NAG Library Manual, Mark 27.3
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NAG CL Interface Introduction
Example description
/* nag_sparseig_feast_complex_herm_solve (f12jrc) Example Program.
 *
 * Copyright 2021 Numerical Algorithms Group.
 *
 * Mark 27.3, 2021.
 */
#include <math.h>
#include <nag.h>

#define X(I, J) x[(J - 1) * pdx + I - 1]
#define Y(I, J) y[(J - 1) * pdy + I - 1]
#define Z(I, J) z[(J - 1) * pdz + I - 1]

int main(void) {
  /* Scalars */
  Integer exit_status = 0;
  Integer i, j, m, n, pdx, pdy, pdz, m0, iter, nconv, irevcm, exit_loop,
      nnza, nnzb, nnzz, nnzzh, npivm, itn, nnzc, nnzch, la;
  double eps, tol, rnorm, emin, emax;
  Complex ze, cone, czero;
  /* Arrays */
  Complex *a = 0, *x = 0, *z = 0, *b = 0;
  double *resid = 0, *d = 0;
  Complex *y = 0, *w = 0, *az = 0, *azh = 0;
  Integer *ipiv = 0, *irowa = 0, *irowb = 0, *icola = 0, *icolb = 0, *icolz = 0,
          *irowz = 0, *istr = 0, *ipivp = 0, *ipivq = 0, *idiag = 0,
          *istrh = 0, *idiagh = 0, *icolzh = 0, *ipivph = 0, *ipivqh = 0,
          *irowzh = 0;
  void *handle = 0;
  /* Nag Types */
  Nag_OrderType order = Nag_ColMajor;
  NagError fail;

  INIT_FAIL(fail);

  /* Output preamble */
  printf("nag_sparseig_feast_complex_herm_solve (f12jrc) ");
  printf("Example Program Results\n\n");
  fflush(stdout);

  /* Skip heading in data file */
  scanf("%*[^\n] ");

  /* Read in the matrix size and the required rank */
  scanf("%" NAG_IFMT "%*[^\n]", &n);
  scanf("%" NAG_IFMT "", &nnza);
  scanf("%" NAG_IFMT "%*[^\n]", &nnzb);

  pdx = n;
  pdy = n;
  pdz = n;
  m0 = n;
  m = MIN(n, 50);
  la = 4 * (nnza + nnzb);

  tol = sqrt(X02AJC);
  cone = nag_complex_create(1.0, 0.0);
  czero = nag_complex_create(0.0, 0.0);

  /* Allocate memory */
  if (!(a = NAG_ALLOC(nnza, Complex)) || !(b = NAG_ALLOC(nnzb, Complex)) ||
      !(icola = NAG_ALLOC(nnza, Integer)) ||
      !(icolb = NAG_ALLOC(nnzb, Integer)) ||
      !(irowa = NAG_ALLOC(nnza, Integer)) ||
      !(irowb = NAG_ALLOC(nnzb, Integer)) ||
      !(x = NAG_ALLOC(pdx * m0, Complex)) ||
      !(y = NAG_ALLOC(pdy * m0, Complex)) ||
      !(z = NAG_ALLOC(pdz * m0, Complex)) || !(resid = NAG_ALLOC(m0, double)) ||
      !(d = NAG_ALLOC(m0, double)) || !(ipiv = NAG_ALLOC(n, Integer)) ||
      !(w = NAG_ALLOC(n, Complex)) || !(az = NAG_ALLOC(la, Complex)) ||
      !(azh = NAG_ALLOC(la, Complex)) || !(icolz = NAG_ALLOC(la, Integer)) ||
      !(irowz = NAG_ALLOC(la, Integer)) || !(icolzh = NAG_ALLOC(la, Integer)) ||
      !(irowzh = NAG_ALLOC(la, Integer)) ||
      !(idiag = NAG_ALLOC(n, Integer)) || !(ipivp = NAG_ALLOC(n, Integer)) ||
      !(ipivq = NAG_ALLOC(n, Integer)) || !(ipivph = NAG_ALLOC(n, Integer)) ||
      !(ipivqh = NAG_ALLOC(n, Integer)) ||
      !(istrh = NAG_ALLOC(n + 1, Integer)) ||
      !(idiagh = NAG_ALLOC(n, Integer)) ||
      !(istr = NAG_ALLOC(n + 1, Integer))) {

    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }

  /* Read in the matrix A from data file */
  for (i = 0; i < nnza; i++)
    scanf(" ( %lf , %lf ) %" NAG_IFMT "%" NAG_IFMT "%*[^\n]", &a[i].re,
          &a[i].im, &irowa[i], &icola[i]);
  scanf("%*[^\n] ");

  /* Read in the matrix B from data file */
  for (i = 0; i < nnzb; i++)
    scanf(" ( %lf , %lf ) %" NAG_IFMT "%" NAG_IFMT "%*[^\n]", &b[i].re,
          &b[i].im, &irowb[i], &icolb[i]);

  /* Initialize data the handle using nag_sparseig_feast_init (f12jac) */
  nag_sparseig_feast_init(&handle, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_sparseig_feast_init (f12jac)\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* Set options using nag_sparseig_feast_option (f12jbc) */
  nag_sparseig_feast_option(handle, "Integration Type = Zolotarev", &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_sparseig_feast_option (f12jbc)\n%s\n", fail.message);
    exit_status = 2;
    goto END;
  }

  emin = -1.0;
  emax = 0.0;
  /* Set the contour using nag_sparseig_feast_symm_contour (f12jec) */
  nag_sparseig_feast_symm_contour(handle, emin, emax, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_sparseig_feast_symm_contour (f12jec)\n%s\n",
           fail.message);
    exit_status = 3;
    goto END;
  }

  exit_loop = 0;
  irevcm = 0;

  do {
    /* Call solver nag_sparseig_feast_complex_herm_solve (f12jrc) */
    nag_sparseig_feast_complex_herm_solve(handle, &irevcm, &ze, n, x, pdx, y,
                                          pdy, &m0, &nconv, d, z, pdz, &eps,
                                          &iter, resid, &fail);

    switch (irevcm) {
    case 1:
      /* Form the sparse matrix ze B-A */
      nnzz = 2 * (nnza + nnzb);
      /* We store it in the arrays az, irowz and icolz */
      for (i = 0; i < nnza; i++) {
        az[i] = nag_complex_subtract(czero, a[i]);
        irowz[i] = irowa[i];
        icolz[i] = icola[i];
        az[nnza + i] = nag_complex_subtract(czero, a[i]);
        irowz[nnza + i] = icola[i];
        icolz[nnza + i] = irowa[i];
      }
      /* Add the elements of ze B */
      for (i = 0; i < nnzb; i++) {
        irowz[2 * nnza + i] = irowb[i];
        icolz[2 * nnza + i] = icolb[i];
        az[2 * nnza + i] = nag_complex_multiply(ze, b[i]);
        irowz[2 * nnza + nnzb + i] = icolb[i];
        icolz[2 * nnza + nnzb + i] = irowb[i];
        az[2 * nnza + nnzb + i] =
            nag_complex_multiply(nag_complex_conjg(ze), b[i]);
      }
      /* Sort the elements into correct coordinate storage format using
       * nag_sparse_complex_gen_sort (f11znc)
       */
      nag_sparse_complex_gen_sort(n, &nnzz, az, irowz, icolz,
                                  Nag_SparseNsym_SumDups,
                                  Nag_SparseNsym_RemoveZeros, istr, &fail);
      /* We have double counted the diagonal elements so halve them */
      for (i = 0; i < nnzz; i++) {
        if (irowz[i] == icolz[i]) {
          az[i].re = 0.5 * az[i].re;
          az[i].im = 0.5 * az[i].im;
        }
      }
      /* Form incomplete LU factorization of ze B - A using
       * nag_sparse_complex_gen_precon_ilu (f11dnc)
       */
      nag_sparse_complex_gen_precon_ilu(n, nnzz, az, la, irowz, icolz, 0, 0.0,
                                        Nag_SparseNsym_PartialPiv,
                                        Nag_SparseNsym_UnModFact, ipivp, ipivq,
                                        istr, idiag, &nnzc, &npivm, &fail);
      if (fail.code != NE_NOERROR) {
        exit_loop = 1;
      }
      break;
    case 2:
      /* Solve the linear system (ze B - A)w = y, with m0 righthand sides */
      for (j = 1; j <= m0; j++) {
        for (i = 1; i <= n; i++) {
          w[i - 1] = Y(i, j);
          /* Initial guess */
          Y(i, j) = cone;
        }
        /* Call linear system solver for a single righthand side
         * nag_sparse_complex_gen_solve_ilu (f11dqc)
         */
        nag_sparse_complex_gen_solve_ilu(
            Nag_SparseNsym_RGMRES, n, nnzz, az, la, irowz, icolz, ipivp, ipivq,
            istr, idiag, w, m, tol, 500, &Y(1, j), &rnorm, &itn, &fail);
      }
      if (fail.code != NE_NOERROR) {
        exit_loop = 1;
      }
      break;
    case 3:
      /* Form the sparse matrix (ze B-A)^H */
      nnzzh = 2 * (nnza + nnzb);
      /* We store it in the arrays azh, irowzh and icolzh */
      for (i = 0; i < nnza; i++) {
        azh[i] = nag_complex_subtract(czero, a[i]);
        irowzh[i] = irowa[i];
        icolzh[i] = icola[i];
        azh[nnza + i] = nag_complex_subtract(czero, a[i]);
        irowzh[nnza + i] = icola[i];
        icolzh[nnza + i] = irowa[i];
      }
      /* Add the elements of (ze B)^H */
      for (i = 0; i < nnzb; i++) {
        irowzh[2 * nnza + i] = irowb[i];
        icolzh[2 * nnza + i] = icolb[i];
        azh[2 * nnza + i] = nag_complex_multiply(nag_complex_conjg(ze), b[i]);
        irowzh[2 * nnza + nnzb + i] = icolb[i];
        icolzh[2 * nnza + nnzb + i] = irowb[i];
        azh[2 * nnza + nnzb + i] = nag_complex_multiply(ze, b[i]);
      }
      /* Sort the elements into correct coordinate storage format using
       * nag_sparse_complex_gen_sort (f11znc)
       */
      nag_sparse_complex_gen_sort(n, &nnzzh, azh, irowzh, icolzh,
                                  Nag_SparseNsym_SumDups,
                                  Nag_SparseNsym_RemoveZeros, istrh, &fail);
      /* We have double counted the diagonal elements so halve them */
      for (i = 0; i < nnzzh; i++) {
        if (irowzh[i] == icolzh[i]) {
          azh[i].re = 0.5 * azh[i].re;
          azh[i].im = 0.5 * azh[i].im;
        }
      }
      /* Form incomplete LU factorization of ze B - A using
       * nag_sparse_complex_gen_precon_ilu (f11dnc)
       */
      nag_sparse_complex_gen_precon_ilu(
          n, nnzzh, azh, la, irowzh, icolzh, 0, 0.0, Nag_SparseNsym_PartialPiv,
          Nag_SparseNsym_UnModFact, ipivph, ipivqh, istrh, idiagh, &nnzch,
          &npivm, &fail);
      if (fail.code != NE_NOERROR) {
        exit_loop = 1;
      }
      break;
    case 4:
      /* Solve the linear system (ze B - A)w = y, with m0 righthand sides */
      for (j = 1; j <= m0; j++) {
        for (i = 1; i <= n; i++) {
          w[i - 1] = Y(i, j);
          /* Initial guess */
          Y(i, j) = cone;
        }
        /* Call linear system solver for a single righthand side
         * nag_sparse_complex_gen_solve_ilu (f11dqc)
         */
        nag_sparse_complex_gen_solve_ilu(Nag_SparseNsym_RGMRES, n, nnzzh, azh,
                                         la, irowzh, icolzh, ipivph, ipivqh,
                                         istrh, idiagh, w, m, tol, 500,
                                         &Y(1, j), &rnorm, &itn, &fail);
      }
      if (fail.code != NE_NOERROR) {
        exit_loop = 1;
      }
      break;
    case 5:
      /* Compute x <- Az*/
      for (j = 1; j <= m0; j++) {
        nag_sparse_complex_herm_matvec(n, nnza, a, irowa, icola,
                                       Nag_SparseSym_NoCheck, &Z(1, j),
                                       &X(1, j), &fail);
      }
      if (fail.code != NE_NOERROR) {
        exit_loop = 1;
      }
      break;
    case 6:
      /* Compute x <- Bz */
      for (j = 1; j <= m0; j++) {
        nag_sparse_complex_herm_matvec(n, nnzb, b, irowb, icolb,
                                       Nag_SparseSym_NoCheck, &Z(1, j),
                                       &X(1, j), &fail);
      }
      if (fail.code != NE_NOERROR) {
        exit_loop = 1;
      }

      break;
    }
  } while (irevcm != 0 && exit_loop == 0);

  if (fail.code != NE_NOERROR) {
    printf("Error during reverse communication solve\n%s\n", fail.message);
    exit_status = 4;
    goto END;
  }

  /* Print solution */
  printf(" Eigenvalues\n");
  for (i = 0; i < nconv; ++i)
    printf("%8.4f%s", d[i], (i + 1) % 8 == 0 ? "\n" : " ");
  printf("\n\n");

  /* Print eigenvectors using nag_file_print_matrix_complex_gen (x04dac) */
  nag_file_print_matrix_complex_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag,
                                    n, nconv, z, pdz, "Eigenvectors", NULL,
                                    &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_file_print_matrix_complex_gen (x04dac)\n%s\n",
           fail.message);
    exit_status = 5;
    goto END;
  }

END:
  NAG_FREE(a);
  NAG_FREE(b);
  NAG_FREE(w);
  NAG_FREE(az);
  NAG_FREE(azh);
  NAG_FREE(x);
  NAG_FREE(y);
  NAG_FREE(z);
  NAG_FREE(resid);
  NAG_FREE(d);
  NAG_FREE(ipiv);
  NAG_FREE(icolz);
  NAG_FREE(irowz);
  NAG_FREE(icola);
  NAG_FREE(irowa);
  NAG_FREE(icolb);
  NAG_FREE(irowb);
  NAG_FREE(icolzh);
  NAG_FREE(irowzh);
  NAG_FREE(idiag);
  NAG_FREE(idiagh);
  NAG_FREE(ipivp);
  NAG_FREE(ipivph);
  NAG_FREE(ipivq);
  NAG_FREE(ipivqh);
  NAG_FREE(idiagh);
  NAG_FREE(istr);
  NAG_FREE(istrh);

  /* Destroy the data handle using nag_sparseig_feast_free (f12jzc) */
  nag_sparseig_feast_free(&handle, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_sparseig_feast_free (f12jzc)\n%s\n", fail.message);
    exit_status = 6;
  }

  return exit_status;
}