NAG Library Manual, Mark 28.7
```#include "dco.hpp"
/* F08KB_A1W_F C++ Header Example Program.
*
* Copyright 2022 Numerical Algorithms Group.
* Mark 28.7, 2022.
*/

#include <iostream>
#include <nag.h>
#include <nagx04.h>
#include <stdio.h>
#include <string>
using namespace std;

int main()
{
int               exit_status = 0;
Integer           ifail = 0;
NagError          fail;
INIT_FAIL(fail);

cout << "F08KB_A1W_F C++ Header Example Program Results\n\n";
// Skip heading in data file
string mystr;
getline(cin, mystr);

Integer m, n;
cin >> m;
cin >> n;

// Allocate arrays containing A and its factorized form, B
// and the solution X.
Integer            lda = m, ldu = m, ldvt = n, lwork;
nagad_a1w_w_rtype *a = 0, *a_in = 0, *s = 0, *u = 0, *vt = 0, *work = 0;
double *           ur = 0, *vtr = 0;
Charlen            lena = 1;
if (!(a = NAG_ALLOC(m * n, nagad_a1w_w_rtype)) ||
!(a_in = NAG_ALLOC(m * n, nagad_a1w_w_rtype)) ||
!(u = NAG_ALLOC(m * m, nagad_a1w_w_rtype)) ||
!(vt = NAG_ALLOC(n * n, nagad_a1w_w_rtype)))
{
cout << "Allocation failure\n";
exit_status = -1;
return exit_status;
}

dco::ga1s<double>::global_tape = dco::ga1s<double>::tape_t::create();

// Read the matrix A, register and copy
double dd;
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++)
{
cin >> dd;
Integer k = i + j * m;
a_in[k]   = dd;
dco::ga1s<double>::global_tape->register_variable(a_in[k]);
a[k] = a_in[k];
}
}

// Create AD configuration data object
ifail = 0;

// Use routine workspace query to get optimal workspace.
ifail = 0;
lwork = -1;
nag::ad::f08kb(ad_handle, "A", "A", m, n, a, lda, s, u, ldu, vt, ldvt, dummy,
lwork, ifail);

lwork = (Integer)dco::value(dummy[0]) + 1;
{
cout << "Allocation failure\n";
exit_status = -2;
goto END;
}

//  Compute the singular values and left and right singular vectors
//  of A (A = U*S*(V**T), m < n)
nag::ad::f08kb(ad_handle, "A", "A", m, n, a, lda, s, u, ldu, vt, ldvt, work,
lwork, ifail);

// Print primal solution
cout.precision(4);
cout.width(12);
cout << " ";
cout << " Singular values:\n";
for (int i = 0; i < m; i++)
{
cout.width(11);
cout << dco::value(s[i]);
}

// Copy primal values to array for printing
if (!(ur = NAG_ALLOC(m * m, double)) || !(vtr = NAG_ALLOC(n * n, double)))
{
cout << "Allocation failure\n";
exit_status = -3;
goto END;
}

for (int i = 0; i < m * m; i++)
{
ur[i] = dco::value(u[i]);
}
for (int j = 0; j < n; j++)
{
Integer k = j * n;
for (int i = 0; i < m; i++)
{
vtr[k] = dco::value(vt[k]);
k++;
}
}

cout << "\n\n";
x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, m, m, ur, ldu,
"Left singular vectors by column", 0, &fail);
cout << "\n";
x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, m, n, vtr, ldvt,
"Right singular vectors by row", 0, &fail);

cout << "\n\n Derivatives calculated: First order adjoints\n";
cout << " Computational mode    : algorithmic\n";

cout << "\n Derivatives of Singular values w.r.t first column of A\n";
// Obtain derivatives for each singular value w.r.t first column of A
cout.setf(ios::scientific, ios::floatfield);
cout.setf(ios::right);
cout.precision(2);
for (int i = 0; i < m; i++)
{
cout << "\n Singular value " << i + 1 << endl;
// Setup evaluation of derivatives via adjoints
double inc = 1.0;
dco::derivative(s[i]) += inc;
dco::ga1s<double>::global_tape->sparse_interpret() = true;
if (ifail != 0)
{
exit_status = 1;
goto END;
}
// Get derivatives
cout.width(10);
cout << " ";
for (int j = 0; j < m; j++)
{
double dsda = dco::derivative(a_in[j]);
cout.width(10);
cout << dsda;
}
cout << endl;
}
END:

ifail = 0;

dco::ga1s<double>::tape_t::remove(dco::ga1s<double>::global_tape);

NAG_FREE(a);
NAG_FREE(a_in);
NAG_FREE(s);
NAG_FREE(u);
NAG_FREE(vt);
NAG_FREE(work);
NAG_FREE(ur);
NAG_FREE(vtr);

return exit_status;
}
```