/* F03BN_T1W_F C++ Header Example Program.
 *
 * Copyright 2022 Numerical Algorithms Group.
 * Mark 28.5, 2022.
 */

#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_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;
  nagad_t1w_w_rtype *a_r = 0, *a_i = 0;
  Complex *          ar   = 0;
  Integer *          ipiv = 0;
  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];
  ipiv                    = new Integer[n];
  ar                      = 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)
    {
      cin >> dr >> di;
      Integer k = i + j * n;
      a_r[k]    = dr;
      a_i[k]    = di;
      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;

  for (int i = 0; i < n; i++)
  {
    for (int j = 0; j < n; j++)
    {
      Integer k = i + j * n;

      for (int r = 0; r < 2; ++r)
      {
        double inc = 1.0;
        if (r == 0)
        {
          dco::derivative(a_r[k]) = inc;
        }
        else
        {
          dco::derivative(a_i[k]) = inc;
        }

        for (int p = 0; p < n; ++p)
        {
          for (int q = 0; q < n; ++q)
          {
            Integer l = p + q * n;
            a[l].real(a_r[l]);
            a[l].imag(a_i[l]);
          }
        }
        // Factorize the matrix A
        ifail = 0;
        nag::ad::f07ar(ad_handle, n, n, a, n, ipiv, ifail);

        if (i == 0 && j == 0 && r == 0)
        {
          // Print Factorization of A
          for (int p = 0; p < n; p++)
          {
            for (int q = 0; q < n; q++)
            {
              int l = p + q * n;

              nagad_t1w_w_rtype akr, aki;
              akr      = real(a[l]);
              aki      = imag(a[l]);
              ar[l].re = dco::value(akr);
              ar[l].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_t1w_w_ctype d;
        Integer           id[2];
        d     = 0;
        ifail = 0;
        nag::ad::f03bn(ad_handle, n, a, n, ipiv, d, id, ifail);

        if (i == 0 && j == 0 && r == 0)
        {
          nagad_t1w_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];
          dr = dr * pow(2.0, id[0]);
          di = di * pow(2.0, id[1]);
          cout << "\n\n value of determinant = (" << dr << "," << di << ")";
          cout << endl;
        }

        // Obtain derivatives
        nagad_t1w_w_rtype dt;
        dt          = real(d);
        double ddr  = dco::derivative(dt);
        double zero = 0.0;
        if (r == 0)
        {
          ar[k].re                = ddr;
          dco::derivative(a_r[k]) = zero;
        }
        else
        {
          ar[k].im                = ddr;
          dco::derivative(a_i[k]) = zero;
        }
      }
    }
  }

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

  // 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;

  delete[] a;
  delete[] a_in;
  delete[] a_r;
  delete[] a_i;
  delete[] ipiv;
  delete[] ar;

  return exit_status;
}