```/* nag_dgesdd (f08kdc) Example Program.
*
* Copyright 2017 Numerical Algorithms Group.
*
* Mark 26.1, 2017.
*/

#include <stdio.h>
#include <nag.h>
#include <nagx04.h>
#include <nag_stdlib.h>
#include <nagf08.h>
#include <nagx02.h>

int main(void)
{

/* Scalars */
double eps, serrbd;
Integer exit_status = 0, i, j, m, n, pda, pdu;

/* Arrays */
double *a = 0, *rcondu = 0, *rcondv = 0, *s = 0, *u = 0;
double *uerrbd = 0, *verrbd = 0;
double dummy[1];

/* Nag Types */
NagError fail;
Nag_OrderType order;

#ifdef NAG_COLUMN_MAJOR
#define A(I, J) a[(J - 1) * pda + I - 1]
#define U(I, J) u[(J - 1) * pdu + I - 1]
order = Nag_ColMajor;
#else
#define A(I, J) a[(I - 1) * pda + J - 1]
#define U(I, J) u[(I - 1) * pdu + J - 1]
order = Nag_RowMajor;
#endif

INIT_FAIL(fail);

printf("nag_dgesdd (f08kdc) Example Program Results\n\n");

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

/* Allocate memory */
if (!(a = NAG_ALLOC(m * n, double)) ||
!(rcondu = NAG_ALLOC(m, double)) ||
!(rcondv = NAG_ALLOC(m, double)) ||
!(s = NAG_ALLOC(MIN(m, n), double)) ||
!(u = NAG_ALLOC(m * m, double)) ||
!(uerrbd = NAG_ALLOC(m, double)) || !(verrbd = NAG_ALLOC(m, double))
)
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

#ifdef NAG_COLUMN_MAJOR
pda = m;
pdu = m;
#else
pda = n;
pdu = MIN(m, n);
#endif

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

/* nag_dgesdd (f08kdc).
* Compute the singular values and left and right singular vectors
* of A (A = U*S*(V^T), m.le.n)
*/
nag_dgesdd(order, Nag_DoOverwrite, m, n, a, pda, s, u, pdu, dummy, 1,
&fail);

if (fail.code != NE_NOERROR) {
printf("Error from nag_dgesdd (f08kdc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Print singular values */
printf("Singular values\n");
for (i = 0; i < m; ++i)
printf(" %7.4f%s", s[i], i % 8 == 7 ? "\n" : "");
printf("\n\n");

/*  Normalize so that first elements of singular vectors u >= 0 */
for (i = 1; i <= m; ++i) {
if (U(1,i)<0.0) {
for (j = 1; j <= m; ++j)
U(j,i) = -U(j,i);
for (j = 1; j <= n; ++j)
A(i,j) = -A(i,j);
}
}
/* Print left and right singular vectors using
* nag_gen_real_mat_print (x04cac).
*/
fflush(stdout);
nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, m, m, u,
pdu, "Left singular vectors", 0, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_gen_real_mat_print (x04cac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
printf("\n");

fflush(stdout);
nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, m, n, a,
pda, "Right singular vectors by row", 0, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_gen_real_mat_print (x04cac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

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

/* compute the approximate error bound for the computed singular values.
* Note that for the 2-norm, s[0] = ||A||
*/
serrbd = eps * s[0];

/* Call nag_ddisna (f08flc) to estimate reciprocal condition numbers for
* the singular vectors.
*/
nag_ddisna(Nag_LeftSingVecs, m, n, s, rcondu, &fail);
nag_ddisna(Nag_RightSingVecs, m, n, s, rcondv, &fail);

/* Compute the error estimates for the singular vectors. */
for (i = 0; i < m; ++i) {
uerrbd[i] = serrbd / rcondu[i];
verrbd[i] = serrbd / rcondv[i];
}

/* Print the approximate error bounds for the singular values and vectors */
printf("\nError estimate for the singular values\n%11.1e\n", serrbd);

printf("\nError estimates for the left singular vectors\n");
for (i = 0; i < m; ++i)
printf(" %10.1e%s", uerrbd[i], i % 6 == 5 ? "\n" : "");

printf("\n\nError estimates for the right singular vectors\n");
for (i = 0; i < m; ++i)
printf(" %10.1e%s", verrbd[i], i % 6 == 5 ? "\n" : "");
printf("\n");

END:
NAG_FREE(a);
NAG_FREE(rcondu);
NAG_FREE(rcondv);
NAG_FREE(s);
NAG_FREE(u);
NAG_FREE(uerrbd);
NAG_FREE(verrbd);

return exit_status;
}

#undef A
```