/* D02PE_A1W_F C++ Header Example Program.
 *
 * Copyright 2020 Numerical Algorithms Group.
 *
 * Mark 27.1, 2020.
 */

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

#ifdef __cplusplus
extern "C"
{
#endif
  static void NAG_CALL f(void * &ad_handle, const nagad_a1w_w_rtype &t,
                         const Integer &n, const nagad_a1w_w_rtype y[],
                         nagad_a1w_w_rtype yp[],
                         Integer iuser[], nagad_a1w_w_rtype ruser[]);
#ifdef __cplusplus
}
#endif

int main(void)
{
  const Integer     n = 2, npts = 8;
  const Integer     liwsav = 130;
  const Integer     lrwsav = 350 + 32 * n;

  Integer           exit_status = 0;

  nagad_a1w_w_rtype *rwsav = 0, *thresh = 0, *ygot = 0, *yinit = 0, *ymax = 0;
  nagad_a1w_w_rtype *ypgot = 0, *y = 0, ruser[1];
  Integer           *iwsav = 0, iuser[1];

  cout << "D02PE_A1W_F C++ Header Example Program Results\n\n";

  thresh = new nagad_a1w_w_rtype [n];
  ygot   = new nagad_a1w_w_rtype [n];
  y      = new nagad_a1w_w_rtype [n];
  yinit  = new nagad_a1w_w_rtype [n];
  ypgot  = new nagad_a1w_w_rtype [n];
  ymax   = new nagad_a1w_w_rtype [n];
  iwsav  = new Integer [liwsav];
  rwsav  = new nagad_a1w_w_rtype [lrwsav];

  // Set initial conditions for ODE and parameters for the integrator.
  Integer           method = 1;
  nagad_a1w_w_rtype tol, hstart, tend, tstart;
  tstart    = 0.0;
  tol       = 1.0e-4;
  tend      = 2.0*nag_math_pi;
  yinit[0]  = 0.0;
  yinit[1]  = 1.0;
  hstart    = 0.0;
  thresh[0] = 1.0e-8;
  thresh[1] = 1.0e-8;
  
  {
    double tolr = nagad_a1w_get_value(tol);
    cout << "\n  Calculation with tol = " << tolr << endl;
  }
  cout.setf(ios::fixed);
  cout.setf(ios::right);
  cout.precision(3);
  {
    double t = nagad_a1w_get_value(tstart);
    cout << "\n    t         y1        y2" << endl;
    cout.width(6); cout << t;
  }
  for (int k = 0; k < n; k++) {
    double yr = nagad_a1w_get_value(yinit[k]);
    cout.width(10); cout << yr;
  }
  cout << endl;

  // Set control for output
  double tinc = 2.0*nag_math_pi / (double) (npts);

  // Create AD tape
  nagad_a1w_ir_create();

  // Create AD configuration data object
  Integer ifail = 0;
  void    *ad_handle = 0;
  x10aa_a1w_f_(ad_handle,ifail);
  
  nagad_a1w_ir_register_variable(&yinit[0]);
  nagad_a1w_ir_register_variable(&yinit[1]);

  y[0] = yinit[0];
  y[1] = yinit[1];
  
  // Initialize Runge-Kutta method for integrating ODE
  ifail = 0;
  d02pq_a1w_f_(ad_handle,n,tstart,tend,y,tol,thresh,method,hstart,
               iwsav,rwsav,ifail);

  nagad_a1w_w_rtype tgot, twant;
  twant = tstart;
  for (int j = 0; j < npts; ++j) {
    twant = twant + tinc;

    ifail = 0;
    d02pe_a1w_f_(ad_handle,f,n,twant,tgot,ygot,ypgot,ymax,iuser,ruser,
                 iwsav,rwsav,ifail);
    cout.width(6); cout << nagad_a1w_get_value(tgot);
    for (int k = 0; k < n; ++k) {
      cout.width(10); cout << nagad_a1w_get_value(ygot[k]);
    }
    cout << endl;
  }

  nagad_a1w_w_rtype hnext, waste;
  Integer           fevals, stepcost, stepsok;
  ifail = 0;
  d02pt_a1w_f_(ad_handle,fevals,stepcost,waste,stepsok,hnext,iwsav,
               rwsav,ifail);
  cout << "\n Cost of the integration in evaluations of f is " << fevals;
  cout << endl;

  // Setup evaluation of derivatives via adjoints.
  double inc = 1.0;
  nagad_a1w_inc_derivative(&ygot[0],inc);
  ifail = 0;
  nagad_a1w_ir_interpret_adjoint(ifail);

  cout << "\n Derivatives calculated: First order adjoints\n";
  cout << " Computational mode    : algorithmic\n";
  
  // Get derivatives
  cout << "\n Derivatives: (solution w.r.t. initial values)\n";

  cout.setf(ios::scientific,ios::floatfield);
  cout.precision(5);
  double dr;
  dr = nagad_a1w_get_derivative(yinit[0]);
  cout << " dy(t)/dy0  = ";
  cout.width(12); cout << dr << endl;
  dr = nagad_a1w_get_derivative(yinit[1]);
  cout << " dy(t)/dy0' = ";
  cout.width(12); cout << dr << endl;

  x10ab_a1w_f_(ad_handle,ifail);
  nagad_a1w_ir_remove();

  delete [] thresh;
  delete [] ygot;
  delete [] y;
  delete [] yinit;
  delete [] ypgot;
  delete [] ymax;
  delete [] iwsav;
  delete [] rwsav;
  return exit_status;
}

static void NAG_CALL f(void * &ad_handle, const nagad_a1w_w_rtype &t,
                       const Integer &n, const nagad_a1w_w_rtype y[],
                       nagad_a1w_w_rtype yp[],
                       Integer iuser[], nagad_a1w_w_rtype ruser[])
{
  yp[0] = y[1];
  yp[1] = -y[0];
}