#include "dco.hpp"
/* F07FE_A1W_F C++ Header Example Program.
 *
 * Copyright 2021 Numerical Algorithms Group.
 * Mark 27.3, 2021.
 */

#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 << "F07FE_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, nrhs;
  cin >> n;
  cin >> nrhs;

  // Allocate arrays containing A and its factorized form, B
  // and the solution X.
  nagad_a1w_w_rtype *a = 0, *ax = 0, *b = 0, *x = 0;
  double *           ar, *xr = 0;
  if (!(a = NAG_ALLOC(n * n, nagad_a1w_w_rtype)) ||
      !(ax = NAG_ALLOC(n * n, nagad_a1w_w_rtype)) ||
      !(b = NAG_ALLOC(n * nrhs, nagad_a1w_w_rtype)) ||
      !(x = NAG_ALLOC(n * nrhs, nagad_a1w_w_rtype)) ||
      !(ar = NAG_ALLOC(n * n, double)) || !(xr = NAG_ALLOC(n * nrhs, double)))
  {
    cout << "Allocation failure\n";
    exit_status = -1;
    goto END;
  }

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

  // Read the lower triangular matrix A, register and copy
  double dd;
  for (int i = 0; i < n; ++i)
  {
    for (int j = 0; j <= i; ++j)
    {
      cin >> dd;
      int k = i + j * n;
      a[k]  = dd;
      dco::ga1s<double>::global_tape->register_variable(a[k]);
      ax[k] = a[k];
    }
  }
  // Read the right-hand-sides, register and copy
  for (int i = 0; i < n; ++i)
  {
    for (int j = 0; j < nrhs; ++j)
    {
      cin >> dd;
      int k = i + j * n;
      b[k]  = dd;
      dco::ga1s<double>::global_tape->register_variable(b[k]);
      x[k] = b[k];
    }
  }

  // Create AD configuration data object
  ifail = 0;

  // Factorize the matrix A
  ifail = 0;
  nag::ad::f07fd(ad_handle, "L", n, ax, n, ifail);

  // Solve the system
  ifail = 0;
  nag::ad::f07fe(ad_handle, "L", n, nrhs, ax, n, x, n, ifail);

  // Print solution
  for (int i = 0; i < n; i++)
  {
    for (int j = 0; j < nrhs; j++)
    {
      int k = i + j * n;
      xr[k] = dco::value(x[k]);
    }
  }
  cout << endl;
  NagError fail;
  INIT_FAIL(fail);
  x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, nrhs, xr, n,
         "  Solution", 0, &fail);

  cout << "\n\n Derivatives calculated: First order adjoints\n";
  cout << " Computational mode    : algorithmic\n";
  cout
      << "\n Derivatives of first column solution x w.r.t first column of b:\n";

  // Obtain derivatives
  for (int i = 0; i < n; i++)
  {

    // Reset adjoints, initialize derivative, and evaluate adjoint
    dco::ga1s<double>::global_tape->zero_adjoints();
    double inc = 1.0;
    dco::derivative(x[i]) += 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++)
    {
      double dd     = dco::derivative(b[j]);
      ar[i + j * n] = dd;
    }
  }
  // Print derivatives
  cout << endl;
  INIT_FAIL(fail);
  x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, ar, n,
         "  Derivatives dX(i,1)/db(j,1)", 0, &fail);

END:

  ifail = 0;

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

  return exit_status;
}