def test_closest(self):
"""
Tests :func:`colour.utilities.array.closest` definition.
"""
a = np.array([
24.31357115, 63.62396289, 55.71528816, 62.70988028, 46.84480573,
25.40026416
])
self.assertEqual(closest(a, 63.05), 62.70988028)
self.assertEqual(closest(a, 24.90), 25.40026416)
self.assertEqual(closest(a, 51.15), 46.84480573)
def test_closest(self):
"""
Tests :func:`colour.utilities.array.closest` definition.
"""
a = np.array([24.31357115,
63.62396289,
55.71528816,
62.70988028,
46.84480573,
25.40026416])
self.assertEqual(closest(a, 63.05), 62.70988028)
self.assertEqual(closest(a, 24.90), 25.40026416)
self.assertEqual(closest(a, 51.15), 46.84480573)
def mesopic_weighting_function(
wavelength,
Lp,
source='Blue Heavy',
method='MOVE',
photopic_lef=SDS_LEFS_PHOTOPIC['CIE 1924 Photopic Standard Observer'],
scotopic_lef=SDS_LEFS_SCOTOPIC['CIE 1951 Scotopic Standard Observer']):
"""
Calculates the mesopic weighting function factor at given wavelength
:math:`\\lambda` using the photopic luminance :math:`L_p`.
Parameters
----------
wavelength : numeric or array_like
Wavelength :math:`\\lambda` to calculate the mesopic weighting function
factor.
Lp : numeric
Photopic luminance :math:`L_p`.
source : unicode, optional
**{'Blue Heavy', 'Red Heavy'}**,
Light source colour temperature.
method : unicode, optional
**{'MOVE', 'LRC'}**,
Method to calculate the weighting factor.
photopic_lef : SpectralDistribution, optional
:math:`V(\\lambda)` photopic luminous efficiency function.
scotopic_lef : SpectralDistribution, optional
:math:`V^\\prime(\\lambda)` scotopic luminous efficiency function.
Returns
-------
numeric or ndarray
Mesopic weighting function factor.
References
----------
:cite:`Wikipedia2005d`
Examples
--------
>>> mesopic_weighting_function(500, 0.2) # doctest: +ELLIPSIS
0.7052200...
"""
mesopic_x_luminance_values = sorted(DATA_MESOPIC_X.keys())
index = mesopic_x_luminance_values.index(
closest(mesopic_x_luminance_values, Lp))
x = DATA_MESOPIC_X[mesopic_x_luminance_values[index]][source][method]
Vm = (1 - x) * scotopic_lef[wavelength] + x * photopic_lef[wavelength]
return Vm
def mesopic_weighting_function(
wavelength,
Lp,
source='Blue Heavy',
method='MOVE',
photopic_lef=PHOTOPIC_LEFS['CIE 1924 Photopic Standard Observer'],
scotopic_lef=SCOTOPIC_LEFS['CIE 1951 Scotopic Standard Observer']):
"""
Calculates the mesopic weighting function factor at given wavelength
:math:`\\lambda` using the photopic luminance :math:`L_p`.
Parameters
----------
wavelength : numeric or array_like
Wavelength :math:`\\lambda` to calculate the mesopic weighting function
factor.
Lp : numeric
Photopic luminance :math:`L_p`.
source : unicode, optional
**{'Blue Heavy', 'Red Heavy'}**,
Light source colour temperature.
method : unicode, optional
**{'MOVE', 'LRC'}**,
Method to calculate the weighting factor.
photopic_lef : SpectralDistribution, optional
:math:`V(\\lambda)` photopic luminous efficiency function.
scotopic_lef : SpectralDistribution, optional
:math:`V^\\prime(\\lambda)` scotopic luminous efficiency function.
Returns
-------
numeric or ndarray
Mesopic weighting function factor.
References
----------
:cite:`Wikipedia2005d`
Examples
--------
>>> mesopic_weighting_function(500, 0.2) # doctest: +ELLIPSIS
0.7052200...
"""
mesopic_x_luminance_values = sorted(MESOPIC_X_DATA.keys())
index = mesopic_x_luminance_values.index(
closest(mesopic_x_luminance_values, Lp))
x = MESOPIC_X_DATA[mesopic_x_luminance_values[index]][source][method]
Vm = (1 - x) * scotopic_lef[wavelength] + x * photopic_lef[wavelength]
return Vm
def mesopic_weighting_function(wavelength,
Lp,
source='Blue Heavy',
method='MOVE',
photopic_lef=PHOTOPIC_LEFS.get(
'CIE 1924 Photopic Standard Observer'),
scotopic_lef=SCOTOPIC_LEFS.get(
'CIE 1951 Scotopic Standard Observer')):
"""
Calculates the mesopic weighting function factor at given wavelength
:math:`\lambda` using the photopic luminance :math:`L_p`.
Parameters
----------
wavelength : numeric or array_like
Wavelength :math:`\lambda` to calculate the mesopic weighting function
factor.
Lp : numeric
Photopic luminance :math:`L_p`.
source : unicode, optional
**{'Blue Heavy', 'Red Heavy'}**,
Light source colour temperature.
method : unicode, optional
**{'MOVE', 'LRC'}**,
Method to calculate the weighting factor.
photopic_lef : SpectralPowerDistribution, optional
:math:`V(\lambda)` photopic luminous efficiency function.
scotopic_lef : SpectralPowerDistribution, optional
:math:`V^\prime(\lambda)` scotopic luminous efficiency function.
Returns
-------
numeric or ndarray
Mesopic weighting function factor.
Examples
--------
>>> mesopic_weighting_function(500, 0.2) # doctest: +ELLIPSIS
0.7052200...
"""
mesopic_x_luminance_values = sorted(MESOPIC_X_DATA.keys())
index = mesopic_x_luminance_values.index(
closest(mesopic_x_luminance_values, Lp))
x = MESOPIC_X_DATA.get(
mesopic_x_luminance_values[index]).get(source).get(method)
Vm = ((1 - x) *
scotopic_lef.get(wavelength) + x * photopic_lef.get(wavelength))
return Vm
def test_closest(self):
"""Test :func:`colour.utilities.array.closest` definition."""
a = np.array([
24.31357115,
63.62396289,
55.71528816,
62.70988028,
46.84480573,
25.40026416,
])
self.assertEqual(closest(a, 63.05), 62.70988028)
self.assertEqual(closest(a, 51.15), 46.84480573)
self.assertEqual(closest(a, 24.90), 25.40026416)
np.testing.assert_almost_equal(
closest(a, np.array([63.05, 51.15, 24.90])),
np.array([62.70988028, 46.84480573, 25.40026416]),
decimal=7,
)
def domain_distance(self, a):
"""
Returns the euclidean distance between given array and independent
domain :math:`x` closest element.
Parameters
----------
a : numeric or array_like
:math:`a` variable to compute the euclidean distance with
independent domain :math:`x` variable.
Returns
-------
numeric or array_like
Euclidean distance between independent domain :math:`x` variable
and given :math:`a` variable.
"""
n = closest(self.domain, a)
return as_numeric(np.abs(a - n))
def domain_distance(self, a: FloatingOrArrayLike) -> FloatingOrNDArray:
"""
Return the euclidean distance between given array and independent
domain :math:`x` closest element.
Parameters
----------
a
Variable :math:`a` to compute the euclidean distance with
independent domain variable :math:`x`.
Returns
-------
:class:`numpy.floating` or :class:`numpy.ndarray`
Euclidean distance between independent domain variable :math:`x`
and given variable :math:`a`.
"""
n = closest(self.domain, a)
return as_float(np.abs(a - n))
def domain_distance(self, a):
"""
Returns the euclidean distance between given array and independent
domain :math:`x` closest element.
Parameters
----------
a : numeric or array_like
:math:`a` variable to compute the euclidean distance with
independent domain :math:`x` variable.
Returns
-------
numeric or array_like
Euclidean distance between independent domain :math:`x` variable
and given :math:`a` variable.
"""
n = closest(self.domain, a)
return as_float(np.abs(a - n))
def matrix_augmented_Cheung2004(RGB, terms=3):
"""
Performs polynomial expansion of given *RGB* colourspace array using
*Cheung et al. (2004)* method.
Parameters
----------
RGB : array_like
*RGB* colourspace array to expand.
terms : int, optional
Number of terms of the expanded polynomial, must be one of
*[3, 5, 7, 8, 10, 11, 14, 16, 17, 19, 20, 22]*.
Returns
-------
ndarray
Expanded *RGB* colourspace array.
Notes
-----
- This definition combines the augmented matrices given in
:cite:`Cheung2004` and :cite:`Westland2004`.
References
----------
:cite:`Cheung2004`, :cite:`Westland2004`
Examples
--------
>>> RGB = np.array([0.17224810, 0.09170660, 0.06416938])
>>> matrix_augmented_Cheung2004(RGB, terms=5) # doctest: +ELLIPSIS
array([ 0.1722481..., 0.0917066..., 0.0641693..., 0.0010136..., 1...])
"""
R, G, B = tsplit(RGB)
tail = ones(R.shape)
existing_terms = np.array([3, 5, 7, 8, 10, 11, 14, 16, 17, 19, 20, 22])
closest_terms = as_int(closest(existing_terms, terms))
if closest_terms != terms:
raise ValueError('"Cheung et al. (2004)" method does not define '
'an augmented matrix with {0} terms, '
'closest augmented matrix has {1} terms!'.format(
terms, closest_terms))
if terms == 3:
return RGB
elif terms == 5:
return tstack([
R,
G,
B,
R * G * B,
tail,
])
elif terms == 7:
return tstack([
R,
G,
B,
R * G,
R * B,
G * B,
tail,
])
elif terms == 8:
return tstack([
R,
G,
B,
R * G,
R * B,
G * B,
R * G * B,
tail,
])
elif terms == 10:
return tstack([
R,
G,
B,
R * G,
R * B,
G * B,
R**2,
G**2,
B**2,
tail,
])
elif terms == 11:
return tstack([
R,
G,
B,
R * G,
R * B,
G * B,
R**2,
G**2,
B**2,
R * G * B,
tail,
])
elif terms == 14:
return tstack([
R,
G,
B,
R * G,
R * B,
G * B,
R**2,
G**2,
B**2,
R * G * B,
R**3,
G**3,
B**3,
tail,
])
elif terms == 16:
return tstack([
R,
G,
B,
R * G,
R * B,
G * B,
R**2,
G**2,
B**2,
R * G * B,
R**2 * G,
G**2 * B,
B**2 * R,
R**3,
G**3,
B**3,
])
elif terms == 17:
return tstack([
R,
G,
B,
R * G,
R * B,
G * B,
R**2,
G**2,
B**2,
R * G * B,
R**2 * G,
G**2 * B,
B**2 * R,
R**3,
G**3,
B**3,
tail,
])
elif terms == 19:
return tstack([
R,
G,
B,
R * G,
R * B,
G * B,
R**2,
G**2,
B**2,
R * G * B,
R**2 * G,
G**2 * B,
B**2 * R,
R**2 * B,
G**2 * R,
B**2 * G,
R**3,
G**3,
B**3,
])
elif terms == 20:
return tstack([
R,
G,
B,
R * G,
R * B,
G * B,
R**2,
G**2,
B**2,
R * G * B,
R**2 * G,
G**2 * B,
B**2 * R,
R**2 * B,
G**2 * R,
B**2 * G,
R**3,
G**3,
B**3,
tail,
])
elif terms == 22:
return tstack([
R,
G,
B,
R * G,
R * B,
G * B,
R**2,
G**2,
B**2,
R * G * B,
R**2 * G,
G**2 * B,
B**2 * R,
R**2 * B,
G**2 * R,
B**2 * G,
R**3,
G**3,
B**3,
R**2 * G * B,
R * G**2 * B,
R * G * B**2,
])
def polynomial_expansion_Finlayson2015(RGB,
degree=1,
root_polynomial_expansion=True):
"""
Performs polynomial expansion of given *RGB* colourspace array using
*Finlayson et al. (2015)* method.
Parameters
----------
RGB : array_like
*RGB* colourspace array to expand.
degree : int, optional
Expanded polynomial degree.
root_polynomial_expansion : bool
Whether to use the root-polynomials set for the expansion.
Returns
-------
ndarray
Expanded *RGB* colourspace array.
References
----------
:cite:`Finlayson2015`
Examples
--------
>>> RGB = np.array([0.17224810, 0.09170660, 0.06416938])
>>> polynomial_expansion_Finlayson2015(RGB, degree=2) # doctest: +ELLIPSIS
array([ 0.1722481..., 0.0917066..., 0.0641693..., 0.1256832..., \
0.0767121...,
0.1051335...])
"""
R, G, B = tsplit(RGB)
# TODO: Generalise polynomial expansion.
existing_degrees = np.array([1, 2, 3, 4])
closest_degree = as_int(closest(existing_degrees, degree))
if closest_degree != degree:
raise ValueError('"Finlayson et al. (2015)" method does not define '
'a polynomial expansion for {0} degree, '
'closest polynomial expansion is {1} degree!'.format(
degree, closest_degree))
if degree == 1:
return RGB
elif degree == 2:
if root_polynomial_expansion:
return tstack([
R,
G,
B,
spow(R * G, 1 / 2),
spow(G * B, 1 / 2),
spow(R * B, 1 / 2),
])
else:
return tstack([
R,
G,
B,
R**2,
G**2,
B**2,
R * G,
G * B,
R * B,
])
elif degree == 3:
if root_polynomial_expansion:
return tstack([
R,
G,
B,
spow(R * G, 1 / 2),
spow(G * B, 1 / 2),
spow(R * B, 1 / 2),
spow(R * G**2, 1 / 3),
spow(G * B**2, 1 / 3),
spow(R * B**2, 1 / 3),
spow(G * R**2, 1 / 3),
spow(B * G**2, 1 / 3),
spow(B * R**2, 1 / 3),
spow(R * G * B, 1 / 3),
])
else:
return tstack([
R,
G,
B,
R**2,
G**2,
B**2,
R * G,
G * B,
R * B,
R**3,
G**3,
B**3,
R * G**2,
G * B**2,
R * B**2,
G * R**2,
B * G**2,
B * R**2,
R * G * B,
])
elif degree == 4:
if root_polynomial_expansion:
return tstack([
R,
G,
B,
spow(R * G, 1 / 2),
spow(G * B, 1 / 2),
spow(R * B, 1 / 2),
spow(R * G**2, 1 / 3),
spow(G * B**2, 1 / 3),
spow(R * B**2, 1 / 3),
spow(G * R**2, 1 / 3),
spow(B * G**2, 1 / 3),
spow(B * R**2, 1 / 3),
spow(R * G * B, 1 / 3),
spow(R**3 * G, 1 / 4),
spow(R**3 * B, 1 / 4),
spow(G**3 * R, 1 / 4),
spow(G**3 * B, 1 / 4),
spow(B**3 * R, 1 / 4),
spow(B**3 * G, 1 / 4),
spow(R**2 * G * B, 1 / 4),
spow(G**2 * R * B, 1 / 4),
spow(B**2 * R * G, 1 / 4),
])
else:
return tstack([
R,
G,
B,
R**2,
G**2,
B**2,
R * G,
G * B,
R * B,
R**3,
G**3,
B**3,
R * G**2,
G * B**2,
R * B**2,
G * R**2,
B * G**2,
B * R**2,
R * G * B,
R**4,
G**4,
B**4,
R**3 * G,
R**3 * B,
G**3 * R,
G**3 * B,
B**3 * R,
B**3 * G,
R**2 * G**2,
G**2 * B**2,
R**2 * B**2,
R**2 * G * B,
G**2 * R * B,
B**2 * R * G,
])
def mesopic_weighting_function(
wavelength: FloatingOrArrayLike,
L_p: Floating,
source: Union[Literal["Blue Heavy", "Red Heavy"], str] = "Blue Heavy",
method: Union[Literal["MOVE", "LRC"], str] = "MOVE",
photopic_lef: Optional[SpectralDistribution] = None,
scotopic_lef: Optional[SpectralDistribution] = None,
) -> FloatingOrNDArray:
"""
Calculate the mesopic weighting function factor :math:`V_m` at given
wavelength :math:`\\lambda` using the photopic luminance :math:`L_p`.
Parameters
----------
wavelength
Wavelength :math:`\\lambda` to calculate the mesopic weighting function
factor.
L_p
Photopic luminance :math:`L_p`.
source
Light source colour temperature.
method
Method to calculate the weighting factor.
photopic_lef
:math:`V(\\lambda)` photopic luminous efficiency function, default to
the *CIE 1924 Photopic Standard Observer*.
scotopic_lef
:math:`V^\\prime(\\lambda)` scotopic luminous efficiency function,
default to the *CIE 1951 Scotopic Standard Observer*.
Returns
-------
:class:`numpy.floating` or :class:`numpy.ndarray`
Mesopic weighting function factor :math:`V_m`.
References
----------
:cite:`Wikipedia2005d`
Examples
--------
>>> mesopic_weighting_function(500, 0.2) # doctest: +ELLIPSIS
0.7052200...
"""
photopic_lef = cast(
SpectralDistribution,
optional(
photopic_lef,
SDS_LEFS_PHOTOPIC["CIE 1924 Photopic Standard Observer"],
),
)
scotopic_lef = cast(
SpectralDistribution,
optional(
scotopic_lef,
SDS_LEFS_SCOTOPIC["CIE 1951 Scotopic Standard Observer"],
),
)
source = validate_method(
source,
["Blue Heavy", "Red Heavy"],
'"{0}" light source colour temperature is invalid, '
"it must be one of {1}!",
)
method = validate_method(method, ["MOVE", "LRC"])
mesopic_x_luminance_values = sorted(DATA_MESOPIC_X.keys())
index = mesopic_x_luminance_values.index(
closest(mesopic_x_luminance_values, L_p))
x = DATA_MESOPIC_X[mesopic_x_luminance_values[index]][source][method]
V_m = (1 - x) * scotopic_lef[wavelength] + x * photopic_lef[wavelength]
return V_m
def augmented_matrix_Cheung2004(RGB, terms=3):
"""
Performs polynomial expansion of given *RGB* colourspace array using
*Cheung et al. (2004)* method.
Parameters
----------
RGB : array_like
*RGB* colourspace array to expand.
terms : int, optional
Number of terms of the expanded polynomial, must be one of
*[3, 5, 7, 8, 10, 11, 14, 16, 17, 19, 20, 22]*.
Returns
-------
ndarray
Expanded *RGB* colourspace array.
Notes
-----
- This definition combines the augmented matrices given in
:cite:`Cheung2004` and :cite:`Westland2004`.
References
----------
:cite:`Cheung2004`, :cite:`Westland2004`
Examples
--------
>>> RGB = np.array([0.17224810, 0.09170660, 0.06416938])
>>> augmented_matrix_Cheung2004(RGB, terms=5) # doctest: +ELLIPSIS
array([ 0.1722481..., 0.0917066..., 0.0641693..., 0.0010136..., 1...])
"""
R, G, B = tsplit(RGB)
ones = np.ones(R.shape)
existing_terms = np.array([3, 5, 7, 8, 10, 11, 14, 16, 17, 19, 20, 22])
closest_terms = as_int(closest(existing_terms, terms))
if closest_terms != terms:
raise ValueError('"Cheung et al. (2004)" method does not define '
'an augmented matrix with {0} terms, '
'closest augmented matrix has {1} terms!'.format(
terms, closest_terms))
if terms == 3:
return RGB
elif terms == 5:
return tstack([R, G, B, R * G * B, ones])
elif terms == 7:
return tstack([R, G, B, R * G, R * B, G * B, ones])
elif terms == 8:
return tstack([R, G, B, R * G, R * B, G * B, R * G * B, ones])
elif terms == 10:
return tstack(
[R, G, B, R * G, R * B, G * B, R ** 2, G ** 2, B ** 2, ones])
elif terms == 11:
return tstack([
R, G, B, R * G, R * B, G * B, R ** 2, G ** 2, B ** 2, R * G * B,
ones
])
elif terms == 14:
return tstack([
R, G, B, R * G, R * B, G * B, R ** 2, G ** 2, B ** 2, R * G * B, R
** 3, G ** 3, B ** 3, ones
])
elif terms == 16:
return tstack([
R, G, B, R * G, R * B, G * B, R ** 2, G ** 2, B ** 2, R * G * B,
R ** 2 * G, G ** 2 * B, B ** 2 * R, R ** 3, G ** 3, B ** 3
])
elif terms == 17:
return tstack([
R, G, B, R * G, R * B, G * B, R ** 2, G ** 2, B ** 2, R * G * B,
R ** 2 * G, G ** 2 * B, B ** 2 * R, R ** 3, G ** 3, B ** 3, ones
])
elif terms == 19:
return tstack([
R, G, B, R * G, R * B, G * B, R ** 2, G ** 2, B ** 2, R * G * B,
R ** 2 * G, G ** 2 * B, B ** 2 * R, R ** 2 * B, G ** 2 * R,
B ** 2 * G, R ** 3, G ** 3, B ** 3
])
elif terms == 20:
return tstack([
R, G, B, R * G, R * B, G * B, R ** 2, G ** 2, B ** 2, R * G * B,
R ** 2 * G, G ** 2 * B, B ** 2 * R, R ** 2 * B, G ** 2 * R,
B ** 2 * G, R ** 3, G ** 3, B ** 3, ones
])
elif terms == 22:
return tstack([
R, G, B, R * G, R * B, G * B, R ** 2, G ** 2, B ** 2, R * G * B,
R ** 2 * G, G ** 2 * B, B ** 2 * R, R ** 2 * B, G ** 2 * R,
B ** 2 * G, R ** 3, G ** 3, B ** 3, R ** 2 * G * B, R * G ** 2 * B,
R * G * B ** 2
])
def polynomial_expansion_Finlayson2015(RGB,
degree=1,
root_polynomial_expansion=True):
"""
Performs polynomial expansion of given *RGB* colourspace array using
*Finlayson et al. (2015)* method.
Parameters
----------
RGB : array_like
*RGB* colourspace array to expand.
degree : int, optional
Expanded polynomial degree.
root_polynomial_expansion : bool
Whether to use the root-polynomials set for the expansion.
Returns
-------
ndarray
Expanded *RGB* colourspace array.
References
----------
:cite:`Finlayson2015`
Examples
--------
>>> RGB = np.array([0.17224810, 0.09170660, 0.06416938])
>>> polynomial_expansion_Finlayson2015(RGB, degree=2) # doctest: +ELLIPSIS
array([ 0.1722481..., 0.0917066..., 0.06416938...\
, 0.0078981..., 0.0029423...,
0.0055265...])
"""
R, G, B = tsplit(RGB)
# TODO: Generalise polynomial expansion.
existing_degrees = np.array([1, 2, 3, 4])
closest_degree = as_int(closest(existing_degrees, degree))
if closest_degree != degree:
raise ValueError('"Finlayson et al. (2015)" method does not define '
'a polynomial expansion for {0} degree, '
'closest polynomial expansion is {1} degree!'.format(
degree, closest_degree))
if degree == 1:
return RGB
elif degree == 2:
if root_polynomial_expansion:
return tstack([
R, G, B, (R * G) ** 1 / 2, (G * B) ** 1 / 2, (R * B) ** 1 / 2
])
else:
return tstack(
[R, G, B, R ** 2, G ** 2, B ** 2, R * G, G * B, R * B])
elif degree == 3:
if root_polynomial_expansion:
return tstack([
R, G, B, (R * G) ** 1 / 2, (G * B) ** 1 / 2, (R * B) ** 1 / 2,
(R * G ** 2) ** 1 / 3, (G * B ** 2) ** 1 / 3,
(R * B ** 2) ** 1 / 3, (G * R ** 2) ** 1 / 3,
(B * G ** 2) ** 1 / 3, (B * R ** 2) ** 1 / 3,
(R * G * B) ** 1 / 3
])
else:
return tstack([
R, G, B, R ** 2, G ** 2, B ** 2, R * G, G * B, R * B, R ** 3, G
** 3, B ** 3, R * G ** 2, G * B ** 2, R * B ** 2, G * R ** 2,
B * G ** 2, B * R ** 2, R * G * B
])
elif degree == 4:
if root_polynomial_expansion:
return tstack([
R, G, B, (R * G) ** 1 / 2, (G * B) ** 1 / 2, (R * B) ** 1 / 2,
(R * G ** 2) ** 1 / 3, (G * B ** 2) ** 1 / 3,
(R * B ** 2) ** 1 / 3, (G * R ** 2) ** 1 / 3,
(B * G ** 2) ** 1 / 3, (B * R ** 2) ** 1 / 3,
(R * G * B) ** 1 / 3, (R ** 3 * G) ** 1 / 4,
(R ** 3 * B) ** 1 / 4, (G ** 3 * R) ** 1 / 4,
(G ** 3 * B) ** 1 / 4, (B ** 3 * R) ** 1 / 4,
(B ** 3 * G) ** 1 / 4, (R ** 2 * G * B) ** 1 / 4,
(G ** 2 * R * B) ** 1 / 4, (B ** 2 * R * G) ** 1 / 4
])
else:
return tstack([
R, G, B, R ** 2, G ** 2, B ** 2, R * G, G * B, R * B, R ** 3, G
** 3, B ** 3, R * G ** 2, G * B ** 2, R * B ** 2, G * R ** 2,
B * G ** 2, B * R ** 2, R * G * B, R ** 4, G ** 4, B ** 4,
R ** 3 * G, R ** 3 * B, G ** 3 * R, G ** 3 * B, B ** 3 * R,
B ** 3 * G, R ** 2 * G ** 2, G ** 2 * B ** 2, R ** 2 * B ** 2,
R ** 2 * G * B, G ** 2 * R * B, B ** 2 * R * G
])
def polynomial_expansion_Finlayson2015(
RGB: ArrayLike,
degree: Literal[1, 2, 3, 4] = 1,
root_polynomial_expansion: Boolean = True,
) -> NDArray:
"""
Perform polynomial expansion of given *RGB* colourspace array using
*Finlayson et al. (2015)* method.
Parameters
----------
RGB
*RGB* colourspace array to expand.
degree
Expanded polynomial degree.
root_polynomial_expansion
Whether to use the root-polynomials set for the expansion.
Returns
-------
:class:`numpy.ndarray`
Expanded *RGB* colourspace array.
References
----------
:cite:`Finlayson2015`
Examples
--------
>>> RGB = np.array([0.17224810, 0.09170660, 0.06416938])
>>> polynomial_expansion_Finlayson2015(RGB, degree=2) # doctest: +ELLIPSIS
array([ 0.1722481..., 0.0917066..., 0.0641693..., 0.1256832..., \
0.0767121...,
0.1051335...])
"""
RGB = as_float_array(RGB)
R, G, B = tsplit(RGB)
# TODO: Generalise polynomial expansion.
existing_degrees = np.array([1, 2, 3, 4])
closest_degree = as_int(closest(existing_degrees, degree))
if closest_degree != degree:
raise ValueError(
f'"Finlayson et al. (2015)" method does not define a polynomial '
f"expansion for {degree} degree, closest polynomial expansion is "
f"{closest_degree} degree!")
if degree == 1:
return RGB
elif degree == 2:
if root_polynomial_expansion:
return tstack([
R,
G,
B,
spow(R * G, 1 / 2),
spow(G * B, 1 / 2),
spow(R * B, 1 / 2),
])
else:
return tstack([
R,
G,
B,
R**2,
G**2,
B**2,
R * G,
G * B,
R * B,
])
elif degree == 3:
if root_polynomial_expansion:
return tstack([
R,
G,
B,
spow(R * G, 1 / 2),
spow(G * B, 1 / 2),
spow(R * B, 1 / 2),
spow(R * G**2, 1 / 3),
spow(G * B**2, 1 / 3),
spow(R * B**2, 1 / 3),
spow(G * R**2, 1 / 3),
spow(B * G**2, 1 / 3),
spow(B * R**2, 1 / 3),
spow(R * G * B, 1 / 3),
])
else:
return tstack([
R,
G,
B,
R**2,
G**2,
B**2,
R * G,
G * B,
R * B,
R**3,
G**3,
B**3,
R * G**2,
G * B**2,
R * B**2,
G * R**2,
B * G**2,
B * R**2,
R * G * B,
])
elif degree == 4:
if root_polynomial_expansion:
return tstack([
R,
G,
B,
spow(R * G, 1 / 2),
spow(G * B, 1 / 2),
spow(R * B, 1 / 2),
spow(R * G**2, 1 / 3),
spow(G * B**2, 1 / 3),
spow(R * B**2, 1 / 3),
spow(G * R**2, 1 / 3),
spow(B * G**2, 1 / 3),
spow(B * R**2, 1 / 3),
spow(R * G * B, 1 / 3),
spow(R**3 * G, 1 / 4),
spow(R**3 * B, 1 / 4),
spow(G**3 * R, 1 / 4),
spow(G**3 * B, 1 / 4),
spow(B**3 * R, 1 / 4),
spow(B**3 * G, 1 / 4),
spow(R**2 * G * B, 1 / 4),
spow(G**2 * R * B, 1 / 4),
spow(B**2 * R * G, 1 / 4),
])
else:
return tstack([
R,
G,
B,
R**2,
G**2,
B**2,
R * G,
G * B,
R * B,
R**3,
G**3,
B**3,
R * G**2,
G * B**2,
R * B**2,
G * R**2,
B * G**2,
B * R**2,
R * G * B,
R**4,
G**4,
B**4,
R**3 * G,
R**3 * B,
G**3 * R,
G**3 * B,
B**3 * R,
B**3 * G,
R**2 * G**2,
G**2 * B**2,
R**2 * B**2,
R**2 * G * B,
G**2 * R * B,
B**2 * R * G,
])
def matrix_augmented_Cheung2004(
RGB: ArrayLike,
terms: Literal[3, 5, 7, 8, 10, 11, 14, 16, 17, 19, 20, 22] = 3,
) -> NDArray:
"""
Perform polynomial expansion of given *RGB* colourspace array using
*Cheung et al. (2004)* method.
Parameters
----------
RGB
*RGB* colourspace array to expand.
terms
Number of terms of the expanded polynomial.
Returns
-------
:class:`numpy.ndarray`
Expanded *RGB* colourspace array.
Notes
-----
- This definition combines the augmented matrices given in
:cite:`Cheung2004` and :cite:`Westland2004`.
References
----------
:cite:`Cheung2004`, :cite:`Westland2004`
Examples
--------
>>> RGB = np.array([0.17224810, 0.09170660, 0.06416938])
>>> matrix_augmented_Cheung2004(RGB, terms=5) # doctest: +ELLIPSIS
array([ 0.1722481..., 0.0917066..., 0.0641693..., 0.0010136..., 1...])
"""
RGB = as_float_array(RGB)
R, G, B = tsplit(RGB)
tail = ones(R.shape)
existing_terms = np.array([3, 5, 7, 8, 10, 11, 14, 16, 17, 19, 20, 22])
closest_terms = as_int(closest(existing_terms, terms))
if closest_terms != terms:
raise ValueError(
f'"Cheung et al. (2004)" method does not define an augmented '
f"matrix with {terms} terms, closest augmented matrix has "
f"{closest_terms} terms!")
if terms == 3:
return RGB
elif terms == 5:
return tstack([
R,
G,
B,
R * G * B,
tail,
])
elif terms == 7:
return tstack([
R,
G,
B,
R * G,
R * B,
G * B,
tail,
])
elif terms == 8:
return tstack([
R,
G,
B,
R * G,
R * B,
G * B,
R * G * B,
tail,
])
elif terms == 10:
return tstack([
R,
G,
B,
R * G,
R * B,
G * B,
R**2,
G**2,
B**2,
tail,
])
elif terms == 11:
return tstack([
R,
G,
B,
R * G,
R * B,
G * B,
R**2,
G**2,
B**2,
R * G * B,
tail,
])
elif terms == 14:
return tstack([
R,
G,
B,
R * G,
R * B,
G * B,
R**2,
G**2,
B**2,
R * G * B,
R**3,
G**3,
B**3,
tail,
])
elif terms == 16:
return tstack([
R,
G,
B,
R * G,
R * B,
G * B,
R**2,
G**2,
B**2,
R * G * B,
R**2 * G,
G**2 * B,
B**2 * R,
R**3,
G**3,
B**3,
])
elif terms == 17:
return tstack([
R,
G,
B,
R * G,
R * B,
G * B,
R**2,
G**2,
B**2,
R * G * B,
R**2 * G,
G**2 * B,
B**2 * R,
R**3,
G**3,
B**3,
tail,
])
elif terms == 19:
return tstack([
R,
G,
B,
R * G,
R * B,
G * B,
R**2,
G**2,
B**2,
R * G * B,
R**2 * G,
G**2 * B,
B**2 * R,
R**2 * B,
G**2 * R,
B**2 * G,
R**3,
G**3,
B**3,
])
elif terms == 20:
return tstack([
R,
G,
B,
R * G,
R * B,
G * B,
R**2,
G**2,
B**2,
R * G * B,
R**2 * G,
G**2 * B,
B**2 * R,
R**2 * B,
G**2 * R,
B**2 * G,
R**3,
G**3,
B**3,
tail,
])
elif terms == 22:
return tstack([
R,
G,
B,
R * G,
R * B,
G * B,
R**2,
G**2,
B**2,
R * G * B,
R**2 * G,
G**2 * B,
B**2 * R,
R**2 * B,
G**2 * R,
B**2 * G,
R**3,
G**3,
B**3,
R**2 * G * B,
R * G**2 * B,
R * G * B**2,
])
