def msds_constant(
k: Floating,
labels: Sequence,
shape: SpectralShape = SPECTRAL_SHAPE_DEFAULT,
**kwargs: Any,
) -> MultiSpectralDistributions:
"""
Return the multi-spectral distributions with given labels and given
spectral shape filled with constant :math:`k` values.
Parameters
----------
k
Constant :math:`k` to fill the multi-spectral distributions with.
labels
Names to use for the :class:`colour.SpectralDistribution` class
instances.
shape
Spectral shape used to create the multi-spectral distributions.
Other Parameters
----------------
kwargs
{:class:`colour.MultiSpectralDistributions`},
See the documentation of the previously listed class.
Returns
-------
:class:`colour.MultiSpectralDistributions`
Constant :math:`k` filled multi-spectral distributions.
Notes
-----
- By default, the multi-spectral distributions will use the shape given
by :attr:`colour.SPECTRAL_SHAPE_DEFAULT` attribute.
Examples
--------
>>> msds = msds_constant(100, labels=['a', 'b', 'c'])
>>> msds.shape
SpectralShape(360.0, 780.0, 1.0)
>>> msds[400]
array([ 100., 100., 100.])
>>> msds.labels # doctest: +SKIP
['a', 'b', 'c']
"""
settings = {"name": f"{k} Constant"}
settings.update(kwargs)
wavelengths = shape.range()
values = full((len(wavelengths), len(labels)), k)
return MultiSpectralDistributions(values,
wavelengths,
labels=labels,
**settings)
def load_TCS_CIE2017(shape: SpectralShape) -> MultiSpectralDistributions:
"""
Load the *CIE 2017 Test Colour Samples* dataset appropriate for the given
spectral shape.
The datasets are cached and won't be loaded again on subsequent calls to
this definition.
Parameters
----------
shape
Spectral shape of the tested illuminant.
Returns
-------
:class:`colour.MultiSpectralDistributions`
*CIE 2017 Test Colour Samples* dataset.
Examples
--------
>>> sds_tcs = load_TCS_CIE2017(SpectralShape(380, 780, 5))
>>> len(sds_tcs.labels)
99
"""
global _CACHE_TCS_CIE2017
interval = shape.interval
attest(
interval in (1, 5),
"Spectral shape interval must be either 1nm or 5nm!",
)
filename = f"tcs_cfi2017_{as_int_scalar(interval)}_nm.csv.gz"
if filename in _CACHE_TCS_CIE2017:
return _CACHE_TCS_CIE2017[filename]
data = np.genfromtxt(str(
os.path.join(RESOURCES_DIRECTORY_CIE2017, filename)),
delimiter=",")
labels = [f"TCS{i} (CIE 2017)" for i in range(99)]
tcs = MultiSpectralDistributions(data[:, 1:], data[:, 0], labels)
_CACHE_TCS_CIE2017[filename] = tcs
return tcs
def tcs_colorimetry_data(
sd_irradiance: SpectralDistribution,
sds_tcs: MultiSpectralDistributions,
cmfs: MultiSpectralDistributions,
) -> Tuple[TCS_ColorimetryData_CIE2017, ...]:
"""
Return the *test colour samples* colorimetry data under given test light
source or reference illuminant spectral distribution for the
*CIE 2017 Colour Fidelity Index* (CFI) computations.
Parameters
----------
sd_irradiance
Test light source or reference illuminant spectral distribution, i.e.
the irradiance emitter.
sds_tcs
*Test colour samples* spectral distributions.
cmfs
Standard observer colour matching functions.
Returns
-------
:class:`tuple`
*Test colour samples* colorimetry data under the given test light
source or reference illuminant spectral distribution.
Examples
--------
>>> delta_E_to_R_f(4.4410383190) # doctest: +ELLIPSIS
70.1208254...
"""
XYZ_w = sd_to_XYZ(sd_ones(), cmfs, sd_irradiance)
Y_b = 20
L_A = 100
surround = VIEWING_CONDITIONS_CIECAM02["Average"]
tcs_data = []
for sd_tcs in sds_tcs.to_sds():
XYZ = sd_to_XYZ(sd_tcs, cmfs, sd_irradiance)
CAM = XYZ_to_CIECAM02(XYZ, XYZ_w, L_A, Y_b, surround, True)
JMh = tstack([CAM.J, CAM.M, CAM.h])
Jpapbp = JMh_CIECAM02_to_CAM02UCS(JMh)
tcs_data.append(
TCS_ColorimetryData_CIE2017(sd_tcs.name, XYZ, CAM, JMh, Jpapbp))
return tuple(tcs_data)
def msds_constant(k, labels, shape=SPECTRAL_SHAPE_DEFAULT, dtype=None):
"""
Returns the multi-spectral distributions with given labels and given
spectral shape filled with constant :math:`k` values.
Parameters
----------
k : numeric
Constant :math:`k` to fill the multi-spectral distributions with.
labels : array_like
Names to use for the :class:`colour.SpectralDistribution` class
instances.
shape : SpectralShape, optional
Spectral shape used to create the multi-spectral distributions.
dtype : type
Data type used for the multi-spectral distributions.
Returns
-------
MultiSpectralDistributions
Constant :math:`k` filled multi-spectral distributions.
Notes
-----
- By default, the multi-spectral distributions will use the shape given
by :attr:`colour.SPECTRAL_SHAPE_DEFAULT` attribute.
Examples
--------
>>> msds = msds_constant(100, labels=['a', 'b', 'c'])
>>> msds.shape
SpectralShape(360.0, 780.0, 1.0)
>>> msds[400]
array([ 100., 100., 100.])
>>> msds.labels # doctest: +SKIP
['a', 'b', 'c']
"""
if dtype is None:
dtype = DEFAULT_FLOAT_DTYPE
wavelengths = shape.range(dtype)
values = full([len(wavelengths), len(labels)], k, dtype)
name = '{0} Constant'.format(k)
return MultiSpectralDistributions(
values, wavelengths, name=name, labels=labels, dtype=dtype)
def load_TCS_CIE2017(shape):
"""
Loads the *CIE 2017 Test Colour Samples* dataset appropriate for the given
spectral shape.
The datasets are cached and won't be loaded again on subsequent calls to
this definition.
Parameters
----------
shape : SpectralShape
Spectral shape of the tested illuminant.
Returns
-------
MultiSpectralDistributions
*CIE 2017 Test Colour Samples* dataset.
Examples
--------
>>> sds_tcs = load_TCS_CIE2017(SpectralShape(interval=5))
>>> len(sds_tcs.labels)
99
"""
global _CACHE_TCS_CIE2017
interval = shape.interval
assert interval in (1, 5), (
'Spectral shape interval must be either 1nm or 5nm!')
filename = 'tcs_cfi2017_{0}_nm.csv.gz'.format(as_int(interval))
if filename in _CACHE_TCS_CIE2017:
return _CACHE_TCS_CIE2017[filename]
data = np.genfromtxt(str(
os.path.join(RESOURCES_DIRECTORY_CIE2017, filename)),
delimiter=',')
labels = ['TCS{0} (CIE 2017)'.format(i) for i in range(99)]
return MultiSpectralDistributions(data[:, 1:], data[:, 0], labels)
0.00413520,
0.78492409,
],
[
0.04727245,
0.32210270,
0.22679484,
0.31613642,
0.11242847,
0.00244144,
],
],
])
MSDS_TWO: MultiSpectralDistributions = MultiSpectralDistributions(
np.transpose(np.reshape(DATA_TWO, [-1, 6])),
SpectralShape(400, 700, 60).range(),
)
TVS_D65_INTEGRATION_MSDS: NDArray = np.array([
[7.50219602, 3.95048275, 8.40152163],
[26.92629005, 15.07170066, 28.71020457],
[16.70060700, 28.21421317, 25.64802044],
[11.57577260, 8.64108703, 6.57740493],
[18.73108262, 35.07369122, 30.14365007],
[45.16559608, 39.61411218, 43.68158810],
[8.17318743, 13.09236381, 25.93755134],
[22.46715798, 19.31066951, 7.95954422],
[6.58106180, 2.52865132, 11.09122159],
[43.91745731, 27.98043364, 11.73313699],
[8.53693599, 19.70195654, 17.70110118],
[23.91114755, 26.21471641, 30.67613685],
[[0.01367208, 0.09127947, 0.01524376, 0.02810712, 0.19176012, 0.04299992],
[0.01591516, 0.31454948, 0.08416876, 0.09071489, 0.71026170, 0.04374762],
[0.00959792, 0.25822842, 0.41388571, 0.22275120, 0.00407416, 0.37439537],
[0.01106279, 0.07090867, 0.02204929, 0.12487984, 0.18168917, 0.00202945],
[0.01791409, 0.29707789, 0.56295109, 0.23752193, 0.00236515, 0.58190280],
[0.10565346, 0.46204320, 0.19180590, 0.56250858, 0.42085907, 0.00270085]],
[[0.04325933, 0.26825359, 0.23732357, 0.05175860, 0.01181048, 0.08233768],
[0.02577249, 0.08305486, 0.04303044, 0.32298771, 0.23022813, 0.00813306],
[0.02484169, 0.12027161, 0.00541695, 0.00654612, 0.18603799, 0.36247808],
[0.01861601, 0.12924391, 0.00785840, 0.40062562, 0.94044405, 0.32133976],
[0.03102159, 0.16815442, 0.37186235, 0.08610666, 0.00413520, 0.78492409],
[0.04727245, 0.32210270, 0.22679484, 0.31613642, 0.11242847, 0.00244144]],
])
MSDS = MultiSpectralDistributions(
np.transpose(np.reshape(MSDS_ARRAY, [-1, 6])),
SpectralShape(400, 700, 60).range())
XYZ_D65_INTEGRATION_MSDS = np.array([
[7.50233492, 3.95038753, 8.40338691],
[26.92687731, 15.07139447, 28.71690972],
[16.70142165, 28.21458593, 25.65389977],
[11.57556582, 8.64089371, 6.57886800],
[18.73219899, 35.07426727, 30.15041858],
[45.16536627, 39.61360393, 43.69092793],
[8.17423105, 13.09267724, 25.94320661],
[22.46636804, 19.31025987, 7.96118575],
[6.58131705, 2.52857864, 11.09362054],
[43.91622393, 27.97952698, 11.73575112],
[8.53774314, 19.70241814, 17.70479540],
[23.91149458, 26.21467120, 30.68294836],
[0.34488011934469100, 0.33148268992224300, 0.32363699470796100],
[0.34191787732329100, 0.33198455035238900, 0.32609730884690000],
[0.33953109298712900, 0.33234117252254500, 0.32812736934018400],
[0.33716950377436700, 0.33291200941553900, 0.32991797595888800],
[0.33617201852771700, 0.33291927969521400, 0.33090790121664900],
[0.33516744343336300, 0.33302767257885600, 0.33180363309599500],
[0.33442162530646300, 0.33317970467326000, 0.33239662725536100],
[0.33400876037640200, 0.33324703097454900, 0.33274078072682400],
[0.33391579279008200, 0.33325934921060100, 0.33282085708148900],
[0.33381845494636700, 0.33327505027938300, 0.33290173128344400],
[0.33367277492845600, 0.33329432844873200, 0.33302596748863200],
[0.33356951340559100, 0.33330942495777500, 0.33311108308149700],
]
)
MSDS_BASIS_FUNCTIONS_sRGB_MALLETT2019: MultiSpectralDistributions = (
MultiSpectralDistributions(
DATA_BASIS_FUNCTIONS_sRGB_MALLETT2019,
SPECTRAL_SHAPE_sRGB_MALLETT2019.range(),
name="Basis Functions - sRGB - Mallett 2019",
labels=("red", "green", "blue"),
)
)
"""
*Mallett and Yuksel (2019)* basis functions for the *sRGB* colourspace.
References
----------
:cite:`Mallett2019`
"""
[0.35760870152308100, 0.32914390227898000, 0.31324730130288600],
[0.34871280010839300, 0.33080872680368200, 0.32047832512463300],
[0.34488011934469100, 0.33148268992224300, 0.32363699470796100],
[0.34191787732329100, 0.33198455035238900, 0.32609730884690000],
[0.33953109298712900, 0.33234117252254500, 0.32812736934018400],
[0.33716950377436700, 0.33291200941553900, 0.32991797595888800],
[0.33617201852771700, 0.33291927969521400, 0.33090790121664900],
[0.33516744343336300, 0.33302767257885600, 0.33180363309599500],
[0.33442162530646300, 0.33317970467326000, 0.33239662725536100],
[0.33400876037640200, 0.33324703097454900, 0.33274078072682400],
[0.33391579279008200, 0.33325934921060100, 0.33282085708148900],
[0.33381845494636700, 0.33327505027938300, 0.33290173128344400],
[0.33367277492845600, 0.33329432844873200, 0.33302596748863200],
[0.33356951340559100, 0.33330942495777500, 0.33311108308149700],
])
MSDS_BASIS_FUNCTIONS_sRGB_MALLETT2019 = MultiSpectralDistributions(
DATA_BASIS_FUNCTIONS_sRGB_MALLETT2019,
SPECTRAL_SHAPE_sRGB_MALLETT2019.range(),
name='Basis Functions - sRGB - Mallett 2019',
labels=('red', 'green', 'blue'))
"""
*Mallett and Yuksel (2019)* basis functions for the *sRGB* colourspace.
References
----------
:cite:`Mallett2019`
MSDS_BASIS_FUNCTIONS_sRGB_MALLETT2019 : MultiSpectralDistributions
"""
def spectral_primary_decomposition_Mallett2019(
colourspace: RGB_Colourspace,
cmfs: Optional[MultiSpectralDistributions] = None,
illuminant: Optional[SpectralDistribution] = None,
metric: Callable = np.linalg.norm,
metric_args: Tuple = tuple(),
optimisation_kwargs: Optional[Dict] = None,
) -> MultiSpectralDistributions:
"""
Perform the spectral primary decomposition as described in *Mallett and
Yuksel (2019)* for given *RGB* colourspace.
Parameters
----------
colourspace
*RGB* colourspace.
cmfs
Standard observer colour matching functions, default to the
*CIE 1931 2 Degree Standard Observer*.
illuminant
Illuminant spectral distribution, default to
*CIE Standard Illuminant D65*.
metric
Function to be minimised, i.e. the objective function.
``metric(basis, *metric_args) -> float``
where ``basis`` is three reflectances concatenated together, each
with a shape matching ``shape``.
metric_args
Additional arguments passed to ``metric``.
optimisation_kwargs
Parameters for :func:`scipy.optimize.minimize` definition.
Returns
-------
:class:`colour.MultiSpectralDistributions`
Basis functions for given *RGB* colourspace.
References
----------
:cite:`Mallett2019`
Notes
-----
- In-addition to the *BT.709* primaries used by the *sRGB* colourspace,
:cite:`Mallett2019` tried *BT.2020*, *P3 D65*, *Adobe RGB 1998*,
*NTSC (1987)*, *Pal/Secam*, *ProPhoto RGB*,
and *Adobe Wide Gamut RGB* primaries, every one of which encompasses a
larger (albeit not-always-enveloping) set of *CIE L\\*a\\*b\\** colours
than BT.709. Of these, only *Pal/Secam* produces a feasible basis,
which is relatively unsurprising since it is very similar to *BT.709*,
whereas the others are significantly larger.
Examples
--------
>>> from colour import MSDS_CMFS, SDS_ILLUMINANTS, SpectralShape
>>> from colour.models import RGB_COLOURSPACE_PAL_SECAM
>>> from colour.utilities import numpy_print_options
>>> cmfs = (
... MSDS_CMFS['CIE 1931 2 Degree Standard Observer'].
... copy().align(SpectralShape(360, 780, 10))
... )
>>> illuminant = SDS_ILLUMINANTS['D65'].copy().align(cmfs.shape)
>>> msds = spectral_primary_decomposition_Mallett2019(
... RGB_COLOURSPACE_PAL_SECAM, cmfs, illuminant, optimisation_kwargs={
... 'options': {'ftol': 1e-5}
... }
... )
>>> with numpy_print_options(suppress=True):
... print(msds) # doctest: +SKIP
[[ 360. 0.3395134... 0.3400214... 0.3204650...]
[ 370. 0.3355246... 0.3338028... 0.3306724...]
[ 380. 0.3376707... 0.3185578... 0.3437715...]
[ 390. 0.3178866... 0.3351754... 0.3469378...]
[ 400. 0.3045154... 0.3248376... 0.3706469...]
[ 410. 0.2935652... 0.2919463... 0.4144884...]
[ 420. 0.1875740... 0.1853729... 0.6270530...]
[ 430. 0.0167983... 0.054483 ... 0.9287186...]
[ 440. 0. ... 0. ... 1. ...]
[ 450. 0. ... 0. ... 1. ...]
[ 460. 0. ... 0. ... 1. ...]
[ 470. 0. ... 0.0458044... 0.9541955...]
[ 480. 0. ... 0.2960917... 0.7039082...]
[ 490. 0. ... 0.5042592... 0.4957407...]
[ 500. 0. ... 0.6655795... 0.3344204...]
[ 510. 0. ... 0.8607541... 0.1392458...]
[ 520. 0. ... 0.9999998... 0.0000001...]
[ 530. 0. ... 1. ... 0. ...]
[ 540. 0. ... 1. ... 0. ...]
[ 550. 0. ... 1. ... 0. ...]
[ 560. 0. ... 0.9924229... 0. ...]
[ 570. 0. ... 0.9970703... 0.0025673...]
[ 580. 0.0396002... 0.9028231... 0.0575766...]
[ 590. 0.7058973... 0.2941026... 0. ...]
[ 600. 1. ... 0. ... 0. ...]
[ 610. 1. ... 0. ... 0. ...]
[ 620. 1. ... 0. ... 0. ...]
[ 630. 1. ... 0. ... 0. ...]
[ 640. 0.9835925... 0.0100166... 0.0063908...]
[ 650. 0.7878949... 0.1265097... 0.0855953...]
[ 660. 0.5987994... 0.2051062... 0.1960942...]
[ 670. 0.4724493... 0.2649623... 0.2625883...]
[ 680. 0.3989806... 0.3007488... 0.3002704...]
[ 690. 0.3666586... 0.3164003... 0.3169410...]
[ 700. 0.3497806... 0.3242863... 0.3259329...]
[ 710. 0.3563736... 0.3232441... 0.3203822...]
[ 720. 0.3362624... 0.3326209... 0.3311165...]
[ 730. 0.3245015... 0.3365982... 0.3389002...]
[ 740. 0.3335520... 0.3320670... 0.3343808...]
[ 750. 0.3441287... 0.3291168... 0.3267544...]
[ 760. 0.3343705... 0.3330132... 0.3326162...]
[ 770. 0.3274633... 0.3305704... 0.3419662...]
[ 780. 0.3475263... 0.3262331... 0.3262404...]]
"""
cmfs, illuminant = handle_spectral_arguments(cmfs, illuminant)
N = len(cmfs.shape)
R_to_XYZ = np.transpose(illuminant.values[..., np.newaxis] * cmfs.values /
(np.sum(cmfs.values[:, 1] * illuminant.values)))
R_to_RGB = np.dot(colourspace.matrix_XYZ_to_RGB, R_to_XYZ)
basis_to_RGB = block_diag(R_to_RGB, R_to_RGB, R_to_RGB)
primaries = np.reshape(np.identity(3), 9)
# Ensure that the reflectances correspond to the correct RGB colours.
colour_match = LinearConstraint(basis_to_RGB, primaries, primaries)
# Ensure that the reflectances are bounded by [0, 1].
energy_conservation = Bounds(np.zeros(3 * N), np.ones(3 * N))
# Ensure that the sum of the three bases is bounded by [0, 1].
sum_matrix = np.transpose(np.tile(np.identity(N), (3, 1)))
sum_constraint = LinearConstraint(sum_matrix, np.zeros(N), np.ones(N))
optimisation_settings = {
"method": "SLSQP",
"constraints": [colour_match, sum_constraint],
"bounds": energy_conservation,
"options": {
"ftol": 1e-10,
},
}
if optimisation_kwargs is not None:
optimisation_settings.update(optimisation_kwargs)
result = minimize(metric,
args=metric_args,
x0=np.zeros(3 * N),
**optimisation_settings)
basis_functions = np.transpose(np.reshape(result.x, (3, N)))
return MultiSpectralDistributions(
basis_functions,
cmfs.shape.range(),
name=f"Basis Functions - {colourspace.name} - Mallett (2019)",
labels=("red", "green", "blue"),
)
def spectral_primary_decomposition_Mallett2019(
colourspace,
cmfs=MSDS_CMFS_STANDARD_OBSERVER[
'CIE 1931 2 Degree Standard Observer'],
illuminant=SDS_ILLUMINANTS['D65'],
metric=np.linalg.norm,
metric_args=tuple(),
optimisation_kwargs=None):
"""
Performs the spectral primary decomposition as described in *Mallett and
Yuksel (2019)* for given *RGB* colourspace.
Parameters
----------
colourspace: RGB_Colourspace
*RGB* colourspace.
cmfs : XYZ_ColourMatchingFunctions, optional
Standard observer colour matching functions.
illuminant : SpectralDistribution, optional
Illuminant spectral distribution.
metric : unicode, optional
Function to be minimised, i.e. the objective function.
``metric(basis, *metric_args) -> float``
where ``basis`` is three reflectances concatenated together, each
with a shape matching ``shape``.
metric_args : tuple, optional
Additional arguments passed to ``metric``.
optimisation_kwargs : dict_like, optional
Parameters for :func:`scipy.optimize.minimize` definition.
Returns
-------
MultiSpectralDistributions
Basis functions for given *RGB* colourspace.
References
----------
:cite:`Mallett2019`
Notes
-----
- In-addition to the *BT.709* primaries used by the *sRGB* colourspace,
:cite:`Mallett2019` tried *BT.2020*, *P3 D65*, *Adobe RGB 1998*,
*NTSC (1987)*, *Pal/Secam*, *ProPhoto RGB*,
and *Adobe Wide Gamut RGB* primaries, every one of which encompasses a
larger (albeit not-always-enveloping) set of *CIE L\\*a\\*b\\** colours
than BT.709. Of these, only *Pal/Secam* produces a feasible basis,
which is relatively unsurprising since it is very similar to *BT.709*,
whereas the others are significantly larger.
Examples
--------
>>> from colour.colorimetry import SpectralShape
>>> from colour.models import RGB_COLOURSPACE_PAL_SECAM
>>> from colour.utilities import numpy_print_options
>>> cmfs = (
... MSDS_CMFS_STANDARD_OBSERVER['CIE 1931 2 Degree Standard Observer'].
... copy().align(SpectralShape(360, 780, 10))
... )
>>> illuminant = SDS_ILLUMINANTS['D65'].copy().align(cmfs.shape)
>>> msds = spectral_primary_decomposition_Mallett2019(
... RGB_COLOURSPACE_PAL_SECAM, cmfs, illuminant, optimisation_kwargs={
... 'options': {'ftol': 1e-5}
... }
... )
>>> with numpy_print_options(suppress=True):
... # Doctests skip for Python 2.x compatibility.
... print(msds) # doctest: +SKIP
[[ 360. 0.3324728... 0.3332663... 0.3342608...]
[ 370. 0.3323307... 0.3327746... 0.3348946...]
[ 380. 0.3341115... 0.3323995... 0.3334889...]
[ 390. 0.3337570... 0.3298092... 0.3364336...]
[ 400. 0.3209352... 0.3218213... 0.3572433...]
[ 410. 0.2881025... 0.2837628... 0.4281346...]
[ 420. 0.1836749... 0.1838893... 0.6324357...]
[ 430. 0.0187212... 0.0529655... 0.9283132...]
[ 440. 0. ... 0. ... 1. ...]
[ 450. 0. ... 0. ... 1. ...]
[ 460. 0. ... 0. ... 1. ...]
[ 470. 0. ... 0.0509556... 0.9490443...]
[ 480. 0. ... 0.2933996... 0.7066003...]
[ 490. 0. ... 0.5001396... 0.4998603...]
[ 500. 0. ... 0.6734805... 0.3265195...]
[ 510. 0. ... 0.8555213... 0.1444786...]
[ 520. 0. ... 0.9999985... 0.0000014...]
[ 530. 0. ... 1. ... 0. ...]
[ 540. 0. ... 1. ... 0. ...]
[ 550. 0. ... 1. ... 0. ...]
[ 560. 0. ... 0.9924229... 0. ...]
[ 570. 0. ... 0.9913344... 0.0083032...]
[ 580. 0.0370289... 0.9145168... 0.0484542...]
[ 590. 0.7100075... 0.2898477... 0.0001446...]
[ 600. 1. ... 0. ... 0. ...]
[ 610. 1. ... 0. ... 0. ...]
[ 620. 1. ... 0. ... 0. ...]
[ 630. 1. ... 0. ... 0. ...]
[ 640. 0.9711347... 0.0137659... 0.0150993...]
[ 650. 0.7996619... 0.1119379... 0.0884001...]
[ 660. 0.6064640... 0.202815 ... 0.1907209...]
[ 670. 0.4662959... 0.2675037... 0.2662005...]
[ 680. 0.4010958... 0.2998989... 0.2990052...]
[ 690. 0.3617485... 0.3208921... 0.3173592...]
[ 700. 0.3496691... 0.3247855... 0.3255453...]
[ 710. 0.3433979... 0.3273540... 0.329248 ...]
[ 720. 0.3358860... 0.3345583... 0.3295556...]
[ 730. 0.3349498... 0.3314232... 0.3336269...]
[ 740. 0.3359954... 0.3340147... 0.3299897...]
[ 750. 0.3310392... 0.3327595... 0.3362012...]
[ 760. 0.3346883... 0.3314158... 0.3338957...]
[ 770. 0.3332167... 0.333371 ... 0.3334122...]
[ 780. 0.3319670... 0.3325476... 0.3354852...]]
"""
if illuminant.shape != cmfs.shape:
runtime_warning(
'Aligning "{0}" illuminant shape to "{1}" colour matching '
'functions shape.'.format(illuminant.name, cmfs.name))
illuminant = illuminant.copy().align(cmfs.shape)
N = len(cmfs.shape)
R_to_XYZ = np.transpose(
np.expand_dims(illuminant.values, axis=1) * cmfs.values /
(np.sum(cmfs.values[:, 1] * illuminant.values)))
R_to_RGB = np.dot(colourspace.matrix_XYZ_to_RGB, R_to_XYZ)
basis_to_RGB = block_diag(R_to_RGB, R_to_RGB, R_to_RGB)
primaries = np.identity(3).reshape(9)
# Ensure the reflectances correspond to the correct RGB colours.
colour_match = LinearConstraint(basis_to_RGB, primaries, primaries)
# Ensure the reflectances are bounded by [0, 1].
energy_conservation = Bounds(np.zeros(3 * N), np.ones(3 * N))
# Ensure the sum of the three bases is bounded by [0, 1].
sum_matrix = np.transpose(np.tile(np.identity(N), (3, 1)))
sum_constraint = LinearConstraint(sum_matrix, np.zeros(N), np.ones(N))
optimisation_settings = {
'method': 'SLSQP',
'constraints': [colour_match, sum_constraint],
'bounds': energy_conservation,
'options': {
'ftol': 1e-10,
}
}
if optimisation_kwargs is not None:
optimisation_settings.update(optimisation_kwargs)
result = minimize(metric,
args=metric_args,
x0=np.zeros(3 * N),
**optimisation_settings)
basis_functions = np.transpose(result.x.reshape(3, N))
return MultiSpectralDistributions(
basis_functions,
cmfs.shape.range(),
name='Basis Functions - {0} - Mallett (2019)'.format(colourspace.name),
labels=('red', 'green', 'blue'))