/* nag_sparse_real_symm_precon_ichol_solve (f11jbc) Example Program.
 *
 * Copyright 2019 Numerical Algorithms Group.
 *
 * Mark 27.0, 2019.
 */

#include <nag.h>

void do_rcm(Integer n, Integer nnz, Integer *irow, Integer *icol,
            double *a, double *y, Integer *istr, Integer *perm_fwd,
            Integer *perm_inv);
int main(void)
{
  /* Scalars */
  Integer exit_status = 0;
  double dscale, dtol;
  Integer i, la, lfill, n, nnz, nnzc, npivm;
  /* Arrays */
  double *a = 0, *x = 0, *y = 0;
  Integer *icol = 0, *ipiv = 0, *irow = 0, *istr = 0,
         *perm_fwd = 0, *perm_inv = 0;
  /* NAG types */
  Nag_SparseSym_Fact mic;
  Nag_SparseSym_Piv pstrat;
  Nag_SparseSym_CheckData check;
  Nag_Sparse_Comm comm;
  NagError fail;

  INIT_FAIL(fail);

  printf("nag_sparse_real_symm_precon_ichol_solve (f11jbc) Example Program Results");
  printf("\n");
  /* Skip heading in data file */
  scanf("%*[^\n]");
  /* Read order of matrix and number of nonzero entries */
  scanf("%" NAG_IFMT "%*[^\n]", &n);
  scanf("%" NAG_IFMT "%*[^\n]", &nnz);

  /* Allocate memory */
  la = 3 * nnz;
  if (!(a = NAG_ALLOC(la, double)) ||
      !(x = NAG_ALLOC(n, double)) ||
      !(y = NAG_ALLOC(n, double)) ||
      !(icol = NAG_ALLOC(la, Integer)) ||
      !(ipiv = NAG_ALLOC(n, Integer)) ||
      !(irow = NAG_ALLOC(la, Integer)) ||
      !(istr = NAG_ALLOC(n + 1, Integer)) ||
      !(perm_fwd = NAG_ALLOC(n, Integer)) ||
      !(perm_inv = NAG_ALLOC(n, Integer))
         )
  {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }

  /* Read the matrix A */
  for (i = 0; i < nnz; i++)
    scanf("%lf%" NAG_IFMT "%" NAG_IFMT "%*[^\n]", &a[i], &irow[i], &icol[i]);
  /* Read the vector y */
  for (i = 0; i < n; i++)
    scanf("%lf", &y[i]);

  lfill = -1;
  dtol = 0.0;
  dscale = 0.0;
  mic = Nag_SparseSym_UnModFact;
  pstrat = Nag_SparseSym_MarkPiv;
  /* Calculate Cholesky factorization using
   * nag_sparse_real_symm_precon_ichol (f11jac).
   */
  nag_sparse_real_symm_precon_ichol(n, nnz, &a, &la, &irow, &icol, lfill, dtol, mic,
                          dscale, pstrat, ipiv, istr, &nnzc, &npivm, &comm,
                          &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_sparse_real_symm_precon_ichol (f11jac).\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }
  /* Check the output value of npivm */
  if (npivm != 0)
    printf("Factorization is not complete \n");
  else {
    /* Solve linear system involving incomplete Cholesky factorization
     *
     *              T T
     *       P L D L P x = y
     *
     * using nag_sparse_real_symm_precon_ichol_solve (f11jbc).
     */
    check = Nag_SparseSym_Check;
    nag_sparse_real_symm_precon_ichol_solve(n, a, la, irow, icol, ipiv, istr,
                                      check, y, x, &fail);
    if (fail.code != NE_NOERROR) {
      printf("Error from nag_sparse_real_symm_precon_ichol_solve (f11jbc).\n%s\n",
             fail.message);
      exit_status = 2;
      goto END;
    }
    /* Output results */
    printf(" Solution of linear system \n");
    for (i = 0; i < n; i++)
      printf("%16.4e\n", x[i]);
    printf("\n");
  }

  /* Repeat with Cuthill-McKee permutation 
   * Compute reverse Cuthill-McKee permutation for bandwidth reduction 
   */
  do_rcm(n, nnz, irow, icol, a, y, istr, perm_fwd, perm_inv);

  SET_FAIL(fail);
  nag_sparse_real_symm_precon_ichol(n, nnz, &a, &la, &irow, &icol, lfill, dtol, mic,
                          dscale, pstrat, ipiv, istr, &nnzc, &npivm, &comm,
                          &fail);
  if (npivm != 0)
    printf("Factorization is not complete \n");
  else {
    check = Nag_SparseSym_Check;
    nag_sparse_real_symm_precon_ichol_solve(n, a, la, irow, icol, ipiv, istr,
                                      check, y, x, &fail);
    printf(" Solution of linear system with Reverse Cuthill-McKee\n");
    for (i = 0; i < n; i++)
      printf("%16.4e\n", x[perm_inv[i] - 1]);
    printf("\n");
  }

END:
  NAG_FREE(a);
  NAG_FREE(x);
  NAG_FREE(y);
  NAG_FREE(icol);
  NAG_FREE(ipiv);
  NAG_FREE(irow);
  NAG_FREE(istr);
  NAG_FREE(perm_fwd);
  NAG_FREE(perm_inv);
  return exit_status;
}

void do_rcm(Integer n, Integer nnz, Integer *irow, Integer *icol,
            double *a, double *y, Integer *istr, Integer *perm_fwd,
            Integer *perm_inv)
{
  Integer j, i, nnz_cs, nnz_scs, info[4], mask[1];
  double *yy;
  Nag_Boolean lopts[5] =
         { Nag_FALSE, Nag_FALSE, Nag_TRUE, Nag_TRUE, Nag_TRUE };
  NagError fail;

  SET_FAIL(fail);
  yy = NAG_ALLOC(n, double);
  /* SCS to CS, must add the upper triangle entries. */
  j = nnz;
  for (i = 0; i < nnz; i++) {
    if (irow[i] > icol[i]) {
      /* strictly lower triangle, add the transposed */
      a[j] = a[i];
      irow[j] = icol[i];
      icol[j] = irow[i];
      j++;
    }
  }
  nnz_cs = j;
  /* Reorder, CS to CCS, icolzp in istr */
  nag_sparse_real_gen_sort(n, &nnz_cs, a, icol, irow, Nag_SparseNsym_FailDups,
                       Nag_SparseNsym_FailZeros, istr, &fail);

  /* Calculate reverse Cuthill-McKee */
  nag_sparse_sym_rcm(n, nnz_cs, istr, irow, lopts, mask, perm_fwd, info,
                     &fail);

  /* compute inverse perm, in perm_inv */
  for (i = 0; i < n; i++)
    perm_inv[perm_fwd[i] - 1] = i + 1;

  /* Apply permutation on column/row indices */
  for (i = 0; i < nnz_cs; i++) {
    icol[i] = perm_inv[icol[i] - 1];
    irow[i] = perm_inv[irow[i] - 1];
  }
  /* restrict to lower triangle, SCS format
   * copying entries upwards
   */
  j = 0;
  for (i = 0; i < nnz_cs; i++) {
    if (irow[i] >= icol[i]) {
      /* non-upper triangle, bubble up */
      a[j] = a[i];
      icol[j] = icol[i];
      irow[j] = irow[i];
      j++;
    }
  }
  nnz_scs = j;
  /*  sort */
  nag_sparse_real_symm_sort(n, &nnz_scs, a, irow, icol, Nag_SparseSym_SumDups,
                      Nag_SparseSym_KeepZeros, istr, &fail);

  /* permute rhs vector */
  for (i = 0; i < n; i++)
    yy[i] = y[perm_fwd[i] - 1];
  for (i = 0; i < n; i++)
    y[i] = yy[i];
  NAG_FREE(yy);
}