Constant Diagonal

gpjax.kernels.computations.constant_diagonal

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

ConstantDiagonalKernelComputation dataclass

Bases: AbstractKernelComputation

__init__() -> None

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

Compute the Gram matrix.

Compute Gram covariance operator of the kernel function.

Parameters:

Name	Type	Description	Default
kernel	Kernel	the kernel function.	required
x	Float[Array, 'N D']	The inputs to the kernel function.	required

Returns

LinearOperator: Gram covariance operator of the kernel function.

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

Compute the diagonal Gram matrix's entries.

For a given kernel, compute the elementwise diagonal of the NxN gram matrix on an input matrix of shape $N\times D$.

Parameters:

Name	Type	Description	Default
kernel	Kernel	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: Float[Array, 'N D'], y: Float[Array, 'M D']) -> Float[Array, 'N M']

Compute the cross-covariance matrix.

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

Parameters:

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

Returns

Float[Array, "N M"]: The computed square Gram matrix.