/* nag_ode_ivp_rk_errass (d02pzc) Example Program.
 *
 * Copyright 1992 Numerical Algorithms Group.
 *
 * Mark 3, 1992.
 * Mark 7 revised, 2001.
 * Mark 8 revised, 2004.
 *
 */

#include <nag.h>
#include <math.h>
#include <stdio.h>
#include <nag_stdlib.h>
#include <nagd02.h>
#include <nagx01.h>

#ifdef __cplusplus
extern "C" {
#endif
  static void f(Integer neq, double t1, double y[], double yp[],
                Nag_User *comm);
#ifdef __cplusplus
}
#endif

#define NEQ 4
#define ZERO 0.0
#define ONE 1.0
#define THREE 3.0
#define ECC 0.7

int main(void)
{
  Integer exit_status=0, i, neq;
  NagError fail;
  Nag_ErrorAssess errass;
  Nag_ODE_RK opt;
  Nag_RK_method method;
  Nag_User comm;
  double errmax, hstart, pi, *rmserr=0, tend, terrmx, tgot, *thres=0, tol;
  double tstart, twant, *ygot=0, *ymax=0, *ypgot=0, *ystart=0;

  INIT_FAIL(fail);

  Vprintf("nag_ode_ivp_rk_errass (d02pzc) Example Program Results\n");

  /* Set initial conditions and input for nag_ode_ivp_rk_setup (d02pvc) */
  neq = NEQ;

  if (neq>=1)
    {
      if ( !( thres = NAG_ALLOC(neq, double)) ||
           !( ygot = NAG_ALLOC(neq, double)) ||
           !( ypgot = NAG_ALLOC(neq, double)) ||
           !( ystart = NAG_ALLOC(neq, double)) ||
           !( ymax = NAG_ALLOC(NEQ, double)) ||
           !( rmserr = NAG_ALLOC(NEQ, double)) )
        {
          Vprintf("Allocation failure\n");
          exit_status = -1;
          goto END;
        }
    }
  else
    {
      exit_status = 1;
      return exit_status;
    }

  /* nag_pi (x01aac).
   * pi
   */
  pi = X01AAC;
  tstart = ZERO;
  ystart[0] = ONE - ECC;
  ystart[1] = ZERO;
  ystart[2] = ZERO;
  ystart[3] = sqrt((ONE+ECC)/(ONE-ECC));
  tend = THREE*pi;
  for (i=0; i<neq; i++)
    thres[i] = 1.0e-10;
  errass = Nag_ErrorAssess_on;
  hstart = ZERO;
  tol = 1.0e-6;
  method  = Nag_RK_7_8;
  /* nag_ode_ivp_rk_setup (d02pvc).
   * Setup function for use with nag_ode_ivp_rk_range (d02pcc)
   * and/or nag_ode_ivp_rk_onestep (d02pdc)
   */
  nag_ode_ivp_rk_setup(neq, tstart, ystart, tend, tol, thres, method,
                       Nag_RK_range, errass, hstart, &opt, &fail);
  if (fail.code != NE_NOERROR)
    {
      Vprintf("Error from nag_ode_ivp_rk_setup (d02pvc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  Vprintf("\nCalculation with tol = %8.1e\n\n",tol);
  Vprintf("    t          y1          y2          y3          y4\n\n");
  Vprintf("%8.3f    %8.4f    %8.4f    %8.4f    %8.4f\n", tstart, ystart[0],
          ystart[1], ystart[2], ystart[3]);

  twant = tend;
  do
    {
      /* nag_ode_ivp_rk_range (d02pcc).
       * Ordinary differential equations solver, initial value
       * problems over a range using Runge-Kutta methods
       */
      nag_ode_ivp_rk_range(neq, f, twant, &tgot, ygot, ypgot, ymax, &opt, &comm,
                           &fail);
    } while (fail.code==NE_RK_PDC_POINTS || fail.code==NE_STIFF_PROBLEM);

  if (fail.code != NE_NOERROR)
    {
      Vprintf("Error from nag_ode_ivp_rk_range (d02pcc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }
  else
    {
      Vprintf("%8.3f    %8.4f    %8.4f    %8.4f    %8.4f\n\n", tgot, ygot[0],
              ygot[1], ygot[2], ygot[3]);
      /* nag_ode_ivp_rk_errass (d02pzc).
       * A function to provide global error assessment during an
       * integration with either nag_ode_ivp_rk_range (d02pcc) or
       * nag_ode_ivp_rk_onestep (d02pdc)
       */
      nag_ode_ivp_rk_errass(neq, rmserr, &errmax, &terrmx, &opt, &fail);
      if (fail.code != NE_NOERROR)
        {
          Vprintf("Error from nag_ode_ivp_rk_errass (d02pzc).\n%s\n",
                  fail.message);
          exit_status = 1;
          goto END;
        }

      Vprintf("Componentwise error assessment\n          ");
      for (i=0; i<neq; i++)
        Vprintf("%9.2e ", rmserr[i]);
      Vprintf("\n\n");
      Vprintf("Worst global error observed was %9.2e - "
              "it occurred at t = %6.3f\n\n", errmax, terrmx);
      Vprintf("Cost of the integration in evaluations of f is %ld\n",
              opt.totfcn);
    }
  /* nag_ode_ivp_rk_free (d02ppc).
   * Freeing function for use with the Runge-Kutta suite (d02p
   * functions)
   */
  nag_ode_ivp_rk_free(&opt);
 END:
  if (thres) NAG_FREE(thres);
  if (ygot) NAG_FREE(ygot);
  if (ypgot) NAG_FREE(ypgot);
  if (ystart) NAG_FREE(ystart);
  if (ymax) NAG_FREE(ymax);
  if (rmserr) NAG_FREE(rmserr);
  return exit_status;
}
static void f(Integer neq, double t, double y[], double yp[], Nag_User *comm)

{
  double r, rp3 ;

  r = sqrt(y[0]*y[0]+y[1]*y[1]);
  rp3 = pow(r, 3.0);
  yp[0] = y[2];
  yp[1] = y[3];
  yp[2] = -y[0]/rp3;
  yp[3] = -y[1]/rp3;
}