NAG Library Manual, Mark 30.1
```/* F07FD_T1W_F C++ Header Example Program.
*
* Copyright 2024 Numerical Algorithms Group.
* Mark 30.1, 2024.
*/

#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;

cout << "F07FD_T1W_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_t1w_w_rtype *a = 0, *ax = 0;
double *           ar = 0, *dr = 0;
a  = new nagad_t1w_w_rtype[n * n];
ax = new nagad_t1w_w_rtype[n * n];
ar = new double[n * n];
dr = new double[n * n];

// 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;
}
}

// Create AD configuration data object
ifail = 0;

double inc = 1.0, zero = 0.0;
;
for (int i = 0; i < n; ++i)
{
dco::derivative(a[i]) = inc;
for (int j = 0; j < n * n; ++j)
{
ax[j] = a[j];
}
// Factorize the matrix A
ifail = 0;

dco::derivative(a[i]) = zero;
for (int j = 0; j < n; ++j)
{
dr[i * n + j] = dco::derivative(ax[j * n + j]);
}
}
// 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 tangents\n";
cout << " Computational mode    : algorithmic\n";
cout << "\n Derivatives of diagonal of L w.r.t first column of A:\n";
cout << endl;
INIT_FAIL(fail);
x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, dr, n,
"  Derivatives dL(i,i)/dA(j,1)", 0, &fail);

ifail = 0;

delete[] a;
delete[] ax;
delete[] ar;
delete[] dr;
return exit_status;
}
```