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+# $Id: ilr.R 120 2011-09-02 14:25:35Z jranke $
+
+# Copyright (C) 2012 René Lehmann, Johannes Ranke
+# Contact: jranke@uni-bremen.de
+
+# This file is part of the R package mkin
+
+# mkin is free software: you can redistribute it and/or modify it under the
+# terms of the GNU General Public License as published by the Free Software
+# Foundation, either version 3 of the License, or (at your option) any later
+# version.
+
+# This program is distributed in the hope that it will be useful, but WITHOUT
+# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+# FOR A PARTICULAR PURPOSE.  See the GNU General Public License for more
+# details.
+
+# You should have received a copy of the GNU General Public License along with
+# this program. If not, see <http://www.gnu.org/licenses/>
+
+ilr <- function(x) {
+  z <- vector()
+  for (i in 1:(length(x) - 1)) {
+    z[i] <- sqrt(i/(i+1)) * log((prod(x[1:i]))^(1/i) / x[i+1])
+  }
+  return(z)
+}
+
+invilr<-function(x) {
+  D <- length(x) + 1
+  z <- c(x, 0)
+  y <- rep(0, D)
+  s <- sqrt(1:D*2:(D+1))
+  q <- z/s
+  y[1] <- sum(q[1:D])
+  for (i in 2:D) {
+    y[i] <- sum(q[i:D]) - sqrt((i-1)/i) * z[i-1]
+  }
+  z <- vector()
+  for (i in 1:D) {
+    z[i] <- exp(y[i])/sum(exp(y))
+  }
+  return(z)
+}