rmvnorm: Draw Multivariate Normals

Description

Fast ways to draw multivariate normals when the variance or precision matrix is sparse.

Usage

rmvnorm.spam(n,mu=rep.int(0, dim(Sigma)[1]), Sigma, Rstruct=NULL, ...)
rmvnorm.prec(n,mu=rep.int(0, dim(Q)[1]), Q, Rstruct=NULL, ...)
rmvnorm.canonical(n, b, Q, Rstruct=NULL, ...)

Arguments

number of observations.

mean vector.

Sigma

covariance matrix of class spam.

precision matrix.

vector determining the mean.

Rstruct

the Cholesky structure of Sigma or Q.

…

arguments passed to chol.

Details

The functions rmvnorm.prec and rmvnorm.canonical do not require sparse precision matrices. For rmvnorm.spam, the differences between regular and sparse covariance matrices are too significant to be implemented here. Often (e.g., in a Gibbs sampler setting), the sparsity structure of the covariance/precision does not change. In such setting, the Cholesky factor can be passed via Rstruct in which only updates are performed (i.e., update.spam.chol.NgPeyton instead of a full chol).

References

See references in chol.

Examples

Run this code

# NOT RUN {
# Generate multivariate from a covariance inverse:
# (usefull for GRMF)
set.seed(13)
n <- 25    # dimension
N <- 1000  # sample size
Sigmainv <- .25^abs(outer(1:n,1:n,"-"))
Sigmainv <- as.spam( Sigmainv, eps=1e-4)


Sigma <- solve( Sigmainv)  # for verification
iidsample <- array(rnorm(N*n),c(n,N))

mvsample <- backsolve( chol(Sigmainv), iidsample)
norm( var(t(mvsample)) - Sigma, type="m")

# compare with:
mvsample <- backsolve( chol(as.matrix( Sigmainv)), iidsample, n)
   #### ,n as patch
norm( var(t(mvsample)) - Sigma, type="m")



# 'solve' step by step:
b <- rnorm( n)
R <- chol(Sigmainv)
norm( backsolve( R, forwardsolve( R, b))-
      solve( Sigmainv, b) )
norm( backsolve( R, forwardsolve( R, diag(n)))- Sigma )


# }