/* F03BN_A1W_F C++ Header Example Program.
 *
 * Copyright 2023 Numerical Algorithms Group.
 * Mark 29.2, 2023.
 */

#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 << "F03BN_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;
  nagad_a1w_w_rtype *a_r = 0, *a_i = 0;
  Complex *          ar   = 0;
  Integer *          ipiv = 0;
  a                       = new nagad_a1w_w_ctype[n * n];
  a_in                    = new nagad_a1w_w_ctype[n * n];
  a_r                     = new nagad_a1w_w_rtype[n * n];
  a_i                     = new nagad_a1w_w_rtype[n * n];
  ipiv                    = new Integer[n];
  ar                      = 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;
  Complex dc;
  for (int i = 0; i < n; ++i)
  {
    for (int j = 0; j < n; ++j)
    {
      cin >> dr >> di;
      Integer k = i + j * n;
      a_r[k]    = dr;
      a_i[k]    = di;
      dco::ga1s<double>::global_tape->register_variable(a_r[k]);
      dco::ga1s<double>::global_tape->register_variable(a_i[k]);
      a[k].real(a_r[k]);
      a[k].imag(a_i[k]);
      ar[k].re = dr;
      ar[k].im = di;
    }
  }

  // Print matrix A
  cout << endl;
  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;

  // Factorize the matrix A
  ifail = 0;
  nag::ad::f07ar(ad_handle, n, n, a, n, ipiv, ifail);

  // Print Factorization of A
  for (int i = 0; i < n; i++)
  {
    for (int j = 0; j < n; j++)
    {
      int k = i + j * n;

      nagad_a1w_w_rtype akr, aki;
      akr      = real(a[k]);
      aki      = imag(a[k]);
      ar[k].re = dco::value(akr);
      ar[k].im = dco::value(aki);
    }
  }
  cout << endl;
  // NagError  fail;
  INIT_FAIL(fail);
  x04dac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, ar, n,
         "  Array A after factorization", 0, &fail);

  nagad_a1w_w_ctype d;
  Integer           id[2];
  ifail = 0;
  nag::ad::f03bn(ad_handle, n, a, n, ipiv, d, id, ifail);

  nagad_a1w_w_rtype dcr, dci;
  dcr = real(d);
  dci = imag(d);
  dr  = dco::value(dcr);
  di  = dco::value(dci);
  cout << " d = (" << dr << "," << di << ") id = ";
  cout << id[0] << ", " << id[1] << endl;
  dr = dr * pow(2.0, id[0]);
  di = di * pow(2.0, id[1]);
  cout << "\n value of determinant = (" << dr << "," << di << ")" << endl;

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

  // Obtain derivatives
  double            inc = 1.0;
  nagad_a1w_w_rtype dt;
  dt = real(d);
  dco::derivative(dt) += inc;
  ifail                                              = 0;
  dco::ga1s<double>::global_tape->sparse_interpret() = true;
  dco::ga1s<double>::global_tape->interpret_adjoint();

  for (int i = 0; i < n; i++)
  {
    for (int j = 0; j < n; j++)
    {
      Integer k  = i + j * n;
      double  dr = dco::derivative(a_r[k]);
      double  di = dco::derivative(a_i[k]);
      ar[k].re   = dr;
      ar[k].im   = di;
    }
  }

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

END:

  ifail = 0;

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

  return exit_status;
}