CARrampsOcl (version 0.1.4)

eigenRW1: Function to compute eigenvalues and eigenvectors of RW1 structure matrix.

Description

Function to compute eigenvalues and eigenvectors of RW1 structure matrix.

Usage

eigenRW1(n)

Arguments

n

dimension of structure matrix

Value

values

eigenvalues

vectors

eigenvectors

References

Kunsch, H.R. (1994), "Robust priors for smoothing andimage restoriation," Annals of the Institute of Statistical Mathematics, 55, no. 1, 1-19.

Examples

## The function is currently defined as
function(n)
{
# compute eigenvals and eigenvects of RW1

w <-( pi/n) * ((n-1):0)
evals <-  2 * (1-cos(w) )

evects <- sin( outer( 1:n, w ) ) - sin( outer( (0:(n-1)), w))
evects[,n] <- rep(1,n)

evects <- apply( evects, 2, function(v) v / sqrt( sum(v^2) ) )

list( values = evals, vectors = evects)

}