/* F08AE_A1W_F C++ Header Example Program.
 *
 * Copyright 2024 Numerical Algorithms Group.
 * Mark 30.3, 2024.
 */

#include <dco.hpp>
#include <iostream>
#include <math.h>
#include <nag.h>
#include <nagad.h>
#include <stdio.h>
#include <string>
using namespace std;

int main()
{
  /* Scalars */
  Integer exit_status = 0;
#ifdef NAG_LOAD_FP
  /* The following line is needed to force the Microsoft linker
     to load floating point support */
  float force_loading_of_ms_float_support = 0;
#endif /* NAG_LOAD_FP */

  cout << "F08AE_A1W_F C++ Header Example Program Results\n\n";

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

  nag::ad::handle_t ad_handle;
  Integer           ifail = 0;

  // Skip heading in data file
  string mystr;
  getline(cin, mystr);

  Integer m, n;
  cin >> m;
  cin >> n;

  Integer pda   = m;
  Integer lwork = 64 * n;

  Integer tau_len;
  if (m < n)
  {
    tau_len = m;
  }
  else
  {
    tau_len = n;
  }

  // Allocate arrays
  nagad_a1w_w_rtype *a = 0, *tau = 0, *a_in = 0, *work = 0;
  double *           r = 0, *drda = 0;
  a    = new nagad_a1w_w_rtype[m * n];
  a_in = new nagad_a1w_w_rtype[m * n];
  tau  = new nagad_a1w_w_rtype[tau_len];
  work = new nagad_a1w_w_rtype[lwork];
  r    = new double[n * n];
  drda = new double[n * m];

  // Read A from data file
  double tmp;
  for (int i = 0; i < m; ++i)
  {
    for (int j = 0; j < n; ++j)
    {
      cin >> tmp;
      a_in[i + j * m] = tmp;
    }
  }

  for (int i = 0; i < m; i++)
  {
    dco::ga1s<double>::global_tape->register_variable(a_in[i]);
  }
  for (int i = 0; i < m * n; i++)
  {
    a[i] = a_in[i];
  }

  nag::ad::f08ae(ad_handle, m, n, a, pda, tau, work, lwork, ifail);
  if (ifail != 0)
  {
    printf("Error from nag::ad::f08ae .\n%" NAG_IFMT " ", ifail);
    exit_status = 1;
    goto END;
  }
  for (int k = 0; k < n; ++k)
  {
    for (int i = 0; i < n; ++i)
    {
      r[i + k * n] = dco::value(a[i + k * m]);
    }
  }
  for (int i = 0; i < n; ++i)
  {
    int l = i * (m + 1);
    dco::ga1s<double>::global_tape->zero_adjoints();
    double inc = 1.0;
    dco::derivative(a[l]) += inc;

    dco::ga1s<double>::global_tape->sparse_interpret() = true;
    dco::ga1s<double>::global_tape->interpret_adjoint();

    for (int j = 0; j < m; ++j)
    {
      int k   = j * n + i;
      drda[k] = dco::derivative(a_in[j]);
    }
  }
  NagError fail;
  INIT_FAIL(fail);
  x04cac(Nag_ColMajor, Nag_UpperMatrix, Nag_NonUnitDiag, n, n, r, n,
         "R from Q factorization of A", 0, &fail);
  printf("\nDerivatives of diagonal of R w.r.t. first col of A\n");
  x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, n, m, drda, n,
         "dR_ii/dA_j1", 0, &fail);

END:

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

  delete[] a;
  delete[] a_in;
  delete[] tau;
  delete[] r;
  delete[] drda;

  return exit_status;
}