def test_as_numeric(self):
"""
Tests :func:`colour.utilities.array.as_numeric` definition.
"""
self.assertEqual(as_numeric(1), 1)
self.assertEqual(as_numeric(np.array([1])), 1)
np.testing.assert_almost_equal(as_numeric(np.array([1, 2, 3])),
np.array([1, 2, 3]))
def test_as_numeric(self):
"""
Tests :func:`colour.utilities.array.as_numeric` definition.
"""
self.assertEqual(as_numeric(1), 1.0)
self.assertEqual(as_numeric(np.array([1])), 1.0)
np.testing.assert_almost_equal(
as_numeric(np.array([1, 2, 3])), np.array([1.0, 2.0, 3.0]))
self.assertIsInstance(as_numeric(1), DEFAULT_FLOAT_DTYPE)
self.assertIsInstance(as_numeric(1, int), int)
def log_decoding_ACEScc(ACEScc):
"""
Defines the *ACEScc* colourspace log decoding / electro-optical transfer
function.
Parameters
----------
ACEScc : numeric or array_like
*ACEScc* non-linear value.
Returns
-------
numeric or ndarray
*ACESccLin* linear value.
Examples
--------
>>> log_decoding_ACEScc(0.413588402492442) # doctest: +ELLIPSIS
0.1799999...
"""
ACEScc = np.asarray(ACEScc)
output = np.where(ACEScc < (9.72 - 15) / 17.52,
(2 ** (ACEScc * 17.52 - 9.72) - 2 ** -16) * 2,
2 ** (ACEScc * 17.52 - 9.72))
output = np.where(ACEScc >= (np.log2(65504) + 9.72) / 17.52,
65504,
output)
return as_numeric(output)
def daylight_locus_function(x_D):
"""
Returns the daylight locus as *xy* chromaticity coordinates.
Parameters
----------
x_D : numeric or array_like
*x* chromaticity coordinates
Returns
-------
numeric or array_like
Daylight locus as *xy* chromaticity coordinates.
References
----------
:cite:`Wyszecki2000a`
Examples
--------
>>> daylight_locus_function(0.31270) # doctest: +ELLIPSIS
0.3291051...
"""
x_D = as_float_array(x_D)
y_D = -3.000 * x_D ** 2 + 2.870 * x_D - 0.275
return as_numeric(y_D)
def log_decoding_VLog(V_out):
"""
Defines the *Panasonic V-Log* log decoding curve / electro-optical transfer
function.
Parameters
----------
V_out : numeric or array_like
Non-linear data :math:`V_{out}`.
Returns
-------
numeric or ndarray
Linear reflection data :math`L_{in}`.
Examples
--------
>>> log_decoding_VLog(0.423311448760136) # doctest: +ELLIPSIS
0.1799999...
"""
V_out = np.asarray(V_out)
cut2 = VLOG_CONSTANTS.cut2
b = VLOG_CONSTANTS.b
c = VLOG_CONSTANTS.c
d = VLOG_CONSTANTS.d
V_out = np.where(V_out < cut2,
(V_out - 0.125) / 5.6,
np.power(10, ((V_out - d) / c)) - b)
return as_numeric(V_out)
def oetf_ROMMRGB(X):
"""
Defines the *ROMM RGB* encoding opto-electronic transfer function
(OETF / OECF).
Parameters
----------
X : numeric or array_like
Linear data :math:`X_{ROMM}`.
Returns
-------
numeric or ndarray
Non-linear data :math:`X'_{ROMM}`.
Examples
--------
>>> oetf_ROMMRGB(0.18) # doctest: +ELLIPSIS
0.3857114...
"""
X = np.asarray(X)
E_t = 16 ** (1.8 / (1 - 1.8))
return as_numeric(np.where(X < E_t,
X * 16,
X ** (1 / 1.8)))
def log_encoding_VLog(L_in):
"""
Defines the *Panasonic V-Log* log encoding curve / opto-electronic transfer
function.
Parameters
----------
L_in : numeric or array_like
Linear reflection data :math`L_{in}`.
Returns
-------
numeric or ndarray
Non-linear data :math:`V_{out}`.
Examples
--------
>>> log_encoding_VLog(0.18) # doctest: +ELLIPSIS
0.4233114...
"""
L_in = np.asarray(L_in)
cut1 = VLOG_CONSTANTS.cut1
b = VLOG_CONSTANTS.b
c = VLOG_CONSTANTS.c
d = VLOG_CONSTANTS.d
L_in = np.where(L_in < cut1,
5.6 * L_in + 0.125,
c * np.log10(L_in + b) + d)
return as_numeric(L_in)
def eotf_BT2020(E_p, is_12_bits_system=False):
"""
Defines *Recommendation ITU-R BT.2020* electro-optical transfer function
(EOTF / EOCF).
Parameters
----------
E_p : numeric or array_like
Non-linear signal :math:`E'`.
is_12_bits_system : bool
*BT.709* *alpha* and *beta* constants are used if system is not 12-bit.
Returns
-------
numeric or ndarray
Resulting voltage :math:`E`.
Examples
--------
>>> eotf_BT2020(0.705515089922121) # doctest: +ELLIPSIS
0.4999999...
"""
E_p = np.asarray(E_p)
a = BT2020_CONSTANTS.alpha(is_12_bits_system)
b = BT2020_CONSTANTS.beta(is_12_bits_system)
return as_numeric(np.where(E_p < oetf_BT2020(b),
E_p / 4.5,
((E_p + (a - 1)) / a) ** (1 / 0.45)))
def log_encoding_SLog3(t):
"""
Defines the *Sony S-Log3* log encoding curve / opto-electronic transfer
function.
Parameters
----------
t : numeric or array_like
Input light level :math:`t` to a camera.
Returns
-------
numeric or ndarray
Camera output code :math:`y`.
Examples
--------
>>> log_encoding_SLog3(0.18) # doctest: +ELLIPSIS
0.4105571...
"""
t = np.asarray(t)
return as_numeric(
np.where(t >= 0.01125000,
(420 + np.log10((t + 0.01) /
(0.18 + 0.01)) * 261.5) / 1023,
(t * (171.2102946929 - 95) / 0.01125000 + 95) / 1023))
def oetf_BT709(L):
"""
Defines *Recommendation ITU-R BT.709-6* opto-electronic transfer function
(OETF / OECF).
Parameters
----------
L : numeric or array_like
*Luminance* :math:`L` of the image.
Returns
-------
numeric or ndarray
Corresponding electrical signal :math:`V`.
Examples
--------
>>> oetf_BT709(0.18) # doctest: +ELLIPSIS
0.4090077...
"""
L = np.asarray(L)
return as_numeric(np.where(L < 0.018,
L * 4.5,
1.099 * (L ** 0.45) - 0.099))
def log_decoding_SLog3(y):
"""
Defines the *Sony S-Log3* log decoding curve / electro-optical transfer
function.
Parameters
----------
y : numeric or array_like
Camera output code :math:`y`.
Returns
-------
numeric or ndarray
Input light level :math:`t` to a camera.
Examples
--------
>>> log_decoding_SLog3(0.410557184750733) # doctest: +ELLIPSIS
0.1...
"""
y = np.asarray(y)
return as_numeric(
np.where(y >= 171.2102946929 / 1023,
((10 ** ((y * 1023 - 420) / 261.5)) *
(0.18 + 0.01) - 0.01),
(y * 1023 - 95) * 0.01125000 / (171.2102946929 - 95)))
def eotf_ROMMRGB(X_p):
"""
Defines the *ROMM RGB* encoding electro-optical transfer function
(EOTF / EOCF).
Parameters
----------
X_p : numeric or array_like
Non-linear data :math:`X'_{ROMM}`.
Returns
-------
numeric or ndarray
Linear data :math:`X_{ROMM}`.
Examples
--------
>>> eotf_ROMMRGB(0.3857114247511376) # doctest: +ELLIPSIS
0.1...
"""
X_p = np.asarray(X_p)
E_t = 16 ** (1.8 / (1 - 1.8))
return as_numeric(np.where(
X_p < oetf_ROMMRGB(E_t),
X_p / 16,
X_p ** 1.8))
def log_encoding_ACEScc(ACEScc_l):
"""
Defines the *ACEScc* colourspace log encoding / opto-electronic transfer
function.
Parameters
----------
ACEScc_l : numeric or array_like
*ACESccLin* linear value.
Returns
-------
numeric or ndarray
*ACEScc* non-linear value.
Examples
--------
>>> log_encoding_ACEScc(0.18) # doctest: +ELLIPSIS
0.4135884...
"""
ACEScc_l = np.asarray(ACEScc_l)
output = np.where(ACEScc_l < 0,
(np.log2(2 ** -15 * 0.5) + 9.72) / 17.52,
(np.log2(2 ** -16 + ACEScc_l * 0.5) + 9.72) / 17.52)
output = np.where(ACEScc_l >= 2 ** -15,
(np.log2(ACEScc_l) + 9.72) / 17.52,
output)
return as_numeric(output)
def oetf_BT2020(E, is_12_bits_system=False):
"""
Defines *Recommendation ITU-R BT.2020* opto-electrical transfer function
(OETF / OECF).
Parameters
----------
E : numeric or array_like
Voltage :math:`E` normalized by the reference white level and
proportional to the implicit light intensity that would be detected
with a reference camera colour channel R, G, B.
is_12_bits_system : bool
*BT.709* *alpha* and *beta* constants are used if system is not 12-bit.
Returns
-------
numeric or ndarray
Resulting non-linear signal :math:`E'`.
Examples
--------
>>> oetf_BT2020(0.18) # doctest: +ELLIPSIS
0.4090077...
"""
E = np.asarray(E)
a = BT2020_CONSTANTS.alpha(is_12_bits_system)
b = BT2020_CONSTANTS.beta(is_12_bits_system)
return as_numeric(np.where(E < b,
E * 4.5,
a * (E ** 0.45) - (a - 1)))
def xy_to_CCT_Hernandez1999(xy):
"""
Returns the correlated colour temperature :math:`T_{cp}` from given
*CIE XYZ* tristimulus values *xy* chromaticity coordinates using
Hernandez-Andres, Lee and Romero (1999) method.
Parameters
----------
xy : array_like
*xy* chromaticity coordinates.
Returns
-------
numeric
Correlated colour temperature :math:`T_{cp}`.
References
----------
.. [10] Hernández-Andrés, J., Lee, R. L., & Romero, J. (1999).
Calculating correlated color temperatures across the entire gamut
of daylight and skylight chromaticities. Applied Optics, 38(27),
5703–5709. doi:10.1364/AO.38.005703
Examples
--------
>>> xy = np.array([0.31270, 0.32900])
>>> xy_to_CCT_Hernandez1999(xy) # doctest: +ELLIPSIS
6500.7420431...
"""
x, y = tsplit(xy)
n = (x - 0.3366) / (y - 0.1735)
CCT = (-949.86315 +
6253.80338 * np.exp(-n / 0.92159) +
28.70599 * np.exp(-n / 0.20039) +
0.00004 * np.exp(-n / 0.07125))
n = np.where(CCT > 50000,
(x - 0.3356) / (y - 0.1691),
n)
CCT = np.where(CCT > 50000,
36284.48953 + 0.00228 * np.exp(-n / 0.07861) +
5.4535e-36 * np.exp(-n / 0.01543),
CCT)
return as_numeric(CCT)
def log_encoding_ERIMMRGB(X,
I_max=255,
E_min=0.001,
E_clip=316.2):
"""
Defines the *ERIMM RGB* log encoding curve / opto-electronic transfer
function (OETF / OECF).
Parameters
----------
X : numeric or array_like
Linear data :math:`X_{ERIMM}`.
I_max : numeric, optional
Maximum code value: 255, 4095, and 650535 for respectively 8-bit,
12-bit and 16-bit per channel.
E_min : numeric, optional
Minimum exposure limit.
E_clip : numeric, optional
Maximum exposure limit.
Returns
-------
numeric or ndarray
Non-linear data :math:`X'_{ERIMM}`.
Examples
--------
>>> log_encoding_ERIMMRGB(0.18) # doctest: +ELLIPSIS
104.5633593...
"""
X = np.asarray(X)
E_t = np.exp(1) * E_min
X_p = np.select(
[X < 0.0,
X <= E_t, X > E_t,
X > E_clip],
[0,
I_max * ((np.log(E_t) - np.log(E_min)) /
(np.log(E_clip) - np.log(E_min))) * (X / E_t),
I_max * ((np.log(X) - np.log(E_min)) /
(np.log(E_clip) - np.log(E_min))),
I_max])
return as_numeric(X_p)
def log_encoding_ACESproxy(ACESproxy_l, bit_depth='10 Bit'):
"""
Defines the *ACESproxy* colourspace log encoding curve / opto-electronic
transfer function.
Parameters
----------
ACESproxy_l : numeric or array_like
*ACESproxyLin* linear value.
bit_depth : unicode, optional
**{'10 Bit', '12 Bit'}**,
*ACESproxy* bit depth.
Returns
-------
numeric or ndarray
*ACESproxy* non-linear value.
Examples
--------
>>> log_encoding_ACESproxy(0.18)
426
"""
ACESproxy_l = np.asarray(ACESproxy_l)
constants = ACES_PROXY_CONSTANTS.get(bit_depth)
CV_min = np.resize(constants.CV_min, ACESproxy_l.shape)
CV_max = np.resize(constants.CV_max, ACESproxy_l.shape)
def float_2_cv(x):
"""
Converts given numeric to code value.
"""
return np.maximum(CV_min, np.minimum(CV_max, np.round(x)))
output = np.where(ACESproxy_l > 2 ** -9.72,
float_2_cv((np.log2(ACESproxy_l) +
constants.mid_log_offset) *
constants.steps_per_stop +
constants.mid_CV_offset),
np.resize(CV_min, ACESproxy_l.shape))
return as_numeric(output, int)
def log_encoding_CanonLog(x, bit_depth=10, out_legal=True, in_reflection=True):
"""
Defines the *Canon Log* log encoding curve / opto-electronic transfer
function.
Parameters
----------
x : numeric or array_like
Linear data :math:`x`.
bit_depth : int, optional
Bit depth used for conversion.
out_legal : bool, optional
Whether the *Canon Log* non-linear data is encoded in legal
range.
in_reflection : bool, optional
Whether the light level :math:`x` to a camera is reflection.
Returns
-------
numeric or ndarray
*Canon Log* non-linear data.
References
----------
- :cite:`Thorpe2012a`
Examples
--------
>>> log_encoding_CanonLog(0.18) * 100 # doctest: +ELLIPSIS
34.3389651...
"""
x = np.asarray(x)
if in_reflection:
x = x / 0.9
clog = np.where(x < log_decoding_CanonLog(0.0730597, bit_depth, False),
-(0.529136 * (np.log10(-x * 10.1596 + 1)) - 0.0730597),
0.529136 * np.log10(10.1596 * x + 1) + 0.0730597)
clog = full_to_legal(clog, bit_depth) if out_legal else clog
return as_numeric(clog)
def log_decoding_ALEXALogC(t,
firmware='SUP 3.x',
method='Linear Scene Exposure Factor',
EI=800):
"""
Defines the *ALEXA Log C* log decoding curve / electro-optical transfer
function.
Parameters
----------
t : numeric or array_like
*ALEXA Log C* encoded data :math:`t`.
firmware : unicode, optional
**{'SUP 3.x', 'SUP 2.x'}**,
Alexa firmware version.
method : unicode, optional
**{'Linear Scene Exposure Factor', 'Normalised Sensor Signal'}**,
Conversion method.
EI : int, optional
Ei.
Returns
-------
numeric or ndarray
Linear data :math:`x`.
References
----------
- :cite:`ARRI2012a`
Examples
--------
>>> log_decoding_ALEXALogC(0.391006832034084) # doctest: +ELLIPSIS
0.18...
"""
t = np.asarray(t)
cut, a, b, c, d, e, f, _e_cut_f = (
ALEXA_LOG_C_CURVE_CONVERSION_DATA[firmware][method][EI])
return as_numeric(
np.where(t > e * cut + f, (np.power(10, (t - d) / c) - b) / a,
(t - f) / e))
def luminance_CIE1976(Lstar, Y_n=100):
"""
Returns the *luminance* :math:`Y` of given *Lightness* :math:`L^*` with
given reference white *luminance* :math:`Y_n`.
Parameters
----------
Lstar : numeric or array_like
*Lightness* :math:`L^*`
Y_n : numeric or array_like
White reference *luminance* :math:`Y_n`.
Returns
-------
numeric or array_like
*luminance* :math:`Y`.
Notes
-----
- Input *Lightness* :math:`L^*` and reference white *luminance*
:math:`Y_n` are in domain [0, 100].
- Output *luminance* :math:`Y` is in range [0, 100].
References
----------
- :cite:`Lindbloom2003d`
- :cite:`Wyszecki2000bd`
Examples
--------
>>> luminance_CIE1976(37.98562910) # doctest: +ELLIPSIS
10.0800000...
>>> luminance_CIE1976(37.98562910, 95) # doctest: +ELLIPSIS
9.5760000...
"""
Lstar = np.asarray(Lstar)
Y_n = np.asarray(Y_n)
Y = as_numeric(
np.where(Lstar > CIE_K * CIE_E,
Y_n * ((Lstar + 16) / 116)**3, Y_n * (Lstar / CIE_K)))
return Y
def log_decoding_ERIMMRGB(X_p,
I_max=255,
E_min=0.001,
E_clip=316.2):
"""
Defines the *ERIMM RGB* log decoding curve / electro-optical transfer
function (EOTF / EOCF).
Parameters
----------
X_p : numeric or array_like
Non-linear data :math:`X'_{ERIMM}`.
I_max : numeric, optional
Maximum code value: 255, 4095, and 650535 for respectively 8-bit,
12-bit and 16-bit per channel.
E_min : numeric, optional
Minimum exposure limit.
E_clip : numeric, optional
Maximum exposure limit.
Returns
-------
numeric or ndarray
Linear data :math:`X_{ERIMM}`.
Examples
--------
>>> log_decoding_ERIMMRGB(104.56335932049294) # doctest: +ELLIPSIS
0.1...
"""
X_p = np.asarray(X_p)
E_t = np.exp(1) * E_min
X = np.where(
X_p <= I_max * ((np.log(E_t) - np.log(E_min)) /
(np.log(E_clip) - np.log(E_min))),
(((np.log(E_clip) - np.log(E_min)) / (np.log(E_t) - np.log(E_min))) *
((X_p * E_t) / I_max)),
np.exp((X_p / I_max) *
(np.log(E_clip) - np.log(E_min)) + np.log(E_min)))
return as_numeric(X)
def log_decoding_ERIMMRGB(X_p,
I_max=255,
E_min=0.001,
E_clip=316.2):
"""
Defines the *ERIMM RGB* log decoding curve / electro-optical transfer
function (EOTF / EOCF).
Parameters
----------
X_p : numeric or array_like
Non-linear data :math:`X'_{ERIMM}`.
I_max : numeric, optional
Maximum code value: 255, 4095 and 650535 for respectively 8-bit,
12-bit and 16-bit per channel.
E_min : numeric, optional
Minimum exposure limit.
E_clip : numeric, optional
Maximum exposure limit.
Returns
-------
numeric or ndarray
Linear data :math:`X_{ERIMM}`.
Examples
--------
>>> log_decoding_ERIMMRGB(104.56335932049294) # doctest: +ELLIPSIS
0.1...
"""
X_p = np.asarray(X_p)
E_t = np.exp(1) * E_min
X = np.where(
X_p <= I_max * ((np.log(E_t) - np.log(E_min)) /
(np.log(E_clip) - np.log(E_min))),
(((np.log(E_clip) - np.log(E_min)) / (np.log(E_t) - np.log(E_min))) *
((X_p * E_t) / I_max)),
np.exp((X_p / I_max) *
(np.log(E_clip) - np.log(E_min)) + np.log(E_min)))
return as_numeric(X)
def xy_to_CCT_Hernandez1999(xy):
"""
Returns the correlated colour temperature :math:`T_{cp}` from given
*CIE XYZ* tristimulus values *xy* chromaticity coordinates using
Hernandez-Andres et al. (1999) method.
Parameters
----------
xy : array_like
*xy* chromaticity coordinates.
Returns
-------
numeric
Correlated colour temperature :math:`T_{cp}`.
References
----------
.. [11] Hernández-Andrés, J., Lee, R. L., & Romero, J. (1999).
Calculating correlated color temperatures across the entire gamut
of daylight and skylight chromaticities. Applied Optics, 38(27),
5703–5709. doi:10.1364/AO.38.005703
Examples
--------
>>> xy = np.array([0.31270, 0.32900])
>>> xy_to_CCT_Hernandez1999(xy) # doctest: +ELLIPSIS
6500.7420431...
"""
x, y = tsplit(xy)
n = (x - 0.3366) / (y - 0.1735)
CCT = (-949.86315 + 6253.80338 * np.exp(-n / 0.92159) +
28.70599 * np.exp(-n / 0.20039) + 0.00004 * np.exp(-n / 0.07125))
n = np.where(CCT > 50000, (x - 0.3356) / (y - 0.1691), n)
CCT = np.where(
CCT > 50000, 36284.48953 + 0.00228 * np.exp(-n / 0.07861) +
5.4535e-36 * np.exp(-n / 0.01543), CCT)
return as_numeric(CCT)
def xy_to_CCT_Hernandez1999(xy):
"""
Returns the correlated colour temperature :math:`T_{cp}` from given
*CIE xy* chromaticity coordinates using *Hernandez-Andres et al. (1999)*
method.
Parameters
----------
xy : array_like
*CIE xy* chromaticity coordinates.
Returns
-------
numeric
Correlated colour temperature :math:`T_{cp}`.
References
----------
:cite:`Hernandez-Andres1999a`
Examples
--------
>>> xy = np.array([0.31270, 0.32900])
>>> xy_to_CCT_Hernandez1999(xy) # doctest: +ELLIPSIS
6500.7420431...
"""
x, y = tsplit(xy)
n = (x - 0.3366) / (y - 0.1735)
CCT = (-949.86315 + 6253.80338 * np.exp(-n / 0.92159) +
28.70599 * np.exp(-n / 0.20039) + 0.00004 * np.exp(-n / 0.07125))
n = np.where(CCT > 50000, (x - 0.3356) / (y - 0.1691), n)
CCT = np.where(
CCT > 50000,
36284.48953 + 0.00228 * np.exp(-n / 0.07861) +
5.4535e-36 * np.exp(-n / 0.01543),
CCT,
)
return as_numeric(CCT)
def log_encoding_ERIMMRGB(X, I_max=255, E_min=0.001, E_clip=316.2):
"""
Defines the *ERIMM RGB* log encoding curve / opto-electronic transfer
function (OETF / OECF).
Parameters
----------
X : numeric or array_like
Linear data :math:`X_{ERIMM}`.
I_max : numeric, optional
Maximum code value: 255, 4095 and 650535 for respectively 8-bit,
12-bit and 16-bit per channel.
E_min : numeric, optional
Minimum exposure limit.
E_clip : numeric, optional
Maximum exposure limit.
Returns
-------
numeric or ndarray
Non-linear data :math:`X'_{ERIMM}`.
References
----------
- :cite:`Spaulding2000b`
Examples
--------
>>> log_encoding_ERIMMRGB(0.18) # doctest: +ELLIPSIS
104.5633593...
"""
X = np.asarray(X)
E_t = np.exp(1) * E_min
X_p = np.select([X < 0.0, X <= E_t, X > E_t, X > E_clip], [
0, I_max * ((np.log(E_t) - np.log(E_min)) /
(np.log(E_clip) - np.log(E_min))) * (X / E_t), I_max *
((np.log(X) - np.log(E_min)) / (np.log(E_clip) - np.log(E_min))), I_max
])
return as_numeric(X_p)
def lightness_CIE1976(Y, Y_n=100):
"""
Returns the *Lightness* :math:`L^*` of given *luminance* :math:`Y` using
given reference white *luminance* :math:`Y_n` as per *CIE 1976*
recommendation.
Parameters
----------
Y : numeric or array_like
*luminance* :math:`Y`.
Y_n : numeric or array_like, optional
White reference *luminance* :math:`Y_n`.
Returns
-------
numeric or array_like
*Lightness* :math:`L^*`.
Notes
-----
- Input *luminance* :math:`Y` and :math:`Y_n` are in domain [0, 100].
- Output *Lightness* :math:`L^*` is in range [0, 100].
References
----------
- :cite:`Lindbloom2003d`
- :cite:`Wyszecki2000bd`
Examples
--------
>>> lightness_CIE1976(10.08) # doctest: +ELLIPSIS
37.9856290...
"""
Y = np.asarray(Y)
Y_n = np.asarray(Y_n)
Lstar = Y / Y_n
Lstar = as_numeric(
np.where(Lstar <= CIE_E, CIE_K * Lstar, 116 * Lstar**(1 / 3) - 16))
return Lstar
def log_encoding_ALEXALogC(x,
firmware='SUP 3.x',
method='Linear Scene Exposure Factor',
EI=800):
"""
Defines the *ALEXA Log C* log encoding curve / opto-electronic transfer
function.
Parameters
----------
x : numeric or array_like
Linear data :math:`x`.
firmware : unicode, optional
**{'SUP 3.x', 'SUP 2.x'}**,
Alexa firmware version.
method : unicode, optional
**{'Linear Scene Exposure Factor', 'Normalised Sensor Signal'}**,
Conversion method.
EI : int, optional
Ei.
Returns
-------
numeric or ndarray
*ALEXA Log C* encoded data :math:`t`.
References
----------
- :cite:`ARRI2012a`
Examples
--------
>>> log_encoding_ALEXALogC(0.18) # doctest: +ELLIPSIS
0.3910068...
"""
x = np.asarray(x)
cut, a, b, c, d, e, f, _e_cut_f = (
ALEXA_LOG_C_CURVE_CONVERSION_DATA[firmware][method][EI])
return as_numeric(np.where(x > cut,
c * np.log10(a * x + b) + d, e * x + f))
def oetf_DICOMGSDF(L):
"""
Defines the *DICOM - Grayscale Standard Display Function* opto-electronic
transfer function (OETF / OECF).
Parameters
----------
L : numeric or array_like
*Luminance* :math:`L`.
Returns
-------
numeric or ndarray
Just-Noticeable Difference (JND) Index, :math:`j` in domain 1 to 1023.
References
----------
- :cite:`NationalElectricalManufacturersAssociation2004b`
Examples
--------
>>> oetf_DICOMGSDF(130.065284012159790) # doctest: +ELLIPSIS
511.9964806...
"""
L = np.asarray(L)
L_lg = np.log10(L)
A = DICOMGSDF_CONSTANTS.A
B = DICOMGSDF_CONSTANTS.B
C = DICOMGSDF_CONSTANTS.C
D = DICOMGSDF_CONSTANTS.D
E = DICOMGSDF_CONSTANTS.E
F = DICOMGSDF_CONSTANTS.F
G = DICOMGSDF_CONSTANTS.G
H = DICOMGSDF_CONSTANTS.H
I = DICOMGSDF_CONSTANTS.I # noqa
L = (A + B * L_lg + C * L_lg ** 2 + D * L_lg ** 3 + E * L_lg ** 4 +
F * L_lg ** 5 + G * L_lg ** 6 + H * L_lg ** 7 + I * L_lg ** 8)
return as_numeric(L)
def oetf_RIMMRGB(X, I_max=255, E_clip=2.0):
"""
Defines the *RIMM RGB* encoding opto-electronic transfer function
(OETF / OECF).
*RIMM RGB* encoding non-linearity is based on that specified by
*Recommendation ITU-R BT.709-6*.
Parameters
----------
X : numeric or array_like
Linear data :math:`X_{RIMM}`.
I_max : numeric, optional
Maximum code value: 255, 4095 and 650535 for respectively 8-bit,
12-bit and 16-bit per channel.
E_clip : numeric, optional
Maximum exposure level.
Returns
-------
numeric or ndarray
Non-linear data :math:`X'_{RIMM}`.
References
----------
- :cite:`Spaulding2000b`
Examples
--------
>>> oetf_RIMMRGB(0.18) # doctest: +ELLIPSIS
74.3768017...
"""
X = np.asarray(X)
V_clip = 1.099 * E_clip**0.45 - 0.099
q = I_max / V_clip
X_p_RIMM = np.select([X < 0.0, X < 0.018, X >= 0.018, X > E_clip],
[0, 4.5 * X, 1.099 * (X**0.45) - 0.099, I_max])
return as_numeric(q * X_p_RIMM)
def __call__(self, x):
"""
Evaluates the Extrapolator at given point(s).
Parameters
----------
x : numeric or array_like
Point(s) to evaluate the Extrapolator at.
Returns
-------
float or ndarray
Extrapolated points value(s).
"""
x = np.atleast_1d(x).astype(np.float_)
xe = as_numeric(self.__evaluate(x))
return xe
def __call__(self, x):
"""
Evaluates the interpolator at given point(s).
Parameters
----------
x : numeric or array_like
Point(s) to evaluate the interpolant at.
Returns
-------
float or ndarray
Interpolated value(s).
"""
x = np.atleast_1d(x).astype(self._dtype)
xi = as_numeric(self._evaluate(x))
return xi
def __call__(self, x):
"""
Evaluates the Extrapolator at given point(s).
Parameters
----------
x : numeric or array_like
Point(s) to evaluate the Extrapolator at.
Returns
-------
float or ndarray
Extrapolated points value(s).
"""
x = np.atleast_1d(x).astype(np.float_)
xe = as_numeric(self._evaluate(x))
return xe
def oetf_RIMMRGB(X, I_max=255, E_clip=2.0):
"""
Defines the *RIMM RGB* encoding opto-electronic transfer function
(OETF / OECF).
*RIMM RGB* encoding non-linearity is based on that specified by
*Recommendation ITU-R BT.709-6*.
Parameters
----------
X : numeric or array_like
Linear data :math:`X_{RIMM}`.
I_max : numeric, optional
Maximum code value: 255, 4095, and 650535 for respectively 8-bit,
12-bit and 16-bit per channel.
E_clip : numeric, optional
Maximum exposure level.
Returns
-------
numeric or ndarray
Non-linear data :math:`X'_{RIMM}`.
Examples
--------
>>> oetf_RIMMRGB(0.18) # doctest: +ELLIPSIS
74.3768017...
"""
X = np.asarray(X)
V_clip = 1.099 * E_clip ** 0.45 - 0.099
q = I_max / V_clip
X_p_RIMM = np.select(
[X < 0.0,
X < 0.018, X >= 0.018,
X > E_clip],
[0, 4.5 * X, 1.099 * (X ** 0.45) - 0.099, I_max])
return as_numeric(q * X_p_RIMM)
def __call__(self, x):
"""
Evaluates the interpolating polynomial at given point(s).
Parameters
----------
x : numeric or array_like
Point(s) to evaluate the interpolant at.
Returns
-------
float or ndarray
Interpolated value(s).
"""
x = np.atleast_1d(x).astype(np.float_)
xi = as_numeric(self._evaluate(x))
return xi
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 test_as_numeric(self):
"""
Tests :func:`colour.utilities.array.as_numeric` definition.
"""
self.assertEqual(as_numeric(1), 1.0)
self.assertEqual(as_numeric(np.array([1])), 1.0)
np.testing.assert_almost_equal(as_numeric(np.array([1, 2, 3])),
np.array([1.0, 2.0, 3.0]))
self.assertIsInstance(as_numeric(1), DEFAULT_FLOAT_DTYPE)
self.assertIsInstance(as_numeric(1, int), int)
self.assertListEqual(as_numeric(['John', 'Doe']), ['John', 'Doe'])
self.assertEqual(as_numeric('John Doe'), 'John Doe')
def eotf_RIMMRGB(X_p, I_max=255, E_clip=2.0):
"""
Defines the *RIMM RGB* encoding electro-optical transfer function
(EOTF / EOCF).
Parameters
----------
X_p : numeric or array_like
Non-linear data :math:`X'_{RIMM}`.
I_max : numeric, optional
Maximum code value: 255, 4095 and 650535 for respectively 8-bit,
12-bit and 16-bit per channel.
E_clip : numeric, optional
Maximum exposure level.
Returns
-------
numeric or ndarray
Linear data :math:`X_{RIMM}`.
References
----------
- :cite:`Spaulding2000b`
Examples
--------
>>> eotf_RIMMRGB(74.37680178131521) # doctest: +ELLIPSIS
0.1...
"""
X_p = np.asarray(X_p)
V_clip = 1.099 * E_clip**0.45 - 0.099
m = V_clip * X_p / I_max
X_RIMM = np.where(X_p < oetf_RIMMRGB(0.018), m / 4.5,
((m + 0.099) / 1.099)**(1 / 0.45))
return as_numeric(X_RIMM)
def oetf_reverse_ARIBSTDB67(E_p, r=0.5):
"""
Defines *ARIB STD-B67 (Hybrid Log-Gamma)* reverse opto-electrical transfer
function (OETF / OECF).
Parameters
----------
E_p : numeric or array_like
Non-linear signal :math:`E'`.
r : numeric, optional
Video level corresponding to reference white level.
Returns
-------
numeric or ndarray
Voltage :math:`E` normalized by the reference white level and
proportional to the implicit light intensity that would be detected
with a reference camera color channel R, G, B.
References
----------
- :cite:`AssociationofRadioIndustriesandBusinesses2015a`
Examples
--------
>>> oetf_reverse_ARIBSTDB67(0.212132034355964) # doctest: +ELLIPSIS
0.1799999...
"""
E_p = np.asarray(E_p)
a = ARIBSTDB67_CONSTANTS.a
b = ARIBSTDB67_CONSTANTS.b
c = ARIBSTDB67_CONSTANTS.c
E = np.where(E_p <= oetf_ARIBSTDB67(1), (E_p / r)**2,
np.exp((E_p - c) / a) + b)
return as_numeric(E)
def oetf_ARIBSTDB67(E, r=0.5):
"""
Defines *ARIB STD-B67 (Hybrid Log-Gamma)* opto-electrical transfer
function (OETF / OECF).
Parameters
----------
E : numeric or array_like
Voltage normalized by the reference white level and proportional to
the implicit light intensity that would be detected with a reference
camera color channel R, G, B.
r : numeric, optional
Video level corresponding to reference white level.
Returns
-------
numeric or ndarray
Resulting non-linear signal :math:`E'`.
References
----------
- :cite:`AssociationofRadioIndustriesandBusinesses2015a`
Examples
--------
>>> oetf_ARIBSTDB67(0.18) # doctest: +ELLIPSIS
0.2121320...
"""
E = np.asarray(E)
a = ARIBSTDB67_CONSTANTS.a
b = ARIBSTDB67_CONSTANTS.b
c = ARIBSTDB67_CONSTANTS.c
E_p = np.where(E <= 1, r * np.sqrt(E), a * np.log(E - b) + c)
return as_numeric(E_p)
def eotf_BT709(V):
"""
Defines *Recommendation ITU-R BT.709-6* electro-optical transfer function
(EOTF / EOCF).
Parameters
----------
V : numeric or array_like
Electrical signal :math:`V`.
Returns
-------
numeric or ndarray
Corresponding *luminance* :math:`L` of the image.
Warning
-------
*Recommendation ITU-R BT.709-6* doesn't specify an electro-optical
transfer function. This definition is used for symmetry in unit tests and
other computations but should not be used as an *EOTF*.
Examples
--------
>>> eotf_BT709(0.409007728864150) # doctest: +ELLIPSIS
0.1...
"""
warning(('*Recommendation ITU-R BT.709-6* doesn\'t specify an '
'electro-optical transfer function. This definition is used '
'for symmetry in unit tests and others computations but should '
'not be used as an *EOTF*!'))
V = np.asarray(V)
return as_numeric(np.where(V < oetf_BT709(0.018),
V / 4.5,
((V + 0.099) / 1.099) ** (1 / 0.45)))
def eotf_RIMMRGB(X_p, I_max=255, E_clip=2.0):
"""
Defines the *RIMM RGB* encoding electro-optical transfer function
(EOTF / EOCF).
Parameters
----------
X_p : numeric or array_like
Non-linear data :math:`X'_{RIMM}`.
I_max : numeric, optional
Maximum code value: 255, 4095, and 650535 for respectively 8-bit,
12-bit and 16-bit per channel.
E_clip : numeric, optional
Maximum exposure level.
Returns
-------
numeric or ndarray
Linear data :math:`X_{RIMM}`.
Examples
--------
>>> eotf_RIMMRGB(74.37680178131521) # doctest: +ELLIPSIS
0.1...
"""
X_p = np.asarray(X_p)
V_clip = 1.099 * E_clip ** 0.45 - 0.099
m = V_clip * X_p / I_max
X_RIMM = np.where(
X_p < oetf_RIMMRGB(0.018),
m / 4.5, ((m + 0.099) / 1.099) ** (1 / 0.45))
return as_numeric(X_RIMM)
def log_encoding_ACEScct(lin_AP1):
"""
Defines the *ACEScct* colourspace log encoding / opto-electronic transfer
function.
Parameters
----------
lin_AP1 : numeric or array_like
*lin_AP1* value.
Returns
-------
numeric or ndarray
*ACEScct* non-linear value.
References
----------
- :cite:`TheAcademyofMotionPictureArtsandSciences2014q`
- :cite:`TheAcademyofMotionPictureArtsandSciences2014r`
- :cite:`TheAcademyofMotionPictureArtsandSciences2016c`
- :cite:`TheAcademyofMotionPictureArtsandSciencese`
Examples
--------
>>> log_encoding_ACEScct(0.18) # doctest: +ELLIPSIS
0.4135884...
"""
constants = ACES_CCT_CONSTANTS
lin_AP1 = np.asarray(lin_AP1)
output = np.where(lin_AP1 <= constants.X_BRK,
constants.A * lin_AP1 + constants.B,
(np.log2(lin_AP1) + 9.72) / 17.52)
return as_numeric(output)
def eotf_BT709(V):
"""
Defines *Recommendation ITU-R BT.709-6* electro-optical transfer function
(EOTF / EOCF).
Parameters
----------
V : numeric or array_like
Electrical signal :math:`V`.
Returns
-------
numeric or ndarray
Corresponding *luminance* :math:`L` of the image.
Warning
-------
*Recommendation ITU-R BT.709-6* doesn't specify an electro-optical
transfer function. This definition is used for symmetry in unit tests and
other computations but should not be used as an *EOTF*.
Examples
--------
>>> eotf_BT709(0.409007728864150) # doctest: +ELLIPSIS
0.1...
"""
warning(('*Recommendation ITU-R BT.709-6* doesn\'t specify an '
'electro-optical transfer function. This definition is used '
'for symmetry in unit tests and others computations but should '
'not be used as an *EOTF*!'))
V = np.asarray(V)
return as_numeric(
np.where(V < oetf_BT709(0.018), V / 4.5,
((V + 0.099) / 1.099)**(1 / 0.45)))
def log_decoding_ACEScct(ACEScct):
"""
Defines the *ACEScct* colourspace log decoding / electro-optical transfer
function.
Parameters
----------
ACEScct : numeric or array_like
*ACEScct* non-linear value.
Returns
-------
numeric or ndarray
*lin_AP1* value.
References
----------
- :cite:`TheAcademyofMotionPictureArtsandSciences2014q`
- :cite:`TheAcademyofMotionPictureArtsandSciences2014r`
- :cite:`TheAcademyofMotionPictureArtsandSciences2016c`
- :cite:`TheAcademyofMotionPictureArtsandSciencese`
Examples
--------
>>> log_decoding_ACEScct(0.413588402492442) # doctest: +ELLIPSIS
0.1799999...
"""
constants = ACES_CCT_CONSTANTS
ACEScct = np.asarray(ACEScct)
output = np.where(ACEScct > constants.Y_BRK, 2**(ACEScct * 17.52 - 9.72),
(ACEScct - constants.B) / constants.A)
return as_numeric(output)
def log_decoding_CanonLog3(clog3_ire):
"""
Defines the *Canon Log 3* log decoding curve / electro-optical transfer
function.
Parameters
----------
clog3_ire : numeric or array_like
*Canon Log 3* non-linear *IRE* data.
Returns
-------
numeric or ndarray
Linear data :math:`x`.
Notes
-----
- Input *Canon Log 3* non-linear *IRE* data should be converted from code
value *CV* to *IRE* as follows: `IRE = (CV - 64) / (940 - 64)`.
Examples
--------
>>> log_decoding_CanonLog3(32.795356721989336 / 100) # doctest: +ELLIPSIS
0.2000000...
"""
clog3_ire = np.asarray(clog3_ire)
x = np.select(
(clog3_ire < 0.04076162, clog3_ire <= 0.105357102,
clog3_ire > 0.105357102),
(-(10**((0.069886632 - clog3_ire) / 0.42889912) - 1) / 14.98325,
(clog3_ire - 0.073059361) / 2.3069815,
(10**((clog3_ire - 0.069886632) / 0.42889912) - 1) / 14.98325))
return as_numeric(x)
def log_encoding_CanonLog3(x):
"""
Defines the *Canon Log 3* log encoding curve / opto-electronic transfer
function.
Parameters
----------
x : numeric or array_like
Linear data :math:`x`.
Returns
-------
numeric or ndarray
*Canon Log 3* non-linear *IRE* data.
Notes
-----
- Output *Canon Log 3* non-linear *IRE* data should be converted to code
value *CV* as follows: `CV = IRE * (940 - 64) + 64`.
Examples
--------
>>> log_encoding_CanonLog3(0.20) * 100 # doctest: +ELLIPSIS
32.7953567...
"""
x = np.asarray(x)
clog3_ire = np.select(
(x < log_decoding_CanonLog3(0.04076162),
x <= log_decoding_CanonLog3(0.105357102),
x > log_decoding_CanonLog3(0.105357102)),
(-(0.42889912 *
(np.log10(-x * 14.98325 + 1)) - 0.069886632), 2.3069815 * x +
0.073059361, 0.42889912 * np.log10(x * 14.98325 + 1) + 0.069886632))
return as_numeric(clog3_ire)
def eotf_ROMMRGB(X_p, I_max=255):
"""
Defines the *ROMM RGB* encoding electro-optical transfer function
(EOTF / EOCF).
Parameters
----------
X_p : numeric or array_like
Non-linear data :math:`X'_{ROMM}`.
I_max : numeric, optional
Maximum code value: 255, 4095 and 650535 for respectively 8-bit,
12-bit and 16-bit per channel.
Returns
-------
numeric or ndarray
Linear data :math:`X_{ROMM}`.
References
----------
- :cite:`ANSI2003a`
- :cite:`Spaulding2000b`
Examples
--------
>>> eotf_ROMMRGB(98.356413311540095) # doctest: +ELLIPSIS
0.1...
"""
X_p = np.asarray(X_p)
E_t = 16**(1.8 / (1 - 1.8))
return as_numeric(
np.where(X_p < 16 * E_t * I_max, X_p / (16 * I_max),
(X_p / I_max)**1.8))
def log_decoding_ACEScc(ACEScc):
"""
Defines the *ACEScc* colourspace log decoding / electro-optical transfer
function.
Parameters
----------
ACEScc : numeric or array_like
*ACEScc* non-linear value.
Returns
-------
numeric or ndarray
*lin_AP1* value.
References
----------
- :cite:`TheAcademyofMotionPictureArtsandSciences2014q`
- :cite:`TheAcademyofMotionPictureArtsandSciences2014r`
- :cite:`TheAcademyofMotionPictureArtsandSciences2014t`
- :cite:`TheAcademyofMotionPictureArtsandSciencese`
Examples
--------
>>> log_decoding_ACEScc(0.413588402492442) # doctest: +ELLIPSIS
0.1799999...
"""
ACEScc = np.asarray(ACEScc)
output = np.where(ACEScc < (9.72 - 15) / 17.52,
(2**(ACEScc * 17.52 - 9.72) - 2**-16) * 2,
2**(ACEScc * 17.52 - 9.72))
output = np.where(ACEScc >= (np.log2(65504) + 9.72) / 17.52, 65504, output)
return as_numeric(output)
def log_encoding_ACEScc(lin_AP1):
"""
Defines the *ACEScc* colourspace log encoding / opto-electronic transfer
function.
Parameters
----------
lin_AP1 : numeric or array_like
*lin_AP1* value.
Returns
-------
numeric or ndarray
*ACEScc* non-linear value.
References
----------
- :cite:`TheAcademyofMotionPictureArtsandSciences2014q`
- :cite:`TheAcademyofMotionPictureArtsandSciences2014r`
- :cite:`TheAcademyofMotionPictureArtsandSciences2014t`
- :cite:`TheAcademyofMotionPictureArtsandSciencese`
Examples
--------
>>> log_encoding_ACEScc(0.18) # doctest: +ELLIPSIS
0.4135884...
"""
lin_AP1 = np.asarray(lin_AP1)
output = np.where(lin_AP1 < 0, (np.log2(2**-16) + 9.72) / 17.52,
(np.log2(2**-16 + lin_AP1 * 0.5) + 9.72) / 17.52)
output = np.where(lin_AP1 >= 2**-15, (np.log2(lin_AP1) + 9.72) / 17.52,
output)
return as_numeric(output)
def oetf_BT709(L):
"""
Defines *Recommendation ITU-R BT.709-6* opto-electronic transfer function
(OETF / OECF).
Parameters
----------
L : numeric or array_like
*Luminance* :math:`L` of the image.
Returns
-------
numeric or ndarray
Corresponding electrical signal :math:`V`.
Examples
--------
>>> oetf_BT709(0.18) # doctest: +ELLIPSIS
0.4090077...
"""
L = np.asarray(L)
return as_numeric(np.where(L < 0.018, L * 4.5, 1.099 * (L**0.45) - 0.099))
def CCT_to_xy_Hernandez1999(CCT, optimisation_kwargs=None, **kwargs):
"""
Returns the *CIE xy* chromaticity coordinates from given correlated colour
temperature :math:`T_{cp}` using *Hernandez-Andres et al. (1999)* method.
Parameters
----------
CCT : numeric or array_like
Correlated colour temperature :math:`T_{cp}`.
optimisation_kwargs : dict_like, optional
Parameters for :func:`scipy.optimize.minimize` definition.
Other Parameters
----------------
\\**kwargs : dict, optional
Keywords arguments for deprecation management.
Returns
-------
ndarray
*CIE xy* chromaticity coordinates.
Warnings
--------
*Hernandez-Andres et al. (1999)* 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
optimization using :func:`scipy.optimize.minimize` definition and thus has
reduced precision and poor performance.
References
----------
:cite:`Hernandez-Andres1999a`
Examples
--------
>>> CCT_to_xy_Hernandez1999(6500.7420431786531) # doctest: +ELLIPSIS
array([ 0.3127..., 0.329...])
"""
optimisation_kwargs = handle_arguments_deprecation(
{
'ArgumentRenamed':
[['optimisation_parameters', 'optimisation_kwargs']],
}, **kwargs).get('optimisation_kwargs', optimisation_kwargs)
usage_warning('"Hernandez-Andres et al. (1999)" method for computing '
'"CIE xy" chromaticity coordinates from given correlated '
'colour temperature is not a bijective function and 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, CCT):
"""
Objective function.
"""
objective = np.linalg.norm(xy_to_CCT_Hernandez1999(xy) - CCT)
return 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=CCS_ILLUMINANTS['CIE 1931 2 Degree Standard Observer']['D65'],
args=(CCT_i, ),
**optimisation_settings).x for CCT_i in CCT
])
return as_numeric(CCT.reshape(shape + [2]))
def gamma_function(a, exponent=1, negative_number_handling='indeterminate'):
"""
Defines a typical gamma encoding / decoding function.
Parameters
----------
a : numeric or array_like
Array to encode / decode.
exponent : numeric or array_like, optional
Encoding / decoding exponent.
negative_number_handling : unicode, optional
**{'Indeterminate', 'Mirror', 'Preserve', 'Clamp'}**,
Defines the behaviour for `a` negative numbers and / or the definition
return value:
- *Indeterminate*: The behaviour will be indeterminate and
definition return value might contain *nans*.
- *Mirror*: The definition return value will be mirrored around
abscissa and ordinate axis, i.e. Blackmagic Design: Davinci Resolve
behaviour.
- *Preserve*: The definition will preserve any negative number in
`a`, i.e. The Foundry Nuke behaviour.
- *Clamp*: The definition will clamp any negative number in `a` to 0.
Returns
-------
numeric or ndarray
Encoded / decoded array.
Raises
------
ValueError
If the negative number handling method is not defined.
Examples
--------
>>> gamma_function(0.18, 2.2) # doctest: +ELLIPSIS
0.0229932...
>>> gamma_function(-0.18, 2.0) # doctest: +ELLIPSIS
0.0323999...
>>> gamma_function(-0.18, 2.2)
nan
>>> gamma_function(-0.18, 2.2, 'Mirror') # doctest: +ELLIPSIS
-0.0229932...
>>> gamma_function(-0.18, 2.2, 'Preserve') # doctest: +ELLIPSIS
-0.1...
>>> gamma_function(-0.18, 2.2, 'Clamp') # doctest: +ELLIPSIS
0.0
"""
a = np.asarray(a)
exponent = np.asarray(exponent)
negative_number_handling = negative_number_handling.lower()
if negative_number_handling == 'indeterminate':
return as_numeric(a**exponent)
elif negative_number_handling == 'mirror':
return as_numeric(np.sign(a) * np.abs(a)**exponent)
elif negative_number_handling == 'preserve':
return as_numeric(np.where(a < 0, a, a**exponent))
elif negative_number_handling == 'clamp':
return as_numeric(np.where(a < 0, 0, a**exponent))
else:
raise ValueError(
'Undefined negative number handling method: "{0}".'.format(
negative_number_handling))
def uv_to_CCT_Krystek1985(uv, optimisation_parameters=None):
"""
Returns the correlated colour temperature :math:`T_{cp}` from given
*CIE UCS* colourspace *uv* chromaticity coordinates using *Krystek (1985)*
method.
Parameters
----------
uv : array_like
*CIE UCS* colourspace *uv* chromaticity coordinates.
optimisation_parameters : dict_like, optional
Parameters for :func:`scipy.optimize.minimize` definition.
Returns
-------
ndarray
Correlated colour temperature :math:`T_{cp}`.
Warnings
--------
*Krystek (1985)* does not give an analytical inverse transformation to
compute the correlated colour temperature :math:`T_{cp}` from given
*CIE UCS* colourspace *uv* chromaticity coordinates, the current
implementation relies on optimization using :func:`scipy.optimize.minimize`
definition and thus has reduced precision and poor performance.
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(np.array([0.20047203, 0.31029290]))
... # doctest: +ELLIPSIS
6504.3894290...
"""
uv = as_float_array(uv)
shape = uv.shape
uv = np.atleast_1d(uv.reshape([-1, 2]))
def objective_function(CCT, uv):
"""
Objective function.
"""
objective = np.linalg.norm(CCT_to_uv_Krystek1985(CCT) - uv)
return objective
optimisation_settings = {
'method': 'Nelder-Mead',
'options': {
'fatol': 1e-10,
},
}
if optimisation_parameters is not None:
optimisation_settings.update(optimisation_parameters)
CCT = as_float_array([
minimize(objective_function,
x0=6500,
args=(uv_i, ),
**optimisation_settings).x for uv_i in uv
])
return as_numeric(CCT.reshape(shape[:-1]))