```/* nag_lapackeig_dgesvd (f08kbc) Example Program.
*
* Copyright 2019 Numerical Algorithms Group.
*
* Mark 27.0, 2019.
*/

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

int main(void)
{

/* Scalars */
double alpha, beta, eps, norm, serrbd;
Integer exit_status = 0, i, j, m, n, pda, pdd, pdu, pdvt;

/* Arrays */
double *a = 0, *d = 0, *rcondu = 0, *rcondv = 0;
double *s = 0, *u = 0, *uerrbd = 0, *verrbd = 0, *vt = 0, *work = 0;

/* 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_lapackeig_dgesvd (f08kbc) 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)) ||
!(d = NAG_ALLOC(m * n, double)) ||
!(rcondu = NAG_ALLOC(n, double)) ||
!(rcondv = NAG_ALLOC(n, double)) ||
!(s = NAG_ALLOC(MIN(m, n), double)) ||
!(u = NAG_ALLOC(m * m, double)) ||
!(uerrbd = NAG_ALLOC(n, double)) ||
!(verrbd = NAG_ALLOC(n, double)) ||
!(vt = NAG_ALLOC(n * n, double)) ||
!(work = NAG_ALLOC(MIN(m, n), double)))
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

pdu = m;
pdvt = n;
#ifdef NAG_COLUMN_MAJOR
pda = m;
pdd = m;
#else
pda = n;
pdd = 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]");

/* Copy a into d */
for (i = 0; i < m * n; i++)
d[i] = a[i];

/* nag_file_print_matrix_real_gen (x04cac)
* Print real general matrix A.
*/
fflush(stdout);
nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, m, n, a,
pda, "Matrix A", 0, &fail);
printf("\n");
if (fail.code != NE_NOERROR) {
printf("Error from nag_file_print_matrix_real_gen (x04cac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_lapackeig_dgesvd (f08kbc).
* Compute the singular values and left and right singular vectors
* of A (A = U*S*(V^T), m.ge.n)
*/
nag_lapackeig_dgesvd(order, Nag_AllU, Nag_AllVT, m, n, a, pda, s, u, pdu, vt, pdvt,
work, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_lapackeig_dgesvd (f08kbc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* U <- U*S */
for (i = 1; i <= m; i++)
for (j = 1; j <= n; j++)
U(i, j) *= s[j - 1];

/* nag_blast_dgemm (f16yac):
* Compute D = D - U*S*V^T from the factorization of A
* and store in d */
alpha = -1.0;
beta = 1.0;
nag_blast_dgemm(order, Nag_NoTrans, Nag_NoTrans, m, n, n, alpha, u, pdu, vt, pdvt,
beta, d, pdd, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_blast_dgemm (f16yac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_blast_dge_norm (f16rac)
* Find norm of matrix D and print warning if it is too large.
*/
nag_blast_dge_norm(order, Nag_OneNorm, m, n, d, pdd, &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;
}

/* nag_machine_precision (x02ajc): the machine precision. */
eps = nag_machine_precision;
if (norm > pow(eps, 0.8)) {
printf("\nNorm of A-(U*S*V^T) is much greater than 0.\n"
"Schur factorization has failed.\n");
exit_status = 1;
goto END;
}
/* Get the machine precision, eps and compute the approximate
* error bound for the computed singular values.
* Note that for the 2-norm, s[0] = norm(A).
*/
serrbd = eps * s[0];

/* Estimate reciprocal condition numbers for the singular vectors using
* nag_lapackeig_ddisna (f08flc).
*/
nag_lapackeig_ddisna(Nag_LeftSingVecs, m, n, s, rcondu, &fail);
nag_lapackeig_ddisna(Nag_RightSingVecs, m, n, s, rcondv, &fail);

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

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

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

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

return exit_status;
}

#undef A
#undef U
```