/* nag_ode_ivp_rk_interp (d02pxc) Example Program.
 *
 * Copyright 1992 Numerical Algorithms Group.
 *
 * Mark 3, 1992.
 * Mark 7 revised, 2001.
 * Mark 8 revised, 2004.
 *
 */

#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 NAG_CALL f(Integer neq, double t1, const 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         exit_status = 0, i, j, neq, nout, nwant;
  NagError        fail;
  Nag_ErrorAssess errass;
  Nag_ODE_RK      opt;
  Nag_RK_method   method;
  Nag_User        comm;
  double          hstart, pi, tend, *thres = 0, tinc, tnow, tol, tstart, twant,
  *ynow = 0;
  double          *ypnow = 0, *ypwant = 0, *ystart = 0, *ywant = 0;

  INIT_FAIL(fail);

  printf("nag_ode_ivp_rk_interp (d02pxc) Example Program Results\n");

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

  if (neq >= 1)
    {
      if (!(thres = NAG_ALLOC(neq, double)) ||
          !(ynow = NAG_ALLOC(neq, double)) ||
          !(ypnow = NAG_ALLOC(neq, double)) ||
          !(ystart = NAG_ALLOC(neq, double)) ||
          !(ywant = NAG_ALLOC(nwant, double)) ||
          !(ypwant = NAG_ALLOC(nwant, double)))
        {
          printf("Allocation failure\n");
          exit_status = -1;
          goto END;
        }
    }
  else
    {
      exit_status = 1;
      return exit_status;
    }

  method = Nag_RK_4_5;
  /* nag_pi (x01aac).
   * pi
   */
  pi = nag_pi;
  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;
      /* 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_onestep, errass, hstart, &opt, &fail);
      if (fail.code != NE_NOERROR)
        {
          printf("Error from nag_ode_ivp_rk_setup (d02pvc).\n%s\n",
                  fail.message);
          exit_status = 1;
          goto END;
        }
      printf("\nCalculation with tol = %10.1e\n\n", tol);
      printf("    t          y1           y2\n\n");
      printf("%8.3f    %8.4f     %8.4f\n", tstart, ystart[0],
              ystart[1]);
      j = nout - 1;
      twant = tend - j*tinc;

      do
        {
          /* nag_ode_ivp_rk_onestep (d02pdc).
           * Ordinary differential equations solver, initial value
           * problems, one time step using Runge-Kutta methods
           */
          nag_ode_ivp_rk_onestep(neq, f, &tnow, ynow, ypnow, &opt, &comm,
                                 &fail);
          if (fail.code != NE_NOERROR)
            {
              printf(
                      "Error from nag_ode_ivp_rk_onestep (d02pdc).\n%s\n",
                      fail.message);
              exit_status = 1;
              goto END;
            }

          while (twant <= tnow)
            {
              /* nag_ode_ivp_rk_interp (d02pxc).
               * Ordinary differential equations solver, computes the
               * solution by interpolation anywhere on an integration step
               * taken by nag_ode_ivp_rk_onestep (d02pdc)
               */
              nag_ode_ivp_rk_interp(neq, twant, Nag_SolDer, nwant, ywant,
                                    ypwant, f, &opt, &comm, &fail);
              if (fail.code != NE_NOERROR)
                {
                  printf(
                          "Error from nag_ode_ivp_rk_interp (d02pxc).\n%s\n",
                          fail.message);
                  exit_status = 1;
                  goto END;
                }

              printf("%8.3f    %8.4f     %8.4f\n", twant, ywant[0],
                      ypwant[0]);
              j = j - 1;
              twant = tend - j*tinc;
            }
        } while (tnow < tend);

      printf("\nCost of the integration in evaluations of f is"
              " %ld\n\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 (ynow) NAG_FREE(ynow);
  if (ypnow) NAG_FREE(ypnow);
  if (ystart) NAG_FREE(ystart);
  if (ywant) NAG_FREE(ywant);
  if (ypwant) NAG_FREE(ypwant);
  return exit_status;
}
static void NAG_CALL f(Integer neq, double t, const double y[], double yp[],
                       Nag_User *comm)

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