NAG Library Manual, Mark 28.3
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NAG CL Interface Introduction
Example description
/* nag_sparse_complex_gen_precon_ssor_solve (f11drc) Example Program.
 *
 * Copyright 2022 Numerical Algorithms Group.
 *
 * Mark 28.3, 2022.
 */
#include <nag.h>
int main(void) {
  /* Scalars */
  Integer exit_status = 0;
  double anorm, omega, sigmax, stplhs, stprhs, tol;
  Integer i, irevcm, iterm, itn, liwork, lwneed, lwork, m, maxitn, monit, n,
      nnz;
  /* Arrays */
  char nag_enum_arg[100];
  Complex *a = 0, *b = 0, *rdiag = 0, *work = 0, *x = 0;
  double *wgt = 0;
  Integer *icol = 0, *irow = 0, *iwork = 0;
  /* NAG types */
  Nag_SparseNsym_CheckData ckdr, ckxn;
  Nag_NormType norm;
  Nag_SparseNsym_PrecType precon;
  Nag_SparseNsym_Method method;
  Nag_TransType trans;
  Nag_SparseNsym_Weight weight;
  NagError fail, fail1;

  INIT_FAIL(fail);
  INIT_FAIL(fail1);

  printf(
      "nag_sparse_complex_gen_precon_ssor_solve (f11drc) Example Program Results");
  printf("\n\n");
  /* Skip heading in data file */
  scanf("%*[^\n]");
  /* Read algorithmic parameters */
  scanf("%" NAG_IFMT "%" NAG_IFMT "%*[^\n]", &n, &m);
  scanf("%" NAG_IFMT "%*[^\n]", &nnz);
  lwork = MAX(121 + n * (3 + m) + m * (m + 5), 120 + 7 * n);
  liwork = 2 * n + 1;
  if (!(a = NAG_ALLOC((nnz), Complex)) || !(b = NAG_ALLOC((n), Complex)) ||
      !(rdiag = NAG_ALLOC((n), Complex)) ||
      !(work = NAG_ALLOC((lwork), Complex)) || !(x = NAG_ALLOC((n), Complex)) ||
      !(wgt = NAG_ALLOC((n), double)) || !(icol = NAG_ALLOC((nnz), Integer)) ||
      !(irow = NAG_ALLOC((nnz), Integer)) ||
      !(iwork = NAG_ALLOC((liwork), Integer))) {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }
  /* Read or initialize the parameters for the iterative solver */
  scanf("%99s%*[^\n]", nag_enum_arg);
  /* nag_enum_name_to_value (x04nac).
   * Converts NAG enum member name to value
   */
  method = (Nag_SparseNsym_Method)nag_enum_name_to_value(nag_enum_arg);
  scanf("%99s%*[^\n]", nag_enum_arg);
  precon = (Nag_SparseNsym_PrecType)nag_enum_name_to_value(nag_enum_arg);
  scanf("%99s%*[^\n]", nag_enum_arg);
  norm = (Nag_NormType)nag_enum_name_to_value(nag_enum_arg);
  scanf("%" NAG_IFMT "%*[^\n]", &iterm);
  scanf("%lf%" NAG_IFMT "%*[^\n]", &tol, &maxitn);
  scanf("%lf%lf%*[^\n]", &anorm, &sigmax);
  scanf("%lf%*[^\n]", &omega);

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

    /* Read rhs vector b and initial approximate solution x */
  for (i = 0; i < n; i++)
    scanf(" ( %lf , %lf )", &b[i].re, &b[i].im);
  scanf("%*[^\n]");
  for (i = 0; i < n; i++)
    scanf(" ( %lf , %lf )", &x[i].re, &x[i].im);
  weight = Nag_SparseNsym_UnWeighted;
  monit = 0;

  /* Call to initialize solver */
  /* nag_sparse_complex_gen_basic_setup (f11brc)
   * Complex sparse non-Hermitian linear systems, setup
   */
  nag_sparse_complex_gen_basic_setup(method, precon, norm, weight, iterm, n, m,
                                     tol, maxitn, anorm, sigmax, monit, &lwneed,
                                     work, lwork, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_sparse_complex_gen_basic_setup (f11brc).\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }
  /* Calculate reciprocal diagonal matrix elements if necessary */
  if (precon == Nag_SparseNsym_Prec) {
    for (i = 0; i < n; i++)
      iwork[i] = 0;
    for (i = 0; i < nnz; i++) {
      if (irow[i] == icol[i]) {
        iwork[irow[i] - 1]++;
        if (nag_complex_equal(a[i], nag_complex_create(0.0, 0.0))) {
          printf("Matrix has a zero diagonal element\n");
          goto END;
        } else {
          rdiag[irow[i] - 1] =
              nag_complex_divide(nag_complex_create(1.0, 0.0), a[i]);
        }
      }
    }
    for (i = 0; i < n; i++) {
      if (iwork[i] == 0) {
        printf("Matrix has a missing diagonal element\n");
        goto END;
      }
      if (iwork[i] >= 2) {
        printf("Matrix has a multiple diagonal element\n");
        goto END;
      }
    }
  }
  /* Call solver repeatedly to solve the equations */
  irevcm = 0;
  ckxn = Nag_SparseNsym_Check;
  ckdr = Nag_SparseNsym_Check;
  while (irevcm != 4) {
    /* nag_sparse_complex_gen_basic_solver (f11bsc).
     * Complex sparse non-Hermitian linear systems, solver routine
     * preconditioned RGMRES, CGS, Bi-CGSTAB or TFQMR method
     */
    nag_sparse_complex_gen_basic_solver(&irevcm, x, b, wgt, work, lwork, &fail);
    switch (irevcm) {
    case 1:
      /* Compute matrix-vector product */
      trans = Nag_NoTrans;
      /* nag_sparse_complex_gen_matvec (f11xnc).
       * Complex sparse non-Hermitian matrix vector multiply
       */
      nag_sparse_complex_gen_matvec(trans, n, nnz, a, irow, icol, ckxn, x, b,
                                    &fail1);
      ckxn = Nag_SparseNsym_NoCheck;
      break;
    case -1:
      /* Compute conjugate transposed matrix-vector product */
      trans = Nag_ConjTrans;
      nag_sparse_complex_gen_matvec(trans, n, nnz, a, irow, icol, ckxn, x, b,
                                    &fail1);
      ckxn = Nag_SparseNsym_NoCheck;
      break;
    case 2:
      /* SSOR preconditioning */
      trans = Nag_NoTrans;
      /* nag_sparse_complex_gen_precon_ssor_solve (f11drc).
       * Solution of linear system involving preconditioning matrix generated
       * by applying SSOR to complex sparse non-Hermitian matrix
       */
      nag_sparse_complex_gen_precon_ssor_solve(
          trans, n, nnz, a, irow, icol, rdiag, omega, ckdr, x, b, &fail1);
      ckdr = Nag_SparseNsym_NoCheck;
      break;
    case 4:
      /* Termination */
      break;
    default:
      goto END;
    }
    if (fail1.code != NE_NOERROR) {
      printf("Error from matrix-vector or preconditioning stage.\n%s\n",
             fail1.message);
      exit_status = 2;
      goto END;
    }
  }
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_sparse_complex_gen_basic_solver (f11bsc).\n%s\n",
           fail.message);
    exit_status = 3;
    goto END;
  }
  /* nag_sparse_complex_gen_basic_diag (f11btc)
   * Complex sparse non-Hermitian linear systems, diagnostic
   */
  nag_sparse_complex_gen_basic_diag(&itn, &stplhs, &stprhs, &anorm, &sigmax,
                                    work, lwork, &fail1);
  printf("Converged in %12" NAG_IFMT " iterations\n", itn);
  printf("Matrix norm         = %11.3e\n", anorm);
  printf("Final residual norm = %11.3e\n\n", stplhs);
  /* Output x */
  printf("%14s\n", "Solution");
  for (i = 0; i < n; i++)
    printf(" ( %13.4e, %13.4e) \n", x[i].re, x[i].im);

END:
  NAG_FREE(a);
  NAG_FREE(b);
  NAG_FREE(rdiag);
  NAG_FREE(work);
  NAG_FREE(x);
  NAG_FREE(wgt);
  NAG_FREE(icol);
  NAG_FREE(irow);
  NAG_FREE(iwork);
  return exit_status;
}