/* nag_pde_parab_1d_cd_ode_remesh (d03psc) 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>

static int ex1(void);
static int ex2(void);

#ifdef __cplusplus
extern "C" {
#endif
static void NAG_CALL uvin1(Integer, Integer, Integer, const double[],
                           const double[], double[], Integer, double[],
                           Nag_Comm *);

static void NAG_CALL uvin2(Integer, Integer, Integer, const double[],
                           const double[], double[], Integer, double[],
                           Nag_Comm *);

static void NAG_CALL pdef1(Integer, double, double, const double[],
                           const double[], Integer, const double[],
                           const double[], double[], double[], double[],
                           double[], Integer *, Nag_Comm *);

static void NAG_CALL pdef2(Integer, double, double, const double[],
                           const double[], Integer, const double[],
                           const double[], double[], double[], double[],
                           double[], Integer *, Nag_Comm *);

static void NAG_CALL bndry1(Integer, Integer, double, const double[],
                            const double[], Integer, const double[],
                            const double[], Integer, double[],
                            Integer *, Nag_Comm *);

static void NAG_CALL bndry2(Integer, Integer, double, const double[],
                            const double[], Integer, const double[],
                            const double[], Integer, double[],
                            Integer *, Nag_Comm *);

static void NAG_CALL monit1(double, Integer, Integer, const double[],
                            const double[], double[], Nag_Comm *);

static void NAG_CALL monit2(double, Integer, Integer, const double[],
                            const double[], double[], Nag_Comm *);


static void NAG_CALL nmflx1(Integer, double, double, Integer,
                            const double[], const double[],
                            const double[], double[], Integer *,
                            Nag_Comm *, Nag_D03_Save *);

static void NAG_CALL nmflx2(Integer, double, double, Integer,
                            const double[], const double[],
                            const double[], double[], Integer *,
                            Nag_Comm *, Nag_D03_Save *);
#ifdef __cplusplus
}
#endif

static void NAG_CALL exact(double, double *, const double *, Integer, Integer);

#define P(I, J)       p[npde*((J) -1)+(I) -1]
#define UE(I, J)      ue[npde*((J) -1)+(I) -1]
#define U(I, J)       u[npde*((J) -1)+(I) -1]
#define UOUT(I, J, K) uout[npde*(intpts*((K) -1)+(J) -1)+(I) -1]

int main(void)
{
  Integer  exit_status_ex1 = 0;
  Integer  exit_status_ex2 = 0;

  printf(
          "nag_pde_parab_1d_cd_ode_remesh (d03psc) Example Program Results\n");
  exit_status_ex1 = ex1();
  exit_status_ex2 = ex2();

  return (exit_status_ex1 == 0 && exit_status_ex2 == 0) ? 0 : 1;
}

int ex1(void)
{
  const Integer npde = 1, npts = 61, ncode = 0, nxi = 0, nxfix = 0, itype = 1;
  const Integer neqn = npde*npts+ncode, intpts = 7, lisave = 25+nxfix+neqn;
  const Integer nwkres = npde*(3*npts+3*npde+32)+7*npts+3, lenode = 11*neqn+50;
  const Integer mlu = 3*npde-1, lrsave = (3*mlu+1)*neqn+nwkres+lenode;
  static double xout[7] = { .2, .3, .4, .5, .6, .7, .8 };
  double        con, dxmesh, tout, trmesh, ts, xratio;
  Integer       exit_status, i, ind, ipminf, it, itask, itol, itrace, m,
                nrmesh;
  Nag_Boolean   remesh;
  double        *algopt = 0, *atol = 0, *rsave = 0, *rtol = 0, *u = 0;
  double        *uout = 0, *x = 0, *xfix = 0, *xi = 0;
  Integer       *isave = 0;
  NagError      fail;
  Nag_Comm      comm;
  Nag_D03_Save  saved;

  INIT_FAIL(fail);
  exit_status = 0;

  /* 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(npde*npts, double)) ||
      !(uout = NAG_ALLOC(npde*intpts*itype, double)) ||
      !(x = NAG_ALLOC(npts, double)) ||
      !(xfix = NAG_ALLOC(1, double)) ||
      !(xi = NAG_ALLOC(1, double)) ||
      !(isave = NAG_ALLOC(lisave, Integer)))
    {
      printf("Allocation failure\n");
      exit_status = 1;
      goto END;
    }

  printf("\n\nExample 1\n\n");

  itrace = 0;
  itol = 1;
  atol[0] = 1.0e-4;
  rtol[0] = 1.0e-4;

  printf("  npts = %4ld", npts);
  printf(" atol = %12.3e", atol[0]);
  printf(" rtol = %12.3e\n\n", rtol[0]);

  /* Initialise mesh */

  for (i = 0; i < npts; ++i) x[i] = i/(npts-1.0);
  xfix[0] = 0.0;

  /* Set remesh parameters */

  remesh = Nag_TRUE;
  nrmesh = 3;
  dxmesh = 0.0;
  trmesh = 0.0;
  con = 2.0/(npts-1.0);
  xratio = 1.5;
  ipminf = 0;

  xi[0] = 0.0;
  ind = 0;
  itask = 1;

  for (i = 0; i < 30; ++i) algopt[i] = 0.0;

  /* b.d.f. integration */

  algopt[0] = 1.0;
  algopt[12] = 0.005;

  /* Loop over output value of t */

  ts = 0.0;
  tout = 0.0;
  for (it = 0; it < 3; ++it)
    {
      tout = 0.1*(it+1);

      /* nag_pde_parab_1d_cd_ode_remesh (d03psc).
       * General system of convection-diffusion PDEs with source
       * terms in conservative form, coupled DAEs, method of
       * lines, upwind scheme using numerical flux function based
       * on Riemann solver, remeshing, one space variable
       */
      nag_pde_parab_1d_cd_ode_remesh(npde, &ts, tout, pdef1, nmflx1, bndry1,
                                     uvin1, u, npts, x, ncode, NULLFN, nxi, xi,
                                     neqn, rtol, atol, itol, Nag_OneNorm,
                                     Nag_LinAlgBand, algopt, remesh, nxfix,
                                     xfix, nrmesh, dxmesh, trmesh, ipminf,
                                     xratio, con, monit1, rsave, lrsave, isave,
                                     lisave, itask, itrace, 0, &ind,
                                     &comm, &saved, &fail);
      if (fail.code != NE_NOERROR)
        {
          printf(
                  "Error from nag_pde_parab_1d_cd_ode_remesh (d03psc).\n%s\n",
                  fail.message);
          exit_status = 1;
          goto END;
        }

      printf(" t = %6.3f\n", ts);
      printf(" x        ");

      for (i = 1; i <= intpts; ++i)
        {
          printf("%9.4f", xout[i-1]);
          printf(i%7 == 0 || i == 7?"\n":"");
        }

      /* Interpolate at output points */

      m = 0;
      /* nag_pde_interp_1d_fd (d03pzc). PDEs, spatial interpolation with
       * nag_pde_parab_1d_cd_ode_remesh (d03psc).
       */
      nag_pde_interp_1d_fd(npde, m, u, npts, x, xout, intpts, itype, uout,
                           &fail);

      if (fail.code != NE_NOERROR)
        {
          printf("Error from nag_pde_interp_1d_fd (d03pzc).\n%s\n",
                  fail.message);
          exit_status = 1;
          goto END;
        }

      printf(" Approx u ");

      for (i = 1; i <= intpts; ++i)
        {
          printf("%9.4f", UOUT(1, i, 1));
          printf(i%7 == 0 || i == 7?"\n":"");
        }
      printf("\n");
    }

  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 (algopt) NAG_FREE(algopt);
  if (atol) NAG_FREE(atol);
  if (rsave) NAG_FREE(rsave);
  if (rtol) NAG_FREE(rtol);
  if (u) NAG_FREE(u);
  if (uout) NAG_FREE(uout);
  if (x) NAG_FREE(x);
  if (xfix) NAG_FREE(xfix);
  if (xi) NAG_FREE(xi);
  if (isave) NAG_FREE(isave);

  return exit_status;
}

static void NAG_CALL uvin1(Integer npde, Integer npts, Integer nxi,
                           const double x[], const double xi[], double u[],
                           Integer ncode, double v[], Nag_Comm *comm)
{
  Integer i;

  for (i = 1; i <= npts; ++i)
    {
      if (x[i-1] > 0.2 && x[i-1] <= 0.4)
        {
          U(1, i) = sin(nag_pi*(5.0*x[i-1]-1.0));
        }
      else
        {
          U(1, i) = 0.0;
        }
    }
  return;
}


static void NAG_CALL pdef1(Integer npde, double t, double x, const double u[],
                           const double ux[], Integer ncode, const double v[],
                           const double vdot[], double p[], double c[],
                           double d[], double s[], Integer *ires,
                           Nag_Comm *comm)
{
  P(1, 1) = 1.0;
  c[0] = 0.002;
  d[0] = ux[0];
  s[0] = 0.0;

  return;
}


static void NAG_CALL bndry1(Integer npde, Integer npts, double t,
                            const double x[], const double u[], Integer ncode,
                            const double v[], const double vdot[],
                            Integer ibnd, double g[], Integer *ires,
                            Nag_Comm *comm)
{
  /* Zero solution at both boundaries */

  if (ibnd == 0)
    {
      g[0] = U(1, 1);
    }
  else
    {
      g[0] = U(1, npts);
    }
  return;
}

static void NAG_CALL monit1(double t, Integer npts, Integer npde,
                            const double x[], const double u[], double fmon[],
                            Nag_Comm *comm)
{
  double  h1, h2, h3;
  Integer i;

  for (i = 2; i <= npts-1; ++i)
    {
      h1 = x[i - 1] - x[i - 2];
      h2 = x[i] - x[i - 1];
      h3 = 0.5* (x[i] - x[i - 2]);

      /* Second derivatives */

      fmon[i-1] = fabs(((U(1, i+1) - U(1, i))/h2 -
                        (U(1, i) - U(1, i-1))/h1)/h3);
    }
  fmon[0] = fmon[1];
  fmon[npts-1] = fmon[npts-2];

  return;
}

static void NAG_CALL nmflx1(Integer npde, double t, double x, Integer ncode,
                            const double v[], const double uleft[],
                            const double uright[], double flux[],
                            Integer *ires, Nag_Comm *comm, Nag_D03_Save *saved)
{
  flux [0] = uleft[0];

  return;
}

int ex2(void)
{
  const Integer npde = 1, npts = 61, ncode = 0, nxi = 0, nxfix = 0, itype = 1;
  const Integer neqn = npde*npts+ ncode, intpts = 7, lisave = 25+nxfix+neqn;
  const Integer nwkres = npde*(3*npts+3*npde+32)+7*npts+3, lenode = 11*neqn+50;
  const Integer mlu = 3*npde-1, lrsave = (3*mlu+1)*neqn+nwkres+lenode;
  static double xout[7] = { 0., .3, .4, .5, .6, .7, 1. };
  double        con, dxmesh, tout, trmesh, ts, xratio;
  Integer       exit_status, i, ind, ipminf, it, itask, itol, itrace, m,
                nrmesh;
  Nag_Boolean   remesh;
  double        *algopt = 0, *atol = 0, *rsave = 0, *rtol = 0, *u = 0, *ue = 0;
  double        *uout = 0, *x = 0, *xfix = 0, *xi = 0;
  Integer       *isave = 0;
  NagError      fail;
  Nag_Comm      comm;
  Nag_D03_Save  saved;

  INIT_FAIL(fail);
  exit_status = 0;

  /* 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(npts, double)) ||
      !(ue = NAG_ALLOC(npde*intpts, double)) ||
      !(uout = NAG_ALLOC(npde*intpts*itype, double)) ||
      !(x = NAG_ALLOC(npts, double)) ||
      !(xfix = NAG_ALLOC(1, double)) ||
      !(xi = NAG_ALLOC(1, double)) ||
      !(isave = NAG_ALLOC(lisave, Integer)))
    {
      printf("Allocation failure\n");
      exit_status = 1;
      goto END;
    }

  printf("\n\nExample 2\n\n");

  itrace = 0;
  itol = 1;
  atol [0] = 5e-4;
  rtol [0] = 0.05;
  printf(" npts = %4ld", npts);
  printf(" atol = %12.3e", atol[0]);
  printf(" rtol = %12.3e\n\n", rtol[0]);

  /* Initialise mesh */

  for (i = 0; i < npts; ++i) x[i] = i/ (npts-1.0);
  xfix [0] = 0.0;

  /* Set remesh parameters */

  remesh = Nag_TRUE;
  nrmesh = 5;
  dxmesh = 0.0;
  trmesh = 0.0;
  con = 1.0/(npts-1.0);
  xratio = 1.5;
  ipminf = 0;
  xi[0] = 0.0;
  ind = 0;
  itask = 1;

  for (i = 0; i < 30; ++i) algopt[ i] = 0.0;

  /* Theta integration */

  algopt[0] = 2.0;
  algopt[5] = 2.0;
  algopt[6] = 2.0;

  /* Max. time step */

  algopt[12] = 0.0025;

  ts = 0.0;
  tout = 0.0;
  for (it = 0; it < 2; ++it)
    {
      tout = 0.2* (it+1);

      /* nag_pde_parab_1d_cd_ode_remesh (d03psc), see above. */
      nag_pde_parab_1d_cd_ode_remesh(npde, &ts, tout, pdef2, nmflx2, bndry2,
                                     uvin2, u, npts, x, ncode, NULLFN, nxi, xi,
                                     neqn, rtol, atol, itol, Nag_OneNorm,
                                     Nag_LinAlgBand, algopt, remesh, nxfix,
                                     xfix, nrmesh, dxmesh, trmesh, ipminf,
                                     xratio, con, monit2, rsave, lrsave, isave,
                                     lisave, itask, itrace, 0, &ind,
                                     &comm, &saved, &fail);
      if (fail.code != NE_NOERROR)
        {
          printf(
                  "Error from nag_pde_parab_1d_cd_ode_remesh (d03psc).\n%s\n",
                  fail.message);
          exit_status = 1;
          goto END;
        }

      printf(" t = %6.3f\n", ts);
      printf("        x        Approx u    Exact u\n\n");

      /* Interpolate at output points */

      m = 0;
      /* nag_pde_interp_1d_fd (d03pzc), see above. */
      nag_pde_interp_1d_fd(npde, m, u, npts, x, xout, intpts, itype, uout,
                           &fail);

      if (fail.code != NE_NOERROR)
        {
          printf("Error from nag_pde_interp_1d_fd (d03pzc).\n%s\n",
                  fail.message);
          exit_status = 1;
          goto END;
        }

      /* Check against exact solution */

      exact(tout, ue, xout, npde, intpts);
      for (i = 1; i <= intpts; ++i)
        {
          printf("   %9.4f", xout[i-1]);
          printf("   %9.4f", UOUT(1, i, 1));
          printf("   %9.4f\n", UE(1, i));
        }
    }

  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 (algopt) NAG_FREE(algopt);
  if (atol) NAG_FREE(atol);
  if (rsave) NAG_FREE(rsave);
  if (rtol) NAG_FREE(rtol);
  if (u) NAG_FREE(u);
  if (ue) NAG_FREE(ue);
  if (uout) NAG_FREE(uout);
  if (x) NAG_FREE(x);
  if (xfix) NAG_FREE(xfix);
  if (xi) NAG_FREE(xi);
  if (isave) NAG_FREE(isave);

  return
    exit_status;
}

static void NAG_CALL uvin2(Integer npde, Integer npts, Integer nxi,
                           const double x[], const double xi[], double u[],
                           Integer ncode, double v[], Nag_Comm *comm)
{
  double t;

  t = 0.0;
  exact(t, u, x, npde, npts);

  return;
}


static void NAG_CALL pdef2(Integer npde, double t, double x, const double u[],
                           const double ux[], Integer ncode, const double v[],
                           const double vdot[], double p[], double c[],
                           double d[], double s[], Integer *ires,
                           Nag_Comm *comm)
{
  P(1, 1) = 1.0;
  c[0] = 0.0;
  d[0] = 0.0;
  s[0] = -100.0*u[0]*(u[0]-1.0)*(u[0]-0.5);

  return;
}

static void NAG_CALL bndry2(Integer npde, Integer npts, double t,
                            const double x [], const double u[],
                            Integer ncode, const double v[],
                            const double vdot [], Integer ibnd, double g[],
                            Integer *ires, Nag_Comm *comm)
{
  /* Solution known to be constant at both boundaries */

  double ue[1];

  if (ibnd == 0)
    {
      exact(t, ue, &x[0], npde, 1);
      g [ 0 ] = UE(1, 1) - U(1, 1);
    }
  else
    {
      exact(t, ue, &x[npts-1], npde, 1);
      g [ 0 ] = UE(1, 1) - U(1, npts);
    }

  return;
}

static void NAG_CALL nmflx2(Integer npde, double t, double x, Integer ncode,
                            const double v [], const double uleft[],
                            const double uright [], double flux[],
                            Integer *ires, Nag_Comm *comm, Nag_D03_Save *saved)
{
  flux [ 0 ] = uleft[0];

  return;
}

static void NAG_CALL monit2(double t, Integer npts, Integer npde,
                            const double x [], const double u [],
                            double fmon[], Nag_Comm *comm)
{
  static double  xa = 0.0;
  static Integer icount = 0;
  double         h1, ux, uxmax, xl, xleft, xmax, xr, xright;
  Integer        i;

  /* Locate shock */

  uxmax = 0.0;
  xmax = 0.0;
  for (i = 2; i <= npts-1; ++i)
    {
      h1 = x [i - 1] - x[i - 2];
      ux = fabs((U(1, i) - U(1, i - 1))/h1);
      if (ux > uxmax)
        {
          uxmax = ux;
          xmax = x [i - 1];
        }
    }

  /* Assign width (on first call only) */

  if (icount == 0)
    {
      icount = 1;
      xleft = xmax - x[0];
      xright = x [npts-1] - xmax;
      if (xleft > xright)
        {
          xa = xright;
        }
      else
        {
          xa = xleft;
        }
    }
  xl = xmax - xa;
  xr = xmax + xa;

  /* Assign monitor function */

  for (i = 0; i < npts; ++i)
    {
      if (x [i] > xl && x[i] < xr)
        {
          fmon [ i ] = 1.0 + cos(nag_pi *(x[i] - xmax)/xa);
        }
      else
        {
          fmon [ i ] = 0.0;
        }
    }
  return;
}

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

  double  del, psi, rm, rn, s;
  Integer i;
  s = 0.1;
  del = 0.01;
  rm = -1.0/del;
  rn = s /del + 1.0;

  for (i = 1; i <= npts; ++i)
    {
      psi = x[i-1] - t;
      if (psi < s)
        {
          U(1, i) = 1.0;
        }
      else
      if (psi > del + s)
        {
          U(1, i) = 0.0;
        }
      else
        {
          U(1, i) = rm*psi + rn;
        }
    }
  return;
}