"""
Kang, Moon, Hong, Lee, Cho and Kim (2002) Correlated Colour Temperature
=======================================================================
Defines the *Kang et al. (2002)* correlated colour temperature :math:`T_{cp}`
computations objects:
- :func:`colour.temperature.xy_to_CCT_Kang2002`: Correlated colour
temperature :math:`T_{cp}` of given *CIE xy* chromaticity coordinates
computation using *Kang, Moon, Hong, Lee, Cho and Kim (2002)* method.
- :func:`colour.temperature.CCT_to_xy_Kang2002`: *CIE xy* chromaticity
coordinates computation of given correlated colour temperature
:math:`T_{cp}` using *Kang, Moon, Hong, Lee, Cho and Kim (2002)* method.
References
----------
- :cite:`Kang2002a` : Kang, B., Moon, O., Hong, C., Lee, H., Cho, B., & Kim,
Y. (2002). Design of advanced color: Temperature control system for HDTV
applications. Journal of the Korean Physical Society, 41(6), 865-871.
"""
from __future__ import annotations
import numpy as np
from scipy.optimize import minimize
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_Kang2002",
"CCT_to_xy_Kang2002",
]
[docs]def xy_to_CCT_Kang2002(
xy: ArrayLike, optimisation_kwargs: Optional[Dict] = None
) -> FloatingOrNDArray:
"""
Return the correlated colour temperature :math:`T_{cp}` from given
*CIE xy* chromaticity coordinates using *Kang et al. (2002)* method.
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
--------
*Kang et al. (2002)* 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:`Kang2002a`
Examples
--------
>>> xy_to_CCT_Kang2002(np.array([0.31342600, 0.32359597]))
... # doctest: +ELLIPSIS
6504.3893128...
"""
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_Kang2002(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_Kang2002(CCT: FloatingOrArrayLike) -> NDArray:
"""
Return the *CIE xy* chromaticity coordinates from given correlated colour
temperature :math:`T_{cp}` using *Kang et al. (2002)* method.
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:`Kang2002a`
Examples
--------
>>> CCT_to_xy_Kang2002(6504.38938305) # doctest: +ELLIPSIS
array([ 0.313426 ..., 0.3235959...])
"""
CCT = as_float_array(CCT)
if np.any(CCT[np.asarray(np.logical_or(CCT < 1667, CCT > 25000))]):
usage_warning(
"Correlated colour temperature must be in domain "
"[1667, 25000], unpredictable results may occur!"
)
CCT_3 = CCT**3
CCT_2 = CCT**2
x = np.where(
CCT <= 4000,
-0.2661239 * 10**9 / CCT_3
- 0.2343589 * 10**6 / CCT_2
+ 0.8776956 * 10**3 / CCT
+ 0.179910,
-3.0258469 * 10**9 / CCT_3
+ 2.1070379 * 10**6 / CCT_2
+ 0.2226347 * 10**3 / CCT
+ 0.24039,
)
x_3 = x**3
x_2 = x**2
cnd_l = [CCT <= 2222, np.logical_and(CCT > 2222, CCT <= 4000), CCT > 4000]
i = -1.1063814 * x_3 - 1.34811020 * x_2 + 2.18555832 * x - 0.20219683
j = -0.9549476 * x_3 - 1.37418593 * x_2 + 2.09137015 * x - 0.16748867
k = 3.0817580 * x_3 - 5.8733867 * x_2 + 3.75112997 * x - 0.37001483
y = np.select(cnd_l, [i, j, k])
return tstack([x, y])