```/* nag_zggsvd3 (f08vqc) Example Program.
*
* Copyright 2017 Numerical Algorithms Group.
*
* Mark 26.2, 2017.
*/

#include <stdio.h>
#include <nag.h>
#include <nagf08.h>
#include <nagx04.h>
#include <nag_stdlib.h>
#include <nagf07.h>
#include <nagx02.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 */
char *clabs = 0, *rlabs = 0;
Complex *a = 0, *b = 0, *q = 0, *u = 0, *v = 0;
double *alpha = 0, *beta = 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_zggsvd3 (f08vqc) 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 (!(clabs = NAG_ALLOC(2, char)) ||
!(rlabs = NAG_ALLOC(2, char)) ||
!(a = NAG_ALLOC(m * n, Complex)) ||
!(b = NAG_ALLOC(p * n, Complex)) ||
!(q = NAG_ALLOC(n * n, Complex)) ||
!(u = NAG_ALLOC(m * m, Complex)) ||
!(v = NAG_ALLOC(p * p, Complex)) ||
!(alpha = NAG_ALLOC(n, double)) ||
!(beta = NAG_ALLOC(n, 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 , %lf )", &A(i, j).re, &A(i, j).im);
scanf("%*[^\n] ");

for (i = 1; i <= p; ++i)
for (j = 1; j <= n; ++j)
scanf(" ( %lf , %lf )", &B(i, j).re, &B(i, j).im);
scanf("%*[^\n] ");

/* nag_zggsvd3 (f08vqc)
* Compute the generalized singular value decomposition of (A, B)
* (A = U*D1*(0 R)*(Q^H), B = V*D2*(0 R)*(Q^H), m.ge.n)
*/
nag_zggsvd3(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_zggsvd3 (f08vqc).\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("Number 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\n", irank);
printf("Finite 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_gen_complx_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag,
m, m, u, pdu, Nag_BracketForm, "%13.4e",
"Unitary matrix U", Nag_IntegerLabels,
0, Nag_IntegerLabels, 0, 80, 0, 0, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_gen_complx_mat_print_comp (x04dbc).\n%s\n",
fail.message);
exit_status = 2;
goto END;
}

printf("\n");
fflush(stdout);
nag_gen_complx_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag,
p, p, v, pdv, Nag_BracketForm, "%13.4e",
"Unitary matrix V", Nag_IntegerLabels,
0, Nag_IntegerLabels, 0, 80, 0, 0, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_gen_complx_mat_print_comp (x04dbc).\n%s\n",
fail.message);
exit_status = 3;
goto END;
}

printf("\n");
fflush(stdout);
nag_gen_complx_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag,
n, n, q, pdq, Nag_BracketForm, "%13.4e",
"Unitary matrix Q", Nag_IntegerLabels,
0, Nag_IntegerLabels, 0, 80, 0, 0, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_gen_complx_mat_print_comp (x04dbc).\n%s\n",
fail.message);
exit_status = 4;
goto END;
}

printf("\n");
fflush(stdout);
nag_gen_complx_mat_print_comp(order, Nag_UpperMatrix, Nag_NonUnitDiag,
irank, irank, &A(1, n - irank + 1), pda,
Nag_BracketForm, "%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_gen_complx_mat_print_comp (x04dbc).\n%s\n",
fail.message);
exit_status = 5;
goto END;
}

/* nag_ztrcon (f07tuc)
* estimate the reciprocal condition number of R
*/
nag_ztrcon(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_ztrcon (f07tuc).\n%s\n", fail.message);
exit_status = 6;
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\n");
printf("%11.1e\n", serrbd);
}
else {
printf("(A^T B^T)^T is not of full rank\n");
}

END:

NAG_FREE(clabs);
NAG_FREE(rlabs);
NAG_FREE(a);
NAG_FREE(b);
NAG_FREE(q);
NAG_FREE(u);
NAG_FREE(v);
NAG_FREE(alpha);
NAG_FREE(beta);
NAG_FREE(iwork);

return exit_status;
}

#undef B
#undef A
```