colour.algebra.interpolation Module

Interpolation

Defines classes for interpolating variables.

class colour.algebra.interpolation.LinearInterpolator1d(x=None, y=None)[source]

Bases: object

Linearly interpolates a 1-D function.

Parameters:
  • x (ndarray) – Independent \(x\) variable values corresponding with \(y\) variable.
  • y (ndarray) – Dependent and already known \(y\) variable values to interpolate.
__call__()[source]

Notes

This class is a wrapper around numpy.interp definition.

Examples

Interpolating a single numeric variable:

>>> y = np.array([5.9200, 9.3700, 10.8135, 4.5100, 69.5900, 27.8007, 86.0500])  
>>> x = np.arange(len(y))
>>> f = LinearInterpolator1d(x, y)
>>> # Doctests ellipsis for Python 2.x compatibility.
>>> f(0.5)  
7.64...

Interpolating an array_like variable:

>>> f([0.25, 0.75])
array([ 6.7825,  8.5075])
__call__(x)[source]

Evaluates the interpolating polynomial at given point(s).

Parameters:x (numeric or array_like) – Point(s) to evaluate the interpolant at.
Returns:Interpolated value(s).
Return type:float or ndarray
x[source]

Property for self.__x private attribute.

Returns:self.__x
Return type:array_like
y[source]

Property for self.__y private attribute.

Returns:self.__y
Return type:array_like
class colour.algebra.interpolation.SplineInterpolator(*args, **kwargs)[source]

Bases: scipy.interpolate.interpolate.interp1d

Interpolates a 1-D function using cubic spline interpolation.

Notes

This class is a wrapper around scipy.interpolate.interp1d class.

class colour.algebra.interpolation.SpragueInterpolator(x=None, y=None)[source]

Bases: object

Constructs a fifth-order polynomial that passes through \(y\) dependent variable.

The Sprague (1880) method is recommended by the CIE for interpolating functions having a uniformly spaced independent variable.

Parameters:
  • x (array_like) – Independent \(x\) variable values corresponding with \(y\) variable.
  • y (array_like) – Dependent and already known \(y\) variable values to interpolate.
__call__()[source]

Notes

The minimum number \(k\) of data points required along the interpolation axis is \(k=6\).

References

[1]CIE 167:2005 Recommended Practice for Tabulating Spectral Data for Use in Colour Computations: 9.2.4 Method of interpolation for uniformly spaced independent variable, ISBN-13: 978-3-901-90641-1
[2]Stephen Westland, Caterina Ripamonti, Vien Cheung, Computational Colour Science Using MATLAB, 2nd Edition, The Wiley-IS&T Series in Imaging Science and Technology, published July 2012, ISBN-13: 978-0-470-66569-5, page 33.

Examples

Interpolating a single numeric variable:

>>> y = np.array([5.9200, 9.3700, 10.8135, 4.5100, 69.5900, 27.8007, 86.0500])  
>>> x = np.arange(len(y))
>>> f = SpragueInterpolator(x, y)
>>> f(0.5)  
7.2185025...

Interpolating an array_like variable:

>>> f([0.25, 0.75])  
array([ 6.7295161...,  7.8140625...])
SPRAGUE_C_COEFFICIENTS = array([[ 884, -1960, 3033, -2648, 1080, -180], [ 508, -540, 488, -367, 144, -24], [ -24, 144, -367, 488, -540, 508], [ -180, 1080, -2648, 3033, -1960, 884]])

Defines the coefficients used to generate extra points for boundaries interpolation.

SPRAGUE_C_COEFFICIENTS : array_like, (4, 6)

References

[3]CIE 167:2005 Recommended Practice for Tabulating Spectral Data for Use in Colour Computations: Table V, ISBN-13: 978-3-901-90641-1
__call__(x)[source]

Evaluates the interpolating polynomial at given point(s).

Parameters:x (numeric or array_like) – Point(s) to evaluate the interpolant at.
Returns:Interpolated value(s).
Return type:numeric or ndarray
x[source]

Property for self.__x private attribute.

Returns:self.__x
Return type:array_like
y[source]

Property for self.__y private attribute.

Returns:self.__y
Return type:array_like