/* nag_zgges (f08xnc) Example Program.
 *
 * Copyright 2011 Numerical Algorithms Group.
 *
 * Mark 23, 2011.
 */

#include <stdio.h>
#include <math.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <naga02.h>
#include <nagf08.h>
#include <nagf16.h>
#include <nagx02.h>
#include <nagx04.h>

int main(void)
{
  /* Scalars */
  Complex           alph, bet, z;
  double            norma, normb, normd, norme, eps, small;
  Integer           i, j, n, sdim, pda, pdb, pdc, pdd, pde, pdvsl, pdvsr;
  Integer           exit_status = 0;

  /* Arrays */
  Complex           *a = 0, *alpha = 0, *b = 0, *beta = 0, *c = 0;
  Complex           *d = 0, *e = 0, *vsl = 0, *vsr = 0;
  Nag_LeftVecsType  jobvsl;
  Nag_RightVecsType jobvsr;
  char              nag_enum_arg[40];

  /* Nag Types */
  NagError          fail;
  Nag_OrderType     order;


#ifdef NAG_COLUMN_MAJOR
#define A(I, J) a[(J-1)*pda + I - 1]
#define B(I, J) b[(J-1)*pdb + 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]
  order = Nag_RowMajor;
#endif

  INIT_FAIL(fail);

  printf("nag_zgges (f08xnc) Example Program Results\n\n");

  /* Skip heading in data file */
  scanf("%*[^\n]");
  scanf("%ld%*[^\n]", &n);
  if (n < 0)
    {
      printf("Invalid n\n");
      exit_status = 1;
      goto END;
    }
  scanf(" %s%*[^\n]", nag_enum_arg);
  /* nag_enum_name_to_value(x04nac).
   * Converts NAG enum member name to value
   */
  jobvsl = (Nag_LeftVecsType) nag_enum_name_to_value(nag_enum_arg);
  scanf(" %s%*[^\n]", nag_enum_arg);
  jobvsr = (Nag_RightVecsType) nag_enum_name_to_value(nag_enum_arg);

  pdvsl = (jobvsl==Nag_LeftVecs?n:1);
  pdvsr = (jobvsr==Nag_RightVecs?n:1);
  pda = n;
  pdb = n;
  pdc = n;
  pdd = pda;
  pde = pdb;
  /* Allocate memory */
  if (!(a = NAG_ALLOC(n*n, Complex)) ||
      !(b = NAG_ALLOC(n*n, Complex)) ||
      !(c = NAG_ALLOC(n*n, Complex)) ||
      !(d = NAG_ALLOC(n*n, Complex)) ||
      !(e = NAG_ALLOC(n*n, Complex)) ||
      !(alpha = NAG_ALLOC(n, Complex)) ||
      !(beta = NAG_ALLOC(n, Complex)) ||
      !(vsl = NAG_ALLOC(pdvsl*pdvsl, Complex)) ||
      !(vsr = NAG_ALLOC(pdvsr*pdvsr, Complex)))
    {
      printf("Allocation failure\n");
      exit_status = -1;
      goto END;
    }

  /* Read in the matrices A and B */
  for (i = 1; i <= n; ++i)
      for (j = 1; j <= n; ++j)
        scanf(" ( %lf , %lf )", &A(i, j).re, &A(i, j).im);
  scanf("%*[^\n]");

  for (i = 1; i <= n; ++i)
      for (j = 1; j <= n; ++j)
        scanf(" ( %lf , %lf )", &B(i, j).re, &B(i, j).im);
  scanf("%*[^\n]");

  /* nag_zge_norm (f16uac): Find norms of input matrices A and B. */
  nag_zge_norm(order, Nag_OneNorm, n, n, a, pda, &norma, &fail);
  nag_zge_norm(order, Nag_OneNorm, n, n, b, pdb, &normb, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_dge_norm (f16rac).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  /* Copy Matrices A and B to D and E respectively: nag_zge_copy (f16tfc),
   * Complex valued general matrix copy.
   */
  nag_zge_copy(order, Nag_NoTrans, n, n, a, pda, d, pdd, &fail);
  nag_zge_copy(order, Nag_NoTrans, n, n, b, pdb, e, pde, &fail);
  
  /* nag_gen_complx_mat_print_comp (x04dbc): Print matrix A */
  fflush(stdout);
  nag_gen_complx_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
                                n, a, pda, Nag_BracketForm, "%6.2f",
                                "Matrix A", Nag_IntegerLabels, 0,
                                Nag_IntegerLabels, 0, 80, 0, 0, &fail);
  printf("\n");
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_gen_complx_mat_print_comp (x04dbc).\n%s\n",
             fail.message);
      exit_status = 1;
      goto END;
    }
  
  /* nag_gen_complx_mat_print_comp (x04dbc): Print matrix B */
  fflush(stdout);
  nag_gen_complx_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
                                n, b, pdb, Nag_BracketForm, "%6.2f",
                                "Matrix B", Nag_IntegerLabels, 0,
                                Nag_IntegerLabels, 0, 80, 0, 0, &fail);
  printf("\n");
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_gen_complx_mat_print_comp (x04dbc).\n%s\n",
             fail.message);
      exit_status = 1;
      goto END;
    }

  /* Find the generalized Schur form using nag_zgges (f08xnc). */
  nag_zgges(order, jobvsl, jobvsr, Nag_NoSortEigVals, Nag_FALSE, n, a, pda, b,
	    pdb, &sdim, alpha, beta, vsl, pdvsl, vsr, pdvsr, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_zgges (f08xnc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  /* Print Eigenvalues */

  /* nag_real_safe_small_number (x02amc), nag_machine_precision (x02ajc) */
  eps = nag_machine_precision;
  small = nag_real_safe_small_number;
  printf("\n     Eigenvalues\n");
  for (j = 0; j < n; ++j)
    {
      printf("%2ld ", j+1);
      if (nag_complex_abs(alpha[j]) * small >=  nag_complex_abs(beta[j]))
	{
	  printf(" numerically infinite or undetermined, alpha = "
		 "(%9.4f, %9.4f), beta = (%9.4f, %9.4f)\n",
		 alpha[j].re, alpha[j].im, beta[j].re, beta[j].im);
	}
      else
	{
	  z = nag_complex_divide(alpha[j], beta[j]);
	  printf(" (%11.4e, %11.4e)\n", z.re, z.im);
	}
    }

  /* Check generalized Schur Form by reconstruction of Schur vectors are
   * available.
   */
  if (jobvsl==Nag_NotLeftVecs || jobvsr==Nag_NotRightVecs)
    {
      /* Cannot check factorization by reconstruction Schur vectors. */
      goto END;
    }

  /* Reconstruct A as Q*S*Z^H and subtract from original (D) using the steps
   * C = Q (Q in vsl) using nag_zge_copy (f16tfc).
   * C = C*S (S in a, upper triangular) using nag_ztrmm (f16zfc).
   * D = D - C*Z^H (Z in vsr) using nag_zgemm (f16zac).
   */
  nag_zge_copy(order, Nag_NoTrans, n, n, vsl, pdvsl, c, pdc, &fail);
  alph = nag_complex(1.0,0.0);
  /* nag_ztrmm (f16zfc)  Triangular complex matrix-matrix multiply. */
  nag_ztrmm(order, Nag_RightSide, Nag_Upper, Nag_NoTrans, Nag_NonUnitDiag, n,
	    n, alph, a, pda, c, pdc, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_ztrmm (f16zfc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  alph = nag_complex(-1.0,0.0);
  bet = nag_complex(1.0,0.0);
  nag_zgemm(order, Nag_NoTrans, Nag_ConjTrans, n, n, n, alph, c, pdc, vsr,
	    pdvsr, bet, d, pdd, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_zgemm (f16zac).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  /* Reconstruct B as Q*T*Z^H and subtract from original (D) using the steps
   * Q = Q*T (Q in vsl, T in b, upper triangular) using nag_ztrmm (f16zfc).
   * E = E - Q*Z^H (Z in vsr) using nag_zgemm (f16zac).
   */
  alph = nag_complex(1.0,0.0);
  /* nag_ztrmm (f16zfc)  Triangular complex matrix-matrix multiply. */
  nag_ztrmm(order, Nag_RightSide, Nag_Upper, Nag_NoTrans, Nag_NonUnitDiag, n,
	    n, alph, b, pdb, vsl, pdvsl, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_ztrmm (f16zfc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }
  alph = nag_complex(-1.0,0.0);
  bet = nag_complex(1.0,0.0);
  nag_zgemm(order, Nag_NoTrans, Nag_ConjTrans, n, n, n, alph, vsl, pdvsl, vsr,
	    pdvsr, bet, e, pde, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_zgemm (f16zac).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  /* Compute norm of difference matrices D and E using 
   * nag_zge_norm (f16uac).
   */
  nag_zge_norm(order, Nag_OneNorm, n, n, d, pdd, &normd, &fail);
  nag_zge_norm(order, Nag_OneNorm, n, n, e, pde, &norme, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_zge_norm (f16uac).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }
  if (MAX(normd,norme) > pow(eps,0.8)*MAX(norma,normb))
    {
      printf("The norm of the error in the reconstructed matrices is greater "
	     "than expected.\nThe Schur factorization has failed.\n");
      exit_status = 1;
    }

 END:
  if (a)     NAG_FREE(a);
  if (b)     NAG_FREE(b);
  if (c)     NAG_FREE(c);
  if (d)     NAG_FREE(d);
  if (e)     NAG_FREE(e);
  if (alpha) NAG_FREE(alpha);
  if (beta)  NAG_FREE(beta);
  if (vsl)   NAG_FREE(vsl);
  if (vsr)   NAG_FREE(vsr);

  return exit_status;
}