NAG Library Manual, Mark 30.1
Interfaces:  FL   CL   CPP   AD
```/* F11BF_A1W_F C++ Header Example Program.
*
* Copyright 2024 Numerical Algorithms Group.
* Mark 30.1, 2024.
*/

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

int main()
{
int               exit_status = 0;
Integer           ifail = 0;

cout << "F11BF_A1W_F C++ Header Example Program Results\n\n";
// Skip heading in data file
string mystr;
getline(cin, mystr);

// Read problem size
Integer n, m;
double  alphar;
cin >> n;
cin >> m;
cin >> alphar;

// Allocate arrays containing A and its factorized form, B
// and the solution X.
nagad_a1w_w_rtype *b = 0, *x = 0, *work = 0;
double *           dx;
Integer            lwork = 2 * m * n + 1000;

if (!(b = NAG_ALLOC(n, nagad_a1w_w_rtype)) ||
!(x = NAG_ALLOC(n, nagad_a1w_w_rtype)) ||
!(work = NAG_ALLOC(lwork, nagad_a1w_w_rtype)) ||
!(dx = NAG_ALLOC(2 * n, double)))
{
cout << "Allocation failure\n";
exit_status = -1;
exit(exit_status);
}

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

nagad_a1w_w_rtype alpha, bb, b1, a, c;
alpha = alphar;

b1 = 12.0;
a  = 1.0;
c  = 1.0;
bb = b1 - 2.0;

dco::ga1s<double>::global_tape->register_variable(alpha);
dco::ga1s<double>::global_tape->register_variable(bb);

// Create AD configuration data object
ifail = 0;

for (int i = 0; i < n; ++i)
{
b[i] = b1 * (i + 1);
x[i] = 3.0;
}
b[n - 1] = b[n - 1] - (n + 1);

b[0] = b[0] + (b1 - 1.0) * alpha;
for (int i = 1; i < n - 1; ++i)
{
b[i] = b[i] + b1 * alpha;
}
b[n - 1] = b[n - 1] + (b1 - 1.0) * alpha;

// Initialize the solver
Integer           iterm = 2, maxitn = 800, monit = 0, lwreq = lwork;
nagad_a1w_w_rtype sigmax = 0.0, anorm = 0.0;
nagad_a1w_w_rtype tol = 1.0e-10;
ifail                 = 0;
nag::ad::f11bd(ad_handle, "RGMRES", "P", "2", "N", iterm, n, m, tol, maxitn,
anorm, sigmax, monit, lwreq, work, lwork, ifail);

// Reverse communication call of solver
Integer           irevcm = 0;

while (irevcm != 4)
{
ifail = 0;
nag::ad::f11be(ad_handle, irevcm, x, b, wgt, work, lwreq, ifail);
if (irevcm != 4)
{
ifail = -1;
if (irevcm == -1)
{
//  b = A^Tx
b[0] = bb * x[0] + a * x[1];
for (int i = 1; i < n - 1; ++i)
{
b[i] = c * x[i - 1] + bb * x[i] + a * x[i + 1];
}
b[n - 1] = c * x[n - 2] + bb * x[n - 1];
}
if (irevcm == 1)
{
// b = Ax
b[0] = bb * x[0] + c * x[1];
for (int i = 1; i < n - 1; ++i)
{
b[i] = a * x[i - 1] + bb * x[i] + c * x[i + 1];
}
b[n - 1] = a * x[n - 2] + bb * x[n - 1];
}
if (irevcm == 2)
{
for (int i = 0; i < n; ++i)
{
b[i] = x[i] / bb;
}
}
}
}

// Obtain information about the computation

Integer           ifail1 = 0, itn;
nag::ad::f11bf(ad_handle, itn, stplhs, stprhs, anorm, sigmax, work, lwreq,
ifail1);

// Print the output data

cout.setf(ios::scientific, ios::floatfield);
cout.precision(2);

cout << " Final Results " << endl;
cout << " Number of iterations for convergence:    " << itn << endl;
cout << " Residual norm:                           ";
cout << dco::value(stplhs) << endl;
cout << " Right-hand side of termination criterion:";
cout << dco::value(stprhs) << endl;
// for iterm=2 anorm is not calculated

cout << "  Solution vector   Residual vector\n";
for (int i = 0; i < n; ++i)
{
cout.width(12);
cout << dco::value(x[i]) << "     ";
cout.width(13);
cout << dco::value(b[i]) << endl;
}

cout << "\n\n Derivatives calculated: First order adjoints\n";
cout << " Computational mode    : algorithmic\n";
cout << "\n Derivatives of X w.r.t alpha and bb:\n";

// Obtain derivatives
for (int i = 0; i < n; i++)
{

// Reset adjoints, initialize derivative, and evaluate adjoint
double inc = 1.0;
dco::derivative(x[i]) += inc;
ifail                                              = 0;
dco::ga1s<double>::global_tape->sparse_interpret() = true;

dx[i]     = dco::derivative(alpha);
dx[n + i] = dco::derivative(bb);
}
// Print derivatives
cout << endl;
NagError fail;
INIT_FAIL(fail);
x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, 2, dx, n,
"      dX/dalpha    dX/dbb", 0, &fail);

ifail = 0;

dco::ga1s<double>::tape_t::remove(dco::ga1s<double>::global_tape);

return exit_status;
}
```