```/* nag_dsygst (f08sec) Example Program.
*
* Copyright 2014 Numerical Algorithms Group.
*
* Mark 7, 2001.
*/

#include <stdio.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <nagf07.h>
#include <nagf08.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        *a = 0, *b = 0, *d = 0, *e = 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_dsygst (f08sec) Example Program Results\n\n");

/* Skip heading in data file */
scanf("%*[^\n] ");
scanf("%ld%*[^\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, double)) ||
!(b = NAG_ALLOC(n * n, double)) ||
!(d = NAG_ALLOC(d_len, double)) ||
!(e = NAG_ALLOC(e_len, double)) ||
!(tau = NAG_ALLOC(tau_len, double)))
{
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", &A(i, j));
}
scanf("%*[^\n] ");
for (i = 1; i <= n; ++i)
{
for (j = i; j <= n; ++j)
scanf("%lf", &B(i, j));
}
scanf("%*[^\n] ");
}
else
{
for (i = 1; i <= n; ++i)
{
for (j = 1; j <= i; ++j)
scanf("%lf", &A(i, j));
}
scanf("%*[^\n] ");
for (i = 1; i <= n; ++i)
{
for (j = 1; j <= i; ++j)
scanf("%lf", &B(i, j));
}
scanf("%*[^\n] ");
}

/* Compute the Cholesky factorization of B */
/* nag_dpotrf (f07fdc).
* Cholesky factorization of real symmetric
* positive-definite matrix
*/
nag_dpotrf(order, uplo, n, b, pdb, &fail);
if (fail.code != NE_NOERROR)
{
printf("Error from nag_dpotrf (f07fdc).\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_dsygst (f08sec).
* Reduction to standard form of real symmetric-definite
* generalized eigenproblem Ax = lambda Bx, ABx = lambda x
* or BAx = lambda x, B factorized by nag_dpotrf (f07fdc)
*/
nag_dsygst(order, Nag_Compute_1, uplo, n, a, pda, b, pdb, &fail);
if (fail.code != NE_NOERROR)
{
printf("Error from nag_dsygst (f08sec).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Reduce C to tridiagonal form T = (Q**T)*C*Q */
/* nag_dsytrd (f08fec).
* Orthogonal reduction of real symmetric matrix to
* symmetric tridiagonal form
*/
nag_dsytrd(order, uplo, n, a, pda, d, e, tau, &fail);
if (fail.code != NE_NOERROR)
{
printf("Error from nag_dsytrd (f08fec).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Calculate the eigenvalues of T (same as C) */
/* nag_dsterf (f08jfc).
* All eigenvalues of real symmetric tridiagonal matrix,
* root-free variant of QL or QR
*/
nag_dsterf(n, d, e, &fail);
if (fail.code != NE_NOERROR)
{
printf("Error from nag_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;
}
```