```/* nag_lapackeig_dsyev (f08fac) Example Program.
*
* Copyright 2019 Numerical Algorithms Group.
*
* Mark 27.0, 2019.
*/

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