"""Functions for converting between color spaces.

The "central" color space in this module is RGB, more specifically the linear
sRGB color space using D65 as a white-point [1]_.  This represents a
standard monitor (w/o gamma correction). For a good FAQ on color spaces see
[2]_.

The API consists of functions to convert to and from RGB as defined above, as
well as a generic function to convert to and from any supported color space
(which is done through RGB in most cases).


Supported color spaces
----------------------
* RGB : Red Green Blue.
        Here the sRGB standard [1]_.
* HSV : Hue, Saturation, Value.
        Uniquely defined when related to sRGB [3]_.
* RGB CIE : Red Green Blue.
        The original RGB CIE standard from 1931 [4]_. Primary colors are 700 nm
        (red), 546.1 nm (blue) and 435.8 nm (green).
* XYZ CIE : XYZ
        Derived from the RGB CIE color space. Chosen such that
        ``x == y == z == 1/3`` at the whitepoint, and all color matching
        functions are greater than zero everywhere.
* LAB CIE : Lightness, a, b
        Colorspace derived from XYZ CIE that is intended to be more
        perceptually uniform
* LUV CIE : Lightness, u, v
        Colorspace derived from XYZ CIE that is intended to be more
        perceptually uniform
* LCH CIE : Lightness, Chroma, Hue
        Defined in terms of LAB CIE.  C and H are the polar representation of
        a and b.  The polar angle C is defined to be on ``(0, 2*pi)``

:author: Nicolas Pinto (rgb2hsv)
:author: Ralf Gommers (hsv2rgb)
:author: Travis Oliphant (XYZ and RGB CIE functions)
:author: Matt Terry (lab2lch)
:author: Alex Izvorski (yuv2rgb, rgb2yuv and related)

:license: modified BSD

References
----------
.. [1] Official specification of sRGB, IEC 61966-2-1:1999.
.. [2] http://www.poynton.com/ColorFAQ.html
.. [3] https://en.wikipedia.org/wiki/HSL_and_HSV
.. [4] https://en.wikipedia.org/wiki/CIE_1931_color_space
"""

from warnings import warn

import numpy as np
from scipy import linalg


from .._shared.utils import (
    _supported_float_type,
    channel_as_last_axis,
    identity,
    reshape_nd,
    slice_at_axis,
)
from ..util import dtype, dtype_limits

# TODO: when minimum numpy dependency is 1.25 use:
# np..exceptions.AxisError instead of AxisError
# and remove this try-except
try:
    from numpy import AxisError
except ImportError:
    from numpy.exceptions import AxisError


def convert_colorspace(arr, fromspace, tospace, *, channel_axis=-1):
    """Convert an image array to a new color space.

    Valid color spaces are:
        'RGB', 'HSV', 'RGB CIE', 'XYZ', 'YUV', 'YIQ', 'YPbPr', 'YCbCr', 'YDbDr'

    Parameters
    ----------
    arr : (..., C=3, ...) array_like
        The image to convert. By default, the final dimension denotes
        channels.
    fromspace : str
        The color space to convert from. Can be specified in lower case.
    tospace : str
        The color space to convert to. Can be specified in lower case.
    channel_axis : int, optional
        This parameter indicates which axis of the array corresponds to
        channels.

        .. versionadded:: 0.19
           ``channel_axis`` was added in 0.19.

    Returns
    -------
    out : (..., C=3, ...) ndarray
        The converted image. Same dimensions as input.

    Raises
    ------
    ValueError
        If fromspace is not a valid color space
    ValueError
        If tospace is not a valid color space

    Notes
    -----
    Conversion is performed through the "central" RGB color space,
    i.e. conversion from XYZ to HSV is implemented as ``XYZ -> RGB -> HSV``
    instead of directly.

    Examples
    --------
    >>> from skimage import data
    >>> img = data.astronaut()
    >>> img_hsv = convert_colorspace(img, 'RGB', 'HSV')
    """
    fromdict = {
        'rgb': identity,
        'hsv': hsv2rgb,
        'rgb cie': rgbcie2rgb,
        'xyz': xyz2rgb,
        'yuv': yuv2rgb,
        'yiq': yiq2rgb,
        'ypbpr': ypbpr2rgb,
        'ycbcr': ycbcr2rgb,
        'ydbdr': ydbdr2rgb,
    }
    todict = {
        'rgb': identity,
        'hsv': rgb2hsv,
        'rgb cie': rgb2rgbcie,
        'xyz': rgb2xyz,
        'yuv': rgb2yuv,
        'yiq': rgb2yiq,
        'ypbpr': rgb2ypbpr,
        'ycbcr': rgb2ycbcr,
        'ydbdr': rgb2ydbdr,
    }

    fromspace = fromspace.lower()
    tospace = tospace.lower()
    if fromspace not in fromdict:
        msg = f'`fromspace` has to be one of {fromdict.keys()}'
        raise ValueError(msg)
    if tospace not in todict:
        msg = f'`tospace` has to be one of {todict.keys()}'
        raise ValueError(msg)

    return todict[tospace](
        fromdict[fromspace](arr, channel_axis=channel_axis), channel_axis=channel_axis
    )


def _prepare_colorarray(arr, force_copy=False, *, channel_axis=-1):
    """Check the shape of the array and convert it to
    floating point representation.
    """
    arr = np.asanyarray(arr)

    if arr.shape[channel_axis] != 3:
        msg = (
            f'the input array must have size 3 along `channel_axis`, '
            f'got {arr.shape}'
        )
        raise ValueError(msg)

    float_dtype = _supported_float_type(arr.dtype)
    if float_dtype == np.float32:
        _func = dtype.img_as_float32
    else:
        _func = dtype.img_as_float64
    return _func(arr, force_copy=force_copy)


def _validate_channel_axis(channel_axis, ndim):
    if not isinstance(channel_axis, int):
        raise TypeError("channel_axis must be an integer")
    if channel_axis < -ndim or channel_axis >= ndim:
        raise AxisError("channel_axis exceeds array dimensions")


def rgba2rgb(rgba, background=(1, 1, 1), *, channel_axis=-1):
    """RGBA to RGB conversion using alpha blending [1]_.

    Parameters
    ----------
    rgba : (..., C=4, ...) array_like
        The image in RGBA format. By default, the final dimension denotes
        channels.
    background : array_like
        The color of the background to blend the image with (3 floats
        between 0 to 1 - the RGB value of the background).
    channel_axis : int, optional
        This parameter indicates which axis of the array corresponds to
        channels.

        .. versionadded:: 0.19
           ``channel_axis`` was added in 0.19.

    Returns
    -------
    out : (..., C=3, ...) ndarray
        The image in RGB format. Same dimensions as input.

    Raises
    ------
    ValueError
        If `rgba` is not at least 2D with shape (..., 4, ...).

    References
    ----------
    .. [1] https://en.wikipedia.org/wiki/Alpha_compositing#Alpha_blending

    Examples
    --------
    >>> from skimage import color
    >>> from skimage import data
    >>> img_rgba = data.logo()
    >>> img_rgb = color.rgba2rgb(img_rgba)
    """
    arr = np.asanyarray(rgba)
    _validate_channel_axis(channel_axis, arr.ndim)
    channel_axis = channel_axis % arr.ndim

    if arr.shape[channel_axis] != 4:
        msg = (
            f'the input array must have size 4 along `channel_axis`, '
            f'got {arr.shape}'
        )
        raise ValueError(msg)

    float_dtype = _supported_float_type(arr.dtype)
    if float_dtype == np.float32:
        arr = dtype.img_as_float32(arr)
    else:
        arr = dtype.img_as_float64(arr)

    background = np.ravel(background).astype(arr.dtype)
    if len(background) != 3:
        raise ValueError(
            'background must be an array-like containing 3 RGB '
            f'values. Got {len(background)} items'
        )
    if np.any(background < 0) or np.any(background > 1):
        raise ValueError('background RGB values must be floats between ' '0 and 1.')
    # reshape background for broadcasting along non-channel axes
    background = reshape_nd(background, arr.ndim, channel_axis)

    alpha = arr[slice_at_axis(slice(3, 4), axis=channel_axis)]
    channels = arr[slice_at_axis(slice(3), axis=channel_axis)]
    out = np.clip((1 - alpha) * background + alpha * channels, a_min=0, a_max=1)
    return out


@channel_as_last_axis()
def rgb2hsv(rgb, *, channel_axis=-1):
    """RGB to HSV color space conversion.

    Parameters
    ----------
    rgb : (..., C=3, ...) array_like
        The image in RGB format. By default, the final dimension denotes
        channels.
    channel_axis : int, optional
        This parameter indicates which axis of the array corresponds to
        channels.

        .. versionadded:: 0.19
           ``channel_axis`` was added in 0.19.

    Returns
    -------
    out : (..., C=3, ...) ndarray
        The image in HSV format. Same dimensions as input.

    Raises
    ------
    ValueError
        If `rgb` is not at least 2-D with shape (..., C=3, ...).

    Notes
    -----
    Conversion between RGB and HSV color spaces results in some loss of
    precision, due to integer arithmetic and rounding [1]_.

    References
    ----------
    .. [1] https://en.wikipedia.org/wiki/HSL_and_HSV

    Examples
    --------
    >>> from skimage import color
    >>> from skimage import data
    >>> img = data.astronaut()
    >>> img_hsv = color.rgb2hsv(img)
    """
    input_is_one_pixel = rgb.ndim == 1
    if input_is_one_pixel:
        rgb = rgb[np.newaxis, ...]

    arr = _prepare_colorarray(rgb, channel_axis=-1)
    out = np.empty_like(arr)

    # -- V channel
    out_v = arr.max(-1)

    # -- S channel
    delta = np.ptp(arr, axis=-1)
    # Ignore warning for zero divided by zero
    old_settings = np.seterr(invalid='ignore')
    out_s = delta / out_v
    out_s[delta == 0.0] = 0.0

    # -- H channel
    # red is max
    idx = arr[..., 0] == out_v
    out[idx, 0] = (arr[idx, 1] - arr[idx, 2]) / delta[idx]

    # green is max
    idx = arr[..., 1] == out_v
    out[idx, 0] = 2.0 + (arr[idx, 2] - arr[idx, 0]) / delta[idx]

    # blue is max
    idx = arr[..., 2] == out_v
    out[idx, 0] = 4.0 + (arr[idx, 0] - arr[idx, 1]) / delta[idx]
    out_h = (out[..., 0] / 6.0) % 1.0
    out_h[delta == 0.0] = 0.0

    np.seterr(**old_settings)

    # -- output
    out[..., 0] = out_h
    out[..., 1] = out_s
    out[..., 2] = out_v

    # # remove NaN
    out[np.isnan(out)] = 0

    if input_is_one_pixel:
        out = np.squeeze(out, axis=0)

    return out


@channel_as_last_axis()
def hsv2rgb(hsv, *, channel_axis=-1):
    """HSV to RGB color space conversion.

    Parameters
    ----------
    hsv : (..., C=3, ...) array_like
        The image in HSV format. By default, the final dimension denotes
        channels.
    channel_axis : int, optional
        This parameter indicates which axis of the array corresponds to
        channels.

        .. versionadded:: 0.19
           ``channel_axis`` was added in 0.19.

    Returns
    -------
    out : (..., C=3, ...) ndarray
        The image in RGB format. Same dimensions as input.

    Raises
    ------
    ValueError
        If `hsv` is not at least 2-D with shape (..., C=3, ...).

    Notes
    -----
    Conversion between RGB and HSV color spaces results in some loss of
    precision, due to integer arithmetic and rounding [1]_.

    References
    ----------
    .. [1] https://en.wikipedia.org/wiki/HSL_and_HSV

    Examples
    --------
    >>> from skimage import data
    >>> img = data.astronaut()
    >>> img_hsv = rgb2hsv(img)
    >>> img_rgb = hsv2rgb(img_hsv)
    """
    arr = _prepare_colorarray(hsv, channel_axis=-1)

    hi = np.floor(arr[..., 0] * 6)
    f = arr[..., 0] * 6 - hi
    p = arr[..., 2] * (1 - arr[..., 1])
    q = arr[..., 2] * (1 - f * arr[..., 1])
    t = arr[..., 2] * (1 - (1 - f) * arr[..., 1])
    v = arr[..., 2]

    hi = np.stack([hi, hi, hi], axis=-1).astype(np.uint8) % 6
    out = np.choose(
        hi,
        np.stack(
            [
                np.stack((v, t, p), axis=-1),
                np.stack((q, v, p), axis=-1),
                np.stack((p, v, t), axis=-1),
                np.stack((p, q, v), axis=-1),
                np.stack((t, p, v), axis=-1),
                np.stack((v, p, q), axis=-1),
            ]
        ),
    )

    return out


# ---------------------------------------------------------------
# Primaries for the coordinate systems
# ---------------------------------------------------------------
cie_primaries = np.array([700, 546.1, 435.8])
sb_primaries = np.array([1.0 / 155, 1.0 / 190, 1.0 / 225]) * 1e5

# ---------------------------------------------------------------
# Matrices that define conversion between different color spaces
# ---------------------------------------------------------------

# From sRGB specification
xyz_from_rgb = np.array(
    [
        [0.412453, 0.357580, 0.180423],
        [0.212671, 0.715160, 0.072169],
        [0.019334, 0.119193, 0.950227],
    ]
)

rgb_from_xyz = linalg.inv(xyz_from_rgb)

# From https://en.wikipedia.org/wiki/CIE_1931_color_space
# Note: Travis's code did not have the divide by 0.17697
xyz_from_rgbcie = (
    np.array([[0.49, 0.31, 0.20], [0.17697, 0.81240, 0.01063], [0.00, 0.01, 0.99]])
    / 0.17697
)

rgbcie_from_xyz = linalg.inv(xyz_from_rgbcie)

# construct matrices to and from rgb:
rgbcie_from_rgb = rgbcie_from_xyz @ xyz_from_rgb
rgb_from_rgbcie = rgb_from_xyz @ xyz_from_rgbcie


gray_from_rgb = np.array([[0.2125, 0.7154, 0.0721], [0, 0, 0], [0, 0, 0]])

yuv_from_rgb = np.array(
    [
        [0.299, 0.587, 0.114],
        [-0.14714119, -0.28886916, 0.43601035],
        [0.61497538, -0.51496512, -0.10001026],
    ]
)

rgb_from_yuv = linalg.inv(yuv_from_rgb)

yiq_from_rgb = np.array(
    [
        [0.299, 0.587, 0.114],
        [0.59590059, -0.27455667, -0.32134392],
        [0.21153661, -0.52273617, 0.31119955],
    ]
)

rgb_from_yiq = linalg.inv(yiq_from_rgb)

ypbpr_from_rgb = np.array(
    [[0.299, 0.587, 0.114], [-0.168736, -0.331264, 0.5], [0.5, -0.418688, -0.081312]]
)

rgb_from_ypbpr = linalg.inv(ypbpr_from_rgb)

ycbcr_from_rgb = np.array(
    [[65.481, 128.553, 24.966], [-37.797, -74.203, 112.0], [112.0, -93.786, -18.214]]
)

rgb_from_ycbcr = linalg.inv(ycbcr_from_rgb)

ydbdr_from_rgb = np.array(
    [[0.299, 0.587, 0.114], [-0.45, -0.883, 1.333], [-1.333, 1.116, 0.217]]
)

rgb_from_ydbdr = linalg.inv(ydbdr_from_rgb)


# CIE LAB constants for Observer=2A, Illuminant=D65
# NOTE: this is actually the XYZ values for the illuminant above.
lab_ref_white = np.array([0.95047, 1.0, 1.08883])

# CIE XYZ tristimulus values of the illuminants, scaled to [0, 1]. For each illuminant I
# we have:
#
#   illuminant[I]['2'] corresponds to the CIE XYZ tristimulus values for the 2 degree
#   field of view.
#
#   illuminant[I]['10'] corresponds to the CIE XYZ tristimulus values for the 10 degree
#   field of view.
#
#   illuminant[I]['R'] corresponds to the CIE XYZ tristimulus values for R illuminants
#   in grDevices::convertColor
#
# The CIE XYZ tristimulus values are calculated from [1], using the formula:
#
#   X = x * ( Y / y )
#   Y = Y
#   Z = ( 1 - x - y ) * ( Y / y )
#
# where Y = 1. The only exception is the illuminant "D65" with aperture angle
# 2, whose coordinates are copied from 'lab_ref_white' for
# backward-compatibility reasons.
#
#     References
#    ----------
#    .. [1] https://en.wikipedia.org/wiki/Standard_illuminant

_illuminants = {
    "A": {
        '2': (1.098466069456375, 1, 0.3558228003436005),
        '10': (1.111420406956693, 1, 0.3519978321919493),
        'R': (1.098466069456375, 1, 0.3558228003436005),
    },
    "B": {
        '2': (0.9909274480248003, 1, 0.8531327322886154),
        '10': (0.9917777147717607, 1, 0.8434930535866175),
        'R': (0.9909274480248003, 1, 0.8531327322886154),
    },
    "C": {
        '2': (0.980705971659919, 1, 1.1822494939271255),
        '10': (0.9728569189782166, 1, 1.1614480488951577),
        'R': (0.980705971659919, 1, 1.1822494939271255),
    },
    "D50": {
        '2': (0.9642119944211994, 1, 0.8251882845188288),
        '10': (0.9672062750333777, 1, 0.8142801513128616),
        'R': (0.9639501491621826, 1, 0.8241280285499208),
    },
    "D55": {
        '2': (0.956797052643698, 1, 0.9214805860173273),
        '10': (0.9579665682254781, 1, 0.9092525159847462),
        'R': (0.9565317453467969, 1, 0.9202554587037198),
    },
    "D65": {
        '2': (0.95047, 1.0, 1.08883),  # This was: `lab_ref_white`
        '10': (0.94809667673716, 1, 1.0730513595166162),
        'R': (0.9532057125493769, 1, 1.0853843816469158),
    },
    "D75": {
        '2': (0.9497220898840717, 1, 1.226393520724154),
        '10': (0.9441713925645873, 1, 1.2064272211720228),
        'R': (0.9497220898840717, 1, 1.226393520724154),
    },
    "E": {'2': (1.0, 1.0, 1.0), '10': (1.0, 1.0, 1.0), 'R': (1.0, 1.0, 1.0)},
}


def xyz_tristimulus_values(*, illuminant, observer, dtype=float):
    """Get the CIE XYZ tristimulus values.

    Given an illuminant and observer, this function returns the CIE XYZ tristimulus
    values [2]_ scaled such that :math:`Y = 1`.

    Parameters
    ----------
    illuminant : {"A", "B", "C", "D50", "D55", "D65", "D75", "E"}
        The name of the illuminant (the function is NOT case sensitive).
    observer : {"2", "10", "R"}
        One of: 2-degree observer, 10-degree observer, or 'R' observer as in
        R function ``grDevices::convertColor`` [3]_.
    dtype : dtype, optional
        Output data type.

    Returns
    -------
    values : array
        Array with 3 elements :math:`X, Y, Z` containing the CIE XYZ tristimulus values
        of the given illuminant.

    Raises
    ------
    ValueError
        If either the illuminant or the observer angle are not supported or
        unknown.

    References
    ----------
    .. [1] https://en.wikipedia.org/wiki/Standard_illuminant#White_points_of_standard_illuminants
    .. [2] https://en.wikipedia.org/wiki/CIE_1931_color_space#Meaning_of_X,_Y_and_Z
    .. [3] https://www.rdocumentation.org/packages/grDevices/versions/3.6.2/topics/convertColor

    Notes
    -----
    The CIE XYZ tristimulus values are calculated from :math:`x, y` [1]_, using the
    formula

    .. math:: X = x / y

    .. math:: Y = 1

    .. math:: Z = (1 - x - y) / y

    The only exception is the illuminant "D65" with aperture angle 2° for
    backward-compatibility reasons.

    Examples
    --------
    Get the CIE XYZ tristimulus values for a "D65" illuminant for a 10 degree field of
    view

    >>> xyz_tristimulus_values(illuminant="D65", observer="10")
    array([0.94809668, 1.        , 1.07305136])
    """
    illuminant = illuminant.upper()
    observer = observer.upper()
    try:
        return np.asarray(_illuminants[illuminant][observer], dtype=dtype)
    except KeyError:
        raise ValueError(
            f'Unknown illuminant/observer combination '
            f'(`{illuminant}`, `{observer}`)'
        )


# Haematoxylin-Eosin-DAB colorspace
# From original Ruifrok's paper: A. C. Ruifrok and D. A. Johnston,
# "Quantification of histochemical staining by color deconvolution,"
# Analytical and quantitative cytology and histology / the International
# Academy of Cytology [and] American Society of Cytology, vol. 23, no. 4,
# pp. 291-9, Aug. 2001.
rgb_from_hed = np.array([[0.65, 0.70, 0.29], [0.07, 0.99, 0.11], [0.27, 0.57, 0.78]])
hed_from_rgb = linalg.inv(rgb_from_hed)

# Following matrices are adapted form the Java code written by G.Landini.
# The original code is available at:
# https://web.archive.org/web/20160624145052/http://www.mecourse.com/landinig/software/cdeconv/cdeconv.html

# Hematoxylin + DAB
rgb_from_hdx = np.array([[0.650, 0.704, 0.286], [0.268, 0.570, 0.776], [0.0, 0.0, 0.0]])
rgb_from_hdx[2, :] = np.cross(rgb_from_hdx[0, :], rgb_from_hdx[1, :])
hdx_from_rgb = linalg.inv(rgb_from_hdx)

# Feulgen + Light Green
rgb_from_fgx = np.array(
    [
        [0.46420921, 0.83008335, 0.30827187],
        [0.94705542, 0.25373821, 0.19650764],
        [0.0, 0.0, 0.0],
    ]
)
rgb_from_fgx[2, :] = np.cross(rgb_from_fgx[0, :], rgb_from_fgx[1, :])
fgx_from_rgb = linalg.inv(rgb_from_fgx)

# Giemsa: Methyl Blue + Eosin
rgb_from_bex = np.array(
    [
        [0.834750233, 0.513556283, 0.196330403],
        [0.092789, 0.954111, 0.283111],
        [0.0, 0.0, 0.0],
    ]
)
rgb_from_bex[2, :] = np.cross(rgb_from_bex[0, :], rgb_from_bex[1, :])
bex_from_rgb = linalg.inv(rgb_from_bex)

# FastRed + FastBlue +  DAB
rgb_from_rbd = np.array(
    [
        [0.21393921, 0.85112669, 0.47794022],
        [0.74890292, 0.60624161, 0.26731082],
        [0.268, 0.570, 0.776],
    ]
)
rbd_from_rgb = linalg.inv(rgb_from_rbd)

# Methyl Green + DAB
rgb_from_gdx = np.array(
    [[0.98003, 0.144316, 0.133146], [0.268, 0.570, 0.776], [0.0, 0.0, 0.0]]
)
rgb_from_gdx[2, :] = np.cross(rgb_from_gdx[0, :], rgb_from_gdx[1, :])
gdx_from_rgb = linalg.inv(rgb_from_gdx)

# Hematoxylin + AEC
rgb_from_hax = np.array(
    [[0.650, 0.704, 0.286], [0.2743, 0.6796, 0.6803], [0.0, 0.0, 0.0]]
)
rgb_from_hax[2, :] = np.cross(rgb_from_hax[0, :], rgb_from_hax[1, :])
hax_from_rgb = linalg.inv(rgb_from_hax)

# Blue matrix Anilline Blue + Red matrix Azocarmine + Orange matrix Orange-G
rgb_from_bro = np.array(
    [
        [0.853033, 0.508733, 0.112656],
        [0.09289875, 0.8662008, 0.49098468],
        [0.10732849, 0.36765403, 0.9237484],
    ]
)
bro_from_rgb = linalg.inv(rgb_from_bro)

# Methyl Blue + Ponceau Fuchsin
rgb_from_bpx = np.array(
    [
        [0.7995107, 0.5913521, 0.10528667],
        [0.09997159, 0.73738605, 0.6680326],
        [0.0, 0.0, 0.0],
    ]
)
rgb_from_bpx[2, :] = np.cross(rgb_from_bpx[0, :], rgb_from_bpx[1, :])
bpx_from_rgb = linalg.inv(rgb_from_bpx)

# Alcian Blue + Hematoxylin
rgb_from_ahx = np.array(
    [[0.874622, 0.457711, 0.158256], [0.552556, 0.7544, 0.353744], [0.0, 0.0, 0.0]]
)
rgb_from_ahx[2, :] = np.cross(rgb_from_ahx[0, :], rgb_from_ahx[1, :])
ahx_from_rgb = linalg.inv(rgb_from_ahx)

# Hematoxylin + PAS
rgb_from_hpx = np.array(
    [[0.644211, 0.716556, 0.266844], [0.175411, 0.972178, 0.154589], [0.0, 0.0, 0.0]]
)
rgb_from_hpx[2, :] = np.cross(rgb_from_hpx[0, :], rgb_from_hpx[1, :])
hpx_from_rgb = linalg.inv(rgb_from_hpx)

# -------------------------------------------------------------
# The conversion functions that make use of the matrices above
# -------------------------------------------------------------


def _convert(matrix, arr):
    """Do the color space conversion.

    Parameters
    ----------
    matrix : array_like
        The 3x3 matrix to use.
    arr : (..., C=3, ...) array_like
        The input array. By default, the final dimension denotes
        channels.

    Returns
    -------
    out : (..., C=3, ...) ndarray
        The converted array. Same dimensions as input.
    """
    arr = _prepare_colorarray(arr)

    return arr @ matrix.T.astype(arr.dtype)


@channel_as_last_axis()
def xyz2rgb(xyz, *, channel_axis=-1):
    """XYZ to RGB color space conversion.

    Parameters
    ----------
    xyz : (..., C=3, ...) array_like
        The image in XYZ format. By default, the final dimension denotes
        channels.
    channel_axis : int, optional
        This parameter indicates which axis of the array corresponds to
        channels.

        .. versionadded:: 0.19
           ``channel_axis`` was added in 0.19.

    Returns
    -------
    out : (..., C=3, ...) ndarray
        The image in RGB format. Same dimensions as input.

    Raises
    ------
    ValueError
        If `xyz` is not at least 2-D with shape (..., C=3, ...).

    Notes
    -----
    The CIE XYZ color space is derived from the CIE RGB color space. Note
    however that this function converts to sRGB.

    References
    ----------
    .. [1] https://en.wikipedia.org/wiki/CIE_1931_color_space

    Examples
    --------
    >>> from skimage import data
    >>> from skimage.color import rgb2xyz, xyz2rgb
    >>> img = data.astronaut()
    >>> img_xyz = rgb2xyz(img)
    >>> img_rgb = xyz2rgb(img_xyz)
    """
    # Follow the algorithm from http://www.easyrgb.com/index.php
    # except we don't multiply/divide by 100 in the conversion
    arr = _convert(rgb_from_xyz, xyz)
    mask = arr > 0.0031308
    arr[mask] = 1.055 * np.power(arr[mask], 1 / 2.4) - 0.055
    arr[~mask] *= 12.92
    np.clip(arr, 0, 1, out=arr)
    return arr


@channel_as_last_axis()
def rgb2xyz(rgb, *, channel_axis=-1):
    """RGB to XYZ color space conversion.

    Parameters
    ----------
    rgb : (..., C=3, ...) array_like
        The image in RGB format. By default, the final dimension denotes
        channels.
    channel_axis : int, optional
        This parameter indicates which axis of the array corresponds to
        channels.

        .. versionadded:: 0.19
           ``channel_axis`` was added in 0.19.

    Returns
    -------
    out : (..., C=3, ...) ndarray
        The image in XYZ format. Same dimensions as input.

    Raises
    ------
    ValueError
        If `rgb` is not at least 2-D with shape (..., C=3, ...).

    Notes
    -----
    The CIE XYZ color space is derived from the CIE RGB color space. Note
    however that this function converts from sRGB.

    References
    ----------
    .. [1] https://en.wikipedia.org/wiki/CIE_1931_color_space

    Examples
    --------
    >>> from skimage import data
    >>> img = data.astronaut()
    >>> img_xyz = rgb2xyz(img)
    """
    # Follow the algorithm from http://www.easyrgb.com/index.php
    # except we don't multiply/divide by 100 in the conversion
    arr = _prepare_colorarray(rgb, channel_axis=-1).copy()
    mask = arr > 0.04045
    arr[mask] = np.power((arr[mask] + 0.055) / 1.055, 2.4)
    arr[~mask] /= 12.92
    return arr @ xyz_from_rgb.T.astype(arr.dtype)


@channel_as_last_axis()
def rgb2rgbcie(rgb, *, channel_axis=-1):
    """RGB to RGB CIE color space conversion.

    Parameters
    ----------
    rgb : (..., C=3, ...) array_like
        The image in RGB format. By default, the final dimension denotes
        channels.
    channel_axis : int, optional
        This parameter indicates which axis of the array corresponds to
        channels.

        .. versionadded:: 0.19
           ``channel_axis`` was added in 0.19.

    Returns
    -------
    out : (..., C=3, ...) ndarray
        The image in RGB CIE format. Same dimensions as input.

    Raises
    ------
    ValueError
        If `rgb` is not at least 2-D with shape (..., C=3, ...).

    References
    ----------
    .. [1] https://en.wikipedia.org/wiki/CIE_1931_color_space

    Examples
    --------
    >>> from skimage import data
    >>> from skimage.color import rgb2rgbcie
    >>> img = data.astronaut()
    >>> img_rgbcie = rgb2rgbcie(img)
    """
    return _convert(rgbcie_from_rgb, rgb)


@channel_as_last_axis()
def rgbcie2rgb(rgbcie, *, channel_axis=-1):
    """RGB CIE to RGB color space conversion.

    Parameters
    ----------
    rgbcie : (..., C=3, ...) array_like
        The image in RGB CIE format. By default, the final dimension denotes
        channels.
    channel_axis : int, optional
        This parameter indicates which axis of the array corresponds to
        channels.

        .. versionadded:: 0.19
           ``channel_axis`` was added in 0.19.

    Returns
    -------
    out : (..., C=3, ...) ndarray
        The image in RGB format. Same dimensions as input.

    Raises
    ------
    ValueError
        If `rgbcie` is not at least 2-D with shape (..., C=3, ...).

    References
    ----------
    .. [1] https://en.wikipedia.org/wiki/CIE_1931_color_space

    Examples
    --------
    >>> from skimage import data
    >>> from skimage.color import rgb2rgbcie, rgbcie2rgb
    >>> img = data.astronaut()
    >>> img_rgbcie = rgb2rgbcie(img)
    >>> img_rgb = rgbcie2rgb(img_rgbcie)
    """
    return _convert(rgb_from_rgbcie, rgbcie)


@channel_as_last_axis(multichannel_output=False)
def rgb2gray(rgb, *, channel_axis=-1):
    """Compute luminance of an RGB image.

    Parameters
    ----------
    rgb : (..., C=3, ...) array_like
        The image in RGB format. By default, the final dimension denotes
        channels.

    Returns
    -------
    out : ndarray
        The luminance image - an array which is the same size as the input
        array, but with the channel dimension removed.

    Raises
    ------
    ValueError
        If `rgb` is not at least 2-D with shape (..., C=3, ...).

    Notes
    -----
    The weights used in this conversion are calibrated for contemporary
    CRT phosphors::

        Y = 0.2125 R + 0.7154 G + 0.0721 B

    If there is an alpha channel present, it is ignored.

    References
    ----------
    .. [1] http://poynton.ca/PDFs/ColorFAQ.pdf

    Examples
    --------
    >>> from skimage.color import rgb2gray
    >>> from skimage import data
    >>> img = data.astronaut()
    >>> img_gray = rgb2gray(img)
    """
    rgb = _prepare_colorarray(rgb)
    coeffs = np.array([0.2125, 0.7154, 0.0721], dtype=rgb.dtype)
    return rgb @ coeffs


def gray2rgba(image, alpha=None, *, channel_axis=-1):
    """Create a RGBA representation of a gray-level image.

    Parameters
    ----------
    image : array_like
        Input image.
    alpha : array_like, optional
        Alpha channel of the output image. It may be a scalar or an
        array that can be broadcast to ``image``. If not specified it is
        set to the maximum limit corresponding to the ``image`` dtype.
    channel_axis : int, optional
        This parameter indicates which axis of the output array will correspond
        to channels.

        .. versionadded:: 0.19
           ``channel_axis`` was added in 0.19.

    Returns
    -------
    rgba : ndarray
        RGBA image. A new dimension of length 4 is added to input
        image shape.
    """
    arr = np.asarray(image)
    if alpha is None:
        _, alpha = dtype_limits(arr, clip_negative=False)
    with np.errstate(over="ignore", under="ignore"):
        alpha_arr = np.asarray(alpha).astype(arr.dtype)
    if not np.array_equal(alpha_arr, alpha):
        warn(
            f'alpha cannot be safely cast to image dtype {arr.dtype.name}', stacklevel=2
        )
    try:
        alpha_arr = np.broadcast_to(alpha_arr, arr.shape)
    except ValueError as e:
        raise ValueError("alpha.shape must match image.shape") from e
    rgba = np.stack((arr,) * 3 + (alpha_arr,), axis=channel_axis)
    return rgba


def gray2rgb(image, *, channel_axis=-1):
    """Create an RGB representation of a gray-level image.

    Parameters
    ----------
    image : array_like
        Input image.
    channel_axis : int, optional
        This parameter indicates which axis of the output array will correspond
        to channels.

    Returns
    -------
    rgb : (..., C=3, ...) ndarray
        RGB image. A new dimension of length 3 is added to input image.

    Notes
    -----
    If the input is a 1-dimensional image of shape ``(M,)``, the output
    will be shape ``(M, C=3)``.
    """
    return np.stack(3 * (image,), axis=channel_axis)


@channel_as_last_axis()
def xyz2lab(xyz, illuminant="D65", observer="2", *, channel_axis=-1):
    """XYZ to CIE-LAB color space conversion.

    Parameters
    ----------
    xyz : (..., C=3, ...) array_like
        The image in XYZ format. By default, the final dimension denotes
        channels.
    illuminant : {"A", "B", "C", "D50", "D55", "D65", "D75", "E"}, optional
        The name of the illuminant (the function is NOT case sensitive).
    observer : {"2", "10", "R"}, optional
        One of: 2-degree observer, 10-degree observer, or 'R' observer as in
        R function grDevices::convertColor.
    channel_axis : int, optional
        This parameter indicates which axis of the array corresponds to
        channels.

        .. versionadded:: 0.19
           ``channel_axis`` was added in 0.19.

    Returns
    -------
    out : (..., C=3, ...) ndarray
        The image in CIE-LAB format. Same dimensions as input.

    Raises
    ------
    ValueError
        If `xyz` is not at least 2-D with shape (..., C=3, ...).
    ValueError
        If either the illuminant or the observer angle is unsupported or
        unknown.

    Notes
    -----
    By default Observer="2", Illuminant="D65". CIE XYZ tristimulus values
    x_ref=95.047, y_ref=100., z_ref=108.883. See function
    :func:`~.xyz_tristimulus_values` for a list of supported illuminants.

    References
    ----------
    .. [1] http://www.easyrgb.com/en/math.php
    .. [2] https://en.wikipedia.org/wiki/CIELAB_color_space

    Examples
    --------
    >>> from skimage import data
    >>> from skimage.color import rgb2xyz, xyz2lab
    >>> img = data.astronaut()
    >>> img_xyz = rgb2xyz(img)
    >>> img_lab = xyz2lab(img_xyz)
    """
    arr = _prepare_colorarray(xyz, channel_axis=-1)

    xyz_ref_white = xyz_tristimulus_values(
        illuminant=illuminant, observer=observer, dtype=arr.dtype
    )

    # scale by CIE XYZ tristimulus values of the reference white point
    arr = arr / xyz_ref_white

    # Nonlinear distortion and linear transformation
    mask = arr > 0.008856
    arr[mask] = np.cbrt(arr[mask])
    arr[~mask] = 7.787 * arr[~mask] + 16.0 / 116.0

    x, y, z = arr[..., 0], arr[..., 1], arr[..., 2]

    # Vector scaling
    L = (116.0 * y) - 16.0
    a = 500.0 * (x - y)
    b = 200.0 * (y - z)

    return np.concatenate([x[..., np.newaxis] for x in [L, a, b]], axis=-1)


@channel_as_last_axis()
def lab2xyz(lab, illuminant="D65", observer="2", *, channel_axis=-1):
    """Convert image in CIE-LAB to XYZ color space.

    Parameters
    ----------
    lab : (..., C=3, ...) array_like
        The input image in CIE-LAB color space.
        Unless `channel_axis` is set, the final dimension denotes the CIE-LAB
        channels.
        The L* values range from 0 to 100;
        the a* and b* values range from -128 to 127.
    illuminant : {"A", "B", "C", "D50", "D55", "D65", "D75", "E"}, optional
        The name of the illuminant (the function is NOT case sensitive).
    observer : {"2", "10", "R"}, optional
        The aperture angle of the observer.
    channel_axis : int, optional
        This parameter indicates which axis of the array corresponds to
        channels.

        .. versionadded:: 0.19
           ``channel_axis`` was added in 0.19.

    Returns
    -------
    out : (..., C=3, ...) ndarray
        The image in XYZ color space, of same shape as input.

    Raises
    ------
    ValueError
        If `lab` is not at least 2-D with shape (..., C=3, ...).
    ValueError
        If either the illuminant or the observer angle are not supported or
        unknown.
    UserWarning
        If any of the pixels are invalid (Z < 0).

    Notes
    -----
    The CIE XYZ tristimulus values are x_ref = 95.047, y_ref = 100., and
    z_ref = 108.883. See function :func:`~.xyz_tristimulus_values` for a list of
    supported illuminants.

    See Also
    --------
    xyz2lab

    References
    ----------
    .. [1] http://www.easyrgb.com/en/math.php
    .. [2] https://en.wikipedia.org/wiki/CIELAB_color_space
    """
    xyz, n_invalid = _lab2xyz(lab, illuminant, observer)
    if n_invalid != 0:
        warn(
            "Conversion from CIE-LAB to XYZ color space resulted in "
            f"{n_invalid} negative Z values that have been clipped to zero",
            stacklevel=3,
        )
    return xyz


def _lab2xyz(lab, illuminant, observer):
    """Convert CIE-LAB to XYZ color space.

    Internal function for :func:`~.lab2xyz` and others. In addition to the
    converted image, return the number of invalid pixels in the Z channel for
    correct warning propagation.

    Returns
    -------
    out : (..., C=3, ...) ndarray
        The image in XYZ format. Same dimensions as input.
    n_invalid : int
        Number of invalid pixels in the Z channel after conversion.
    """
    arr = _prepare_colorarray(lab, channel_axis=-1).copy()

    L, a, b = arr[..., 0], arr[..., 1], arr[..., 2]
    y = (L + 16.0) / 116.0
    x = (a / 500.0) + y
    z = y - (b / 200.0)

    invalid = np.atleast_1d(z < 0).nonzero()
    n_invalid = invalid[0].size
    if n_invalid != 0:
        # Warning should be emitted by caller
        if z.ndim > 0:
            z[invalid] = 0
        else:
            z = 0

    out = np.stack([x, y, z], axis=-1)

    mask = out > 0.2068966
    out[mask] = np.power(out[mask], 3.0)
    out[~mask] = (out[~mask] - 16.0 / 116.0) / 7.787

    # rescale to the reference white (illuminant)
    xyz_ref_white = xyz_tristimulus_values(illuminant=illuminant, observer=observer)
    out *= xyz_ref_white
    return out, n_invalid


@channel_as_last_axis()
def rgb2lab(rgb, illuminant="D65", observer="2", *, channel_axis=-1):
    """Conversion from the sRGB color space (IEC 61966-2-1:1999)
    to the CIE Lab colorspace under the given illuminant and observer.

    Parameters
    ----------
    rgb : (..., C=3, ...) array_like
        The image in RGB format. By default, the final dimension denotes
        channels.
    illuminant : {"A", "B", "C", "D50", "D55", "D65", "D75", "E"}, optional
        The name of the illuminant (the function is NOT case sensitive).
    observer : {"2", "10", "R"}, optional
        The aperture angle of the observer.
    channel_axis : int, optional
        This parameter indicates which axis of the array corresponds to
        channels.

        .. versionadded:: 0.19
           ``channel_axis`` was added in 0.19.

    Returns
    -------
    out : (..., C=3, ...) ndarray
        The image in Lab format. Same dimensions as input.

    Raises
    ------
    ValueError
        If `rgb` is not at least 2-D with shape (..., C=3, ...).

    Notes
    -----
    RGB is a device-dependent color space so, if you use this function, be
    sure that the image you are analyzing has been mapped to the sRGB color
    space.

    This function uses rgb2xyz and xyz2lab.
    By default Observer="2", Illuminant="D65". CIE XYZ tristimulus values
    x_ref=95.047, y_ref=100., z_ref=108.883. See function
    :func:`~.xyz_tristimulus_values` for a list of supported illuminants.

    References
    ----------
    .. [1] https://en.wikipedia.org/wiki/Standard_illuminant
    """
    return xyz2lab(rgb2xyz(rgb), illuminant, observer)


@channel_as_last_axis()
def lab2rgb(lab, illuminant="D65", observer="2", *, channel_axis=-1):
    """Convert image in CIE-LAB to sRGB color space.

    Parameters
    ----------
    lab : (..., C=3, ...) array_like
        The input image in CIE-LAB color space.
        Unless `channel_axis` is set, the final dimension denotes the CIE-LAB
        channels.
        The L* values range from 0 to 100;
        the a* and b* values range from -128 to 127.
    illuminant : {"A", "B", "C", "D50", "D55", "D65", "D75", "E"}, optional
        The name of the illuminant (the function is NOT case sensitive).
    observer : {"2", "10", "R"}, optional
        The aperture angle of the observer.
    channel_axis : int, optional
        This parameter indicates which axis of the array corresponds to
        channels.

        .. versionadded:: 0.19
           ``channel_axis`` was added in 0.19.

    Returns
    -------
    out : (..., C=3, ...) ndarray
        The image in sRGB color space, of same shape as input.

    Raises
    ------
    ValueError
        If `lab` is not at least 2-D with shape (..., C=3, ...).

    Notes
    -----
    This function uses :func:`~.lab2xyz` and :func:`~.xyz2rgb`.
    The CIE XYZ tristimulus values are x_ref = 95.047, y_ref = 100., and
    z_ref = 108.883. See function :func:`~.xyz_tristimulus_values` for a list of
    supported illuminants.

    See Also
    --------
    rgb2lab

    References
    ----------
    .. [1] https://en.wikipedia.org/wiki/Standard_illuminant
    .. [2] https://en.wikipedia.org/wiki/CIELAB_color_space
    """
    xyz, n_invalid = _lab2xyz(lab, illuminant, observer)
    if n_invalid != 0:
        warn(
            "Conversion from CIE-LAB, via XYZ to sRGB color space resulted in "
            f"{n_invalid} negative Z values that have been clipped to zero",
            stacklevel=3,
        )
    return xyz2rgb(xyz)


@channel_as_last_axis()
def xyz2luv(xyz, illuminant="D65", observer="2", *, channel_axis=-1):
    """XYZ to CIE-Luv color space conversion.

    Parameters
    ----------
    xyz : (..., C=3, ...) array_like
        The image in XYZ format. By default, the final dimension denotes
        channels.
    illuminant : {"A", "B", "C", "D50", "D55", "D65", "D75", "E"}, optional
        The name of the illuminant (the function is NOT case sensitive).
    observer : {"2", "10", "R"}, optional
        The aperture angle of the observer.
    channel_axis : int, optional
        This parameter indicates which axis of the array corresponds to
        channels.

        .. versionadded:: 0.19
           ``channel_axis`` was added in 0.19.

    Returns
    -------
    out : (..., C=3, ...) ndarray
        The image in CIE-Luv format. Same dimensions as input.

    Raises
    ------
    ValueError
        If `xyz` is not at least 2-D with shape (..., C=3, ...).
    ValueError
        If either the illuminant or the observer angle are not supported or
        unknown.

    Notes
    -----
    By default XYZ conversion weights use observer=2A. Reference whitepoint
    for D65 Illuminant, with XYZ tristimulus values of ``(95.047, 100.,
    108.883)``. See function :func:`~.xyz_tristimulus_values` for a list of supported
    illuminants.

    References
    ----------
    .. [1] http://www.easyrgb.com/en/math.php
    .. [2] https://en.wikipedia.org/wiki/CIELUV

    Examples
    --------
    >>> from skimage import data
    >>> from skimage.color import rgb2xyz, xyz2luv
    >>> img = data.astronaut()
    >>> img_xyz = rgb2xyz(img)
    >>> img_luv = xyz2luv(img_xyz)
    """
    input_is_one_pixel = xyz.ndim == 1
    if input_is_one_pixel:
        xyz = xyz[np.newaxis, ...]

    arr = _prepare_colorarray(xyz, channel_axis=-1)

    # extract channels
    x, y, z = arr[..., 0], arr[..., 1], arr[..., 2]

    eps = np.finfo(arr.dtype).eps

    # compute y_r and L
    xyz_ref_white = xyz_tristimulus_values(
        illuminant=illuminant, observer=observer, dtype=arr.dtype
    )
    L = y / xyz_ref_white[1]
    mask = L > 0.008856
    L[mask] = 116.0 * np.cbrt(L[mask]) - 16.0
    L[~mask] = 903.3 * L[~mask]

    uv_weights = np.array([1, 15, 3], dtype=arr.dtype)
    u0 = 4 * xyz_ref_white[0] / (uv_weights @ xyz_ref_white)
    v0 = 9 * xyz_ref_white[1] / (uv_weights @ xyz_ref_white)

    # u' and v' helper functions
    def fu(X, Y, Z):
        return (4.0 * X) / (X + 15.0 * Y + 3.0 * Z + eps)

    def fv(X, Y, Z):
        return (9.0 * Y) / (X + 15.0 * Y + 3.0 * Z + eps)

    # compute u and v using helper functions
    u = 13.0 * L * (fu(x, y, z) - u0)
    v = 13.0 * L * (fv(x, y, z) - v0)

    out = np.stack([L, u, v], axis=-1)

    if input_is_one_pixel:
        out = np.squeeze(out, axis=0)

    return out


@channel_as_last_axis()
def luv2xyz(luv, illuminant="D65", observer="2", *, channel_axis=-1):
    """CIE-Luv to XYZ color space conversion.

    Parameters
    ----------
    luv : (..., C=3, ...) array_like
        The image in CIE-Luv format. By default, the final dimension denotes
        channels.
    illuminant : {"A", "B", "C", "D50", "D55", "D65", "D75", "E"}, optional
        The name of the illuminant (the function is NOT case sensitive).
    observer : {"2", "10", "R"}, optional
        The aperture angle of the observer.
    channel_axis : int, optional
        This parameter indicates which axis of the array corresponds to
        channels.

        .. versionadded:: 0.19
           ``channel_axis`` was added in 0.19.

    Returns
    -------
    out : (..., C=3, ...) ndarray
        The image in XYZ format. Same dimensions as input.

    Raises
    ------
    ValueError
        If `luv` is not at least 2-D with shape (..., C=3, ...).
    ValueError
        If either the illuminant or the observer angle are not supported or
        unknown.

    Notes
    -----
    XYZ conversion weights use observer=2A. Reference whitepoint for D65
    Illuminant, with XYZ tristimulus values of ``(95.047, 100., 108.883)``. See
    function :func:`~.xyz_tristimulus_values` for a list of supported illuminants.

    References
    ----------
    .. [1] http://www.easyrgb.com/en/math.php
    .. [2] https://en.wikipedia.org/wiki/CIELUV
    """
    arr = _prepare_colorarray(luv, channel_axis=-1).copy()

    L, u, v = arr[..., 0], arr[..., 1], arr[..., 2]

    eps = np.finfo(arr.dtype).eps

    # compute y
    y = L.copy()
    mask = y > 7.999625
    y[mask] = np.power((y[mask] + 16.0) / 116.0, 3.0)
    y[~mask] = y[~mask] / 903.3
    xyz_ref_white = xyz_tristimulus_values(
        illuminant=illuminant, observer=observer, dtype=arr.dtype
    )
    y *= xyz_ref_white[1]

    # reference white x,z
    uv_weights = np.array([1, 15, 3], dtype=arr.dtype)
    u0 = 4 * xyz_ref_white[0] / (uv_weights @ xyz_ref_white)
    v0 = 9 * xyz_ref_white[1] / (uv_weights @ xyz_ref_white)

    # compute intermediate values
    a = u0 + u / (13.0 * L + eps)
    b = v0 + v / (13.0 * L + eps)
    c = 3 * y * (5 * b - 3)

    # compute x and z
    z = ((a - 4) * c - 15 * a * b * y) / (12 * b)
    x = -(c / b + 3.0 * z)

    return np.concatenate([q[..., np.newaxis] for q in [x, y, z]], axis=-1)


@channel_as_last_axis()
def rgb2luv(rgb, *, channel_axis=-1):
    """RGB to CIE-Luv color space conversion.

    Parameters
    ----------
    rgb : (..., C=3, ...) array_like
        The image in RGB format. By default, the final dimension denotes
        channels.
    channel_axis : int, optional
        This parameter indicates which axis of the array corresponds to
        channels.

        .. versionadded:: 0.19
           ``channel_axis`` was added in 0.19.

    Returns
    -------
    out : (..., C=3, ...) ndarray
        The image in CIE Luv format. Same dimensions as input.

    Raises
    ------
    ValueError
        If `rgb` is not at least 2-D with shape (..., C=3, ...).

    Notes
    -----
    This function uses rgb2xyz and xyz2luv.

    References
    ----------
    .. [1] http://www.easyrgb.com/en/math.php
    .. [2] https://en.wikipedia.org/wiki/CIELUV
    """
    return xyz2luv(rgb2xyz(rgb))


@channel_as_last_axis()
def luv2rgb(luv, *, channel_axis=-1):
    """Luv to RGB color space conversion.

    Parameters
    ----------
    luv : (..., C=3, ...) array_like
        The image in CIE Luv format. By default, the final dimension denotes
        channels.

    Returns
    -------
    out : (..., C=3, ...) ndarray
        The image in RGB format. Same dimensions as input.

    Raises
    ------
    ValueError
        If `luv` is not at least 2-D with shape (..., C=3, ...).

    Notes
    -----
    This function uses luv2xyz and xyz2rgb.
    """
    return xyz2rgb(luv2xyz(luv))


@channel_as_last_axis()
def rgb2hed(rgb, *, channel_axis=-1):
    """RGB to Haematoxylin-Eosin-DAB (HED) color space conversion.

    Parameters
    ----------
    rgb : (..., C=3, ...) array_like
        The image in RGB format. By default, the final dimension denotes
        channels.
    channel_axis : int, optional
        This parameter indicates which axis of the array corresponds to
        channels.

        .. versionadded:: 0.19
           ``channel_axis`` was added in 0.19.

    Returns
    -------
    out : (..., C=3, ...) ndarray
        The image in HED format. Same dimensions as input.

    Raises
    ------
    ValueError
        If `rgb` is not at least 2-D with shape (..., C=3, ...).

    References
    ----------
    .. [1] A. C. Ruifrok and D. A. Johnston, "Quantification of histochemical
           staining by color deconvolution.," Analytical and quantitative
           cytology and histology / the International Academy of Cytology [and]
           American Society of Cytology, vol. 23, no. 4, pp. 291-9, Aug. 2001.

    Examples
    --------
    >>> from skimage import data
    >>> from skimage.color import rgb2hed
    >>> ihc = data.immunohistochemistry()
    >>> ihc_hed = rgb2hed(ihc)
    """
    return separate_stains(rgb, hed_from_rgb)


@channel_as_last_axis()
def hed2rgb(hed, *, channel_axis=-1):
    """Haematoxylin-Eosin-DAB (HED) to RGB color space conversion.

    Parameters
    ----------
    hed : (..., C=3, ...) array_like
        The image in the HED color space. By default, the final dimension
        denotes channels.
    channel_axis : int, optional
        This parameter indicates which axis of the array corresponds to
        channels.

        .. versionadded:: 0.19
           ``channel_axis`` was added in 0.19.

    Returns
    -------
    out : (..., C=3, ...) ndarray
        The image in RGB. Same dimensions as input.

    Raises
    ------
    ValueError
        If `hed` is not at least 2-D with shape (..., C=3, ...).

    References
    ----------
    .. [1] A. C. Ruifrok and D. A. Johnston, "Quantification of histochemical
           staining by color deconvolution.," Analytical and quantitative
           cytology and histology / the International Academy of Cytology [and]
           American Society of Cytology, vol. 23, no. 4, pp. 291-9, Aug. 2001.

    Examples
    --------
    >>> from skimage import data
    >>> from skimage.color import rgb2hed, hed2rgb
    >>> ihc = data.immunohistochemistry()
    >>> ihc_hed = rgb2hed(ihc)
    >>> ihc_rgb = hed2rgb(ihc_hed)
    """
    return combine_stains(hed, rgb_from_hed)


@channel_as_last_axis()
def separate_stains(rgb, conv_matrix, *, channel_axis=-1):
    """RGB to stain color space conversion.

    Parameters
    ----------
    rgb : (..., C=3, ...) array_like
        The image in RGB format. By default, the final dimension denotes
        channels.
    conv_matrix : ndarray
        The stain separation matrix as described by G. Landini [1]_.
    channel_axis : int, optional
        This parameter indicates which axis of the array corresponds to
        channels.

        .. versionadded:: 0.19
           ``channel_axis`` was added in 0.19.

    Returns
    -------
    out : (..., C=3, ...) ndarray
        The image in stain color space. Same dimensions as input.

    Raises
    ------
    ValueError
        If `rgb` is not at least 2-D with shape (..., C=3, ...).

    Notes
    -----
    Stain separation matrices available in the ``color`` module and their
    respective colorspace:

    * ``hed_from_rgb``: Hematoxylin + Eosin + DAB
    * ``hdx_from_rgb``: Hematoxylin + DAB
    * ``fgx_from_rgb``: Feulgen + Light Green
    * ``bex_from_rgb``: Giemsa stain : Methyl Blue + Eosin
    * ``rbd_from_rgb``: FastRed + FastBlue +  DAB
    * ``gdx_from_rgb``: Methyl Green + DAB
    * ``hax_from_rgb``: Hematoxylin + AEC
    * ``bro_from_rgb``: Blue matrix Anilline Blue + Red matrix Azocarmine\
                        + Orange matrix Orange-G
    * ``bpx_from_rgb``: Methyl Blue + Ponceau Fuchsin
    * ``ahx_from_rgb``: Alcian Blue + Hematoxylin
    * ``hpx_from_rgb``: Hematoxylin + PAS

    This implementation borrows some ideas from DIPlib [2]_, e.g. the
    compensation using a small value to avoid log artifacts when
    calculating the Beer-Lambert law.

    References
    ----------
    .. [1] https://web.archive.org/web/20160624145052/http://www.mecourse.com/landinig/software/cdeconv/cdeconv.html
    .. [2] https://github.com/DIPlib/diplib/
    .. [3] A. C. Ruifrok and D. A. Johnston, “Quantification of histochemical
           staining by color deconvolution,” Anal. Quant. Cytol. Histol., vol.
           23, no. 4, pp. 291–299, Aug. 2001.

    Examples
    --------
    >>> from skimage import data
    >>> from skimage.color import separate_stains, hdx_from_rgb
    >>> ihc = data.immunohistochemistry()
    >>> ihc_hdx = separate_stains(ihc, hdx_from_rgb)
    """
    rgb = _prepare_colorarray(rgb, force_copy=True, channel_axis=-1)
    np.maximum(rgb, 1e-6, out=rgb)  # avoiding log artifacts
    log_adjust = np.log(1e-6)  # used to compensate the sum above

    stains = (np.log(rgb) / log_adjust) @ conv_matrix

    np.maximum(stains, 0, out=stains)

    return stains


@channel_as_last_axis()
def combine_stains(stains, conv_matrix, *, channel_axis=-1):
    """Stain to RGB color space conversion.

    Parameters
    ----------
    stains : (..., C=3, ...) array_like
        The image in stain color space. By default, the final dimension denotes
        channels.
    conv_matrix : ndarray
        The stain separation matrix as described by G. Landini [1]_.
    channel_axis : int, optional
        This parameter indicates which axis of the array corresponds to
        channels.

        .. versionadded:: 0.19
           ``channel_axis`` was added in 0.19.

    Returns
    -------
    out : (..., C=3, ...) ndarray
        The image in RGB format. Same dimensions as input.

    Raises
    ------
    ValueError
        If `stains` is not at least 2-D with shape (..., C=3, ...).

    Notes
    -----
    Stain combination matrices available in the ``color`` module and their
    respective colorspace:

    * ``rgb_from_hed``: Hematoxylin + Eosin + DAB
    * ``rgb_from_hdx``: Hematoxylin + DAB
    * ``rgb_from_fgx``: Feulgen + Light Green
    * ``rgb_from_bex``: Giemsa stain : Methyl Blue + Eosin
    * ``rgb_from_rbd``: FastRed + FastBlue +  DAB
    * ``rgb_from_gdx``: Methyl Green + DAB
    * ``rgb_from_hax``: Hematoxylin + AEC
    * ``rgb_from_bro``: Blue matrix Anilline Blue + Red matrix Azocarmine\
                        + Orange matrix Orange-G
    * ``rgb_from_bpx``: Methyl Blue + Ponceau Fuchsin
    * ``rgb_from_ahx``: Alcian Blue + Hematoxylin
    * ``rgb_from_hpx``: Hematoxylin + PAS

    References
    ----------
    .. [1] https://web.archive.org/web/20160624145052/http://www.mecourse.com/landinig/software/cdeconv/cdeconv.html
    .. [2] A. C. Ruifrok and D. A. Johnston, “Quantification of histochemical
           staining by color deconvolution,” Anal. Quant. Cytol. Histol., vol.
           23, no. 4, pp. 291–299, Aug. 2001.

    Examples
    --------
    >>> from skimage import data
    >>> from skimage.color import (separate_stains, combine_stains,
    ...                            hdx_from_rgb, rgb_from_hdx)
    >>> ihc = data.immunohistochemistry()
    >>> ihc_hdx = separate_stains(ihc, hdx_from_rgb)
    >>> ihc_rgb = combine_stains(ihc_hdx, rgb_from_hdx)
    """
    stains = _prepare_colorarray(stains, channel_axis=-1)

    # log_adjust here is used to compensate the sum within separate_stains().
    log_adjust = -np.log(1e-6)
    log_rgb = -(stains * log_adjust) @ conv_matrix
    rgb = np.exp(log_rgb)

    return np.clip(rgb, a_min=0, a_max=1)


@channel_as_last_axis()
def lab2lch(lab, *, channel_axis=-1):
    """Convert image in CIE-LAB to CIE-LCh color space.

    CIE-LCh is the cylindrical representation of the CIE-LAB (Cartesian) color
    space.

    Parameters
    ----------
    lab : (..., C=3, ...) array_like
        The input image in CIE-LAB color space.
        Unless `channel_axis` is set, the final dimension denotes the CIE-LAB
        channels.
        The L* values range from 0 to 100;
        the a* and b* values range from -128 to 127.
    channel_axis : int, optional
        This parameter indicates which axis of the array corresponds to
        channels.

        .. versionadded:: 0.19
           ``channel_axis`` was added in 0.19.

    Returns
    -------
    out : (..., C=3, ...) ndarray
        The image in CIE-LCh color space, of same shape as input.

    Raises
    ------
    ValueError
        If `lab` does not have at least 3 channels (i.e., L*, a*, and b*).

    Notes
    -----
    The h channel (i.e., hue) is expressed as an angle in range ``(0, 2*pi)``.

    See Also
    --------
    lch2lab

    References
    ----------
    .. [1] http://www.easyrgb.com/en/math.php
    .. [2] https://en.wikipedia.org/wiki/CIELAB_color_space
    .. [3] https://en.wikipedia.org/wiki/HCL_color_space

    Examples
    --------
    >>> from skimage import data
    >>> from skimage.color import rgb2lab, lab2lch
    >>> img = data.astronaut()
    >>> img_lab = rgb2lab(img)
    >>> img_lch = lab2lch(img_lab)
    """
    lch = _prepare_lab_array(lab)

    a, b = lch[..., 1], lch[..., 2]
    lch[..., 1], lch[..., 2] = _cart2polar_2pi(a, b)
    return lch


def _cart2polar_2pi(x, y):
    """convert cartesian coordinates to polar (uses non-standard theta range!)

    NON-STANDARD RANGE! Maps to ``(0, 2*pi)`` rather than usual ``(-pi, +pi)``
    """
    r, t = np.hypot(x, y), np.arctan2(y, x)
    t += np.where(t < 0.0, 2 * np.pi, 0)
    return r, t


@channel_as_last_axis()
def lch2lab(lch, *, channel_axis=-1):
    """Convert image in CIE-LCh to CIE-LAB color space.

    CIE-LCh is the cylindrical representation of the CIE-LAB (Cartesian) color
    space.

    Parameters
    ----------
    lch : (..., C=3, ...) array_like
        The input image in CIE-LCh color space.
        Unless `channel_axis` is set, the final dimension denotes the CIE-LAB
        channels.
        The L* values range from 0 to 100;
        the C values range from 0 to 100;
        the h values range from 0 to ``2*pi``.
    channel_axis : int, optional
        This parameter indicates which axis of the array corresponds to
        channels.

        .. versionadded:: 0.19
           ``channel_axis`` was added in 0.19.

    Returns
    -------
    out : (..., C=3, ...) ndarray
        The image in CIE-LAB format, of same shape as input.

    Raises
    ------
    ValueError
        If `lch` does not have at least 3 channels (i.e., L*, C, and h).

    Notes
    -----
    The h channel (i.e., hue) is expressed as an angle in range ``(0, 2*pi)``.

    See Also
    --------
    lab2lch

    References
    ----------
    .. [1] http://www.easyrgb.com/en/math.php
    .. [2] https://en.wikipedia.org/wiki/HCL_color_space
    .. [3] https://en.wikipedia.org/wiki/CIELAB_color_space

    Examples
    --------
    >>> from skimage import data
    >>> from skimage.color import rgb2lab, lch2lab, lab2lch
    >>> img = data.astronaut()
    >>> img_lab = rgb2lab(img)
    >>> img_lch = lab2lch(img_lab)
    >>> img_lab2 = lch2lab(img_lch)
    """
    lch = _prepare_lab_array(lch)

    c, h = lch[..., 1], lch[..., 2]
    lch[..., 1], lch[..., 2] = c * np.cos(h), c * np.sin(h)
    return lch


def _prepare_lab_array(arr, force_copy=True):
    """Ensure input for lab2lch and lch2lab is well-formed.

    Input array must be in floating point and have at least 3 elements in the
    last dimension. Returns a new array by default.
    """
    arr = np.asarray(arr)
    shape = arr.shape
    if shape[-1] < 3:
        raise ValueError('Input image has less than 3 channels.')
    float_dtype = _supported_float_type(arr.dtype)
    if float_dtype == np.float32:
        _func = dtype.img_as_float32
    else:
        _func = dtype.img_as_float64
    return _func(arr, force_copy=force_copy)


@channel_as_last_axis()
def rgb2yuv(rgb, *, channel_axis=-1):
    """RGB to YUV color space conversion.

    Parameters
    ----------
    rgb : (..., C=3, ...) array_like
        The image in RGB format. By default, the final dimension denotes
        channels.
    channel_axis : int, optional
        This parameter indicates which axis of the array corresponds to
        channels.

        .. versionadded:: 0.19
           ``channel_axis`` was added in 0.19.

    Returns
    -------
    out : (..., C=3, ...) ndarray
        The image in YUV format. Same dimensions as input.

    Raises
    ------
    ValueError
        If `rgb` is not at least 2-D with shape (..., C=3, ...).

    Notes
    -----
    Y is between 0 and 1.  Use YCbCr instead of YUV for the color space
    commonly used by video codecs, where Y ranges from 16 to 235.

    References
    ----------
    .. [1] https://en.wikipedia.org/wiki/YUV
    """
    return _convert(yuv_from_rgb, rgb)


@channel_as_last_axis()
def rgb2yiq(rgb, *, channel_axis=-1):
    """RGB to YIQ color space conversion.

    Parameters
    ----------
    rgb : (..., C=3, ...) array_like
        The image in RGB format. By default, the final dimension denotes
        channels.
    channel_axis : int, optional
        This parameter indicates which axis of the array corresponds to
        channels.

        .. versionadded:: 0.19
           ``channel_axis`` was added in 0.19.

    Returns
    -------
    out : (..., C=3, ...) ndarray
        The image in YIQ format. Same dimensions as input.

    Raises
    ------
    ValueError
        If `rgb` is not at least 2-D with shape (..., C=3, ...).
    """
    return _convert(yiq_from_rgb, rgb)


@channel_as_last_axis()
def rgb2ypbpr(rgb, *, channel_axis=-1):
    """RGB to YPbPr color space conversion.

    Parameters
    ----------
    rgb : (..., C=3, ...) array_like
        The image in RGB format. By default, the final dimension denotes
        channels.
    channel_axis : int, optional
        This parameter indicates which axis of the array corresponds to
        channels.

        .. versionadded:: 0.19
           ``channel_axis`` was added in 0.19.

    Returns
    -------
    out : (..., C=3, ...) ndarray
        The image in YPbPr format. Same dimensions as input.

    Raises
    ------
    ValueError
        If `rgb` is not at least 2-D with shape (..., C=3, ...).

    References
    ----------
    .. [1] https://en.wikipedia.org/wiki/YPbPr
    """
    return _convert(ypbpr_from_rgb, rgb)


@channel_as_last_axis()
def rgb2ycbcr(rgb, *, channel_axis=-1):
    """RGB to YCbCr color space conversion.

    Parameters
    ----------
    rgb : (..., C=3, ...) array_like
        The image in RGB format. By default, the final dimension denotes
        channels.
    channel_axis : int, optional
        This parameter indicates which axis of the array corresponds to
        channels.

        .. versionadded:: 0.19
           ``channel_axis`` was added in 0.19.

    Returns
    -------
    out : (..., C=3, ...) ndarray
        The image in YCbCr format. Same dimensions as input.

    Raises
    ------
    ValueError
        If `rgb` is not at least 2-D with shape (..., C=3, ...).

    Notes
    -----
    Y is between 16 and 235. This is the color space commonly used by video
    codecs; it is sometimes incorrectly called "YUV".

    References
    ----------
    .. [1] https://en.wikipedia.org/wiki/YCbCr
    """
    arr = _convert(ycbcr_from_rgb, rgb)
    arr[..., 0] += 16
    arr[..., 1] += 128
    arr[..., 2] += 128
    return arr


@channel_as_last_axis()
def rgb2ydbdr(rgb, *, channel_axis=-1):
    """RGB to YDbDr color space conversion.

    Parameters
    ----------
    rgb : (..., C=3, ...) array_like
        The image in RGB format. By default, the final dimension denotes
        channels.
    channel_axis : int, optional
        This parameter indicates which axis of the array corresponds to
        channels.

        .. versionadded:: 0.19
           ``channel_axis`` was added in 0.19.

    Returns
    -------
    out : (..., C=3, ...) ndarray
        The image in YDbDr format. Same dimensions as input.

    Raises
    ------
    ValueError
        If `rgb` is not at least 2-D with shape (..., C=3, ...).

    Notes
    -----
    This is the color space commonly used by video codecs. It is also the
    reversible color transform in JPEG2000.

    References
    ----------
    .. [1] https://en.wikipedia.org/wiki/YDbDr
    """
    arr = _convert(ydbdr_from_rgb, rgb)
    return arr


@channel_as_last_axis()
def yuv2rgb(yuv, *, channel_axis=-1):
    """YUV to RGB color space conversion.

    Parameters
    ----------
    yuv : (..., C=3, ...) array_like
        The image in YUV format. By default, the final dimension denotes
        channels.

    Returns
    -------
    out : (..., C=3, ...) ndarray
        The image in RGB format. Same dimensions as input.

    Raises
    ------
    ValueError
        If `yuv` is not at least 2-D with shape (..., C=3, ...).

    References
    ----------
    .. [1] https://en.wikipedia.org/wiki/YUV
    """
    return _convert(rgb_from_yuv, yuv)


@channel_as_last_axis()
def yiq2rgb(yiq, *, channel_axis=-1):
    """YIQ to RGB color space conversion.

    Parameters
    ----------
    yiq : (..., C=3, ...) array_like
        The image in YIQ format. By default, the final dimension denotes
        channels.
    channel_axis : int, optional
        This parameter indicates which axis of the array corresponds to
        channels.

        .. versionadded:: 0.19
           ``channel_axis`` was added in 0.19.

    Returns
    -------
    out : (..., C=3, ...) ndarray
        The image in RGB format. Same dimensions as input.

    Raises
    ------
    ValueError
        If `yiq` is not at least 2-D with shape (..., C=3, ...).
    """
    return _convert(rgb_from_yiq, yiq)


@channel_as_last_axis()
def ypbpr2rgb(ypbpr, *, channel_axis=-1):
    """YPbPr to RGB color space conversion.

    Parameters
    ----------
    ypbpr : (..., C=3, ...) array_like
        The image in YPbPr format. By default, the final dimension denotes
        channels.
    channel_axis : int, optional
        This parameter indicates which axis of the array corresponds to
        channels.

        .. versionadded:: 0.19
           ``channel_axis`` was added in 0.19.

    Returns
    -------
    out : (..., C=3, ...) ndarray
        The image in RGB format. Same dimensions as input.

    Raises
    ------
    ValueError
        If `ypbpr` is not at least 2-D with shape (..., C=3, ...).

    References
    ----------
    .. [1] https://en.wikipedia.org/wiki/YPbPr
    """
    return _convert(rgb_from_ypbpr, ypbpr)


@channel_as_last_axis()
def ycbcr2rgb(ycbcr, *, channel_axis=-1):
    """YCbCr to RGB color space conversion.

    Parameters
    ----------
    ycbcr : (..., C=3, ...) array_like
        The image in YCbCr format. By default, the final dimension denotes
        channels.
    channel_axis : int, optional
        This parameter indicates which axis of the array corresponds to
        channels.

        .. versionadded:: 0.19
           ``channel_axis`` was added in 0.19.

    Returns
    -------
    out : (..., C=3, ...) ndarray
        The image in RGB format. Same dimensions as input.

    Raises
    ------
    ValueError
        If `ycbcr` is not at least 2-D with shape (..., C=3, ...).

    Notes
    -----
    Y is between 16 and 235. This is the color space commonly used by video
    codecs; it is sometimes incorrectly called "YUV".

    References
    ----------
    .. [1] https://en.wikipedia.org/wiki/YCbCr
    """
    arr = ycbcr.copy()
    arr[..., 0] -= 16
    arr[..., 1] -= 128
    arr[..., 2] -= 128
    return _convert(rgb_from_ycbcr, arr)


@channel_as_last_axis()
def ydbdr2rgb(ydbdr, *, channel_axis=-1):
    """YDbDr to RGB color space conversion.

    Parameters
    ----------
    ydbdr : (..., C=3, ...) array_like
        The image in YDbDr format. By default, the final dimension denotes
        channels.
    channel_axis : int, optional
        This parameter indicates which axis of the array corresponds to
        channels.

        .. versionadded:: 0.19
           ``channel_axis`` was added in 0.19.

    Returns
    -------
    out : (..., C=3, ...) ndarray
        The image in RGB format. Same dimensions as input.

    Raises
    ------
    ValueError
        If `ydbdr` is not at least 2-D with shape (..., C=3, ...).

    Notes
    -----
    This is the color space commonly used by video codecs, also called the
    reversible color transform in JPEG2000.

    References
    ----------
    .. [1] https://en.wikipedia.org/wiki/YDbDr
    """
    return _convert(rgb_from_ydbdr, ydbdr)
