Eigen

gpjax.kernels.computations.eigen

Kernel = tp.TypeVar('Kernel', bound='gpjax.kernels.base.AbstractKernel') module-attribute

EigenKernelComputation dataclass

Bases: AbstractKernelComputation

Eigen kernel computation class. Kernels who operate on an eigen-decomposed structure should use this computation object.

gram(kernel: Kernel, x: Num[Array, 'N D']) -> LinearOperator

Compute Gram covariance operator of the kernel function.

Parameters:

Name	Type	Description	Default
kernel	AbstractKernel	the kernel function.	required
x	Num[Array, 'N N']	The inputs to the kernel function.	required

Returns

LinearOperator: Gram covariance operator of the kernel function.

diagonal(kernel: Kernel, inputs: Num[Array, 'N D']) -> Diagonal

For a given kernel, compute the elementwise diagonal of the NxN gram matrix on an input matrix of shape NxD.

Parameters:

Name	Type	Description	Default
kernel	AbstractKernel	the kernel function.	required
inputs	Float[Array, 'N D']	The input matrix.	required

Returns

Diagonal: The computed diagonal variance entries.

cross_covariance(kernel: Kernel, x: Num[Array, 'N D'], y: Num[Array, 'M D']) -> Float[Array, 'N M']

Compute the cross-covariance matrix.

For an $N\times D$ and $M\times D$ pair of matrices, evaluate the $N \times M$ cross-covariance matrix.

Parameters:

Name	Type	Description	Default
kernel	Kernel	the kernel function.	required
x	Num[Array, 'N D']	The input matrix.	required
y	Num[Array, 'M D']	The input matrix.	required

Returns:

Name	Type	Description
_type_	Float[Array, 'N M']	description