/* nag_trans_hessenberg_controller (g13exc) Example Program.
 *
 * Copyright 1993 Numerical Algorithms Group
 *
 * Mark 3, 1993
 * Mark 8 revised, 2004.
 */

#include <nag.h>
#include <stdio.h>
#include <nag_stdlib.h>
#include <nagg13.h>

#define A(I, J) a[(I) *tda + J]
#define B(I, J) b[(I) *tdb + J]
#define U(I, J) u[(I) *tdu + J]
int main(void)
{
  Integer            exit_status = 0, i, j, m, n, tda, tdb, tdu;
  double             *a = 0, *b = 0, one = 1.0, *u = 0, zero = 0.0;
  Nag_ControllerForm reduceto;
  NagError           fail;

  INIT_FAIL(fail);

  printf(
          "nag_trans_hessenberg_controller (g13exc) Example Program Results\n");

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

  scanf("%ld%ld", &n, &m);
  if (n >= 1 || m >= 1)
    {
      if (!(a = NAG_ALLOC(n*n, double)) ||
          !(b = NAG_ALLOC(n*m, double)) ||
          !(u = NAG_ALLOC(n*n, double)))
        {
          printf("Allocation failure\n");
          exit_status = -1;
          goto END;
        }
      tda = n;
      tdb = m;
      tdu = n;
    }
  else
    {
      printf("Invalid n or m.\n");
      exit_status = 1;
      return exit_status;
    }
  reduceto = Nag_UH_Controller;

  for (j = 0; j < n; ++j)
    for (i = 0; i < n; ++i)
      scanf("%lf", &A(i, j));
  for (j = 0; j < m; ++j)
    for (i = 0; i < n; ++i)
      scanf("%lf", &B(i, j));

  if (u) /* Initialise U as the identity matrix. */
    for (i = 0; i < n; ++i)
      {
        for (j = 0; j < n; ++j)
          U(i, j) = zero;
        U(i, i) = one;
      }

  /* Reduce the pair (B,A) to reduceto controller Hessenberg form. */
  /* nag_trans_hessenberg_controller (g13exc).
   * Unitary state-space transformation to reduce (BA) to
   * lower or upper controller Hessenberg form
   */
  nag_trans_hessenberg_controller(n, m, reduceto, a, tda, b, tdb, u, tdu,
                                  &fail);
  if (fail.code != NE_NOERROR)
    {
      printf(
              "Error from nag_trans_hessenberg_controller (g13exc).\n%s\n",
              fail.message);
      exit_status = 1;
      goto END;
    }

  printf("\nThe transformed state transition matrix is\n\n");
  for (i = 0; i < n; ++i)
    {
      for (j = 0; j < n; ++j)
        printf("%8.4f ", A(i, j));
      printf("\n");
    }

  printf("\nThe transformed input matrix is\n\n");
  for (i = 0; i < n; ++i)
    {
      for (j = 0; j < m; ++j)
        printf("%8.4f ", B(i, j));
      printf("\n");
    }
  if (u)
    {
      printf("\nThe matrix that reduces (B,A) to ");
      printf("controller Hessenberg form is\n\n");
      for (i = 0; i < n; ++i)
        {
          for (j = 0; j < n; ++j)
            printf("%8.4f ", U(i, j));
          printf("\n");
        }
    }
 END:
  if (a) NAG_FREE(a);
  if (b) NAG_FREE(b);
  if (u) NAG_FREE(u);
  return exit_status;
}