API Reference

Covariance matrix representations and priors for large scale inverse problems.

Abstract Covariance class

The common interface CovarianceMatrix can be seen as a extension of the class scipy.stats.Covariance as it inherits from it (thus making it compatible with all scipy.stats functions and classes) and dope it with LinearOperator capabilities.

CovarianceMatrix(*args, **kwargs)

Abstract representation of a covariance matrix.

Full-rank covariance matrix decomposition

Several full-rank representation of covariance matrices.

CovViaDiagonal(*args, **kwargs)	Representation of a covariance matrix via its diagonal.
CovViaCholesky(*args, **kwargs)	Representation of a covariance via a Cholesky factorization.
CovViaSparseCholesky(*args, **kwargs)	Representation of a covariance via a sparse Cholesky factorization.
CovViaPrecisionCholesky(*args, **kwargs)	Representation of a covariance via the Cholesky factorization of its inverse (aka the precision matrix).
CovViaSparsePrecisionCholesky(*args, **kwargs)	Representation of a covariance via the sparse Cholesky factorization of its sparse inverse (aka the precision matrix).

Low-rank approximations

Several low-rank (approximate) representation of covariance matrices.

CovViaEigenFactorization(*args, **kwargs)	Representation of a covariance provided via eigenfactorization
CovViaEnsemble(*args, **kwargs)	Represents a covariance matrix as an ensemble of realizations.

Kernel based approximations

Low-rank approximations from a given Kernel. Only provides the linear operations capabilities (no sampling not statistical calculations).

CovKernelAsLinop(*args, **kwargs)	Abstract class providing linear operator capability from a kernel definition.
CovKernelAsLinopViaFFT(*args, **kwargs)	Represents a fast fourier transform covariance matrix.

Matrix compression

Allow to factorize CovarianceMatrix and CovKernelAsLinop using Eigen low-rank approximation.

get_linop_eigen_factorization(linop, size, n_pc)	Compute Eigenmodes of the covariance.
eigen_factorize_cov_mat(cov_mat, n_pc[, ...])	Return an eigen factorized covariance matrix from the input covariance matrix.

Sparse Helpers

Helper to work with sparse matrices and covariances.

SparseCholeskyFactor(*args, **kwargs)

Sparse Cholesky factor of a matrix \(\mathbf{A}\).

Working with priors and trends

To represent trend through drift matrix. To use along with geostatistical regularizator.

PriorTerm()	Represent a prior term for the geostatistical regularization.
NullPriorTerm()	Represent a null prior term.
ConstantPriorTerm(prior_values)	Represent a prior (no influence of beta).
MeanPriorTerm()	Represent a mean prior.
EnsembleMeanPriorTerm(shape)	Represent a mean prior.
DriftMatrix(mat[, beta])	Represent a drift matrix prior term.
ConstantDriftMatrix(n_pts)	Represent a constant drift matrix (trend).
LinearDriftMatrix(pts)	Represent a linear drift matrix (trend).

Other utility functions

To work with covariance matrices and low rank approximations.

get_explained_var(eigval[, cov_mat, ...])

Return the variance explained by each eigen value.

Test data

Functions providing test data.

load_precision_example_4225x()
load_precision_example_4225x_SCF()
get_SPD_sparse_n11_example(seed)	Create a symmetric positive definite matrix of shape(11, 11).
get_SPD_sparse_example(n, seed[, diag_mean])	Create a symmetric positive definite matrix.