NAG Library Manual, Mark 28.3
```/* F11DB_T1W_F C++ Header Example Program.
*
* Copyright 2022 Numerical Algorithms Group.
* Mark 28.3, 2022.
*/
#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 << "F11DB_T1W_F C++ Header Example Program Results\n\n";
// Skip heading in data file
string mystr;
getline(cin, mystr);

// Read order of matrix and number of nonzero entries
Integer n, nnz;
cin >> n;
cin >> nnz;

Integer            la     = 2 * nnz;
Integer            liwork = 7 * n + 2;
nagad_t1w_w_rtype *a = 0, *x = 0, *y = 0;
double *           ar = 0, *yr = 0, *dxdy = 0;
Integer *          icol = 0, *idiag = 0, *ipivp = 0, *ipivq = 0, *irow = 0;
Integer *          istr = 0, *iwork = 0;

icol  = new Integer[la];
idiag = new Integer[n];
ipivp = new Integer[n];
ipivq = new Integer[n];
irow  = new Integer[la];
istr  = new Integer[n + 1];
iwork = new Integer[liwork];
ar    = new double[la];
yr    = new double[n];
dxdy  = new double[n * n];

for (int i = 0; i < nnz; i++)
{
cin >> ar[i] >> irow[i] >> icol[i];
a[i] = ar[i];
}

for (int i = 0; i < n; i++)
{
cin >> yr[i];
y[i] = yr[i];
}

// Create AD configuration data object
ifail = 0;

// Calculate LU factorization

Integer           lfill = -1;
Integer           nnzc, npivm;
dtol  = 0.0;
ifail = 0;
ipivp, ipivq, istr, idiag, nnzc, npivm, iwork, liwork, ifail);

// Check value of npivm

if (npivm > 0)
{
cout << " Factorization is not complete" << endl;
}
else
{

//       Solve P L D U x = y

double inc = 1.0, zero = 0.0;
for (int i = 0; i < n; i++)
{

for (int j = 0; j < n; j++)
{
y[j] = yr[j];
}
dco::derivative(y[i]) = inc;

ifail = 0;
idiag, "C", y, x, ifail);

for (int j = 0; j < n; j++)
{
Integer k = j + i * n;
dxdy[k]   = dco::derivative(x[j]);
}
dco::derivative(y[i]) = zero;
}
// Output results
cout.setf(ios::scientific, ios::floatfield);
cout.precision(4);
cout << "  Solution vector" << endl;
for (int i = 0; i < n; ++i)
{
cout.width(12);
cout << dco::value(x[i]) << "     ";
}

cout << "\n\n Derivatives calculated: First order tangents\n";
cout << " Computational mode    : algorithmic\n";
cout << "\n Derivatives of solution X w.r.t RHS Y:\n";

// Print derivatives
cout << endl;
NagError fail;
INIT_FAIL(fail);
x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, dxdy, n,
"       dx_i/dy_j", 0, &fail);
}

ifail = 0;

delete[] a;
delete[] x;
delete[] y;
delete[] icol;
delete[] idiag;
delete[] ipivp;
delete[] ipivq;
delete[] irow;
delete[] istr;
delete[] iwork;
delete[] ar;
delete[] yr;
delete[] dxdy;

return exit_status;
}
```