NAG Library Manual, Mark 27.2
```#include "dco.hpp"
/* F07FE_A1W_F C++ Header Example Program.
*
* Copyright 2021 Numerical Algorithms Group.
* Mark 27.2, 2021.
*/

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

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

cout << "F07FE_A1W_F C++ Header Example Program Results\n\n";
// Skip heading in data file
string mystr;
getline(cin, mystr);

// Read problem size and number of right-hand-sides
Integer n, nrhs;
cin >> n;
cin >> nrhs;

// Allocate arrays containing A and its factorized form, B
// and the solution X.
nagad_a1w_w_rtype *a = 0, *ax = 0, *b = 0, *x = 0;
double *           ar, *xr = 0;
if (!(a = NAG_ALLOC(n * n, nagad_a1w_w_rtype)) ||
!(ax = NAG_ALLOC(n * n, nagad_a1w_w_rtype)) ||
!(b = NAG_ALLOC(n * nrhs, nagad_a1w_w_rtype)) ||
!(x = NAG_ALLOC(n * nrhs, nagad_a1w_w_rtype)) ||
!(ar = NAG_ALLOC(n * n, double)) || !(xr = NAG_ALLOC(n * nrhs, double)))
{
cout << "Allocation failure\n";
exit_status = -1;
goto END;
}

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

// Read the lower triangular matrix A, register and copy
double dd;
for (int i = 0; i < n; ++i)
{
for (int j = 0; j <= i; ++j)
{
cin >> dd;
int k = i + j * n;
a[k]  = dd;
dco::ga1s<double>::global_tape->register_variable(a[k]);
ax[k] = a[k];
}
}
// Read the right-hand-sides, register and copy
for (int i = 0; i < n; ++i)
{
for (int j = 0; j < nrhs; ++j)
{
cin >> dd;
int k = i + j * n;
b[k]  = dd;
dco::ga1s<double>::global_tape->register_variable(b[k]);
x[k] = b[k];
}
}

// Create AD configuration data object
ifail = 0;

// Factorize the matrix A
ifail = 0;

// Solve the system
ifail = 0;

// Print solution
for (int i = 0; i < n; i++)
{
for (int j = 0; j < nrhs; j++)
{
int k = i + j * n;
xr[k] = dco::value(x[k]);
}
}
cout << endl;
NagError fail;
INIT_FAIL(fail);
x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, nrhs, xr, n,
"  Solution", 0, &fail);

cout << "\n\n Derivatives calculated: First order adjoints\n";
cout << " Computational mode    : algorithmic\n";
cout
<< "\n Derivatives of first column solution x w.r.t first column of b:\n";

// Obtain derivatives
for (int i = 0; i < n; i++)
{

double inc = 1.0;
dco::derivative(x[i]) += inc;
ifail                                              = 0;
dco::ga1s<double>::global_tape->sparse_interpret() = true;

for (int j = 0; j < n; j++)
{
double dd     = dco::derivative(b[j]);
ar[i + j * n] = dd;
}
}
// Print derivatives
cout << endl;
INIT_FAIL(fail);
x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, ar, n,
"  Derivatives dX(i,1)/db(j,1)", 0, &fail);

END:
// Remove computational data object and tape
ifail = 0;