/* nag_lapackeig_dstev (f08jac) Example Program.
 *
 * Copyright 2024 Numerical Algorithms Group.
 *
 * Mark 30.1, 2024.
 */

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

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

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

  INIT_FAIL(fail);

  printf("nag_lapackeig_dstev (f08jac) Example Program Results\n\n");

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

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

  pdz = n;
  /* Read the diagonal and off-diagonal elements of the matrix A
   * from data file.
   */
  for (i = 0; i < n; ++i)
    scanf("%lf", &d[i]);
  scanf("%*[^\n]");

  for (i = 0; i < n - 1; ++i)
    scanf("%lf", &e[i]);
  scanf("%*[^\n]");

  /* nag_lapackeig_dstev (f08jac).
   * Solve the symmetric tridiagonal eigenvalue problem.
   */
  nag_lapackeig_dstev(order, Nag_DoBoth, n, d, e, z, pdz, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_dstev (f08jac).\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 solution */
  printf("Eigenvalues\n");
  for (i = 0; i < n; ++i)
    printf("%8.4f%s", d[i], (i + 1) % 8 == 0 ? "\n" : " ");
  printf("\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, 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;
  }

  /* 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 {|d[i]|, i=0..n-1}, and since
   * the eigenvalues are in ascending order ||A|| = max( |d[0]|, |d[n-1]|).
   */
  eps = nag_machine_precision;
  eerrbd = eps * MAX(fabs(d[0]), fabs(d[n - 1]));

  /* nag_lapackeig_ddisna (f08flc).
   * Estimate reciprocal condition numbers for the eigenvectors.
   */
  nag_lapackeig_ddisna(Nag_EigVecs, n, n, d, 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", eerrbd);
  printf("\nError 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(d);
  NAG_FREE(e);
  NAG_FREE(rcondz);
  NAG_FREE(z);
  NAG_FREE(zerrbd);

  return exit_status;
}

#undef Z