fmesher (version 0.3.0)

fm_qinv: Sparse partial inverse

Description

Compute sparse partial matrix inverse. As of 0.2.0.9010, an R implementation of the Takahashi recursion method, unless a special build of the fmesher package is used.

Usage

fm_qinv(A)

Value

A sparse symmetric matrix, with the elements of the inverse of A

for the non-zero pattern of A plus potential Cholesky in-fill locations.

Arguments

A

A sparse symmetric positive definite matrix

Examples

A <- Matrix::Matrix(
  c(2, -1, 0, 0, -1, 2, -1, 0, 0, -1, 2, -1, 0, 0, -1, 2),
  4,
  4
)
# Partial inverse:
(S <- fm_qinv(A))
# Full inverse (not guaranteed to be symmetric):
(S2 <- solve(A))
# Matrix symmetry:
c(sum((S - Matrix::t(S))^2), sum((S2 - Matrix::t(S2))^2))
# Accuracy (not that S2 is non-symmetric, and S may be more accurate):
sum((S - S2)[S != 0]^2)