/* nag_zggevx (f08wpc) Example Program.
 *
 * NAGPRODCODE Version.
 *
 * Copyright 2016 Numerical Algorithms Group.
 *
 * Mark 26, 2016.
 */

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

int main(void)
{
  /* Scalars */
  Complex z;
  double abnorm, abnrm, bbnrm, eps, small, tol;
  Integer i, ihi, ilo, j, n, pda, pdb, pdvl, pdvr;
  Integer exit_status = 0;

  /* Arrays */
  Complex *a = 0, *alpha = 0, *b = 0, *beta = 0, *vl = 0, *vr = 0;
  double *lscale = 0, *rconde = 0, *rcondv = 0, *rscale = 0;
  char nag_enum_arg[40];

  /* Nag Types */
  NagError fail;
  Nag_OrderType order;
  Nag_LeftVecsType jobvl;
  Nag_RightVecsType jobvr;
  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_zggevx (f08wpc) Example Program Results\n");

  /* Skip heading in data file */
  scanf("%*[^\n]");
  scanf("%" NAG_IFMT "%*[^\n]", &n);
  if (n < 0) {
    printf("Invalid n\n");
    exit_status = 1;
    goto END;
  }
  scanf(" %39s%*[^\n]", nag_enum_arg);
  /* nag_enum_name_to_value (x04nac).
   * Converts NAG enum member name to value
   */
  jobvl = (Nag_LeftVecsType) nag_enum_name_to_value(nag_enum_arg);
  scanf(" %39s%*[^\n]", nag_enum_arg);
  jobvr = (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);

  pda = n;
  pdb = n;
  pdvl = (jobvl == Nag_LeftVecs ? n : 1);
  pdvr = (jobvr == Nag_RightVecs ? n : 1);

  /* Allocate memory */
  if (!(a = NAG_ALLOC(n * n, Complex)) ||
      !(b = NAG_ALLOC(n * n, Complex)) ||
      !(alpha = NAG_ALLOC(n, Complex)) ||
      !(beta = NAG_ALLOC(n, Complex)) ||
      !(vl = NAG_ALLOC(pdvl * pdvl, Complex)) ||
      !(vr = NAG_ALLOC(pdvr * pdvr, Complex)) ||
      !(lscale = NAG_ALLOC(n, double)) ||
      !(rconde = NAG_ALLOC(n, double)) ||
      !(rcondv = NAG_ALLOC(n, double)) || !(rscale = NAG_ALLOC(n, double)))
  {
    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]");

  /* Solve the generalized eigenvalue problem using nag_zggevx (f08wpc). */
  nag_zggevx(order, Nag_BalanceBoth, jobvl, jobvr, sense, n, a, pda, b, pdb,
             alpha, beta, vl, pdvl, vr, pdvr, &ilo, &ihi, lscale, rscale,
             &abnrm, &bbnrm, rconde, rcondv, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_zggevx (f08wpc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* nag_real_safe_small_number (x02amc), nag_machine_precision (x02ajc) */
  eps = nag_machine_precision;
  small = nag_real_safe_small_number;
  if (abnrm == 0.0)
    abnorm = ABS(bbnrm);
  else if (bbnrm == 0.0)
    abnorm = ABS(abnrm);
  else if (ABS(abnrm) >= ABS(bbnrm))
    abnorm = ABS(abnrm) * sqrt(1.0 + (bbnrm / abnrm) * (bbnrm / abnrm));
  else
    abnorm = ABS(bbnrm) * sqrt(1.0 + (abnrm / bbnrm) * (abnrm / bbnrm));

  tol = eps * abnorm;

  /* Print out eigenvalues and associated condition number and bounds */
  if (sense != Nag_NotRCond)
    printf("\n R = Reciprocal condition number, E = Error bound\n\n");
  printf("%22s", "Eigenvalues");
  if (sense == Nag_RCondEigVals || sense == Nag_RCondBoth)
    printf("%15s%10s", "R", "E");
  printf("\n");
  for (j = 0; j < n; ++j) {
    /* Print out information on the j-th eigenvalue */
    if (nag_complex_abs(alpha[j]) * small >= nag_complex_abs(beta[j])) {
      printf("%2" NAG_IFMT " is numerically infinite or undetermined\n",
             j + 1);
      printf("   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("%2" NAG_IFMT " (%13.4e, %13.4e)", j + 1, z.re, z.im);
      if (sense == Nag_RCondEigVals || sense == Nag_RCondBoth) {
        printf(" %10.1e", rconde[j]);
        if (rconde[j] > 0.0)
          printf(" %9.1e", tol / rconde[j]);
        else
          printf(" infinite");
      }
      printf("\n");
    }
  }

  /* Print out information on the eigenvectors as requested */
  if (jobvl == Nag_LeftVecs) {
    printf("\n");
    /* Print left eigenvectors using nag_gen_complx_mat_print (x04dac). */
    fflush(stdout);
    nag_gen_complx_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
                             n, vl, pdvl, "    Left eigenvectors (columns)",
                             0, &fail);
  }
  if (jobvr == Nag_RightVecs && fail.code == NE_NOERROR) {
    printf("\n");
    /* Print rightt eigenvectors using nag_gen_complx_mat_print (x04dac). */
    fflush(stdout);
    nag_gen_complx_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
                             n, vr, pdvr, "    Right eigenvectors (columns)",
                             0, &fail);
  }
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_gen_complx_mat_print (x04dac).\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }
  if (sense == Nag_RCondEigVecs || sense == Nag_RCondBoth) {
    printf("%2s", "R");
    for (j = 0; j < n; ++j)
      printf(" %8.1e", rcondv[j]);
    printf("\n%2s", "E");
    for (j = 0; j < n; ++j) {
      if (rcondv[j] > 0.0)
        printf(" %8.1e", tol / rcondv[j]);
      else
        printf(" infinite");
    }
    printf("\n");
  }

END:
  NAG_FREE(a);
  NAG_FREE(b);
  NAG_FREE(alpha);
  NAG_FREE(beta);
  NAG_FREE(vl);
  NAG_FREE(vr);
  NAG_FREE(lscale);
  NAG_FREE(rconde);
  NAG_FREE(rcondv);
  NAG_FREE(rscale);

  return exit_status;
}