spam (version 0.15-5)

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(0, nrow(Sigma)), Sigma,...) 
rmvnorm.prec(n,mu=rep(0, nrow(Q)), Q, ...) 
rmvnorm.canonical(n, b, Q, ...)

Arguments

n

number of observations.

mu

mean vector.

Sigma

covariance matrix of class spam.

Q

precision matrix.

b

vector determining the mean.

...

arguments passed to chol.

References

See references in chol.

See Also

chol and ordering.

Examples

# Generate multivariate form 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="HS")

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



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