particleiterator.hpp

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/* Copyright (c) 2005-2011 Taneli Kalvas. All rights reserved.
 *
 * You can redistribute this software and/or modify it under the terms
 * of the GNU General Public License as published by the Free Software
 * Foundation; either version 2 of the License, or (at your option)
 * any later version.
 * 
 * This library is distributed in the hope that it will be useful, but
 * WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
 * General Public License for more details.
 * 
 * You should have received a copy of the GNU General Public License
 * along with this library (file "COPYING" included in the package);
 * if not, write to the Free Software Foundation, Inc., 51 Franklin
 * Street, Fifth Floor, Boston, MA 02110-1301 USA
 * 
 * If you have questions about your rights to use or distribute this
 * software, please contact Berkeley Lab's Technology Transfer
 * Department at TTD@lbl.gov. Other questions, comments and bug
 * reports should be sent directly to the author via email at
 * taneli.kalvas@jyu.fi.
 * 
 * NOTICE. This software was developed under partial funding from the
 * U.S.  Department of Energy.  As such, the U.S. Government has been
 * granted for itself and others acting on its behalf a paid-up,
 * nonexclusive, irrevocable, worldwide license in the Software to
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#ifndef PARTICLEITERATOR_HPP
#define PARTICLEITERATOR_HPP 1


#include <vector>
#include <iostream>
#include <algorithm>
#include <iomanip>
#include <gsl/gsl_odeiv.h>
#include <gsl/gsl_poly.h>
#include "geometry.hpp"
#include "trajectory.hpp"
#include "particles.hpp"
#include "vectorfield.hpp"
#include "scalarfield.hpp"
#include "scharge.hpp"
#include "scheduler.hpp"
#include "polysolver.hpp"
#include "particledatabase.hpp"


//#define DEBUG_PARTICLE_ITERATOR 1


enum particle_iterator_type_e {
    PARTICLE_ITERATOR_ADAPTIVE = 0,
    PARTICLE_ITERATOR_FIXED_STEP_LEN
};


template <class PP> class ColData {
public:
    PP                _x;         
    int               _dir;       
    ColData( PP x, int dir ) : _x(x), _dir(dir) {}
    
    bool operator<( const ColData &cd ) const {
        return( _x[0] < cd._x[0] );
    }

    static void build_coldata_linear( std::vector<ColData> &coldata, const Mesh &mesh,
                                      const PP &x1, const PP &x2 ) {
        
        coldata.clear();

        for( size_t a = 0; a < PP::dim(); a++ ) {
            
            int a1 = (int)floor( (x1[2*a+1]-mesh.origo(a))/mesh.h() );
            int a2 = (int)floor( (x2[2*a+1]-mesh.origo(a))/mesh.h() );
            if( a1 > a2 ) {
                int a = a2;
                a2 = a1;
                a1 = a;
            }
            
            for( int b = a1+1; b <= a2; b++ ) {
        
                // Save intersection coordinates
                double K = (b*mesh.h() + mesh.origo(a) - x1[2*a+1]) / 
                    (x2[2*a+1] - x1[2*a+1]);
                if( K < 0.0 ) K = 0.0;
                else if( K > 1.0 ) K = 1.0;
                //std::cout << "Found valid root: " << K << "\n";

                if( x2[2*a+1] > x1[2*a+1] )
                    coldata.push_back( ColData( x1 + (x2-x1)*K, a+1 ) );
                else
                    coldata.push_back( ColData( x1 + (x2-x1)*K, -a-1 ) );
            }
        }

        // Sort intersections in increasing time order
        sort( coldata.begin(), coldata.end() );
    }

    static void build_coldata_poly( std::vector<ColData> &coldata, const Mesh &mesh,
                                    const PP &x1, const PP &x2 ) {
        
#ifdef DEBUG_PARTICLE_ITERATOR
        std::cout << "Building coldata using polynomial interpolation\n";
#endif

        coldata.clear();

        // Construct trajectory representation
        TrajectoryRep1D traj[PP::dim()];
        for( size_t a = 0; a < PP::dim(); a++ ) {
            traj[a].construct( x2[0]-x1[0], 
                               x1[2*a+1], x1[2*a+2], 
                               x2[2*a+1], x2[2*a+2] );
        }

        // Solve trajectory intersections
        for( size_t a = 0; a < PP::dim(); a++ ) {

            // Mesh number of x1 (start point)
            int i = (int)floor( (x1[2*a+1]-mesh.origo(a))/mesh.h() );
            
            // Search to negative (dj = -1) and positive (dj = +1) mesh directions
            for( int dj = -1; dj <= 1; dj += 2 ) {
                int j = i;
                if( dj == +1 )
                    j = i+1;
                int Kcount;  // Solution counter
                double K[3]; // Solution array
                while( 1 ) {

                    // Intersection point
                    double val = mesh.origo(a) + mesh.h() * j;
                    if( val < mesh.origo(a) )
                        break;
                    else if( val > mesh.max(a) )
                        break;

#ifdef DEBUG_PARTICLE_ITERATOR
                    std::cout << "  Searching intersections at coord(" << a << ") = " << val << "\n";
#endif
                    Kcount = traj[a].solve( K, val );
                    if( Kcount == 0 )
                        break; // No valid roots

#ifdef DEBUG_PARTICLE_ITERATOR
                    std::cout << "  Found " << Kcount << " valid roots: ";
                    for( int p = 0; p < Kcount; p++ )
                        std::cout << K[p] << " ";
                    std::cout << "\n";
#endif

                    // Save roots to coldata
                    for( int b = 0; b < Kcount; b++ ) {
                        PP xcol;
                        double x, v;
                        xcol(0) = x1[0] + K[b]*(x2[0]-x1[0]);
                        for( size_t c = 0; c < PP::dim(); c++ ) {
                            traj[c].coord( x, v, K[b] );
                            if( a == c )
                                xcol[2*c+1] = val; // limit numerical inaccuracy
                            else
                                xcol[2*c+1] = x;
                            xcol[2*c+2] = v;
                        }
                        if( mesh.geom_mode() == MODE_CYL )
                            xcol[5] = x1[5] + K[b]*(x2[5]-x1[5]);
                        if( xcol[2*a+2] >= 0.0 )
                            coldata.push_back( ColData( xcol, a+1 ) );
                        else
                            coldata.push_back( ColData( xcol, -a-1 ) );
                    }

                    j += dj;
                }
            }
        }

        // Sort intersections in increasing time order
        sort( coldata.begin(), coldata.end() );

#ifdef DEBUG_PARTICLE_ITERATOR
        std::cout << "  Coldata built\n";
#endif
    }

};


template <class PP> class ParticleIterator {

    gsl_odeiv_system           _system;    
    gsl_odeiv_step            *_step;      
    gsl_odeiv_control         *_control;   
    gsl_odeiv_evolve          *_evolve;    
    particle_iterator_type_e   _type;      
    bool                       _polyint;   
    double                     _epsabs;    
    double                     _epsrel;    
    uint32_t                   _maxsteps;  
    double                     _maxt;      
    uint32_t                   _trajdiv;   
    bool                       _mirror[6]; 
    ParticleIteratorData       _pidata;    
    const TrajectoryHandlerCallback *_thand_cb; 
    const TrajectoryEndCallback     *_tend_cb;  
    const TrajectoryEndCallback     *_bsup_cb;  
    ParticleDataBase          *_pdb;            
    pthread_mutex_t           *_scharge_mutex;  
    PP                         _xi;        
    std::vector<PP>            _traj;      
    std::vector<ColData<PP> >  _coldata;   
    ParticleStatistics         _stat;      
    bool check_collision( Particle<PP> &particle, const PP &x1, const PP &x2, PP &status_x ) {

        // If inside solid, bracket for collision point
        Vec3D v2 = x2.location();
        int32_t bound = _pidata._geom->inside( v2 );
        if( bound < 7 )
            return( true ); // No collision happened.
        Vec3D vc;
        Vec3D v1 = x1.location();
        double K = _pidata._geom->bracket_surface( bound, v2, v1, vc );

        // Calculate new PP
        for( size_t a = 0; a < PP::size(); a++ )
            status_x[a] = x2[a] + K*(x1[a]-x2[a]);

        // Remove all points from trajectory after time status_x[0].
        for( size_t a = _traj.size()-1; a > 0; a-- ) {
            if( _traj[a][0] > status_x[0] )
                _traj.pop_back();
            else
                break;
        }

        // Save last trajectory point and update status
        //_traj.push_back( status_x );
        particle.set_status( PARTICLE_COLL );

        // Update collision statistics for boundary
        _stat.add_bound_collision( bound, particle.IQ() );

        return( false ); // Collision happened.
    }


    void handle_mirror( size_t c, int i[3], size_t a, int border, PP &x2 ) {

#ifdef DEBUG_PARTICLE_ITERATOR
        std::cout << "    handle_mirror( c = " << c 
                  << ", i = (" << i[0] << ", " << i[1] << ", " << i[2]
                  << "), a = " << a << ", border = " << border 
                  << ")\n";
#endif

        double xmirror;
        if( border < 0 ) {
            xmirror = _pidata._geom->origo(a);
            i[a] = -i[a]-1;
        } else {
            xmirror = _pidata._geom->max(a);
            i[a] = 2*_pidata._geom->size(a)-i[a]-3;
        }

#ifdef DEBUG_PARTICLE_ITERATOR
        std::cout << "    xmirror = " << xmirror << "\n";
        std::cout << "    i = (" << i[0] << ", " << i[1] << ", " << i[2] << ")\n";
        std::cout << "    xi = " << _xi << "\n";
#endif
        
        // Check if found edge at first encounter
        bool caught_at_boundary = false;
        if( _coldata[c]._dir == border*((int)a+1) && 
            ( i[a] == 0 || i[a] == (int)_pidata._geom->size(a)-2 ) ) {
            caught_at_boundary = true;
#ifdef DEBUG_PARTICLE_ITERATOR
            std::cout << "   caught_at_boundary\n";
#endif
        }

        // Mirror traj back to _xi
        if( caught_at_boundary ) {
            _traj.push_back( _coldata[c]._x );
        } else {
            for( int b = _traj.size()-1; b > 0; b-- ) {
                if( _traj[b][0] >= _xi[0] ) {
                    
#ifdef DEBUG_PARTICLE_ITERATOR
                    std::cout << "    mirroring traj[" << b << "] = " << _traj[b] << "\n";
#endif
                    _traj[b][2*a+1] = 2.0*xmirror - _traj[b][2*a+1];
                    _traj[b][2*a+2] *= -1.0;
                } else
                    break;
            }
        }

        // Mirror rest of the coldata
        for( size_t b = c; b < _coldata.size(); b++ ) {
            if( (size_t)abs(_coldata[b]._dir) == a+1 )
                _coldata[b]._dir *= -1;
            _coldata[b]._x[2*a+1] = 2.0*xmirror - _coldata[b]._x[2*a+1];
            _coldata[b]._x[2*a+2] *= -1.0;
        }

        if( caught_at_boundary )
            _traj.push_back( _coldata[c]._x );

        // Mirror calculation point
        x2[2*a+1] = 2.0*xmirror - x2[2*a+1];
        x2[2*a+2] *= -1.0;
        
        // Coordinates changed, reset integrator
        gsl_odeiv_step_reset( _step );
        gsl_odeiv_evolve_reset( _evolve );
    }


    void handle_collision( Particle<PP> &particle, uint32_t bound, size_t c, PP &status_x ) {

#ifdef DEBUG_PARTICLE_ITERATOR
        std::cout << "    handle_collision()\n";
#endif

        //_traj.push_back( _coldata[c]._x );
        status_x = _coldata[c]._x;
        particle.set_status( PARTICLE_OUT );
        _stat.add_bound_collision( bound, particle.IQ() );
    }


    bool handle_trajectory_advance( Particle<PP> &particle, size_t c, int i[3], PP &x2 ) {

        // Check for collisions with solids and advance coordinates i.
        if( PP::dim() == 2 ) {
            if( _coldata[c]._dir == -1 ) {
                if( ( abs(_pidata._geom->mesh(i[0],  i[1]  )) >= 7 || 
                      abs(_pidata._geom->mesh(i[0],  i[1]+1)) >= 7 ) &&
                    !check_collision( particle, _xi, _coldata[c]._x, x2 ) )
                    return( false );
                i[0]--;
            } else if( _coldata[c]._dir == +1 ) {
                if( ( abs(_pidata._geom->mesh(i[0]+1,i[1]  )) >= 7 || 
                      abs(_pidata._geom->mesh(i[0]+1,i[1]+1)) >= 7 ) &&
                    !check_collision( particle, _xi, _coldata[c]._x, x2 ) )
                    return( false );
                i[0]++;
            } else if( _coldata[c]._dir == -2 ) {
                if( ( abs(_pidata._geom->mesh(i[0],  i[1]  )) >= 7 || 
                      abs(_pidata._geom->mesh(i[0]+1,i[1]  )) >= 7 ) &&
                    !check_collision( particle, _xi, _coldata[c]._x, x2 ) )
                    return( false );
                i[1]--;
            } else {
                if( ( abs(_pidata._geom->mesh(i[0],  i[1]+1)) >= 7 || 
                      abs(_pidata._geom->mesh(i[0]+1,i[1]+1)) >= 7 ) &&
                    !check_collision( particle, _xi, _coldata[c]._x, x2 ) )
                    return( false );
                i[1]++;
            }
        } else if( PP::dim() == 3 ) {
            if( _coldata[c]._dir == -1 ) {
                if( ( abs(_pidata._geom->mesh(i[0],  i[1],  i[2]  )) >= 7 || 
                      abs(_pidata._geom->mesh(i[0],  i[1]+1,i[2]  )) >= 7 ||
                      abs(_pidata._geom->mesh(i[0],  i[1],  i[2]+1)) >= 7 ||
                      abs(_pidata._geom->mesh(i[0],  i[1]+1,i[2]+1)) >= 7 ) &&
                    !check_collision( particle, _xi, _coldata[c]._x, x2 ) )
                    return( false );
                i[0]--;
            } else if( _coldata[c]._dir == +1 ) {
                if( ( abs(_pidata._geom->mesh(i[0]+1,i[1],  i[2]  )) >= 7 || 
                      abs(_pidata._geom->mesh(i[0]+1,i[1]+1,i[2]  )) >= 7 ||
                      abs(_pidata._geom->mesh(i[0]+1,i[1],  i[2]+1)) >= 7 ||
                      abs(_pidata._geom->mesh(i[0]+1,i[1]+1,i[2]+1)) >= 7 ) &&
                    !check_collision( particle, _xi, _coldata[c]._x, x2 ) )
                    return( false );
                i[0]++;
            } else if( _coldata[c]._dir == -2 ) {
                if( ( abs(_pidata._geom->mesh(i[0],  i[1],i[2]  )) >= 7 || 
                      abs(_pidata._geom->mesh(i[0]+1,i[1],i[2]  )) >= 7 ||
                      abs(_pidata._geom->mesh(i[0],  i[1],i[2]+1)) >= 7 ||
                      abs(_pidata._geom->mesh(i[0]+1,i[1],i[2]+1)) >= 7 ) &&
                    !check_collision( particle, _xi, _coldata[c]._x, x2 ) )
                    return( false );
                i[1]--;
            } else if( _coldata[c]._dir == +2 ) {
                if( ( abs(_pidata._geom->mesh(i[0],  i[1]+1,i[2]  )) >= 7 || 
                      abs(_pidata._geom->mesh(i[0]+1,i[1]+1,i[2]  )) >= 7 ||
                      abs(_pidata._geom->mesh(i[0],  i[1]+1,i[2]+1)) >= 7 ||
                      abs(_pidata._geom->mesh(i[0]+1,i[1]+1,i[2]+1)) >= 7 ) &&
                    !check_collision( particle, _xi, _coldata[c]._x, x2 ) )
                    return( false );
                i[1]++;
            } else if( _coldata[c]._dir == -3 ) {
                if( ( abs(_pidata._geom->mesh(i[0],  i[1],  i[2]  )) >= 7 || 
                      abs(_pidata._geom->mesh(i[0]+1,i[1],  i[2]  )) >= 7 ||
                      abs(_pidata._geom->mesh(i[0],  i[1]+1,i[2])) >= 7 ||
                      abs(_pidata._geom->mesh(i[0]+1,i[1]+1,i[2])) >= 7 ) &&
                    !check_collision( particle, _xi, _coldata[c]._x, x2 ) )
                    return( false );
                i[2]--;
            } else {
                if( ( abs(_pidata._geom->mesh(i[0],  i[1],  i[2]+1)) >= 7 || 
                      abs(_pidata._geom->mesh(i[0]+1,i[1],  i[2]+1)) >= 7 ||
                      abs(_pidata._geom->mesh(i[0],  i[1]+1,i[2]+1)) >= 7 ||
                      abs(_pidata._geom->mesh(i[0]+1,i[1]+1,i[2]+1)) >= 7 ) &&
                    !check_collision( particle, _xi, _coldata[c]._x, x2 ) )
                    return( false );
                i[2]++;
            }
        } else {
            throw( Error( ERROR_LOCATION, "unsupported dimension number" ) );
        }
        
        // Check for collisions/mirroring with simulation boundary. Here
        // coordinates i are already advanced to next mesh.
        for( size_t a = 0; a < PP::dim(); a++ ) {

            if( i[a] < 0 ) {
                if( _mirror[2*a] )
                    handle_mirror( c, i, a, -1, x2 );
                else {
                    handle_collision( particle, 1+2*a, c, x2 );
                    return( false );
                }
            } else if( i[a] >= (_pidata._geom->size(a)-1) ) {
                if( _mirror[2*a+1] )
                    handle_mirror( c, i, a, +1, x2 );
                else {
                    handle_collision( particle, 2+2*a, c, x2 );
                    return( false );
                }
            }
        }

        return( true );
    }

    bool limit_trajectory_advance( const PP &x1, PP &x2 ) {

        bool touched = false;

        for( size_t a = 0; a < PP::dim(); a++ ) {

            double lim1 = _pidata._geom->origo(a) - 
                (_pidata._geom->size(a)-1)*_pidata._geom->h();
            double lim2 = _pidata._geom->origo(a) + 
                2*(_pidata._geom->size(a)-1)*_pidata._geom->h();

            if( x2[2*a+1] < lim1 ) {
                
                double K = (lim1 - x1[2*a+1]) / (x2[2*a+1] - x1[2*a+1]);
                x2 = x1 + K*(x2-x1);
                touched = true;
#ifdef DEBUG_PARTICLE_ITERATOR
                std::cout << "Limiting step to:\n";
                std::cout << "  x2: " << x2 << "\n";
#endif
            } else if(x2[2*a+1] > lim2 ) {

                double K = (lim2 - x1[2*a+1]) / (x2[2*a+1] - x1[2*a+1]);
                x2 = x1 + K*(x2-x1);
                touched = true;
#ifdef DEBUG_PARTICLE_ITERATOR
                std::cout << "Limiting step to:\n";
                std::cout << "  x2: " << x2 << "\n";
#endif
            }
        }

        return( touched );
    }

    bool handle_trajectory( Particle<PP> &particle, const PP &x1, PP &x2, 
                            bool force_linear, bool first_step ) {

#ifdef DEBUG_PARTICLE_ITERATOR
        std::cout << "Handle trajectory from x1 to x2:\n";
        std::cout << "  x1: " << x1 << "\n";
        std::cout << "  x2: " << x2 << "\n";
#endif

        // Limit trajectory advance to double the simulation box
        // If limitation done, force to linear interpolation
        if( limit_trajectory_advance( x1, x2 ) )
            force_linear = true;

        // Make coldata
        if( _polyint && !force_linear )
            ColData<PP>::build_coldata_poly( _coldata, *_pidata._geom, x1, x2 );
        else
            ColData<PP>::build_coldata_linear( _coldata, *_pidata._geom, x1, x2 );

        // TODO
        // Remove entrance to geometry if coming from outside or make
        // code to skip the collision detection for these particles

        // No intersections, nothing to do
        if( _coldata.size() == 0 ) {
#ifdef DEBUG_PARTICLE_ITERATOR
            std::cout << "No coldata\n";
#endif
            return( true );
        }

        // Starting mesh index
        int i[3] = {0, 0, 0};
        for( size_t cdir = 0; cdir < PP::dim(); cdir++ )
            i[cdir] = (int)floor( (x1[2*cdir+1]-_pidata._geom->origo(cdir))/_pidata._geom->h() );

        // Process intersection points
#ifdef DEBUG_PARTICLE_ITERATOR
        std::cout << "Process coldata points:\n";
#endif
        for( size_t a = 0; a < _coldata.size(); a++ ) {

#ifdef DEBUG_PARTICLE_ITERATOR
            std::cout << "  Coldata " << std::setw(4) << a << ": " 
                      << _coldata[a]._x << ", " 
                      << std::setw(3) << i[0] << " "
                      << std::setw(3) << i[1] << " "
                      << std::setw(3) << i[2] << " "
                      << std::setw(3) << _coldata[a]._dir << "\n";
#endif

            // Advance particle in mesh, check for possible collisions and
            // do mirroring.
            handle_trajectory_advance( particle, a, i, x2 );

            // Update space charge for one mesh.
            if( _pidata._scharge )
                scharge_add_from_trajectory( *_pidata._scharge, _scharge_mutex, particle.IQ(), 
                                             _xi, _coldata[a]._x );

            // Call trajectory handler callback
            if( _thand_cb )
                (*_thand_cb)( &particle, &_coldata[a]._x, &x2 );

#ifdef DEBUG_PARTICLE_ITERATOR
            if( particle.get_status() == PARTICLE_OUT ) {
                std::cout << "  Particle out\n";
                std::cout << "  x = " << x2 << "\n";
            } else if( particle.get_status() == PARTICLE_COLL ) {
                std::cout << "  Particle collided\n";
                std::cout << "  x = " << x2 << "\n";
            }
#endif
            // Clear coldata and exit if particle collided.
            if( particle.get_status() != PARTICLE_OK ) {
                _traj.push_back( x2 );
                _coldata.clear();
                return( false );
            }

            // Update last intersection point xi.
            _xi = _coldata[a]._x;
        }

#ifdef DEBUG_PARTICLE_ITERATOR
        std::cout << "Coldata done\n";
#endif
        _coldata.clear();
        return( true );
    }


     bool axis_mirror_required( const PP &x2 ) {
         return( _pidata._geom->geom_mode() == MODE_CYL && 
                 x2[4] < 0.0 && 
                 x2[3] <= 0.01*_pidata._geom->h() &&
                 x2[3]*fabs(x2[5]) <= 1.0e-9*fabs(x2[4]) );
                 
     }


    bool handle_axis_mirror_step( Particle<PP> &particle, const PP &x1, PP &x2 ) {

        // Get acceleration at x2
        double dxdt[5];
        PP::get_derivatives( x2[0], &x2[1], dxdt, (void *)&_pidata );

        // Calculate crossover point assuming zero acceleration in
        // r-direction and constant acceleration in x-direction
        double dt = -x2[3]/x2[4];
        PP xc;
        xc[0] = x2[0]+dt;
        xc[1] = x2[1]+(x2[2]+0.5*dxdt[1]*dt)*dt;
        xc[2] = x2[2];
        xc[3] = x2[3]+x2[4]*dt;
        xc[4] = x2[4];
        xc[5] = x2[5];

        // Mirror x2 to x3
        PP x3 = 2*xc - x2;
        x3[3] *= -1.0;
        x3[4] *= -1.0;
        x3[5] *= -1.0;

#ifdef DEBUG_PARTICLE_ITERATOR
        std::cout << "Particle mirror:\n";
        std::cout << "  x1: " << x1 << "\n";
        std::cout << "  x2: " << x2 << "\n";
        std::cout << "  xc: " << xc << "\n";
        std::cout << "  x3: " << x3 << "\n";
#endif
        
        // Handle step with linear interpolation to avoid going to r<=0
        if( !handle_trajectory( particle, x2, x3, true, false ) )
            return( false ); // Particle done

        // Save trajectory calculation points
        _traj.push_back( x2 );
        _traj.push_back( xc );
        xc[4] *= -1.0;
        xc[5] *= -1.0;
        _traj.push_back( xc );
        
        // Next step not a continuation of previous one, reset
        // integrator
        gsl_odeiv_step_reset( _step );
        gsl_odeiv_evolve_reset( _evolve );

        // Continue iteration at mirrored point
        x2 = x3;
        return( true );
    }
    
    bool check_particle_definition( PP &x ) {

#ifdef DEBUG_PARTICLE_ITERATOR
        std::cout << "Particle defined at:\n";
        std::cout << "  x = " << x << "\n";
#endif

        // Check if inside solids or outside simulation geometry box.
        if( _pidata._geom->inside( x.location() ) )
            return( false );

        // Check if particle on simulation geometry border and directed outwards
        /*
        for( size_t a = 0; a < PP::dim(); a++ ) {
            if( x[2*a+1] == _pidata._geom->origo(a) && x[2*a+2] < 0.0 ) {
                if( _mirror[2*a] ) {
                    x[2*a+2] *= -1.0;
#ifdef DEBUG_PARTICLE_ITERATOR
        std::cout << "Mirroring to:\n";
        std::cout << "  x = " << x << "\n";
#endif
                } else {
                    return( false );
                }

            } else if( x[2*a+1] == _pidata._geom->max(a) & x[2*a+2] > 0.0 ) {
                if( _mirror[2*a+1] ) {
                    x[2*a+2] *= -1.0;
#ifdef DEBUG_PARTICLE_ITERATOR
        std::cout << "Mirroring to:\n";
        std::cout << "  x = " << x << "\n";
#endif
                } else {
                    return( false );
                }
            }
        }

#ifdef DEBUG_PARTICLE_ITERATOR
        std::cout << "Definition ok\n";
#endif

        */
        return( true );
    }
    
    double calculate_dt( const PP &x, const double *dxdt ) {

        double spd = 0.0, acc = 0.0;

        for( size_t a = 0; a < (PP::size()-1)/2; a++ ) {
            //std::cout << "spd += " << dxdt[2*a]*dxdt[2*a] << "\n";
            spd += dxdt[2*a]*dxdt[2*a];
            //std::cout << "acc += " << dxdt[2*a+1]*dxdt[2*a+1] << "\n";
            acc += dxdt[2*a+1]*dxdt[2*a+1];
        }
        if( _pidata._geom->geom_mode() == MODE_CYL ) {
            //std::cout << "MODE_CYL\n";
            //std::cout << "spd += " << x[3]*x[3]*x[5]*x[5] << "\n";
            spd += x[3]*x[3]*x[5]*x[5];
            //std::cout << "acc += " << x[3]*x[3]*dxdt[4]*dxdt[4] << "\n";
            acc += x[3]*x[3]*dxdt[4]*dxdt[4];
        }
        //std::cout << "spd = " << sqrt(spd) << "\n";
        //std::cout << "acc = " << sqrt(acc) << "\n";
        spd = _pidata._geom->h() / sqrt(spd);
        acc = sqrt( 2.0*_pidata._geom->h() / sqrt(acc) );

        return( spd < acc ? spd : acc );
    }

public:

    ParticleIterator( particle_iterator_type_e type, double epsabs, double epsrel, 
                      bool polyint, uint32_t maxsteps, double maxt, 
                      uint32_t trajdiv, bool mirror[6], ScalarField *scharge, 
                      pthread_mutex_t *scharge_mutex,
                      const VectorField *efield, const VectorField *bfield, 
                      const Geometry *geom ) 
        : _type(type), _polyint(polyint), _epsabs(epsabs), _epsrel(epsrel), _maxsteps(maxsteps), _maxt(maxt), 
          _trajdiv(trajdiv), _pidata(scharge,efield,bfield,geom), 
          _thand_cb(0), _tend_cb(0), _bsup_cb(0), _pdb(0), _scharge_mutex(scharge_mutex), 
          _stat(geom->number_of_boundaries()) {
        
        // Initialize mirroring
        _mirror[0] = mirror[0];
        _mirror[1] = mirror[1];
        _mirror[2] = mirror[2];
        _mirror[3] = mirror[3];
        _mirror[4] = mirror[4];
        _mirror[5] = mirror[5];

        // Initialize system of ordinary differential equations (ODE)
        _system.jacobian  = NULL;
        _system.params    = (void *)&_pidata;
        _system.function  = PP::get_derivatives;
        _system.dimension = PP::size()-1; // Time is not part of differential equation dimensions

        // Make scale
        // 2D:  x vx y vy
        // Cyl: x vx r vr omega
        // 3D:  x vx y vy z vz
        double scale_abs[PP::size()-1];
        for( uint32_t a = 0; a < (uint32_t)PP::size()-2; a+=2 ) {
            scale_abs[a+0] = 1.0;
            scale_abs[a+1] = 1.0e6;
        }
        if( _pidata._geom->geom_mode() == MODE_CYL )
            scale_abs[4] = 1.0;

        // Initialize ODE solver
        _step    = gsl_odeiv_step_alloc( gsl_odeiv_step_rkck, _system.dimension );
        //_control = gsl_odeiv_control_standard_new( _epsabs, _epsrel, 1.0, 1.0 );
        _control = gsl_odeiv_control_scaled_new( _epsabs, _epsrel, 1.0, 1.0, scale_abs, PP::size()-1 );
        _evolve  = gsl_odeiv_evolve_alloc( _system.dimension );
    }


    ~ParticleIterator() {
        gsl_odeiv_evolve_free( _evolve );
        gsl_odeiv_control_free( _control );
        gsl_odeiv_step_free( _step );
    }


    void set_trajectory_handler_callback( const TrajectoryHandlerCallback *thand_cb ) {
        _thand_cb = thand_cb;
    }


    void set_trajectory_end_callback( const TrajectoryEndCallback *tend_cb, ParticleDataBase *pdb ) {
        _tend_cb = tend_cb;
        _pdb = pdb;
    }


    void set_bfield_suppression_callback( const CallbackFunctorD_V *bsup_cb ) {
        _pidata.set_bfield_suppression_callback( bsup_cb );
    }

    const ParticleStatistics &get_statistics( void ) const {
        return( _stat );
    }

    
    void operator()( Particle<PP> *particle, uint32_t pi ) {

        // Check particle status
        if( particle->get_status() != PARTICLE_OK )
            return;

        // Copy starting point to x and 
        PP x = particle->x();

        // Check particle definition
        if( !check_particle_definition( x ) ) {
            particle->set_status( PARTICLE_BADDEF );
            _stat.inc_end_baddef();
            return;
        }
        particle->x() = x;

        // Reset trajectory and save first trajectory point.
        _traj.clear();
        _traj.push_back( x );
#ifdef DEBUG_PARTICLE_ITERATOR
        std::cout << x[0] << " " 
                  << x[1] << " " 
                  << x[2] << " " 
                  << x[3] << " " 
                  << x[4] << "\n";
#endif
        _pidata._qm = particle->qm();
        _xi = x;

        // Reset integrator
        gsl_odeiv_step_reset( _step );
        gsl_odeiv_evolve_reset( _evolve );
        
        // Make initial guess for step size
        //std::cout << "Guess dt ------------------------------------------------\n";
        double dxdt[PP::size()-1];
        PP::get_derivatives( 0.0, &x[1], dxdt, (void *)&_pidata );
        double dt = calculate_dt( x, dxdt );

#ifdef DEBUG_PARTICLE_ITERATOR
        std::cout << "dxdt = ";
        for( size_t a = 0; a < PP::size()-1; a++ )
            std::cout  << dxdt[a] << " ";
        std::cout << "\n";
        std::cout << "dt = " << dt << "\n";
        std::cout << "*** Starting iteration\n";
#endif
        
        // Iterate ODEs until maximum steps are done, time is used 
        // or particle collides.
        PP x2;
        size_t nstp = 0; // Steps taken
        while( nstp < _maxsteps && x[0] < _maxt ) {

#ifdef DEBUG_PARTICLE_ITERATOR
            std::cout << "\n*** Step ***\n";
            std::cout << "  x  = " << x2 << "\n";
            std::cout << "  dt = " << dt << " (proposed)\n";
#endif
            
            // Take a step.
            x2 = x;

            while( true ) {
                int retval = gsl_odeiv_evolve_apply( _evolve, _control, _step, &_system, 
                                                     &x2[0], _maxt, &dt, &x2[1] );
                if( retval == IBSIMU_DERIV_ERROR ) {
#ifdef DEBUG_PARTICLE_ITERATOR
                    std::cout << "Step rejected\n";
                    std::cout << "  x2 = " << x2 << "\n";
                    std::cout << "  dt = " << dt << "\n";
#endif
                    x2[0] = x[0]; // Reset time (this shouldn't be necessary - there 
                                  // is a bug in GSL-1.12, report has been sent)
                    dt *= 0.5;
                    if( dt == 0.0 )
                        throw( Error( ERROR_LOCATION, "too small step size" ) );
                    //nstp++;
                    continue;
                } else if( retval == GSL_SUCCESS ) {
                    break;
                } else {
                    throw( Error( ERROR_LOCATION, "gsl_odeiv_evolve_apply failed" ) );
                }
            }
            
            // Check step count number and step size validity
            if( nstp >= _maxsteps )
                break;
            if( x2[0] == x[0] )
                throw( Error( ERROR_LOCATION, "too small step size" ) );

#ifdef DEBUG_PARTICLE_ITERATOR
            std::cout << "Step accepted from x1 to x2:\n";
            std::cout << "  dt = " << dt << " (taken)\n";
            std::cout << "  x1 = " << x << "\n";
            std::cout << "  x2 = " << x2 << "\n";
#endif

            // Handle collisions and space charge of step.
            if( !handle_trajectory( *particle, x, x2, false, nstp == 0 ) ) {
                x = x2;
                break; // Particle done
            }

            // Check if particle mirroring is required to avoid 
            // singularity at symmetry axis.
            if( axis_mirror_required( x2 ) ) {
                if( !handle_axis_mirror_step( *particle, x, x2 ) )
                    break; // Particle done
            }

            // Propagate coordinates
            x = x2;

            // Save trajectory point
            _traj.push_back( x2 );
            
            // Increase step count.
            nstp++;
        }

#ifdef DEBUG_PARTICLE_ITERATOR
        std::cout << "\n*** Done stepping ***\n";
#endif

        // Check if step count or time limited 
        if( nstp == _maxsteps ) {
            particle->set_status( PARTICLE_NSTP );
            _stat.inc_end_step();
        } else if( x[0] >= _maxt ) {
            particle->set_status( PARTICLE_TIME );
            _stat.inc_end_time();
        }

        // Save step count
        _stat.inc_sum_steps( nstp );

        // Save trajectory of current particle
        if( _trajdiv != 0 && pi % _trajdiv == 0 )
            particle->copy_trajectory( _traj );

        // Save last particle location
        particle->x() = x;

        // Call trajectory end callback
        if( _tend_cb )
            (*_tend_cb)( particle, _pdb );
    }

};


#endif