# Source code for colour.temperature.mccamy1992

```"""
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
"""

from __future__ import annotations

import numpy as np
from scipy.optimize import minimize

from colour.algebra import sdiv, sdiv_mode
from colour.colorimetry import CCS_ILLUMINANTS
from colour.hints import ArrayLike, NDArrayFloat
from colour.utilities import as_float_array, as_float, 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: ArrayLike) -> NDArrayFloat:
"""
Return the correlated colour temperature :math:`T_{cp}` from given
*CIE xy* chromaticity coordinates using *McCamy (1992)* method.

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

Returns
-------
:class:`numpy.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)

with sdiv_mode():
n = sdiv(x - 0.3320, y - 0.1858)

CCT = -449 * n**3 + 3525 * n**2 - 6823.3 * n + 5520.33

return as_float(CCT)

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

Parameters
----------
CCT
Correlated colour temperature :math:`T_{cp}`.
optimisation_kwargs
Parameters for :func:`scipy.optimize.minimize` definition.

Returns
-------
:class:`numpy.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
optimisation 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: NDArrayFloat, CCT: NDArrayFloat
) -> NDArrayFloat:
"""Objective function."""

objective = np.linalg.norm(xy_to_CCT_McCamy1992(xy) - CCT)

return as_float(objective)

optimisation_settings = {
"options": {
"fatol": 1e-10,
},
}
if optimisation_kwargs is not None:
optimisation_settings.update(optimisation_kwargs)

xy = 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 np.reshape(xy, ([*shape, 2]))
```