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+#' Transform formation fractions as in the first published mkin version
+#'
+#' The transformed fractions can be restricted between 0 and 1 in model
+#' optimisations. Therefore this transformation was used originally in mkin. It
+#' was later replaced by the [ilr] transformation because the ilr transformed
+#' fractions can assumed to follow normal distribution. As the ilr
+#' transformation is not available in [RxODE] and can therefore not be used in
+#' the nlmixr modelling language, this transformation is currently used for
+#' translating mkin models with formation fractions to more than one target
+#' compartment for fitting with nlmixr in [nlmixr_model]. However,
+#' this implementation cannot be used there, as it is not accessible
+#' from RxODE.
+#'
+#' @param ff Vector of untransformed formation fractions. The sum
+#'   must be smaller or equal to one
+#' @param ff_trans Vector of transformed formation fractions that can be
+#'   restricted to the interval from 0 to 1
+#' @return A vector of the transformed formation fractions
+#' @export
+#' @examples
+#' ff_example <- c(
+#'   0.10983681, 0.09035905, 0.08399383
+#' )
+#' ff_example_trans <- tffm0(ff_example)
+#' invtffm0(ff_example_trans)
+tffm0 <- function(ff) {
+  n <- length(ff)
+  res <- numeric(n)
+  f_remaining <- 1
+  for (i in 1:n) {
+    res[i] <- ff[i]/f_remaining
+    f_remaining <- f_remaining - ff[i]
+  }
+  return(res)
+}
+#' @rdname tffm0
+#' @export
+#' @return A vector of backtransformed formation fractions for natural use in degradation models
+invtffm0 <- function(ff_trans) {
+  n <- length(ff_trans)
+  res <- numeric(n)
+  f_remaining <- 1
+  for (i in 1:n) {
+    res[i] <- ff_trans[i] * f_remaining
+    f_remaining <- f_remaining - res[i]
+  }
+  return(res)
+}