/* nag_pde_parab_1d_keller_ode (d03pkc) Example Program.
 *
 * Copyright 2014 Numerical Algorithms Group.
 *
 * Mark 7, 2001.
 * Mark 7b revised, 2004.
 */

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

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

static void NAG_CALL bndary(Integer npde, double t, Integer ibnd, Integer nobc,
                            const double u[], const double ut[], Integer ncode,
                            const double v[], const double vdot[],
                            double res[], Integer *ires, Nag_Comm *);

static void NAG_CALL odedef(Integer, double, Integer, const double[],
                            const double[], Integer, const double[],
                            const double[], const double[], const double[],
                            double[], Integer *, Nag_Comm *);

static void NAG_CALL uvinit(Integer npde, Integer npts, double *x, double *u,
                            Integer ncode, Integer neqn, double ts);

static void NAG_CALL exact(double, Integer, Integer, double *, double *);
#ifdef __cplusplus
}
#endif

#define UCP(I, J) ucp[npde*((J) -1)+(I) -1]

int main(void)
{
  const Integer npde = 2, npts = 21, ncode = 1, nxi = 1, nleft = 1;
  const Integer neqn = npde*npts+ncode, lisave = 24;
  const Integer nwkres = npde*(npts+6*nxi+3*npde+15)+ncode+nxi+7*npts+2;
  const Integer lenode = 11*neqn+50, lrsave = neqn*neqn+neqn+nwkres+lenode;
  static double ruser[3] = {-1.0, -1.0, -1.0};
  double        tout, ts;
  Integer       exit_status = 0, i, ind, it, itask, itol, itrace;
  Nag_Boolean   theta;
  double        *algopt = 0, *atol = 0, *exy = 0, *rsave = 0, *rtol = 0;
  double        *u = 0, *x = 0, *xi = 0;
  Integer       *isave = 0;
  NagError      fail;
  Nag_Comm      comm;
  Nag_D03_Save  saved;

  INIT_FAIL(fail);

  printf(
          "nag_pde_parab_1d_keller_ode (d03pkc) Example Program Results\n\n");

  /* For communication with user-supplied functions: */
  comm.user = ruser;

  /* Allocate memory */

  if (!(algopt = NAG_ALLOC(30, double)) ||
      !(atol = NAG_ALLOC(1, double)) ||
      !(exy = NAG_ALLOC(neqn, double)) ||
      !(rsave = NAG_ALLOC(lrsave, double)) ||
      !(rtol = NAG_ALLOC(1, double)) ||
      !(u = NAG_ALLOC(neqn, double)) ||
      !(x = NAG_ALLOC(npts, double)) ||
      !(xi = NAG_ALLOC(nxi, double)) ||
      !(isave = NAG_ALLOC(lisave, Integer)))
    {
      printf("Allocation failure\n");
      exit_status = 1;
      goto END;
    }

  itrace = 0;
  itol = 1;
  atol[0] = 1e-4;
  rtol[0] = atol[0];

  printf("  Accuracy requirement =%12.3e", atol[0]);
  printf(" Number of points = %3ld\n\n", npts);

  /* Set spatial-mesh points */

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

  xi[0] = 1.0;
  ind = 0;
  itask = 1;

  /* Set THETA to TRUE if the Theta integrator is required */

  theta = Nag_FALSE;
  for (i = 0; i < 30; ++i) algopt[i] = 0.0;
  if (theta)
    {
      algopt[0] = 2.0;
    }
  else
    {
      algopt[0] = 0.0;
    }
  algopt[0] = 1.0;
  algopt[12] = 0.005;

  /* Loop over output value of t */

  ts = 1e-4;
  tout = 0.0;
  printf("  x        %9.3f%9.3f%9.3f%9.3f%9.3f\n\n",
          x[0], x[4], x[8], x[12], x[20]);

  uvinit(npde, npts, x, u, ncode, neqn, ts);

  for (it = 0; it < 5; ++it)
    {
      tout = 0.1*pow(2.0, (it+1.0));
      /* nag_pde_parab_1d_keller_ode (d03pkc).
       * General system of first-order PDEs, coupled DAEs, method
       * of lines, Keller box discretisation, one space variable
       */
      nag_pde_parab_1d_keller_ode(npde, &ts, tout, pdedef, bndary, u, npts, x,
                                  nleft, ncode, odedef, nxi, xi, neqn, rtol,
                                  atol, itol, Nag_TwoNorm, Nag_LinAlgFull,
                                  algopt, rsave, lrsave, isave, lisave, itask,
                                  itrace, 0, &ind, &comm, &saved, &fail);

      if (fail.code != NE_NOERROR)
        {
          printf(
                  "Error from nag_pde_parab_1d_keller_ode (d03pkc).\n%s\n",
                  fail.message);
          exit_status = 1;
          goto END;
        }

      /* Check against the exact solution */

      exact(tout, neqn, npts, x, exy);

      printf(" t = %6.3f\n", ts);
      printf(" App.  sol.  %7.3f%9.3f%9.3f%9.3f%9.3f",
              u[0], u[8], u[16], u[24], u[40]);
      printf("  ODE sol. =%8.3f\n", u[42]);
      printf(" Exact sol.  %7.3f%9.3f%9.3f%9.3f%9.3f",
              exy[0], exy[8], exy[16], exy[24], exy[40]);
      printf("  ODE sol. =%8.3f\n\n", ts);
    }
  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:
  NAG_FREE(algopt);
  NAG_FREE(atol);
  NAG_FREE(exy);
  NAG_FREE(rsave);
  NAG_FREE(rtol);
  NAG_FREE(u);
  NAG_FREE(x);
  NAG_FREE(xi);
  NAG_FREE(isave);

  return exit_status;
}


static void NAG_CALL uvinit(Integer npde, Integer npts, double *x,
                            double *u, Integer ncode, Integer neqn,
                            double ts)
{
  Integer i, k;

  /* Routine for PDE initial values */

  k = 0;
  for (i = 0; i < npts; ++i)
    {
      u[k] = exp(ts*(1.0-x[i])) - 1.0;
      u[k+1] = -ts *exp(ts *(1.0-x[i]));
      k += 2;
    }
  u[neqn-1] = ts;

  return;
}

static void NAG_CALL odedef(Integer npde, double t, Integer ncode,
                            const double v[], const double vdot[], Integer nxi,
                            const double xi[], const double ucp[],
                            const double ucpx[], const double ucpt[],
                            double f[], Integer *ires, Nag_Comm *comm)
{
  if (comm->user[0] == -1.0)
    {
      printf("(User-supplied callback odedef, first invocation.)\n");
      comm->user[0] = 0.0;
    }
  if (*ires == -1)
    {
      f[0] = vdot[0];
    }
  else
    {
      f[0] = vdot[0] - v[0]*UCP(1, 1) - UCP(2, 1) - 1.0 - t;
    }
  return;
}

static void NAG_CALL pdedef(Integer npde, double t, double x, const double u[],
                            const double ut[], const double ux[],
                            Integer ncode, const double v[],
                            const double vdot[], double res[],
                            Integer *ires, Nag_Comm *comm)
{
  if (comm->user[1] == -1.0)
    {
      printf("(User-supplied callback pdedef, first invocation.)\n");
      comm->user[1] = 0.0;
    }
  if (*ires == -1)
    {
      res[0] = v[0]*v[0]*ut[0] - x*u[1]* v[0]*vdot[0];
      res[1] = 0.0;
    }
  else
    {
      res[0] = v[0]*v[0]*ut[0] - x*u[1]* v[0]*vdot[0] - ux[1];
      res[1] = u[1] - ux[0];
    }
  return;
}

static void NAG_CALL bndary(Integer npde, double t, Integer ibnd, Integer nobc,
                            const double u[], const double ut[], Integer ncode,
                            const double v[], const double vdot[],
                            double res[], Integer *ires, Nag_Comm *comm)
{
  if (comm->user[2] == -1.0)
    {
      printf("(User-supplied callback bndary, first invocation.)\n");
      comm->user[2] = 0.0;
    }
  if (ibnd == 0)
    {
      if (*ires == -1)
        {
          res[0] = 0.0;
        }
      else
        {
          res[0] = u[1] + v[0]* exp(t);
        }
    }
  else
    {
      if (*ires == -1)
        {
          res[0] = v[0]* vdot[0 ];
        }
      else
        {
          res[0] = u[1] + v[0]* vdot[0 ];
        }
    }
  return;
}

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

  Integer i, k;

  k = 0;
  for (i = 0; i < npts; ++i)
    {
      u [k] = exp(time* (1.0-x[i])) - 1.0;
      k += 2;
    }
  return;
}