/* nag_lapackeig_dsyev (f08fac) Example Program.
 *
 * Copyright 2024 Numerical Algorithms Group.
 *
 * Mark 30.3, 2024.
 */

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

int main(void) {
  /* Scalars */
  double eerrbd, eps;
  Integer i, j, n, pda;
  Integer exit_status = 0;
  /* Arrays */
  double *a = 0, *rcondz = 0, *w = 0, *zerrbd = 0;
  /* Nag Types */
  Nag_OrderType order;
  NagError fail;

#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_dsyev (f08fac) Example Program Results\n\n");

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

  /* Allocate memory */
  if (!(a = NAG_ALLOC(n * n, double)) || !(rcondz = NAG_ALLOC(n, double)) ||
      !(w = NAG_ALLOC(n, double)) || !(zerrbd = NAG_ALLOC(n, double))) {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }
  pda = n;

  /* Read the upper triangular part of the matrix A from data file */
  for (i = 1; i <= n; ++i)
    for (j = i; j <= n; ++j)
      scanf("%lf", &A(i, j));
  scanf("%*[^\n]");

  /* nag_lapackeig_dsyev (f08fac).
   * Solve the symmetric eigenvalue problem.
   */
  nag_lapackeig_dsyev(order, Nag_DoBoth, Nag_Upper, n, a, pda, w, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_dsyev (f08fac).\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--)
      A(i, j) = A(i, j) / A(1, j);

  /* Print solution */
  printf("Eigenvalues\n");
  for (j = 0; j < n; ++j)
    printf("%8.4f%s", w[j], (j + 1) % 8 == 0 ? "\n" : " ");
  printf("\n\n");

  /* nag_file_print_matrix_real_gen (x04cac).
   * Print eigenvectors.
   */
  fflush(stdout);
  nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
                                 n, a, pda, "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;
  }

  /* Get the machine precision, eps, using nag_machine_precision (X02AJC)
   * and compute the approximate error bound for the computed eigenvalues.
   * Note that for the 2-norm, ||A|| = max {|w[i]|, i=0..n-1}, and since
   * the eigenvalues are in ascending order ||A|| = max( |w[0]|, |w[n-1]|).
   */
  eps = nag_machine_precision;
  eerrbd = eps * MAX(fabs(w[0]), fabs(w[n - 1]));

  /* nag_lapackeig_ddisna (f08flc).
   * Estimate reciprocal condition numbers for the eigenvectors.
   */
  nag_lapackeig_ddisna(Nag_EigVecs, n, n, w, rcondz, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_ddisna (f08flc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* Compute the error estimates for the eigenvectors */
  for (i = 0; i < n; ++i)
    zerrbd[i] = eerrbd / rcondz[i];

  /* Print the approximate error bounds for the eigenvalues and vectors */
  printf("\nError estimate for the eigenvalues\n");
  printf("%11.1e\n\n", eerrbd);
  printf("Error estimates for the eigenvectors\n");
  for (i = 0; i < n; ++i)
    printf("%11.1e%s", zerrbd[i], (i + 1) % 6 == 0 || i == n - 1 ? "\n" : " ");

END:
  NAG_FREE(a);
  NAG_FREE(rcondz);
  NAG_FREE(w);
  NAG_FREE(zerrbd);

  return exit_status;
}

#undef A