Source code for colour.temperature.cie_d

"""
CIE Illuminant D Series Correlated Colour Temperature
=====================================================

Defines the *CIE Illuminant D Series* correlated colour temperature
:math:`T_{cp} computations objects:

-   :func:`colour.temperature.xy_to_CCT_CIE_D`: Correlated colour temperature
    :math:`T_{cp}` computation of a *CIE Illuminant D Series* from its *CIE xy*
    chromaticity coordinates.
-   :func:`colour.temperature.CCT_to_xy_CIE_D`: *CIE xy* chromaticity
    coordinates computation of a *CIE Illuminant D Series* from its correlated
    colour temperature :math:`T_{cp}`.

References
----------
-   :cite:`Wyszecki2000z` : Wyszecki, Gùˆnther, & Stiles, W. S. (2000). CIE
    Method of Calculating D-Illuminants. In Color Science: Concepts and
    Methods, Quantitative Data and Formulae (pp. 145-146). Wiley.
    ISBN:978-0-471-39918-6
"""

from __future__ import annotations

import numpy as np
from scipy.optimize import minimize

from colour.colorimetry import daylight_locus_function
from colour.hints import (
    ArrayLike,
    Dict,
    FloatingOrArrayLike,
    FloatingOrNDArray,
    NDArray,
    Optional,
)
from colour.utilities import as_float_array, as_float, tstack, 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_CIE_D",
    "CCT_to_xy_CIE_D",
]


[docs]def xy_to_CCT_CIE_D( xy: ArrayLike, optimisation_kwargs: Optional[Dict] = None ) -> FloatingOrNDArray: """ Return the correlated colour temperature :math:`T_{cp}` of a *CIE Illuminant D Series* from its *CIE xy* chromaticity coordinates. Parameters ---------- xy *CIE xy* chromaticity coordinates. optimisation_kwargs Parameters for :func:`scipy.optimize.minimize` definition. Returns ------- :class:`numpy.floating` or :class:`numpy.ndarray` Correlated colour temperature :math:`T_{cp}`. Warnings -------- The *CIE Illuminant D Series* method does not give an analytical inverse transformation to compute the correlated colour temperature :math:`T_{cp}` from given *CIE xy* chromaticity coordinates, the current implementation relies on optimization using :func:`scipy.optimize.minimize` definition and thus has reduced precision and poor performance. References ---------- :cite:`Wyszecki2000z` Examples -------- >>> xy_to_CCT_CIE_D(np.array([0.31270775, 0.32911283])) ... # doctest: +ELLIPSIS 6504.3895840... """ xy = as_float_array(xy) shape = xy.shape xy = np.atleast_1d(xy.reshape([-1, 2])) def objective_function( CCT: FloatingOrArrayLike, xy: ArrayLike ) -> FloatingOrNDArray: """Objective function.""" objective = np.linalg.norm(CCT_to_xy_CIE_D(CCT) - xy) return as_float(objective) optimisation_settings = { "method": "Nelder-Mead", "options": { "fatol": 1e-10, }, } if optimisation_kwargs is not None: optimisation_settings.update(optimisation_kwargs) CCT = as_float_array( [ minimize( objective_function, x0=6500, args=(xy_i,), **optimisation_settings, ).x for xy_i in as_float_array(xy) ] ) return as_float(np.reshape(CCT, shape[:-1]))
[docs]def CCT_to_xy_CIE_D(CCT: FloatingOrArrayLike) -> NDArray: """ Return the *CIE xy* chromaticity coordinates of a *CIE Illuminant D Series* from its correlated colour temperature :math:`T_{cp}`. Parameters ---------- CCT Correlated colour temperature :math:`T_{cp}`. Returns ------- :class:`numpy.ndarray` *CIE xy* chromaticity coordinates. Raises ------ ValueError If the correlated colour temperature is not in appropriate domain. References ---------- :cite:`Wyszecki2000z` Examples -------- >>> CCT_to_xy_CIE_D(6504.38938305) # doctest: +ELLIPSIS array([ 0.3127077..., 0.3291128...]) """ CCT = as_float_array(CCT) if np.any(CCT[np.asarray(np.logical_or(CCT < 4000, CCT > 25000))]): usage_warning( "Correlated colour temperature must be in domain " "[4000, 25000], unpredictable results may occur!" ) CCT_3 = CCT**3 CCT_2 = CCT**2 x = np.where( CCT <= 7000, -4.607 * 10**9 / CCT_3 + 2.9678 * 10**6 / CCT_2 + 0.09911 * 10**3 / CCT + 0.244063, -2.0064 * 10**9 / CCT_3 + 1.9018 * 10**6 / CCT_2 + 0.24748 * 10**3 / CCT + 0.23704, ) y = daylight_locus_function(x) return tstack([x, y])