```/* nag_lapackeig_dsptrd (f08gec) Example Program.
*
* Copyright 2019 Numerical Algorithms Group.
*
* Mark 27.0, 2019.
*/

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

int main(void)
{
/* Scalars */
Integer ap_len, i, j, n, 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 *ap = 0, *d = 0, *e = 0, *tau = 0, *z = 0;

#ifdef NAG_COLUMN_MAJOR
#define A_UPPER(I, J) ap[J * (J - 1) / 2 + I - 1]
#define A_LOWER(I, J) ap[(2 * n - J) * (J - 1) / 2 + I - 1]
#define Z(I, J) z[(J - 1) * pdz + I - 1]
order = Nag_ColMajor;
#else
#define A_LOWER(I, J) ap[I * (I - 1) / 2 + J - 1]
#define A_UPPER(I, J) ap[(2 * n - I) * (I - 1) / 2 + J - 1]
#define Z(I, J) z[(I - 1) * pdz + J - 1]
order = Nag_RowMajor;
#endif

INIT_FAIL(fail);

printf("nag_lapackeig_dsptrd (f08gec) Example Program Results\n\n");

/* Skip heading in data file */
scanf("%*[^\n] ");
scanf("%" NAG_IFMT "%*[^\n] ", &n);
#ifdef NAG_COLUMN_MAJOR
pdz = n;
#else
pdz = n;
#endif
ap_len = n * (n + 1) / 2;
tau_len = n - 1;
d_len = n;
e_len = n - 1;
/* Allocate memory */
if (!(ap = NAG_ALLOC(ap_len, 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_UPPER(i, j));
}
scanf("%*[^\n] ");
}
else {
for (i = 1; i <= n; ++i) {
for (j = 1; j <= i; ++j)
scanf("%lf", &A_LOWER(i, j));
}
scanf("%*[^\n] ");
}

/* Reduce A to tridiagonal form T = (Q^T)*A*Q */
/* nag_lapackeig_dsptrd (f08gec).
* Orthogonal reduction of real symmetric matrix to
* symmetric tridiagonal form, packed storage
*/
nag_lapackeig_dsptrd(order, uplo, n, ap, d, e, tau, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_dsptrd (f08gec).\n%s\n", fail.message);
exit_status = 1;
}

/* Form Q explicitly, storing the result in Z */
/* nag_lapackeig_dopgtr (f08gfc).
* Generate orthogonal transformation matrix from reduction
* to tridiagonal form determined by nag_lapackeig_dsptrd (f08gec)
*/
nag_lapackeig_dopgtr(order, uplo, n, ap, tau, z, pdz, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_dopgtr (f08gfc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Calculate all the eigenvalues and eigenvectors of A */
/* nag_lapackeig_dsteqr (f08jec).
* All eigenvalues and eigenvectors of real symmetric
* tridiagonal matrix, reduced from real symmetric matrix
* using implicit QL or QR
*/
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(ap);
NAG_FREE(d);
NAG_FREE(e);
NAG_FREE(tau);
NAG_FREE(z);

return exit_status;
}
```