colour.algebra.interpolation Module¶

Interpolation¶

Defines classes for interpolating variables.

• LinearInterpolator1d: 1-D function linear interpolation.
• SpragueInterpolator: 1-D function fifth-order polynomial interpolation.

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.

See also

SpragueInterpolator

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.

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]¶

See also

LinearInterpolator1d

Notes

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

References

[1]	CIE TC 1-38. (2005). 9.2.4 Method of interpolation for uniformly spaced independent variable. In CIE 167:2005 Recommended Practice for Tabulating Spectral Data for Use in Colour Computations (pp. 1–27). ISBN:978-3-901-90641-1

[2]	Westland, S., Ripamonti, C., & Cheung, V. (2012). Interpolation Methods. In Computational Colour Science Using MATLAB (2nd ed., pp. 29–37). ISBN:978-0-470-66569-5

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 TC 1-38. (2005). Table V. Values of the c-coefficients of Equ.s 6 and 7. In CIE 167:2005 Recommended Practice for Tabulating Spectral Data for Use in Colour Computations (p. 19). ISBN: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