NAG Library Manual, Mark 27.3
```/* nag_lapackeig_zhetrd (f08fsc) 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, 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];
Complex *a = 0, *tau = 0, *z = 0;
double *d = 0, *e = 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_zhetrd (f08fsc) Example Program Results\n");

/* Skip heading in data file */
scanf("%*[^\n] ");
scanf("%" NAG_IFMT "%*[^\n] ", &n);
#ifdef NAG_COLUMN_MAJOR
pda = n;
pdz = n;
#else
pda = n;
pdz = n;
#endif

tau_len = n - 1;
d_len = n;
e_len = n - 1;
/* Allocate memory */
if (!(a = NAG_ALLOC(n * n, Complex)) ||
!(tau = NAG_ALLOC(tau_len, Complex)) ||
!(z = NAG_ALLOC(n * n, Complex)) || !(d = NAG_ALLOC(d_len, double)) ||
!(e = NAG_ALLOC(e_len, 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 , %lf )", &A(i, j).re, &A(i, j).im);
}
scanf("%*[^\n] ");
} else {
for (i = 1; i <= n; ++i) {
for (j = 1; j <= i; ++j)
scanf(" ( %lf , %lf )", &A(i, j).re, &A(i, j).im);
}
scanf("%*[^\n] ");
}

/* Reduce A to tridiagonal form T = (Q^H)*A*Q */
/* nag_lapackeig_zhetrd (f08fsc).
* Unitary reduction of complex Hermitian matrix to real
* symmetric tridiagonal form
*/
nag_lapackeig_zhetrd(order, uplo, n, a, pda, d, e, tau, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_zhetrd (f08fsc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Copy A into Z */
if (uplo == Nag_Upper) {
for (i = 1; i <= n; ++i) {
for (j = i; j <= n; ++j) {
Z(i, j).re = A(i, j).re;
Z(i, j).im = A(i, j).im;
}
}
} else {
for (i = 1; i <= n; ++i) {
for (j = 1; j <= i; ++j) {
Z(i, j).re = A(i, j).re;
Z(i, j).im = A(i, j).im;
}
}
}
/* Form Q explicitly, storing the result in Z */
/* nag_lapackeig_zungtr (f08ftc).
* Generate unitary transformation matrix from reduction to
* tridiagonal form determined by nag_lapackeig_zhetrd (f08fsc)
*/
nag_lapackeig_zungtr(order, uplo, n, z, pdz, tau, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_zungtr (f08ftc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Calculate all the eigenvalues and eigenvectors of A */
/* nag_lapackeig_zsteqr (f08jsc).
* All eigenvalues and eigenvectors of real symmetric
* tridiagonal matrix, reduced from complex Hermitian
* matrix, using implicit QL or QR
*/
nag_lapackeig_zsteqr(order, Nag_UpdateZ, n, d, e, z, pdz, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_zsteqr (f08jsc).\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) = nag_complex_divide(Z(i, j), Z(1, j));
}
}
/* Print eigenvalues and eigenvectors */
printf("\nEigenvalues\n");
for (i = 1; i <= n; ++i)
printf("%9.4f%s", d[i - 1], i % 4 == 0 ? "\n" : " ");
printf("\n");
/* nag_file_print_matrix_complex_gen_comp (x04dbc).
* Print complex general matrix (comprehensive)
*/
fflush(stdout);
nag_file_print_matrix_complex_gen_comp(
order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, z, pdz, Nag_BracketForm,
"%7.4f", "Eigenvectors", Nag_NoLabels, 0, Nag_IntegerLabels, 0, 80, 0, 0,
&fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_file_print_matrix_complex_gen_comp (x04dbc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}
END:
NAG_FREE(a);
NAG_FREE(tau);
NAG_FREE(z);
NAG_FREE(d);
NAG_FREE(e);

return exit_status;
}
```