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

In inbo/INLA: Full Bayesian Analysis of Latent Gaussian Models using Integrated Nested Laplace Approximations

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())
 

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.

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 [e-mail]

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 = INLA:::inla.tempfile()
 write(t(cbind(Q@i+1L,  Q@j+1L,  Q@x)), ncol=3, file=filename)
 Qinv = inla.qinv(filename)
 unlink(filename)
 

inbo/INLA documentation built on Dec. 6, 2019, 9:51 a.m.