NAG Library Manual, Mark 30.1
```/* nag_lapackeig_dtgsen (f08ygc) Example Program.
*
* Copyright 2024 Numerical Algorithms Group.
*
* Mark 30.1, 2024.
*/

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

int main(void) {

/* Scalars */
double pl, pr, small;
Integer i, ijob, j, m, n, pdq, pds, pdt, pdz;
Integer exit_status = 0;

/* Arrays */
double *alphai = 0, *alphar = 0, *beta = 0, *q = 0, *s = 0, *t = 0, *z = 0;
double dif[2];
char nag_enum_arg[40];

/* Nag Types */
NagError fail;
Nag_OrderType order;
Nag_Boolean wantq, wantz;
Nag_Boolean *select = 0;

#ifdef NAG_COLUMN_MAJOR
#define S(I, J) s[(J - 1) * pds + I - 1]
#define T(I, J) t[(J - 1) * pdt + I - 1]
#define Q(I, J) q[(J - 1) * pdq + I - 1]
#define Z(I, J) z[(J - 1) * pdz + I - 1]
order = Nag_ColMajor;
#else
#define S(I, J) s[(I - 1) * pds + J - 1]
#define T(I, J) t[(I - 1) * pdt + J - 1]
#define Q(I, J) q[(I - 1) * pdq + J - 1]
#define Z(I, J) z[(I - 1) * pdz + J - 1]
order = Nag_RowMajor;
#endif

INIT_FAIL(fail);

printf("nag_lapackeig_dtgsen (f08ygc) Example Program Results\n\n");

/* Skip heading in data file */
scanf("%*[^\n]");
scanf("%" NAG_IFMT "%" NAG_IFMT "%*[^\n]", &n, &ijob);
if (n < 0 || ijob < 0 || ijob > 5) {
printf("Invalid n or ijob\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
*/
wantq = (Nag_Boolean)nag_enum_name_to_value(nag_enum_arg);
scanf(" %39s%*[^\n]", nag_enum_arg);
wantz = (Nag_Boolean)nag_enum_name_to_value(nag_enum_arg);

pds = n;
pdt = n;
pdq = (wantq ? n : 1);
pdz = (wantz ? n : 1);

/* Allocate memory */
if (!(s = NAG_ALLOC(n * n, double)) || !(t = NAG_ALLOC(n * n, double)) ||
!(alphai = NAG_ALLOC(n, double)) || !(alphar = NAG_ALLOC(n, double)) ||
!(beta = NAG_ALLOC(n, double)) || !(select = NAG_ALLOC(n, Nag_Boolean)) ||
!(q = NAG_ALLOC(pdq * pdq, double)) ||
!(z = NAG_ALLOC(pdz * pdz, double))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

/* nag_enum_name_to_value (x04nac).
* Converts NAG enum member name to value
*/
for (i = 0; i < n; ++i) {
scanf("%39s", nag_enum_arg);
select[i] = (Nag_Boolean)nag_enum_name_to_value(nag_enum_arg);
}
scanf("%*[^\n]");

/* Read S, T, Q, Z and the logical array select from data file */
for (i = 1; i <= n; ++i)
for (j = 1; j <= n; ++j)
scanf("%lf", &S(i, j));
scanf("%*[^\n]");
for (i = 1; i <= n; ++i)
for (j = 1; j <= n; ++j)
scanf("%lf", &T(i, j));
scanf("%*[^\n]");

if (wantq) {
for (i = 1; i <= n; ++i)
for (j = 1; j <= n; ++j)
scanf("%lf", &Q(i, j));
scanf("%*[^\n]");
}
if (wantz) {
for (i = 1; i <= n; ++i)
for (j = 1; j <= n; ++j)
scanf("%lf", &Z(i, j));
scanf("%*[^\n]");
}

/* Reorder the Schur factors S and T and update the matrices Q and Z */
nag_lapackeig_dtgsen(order, ijob, wantq, wantz, select, n, s, pds, t, pdt,
alphar, alphai, beta, q, pdq, z, pdz, &m, &pl, &pr, dif,
&fail);

if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_dtgsen (f08ygc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_machine_real_safe (x02amc). */
small = nag_machine_real_safe;

/* Print the eigenvalues */
printf("Selected Eigenvalues\n");
for (j = 0; j < m; ++j) {
printf("%2" NAG_IFMT " ", j + 1);
if ((fabs(alphar[j]) + fabs(alphai[j])) * small >= fabs(beta[j]))
printf("  infinite or undetermined, alpha = (%13.4e, %13.4e), "
"beta = %13.4e\n",
alphar[j], alphai[j], beta[j]);
else if (alphai[j] == 0.0)
printf("  %12.4e\n", alphar[j] / beta[j]);
else
printf("  (%13.4e, %13.4e)\n", alphar[j] / beta[j], alphai[j] / beta[j]);
}

if (ijob == 1 || ijob == 4 || ijob == 5) {
printf("\n");
printf("For the selected eigenvalues,\nthe reciprocals of projection "
"norms onto the deflating subspaces are\n");
printf(" for left  subspace, pl = %11.2e\n for right subspace, pr = "
"%11.2e\n\n",
pl, pr);
}
if (ijob > 1) {
printf(" upper bound on Difu    = %11.2e\n", dif[0]);
printf(" upper bound on Difl    = %11.2e\n", dif[1]);
if (ijob == 2 || ijob == 4) {
printf("\nUpper bounds on Difl, Difu are based on the Frobenius norm\n");
}
if (ijob == 3 || ijob == 5) {
printf("\nUpper bounds on Difl, Difu are based on the one norm.\n");
}
}

END:
NAG_FREE(s);
NAG_FREE(t);
NAG_FREE(alphai);
NAG_FREE(alphar);
NAG_FREE(beta);
NAG_FREE(select);
NAG_FREE(q);
NAG_FREE(z);

return exit_status;
}
```