Takahashi_Davis: Compute the Takahashi equations

In andrewzm/linalg: Linalg functions

Description

This function is wrapper for the Takahashi equations required to compute the marginal variances from the Cholesky factor of a precision matrix. The equations themselves are implemented in C using the SparseSuite package of Timothy Davis.

Usage

Takahashi_Davis(Q, return_perm_chol = 0, cholQp = matrix(0, 0, 0), P = 0)

Arguments

Q	precision matrix (sparse or dense)
return_perm_chol	if 1 returns the permuted Cholesky factor (not advisable for large systems)
cholQp	the permuted Cholesky factor of Q (if known already)
P	the pivot matrix (if known already)

Value

if return_perm_chol == 0, returns the partial matrix inverse of Q, where the non-zero elements correspond to those in the Cholesky factor. If !(return_perm_chol == 0), returns a list with three elements, S (the partial matrix inverse), Lp (the Cholesky factor of the permuted matrix) and P (the permutation matrix)

References

Yogin E. Campbell and Timothy A Davis (1995). Computing the sparse inverse subset: an inverse multifrontal approach. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.37.9276&rep=rep1&type=pdf

Examples

require(Matrix)
Q = sparseMatrix(i=c(1,1,2,2),j=c(1,2,1,2),x=c(0.1,0.2,0.2,1))
X <- cholPermute(Q)
S_partial = Takahashi_Davis(Q,cholQp = X$Qpermchol,P=X$P)

andrewzm/linalg documentation built on May 10, 2019, 11:15 a.m.