/* nag_pde_parab_1d_fd_ode_remesh (d03ppc) 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>

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

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

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

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

static void exact(double, double *, Integer, double *, Nag_Comm *);

#define P(I,J) p[npde*((J)-1)+(I)-1]
#define R(I,J) r[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)
{
  const Integer npde=1, npts=61, ncode=0, m=0, nxi=0, nxfix=0, itype=1, 
    neqn=npde*npts+ncode, intpts=5, lisave=25+nxfix, 
    nwkres=npde*(npts+3*npde+21)+7*npts+nxfix+3, lenode=11*neqn+50, 
    lrsave=neqn*neqn+neqn+nwkres+lenode;
  double con, dxmesh, e, tout, trmesh, ts, xratio;
  Integer exit_status, i, ind, ipminf, it, itask, itol, itrace, nrmesh;
  Boolean remesh, theta;
  double *algopt=0, *atol=0, *rsave=0, *rtol=0, *u=0, *ue=0, 
    *uout=0, *x=0, *xfix=0, *xi=0, *xout=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(neqn, double)) ||
       !(ue = NAG_ALLOC(intpts, double)) ||
       !(uout = NAG_ALLOC(npde*intpts*itype, double)) ||
       !(x = NAG_ALLOC(npts, double)) ||
       !(xfix = NAG_ALLOC(1, double)) ||
       !(xi = NAG_ALLOC(1, double)) ||
       !(xout = NAG_ALLOC(intpts, double)) ||
       !(isave = NAG_ALLOC(lisave, Integer)) )
    {
      Vprintf("Allocation failure\n");
      exit_status = 1;
      goto END;
    }
    
  Vprintf("d03ppc Example Program Results\n\n");
  e = 0.005;
  comm.p = (Pointer)&e;
  itrace = 0;
  itol = 1;
  atol[0] = 5e-5;
  rtol[0] = atol[0];
    
  Vprintf("  Accuracy requirement =%10.3e", atol[0]);
  Vprintf(" Number of points = %3ld\n\n", npts);

  /* Initialise mesh */

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

  /* Set remesh parameters */

  remesh = TRUE;
  nrmesh = 3;
  dxmesh = 0.5;
  trmesh = 0.0;
  con = 2.0/(npts-1.0);
  xratio = 1.5;
  ipminf = 0;

  Vprintf("  Remeshing every %3ld time steps\n\n", nrmesh);
  Vprintf("  e =%8.3f\n\n\n", e);

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

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

  theta = 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 = 0.0;
  tout = 0.0;
  for (it = 0; it < 5; ++it) 
    {
      tout = 0.2*(it+1);

      d03ppc(npde, m, &ts, tout, pdedef, bndary, uvinit, u, npts, 
             x, ncode, d03pck, nxi, xi, neqn, rtol, atol, itol, 
             Nag_TwoNorm, Nag_LinAlgFull, algopt, remesh, nxfix, 
             xfix, nrmesh, dxmesh, trmesh, ipminf, xratio, con, 
             monitf, rsave, lrsave, isave, lisave, itask, itrace, 
             0, &ind, &comm, &saved, &fail);

      if (fail.code != NE_NOERROR)
        {
          Vprintf("Error from d03ppc.\n%s\n", fail.message);
          exit_status = 1;
          goto END;
        }

      /* Set output points */

      switch (it)
        {
        case 0:
          for (i = 0; i < 5; ++i) xout[i] = 0.3+0.1*i;
          break;
        case 1:
          for (i = 0; i < 5; ++i) xout[i] = 0.4+0.1*i;
          break;
        case 2:
          for (i = 0; i < 5; ++i) xout[i] = 0.6+0.05*i;
          break;
        case 3:
          for (i = 0; i < 5; ++i) xout[i] = 0.7+0.05*i;
          break;
        case 4:
          for (i = 0; i < 5; ++i) xout[i] = 0.8+0.05*i;
          break;
        }

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

      for (i = 0; i < 5; ++i) 
        {
          Vprintf("%9.4f", xout[i]);
          Vprintf((i+1)%5 == 0 || i == 4 ?"\n":" ");
        }

      /* Interpolate at output points */

      d03pzc(npde, m, u, npts, x, xout, intpts, itype, uout, &fail);

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

      /* Check against exact solution */

      exact(ts, xout, intpts, ue, &comm);

      Vprintf(" Approx sol. ");

      for (i = 1; i <= intpts; ++i) 
        {
          Vprintf("%9.4f", UOUT(1,i,1));
          Vprintf(i%5 == 0 || i == 5 ?"\n":" ");
        }       

      Vprintf(" Exact  sol. ");

      for (i = 1; i <= intpts; ++i) 
        {
          Vprintf("%9.4f", ue[i-1]);
          Vprintf(i%5 == 0 || i == 5 ?"\n":" ");
        }
      Vprintf("\n");
    }

  Vprintf(" Number of integration steps in time = %6ld\n", isave[0]);
  Vprintf(" Number of function evaluations = %6ld\n", isave[1]);
  Vprintf(" Number of Jacobian evaluations = %6ld\n", isave[2]);
  Vprintf(" 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 (xout) NAG_FREE(xout);
  if (isave) NAG_FREE(isave);

  return exit_status;
}


static void uvinit(Integer npde, Integer npts, Integer nxi, const double x[], 
                   const double xi[], double u[], Integer ncode, double v[], 
                   Nag_Comm *comm)
{
  double *e = (double *)comm->p;
  double a, b, c, t;
  Integer i;

  t = 0.0;
  for (i = 1; i <= npts; ++i) 
    {
      a = (x[i-1] - 0.25 - 0.75*t)/(*e*4.0);
      b = (0.9*x[i-1] - 0.325 - 0.495*t)/(*e*2.0);
      if (a > 0.0 && a > b) 
        {
          a = exp(-a);
          c = (0.8*x[i-1] - 0.4 - 0.24*t)/(*e*4.0);
          c = exp(c);
          U(1, i) = (0.1*c + 0.5 + a)/(c + 1.0 + a);
        } else if (b > 0.0 && b >= a) {
          b = exp(-b);
          c = (-0.8*x[i-1] + 0.4 + 0.24*t)/(*e*4.0);
          c = exp(c);
          U(1, i) = (0.5*c + 0.1 + b)/(c + 1.0 + b);
        } else {
          a = exp(a);
          b = exp(b);
          U(1, i) = (0.5*a + 1.0 + 0.1*b)/(a + 1.0 + b);
        }
    }
  return;
}


static void pdedef(Integer npde, double t, double x, 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)
{
  double *e = (double *)comm->p;

  P(1, 1) = 1.0;
  r[0] = *e*ux[0];
  q[0] = u[0]*ux[0];

  return;
}


static void 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)
{
  double a, b, c, ue, x;
  double *e = (double *)comm->p;

  beta[0] = 0.0;
  if (ibnd == 0) 
    {
      x = 0.0;
      a = (x - 0.25 - 0.75*t)/(*e*4.0);
      b = (0.9*x - 0.325 - 0.495*t)/(*e*2.0);
      if (a > 0. && a > b) 
        {
          a = exp(-a);
          c = (0.8*x - 0.4 - 0.24*t)/(*e*4.0);
          c = exp(c);
          ue = (0.1*c + 0.5 + a)/(c + 1.0 + a);
        } else if (b > 0.0 && b >= a) {
          b = exp(-b);
          c = (-0.8*x + 0.4 + 0.24*t)/(*e*4.0);
          c = exp(c);
          ue = (0.5*c + 0.1 + b)/(c + 1.0 + b);
        } else {
          a = exp(a);
          b = exp(b);
          ue = (0.5*a + 1.0 + 0.1*b)/(a + 1.0 + b);
        }
    } else {
      x = 1.0;
      a = (x - 0.25 - 0.75*t)/(*e*4.0);
      b = (0.9*x - 0.325 - 0.495*t)/(*e*2.0);
      if (a > 0.0 && a > b) 
        {
          a = exp(-a);
          c = (0.8*x - 0.4 - 0.24*t)/(*e*4.0);
          c = exp(c);
          ue = (0.1*c + 0.5 + a)/(c + 1.0 + a);
        } else if (b > 0.0 && b >= a) {
          b = exp(-b);
          c = (-0.8*x + 0.4 + 0.24*t)/(*e*4.0);
          c = exp(c);
          ue = (0.5*c + 0.1 + b)/(c + 1.0 + b);
        } else {
          a = exp(a);
          b = exp(b);
          ue = (0.5*a + 1.0 + 0.1*b)/(a + 1.0 + b);
        }
    }
  gamma[0] = u[0] - ue;

  return;
}


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

  double a, b, c;
  double *e = (double *)comm->p;
  Integer i;

  for (i = 0; i < npts; ++i) 
    {
      a = (x[i] - 0.25 - 0.75*t)/(*e*4.0);
      b = (0.9*x[i] - 0.325 - 0.495*t)/(*e*2.0);
      if (a > 0. && a > b) 
        {
          a = exp(-a);
          c = (0.8*x[i] - 0.4 - 0.24*t)/(*e*4.0);
          c = exp(c);
          u[i] = (0.1*c + 0.5 + a)/(c + 1.0 + a);
        } else if (b > 0. && b >= a) {
          b = exp(-b);
          c = (-0.8*x[i] + 0.4 + 0.24*t)/(*e*4.0);
          c = exp(c);
          u[i] = (0.5*c + 0.1 + b)/(c + 1.0 + b);
        } else {
          a = exp(a);
          b = exp(b);
          u[i] = (0.5*a + 1.0 + 0.1*b)/(a + 1.0 + b);
        }
    }
  return;
}


static void monitf(double t, Integer npts, Integer npde, const double x[], 
                   const double u[], const double r[], double fmon[], 
                   Nag_Comm *comm)
{
  double drdx, h;
  Integer i, k, l;

  for (i = 1; i <= npts-1; ++i) 
    {
      k = i-1; if (i == 1) k = 1;
      l = i+1;
      h = 0.5*(x[l-1] - x[k-1]);

      /* Second derivative */

      drdx = (R(1, i+1) - R(1, i))/h;
      fmon[i-1] = drdx; if (fmon[i-1] < 0) fmon[i-1] = -drdx;
    }
  fmon[npts-1] = fmon[npts-2];

  return;
}