/* nag_dgebal (f08nhc) Example Program.
 *
 * Copyright 2014 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       firstnz, i, ihi, ilo, j, m, n, pda, pdh, pdvr;
  Integer       scale_len, tau_len, wi_len, wr_len;
  Integer       exit_status = 0;
  NagError      fail;
  Nag_OrderType order;
  /* Arrays */
  double        *a = 0, *h = 0, *scale = 0, *tau = 0, *vl = 0, *vr = 0;
  double        *wi = 0, *wr = 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);

  printf("nag_dgebal (f08nhc) Example Program Results\n\n");

  /* Skip heading in data file */
  scanf("%*[^\n] ");
  scanf("%ld%*[^\n] ", &n);

  pda = n;
  pdh = n;
  pdvr = n;
  scale_len = n;
  tau_len = n;
  wi_len = n;
  wr_len = n;

  /* Allocate memory */
  if (!(a = NAG_ALLOC(n * n, double)) ||
      !(h = NAG_ALLOC(n * n, double)) ||
      !(scale = NAG_ALLOC(scale_len, double)) ||
      !(tau = NAG_ALLOC(tau_len, double)) ||
      !(vl = NAG_ALLOC(1 * 1, double)) ||
      !(vr = NAG_ALLOC(n * n, double)) ||
      !(wi = NAG_ALLOC(wi_len, double)) ||
      !(wr = NAG_ALLOC(wr_len, double)) ||
      !(select = NAG_ALLOC(1, Nag_Boolean)))
    {
      printf("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)
        scanf("%lf", &A(i, j));
    }
  scanf("%*[^\n] ");

  /* Balance A */
  /* nag_dgebal (f08nhc).
   * Balance real general matrix
   */
  nag_dgebal(order, Nag_DoBoth, n, a, pda, &ilo, &ihi, scale, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_dgebal (f08nhc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  /* Reduce A to upper Hessenberg form H = (Q**T)*A*Q */
  /* nag_dgehrd (f08nec).
   * Orthogonal reduction of real general matrix to upper
   * Hessenberg form
   */
  nag_dgehrd(order, n, ilo, ihi, a, pda, tau, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_dgehrd (f08nec).\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) = A(i, j);
          VR(i, j) = A(i, j);
        }
    }

  /* Form Q explicitly, storing the result in VR */
  /* nag_dorghr (f08nfc).
   * Generate orthogonal transformation matrix from reduction
   * to Hessenberg form determined by nag_dgehrd (f08nec)
   */
  nag_dorghr(order, n, 1, n, vr, pdvr, tau, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_dorghr (f08nfc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  /* Calculate the eigenvalues and Schur factorization of A */
  /* nag_dhseqr (f08pec).
   * Eigenvalues and Schur factorization of real upper
   * Hessenberg matrix reduced from real general matrix
   */
  nag_dhseqr(order, Nag_Schur, Nag_UpdateZ, n, ilo, ihi, h, pdh,
             wr, wi, vr, pdvr, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_dhseqr (f08pec).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }
  printf(" Eigenvalues\n");
  for (i = 1; i <= n; ++i)
    printf("(%8.4f,%8.4f)\n", wr[i - 1], wi[i - 1]);
  /* Calculate the eigenvectors of A, storing the result in VR */
  /* nag_dtrevc (f08qkc).
   * Left and right eigenvectors of real upper
   * quasi-triangular matrix
   */
  nag_dtrevc(order, Nag_RightSide, Nag_BackTransform, select, n,
             h, pdh, vl, 1, vr, pdvr, n, &m, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_dtrevc (f08qkc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }
  /* nag_dgebak (f08njc).
   * Transform eigenvectors of real balanced matrix to those
   * of original matrix supplied to nag_dgebal (f08nhc)
   */
  nag_dgebak(order, Nag_DoBoth, Nag_RightSide, n, ilo, ihi, scale,
             m, vr, pdvr, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_dgebak (f08njc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }
      
  /* Normalize the left eigenvectors */
  for(j=1; j<=n; j++)
    {
      
      for(i=n; i>=1; i--)
        {
          if(VR(i, j) != 0)
            {
              firstnz = i;
            }
        }
      for(i=n; i>=1; i--)
        {
          VR(i, j) = VR(i, j) / VR(firstnz,j);
        }
    }
  
  /* Print eigenvectors */
  printf("\n");
  /* 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, m, vr,
                         pdvr, "Contents of array VR", 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;
    }
 END:
  NAG_FREE(a);
  NAG_FREE(h);
  NAG_FREE(scale);
  NAG_FREE(tau);
  NAG_FREE(vl);
  NAG_FREE(vr);
  NAG_FREE(wi);
  NAG_FREE(wr);
  NAG_FREE(select);

  return exit_status;
}