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, Günther, & 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, NDArrayFloat
from colour.utilities import as_float, as_float_array, tstack, usage_warning

__author__ = "Colour Developers"
__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: dict | None = None
) -> NDArrayFloat:
"""
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.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 optimisation 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(np.reshape(xy, (-1, 2)))

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

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

return as_float(objective)

optimisation_settings = {
"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 xy
]
)

return as_float(np.reshape(CCT, shape[:-1]))

[docs]
def CCT_to_xy_CIE_D(CCT: ArrayLike) -> NDArrayFloat:
"""
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 = as_float(
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])

```