/* nag_pde_parab_1d_keller (d03pec) Example Program.
 *
 * Copyright 2001 Numerical Algorithms Group.
 *
 * Mark 7, 2001.
 */

#include <stdio.h>
#include <math.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <nagd03.h>
#include <nagx01.h>

#ifdef __cplusplus
extern "C" {
#endif
static void NAG_CALL pdedef(Integer, double, double, const double[],
                            const double[], const double[], double[],
                            Integer *, Nag_Comm *);
static void NAG_CALL bndary(Integer, double, Integer, Integer, const double[],
                            const double[], double[], Integer *, Nag_Comm *);
static void NAG_CALL exact(double, Integer, Integer, double *, double *);
static void NAG_CALL uinit(Integer, Integer, double *, double *);
#ifdef __cplusplus
}
#endif

#define U(I, J)  u[npde*((J) -1)+(I) -1]
#define EU(I, J) eu[npde*((J) -1)+(I) -1]

int main(void)
{
  const Integer npde = 2, npts = 41, nleft = 1, neqn = npde*npts;
  const Integer lisave = neqn+24, nwkres = npde*(npts+21+3*npde)+7*npts+4;
  const Integer lrsave = 11*neqn+(4*npde+nleft+2)*neqn+50+nwkres;
  Integer       exit_status = 0, i, ind, it, itask, itrace;
  double        acc, tout, ts;
  double        *eu = 0, *rsave = 0, *u = 0, *x = 0;
  Integer       *isave = 0;
  NagError      fail;
  Nag_Comm      comm;
  Nag_D03_Save  saved;

  INIT_FAIL(fail);

  printf(
          "nag_pde_parab_1d_keller (d03pec) Example Program Results\n\n");

  /* Allocate memory */

  if (!(eu = NAG_ALLOC(npde*npts, double)) ||
      !(rsave = NAG_ALLOC(lrsave, double)) ||
      !(u = NAG_ALLOC(npde*npts, double)) ||
      !(x = NAG_ALLOC(npts, double)) ||
      !(isave = NAG_ALLOC(lisave, Integer)))
    {
      printf("Allocation failure\n");
      exit_status = 1;
      goto END;
    }

  itrace = 0;
  acc = 1e-6;

  printf("  Accuracy requirement =%12.3e", acc);
  printf(" Number of points = %3ld\n\n", npts);

  /* Set spatial-mesh points */

  for (i = 0; i < npts; ++i) x[i] = i/(npts-1.0);

  printf(" x        ");
  printf("%10.4f%10.4f%10.4f%10.4f%10.4f\n\n",
          x[4], x[12], x[20], x[28], x[36]);

  ind = 0;
  itask = 1;

  uinit(npde, npts, x, u);

  /* Loop over output value of t */

  ts = 0.0;
  tout = 0.0;
  for (it = 0; it < 5; ++it)
    {
      tout = 0.2*(it+1);
      /* nag_pde_parab_1d_keller (d03pec).
       * General system of first-order PDEs, method of lines,
       * Keller box discretisation, one space variable
       */
      nag_pde_parab_1d_keller(npde, &ts, tout, pdedef, bndary, u, npts, x,
                              nleft, acc, rsave, lrsave, isave, lisave, itask,
                              itrace, 0, &ind, &comm, &saved, &fail);

      if (fail.code != NE_NOERROR)
        {
          printf("Error from nag_pde_parab_1d_keller (d03pec).\n%s\n",
                  fail.message);
          exit_status = 1;
          goto END;
        }

      /* Check against the exact solution */

      exact(tout, npde, npts, x, eu);

      printf(" t = %5.2f\n", ts);
      printf(" Approx u1");
      printf("%10.4f%10.4f%10.4f%10.4f%10.4f\n",
              U(1, 5), U(1, 13), U(1, 21), U(1, 29), U(1, 37));

      printf(" Exact  u1");
      printf("%10.4f%10.4f%10.4f%10.4f%10.4f\n",
              EU(1, 5), EU(1, 13), EU(1, 21), EU(1, 29), EU(1, 37));

      printf(" Approx u2");
      printf("%10.4f%10.4f%10.4f%10.4f%10.4f\n",
              U(2, 5), U(2, 13), U(2, 21), U(2, 29), U(2, 37));

      printf(" Exact  u2");
      printf("%10.4f%10.4f%10.4f%10.4f%10.4f\n\n",
              EU(2, 5), EU(2, 13), EU(2, 21), EU(2, 29), EU(2, 37));
    }
  printf(" Number of integration steps in time = %6ld\n", isave[0]);
  printf(" Number of function evaluations = %6ld\n", isave[1]);
  printf(" Number of Jacobian evaluations =%6ld\n", isave[2]);
  printf(" Number of iterations = %6ld\n\n", isave[4]);

 END:
  if (eu) NAG_FREE(eu);
  if (rsave) NAG_FREE(rsave);
  if (u) NAG_FREE(u);
  if (x) NAG_FREE(x);
  if (isave) NAG_FREE(isave);

  return exit_status;
}



static void NAG_CALL pdedef(Integer npde, double t, double x, const double u[],
                            const double udot[], const double dudx[], double
                            res[], Integer *ires, Nag_Comm *comm)
{
  if (*ires == -1)
    {
      res[0] = udot[0];
      res[1] = udot[1];
    }
  else
    {
      res[0] = udot[0] + dudx[0] + dudx[1];
      res[1] = udot[1] + 4.0*dudx[0] + dudx[1];
    }
  return;
}


static void NAG_CALL bndary(Integer npde, double t, Integer ibnd, Integer nobc,
                            const double u[], const double udot[],
                            double res[], Integer *ires, Nag_Comm *comm)
{
  if (ibnd == 0)
    {
      if (*ires == -1)
        {
          res[0] = 0.0;
        }
      else
        {
          res[0] = u[0] - 0.5*(exp(t) + exp(-3.0*t))
                   - 0.25*(sin(-3.0*t) - sin(t));
        }
    }
  else
    {
      if (*ires == -1)
        {
          res[0] = 0.0;
        }
      else
        {
          res[0] = u[1] - exp(1.0 - 3.0*t) + exp(t + 1.0)
                   - 0.5*(sin(1.0 - 3.0*t) + sin(
                            t + 1.0));
        }
    }
  return;
}

static void NAG_CALL uinit(Integer npde, Integer npts, double *x, double *u)
{
  /* Routine for PDE initial values */

  Integer i;

  for (i = 1; i <= npts; ++i)
    {
      U(1, i) = exp(x[i-1]);
      U(2, i) = sin(x[i-1]);
    }
  return;
}

static void NAG_CALL exact(double t, Integer npde, Integer npts, double *x,
                           double *u)
{
  /* Exact solution (for comparison purposes) */

  Integer i;

  for (i = 1; i <= npts; ++i)
    {
      U(1, i) = 0.5*(exp(x[i-1] + t) + exp(x[i-1] - 3.0*t)) +
                0.25*(sin(x[i-1] - 3.0*t) - sin(x[i-1] + t));
      U(2, i) = exp(x[i-1] - 3.0*t) - exp(x[i-1] + t) +
                0.5*(sin(x[i-1] - 3.0*t) + sin(x[i-1] + t));
    }
  return;
}