AbstractCovarianceKernel

class pmrf.stats.AbstractCovarianceKernel(*, name: str | None = None, metadata: Any = None)

Bases: Module

Abstract base class for covariance kernel functions.

These kernels are used in a Gaussian Process for discrepancy modeling.

__add__(other: AbstractCovarianceKernel) → AbstractCovarianceKernel

abstractmethod __call__(x1: Array, x2: Array, key=None) → Array

Evaluate the kernel between two points.

Parameters:

• x1 (jnp.ndarray) – First input point.

• x2 (jnp.ndarray) – Second input point.

• key (jax.random.PRNGKey, optional) – Random key for stochastic kernels.

Returns:

Kernel covariance scalar.

Return type:

jnp.ndarray

__mul__(other: AbstractCovarianceKernel | TypeAliasForwardRef('Param') | float) → AbstractCovarianceKernel

gram(x: Array, *, jitter: float = 0.0) → Array

Build the Gram (covariance) matrix of this kernel evaluated at x.

Equivalent to pmrf.stats.covariance_kernels.gram(self, x, jitter=jitter).

Parameters:

• x (jnp.ndarray) – The input points, of shape (N,) or (N, d).

• jitter (float, default=0.0) – A small scalar added to the diagonal for numerical stability.

Returns:

The Gram matrix, of shape (*batch_shape, N, N).

Return type:

jnp.ndarray