NAG Library Manual, Mark 27.3
```/* nag_lapackeig_dsteqr (f08jec) Example Program.
*
* Copyright 2021 Numerical Algorithms Group.
*
* Mark 27.3, 2021.
*/

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

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

#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_dsteqr (f08jec) Example Program Results\n\n");

/* Skip heading in data file */
scanf("%*[^\n] ");
scanf("%" NAG_IFMT "%*[^\n] ", &n);
pdz = n;
d_len = n;
e_len = n - 1;

/* Allocate memory */
if (!(z = NAG_ALLOC(n * n, double)) || !(d = NAG_ALLOC(d_len, double)) ||
!(e = NAG_ALLOC(e_len, double))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
/* Read T from data file */
for (i = 0; i < d_len; ++i)
scanf("%lf", &d[i]);
for (i = 0; i < e_len; ++i)
scanf("%lf", &e[i]);
/* Calculate all the eigenvalues and eigenvectors of tridiagonal matrix T,
* reduced from real symmetric matrix using nag_lapackeig_dsteqr (f08jec).
*/
nag_lapackeig_dsteqr(order, Nag_InitZ, 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;
}

/* Standardize the eigenvectors so that first elements are non-negative. */
for (j = 1; j <= n; j++) {
if (Z(1, j) < 0.0) {
for (i = 1; i <= n; i++)
Z(i, j) = -Z(i, j);
}
}

/* Print eigenvalues and eigenvectors */
printf(" Eigenvalues\n");
for (i = 0; i < n; ++i)
printf("  %7.4f", d[i]);
printf("\n\n");

/* Print real general matrix Z using easy-to-use
* nag_file_print_matrix_real_gen (x04cac).
*/
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;
}

END:
NAG_FREE(d);
NAG_FREE(e);
NAG_FREE(z);
return exit_status;
}
```