```/* nag_dgejsv (f08khc) Example Program.
*
* Copyright 2014 Numerical Algorithms Group.
*
* Mark 23, 2011.
*/

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

int main(void)
{
/* Scalars */
double            eps, serrbd;
Integer           exit_status = 0;
Integer           pda, pdu, pdv;
Integer           i, j, m, n, n_uvecs, n_vvecs;
/* Arrays */
double            *a = 0, *rcondu = 0, *rcondv = 0, *s = 0, *u = 0, *v = 0;
double            work[7];
Integer           iwork[3];
char              nag_enum_arg[40];

/* Nag Types */
Nag_OrderType     order;
Nag_Preprocess    joba;
Nag_LeftVecsType  jobu;
Nag_RightVecsType jobv;
Nag_ZeroCols      jobr;
Nag_TransType     jobt;
Nag_Perturb       jobp;
NagError          fail;

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

INIT_FAIL(fail);

printf("nag_dgejsv (f08khc) Example Program Results\n\n");

jobu = Nag_LeftSpan;
jobv = Nag_RightVecs;
jobr = Nag_ZeroColsRestrict;
jobt = Nag_NoTrans;
jobp = Nag_PerturbOff;

/* Skip heading in data file*/
scanf("%*[^\n]");
scanf("%ld%ld%*[^\n]", &m, &n);

if (n < 0 || m < n)
{
printf("Invalid n or nrhs\n");
exit_status = 1;
goto END;;
}

/* Read Nag type arguments by name and convert to value */
scanf(" %39s%*[^\n]", nag_enum_arg);
/* nag_enum_name_to_value (x04nac).
* Converts NAG enum member name to value
*/
joba = (Nag_Preprocess) nag_enum_name_to_value(nag_enum_arg);
scanf(" %39s%*[^\n]", nag_enum_arg);
jobu = (Nag_LeftVecsType) nag_enum_name_to_value(nag_enum_arg);
scanf(" %39s%*[^\n]", nag_enum_arg);
jobv = (Nag_RightVecsType) nag_enum_name_to_value(nag_enum_arg);
scanf(" %39s%*[^\n]", nag_enum_arg);
jobr = (Nag_ZeroCols) nag_enum_name_to_value(nag_enum_arg);
scanf(" %39s%*[^\n]", nag_enum_arg);
jobt = (Nag_TransType) nag_enum_name_to_value(nag_enum_arg);
scanf(" %39s%*[^\n]", nag_enum_arg);
jobp = (Nag_Perturb) nag_enum_name_to_value(nag_enum_arg);

/* Size of u and v depends on some of the above Nag type arguments. */
n_uvecs = 1;
if (jobu==Nag_LeftVecs) {
n_uvecs = m;
} else if (jobu==Nag_LeftSpan) {
n_uvecs = n;
} else if (jobu==Nag_NotLeftWork && jobv==Nag_RightVecs &&
jobt==Nag_Trans && m==n) {
n_uvecs = m;
}
if (jobv==Nag_NotRightVecs) {
n_vvecs = 1;
} else {
n_vvecs = n;
}
#ifdef NAG_COLUMN_MAJOR
pda = m;
pdu = m;
pdv = n;
#else
pda = n;
pdu = n_uvecs;
pdv = n_vvecs;
#endif

if (!(a      = NAG_ALLOC(m*n, double)) ||
!(rcondu = NAG_ALLOC(m, double)) ||
!(rcondv = NAG_ALLOC(m, double)) ||
!(s      = NAG_ALLOC(n, double)) ||
!(u      = NAG_ALLOC(m*n_uvecs, double)) ||
!(v      = NAG_ALLOC(n_vvecs*n_vvecs, double)))
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}

/* 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_dgejsv (f08khc)
* Compute the singular values and left and right singular vectors
* of A (A = U*S*V^T, m>=n).
*/
nag_dgejsv(order, joba, jobu, jobv, jobr, jobt, jobp, m, n, a, pda, s, u, pdu,
v, pdv, work, iwork, &fail);
if (fail.code != NE_NOERROR)
{
printf("Error from nag_dgejsv (f08khc).\n%s\n", fail.message);
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).
*/
eps = nag_machine_precision;
serrbd = eps * s[0];

/* Print (possibly scaled) singular values. */
if (fabs(work[0] - work[1]) < 2.0 * eps)
{
/* No scaling required*/
printf("Singular values\n");
for (j = 0; j < n; j++) printf("%8.4f", s[j]);
}
else
{
printf("Scaled singular values\n");
for (j = 0; j < n; j++) printf("%8.4f", s[j]);
printf("\nFor true singular values, multiply by a/b,\n");
printf("where a = %f and b = %f", work[0], work[1]);
}
printf("\n\n");

/* Print left and right (spanning) singular vectors, if requested.  using
* nag_gen_real_mat_print (x04cac)
* Print real general matrix (easy-to-use)
*/
if (jobu==Nag_LeftVecs || jobu==Nag_LeftSpan) {
fflush(stdout);
nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, m, n, 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;
}
}
if (jobv==Nag_RightVecs || jobv==Nag_RightVecsJRots) {
printf("\n");
fflush(stdout);
nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, v,
pdv, "Right 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;
}
}

/* nag_ddisna (f08flc)
* Estimate reciprocal condition numbers for the singular vectors.
*/
nag_ddisna(Nag_LeftSingVecs, m, n, s, rcondu, &fail);
if (fail.code == NE_NOERROR)
nag_ddisna(Nag_RightSingVecs, m, n, s, rcondv, &fail);
if (fail.code != NE_NOERROR)
{
printf("Error from nag_ddisna (f08flc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

if (joba==Nag_ColpivRrankCond || joba==Nag_FullpivRrankCond) {
printf("\n\nEstimate of the condition number of column equilibrated A\n");
printf("%11.1e", work[2]);
}

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

printf("\n\nError estimates for left singular vectors\n");
for (i = 0; i < n; i++) printf("%11.1e", serrbd/rcondu[i]);

printf("\n\nError estimates for right singular vectors\n");
for (i = 0; i < n; i++) printf("%11.1e", serrbd/rcondv[i]);
printf("\n");

END:
NAG_FREE(a);
NAG_FREE(rcondu);
NAG_FREE(rcondv);
NAG_FREE(s);
NAG_FREE(u);
NAG_FREE(v);

return exit_status;
}
```