NAG Library Manual, Mark 27.2
```/* nag_lapackeig_dsytrd (f08fec) Example Program.
*
* Copyright 2021 Numerical Algorithms Group.
*
* Mark 27.2, 2021.
*/

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

int main(void) {
/* Scalars */
Integer i, j, n, pda, 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 *a = 0, *d = 0, *e = 0, *tau = 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_dsytrd (f08fec) 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)) || !(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;
}

/* Copy A into Z using  nag_blast_dtr_copy (f16qec). */
nag_blast_dtr_copy(order, uplo, Nag_NoTrans, Nag_NonUnitDiag, n, a, pda, z,
pdz, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from dtr_copy.\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Form Q explicitly, storing the result in z using  nag_lapackeig_dorgtr
* (f08ffc). */
nag_lapackeig_dorgtr(order, uplo, n, z, pdz, tau, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_dorgtr (f08ffc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Calculate all the eigenvalues and eigenvectors of matrix A */
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(a);
NAG_FREE(d);
NAG_FREE(e);
NAG_FREE(tau);
NAG_FREE(z);

return exit_status;
}
```