# Source code for colour.temperature.mccamy1992

```# -*- coding: utf-8 -*-
"""
McCamy (1992) Correlated Colour Temperature
===========================================

Defines the *McCamy (1992)* correlated colour temperature :math:`T_{cp}`
computations objects:

-   :func:`colour.temperature.xy_to_CCT_McCamy1992`: Correlated colour
temperature :math:`T_{cp}` computation of given *CIE xy* chromaticity
coordinates using *McCamy (1992)* method.
-   :func:`colour.temperature.xy_to_CCT_McCamy1992`: *CIE xy* chromaticity
coordinates computation of given correlated colour temperature
:math:`T_{cp}` using *McCamy (1992)* method.

References
----------
-   :cite:`Wikipedia2001` : Wikipedia. (2001). Approximation. Retrieved June
28, 2014, from http://en.wikipedia.org/wiki/Color_temperature#Approximation
"""

import numpy as np
from scipy.optimize import minimize

from colour.colorimetry import CCS_ILLUMINANTS
from colour.utilities import as_float_array, as_numeric, tsplit, usage_warning

__author__ = 'Colour Developers'
__maintainer__ = 'Colour Developers'
__email__ = 'colour-developers@colour-science.org'
__status__ = 'Production'

__all__ = ['xy_to_CCT_McCamy1992', 'CCT_to_xy_McCamy1992']

[docs]def xy_to_CCT_McCamy1992(xy):
"""
Returns the correlated colour temperature :math:`T_{cp}` from given
*CIE xy* chromaticity coordinates using *McCamy (1992)* method.

Parameters
----------
xy : array_like
*CIE xy* chromaticity coordinates.

Returns
-------
numeric or ndarray
Correlated colour temperature :math:`T_{cp}`.

References
----------
:cite:`Wikipedia2001`

Examples
--------
>>> import numpy as np
>>> xy = np.array([0.31270, 0.32900])
>>> xy_to_CCT_McCamy1992(xy)  # doctest: +ELLIPSIS
6505.0805913...
"""

x, y = tsplit(xy)

n = (x - 0.3320) / (y - 0.1858)
CCT = -449 * n ** 3 + 3525 * n ** 2 - 6823.3 * n + 5520.33

return CCT

[docs]def CCT_to_xy_McCamy1992(CCT, optimisation_kwargs=None):
"""
Returns the *CIE xy* chromaticity coordinates from given correlated colour
temperature :math:`T_{cp}` using *McCamy (1992)* method.

Parameters
----------
CCT : numeric or array_like
Correlated colour temperature :math:`T_{cp}`.
optimisation_kwargs : dict_like, optional
Parameters for :func:`scipy.optimize.minimize` definition.

Returns
-------
ndarray
*CIE xy* chromaticity coordinates.

Warnings
--------
*McCamy (1992)* 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:`Wikipedia2001`

Examples
--------
>>> CCT_to_xy_McCamy1992(6505.0805913074782)  # doctest: +ELLIPSIS
array([ 0.3127...,  0.329...])
"""

usage_warning('"McCamy (1992)" 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.')

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_McCamy1992(xy) - CCT)

return 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=CCS_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 + ))
```