in ("size", "fontsize")):
            self._title_dict[loc]._ultraplot_manual_size = True
        kw.update(kwargs)
        self._title_dict[loc].update(kw)

    def _update_title_position(self, renderer):
        """
        Update the position of inset titles and outer titles. This is called
        by matplotlib at drawtime.
        """
        # Update title positions
        # NOTE: Critical to do this every time in case padding changes or
        # we added or removed an a-b-c label in the same position as a title
        width, height = self._get_size_inches()
        if width <= 0 or height <= 0:
            return
        x_pad = self._title_pad / (72 * width)
        y_pad = self._title_pad / (72 * height)
        for loc, obj in self._title_dict.items():
            if loc == "abc":  # redirect
                loc = self._abc_loc
            xy = _get_pos_from_locator(loc, x_pad, y_pad)
            obj.set_position(xy)

        # Get title padding. Push title above tick marks since matplotlib ignores them.
        # This is known matplotlib problem but especially annoying with top panels.
        # NOTE: See axis.get_ticks_position for inspiration
        pad = self._title_pad
        # Horizontal separation between abc label and title when co-located (in points)
        abc_title_sep_pts = self._abc_title_pad
        if self.xaxis.get_visible() and any(
            tick.tick2line.get_visible() and not tick.label2.get_visible()
            for tick in self.xaxis.majorTicks
        ):
            pad += self.xaxis.get_tick_padding()

        # Avoid applying padding on every draw in case it is expensive to change
        # the title Text transforms every time.
        pad_current = self._title_pad_current
        if pad_current is None or not np.isclose(pad, pad_current):
            self._title_pad_current = pad
            self._set_title_offset_trans(pad)

        # Adjust the above-axes positions with builtin algorithm
        # WARNING: Make sure the name of this private function doesn't change
        super()._update_title_position(renderer)

        # Sync the title position with the a-b-c label position
        aobj = self._title_dict["abc"]
        tobj = self._title_dict[self._abc_loc]
        aobj.set_transform(tobj.get_transform())
        aobj.set_position(tobj.get_position())
        aobj.set_ha(tobj.get_ha())
        aobj.set_va(tobj.get_va())

        # Offset title away from a-b-c label
        # NOTE: Title texts all use axes transform in x-direction
        # We need to convert padding values from points to axes coordinates (0-1 normalized)
        atext, ttext = aobj.get_text(), tobj.get_text()
        awidth = twidth = 0
        width_inches = self._get_size_inches()[0]

        # Convert abc-title separation from points to axes coordinates
        # This is the spacing BETWEEN abc and title when they share the same location
        abc_title_sep = (abc_title_sep_pts / 72) / width_inches

        # Convert user's horizontal offset from points to axes coordinates
        # This is the user-specified shift for the abc label position (via abcpad parameter)
        abc_offset = (self._abc_pad / 72) / width_inches

        ha = aobj.get_ha()

        # Get dimensions of non-empty elements
        if atext and aobj.get_figure() is not None:
            awidth = (
                aobj.get_window_extent(renderer)
                .transformed(self.transAxes.inverted())
                .width
            )
        if ttext and tobj.get_figure() is not None:
            twidth = (
                tobj.get_window_extent(renderer)
                .transformed(self.transAxes.inverted())
                .width
            )

        # Shrink the title font if both texts share a location and would overflow
        if (
            atext
            and ttext
            and self._abc_loc == self._title_loc
            and twidth > 0
            and not getattr(tobj, "_ultraplot_manual_size", False)
        ):
            scale = 1
            base_x = tobj.get_position()[0]
            if ha == "left":
                available = 1 - (base_x + awidth + abc_title_sep)
                if available < twidth and available > 0:
                    scale = available / twidth
            elif ha == "right":
                available = base_x + abc_offset - abc_title_sep - awidth
                if available < twidth and available > 0:
                    scale = available / twidth
            elif ha == "center":
                # Conservative fit for centered titles sharing the abc location
                left_room = base_x - 0.5 * (awidth + abc_title_sep)
                right_room = 1 - (base_x + 0.5 * (awidth + abc_title_sep))
                max_room = min(left_room, right_room)
                if max_room < twidth / 2 and max_room > 0:
                    scale = (2 * max_room) / twidth

            if scale < 1:
                tobj.set_fontsize(tobj.get_fontsize() * scale)
                twidth *= scale

        # Calculate offsets based on alignment and content
        aoffset = toffset = 0
        if atext and ttext:
            if ha == "left":
                toffset = awidth + abc_title_sep
            elif ha == "right":
                aoffset = -(twidth + abc_title_sep)
            elif ha == "center":
                toffset = 0.5 * (awidth + abc_title_sep)
                aoffset = -0.5 * (twidth + abc_title_sep)

        # Apply positioning adjustments
        # For abc label: apply offset from co-located title + user's horizontal offset
        if atext:
            aobj.set_x(
                aobj.get_position()[0]
                + aoffset
                + abc_offset  # User's horizontal shift (from abcpad parameter)
            )
        if ttext:
            tobj.set_x(tobj.get_position()[0] + toffset)

        # Shrink title if it overlaps the abc label at a different location
        if (
            atext
            and self._abc_loc != self._title_loc
            and not getattr(
                self._title_dict[self._title_loc], "_ultraplot_manual_size", False
            )
        ):
            title_obj = self._title_dict[self._title_loc]
            title_text = title_obj.get_text()
            if title_text:
                abc_bbox = aobj.get_window_extent(renderer).transformed(
                    self.transAxes.inverted()
                )
                title_bbox = title_obj.get_window_extent(renderer).transformed(
                    self.transAxes.inverted()
                )
                ax0, ax1 = abc_bbox.x0, abc_bbox.x1
                tx0, tx1 = title_bbox.x0, title_bbox.x1
                if tx0 < ax1 + abc_title_sep and tx1 > ax0 - abc_title_sep:
                    base_x = title_obj.get_position()[0]
                    ha = title_obj.get_ha()
                    max_width = 0
                    if ha == "left":
                        if base_x <= ax0 - abc_title_sep:
                            max_width = (ax0 - abc_title_sep) - base_x
                    elif ha == "right":
                        if base_x >= ax1 + abc_title_sep:
                            max_width = base_x - (ax1 + abc_title_sep)
                    elif ha == "center":
                        if base_x >= ax1 + abc_title_sep:
                            max_width = 2 * (base_x - (ax1 + abc_title_sep))
                        elif base_x <= ax0 - abc_title_sep:
                            max_width = 2 * ((ax0 - abc_title_sep) - base_x)
                    if 0 < max_width < title_bbox.width:
                        scale = max_width / title_bbox.width
                        title_obj.set_fontsize(title_obj.get_fontsize() * scale)

    def _update_super_title(self, suptitle=None, **kwargs):
        """
        Update the figure super title.
        """
        # NOTE: This is actually *figure-wide* setting, but that line gets blurred
        # where we have shared axes, spanning labels, etc. May cause redundant
        # assignments if using SubplotGrid.format() but this is fast so nbd.
        if self.number is None:
            # NOTE: Kludge prevents changed *figure-wide* settings from getting
            # overwritten when user makes a new panels or insets. Funky limitation but
            # kind of makes sense to make these inaccessible from panels.
            return
        kw = rc.fill(
            {
                "size": "suptitle.size",
                "weight": "suptitle.weight",
                "color": "suptitle.color",
                "family": "font.family",
            },
            context=True,
        )
        kw.update(kwargs)
        if suptitle or kw:
            self.figure._update_super_title(suptitle, **kw)

    def _update_super_labels(self, side, labels=None, **kwargs):
        """
        Update the figure super labels.
        """
        fig = self.figure
        if self.number is None:
            return  # NOTE: see above
        kw = rc.fill(
            {
                "color": side + "label.color",
                "rotation": side + "label.rotation",
                "size": side + "label.size",
                "weight": side + "label.weight",
                "family": "font.family",
            },
            context=True,
        )
        kw.update(kwargs)
        if labels or kw:
            fig._update_super_labels(side, labels, **kw)

    @staticmethod
    def get_center_of_axes(axes=None):
        positions = [ax.get_position() for ax in axes]
        # get the outermost coordinates
        box = mtransforms.Bbox.from_extents(
            min(p.bounds[0] for p in positions),
            min(p.bounds[1] for p in positions),
            max(p.bounds[0] + p.bounds[2] for p in positions),
            max(p.bounds[1] + p.bounds[3] for p in positions),
        )
        return box

    def _update_share_labels(self, axes=None, target="x"):
        """Update shared axis labels for a group of axes.

        Parameters
        ----------
        axes : list of int or list of Axes, optional
                The axes indices or Axes objects to share labels between
        target : {'x', 'y'}, optional
                Which axis labels to share ('x' for x-axis, 'y' for     y-axis)
        """
        if axes is False:
            self.figure._clear_share_label_groups([self], target=target)
            return
        if axes is None or not len(list(axes)):
            return

        # Convert indices to actual axes objects
        if isinstance(axes[0], int):
            axes = [self.figure.axes[i] for i in axes]
        axes = [
            ax._get_topmost_axes() if hasattr(ax, "_get_topmost_axes") else ax
            for ax in axes
            if ax is not None
        ]
        if len(axes) < 2:
            return
        # Preserve order while de-duplicating
        seen = set()
        unique = []
        for ax in axes:
            ax_id = id(ax)
            if ax_id in seen:
                continue
            seen.add(ax_id)
            unique.append(ax)
        axes = unique
        if len(axes) < 2:
            return

        # Prefer figure-managed spanning labels when possible
        if all(isinstance(ax, maxes.SubplotBase) for ax in axes):
            self.figure._register_share_label_group(axes, target=target, source=self)
            return

        # Get the center position of the axes group
        if box := self.get_center_of_axes(axes):
            # Reuse existing label if possible
            if target == "x":
                label = axes[0].xaxis.label
                # Update position and properties
                label.set_position(((box.bounds[0] + box.bounds[2]) / 2, box.bounds[1]))
            else:  # y-axis
                label = axes[0].yaxis.label
                # Update position and properties
                label.set_position((box.bounds[0], (box.bounds[1] + box.bounds[3]) / 2))

            label.set_ha("center")
            label.set_va("center")

            # Share the same label object across all axes
            # Skip first axes since we used its    label
            for ax in axes[1:]:
                if target == "x":
                    ax.xaxis.label = label
                else:
                    ax.yaxis.label = label

    @docstring._snippet_manager
    def format(
        self,
        *,
        title=None,
        title_kw=None,
        abc_kw=None,
        ltitle=None,
        lefttitle=None,
        ctitle=None,
        centertitle=None,
        rtitle=None,
        righttitle=None,
        ultitle=None,
        upperlefttitle=None,
        uctitle=None,
        uppercentertitle=None,
        urtitle=None,
        upperrighttitle=None,
        lltitle=None,
        lowerlefttitle=None,
        lctitle=None,
        lowercentertitle=None,
        lrtitle=None,
        lowerrighttitle=None,
        share_xlabels=None,
        share_ylabels=None,
        **kwargs,
    ):
        """
        Modify the a-b-c label, axes title(s), and background patch,
        and call `ultraplot.figure.Figure.format` on the axes figure.

        Parameters
        ----------
        %(axes.format)s

        Important
        ---------
        `abc`, `abcloc`, `titleloc`, `titleabove`, `titlepad`, and
        `abctitlepad` are actually :ref:`configuration settings <ug_config>`.
        We explicitly document these arguments here because it is common to
        change them for specific axes. But many :ref:`other configuration
        settings <ug_format>` can be passed to ``format`` too.

        Other parameters
        ----------------
        %(figure.format)s
        %(rc.format)s

        See also
        --------
        ultraplot.axes.CartesianAxes.format
        ultraplot.axes.PolarAxes.format
        ultraplot.axes.GeoAxes.format
        ultraplot.figure.Figure.format
        ultraplot.gridspec.SubplotGrid.format
        ultraplot.config.Configurator.context
        """
        skip_figure = kwargs.pop("skip_figure", False)  # internal keyword arg
        params = _pop_params(kwargs, self.figure._format_signature)

        # Initiate context block
        rc_kw, rc_mode = _pop_rc(kwargs)
        with rc.context(rc_kw, mode=rc_mode):
            # Behavior of titles in presence of panels
            above = rc.find("title.above", context=True)
            if above is not None:
                self._title_above = above  # used for future titles

            # Update a-b-c label and titles
            abc_kw = abc_kw or {}
            title_kw = title_kw or {}
            self._update_share_labels(share_xlabels, target="x")
            self._update_share_labels(share_ylabels, target="y")
            if (pad := kwargs.pop("abcpad", None)) is not None:
                self._abc_pad = units(pad)
            self._update_abc(**abc_kw)
            self._update_title(None, title, **title_kw)
            self._update_title(
                "left",
                _not_none(ltitle=ltitle, lefttitle=lefttitle),
                **title_kw,
            )
            self._update_title(
                "center",
                _not_none(ctitle=ctitle, centertitle=centertitle),
                **title_kw,
            )
            self._update_title(
                "right",
                _not_none(rtitle=rtitle, righttitle=righttitle),
                **title_kw,
            )
            self._update_title(
                "upper left",
                _not_none(ultitle=ultitle, upperlefttitle=upperlefttitle),
                **title_kw,
            )
            self._update_title(
                "upper center",
                _not_none(uctitle=uctitle, uppercentertitle=uppercentertitle),
                **title_kw,
            )
            self._update_title(
                "upper right",
                _not_none(urtitle=urtitle, upperrighttitle=upperrighttitle),
                **title_kw,
            )
            self._update_title(
                "lower left",
                _not_none(lltitle=lltitle, lowerlefttitle=lowerlefttitle),
                **title_kw,
            )
            self._update_title(
                "lower center",
                _not_none(lctitle=lctitle, lowercentertitle=lowercentertitle),
                **title_kw,
            )
            self._update_title(
                "lower right",
                _not_none(lrtitle=lrtitle, lowerrighttitle=lowerrighttitle),
                **title_kw,
            )

            # Update the axes style
            # NOTE: This will also raise an error if unknown args are encountered
            cycle = rc.find("axes.prop_cycle", context=True)
            if cycle is not None:
                self.set_prop_cycle(cycle)
            self._update_background(**kwargs)

        # Update super labels and super title
        # NOTE: To avoid resetting figure-wide settings when new axes are created
        # we only proceed if using the default context mode. Simliar to geo.py
        if skip_figure:  # avoid recursion
            return
        if rc_mode == 1:  # avoid resetting
            return
        self.figure.format(rc_kw=rc_kw, rc_mode=rc_mode, skip_axes=True, **params)

    def draw(self, renderer=None, *args, **kwargs):
        # Perform extra post-processing steps
        # NOTE: In *principle* these steps go here but should already be complete
        # because auto_layout() (called by figure pre-processor) has to run them
        # before aligning labels. So these are harmless no-ops.
        self._add_queued_guides()
        self._apply_title_above()
        if self._colorbar_fill:
            self._colorbar_fill.update_ticks(manual_only=True)  # only if needed
        if self._inset_parent is not None and self._inset_zoom:
            self.indicate_inset_zoom()
        super().draw(renderer, *args, **kwargs)

    def get_tightbbox(self, renderer, *args, **kwargs):
        # Perform extra post-processing steps
        # NOTE: This should be updated alongside draw(). We also cache the resulting
        # bounding box to speed up tight layout calculations (see _range_tightbbox).
        self._add_queued_guides()
        self._apply_title_above()
        if self._colorbar_fill:
            self._colorbar_fill.update_ticks(manual_only=True)  # only if needed
        if self._inset_parent is not None and self._inset_zoom:
            self.indicate_inset_zoom()
        self._tight_bbox = super().get_tightbbox(renderer, *args, **kwargs)
        return self._tight_bbox

    def get_default_bbox_extra_artists(self):
        # Further restrict artists to those with disabled clipping
        # or use the axes bounding box or patch path for clipping.
        # NOTE: Critical to ignore x and y axis, spines, and all child axes.
        # For some reason these have clipping 'enabled' but it is not respected.
        # NOTE: Matplotlib already tries to do this inside get_tightbbox() but
        # their approach fails for cartopy axes clipped by paths and not boxes.
        return [
            artist
            for artist in super().get_default_bbox_extra_artists()
            if not self._artist_fully_clipped(artist)
        ]

    def set_prop_cycle(self, *args, **kwargs):
        # Silent override. This is a strict superset of matplotlib functionality.
        # Includes both ultraplot syntax with positional arguments interpreted as
        # color arguments and oldschool matplotlib cycler(key, value) syntax.
        if len(args) == 2 and isinstance(args[0], str) and np.iterable(args[1]):
            if _pop_props({args[0]: object()}, "line"):  # if a valid line property
                kwargs = {args[0]: args[1]}  # pass as keyword argument
                args = ()
        cycle = self._active_cycle = constructor.Cycle(*args, **kwargs)
        return super().set_prop_cycle(cycle)  # set the property cycler after validation

    def _is_panel_group_member(self, other: "Axes") -> bool:
        """
        Determine if the current axes and another axes belong to the same panel group.

        Two axes belong to the same panel group if any of the following is true:
        1. One axis is the parent of the other
        2. Both axes are panels sharing the same parent

        Parameters
        ----------
        other : Axes
            The other axes to compare with

        Returns
        -------
        bool
            True if both axes belong to the same panel group, False otherwise
        """
        # Case 1: self is a panel of other (other is the parent)
        if self._panel_parent is other:
            return True

        # Case 2: other is a panel of self (self is the parent)
        if other._panel_parent is self:
            return True

        # Case 3: both are panels of the same parent
        if (
            self._panel_parent
            and other._panel_parent
            and self._panel_parent is other._panel_parent
        ):
            return True
        # Not in the same panel group
        return False

    def _label_key(self, side: str) -> str:
        """
        Map requested side name to the correct tick_params key across mpl versions.

        This accounts for the API change around Matplotlib 3.10 where labeltop/labelbottom
        became first-class tick parameter keys. For older versions, these map to
        labelright/labelleft respectively.
        """
        from packaging import version

        from ..internals import _version_mpl

        # TODO: internal deprecation warning when we drop 3.9, we need to remove this

        use_new = version.parse(str(_version_mpl)) >= version.parse("3.10")
        if side == "labeltop":
            return "labeltop" if use_new else "labelright"
        if side == "labelbottom":
            return "labelbottom" if use_new else "labelleft"
        # "labelleft" and "labelright" are stable across versions
        return side

    def _is_ticklabel_on(self, side: str) -> bool:
        """
        Check if tick labels are on for the specified sides.
        """
        # NOTE: This is a helper function to check if tick labels are on
        # for the specified sides. It returns True if any of the specified
        # sides have tick labels turned on.
        axis = self.xaxis
        if side in ["labelleft", "labelright"]:
            axis = self.yaxis
        label = "label1"
        if side in ["labelright", "labeltop"]:
            label = "label2"

        return axis.get_tick_params().get(self._label_key(side), False)

    @docstring._snippet_manager
    def inset(self, *args, **kwargs):
        """
        %(axes.inset)s
        """
        return self._add_inset_axes(*args, **kwargs)

    @docstring._snippet_manager
    def inset_axes(self, *args, **kwargs):
        """
        %(axes.inset)s
        """
        return self._add_inset_axes(*args, **kwargs)

    @override
    @docstring._snippet_manager
    def indicate_inset_zoom(self, **kwargs):
        """
        %(axes.indicate_inset)s
        """

        # Add the inset indicators
        parent = self._inset_parent
        if not parent:
            raise ValueError("This command can only be called from an inset axes.")

        kwargs.update(_pop_props(kwargs, "patch"))  # impose alternative defaults

        if not self._inset_zoom_artists:
            kwargs.setdefault("zorder", 3.5)
            kwargs.setdefault("linewidth", rc["axes.linewidth"])
            kwargs.setdefault("edgecolor", rc["axes.edgecolor"])

        xlim, ylim = self.get_xlim(), self.get_ylim()
        bounds = (xlim[0], ylim[0], xlim[1] - xlim[0], ylim[1] - ylim[0])

        return self._format_inset(bounds, parent, **kwargs)

    @docstring._snippet_manager
    def panel(self, side=None, **kwargs):
        """
        %(axes.panel)s
        """
        return self.figure._add_axes_panel(self, side, **kwargs)

    @docstring._snippet_manager
    def panel_axes(self, side=None, **kwargs):
        """
        %(axes.panel)s
        """
        return self.figure._add_axes_panel(self, side, **kwargs)

    @docstring._obfuscate_params
    @docstring._snippet_manager
    def colorbar(self, mappable, values=None, loc=None, location=None, **kwargs):
        """
        Add an inset colorbar or an outer colorbar along the edge of the axes.

        Parameters
        ----------
        %(axes.colorbar_args)s
        loc, location : int or str, default: :rc:`colorbar.loc`
            The colorbar location. Valid location keys are shown in the below table.

            .. _colorbar_table:

            ==================  =======================================
            Location            Valid keys
            ==================  =======================================
            outer left          ``'left'``, ``'l'``
            outer right         ``'right'``, ``'r'``
            outer bottom        ``'bottom'``, ``'b'``
            outer top           ``'top'``, ``'t'``
            default inset       ``'best'``, ``'inset'``, ``'i'``, ``0``
            upper right inset   ``'upper right'``, ``'ur'``, ``1``
            upper left inset    ``'upper left'``, ``'ul'``, ``2``
            lower left inset    ``'lower left'``, ``'ll'``, ``3``
            lower right inset   ``'lower right'``, ``'lr'``, ``4``
            "filled"            ``'fill'``
            ==================  =======================================

        shrink
            Alias for `length`. This is included for consistency with
            `matplotlib.figure.Figure.colorbar`.
        length \\
: float or unit-spec, default: :rc:`colorbar.length` or :rc:`colorbar.insetlength`
            The colorbar length. For outer colorbars, units are relative to the axes
            width or height (default is :rcraw:`colorbar.length`). For inset
            colorbars, floats interpreted as em-widths and strings interpreted
            by `~ultraplot.utils.units` (default is :rcraw:`colorbar.insetlength`).
        width : unit-spec, default: :rc:`colorbar.width` or :rc:`colorbar.insetwidth`
            The colorbar width. For outer colorbars, floats are interpreted as inches
            (default is :rcraw:`colorbar.width`). For inset colorbars, floats are
            interpreted as em-widths (default is :rcraw:`colorbar.insetwidth`).
            Strings are interpreted by `~ultraplot.utils.units`.
        %(axes.colorbar_space)s
            Has no visible effect if `length` is ``1``.

        Other parameters
        ----------------
        %(axes.colorbar_kwargs)s

        See also
        --------
        ultraplot.figure.Figure.colorbar
        matplotlib.figure.Figure.colorbar
        """
        # Translate location and possibly infer from orientation. Also optionally
        # infer align setting from keywords stored on object.
        orientation = kwargs.get("orientation", None)
        kwargs = guides._flush_guide_kw(mappable, "colorbar", kwargs)
        loc = _not_none(loc=loc, location=location)
        if orientation is not None:  # possibly infer loc from orientation
            if orientation not in ("vertical", "horizontal"):
                raise ValueError(
                    f"Invalid colorbar orientation {orientation!r}. Must be 'vertical' or 'horizontal'."
                )  # noqa: E501
            if loc is None:
                loc = {"vertical": "right", "horizontal": "bottom"}[orientation]
        loc = _translate_loc(loc, "colorbar", default=rc["colorbar.loc"])
        align = kwargs.pop("align", None)
        align = _translate_loc(align, "align", default="center")

        # Either draw right now or queue up for later. The queue option lets us
        # successively append objects (e.g. lines) to a colorbar artist list.
        queue = kwargs.pop("queue", False)
        if queue:
            self._register_guide("colorbar", (mappable, values), (loc, align), **kwargs)
        else:
            return self._add_colorbar(mappable, values, loc=loc, align=align, **kwargs)

    @docstring._concatenate_inherited  # also obfuscates params
    @docstring._snippet_manager
    def legend(
        self,
        handles=None,
        labels=None,
        loc=None,
        location=None,
        span: Optional[Union[int, Tuple[int, int]]] = None,
        row: Optional[int] = None,
        col: Optional[int] = None,
        rows: Optional[Union[int, Tuple[int, int]]] = None,
        cols: Optional[Union[int, Tuple[int, int]]] = None,
        **kwargs,
    ):
        """
        Add an inset legend or outer legend along the edge of the axes.

        Parameters
        ----------
        %(axes.legend_args)s
        loc, location : int or str, default: :rc:`legend.loc`
            The legend location. Valid location keys are shown in the below table.

            .. _legend_table:

            ==================  =======================================
            Location            Valid keys
            ==================  =======================================
            outer left          ``'left'``, ``'l'``
            outer right         ``'right'``, ``'r'``
            outer bottom        ``'bottom'``, ``'b'``
            outer top           ``'top'``, ``'t'``
            "best" inset        ``'best'``, ``'inset'``, ``'i'``, ``0``
            upper right inset   ``'upper right'``, ``'ur'``, ``1``
            upper left inset    ``'upper left'``, ``'ul'``, ``2``
            lower left inset    ``'lower left'``, ``'ll'``, ``3``
            lower right inset   ``'lower right'``, ``'lr'``, ``4``
            center left inset   ``'center left'``, ``'cl'``, ``5``
            center right inset  ``'center right'``, ``'cr'``, ``6``
            lower center inset  ``'lower center'``, ``'lc'``, ``7``
            upper center inset  ``'upper center'``, ``'uc'``, ``8``
            center inset        ``'center'``, ``'c'``, ``9``
            "filled"            ``'fill'``
            ==================  =======================================

        width : unit-spec, optional
            For outer legends only. The space allocated for the legend
            box. This does nothing if the :ref:`tight layout algorithm
            <ug_tight>` is active for the figure.
            %(units.in)s
        %(axes.legend_space)s

        Other parameters
        ----------------
        %(axes.legend_kwargs)s

        See also
        --------
        ultraplot.figure.Figure.legend
        matplotlib.axes.Axes.legend
        """
        # Translate location and possibly infer from orientation. Also optionally
        # infer align setting from keywords stored on object.
        kwargs = guides._flush_guide_kw(handles, "legend", kwargs)
        loc = _not_none(loc=loc, location=location)
        loc = _translate_loc(loc, "legend", default=rc["legend.loc"])
        align = kwargs.pop("align", None)
        align = _translate_loc(align, "align", default="center")

        # Either draw right now or queue up for later. Handles can be successively
        # added to a single location this way. Used for on-the-fly legends.
        queue = kwargs.pop("queue", False)
        if queue:
            self._register_guide("legend", (handles, labels), (loc, align), **kwargs)
        else:
            return self._add_legend(
                handles,
                labels,
                loc=loc,
                align=align,
                span=span,
                row=row,
                col=col,
                rows=rows,
                cols=cols,
                **kwargs,
            )

    @docstring._concatenate_inherited
    @docstring._snippet_manager
    def text(
        self,
        *args,
        border=False,
        bbox=False,
        bordercolor="w",
        borderwidth=2,
        borderinvert=False,
        borderstyle="miter",
        bboxcolor="w",
        bboxstyle="round",
        bboxalpha=0.5,
        bboxpad=None,
        **kwargs,
    ):
        """
        Add text to the axes.

        Parameters
        ----------
        x, y, [z] : float
            The coordinates for the text. `~ultraplot.axes.ThreeAxes` accept an
            optional third coordinate. If only two are provided this automatically
            redirects to the `~mpl_toolkits.mplot3d.Axes3D.text2D` method.
        s, text : str
            The string for the text.
        %(axes.transform)s

        Other parameters
        ----------------
        border : bool, default: False
            Whether to draw border around text.
        borderwidth : float, default: 2
            The width of the text border.
        bordercolor : color-spec, default: 'w'
            The color of the text border.
        borderinvert : bool, optional
            If ``True``, the text and border colors are swapped.
        borderstyle : {'miter', 'round', 'bevel'}, optional
            The `line join style \\
<https://matplotlib.org/stable/gallery/lines_bars_and_markers/joinstyle.html>`__
            used for the border.
        bbox : bool, default: False
            Whether to draw a bounding box around text.
        bboxcolor : color-spec, default: 'w'
            The color of the text bounding box.
        bboxstyle : boxstyle, default: 'round'
            The style of the bounding box.
        bboxalpha : float, default: 0.5
            The alpha for the bounding box.
        bboxpad : float, default: :rc:`title.bboxpad`
            The padding for the bounding box.
        %(artist.text)s

        **kwargs
            Passed to `matplotlib.axes.Axes.text`.

        See also
        --------
        matplotlib.axes.Axes.text
        """
        # Translate positional args
        # Audo-redirect to text2D for 3D axes if not enough arguments passed
        # NOTE: The transform must be passed positionally for 3D axes with 2D coords
        keys = "xy"
        func = super().text
        if self._name == "three":
            if len(args) >= 4 or "z" in kwargs:
                keys += "z"
            else:
                func = self.text2D
        keys = (*keys, ("s", "text"), "transform")
        args, kwargs = _kwargs_to_args(keys, *args, **kwargs)
        *args, transform = args
        if any(arg is None for arg in args):
            raise TypeError("Missing required positional argument.")
        if transform is None:
            transform = self.transData
        else:
            transform = self._get_transform(transform)
        with warnings.catch_warnings():  # ignore duplicates (internal issues?)
            warnings.simplefilter("ignore", warnings.UltraPlotWarning)
            kwargs.update(_pop_props(kwargs, "text"))

        # Update the text object using a monkey patch
        obj = func(*args, transform=transform, **kwargs)
        obj.update = labels._update_label.__get__(obj)
        obj.update(
            {
                "border": border,
                "bordercolor": bordercolor,
                "borderinvert": borderinvert,
                "borderwidth": borderwidth,
                "borderstyle": borderstyle,
                "bbox": bbox,
                "bboxcolor": bboxcolor,
                "bboxstyle": bboxstyle,
                "bboxalpha": bboxalpha,
                "bboxpad": bboxpad,
            }
        )
        return obj

    def _toggle_spines(self, spines: Union[bool, Iterable, str]):
        """
        Turns spines on or off depending on input. Spines can be a list such as ['left', 'right'] etc
        """
        if spines:
            match spines:
                case str():
                    toggle_spines = {spines: True}
                case IterableType():
                    toggle_spines = {spine: True for spine in spines}
                case bool():
                    toggler = spines
                    toggle_spines = {spine: toggler for spine in self.spines}
                case _:
                    raise ValueError(
                        f"Invalid input for spines. Received {type(spines)} expecting iterable, string or boolean"
                    )
            for side, spine in self.spines.items():
                spine.set_visible(False)
                if side in toggle_spines:
                    spine.set_visible(True)
        else:
            for spine in self.spines.values():
                spine.set_visible(False)

    def _iter_axes(self, hidden=False, children=False, panels=True):
        """
        Return a list of visible axes, panel axes, and child axes of both.

        Parameters
        ----------
        hidden : bool, optional
            Whether to include "hidden" panels.
        children : bool, optional
            Whether to include children. Note this now includes "twin" axes.
        panels : bool or str or sequence of str, optional
            Whether to include panels or the panels to include.
        """
        # Parse panels
        if panels is False:
            panels = ()
        elif panels is True or panels is None:
            panels = ("left", "right", "bottom", "top")
        elif isinstance(panels, str):
            panels = (panels,)
        if not set(panels) <= {"left", "right", "bottom", "top"}:
            raise ValueError(f"Invalid sides {panels!r}.")
        # Iterate
        axs = (self, *(ax for side in panels for ax in self._panel_dict[side]))
        for iax in axs:
            if not hidden and iax._panel_hidden:
                continue  # ignore hidden panel and its colorbar/legend child
            iaxs = (iax, *(iax.child_axes if children else ()))
            for jax in iaxs:
                if not jax.get_visible():
                    continue  # safety first
                yield jax

    @property
    def number(self):
        """
        The axes number. This controls the order of a-b-c labels and the
        order of appearance in the :class:`~ultraplot.gridspec.SubplotGrid` returned
        by `~ultraplot.figure.Figure.subplots`.
        """
        return self._number

    @number.setter
    def number(self, num):
        if num is None or isinstance(num, Integral) and num > 0:
            self._number = num
        else:
            raise ValueError(f"Invalid number {num!r}. Must be integer >=1.")


# Apply signature obfuscation after storing previous signature
# NOTE: This is needed for __init__
Axes._format_signatures = {Axes: inspect.signature(Axes.format)}
Axes.format = docstring._obfuscate_kwargs(Axes.format)


def _get_pos_from_locator(
    loc: str,
    x_pad: float,
    y_pad: float,
) -> tuple[float, float]:
    """
    Helper function to map string locators to x and y coordinates.
    """
    # Set x-coordinate based on horizontal position
    x, y = 0, 1
    match loc:
        case "left" | "outer left":
            x = 0
        case "center":
            x = 0.5
        case "right" | "outer right":
            x = 1
        case "upper center" | "lower center":
            x = 0.5
        case "upper left" | "lower left":
            x = x_pad
        case "upper right" | "lower right":
            x = 1 - x_pad

    # Set y-coordinate based on vertical position
    match loc:
        case "upper left" | "upper right" | "upper center":
            y = 1 - y_pad
        case "lower left" | "lower right" | "lower center":
            y = y_pad
    return (x, y)


def _get_axis_for(
    labelloc: str,
    loc: str,
    *,
    ax: Axes,
    orientation: str,
) -> Axes:
    """
    Helper function to determine the axis for a label.
    Particularly used for colorbars but can be used for other purposes
    """

    def get_short_or_long(which):
        if hasattr(ax, f"{which}_axis"):
            return getattr(ax, f"{which}_axis")
        return getattr(ax, f"_{which}_axis")()

    short = get_short_or_long("short")
    long = get_short_or_long("long")

    label_axis = None
    # For fill or none, we use default locations.
    # This would be the long axis for horizontal orientation
    # and the short axis for vertical orientation.
    if not isinstance(labelloc, str):
        label_axis = long
    # if the orientation is horizontal,
    # the short axis is the y-axis, and the long axis is the
    # x-axis. The inverse holds true for vertical orientation.
    elif "left" in labelloc or "right" in labelloc:
        # Vertical label, use short axis
        label_axis = short if orientation == "horizontal" else long
    elif "top" in labelloc or "bottom" in labelloc:
        label_axis = long if orientation == "horizontal" else short

    if label_axis is None:
        raise ValueError(
            f"Could not determine label axis for {labelloc=}, with {orientation=}."
        )
    return label_axis


def _determine_label_rotation(
    labelrotation: str | Number,
    labelloc: str,
    orientation: str,
    kw_label: MutableMapping,
):
    """
    Note we update kw_label in place.
    """
    if labelrotation == "auto":
        # Automatically determine label rotation based on location, we also align the label to make it look
        # extra nice for 90 degree rotations
        if orientation == "horizontal":
            if labelloc in ["left", "right"]:
                labelrotation = 90 if "left" in labelloc else -90
                kw_label["ha"] = "center"
                kw_label["va"] = "bottom" if "left" in labelloc else "bottom"
            elif labelloc in ["top", "bottom"]:
                labelrotation = 0
                kw_label["ha"] = "center"
                kw_label["va"] = "bottom" if "top" in labelloc else "top"
        elif orientation == "vertical":
            if labelloc in ["left", "right"]:
                labelrotation = 90 if "left" in labelloc else -90
                kw_label["ha"] = "center"
                kw_label["va"] = "bottom" if "left" in labelloc else "bottom"
            elif labelloc in ["top", "bottom"]:
                labelrotation = 0
                kw_label["ha"] = "center"
                kw_label["va"] = "bottom" if "top" in labelloc else "top"

    if not isinstance(labelrotation, (int, float)):
        raise ValueError(
            f"Label rotation must be a number or 'auto', got {labelrotation!r}."
        )
    kw_label.update({"rotation": labelrotation})