NAG Library Manual, Mark 30.2
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NAG CL Interface Introduction
Example description
/* nag_sparseig_feast_poly_gen_solve (f12jvc) Example Program.
 *
 * Copyright 2024 Numerical Algorithms Group.
 *
 * Mark 30.2, 2024.
 */
#include <math.h>
#include <nag.h>

#define A(I, J) a[I + J * nnzmax]
#define IROW(I, J) irow[I + J * nnzmax]
#define ICOL(I, J) icol[I + J * nnzmax]
#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, k, pdx, pdy, pdz, m0, iter, nconv, irevcm,
      exit_loop, nnzz, nnzzh, npivm, itn, nnzc, nnzch, ccn, deg, nnzmax, nnzsum,
      ind, la;
  double eps, tol, rnorm;
  Complex ze, cone;
  /* Arrays */
  Complex *a = 0, *x = 0, *z = 0, *w = 0, *zedge = 0, *d = 0;
  double *resid = 0;
  Complex *y = 0, *az = 0, *azh = 0;
  Integer *ipiv = 0, *irow = 0, *icol = 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,
          *nedge = 0, *tedge = 0, *nnza = 0;
  void *handle = 0;
  /* Nag Types */
  Nag_OrderType order = Nag_ColMajor;
  NagError fail;

  INIT_FAIL(fail);

  /* Output preamble */
  printf("nag_sparseig_feast_poly_gen_solve (f12jvc) ");
  printf("Example Program Results\n\n");
  fflush(stdout);

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

  /* Read in the matrix size and the degree */
  scanf("%" NAG_IFMT "", &n);
  scanf("%" NAG_IFMT "", &deg);
  scanf("%*[^\n]");

  /* Initial memory allocation */
  if (!(nnza = NAG_ALLOC(deg + 1, Integer))) {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }

  nnzmax = 0;
  nnzsum = 0;
  for (i = 0; i < deg + 1; i++) {
    scanf("%" NAG_IFMT "", &nnza[i]);
    nnzsum += nnza[i];
    nnzmax = MAX(nnzmax, nnza[i]);
  }
  scanf("%*[^\n]");

  pdx = n;
  pdy = n;
  pdz = n;
  m0 = n;
  m = MIN(n, 50);
  la = 2 * (nnzsum);

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

  /* Memory allocation */
  if (!(a = NAG_ALLOC(nnzmax * (deg + 1), Complex)) ||
      !(icol = NAG_ALLOC(nnzmax * (deg + 1), Integer)) ||
      !(irow = NAG_ALLOC(nnzmax * (deg + 1), Integer)) ||
      !(x = NAG_ALLOC(pdx * 2 * m0, Complex)) ||
      !(y = NAG_ALLOC(pdy * m0, Complex)) ||
      !(z = NAG_ALLOC(pdz * 2 * m0, Complex)) ||
      !(resid = NAG_ALLOC(2 * m0, double)) || !(d = NAG_ALLOC(m0, Complex)) ||
      !(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 = -2;
  goto END;
}

/* Read in the matrices from data file */
for (j = 0; j < deg + 1; j++) {
  for (i = 0; i < nnza[j]; i++)
    scanf(" ( %lf , %lf ) %" NAG_IFMT "%" NAG_IFMT "%*[^\n]", &A(i, j).re,
          &A(i, j).im, &IROW(i, j), &ICOL(i, j));
}

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

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

/* Define arrays for the custom contour */
ccn = 2;
if (!(nedge = NAG_ALLOC(ccn, Integer)) || !(tedge = NAG_ALLOC(ccn, Integer)) ||
    !(zedge = NAG_ALLOC(ccn, Complex))) {
  exit_status = -3;
  goto END;
}

zedge[0] = nag_complex_create(-1.5, -0.5);
zedge[1] = nag_complex_create(0.5, 1.5);

tedge[0] = 100;
tedge[1] = 0;

nedge[0] = 20;
nedge[1] = 10;

/* Generate the contour using nag_sparseig_feast_custom_contour (f12jgc) */
nag_sparseig_feast_custom_contour(handle, ccn, nedge, tedge, zedge, &fail);
if (fail.code != NE_NOERROR) {
  printf("Error from nag_sparseig_feast_custom_contour (f12jgc)\n%s\n",
         fail.message);
  exit_status = 3;
  goto END;
}

exit_loop = 0;
irevcm = 0;

do {
  /* Call solver nag_sparseig_feast_poly_gen_solve (f12jrc) */
  nag_sparseig_feast_poly_gen_solve(handle, &irevcm, deg, &ze, n, x, pdx, y,
                                    pdy, &k, &m0, &nconv, d, z, pdz, &eps,
                                    &iter, resid, &fail);
  switch (irevcm) {
  case 1:
    /* Form the sparse matrix \sum ze^i A_i */
    nnzz = nnzsum;
    ind = 0;
    for (i = 0; i < deg + 1; i++) {
      for (j = 0; j < nnza[i]; j++) {
        az[ind] = nag_complex_multiply(nag_complex_i_power(ze, i), A(j, i));
        irowz[ind] = IROW(j, i);
        icolz[ind] = ICOL(j, i);
        ind++;
      }
    }
    /* 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);
    /* Form incomplete LU factorization of \sum ze^i A_i 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 (\sum ze^i A_i) 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 (\sum ze^i A_i)^H */
    nnzzh = nnzsum;
    ind = 0;
    for (i = 0; i < deg + 1; i++) {
      for (j = 0; j < nnza[i]; j++) {
        azh[ind] = nag_complex_conjg(
            nag_complex_multiply(nag_complex_i_power(ze, i), A(j, i)));
        irowzh[ind] = ICOL(j, i);
        icolzh[ind] = IROW(j, i);
        ind++;
      }
    }
    /* 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);
    /* Form incomplete LU factorization of (\sum ze^i A_i)^H 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 (\sum ze^i A_i)^H 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 <- A_k z */
    for (j = 1; j <= m0; j++) {
      nag_sparse_complex_gen_matvec(
          Nag_NoTrans, n, nnza[k], &A(0, k), &IROW(0, k), &ICOL(0, k),
          Nag_SparseNsym_NoCheck, &Z(1, j), &X(1, j), &fail);
    }
    if (fail.code != NE_NOERROR) {
      exit_loop = 1;
    }
    break;
  case 6:
    /* Compute x <- (A_k)^H z */
    for (j = 1; j <= m0; j++) {
      nag_sparse_complex_gen_matvec(
          Nag_ConjTrans, n, nnza[k], &A(0, k), &IROW(0, k), &ICOL(0, k),
          Nag_SparseNsym_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) {
  if (d[i].im == 0.0)
    printf("%13.4e%s", d[i].re, (i + 1) % 4 == 0 ? "\n" : " ");
  else
    printf(" (%13.4e, %13.4e)%s", d[i].re, d[i].im,
           (i + 1) % 4 == 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, "Right 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;
}
nag_file_print_matrix_complex_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
                                  nconv, &z[m0 * pdz], pdz, "Left 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 = 6;
  goto END;
}

END : NAG_FREE(a);
NAG_FREE(w);
NAG_FREE(az);
NAG_FREE(azh);
NAG_FREE(nnza);
NAG_FREE(x);
NAG_FREE(y);
NAG_FREE(z);
NAG_FREE(resid);
NAG_FREE(d);
NAG_FREE(ipiv);
NAG_FREE(icolz);
NAG_FREE(nedge);
NAG_FREE(tedge);
NAG_FREE(zedge);
NAG_FREE(irowz);
NAG_FREE(icol);
NAG_FREE(irow);
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 = 7;
}

return exit_status;
}