colour.SpectralDistribution¶

class colour.SpectralDistribution(data=None, domain=None, **kwargs)[source]¶

Bases: colour.continuous.signal.Signal

Defines the spectral distribution: the base object for spectral computations.

The spectral distribution will be initialised according to CIE 15:2004 recommendation: the method developed by Sprague (1880) will be used for interpolating functions having a uniformly spaced independent variable and the Cubic Spline method for non-uniformly spaced independent variable. Extrapolation is performed according to CIE 167:2005 recommendation.

Important

Specific documentation about getting, setting, indexing and slicing the spectral power distribution values is available in the Spectral Representation and Continuous Signal section.

Parameters

data (Series or Signal, SpectralDistribution or array_like or dict_like, optional) – Data to be stored in the spectral distribution.
domain (array_like, optional) – Values to initialise the colour.SpectralDistribution.wavelength attribute with. If both data and domain arguments are defined, the latter will be used to initialise the colour.SpectralDistribution.wavelength attribute.
name (unicode, optional) – Spectral distribution name.
interpolator (object, optional) – Interpolator class type to use as interpolating function.
interpolator_kwargs (dict_like, optional) – Arguments to use when instantiating the interpolating function.
extrapolator (object, optional) – Extrapolator class type to use as extrapolating function.
extrapolator_kwargs (dict_like, optional) – Arguments to use when instantiating the extrapolating function.
strict_name (unicode, optional) – Spectral distribution name for figures, default to colour.SpectralDistribution.name attribute value.

Attributes

strict_name
wavelengths
values
shape

Methods

__init__()
interpolate()
extrapolate()
align()
trim()
normalise()

References

[], [], []

Examples

Instantiating a spectral distribution with a uniformly spaced independent variable:

>>> from colour.utilities import numpy_print_options
>>> data = {
...     500: 0.0651,
...     520: 0.0705,
...     540: 0.0772,
...     560: 0.0870,
...     580: 0.1128,
...     600: 0.1360
... }
>>> with numpy_print_options(suppress=True):
...     SpectralDistribution(data)  
SpectralDistribution([[ 500.    ,    0.0651],
                      [ 520.    ,    0.0705],
                      [ 540.    ,    0.0772],
                      [ 560.    ,    0.087 ],
                      [ 580.    ,    0.1128],
                      [ 600.    ,    0.136 ]],
                     interpolator=SpragueInterpolator,
                     interpolator_kwargs={},
                     extrapolator=Extrapolator,
                     extrapolator_kwargs={...})

Instantiating a spectral distribution with a non-uniformly spaced independent variable:

>>> data[510] = 0.31416
>>> with numpy_print_options(suppress=True):
...     SpectralDistribution(data)  
SpectralDistribution([[ 500.     ,    0.0651 ],
                      [ 510.     ,    0.31416],
                      [ 520.     ,    0.0705 ],
                      [ 540.     ,    0.0772 ],
                      [ 560.     ,    0.087  ],
                      [ 580.     ,    0.1128 ],
                      [ 600.     ,    0.136  ]],
                     interpolator=CubicSplineInterpolator,
                     interpolator_kwargs={},
                     extrapolator=Extrapolator,
                     extrapolator_kwargs={...})

Instantiation with a Pandas Series:

>>> from colour.utilities import is_pandas_installed
>>> if is_pandas_installed():
...     from pandas import Series
...     print(SpectralDistribution(Series(data)))  
[[  5.0000000...e+02   6.5100000...e-02]
 [  5.2000000...e+02   7.0500000...e-02]
 [  5.4000000...e+02   7.7200000...e-02]
 [  5.6000000...e+02   8.7000000...e-02]
 [  5.8000000...e+02   1.1280000...e-01]
 [  6.0000000...e+02   1.3600000...e-01]
 [  5.1000000...e+02   3.1416000...e-01]]

__init__(data=None, domain=None, **kwargs)[source]¶

property strict_name¶

Getter and setter property for the spectral distribution strict name.

Parameters: value (unicode) – Value to set the spectral distribution strict name with.
Returns: Spectral distribution strict name.
Return type: unicode

property wavelengths¶

Getter and setter property for the spectral distribution wavelengths \(\lambda_n\).

Parameters: value (array_like) – Value to set the spectral distribution wavelengths \(\lambda_n\) with.
Returns: Spectral distribution wavelengths \(\lambda_n\).
Return type: ndarray

property values¶

Getter and setter property for the spectral distribution values.

Parameters: value (array_like) – Value to set the spectral distribution wavelengths values with.
Returns: Spectral distribution values.
Return type: ndarray

property shape¶

Getter property for the spectral distribution shape.

Returns: Spectral distribution shape.
Return type: SpectralShape

Notes

A spectral distribution with a non-uniformly spaced independent variable have multiple intervals, in that case colour.SpectralDistribution.shape attribute returns the minimum interval size.

Examples

Shape of a spectral distribution with a uniformly spaced independent variable:

>>> data = {
...     500: 0.0651,
...     520: 0.0705,
...     540: 0.0772,
...     560: 0.0870,
...     580: 0.1128,
...     600: 0.1360
... }
>>> SpectralDistribution(data).shape
SpectralShape(500.0, 600.0, 20.0)

Shape of a spectral distribution with a non-uniformly spaced independent variable:

>>> data[510] = 0.31416
>>> SpectralDistribution(data).shape
SpectralShape(500.0, 600.0, 10.0)

interpolate(shape, interpolator=None, interpolator_kwargs=None, **kwargs)[source]¶

Interpolates the spectral distribution in-place according to CIE 167:2005 recommendation (if the interpolator has not been changed at instantiation time) or given interpolation arguments.

The logic for choosing the interpolator class when interpolator is not given is as follows:

if self.interpolator not in (SpragueInterpolator,
                             CubicSplineInterpolator):
    interpolator = self.interpolator
elif self.is_uniform():
    interpolator = SpragueInterpolator
else:
    interpolator = CubicSplineInterpolator

The logic for choosing the interpolator keyword arguments when interpolator_kwargs is not given is as follows:

if self.interpolator not in (SpragueInterpolator,
                             CubicSplineInterpolator):
    interpolator_kwargs = self.interpolator_kwargs
else:
    interpolator_kwargs = {}

Parameters

shape (SpectralShape, optional) – Spectral shape used for interpolation.
interpolator (object, optional) – Interpolator class type to use as interpolating function.
interpolator_kwargs (dict_like, optional) – Arguments to use when instantiating the interpolating function.
**kwargs (dict, optional) – Keywords arguments for deprecation management.

Returns

Interpolated spectral distribution.

Return type

SpectralDistribution

Notes

Interpolation will be performed over boundaries range, if you need to extend the range of the spectral distribution use the colour.SpectralDistribution.extrapolate() or colour.SpectralDistribution.align() methods.

Warning

Cubic Spline interpolator requires at least 3 wavelengths \(\lambda_n\) for interpolation.
Sprague (1880) interpolator requires at least 6 wavelengths \(\lambda_n\) for interpolation.

References

[]

Examples

Spectral distribution with a uniformly spaced independent variable uses Sprague (1880) interpolation:

>>> from colour.utilities import numpy_print_options
>>> data = {
...     500: 0.0651,
...     520: 0.0705,
...     540: 0.0772,
...     560: 0.0870,
...     580: 0.1128,
...     600: 0.1360
... }
>>> sd = SpectralDistribution(data)
>>> with numpy_print_options(suppress=True):
...     print(sd.interpolate(SpectralShape(interval=1)))
... 
[[ 500.            0.0651   ...]
 [ 501.            0.0653522...]
 [ 502.            0.0656105...]
 [ 503.            0.0658715...]
 [ 504.            0.0661328...]
 [ 505.            0.0663929...]
 [ 506.            0.0666509...]
 [ 507.            0.0669069...]
 [ 508.            0.0671613...]
 [ 509.            0.0674150...]
 [ 510.            0.0676692...]
 [ 511.            0.0679253...]
 [ 512.            0.0681848...]
 [ 513.            0.0684491...]
 [ 514.            0.0687197...]
 [ 515.            0.0689975...]
 [ 516.            0.0692832...]
 [ 517.            0.0695771...]
 [ 518.            0.0698787...]
 [ 519.            0.0701870...]
 [ 520.            0.0705   ...]
 [ 521.            0.0708155...]
 [ 522.            0.0711336...]
 [ 523.            0.0714547...]
 [ 524.            0.0717789...]
 [ 525.            0.0721063...]
 [ 526.            0.0724367...]
 [ 527.            0.0727698...]
 [ 528.            0.0731051...]
 [ 529.            0.0734423...]
 [ 530.            0.0737808...]
 [ 531.            0.0741203...]
 [ 532.            0.0744603...]
 [ 533.            0.0748006...]
 [ 534.            0.0751409...]
 [ 535.            0.0754813...]
 [ 536.            0.0758220...]
 [ 537.            0.0761633...]
 [ 538.            0.0765060...]
 [ 539.            0.0768511...]
 [ 540.            0.0772   ...]
 [ 541.            0.0775527...]
 [ 542.            0.0779042...]
 [ 543.            0.0782507...]
 [ 544.            0.0785908...]
 [ 545.            0.0789255...]
 [ 546.            0.0792576...]
 [ 547.            0.0795917...]
 [ 548.            0.0799334...]
 [ 549.            0.0802895...]
 [ 550.            0.0806671...]
 [ 551.            0.0810740...]
 [ 552.            0.0815176...]
 [ 553.            0.0820049...]
 [ 554.            0.0825423...]
 [ 555.            0.0831351...]
 [ 556.            0.0837873...]
 [ 557.            0.0845010...]
 [ 558.            0.0852763...]
 [ 559.            0.0861110...]
 [ 560.            0.087    ...]
 [ 561.            0.0879383...]
 [ 562.            0.0889300...]
 [ 563.            0.0899793...]
 [ 564.            0.0910876...]
 [ 565.            0.0922541...]
 [ 566.            0.0934760...]
 [ 567.            0.0947487...]
 [ 568.            0.0960663...]
 [ 569.            0.0974220...]
 [ 570.            0.0988081...]
 [ 571.            0.1002166...]
 [ 572.            0.1016394...]
 [ 573.            0.1030687...]
 [ 574.            0.1044972...]
 [ 575.            0.1059186...]
 [ 576.            0.1073277...]
 [ 577.            0.1087210...]
 [ 578.            0.1100968...]
 [ 579.            0.1114554...]
 [ 580.            0.1128   ...]
 [ 581.            0.1141333...]
 [ 582.            0.1154495...]
 [ 583.            0.1167424...]
 [ 584.            0.1180082...]
 [ 585.            0.1192452...]
 [ 586.            0.1204536...]
 [ 587.            0.1216348...]
 [ 588.            0.1227915...]
 [ 589.            0.1239274...]
 [ 590.            0.1250465...]
 [ 591.            0.1261531...]
 [ 592.            0.1272517...]
 [ 593.            0.1283460...]
 [ 594.            0.1294393...]
 [ 595.            0.1305340...]
 [ 596.            0.1316310...]
 [ 597.            0.1327297...]
 [ 598.            0.1338277...]
 [ 599.            0.1349201...]
 [ 600.            0.136    ...]]

Spectral distribution with a non-uniformly spaced independent variable uses Cubic Spline interpolation:

>>> sd = SpectralDistribution(data)
>>> sd[510] = np.pi / 10
>>> with numpy_print_options(suppress=True):
...     print(sd.interpolate(SpectralShape(interval=1)))
... 
[[ 500.            0.0651   ...]
 [ 501.            0.1365202...]
 [ 502.            0.1953263...]
 [ 503.            0.2423724...]
 [ 504.            0.2785126...]
 [ 505.            0.3046010...]
 [ 506.            0.3214916...]
 [ 507.            0.3300387...]
 [ 508.            0.3310962...]
 [ 509.            0.3255184...]
 [ 510.            0.3141592...]
 [ 511.            0.2978729...]
 [ 512.            0.2775135...]
 [ 513.            0.2539351...]
 [ 514.            0.2279918...]
 [ 515.            0.2005378...]
 [ 516.            0.1724271...]
 [ 517.            0.1445139...]
 [ 518.            0.1176522...]
 [ 519.            0.0926962...]
 [ 520.            0.0705   ...]
 [ 521.            0.0517370...]
 [ 522.            0.0363589...]
 [ 523.            0.0241365...]
 [ 524.            0.0148407...]
 [ 525.            0.0082424...]
 [ 526.            0.0041126...]
 [ 527.            0.0022222...]
 [ 528.            0.0023421...]
 [ 529.            0.0042433...]
 [ 530.            0.0076966...]
 [ 531.            0.0124729...]
 [ 532.            0.0183432...]
 [ 533.            0.0250785...]
 [ 534.            0.0324496...]
 [ 535.            0.0402274...]
 [ 536.            0.0481829...]
 [ 537.            0.0560870...]
 [ 538.            0.0637106...]
 [ 539.            0.0708246...]
 [ 540.            0.0772   ...]
 [ 541.            0.0826564...]
 [ 542.            0.0872086...]
 [ 543.            0.0909203...]
 [ 544.            0.0938549...]
 [ 545.            0.0960760...]
 [ 546.            0.0976472...]
 [ 547.            0.0986321...]
 [ 548.            0.0990942...]
 [ 549.            0.0990971...]
 [ 550.            0.0987043...]
 [ 551.            0.0979794...]
 [ 552.            0.0969861...]
 [ 553.            0.0957877...]
 [ 554.            0.0944480...]
 [ 555.            0.0930304...]
 [ 556.            0.0915986...]
 [ 557.            0.0902161...]
 [ 558.            0.0889464...]
 [ 559.            0.0878532...]
 [ 560.            0.087    ...]
 [ 561.            0.0864371...]
 [ 562.            0.0861623...]
 [ 563.            0.0861600...]
 [ 564.            0.0864148...]
 [ 565.            0.0869112...]
 [ 566.            0.0876336...]
 [ 567.            0.0885665...]
 [ 568.            0.0896945...]
 [ 569.            0.0910020...]
 [ 570.            0.0924735...]
 [ 571.            0.0940936...]
 [ 572.            0.0958467...]
 [ 573.            0.0977173...]
 [ 574.            0.0996899...]
 [ 575.            0.1017491...]
 [ 576.            0.1038792...]
 [ 577.            0.1060649...]
 [ 578.            0.1082906...]
 [ 579.            0.1105408...]
 [ 580.            0.1128   ...]
 [ 581.            0.1150526...]
 [ 582.            0.1172833...]
 [ 583.            0.1194765...]
 [ 584.            0.1216167...]
 [ 585.            0.1236884...]
 [ 586.            0.1256760...]
 [ 587.            0.1275641...]
 [ 588.            0.1293373...]
 [ 589.            0.1309798...]
 [ 590.            0.1324764...]
 [ 591.            0.1338114...]
 [ 592.            0.1349694...]
 [ 593.            0.1359349...]
 [ 594.            0.1366923...]
 [ 595.            0.1372262...]
 [ 596.            0.1375211...]
 [ 597.            0.1375614...]
 [ 598.            0.1373316...]
 [ 599.            0.1368163...]
 [ 600.            0.136    ...]]

extrapolate(shape, extrapolator=None, extrapolator_kwargs=None, **kwargs)[source]¶

Extrapolates the spectral distribution in-place according to CIE 15:2004 and CIE 167:2005 recommendations or given extrapolation arguments.

Parameters

shape (SpectralShape) – Spectral shape used for extrapolation.
extrapolator (object, optional) – Extrapolator class type to use as extrapolating function.
extrapolator_kwargs (dict_like, optional) – Arguments to use when instantiating the extrapolating function.
**kwargs (dict, optional) – Keywords arguments for deprecation management.

Returns

Extrapolated spectral distribution.

Return type

SpectralDistribution

References

[], []

Examples

>>> from colour.utilities import numpy_print_options
>>> data = {
...     500: 0.0651,
...     520: 0.0705,
...     540: 0.0772,
...     560: 0.0870,
...     580: 0.1128,
...     600: 0.1360
... }
>>> sd = SpectralDistribution(data)
>>> sd.extrapolate(SpectralShape(400, 700)).shape
SpectralShape(400.0, 700.0, 20.0)
>>> with numpy_print_options(suppress=True):
...     print(sd)
[[ 400.        0.0651]
 [ 420.        0.0651]
 [ 440.        0.0651]
 [ 460.        0.0651]
 [ 480.        0.0651]
 [ 500.        0.0651]
 [ 520.        0.0705]
 [ 540.        0.0772]
 [ 560.        0.087 ]
 [ 580.        0.1128]
 [ 600.        0.136 ]
 [ 620.        0.136 ]
 [ 640.        0.136 ]
 [ 660.        0.136 ]
 [ 680.        0.136 ]
 [ 700.        0.136 ]]

align(shape, interpolator=None, interpolator_kwargs=None, extrapolator=None, extrapolator_kwargs=None, **kwargs)[source]¶

Aligns the spectral distribution in-place to given spectral shape: Interpolates first then extrapolates to fit the given range.

Interpolation is performed according to CIE 167:2005 recommendation (if the interpolator has not been changed at instantiation time) or given interpolation arguments.

The logic for choosing the interpolator class when interpolator is not given is as follows:

if self.interpolator not in (SpragueInterpolator,
                             CubicSplineInterpolator):
    interpolator = self.interpolator
elif self.is_uniform():
    interpolator = SpragueInterpolator
else:
    interpolator = CubicSplineInterpolator

The logic for choosing the interpolator keyword arguments when interpolator_kwargs is not given is as follows:

if self.interpolator not in (SpragueInterpolator,
                             CubicSplineInterpolator):
    interpolator_kwargs = self.interpolator_kwargs
else:
    interpolator_kwargs = {}

Parameters

shape (SpectralShape) – Spectral shape used for alignment.
interpolator (object, optional) – Interpolator class type to use as interpolating function.
interpolator_kwargs (dict_like, optional) – Arguments to use when instantiating the interpolating function.
extrapolator (object, optional) – Extrapolator class type to use as extrapolating function.
extrapolator_kwargs (dict_like, optional) – Arguments to use when instantiating the extrapolating function.
**kwargs (dict, optional) – Keywords arguments for deprecation management.

Returns

Aligned spectral distribution.

Return type

SpectralDistribution

Examples

>>> from colour.utilities import numpy_print_options
>>> data = {
...     500: 0.0651,
...     520: 0.0705,
...     540: 0.0772,
...     560: 0.0870,
...     580: 0.1128,
...     600: 0.1360
... }
>>> sd = SpectralDistribution(data)
>>> with numpy_print_options(suppress=True):
...     print(sd.align(SpectralShape(505, 565, 1)))
... 
[[ 505.            0.0663929...]
 [ 506.            0.0666509...]
 [ 507.            0.0669069...]
 [ 508.            0.0671613...]
 [ 509.            0.0674150...]
 [ 510.            0.0676692...]
 [ 511.            0.0679253...]
 [ 512.            0.0681848...]
 [ 513.            0.0684491...]
 [ 514.            0.0687197...]
 [ 515.            0.0689975...]
 [ 516.            0.0692832...]
 [ 517.            0.0695771...]
 [ 518.            0.0698787...]
 [ 519.            0.0701870...]
 [ 520.            0.0705   ...]
 [ 521.            0.0708155...]
 [ 522.            0.0711336...]
 [ 523.            0.0714547...]
 [ 524.            0.0717789...]
 [ 525.            0.0721063...]
 [ 526.            0.0724367...]
 [ 527.            0.0727698...]
 [ 528.            0.0731051...]
 [ 529.            0.0734423...]
 [ 530.            0.0737808...]
 [ 531.            0.0741203...]
 [ 532.            0.0744603...]
 [ 533.            0.0748006...]
 [ 534.            0.0751409...]
 [ 535.            0.0754813...]
 [ 536.            0.0758220...]
 [ 537.            0.0761633...]
 [ 538.            0.0765060...]
 [ 539.            0.0768511...]
 [ 540.            0.0772   ...]
 [ 541.            0.0775527...]
 [ 542.            0.0779042...]
 [ 543.            0.0782507...]
 [ 544.            0.0785908...]
 [ 545.            0.0789255...]
 [ 546.            0.0792576...]
 [ 547.            0.0795917...]
 [ 548.            0.0799334...]
 [ 549.            0.0802895...]
 [ 550.            0.0806671...]
 [ 551.            0.0810740...]
 [ 552.            0.0815176...]
 [ 553.            0.0820049...]
 [ 554.            0.0825423...]
 [ 555.            0.0831351...]
 [ 556.            0.0837873...]
 [ 557.            0.0845010...]
 [ 558.            0.0852763...]
 [ 559.            0.0861110...]
 [ 560.            0.087    ...]
 [ 561.            0.0879383...]
 [ 562.            0.0889300...]
 [ 563.            0.0899793...]
 [ 564.            0.0910876...]
 [ 565.            0.0922541...]]

trim(shape)[source]¶

Trims the spectral distribution wavelengths to given spectral shape.

Parameters: shape (SpectralShape) – Spectral shape used for trimming.
Returns: Trimmed spectral distribution.
Return type: SpectralDistribution

Examples

>>> from colour.utilities import numpy_print_options
>>> data = {
...     500: 0.0651,
...     520: 0.0705,
...     540: 0.0772,
...     560: 0.0870,
...     580: 0.1128,
...     600: 0.1360
... }
>>> sd = SpectralDistribution(data)
>>> sd = sd.interpolate(SpectralShape(interval=1))
>>> with numpy_print_options(suppress=True):
...     print(sd.trim(SpectralShape(520, 580, 5)))
... 
[[ 520.            0.0705   ...]
 [ 521.            0.0708155...]
 [ 522.            0.0711336...]
 [ 523.            0.0714547...]
 [ 524.            0.0717789...]
 [ 525.            0.0721063...]
 [ 526.            0.0724367...]
 [ 527.            0.0727698...]
 [ 528.            0.0731051...]
 [ 529.            0.0734423...]
 [ 530.            0.0737808...]
 [ 531.            0.0741203...]
 [ 532.            0.0744603...]
 [ 533.            0.0748006...]
 [ 534.            0.0751409...]
 [ 535.            0.0754813...]
 [ 536.            0.0758220...]
 [ 537.            0.0761633...]
 [ 538.            0.0765060...]
 [ 539.            0.0768511...]
 [ 540.            0.0772   ...]
 [ 541.            0.0775527...]
 [ 542.            0.0779042...]
 [ 543.            0.0782507...]
 [ 544.            0.0785908...]
 [ 545.            0.0789255...]
 [ 546.            0.0792576...]
 [ 547.            0.0795917...]
 [ 548.            0.0799334...]
 [ 549.            0.0802895...]
 [ 550.            0.0806671...]
 [ 551.            0.0810740...]
 [ 552.            0.0815176...]
 [ 553.            0.0820049...]
 [ 554.            0.0825423...]
 [ 555.            0.0831351...]
 [ 556.            0.0837873...]
 [ 557.            0.0845010...]
 [ 558.            0.0852763...]
 [ 559.            0.0861110...]
 [ 560.            0.087    ...]
 [ 561.            0.0879383...]
 [ 562.            0.0889300...]
 [ 563.            0.0899793...]
 [ 564.            0.0910876...]
 [ 565.            0.0922541...]
 [ 566.            0.0934760...]
 [ 567.            0.0947487...]
 [ 568.            0.0960663...]
 [ 569.            0.0974220...]
 [ 570.            0.0988081...]
 [ 571.            0.1002166...]
 [ 572.            0.1016394...]
 [ 573.            0.1030687...]
 [ 574.            0.1044972...]
 [ 575.            0.1059186...]
 [ 576.            0.1073277...]
 [ 577.            0.1087210...]
 [ 578.            0.1100968...]
 [ 579.            0.1114554...]
 [ 580.            0.1128   ...]]

normalise(factor=1)[source]¶

Normalises the spectral distribution using given normalization factor.

Parameters: factor (numeric, optional) – Normalization factor
Returns: Normalised spectral distribution.
Return type: SpectralDistribution

Examples

>>> from colour.utilities import numpy_print_options
>>> data = {
...     500: 0.0651,
...     520: 0.0705,
...     540: 0.0772,
...     560: 0.0870,
...     580: 0.1128,
...     600: 0.1360
... }
>>> sd = SpectralDistribution(data)
>>> with numpy_print_options(suppress=True):
...     print(sd.normalise())  
[[ 500.            0.4786764...]
 [ 520.            0.5183823...]
 [ 540.            0.5676470...]
 [ 560.            0.6397058...]
 [ 580.            0.8294117...]
 [ 600.            1.       ...]]

__repr__()¶

Returns an ellipsis string representation of the continuous signal for documentation purposes.

Returns: Ellipsis string representation.
Return type: unicode