/* nag_lapackeig_zgees (f08pnc) Example Program.
 *
 * Copyright 2023 Numerical Algorithms Group.
 *
 * Mark 29.3, 2023.
 */

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

int main(void) {

  /* Scalars */
  Complex alpha, beta;
  double anorm, eps, norm;
  Integer i, j, n, pda, pdc, pdd, pdvs, sdim;
  Integer exit_status = 0;

  /* Arrays */
  Complex *a = 0, *c = 0, *d = 0, *vs = 0, *w = 0;

  /* Nag Types */
  NagError fail;
  Nag_OrderType order;

#ifdef NAG_COLUMN_MAJOR
#define A(I, J) a[(J - 1) * pda + I - 1]
  order = Nag_ColMajor;
#else
#define A(I, J) a[(I - 1) * pda + J - 1]
  order = Nag_RowMajor;
#endif

  INIT_FAIL(fail);

  printf("nag_lapackeig_zgees (f08pnc) 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;
  }

  pda = n;
  pdc = n;
  pdd = n;
  pdvs = n;
  /* Allocate memory */
  if (!(a = NAG_ALLOC(n * n, Complex)) || !(c = NAG_ALLOC(n * n, Complex)) ||
      !(d = NAG_ALLOC(n * n, Complex)) || !(vs = NAG_ALLOC(n * n, Complex)) ||
      !(w = NAG_ALLOC(n, Complex))) {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }

  /* Read in the matrix A */
  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]");

  /* Copy A to D: 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_norm (f16uac): Find norm of matrix A for use later
   * in relative error test.
   */
  nag_blast_zge_norm(order, Nag_OneNorm, n, n, a, pda, &anorm, &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 matrix A. */
  fflush(stdout);
  nag_file_print_matrix_complex_gen_comp(
      order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, a, pda, Nag_BracketForm,
      "%7.4f", "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;
  }

  /* Find the Schur factorization of A using nag_lapackeig_zgees (f08pnc). */
  nag_lapackeig_zgees(order, Nag_Schur, Nag_NoSortEigVals, NULLFN, n, a, pda,
                      &sdim, w, vs, pdvs, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_zgees (f08pnc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* Reconstruct A from Schur Factorization Z*T*ConjTrans(Z) where T is upper
   * triangular and stored in A. This can be done using the following steps:
   * i.  C = Z*T (nag_blast_zgemm, f16zac),
   * ii. D = D-C*ConjTrans(Z) (nag_blast_zgemm, f16zac).
   */
  alpha = nag_complex_create(1.0, 0.0);
  beta = nag_complex_create(0.0, 0.0);
  nag_blast_zgemm(order, Nag_NoTrans, Nag_NoTrans, n, n, n, alpha, vs, pdvs, a,
                  pda, beta, c, pdc, &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_zgemm (f16zac):
   * Compute D = A - C*Z^H.
   */
  alpha = nag_complex_create(-1.0, 0.0);
  beta = nag_complex_create(1.0, 0.0);
  nag_blast_zgemm(order, Nag_NoTrans, Nag_ConjTrans, n, n, n, alpha, c, pdc, vs,
                  pdvs, beta, 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;
  }

  /* nag_blast_zge_norm (f16uac): Find norm of difference matrix D and print
   * warning if it is too large relative to norm of A.
   */
  nag_blast_zge_norm(order, Nag_OneNorm, n, n, d, pdd, &norm, &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 (norm > pow(eps, 0.8) * MAX(anorm, 1.0)) {
    printf("||A-(Z*T*Z^H)||/||A|| is larger than expected.\n"
           "Schur factorization has failed.\n");
    exit_status = 1;
    goto END;
  }

  /* Print details on eigenvalues */
  printf("Eigenvalues\n");
  for (i = 0; i < n; i++)
    printf("%4" NAG_IFMT "   (%7.4f,%7.4f)\n", i + 1, w[i].re, w[i].im);

END:
  NAG_FREE(a);
  NAG_FREE(c);
  NAG_FREE(d);
  NAG_FREE(vs);
  NAG_FREE(w);

  return exit_status;
}