covmats.CovarianceMatrix

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

Abstract representation of a covariance matrix.

Calculations involving covariance matrices (e.g. data whitening, multivariate normal function evaluation) are often performed more efficiently using a decomposition of the covariance matrix instead of the covariance matrix itself. This class allows the user to construct an object representing a covariance matrix using any of several decompositions and perform calculations using a common interface.

Note

The CovarianceMatrix class cannot be instantiated directly. Instead, use one of the derived class:

• CovViaDiagonal

• CovViaCholesky

• CovViaSparseCholesky

• CovViaPrecisionCholesky

• CovViaSparsePrecisionCholesky

• CovViaEigenFactorization

• CovViaEnsemble

Notes

None of the Covariance child implementation supports singular or indefinite covariance matrices. Otherwise, they would not be invertible, colorizing and whitening would not well defined.

__init__() → None

Initialize the instance.

Properties

H	Hermitian adjoint.
T	Transpose this linear operator.
covariance	Explicit dense representation of the covariance matrix.
log_pdet	Log of the pseudo-determinant of the covariance matrix.
n_pts	Number of points in the domain (n).
ndim
precision	Explicit dense representation of the precision matrix with shape (n, n).
rank	Rank of the covariance matrix.
shape	Shape of the covariance matrix (n, n).
subspace_size	Subspace size of the covariance matrix.

Methods

adjoint	Hermitian adjoint.
colorize	Perform a colorizing transformation on data.
dot	Matrix-matrix or matrix-vector multiplication.
from_cholesky	Representation of a covariance provided via choleksy factorization.
from_diagonal	Representation of a covariance provided via diagonal.
from_eigendecomposition	Representation of a covariance provided via eigendecomposition.
from_precision	Return a representation of a covariance from its precision matrix.
get_diagonal	Return the diagonal entries of the matrix (variances) as a vector (n,).
get_trace	Return the trace of the covariance matrix (sum of diagonal elements).
matmat	Matrix-matrix multiplication.
matvec	Matrix-vector multiplication.
rmatmat	Adjoint matrix-matrix multiplication.
rmatvec	Adjoint matrix-vector multiplication.
sample_mvnormal	Draw samples from the multivariate normal N(0, A).
solve	Solve Ax = b, with A, the current covariance matrix instance.
todense	Explicit dense representation of the covariance matrix with shape (n, n).
transpose	Transpose this linear operator.
whiten	Perform a whitening transformation on data.