```/* nag_dggevx (f08wbc) Example Program.
*
* Copyright 2014 Numerical Algorithms Group.
*
* Mark 23, 2011.
*/

#include <math.h>
#include <stdio.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <nagf08.h>
#include <nagx02.h>
#include <naga02.h>
int main(void)
{
/* Scalars */
Complex           eig, eigl, eigr;
double            abnorm, abnrm, bbnrm, eps, sign, small, tol;
Integer           i, ihi, ilo, j, k, n, pda, pdb, pdvl, pdvr;
Integer           exit_status = 0;

/* Arrays */
double            *a = 0, *alphai = 0, *alphar = 0, *b = 0, *beta = 0;
double            *lscale = 0, *rconde = 0, *rcondv = 0, *rscale = 0;
double            *vl = 0, *vr = 0;
char              nag_enum_arg[40];

/* Nag Types */
NagError          fail;
Nag_OrderType     order;
Nag_LeftVecsType  jobvl;
Nag_RightVecsType jobvr;
Nag_RCondType     sense;

#ifdef NAG_COLUMN_MAJOR
#define A(I, J)  a[(J-1)*pda + I - 1]
#define B(I, J)  b[(J-1)*pdb + I - 1]
#define VL(I, J) vl[(J-1)*pdvl + I - 1]
#define VR(I, J) vr[(J-1)*pdvr + 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]
#define VL(I, J) vl[(I-1)*pdvl + J - 1]
#define VR(I, J) vr[(I-1)*pdvr + J - 1]
order = Nag_RowMajor;
#endif

INIT_FAIL(fail);

printf("nag_dggevx (f08wbc) Example Program Results\n");

/* Skip heading in data file */
scanf("%*[^\n]");
scanf("%ld%*[^\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
*/
jobvl = (Nag_LeftVecsType) nag_enum_name_to_value(nag_enum_arg);
scanf(" %39s%*[^\n]", nag_enum_arg);
jobvr = (Nag_RightVecsType) nag_enum_name_to_value(nag_enum_arg);
scanf(" %39s%*[^\n]", nag_enum_arg);
sense = (Nag_RCondType) nag_enum_name_to_value(nag_enum_arg);

pda = n;
pdb = n;
pdvl = (jobvl==Nag_LeftVecs?n:1);
pdvr = (jobvr==Nag_RightVecs?n:1);

/* Allocate memory */
if (!(a      = NAG_ALLOC(n*n, double)) ||
!(alphai = NAG_ALLOC(n, double)) ||
!(alphar = NAG_ALLOC(n, double)) ||
!(b      = NAG_ALLOC(n*n, double)) ||
!(beta   = NAG_ALLOC(n, double)) ||
!(lscale = NAG_ALLOC(n, double)) ||
!(rconde = NAG_ALLOC(n, double)) ||
!(rcondv = NAG_ALLOC(n, double)) ||
!(rscale = NAG_ALLOC(n, double)) ||
!(vl     = NAG_ALLOC(pdvl*pdvl, double)) ||
!(vr     = NAG_ALLOC(pdvr*pdvr, double)))
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

/* Read in the matrices A and B */
for (i = 1; i <= n; ++i)
for (j = 1; j <= n; ++j) scanf("%lf", &A(i, j));
scanf("%*[^\n]");
for (i = 1; i <= n; ++i)
for (j = 1; j <= n; ++j) scanf("%lf", &B(i, j));
scanf("%*[^\n]");

/* Solve the generalized eigenvalue problem using nag_dggevx (f08wbc). */
nag_dggevx(order, Nag_BalanceBoth, jobvl, jobvr, sense, n, a, pda, b, pdb,
alphar, alphai, beta, vl, pdvl, vr, pdvr, &ilo, &ihi, lscale,
rscale, &abnrm, &bbnrm, rconde, rcondv, &fail);
if (fail.code != NE_NOERROR)
{
printf("Error from nag_dggevx (f08wbc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_real_safe_small_number (x02amc), nag_machine_precision (x02ajc) */
eps = nag_machine_precision;
small = nag_real_safe_small_number;
if (abnrm == 0.0)
abnorm = ABS(bbnrm);
else if (bbnrm == 0.0)
abnorm = ABS(abnrm);
else if (ABS(abnrm) >= ABS(bbnrm))
abnorm = ABS(abnrm)*sqrt(1.0+(bbnrm/abnrm)*(bbnrm/abnrm));
else
abnorm = ABS(bbnrm)*sqrt(1.0+(abnrm/bbnrm)*(abnrm/bbnrm));

tol = eps * abnorm;

/* Print out eigenvalues and vectors and associated condition
* number and bounds.
*/
for (j = 0; j < n; ++j)
{
/* Print out information on the jth eigenvalue */
printf("\n");
if ((fabs(alphar[j]) + fabs(alphai[j])) * small >= fabs(beta[j]))
{
printf("Eigenvalue %2ld is numerically infinite or "
"undetermined\n", j+1);
printf("alpha = (%13.4e, %13.4e), beta = %13.4e\n", alphar[j],
alphai[j], beta[j]);
}
else if (alphai[j] == 0.0)
{
printf("Eigenvalue %2ld = %13.4e\n", j+1, alphar[j]/beta[j]);
}
else
{
eig.re = alphar[j]/beta[j], eig.im = alphai[j]/beta[j];
printf("Eigenvalue %2ld = (%13.4e, %13.4e)\n", j+1, eig.re,
eig.im);
}
if (sense==Nag_RCondEigVals || sense==Nag_RCondBoth) {
printf("\n Reciprocal condition number = %10.1e\n",  rconde[j]);

if ( rconde[j] > 0.0)
printf(" Error bound                 = %10.1e\n",  tol/rconde[j]);
else
printf(" Error bound is infinite\n");
}
printf("\n\n");
/* Normalize and print out information on the jth eigenvector(s) */
if (jobvl==Nag_LeftVecs) printf("%21s%8s", "Left Eigenvector", "");
if (jobvr==Nag_RightVecs) printf("%21s", "Right Eigenvector");
printf(" %2ld\n", j+1);
if (alphai[j] == 0.0)
for (i = 1; i <= n; ++i) {
if (jobvl==Nag_LeftVecs)
printf("%7s%13.4e%12s", "", VL(i, j+1)/VL(n, j+1), "");
if (jobvr==Nag_RightVecs)
printf("%7s%13.4e", "", VR(i, j+1)/VR(n, j+1));
printf("\n");
}
else
{
k = (alphai[j]>0.0?j+1:j);
sign = (alphai[j]>0.0?1.0:-1.0);
if (jobvl==Nag_LeftVecs) eigl = nag_complex(VL(n,k), VL(n,k+1));
if (jobvr==Nag_RightVecs) eigr = nag_complex(VR(n,k), VR(n,k+1));
for (i = 1; i <= n; ++i)
{
if (jobvl==Nag_LeftVecs) {
eig = nag_complex_divide(nag_complex(VL(i,k), VL(i,k+1)),
eigl);
printf(" (%13.4e,%13.4e) ", eig.re, sign*eig.im);
}
if (jobvr==Nag_RightVecs) {
eig = nag_complex_divide(nag_complex(VR(i,k), VR(i,k+1)),
eigr);
printf(" (%13.4e,%13.4e)", eig.re, sign*eig.im);
}
printf("\n");
}
}

if (sense==Nag_RCondEigVecs || sense==Nag_RCondBoth) {
printf("\n Reciprocal condition number = %10.1e\n", rcondv[j]);

if (rcondv[j] > 0.0)
printf(" Error bound                 = %10.1e\n\n", tol/rcondv[j]);
else
printf(" Error bound is infinite\n\n");
}
}

END:
NAG_FREE(a);
NAG_FREE(alphai);
NAG_FREE(alphar);
NAG_FREE(b);
NAG_FREE(beta);
NAG_FREE(lscale);
NAG_FREE(rconde);
NAG_FREE(rcondv);
NAG_FREE(rscale);
NAG_FREE(vl);
NAG_FREE(vr);

return exit_status;
}
```