SelectedInversion.jl

About

Sparse factorizations let us solve linear systems involving the inverse efficiently, but some applications need a bunch of entries of the inverse itself. Selected inversion computes exactly those entries that correspond to nonzeros in the factorization.

The package interfaces directly with CHOLMOD-based Cholesky factorizations, and supports LDLFactorizations.jl through a package extension. The algorithms are based on SelInv, and the simplicial formulation is equivalent to the Takahashi recursions.

Installation

SelectedInversion.jl is a registered Julia package:

] add SelectedInversion

Usage

using SelectedInversion

A = ... # some sparse matrix
Z, p = selinv(A) # selected inverse and corresponding permutation vector

The nonzero entries of Z match the corresponding entries in inv(A[p, p]).