/* nag_zggevx (f08wpc) Example Program.
 *
 * Copyright 2017 Numerical Algorithms Group.
 *
 * Mark 26.2, 2017.
 */

#include <stdio.h>
#include <math.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <naga02.h>
#include <nagf08.h>
#include <nagm01.h>
#include <nagx02.h>

#ifdef __cplusplus
extern "C"
{
#endif
  static Integer NAG_CALL compare(const Nag_Pointer a, const Nag_Pointer b);
  static Integer normalize_vectors(Integer n, Complex v[], Complex e[],
                                   size_t rank[]);
  static Integer sort_values (Integer n, Complex alpha[],
                              Complex beta[], Complex e[],
                              double rconde[], double rcondv[],
                              size_t rank[], double emod[]);
#ifdef __cplusplus
}
#endif

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, verbose = 0;

  /* Arrays */
  Complex *a = 0, *alpha = 0, *b = 0, *beta = 0, *vl = 0, *vr = 0;
  Complex *e = 0;
  double *emod = 0;
  size_t *rank = 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)) ||
      !(e = NAG_ALLOC(n, Complex)) ||
      !(emod = NAG_ALLOC(n, double)) ||
      !(rank = NAG_ALLOC(n, size_t)) ||
      !(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 (verbose && sense != Nag_NotRCond)
    printf("\n R = Reciprocal condition number, E = Error bound\n");
  printf("\n");
  printf("%22s", "Eigenvalues");

  /* Sort values by decreasing modulus and store in e[] */
  exit_status=sort_values(n, alpha, beta, e, rconde, rcondv, rank, emod);

  if (verbose && (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 (verbose && (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");
    }
  }

  if (jobvl == Nag_LeftVecs) {
    exit_status = normalize_vectors(n, vl, e, rank);
  }
  if (jobvr == Nag_RightVecs && exit_status == 0) {
    exit_status = normalize_vectors(n, vr, e, rank);
  }

  /* 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 right 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 (verbose && (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);
  NAG_FREE(e);
  NAG_FREE(emod);
  NAG_FREE(rank);

  return exit_status;
}

static Integer normalize_vectors(Integer n, Complex v[], Complex e[],
                                 size_t rank[])
{

  Complex           scal;
  double            r, rr;
  Integer           errors = 0, i, j, k;
  NagError          fail;

  INIT_FAIL(fail);

#ifdef NAG_COLUMN_MAJOR
#define V(I, J)  v[(J-1)*n + I - 1]
#else
#define V(I, J)  v[(I-1)*n + J - 1]
#endif
  /* Re-normalize the eigenvectors, largest absolute element real */
  for (i=1; i<=n; i++) {
    k = 0;
    r = -1.0;
    for (j=1; j<=n; j++) {
      rr = nag_complex_abs(V(j,i));
      if (rr>r) {
        r = rr;
        k = j;
      }
    }
    scal.re = V(k,i).re/(r*r);
    scal.im = -V(k,i).im/(r*r);
    for (j=1; j<=n; j++) {
      V(j,i) = nag_complex_multiply(V(j,i),scal);
    }
    V(k,i).re = 1.0;
    V(k,i).im = 0.0;
  }
  /* Sort eigenvectors according to rank */
  for (i=1; i<=n; i++) {
    for (j=1; j<=n; j++)
      e[j-1] = V(i,j);

    /* Sort eigenvector row i using nag_reorder_vector (m01esc). */
    nag_reorder_vector((Pointer) e, (size_t) n, sizeof(Complex),
                       (ptrdiff_t) sizeof(Complex), rank, &fail);
    if (fail.code != NE_NOERROR) {
      printf("Error from nag_reorder_vector (m01esc).\n%s\n", fail.message);
      errors = 5;
      goto END;
    }
    for (j=1; j<=n; j++)
      V(i,j) = e[j-1];
  }
#undef V
 END:
  return errors;
}

static Integer sort_values (Integer n, Complex alpha[], Complex beta[],
                            Complex e[], double rconde[], double rcondv[],
                            size_t rank[], double emod[])
{
  Integer       i, exit_status = 0;
  NagError      fail;

  INIT_FAIL(fail);

  for (i = 0; i < n; ++i) {
    /* nag_complex_divide (a02cdc): Quotient of two complex numbers;
     * nag_complex_abs (a02ddc): Moduli of complex number.
     */
    e[i] = nag_complex_divide(alpha[i], beta[i]);
    emod[i] = nag_complex_abs(e[i]);
  }
  /* Rank sort eigenvalues by absolute values using
   * nag_rank_sort (m01dsc).
   */
  nag_rank_sort((Pointer) emod, (size_t) n, (ptrdiff_t) (sizeof(double)),
                compare, Nag_Descending, rank, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_rank_sort (m01dsc).\n%s\n", fail.message);
    exit_status = 10;
    goto END;
  }
  /* Turn ranks into indices using nag_make_indices (m01zac). */
  nag_make_indices(rank, (size_t) n, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_make_indices (m01zac).\n%s\n", fail.message);
    exit_status = 11;
    goto END;
  }
  /* Sort eigenvalues using nag_reorder_vector (m01esc). */
  nag_reorder_vector((Pointer) e, (size_t) n, sizeof(Complex),
                     (ptrdiff_t) sizeof(Complex), rank, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_reorder_vector (m01esc).\n%s\n", fail.message);
    exit_status = 12;
    goto END;
  }
  nag_reorder_vector((Pointer) alpha, (size_t) n, sizeof(Complex),
                     (ptrdiff_t) sizeof(Complex), rank, &fail);
  nag_reorder_vector((Pointer) beta, (size_t) n, sizeof(Complex),
                     (ptrdiff_t) sizeof(Complex), rank, &fail);
  nag_reorder_vector((Pointer) rconde, (size_t) n, sizeof(double),
                     (ptrdiff_t) sizeof(double), rank, &fail);
  nag_reorder_vector((Pointer) rcondv, (size_t) n, sizeof(double),
                     (ptrdiff_t) sizeof(double), rank, &fail);
 END:
  return exit_status;
}

static Integer NAG_CALL compare(const Nag_Pointer a, const Nag_Pointer b)
{
  double x = *((const double *) a) - *((const double *) b);
  return (x < 0.0 ? -1 : (x == 0.0 ? 0 : 1));
}