NAG Library Manual, Mark 27.2
```/* C05RB_A1W_F C++ Header Example Program.
*
* Copyright 2021 Numerical Algorithms Group.
* Mark 27.2, 2021.
*/

#include <dco.hpp>
#include <iostream>
#include <math.h>
#include <nag.h>
#include <nagx02.h>
#include <nagx04.h>
#include <stdio.h>
#include <string>
using namespace std;

extern "C"
{
static void NAG_CALL fcn(void *&                 ad_handle,
const Integer &         n,
Integer                 iuser[],
Integer &               iflag);
}

int main(void)
{
// Scalars
int           exit_status = 0;
const Integer n           = 7;

cout << "C05RB_A1W_F C++ Header Example Program Results\n\n";

// problem parameters and starting value

r[0] = -1.0;
r[1] = 3.0;
r[2] = -2.0;
r[3] = -2.0;
r[4] = -1.0;

for (int i = 0; i < n; ++i)
{
x[i] = -1.0;
}

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

// Create AD configuration data object
Integer ifail     = 0;

// Register variables to differentiate w.r.t.
for (int i = 0; i < 5; ++i)
{
dco::ga1s<double>::global_tape->register_variable(r[i]);
}

nagad_a1w_w_rtype fvec[n], fjac[n * n], xtol;
Integer           iuser[1];

xtol  = sqrt(X02AJC);
ifail = 0;
ifail);

cout.setf(ios::scientific, ios::floatfield);
cout.precision(4);
cout << "           Solution:\n";
for (int i = 0; i < n; ++i)
{
cout.width(10);
cout << i + 1;
cout.width(20);
cout << dco::value(x[i]) << endl;
}

cout << "\n Derivatives calculated: First order adjoints\n";
cout << " Computational mode    : algorithmic\n";
cout << "\n Derivatives are of solution w.r.t function params\n\n";

// Setup evaluation of derivatives via adjoints
double dr[5 * n];
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 < 5; ++j)
{
int k = j * n + i;
dr[k] = dco::derivative(r[j]);
}
}

NagError fail;
INIT_FAIL(fail);
x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, 5, dr, n,
"    dx/druser", 0, &fail);

// Remove computational data object and tape
dco::ga1s<double>::tape_t::remove(dco::ga1s<double>::global_tape);

return exit_status;
}

static void NAG_CALL fcn(void *&                 ad_handle,
const Integer &         n,
Integer                 iuser[],
Integer &               iflag)
{
if (iflag != 2)
{
for (int i = 0; i < n; ++i)
{
fvec[i] = (ruser[1] + ruser[2] * x[i]) * x[i] - ruser[4];
}
for (int i = 1; i < n; ++i)
{
fvec[i] = fvec[i] + ruser[0] * x[i - 1];
}
for (int i = 0; i < n - 1; ++i)
{
fvec[i] = fvec[i] + ruser[3] * x[i + 1];
}
}
else
{
for (int i = 0; i < n * n; ++i)
{
fjac[i] = 0.0;
}
fjac[0] = ruser[1] + 2.0 * ruser[2] * x[0];
fjac[n] = ruser[3];
for (int i = 1; i < n - 1; ++i)
{
int k       = i * n + i;
fjac[k - n] = ruser[0];
fjac[k]     = ruser[1] + 2.0 * ruser[2] * x[i];
fjac[k + n] = ruser[3];
}
fjac[n * n - n - 1] = ruser[0];
fjac[n * n - 1]     = ruser[1] + 2.0 * ruser[2] * x[n - 1];
}
iflag = 0;
return;
}
```