NAG Library Manual, Mark 28.5
Interfaces:  FL   CL   CPP   AD
```#include "dco.hpp"
/* F07AJ_A1W_F C++ Header Example Program.
*
* Copyright 2022 Numerical Algorithms Group.
* Mark 28.5, 2022.
*/

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

int main()
{
int               exit_status = 0;
nag::ad::handle_t ad_handle;
Integer           ifail = 0;

cout << "F07AJ_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, *work = 0;
double *           ar    = 0;
Integer *          ipiv  = 0;
Integer            lwork = 64 * n;
if (!(a = NAG_ALLOC(n * n, nagad_a1w_w_rtype)) ||
!(a_in = NAG_ALLOC(n * n, nagad_a1w_w_rtype)) ||
!(work = NAG_ALLOC(lwork, nagad_a1w_w_rtype)) ||
!(ipiv = NAG_ALLOC(n, Integer)) || !(ar = NAG_ALLOC(n * n, double)))
{
cout << "Allocation failure\n";
exit_status = -1;
goto END;
}

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

// Read the lower triangular matrix A, register and copy
double dd;
for (int i = 0; i < n; ++i)
{
for (int j = 0; 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];
}
}

// Print matrix A
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
Integer k = i + j * n;
ar[k]     = dco::value(a[k]);
}
}
cout << endl;
NagError fail;
INIT_FAIL(fail);
x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, ar, n, "  A",
0, &fail);

// Create AD configuration data object
ifail = 0;

// Factorize the matrix A
ifail = 0;
nag::ad::f07ad(ad_handle, n, n, a, n, ipiv, ifail);

// Invert A
ifail = 0;
nag::ad::f07aj(ad_handle, n, a, n, ipiv, work, lwork, ifail);

// Print Inverse
for (int i = 0; i < n; i++)
{
for (int j = 0; 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_GeneralMatrix, Nag_NonUnitDiag, n, n, ar, n,
"  Inverse", 0, &fail);

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

// Obtain derivatives
for (int i = 0; i < n; i++)
{

// Reset adjoints, initialize derivative, and evaluate adjoint
dco::ga1s<double>::global_tape->zero_adjoints();
double  inc = 1.0;
Integer k   = i * n + i;
dco::derivative(a[k]) += inc;
ifail                                              = 0;
dco::ga1s<double>::global_tape->sparse_interpret() = true;
dco::ga1s<double>::global_tape->interpret_adjoint();

for (int j = 0; j < n; j++)
{
Integer k     = j + j * n;
double  dd    = dco::derivative(a_in[k]);
ar[i + j * n] = dd;
}
}
// Print derivatives
cout << endl;
INIT_FAIL(fail);
x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, ar, n,
"           dai(i,i)/da(j,j)", 0, &fail);

END:

ifail = 0;

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

return exit_status;
}
```