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.

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