`ilr` <-
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]))
} 
invisible(x.ilr)
}