/* F01EF_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 << "F01EF_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_rtype *a = 0, *a_in = 0;
  double *           ar = 0;

  a    = new nagad_a1w_w_rtype[n * n];
  a_in = new nagad_a1w_w_rtype[n * n];
  ar   = new double[n * n];

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

  // Read the matrix A, register and copy
  double dd;
  for (int i = 0; i < n; ++i)
  {
    for (int j = i; j < n; ++j)
    {
      cin >> dd;
      Integer k = i + j * n;
      a_in[k]   = dd;
      if (i == j)
      {
        dco::ga1s<double>::global_tape->register_variable(a_in[k]);
      }
      a[k]  = a_in[k];
      ar[k] = dco::value(a[k]);
    }
  }

  ifail = 0;
  auto f = [&](nag::ad::handle_t &     ad_handle,
            Integer &               iflag,
            const Integer &         n,
            const nagad_a1w_w_rtype *x,
            nagad_a1w_w_rtype *fx)
          {
            for (int i = 0; i < n; ++i)
            {
              fx[i] = cos(x[i]);
            }
          };
  // Find f(A)
  Integer           iflag = 0;
  nag::ad::f01ef(ad_handle, "U", n, a, n, f, iflag, ifail);

  // Print f(A)
  for (int i = 0; i < n; i++)
  {
    for (int j = i; j < n; j++)
    {
      int k = i + j * n;
      ar[k] = dco::value(a[k]);
    }
  }

  cout << endl;
  NagError fail;
  INIT_FAIL(fail);
  x04cac(Nag_ColMajor, Nag_UpperMatrix, Nag_NonUnitDiag, n, n, ar, n, "  f(A)",
         0, &fail);

  cout << "\n\n Derivatives calculated: First order adjoints\n";
  cout << " Computational mode    : algorithmic\n";
  cout << "\n Derivatives of diagonal of f(A) w.r.t diagonal of 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;
      dco::derivative(a[k]) += 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(a_in[l]);
      ar[p]      = dd;
    }
  }

  // Print derivatives
  cout << endl;
  INIT_FAIL(fail);
  x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, ar, n,
         "     d(fA(i,i)/dA(j,j)", 0, &fail);

  ifail = 0;

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

  return exit_status;
}