"isomLR" <- function(x){ x.ilr=matrix(NA,nrow=nrow(x),ncol=ncol(x)-1) D=ncol(x) for (i in 1:ncol(x.ilr)){ x.ilr[,i]=sqrt((D-i)/(D-i+1))*log(((apply(as.matrix(x[,(i+1):D,drop=FALSE]),1,prod))^(1/(D-i)))/(x[,i])) } return(x.ilr) }