# -*- coding: utf-8 -*-
"""
Hernandez-Andres, Lee and Romero (1999) Correlated Colour Temperature
=====================================================================
Defines *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.
See Also
--------
`Colour Temperature & Correlated Colour Temperature Jupyter Notebook
<http://nbviewer.jupyter.org/github/colour-science/colour-notebooks/\
blob/master/notebooks/temperature/cct.ipynb>`_
References
----------
- :cite:`Hernandez-Andres1999a` : Hernandez-Andres, 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 division, unicode_literals
import numpy as np
from scipy.optimize import minimize
from colour.colorimetry import ILLUMINANTS
from colour.utilities import as_float_array, as_numeric, tsplit, usage_warning
__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013-2020 - 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']
[docs]def xy_to_CCT_Hernandez1999(xy):
"""
Returns the correlated colour temperature :math:`T_{cp}` from given
*CIE xy* chromaticity coordinates using *Hernandez-Andres et al. (1999)*
method.
Parameters
----------
xy : array_like
*CIE xy* chromaticity coordinates.
Returns
-------
numeric
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)
n = (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_numeric(CCT)
[docs]def CCT_to_xy_Hernandez1999(CCT, optimisation_parameters=None):
"""
Returns the *CIE xy* chromaticity coordinates from given correlated colour
temperature :math:`T_{cp}` using *Hernandez-Andres et al. (1999)* method.
Parameters
----------
CCT : numeric or array_like
Correlated colour temperature :math:`T_{cp}`.
optimisation_parameters : dict_like, optional
Parameters for :func:`scipy.optimize.minimize` definition.
Returns
-------
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
optimization 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 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, CCT):
"""
Objective function.
"""
objective = np.linalg.norm(xy_to_CCT_Hernandez1999(xy) - CCT)
return objective
optimisation_settings = {
'method': 'Nelder-Mead',
'options': {
'fatol': 1e-10,
},
}
if optimisation_parameters is not None:
optimisation_settings.update(optimisation_parameters)
CCT = as_float_array([
minimize(
objective_function,
x0=ILLUMINANTS['CIE 1931 2 Degree Standard Observer']['D65'],
args=(CCT_i, ),
**optimisation_settings).x for CCT_i in CCT
])
return as_numeric(CCT.reshape(shape + [2]))