NAG Library Manual, Mark 27.2
```/* F07AD_T1W_F C++ Header Example Program.
*
* Copyright 2021 Numerical Algorithms Group.
* Mark 27.2, 2021.
*/

#include <dco.hpp>
#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;

// Skip heading in data file
string mystr;
getline(cin, mystr);

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

// Allocate arrays containing A and its factorized form, B
// and the solution X.
nagad_t1w_w_rtype *a = 0, *a_in = 0, *work = 0;
double *           ar    = 0;
Integer *          ipiv  = 0;
Integer            lwork = 64 * n;
a                        = new nagad_t1w_w_rtype[n * n];
a_in                     = new nagad_t1w_w_rtype[n * n];
ipiv                     = new Integer[n];
ar                       = new double[n * n];

// Read the matrix A, register and copy
double dd;
for (int i = 0; i < n; ++i)
{
for (int j = 0; j < n; ++j)
{
cin >> dd;
Integer k = i + j * n;
a_in[k]   = dd;
ar[k]     = dd;
}
}

// Print matrix A
cout << endl;
NagError fail;
INIT_FAIL(fail);
x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, ar, n, "  A",
0, &fail);

// Create AD configuration data object
ifail = 0;

for (int l = 0; l < n; ++l)
{
{
double  inc              = 1.0;
Integer k                = l * n + l;
dco::derivative(a_in[k]) = inc;
}
for (int k = 0; k < n * n; ++k)
{
a[k] = a_in[k];
}
// Factorize the matrix A
ifail = 0;

// Invert A
ifail = 0;

if (l == 0)
{
// Print Inverse
for (int k = 0; k < n * n; k++)
{
ar[k] = dco::value(a[k]);
}
cout << endl;
x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, ar, n,
"  Inverse", 0, &fail);
}
{
double  zero             = 0.0;
Integer k                = l * n + l;
dco::derivative(a_in[k]) = zero;
}
for (int j = 0; j < n; j++)
{
Integer k     = j + j * n;
double  dd    = dco::derivative(a[k]);
ar[l * n + j] = dd;
}
}

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

// Print derivatives
cout << endl;
x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, ar, n,
"           dai(i,i)/da(j,j)", 0, &fail);

// Remove computational data object
ifail = 0;