NAG Library Manual, Mark 27.2
```#include "dco.hpp"
/* F07CE_A1W_F C++ Header Example Program.
*
* Copyright 2021 Numerical Algorithms Group.
* Mark 27.2, 2021.
*/

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

int main(void)
{
int     exit_status = 0;
Integer nrhs = 1, ifail = 0;

cout << "F07CE_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;
cin >> nrhs;

// Allocate arrays containing A and its factorized form, B
// and the solution X.
nagad_a1w_w_rtype *dl = 0, *d = 0, *du = 0, *du2 = 0, *b = 0;
nagad_a1w_w_rtype *dlf = 0, *df = 0, *duf = 0, *x = 0;
double *           sol  = 0;
Integer *          ipiv = 0;
Integer            n1 = n - 1, n2 = n - 2;
if (!(dl = NAG_ALLOC(n1, nagad_a1w_w_rtype)) ||
!(b = NAG_ALLOC(n * nrhs, nagad_a1w_w_rtype)) ||
!(ipiv = NAG_ALLOC(n, Integer)) ||
!(x = NAG_ALLOC(n * n, nagad_a1w_w_rtype)) ||
!(sol = NAG_ALLOC(n * n, double)))
{
cout << "Allocation failure\n";
exit_status = -1;
goto END;
}

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

// Read the tridiagonal matrix A and right hand side B, register and copy
double dd;
for (int i = 0; i < n1; i++)
{
cin >> dd;
du[i] = dd;
dco::ga1s<double>::global_tape->register_variable(du[i]);
duf[i] = du[i];
}
for (int i = 0; i < n; i++)
{
cin >> dd;
d[i] = dd;
dco::ga1s<double>::global_tape->register_variable(d[i]);
df[i] = d[i];
}
for (int i = 0; i < n1; i++)
{
cin >> dd;
dl[i] = dd;
dco::ga1s<double>::global_tape->register_variable(dl[i]);
dlf[i] = dl[i];
}
for (int i = 0; i < n; i++)
{
for (int j = 0; j < nrhs; j++)
{
cin >> dd;
int k = i + j * n;
b[k]  = dd;
dco::ga1s<double>::global_tape->register_variable(b[k]);
x[k] = b[k];
}
}

// Create AD configuration data object
ifail = 0;

// Factorize the tridiagonal matrix A
ifail = 0;

// Solve the equations Ax = b for x
ifail = 0;
nag::ad::f07ce(ad_handle, "N", n, nrhs, dlf, df, duf, du2, ipiv, x, n, ifail);

// Print primal solution
for (int i = 0; i < n * nrhs; i++)
{
sol[i] = dco::value(x[i]);
}
cout << "\n\n";
NagError fail;
INIT_FAIL(fail);
x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, nrhs, sol, n,
"  Solution", 0, &fail);

cout << "\n\n Derivatives calculated: First order adjoints\n";
cout << " Computational mode    : algorithmic\n";
cout << "\n Derivatives of first solution column w.r.t. inputs:\n";

// Obtain derivatives for each output solution point

cout.setf(ios::scientific, ios::floatfield);
cout.setf(ios::right);
cout.precision(2);
for (int i = 0; i < n; i++)
{
cout << "\n  Solution point " << i + 1 << endl;

double inc = 1.0;
dco::derivative(x[i]) += inc;
dco::ga1s<double>::global_tape->sparse_interpret() = true;
if (ifail != 0)
{
exit_status = 3;
goto END;
}

cout << "      dx/d(du) : ";
cout.width(10);
cout << " ";
for (int j = 0; j < n1; j++)
{
double dd = dco::derivative(du[j]);
cout.width(10);
cout << dd;
}

cout << "\n      dx/d(d)  : ";
for (int j = 0; j < n; j++)
{
double dd = dco::derivative(d[j]);
cout.width(10);
cout << dd;
}

cout << "\n      dx/d(dl) : ";
for (int j = 0; j < n1; j++)
{
double dd = dco::derivative(dl[j]);
cout.width(10);
cout << dd;
}
cout << "\n      dx/d(b)  : ";
for (int j = 0; j < n; j++)
{
double dd = dco::derivative(b[j]);
cout.width(10);
cout << dd;
}
cout << endl;
}

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