NAG Library Manual, Mark 28.5
```/* F07CD_T1W_F C++ Header Example Program.
*
* Copyright 2022 Numerical Algorithms Group.
* Mark 28.5, 2022.
*/

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

int main()
{
int               exit_status = 0;
Integer           nrhs = 1, ifail = 0;
NagError          fail;
INIT_FAIL(fail);

cout << "F07CD_T1W_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_t1w_w_rtype *dl = 0, *d = 0, *du = 0, *du2 = 0, *b = 0;
nagad_t1w_w_rtype *dlf = 0, *df = 0, *duf = 0, *x = 0;
double *           sol = 0, *dxdu = 0, *dxdd = 0, *dxdl = 0, *dxdb = 0;
Integer *          ipiv = 0;
Integer            n1 = n - 1, n2 = n - 2;
b    = new nagad_t1w_w_rtype[n * nrhs];
ipiv = new Integer[n];
x    = new nagad_t1w_w_rtype[n * n];
sol  = new double[n * n];
dxdu = new double[n * n1];
dxdd = new double[n * n];
dxdl = new double[n * n1];
dxdb = new double[n * n];

// 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;
}
for (int i = 0; i < n; i++)
{
cin >> dd;
d[i] = dd;
}
for (int i = 0; i < n1; i++)
{
cin >> dd;
dl[i] = dd;
}
for (int i = 0; i < n; i++)
{
for (int j = 0; j < nrhs; j++)
{
cin >> dd;
int k = i + j * n;
b[k]  = dd;
}
}

// Create AD configuration data object
ifail = 0;

double inc = 1.0, zero = 0.0;
for (int i = 0; i < 4 * n - 2; ++i)
{
int k = i;
if (i < n1)
{
dco::derivative(du[i]) = inc;
}
else if (i < n + n1)
{
k                     = i - n1;
dco::derivative(d[k]) = inc;
}
else if (i < n + n1 + n1)
{
k                      = i - n - n1;
dco::derivative(dl[k]) = inc;
}
else
{
k                     = i - n - n1 - n1;
dco::derivative(b[k]) = inc;
}
for (int j = 0; j < n1; ++j)
{
dlf[j] = dl[j];
df[j]  = d[j];
duf[j] = du[j];
x[j]   = b[j];
}
df[n1] = d[n1];
x[n1]  = b[n1];
// Factorize the tridiagonal matrix A
ifail = 0;

// Solve the equations Ax = b for x
ifail = 0;
ifail);

if (i == 0)
{
// Print primal solution
for (int j = 0; j < n * nrhs; ++j)
{
sol[j] = dco::value(x[j]);
}
cout << "\n\n";
x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, nrhs, sol, n,
"  Solution", 0, &fail);
}
if (i < n1)
{
dco::derivative(du[k]) = zero;
for (int j = 0; j < n; ++j)
{
dxdu[j + k * n] = dco::derivative(x[j]);
}
}
else if (i < n + n1)
{
dco::derivative(d[k]) = zero;
for (int j = 0; j < n; ++j)
{
dxdd[j + k * n] = dco::derivative(x[j]);
}
}
else if (i < n + n1 + n1)
{
dco::derivative(dl[k]) = zero;
for (int j = 0; j < n; ++j)
{
dxdl[j + k * n] = dco::derivative(x[j]);
}
}
else
{
dco::derivative(b[k]) = zero;
for (int j = 0; j < n; ++j)
{
dxdb[j + k * n] = dco::derivative(x[j]);
}
}
}
cout << "\n\n Derivatives calculated: First order tangents\n";
cout << " Computational mode    : algorithmic\n";
cout << "\n Derivatives of first solution column w.r.t. inputs:\n";

cout << "\n";
x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n1, dxdu, n,
"  d(du(i))/dx(j)", 0, &fail);
cout << "\n";
x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, dxdd, n,
"  d(d(i))/dx(j)", 0, &fail);
cout << "\n";
x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n1, dxdl, n,
"  d(dl(i))/dx(j)", 0, &fail);
cout << "\n";
x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, dxdb, n,
"  d(b(i))/dx(j)", 0, &fail);

ifail = 0;

delete[] dl;
delete[] d;
delete[] du;
delete[] du2;
delete[] dlf;
delete[] df;
delete[] duf;
delete[] b;
delete[] ipiv;
delete[] x;
delete[] sol;
delete[] dxdu;
delete[] dxdd;
delete[] dxdl;
delete[] dxdb;
return exit_status;
}
```