```/* nag_lapackeig_dormtr (f08fgc) Example Program.
*
* Copyright 2019 Numerical Algorithms Group.
*
* Mark 27.0, 2019.
*/

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

int main(void)
{
/* Scalars */
Integer i, j, m, n, nsplit, pda, pdz, d_len, e_len, tau_len;
Integer exit_status = 0;
double vl = 0.0, vu = 0.0;
NagError fail;
Nag_UploType uplo;
Nag_OrderType order;
/* Arrays */
char nag_enum_arg[40];
Integer *iblock = 0, *ifailv = 0, *isplit = 0;
double *a = 0, *d = 0, *e = 0, *tau = 0, *w = 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_dormtr (f08fgc) 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)) ||
!(iblock = NAG_ALLOC(n, Integer)) ||
!(ifailv = NAG_ALLOC(n, Integer)) ||
!(isplit = NAG_ALLOC(n, Integer)) ||
!(w = NAG_ALLOC(n, 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;
goto END;
}
/* Calculate the two smallest eigenvalues of T (same as A) */
/* nag_lapackeig_dstebz (f08jjc).
* Selected eigenvalues of real symmetric tridiagonal matrix
* by bisection
*/
nag_lapackeig_dstebz(Nag_Indices, Nag_ByBlock, n, vl, vu, 1, 2, 0.0,
d, e, &m, &nsplit, w, iblock, isplit, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_dstebz (f08jjc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Print eigenvalues */
printf("Eigenvalues\n");
for (i = 0; i < m; ++i)
printf("%8.4f%s", w[i], (i + 1) % 8 == 0 ? "\n" : " ");
printf("\n\n");
/* Calculate the eigenvectors of T storing the result in Z */
/* nag_lapackeig_dstein (f08jkc).
* Selected eigenvectors of real symmetric tridiagonal
* matrix by inverse iteration, storing eigenvectors in real
* array
*/
nag_lapackeig_dstein(order, n, d, e, m, w, iblock, isplit, z, pdz, ifailv, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_dstein (f08jkc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Calculate all the eigenvectors of A = Q*(eigenvectors of T) */
/* nag_lapackeig_dormtr (f08fgc).
* Apply orthogonal transformation determined by nag_lapackeig_dsytrd
* (f08fec)
*/
nag_lapackeig_dormtr(order, Nag_LeftSide, uplo, Nag_NoTrans, n, m, a, pda,
tau, z, pdz, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_dormtr (f08fgc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Normalize the eigenvectors */
for (j = 1; j <= m; j++) {
for (i = n; i >= 1; i--) {
Z(i, j) = Z(i, j) / Z(1, j);
}
}
/* Print eigenvectors */
/* 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, m, 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(iblock);
NAG_FREE(ifailv);
NAG_FREE(isplit);
NAG_FREE(tau);
NAG_FREE(w);
NAG_FREE(z);

return exit_status;
}
```