NAG Library Manual, Mark 30.1
```#include "dco.hpp"
/* F07FD_A1W_F C++ Header Example Program.
*
* Copyright 2024 Numerical Algorithms Group.
* Mark 30.1, 2024.
*/

#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;

cout << "F07FD_A1W_F C++ Header Example Program Results\n\n";
// Skip heading in data file
string mystr;
getline(cin, mystr);

Integer n;
cin >> n;

// Allocate arrays containing A and its factorized form, B
// and the solution X.
nagad_a1w_w_rtype *a = 0, *ax = 0;
double *           ar;
if (!(a = NAG_ALLOC(n * n, nagad_a1w_w_rtype)) ||
!(ax = NAG_ALLOC(n * n, nagad_a1w_w_rtype)) ||
!(ar = NAG_ALLOC(n * n, 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];
}
}

// Create AD configuration data object
ifail = 0;

// Factorize the matrix A
ifail = 0;

// Print Factor
for (int i = 0; i < n; i++)
{
for (int j = 0; j <= i; j++)
{
int k = i + j * n;
ar[k] = dco::value(ax[k]);
}
}
cout << endl;
NagError fail;
INIT_FAIL(fail);
x04cac(Nag_ColMajor, Nag_LowerMatrix, Nag_NonUnitDiag, n, n, ar, n,
"  Factor", 0, &fail);

cout << "\n\n Derivatives calculated: First order adjoints\n";
cout << " Computational mode    : algorithmic\n";
cout << "\n Derivatives of diagonal of L w.r.t first column of A:\n";

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

double inc = 1.0;
int    k   = i + i * n;
dco::derivative(ax[k]) += inc;
ifail                                              = 0;
dco::ga1s<double>::global_tape->sparse_interpret() = true;

for (int j = 0; j < n; j++)
{
double dd     = dco::derivative(a[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 dL(i,i)/dA(j,1)", 0, &fail);

END:

ifail = 0;

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

return exit_status;
}
```