/* nag_zggesx (f08xpc) Example Program.
 *
 * Copyright 2014 Numerical Algorithms Group.
 *
 * Mark 25, 2014.
 */

#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>

#ifdef __cplusplus
extern "C" {
#endif
  static Nag_Boolean NAG_CALL selctg(const Complex a, const Complex b);
#ifdef __cplusplus
}
#endif

int main(void)
{

  /* Scalars */
  Complex             alph, bet, z;
  double              abnorm, norma, normb, normd, norme, eps, tol;
  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, *d = 0; 
  Complex             *e = 0, *vsl = 0, *vsr = 0;
  double              rconde[2], rcondv[2];
  char                nag_enum_arg[40];

  /* Nag Types */
  NagError            fail;
  Nag_OrderType       order;
  Nag_LeftVecsType    jobvsl;
  Nag_RightVecsType   jobvsr;
  Nag_SortEigValsType sort = Nag_SortEigVals;
  Nag_RCondType       sense;

#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_zggesx (f08xpc) 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;
      return exit_status;
    }
  scanf(" %39s%*[^\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(" %39s%*[^\n]", nag_enum_arg);
  jobvsr = (Nag_RightVecsType) nag_enum_name_to_value(nag_enum_arg);
  scanf(" %39s%*[^\n]", nag_enum_arg);
  sense = (Nag_RCondType) 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 = n;
  pde = n;
  /* 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]");

  /* Copy matrices A and B to matrices D and E using nag_zge_copy (f16tfc),
   * Complex valued general matrix copy.
   * The copies will be used as comparison against reconstructed matrices.
   */
  nag_zge_copy(order, Nag_NoTrans, n, n, a, pda, d, pdd, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_zge_copy (f16tfc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }
  nag_zge_copy(order, Nag_NoTrans, n, n, b, pdb, e, pde, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_zge_copy (f16tfc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

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

  /* nag_gen_complx_mat_print_comp (x04dbc): Print matrices A and B. */
  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;
    }
  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_zggesx (f08xpc). */
  nag_zggesx(order, jobvsl, jobvsr, sort, selctg, sense, n, a, pda, b, pdb,
             &sdim, alpha, beta, vsl, pdvsl, vsr, pdvsr, rconde, rcondv, &fail);

  if (fail.code != NE_NOERROR && fail.code != NE_SCHUR_REORDER_SELECT)
    {
      printf("Error from nag_zggesx (f08xpc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  /* 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 (E) 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;
    }

  /* nag_zge_norm (f16uac): Find norms of difference matrices D and E. */
  nag_zge_norm(order, Nag_FrobeniusNorm, n, n, d, pdd, &normd, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_zge_norm (f16uac).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }
  nag_zge_norm(order, Nag_FrobeniusNorm, 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;
    }

  /* Get the machine precision, using nag_machine_precision (x02ajc) */
  eps = nag_machine_precision;
  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;
      goto END;
    }

  /* Print details on eigenvalues */
  printf("Number of sorted eigenvalues = %4ld\n\n", sdim);
  if (fail.code == NE_SCHUR_REORDER_SELECT) {
    printf("*** Note that rounding errors mean that leading eigenvalues in the"
           " generalized\n    Schur form no longer satisfy selctg = Nag_TRUE"
           "\n\n");
  } else {
    printf("The selected eigenvalues are:\n");
    for (i=0;i<sdim;i++) {
      if (beta[i].re != 0.0 || beta[i].im != 0.0) {
        z = nag_complex_divide(alpha[i], beta[i]);
        printf("%3ld (%13.4e, %13.4e)\n", i+1, z.re, z.im);
      }
      else
        printf("%3ld Eigenvalue is infinite\n", i + 1);
    }
  }

  abnorm = sqrt(pow(norma, 2) + pow(normb, 2));
  tol = eps*abnorm;

  if (sense==Nag_RCondEigVals || sense==Nag_RCondBoth) {
    /* Print out the reciprocal condition number and error bound */
    printf("\n");
    printf("For the selected eigenvalues,\nthe reciprocals of projection "
           "norms onto the deflating subspaces are\n");
    printf(" for left  subspace, rcond = %10.1e\n for right subspace, rcond = "
           "%10.1e\n\n", rconde[0], rconde[1]);
    printf(" asymptotic error bound    = %10.1e\n\n", tol / rconde[0]);
  }
  if (sense==Nag_RCondEigVecs || sense==Nag_RCondBoth) {
    /* Print out the reciprocal condition numbers and error bound. */
     printf("For the left and right deflating subspaces,\n");
    printf("reciprocal condition numbers are:\n");
    printf(" for left  subspace, rcond = %10.1e\n for right subspace, rcond = "
           "%10.1e\n\n", rcondv[0], rcondv[1]);
    printf(" approximate error bound   = %10.1e\n", tol / rcondv[1]);
  }
  
 END:
  NAG_FREE(a);
  NAG_FREE(b);
  NAG_FREE(c);
  NAG_FREE(d);
  NAG_FREE(e);
  NAG_FREE(alpha);
  NAG_FREE(beta);
  NAG_FREE(vsl);
  NAG_FREE(vsr);

  return exit_status;
}

static Nag_Boolean NAG_CALL selctg(const Complex a, const Complex b)
{
  /* Boolean function selctg for use with nag_zggesx (f08xpc)
   * Returns the value Nag_TRUE if the absolute value of the eigenvalue
   * a/b < 6.0
   */

  return (nag_complex_abs(a) < 6.0*nag_complex_abs(b) ? Nag_TRUE : Nag_FALSE);
}