NAG Library Manual, Mark 27.2
```/* F03BA_A1W_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;

cout << "F03BA_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;
cin >> n;

// Allocate arrays containing A and its factorized form, B
// and the solution X.
nagad_a1w_w_rtype *a = 0, *a_in = 0;
double *           ar   = 0;
Integer *          ipiv = 0;
a                       = new nagad_a1w_w_rtype[n * n];
a_in                    = new nagad_a1w_w_rtype[n * n];
ipiv                    = new Integer[n];
ar                      = new double[n * n];

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

// 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;
dco::ga1s<double>::global_tape->register_variable(a_in[k]);
a[k]  = a_in[k];
ar[k] = dco::value(a[k]);
}
}

// 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;

// Factorize the matrix A
ifail = 0;

// Print Factorization of A
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
int k = i + j * n;
ar[k] = dco::value(a[k]);
}
}
cout << endl;
// NagError  fail;
INIT_FAIL(fail);
x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, ar, n,
"  Array A after factorization", 0, &fail);

Integer           id;
ifail = 0;

cout << "\n d = " << dco::value(d) << " id = " << id << endl;
cout << "\n value of determinant = " << dco::value(d) * pow(2.0, id);
cout << endl;

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

// Obtain derivatives
double inc = 1.0;
dco::derivative(d) += inc;
ifail                                              = 0;
dco::ga1s<double>::global_tape->sparse_interpret() = true;

for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
Integer k  = i + j * n;
double  dd = dco::derivative(a_in[k]);
ar[k]      = dd;
}
}

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

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