qinv {INLA}R Documentation

Computes (parts of) the inverse of a SPD sparse matrix

Description

This routine use the GMRFLib implementation which compute parts of the inverse of a SPD sparse matrix. The diagonal and values for the neighbours in the inverse, are provided.

Usage

inla.qinv(Q, constr, reordering = INLA::inla.reorderings(), num.threads = NULL)

Arguments

Q

A SPD matrix, either as a (dense) matrix or sparseMatrix.

constr

Optional linear constraints; see ?INLA::f and argument extraconstr

reordering

The type of reordering algorithm to be used for TAUCS; either one of the names listed in inla.reorderings() or the output from inla.qreordering(Q). The default is "auto" which try several reordering algorithm and use the best one for this particular matrix.

num.threads

Maximum number of threads the inla-program will use, or as 'A:B' defining the number threads in the outer (A) and inner (B) layer for nested parallelism.

Value

inla.qinv returns a sparseMatrix of type dgTMatrix with the diagonal and values for the neigbours in the inverse. Note that the full inverse is NOT provided!

Author(s)

Havard Rue hrue@r-inla.org

Examples



 ## dense matrix example
 n = 10
 A = matrix(runif(n^2), n, n)
 Q = A %*% t(A)
 print(mean(abs(inla.qinv(Q) - solve(Q))))

 ## sparse matrix example
 rho = 0.9
 Q = toeplitz(c(1+rho^2, -rho,  rep(0, n-3), -rho)) / (1-rho^2)
 Q = inla.as.dgTMatrix(Q)
 Q.inv = inla.qinv(Q)

 ## compute the marginal variances as a vector from a precision matrix
 marginal.variances = diag(inla.qinv(Q))

 ## read the sparse matrix from a file in the 'i, j, value' format
 filename = tempfile()
 write(t(cbind(Q@i+1L,  Q@j+1L,  Q@x)), ncol=3, file=filename)
 Qinv = inla.qinv(filename)
 unlink(filename)
[Package INLA version 25.10.19 Index]