saealib.MultiquadricKernel#

class saealib.MultiquadricKernel(*, length_scale=None)[source]#

Bases: RBFKernel

Multiquadric radial basis function kernel.

This conditionally positive definite kernel has order 0 and requires a constant polynomial term for a well-posed system. Based on [16].

Parameters:

length_scale (float or None) – Shape parameter (denoted gamma in the paper), in the same distance units as the input data. None resolves to the median pairwise training-point distance at fit time.

Methods

__init__

evaluate

Evaluate the multiquadric kernel sqrt(r**2 + length_scale**2).

pairwise

Evaluate the kernel between every row of x1 and x2.

resolve

Resolve length_scale from training data if unset.

validate

Validate length_scale.

Method Details

MultiquadricKernel.__init__(*, length_scale=None)#
Parameters:

length_scale (float | None)

Return type:

None

MultiquadricKernel.evaluate(r)[source]#

Evaluate the multiquadric kernel sqrt(r**2 + length_scale**2).

Parameters:

r (ndarray)

Return type:

ndarray

MultiquadricKernel.pairwise(x1, x2)#

Evaluate the kernel between every row of x1 and x2.

Parameters:

  • x1 (ndarray)

  • x2 (ndarray)

Return type:

ndarray

MultiquadricKernel.resolve(train_x)[source]#

Resolve length_scale from training data if unset.

Parameters:

train_x (ndarray)

Return type:

Self

MultiquadricKernel.validate()[source]#

Validate length_scale.

Return type:

None