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/*  SCCS @(#)cholesky2.c      5.2 10/27/98
** subroutine to do Cholesky decompostion on a matrix: C = FDF'
**   where F is lower triangular with 1's on the diagonal, and D is diagonal
** arguments are:
**     n         the size of the matrix to be factored
**     **matrix  a ragged array containing an n by n submatrix to be factored
**     toler     the threshold value for detecting "singularity"
**  The factorization is returned in the lower triangle, D occupies the
**    diagonal and the upper triangle is left undisturbed.
**    The lower triangle need not be filled in at the start.
**  Return value:  the rank of the matrix (non-negative definite), or -rank
**     it not SPD or NND
**  If a column is deemed to be redundant, then that diagonal is set to zero.
**   Terry Therneau

int cholesky2(double **matrix, int n, double toler)
    double temp;
    int  i,j,k;
    double eps, pivot;
    int rank;
    int nonneg;

    eps =0;
    for (i=0; i<n; i++) {
      if (matrix[i][i] > eps)  eps = matrix[i][i];
      for (j=(i+1); j<n; j++)  matrix[j][i] = matrix[i][j];
    eps *= toler;

    rank =0;
    for (i=0; i<n; i++) {
      pivot = matrix[i][i];
      if (pivot < eps) {
          matrix[i][i] =0;
          if (pivot < -8*eps) nonneg= -1;
      else  {
          for (j=(i+1); j<n; j++) {
            temp = matrix[j][i]/pivot;
            matrix[j][i] = temp;
            matrix[j][j] -= temp*temp*pivot;
            for (k=(j+1); k<n; k++) matrix[k][j] -= temp*matrix[k][i];
    return(rank * nonneg);

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