/* nag_lapackeig_zunghr (f08ntc) 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 norm;
  Integer i, j, n, pda, pdc, pdd, pdz, tau_len, w_len;
  Integer exit_status = 0;
  NagError fail;
  Nag_OrderType order;
  /* Arrays */
  Complex *a = 0, *c = 0, *d = 0, *tau = 0, *w = 0, *z = 0;

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

  INIT_FAIL(fail);

  printf("nag_lapackeig_zunghr (f08ntc) Example Program Results\n\n");

  /* Skip heading in data file */
  scanf("%*[^\n] ");
  scanf("%" NAG_IFMT "%*[^\n] ", &n);
#ifdef NAG_COLUMN_MAJOR
  pda = n;
  pdc = n;
  pdd = n;
  pdz = n;
#else
  pda = n;
  pdc = n;
  pdd = n;
  pdz = n;
#endif
  tau_len = n - 1;
  w_len = n;

  /* Allocate memory */
  if (!(a = NAG_ALLOC(n * n, Complex)) || !(c = NAG_ALLOC(n * n, Complex)) ||
      !(d = NAG_ALLOC(n * n, Complex)) ||
      !(tau = NAG_ALLOC(tau_len, Complex)) ||
      !(w = NAG_ALLOC(w_len, Complex)) || !(z = NAG_ALLOC(n * n, Complex))) {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }

  /* Read A from data file */
  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 into D */
  for (i = 1; i <= n; ++i) {
    for (j = 1; j <= n; ++j) {
      D(i, j).re = A(i, j).re;
      D(i, j).im = A(i, j).im;
    }
  }

  /* 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;
  }

  /* Reduce A to upper Hessenberg form H = (Q^T)*A*Q */
  /* nag_lapackeig_zgehrd (f08nsc).
   * Unitary reduction of complex general matrix to upper
   * Hessenberg form
   */
  nag_lapackeig_zgehrd(order, n, 1, n, a, pda, tau, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_zgehrd (f08nsc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* Copy A into Z */
  for (i = 1; i <= n; ++i) {
    for (j = 1; j <= n; ++j) {
      Z(i, j).re = A(i, j).re;
      Z(i, j).im = A(i, j).im;
    }
  }

  /* Form Q explicitly, storing the result in Z */
  /* nag_lapackeig_zunghr (f08ntc).
   * Generate unitary transformation matrix from reduction to
   * Hessenberg form determined by nag_lapackeig_zgehrd (f08nsc)
   */
  nag_lapackeig_zunghr(order, n, 1, n, z, pdz, tau, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_zunghr (f08ntc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* Calculate the Schur factorization of H = Y*T*(Y^T) and form */
  /* Q*Y explicitly, storing the result in Z */

  /* Note that A = Z*T*(Z^T), where Z = Q*Y */
  /* nag_lapackeig_zhseqr (f08psc).
   * Eigenvalues and Schur factorization of complex upper
   * Hessenberg matrix reduced from complex general matrix
   */
  nag_lapackeig_zhseqr(order, Nag_Schur, Nag_UpdateZ, n, 1, n, a, pda, w, z,
                       pdz, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_zhseqr (f08psc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* nag_blast_zgemm (f16zac): Compute A - Z*T*Z^H from the factorization of */
  /* A and store in matrix D */
  alpha.re = 1.0;
  alpha.im = 0.0;
  beta.re = 0.0;
  beta.im = 0.0;
  nag_blast_zgemm(order, Nag_NoTrans, Nag_NoTrans, n, n, n, alpha, z, pdz, 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;
  }
  alpha.re = -1.0;
  beta.re = 1.0;
  nag_blast_zgemm(order, Nag_NoTrans, Nag_ConjTrans, n, n, n, alpha, c, pdc, z,
                  pdz, 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 matrix D and print warning if */
  /* it is too large */
  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;
  }
  if (norm > pow(x02ajc(), 0.8)) {
    printf("%s\n%s\n", "Norm of A-(Z*T*Z^H) is much greater than 0.",
           "Schur factorization has failed.");
  }

END:
  NAG_FREE(a);
  NAG_FREE(c);
  NAG_FREE(d);
  NAG_FREE(tau);
  NAG_FREE(w);
  NAG_FREE(z);

  return exit_status;
}