NAG Library Manual, Mark 27.2
```/* E04UE_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 <stdio.h>
#include <string>
using namespace std;

extern "C"
{
static void NAG_CALL objfun(void *&                 ad_handle,
Integer &               mode,
const Integer &         n,
const Integer &         nstate,
Integer                 iuser[],
static void NAG_CALL confun(void *&                 ad_handle,
Integer &               mode,
const Integer &         ncnln,
const Integer &         n,
const Integer &         ldcj,
const Integer           needc[],
const Integer &         nstate,
Integer                 iuser[],
}

int main(void)
{
// Scalars
int exit_status = 0;

cout << "E04UE_A1W_F C++ Header Example Program Results\n\n";

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

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

// Skip first line of data file
string mystr;
getline(cin, mystr);

Integer n, nclin, ncnln;
cin >> n;
cin >> nclin;
cin >> ncnln;

Integer liwork = 3 * n + nclin + 2 * ncnln;
Integer lda = nclin, sda = n, ldcj = ncnln, ldr = n;
Integer lwork;

lwork = 20 * n;
if (nclin > 0 || ncnln > 0)
{
lwork = lwork + 2 * n * n;
if (nclin > 0)
{
lwork = lwork + 11 * nclin;
;
}
if (ncnln > 0)
{
lwork = lwork + n * nclin + 2 * n * ncnln + 21 * ncnln;
}
}
if (ncnln > 0)
{
lwork = lwork + n * nclin + (2 * n + 21) * ncnln;
}
Integer            lb = n + nclin + ncnln;
nagad_a1w_w_rtype *a = 0, *bl = 0, *bu = 0, *c = 0, *cjac = 0;
nagad_a1w_w_rtype *objgrd = 0, *clamda = 0, *r = 0, *x = 0, *work = 0,
*rwsav = 0;
Integer *istate = 0, *iwork = 0, *iwsav = 0;
logical *lwsav = 0;
a              = new nagad_a1w_w_rtype[lda * sda];
cjac           = new nagad_a1w_w_rtype[ncnln * n];
r              = new nagad_a1w_w_rtype[ldr * n];
lwsav          = new logical[120];
istate         = new Integer[lb];
iwork          = new Integer[liwork];
iwsav          = new Integer[610];

// Read problem parameters and register for differentiation
double yr;
for (int i = 0; i < nclin; i++)
{
for (int j = 0; j < sda; j++)
{
Integer k = i + j * nclin;
cin >> yr;
a[k] = yr;
}
}
for (int i = 0; i < lb; i++)
{
cin >> yr;
bl[i] = yr;
}
for (int i = 0; i < lb; i++)
{
cin >> yr;
bu[i] = yr;
}
for (int i = 0; i < n; i++)
{
cin >> yr;
x[i] = yr;
}
for (int i = 0; i < 3; i++)
{
ruser[i] = 1.0;
dco::ga1s<double>::global_tape->register_variable(ruser[i]);
}

// Initialize sav arrays
ifail = 0;
char cwsav[1];
nag::ad::e04wb("E04UCA", cwsav, 1, lwsav, 120, iwsav, 610, rwsav, 475, ifail);

// Solve the problem
Integer           iter, iuser[1];
ifail = -1;
objfun, iter, istate, c, cjac, clamda, objf, objgrd, r, x,
iwork, liwork, work, lwork, -1, iuser, -1, ruser, lwsav, iwsav,
rwsav, ifail);

// Primal results
double inc = 1.0;
cout.setf(ios::scientific, ios::floatfield);
if (ifail == 0 || ifail > 1)
{
cout.precision(4);
cout << "\n Optimal objective function value = ";
cout.width(12);
cout << dco::value(objf);
cout << "\n Solution point = ";
for (int i = 0; i < n; i++)
{
cout.width(12);
cout << dco::value(x[i]);
}
cout << endl;
}
else
{
cout << "nag::ad::e04uc failed with ifail = " << ifail << endl;
goto END;
}

cout << "\n Derivatives calculated: First order adjoints\n";
cout << " Computational mode    : algorithmic\n\n";
cout << " Derivatives:\n\n";

// Setup evaluation of derivatives of objf via adjoints.
dco::derivative(objf) += inc;
ifail                                              = 0;
dco::ga1s<double>::global_tape->sparse_interpret() = true;

// Get derivatives of objf w.r.t. ruser
cout << "  derivatives of x[0] w.r.t ruser[0:2]:\n";
for (int i = 0; i < 3; i++)
{
double d = dco::derivative(ruser[i]);
cout.width(12);
cout << d;
if (i % 4 == 3)
{
cout << endl;
}
}
cout << endl;
END:
// Remove computational data object and tape
dco::ga1s<double>::tape_t::remove(dco::ga1s<double>::global_tape);

delete[] a;
delete[] bl;
delete[] bu;
delete[] c;
delete[] cjac;
delete[] clamda;
delete[] r;
delete[] x;
delete[] objgrd;
delete[] work;
delete[] rwsav;
delete[] lwsav;
delete[] istate;
delete[] iwork;
delete[] iwsav;
return exit_status;
}

static void NAG_CALL objfun(void *&                 ad_handle,
Integer &               mode,
const Integer &         n,
const Integer &         nstate,
Integer                 iuser[],
{
if (mode == 0 || mode == 2)
{
objf =
x[0] * x[3] * (ruser[0] * x[0] + ruser[1] * x[1] + ruser[2] * x[2]) +
x[2];
}
if (mode == 1 || mode == 2)
{
objgrd[0] =
x[3] * (2.0 * ruser[0] * x[0] + ruser[1] * x[1] + ruser[2] * x[2]);
objgrd[1] = x[0] * x[3] * ruser[1];
objgrd[2] = x[0] * x[3] * ruser[2] + 1.0;
objgrd[3] = x[0] * (ruser[0] * x[0] + ruser[1] * x[1] + ruser[2] * x[2]);
}
return;
}
static void NAG_CALL confun(void *&                 ad_handle,
Integer &               mode,
const Integer &         ncnln,
const Integer &         n,
const Integer &         ldcj,
const Integer           needc[],
const Integer &         nstate,
Integer                 iuser[],
{
if (nstate == 1)
{
for (int i = 0; i < ncnln * n; ++i)
{
cjac[i] = 0.0;
}
}
if (needc[0] > 0)
{
if (mode == 0 || mode == 2)
{
c[0] = x[0] * x[0] + x[1] * x[1] + x[2] * x[2] + x[3] * x[3];
}
if (mode == 1 || mode == 2)
{
cjac[0]         = x[0] + x[0];
cjac[ncnln]     = x[1] + x[1];
cjac[2 * ncnln] = x[2] + x[2];
cjac[3 * ncnln] = x[3] + x[3];
}
}
if (needc[1] > 0)
{
if (mode == 0 || mode == 2)
{
c[1] = x[0] * x[1] * x[2] * x[3];
}
if (mode == 1 || mode == 2)
{
cjac[1]             = x[1] * x[2] * x[3];
cjac[ncnln + 1]     = x[0] * x[2] * x[3];
cjac[2 * ncnln + 1] = x[0] * x[1] * x[3];
cjac[3 * ncnln + 1] = x[0] * x[1] * x[2];
}
}
return;
}
```