# colour.KernelInterpolator¶

class colour.KernelInterpolator(x, y, window=3, kernel=<function kernel_lanczos>, kernel_args=None, padding_args=None, dtype=<class 'numpy.float64'>)[source]

Kernel based interpolation of a 1-D function.

The reconstruction of a continuous signal can be described as a linear convolution operation. Interpolation can be expressed as a convolution of the given discrete function $$g(x)$$ with some continuous interpolation kernel $$k(w)$$:

$$\hat{g}(w_0) = [k * g](w_0) = \sum_{x=-\infty}^{\infty}k(w_0 - x)\cdot g(x)$$

Parameters: x (array_like) – Independent $$x$$ variable values corresponding with $$y$$ variable. y (array_like) – Dependent and already known $$y$$ variable values to interpolate. window (int, optional) – Width of the window in samples on each side. kernel (callable, optional) – Kernel to use for interpolation. kernel_args (dict, optional) – Arguments to use when calling the kernel. padding_args (dict, optional) – Arguments to use when padding $$y$$ variable values with the np.pad() definition. dtype (type) – Data type used for internal conversions.
x
y
window
kernel
kernel_args
padding_args
__call__()[source]

References

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 = KernelInterpolator(x, y)
>>> f(0.5)  # doctest: +ELLIPSIS
6.9411400...


Interpolating an array_like variable:

>>> f([0.25, 0.75])  # doctest: +ELLIPSIS
array([ 6.1806208...,  8.0823848...])


Using a different lanczos kernel:

>>> f = KernelInterpolator(x, y, kernel=kernel_sinc)
>>> f([0.25, 0.75])  # doctest: +ELLIPSIS
array([ 6.5147317...,  8.3965466...])


Using a different window size:

>>> f = KernelInterpolator(
...     x,
...     y,
...     window=16,
...     kernel=kernel_lanczos,
...     kernel_args={'a': 16})
>>> f([0.25, 0.75])  # doctest: +ELLIPSIS
array([ 5.3961792...,  5.6521093...])

__init__(x, y, window=3, kernel=<function kernel_lanczos>, kernel_args=None, padding_args=None, dtype=<class 'numpy.float64'>)[source]

Initialize self. See help(type(self)) for accurate signature.

Methods

 __init__(x, y[, window, kernel, …]) Initialize self.

Attributes

 kernel Getter and setter property for the kernel callable. kernel_args Getter and setter property for the kernel call time arguments. padding_args Getter and setter property for the kernel call time arguments. window Getter and setter property for the window. x Getter and setter property for the independent $$x$$ variable. y Getter and setter property for the dependent and already known $$y$$ variable.