colour.KernelInterpolator¶

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

Bases: object

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

[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...])

property kernel

Getter and setter property for the kernel callable.

Parameters: value (callable) – Value to set the kernel callable.
Returns: Kernel callable.
Return type: callable

property kernel_args

Getter and setter property for the kernel call time arguments.

Parameters: value (dict) – Value to call the interpolation kernel with.
Returns: Kernel call time arguments.
Return type: dict

property padding_args

Getter and setter property for the kernel call time arguments.

Parameters: value (dict) – Value to call the interpolation kernel with.
Returns: Kernel call time arguments.
Return type: dict

property window

Getter and setter property for the window.

Parameters: value (int) – Value to set the window with.
Returns: Window.
Return type: int

property x

Getter and setter property for the independent \(x\) variable.

Parameters: value (array_like) – Value to set the independent \(x\) variable with.
Returns: Independent \(x\) variable.
Return type: array_like

property y

Getter and setter property for the dependent and already known \(y\) variable.

Parameters: value (array_like) – Value to set the dependent and already known \(y\) variable with.
Returns: Dependent and already known \(y\) variable.
Return type: array_like