Source code for colour.temperature.krystek1985

# -*- coding: utf-8 -*-
"""
Krystek (1985) Correlated Colour Temperature
============================================

Defines the *Krystek (1985)* correlated colour temperature :math:`T_{cp}`
computations objects:

-   :func:`colour.temperature.uv_to_CCT_Krystek1985`: Correlated colour
    temperature :math:`T_{cp}` computation of given *CIE UCS* colourspace *uv*
    chromaticity coordinates using *Krystek (1985)* method.
-   :func:`colour.temperature.CCT_to_uv_Krystek1985`: *CIE UCS* colourspace
    *uv* chromaticity coordinates computation of given correlated colour
    temperature :math:`T_{cp}` using *Krystek (1985)* method.

References
----------
-   :cite:`Krystek1985b` : Krystek, M. (1985). An algorithm to calculate
    correlated colour temperature. Color Research & Application, 10(1), 38-40.
    doi:10.1002/col.5080100109
"""

import numpy as np
from scipy.optimize import minimize

from colour.utilities import as_float_array, as_numeric, tstack

__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013-2021 - 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__ = ['uv_to_CCT_Krystek1985', 'CCT_to_uv_Krystek1985']


[docs]def uv_to_CCT_Krystek1985(uv, optimisation_kwargs=None): """ Returns the correlated colour temperature :math:`T_{cp}` from given *CIE UCS* colourspace *uv* chromaticity coordinates using *Krystek (1985)* method. Parameters ---------- uv : array_like *CIE UCS* colourspace *uv* chromaticity coordinates. optimisation_kwargs : dict_like, optional Parameters for :func:`scipy.optimize.minimize` definition. Returns ------- ndarray Correlated colour temperature :math:`T_{cp}`. Warnings -------- *Krystek (1985)* does not give an analytical inverse transformation to compute the correlated colour temperature :math:`T_{cp}` from given *CIE UCS* colourspace *uv* chromaticity coordinates, the current implementation relies on optimization using :func:`scipy.optimize.minimize` definition and thus has reduced precision and poor performance. Notes ----- - *Krystek (1985)* method computations are valid for correlated colour temperature :math:`T_{cp}` normalised to domain [1000, 15000]. References ---------- :cite:`Krystek1985b` Examples -------- >>> uv_to_CCT_Krystek1985(np.array([0.20047203, 0.31029290])) ... # doctest: +ELLIPSIS 6504.3894290... """ uv = as_float_array(uv) shape = uv.shape uv = np.atleast_1d(uv.reshape([-1, 2])) def objective_function(CCT, uv): """ Objective function. """ objective = np.linalg.norm(CCT_to_uv_Krystek1985(CCT) - uv) return 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=(uv_i, ), **optimisation_settings).x for uv_i in uv ]) return as_numeric(CCT.reshape(shape[:-1]))
[docs]def CCT_to_uv_Krystek1985(CCT): """ Returns the *CIE UCS* colourspace *uv* chromaticity coordinates from given correlated colour temperature :math:`T_{cp}` using *Krystek (1985)* method. Parameters ---------- CCT : array_like Correlated colour temperature :math:`T_{cp}`. Returns ------- ndarray *CIE UCS* colourspace *uv* chromaticity coordinates. Notes ----- - *Krystek (1985)* method computations are valid for correlated colour temperature :math:`T_{cp}` normalised to domain [1000, 15000]. References ---------- :cite:`Krystek1985b` Examples -------- >>> CCT_to_uv_Krystek1985(6504.38938305) # doctest: +ELLIPSIS array([ 0.2004720..., 0.3102929...]) """ T = as_float_array(CCT) T_2 = T ** 2 u = ( (0.860117757 + 1.54118254 * 10 ** -4 * T + 1.28641212 * 10 ** -7 * T_2) / (1 + 8.42420235 * 10 ** -4 * T + 7.08145163 * 10 ** -7 * T_2)) v = ( (0.317398726 + 4.22806245 * 10 ** -5 * T + 4.20481691 * 10 ** -8 * T_2) / (1 - 2.89741816 * 10 ** -5 * T + 1.61456053 * 10 ** -7 * T_2)) return tstack([u, v])