/* D02PR_T1W_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_t1w_w_rtype &t,
                         const Integer &n, const nagad_t1w_w_rtype y[],
                         nagad_t1w_w_rtype yp[],
                         Integer iuser[], nagad_t1w_w_rtype ruser[]);
#ifdef __cplusplus
}
#endif

int main(void)
{
  const Integer     n = 4, npts = 6;
  const Integer     liwsav = 130;
  const Integer     lrwsav = 350 + 32 * n;

  Integer           exit_status = 0;

  nagad_t1w_w_rtype *rwsav = 0, *thresh = 0, *ynow = 0;
  nagad_t1w_w_rtype *ypnow = 0, *y = 0, ruser[1];
  Integer           *iwsav = 0, iuser[1];

  cout << "D02PR_T1W_F C++ Header Example Program Results\n\n";

  thresh = new nagad_t1w_w_rtype [n];
  ynow   = new nagad_t1w_w_rtype [n];
  y      = new nagad_t1w_w_rtype [n];
  ypnow  = new nagad_t1w_w_rtype [n];
  iwsav  = new Integer [liwsav];
  rwsav  = new nagad_t1w_w_rtype [lrwsav];

  // Set initial conditions for ODE and parameters for the integrator.
  Integer           method = -3;
  nagad_t1w_w_rtype eps, tol, hstart, tend, tstart;
  eps       = 0.7;
  tstart    = 0.0;
  tol       = 1.0e-4;
  tend      = 6.0*nag_math_pi;
  hstart    = 0.0;
  for (int k = 0; k < n; k++) {
    thresh[k] = 1.0e-10;
  }
  
  {
    double tolr = nagad_t1w_get_value(tol);
    cout << "\n  Calculation with tol = " << tolr << endl;
  }
  cout.setf(ios::fixed);
  cout.setf(ios::right);
  cout.precision(3);
  {
    double t = nagad_t1w_get_value(tstart);
    cout << "\n    t         y1        y2" << endl;
    cout.width(6); cout << t;
  }

  // Create AD configuration data object
  Integer ifail = 0;
  void    *ad_handle = 0;
  x10aa_t1w_f_(ad_handle,ifail);
  
  double inc = 1.0;
  nagad_t1w_inc_derivative(&eps,inc);

  y[0] = 1.0 - eps;
  y[1] = 0.0;
  y[2] = 0.0;
  y[3] = sqrt((1.0+eps)/(1.0-eps));
  for (int k = 0; k < n; k++) {
    double yr = nagad_t1w_get_value(y[k]);
    cout.width(10); cout << yr;
  }
  cout << endl;

  nagad_t1w_w_rtype tnow, twant, tinc;
  tinc = (tend-tstart)/( (double) npts);
  twant = tstart + tinc;
  
  // Initialize Runge-Kutta method for integrating ODE
  ifail = 0;
  d02pq_t1w_f_(ad_handle,n,tstart,twant,y,tol,thresh,method,hstart,
               iwsav,rwsav,ifail);

  do {
    ifail = 0;
    d02pf_t1w_f_(ad_handle,f,n,tnow,ynow,ypnow,iuser,ruser,
                 iwsav,rwsav,ifail);
    if (tnow==twant) {
      cout.width(6); cout << nagad_t1w_get_value(tnow);
      for (int k = 0; k < n; ++k) {
        cout.width(10); cout << nagad_t1w_get_value(ynow[k]);
      }
      cout << endl;
      twant = twant + tinc;
      ifail = 0;
      d02pr_t1w_f_(ad_handle,twant,iwsav,rwsav,ifail);
    }
  } while (tnow<tend);

  nagad_t1w_w_rtype hnext, waste;
  Integer           fevals, stepcost, stepsok;
  ifail = 0;
  d02pt_t1w_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;

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

  cout.setf(ios::scientific,ios::floatfield);
  cout.precision(5);
  double deps;
  deps = nagad_t1w_get_derivative(ynow[0]);
  cout << " dy(t)/deps = ";
  cout.width(12); cout << deps << endl;

  ifail =0;
  x10ab_t1w_f_(ad_handle,ifail);

  delete [] thresh;
  delete [] ynow;
  delete [] y;
  delete [] ypnow;
  delete [] iwsav;
  delete [] rwsav;
  return exit_status;
}

static void NAG_CALL f(void * &ad_handle, const nagad_t1w_w_rtype &t,
                       const Integer &n, const nagad_t1w_w_rtype y[],
                       nagad_t1w_w_rtype yp[],
                       Integer iuser[], nagad_t1w_w_rtype ruser[])
{
  nagad_t1w_w_rtype r;
  r = 1.0/sqrt(y[0]*y[0]+y[1]*y[1]);
  r = r*r*r;
  yp[0] = y[2];
  yp[1] = y[3];
  yp[2] = -y[0]*r;
  yp[3] = -y[1]*r;
}