Base

gpjax.kernels.computations.base

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

AbstractKernelComputation dataclass

Abstract class for kernel computations.

__init__() -> None

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.

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

For a given kernel, compute the NxM gram matrix on an a pair of input matrices with shape NxD and MxD.

Parameters:

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

Returns

Float[Array, "N M"]: The computed cross-covariance.

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.