/* nag_lapackeig_zhetrd (f08fsc) Example Program.
 *
 * Copyright 2024 Numerical Algorithms Group.
 *
 * Mark 30.3, 2024.
 */

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

int main(void) {
  /* Scalars */
  Integer i, j, n, pda, pdz, d_len, e_len, tau_len;
  Integer exit_status = 0;
  NagError fail;
  Nag_UploType uplo;
  Nag_OrderType order;
  /* Arrays */
  char nag_enum_arg[40];
  Complex *a = 0, *tau = 0, *z = 0;
  double *d = 0, *e = 0;

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

  INIT_FAIL(fail);

  printf("nag_lapackeig_zhetrd (f08fsc) Example Program Results\n");

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

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

  /* Read A from data file */
  scanf("%39s%*[^\n] ", nag_enum_arg);
  /* nag_enum_name_to_value (x04nac).
   * Converts NAG enum member name to value
   */
  uplo = (Nag_UploType)nag_enum_name_to_value(nag_enum_arg);
  if (uplo == Nag_Upper) {
    for (i = 1; i <= n; ++i) {
      for (j = i; j <= n; ++j)
        scanf(" ( %lf , %lf )", &A(i, j).re, &A(i, j).im);
    }
    scanf("%*[^\n] ");
  } else {
    for (i = 1; i <= n; ++i) {
      for (j = 1; j <= i; ++j)
        scanf(" ( %lf , %lf )", &A(i, j).re, &A(i, j).im);
    }
    scanf("%*[^\n] ");
  }

  /* Reduce A to tridiagonal form T = (Q^H)*A*Q */
  /* nag_lapackeig_zhetrd (f08fsc).
   * Unitary reduction of complex Hermitian matrix to real
   * symmetric tridiagonal form
   */
  nag_lapackeig_zhetrd(order, uplo, n, a, pda, d, e, tau, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_zhetrd (f08fsc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* Copy A into Z */
  if (uplo == Nag_Upper) {
    for (i = 1; i <= n; ++i) {
      for (j = i; j <= n; ++j) {
        Z(i, j).re = A(i, j).re;
        Z(i, j).im = A(i, j).im;
      }
    }
  } else {
    for (i = 1; i <= n; ++i) {
      for (j = 1; j <= i; ++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_zungtr (f08ftc).
   * Generate unitary transformation matrix from reduction to
   * tridiagonal form determined by nag_lapackeig_zhetrd (f08fsc)
   */
  nag_lapackeig_zungtr(order, uplo, n, z, pdz, tau, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_zungtr (f08ftc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* Calculate all the eigenvalues and eigenvectors of A */
  /* nag_lapackeig_zsteqr (f08jsc).
   * All eigenvalues and eigenvectors of real symmetric
   * tridiagonal matrix, reduced from complex Hermitian
   * matrix, using implicit QL or QR
   */
  nag_lapackeig_zsteqr(order, Nag_UpdateZ, n, d, e, z, pdz, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_zsteqr (f08jsc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }
  /* Normalize the eigenvectors */
  for (j = 1; j <= n; j++) {
    for (i = n; i >= 1; i--) {
      Z(i, j) = nag_complex_divide(Z(i, j), Z(1, j));
    }
  }
  /* Print eigenvalues and eigenvectors */
  printf("\nEigenvalues\n");
  for (i = 1; i <= n; ++i)
    printf("%9.4f%s", d[i - 1], i % 4 == 0 ? "\n" : " ");
  printf("\n");
  /* nag_file_print_matrix_complex_gen_comp (x04dbc).
   * Print complex general matrix (comprehensive)
   */
  fflush(stdout);
  nag_file_print_matrix_complex_gen_comp(
      order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, z, pdz, Nag_BracketForm,
      "%7.4f", "Eigenvectors", Nag_NoLabels, 0, Nag_IntegerLabels, 0, 80, 0, 0,
      &fail);
  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;
  }
END:
  NAG_FREE(a);
  NAG_FREE(tau);
  NAG_FREE(z);
  NAG_FREE(d);
  NAG_FREE(e);

  return exit_status;
}