/* nag_lapackeig_dormtr (f08fgc) Example Program.
 *
 * Copyright 2024 Numerical Algorithms Group.
 *
 * Mark 30.2, 2024.
 */

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

int main(void) {
  /* Scalars */
  Integer i, j, m, n, nsplit, pda, pdz, d_len, e_len, tau_len;
  Integer exit_status = 0;
  double vl = 0.0, vu = 0.0;
  NagError fail;
  Nag_UploType uplo;
  Nag_OrderType order;
  /* Arrays */
  char nag_enum_arg[40];
  Integer *iblock = 0, *ifailv = 0, *isplit = 0;
  double *a = 0, *d = 0, *e = 0, *tau = 0, *w = 0, *z = 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_dormtr (f08fgc) Example Program Results\n\n");

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

  tau_len = n - 1;
  d_len = n;
  e_len = n - 1;
  /* Allocate memory */
  if (!(a = NAG_ALLOC(n * n, double)) || !(d = NAG_ALLOC(d_len, double)) ||
      !(e = NAG_ALLOC(e_len, double)) || !(iblock = NAG_ALLOC(n, Integer)) ||
      !(ifailv = NAG_ALLOC(n, Integer)) || !(isplit = NAG_ALLOC(n, Integer)) ||
      !(w = NAG_ALLOC(n, 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(i, j));
    }
    scanf("%*[^\n] ");
  } else {
    for (i = 1; i <= n; ++i) {
      for (j = 1; j <= i; ++j)
        scanf("%lf", &A(i, j));
    }
    scanf("%*[^\n] ");
  }

  /* Reduce A to tridiagonal form T = (Q^T)*A*Q */
  /* nag_lapackeig_dsytrd (f08fec).
   * Orthogonal reduction of real symmetric matrix to
   * symmetric tridiagonal form
   */
  nag_lapackeig_dsytrd(order, uplo, n, a, pda, d, e, tau, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_dsytrd (f08fec).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }
  /* Calculate the two smallest eigenvalues of T (same as A) */
  /* nag_lapackeig_dstebz (f08jjc).
   * Selected eigenvalues of real symmetric tridiagonal matrix
   * by bisection
   */
  nag_lapackeig_dstebz(Nag_Indices, Nag_ByBlock, n, vl, vu, 1, 2, 0.0, d, e, &m,
                       &nsplit, w, iblock, isplit, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_dstebz (f08jjc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* Print eigenvalues */
  printf("Eigenvalues\n");
  for (i = 0; i < m; ++i)
    printf("%8.4f%s", w[i], (i + 1) % 8 == 0 ? "\n" : " ");
  printf("\n\n");
  /* Calculate the eigenvectors of T storing the result in Z */
  /* nag_lapackeig_dstein (f08jkc).
   * Selected eigenvectors of real symmetric tridiagonal
   * matrix by inverse iteration, storing eigenvectors in real
   * array
   */
  nag_lapackeig_dstein(order, n, d, e, m, w, iblock, isplit, z, pdz, ifailv,
                       &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_dstein (f08jkc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }
  /* Calculate all the eigenvectors of A = Q*(eigenvectors of T) */
  /* nag_lapackeig_dormtr (f08fgc).
   * Apply orthogonal transformation determined by nag_lapackeig_dsytrd
   * (f08fec)
   */
  nag_lapackeig_dormtr(order, Nag_LeftSide, uplo, Nag_NoTrans, n, m, a, pda,
                       tau, z, pdz, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_dormtr (f08fgc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }
  /* Normalize the eigenvectors */
  for (j = 1; j <= m; j++) {
    for (i = n; i >= 1; i--) {
      Z(i, j) = Z(i, j) / Z(1, j);
    }
  }
  /* Print eigenvectors */
  /* 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,
                                 m, 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(a);
  NAG_FREE(d);
  NAG_FREE(e);
  NAG_FREE(iblock);
  NAG_FREE(ifailv);
  NAG_FREE(isplit);
  NAG_FREE(tau);
  NAG_FREE(w);
  NAG_FREE(z);

  return exit_status;
}