/* nag_tsa_trans_hessenberg_controller (g13exc) Example Program.
 *
 * Copyright 2022 Numerical Algorithms Group
 *
 * Mark 28.3, 2022.
 */

#include <nag.h>
#include <stdio.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_tsa_trans_hessenberg_controller (g13exc) Example Program Results\n");

  /* Skip the heading in the data file and read the data. */
  scanf("%*[^\n]");
  scanf("%" NAG_IFMT "%" NAG_IFMT "", &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) /* Initialize 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_tsa_trans_hessenberg_controller (g13exc).
   * Unitary state-space transformation to reduce (BA) to
   * lower or upper controller Hessenberg form
   */
  nag_tsa_trans_hessenberg_controller(n, m, reduceto, a, tda, b, tdb, u, tdu,
                                      &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_tsa_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:
  NAG_FREE(a);
  NAG_FREE(b);
  NAG_FREE(u);
  return exit_status;
}