hernandez1999.py

"""
Hernandez-Andres, Lee and Romero (1999) Correlated Colour Temperature
=====================================================================

Defines the *Hernandez-Andres et al. (1999)* correlated colour temperature
:math:`T_{cp}` computations objects:

-   :func:`colour.temperature.xy_to_CCT_Hernandez1999`: Correlated colour
    temperature :math:`T_{cp}` computation of given *CIE xy* chromaticity
    coordinates using *Hernandez-Andres, Lee and Romero (1999)* method.
-   :func:`colour.temperature.CCT_to_xy_Hernandez1999`: *CIE xy* chromaticity
    coordinates computation of given correlated colour temperature
    :math:`T_{cp}` using *Hernandez-Andres, Lee and Romero (1999)* method.

References
----------
-   :cite:`Hernandez-Andres1999a` : Hernández-Andrés, J., Lee, R. L., &
    Romero, J. (1999). Calculating correlated color temperatures across the
    entire gamut of daylight and skylight chromaticities. Applied Optics,
    38(27), 5703. doi:10.1364/AO.38.005703
"""

from __future__ import annotations

import numpy as np
from scipy.optimize import minimize

from colour.algebra import sdiv, sdiv_mode
from colour.colorimetry import CCS_ILLUMINANTS
from colour.hints import ArrayLike, NDArrayFloat
from colour.utilities import as_float_array, as_float, tsplit, usage_warning

__author__ = "Colour Developers"
__copyright__ = "Copyright 2013 Colour Developers"
__license__ = "New BSD License - https://opensource.org/licenses/BSD-3-Clause"
__maintainer__ = "Colour Developers"
__email__ = "colour-developers@colour-science.org"
__status__ = "Production"

__all__ = [
    "xy_to_CCT_Hernandez1999",
    "CCT_to_xy_Hernandez1999",
]


def xy_to_CCT_Hernandez1999(xy: ArrayLike) -> NDArrayFloat:
    """
    Return the correlated colour temperature :math:`T_{cp}` from given
    *CIE xy* chromaticity coordinates using *Hernandez-Andres et al. (1999)*
    method.

    Parameters
    ----------
    xy
        *CIE xy* chromaticity coordinates.

    Returns
    -------
    :class:`numpy.ndarray`
        Correlated colour temperature :math:`T_{cp}`.

    References
    ----------
    :cite:`Hernandez-Andres1999a`

    Examples
    --------
    >>> xy = np.array([0.31270, 0.32900])
    >>> xy_to_CCT_Hernandez1999(xy)  # doctest: +ELLIPSIS
    6500.7420431...
    """

    x, y = tsplit(xy)

    with sdiv_mode():
        n = sdiv(x - 0.3366, y - 0.1735)

    CCT = (
        -949.86315
        + 6253.80338 * np.exp(-n / 0.92159)
        + 28.70599 * np.exp(-n / 0.20039)
        + 0.00004 * np.exp(-n / 0.07125)
    )

    n = np.where(CCT > 50000, (x - 0.3356) / (y - 0.1691), n)

    CCT = np.where(
        CCT > 50000,
        36284.48953
        + 0.00228 * np.exp(-n / 0.07861)
        + 5.4535e-36 * np.exp(-n / 0.01543),
        CCT,
    )

    return as_float(CCT)


def CCT_to_xy_Hernandez1999(
    CCT: ArrayLike, optimisation_kwargs: dict | None = None
) -> NDArrayFloat:
    """
    Return the *CIE xy* chromaticity coordinates from given correlated colour
    temperature :math:`T_{cp}` using *Hernandez-Andres et al. (1999)* method.

    Parameters
    ----------
    CCT
        Correlated colour temperature :math:`T_{cp}`.
    optimisation_kwargs
        Parameters for :func:`scipy.optimize.minimize` definition.

    Returns
    -------
    :class:`numpy.ndarray`
        *CIE xy* chromaticity coordinates.

    Warnings
    --------
    *Hernandez-Andres et al. (1999)* method for computing *CIE xy* chromaticity
    coordinates from given correlated colour temperature is not a bijective
    function and might produce unexpected results. It is given for consistency
    with other correlated colour temperature computation methods but should be
    avoided for practical applications. The current implementation relies on
    optimisation using :func:`scipy.optimize.minimize` definition and thus has
    reduced precision and poor performance.

    References
    ----------
    :cite:`Hernandez-Andres1999a`

    Examples
    --------
    >>> CCT_to_xy_Hernandez1999(6500.7420431786531)  # doctest: +ELLIPSIS
    array([ 0.3127...,  0.329...])
    """

    usage_warning(
        '"Hernandez-Andres et al. (1999)" method for computing "CIE xy" '
        "chromaticity coordinates from given correlated colour temperature is "
        "not a bijective function and might produce unexpected results. It is "
        "given for consistency with other correlated colour temperature "
        "computation methods but should be avoided for practical applications."
    )

    CCT = as_float_array(CCT)
    shape = list(CCT.shape)
    CCT = np.atleast_1d(CCT.reshape([-1, 1]))

    def objective_function(
        xy: NDArrayFloat, CCT: NDArrayFloat
    ) -> NDArrayFloat:
        """Objective function."""

        objective = np.linalg.norm(xy_to_CCT_Hernandez1999(xy) - CCT)

        return as_float(objective)

    optimisation_settings = {
        "method": "Nelder-Mead",
        "options": {
            "fatol": 1e-10,
        },
    }
    if optimisation_kwargs is not None:
        optimisation_settings.update(optimisation_kwargs)

    xy = as_float_array(
        [
            minimize(
                objective_function,
                x0=CCS_ILLUMINANTS["CIE 1931 2 Degree Standard Observer"][
                    "D65"
                ],
                args=(CCT_i,),
                **optimisation_settings,
            ).x
            for CCT_i in CCT
        ]
    )

    return np.reshape(xy, ([*shape, 2]))