Add the CeCILL licence version 2.1 in french and english

R/multivariate.R

+#'
+#' @import MASS
+#'
+NULL
+
+library(MASS)
+
+#' Project a distance matrix in a euclidean space (NMDS).
+#'
+#' @author Eric Coissac
+#' @author Christelle Gonindard-Melodelima
+#' @export
+nmds = function(distances,
+                maxit = 50, trace = TRUE,
+                tol = 0.001, p = 2) {
+  if (inherits(distances,"matrix"))
+    distances=as.dist(distances)
+
+  stopifnot(inherits(distances,"dist"))
+
+  k = attr(distances,"Size") - 1
+
+  n = isoMDS(distances,
+             k=k,
+             maxit = maxit,
+             trace = trace,
+             tol = tol,
+             p=p)
+
+  p = n$points
+  attr(p,"stress") = n$stress
+  attr(x,"method")="nmds"
+
+  return(p)
+}
+
+#' Project a distance matrix in a euclidean space (PCOA).
+#'
+#' @author Eric Coissac
+#' @author Christelle Gonindard-Melodelima
+#' @export
+pcoa = function(distances) {
+  if (inherits(distances,"matrix"))
+    distances=as.dist(distances)
+
+  stopifnot(inherits(distances,"dist"))
+
+  k = attr(distances,"Size") - 1
+  x = cmdscale(distances,k=k)
+  attr(x,"method")="pcoa"
+
+  return()
+}
+
+#' Project a set of points in a euclidean space (PCA).
+#'
+#' @author Eric Coissac
+#' @author Christelle Gonindard-Melodelima
+#' @export
+pca = function(data,scale=FALSE) {
+  k = min(nrow(data)-1,ncol(data))
+  p = prcomp(data,
+             retx = TRUE,
+             center = TRUE,
+             scale. = scale,
+             tol=0)
+
+  x = p$x
+  attr(x,"method")="pca"
+
+  return(x)
+}
+
+#' Double centering of a matrix.
+#'
+#' colSums and rowSums of the returned matrix are all equal to zero.
+#'
+#' Inspired from the algorithm described in stackoverflow
+#' \url{https://stackoverflow.com/questions/43639063/double-centering-in-r}
+#'
+#' @export
+bicentered = function(m) {
+
+  # compute the row-wise and column-wise mean matrices
+  R = m*0 + rowMeans(m)
+  C = t(m*0 + colMeans(m))
+
+  # substract them and add the grand mean
+  return(m - R - C + mean(m[]))
+}
+
+#' Test if the distance matrix is euclidean.
+#'
+#' Actually a simplified version of the ADE4 implementation
+#' (\code{\link[ade4]{is.euclid}}).
+#'
+#' @author Eric Coissac
+#' @author Christelle Gonindard-Melodelima
+#' @export
+is.euclid = function (distances, tol = 1e-07)
+{
+  if (!inherits(distances, "dist"))
+    stop("Object of class 'dist' expected")
+
+  if (any(distances < tol))
+    warning("Zero distance(s)")
+
+  distances <- as.matrix(distances)
+  n <- ncol(distances)
+  delta <- -0.5 * ProcMod::bicenter(distances * distances)
+  lambda <- eigen(delta, symmetric = TRUE, only.values = TRUE)$values
+  w0 <- lambda[n]/lambda[1]
+  return((w0 > -tol))
+}
+
+#' Project a distance matrix in a euclidean space.
+#'
+#' Project a set of points defined by a distance matrix in
+#' an eucleadean space. If the used distance is a metric,
+#' this is done using the \code{\link[ProcMod]{pcoa}} function,
+#' otherwise the \code{\link[ProcMod]{nmds}} is used.
+#'
+#' @author Eric Coissac
+#' @author Christelle Gonindard-Melodelima
+#' @export
+dist2orthospace = function(distances, tol = 1e-07) {
+  if (inherits(distances,"matrix"))
+    distances=as.dist(distances)
+
+  if (ProcMod::is.euclid(distances,tol = tol))
+    return(ProcMod::pcoa(distances))
+  else
+    return(ProcMod::nmds(distances))
+}