/* F01FJ_A1W_F C++ Header Example Program.
 *
 * Copyright 2024 Numerical Algorithms Group.
 * Mark 30.1, 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;
}