Source code for colour.temperature.krystek1985
"""
Krystek (1985) Correlated Colour Temperature
============================================
Define the *Krystek (1985)* correlated colour temperature :math:`T_{cp}`
computation objects.
- :func:`colour.temperature.uv_to_CCT_Krystek1985`: Compute correlated
colour temperature :math:`T_{cp}` from specified *CIE UCS* colourspace
*uv* chromaticity coordinates using the *Krystek (1985)* method.
- :func:`colour.temperature.CCT_to_uv_Krystek1985`: Compute *CIE UCS*
colourspace *uv* chromaticity coordinates from specified correlated
colour temperature :math:`T_{cp}` using the *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
"""
from __future__ import annotations
import typing
if typing.TYPE_CHECKING:
from colour.hints import ArrayLike, NDArrayFloat
from colour.temperature.common import (
CCT_INVERSION_GRID_SAMPLES,
solve_CCT_Newton,
x0_CCT_grid,
)
from colour.utilities import (
array_namespace,
as_float,
as_float_array,
optional,
tstack,
usage_warning,
)
__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_Krystek1985",
"CCT_to_uv_Krystek1985",
]
[docs]
def uv_to_CCT_Krystek1985(
uv: ArrayLike, optimisation_kwargs: dict | None = None
) -> NDArrayFloat:
"""
Compute the correlated colour temperature :math:`T_{cp}` from the
specified *CIE UCS* colourspace *uv* chromaticity coordinates using
*Krystek (1985)* method.
Parameters
----------
uv
*CIE UCS* colourspace *uv* chromaticity coordinates.
optimisation_kwargs
Inversion parameters forwarded to
:func:`colour.temperature.x0_CCT_grid` and
:func:`colour.temperature.solve_CCT_Newton`. Accepted keys are
``samples`` (grid density for the initial guess, default
:attr:`colour.temperature.CCT_INVERSION_GRID_SAMPLES`),
``newton_iterations``, ``backtrack_iterations`` and ``tolerance``
(forwarded to :func:`solve_CCT_Newton`).
Returns
-------
:class:`numpy.ndarray`
Correlated colour temperature :math:`T_{cp}`.
Warnings
--------
*Krystek (1985)* does not provide an analytical inverse transformation
to compute the correlated colour temperature :math:`T_{cp}` from the
specified *CIE UCS* colourspace *uv* chromaticity coordinates. The
current implementation seeds a damped *Gauss-Newton* iteration with a
nearest-neighbour lookup against a coarse grid sampled from the
analytical forward, vectorised across all input samples.
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([0.20047203, 0.31029290]) # doctest: +ELLIPSIS
np.float64(6504.389416...)
"""
optimisation_kwargs = dict(optional(optimisation_kwargs, {}))
uv = as_float_array(uv)
x0 = x0_CCT_grid(
CCT_to_uv_Krystek1985,
uv,
(1000.0, 15000.0),
samples=optimisation_kwargs.pop("samples", CCT_INVERSION_GRID_SAMPLES),
)
return as_float(
solve_CCT_Newton(CCT_to_uv_Krystek1985, uv, x0=x0, **optimisation_kwargs)
)
[docs]
def CCT_to_uv_Krystek1985(CCT: ArrayLike) -> NDArrayFloat:
"""
Compute the *CIE UCS* colourspace *uv* chromaticity coordinates from the
specified correlated colour temperature :math:`T_{cp}` using the
*Krystek (1985)* method.
Parameters
----------
CCT
Correlated colour temperature :math:`T_{cp}`.
Returns
-------
:class:`numpy.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)
xp = array_namespace(T)
if xp.any(xp.logical_or(T < 1000, T > 15000)):
usage_warning(
"Correlated colour temperature must be in domain "
"[1000, 15000], unpredictable results may occur!"
)
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])
