/* nag_lapackeig_zgges (f08xnc) Example Program.
 *
 * Copyright 2019 Numerical Algorithms Group.
 *
 * Mark 27.0, 2019.
 */

#include <stdio.h>
#include <math.h>
#include <nag.h>

int main(void)
{

  /* Scalars */
  Complex alph, bet, z;
  double norma, normb, normd, norme, eps;
  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_lapackeig_zgges (f08xnc) Example Program Results\n\n");

  /* Skip heading in data file */
  scanf("%*[^\n]");
  scanf("%" NAG_IFMT "%*[^\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);

  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 A and B to D and E respectively: nag_blast_zge_copy (f16tfc),
   * Complex valued general matrix copy.
   */
  nag_blast_zge_copy(order, Nag_NoTrans, n, n, a, pda, d, pdd, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_blast_zge_copy (f16tfc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }
  nag_blast_zge_copy(order, Nag_NoTrans, n, n, b, pdb, e, pde, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_blast_zge_copy (f16tfc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }
  /* nag_blast_zge_norm (f16uac): Find norms of input matrices A and B. */
  nag_blast_zge_norm(order, Nag_OneNorm, n, n, a, pda, &norma, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_blast_zge_norm (f16uac).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }
  nag_blast_zge_norm(order, Nag_OneNorm, n, n, b, pdb, &normb, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_blast_zge_norm (f16uac).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* nag_file_print_matrix_complex_gen_comp (x04dbc): Print matrices A and B. */
  fflush(stdout);
  nag_file_print_matrix_complex_gen_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_file_print_matrix_complex_gen_comp (x04dbc).\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }
  fflush(stdout);
  nag_file_print_matrix_complex_gen_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_file_print_matrix_complex_gen_comp (x04dbc).\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }

  /* Find the generalized Schur form using nag_lapackeig_zgges (f08xnc). */
  nag_lapackeig_zgges(order, jobvsl, jobvsr, Nag_NoSortEigVals, NULLFN, n, a, pda, b,
            pdb, &sdim, alpha, beta, vsl, pdvsl, vsr, pdvsr, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_zgges (f08xnc).\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_blast_zge_copy (f16tfc).
   * C = C*S (S in a, upper triangular) using nag_blast_ztrmm (f16zfc).
   * D = D - C*Z^H (Z in vsr) using nag_blast_zgemm (f16zac).
   */
  nag_blast_zge_copy(order, Nag_NoTrans, n, n, vsl, pdvsl, c, pdc, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_blast_zge_copy (f16tfc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }
  alph = nag_complex_create(1.0, 0.0);
  /* nag_blast_ztrmm (f16zfc)  Triangular complex matrix-matrix multiply. */
  nag_blast_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_blast_ztrmm (f16zfc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }
  alph = nag_complex_create(-1.0, 0.0);
  bet = nag_complex_create(1.0, 0.0);
  nag_blast_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_blast_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_blast_ztrmm (f16zfc).
   * E = E - Q*Z^H (Z in vsr) using nag_blast_zgemm (f16zac).
   */
  alph = nag_complex_create(1.0, 0.0);
  nag_blast_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_blast_ztrmm (f16zfc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }
  alph = nag_complex_create(-1.0, 0.0);
  bet = nag_complex_create(1.0, 0.0);
  nag_blast_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_blast_zgemm (f16zac).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* nag_blast_zge_norm (f16uac): Find norms of difference matrices D and E. */
  nag_blast_zge_norm(order, Nag_OneNorm, n, n, d, pdd, &normd, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_blast_zge_norm (f16uac).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }
  nag_blast_zge_norm(order, Nag_OneNorm, n, n, e, pde, &norme, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_blast_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("Generalized eigenvalues are:\n");
  for (i = 0; i < n; i++) {
    if (beta[i].re != 0.0 || beta[i].im != 0.0) {
      z = nag_complex_divide(alpha[i], beta[i]);
      printf("%3" NAG_IFMT " (%13.4e, %13.4e)\n", i + 1, z.re, z.im);
    }
    else
      printf("%3" NAG_IFMT " Eigenvalue is infinite\n", i + 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;
}