/* F01FJ_A1W_F C++ Header Example Program.
*
* Copyright 2024 Numerical Algorithms Group.
* Mark 30.0, 2024.
*/
#include <dco.hpp>
#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 << "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];
// Create AD tape
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;
nag::ad::f01fj(ad_handle, n, a, n, ifail);
// 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++)
{
dco::ga1s<double>::global_tape->zero_adjoints();
double inc = 1.0;
Integer k = i * n + i;
nagad_a1w_w_rtype avr;
avr = real(a[k]);
dco::derivative(avr) += 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 l = j + j * n, p = i + j * n;
double dd = dco::derivative(ai[l]);
ac[p].re = dd;
}
dco::ga1s<double>::global_tape->zero_adjoints();
nagad_a1w_w_rtype avi;
avi = imag(a[k]);
dco::derivative(avi) += 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 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);
ifail = 0;
dco::ga1s<double>::tape_t::remove(dco::ga1s<double>::global_tape);
return exit_status;
}