NAG Library Manual, Mark 27.3
Interfaces:  FL   CL   CPP   AD
```/* F07AW_T1W_F C++ Header Example Program.
*
* Copyright 2021 Numerical Algorithms Group.
* Mark 27.3, 2021.
*/

#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 << "F07AW_T1W_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_t1w_w_ctype *a = 0, *a_in = 0, *work = 0;
nagad_t1w_w_rtype *a_r = 0, *a_i = 0;
Complex *          ar = 0, *drda = 0, *dida = 0;
Integer *          ipiv  = 0;
Integer            lwork = 64 * n;
a                        = new nagad_t1w_w_ctype[n * n];
a_in                     = new nagad_t1w_w_ctype[n * n];
a_r                      = new nagad_t1w_w_rtype[n * n];
a_i                      = new nagad_t1w_w_rtype[n * n];
work                     = new nagad_t1w_w_ctype[lwork];
ipiv                     = new Integer[n];
ar                       = new Complex[n * n];
drda                     = new Complex[n * n];
dida                     = new Complex[n * n];

// Read the matrix A, register and copy
double dr, di;
for (int i = 0; i < n; ++i)
{
for (int j = 0; j < n; ++j)
{
Integer k = i + j * n;
cin >> dr >> di;
a_r[k]   = dr;
a_i[k]   = di;
ar[k].re = dr;
ar[k].im = di;
}
}

// Print matrix A
NagError fail;
INIT_FAIL(fail);
x04dac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, ar, n, "  A",
0, &fail);

// Create AD configuration data object
ifail = 0;

for (int i = 0; i < 2 * n; ++i)
{
Integer k;
double  inc = 1.0;
if (i < n)
{
k                       = i * (n + 1);
dco::derivative(a_r[k]) = inc;
}
else
{
k                       = (i - n) * (n + 1);
dco::derivative(a_i[k]) = inc;
}
for (int j = 0; j < n * n; ++j)
{
a[j].real(a_r[j]);
a[j].imag(a_i[j]);
}
// Factorize the matrix A
ifail = 0;
nag::ad::f07ar(ad_handle, n, n, a, n, ipiv, ifail);

// Invert A
ifail = 0;
nag::ad::f07aw(ad_handle, n, a, n, ipiv, work, lwork, ifail);

double zero = 0.0;
if (i < n)
{
dco::derivative(a_r[k]) = zero;
}
else
{
dco::derivative(a_i[k]) = zero;
}

for (int j = 0; j < n; j++)
{
Integer           p = j + j * n;
dar                 = real(a[p]);
dai                 = imag(a[p]);
double da           = dco::derivative(dar);
double di           = dco::derivative(dai);
if (i < n)
{
Integer l  = j + i * n;
drda[l].re = da;
drda[l].im = di;
}
else
{
Integer l  = j + (i - n) * n;
dida[l].re = da;
dida[l].im = di;
}
}
}

// Print Inverse
for (int i = 0; i < n * n; i++)
{
akr      = real(a[i]);
aki      = imag(a[i]);
ar[i].re = dco::value(akr);
ar[i].im = dco::value(aki);
}
cout << endl;
// NagError  fail;
INIT_FAIL(fail);
x04dac(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";

// Print derivatives
cout << endl;
INIT_FAIL(fail);
x04dac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, drda, n,
"   d(real(ai(i,i)))/da(j,j)", 0, &fail);

cout << endl;
INIT_FAIL(fail);
x04dac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, dida, n,
"   d(real(ai(i,i)))/da(j,j)", 0, &fail);

ifail = 0;

delete[] a;
delete[] a_in;
delete[] a_r;
delete[] a_i;
delete[] work;
delete[] ipiv;
delete[] ar;
delete[] drda;
delete[] dida;
return exit_status;
}
```