/* nag_zgebal (f08nvc) 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, j, m, n, pda, pdh, pdvr;
  Integer  scale_len, tau_len, w_len;
  Integer  exit_status=0;
  NagError fail;
  Nag_OrderType order;
  /* Arrays */
  Complex *a=0, *h=0, *tau=0, *vl=0, *vr=0, *w=0;
  double  *scale=0;
  Nag_Boolean *select=0;

#ifdef NAG_COLUMN_MAJOR
#define A(I,J) a[(J-1)*pda + I - 1]
#define H(I,J) h[(J-1)*pdh + I - 1]
#define VR(I,J) vr[(J-1)*pdvr + I - 1]
  order = Nag_ColMajor;
#else
#define A(I,J) a[(I-1)*pda + J - 1]
#define H(I,J) h[(I-1)*pdh + J - 1]
#define VR(I,J) vr[(I-1)*pdvr + J - 1]
  order = Nag_RowMajor;
#endif

  INIT_FAIL(fail);
  Vprintf("nag_zgebal (f08nvc) Example Program Results\n\n");

  /* Skip heading in data file */
  Vscanf("%*[^\n] ");
  Vscanf("%ld%*[^\n] ", &n);
#ifdef NAG_COLUMN_MAJOR
  pda = n;
  pdh = n;
  pdvr = n;
#else
  pda = n;
  pdh = n;
  pdvr = n;
#endif
  scale_len = n;
  tau_len = n;
  w_len = n;

  /* Allocate memory */
  if ( !(a = NAG_ALLOC(n * n, Complex)) ||
       !(h = NAG_ALLOC(n * n, Complex)) ||
       !(scale = NAG_ALLOC(scale_len, double)) ||
       !(tau = NAG_ALLOC(tau_len, Complex)) ||
       !(vl = NAG_ALLOC(1 * 1, Complex)) ||
       !(vr = NAG_ALLOC(n * n, Complex)) ||
       !(w = NAG_ALLOC(w_len, Complex)) ||
       !(select = NAG_ALLOC(1, Nag_Boolean)) )
    {
      Vprintf("Allocation failure\n");
      exit_status = -1;
      goto END;
    }

  /* Read 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] ");

  /* Balance A */
  /* nag_zgebal (f08nvc).
   * Balance complex general matrix
   */
  nag_zgebal(order, Nag_DoBoth, n, a, pda, &ilo, &ihi, scale, &fail);
  if (fail.code != NE_NOERROR)
    {
      Vprintf("Error from nag_zgebal (f08nvc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  /* Reduce A to upper Hessenberg form H = (Q**H)*A*Q */
  /* nag_zgehrd (f08nsc).
   * Unitary reduction of complex general matrix to upper
   * Hessenberg form
   */
  nag_zgehrd(order, n, ilo, ihi, a, pda, tau, &fail);
  if (fail.code != NE_NOERROR)
    {
      Vprintf("Error from nag_zgehrd (f08nsc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  /* Copy A to H and VR */
  for (i = 1; i <= n; ++i)
    {
      for (j = 1; j <= n; ++j)
        {
          H(i,j).re = A(i,j).re;
          H(i,j).im = A(i,j).im;
          VR(i,j).re = A(i,j).re;
          VR(i,j).im = A(i,j).im;
        }
    }

  /* Form Q explicitly, storing the result in VR */
  /* nag_zunghr (f08ntc).
   * Generate unitary transformation matrix from reduction to
   * Hessenberg form determined by nag_zgehrd (f08nsc)
   */
  nag_zunghr(order, n, 1, n, vr, pdvr, tau, &fail);
  if (fail.code != NE_NOERROR)
    {
      Vprintf("Error from nag_zunghr (f08ntc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  /* Calculate the eigenvalues and Schur factorization of A */
  /* nag_zhseqr (f08psc).
   * Eigenvalues and Schur factorization of complex upper
   * Hessenberg matrix reduced from complex general matrix
   */
  nag_zhseqr(order, Nag_Schur, Nag_UpdateZ, n, ilo, ihi, h, pdh,
             w, vr, pdvr, &fail);
  if (fail.code != NE_NOERROR)
    {
      Vprintf("Error from nag_zhseqr (f08psc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }
  Vprintf(" Eigenvalues\n");
  for (i = 0; i < n; ++i)
    Vprintf(" (%7.4f,%7.4f)", w[i].re, w[i].im);
  Vprintf("\n");
  /* Calculate the eigenvectors of A, storing the result in VR */
  /* nag_ztrevc (f08qxc).
   * Left and right eigenvectors of complex upper triangular
   * matrix
   */
  nag_ztrevc(order, Nag_RightSide, Nag_BackTransform, select, n,
             h, pdh, vl, 1, vr, pdvr, n, &m, &fail);
  if (fail.code != NE_NOERROR)
    {
      Vprintf("Error from nag_ztrevc (f08qxc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }
  /* nag_zgebak (f08nwc).
   * Transform eigenvectors of complex balanced matrix to
   * those of original matrix supplied to nag_zgebal (f08nvc)
   */
  nag_zgebak(order, Nag_DoBoth, Nag_RightSide, n, ilo, ihi, scale,
             m, vr, pdvr, &fail);
  if (fail.code != NE_NOERROR)
    {
      Vprintf("Error from nag_zgebak (f08nwc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  /* Print eigenvectors */
  Vprintf("\n");
  /* nag_gen_complx_mat_print_comp (x04dbc).
   * Print complex general matrix (comprehensive)
   */
  nag_gen_complx_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
                                m, vr, pdvr, Nag_BracketForm, "%7.4f",
                                "Contents of array VR", 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;
    }
 END:
  if (a) NAG_FREE(a);
  if (h) NAG_FREE(h);
  if (scale) NAG_FREE(scale);
  if (tau) NAG_FREE(tau);
  if (vl) NAG_FREE(vl);
  if (vr) NAG_FREE(vr);
  if (w) NAG_FREE(w);
  if (select) NAG_FREE(select);

  return exit_status;
}