/* nag_ode_ivp_rk_interp(d02pxc) Example Program
 *
 * Copyright 1992 Numerical Algorithms Group.
 *
 * Mark 3, 1992.
 * Mark 7 revised, 2001.
 *
 */

#include <nag.h>
#include <stdio.h>
#include <nag_stdlib.h>
#include <math.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 2
#define NWANT 1
#define ZERO 0.0
#define ONE 1.0
#define TWO 2.0
#define FOUR 4.0

int main(void)
{
  Integer neq, nwant;
  double hstart, pi, tnow, tend, tol, tstart, tinc, twant;
  Integer i, j, nout;
  double thres[NEQ], ynow[NEQ], ypnow[NEQ], ystart[NEQ], ywant[NWANT];
  double ypwant[NWANT];
  Nag_RK_method method;
  Nag_ErrorAssess errass;
  Nag_ODE_RK opt;
  Nag_User comm;

  Vprintf("d02pxc Example Program Results\n");

  /* Set initial conditions and input for d02pvc */
  neq = NEQ;
  method  = Nag_RK_4_5;
  pi = X01AAC;
  tstart = ZERO;
  ystart[0] = ZERO;
  ystart[1] = ONE;
  tend = TWO*pi;
  for (i=0; i<neq; i++)
    thres[i] = 1.0e-8;
  errass = Nag_ErrorAssess_off;
  hstart = ZERO;

  /*
   * Set control for output
   */
  nwant = NWANT;
  nout = 16;
  tinc = tend/nout;
  for (i=1; i<=2; i++)
    {
      if (i==1)
        tol = 1.0e-3;
      else
        tol = 1.0e-4;
      d02pvc(neq, tstart, ystart, tend, tol, thres, method,
             Nag_RK_onestep, errass, hstart, &opt, NAGERR_DEFAULT);

      Vprintf("\nCalculation with tol = %8.1e\n\n",tol);
      Vprintf("    t          y1           y2\n\n");
      Vprintf("%8.3f    %8.4f     %8.4f\n", tstart, ystart[0], ystart[1]);
      j = nout - 1;
      twant = tend - j*tinc;

      do
        {
          d02pdc(neq, f, &tnow, ynow, ypnow, &opt, &comm, NAGERR_DEFAULT);
          while (twant<=tnow)
            {
              d02pxc(neq, twant, Nag_SolDer, nwant, ywant, ypwant, f,
                     &opt, &comm, NAGERR_DEFAULT);
              Vprintf("%8.3f    %8.4f     %8.4f\n", twant, ywant[0],
                      ypwant[0]);
              j = j - 1;
              twant = tend - j*tinc;
            }
        } while (tnow<tend);

      Vprintf("\nCost of the integration in evaluations of f is %ld\n\n",
              opt.totfcn);
      d02ppc(&opt);
    }
  return EXIT_SUCCESS;
}
static void f(Integer neq, double t, double y[], double yp[], Nag_User *comm)

{
  yp[0] = y[1];
  yp[1] = -y[0];
}