```/* nag_dgesvj (f08kjc) Example Program.
*
* Copyright 2017 Numerical Algorithms Group.
*
* Mark 26.1, 2017.
*/

#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, ctol;
Integer exit_status = 0;
Integer i, j, lwork, m, mv, n, n_vrows, n_vcols, pda, pdv, ranka;

/* Arrays */
double *a = 0, *rcondu = 0, *rcondv = 0, *s = 0, *v = 0, *work = 0;
char nag_enum_arg[40];

/* Nag Types */
Nag_OrderType order;
Nag_MatrixType joba;
Nag_LeftVecsType jobu;
Nag_RightVecsType jobv;
NagError fail;

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

INIT_FAIL(fail);

printf("nag_dgesvj (f08kjc) Example Program Results\n\n");

/* Skip heading in data file */
scanf("%*[^\n]");
scanf("%" NAG_IFMT "%" NAG_IFMT "%*[^\n]", &m, &n);
if (n < 0 || m < n) {
printf("Invalid m or n\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_MatrixType) 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);

n_vcols = n;
n_vrows = n;
mv = 0;
if (jobv == Nag_RightVecsMV) {
scanf("%" NAG_IFMT, &mv);
n_vrows = mv;
}
else if (jobv == Nag_NotRightVecs) {
n_vrows = 1;
n_vcols = 1;
}
scanf("%*[^\n]");

#ifdef NAG_COLUMN_MAJOR
pda = m;
pdv = n_vrows;
#else
pda = n;
pdv = n_vcols;
#endif
lwork = 6;

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

/* Read the m by n matrix A from data file */
if (joba == Nag_GeneralMatrix) {
for (i = 1; i <= m; i++)
for (j = 1; j <= n; j++)
scanf("%lf", &A(i, j));
}
else if (joba == Nag_UpperMatrix) {
for (i = 1; i <= m; i++)
for (j = i; j <= n; j++)
scanf("%lf", &A(i, j));
}
else {
for (i = 1; i <= m; i++)
for (j = 1; j <= i; j++)
scanf("%lf", &A(i, j));
}
scanf("%*[^\n]");
/* jobv==Nag_RightVecsMV means that the first mv rows of v must be set. */
if (jobv == Nag_RightVecsMV) {
for (i = 1; i <= mv; i++)
for (j = 1; j <= n; j++)
scanf("%lf", &V(i, j));
scanf("%*[^\n]");
}
ctol = 10.0;
/* nag_dgesvj (f08kjc)
* Compute the singular values and left and right singular vectors
* of A (A = U*S*V, m>=n).
*/
nag_dgesvj(order, joba, jobu, jobv, m, n, a, pda, s, mv, v, pdv, ctol,
work, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dgesvj (f08kjc).\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 solution */
printf("Singular values\n   ");
for (j = 0; j < n; j++)
printf("%8.4f", s[j]);
printf("\n\n");
if (fabs(work[0] - 1.0) > eps)
printf("Values need scaling by factor = %13.5e\n\n", work[0]);

ranka = (Integer) work[1];
printf("Rank of A = %5" NAG_IFMT "\n\n", ranka);
if (jobu != Nag_NotLeftVecs) {
/* nag_gen_real_mat_print (x04cac)
* Print real general matrix (easy-to-use)
*/
fflush(stdout);
nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, m,
ranka, a, pda, "Left spanning 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) {
printf("\n");
fflush(stdout);
nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, v,
pdv, "Right singular vectors", 0, &fail);
}
else if (jobv == Nag_RightVecsMV) {
printf("\n");
fflush(stdout);
nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, mv, n,
v, pdv,
"Right singular vectors applied to input V", 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);
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;
}

/* Print the approximate error bounds for the singular values and vectors. */
printf("\nError estimate for the singular values\n");
printf("%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(v);
NAG_FREE(work);

return exit_status;
}
```