/* F01EF_T1W_F C++ Header Example Program.
 *
 * Copyright 2022 Numerical Algorithms Group.
 * Mark 28.4, 2022.
 */

#include <dco.hpp>
#include <iostream>
#include <nag.h>
#include <nagad.h>
#include <nagx04.h>
#include <stdio.h>
#include <string>
using namespace std;
extern "C"
{
  static void NAG_CALL f(nag::ad::handle_t &     ad_handle,
                         Integer &               iflag,
                         const Integer &         n,
                         const nagad_t1w_w_rtype x[],
                         nagad_t1w_w_rtype       fx[],
                         Integer                 iuser[],
                         nagad_t1w_w_rtype       ruser[]);
}
int main()
{
  int               exit_status = 0;
  nag::ad::handle_t ad_handle;
  Integer           ifail = 0;
  NagError          fail;
  INIT_FAIL(fail);

  cout << "F01EF_T1W_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_t1w_w_rtype *a = 0, *a_in = 0;
  double *           ar = 0;

  a    = new nagad_t1w_w_rtype[n * n];
  a_in = new nagad_t1w_w_rtype[n * n];
  ar   = new double[n * n];

  // 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;
    }
  }

  ifail = 0;
  auto f = [&](nag::ad::handle_t &     ad_handle,
            Integer &               iflag,
            const Integer &         n,
            const nagad_t1w_w_rtype *x,
            nagad_t1w_w_rtype *fx)
          {
            for (int i = 0; i < n; ++i)
            {
              fx[i] = cos(x[i]);
            }
          };
  // Find f(A)
  Integer           iflag = 0;

  for (int i = 0; i < n; i++)
  {
    {
      double  inc              = 1.0;
      Integer k                = i * n + i;
      dco::derivative(a_in[k]) = inc;
    }
    for (int j = 0; j < n; ++j)
    {
      for (int l = j; l < n; ++l)
      {
        Integer k = j + l * n;
        a[k]      = a_in[k];
      }
    }
    ifail = 0;
    nag::ad::f01ef(ad_handle, "U", n, a, n, f, iflag, ifail);

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

      cout << endl;
      x04cac(Nag_ColMajor, Nag_UpperMatrix, Nag_NonUnitDiag, n, n, ar, n,
             "  Exp(A)", 0, &fail);
    }
    for (int j = 0; j < n; j++)
    {
      Integer l = j + j * n, p = j + i * n;
      double  dd = dco::derivative(a[l]);
      ar[p]      = dd;
    }
    {
      double  zero             = 0.0;
      Integer k                = i * n + i;
      dco::derivative(a_in[k]) = zero;
    }
  }

  cout << "\n\n Derivatives calculated: First order tangents\n";
  cout << " Computational mode    : algorithmic\n";
  cout << "\n Derivatives of diagonal of f(A) w.r.t diagonal of A:\n";

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

  ifail = 0;

  delete[] a;
  delete[] a_in;
  delete[] ar;

  return exit_status;
}
static void NAG_CALL f(nag::ad::handle_t &     ad_handle,
                       Integer &               iflag,
                       const Integer &         n,
                       const nagad_t1w_w_rtype x[],
                       nagad_t1w_w_rtype       fx[],
                       Integer                 iuser[],
                       nagad_t1w_w_rtype       ruser[])
{
  for (int i = 0; i < n; ++i)
  {
    fx[i] = cos(x[i]);
  }
}