```/* nag_zggev3 (f08wqc) Example Program.
*
* Copyright 2017 Numerical Algorithms Group.
*
* Mark 26.1, 2017.
*/

#include <stdio.h>
#include <math.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <naga02.h>
#include <nagf08.h>
#include <nagm01.h>
#include <nagx02.h>
#include <nagx04.h>

#ifdef __cplusplus
extern "C"
{
#endif
static Integer NAG_CALL compare(const Nag_Pointer a, const Nag_Pointer b);
static Integer normalize_vectors(Integer n, Complex v[], size_t rank[],
const char *title);
static Integer sort_values (Integer n, Complex e[], size_t rank[],
double emod[]);
#ifdef __cplusplus
}
#endif

int main(void)
{
/* Scalars */
Integer           i, isinf, j, n, pda, pdb, pdvl, pdvr;
Integer           exit_status = 0;

/* Arrays */
Complex           *a = 0, *alpha = 0, *b = 0, *beta = 0, *vl = 0, *vr = 0;
double            *emod = 0;
size_t            *rank = 0;
char              nag_enum_arg[40];

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

INIT_FAIL(fail);

printf("nag_zggev3 (f08wqc) Example Program Results\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;
}

#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
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);

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

/* Allocate memory */
if (!(a = NAG_ALLOC(n * n, Complex)) ||
!(alpha = NAG_ALLOC(n, Complex)) ||
!(b = NAG_ALLOC(n * n, Complex)) ||
!(beta = NAG_ALLOC(n, Complex)) ||
!(emod = NAG_ALLOC(n, double)) ||
!(rank = NAG_ALLOC(n, size_t)) ||
!(vl = NAG_ALLOC(pdvl * pdvl, Complex)) ||
!(vr = NAG_ALLOC(pdvr * pdvr, Complex)))
{
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 , %lf )", &A(i, j).re, &A(i, j).im);
scanf("%*[^\n]");
for (i = 1; i <= n; ++i)
for (j = 1; j <= n; ++j)
scanf(" ( %lf , %lf )", &B(i, j).re, &B(i, j).im);
scanf("%*[^\n]");

/* Solve the generalized eigenvalue problem Ax = lambda Bx using the
* level 3 blocked routine nag_zggev3 (f08wqc) which returns:
*  - eigenvalues as alpha[]./beta[];
*  - left and right eigenvectors in vl and vr respectively.
*/
/* Solve the generalized eigenvalue problem using nag_zggev3 (f08wqc). */
nag_zggev3(order, jobvl, jobvr, n, a, pda, b, pdb, alpha, beta, vl, pdvl, vr,
pdvr, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_zggev3 (f08wqc).\n%s\n", fail.message);
exit_status = 2;
goto END;
}

isinf = 0;
for (j = 0; j < n; ++j) {
/* Check for infinite eigenvalues */
if (nag_complex_abs(beta[j]) < x02ajc()) {
isinf  = j + 1;
} else {
alpha[j] = nag_complex_divide(alpha[j],beta[j]);
}
}
if (isinf) {
printf("Eigenvalue %2" NAG_IFMT " is numerically infinite.\n",isinf);
} else {

/* Sort values by decreasing modulus and store in e[] */
exit_status=sort_values(n, alpha, rank, emod);

/* Print the (finite) eigenvalues
* using nag_gen_complx_mat_print (x04dac).
*/
fflush(stdout);
printf("\n");
nag_gen_complx_mat_print(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag,
1, n, alpha, 1, "Eigenvalues:", NULL, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_gen_complx_mat_print (x04dac).\n%s\n",
fail.message);
exit_status = 3;
goto END;
}
}

/* Re-normalize, sort and print the eigenvectors */
if (jobvl == Nag_LeftVecs) {
exit_status = normalize_vectors(n, vl, rank, "Left Eigenvectors:");
if (exit_status) goto END;
}
if (jobvr == Nag_RightVecs) {
exit_status = normalize_vectors(n, vr, rank, "Right Eigenvectors:");
}

END:
NAG_FREE(a);
NAG_FREE(alpha);
NAG_FREE(b);
NAG_FREE(beta);
NAG_FREE(vl);
NAG_FREE(vr);
NAG_FREE(emod);
NAG_FREE(rank);

return exit_status;
}

static Integer normalize_vectors(Integer n, Complex v[], size_t rank[],
const char *title)
{

Complex           scal;
double            r, rr, rnrm;
Integer           errors = 0, i, j, k, stride;
Nag_OrderType     order;
NagError          fail;

INIT_FAIL(fail);

#ifdef NAG_COLUMN_MAJOR
#define V(I, J)  v[(J-1)*n + I - 1]
order = Nag_ColMajor;
stride = n;
#else
#define V(I, J)  v[(I-1)*n + J - 1]
order = Nag_RowMajor;
stride = 1;
#endif
/* Re-normalize the eigenvectors, largest absolute element real */
for (i=1; i<=n; i++) {
k = 0;
r = -1.0;
rnrm = 0.0;
for (j=1; j<=n; j++) {
rr = nag_complex_abs(V(j,i));
rnrm = rnrm + rr*rr;
if (rr>r) {
r = rr;
k = j;
}
}
rnrm = sqrt(rnrm);
r = r*rnrm;
scal.re = V(k,i).re/r;
scal.im = -V(k,i).im/r;
for (j=1; j<=n; j++) {
V(j,i) = nag_complex_multiply(V(j,i),scal);
}
V(k,i).im = 0.0;
}
/* Sort eigenvectors */
for (i=1; i<=n; i++) {

/* Sort eigenvector row i using nag_reorder_vector (m01esc). */
nag_reorder_vector((Pointer) &V(i,1), (size_t) n, sizeof(Complex),
(ptrdiff_t) (stride*sizeof(Complex)), rank, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_reorder_vector (m01esc).\n%s\n", fail.message);
errors = 5;
goto END;
}
}

printf("\n");
/* Print eigenvectors using nag_gen_complx_mat_print (x04dac). */
fflush(stdout);
nag_gen_complx_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
n, v, n, title, 0, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_gen_complx_mat_print (x04dac).\n%s\n",
fail.message);
errors = 5;
}
END:
#undef V
return errors;
}
static Integer sort_values (Integer n, Complex e[], size_t rank[],
double emod[])
{
Integer       i, exit_status = 0;
NagError      fail;

INIT_FAIL(fail);

for (i = 0; i < n; ++i) {
/* nag_complex_abs (a02ddc): Moduli of complex number. */
emod[i] = nag_complex_abs(e[i]);
}
/* Rank sort eigenvalues by absolute values using
* nag_rank_sort (m01dsc).
*/
nag_rank_sort((Pointer) emod, (size_t) n, (ptrdiff_t) (sizeof(double)),
compare, Nag_Descending, rank, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_rank_sort (m01dsc).\n%s\n", fail.message);
exit_status = 10;
goto END;
}
/* Turn ranks into indices using nag_make_indices (m01zac). */
nag_make_indices(rank, (size_t) n, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_make_indices (m01zac).\n%s\n", fail.message);
exit_status = 11;
goto END;
}
/* Sort eigenvalues using nag_reorder_vector (m01esc). */
nag_reorder_vector((Pointer) e, (size_t) n, sizeof(Complex),
(ptrdiff_t) sizeof(Complex), rank, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_reorder_vector (m01esc).\n%s\n", fail.message);
exit_status = 12;
goto END;
}
END:
return exit_status;
}

static Integer NAG_CALL compare(const Nag_Pointer a, const Nag_Pointer b)
{
double x = *((const double *) a) - *((const double *) b);
return (x < 0.0 ? -1 : (x == 0.0 ? 0 : 1));
}
```