/* nag_zhgeqz (f08xsc) Example Program.
 *
 * Copyright 2001 Numerical Algorithms Group.
 *
 * Mark 7, 2001.
 */

#include <stdio.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <naga02.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 */
  Complex *a=0, *alpha=0, *b=0, *beta=0, *q=0, *tau=0, *z=0;
  Complex e;
  double *lscale=0, *rscale=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);
  Vprintf("nag_zhgeqz (f08xsc) Example Program Results\n\n");
  /* Skip heading in data file */
  Vscanf("%*[^\n] ");
  Vscanf("%ld%*[^\n] ", &n);
#ifdef NAG_COLUMN_MAJOR
  pda = n;
  pdb = n;
#else
  pda = n;
  pdb = n;
#endif
  alpha_len = n;
  beta_len = n;
  scale_len = n;
  tau_len = n;

  /* Allocate memory */
  if ( !(a = NAG_ALLOC(n * n, Complex)) ||
       !(alpha = NAG_ALLOC(alpha_len, Complex)) ||
       !(b = NAG_ALLOC(n * n, Complex)) ||
       !(beta = NAG_ALLOC(beta_len, Complex)) ||
       !(q = NAG_ALLOC(1 * 1, Complex)) ||
       !(tau = NAG_ALLOC(tau_len, Complex)) ||
       !(lscale = NAG_ALLOC(scale_len, double)) ||
       !(rscale = NAG_ALLOC(scale_len, double)) ||
       !(z = NAG_ALLOC(1 * 1, Complex)) )
    {
      Vprintf("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)
        Vscanf(" ( %lf, %lf ) ", &A(i,j).re, &A(i,j).im);
    }
  Vscanf("%*[^\n] ");

  /* READ matrix B from data file */
  for (i = 1; i <= n; ++i)
    {
      for (j = 1; j <= n; ++j)
        Vscanf(" ( %lf, %lf ) ", &B(i,j).re, &B(i,j).im);
    }
  Vscanf("%*[^\n] ");
  /* Balance matrix pair (A,B) */
  /* nag_zggbal (f08wvc).
   * Balance a pair of complex general matrices
   */
  nag_zggbal(order, Nag_DoBoth, n, a, pda, b, pdb, &ilo, &ihi, lscale,
             rscale, &fail);
  if (fail.code != NE_NOERROR)
    {
      Vprintf("Error from nag_zggbal (f08wvc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  /* Matrix A after balancing */
  /* nag_gen_complx_mat_print_comp (x04dbc).
   * Print complex general matrix (comprehensive)
   */
  nag_gen_complx_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
                                n, a, pda, Nag_BracketForm, "%7.4f",
                                "Matrix A after balancing",
                                Nag_IntegerLabels, 0, Nag_IntegerLabels, 0, 80,
                                0, 0, &fail);
  if (fail.code != NE_NOERROR)
    {
      Vprintf("Error from nag_gen_complx_mat_print_comp (x04dbc).\n%s\n",
              fail.message);
      exit_status = 1;
      goto END;
    }
  Vprintf("\n");

  /* Matrix B after balancing */
  /* nag_gen_complx_mat_print_comp (x04dbc), see above. */
  nag_gen_complx_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
                                n, b, pdb, Nag_BracketForm, "%7.4f",
                                "Matrix B after balancing",
                                Nag_IntegerLabels, 0, Nag_IntegerLabels, 0, 80,
                                0, 0, &fail);
  if (fail.code != NE_NOERROR)
    {
      Vprintf("Error from nag_gen_complx_mat_print_comp (x04dbc).\n%s\n",
              fail.message);
      exit_status = 1;
      goto END;
    }
  Vprintf("\n");

  /* Reduce B to triangular form using QR */
  irows = ihi + 1 - ilo;
  /* nag_zgeqrf (f08asc).
   * QR factorization of complex general rectangular matrix
   */
  nag_zgeqrf(order, irows, irows, &B(ilo, ilo), pdb, tau, &fail);
  if (fail.code != NE_NOERROR)
    {
      Vprintf("Error from nag_zgeqrf (f08asc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  /* Apply the orthogonal transformation to matrix A */
  /* nag_zunmqr (f08auc).
   * Apply unitary transformation determined by nag_zgeqrf
   * (f08asc) or nag_zgeqpf (f08bsc)
   */
  nag_zunmqr(order, Nag_LeftSide, Nag_ConjTrans, irows, irows, irows,
             &B(ilo, ilo), pdb, tau, &A(ilo, ilo), pda, &fail);
  if (fail.code != NE_NOERROR)
    {
      Vprintf("Error from nag_zunmqr (f08auc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  /* Compute the generalized Hessenberg form of (A,B) */
  /* nag_zgghrd (f08wsc).
   * Unitary reduction of a pair of complex general matrices
   * to generalized upper Hessenberg form
   */
  nag_zgghrd(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)
    {
      Vprintf("Error from nag_zgghrd (f08wsc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  /* Matrix A in generalized Hessenberg form */
  /* nag_gen_complx_mat_print_comp (x04dbc), see above. */
  nag_gen_complx_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
                                n, a, pda, Nag_BracketForm, "%7.3f",
                                "Matrix A in Hessenberg form",
                                Nag_IntegerLabels, 0, Nag_IntegerLabels, 0, 80,
                                0, 0, &fail);
  if (fail.code != NE_NOERROR)
    {
      Vprintf("Error from nag_gen_complx_mat_print_comp (x04dbc).\n%s\n",
              fail.message);
      exit_status = 1;
      goto END;
    }
  Vprintf("\n");
  /* Matrix B in generalized Hessenberg form */
  /* nag_gen_complx_mat_print_comp (x04dbc), see above. */
  nag_gen_complx_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
                                n, b, pdb, Nag_BracketForm, "%7.3f",
                                "Matrix B is triangular",
                                Nag_IntegerLabels, 0, Nag_IntegerLabels, 0, 80,
                                0, 0, &fail);
  if (fail.code != NE_NOERROR)
    {
      Vprintf("Error from nag_gen_complx_mat_print_comp (x04dbc).\n%s\n",
              fail.message);
      exit_status = 1;
      goto END;
    }

  /* Compute the generalized Schur form */
  /* nag_zhgeqz (f08xsc).
   * Eigenvalues and generalized Schur factorization of
   * complex generalized upper Hessenberg form reduced from a
   * pair of complex general matrices
   */
  nag_zhgeqz(order, Nag_EigVals, Nag_NotQ, Nag_NotZ, n, ilo, ihi, a,
             pda, b, pdb, alpha, beta, q, 1, z, 1, &fail);
  if (fail.code != NE_NOERROR)
    {
      Vprintf("Error from nag_zhgeqz (f08xsc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  /* Print the generalized eigenvalues */
  Vprintf("\n Generalized eigenvalues\n");
  for (i = 0; i < n; ++i)
    {
      if (beta[i].re != 0.0 || beta[i].im != 0.0)
        {
          /* nag_complex_divide (a02cdc).
           * Quotient of two complex numbers
           */
          e = nag_complex_divide(alpha[i], beta[i]);

          Vprintf(" %4ld     (%7.3f,%7.3f)\n", i+1, e.re, e.im);
        }
      else
        Vprintf(" %4ld     Infinite eigenvalue\n", i+1);
    }
 END:
  if (a) NAG_FREE(a);
  if (alpha) NAG_FREE(alpha);
  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;
}