NAG Library Manual, Mark 28.5
```/* F06PA_A1W_F C++ Header Example Program.
*
* Copyright 2022 Numerical Algorithms Group.
* Mark 28.5, 2022.
*/

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

int main()
{
int               exit_status = 0;
Integer           ifail = 0;

cout << "F06PA_A1W_F C++ Header Example Program Results\n\n";
// Skip heading in data file
string mystr;
getline(cin, mystr);

// Read problem size and parameters
Integer m, n;
cin >> m >> n;
double alphar, betar;
cin >> alphar >> betar;
alpha = alphar;
beta  = betar;

// Allocate arrays containing A and its factorized form, B
// and the solution X.
nagad_a1w_w_rtype *a = 0, *b = 0, *y = 0;
double *           ar = 0, *br = 0, *yr = 0, *da = 0, *db = 0;
a  = new nagad_a1w_w_rtype[m * n];
ar = new double[m * n];
br = new double[m];
yr = new double[n];
da = new double[n];
db = new double[n];

double dd;
for (int i = 0; i < m; ++i)
{
for (int j = 0; j < n; ++j)
{
cin >> dd;
Integer k = i + j * m;
ar[k]     = dd;
a[k]      = dd;
}
}
for (int i = 0; i < m; ++i)
{
cin >> dd;
br[i] = dd;
b[i]  = dd;
}
for (int i = 0; i < n; ++i)
{
yr[i] = 1.0;
y[i]  = 1.0;
}

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

// Create AD configuration data object
ifail = 0;

dco::ga1s<double>::global_tape->register_variable(alpha);
dco::ga1s<double>::global_tape->register_variable(beta);

for (int i = 0; i < n; ++i)
{
yr[i] = dco::value(y[i]);
}

//  y = beta*y + alpha*A^T*b
ifail = 0;
nag::ad::f06pa(ad_handle, "T", m, n, alpha, a, m, b, 1, beta, y, 1, ifail);

for (int i = 0; i < n; ++i)
{
yr[i] = dco::value(y[i]);
}

cout << endl;
NagError fail;
INIT_FAIL(fail);
x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, 1, yr, n,
"  Array y after update", 0, &fail);

cout << "\n\n Derivatives calculated: First order adjoints\n";
cout << " Computational mode    : algorithmic\n";
cout << "\n Derivatives of y w.r.t alpha and beta:\n";

for (int i = 0; i < n; ++i)
{
double inc = 1.0;
dco::derivative(y[i]) += inc;
ifail                                              = 0;
dco::ga1s<double>::global_tape->sparse_interpret() = true;
da[i] = dco::derivative(alpha);
db[i] = dco::derivative(beta);
}

// Print derivatives
cout << endl;
x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, 1, n, da, 1,
"           dy/dalpha", 0, &fail);
cout << endl;
x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, 1, n, db, 1,
"           dy/dbeta", 0, &fail);

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

return exit_status;
}
```