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zeta2.coef<-function(mat,H,r,indices,tolval=10*.Machine$double.eps,tolsym=1000*.Machine$double.eps)
{
# Function zeta_2.coef
# Computes the zeta^2 index of "effect magnitude".
# This criterion is equivalent to the maximization of Hotteling-Lawley trace statistic.
# Expected input: a variance-covariance (or correlation) matrix,
# Effect descrption matrix (H) and its rank (r)
# error checking
# mat and indices
if (sum(!(as.integer(indices) == indices)) > 0) stop("\n The variable indices must be integers")
p <- dim(mat)[2]
validmat(mat,p,tolval,tolsym,allowsingular=TRUE,algorithm="none")
# checks on r and H
validnovcrit(mat,criterion="ZETA_2",H,r,p,tolval,tolsym)
# Computing the criterion value
tr<-function(mat){sum(diag(mat))}
zeta2.1d<-function(mat,H,r,indices){
l <- min(r,length(indices))
V <-tr(solve(mat[indices,indices]-H[indices,indices],H[indices,indices]))
V/(V+l)
}
dimension<-length(dim(indices))
if (dimension > 1){
zeta2.2d<-function(mat,H,r,subsets){
apply(subsets,1,function(indices){
zeta2.1d(mat,H,r,indices)})
}
if (dimension > 2) {
zeta2.3d<-function(mat,H,r,array3d){
apply(array3d,3,function(subsets){zeta2.2d(mat,H,r,subsets)})
}
output<-zeta2.3d(mat,H=H,r,indices)
}
if (dimension == 2) {output<-zeta2.2d(mat=mat,H,r,indices)}
}
if (dimension < 2) {output<-zeta2.1d(mat,H,r,indices)}
output
}
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