/* nag_lapackeig_zggev3 (f08wqc) Example Program.
 *
 * Copyright 2021 Numerical Algorithms Group.
 *
 * Mark 27.2, 2021.
 */

#include <math.h>
#include <nag.h>
#include <stdio.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[], size_t rank[],
                                 const char *title);
static Integer sort_values(Integer n, Complex e[], size_t rank[],
                           double emod[]);
#ifdef __cplusplus
}
#endif

int main(void) {
  /* Scalars */
  Integer i, isinf, 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 *emod = 0;
  size_t *rank = 0;
  char nag_enum_arg[40];

  /* Nag Types */
  NagError fail;
  Nag_OrderType order;
  Nag_LeftVecsType jobvl;
  Nag_RightVecsType jobvr;

  INIT_FAIL(fail);

  printf("nag_lapackeig_zggev3 (f08wqc) 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;
  }

#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
  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);

  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)) || !(alpha = NAG_ALLOC(n, Complex)) ||
      !(b = NAG_ALLOC(n * n, Complex)) || !(beta = 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))) {
    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 Ax = lambda Bx using the
   * level 3 blocked routine nag_lapackeig_zggev3 (f08wqc) which returns:
   *  - eigenvalues as alpha[]./beta[];
   *  - left and right eigenvectors in vl and vr respectively.
   */
  /* Solve the generalized eigenvalue problem using nag_lapackeig_zggev3
   * (f08wqc). */
  nag_lapackeig_zggev3(order, jobvl, jobvr, n, a, pda, b, pdb, alpha, beta, vl,
                       pdvl, vr, pdvr, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_zggev3 (f08wqc).\n%s\n", fail.message);
    exit_status = 2;
    goto END;
  }

  isinf = 0;
  for (j = 0; j < n; ++j) {
    /* Check for infinite eigenvalues */
    if (nag_complex_abs(beta[j]) < x02ajc()) {
      isinf = j + 1;
    } else {
      alpha[j] = nag_complex_divide(alpha[j], beta[j]);
    }
  }
  if (isinf) {
    printf("Eigenvalue %2" NAG_IFMT " is numerically infinite.\n", isinf);
  } else {

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

    /* Print the (finite) eigenvalues
     * using nag_file_print_matrix_complex_gen (x04dac).
     */
    fflush(stdout);
    printf("\n");
    nag_file_print_matrix_complex_gen(Nag_ColMajor, Nag_GeneralMatrix,
                                      Nag_NonUnitDiag, 1, n, alpha, 1,
                                      "Eigenvalues:", NULL, &fail);
    if (fail.code != NE_NOERROR) {
      printf("Error from nag_file_print_matrix_complex_gen (x04dac).\n%s\n",
             fail.message);
      exit_status = 3;
      goto END;
    }
  }

  /* Re-normalize, sort and print the eigenvectors */
  if (jobvl == Nag_LeftVecs) {
    exit_status = normalize_vectors(n, vl, rank, "Left Eigenvectors:");
    if (exit_status)
      goto END;
  }
  if (jobvr == Nag_RightVecs) {
    exit_status = normalize_vectors(n, vr, rank, "Right Eigenvectors:");
  }

END:
  NAG_FREE(a);
  NAG_FREE(alpha);
  NAG_FREE(b);
  NAG_FREE(beta);
  NAG_FREE(vl);
  NAG_FREE(vr);
  NAG_FREE(emod);
  NAG_FREE(rank);

  return exit_status;
}

static Integer normalize_vectors(Integer n, Complex v[], size_t rank[],
                                 const char *title) {

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

  INIT_FAIL(fail);

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

    /* Sort eigenvector row i using nag_sort_reorder_vector (m01esc). */
    nag_sort_reorder_vector((Pointer)&V(i, 1), (size_t)n, sizeof(Complex),
                            (ptrdiff_t)(stride * sizeof(Complex)), rank, &fail);
    if (fail.code != NE_NOERROR) {
      printf("Error from nag_sort_reorder_vector (m01esc).\n%s\n",
             fail.message);
      errors = 5;
      goto END;
    }
  }

  printf("\n");
  /* Print eigenvectors using nag_file_print_matrix_complex_gen (x04dac). */
  fflush(stdout);
  nag_file_print_matrix_complex_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag,
                                    n, n, v, n, title, 0, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_file_print_matrix_complex_gen (x04dac).\n%s\n",
           fail.message);
    errors = 5;
  }
END:
#undef V
  return errors;
}
static Integer sort_values(Integer n, Complex e[], size_t rank[],
                           double emod[]) {
  Integer i, exit_status = 0;
  NagError fail;

  INIT_FAIL(fail);

  for (i = 0; i < n; ++i) {
    /* nag_complex_abs (a02ddc): Moduli of complex number. */
    emod[i] = nag_complex_abs(e[i]);
  }
  /* Rank sort eigenvalues by absolute values using
   * nag_sort_rank_sort (m01dsc).
   */
  nag_sort_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_sort_rank_sort (m01dsc).\n%s\n", fail.message);
    exit_status = 10;
    goto END;
  }
  /* Turn ranks into indices using nag_sort_permute_invert (m01zac). */
  nag_sort_permute_invert(rank, (size_t)n, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_sort_permute_invert (m01zac).\n%s\n", fail.message);
    exit_status = 11;
    goto END;
  }
  /* Sort eigenvalues using nag_sort_reorder_vector (m01esc). */
  nag_sort_reorder_vector((Pointer)e, (size_t)n, sizeof(Complex),
                          (ptrdiff_t)sizeof(Complex), rank, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_sort_reorder_vector (m01esc).\n%s\n", fail.message);
    exit_status = 12;
    goto END;
  }
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));
}