NAG Library Manual, Mark 28.7
```/* nag_lapackeig_dtgsja (f08yec) Example Program.
*
* Copyright 2022 Numerical Algorithms Group.
*
* Mark 28.7, 2022.
*/

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

int main(void) {
/* Scalars */
double norma, normb, eps, tola, tolb;
Integer i, irank, j, k, l, m, n, ncycle, p, pda, pdb, pdq, pdu, pdv;
Integer printq, printr, printu, printv, vsize;
Integer exit_status = 0;

/* Arrays */
double *a = 0, *alpha = 0, *b = 0, *beta = 0, *q = 0, *u = 0, *v = 0;
char nag_enum_arg[40];

/* Nag Types */
NagError fail;
Nag_OrderType order;
Nag_ComputeUType jobu;
Nag_ComputeVType jobv;
Nag_ComputeQType jobq;
Nag_MatrixType genmat = Nag_GeneralMatrix, upmat = Nag_UpperMatrix;
Nag_DiagType diag = Nag_NonUnitDiag;
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_dtgsja (f08yec) Example Program Results\n\n");

/* Skip heading in data file */
scanf("%*[^\n]");
scanf("%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "%*[^\n]", &m, &n, &p);
if (m < 0 || n < 0 || p < 0) {
printf("Invalid m, n or p\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
*/
jobu = (Nag_ComputeUType)nag_enum_name_to_value(nag_enum_arg);
scanf(" %39s%*[^\n]", nag_enum_arg);
jobv = (Nag_ComputeVType)nag_enum_name_to_value(nag_enum_arg);
scanf(" %39s%*[^\n]", nag_enum_arg);
jobq = (Nag_ComputeQType)nag_enum_name_to_value(nag_enum_arg);

pdu = (jobu != Nag_NotU ? m : 1);
pdv = (jobv != Nag_NotV ? p : 1);
pdq = (jobq != Nag_NotQ ? n : 1);
vsize = (jobv != Nag_NotV ? p * m : 1);
#ifdef NAG_COLUMN_MAJOR
pda = m;
pdb = p;
#else
pda = n;
pdb = n;
#endif

/* 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)) ||
!(alpha = NAG_ALLOC(n, double)) || !(beta = NAG_ALLOC(n, double)) ||
!(q = NAG_ALLOC(pdq * pdq, double)) ||
!(u = NAG_ALLOC(pdu * pdu, double)) || !(v = NAG_ALLOC(vsize, 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]");

nag_blast_dge_norm(order, Nag_FrobeniusNorm, m, n, a, pda, &norma, &fail);
nag_blast_dge_norm(order, Nag_FrobeniusNorm, p, n, b, pdb, &normb, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_blast_dge_norm (f16rac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Compute tola and tolb using nag_machine_precision (x02ajc) */
eps = nag_machine_precision;
tola = MAX(m, n) * norma * eps;
tolb = MAX(p, n) * normb * eps;

/* Preprocess step:
* compute transformations to reduce (A, B) to upper triangular form
* (A = U1*S*(Q1^T), B = V1*T*(Q1^T))
* using nag_lapackeig_dggsvp (f08vec).
*/
nag_lapackeig_dggsvp(order, jobu, jobv, jobq, 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_dggsvp (f08vec).\n%s\n", fail.message);
exit_status = 1;
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, jobu, jobv, jobq, 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 = 1;
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 && jobu != Nag_NotU) {
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 && jobv != Nag_NotV) {
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 && jobq != Nag_NotQ) {
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 = 1;
}

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;
}
```