/* nag_ztgevc (f08yxc) 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, icols, ihi, ilo, irows, j, m, n,pda, pdb, pdq, pdz;
  Integer  alpha_len, beta_len, scale_len, tau_len, select_len;
  Integer  exit_status=0;
  Complex  e;
  Nag_Boolean  ileft, iright;

  NagError fail;
  Nag_OrderType order;
  /* Arrays */
  Complex *a=0, *alpha=0, *b=0, *beta=0, *q=0, *tau=0, *z=0;
  double  *lscale=0, *rscale=0;
  Nag_Boolean *select=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]
#define Q(I,J) q[(J-1)*pdq + I - 1]
#define Z(I,J) z[(J-1)*pdz + 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]
#define Q(I,J) q[(I-1)*pdq + J - 1]
#define Z(I,J) z[(I-1)*pdz + J - 1]
  order = Nag_RowMajor;
#endif

  INIT_FAIL(fail);
  Vprintf("nag_ztgevc (f08yxc) Example Program Results\n\n");

  /* ILEFT  is TRUE if left  eigenvectors are required */
  /* IRIGHT is TRUE if right eigenvectors are required */
  ileft = Nag_TRUE;
  iright = Nag_TRUE;

  /* Skip heading in data file */
  Vscanf("%*[^\n] ");

  Vscanf("%ld%*[^\n] ", &n);
#ifdef NAG_COLUMN_MAJOR
  pda = n;
  pdb = n;
  pdq = n;
  pdz = n;
#else
  pda = n;
  pdb = n;
  pdq = n;
  pdz = n;
#endif
  alpha_len = n;
  beta_len = n;
  scale_len = n;
  tau_len = n;
  select_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)) ||
      !(lscale = NAG_ALLOC(scale_len, double)) ||
      !(rscale = NAG_ALLOC(scale_len, double)) ||
      !(q = NAG_ALLOC(n * n, Complex)) ||
      !(tau = NAG_ALLOC(tau_len, Complex)) ||
      !(z = NAG_ALLOC(n * n, Complex)) ||
      !(select = NAG_ALLOC(select_len, Nag_Boolean)) )
    {
      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;
    }
  /* 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;
  icols = n + 1 - ilo;
  /* nag_zgeqrf (f08asc).
   * QR factorization of complex general rectangular matrix
   */
  nag_zgeqrf(order, irows, icols, &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, icols, 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;
    }

  /* Initialize Q (if left eigenvectors are required) */
  if (ileft)
    {
      for (i = 1; i <= n; ++i)
        {
          for (j = 1; j <= n; ++j)
            {
              Q(i,j).re = 0.0;
              Q(i,j).im = 0.0;
            }
          Q(i,i).re = 1.0;
        }
      for (i = ilo+1; i <= ilo+irows-1; ++i)
        {
          for (j = ilo; j <= MIN(i,ilo+irows-2); ++j)
            {
              Q(i,j).re = B(i,j).re;
              Q(i,j).im = B(i,j).im;
            }
        }
      /* nag_zungqr (f08atc).
       * Form all or part of unitary Q from QR factorization
       * determined by nag_zgeqrf (f08asc) or nag_zgeqpf (f08bsc)
       */
      nag_zungqr(order, irows, irows, irows, &Q(ilo, ilo), pdq, tau,
                 &fail);
      if (fail.code != NE_NOERROR)
        {
          Vprintf("Error from nag_zungqr (f08atc).\n%s\n", fail.message);
          exit_status = 1;
          goto END;
        }
    }

  /* Initialize Z (if right eigenvectors are required) */
  if (iright)
    {
      for (i = 1; i <= n; ++i)
        {
          for (j = 1; j <= n; ++j)
            {
              Z(i,j).re = 0.0;
              Z(i,j).im = 0.0;
            }
          Z(i,i).re = 1.0;
        }
    }

  /* 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_UpdateSchur, Nag_UpdateZ, n, ilo, ihi, a, pda,
             b, pdb, q, pdq, z, pdz, &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 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;
    }

  /* Compute the generalized Schur form */
  /* The Schur form also gives parameters */
  /* required to compute generalized eigenvalues */
  /* 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_Schur, Nag_AccumulateQ, Nag_AccumulateZ, n, ilo, ihi, a,
             pda, b, pdb, alpha, beta, q, pdq, z, pdz, &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 eigenvalue parameters */
  Vprintf("\n Generalized eigenvalues\n");
  for (i = 1; i <= n; ++i)
    {
      if (beta[i-1].re != 0.0 || beta[i-1].im != 0.0)
        {
          /* nag_complex_divide (a02cdc).
           * Quotient of two complex numbers
           */
          e = nag_complex_divide(alpha[i - 1], beta[i - 1]);
          Vprintf(" %4ld     (%7.3f,%7.3f)\n", i, e.re, e.im);
        }
      else
        Vprintf(" %4ldEigenvalue is infinite\n", i);
    }
  Vprintf("\n");

  /* Compute left and right generalized eigenvectors */
  /* of the balanced matrix */
  /* nag_ztgevc (f08yxc).
   * Left and right eigenvectors of a pair of complex upper
   * triangular matrices
   */
  nag_ztgevc(order, Nag_BothSides, Nag_BackTransform, select, n, a, pda,
             b, pdb, q, pdq, z, pdz, n, &m, &fail);
  if (fail.code != NE_NOERROR)
    {
      Vprintf("Error from nag_ztgevc (f08yxc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }
  if (iright)
    {

      /* Compute right eigenvectors of the original matrix */
      /* nag_zggbak (f08wwc).
       * Transform eigenvectors of a pair of complex balanced
       * matrices to those of original matrix pair supplied to
       * nag_zggbal (f08wvc)
       */
      nag_zggbak(order, Nag_DoBoth, Nag_RightSide, n, ilo, ihi, lscale,
                 rscale, n, z, pdz, &fail);
      if (fail.code != NE_NOERROR)
        {
          Vprintf("Error from nag_zggbak (f08wwc).\n%s\n", fail.message);
          exit_status = 1;
          goto END;
        }

      /* Print the right eigenvectors */
      /* nag_gen_complx_mat_print_comp (x04dbc), see above. */
      nag_gen_complx_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag,
                                    n, n, z, pdz, Nag_BracketForm, "%7.4f",
                                    "Right eigenvectors", 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");
    }

  /* Compute left eigenvectors of the original matrix */
  if (ileft)
    {
      /* nag_zggbak (f08wwc), see above. */
      nag_zggbak(order, Nag_DoBoth, Nag_LeftSide, n, ilo, ihi, lscale,
                 rscale, n, q, pdq, &fail);
      if (fail.code != NE_NOERROR)
        {
          Vprintf("Error from nag_zggbak (f08wwc).\n%s\n", fail.message);
          exit_status = 1;
          goto END;
        }

      /* Print the left eigenvectors */
      /* nag_gen_complx_mat_print_comp (x04dbc), see above. */
      nag_gen_complx_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag,
                                    n, n, q, pdq, Nag_BracketForm, "%7.4f",
                                    "Left eigenvectors", 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 (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);
  if (select) NAG_FREE(select);

  return exit_status;
}