##  Copyright (C) 2007 Andrés Baselga   <baselga@mncn.csic.es>
##                     Gilles Niccolini <nicolin@unice.fr>
##
##  This program 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 2 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, write to the Free Software
##  Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
minbibj<-function(matrix) {
  ## nr is the number of rows
  nr<-dim(matrix)[1];
  ## This variable contains the sum of 'min(bi,bj)' on row pairs.
  sumbibj<-0.;
  ## We 'loop' on every different row pairs.
  for(i in 1:nr-1) {
    for(j in (i+1):nr) {
      ## 'bi' and 'bj' are respectively the number of species appearing
      ## only in the ith and the jth site (row).
      bi<-sum(matrix[i,]&(!matrix[j,]));
      bj<-sum(matrix[j,]&(!matrix[i,]));
      ## We sum up 'min(bi,bj)' on every different pair of rows.
      sumbibj<-sumbibj+min(bi,bj);
    }
  }
  ## We return the sum
  sumbibj;
}
zeroColumn<-function(matrix) {
  sum<-0;
  nc<-dim(matrix)[2];
  for(i in 1:nc) if(!sum(matrix[,i])) sum<-sum+1;
  if(sum!=0)
    warning(sum," missing species. This fact does not affect the result since total number of species is calculated excluding these columns.",call.=FALSE,immediate.=TRUE);
  sum
}
Simpson.multi<-function(x) {
  ## x must be a data frame
  matrix<-as.matrix(x);
  ## Si is the number of species present in the ith site. We sum all
  ## these values.
  sumSi<-sum(matrix);
  ## St is the total number of species in all sites, thus the number of columns, excepting if a given
  ## species is not present at all (in any site), so we must not count this column
  ## out.
  St<-ncol(matrix)-zeroColumn(matrix);
  ## 'a' is the number of species shared for at least two sites
  a<-sumSi-St;
  index<-a/(minbibj(matrix)+a);
  if(any(matrix>1))
    warning("The table contains values >1: the result may be meaningless.",call.=FALSE,immediate. = TRUE);
  if(any(matrix<0))
    warning("The table contains values <0: the result may be meaningless.",call.=FALSE,immediate. = TRUE);  
  result<-c("Simpson-based Multiple-site Similarity: ", index);
  noquote(result);
}