/* nag_pde_parab_1d_coll_ode (d03pjc) Example Program.
 *
 * Copyright 2017 Numerical Algorithms Group.
 *
 * Mark 26.2, 2017.
 */

#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, const double[], Integer, const
                              double[], const double[], Integer,
                              const double[], const double[], double[],
                              double[], double[], Integer *, Nag_Comm *);
  static void NAG_CALL bndary(Integer, double, const double[], const double[],
                              Integer, const double[], const double[],
                              Integer, double[], double[], Integer *,
                              Nag_Comm *);
  static void NAG_CALL odedef(Integer, double, Integer, const double[],
                              const double[], Integer, const double[],
                              const double[], const double[], const double[],
                              const double[], const double[], double[],
                              Integer *, Nag_Comm *);
  static void NAG_CALL uvinit(Integer, Integer, const double[], double[],
                              Integer, double[], Nag_Comm *);
#ifdef __cplusplus
}
#endif

#define U(I, J)    u[npde*((J) -1)+(I) -1]
#define UX(I, J)   ux[npde*((J) -1)+(I) -1]
#define UCP(I, J)  ucp[npde*((J) -1)+(I) -1]
#define UCPX(I, J) ucpx[npde*((J) -1)+(I) -1]
#define P(I, J, K) p[npde*(npde*((K) -1)+(J) -1)+(I) -1]
#define Q(I, J)    q[npde*((J) -1)+(I) -1]
#define R(I, J)    r[npde*((J) -1)+(I) -1]

int main(void)
{
  /* Constant scalars */
  const Integer print_stat = 0;
  const Integer npde = 1, ncode = 1, npoly = 3, m = 0, nbkpts = 30;
  const Integer nel = nbkpts - 1, npts = nel * npoly + 1;
  const Integer neqn = npde*npts + ncode;
  const Integer nxi = 1, lisave = 24, npl1 = npoly + 1;
  const Integer nwkres = npl1*(3*npl1 + npde*(npde + 6) + nbkpts + 1) +
                         8*npde + nxi*(5*npde + 1) + ncode + 3;
  const Integer lenode = 11 * neqn + 50;
  const Integer lrsave =  neqn*neqn + neqn + nwkres + lenode;

  /* Constant arrays */
  static double ruser[4] = { -1.0, -1.0, -1.0, -1.0 };

  /* Scalars */
  double       tout, ts;
  Integer      exit_status = 0, i, ind, it, itask, itol, itrace;
  Nag_Boolean  theta;

  /* Arrays */
  double       *algopt = 0, *atol = 0, *rsave = 0, *rtol = 0;
  double       *u = 0, *x = 0, *xbkpts = 0, *xi = 0;
  Integer      *isave = 0;

  /* Nag Types */
  NagError     fail;
  Nag_Comm     comm;
  Nag_D03_Save saved;

  INIT_FAIL(fail);

  printf(" nag_pde_parab_1d_coll_ode (d03pjc) Example Program Results\n");

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

  /* Allocate memory */

  if (!(algopt = NAG_ALLOC(30, double)) ||
      !(atol = NAG_ALLOC(1, double)) ||
      !(rsave = NAG_ALLOC(lrsave, double)) ||
      !(rtol = NAG_ALLOC(1, double)) ||
      !(u = NAG_ALLOC(neqn, double)) ||
      !(x = NAG_ALLOC(npts, double)) ||
      !(xbkpts = NAG_ALLOC(nbkpts, 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-5;
  rtol[0] = atol[0];
  printf("\n  Simple coupled PDE using BDF\n\n");
  printf("   Degree of Polynomial =%4" NAG_IFMT "\n", npoly);
  printf("   Number of elements   =%4" NAG_IFMT "\n", nbkpts - 1);
  printf("   Accuracy requirement =%12.3e\n", atol[0]);
  printf("   Number of points     =%4" NAG_IFMT "\n\n", npts);

  /* Set break-points */

  for (i = 0; i < nbkpts; ++i)
    xbkpts[i] = i / (nbkpts - 1.0);

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

  /* Set theta = 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;
  }

  /* Loop over output value of t */

  ts = 1.e-4;
  comm.p = (Pointer) &ts;

  printf("%7s%8s%s\n", "time", "", "solution at x=0");

  tout = 0.1;
  for (it = 0; it < 5; ++it) {
    tout = tout + tout;
    /* nag_pde_parab_1d_coll_ode (d03pjc).
     * General system of parabolic PDEs, coupled DAEs, method of
     * lines, Chebyshev C^0 collocation, one space variable
     */
    nag_pde_parab_1d_coll_ode(npde, m, &ts, tout, pdedef, bndary, u, nbkpts,
                              xbkpts, npoly, npts, x, ncode, odedef, nxi, xi,
                              neqn, uvinit, 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_coll_ode (d03pjc).\n%s\n",
             fail.message);
      exit_status = 1;
      goto END;
    }

    printf("%7.1f%15s%6.2f\n", ts, "", u[0]);
  }
  if (print_stat) {
    printf(" Number of integration steps in time = %6" NAG_IFMT "\n", isave[0]);
    printf(" Number of function evaluations = %6" NAG_IFMT "\n", isave[1]);
    printf(" Number of Jacobian evaluations =%6" NAG_IFMT "\n", isave[2]);
    printf(" Number of iterations = %6" NAG_IFMT "\n\n", isave[4]);
  }
END:
  NAG_FREE(algopt);
  NAG_FREE(atol);
  NAG_FREE(rsave);
  NAG_FREE(rtol);
  NAG_FREE(u);
  NAG_FREE(x);
  NAG_FREE(xbkpts);
  NAG_FREE(xi);
  NAG_FREE(isave);

  return exit_status;
}

static void NAG_CALL uvinit(Integer npde, Integer npts, const double x[],
                            double u[], Integer ncode, double v[],
                            Nag_Comm *comm)
{
  /* Routine for PDE initial values (start time is 0.1e-6) */

  double *ts = (double *) comm->p;
  Integer i;

  if (comm->user[0] == -1.0) {
    /* printf("(User-supplied callback uvinit, first invocation.)\n"); */
    comm->user[0] = 0.0;
  }
  v[0] = *ts;
  for (i = 1; i <= npts; ++i)
    U(1, i) = exp(*ts * (1.0 - x[i - 1])) - 1.0;
  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 rcp[], const double ucpt[],
                            const double ucptx[], double f[], Integer *ires,
                            Nag_Comm *comm)
{
  if (comm->user[1] == -1.0) {
    /* printf("(User-supplied callback odedef, first invocation.)\n"); */
    comm->user[1] = 0.0;
  }
  if (*ires == 1) {
    f[0] = vdot[0] - v[0] * UCP(1, 1) - UCPX(1, 1) - 1.0 - t;
  }
  else if (*ires == -1) {
    f[0] = vdot[0];
  }
  return;
}

static void NAG_CALL pdedef(Integer npde, double t, const double x[],
                            Integer nptl, const double u[], const double ux[],
                            Integer ncode, const double v[],
                            const double vdot[], double p[], double q[],
                            double r[], Integer *ires, Nag_Comm *comm)
{
  Integer i;
  if (comm->user[2] == -1.0) {
    /* printf("(User-supplied callback pdedef, first invocation.)\n"); */
    comm->user[2] = 0.0;
  }
  for (i = 1; i <= nptl; ++i) {
    P(1, 1, i) = v[0] * v[0];
    R(1, i) = UX(1, i);
    Q(1, i) = -x[i - 1] * UX(1, i) * v[0] * vdot[0];
  }
  return;
}

static void NAG_CALL bndary(Integer npde, double t, const double u[],
                            const double ux[], Integer ncode,
                            const double v[], const double vdot[],
                            Integer ibnd, double beta[], double gamma[],
                            Integer *ires, Nag_Comm *comm)
{
  if (comm->user[3] == -1.0) {
    /* printf("(User-supplied callback bndary, first invocation.)\n"); */
    comm->user[3] = 0.0;
  }
  beta[0] = 1.0;
  if (ibnd == 0) {
    gamma[0] = -v[0] * exp(t);
  }
  else {
    gamma[0] = -v[0] * vdot[0];
  }
  return;
}