/* nag_lapackeig_dopgtr (f08gfc) Example Program.
 *
 * Copyright 2022 Numerical Algorithms Group.
 *
 * Mark 28.3, 2022.
 */

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

int main(void) {
  /* Scalars */
  Integer ap_len, i, j, n, 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];
  double *ap = 0, *d = 0, *e = 0, *tau = 0, *z = 0;

#ifdef NAG_COLUMN_MAJOR
#define A_UPPER(I, J) ap[J * (J - 1) / 2 + I - 1]
#define A_LOWER(I, J) ap[(2 * n - J) * (J - 1) / 2 + I - 1]
#define Z(I, J) z[(J - 1) * pdz + I - 1]
  order = Nag_ColMajor;
#else
#define A_LOWER(I, J) ap[I * (I - 1) / 2 + J - 1]
#define A_UPPER(I, J) ap[(2 * n - I) * (I - 1) / 2 + J - 1]
#define Z(I, J) z[(I - 1) * pdz + J - 1]
  order = Nag_RowMajor;
#endif

  INIT_FAIL(fail);

  printf("nag_lapackeig_dopgtr (f08gfc) Example Program Results\n\n");

  /* Skip heading in data file */
  scanf("%*[^\n] ");
  scanf("%" NAG_IFMT "%*[^\n] ", &n);
#ifdef NAG_COLUMN_MAJOR
  pdz = n;
#else
  pdz = n;
#endif
  ap_len = n * (n + 1) / 2;
  tau_len = n - 1;
  d_len = n;
  e_len = n - 1;
  /* Allocate memory */
  if (!(ap = NAG_ALLOC(ap_len, double)) || !(d = NAG_ALLOC(d_len, double)) ||
      !(e = NAG_ALLOC(e_len, double)) || !(tau = NAG_ALLOC(tau_len, double)) ||
      !(z = NAG_ALLOC(n * n, 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", &A_UPPER(i, j));
    }
    scanf("%*[^\n] ");
  } else {
    for (i = 1; i <= n; ++i) {
      for (j = 1; j <= i; ++j)
        scanf("%lf", &A_LOWER(i, j));
    }
    scanf("%*[^\n] ");
  }

  /* Reduce A to tridiagonal form T = (Q^T)*A*Q */
  /* nag_lapackeig_dsptrd (f08gec).
   * Orthogonal reduction of real symmetric matrix to
   * symmetric tridiagonal form, packed storage
   */
  nag_lapackeig_dsptrd(order, uplo, n, ap, d, e, tau, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_dsptrd (f08gec).\n%s\n", fail.message);
    exit_status = 1;
  }

  /* Form Q explicitly, storing the result in Z */
  /* nag_lapackeig_dopgtr (f08gfc).
   * Generate orthogonal transformation matrix from reduction
   * to tridiagonal form determined by nag_lapackeig_dsptrd (f08gec)
   */
  nag_lapackeig_dopgtr(order, uplo, n, ap, tau, z, pdz, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_dopgtr (f08gfc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* Calculate all the eigenvalues and eigenvectors of A */
  /* nag_lapackeig_dsteqr (f08jec).
   * All eigenvalues and eigenvectors of real symmetric
   * tridiagonal matrix, reduced from real symmetric matrix
   * using implicit QL or QR
   */
  nag_lapackeig_dsteqr(order, Nag_UpdateZ, n, d, e, z, pdz, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_dsteqr (f08jec).\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) = Z(i, j) / Z(1, j);
    }
  }
  /* Print eigenvalues and eigenvectors */
  printf("Eigenvalues\n");
  for (i = 1; i <= n; ++i)
    printf("%8.4f%s", d[i - 1], i % 8 == 0 ? "\n" : " ");
  printf("\n\n");
  /* nag_file_print_matrix_real_gen (x04cac).
   * Print real general matrix (easy-to-use)
   */
  fflush(stdout);
  nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
                                 n, z, pdz, "Eigenvectors", 0, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_file_print_matrix_real_gen (x04cac).\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }
END:
  NAG_FREE(ap);
  NAG_FREE(d);
  NAG_FREE(e);
  NAG_FREE(tau);
  NAG_FREE(z);

  return exit_status;
}