```/* nag_dorgbr (f08kfc) Example Program.
*
* NAGPRODCODE Version.
*
* Copyright 2016 Numerical Algorithms Group.
*
* Mark 26, 2016.
*/

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

int main(void)
{
/* Scalars */
Integer i, ic, j, m, n, pda, pdc, pdu, pdvt, d_len;
Integer e_len, tauq_len, taup_len;
Integer exit_status = 0;
NagError fail;
Nag_OrderType order;
/* Arrays */
double *a = 0, *c = 0, *d = 0, *e = 0, *taup = 0, *tauq = 0, *u = 0;
double *vt = 0;

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

INIT_FAIL(fail);

printf("nag_dorgbr (f08kfc) Example Program Results\n\n");

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

for (ic = 1; ic <= 2; ++ic) {
scanf("%" NAG_IFMT "%" NAG_IFMT "%*[^\n] ", &m, &n);

#ifdef NAG_COLUMN_MAJOR
pda = m;
pdu = m;
pdvt = m;
#else
pda = n;
pdu = n;
pdvt = n;
#endif
pdc = n;
d_len = n;
e_len = n - 1;
tauq_len = n;
taup_len = n;

/* Allocate memory */
if (!(a = NAG_ALLOC(m * n, double)) ||
!(c = NAG_ALLOC(n * n, double)) ||
!(d = NAG_ALLOC(d_len, double)) ||
!(e = NAG_ALLOC(e_len, double)) ||
!(taup = NAG_ALLOC(taup_len, double)) ||
!(tauq = NAG_ALLOC(tauq_len, double)) ||
!(u = NAG_ALLOC(m * n, double)) || !(vt = NAG_ALLOC(m * n, double)))
{
printf("Allocation failure\n");
exit_status = -1;
goto END;
}
/* Read A from data file */
for (i = 1; i <= m; ++i) {
for (j = 1; j <= n; ++j)
scanf("%lf", &A(i, j));
}
scanf("%*[^\n] ");

/* Reduce A to bidiagonal form using  nag_dgebrd (f08kec). */
nag_dgebrd(order, m, n, a, pda, d, e, tauq, taup, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dgebrd (f08kec).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
if (m >= n) {
/* Example 1 */
/* Copy A to VT and U */
for (i = 1; i <= n; ++i) {
for (j = i; j <= n; ++j)
VT(i, j) = A(i, j);
}
for (i = 1; i <= m; ++i) {
for (j = 1; j <= MIN(i, n); ++j)
U(i, j) = A(i, j);
}
/* nag_dorgbr (f08kfc):                                 */
/*       Form P^T explicitly, storing the result in VT */
nag_dorgbr(order, Nag_FormP, n, n, m, vt, pdvt, taup, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dorgbr (f08kfc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_dorgbr (f08kfc):                             */
/*       Form Q explicitly, storing the result in U */
nag_dorgbr(order, Nag_FormQ, m, n, n, u, pdu, tauq, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dorgbr (f08kfc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* nag_dbdsqr (f08mec): Compute the SVD of A.        */
nag_dbdsqr(order, Nag_Upper, n, n, m, 0, d, e, vt, pdvt, u,
pdu, c, pdc, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dbdsqr (f08mec).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Print singular values, left & right singular vectors */
printf("\n Example 1: singular values\n");
for (i = 1; i <= n; ++i)
printf("%8.4f%s", d[i - 1], i % 8 == 0 ? "\n" : " ");
printf("\n\n");

/* nag_gen_real_mat_print (x04cac): Print VT. */
fflush(stdout);
nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag,
n, n, vt, pdvt,
"Example 1: 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;
}
printf("\n");

/* nag_gen_real_mat_print (x04cac): Print U. */
fflush(stdout);
nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag,
m, n, u, pdu,
"Example 1: left singular vectors, by column",
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;
}
}
else {
/* Example 2 */
/* Copy A to VT and U */
for (i = 1; i <= m; ++i) {
for (j = i; j <= n; ++j)
VT(i, j) = A(i, j);
}
for (i = 1; i <= m; ++i) {
for (j = 1; j <= i; ++j)
U(i, j) = A(i, j);
}
/* nag_dorgbr (f08kfc):                                  */
/*        Form P^T explicitly, storing the result in VT */
nag_dorgbr(order, Nag_FormP, m, n, m, vt, pdvt, taup, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dorgbr (f08kfc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* nag_dorgbr (f08kfc):                              */
/*        Form Q explicitly, storing the result in U */
nag_dorgbr(order, Nag_FormQ, m, m, n, u, pdu, tauq, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dorgbr (f08kfc).\n%s\n", fail.message);
exit_status = 1;
goto END;
}
/* nag_dbdsqr (f08mec): Compute the SVD of A */
nag_dbdsqr(order, Nag_Lower, m, n, m, 0, d, e, vt, pdvt, u,
pdu, c, pdc, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_dbdsqr (f08mec).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

/* Print singular values, left & right singular vectors */
printf("\n Example 2: singular values\n");
for (i = 1; i <= m; ++i)
printf("%8.4f%s", d[i - 1], i % 8 == 0 ? "\n" : " ");
printf("\n\n");
/* nag_gen_real_mat_print (x04cac): Print VT */
fflush(stdout);
nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag,
m, n, vt, pdvt,
"Example 2: 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;
}
printf("\n");
/* nag_gen_real_mat_print (x04cac): print U */
fflush(stdout);
nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag,
m, m, u, pdu,
"Example 2: left singular vectors, by column",
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;
}
}
END:
NAG_FREE(a);
NAG_FREE(c);
NAG_FREE(d);
NAG_FREE(e);
NAG_FREE(taup);
NAG_FREE(tauq);
NAG_FREE(u);
NAG_FREE(vt);
}
return exit_status;
}

#undef A
#undef U
#undef VT
```