"""
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):
        """
        *linthresh*:
        The range within which the plot is linear (to
        avoid having the plot go to infinity around zero).

        *linscale*:
        This allows the linear range (-*linthresh* to *linthresh*)
        to be stretched relative to the logarithmic range.  Its
        value is the number of decades to use for each half of the
        linear range.  For example, when *linscale* == 1.0 (the
        default), the space used for the positive and negative
        halves of the linear range will be equal to one decade in
        the logarithmic range. Defaults to 1.
        """
        Normalize.__init__(self, vmin, vmax, clip)
        self.linthresh = float(linthresh)
        self._linscale_adj = (linscale / (1.0 - np.e ** -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))
        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.exp(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
