NAG Library Manual, Mark 27.2
Interfaces:  FL   CL   CPP   AD
```/* C05QD_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 <nagad.h>
#include <nagx02.h>
#include <nagx04.h>
#include <stdio.h>
#include <string>
using namespace std;

int main(void)
{
// Scalars
int           exit_status = 0;
const Integer mode = 2, n = 7;

cout << "C05QD_A1W_F C++ Header Example Program Results\n\n";

// problem parameters and starting value
nagad_a1w_w_rtype ruser[5], x[7];

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

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

// Create AD tape
dco::ga1s<double>::global_tape = dco::ga1s<double>::tape_t::create();

// Create AD configuration data object
Integer ifail     = 0;
void *  ad_handle = 0;
nag::ad::x10aa(ad_handle, ifail);

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

// Call AD routine
nagad_a1w_w_rtype diag[n], epsfcn, fjac[n * n], factor, fvec[n], qtf[n],
r[n * (n + 1) / 2], rwsav[4 * n + 10], xtol;
Integer irevcm, iwsav[17], ml, mu;

xtol   = sqrt(X02AJC);
factor = 100.;
for (int i = 0; i < n; ++i)
{
diag[i] = 1.;
}
ml     = 1;
mu     = 1;
epsfcn = 0.;

irevcm = 0;

do
{
ifail = 0;
nag::ad::c05qd(ad_handle, irevcm, n, x, fvec, xtol, ml, mu, epsfcn, mode,
diag, factor, fjac, r, qtf, iwsav, rwsav, ifail);

switch (irevcm)
{
case 1:
// Monitoring exit
continue;
case 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];
}
break;
}
}
while (irevcm != 0);

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)
{

dco::ga1s<double>::global_tape->zero_adjoints();
double inc            = 1.0;
dco::derivative(x[i]) = inc;

ifail                                              = 0;
dco::ga1s<double>::global_tape->sparse_interpret() = true;
dco::ga1s<double>::global_tape->interpret_adjoint();

for (int j = 0; j < 5; ++j)
{
int k = j * n + i;
dr[k] = dco::derivative(ruser[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
nag::ad::x10ab(ad_handle, ifail);
dco::ga1s<double>::tape_t::remove(dco::ga1s<double>::global_tape);

return exit_status;
}
```