NAG Library Manual, Mark 27.2
```/* nag_lapackeig_zhgeqz (f08xsc) Example Program.
*
* Copyright 2021 Numerical Algorithms Group.
*
* Mark 27.2, 2021.
*/

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

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

int main(void) {
/* Scalars */
Integer i, ihi, ilo, irows, j, n, pda, pdb, ninf;
Integer exit_status = 0;

/* Arrays */
Complex *a = 0, *alpha = 0, *b = 0, *beta = 0, *q = 0, *tau = 0;
Complex *z = 0, *e = 0;
double *lscale = 0, *rscale = 0, *emod = 0;
size_t *rank = 0;

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

#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_zhgeqz (f08xsc) Example Program Results\n\n");
/* Skip heading in data file */
scanf("%*[^\n] ");
scanf("%" NAG_IFMT "%*[^\n] ", &n);
pda = n;
pdb = n;

/* Allocate memory */
if (!(a = NAG_ALLOC(n * n, Complex)) || !(b = NAG_ALLOC(n * n, Complex)) ||
!(alpha = NAG_ALLOC(n, Complex)) || !(beta = NAG_ALLOC(n, Complex)) ||
!(q = NAG_ALLOC(1 * 1, Complex)) || !(tau = NAG_ALLOC(n, Complex)) ||
!(lscale = NAG_ALLOC(n, double)) || !(rscale = NAG_ALLOC(n, double)) ||
!(rank = NAG_ALLOC(n, size_t)) || !(emod = NAG_ALLOC(n, double)) ||
!(e = NAG_ALLOC(n, Complex)) || !(z = NAG_ALLOC(1 * 1, Complex))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

/* READ matrix A from data file */
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] ");

/* READ matrix B from data file */
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] ");
/* Balance matrix pair (A,B) */
/* nag_lapackeig_zggbal (f08wvc).
* Balance a pair of complex general matrices
*/
nag_lapackeig_zggbal(order, Nag_DoBoth, n, a, pda, b, pdb, &ilo, &ihi, lscale,
rscale, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_zggbal (f08wvc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Matrix A after balancing */
/* nag_file_print_matrix_complex_gen_comp (x04dbc).
* Print complex general matrix (comprehensive)
*/
fflush(stdout);
nag_file_print_matrix_complex_gen_comp(
order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, a, pda, Nag_BracketForm,
"%7.4f", "Matrix A after balancing", Nag_IntegerLabels, 0,
Nag_IntegerLabels, 0, 80, 0, 0, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_file_print_matrix_complex_gen_comp (x04dbc).\n%s\n",
fail.message);
exit_status = 2;
goto END;
}
printf("\n");

/* Matrix B after balancing */
/* nag_file_print_matrix_complex_gen_comp (x04dbc), see above. */
fflush(stdout);
nag_file_print_matrix_complex_gen_comp(
order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, b, pdb, Nag_BracketForm,
"%7.4f", "Matrix B after balancing", Nag_IntegerLabels, 0,
Nag_IntegerLabels, 0, 80, 0, 0, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_file_print_matrix_complex_gen_comp (x04dbc).\n%s\n",
fail.message);
exit_status = 3;
goto END;
}
printf("\n");

/* Reduce B to triangular form using QR */
irows = ihi + 1 - ilo;
/* nag_lapackeig_zgeqrf (f08asc).
* QR factorization of complex general rectangular matrix
*/
nag_lapackeig_zgeqrf(order, irows, irows, &B(ilo, ilo), pdb, tau, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_zgeqrf (f08asc).\n%s\n", fail.message);
exit_status = 4;
goto END;
}

/* Apply the orthogonal transformation to matrix A */
/* nag_lapackeig_zunmqr (f08auc).
* Apply unitary transformation determined by nag_lapackeig_zgeqrf
* (f08asc) or nag_lapackeig_zgeqpf (f08bsc)
*/
nag_lapackeig_zunmqr(order, Nag_LeftSide, Nag_ConjTrans, irows, irows, irows,
&B(ilo, ilo), pdb, tau, &A(ilo, ilo), pda, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_zunmqr (f08auc).\n%s\n", fail.message);
exit_status = 5;
goto END;
}

/* Compute the generalized Hessenberg form of (A,B) */
/* nag_lapackeig_zgghd3 (f08wtc).
* Unitary reduction of a pair of complex general matrices
* to generalized upper Hessenberg form
*/
nag_lapackeig_zgghd3(order, Nag_NotQ, Nag_NotZ, irows, 1, irows, &A(ilo, ilo),
pda, &B(ilo, ilo), pdb, q, 1, z, 1, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_zgghd3 (f08wtc).\n%s\n", fail.message);
exit_status = 6;
goto END;
}

/* Matrix A in generalized Hessenberg form */
/* nag_file_print_matrix_complex_gen_comp (x04dbc), see above. */
fflush(stdout);
nag_file_print_matrix_complex_gen_comp(
order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, a, pda, Nag_BracketForm,
"%7.3f", "Matrix A in Hessenberg form", Nag_IntegerLabels, 0,
Nag_IntegerLabels, 0, 80, 0, 0, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_file_print_matrix_complex_gen_comp (x04dbc).\n%s\n",
fail.message);
exit_status = 7;
goto END;
}
printf("\n");
/* Matrix B in generalized Hessenberg form */
/* nag_file_print_matrix_complex_gen_comp (x04dbc), see above. */
fflush(stdout);
nag_file_print_matrix_complex_gen_comp(
order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, b, pdb, Nag_BracketForm,
"%7.3f", "Matrix B is triangular", Nag_IntegerLabels, 0,
Nag_IntegerLabels, 0, 80, 0, 0, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_file_print_matrix_complex_gen_comp (x04dbc).\n%s\n",
fail.message);
exit_status = 8;
goto END;
}

/* Compute the generalized Schur form */
/* nag_lapackeig_zhgeqz (f08xsc).
* Eigenvalues and generalized Schur factorization of
* complex generalized upper Hessenberg form reduced from a
* pair of complex general matrices
*/
nag_lapackeig_zhgeqz(order, Nag_EigVals, Nag_NotQ, Nag_NotZ, n, ilo, ihi, a,
pda, b, pdb, alpha, beta, q, 1, z, 1, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_zhgeqz (f08xsc).\n%s\n", fail.message);
exit_status = 9;
goto END;
}

/* Print the generalized eigenvalues */
printf("\n Generalized eigenvalues\n");
ninf = 0;
for (i = 0; i < n; ++i) {
if (beta[i].re == 0.0) {
ninf = ninf + 1;
printf(" %4" NAG_IFMT "     Infinite eigenvalue\n", i + 1);
}
}
if (ninf == 0) {
/* Sort values by decreasing modulus and store in e[] */
exit_status = sort_values(n, alpha, beta, e, rank, emod);
for (i = 0; i < n; ++i) {
printf(" %4" NAG_IFMT "     (%7.3f,%7.3f)\n", i + 1, e[i].re, e[i].im);
}
}
END:
NAG_FREE(a);
NAG_FREE(alpha);
NAG_FREE(b);
NAG_FREE(beta);
NAG_FREE(lscale);
NAG_FREE(q);
NAG_FREE(rank);
NAG_FREE(rscale);
NAG_FREE(tau);
NAG_FREE(e);
NAG_FREE(emod);
NAG_FREE(z);

return exit_status;
}
static Integer sort_values(Integer n, Complex alpha[], Complex beta[],
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_divide (a02cdc): Quotient of two complex numbers;
* nag_complex_abs (a02ddc): Moduli of complex number.
*/
e[i] = nag_complex_divide(alpha[i], beta[i]);
emod[i] = nag_complex_abs(e[i]);
}
/* Rank sort eigenvalues by absolute values using
* nag_sort_rank_sort (m01dsc).
*/
nag_sort_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_sort_rank_sort (m01dsc).\n%s\n", fail.message);
exit_status = 10;
goto END;
}
/* Turn ranks into indices using nag_sort_permute_invert (m01zac). */
nag_sort_permute_invert(rank, (size_t)n, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_sort_permute_invert (m01zac).\n%s\n", fail.message);
exit_status = 11;
goto END;
}
/* Sort eigenvalues using nag_sort_reorder_vector (m01esc). */
nag_sort_reorder_vector((Pointer)e, (size_t)n, sizeof(Complex),
(ptrdiff_t)sizeof(Complex), rank, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_sort_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));
}
```