covmats.SparseCholeskyFactor

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

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

Factorization

It relies on the \(\mathbf{LDL}^{\mathrm{T}} =\) \(\mathbf{PAP}^{\mathrm{T}}\) factorization where

• \(\mathbf{L}\) is the sparse lower triangle with unit diagonal.

• \(\mathbf{D}\) is the sparse diagonal matrix with diagonal entries.

• \(\mathbf{P}\) is the rows permutation vector.

Note

Since this code is released under BSD 3-Clause License, it is not possible to include sparse factors provided by scikit-sparse, as it depends on external libraries with GPL licenses, such as SuiteSparse. The main goal of this implementation is therefore to mimic useful features while preserving the BSD 3-Clause License compatibility.

Examples

>>> from your_module import SparseCholeskyFactor
>>> L, D, P = ...  # sparse matrices
>>> factor = SparseCholeskyFactor(L, D, P)
>>> factor.matvec(x)
array([...])

__init__(L: sparray, D: sparray, P: _Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | complex | bytes | str | _NestedSequence[complex | bytes | str]) → None

Initialize the instance.

Parameters:

• L (sp.sparse.sparray) – Sparse lower triangle \(\mathbf{L}\) of the factorization.

• D (sp.sparse.sparray) – Sparse diagonal matrix \(\mathbf{{D}}\) of the factorization.

• P (ArrayLike) – 1D vector \(\mathbf{{P}}\) storing rows permutations of the factorization.

Raises:

ValueError – If the dimensions of L, D and P do not match.

Properties

D	Sparse diagonal matrix \(\mathbf{D}\) of the factorization.
H	Hermitian adjoint.
L	Sparse lower triangle \(\mathbf{L}\) with unit diagonal of the factorization.
P	1D vector \(\mathbf{P}\) storing rows permutations of the factorization.
Pt	1D vector \(\mathbf{P}\) storing rows back-permutations of the factorization.
T	Transpose this linear operator.
invD	Inverse of \(\mathbf{D}\) in the factorization.
log_pdet	Log of the pseudo-determinant of the covariance matrix.
mat	Return \(\mathbf{A}\) as a dense array.
n_pts	Number of points in the domain (n).
ndim
shape	Shape of the square matrix (n, n).
sqrtD	Squared root of \(\mathbf{D}\) in the factorization.
sqrtinvD	Squared root inverse of \(\mathbf{D}\) in the factorization.

Methods

adjoint	Hermitian adjoint.
apply_P	Apply the permutation of rows.
apply_Pt	Apply the reverse permutation of rows.
colorize	Perform a colorizing transformation on data.
colorize_inv	Perform a colorizing transformation on data as in SparseCholeskyFactor:colorize() but for the inverse \(\mathbf{A}^{-1}\).
dot	Matrix-matrix or matrix-vector multiplication.
get_diagonal	Return the diagonal entries of the matrix \(\mathbf{A}\).
get_invdiagonal	Return the diagonal entries of the inverse matrix \(\mathbf{A}^{-1}\).
inv	Return the inverse \(\mathbf{A}^{-1}\) as a dense array.
matmat	Matrix-matrix multiplication.
matvec	Matrix-vector multiplication.
rmatmat	Adjoint matrix-matrix multiplication.
rmatvec	Adjoint matrix-vector multiplication.
solve	Return \(\mathbf{x} = \mathbf{A}^{-1} \mathbf{b}.\)
todense	Return \(\mathbf{A}\) as a dense array.
transpose	Transpose this linear operator.
whiten	Perform a whitening transformation on data.
whiten_inv	Perform a whitening transformation on data as in SparseCholeskyFactor:whiten() but for the inverse \(\mathbf{A}^{-1}\).