NAG Library Manual, Mark 29.2
Interfaces:  FL   CL   CPP   AD
```/* F01EF_A1W_F C++ Header Example Program.
*
* Copyright 2023 Numerical Algorithms Group.
* Mark 29.2, 2023.
*/

#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;

cout << "F01EF_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_rtype *a = 0, *a_in = 0;
double *           ar = 0;

a    = new nagad_a1w_w_rtype[n * n];
a_in = new nagad_a1w_w_rtype[n * n];
ar   = new double[n * n];

// Create AD tape
dco::ga1s<double>::global_tape = dco::ga1s<double>::tape_t::create();

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

ifail = 0;
Integer &               iflag,
const Integer &         n,
{
for (int i = 0; i < n; ++i)
{
fx[i] = cos(x[i]);
}
};
// Find f(A)
Integer           iflag = 0;
nag::ad::f01ef(ad_handle, "U", n, a, n, f, iflag, ifail);

// Print f(A)
for (int i = 0; i < n; i++)
{
for (int j = i; j < n; j++)
{
int k = i + j * n;
ar[k] = dco::value(a[k]);
}
}

cout << endl;
NagError fail;
INIT_FAIL(fail);
x04cac(Nag_ColMajor, Nag_UpperMatrix, Nag_NonUnitDiag, n, n, ar, n, "  f(A)",
0, &fail);

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

// Obtain derivatives
for (int i = 0; i < n; i++)
{
{
double  inc = 1.0;
Integer k   = i * n + i;
dco::derivative(a[k]) += 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(a_in[l]);
ar[p]      = dd;
}
}

// Print derivatives
cout << endl;
INIT_FAIL(fail);
x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, ar, n,
"     d(fA(i,i)/dA(j,j)", 0, &fail);

ifail = 0;

dco::ga1s<double>::tape_t::remove(dco::ga1s<double>::global_tape);

return exit_status;
}
```