NAG Library Manual, Mark 30.1
```/* nag_lapackeig_dggsvp3 (f08vgc) Example Program.
*
* Copyright 2024 Numerical Algorithms Group.
*
* Mark 30.1, 2024.
*/

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

int main(void) {
/* Scalars */
double eps, norm, tola, tolb;
Integer i, irank, j, k, l, m, n, ncycle, p, pda, pdb, pdq, pdu, pdv;
Integer printq, printr, printu, printv;
Integer exit_status = 0;
/* Arrays */
double *a = 0, *b = 0, *q = 0, *u = 0, *v = 0, *alpha = 0, *beta = 0;

/* Nag Types */
NagError fail;
Nag_OrderType order;
Nag_DiagType diag = Nag_NonUnitDiag;
Nag_MatrixType genmat = Nag_GeneralMatrix, upmat = Nag_UpperMatrix;
Nag_LabelType intlab = Nag_IntegerLabels;

#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_dggsvp3 (f08vgc) Example Program Results\n\n");

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

#ifdef NAG_COLUMN_MAJOR
pda = m;
pdb = p;
pdv = p;
#else
pda = n;
pdb = n;
pdv = m;
#endif
pdq = n;
pdu = m;

/* Read in 0s or 1s to determine whether matrices U, V, Q or R are to be
* printed.
*/
scanf("%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "%*[^\n]", &printu,
&printv, &printq, &printr);

/* Allocate memory */
if (!(a = NAG_ALLOC(m * n, double)) || !(b = NAG_ALLOC(p * n, double)) ||
!(q = NAG_ALLOC(n * n, double)) || !(u = NAG_ALLOC(m * m, double)) ||
!(v = NAG_ALLOC(n * n, double)) || !(alpha = NAG_ALLOC(n, double)) ||
!(beta = NAG_ALLOC(n, double))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

/* Read the m by n matrix A and p by n matrix B from data file */
for (i = 1; i <= m; ++i)
for (j = 1; j <= n; ++j)
scanf("%lf", &A(i, j));
scanf("%*[^\n]");
for (i = 1; i <= p; ++i)
for (j = 1; j <= n; ++j)
scanf("%lf", &B(i, j));
scanf("%*[^\n]");

/* get norms of A and B using nag_blast_dge_norm (f16rac). */
nag_blast_dge_norm(order, Nag_OneNorm, m, n, a, pda, &norm, &fail);
nag_blast_dge_norm(order, Nag_OneNorm, p, n, b, pdb, &norm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_blast_dge_norm (f16rac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Get the machine precision, using nag_machine_precision (x02ajc) */
eps = nag_machine_precision;

tola = MAX(m, n) * norm * eps;
tolb = MAX(p, n) * norm * eps;

/* Compute the factorization of (A, B) (A = U*S*(Q^T), B = V*T*(Q^T))
* using nag_lapackeig_dggsvp3 (f08vgc).
*/
nag_lapackeig_dggsvp3(order, Nag_AllU, Nag_ComputeV, Nag_ComputeQ, m, p, n, a,
pda, b, pdb, tola, tolb, &k, &l, u, pdu, v, pdv, q, pdq,
&fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_dggsvp3 (f08vgc).\n%s\n", fail.message);
exit_status = 2;
goto END;
}

/* Compute the generalized singular value decomposition of preprocessed (A,B)
* (A = U*D1*(0 R)*(Q^T), B = V*D2*(0 R)*(Q^T))
* using nag_lapackeig_dtgsja (f08yec). */
nag_lapackeig_dtgsja(order, Nag_AllU, Nag_ComputeV, Nag_ComputeQ, m, p, n, k,
l, a, pda, b, pdb, tola, tolb, alpha, beta, u, pdu, v,
pdv, q, pdq, &ncycle, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_dtgsja (f08yec).\n%s\n", fail.message);
exit_status = 3;
goto END;
}

/* Print the generalized singular value pairs alpha, beta */
irank = MIN(k + l, m);
printf("Number of infinite generalized singular values (k): %5" NAG_IFMT "\n",
k);
printf("Number of   finite generalized singular values (l): %5" NAG_IFMT "\n",
l);
printf("Effective Numerical rank  of  ( A^T B^T)^T   (k+l): %5" NAG_IFMT "\n",
irank);
printf("\nFinite generalized singular values:\n");

for (j = k; j < irank; ++j)
printf("%45s%12.4e\n", "", alpha[j] / beta[j]);

printf("\nNumber of cycles of the Kogbetliantz method: %12" NAG_IFMT "\n\n",
ncycle);

if (printu) {
fflush(stdout);
nag_file_print_matrix_real_gen_comp(order, genmat, diag, m, m, u, pdu,
"%13.4e", "Orthogonal matrix U", intlab,
NULL, intlab, NULL, 80, 0, NULL, &fail);
if (fail.code != NE_NOERROR)
goto PRINTERR;
printf("\n");
}
if (printv) {
fflush(stdout);
nag_file_print_matrix_real_gen_comp(order, genmat, diag, p, p, v, pdv,
"%13.4e", "Orthogonal matrix V", intlab,
NULL, intlab, NULL, 80, 0, NULL, &fail);
if (fail.code != NE_NOERROR)
goto PRINTERR;
printf("\n");
}
if (printq) {
fflush(stdout);
nag_file_print_matrix_real_gen_comp(order, genmat, diag, n, n, q, pdq,
"%13.4e", "Orthogonal matrix Q", intlab,
NULL, intlab, NULL, 80, 0, NULL, &fail);
if (fail.code != NE_NOERROR)
goto PRINTERR;
printf("\n");
}
if (printr) {
fflush(stdout);
nag_file_print_matrix_real_gen_comp(
order, upmat, diag, irank, irank, &A(1, n - irank + 1), pda, "%13.4e",
"Nonsingular upper triangular matrix R", intlab, NULL, intlab, NULL, 80,
0, NULL, &fail);
}
PRINTERR:
if (fail.code != NE_NOERROR) {
printf("Error from nag_file_print_matrix_real_gen_comp (x04cbc).\n%s\n",
fail.message);
exit_status = 4;
}

END:
NAG_FREE(a);
NAG_FREE(alpha);
NAG_FREE(b);
NAG_FREE(beta);
NAG_FREE(q);
NAG_FREE(u);
NAG_FREE(v);

return exit_status;
}
```