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    /*
       MSORT.I
       Multiple key sort routine.

       $Id$
     */
    /*    Copyright (c) 1994.  The Regents of the University of California.
                        All rights reserved.  */

    func msort (x, ..)
    /* DOCUMENT msort(x1, x2, x3, ...)

         returns an index list which sorts the array X1 into increasing

         order.  Where X1 values are equal, the list will sort X2 into
         increasing order.  Where both X1 and X2 are equal, X3 will be

         in increasing order, and so on.  Finally, where all of the keys
         are equal, the returned list will leave the order unchanged
         from the input keys.

         The Xi may be numbers or strings (e.g.- X1 could be an integer
         while X2 was a string, and X3 was a real).  The Xi must all be
         conformable, and each dimension of X1 must be as large as the
         corresponding dimension of any otehr Xi.

         Hence, msort(x) will return the same list as sort(x), except

         where the values of x are equal, in which case msort leaves

         the order unchanged, while sort non-deterministically permutes
         equal elements.  This feature may cost a factor of two in speed,

         so don't use it unless you really need it.  In general, msort

         will call sort up to twice per input argument.

       SEE ALSO: sort, msort_rank
     */
    {
      mxrank= numberof(x)-1;
      local list;
      rank= msort_rank(x, list);
      if (max(rank)==mxrank) return list;

      norm= 1.0/(mxrank+1.0);

      if (1.0+norm == 1.0) error, pr1(mxrank+1)+" is too large an array";

      n= more_args();
      while (n--) {
        x= next_arg();

        rank+= msort_rank(x)*norm;     /* adjust rank for next key */

        rank= msort_rank(rank, list);  /* renormalize adjusted rank */
        if (max(rank)==mxrank) return list;
      }

      /* use indgen as final key guaranteed to break up any remaining
         equal values */

      return sort(rank+indgen(0:mxrank)*norm);
    }

    func msort_rank (x, &list)
    /* DOCUMENT msort_rank(x)
                msort_rank(x, list)
         returns a list of longs the same size and shape as X, whose
         values are the "rank" of the corresponding element of X among
         all the elements of X -- the smallest element has rank 0 and
         the largest has the largest rank, which is equal to one less

         than the number of distinct values in the array X.

         If LIST is present, it is set to the order list returned by
         sort(x(*)).

       SEE ALSO: msort, sort
     */
    {

      rank= array(0, dimsof(x));

      if (numberof(x)<2) return rank;
      void= use_origins(0);
      list= sort(x(*));
      x= x(list);
      x= (x(1:-1)!=x(2:0))(cum);  /* NOT dif -- x may be strings */
      rank(list)= x;
      return rank;
    }