text: """
  A module for converting numbers or color arguments to *RGB* or *RGBA*.
  
  *RGB* and *RGBA* are sequences of, respectively, 3 or 4 floats in the
  range 0-1.
  
  This module includes functions and classes for color specification
  conversions, and for mapping numbers to colors in a 1-D array of colors called
  a colormap.
  
  Mapping data onto colors using a colormap typically involves two steps:
  a data array is first mapped onto the range 0-1 using a subclass of
  :class:`Normalize`, then this number is mapped to a color using
  a subclass of :class:`Colormap`.  Two are provided here:
  :class:`LinearSegmentedColormap`, which uses piecewise-linear interpolation
  to define colormaps, and :class:`ListedColormap`, which makes a colormap
  from a list of colors.
  
  .. seealso::
  
    :doc:`/tutorials/colors/colormap-manipulation` for examples of how to
    make colormaps and
  
    :doc:`/tutorials/colors/colormaps` for a list of built-in colormaps.
  
    :doc:`/tutorials/colors/colormapnorms` for more details about data
    normalization
  
    More colormaps are available at palettable_.
  
  The module also provides functions for checking whether an object can be
  interpreted as a color (:func:`is_color_like`), for converting such an object
  to an RGBA tuple (:func:`to_rgba`) or to an HTML-like hex string in the
  `#rrggbb` format (:func:`to_hex`), and a sequence of colors to an `(n, 4)`
  RGBA array (:func:`to_rgba_array`).  Caching is used for efficiency.
  
  Matplotlib recognizes the following formats to specify a color:
  
  * an RGB or RGBA (red, green, blue, alpha) tuple of float values in closed
    interval ``[0, 1]`` (e.g., ``(0.1, 0.2, 0.5)`` or ``(0.1, 0.2, 0.5, 0.3)``);
  * a hex RGB or RGBA string (e.g., ``'#0f0f0f'`` or ``'#0f0f0f80'``;
    case-insensitive);
  * a shorthand hex RGB or RGBA string, equivalent to the hex RGB or RGBA
    string obtained by duplicating each character, (e.g., ``'#abc'``, equivalent
    to ``'#aabbcc'``, or ``'#abcd'``, equivalent to ``'#aabbccdd'``;
    case-insensitive);
  * a string representation of a float value in ``[0, 1]`` inclusive for gray
    level (e.g., ``'0.5'``);
  * one of ``{'b', 'g', 'r', 'c', 'm', 'y', 'k', 'w'}``, they are the single
    character short-hand notations for blue, green, red, cyan, magenta, yellow,
    black, and white.
  * a X11/CSS4 color name (case-insensitive);
  * a name from the `xkcd color survey`_, prefixed with ``'xkcd:'`` (e.g.,
    ``'xkcd:sky blue'``; case insensitive);
  * one of the Tableau Colors from the 'T10' categorical palette (the default
    color cycle): ``{'tab:blue', 'tab:orange', 'tab:green', 'tab:red',
    'tab:purple', 'tab:brown', 'tab:pink', 'tab:gray', 'tab:olive', 'tab:cyan'}``
    (case-insensitive);
  * a "CN" color spec, i.e. `'C'` followed by a number, which is an index into
    the default property cycle (``matplotlib.rcParams['axes.prop_cycle']``); the
    indexing is intended to occur at rendering time, and defaults to black if the
    cycle does not include color.
  
  .. _palettable: https://jiffyclub.github.io/palettable/
  .. _xkcd color survey: https://xkcd.com/color/rgb/
  """
  
  from collections.abc import Sized
  import functools
  import itertools
  import re
  
  import numpy as np
  import matplotlib.cbook as cbook
  from matplotlib import docstring
  from ._color_data import BASE_COLORS, TABLEAU_COLORS, CSS4_COLORS, XKCD_COLORS
  
  
  class _ColorMapping(dict):
      def __init__(self, mapping):
          super().__init__(mapping)
          self.cache = {}
  
      def __setitem__(self, key, value):
          super().__setitem__(key, value)
          self.cache.clear()
  
      def __delitem__(self, key):
          super().__delitem__(key)
          self.cache.clear()
  
  
  _colors_full_map = {}
  # Set by reverse priority order.
  _colors_full_map.update(XKCD_COLORS)
  _colors_full_map.update({k.replace('grey', 'gray'): v
                           for k, v in XKCD_COLORS.items()
                           if 'grey' in k})
  _colors_full_map.update(CSS4_COLORS)
  _colors_full_map.update(TABLEAU_COLORS)
  _colors_full_map.update({k.replace('gray', 'grey'): v
                           for k, v in TABLEAU_COLORS.items()
                           if 'gray' in k})
  _colors_full_map.update(BASE_COLORS)
  _colors_full_map = _ColorMapping(_colors_full_map)
  
  
  def get_named_colors_mapping():
      """Return the global mapping of names to named colors."""
      return _colors_full_map
  
  
  def _sanitize_extrema(ex):
      if ex is None:
          return ex
      try:
          ret = ex.item()
      except AttributeError:
          ret = float(ex)
      return ret
  
  
  def _is_nth_color(c):
      """Return whether *c* can be interpreted as an item in the color cycle."""
      return isinstance(c, str) and re.match(r"\AC[0-9]+\Z", c)
  
  
  def is_color_like(c):
      """Return whether *c* can be interpreted as an RGB(A) color."""
      # Special-case nth color syntax because it cannot be parsed during setup.
      if _is_nth_color(c):
          return True
      try:
          to_rgba(c)
      except ValueError:
          return False
      else:
          return True
  
  
  def same_color(c1, c2):
      """
      Compare two colors to see if they are the same.
  
      Parameters
      ----------
      c1, c2 : Matplotlib colors
  
      Returns
      -------
      bool
          ``True`` if *c1* and *c2* are the same color, otherwise ``False``.
      """
      return (to_rgba_array(c1) == to_rgba_array(c2)).all()
  
  
  def to_rgba(c, alpha=None):
      """
      Convert *c* to an RGBA color.
  
      Parameters
      ----------
      c : Matplotlib color or ``np.ma.masked``
  
      alpha : scalar, optional
          If *alpha* is not ``None``, it forces the alpha value, except if *c* is
          ``"none"`` (case-insensitive), which always maps to ``(0, 0, 0, 0)``.
  
      Returns
      -------
      tuple
          Tuple of ``(r, g, b, a)`` scalars.
      """
      # Special-case nth color syntax because it should not be cached.
      if _is_nth_color(c):
          from matplotlib import rcParams
          prop_cycler = rcParams['axes.prop_cycle']
          colors = prop_cycler.by_key().get('color', ['k'])
          c = colors[int(c[1:]) % len(colors)]
      try:
          rgba = _colors_full_map.cache[c, alpha]
      except (KeyError, TypeError):  # Not in cache, or unhashable.
          rgba = None
      if rgba is None:  # Suppress exception chaining of cache lookup failure.
          rgba = _to_rgba_no_colorcycle(c, alpha)
          try:
              _colors_full_map.cache[c, alpha] = rgba
          except TypeError:
              pass
      return rgba
  
  
  def _to_rgba_no_colorcycle(c, alpha=None):
      """Convert *c* to an RGBA color, with no support for color-cycle syntax.
  
      If *alpha* is not ``None``, it forces the alpha value, except if *c* is
      ``"none"`` (case-insensitive), which always maps to ``(0, 0, 0, 0)``.
      """
      orig_c = c
      if c is np.ma.masked:
          return (0., 0., 0., 0.)
      if isinstance(c, str):
          if c.lower() == "none":
              return (0., 0., 0., 0.)
          # Named color.
          try:
              # This may turn c into a non-string, so we check again below.
              c = _colors_full_map[c]
          except KeyError:
              try:
                  c = _colors_full_map[c.lower()]
              except KeyError:
                  pass
              else:
                  if len(orig_c) == 1:
                      cbook.warn_deprecated(
                          "3.1", message="Support for uppercase "
                          "single-letter colors is deprecated since Matplotlib "
                          "%(since)s and will be removed %(removal)s; please "
                          "use lowercase instead.")
      if isinstance(c, str):
          # hex color in #rrggbb format.
          match = re.match(r"\A#[a-fA-F0-9]{6}\Z", c)
          if match:
              return (tuple(int(n, 16) / 255
                            for n in [c[1:3], c[3:5], c[5:7]])
                      + (alpha if alpha is not None else 1.,))
          # hex color in #rgb format, shorthand for #rrggbb.
          match = re.match(r"\A#[a-fA-F0-9]{3}\Z", c)
          if match:
              return (tuple(int(n, 16) / 255
                            for n in [c[1]*2, c[2]*2, c[3]*2])
                      + (alpha if alpha is not None else 1.,))
          # hex color with alpha in #rrggbbaa format.
          match = re.match(r"\A#[a-fA-F0-9]{8}\Z", c)
          if match:
              color = [int(n, 16) / 255
                       for n in [c[1:3], c[3:5], c[5:7], c[7:9]]]
              if alpha is not None:
                  color[-1] = alpha
              return tuple(color)
          # hex color with alpha in #rgba format, shorthand for #rrggbbaa.
          match = re.match(r"\A#[a-fA-F0-9]{4}\Z", c)
          if match:
              color = [int(n, 16) / 255
                       for n in [c[1]*2, c[2]*2, c[3]*2, c[4]*2]]
              if alpha is not None:
                  color[-1] = alpha
              return tuple(color)
          # string gray.
          try:
              c = float(c)
          except ValueError:
              pass
          else:
              if not (0 <= c <= 1):
                  raise ValueError(
                      f"Invalid string grayscale value {orig_c!r}. "
                      f"Value must be within 0-1 range")
              return c, c, c, alpha if alpha is not None else 1.
          raise ValueError(f"Invalid RGBA argument: {orig_c!r}")
      # tuple color.
      c = np.array(c)
      if not np.can_cast(c.dtype, float, "same_kind") or c.ndim != 1:
          # Test the dtype explicitly as `map(float, ...)`, `np.array(...,
          # float)` and `np.array(...).astype(float)` all convert "0.5" to 0.5.
          # Test dimensionality to reject single floats.
          raise ValueError(f"Invalid RGBA argument: {orig_c!r}")
      # Return a tuple to prevent the cached value from being modified.
      c = tuple(c.astype(float))
      if len(c) not in [3, 4]:
          raise ValueError("RGBA sequence should have length 3 or 4")
      if len(c) == 3 and alpha is None:
          alpha = 1
      if alpha is not None:
          c = c[:3] + (alpha,)
      if any(elem < 0 or elem > 1 for elem in c):
          raise ValueError("RGBA values should be within 0-1 range")
      return c
  
  
  def to_rgba_array(c, alpha=None):
      """Convert *c* to a (n, 4) array of RGBA colors.
  
      If *alpha* is not ``None``, it forces the alpha value.  If *c* is
      ``"none"`` (case-insensitive) or an empty list, an empty array is returned.
      If *c* is a masked array, an ndarray is returned with a (0, 0, 0, 0)
      row for each masked value or row in *c*.
      """
      # Special-case inputs that are already arrays, for performance.  (If the
      # array has the wrong kind or shape, raise the error during one-at-a-time
      # conversion.)
      if (isinstance(c, np.ndarray) and c.dtype.kind in "if"
              and c.ndim == 2 and c.shape[1] in [3, 4]):
          mask = c.mask.any(axis=1) if np.ma.is_masked(c) else None
          c = np.ma.getdata(c)
          if c.shape[1] == 3:
              result = np.column_stack([c, np.zeros(len(c))])
              result[:, -1] = alpha if alpha is not None else 1.
          elif c.shape[1] == 4:
              result = c.copy()
              if alpha is not None:
                  result[:, -1] = alpha
          if mask is not None:
              result[mask] = 0
          if np.any((result < 0) | (result > 1)):
              raise ValueError("RGBA values should be within 0-1 range")
          return result
      # Handle single values.
      # Note that this occurs *after* handling inputs that are already arrays, as
      # `to_rgba(c, alpha)` (below) is expensive for such inputs, due to the need
      # to format the array in the ValueError message(!).
      if cbook._str_lower_equal(c, "none"):
          return np.zeros((0, 4), float)
      try:
          return np.array([to_rgba(c, alpha)], float)
      except (ValueError, TypeError):
          pass
  
      # Convert one at a time.
      if isinstance(c, str):
          # Single string as color sequence.
          # This is deprecated and will be removed in the future.
          try:
              result = np.array([to_rgba(cc, alpha) for cc in c])
          except ValueError:
              raise ValueError(
                  "'%s' is neither a valid single color nor a color sequence "
                  "consisting of single character color specifiers such as "
                  "'rgb'. Note also that the latter is deprecated." % c)
          else:
              cbook.warn_deprecated("3.2", message="Using a string of single "
                                    "character colors as a color sequence is "
                                    "deprecated. Use an explicit list instead.")
              return result
  
      if len(c) == 0:
          return np.zeros((0, 4), float)
      else:
          return np.array([to_rgba(cc, alpha) for cc in c])
  
  
  def to_rgb(c):
      """Convert *c* to an RGB color, silently dropping the alpha channel."""
      return to_rgba(c)[:3]
  
  
  def to_hex(c, keep_alpha=False):
      """
      Convert *c* to a hex color.
  
      Uses the ``#rrggbb`` format if *keep_alpha* is False (the default),
      ``#rrggbbaa`` otherwise.
      """
      c = to_rgba(c)
      if not keep_alpha:
          c = c[:3]
      return "#" + "".join(format(int(round(val * 255)), "02x") for val in c)
  
  
  ### Backwards-compatible color-conversion API
  
  
  cnames = CSS4_COLORS
  hexColorPattern = re.compile(r"\A#[a-fA-F0-9]{6}\Z")
  rgb2hex = to_hex
  hex2color = to_rgb
  
  
  class ColorConverter:
      """
      This class is only kept for backwards compatibility.
  
      Its functionality is entirely provided by module-level functions.
      """
      colors = _colors_full_map
      cache = _colors_full_map.cache
      to_rgb = staticmethod(to_rgb)
      to_rgba = staticmethod(to_rgba)
      to_rgba_array = staticmethod(to_rgba_array)
  
  
  colorConverter = ColorConverter()
  
  
  ### End of backwards-compatible color-conversion API
  
  
  def _create_lookup_table(N, data, gamma=1.0):
      r"""Create an *N* -element 1-d lookup table.
  
      This assumes a mapping :math:`f : [0, 1] \rightarrow [0, 1]`. The returned
      data is an array of N values :math:`y = f(x)` where x is sampled from
      [0, 1].
  
      By default (*gamma* = 1) x is equidistantly sampled from [0, 1]. The
      *gamma* correction factor :math:`\gamma` distorts this equidistant
      sampling by :math:`x \rightarrow x^\gamma`.
  
      Parameters
      ----------
      N : int
          The number of elements of the created lookup table.
          This must be N >= 1.
      data : Mx3 array-like or callable
          Defines the mapping :math:`f`.
  
          If a Mx3 array-like, the rows define values (x, y0, y1). The x values
          must start with x=0, end with x=1, and all x values be in increasing
          order.
  
          A value between :math:`x_i` and :math:`x_{i+1}` is mapped to the range
          :math:`y^1_{i-1} \ldots y^0_i` by linear interpolation.
  
          For the simple case of a y-continuous mapping, y0 and y1 are identical.
  
          The two values of y are to allow for discontinuous mapping functions.
          E.g. a sawtooth with a period of 0.2 and an amplitude of 1 would be::
  
              [(0, 1, 0), (0.2, 1, 0), (0.4, 1, 0), ..., [(1, 1, 0)]
  
          In the special case of ``N == 1``, by convention the returned value
          is y0 for x == 1.
  
          If *data* is a callable, it must accept and return numpy arrays::
  
             data(x : ndarray) -> ndarray
  
          and map values between 0 - 1 to 0 - 1.
      gamma : float
          Gamma correction factor for input distribution x of the mapping.
  
          See also https://en.wikipedia.org/wiki/Gamma_correction.
  
      Returns
      -------
      lut : array
          The lookup table where ``lut[x * (N-1)]`` gives the closest value
          for values of x between 0 and 1.
  
      Notes
      -----
      This function is internally used for `.LinearSegmentedColormaps`.
      """
  
      if callable(data):
          xind = np.linspace(0, 1, N) ** gamma
          lut = np.clip(np.array(data(xind), dtype=float), 0, 1)
          return lut
  
      try:
          adata = np.array(data)
      except Exception:
          raise TypeError("data must be convertible to an array")
      shape = adata.shape
      if len(shape) != 2 or shape[1] != 3:
          raise ValueError("data must be nx3 format")
  
      x = adata[:, 0]
      y0 = adata[:, 1]
      y1 = adata[:, 2]
  
      if x[0] != 0. or x[-1] != 1.0:
          raise ValueError(
              "data mapping points must start with x=0 and end with x=1")
      if (np.diff(x) < 0).any():
          raise ValueError("data mapping points must have x in increasing order")
      # begin generation of lookup table
      if N == 1:
          # convention: use the y = f(x=1) value for a 1-element lookup table
          lut = np.array(y0[-1])
      else:
          x = x * (N - 1)
          xind = (N - 1) * np.linspace(0, 1, N) ** gamma
          ind = np.searchsorted(x, xind)[1:-1]
  
          distance = (xind[1:-1] - x[ind - 1]) / (x[ind] - x[ind - 1])
          lut = np.concatenate([
              [y1[0]],
              distance * (y0[ind] - y1[ind - 1]) + y1[ind - 1],
              [y0[-1]],
          ])
      # ensure that the lut is confined to values between 0 and 1 by clipping it
      return np.clip(lut, 0.0, 1.0)
  
  
  @cbook.deprecated("3.2",
                    addendum='This is not considered public API any longer.')
  @docstring.copy(_create_lookup_table)
  def makeMappingArray(N, data, gamma=1.0):
      return _create_lookup_table(N, data, gamma)
  
  
  class Colormap:
      """
      Baseclass for all scalar to RGBA mappings.
  
      Typically Colormap instances are used to convert data values (floats) from
      the interval ``[0, 1]`` to the RGBA color that the respective Colormap
      represents. For scaling of data into the ``[0, 1]`` interval see
      :class:`matplotlib.colors.Normalize`. It is worth noting that
      :class:`matplotlib.cm.ScalarMappable` subclasses make heavy use of this
      ``data->normalize->map-to-color`` processing chain.
  
      """
      def __init__(self, name, N=256):
          """
          Parameters
          ----------
          name : str
              The name of the colormap.
          N : int
              The number of rgb quantization levels.
  
          """
          self.name = name
          self.N = int(N)  # ensure that N is always int
          self._rgba_bad = (0.0, 0.0, 0.0, 0.0)  # If bad, don't paint anything.
          self._rgba_under = None
          self._rgba_over = None
          self._i_under = self.N
          self._i_over = self.N + 1
          self._i_bad = self.N + 2
          self._isinit = False
  
          #: When this colormap exists on a scalar mappable and colorbar_extend
          #: is not False, colorbar creation will pick up ``colorbar_extend`` as
          #: the default value for the ``extend`` keyword in the
          #: :class:`matplotlib.colorbar.Colorbar` constructor.
          self.colorbar_extend = False
  
      def __call__(self, X, alpha=None, bytes=False):
          """
          Parameters
          ----------
          X : scalar, ndarray
              The data value(s) to convert to RGBA.
              For floats, X should be in the interval ``[0.0, 1.0]`` to
              return the RGBA values ``X*100`` percent along the Colormap line.
              For integers, X should be in the interval ``[0, Colormap.N)`` to
              return RGBA values *indexed* from the Colormap with index ``X``.
          alpha : float, None
              Alpha must be a scalar between 0 and 1, or None.
          bytes : bool
              If False (default), the returned RGBA values will be floats in the
              interval ``[0, 1]`` otherwise they will be uint8s in the interval
              ``[0, 255]``.
  
          Returns
          -------
          Tuple of RGBA values if X is scalar, otherwise an array of
          RGBA values with a shape of ``X.shape + (4, )``.
  
          """
          # See class docstring for arg/kwarg documentation.
          if not self._isinit:
              self._init()
          mask_bad = None
          if np.ma.is_masked(X):
              mask_bad = X.mask
          elif np.any(np.isnan(X)):
              # mask nan's
              mask_bad = np.isnan(X)
  
          xa = np.array(X, copy=True)
          # Fill bad values to avoid warnings
          # in the boolean comparisons below.
          if mask_bad is not None:
              xa[mask_bad] = 0.
  
          # Calculations with native byteorder are faster, and avoid a
          # bug that otherwise can occur with putmask when the last
          # argument is a numpy scalar.
          if not xa.dtype.isnative:
              xa = xa.byteswap().newbyteorder()
  
          if xa.dtype.kind == "f":
              xa *= self.N
              # Negative values are out of range, but astype(int) would truncate
              # them towards zero.
              xa[xa < 0] = -1
              # xa == 1 (== N after multiplication) is not out of range.
              xa[xa == self.N] = self.N - 1
              # Avoid converting large positive values to negative integers.
              np.clip(xa, -1, self.N, out=xa)
              xa = xa.astype(int)
          # Set the over-range indices before the under-range;
          # otherwise the under-range values get converted to over-range.
          xa[xa > self.N - 1] = self._i_over
          xa[xa < 0] = self._i_under
          if mask_bad is not None:
              xa[mask_bad] = self._i_bad
  
          if bytes:
              lut = (self._lut * 255).astype(np.uint8)
          else:
              lut = self._lut.copy()  # Don't let alpha modify original _lut.
  
          if alpha is not None:
              alpha = np.clip(alpha, 0, 1)
              if bytes:
                  alpha = int(alpha * 255)
              if (lut[-1] == 0).all():
                  lut[:-1, -1] = alpha
                  # All zeros is taken as a flag for the default bad
                  # color, which is no color--fully transparent.  We
                  # don't want to override this.
              else:
                  lut[:, -1] = alpha
                  # If the bad value is set to have a color, then we
                  # override its alpha just as for any other value.
  
          rgba = lut.take(xa, axis=0, mode='clip')
          if not np.iterable(X):
              # Return a tuple if the input was a scalar
              rgba = tuple(rgba)
          return rgba
  
      def __copy__(self):
          """Create new object with the same class, update attributes
          """
          cls = self.__class__
          cmapobject = cls.__new__(cls)
          cmapobject.__dict__.update(self.__dict__)
          if self._isinit:
              cmapobject._lut = np.copy(self._lut)
          return cmapobject
  
      def set_bad(self, color='k', alpha=None):
          """Set color to be used for masked values.
          """
          self._rgba_bad = to_rgba(color, alpha)
          if self._isinit:
              self._set_extremes()
  
      def set_under(self, color='k', alpha=None):
          """
          Set the color for low out-of-range values when ``norm.clip = False``.
          """
          self._rgba_under = to_rgba(color, alpha)
          if self._isinit:
              self._set_extremes()
  
      def set_over(self, color='k', alpha=None):
          """
          Set the color for high out-of-range values when ``norm.clip = False``.
          """
          self._rgba_over = to_rgba(color, alpha)
          if self._isinit:
              self._set_extremes()
  
      def _set_extremes(self):
          if self._rgba_under:
              self._lut[self._i_under] = self._rgba_under
          else:
              self._lut[self._i_under] = self._lut[0]
          if self._rgba_over:
              self._lut[self._i_over] = self._rgba_over
          else:
              self._lut[self._i_over] = self._lut[self.N - 1]
          self._lut[self._i_bad] = self._rgba_bad
  
      def _init(self):
          """Generate the lookup table, self._lut"""
          raise NotImplementedError("Abstract class only")
  
      def is_gray(self):
          if not self._isinit:
              self._init()
          return (np.all(self._lut[:, 0] == self._lut[:, 1]) and
                  np.all(self._lut[:, 0] == self._lut[:, 2]))
  
      def _resample(self, lutsize):
          """
          Return a new color map with *lutsize* entries.
          """
          raise NotImplementedError()
  
      def reversed(self, name=None):
          """
          Make a reversed instance of the Colormap.
  
          .. note:: Function not implemented for base class.
  
          Parameters
          ----------
          name : str, optional
              The name for the reversed colormap. If it's None the
              name will be the name of the parent colormap + "_r".
  
          See Also
          --------
          LinearSegmentedColormap.reversed
          ListedColormap.reversed
          """
          raise NotImplementedError()
  
  
  class LinearSegmentedColormap(Colormap):
      """
      Colormap objects based on lookup tables using linear segments.
  
      The lookup table is generated using linear interpolation for each
      primary color, with the 0-1 domain divided into any number of
      segments.
      """
  
      def __init__(self, name, segmentdata, N=256, gamma=1.0):
          """
          Create color map from linear mapping segments
  
          segmentdata argument is a dictionary with a red, green and blue
          entries. Each entry should be a list of *x*, *y0*, *y1* tuples,
          forming rows in a table. Entries for alpha are optional.
  
          Example: suppose you want red to increase from 0 to 1 over
          the bottom half, green to do the same over the middle half,
          and blue over the top half.  Then you would use::
  
              cdict = {'red':   [(0.0,  0.0, 0.0),
                                 (0.5,  1.0, 1.0),
                                 (1.0,  1.0, 1.0)],
  
                       'green': [(0.0,  0.0, 0.0),
                                 (0.25, 0.0, 0.0),
                                 (0.75, 1.0, 1.0),
                                 (1.0,  1.0, 1.0)],
  
                       'blue':  [(0.0,  0.0, 0.0),
                                 (0.5,  0.0, 0.0),
                                 (1.0,  1.0, 1.0)]}
  
          Each row in the table for a given color is a sequence of
          *x*, *y0*, *y1* tuples.  In each sequence, *x* must increase
          monotonically from 0 to 1.  For any input value *z* falling
          between *x[i]* and *x[i+1]*, the output value of a given color
          will be linearly interpolated between *y1[i]* and *y0[i+1]*::
  
              row i:   x  y0  y1
                             /
                            /
              row i+1: x  y0  y1
  
          Hence y0 in the first row and y1 in the last row are never used.
  
          See Also
          --------
          LinearSegmentedColormap.from_list
              Static method; factory function for generating a smoothly-varying
              LinearSegmentedColormap.
  
          makeMappingArray
              For information about making a mapping array.
          """
          # True only if all colors in map are identical; needed for contouring.
          self.monochrome = False
          Colormap.__init__(self, name, N)
          self._segmentdata = segmentdata
          self._gamma = gamma
  
      def _init(self):
          self._lut = np.ones((self.N + 3, 4), float)
          self._lut[:-3, 0] = _create_lookup_table(
              self.N, self._segmentdata['red'], self._gamma)
          self._lut[:-3, 1] = _create_lookup_table(
              self.N, self._segmentdata['green'], self._gamma)
          self._lut[:-3, 2] = _create_lookup_table(
              self.N, self._segmentdata['blue'], self._gamma)
          if 'alpha' in self._segmentdata:
              self._lut[:-3, 3] = _create_lookup_table(
                  self.N, self._segmentdata['alpha'], 1)
          self._isinit = True
          self._set_extremes()
  
      def set_gamma(self, gamma):
          """
          Set a new gamma value and regenerate color map.
          """
          self._gamma = gamma
          self._init()
  
      @staticmethod
      def from_list(name, colors, N=256, gamma=1.0):
          """
          Make a linear segmented colormap with *name* from a sequence
          of *colors* which evenly transitions from colors[0] at val=0
          to colors[-1] at val=1.  *N* is the number of rgb quantization
          levels.
          Alternatively, a list of (value, color) tuples can be given
          to divide the range unevenly.
          """
  
          if not np.iterable(colors):
              raise ValueError('colors must be iterable')
  
          if (isinstance(colors[0], Sized) and len(colors[0]) == 2
                  and not isinstance(colors[0], str)):
              # List of value, color pairs
              vals, colors = zip(*colors)
          else:
              vals = np.linspace(0, 1, len(colors))
  
          cdict = dict(red=[], green=[], blue=[], alpha=[])
          for val, color in zip(vals, colors):
              r, g, b, a = to_rgba(color)
              cdict['red'].append((val, r, r))
              cdict['green'].append((val, g, g))
              cdict['blue'].append((val, b, b))
              cdict['alpha'].append((val, a, a))
  
          return LinearSegmentedColormap(name, cdict, N, gamma)
  
      def _resample(self, lutsize):
          """
          Return a new color map with *lutsize* entries.
          """
          return LinearSegmentedColormap(self.name, self._segmentdata, lutsize)
  
      # Helper ensuring picklability of the reversed cmap.
      @staticmethod
      def _reverser(func, x):
          return func(1 - x)
  
      def reversed(self, name=None):
          """
          Make a reversed instance of the Colormap.
  
          Parameters
          ----------
          name : str, optional
              The name for the reversed colormap. If it's None the
              name will be the name of the parent colormap + "_r".
  
          Returns
          -------
          LinearSegmentedColormap
              The reversed colormap.
          """
          if name is None:
              name = self.name + "_r"
  
          # Using a partial object keeps the cmap picklable.
          data_r = {key: (functools.partial(self._reverser, data)
                          if callable(data) else
                          [(1.0 - x, y1, y0) for x, y0, y1 in reversed(data)])
                    for key, data in self._segmentdata.items()}
  
          return LinearSegmentedColormap(name, data_r, self.N, self._gamma)
  
  
  class ListedColormap(Colormap):
      """
      Colormap object generated from a list of colors.
  
      This may be most useful when indexing directly into a colormap,
      but it can also be used to generate special colormaps for ordinary
      mapping.
  
      Parameters
      ----------
      colors : list, array
          List of Matplotlib color specifications, or an equivalent Nx3 or Nx4
          floating point array (*N* rgb or rgba values).
      name : str, optional
          String to identify the colormap.
      N : int, optional
          Number of entries in the map. The default is *None*, in which case
          there is one colormap entry for each element in the list of colors.
          If ::
  
              N < len(colors)
  
          the list will be truncated at *N*. If ::
  
              N > len(colors)
  
          the list will be extended by repetition.
      """
      def __init__(self, colors, name='from_list', N=None):
          self.monochrome = False  # Are all colors identical? (for contour.py)
          if N is None:
              self.colors = colors
              N = len(colors)
          else:
              if isinstance(colors, str):
                  self.colors = [colors] * N
                  self.monochrome = True
              elif np.iterable(colors):
                  if len(colors) == 1:
                      self.monochrome = True
                  self.colors = list(
                      itertools.islice(itertools.cycle(colors), N))
              else:
                  try:
                      gray = float(colors)
                  except TypeError:
                      pass
                  else:
                      self.colors = [gray] * N
                  self.monochrome = True
          Colormap.__init__(self, name, N)
  
      def _init(self):
          self._lut = np.zeros((self.N + 3, 4), float)
          self._lut[:-3] = to_rgba_array(self.colors)
          self._isinit = True
          self._set_extremes()
  
      def _resample(self, lutsize):
          """
          Return a new color map with *lutsize* entries.
          """
          colors = self(np.linspace(0, 1, lutsize))
          return ListedColormap(colors, name=self.name)
  
      def reversed(self, name=None):
          """
          Make a reversed instance of the Colormap.
  
          Parameters
          ----------
          name : str, optional
              The name for the reversed colormap. If it's None the
              name will be the name of the parent colormap + "_r".
  
          Returns
          -------
          ListedColormap
              A reversed instance of the colormap.
          """
          if name is None:
              name = self.name + "_r"
  
          colors_r = list(reversed(self.colors))
          return ListedColormap(colors_r, name=name, N=self.N)
  
  
  class Normalize:
      """
      A class which, when called, can normalize data into
      the ``[0.0, 1.0]`` interval.
  
      """
      def __init__(self, vmin=None, vmax=None, clip=False):
          """
          If *vmin* or *vmax* is not given, they are initialized from the
          minimum and maximum value respectively of the first input
          processed.  That is, *__call__(A)* calls *autoscale_None(A)*.
          If *clip* is *True* and the given value falls outside the range,
          the returned value will be 0 or 1, whichever is closer.
          Returns 0 if ::
  
              vmin==vmax
  
          Works with scalars or arrays, including masked arrays.  If
          *clip* is *True*, masked values are set to 1; otherwise they
          remain masked.  Clipping silently defeats the purpose of setting
          the over, under, and masked colors in the colormap, so it is
          likely to lead to surprises; therefore the default is
          *clip* = *False*.
          """
          self.vmin = _sanitize_extrema(vmin)
          self.vmax = _sanitize_extrema(vmax)
          self.clip = clip
  
      @staticmethod
      def process_value(value):
          """
          Homogenize the input *value* for easy and efficient normalization.
  
          *value* can be a scalar or sequence.
  
          Returns *result*, *is_scalar*, where *result* is a
          masked array matching *value*.  Float dtypes are preserved;
          integer types with two bytes or smaller are converted to
          np.float32, and larger types are converted to np.float64.
          Preserving float32 when possible, and using in-place operations,
          can greatly improve speed for large arrays.
  
          Experimental; we may want to add an option to force the
          use of float32.
          """
          is_scalar = not np.iterable(value)
          if is_scalar:
              value = [value]
          dtype = np.min_scalar_type(value)
          if np.issubdtype(dtype, np.integer) or dtype.type is np.bool_:
              # bool_/int8/int16 -> float32; int32/int64 -> float64
              dtype = np.promote_types(dtype, np.float32)
          # ensure data passed in as an ndarray subclass are interpreted as
          # an ndarray. See issue #6622.
          mask = np.ma.getmask(value)
          data = np.asarray(value)
          result = np.ma.array(data, mask=mask, dtype=dtype, copy=True)
          return result, is_scalar
  
      def __call__(self, value, clip=None):
          """
          Normalize *value* data in the ``[vmin, vmax]`` interval into
          the ``[0.0, 1.0]`` interval and return it.  *clip* defaults
          to *self.clip* (which defaults to *False*).  If not already
          initialized, *vmin* and *vmax* are initialized using
          *autoscale_None(value)*.
          """
          if clip is None:
              clip = self.clip
  
          result, is_scalar = self.process_value(value)
  
          self.autoscale_None(result)
          # Convert at least to float, without losing precision.
          (vmin,), _ = self.process_value(self.vmin)
          (vmax,), _ = self.process_value(self.vmax)
          if vmin == vmax:
              result.fill(0)   # Or should it be all masked?  Or 0.5?
          elif vmin > vmax:
              raise ValueError("minvalue must be less than or equal to maxvalue")
          else:
              if clip:
                  mask = np.ma.getmask(result)
                  result = np.ma.array(np.clip(result.filled(vmax), vmin, vmax),
                                       mask=mask)
              # ma division is very slow; we can take a shortcut
              resdat = result.data
              resdat -= vmin
              resdat /= (vmax - vmin)
              result = np.ma.array(resdat, mask=result.mask, copy=False)
          if is_scalar:
              result = result[0]
          return result
  
      def inverse(self, value):
          if not self.scaled():
              raise ValueError("Not invertible until scaled")
          (vmin,), _ = self.process_value(self.vmin)
          (vmax,), _ = self.process_value(self.vmax)
  
          if np.iterable(value):
              val = np.ma.asarray(value)
              return vmin + val * (vmax - vmin)
          else:
              return vmin + value * (vmax - vmin)
  
      def autoscale(self, A):
          """Set *vmin*, *vmax* to min, max of *A*."""
          A = np.asanyarray(A)
          self.vmin = A.min()
          self.vmax = A.max()
  
      def autoscale_None(self, A):
          """Autoscale only None-valued vmin or vmax."""
          A = np.asanyarray(A)
          if self.vmin is None and A.size:
              self.vmin = A.min()
          if self.vmax is None and A.size:
              self.vmax = A.max()
  
      def scaled(self):
          """Return whether vmin and vmax are set."""
          return self.vmin is not None and self.vmax is not None
  
  
  class TwoSlopeNorm(Normalize):
      def __init__(self, vcenter, vmin=None, vmax=None):
          """
          Normalize data with a set center.
  
          Useful when mapping data with an unequal rates of change around a
          conceptual center, e.g., data that range from -2 to 4, with 0 as
          the midpoint.
  
          Parameters
          ----------
          vcenter : float
              The data value that defines ``0.5`` in the normalization.
          vmin : float, optional
              The data value that defines ``0.0`` in the normalization.
              Defaults to the min value of the dataset.
          vmax : float, optional
              The data value that defines ``1.0`` in the normalization.
              Defaults to the the max value of the dataset.
  
          Examples
          --------
          This maps data value -4000 to 0., 0 to 0.5, and +10000 to 1.0; data
          between is linearly interpolated::
  
              >>> import matplotlib.colors as mcolors
              >>> offset = mcolors.TwoSlopeNorm(vmin=-4000.,
                                                vcenter=0., vmax=10000)
              >>> data = [-4000., -2000., 0., 2500., 5000., 7500., 10000.]
              >>> offset(data)
              array([0., 0.25, 0.5, 0.625, 0.75, 0.875, 1.0])
          """
  
          self.vcenter = vcenter
          self.vmin = vmin
          self.vmax = vmax
          if vcenter is not None and vmax is not None and vcenter >= vmax:
              raise ValueError('vmin, vcenter, and vmax must be in '
                               'ascending order')
          if vcenter is not None and vmin is not None and vcenter <= vmin:
              raise ValueError('vmin, vcenter, and vmax must be in '
                               'ascending order')
  
      def autoscale_None(self, A):
          """
          Get vmin and vmax, and then clip at vcenter
          """
          super().autoscale_None(A)
          if self.vmin > self.vcenter:
              self.vmin = self.vcenter
          if self.vmax < self.vcenter:
              self.vmax = self.vcenter
  
      def __call__(self, value, clip=None):
          """
          Map value to the interval [0, 1]. The clip argument is unused.
          """
          result, is_scalar = self.process_value(value)
          self.autoscale_None(result)  # sets self.vmin, self.vmax if None
  
          if not self.vmin <= self.vcenter <= self.vmax:
              raise ValueError("vmin, vcenter, vmax must increase monotonically")
          result = np.ma.masked_array(
              np.interp(result, [self.vmin, self.vcenter, self.vmax],
                        [0, 0.5, 1.]), mask=np.ma.getmask(result))
          if is_scalar:
              result = np.atleast_1d(result)[0]
          return result
  
  
  @cbook.deprecation.deprecated('3.2', alternative='TwoSlopeNorm')
  class DivergingNorm(TwoSlopeNorm):
      ...
  
  
  class LogNorm(Normalize):
      """Normalize a given value to the 0-1 range on a log scale."""
  
      def _check_vmin_vmax(self):
          if self.vmin > self.vmax:
              raise ValueError("minvalue must be less than or equal to maxvalue")
          elif self.vmin <= 0:
              raise ValueError("minvalue must be positive")
  
      def __call__(self, value, clip=None):
          if clip is None:
              clip = self.clip
  
          result, is_scalar = self.process_value(value)
  
          result = np.ma.masked_less_equal(result, 0, copy=False)
  
          self.autoscale_None(result)
          self._check_vmin_vmax()
          vmin, vmax = self.vmin, self.vmax
          if vmin == vmax:
              result.fill(0)
          else:
              if clip:
                  mask = np.ma.getmask(result)
                  result = np.ma.array(np.clip(result.filled(vmax), vmin, vmax),
                                       mask=mask)
              # in-place equivalent of above can be much faster
              resdat = result.data
              mask = result.mask
              if mask is np.ma.nomask:
                  mask = (resdat <= 0)
              else:
                  mask |= resdat <= 0
              np.copyto(resdat, 1, where=mask)
              np.log(resdat, resdat)
              resdat -= np.log(vmin)
              resdat /= (np.log(vmax) - np.log(vmin))
              result = np.ma.array(resdat, mask=mask, copy=False)
          if is_scalar:
              result = result[0]
          return result
  
      def inverse(self, value):
          if not self.scaled():
              raise ValueError("Not invertible until scaled")
          self._check_vmin_vmax()
          vmin, vmax = self.vmin, self.vmax
  
          if np.iterable(value):
              val = np.ma.asarray(value)
              return vmin * np.ma.power((vmax / vmin), val)
          else:
              return vmin * pow((vmax / vmin), value)
  
      def autoscale(self, A):
          # docstring inherited.
          super().autoscale(np.ma.masked_less_equal(A, 0, copy=False))
  
      def autoscale_None(self, A):
          # docstring inherited.
          super().autoscale_None(np.ma.masked_less_equal(A, 0, copy=False))
  
  
  class SymLogNorm(Normalize):
      """
      The symmetrical logarithmic scale is logarithmic in both the
      positive and negative directions from the origin.
  
      Since the values close to zero tend toward infinity, there is a
      need to have a range around zero that is linear.  The parameter
      *linthresh* allows the user to specify the size of this range
      (-*linthresh*, *linthresh*).
      """
      def __init__(self, linthresh, linscale=1.0, vmin=None, vmax=None,
                   clip=False, *, base=None):
          """
          Parameters
          ----------
          linthresh : float
              The range within which the plot is linear (to avoid having the plot
              go to infinity around zero).
          linscale : float, default: 1
              This allows the linear range (-*linthresh* to *linthresh*)
              to be stretched relative to the logarithmic range. Its
              value is the number of powers of *base* to use for each
              half of the linear range.
  
              For example, when *linscale* == 1.0 (the default) and
              ``base=10``, then space used for the positive and negative
              halves of the linear range will be equal to a decade in
              the logarithmic.
  
          base : float, default: None
              If not given, defaults to ``np.e`` (consistent with prior
              behavior) and warns.
  
              In v3.3 the default value will change to 10 to be consistent with
              `.SymLogNorm`.
  
              To suppress the warning pass *base* as a keyword argument.
  
          """
          Normalize.__init__(self, vmin, vmax, clip)
          if base is None:
              self._base = np.e
              cbook.warn_deprecated("3.3", message="default base may change "
                  "from np.e to 10.  To suppress this warning specify the base "
                  "keyword argument.")
          else:
              self._base = base
          self._log_base = np.log(self._base)
  
          self.linthresh = float(linthresh)
          self._linscale_adj = (linscale / (1.0 - self._base ** -1))
          if vmin is not None and vmax is not None:
              self._transform_vmin_vmax()
  
      def __call__(self, value, clip=None):
          if clip is None:
              clip = self.clip
  
          result, is_scalar = self.process_value(value)
          self.autoscale_None(result)
          vmin, vmax = self.vmin, self.vmax
  
          if vmin > vmax:
              raise ValueError("minvalue must be less than or equal to maxvalue")
          elif vmin == vmax:
              result.fill(0)
          else:
              if clip:
                  mask = np.ma.getmask(result)
                  result = np.ma.array(np.clip(result.filled(vmax), vmin, vmax),
                                       mask=mask)
              # in-place equivalent of above can be much faster
              resdat = self._transform(result.data)
              resdat -= self._lower
              resdat /= (self._upper - self._lower)
  
          if is_scalar:
              result = result[0]
          return result
  
      def _transform(self, a):
          """Inplace transformation."""
          with np.errstate(invalid="ignore"):
              masked = np.abs(a) > self.linthresh
          sign = np.sign(a[masked])
          log = (self._linscale_adj +
                 np.log(np.abs(a[masked]) / self.linthresh) / self._log_base)
          log *= sign * self.linthresh
          a[masked] = log
          a[~masked] *= self._linscale_adj
          return a
  
      def _inv_transform(self, a):
          """Inverse inplace Transformation."""
          masked = np.abs(a) > (self.linthresh * self._linscale_adj)
          sign = np.sign(a[masked])
          exp = np.power(self._base,
                         sign * a[masked] / self.linthresh - self._linscale_adj)
          exp *= sign * self.linthresh
          a[masked] = exp
          a[~masked] /= self._linscale_adj
          return a
  
      def _transform_vmin_vmax(self):
          """Calculates vmin and vmax in the transformed system."""
          vmin, vmax = self.vmin, self.vmax
          arr = np.array([vmax, vmin]).astype(float)
          self._upper, self._lower = self._transform(arr)
  
      def inverse(self, value):
          if not self.scaled():
              raise ValueError("Not invertible until scaled")
          val = np.ma.asarray(value)
          val = val * (self._upper - self._lower) + self._lower
          return self._inv_transform(val)
  
      def autoscale(self, A):
          # docstring inherited.
          super().autoscale(A)
          self._transform_vmin_vmax()
  
      def autoscale_None(self, A):
          # docstring inherited.
          super().autoscale_None(A)
          self._transform_vmin_vmax()
  
  
  class PowerNorm(Normalize):
      """
      Linearly map a given value to the 0-1 range and then apply
      a power-law normalization over that range.
      """
      def __init__(self, gamma, vmin=None, vmax=None, clip=False):
          Normalize.__init__(self, vmin, vmax, clip)
          self.gamma = gamma
  
      def __call__(self, value, clip=None):
          if clip is None:
              clip = self.clip
  
          result, is_scalar = self.process_value(value)
  
          self.autoscale_None(result)
          gamma = self.gamma
          vmin, vmax = self.vmin, self.vmax
          if vmin > vmax:
              raise ValueError("minvalue must be less than or equal to maxvalue")
          elif vmin == vmax:
              result.fill(0)
          else:
              if clip:
                  mask = np.ma.getmask(result)
                  result = np.ma.array(np.clip(result.filled(vmax), vmin, vmax),
                                       mask=mask)
              resdat = result.data
              resdat -= vmin
              resdat[resdat < 0] = 0
              np.power(resdat, gamma, resdat)
              resdat /= (vmax - vmin) ** gamma
  
              result = np.ma.array(resdat, mask=result.mask, copy=False)
          if is_scalar:
              result = result[0]
          return result
  
      def inverse(self, value):
          if not self.scaled():
              raise ValueError("Not invertible until scaled")
          gamma = self.gamma
          vmin, vmax = self.vmin, self.vmax
  
          if np.iterable(value):
              val = np.ma.asarray(value)
              return np.ma.power(val, 1. / gamma) * (vmax - vmin) + vmin
          else:
              return pow(value, 1. / gamma) * (vmax - vmin) + vmin
  
  
  class BoundaryNorm(Normalize):
      """
      Generate a colormap index based on discrete intervals.
  
      Unlike `Normalize` or `LogNorm`, `BoundaryNorm` maps values to integers
      instead of to the interval 0-1.
  
      Mapping to the 0-1 interval could have been done via piece-wise linear
      interpolation, but using integers seems simpler, and reduces the number of
      conversions back and forth between integer and floating point.
      """
      def __init__(self, boundaries, ncolors, clip=False):
          """
          Parameters
          ----------
          boundaries : array-like
              Monotonically increasing sequence of boundaries
          ncolors : int
              Number of colors in the colormap to be used
          clip : bool, optional
              If clip is ``True``, out of range values are mapped to 0 if they
              are below ``boundaries[0]`` or mapped to ncolors - 1 if they are
              above ``boundaries[-1]``.
  
              If clip is ``False``, out of range values are mapped to -1 if
              they are below ``boundaries[0]`` or mapped to ncolors if they are
              above ``boundaries[-1]``. These are then converted to valid indices
              by :meth:`Colormap.__call__`.
  
          Notes
          -----
          *boundaries* defines the edges of bins, and data falling within a bin
          is mapped to the color with the same index.
  
          If the number of bins doesn't equal *ncolors*, the color is chosen
          by linear interpolation of the bin number onto color numbers.
          """
          self.clip = clip
          self.vmin = boundaries[0]
          self.vmax = boundaries[-1]
          self.boundaries = np.asarray(boundaries)
          self.N = len(self.boundaries)
          self.Ncmap = ncolors
          if self.N - 1 == self.Ncmap:
              self._interp = False
          else:
              self._interp = True
  
      def __call__(self, value, clip=None):
          if clip is None:
              clip = self.clip
  
          xx, is_scalar = self.process_value(value)
          mask = np.ma.getmaskarray(xx)
          xx = np.atleast_1d(xx.filled(self.vmax + 1))
          if clip:
              np.clip(xx, self.vmin, self.vmax, out=xx)
              max_col = self.Ncmap - 1
          else:
              max_col = self.Ncmap
          iret = np.zeros(xx.shape, dtype=np.int16)
          for i, b in enumerate(self.boundaries):
              iret[xx >= b] = i
          if self._interp:
              scalefac = (self.Ncmap - 1) / (self.N - 2)
              iret = (iret * scalefac).astype(np.int16)
          iret[xx < self.vmin] = -1
          iret[xx >= self.vmax] = max_col
          ret = np.ma.array(iret, mask=mask)
          if is_scalar:
              ret = int(ret[0])  # assume python scalar
          return ret
  
      def inverse(self, value):
          """
          Raises
          ------
          ValueError
              BoundaryNorm is not invertible, so calling this method will always
              raise an error
          """
          raise ValueError("BoundaryNorm is not invertible")
  
  
  class NoNorm(Normalize):
      """
      Dummy replacement for `Normalize`, for the case where we want to use
      indices directly in a `~matplotlib.cm.ScalarMappable`.
      """
      def __call__(self, value, clip=None):
          return value
  
      def inverse(self, value):
          return value
  
  
  def rgb_to_hsv(arr):
      """
      Convert float rgb values (in the range [0, 1]), in a numpy array to hsv
      values.
  
      Parameters
      ----------
      arr : (..., 3) array-like
         All values must be in the range [0, 1]
  
      Returns
      -------
      hsv : (..., 3) ndarray
         Colors converted to hsv values in range [0, 1]
      """
      arr = np.asarray(arr)
  
      # check length of the last dimension, should be _some_ sort of rgb
      if arr.shape[-1] != 3:
          raise ValueError("Last dimension of input array must be 3; "
                           "shape {} was found.".format(arr.shape))
  
      in_shape = arr.shape
      arr = np.array(
          arr, copy=False,
          dtype=np.promote_types(arr.dtype, np.float32),  # Don't work on ints.
          ndmin=2,  # In case input was 1D.
      )
      out = np.zeros_like(arr)
      arr_max = arr.max(-1)
      ipos = arr_max > 0
      delta = arr.ptp(-1)
      s = np.zeros_like(delta)
      s[ipos] = delta[ipos] / arr_max[ipos]
      ipos = delta > 0
      # red is max
      idx = (arr[..., 0] == arr_max) & ipos
      out[idx, 0] = (arr[idx, 1] - arr[idx, 2]) / delta[idx]
      # green is max
      idx = (arr[..., 1] == arr_max) & ipos
      out[idx, 0] = 2. + (arr[idx, 2] - arr[idx, 0]) / delta[idx]
      # blue is max
      idx = (arr[..., 2] == arr_max) & ipos
      out[idx, 0] = 4. + (arr[idx, 0] - arr[idx, 1]) / delta[idx]
  
      out[..., 0] = (out[..., 0] / 6.0) % 1.0
      out[..., 1] = s
      out[..., 2] = arr_max
  
      return out.reshape(in_shape)
  
  
  def hsv_to_rgb(hsv):
      """
      Convert hsv values to rgb.
  
      Parameters
      ----------
      hsv : (..., 3) array-like
         All values assumed to be in range [0, 1]
  
      Returns
      -------
      rgb : (..., 3) ndarray
         Colors converted to RGB values in range [0, 1]
      """
      hsv = np.asarray(hsv)
  
      # check length of the last dimension, should be _some_ sort of rgb
      if hsv.shape[-1] != 3:
          raise ValueError("Last dimension of input array must be 3; "
                           "shape {shp} was found.".format(shp=hsv.shape))
  
      in_shape = hsv.shape
      hsv = np.array(
          hsv, copy=False,
          dtype=np.promote_types(hsv.dtype, np.float32),  # Don't work on ints.
          ndmin=2,  # In case input was 1D.
      )
  
      h = hsv[..., 0]
      s = hsv[..., 1]
      v = hsv[..., 2]
  
      r = np.empty_like(h)
      g = np.empty_like(h)
      b = np.empty_like(h)
  
      i = (h * 6.0).astype(int)
      f = (h * 6.0) - i
      p = v * (1.0 - s)
      q = v * (1.0 - s * f)
      t = v * (1.0 - s * (1.0 - f))
  
      idx = i % 6 == 0
      r[idx] = v[idx]
      g[idx] = t[idx]
      b[idx] = p[idx]
  
      idx = i == 1
      r[idx] = q[idx]
      g[idx] = v[idx]
      b[idx] = p[idx]
  
      idx = i == 2
      r[idx] = p[idx]
      g[idx] = v[idx]
      b[idx] = t[idx]
  
      idx = i == 3
      r[idx] = p[idx]
      g[idx] = q[idx]
      b[idx] = v[idx]
  
      idx = i == 4
      r[idx] = t[idx]
      g[idx] = p[idx]
      b[idx] = v[idx]
  
      idx = i == 5
      r[idx] = v[idx]
      g[idx] = p[idx]
      b[idx] = q[idx]
  
      idx = s == 0
      r[idx] = v[idx]
      g[idx] = v[idx]
      b[idx] = v[idx]
  
      rgb = np.stack([r, g, b], axis=-1)
  
      return rgb.reshape(in_shape)
  
  
  def _vector_magnitude(arr):
      # things that don't work here:
      #  * np.linalg.norm
      #    - doesn't broadcast in numpy 1.7
      #    - drops the mask from ma.array
      #  * using keepdims - broken on ma.array until 1.11.2
      #  * using sum - discards mask on ma.array unless entire vector is masked
  
      sum_sq = 0
      for i in range(arr.shape[-1]):
          sum_sq += np.square(arr[..., i, np.newaxis])
      return np.sqrt(sum_sq)
  
  
  class LightSource:
      """
      Create a light source coming from the specified azimuth and elevation.
      Angles are in degrees, with the azimuth measured
      clockwise from north and elevation up from the zero plane of the surface.
  
      The :meth:`shade` is used to produce "shaded" rgb values for a data array.
      :meth:`shade_rgb` can be used to combine an rgb image with
      The :meth:`shade_rgb`
      The :meth:`hillshade` produces an illumination map of a surface.
      """
      def __init__(self, azdeg=315, altdeg=45, hsv_min_val=0, hsv_max_val=1,
                   hsv_min_sat=1, hsv_max_sat=0):
          """
          Specify the azimuth (measured clockwise from south) and altitude
          (measured up from the plane of the surface) of the light source
          in degrees.
  
          Parameters
          ----------
          azdeg : number, optional
              The azimuth (0-360, degrees clockwise from North) of the light
              source. Defaults to 315 degrees (from the northwest).
          altdeg : number, optional
              The altitude (0-90, degrees up from horizontal) of the light
              source.  Defaults to 45 degrees from horizontal.
  
          Notes
          -----
          For backwards compatibility, the parameters *hsv_min_val*,
          *hsv_max_val*, *hsv_min_sat*, and *hsv_max_sat* may be supplied at
          initialization as well.  However, these parameters will only be used if
          "blend_mode='hsv'" is passed into :meth:`shade` or :meth:`shade_rgb`.
          See the documentation for :meth:`blend_hsv` for more details.
          """
          self.azdeg = azdeg
          self.altdeg = altdeg
          self.hsv_min_val = hsv_min_val
          self.hsv_max_val = hsv_max_val
          self.hsv_min_sat = hsv_min_sat
          self.hsv_max_sat = hsv_max_sat
  
      @property
      def direction(self):
          """The unit vector direction towards the light source."""
          # Azimuth is in degrees clockwise from North. Convert to radians
          # counterclockwise from East (mathematical notation).
          az = np.radians(90 - self.azdeg)
          alt = np.radians(self.altdeg)
          return np.array([
              np.cos(az) * np.cos(alt),
              np.sin(az) * np.cos(alt),
              np.sin(alt)
          ])
  
      def hillshade(self, elevation, vert_exag=1, dx=1, dy=1, fraction=1.):
          """
          Calculates the illumination intensity for a surface using the defined
          azimuth and elevation for the light source.
  
          This computes the normal vectors for the surface, and then passes them
          on to `shade_normals`
  
          Parameters
          ----------
          elevation : array-like
              A 2d array (or equivalent) of the height values used to generate an
              illumination map
          vert_exag : number, optional
              The amount to exaggerate the elevation values by when calculating
              illumination. This can be used either to correct for differences in
              units between the x-y coordinate system and the elevation
              coordinate system (e.g. decimal degrees vs. meters) or to
              exaggerate or de-emphasize topographic effects.
          dx : number, optional
              The x-spacing (columns) of the input *elevation* grid.
          dy : number, optional
              The y-spacing (rows) of the input *elevation* grid.
          fraction : number, optional
              Increases or decreases the contrast of the hillshade.  Values
              greater than one will cause intermediate values to move closer to
              full illumination or shadow (and clipping any values that move
              beyond 0 or 1). Note that this is not visually or mathematically
              the same as vertical exaggeration.
  
          Returns
          -------
          intensity : ndarray
              A 2d array of illumination values between 0-1, where 0 is
              completely in shadow and 1 is completely illuminated.
          """
  
          # Because most image and raster GIS data has the first row in the array
          # as the "top" of the image, dy is implicitly negative.  This is
          # consistent to what `imshow` assumes, as well.
          dy = -dy
  
          # compute the normal vectors from the partial derivatives
          e_dy, e_dx = np.gradient(vert_exag * elevation, dy, dx)
  
          # .view is to keep subclasses
          normal = np.empty(elevation.shape + (3,)).view(type(elevation))
          normal[..., 0] = -e_dx
          normal[..., 1] = -e_dy
          normal[..., 2] = 1
          normal /= _vector_magnitude(normal)
  
          return self.shade_normals(normal, fraction)
  
      def shade_normals(self, normals, fraction=1.):
          """
          Calculates the illumination intensity for the normal vectors of a
          surface using the defined azimuth and elevation for the light source.
  
          Imagine an artificial sun placed at infinity in some azimuth and
          elevation position illuminating our surface. The parts of the surface
          that slope toward the sun should brighten while those sides facing away
          should become darker.
  
          Parameters
          ----------
          fraction : number, optional
              Increases or decreases the contrast of the hillshade.  Values
              greater than one will cause intermediate values to move closer to
              full illumination or shadow (and clipping any values that move
              beyond 0 or 1). Note that this is not visually or mathematically
              the same as vertical exaggeration.
  
          Returns
          -------
          intensity : ndarray
              A 2d array of illumination values between 0-1, where 0 is
              completely in shadow and 1 is completely illuminated.
          """
  
          intensity = normals.dot(self.direction)
  
          # Apply contrast stretch
          imin, imax = intensity.min(), intensity.max()
          intensity *= fraction
  
          # Rescale to 0-1, keeping range before contrast stretch
          # If constant slope, keep relative scaling (i.e. flat should be 0.5,
          # fully occluded 0, etc.)
          if (imax - imin) > 1e-6:
              # Strictly speaking, this is incorrect. Negative values should be
              # clipped to 0 because they're fully occluded. However, rescaling
              # in this manner is consistent with the previous implementation and
              # visually appears better than a "hard" clip.
              intensity -= imin
              intensity /= (imax - imin)
          intensity = np.clip(intensity, 0, 1)
  
          return intensity
  
      def shade(self, data, cmap, norm=None, blend_mode='overlay', vmin=None,
                vmax=None, vert_exag=1, dx=1, dy=1, fraction=1, **kwargs):
          """
          Combine colormapped data values with an illumination intensity map
          (a.k.a.  "hillshade") of the values.
  
          Parameters
          ----------
          data : array-like
              A 2d array (or equivalent) of the height values used to generate a
              shaded map.
          cmap : `~matplotlib.colors.Colormap` instance
              The colormap used to color the *data* array. Note that this must be
              a `~matplotlib.colors.Colormap` instance.  For example, rather than
              passing in `cmap='gist_earth'`, use
              `cmap=plt.get_cmap('gist_earth')` instead.
          norm : `~matplotlib.colors.Normalize` instance, optional
              The normalization used to scale values before colormapping. If
              None, the input will be linearly scaled between its min and max.
          blend_mode : {'hsv', 'overlay', 'soft'} or callable, optional
              The type of blending used to combine the colormapped data
              values with the illumination intensity.  Default is
              "overlay".  Note that for most topographic surfaces,
              "overlay" or "soft" appear more visually realistic. If a
              user-defined function is supplied, it is expected to
              combine an MxNx3 RGB array of floats (ranging 0 to 1) with
              an MxNx1 hillshade array (also 0 to 1).  (Call signature
              `func(rgb, illum, **kwargs)`) Additional kwargs supplied
              to this function will be passed on to the *blend_mode*
              function.
          vmin : scalar or None, optional
              The minimum value used in colormapping *data*. If *None* the
              minimum value in *data* is used. If *norm* is specified, then this
              argument will be ignored.
          vmax : scalar or None, optional
              The maximum value used in colormapping *data*. If *None* the
              maximum value in *data* is used. If *norm* is specified, then this
              argument will be ignored.
          vert_exag : number, optional
              The amount to exaggerate the elevation values by when calculating
              illumination. This can be used either to correct for differences in
              units between the x-y coordinate system and the elevation
              coordinate system (e.g. decimal degrees vs. meters) or to
              exaggerate or de-emphasize topography.
          dx : number, optional
              The x-spacing (columns) of the input *elevation* grid.
          dy : number, optional
              The y-spacing (rows) of the input *elevation* grid.
          fraction : number, optional
              Increases or decreases the contrast of the hillshade.  Values
              greater than one will cause intermediate values to move closer to
              full illumination or shadow (and clipping any values that move
              beyond 0 or 1). Note that this is not visually or mathematically
              the same as vertical exaggeration.
          Additional kwargs are passed on to the *blend_mode* function.
  
          Returns
          -------
          rgba : ndarray
              An MxNx4 array of floats ranging between 0-1.
          """
          if vmin is None:
              vmin = data.min()
          if vmax is None:
              vmax = data.max()
          if norm is None:
              norm = Normalize(vmin=vmin, vmax=vmax)
  
          rgb0 = cmap(norm(data))
          rgb1 = self.shade_rgb(rgb0, elevation=data, blend_mode=blend_mode,
                                vert_exag=vert_exag, dx=dx, dy=dy,
                                fraction=fraction, **kwargs)
          # Don't overwrite the alpha channel, if present.
          rgb0[..., :3] = rgb1[..., :3]
          return rgb0
  
      def shade_rgb(self, rgb, elevation, fraction=1., blend_mode='hsv',
                    vert_exag=1, dx=1, dy=1, **kwargs):
          """
          Use this light source to adjust the colors of the *rgb* input array to
          give the impression of a shaded relief map with the given `elevation`.
  
          Parameters
          ----------
          rgb : array-like
              An (M, N, 3) RGB array, assumed to be in the range of 0 to 1.
          elevation : array-like
              An (M, N) array of the height values used to generate a shaded map.
          fraction : number
              Increases or decreases the contrast of the hillshade.  Values
              greater than one will cause intermediate values to move closer to
              full illumination or shadow (and clipping any values that move
              beyond 0 or 1). Note that this is not visually or mathematically
              the same as vertical exaggeration.
          blend_mode : {'hsv', 'overlay', 'soft'} or callable, optional
              The type of blending used to combine the colormapped data values
              with the illumination intensity.  For backwards compatibility, this
              defaults to "hsv". Note that for most topographic surfaces,
              "overlay" or "soft" appear more visually realistic. If a
              user-defined function is supplied, it is expected to combine an
              MxNx3 RGB array of floats (ranging 0 to 1) with an MxNx1 hillshade
              array (also 0 to 1).  (Call signature `func(rgb, illum, **kwargs)`)
              Additional kwargs supplied to this function will be passed on to
              the *blend_mode* function.
          vert_exag : number, optional
              The amount to exaggerate the elevation values by when calculating
              illumination. This can be used either to correct for differences in
              units between the x-y coordinate system and the elevation
              coordinate system (e.g. decimal degrees vs. meters) or to
              exaggerate or de-emphasize topography.
          dx : number, optional
              The x-spacing (columns) of the input *elevation* grid.
          dy : number, optional
              The y-spacing (rows) of the input *elevation* grid.
          Additional kwargs are passed on to the *blend_mode* function.
  
          Returns
          -------
          shaded_rgb : ndarray
              An (m, n, 3) array of floats ranging between 0-1.
          """
          # Calculate the "hillshade" intensity.
          intensity = self.hillshade(elevation, vert_exag, dx, dy, fraction)
          intensity = intensity[..., np.newaxis]
  
          # Blend the hillshade and rgb data using the specified mode
          lookup = {
                  'hsv': self.blend_hsv,
                  'soft': self.blend_soft_light,
                  'overlay': self.blend_overlay,
                  }
          if blend_mode in lookup:
              blend = lookup[blend_mode](rgb, intensity, **kwargs)
          else:
              try:
                  blend = blend_mode(rgb, intensity, **kwargs)
              except TypeError:
                  raise ValueError('"blend_mode" must be callable or one of {}'
                                   .format(lookup.keys))
  
          # Only apply result where hillshade intensity isn't masked
          if hasattr(intensity, 'mask'):
              mask = intensity.mask[..., 0]
              for i in range(3):
                  blend[..., i][mask] = rgb[..., i][mask]
  
          return blend
  
      def blend_hsv(self, rgb, intensity, hsv_max_sat=None, hsv_max_val=None,
                    hsv_min_val=None, hsv_min_sat=None):
          """
          Take the input data array, convert to HSV values in the given colormap,
          then adjust those color values to give the impression of a shaded
          relief map with a specified light source.  RGBA values are returned,
          which can then be used to plot the shaded image with imshow.
  
          The color of the resulting image will be darkened by moving the (s, v)
          values (in hsv colorspace) toward (hsv_min_sat, hsv_min_val) in the
          shaded regions, or lightened by sliding (s, v) toward (hsv_max_sat,
          hsv_max_val) in regions that are illuminated.  The default extremes are
          chose so that completely shaded points are nearly black (s = 1, v = 0)
          and completely illuminated points are nearly white (s = 0, v = 1).
  
          Parameters
          ----------
          rgb : ndarray
              An MxNx3 RGB array of floats ranging from 0 to 1 (color image).
          intensity : ndarray
              An MxNx1 array of floats ranging from 0 to 1 (grayscale image).
          hsv_max_sat : number, optional
              The maximum saturation value that the *intensity* map can shift the
              output image to. Defaults to 1.
          hsv_min_sat : number, optional
              The minimum saturation value that the *intensity* map can shift the
              output image to. Defaults to 0.
          hsv_max_val : number, optional
              The maximum value ("v" in "hsv") that the *intensity* map can shift
              the output image to. Defaults to 1.
          hsv_min_val : number, optional
              The minimum value ("v" in "hsv") that the *intensity* map can shift
              the output image to. Defaults to 0.
  
          Returns
          -------
          rgb : ndarray
              An MxNx3 RGB array representing the combined images.
          """
          # Backward compatibility...
          if hsv_max_sat is None:
              hsv_max_sat = self.hsv_max_sat
          if hsv_max_val is None:
              hsv_max_val = self.hsv_max_val
          if hsv_min_sat is None:
              hsv_min_sat = self.hsv_min_sat
          if hsv_min_val is None:
              hsv_min_val = self.hsv_min_val
  
          # Expects a 2D intensity array scaled between -1 to 1...
          intensity = intensity[..., 0]
          intensity = 2 * intensity - 1
  
          # Convert to rgb, then rgb to hsv
          hsv = rgb_to_hsv(rgb[:, :, 0:3])
          hue, sat, val = np.moveaxis(hsv, -1, 0)
  
          # Modify hsv values (in place) to simulate illumination.
          # putmask(A, mask, B) <=> A[mask] = B[mask]
          np.putmask(sat, (np.abs(sat) > 1.e-10) & (intensity > 0),
                     (1 - intensity) * sat + intensity * hsv_max_sat)
          np.putmask(sat, (np.abs(sat) > 1.e-10) & (intensity < 0),
                     (1 + intensity) * sat - intensity * hsv_min_sat)
          np.putmask(val, intensity > 0,
                     (1 - intensity) * val + intensity * hsv_max_val)
          np.putmask(val, intensity < 0,
                     (1 + intensity) * val - intensity * hsv_min_val)
          np.clip(hsv[:, :, 1:], 0, 1, out=hsv[:, :, 1:])
  
          # Convert modified hsv back to rgb.
          return hsv_to_rgb(hsv)
  
      def blend_soft_light(self, rgb, intensity):
          """
          Combines an rgb image with an intensity map using "soft light"
          blending.  Uses the "pegtop" formula.
  
          Parameters
          ----------
          rgb : ndarray
              An MxNx3 RGB array of floats ranging from 0 to 1 (color image).
          intensity : ndarray
              An MxNx1 array of floats ranging from 0 to 1 (grayscale image).
  
          Returns
          -------
          rgb : ndarray
              An MxNx3 RGB array representing the combined images.
          """
          return 2 * intensity * rgb + (1 - 2 * intensity) * rgb**2
  
      def blend_overlay(self, rgb, intensity):
          """
          Combines an rgb image with an intensity map using "overlay" blending.
  
          Parameters
          ----------
          rgb : ndarray
              An MxNx3 RGB array of floats ranging from 0 to 1 (color image).
          intensity : ndarray
              An MxNx1 array of floats ranging from 0 to 1 (grayscale image).
  
          Returns
          -------
          rgb : ndarray
              An MxNx3 RGB array representing the combined images.
          """
          low = 2 * intensity * rgb
          high = 1 - 2 * (1 - intensity) * (1 - rgb)
          return np.where(rgb <= 0.5, low, high)
  
  
  def from_levels_and_colors(levels, colors, extend='neither'):
      """
      A helper routine to generate a cmap and a norm instance which
      behave similar to contourf's levels and colors arguments.
  
      Parameters
      ----------
      levels : sequence of numbers
          The quantization levels used to construct the :class:`BoundaryNorm`.
          Value ``v`` is quantized to level ``i`` if ``lev[i] <= v < lev[i+1]``.
      colors : sequence of colors
          The fill color to use for each level. If `extend` is "neither" there
          must be ``n_level - 1`` colors. For an `extend` of "min" or "max" add
          one extra color, and for an `extend` of "both" add two colors.
      extend : {'neither', 'min', 'max', 'both'}, optional
          The behaviour when a value falls out of range of the given levels.
          See :func:`~matplotlib.pyplot.contourf` for details.
  
      Returns
      -------
      cmap : `~matplotlib.colors.Normalize`
      norm : `~matplotlib.colors.Colormap`
      """
      slice_map = {
          'both': slice(1, -1),
          'min': slice(1, None),
          'max': slice(0, -1),
          'neither': slice(0, None),
      }
      cbook._check_in_list(slice_map, extend=extend)
      color_slice = slice_map[extend]
  
      n_data_colors = len(levels) - 1
      n_expected = n_data_colors + color_slice.start - (color_slice.stop or 0)
      if len(colors) != n_expected:
          raise ValueError(
              f'With extend == {extend!r} and {len(levels)} levels, '
              f'expected {n_expected} colors, but got {len(colors)}')
  
      cmap = ListedColormap(colors[color_slice], N=n_data_colors)
  
      if extend in ['min', 'both']:
          cmap.set_under(colors[0])
      else:
          cmap.set_under('none')
  
      if extend in ['max', 'both']:
          cmap.set_over(colors[-1])
      else:
          cmap.set_over('none')
  
      cmap.colorbar_extend = extend
  
      norm = BoundaryNorm(levels, ncolors=n_data_colors)
      return cmap, norm
  