# colour.SpragueInterpolator¶

class colour.SpragueInterpolator(x: ArrayLike, y: ArrayLike, dtype: Optional[Type[DTypeNumber]] = None)[source]

Bases: object

Construct 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 (ArrayLike) – Independent $$x$$ variable values corresponding with $$y$$ variable.

• y (ArrayLike) – Dependent and already known $$y$$ variable values to interpolate.

• dtype (Optional[Type[DTypeNumber]]) – Data type used for internal conversions.

Attributes

Methods

Notes

• The minimum number $$k$$ of data points required along the interpolation axis is $$k=6$$.

References

, [WRC12e]

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 ArrayLike 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, (4, 6)

References

__init__(x: ArrayLike, y: ArrayLike, dtype: Optional[Type[DTypeNumber]] = None)[source]
Parameters
• x (ArrayLike) –

• y (ArrayLike) –

• dtype (Optional[Type[DTypeNumber]]) –

property x: numpy.ndarray

Getter and setter property for the independent $$x$$ variable.

Parameters

value – Value to set the independent $$x$$ variable with.

Returns

Independent $$x$$ variable.

Return type

numpy.ndarray

property y: numpy.ndarray

Getter and setter property for the dependent and already known $$y$$ variable.

Parameters

value – Value to set the dependent and already known $$y$$ variable with.

Returns

Dependent and already known $$y$$ variable.

Return type

numpy.ndarray

__call__(x: FloatingOrArrayLike) FloatingOrNDArray[source]

Evaluate the interpolating polynomial at given point(s).

Parameters

x (FloatingOrArrayLike) – Point(s) to evaluate the interpolant at.

Returns

Interpolated value(s).

Return type
__weakref__

list of weak references to the object (if defined)