R: Solve the equation X = AQ^-1t(A) under permutations

cholsolveAQinvAT {sparseinv} | R Documentation

## Solve the equation X = AQ^-1t(A) under permutations

### Description

This function is a wrapper of `solve()` for finding `X = AQ^{-1}t(A)` when the permuted Cholesky factor of Q is known. #'

### Usage

    cholsolveAQinvAT(Q = NULL, A = NULL, Lp = NULL, P = NULL)

### Arguments

`Q` | matrix (if of class `Matrix` needs to be column-compressed, i.e., `dgCMatrix` or `dsCMatrix`)), the Cholesky factor of which needs to be found
`A` | sparse or dense matrix
`Lp` | the lower Cholesky factor of a permuted Q
`P` | the permutation matrix

### Value

x solution to `X = AQ^{-1}t(A)`

### References

Havard Rue and Leonhard Held (2005). Gaussian Markov Random Fields: Theory and Applications. Chapman & Hall/CRC Press

### 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)
    y <- matrix(c(1,2), 2, 1)
    A <- y %*% t(y)
    cholsolveAQinvAT(Q,A,X$Qpermchol,X$P)

[Package sparseinv version 0.1.3 Index]