iso_new <- function(x){ # PF, 05.04.2007 # isometric transformation # INPUT: # x ... compositional data # OUTPUT # x.iso ... 2 columns matrix # isometric transformation according to paper: x.iso=matrix(NA,nrow=nrow(x),ncol=ncol(x)-1) for (l in 1:nrow(x.iso)){ for (i in 1:ncol(x.iso)){ x.iso[l,i]=sqrt((i)/(i+1))*log(((prod(x[l,1:i]))^(1/i))/(x[l,i+1])) } } return(x.iso) }