NAG Library Manual, Mark 27.2
```/* F01FJ_A1W_F C++ Header Example Program.
*
* Copyright 2021 Numerical Algorithms Group.
* Mark 27.2, 2021.
*/

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

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

cout << "F01FJ_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;

// Allocate arrays containing A and its factorized form, B
// and the solution X.
nagad_a1w_w_ctype *a = 0, *a_in = 0;
Complex *          ac = 0;
nagad_a1w_w_rtype *ar = 0, *ai = 0;

a    = new nagad_a1w_w_ctype[n * n];
a_in = new nagad_a1w_w_ctype[n * n];
ar   = new nagad_a1w_w_rtype[n * n];
ai   = new nagad_a1w_w_rtype[n * n];
ac   = new Complex[n * n];

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

// Read the matrix A, register and copy
double dr, di;
for (int i = 0; i < n; ++i)
{
for (int j = 0; j < n; ++j)
{
cin >> dr >> di;
Integer k = i + j * n;
ar[k]     = dr;
ai[k]     = di;
if (i == j)
{
dco::ga1s<double>::global_tape->register_variable(ai[k]);
}
a[k].real(ar[k]);
a[k].imag(ai[k]);
}
}

// Create AD configuration data object
ifail = 0;

// Find log(A)
ifail = 0;

// Print log(A)
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
int k = i + j * n;

ac[k].re = dco::value(real(a[k]));
ac[k].im = dco::value(imag(a[k]));
}
}

cout << endl;
NagError fail;
INIT_FAIL(fail);
x04dac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, ac, n,
"  Log(A)", 0, &fail);

cout << "\n\n Derivatives calculated: First order adjoints\n";
cout << " Computational mode    : algorithmic\n";
cout << "\n Derivatives of diagional of log(A) w.r.t diagonal of imag(A):\n";

// Obtain derivatives
for (int i = 0; i < n; i++)
{
double            inc = 1.0;
Integer           k   = i * n + i;
avr = real(a[k]);
dco::derivative(avr) += inc;

ifail                                              = 0;
dco::ga1s<double>::global_tape->sparse_interpret() = true;

for (int j = 0; j < n; j++)
{
Integer l = j + j * n, p = i + j * n;
double  dd = dco::derivative(ai[l]);
ac[p].re   = dd;
}

avi = imag(a[k]);
dco::derivative(avi) += inc;

ifail                                              = 0;
dco::ga1s<double>::global_tape->sparse_interpret() = true;

for (int j = 0; j < n; j++)
{
Integer l = j + j * n, p = i + j * n;
double  dd = dco::derivative(ai[l]);
ac[p].im   = dd;
}
}

// Print derivatives
cout << endl;
INIT_FAIL(fail);
x04dac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, ac, n,
"     d(logA(i,i)/dImag(A(j,j))", 0, &fail);

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