NAG Library Manual, Mark 28.4
```/* nag_lapackeig_zhegst (f08ssc) Example Program.
*
* Copyright 2022 Numerical Algorithms Group.
*
* Mark 28.4, 2022.
*/

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

int main(void) {
/* Scalars */
Integer i, j, n, pda, pdb, 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 *d = 0, *e = 0;
Complex *a = 0, *b = 0, *tau = 0;

#ifdef NAG_COLUMN_MAJOR
#define A(I, J) a[(J - 1) * pda + I - 1]
#define B(I, J) b[(J - 1) * pdb + I - 1]
order = Nag_ColMajor;
#else
#define A(I, J) a[(I - 1) * pda + J - 1]
#define B(I, J) b[(I - 1) * pdb + J - 1]
order = Nag_RowMajor;
#endif

INIT_FAIL(fail);

printf("nag_lapackeig_zhegst (f08ssc) Example Program Results\n\n");

/* Skip heading in data file */
scanf("%*[^\n] ");
scanf("%" NAG_IFMT "%*[^\n] ", &n);
#ifdef NAG_COLUMN_MAJOR
pda = n;
pdb = n;
#else
pda = n;
pdb = n;
#endif
d_len = n;
e_len = n - 1;
tau_len = n - 1;

/* Allocate memory */
if (!(a = NAG_ALLOC(n * n, Complex)) || !(b = NAG_ALLOC(n * n, Complex)) ||
!(d = NAG_ALLOC(d_len, double)) || !(e = NAG_ALLOC(e_len, double)) ||
!(tau = NAG_ALLOC(tau_len, Complex))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
/* Read A and B 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] ");
for (i = 1; i <= n; ++i) {
for (j = i; j <= n; ++j)
scanf(" ( %lf , %lf )", &B(i, j).re, &B(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] ");
for (i = 1; i <= n; ++i) {
for (j = 1; j <= i; ++j)
scanf(" ( %lf , %lf )", &B(i, j).re, &B(i, j).im);
}
scanf("%*[^\n] ");
}

/* Compute the Cholesky factorization of B */
/* nag_lapacklin_zpotrf (f07frc).
* Cholesky factorization of complex Hermitian
* positive-definite matrix
*/
nag_lapacklin_zpotrf(order, uplo, n, b, pdb, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapacklin_zpotrf (f07frc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Reduce the problem to standard form C*y = lambda*y, storing */
/* the result in A */
/* nag_lapackeig_zhegst (f08ssc).
* Reduction to standard form of complex Hermitian-definite
* generalized eigenproblem Ax = lambda Bx, ABx = lambda x
* or BAx = lambda x, B factorized by nag_lapacklin_zpotrf (f07frc)
*/
nag_lapackeig_zhegst(order, Nag_Compute_1, uplo, n, a, pda, b, pdb, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_zhegst (f08ssc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Reduce C to tridiagonal form T = (Q^T)*C*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;
}
/* Calculate the eigenvalues of T (same as C) */
/* nag_lapackeig_dsterf (f08jfc).
* All eigenvalues of real symmetric tridiagonal matrix,
* root-free variant of QL or QR
*/
nag_lapackeig_dsterf(n, d, e, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_dsterf (f08jfc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Print eigenvalues */
printf("Eigenvalues\n");
for (i = 1; i <= n; ++i)
printf("%8.4f%s", d[i - 1], i % 9 == 0 ? "\n" : " ");
printf("\n");
END:
NAG_FREE(a);
NAG_FREE(b);
NAG_FREE(d);
NAG_FREE(e);
NAG_FREE(tau);

return exit_status;
}
```