/* nag_dhgeqz (f08xec) Example Program.
 *
 * Copyright 2001 Numerical Algorithms Group.
 *
 * Mark 7, 2001.
 */

#include <stdio.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <nagf08.h>
#include <nagx04.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_dhgeqz (f08xec) Example Program Results\n\n");
  /* Skip heading in data file */
  scanf("%*[^\n] ");
  scanf("%ld%*[^\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_dggbal (f08whc).
   * Balance a pair of real general matrices
   */
  nag_dggbal(order, Nag_DoBoth, n, a, pda, b, pdb, &ilo, &ihi, lscale,
             rscale, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_dggbal (f08whc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

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

  /* Matrix B after balancing */
  /* nag_gen_real_mat_print (x04cac), see above. */
  fflush(stdout);
  nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, b,
                         pdb, "Matrix B after balancing", 0, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_gen_real_mat_print (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_dgeqrf (f08aec).
   * QR factorization of real general rectangular matrix
   */
  nag_dgeqrf(order, irows, irows, &B(ilo, ilo), pdb, tau, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_dgeqrf (f08aec).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  /* Apply the orthogonal transformation to matrix A */
  /* nag_dormqr (f08agc).
   * Apply orthogonal transformation determined by nag_dgeqrf
   * (f08aec) or nag_dgeqpf (f08bec)
   */
  nag_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_dormqr (f08agc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  /* Compute the generalized Hessenberg form of (A,B) */
  /* nag_dgghrd (f08wec).
   * Orthogonal reduction of a pair of real general matrices
   * to generalized upper Hessenberg form
   */
  nag_dgghrd(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_dgghrd (f08wec).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

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

  /* Compute the generalized Schur form */
  /* nag_dhgeqz (f08xec).
   * Eigenvalues and generalized Schur factorization of real
   * generalized upper Hessenberg form reduced from a pair of
   * real general matrices
   */
  nag_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_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(" %4ld     (%7.3f,%7.3f)\n", i,
                  alphar[i-1]/beta[i-1], alphai[i-1]/beta[i-1]);
        }
      else
        printf(" %4ldEigenvalue is infinite\n", i);
    }
 END:
  if (a) NAG_FREE(a);
  if (alphai) NAG_FREE(alphai);
  if (alphar) NAG_FREE(alphar);
  if (b) NAG_FREE(b);
  if (beta) NAG_FREE(beta);
  if (lscale) NAG_FREE(lscale);
  if (q) NAG_FREE(q);
  if (rscale) NAG_FREE(rscale);
  if (tau) NAG_FREE(tau);
  if (z) NAG_FREE(z);

  return exit_status;
}