colour.KernelInterpolator#

class colour.KernelInterpolator(x: ArrayLike, y: ArrayLike, window: float = 3, kernel: Callable = kernel_lanczos, kernel_kwargs: dict | None = None, padding_kwargs: dict | None = None, dtype: Type[DTypeReal] | None = None, *args: Any, **kwargs: Any)[source]#

Bases: object

Perform kernel-based interpolation of a 1-D function.

Reconstruct a continuous signal from discrete samples using linear convolution. Express interpolation as the convolution of the specified discrete function \(g(x)\) with a 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 (ArrayLike) – Independent \(x\) variable values corresponding with \(y\) variable.

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

  • window (float) – Width of the window in samples on each side.

  • kernel (Callable) – Kernel to use for interpolation.

  • kernel_kwargs (dict | None) – Arguments to use when calling the kernel.

  • padding_kwargs (dict | None) – Arguments to use when padding \(y\) variable values with the np.pad() definition.

  • dtype (Type[DTypeReal] | None) – Data type used for internal conversions.

  • args (Any)

  • kwargs (Any)

Attributes

Methods

References

[BB09], [Wikipedia05a]

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)
np.float64(6.9411400...)

Interpolating an ArrayLike 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_kwargs={"a": 16}
... )
>>> f([0.25, 0.75])
array([5.3961792..., 5.6521093...])
__init__(x: ArrayLike, y: ArrayLike, window: float = 3, kernel: Callable = kernel_lanczos, kernel_kwargs: dict | None = None, padding_kwargs: dict | None = None, dtype: Type[DTypeReal] | None = None, *args: Any, **kwargs: Any) → None[source]#
Parameters:
Return type:

None

property x: NDArrayFloat#

Getter and setter 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: NDArrayFloat#

Getter and setter 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

property window: float#

Getter and setter for the filtering window size for the moving average.

The window determines the number of samples used in the moving average calculation. A larger window produces smoother results with greater lag, while a smaller window yields more responsive but potentially noisier output.

Parameters:

value – Value to set the window with.

Returns:

Window size for the moving average filter.

Return type:

float

property kernel: Callable#

Getter and setter for the kernel callable for the interpolator.

Parameters:

value – Value to set the callable object to use as the interpolation kernel with. Must be a callable that accepts numeric arguments.

Returns:

Callable object to use as the interpolation kernel.

Return type:

Callable

Raises:

AssertionError – If the provided value is not callable.

property kernel_kwargs: dict#

Getter and setter for the kernel keyword arguments for the convolution operation.

Parameters:

value – Value to set the keyword arguments to pass to the kernel function with.

Returns:

Keyword arguments to pass to the kernel function.

Return type:

dict

Raises:

AssertionError – If the provided value is not a :class:’dict` class instance.

property padding_kwargs: dict#

Getter and setter for the padding keyword arguments for edge handling.

Parameters:

value – Value to set the keyword arguments to pass to the padding function when handling edges during interpolation.

Returns:

Keyword arguments to pass to the padding function when handling edges during interpolation.

Return type:

dict

Raises:

AssertionError – If the provided value is not a dict class instance.

__call__(x: ArrayLike) → NDArrayFloat[source]#

Evaluate the interpolator at specified point(s).

Parameters:

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

Returns:

Interpolated value(s).

Return type:

numpy.ndarray

__weakref__#

list of weak references to the object