/* F08AH_A1W_F C++ Header Example Program.
 *
 * Copyright 2023 Numerical Algorithms Group.
 * Mark 29.2, 2023.
 */

#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;

  cout << "F08AH_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, *work = 0, *a_in = 0;
  double *           l = 0, *dlda = 0;
  a    = new nagad_a1w_w_rtype[m * n];
  work = new nagad_a1w_w_rtype[lwork];
  a_in = new nagad_a1w_w_rtype[m * n];
  tau  = new nagad_a1w_w_rtype[tau_len];
  l    = new double[m * m];
  dlda = new double[m * n];

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

  nag::ad::f08ah(ad_handle, m, n, a, pda, tau, work, lwork, ifail);
  if (ifail != 0)
  {
    printf("Error from F08AH_A1W_F .\n%" NAG_IFMT " ", ifail);
    exit_status = 1;
    goto END;
  }

  for (int i = 0; i < m * m; ++i)
  {
    l[i] = dco::value(a[i]);
  }

  for (int i = 0; i < m; ++i)
  {
    double d_one = 1.0;
    int    ld    = i * (m + 1);
    dco::ga1s<double>::global_tape->zero_adjoints();
    dco::derivative(a[ld]) += d_one;

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

    for (int j = 0; j < n; ++j)
    {
      int k   = j * m + i;
      dlda[k] = dco::derivative(a_in[j * m]);
    }
  }
  NagError fail;
  INIT_FAIL(fail);
  x04cac(Nag_ColMajor, Nag_LowerMatrix, Nag_NonUnitDiag, m, m, l, m,
         "L from Q factorization of A", 0, &fail);
  printf("\nDerivatives of diagonal of L w.r.t. first row of A\n");
  x04cac(Nag_ColMajor, Nag_GeneralMatrix, Nag_NonUnitDiag, m, n, dlda, m,
         "dL_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[] l;
  delete[] dlda;
  return exit_status;
}