```/* nag_dsygv (f08sac) Example Program.
*
* NAGPRODCODE Version.
*
* Copyright 2016 Numerical Algorithms Group.
*
* Mark 26, 2016.
*/

#include <math.h>
#include <stdio.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <nagf07.h>
#include <nagf08.h>
#include <nagf16.h>
#include <nagx04.h>
#include <nagx02.h>

int main(void)
{

/* Scalars */
double anorm, bnorm, eps, rcond, rcondb, t1, t2, t3;
Integer exit_status = 0, i, j, n, pda, pdb;

/* Arrays */
double *a = 0, *b = 0, *eerbnd = 0, *rcondz = 0, *w = 0, *zerbnd = 0;
char nag_enum_arg[40];

/* Nag Types */
NagError fail;
Nag_OrderType order;
Nag_UploType uplo;

#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_dsygv (f08sac) Example Program Results\n\n");

/* Skip heading in data file */
scanf("%*[^\n]");
scanf("%" NAG_IFMT "%*[^\n]", &n);
if (n < 0) {
printf("Invalid n\n");
exit_status = 1;
goto END;;
}
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);

pda = n;
pdb = n;
/* Allocate memory */
if (!(a = NAG_ALLOC(n * n, double)) ||
!(b = NAG_ALLOC(n * n, double)) ||
!(eerbnd = NAG_ALLOC(n, double)) ||
!(rcondz = NAG_ALLOC(n, double)) ||
!(w = NAG_ALLOC(n, double)) || !(zerbnd = NAG_ALLOC(n, double)))
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

/* Read the triangular parts of the matrices A and B */
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));
}
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 one-norms of the symmetric matrices A and B */
nag_dsy_norm(order, Nag_OneNorm, uplo, n, a, pda, &anorm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dsy_norm (f16rcc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

nag_dsy_norm(order, Nag_OneNorm, uplo, n, b, pdb, &bnorm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dsy_norm (f16rcc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Solve the generalized symmetric eigenvalue problem  A*x = lambda*B*x
* using nag_dsygv (f08sac).
*/
nag_dsygv(order, 1, Nag_DoBoth, uplo, n, a, pda, b, pdb, w, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dsygv (f08sac).\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--)
A(i, j) = A(i, j) / A(1, j);

/* Print eigensolution */
printf(" Eigenvalues\n   ");
for (j = 0; j < n; ++j)
printf(" %10.4f%s", w[j], j % 6 == 5 ? "\n" : "");
printf("\n\n");

/* Print the normalized eigenvectors using nag_gen_real_mat_print (x04cac). */
fflush(stdout);
nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, a,
pda, "Eigenvectors", 0, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_gen_real_mat_print (x04cac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Estimate the reciprocal condition number of the Cholesky factor of B.
* nag_dtrcon (f07tgc)
* Note that: cond(B) = 1.0/(rcond*rcond)
*/
nag_dtrcon(order, Nag_OneNorm, uplo, Nag_NonUnitDiag, n, b, pdb, &rcond,
&fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dtrcon (f07tgc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
rcondb = rcond * rcond;
printf("\nEstimate of reciprocal condition number for B\n%15.1e\n", rcondb);

/* Get the machine precision, using nag_machine_precision (x02ajc) */
eps = nag_machine_precision;
if (rcond < eps) {
printf("\nB is very ill-conditioned, error estimates have not been "
"computed\n");
goto END;
}

/* Estimate reciprocal condition numbers for the eigenvectors of A-lambda*B
* nag_ddisna (f08flc).
*/
nag_ddisna(Nag_EigVecs, n, n, w, rcondz, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_ddisna (f08flc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Compute the error estimates for the eigenvalues and eigenvectors */
t1 = eps / rcondb;
t2 = anorm / bnorm;
t3 = t2 / rcond;
for (i = 0; i < n; ++i) {
eerbnd[i] = t1 * (t2 + fabs(w[i]));
zerbnd[i] = t1 * (t3 + fabs(w[i])) / rcondz[i];
}

/* Print the approximate error bounds for the eigenvalues and vectors */
printf("\nError estimates for the eigenvalues\n    ");
for (i = 0; i < n; ++i)
printf(" %10.1e%s", eerbnd[i], i % 6 == 5 ? "\n" : "");

printf("\n\nError estimates for the eigenvectors\n    ");
for (i = 0; i < n; ++i)
printf(" %10.1e%s", zerbnd[i], i % 6 == 5 ? "\n" : "");
printf("\n");

END:
NAG_FREE(a);
NAG_FREE(b);
NAG_FREE(eerbnd);
NAG_FREE(rcondz);
NAG_FREE(w);
NAG_FREE(zerbnd);

return exit_status;
}
```