/* F01EJ_A1W_F C++ Header Example Program.
 *
 * Copyright 2023 Numerical Algorithms Group.
 * Mark 29.0, 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()
{
  cout << "F01EJ_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.
  std::vector<dco::ga1s<double>::type> a(n*n), a_in(n*n);
  std::vector<double> ar(n*n);

  // Create AD tape
  dco::ga1s<double>::global_tape = dco::ga1s<double>::tape_t::create();

  // Read the matrix A
  for (int i = 0; i < n; ++i)
  {
    for (int j = 0; j < n; ++j)
    {
      Integer k = i + j * n;
      cin >> a_in[k];
    }
  }
  // Register and copy
  dco::ga1s<double>::global_tape->register_variable(a_in);
  a  = a_in;
  
  // Find log(A)
  dco::ga1s<double>::type imnorm;
  Integer ifail = 0;
  nag::ad::handle_t ad_handle;
  nag::ad::f01ej(ad_handle, n, a.data(), n, imnorm, ifail);

  // Print log(A)
  ar = dco::value(a);
  cout << endl;
  NagError fail;
  INIT_FAIL(fail);
  x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, ar.data(), 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 A:\n";

  // Obtain derivatives
  for (int i = 0; i < n; i++)
  {
    Integer k = i * n + i;
    dco::derivative(a[k]) = 1.0;
    dco::ga1s<double>::global_tape->interpret_adjoint();
    
    for (int j = 0; j < n; j++)
    {
      Integer l = j + j * n, p = i + j * n;
      ar[p]     = dco::derivative(a_in[l]);
    }
    dco::ga1s<double>::global_tape->zero_adjoints();
  }

  cout << endl;
  INIT_FAIL(fail);
  x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, ar.data(), n,
         "     d(logA(i,i)/dA(j,j)", 0, &fail);

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

  return 0;
}