Dense

gpjax.kernels.computations.dense

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

DenseKernelComputation

Bases: AbstractKernelComputation

Dense kernel computation class. Operations with the kernel assume a dense gram matrix structure.

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: 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 cross-covariance.