/* D02PU_P0W_F C++ Header Example Program.
 *
 * Copyright 2021 Numerical Algorithms Group.
 *
 * Mark 27.2, 2021.
 */

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

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

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

  Integer exit_status = 0;

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

  cout << "D02PU_P0W_F C++ Header Example Program Results\n\n";

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

  // Set initial conditions for ODE and parameters for the integrator.
  Integer method = 3;
  double  tol, hstart, tend, tstart, eps;
  eps    = 0.7;
  tstart = 0.0;
  tol    = 1.0e-6;
  tend   = 3.0 * nag_math_pi;
  hstart = 0.0;
  for (int i = 0; i < n; ++i)
    {
      thresh[i] = 1.0e-10;
    }

  cout << "\n  Calculation with tol = " << tol << endl;

  cout.setf(ios::fixed);
  cout.setf(ios::right);
  cout.precision(3);
  cout << "\n    t         y1         y2         y3         y4" << endl;
  cout.width(6);
  cout << tstart;

  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++)
    {
      cout.width(11);
      cout << y[k];
    }
  cout << endl;

  // Initialize Runge-Kutta method for integrating ODE
  Integer ifail     = 0;
  void *  ad_handle = 0;
  nag::ad::d02pq(ad_handle, n, tstart, tend, y, tol, thresh, method, hstart,
                 iwsav, rwsav, ifail);

  double tgot, twant;
  twant = tend;

  ifail = 2;
  while (ifail > 1 && ifail < 5)
    {
      ifail = -1;
      nag::ad::d02pe(ad_handle, f, n, twant, tgot, ygot, ypgot, ymax, -1, iuser,
                     -1, ruser, iwsav, rwsav, ifail);
    }

  if (ifail == 0)
    {
      cout.width(6);
      cout << tgot;
      for (int k = 0; k < n; ++k)
        {
          cout.width(11);
          cout << ygot[k];
        }
      cout << endl;

      // Get Error estimates
      double errmax, terrmx;
      ifail = 0;
      nag::ad::d02pu(ad_handle, n, rmserr, errmax, terrmx, iwsav, rwsav, ifail);

      cout.setf(ios::scientific, ios::floatfield);
      cout.precision(2);
      cout << "\n Componentwise error assessment\n        ";
      for (int k = 0; k < n; ++k)
        {
          cout.width(11);
          cout << rmserr[k];
        }
      cout << endl;
      cout.precision(3);
      cout << "\n Worst global error observed was ";
      cout.width(9);
      cout << errmax << endl;
      cout << "              it occurred at T = ";
      cout.width(8);
      cout << terrmx << endl;

      double  hnext, waste;
      Integer fevals, stepcost, stepsok;
      ifail = 0;
      nag::ad::d02pt(ad_handle, fevals, stepcost, waste, stepsok, hnext, iwsav,
                     rwsav, ifail);
      cout << "\n Cost of the integration in evaluations of f is " << fevals;
      cout << endl;
    }
  delete[] thresh;
  delete[] ygot;
  delete[] y;
  delete[] ypgot;
  delete[] ymax;
  delete[] iwsav;
  delete[] rwsav;
  delete[] rmserr;
  return exit_status;
}

static void NAG_CALL f(void *&        ad_handle,
                       const double & t,
                       const Integer &n,
                       const double   y[],
                       double         yp[],
                       Integer        iuser[],
                       double         ruser[])
{
  double 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;
}