NAG Library Manual, Mark 28.4
```/* F08KP_A1W_F C++ Header Example Program.
*
* Copyright 2022 Numerical Algorithms Group.
* Mark 28.4, 2022.
*/

#include <dco.hpp>
#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 << "F08KP_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_ctype *a = 0, *u = 0, *vt = 0, *work = 0, dummy[1];
nagad_a1w_w_rtype *ar = 0, *ai = 0, *s = 0, *rwork = 0;
Complex *          uc = 0, *vtc = 0, *dsda = 0;
Charlen            lena = 1;
a                       = new nagad_a1w_w_ctype[m * n];
ar                      = new nagad_a1w_w_rtype[m * n];
ai                      = new nagad_a1w_w_rtype[m * n];
rwork                   = new nagad_a1w_w_rtype[5 * n];
dsda                    = new Complex[n * m];
u                       = new nagad_a1w_w_ctype[m * m];
vt                      = new nagad_a1w_w_ctype[n * n];

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

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

// Create AD configuration data object
ifail = 0;

// Use routine workspace query to get optimal workspace.
ifail = 0;
lwork = -1;
nag::ad::f08kp(ad_handle, "A", "A", m, n, a, lda, s, u, ldu, vt, ldvt, dummy,
lwork, rwork, ifail);

lwork = (Integer)dco::value(real(dummy[0])) + 1;

//  Compute the singular values and left and right singular vectors
//  of A (A = U*S*(V**T), m < n)
nag::ad::f08kp(ad_handle, "A", "A", m, n, a, lda, s, u, ldu, vt, ldvt, work,
lwork, rwork, ifail);

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

// Copy primal values to array for printing
uc  = new Complex[m * m];
vtc = new Complex[n * n];

for (int i = 0; i < m * m; i++)
{
uc[i].re = dco::value(real(u[i]));
uc[i].im = dco::value(imag(u[i]));
}
for (int i = 0; i < n * n; i++)
{
vtc[i].re = dco::value(real(vt[i]));
vtc[i].im = dco::value(imag(vt[i]));
}

cout << "\n\n";
x04dac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, m, m, uc, m,
"Left singular vectors by column", 0, &fail);
cout << "\n";
x04dac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, vtc, n,
"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 < n; i++)
{
// Setup evaluation of derivatives via adjoints
double inc = 1.0;
dco::derivative(s[i]) += inc;
ifail                                              = 0;
dco::ga1s<double>::global_tape->sparse_interpret() = true;

// Get derivatives
for (int j = 0; j < m; j++)
{
dsda[i + n * j].re = dco::derivative(ar[j]);
dsda[i + n * j].im = dco::derivative(ai[j]);
}
}
cout << "\n";
x04dac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, m, dsda, n,
" dS_i/dA_j1", 0, &fail);

ifail = 0;

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

delete[] a;
delete[] ar;
delete[] ai;
delete[] s;
delete[] u;
delete[] vt;
delete[] work;
delete[] rwork;
delete[] uc;
delete[] vtc;
delete[] dsda;

return exit_status;
}
```