R: Solve the equation Qx = y

cholsolve {sparseinv} | R Documentation

## Solve the equation Qx = y

### Description

This function is similar to `solve(Q,y)` but with the added benefit that it allows for permuted matrices. This function does the job in order to minimise user error when attempting to re-permute the matrices prior or after solving. The user also has an option for the permuted Cholesky factorisation of Q to be carried out internally.

### Usage

    cholsolve(Q = NULL, y = NULL, perm = FALSE, cholQ = NULL,
      cholQp = 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
`y` | matrix with the same number of rows as Q
`perm` | if FLASE no permutation is carried out, if TRUE permuted Cholesky factors are used
`cholQ` | the lower Cholesky factor of Q (if known already)
`cholQp` | the lower Cholesky factor of a permuted Q (if known already)
`P` | the permutation matrix (if known already)

### Value

x solution to Qx = y

### 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))
    y = matrix(c(1, 2), 2, 1)
    cholsolve(Q, y)

[Package sparseinv version 0.1.3 Index]