covmats.CovKernelAsLinopViaFFT

class covmats.CovKernelAsLinopViaFFT(*args, **kwargs)

Represents a fast fourier transform covariance matrix.

FFT based operations if kernel is stationary or translation invariant and points are on a regular grid.

Notes

This FFT-based code is a reimplementation of Arvind Saibaba’s work (https://github.com/arvindks/kle).

TODO: add references.

__init__(kernel, mesh_dim: float | ndarray[tuple[Any, ...], dtype[float64]] | Sequence[float], domain_shape: int | ndarray[tuple[Any, ...], dtype[int64]] | Sequence[int], len_scale: ndarray[tuple[Any, ...], dtype[float64]], nugget: float = 0.0, k: int = 100, is_use_preconditioner: bool = False) → None

Initialize the instance.

Parameters:

• kernel (_type_) – _description_

• mesh_dim (Union[NDArrayInt, Tuple[float, float]]) – _description_

• domain_shape (Union[NDArrayInt, Tuple[int, int]]) – _description_

• len_scale (NDArrayFloat) – _description_

• nugget (float, optional) – _description_, by default 0.0

• k (int, optional) – Number of local centers in the preconditioner. Controls the sparity of the preconditioner. It should be inferior to the number of points. By default 100.

• is_use_preconditioner (bool) – Whether to build the preconditioner at instance creation and use it to solve Ax = b systems. The default is False.

Properties

H	Hermitian adjoint.
T	Transpose this linear operator.
count
n_pts	Return the number of points covered.
ndim
solvematvecs

Methods

adjoint	Hermitian adjoint.
dot	Matrix-matrix or matrix-vector multiplication.
get_diagonal	Return the diagonal entries of the matrix (variances).
itercount	Return the number of counts.
matmat	Matrix-matrix multiplication.
matvec	Matrix-vector multiplication.
reset_comptors	Set the comptors to zero.
rmatmat	Adjoint matrix-matrix multiplication.
rmatvec	Adjoint matrix-vector multiplication.
solve	Solve Ax = b, with A, the current covariance matrix instance.
todense	Explicit dense representation of the covariance matrix.
transpose	Transpose this linear operator.