Source code for colour.temperature.planck1900
"""
Blackbody - Planck (1900) - Correlated Colour Temperature
=========================================================
Defines the *Planck (1900)* correlated colour temperature :math:`T_{cp}`
computations objects based on the spectral radiance of a planckian radiator:
- :func:`colour.temperature.uv_to_CCT_Planck1900`
- :func:`colour.temperature.CCT_to_uv_Planck1900`
References
----------
- :cite:`CIETC1-482004i` : CIE TC 1-48. (2004). APPENDIX E. INFORMATION ON
THE USE OF PLANCK'S EQUATION FOR STANDARD AIR. In CIE 015:2004 Colorimetry,
3rd Edition (pp. 77-82). ISBN:978-3-901906-33-6
"""
from __future__ import annotations
import numpy as np
from scipy.optimize import minimize
from colour.colorimetry import (
MultiSpectralDistributions,
handle_spectral_arguments,
msds_to_XYZ_integration,
planck_law,
)
from colour.hints import ArrayLike, NDArrayFloat
from colour.models import UCS_to_uv, XYZ_to_UCS
from colour.utilities import as_float, as_float_array
__author__ = "Colour Developers"
__copyright__ = "Copyright 2013 Colour Developers"
__license__ = "BSD-3-Clause - https://opensource.org/licenses/BSD-3-Clause"
__maintainer__ = "Colour Developers"
__email__ = "colour-developers@colour-science.org"
__status__ = "Production"
__all__ = [
"uv_to_CCT_Planck1900",
"CCT_to_uv_Planck1900",
]
[docs]
def uv_to_CCT_Planck1900(
uv: ArrayLike,
cmfs: MultiSpectralDistributions | None = None,
optimisation_kwargs: dict | None = None,
) -> NDArrayFloat:
"""
Return the correlated colour temperature :math:`T_{cp}` of a blackbody from
given *CIE UCS* colourspace *uv* chromaticity coordinates and colour
matching functions.
Parameters
----------
uv
*CIE UCS* colourspace *uv* chromaticity coordinates.
cmfs
Standard observer colour matching functions, default to the
*CIE 1931 2 Degree Standard Observer*.
optimisation_kwargs
Parameters for :func:`scipy.optimize.minimize` definition.
Returns
-------
:class:`numpy.ndarray`
Correlated colour temperature :math:`T_{cp}`.
Warnings
--------
The current implementation relies on optimisation using
:func:`scipy.optimize.minimize` definition and thus has reduced precision
and poor performance.
References
----------
:cite:`CIETC1-482004i`
Examples
--------
>>> uv_to_CCT_Planck1900(np.array([0.20042808, 0.31033343]))
... # doctest: +ELLIPSIS
6504.0000617...
"""
uv = as_float_array(uv)
cmfs, _illuminant = handle_spectral_arguments(cmfs)
shape = uv.shape
uv = np.atleast_1d(np.reshape(uv, (-1, 2)))
def objective_function(CCT: NDArrayFloat, uv: NDArrayFloat) -> NDArrayFloat:
"""Objective function."""
objective = np.linalg.norm(CCT_to_uv_Planck1900(CCT, cmfs) - uv)
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=(uv_i,),
**optimisation_settings,
).x
for uv_i in uv
]
)
return as_float(np.reshape(CCT, shape[:-1]))
[docs]
def CCT_to_uv_Planck1900(
CCT: ArrayLike, cmfs: MultiSpectralDistributions | None = None
) -> NDArrayFloat:
"""
Return the *CIE UCS* colourspace *uv* chromaticity coordinates from given
correlated colour temperature :math:`T_{cp}` and colour matching functions
using the spectral radiance of a blackbody at the given thermodynamic
temperature.
Parameters
----------
CCT
Colour temperature :math:`T_{cp}`.
cmfs
Standard observer colour matching functions, default to the
*CIE 1931 2 Degree Standard Observer*.
Returns
-------
:class:`numpy.ndarray`
*CIE UCS* colourspace *uv* chromaticity coordinates.
References
----------
:cite:`CIETC1-482004i`
Examples
--------
>>> CCT_to_uv_Planck1900(6504) # doctest: +ELLIPSIS
array([ 0.2004280..., 0.3103334...])
"""
CCT = as_float_array(CCT)
cmfs, _illuminant = handle_spectral_arguments(cmfs)
XYZ = msds_to_XYZ_integration(
np.transpose(planck_law(cmfs.wavelengths * 1e-9, np.ravel(CCT)) * 1e-9),
cmfs,
shape=cmfs.shape,
)
UVW = XYZ_to_UCS(XYZ)
uv = UCS_to_uv(UVW)
return np.reshape(uv, [*list(CCT.shape), 2])