colour.KernelInterpolator

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

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__()

References

[BB09], [Wik05c]

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)  
6.9411400...

Interpolating an array_like variable:

>>> f([0.25, 0.75])  
array([ 6.1806208...,  8.0823848...])

Using a different lanczos kernel:

>>> f = KernelInterpolator(x, y, kernel=kernel_sinc)
>>> f([0.25, 0.75])  
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])  
array([ 5.3961792...,  5.6521093...])

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

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.