NAG Library Manual, Mark 28.4
```/* F08KE_T1W_F C++ Header Example Program.
*
* Copyright 2022 Numerical Algorithms Group.
* Mark 28.4, 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           ifail = 0;
NagError          fail;
INIT_FAIL(fail);

cout << "F08KE_T1W_F C++ Header Example Program Results\n\n";
// Skip heading in data file
string mystr;
getline(cin, mystr);

Integer m, n;
cin >> m;
cin >> n;

// Allocate arrays containing A and its factorized form, B
// and the solution X.
Integer            lda = m, lwork = 64 * (m + n);
nagad_t1w_w_rtype *a = 0, *a_in = 0, *d = 0, *e = 0, *taup = 0, *tauq,
*work = 0;
double *dd = 0, *de = 0;
a    = new nagad_t1w_w_rtype[m * n];
a_in = new nagad_t1w_w_rtype[m * n];
e    = new nagad_t1w_w_rtype[n - 1];
dd   = new double[m * n];
de   = new double[m * n - n];

// Read the matrix A, register and copy
double ddd;
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++)
{
Integer k = i + j * m;
cin >> ddd;
a_in[k] = ddd;
}
}

// Create AD configuration data object
ifail = 0;

double inc = 1.0, zero = 0.0;
for (int i = 0; i < m; ++i)
{
dco::derivative(a_in[i]) = inc;
for (int j = 0; j < m * n; ++j)
{
a[j] = a_in[j];
}
// reduce A to bidiagonal form
ifail = 0;
ifail);
dco::derivative(a_in[i]) = zero;
for (int j = 0; j < n; ++j)
{
dd[j + i * n] = dco::derivative(d[j]);
}
for (int j = 0; j < n - 1; ++j)
{
de[j + i * (n - 1)] = dco::derivative(e[j]);
}
}

// Print bidiagonal form
cout.precision(4);
cout << " Diagonal:" << endl;
cout.width(12);
cout << " ";
for (int i = 0; i < n; i++)
{
cout.width(11);
cout << dco::value(d[i]);
}
cout << endl;
if (m > n)
{
cout << " Superdiagonal:" << endl;
}
else
{
cout << " Subdiagonal:" << endl;
}
cout.width(12);
cout << " ";
for (int i = 0; i < n - 1; i++)
{
cout.width(11);
cout << dco::value(e[i]);
}

cout << "\n\n Derivatives calculated: First order tangents\n";
cout << " Computational mode    : algorithmic\n";

cout << "\n Derivatives of d/e w.r.t first column of A\n";

cout << "\n\n";
x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, m, dd, n,
"  dD_i/dA_j1", 0, &fail);
cout << "\n";
x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n - 1, m, de, n - 1,
" dE_i/DA_j1", 0, &fail);

delete[] a;
delete[] a_in;
delete[] d;
delete[] e;
delete[] taup;
delete[] tauq;
delete[] work;
delete[] dd;
delete[] de;
return exit_status;
}
```