NAG Library Manual, Mark 28.5
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NAG CL Interface Introduction
Example description
/* nag_lapackeig_dhgeqz (f08xec) Example Program.
 *
 * Copyright 2022 Numerical Algorithms Group.
 *
 * Mark 28.5, 2022.
 */

#include <nag.h>
#include <stdio.h>

int main(void) {
  /* Scalars */
  Integer i, ihi, ilo, irows, j, n, pda, pdb;
  Integer alpha_len, beta_len, scale_len, tau_len;
  Integer exit_status = 0;

  NagError fail;
  Nag_OrderType order;
  /* Arrays */
  double *a = 0, *alphai = 0, *alphar = 0, *b = 0, *beta = 0;
  double *lscale = 0, *q = 0, *rscale = 0, *tau = 0, *z = 0;

#ifdef NAG_COLUMN_MAJOR
#define A(I, J) a[(J - 1) * pda + I - 1]
#define B(I, J) b[(J - 1) * pdb + I - 1]
  order = Nag_ColMajor;
#else
#define A(I, J) a[(I - 1) * pda + J - 1]
#define B(I, J) b[(I - 1) * pdb + J - 1]
  order = Nag_RowMajor;
#endif

  INIT_FAIL(fail);

  printf("nag_lapackeig_dhgeqz (f08xec) Example Program Results\n\n");
  /* Skip heading in data file */
  scanf("%*[^\n] ");
  scanf("%" NAG_IFMT "%*[^\n] ", &n);
  pda = n;
  pdb = n;
  alpha_len = n;
  beta_len = n;
  scale_len = n;
  tau_len = n;

  /* Allocate memory */
  if (!(a = NAG_ALLOC(n * n, double)) ||
      !(alphai = NAG_ALLOC(alpha_len, double)) ||
      !(alphar = NAG_ALLOC(alpha_len, double)) ||
      !(b = NAG_ALLOC(n * n, double)) ||
      !(beta = NAG_ALLOC(beta_len, double)) ||
      !(lscale = NAG_ALLOC(scale_len, double)) ||
      !(q = NAG_ALLOC(1 * 1, double)) ||
      !(rscale = NAG_ALLOC(scale_len, double)) ||
      !(tau = NAG_ALLOC(tau_len, double)) || !(z = NAG_ALLOC(1 * 1, double))) {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }

  /* READ matrix A from data file */
  for (i = 1; i <= n; ++i) {
    for (j = 1; j <= n; ++j)
      scanf("%lf", &A(i, j));
  }
  scanf("%*[^\n] ");

  /* READ matrix B from data file */
  for (i = 1; i <= n; ++i) {
    for (j = 1; j <= n; ++j)
      scanf("%lf", &B(i, j));
  }
  scanf("%*[^\n] ");
  /* Balance matrix pair (A,B) */
  /* nag_lapackeig_dggbal (f08whc).
   * Balance a pair of real general matrices
   */
  nag_lapackeig_dggbal(order, Nag_DoBoth, n, a, pda, b, pdb, &ilo, &ihi, lscale,
                       rscale, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_dggbal (f08whc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* Matrix A after balancing */
  /* nag_file_print_matrix_real_gen (x04cac).
   * Print real general matrix (easy-to-use)
   */
  fflush(stdout);
  nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
                                 n, a, pda, "Matrix A after balancing", 0,
                                 &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_file_print_matrix_real_gen (x04cac).\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }
  printf("\n");

  /* Matrix B after balancing */
  /* nag_file_print_matrix_real_gen (x04cac), see above. */
  fflush(stdout);
  nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
                                 n, b, pdb, "Matrix B after balancing", 0,
                                 &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_file_print_matrix_real_gen (x04cac).\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }
  printf("\n");

  /* Reduce B to triangular form using QR */
  irows = ihi + 1 - ilo;
  /* nag_lapackeig_dgeqrf (f08aec).
   * QR factorization of real general rectangular matrix
   */
  nag_lapackeig_dgeqrf(order, irows, irows, &B(ilo, ilo), pdb, tau, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_dgeqrf (f08aec).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* Apply the orthogonal transformation to matrix A */
  /* nag_lapackeig_dormqr (f08agc).
   * Apply orthogonal transformation determined by nag_lapackeig_dgeqrf
   * (f08aec) or nag_lapackeig_dgeqpf (f08bec)
   */
  nag_lapackeig_dormqr(order, Nag_LeftSide, Nag_Trans, irows, irows, irows,
                       &B(ilo, ilo), pdb, tau, &A(ilo, ilo), pda, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_dormqr (f08agc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* Compute the generalized Hessenberg form of (A,B) */
  /* nag_lapackeig_dgghd3 (f08wfc).
   * Orthogonal reduction of a pair of real general matrices
   * to generalized upper Hessenberg form
   */
  nag_lapackeig_dgghd3(order, Nag_NotQ, Nag_NotZ, irows, 1, irows, &A(ilo, ilo),
                       pda, &B(ilo, ilo), pdb, q, 1, z, 1, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_dgghd3 (f08wfc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* Matrix A in generalized Hessenberg form */
  /* nag_file_print_matrix_real_gen (x04cac), see above. */
  fflush(stdout);
  nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
                                 n, a, pda, "Matrix A in Hessenberg form", 0,
                                 &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_file_print_matrix_real_gen (x04cac).\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }
  printf("\n");
  /* Matrix B in generalized Hessenberg form */
  /* nag_file_print_matrix_real_gen (x04cac), see above. */
  fflush(stdout);
  nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
                                 n, b, pdb, "Matrix B is triangular", 0, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_file_print_matrix_real_gen (x04cac).\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }

  /* Compute the generalized Schur form */
  /* nag_lapackeig_dhgeqz (f08xec).
   * Eigenvalues and generalized Schur factorization of real
   * generalized upper Hessenberg form reduced from a pair of
   * real general matrices
   */
  nag_lapackeig_dhgeqz(order, Nag_EigVals, Nag_NotQ, Nag_NotZ, n, ilo, ihi, a,
                       pda, b, pdb, alphar, alphai, beta, q, 1, z, 1, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_dhgeqz (f08xec).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* Print the generalized eigenvalues */
  printf("\n Generalized eigenvalues\n");
  for (i = 1; i <= n; ++i) {
    if (beta[i - 1] != 0.0) {
      printf(" %4" NAG_IFMT "     (%7.3f,%7.3f)\n", i,
             alphar[i - 1] / beta[i - 1], alphai[i - 1] / beta[i - 1]);
    } else
      printf(" %4" NAG_IFMT "Eigenvalue is infinite\n", i);
  }
END:
  NAG_FREE(a);
  NAG_FREE(alphai);
  NAG_FREE(alphar);
  NAG_FREE(b);
  NAG_FREE(beta);
  NAG_FREE(lscale);
  NAG_FREE(q);
  NAG_FREE(rscale);
  NAG_FREE(tau);
  NAG_FREE(z);

  return exit_status;
}