```/* nag_lapackeig_dggsvd (f08vac) Example Program.
*
* Copyright 2020 Numerical Algorithms Group.
*
* Mark 27.1, 2020.
*/

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

int main(void) {

/* Scalars */
double d, eps, rcond, serrbd;
Integer exit_status = 0, i, irank, j, k, l, m, n, p, pda, pdb, pdq, pdu, pdv;
NagError fail;
Nag_OrderType order;

/* Arrays */
double *a = 0, *alpha = 0, *b = 0, *beta = 0, *q = 0, *u = 0, *v = 0;
Integer *iwork = 0;

#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_dggsvd (f08vac) 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 <= 10 && n <= 10 && p <= 10) {
/* Allocate memory */
if (!(a = NAG_ALLOC(m * n, double)) || !(alpha = NAG_ALLOC(n, double)) ||
!(b = NAG_ALLOC(p * n, double)) || !(beta = NAG_ALLOC(n, double)) ||
!(q = NAG_ALLOC(n * n, double)) || !(u = NAG_ALLOC(m * m, double)) ||
!(v = NAG_ALLOC(p * p, double)) || !(iwork = NAG_ALLOC(n, Integer))) {
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
#ifdef NAG_COLUMN_MAJOR
pda = m;
pdb = p;
pdq = n;
pdu = m;
pdv = p;
#else
pda = n;
pdb = n;
pdq = n;
pdu = m;
pdv = p;
#endif
} else {
printf("m and/or n too small\n");
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_lapackeig_dggsvd (f08vac)
* Compute the generalized singular value decomposition of (A, B)
* (A = U*D1*(0 R)*(Q^T), B = V*D2*(0 R)*(Q^T), m.ge.n)
*/

nag_lapackeig_dggsvd(order, Nag_AllU, Nag_ComputeV, Nag_ComputeQ, m, n, p, &k,
&l, a, pda, b, pdb, alpha, beta, u, pdu, v, pdv, q, pdq,
iwork, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_dggsvd (f08vac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* Print solution */
irank = k + l;

printf("Number of infinite generalized singular values (k)\n");
printf("%5" NAG_IFMT "\n", k);
printf("\nNumber of finite generalized singular values (l)\n");
printf("%5" NAG_IFMT "\n", l);
printf("Numerical rank of ( A^T B^T)^T   (k+l)\n");
printf("%5" NAG_IFMT "\n", irank);

printf("\nFinite generalized singular values\n");
for (j = k; j < irank; ++j) {
d = alpha[j] / beta[j];
printf("%13.4e%s", d, (j + 1) % 8 == 0 || (j + 1) == irank ? "\n" : " ");
}

printf("\n");
fflush(stdout);
nag_file_print_matrix_real_gen_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag,
m, m, u, pdu, "%13.4e",
"Orthogonal matrix U", Nag_IntegerLabels,
0, Nag_IntegerLabels, 0, 80, 0, 0, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_file_print_matrix_real_gen_comp (x04cbc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

printf("\n");
fflush(stdout);
nag_file_print_matrix_real_gen_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag,
p, p, v, pdv, "%13.4e",
"Orthogonal matrix V", Nag_IntegerLabels,
0, Nag_IntegerLabels, 0, 80, 0, 0, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_file_print_matrix_real_gen_comp (x04cbc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

printf("\n");
fflush(stdout);
nag_file_print_matrix_real_gen_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag,
n, n, q, pdq, "%13.4e",
"Orthogonal matrix Q", Nag_IntegerLabels,
0, Nag_IntegerLabels, 0, 80, 0, 0, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_file_print_matrix_real_gen_comp (x04cbc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

printf("\n");
fflush(stdout);
nag_file_print_matrix_real_gen_comp(
order, Nag_UpperMatrix, Nag_NonUnitDiag, irank, irank,
&A(1, n - irank + 1), pda, "%13.4e",
"Nonsingular upper triangular matrix R", Nag_IntegerLabels, 0,
Nag_IntegerLabels, 0, 80, 0, 0, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_file_print_matrix_real_gen_comp (x04cbc).\n%s\n",
fail.message);
exit_status = 1;
goto END;
}

/* nag_lapacklin_dtrcon (f07tgc)
* estimate the reciprocal condition number of R
*/

nag_lapacklin_dtrcon(order, Nag_InfNorm, Nag_Upper, Nag_NonUnitDiag, irank,
&A(1, n - irank + 1), pda, &rcond, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapacklin_dtrcon (f07tgc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

printf("\nEstimate of reciprocal condition number for R\n");
printf("%11.1e\n\n", rcond);

/* So long as irank = n, get the machine precision, eps, and compute the
* approximate error bound for the computed generalized singular values
*/
if (irank == n) {
eps = nag_machine_precision;
serrbd = eps / rcond;
printf("Error estimate for the generalized singular values");
printf("\n%11.1e\n", serrbd);
} else {
printf("( A^T B^T)^T is not of full rank\n");
}

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

return exit_status;
}

#undef B
#undef A
```