source: git/external/fastjet/LazyTiling9.cc@ ee0763a

//FJSTARTHEADER
// $Id: LazyTiling9.cc 3808 2015-02-20 11:24:53Z soyez $
//
// Copyright (c) 2005-2014, Matteo Cacciari, Gavin P. Salam and Gregory Soyez
//
//----------------------------------------------------------------------
// This file is part of FastJet.
//
//  FastJet is free software; you can redistribute it 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.
//
//  The algorithms that underlie FastJet have required considerable
//  development. They are described in the original FastJet paper,
//  hep-ph/0512210 and in the manual, arXiv:1111.6097. If you use
//  FastJet as part of work towards a scientific publication, please
//  quote the version you use and include a citation to the manual and
//  optionally also to hep-ph/0512210.
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//  FastJet is distributed in the hope that it will be useful,
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//  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
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//----------------------------------------------------------------------
//FJENDHEADER


#include <iomanip>
#include <limits>
#include <cmath>
#include "fastjet/internal/LazyTiling9.hh"
#include "fastjet/internal/TilingExtent.hh"
using namespace std;

// uncomment the line below to use TilingExtent in LazyTiling9
#define _FASTJET_TILING2_USE_TILING_ANALYSIS_

FASTJET_BEGIN_NAMESPACE      // defined in fastjet/internal/base.hh



LazyTiling9::LazyTiling9(ClusterSequence & cs) :
  _cs(cs), _jets(cs.jets())
  //, _minheap(_jets.size()) 
{
#ifdef INSTRUMENT2
  _ncall = 0; // gps tmp
  _ncall_dtt = 0; // gps tmp
#endif // INSTRUMENT2
  _Rparam = cs.jet_def().R();
  _R2 = _Rparam * _Rparam;
  _invR2 = 1.0 / _R2;
  _initialise_tiles();
}


//----------------------------------------------------------------------
/// Set up the tiles:
///  - decide the range in eta
///  - allocate the tiles
///  - set up the cross-referencing info between tiles
///
/// The neighbourhood of a tile is set up as follows
///
///           LRR
///           LXR
///           LLR
///
/// such that tiles is an array containing XLLLLRRRR with pointers
///                                         |   \ RH_tiles
///                                         \ surrounding_tiles
///
/// with appropriate precautions when close to the edge of the tiled
/// region.
///
void LazyTiling9::_initialise_tiles() {

  // first decide tile sizes (with a lower bound to avoid huge memory use with
  // very small R)
  double default_size = max(0.1,_Rparam);
  _tile_size_eta = default_size;
  // it makes no sense to go below 3 tiles in phi -- 3 tiles is
  // sufficient to make sure all pair-wise combinations up to pi in
  // phi are possible
  _n_tiles_phi   = max(3,int(floor(twopi/default_size)));
  _tile_size_phi = twopi / _n_tiles_phi; // >= _Rparam and fits in 2pi

#ifdef _FASTJET_TILING2_USE_TILING_ANALYSIS_
  // testing
  TilingExtent tiling_analysis(_cs);
  _tiles_eta_min = tiling_analysis.minrap();
  _tiles_eta_max = tiling_analysis.maxrap();
  //cout << "Using timing analysis " << " " << _tiles_eta_min << " " << _tiles_eta_max << endl;
#else
  // always include zero rapidity in the tiling region
  _tiles_eta_min = 0.0;
  _tiles_eta_max = 0.0;
  // but go no further than following
  const double maxrap = 7.0;
  
  // and find out how much further one should go
  for(unsigned int i = 0; i < _jets.size(); i++) {
    double eta = _jets[i].rap();
    // first check if eta is in range -- to avoid taking into account
    // very spurious rapidities due to particles with near-zero kt.
    if (abs(eta) < maxrap) {
      if (eta < _tiles_eta_min) {_tiles_eta_min = eta;}
      if (eta > _tiles_eta_max) {_tiles_eta_max = eta;}
    }
  }
  //cout << "NOT using timing analysis " << " " << _tiles_eta_min << " " << _tiles_eta_max << endl;
#endif

  // Now adjust the values for the rapidity ("eta") range.
  //
  // When tile_size_eta is large, we have two options:
  // - always have at least two tiles in rapidity (FASTJET_LAZY9_MIN2TILESY),
  //   currently split down the middle of the rapidity extent of the particles
  // - take whatever we get from the original 
  //   _tiles_ieta_min[max] = int(floor(_tiles_eta_min[max]/_tile_size_eta));
  //   which will sometimes leave us with just one tile in Y; 
  //
  // For events that are symetric in Y this should not change
  // anything, but for asymmetric ones FASTJET_LAZY9_MIN2TILESY may be
  // a bit faster.
  // 
#define FASTJET_LAZY9_MIN2TILESY
#ifdef FASTJET_LAZY9_MIN2TILESY
   if (_tiles_eta_max - _tiles_eta_min < 2*_tile_size_eta) {
     // if we have a rapidity coverage that is small compared to the
     // tile size then we can adjust the grid in rapidity so as to
     // have exactly 3 tiles. This can give relevant speed improvements 
     // for large R jets
     _tile_size_eta = (_tiles_eta_max - _tiles_eta_min)/2;
     _tiles_ieta_min = 0;
     _tiles_ieta_max = 1;
     // the eta max value is being taken as the lower edge of the
     // highest-y tile
     _tiles_eta_max -= _tile_size_eta;
   } else {
#endif //FASTJET_LAZY9_MIN2TILESY
  _tiles_ieta_min = int(floor(_tiles_eta_min/_tile_size_eta));
  _tiles_ieta_max = int(floor( _tiles_eta_max/_tile_size_eta));
  _tiles_eta_min = _tiles_ieta_min * _tile_size_eta;
  _tiles_eta_max = _tiles_ieta_max * _tile_size_eta;
#ifdef FASTJET_LAZY9_MIN2TILESY
   }
#endif

  _tile_half_size_eta = _tile_size_eta * 0.5;
  _tile_half_size_phi = _tile_size_phi * 0.5;

  // set up information about whether we need to allow for "periodic" 
  // wrapping tests in delta_phi calculations
  vector<bool> use_periodic_delta_phi(_n_tiles_phi, false);
  if (_n_tiles_phi <= 3) {
    fill(use_periodic_delta_phi.begin(), use_periodic_delta_phi.end(), true);
  } else {
    use_periodic_delta_phi[0] = true;
    use_periodic_delta_phi[_n_tiles_phi-1] = true;
  }

  // allocate the tiles
  _tiles.resize((_tiles_ieta_max-_tiles_ieta_min+1)*_n_tiles_phi);

  // now set up the cross-referencing between tiles
  for (int ieta = _tiles_ieta_min; ieta <= _tiles_ieta_max; ieta++) {
    for (int iphi = 0; iphi < _n_tiles_phi; iphi++) {
      Tile2 * tile = & _tiles[_tile_index(ieta,iphi)];
      // no jets in this tile yet
      tile->head = NULL; // first element of tiles points to itself
      tile->begin_tiles[0] =  tile;
      Tile2 ** pptile = & (tile->begin_tiles[0]);
      pptile++;
      //
      // set up L's in column to the left of X
      tile->surrounding_tiles = pptile;
      if (ieta > _tiles_ieta_min) {
        // with the itile subroutine, we can safely run tiles from
        // idphi=-1 to idphi=+1, because it takes care of
        // negative and positive boundaries
        for (int idphi = -1; idphi <=+1; idphi++) {
          *pptile = & _tiles[_tile_index(ieta-1,iphi+idphi)];
          pptile++;
        }       
      }
      // now set up last L (below X)
      *pptile = & _tiles[_tile_index(ieta,iphi-1)];
      pptile++;
      // set up first R (above X)
      tile->RH_tiles = pptile;
      *pptile = & _tiles[_tile_index(ieta,iphi+1)];
      pptile++;
      // set up remaining R's, to the right of X
      if (ieta < _tiles_ieta_max) {
        for (int idphi = -1; idphi <= +1; idphi++) {
          *pptile = & _tiles[_tile_index(ieta+1,iphi+idphi)];
          pptile++;
        }       
      }
      // now put semaphore for end tile
      tile->end_tiles = pptile;
      // finally make sure tiles are untagged
      tile->tagged = false;
      // and store the information about periodicity in phi
      tile->use_periodic_delta_phi = use_periodic_delta_phi[iphi];
      // and ensure max distance is sensibly initialised
      tile->max_NN_dist = 0;
      // and also position of centre of tile
      tile->eta_centre = (ieta-_tiles_ieta_min+0.5)*_tile_size_eta + _tiles_eta_min;
      tile->phi_centre = (iphi+0.5)*_tile_size_phi;
    }
  }

}

//----------------------------------------------------------------------
/// return the tile index corresponding to the given eta,phi point
int LazyTiling9::_tile_index(const double eta, const double phi) const {
  int ieta, iphi;
  if      (eta <= _tiles_eta_min) {ieta = 0;}
  else if (eta >= _tiles_eta_max) {ieta = _tiles_ieta_max-_tiles_ieta_min;}
  else {
    //ieta = int(floor((eta - _tiles_eta_min) / _tile_size_eta));
    ieta = int(((eta - _tiles_eta_min) / _tile_size_eta));
    // following needed in case of rare but nasty rounding errors
    if (ieta > _tiles_ieta_max-_tiles_ieta_min) {
      ieta = _tiles_ieta_max-_tiles_ieta_min;} 
  }
  // allow for some extent of being beyond range in calculation of phi
  // as well
  //iphi = (int(floor(phi/_tile_size_phi)) + _n_tiles_phi) % _n_tiles_phi;
  // with just int and no floor, things run faster but beware
  iphi = int((phi+twopi)/_tile_size_phi) % _n_tiles_phi;
  return (iphi + ieta * _n_tiles_phi);
}


//----------------------------------------------------------------------
// sets up information regarding the tiling of the given jet
inline void LazyTiling9::_tj_set_jetinfo( TiledJet * const jet,
                                              const int _jets_index) {
  // first call the generic setup
  _bj_set_jetinfo<>(jet, _jets_index);

  // Then do the setup specific to the tiled case.

  // Find out which tile it belonds to
  jet->tile_index = _tile_index(jet->eta, jet->phi);

  // Insert it into the tile's linked list of jets
  Tile2 * tile = &_tiles[jet->tile_index];
  jet->previous   = NULL;
  jet->next       = tile->head;
  if (jet->next != NULL) {jet->next->previous = jet;}
  tile->head      = jet;
}


//----------------------------------------------------------------------
void LazyTiling9::_bj_remove_from_tiles(TiledJet * const jet) {
  Tile2 * tile = & _tiles[jet->tile_index];

  if (jet->previous == NULL) {
    // we are at head of the tile, so reset it.
    // If this was the only jet on the tile then tile->head will now be NULL
    tile->head = jet->next;
  } else {
    // adjust link from previous jet in this tile
    jet->previous->next = jet->next;
  }
  if (jet->next != NULL) {
    // adjust backwards-link from next jet in this tile
    jet->next->previous = jet->previous;
  }
}


//----------------------------------------------------------------------
/// output the contents of the tiles
void LazyTiling9::_print_tiles(TiledJet * briefjets ) const {
  for (vector<Tile2>::const_iterator tile = _tiles.begin(); 
       tile < _tiles.end(); tile++) {
    cout << "Tile " << tile - _tiles.begin()<<" = ";
    vector<int> list;
    for (TiledJet * jetI = tile->head; jetI != NULL; jetI = jetI->next) {
      list.push_back(jetI-briefjets);
      //cout <<" "<<jetI-briefjets;
    }
    sort(list.begin(),list.end());
    for (unsigned int i = 0; i < list.size(); i++) {cout <<" "<<list[i];}
    cout <<"\n";
  }
}


//----------------------------------------------------------------------
/// Add to the vector tile_union the tiles that are in the neighbourhood
/// of the specified tile_index, including itself -- start adding
/// from position n_near_tiles-1, and increase n_near_tiles as
/// you go along (could have done it more C++ like with vector with reserved
/// space, but fear is that it would have been slower, e.g. checking
/// for end of vector at each stage to decide whether to resize it)
void LazyTiling9::_add_neighbours_to_tile_union(const int tile_index, 
               vector<int> & tile_union, int & n_near_tiles) const {
  for (Tile2 * const * near_tile = _tiles[tile_index].begin_tiles; 
       near_tile != _tiles[tile_index].end_tiles; near_tile++){
    // get the tile number
    tile_union[n_near_tiles] = *near_tile - & _tiles[0];
    n_near_tiles++;
  }
}


//----------------------------------------------------------------------
/// Like _add_neighbours_to_tile_union, but only adds neighbours if 
/// their "tagged" status is false; when a neighbour is added its
/// tagged status is set to true.
inline void LazyTiling9::_add_untagged_neighbours_to_tile_union(
               const int tile_index, 
               vector<int> & tile_union, int & n_near_tiles)  {
  for (Tile2 ** near_tile = _tiles[tile_index].begin_tiles; 
       near_tile != _tiles[tile_index].end_tiles; near_tile++){
    if (! (*near_tile)->tagged) {
      (*near_tile)->tagged = true;
      // get the tile number
      tile_union[n_near_tiles] = *near_tile - & _tiles[0];
      n_near_tiles++;
    }
  }
}

//----------------------------------------------------------------------
/// Like _add_neighbours_to_tile_union, but adds tiles that are
/// "neighbours" of a jet (rather than a tile) and only if a
/// neighbouring tile's max_NN_dist is >= the distance between the jet
/// and the nearest point on the tile. It ignores tiles that have
/// already been tagged.
inline void LazyTiling9::_add_untagged_neighbours_to_tile_union_using_max_info(
               const TiledJet * jet, 
               vector<int> & tile_union, int & n_near_tiles)  {
  Tile2 & tile = _tiles[jet->tile_index];
  
  for (Tile2 ** near_tile = tile.begin_tiles; near_tile != tile.end_tiles; near_tile++){
    if ((*near_tile)->tagged) continue;
    // here we are not allowed to miss a tile due to some rounding
    // error. We therefore allow for a margin of security
    double dist = _distance_to_tile(jet, *near_tile) - tile_edge_security_margin;
    // cout << "      max info looked at tile " << *near_tile - &_tiles[0] 
    //   << ", dist = " << dist << " " << (*near_tile)->max_NN_dist
    //   << endl;
    if (dist > (*near_tile)->max_NN_dist) continue;

    // cout << "      max info tagged tile " << *near_tile - &_tiles[0] << endl;
    (*near_tile)->tagged = true;
    // get the tile number
    tile_union[n_near_tiles] = *near_tile - & _tiles[0];
    n_near_tiles++;
  }
}

////--------TMPTMPTMPTMPTMP-----GPS TEMP--------------------
//ostream & operator<<(ostream & ostr, const TiledJet & jet) {
//  ostr << "j" << setw(3) << jet._jets_index << ":pt2,rap,phi=" ; ostr.flush();
//  ostr     << jet.kt2 << ","; ostr.flush();
//  ostr     << jet.eta << ","; ostr.flush();
//  ostr     << jet.phi; ostr.flush();
//  ostr     << ", tile=" << jet.tile_index; ostr.flush();
//  return ostr;
//}


//----------------------------------------------------------------------
/// returns a particle's distance to the edge of the specified tile
inline double LazyTiling9::_distance_to_tile(const TiledJet * bj, const Tile2 * tile) 
#ifdef INSTRUMENT2
   {
  _ncall_dtt++; // GPS tmp
#else
  const {
#endif // INSTRUMENT2
  // Note the careful way of checking the minimum potential deta:
  // unlike the phi case below, we don't calculate the distance to the
  // centre and subtract spacing/2. This is because of issue of
  // boundary tiles, which can extend far beyond spacing/2 in eta. 
  // Using the positions of tile centers should instead be safe.
  double deta;
  if (_tiles[bj->tile_index].eta_centre == tile->eta_centre) deta = 0;
  //else   deta = std::abs(bj->eta - tile->eta_centre) - 0.5*_tile_size_eta;
  else   deta = std::abs(bj->eta - tile->eta_centre) - _tile_half_size_eta;
  // ------
  //   |
  // A | B
  // ------
  //   |
  // C | D
  // ------

  double dphi = std::abs(bj->phi - tile->phi_centre);
  if (dphi > pi) dphi = twopi-dphi;
  dphi -= _tile_half_size_phi;
  //dphi -= 0.5*_tile_size_phi;
  if (dphi < 0) dphi = 0;

  return dphi*dphi + deta*deta;
}




//----------------------------------------------------------------------
/// looks at distance between jetX and jetI and updates the NN
/// information if relevant; also pushes identity of jetI onto
/// the vector of jets for minheap, to signal that it will have
/// to be handled later.
///
/// GPS TEMP GPS TMP: REMOVE THIS LATER: EVEN LABELLED AS INLINE, THE
/// CALL ADDS A SUBSTANTIAL PENALTY...
inline void LazyTiling9::_update_jetX_jetI_NN(TiledJet * jetX, TiledJet * jetI, vector<TiledJet *> & jets_for_minheap) {
  double dist = _bj_dist(jetI,jetX);
  if (dist < jetI->NN_dist) {
    if (jetI != jetX) {
      jetI->NN_dist = dist;
      jetI->NN = jetX;
      // label jetI as needing heap action...
      if (!jetI->minheap_update_needed()) {
        jetI->label_minheap_update_needed();
        jets_for_minheap.push_back(jetI);
      }
    }
  }
  if (dist < jetX->NN_dist) {
    if (jetI != jetX) {
      jetX->NN_dist = dist;
      jetX->NN      = jetI;}
  }
}


inline void LazyTiling9::_set_NN(TiledJet * jetI, 
                              vector<TiledJet *> & jets_for_minheap) {
  jetI->NN_dist = _R2;
  jetI->NN      = NULL;
  // label jetI as needing heap action...
  if (!jetI->minheap_update_needed()) {
    jetI->label_minheap_update_needed();
    jets_for_minheap.push_back(jetI);}
  // now go over tiles that are neighbours of I (include own tile)
  Tile2 * tile_ptr = &_tiles[jetI->tile_index];
  //if (tile_ptr->is_near_zero_phi(_tile_size_phi)) {
    for (Tile2 ** near_tile  = tile_ptr->begin_tiles; 
         near_tile != tile_ptr->end_tiles; near_tile++) {
      // for own tile, this will be zero automatically: should we be clever
      // and skip the test? (With some doubling of code?)
      if (jetI->NN_dist < _distance_to_tile(jetI, *near_tile)) continue;
      // and then over the contents of that tile
      for (TiledJet * jetJ  = (*near_tile)->head; 
           jetJ != NULL; jetJ = jetJ->next) {
        double dist = _bj_dist(jetI,jetJ);
        if (dist < jetI->NN_dist && jetJ != jetI) {
          jetI->NN_dist = dist; jetI->NN = jetJ;
        }
      }
    }
  // } else {
  //   // second copy that exploits the fact that for this tile we needn't worry
  //   // about periodicity
  //   for (Tile2 ** near_tile  = tile_ptr->begin_tiles; 
  //        near_tile != tile_ptr->end_tiles; near_tile++) {
  //     // for own tile, this will be zero automatically: should we be clever
  //     // and skip the test? (With some doubling of code?)
  //     if (jetI->NN_dist < _distance_to_tile(jetI, *near_tile)) continue;
  //     // and then over the contents of that tile
  //     for (TiledJet * jetJ  = (*near_tile)->head; 
  //          jetJ != NULL; jetJ = jetJ->next) {
  //       double dist = _bj_dist_not_periodic(jetI,jetJ);
  //       if (dist < jetI->NN_dist && jetJ != jetI) {
  //         jetI->NN_dist = dist; jetI->NN = jetJ;
  //       }
  //     }
  //   }
  // }
}


void LazyTiling9::run() {

  //_initialise_tiles();

  int n = _jets.size();
  if (n == 0) return; 

  TiledJet * briefjets = new TiledJet[n];
  TiledJet * jetA = briefjets, * jetB;
  // avoid warning about uninitialised oldB below; 
  // only valid for n>=1 (hence the test n==0 test above)
  TiledJet oldB = briefjets[0]; 

  // will be used quite deep inside loops, but declare it here so that
  // memory (de)allocation gets done only once
  vector<int> tile_union(3*n_tile_neighbours);
  
  // initialise the basic jet info 
  for (int i = 0; i< n; i++) {
    _tj_set_jetinfo(jetA, i);
    //cout << i<<": "<<jetA->tile_index<<"\n";
    jetA++; // move on to next entry of briefjets
  }
  TiledJet * head = briefjets; // a nicer way of naming start


  // // count the contents of the tiles
  // for (int ieta = _tiles_ieta_min; ieta <= _tiles_ieta_max; ieta++) {
  //   for (int iphi = 0; iphi < _n_tiles_phi; iphi++) {
  //     Tile2 * tile = & _tiles[_tile_index(ieta,iphi)];
  //     int njets = 0;
  //     const TiledJet * jet = tile->head;
  //     while (jet != 0) {
  //       njets++;
  //       jet = jet->next;
  //     }
  //     cout << ieta 
  //          << " " << iphi 
  //          << " " << tile->jet_count()
  //          << endl;
  //   }
  // }


  // set up the initial nearest neighbour information
  vector<Tile2>::iterator tile;
  for (tile = _tiles.begin(); tile != _tiles.end(); tile++) {
    // first do it on this tile
    for (jetA = tile->head; jetA != NULL; jetA = jetA->next) {
      for (jetB = tile->head; jetB != jetA; jetB = jetB->next) {
        double dist = _bj_dist_not_periodic(jetA,jetB);
        if (dist < jetA->NN_dist) {jetA->NN_dist = dist; jetA->NN = jetB;}
        if (dist < jetB->NN_dist) {jetB->NN_dist = dist; jetB->NN = jetA;}
      }
    }
    for (jetA = tile->head; jetA != NULL; jetA = jetA->next) {
      if (jetA->NN_dist > tile->max_NN_dist) tile->max_NN_dist = jetA->NN_dist;
    }
  }
  for (tile = _tiles.begin(); tile != _tiles.end(); tile++) {
    if (tile->use_periodic_delta_phi) {
      // then do it for RH tiles; 
      for (Tile2 ** RTile = tile->RH_tiles; RTile != tile->end_tiles; RTile++) {
        for (jetA = tile->head; jetA != NULL; jetA = jetA->next) {
          double dist_to_tile = _distance_to_tile(jetA, *RTile);
          // it only makes sense to do a tile if jetA is close enough to the Rtile
          // either for a jet in the Rtile to be closer to jetA than it's current NN
          // or if jetA could be closer to something in the Rtile than the largest
          // NN distance within the RTile.
          //
          // GPS note: also tried approach where we perform only the
          //           first test and run over all surrounding tiles
          //           (not just RH ones). The test is passed less
          //           frequently, but one is running over more tiles
          //           and on balance, for the trial event we used, it's
          //           a bit slower.
          bool relevant_for_jetA  = dist_to_tile <= jetA->NN_dist;
          bool relevant_for_RTile = dist_to_tile <= (*RTile)->max_NN_dist;
          if (relevant_for_jetA || relevant_for_RTile) {
            for (jetB = (*RTile)->head; jetB != NULL; jetB = jetB->next) {
              double dist = _bj_dist(jetA,jetB);
              if (dist < jetA->NN_dist) {jetA->NN_dist = dist; jetA->NN = jetB;}
              if (dist < jetB->NN_dist) {jetB->NN_dist = dist; jetB->NN = jetA;}
            }
          } 
        }
      }
    } else {
      // this second version of the code uses the faster
      // "not_periodic" version because it knows that the tile is
      // sufficiently far from the edge.
      for (Tile2 ** RTile = tile->RH_tiles; RTile != tile->end_tiles; RTile++) {
        for (jetA = tile->head; jetA != NULL; jetA = jetA->next) {
          double dist_to_tile = _distance_to_tile(jetA, *RTile);
          bool relevant_for_jetA  = dist_to_tile <= jetA->NN_dist;
          bool relevant_for_RTile = dist_to_tile <= (*RTile)->max_NN_dist;
          if (relevant_for_jetA || relevant_for_RTile) {
            for (jetB = (*RTile)->head; jetB != NULL; jetB = jetB->next) {
              double dist = _bj_dist_not_periodic(jetA,jetB);
              if (dist < jetA->NN_dist) {jetA->NN_dist = dist; jetA->NN = jetB;}
              if (dist < jetB->NN_dist) {jetB->NN_dist = dist; jetB->NN = jetA;}
            }
          } 
        }
      }
    }
    // no need to do it for LH tiles, since they are implicitly done
    // when we set NN for both jetA and jetB on the RH tiles.
  }
  // Now update the max_NN_dist within each tile. Not strictly
  // necessary, because existing max_NN_dist is an upper bound.  but
  // costs little and may give some efficiency gain later.
  for (tile = _tiles.begin(); tile != _tiles.end(); tile++) {
    tile->max_NN_dist = 0;
    for (jetA = tile->head; jetA != NULL; jetA = jetA->next) {
      if (jetA->NN_dist > tile->max_NN_dist) tile->max_NN_dist = jetA->NN_dist;
    }
  }

#ifdef INSTRUMENT2
  cout << "intermediate ncall, dtt = " << _ncall << " " << _ncall_dtt << endl; // GPS tmp
#endif // INSTRUMENT2

  vector<double> diJs(n);
  for (int i = 0; i < n; i++) {
    diJs[i] = _bj_diJ(&briefjets[i]);
    briefjets[i].label_minheap_update_done();
  }
  MinHeap minheap(diJs);
  // have a stack telling us which jets we'll have to update on the heap
  vector<TiledJet *> jets_for_minheap;
  jets_for_minheap.reserve(n); 

  // now run the recombination loop
  int history_location = n-1;
  while (n > 0) {

    double diJ_min = minheap.minval() *_invR2;
    jetA = head + minheap.minloc();

    // do the recombination between A and B
    history_location++;
    jetB = jetA->NN;

    if (jetB != NULL) {
      // jet-jet recombination
      // If necessary relabel A & B to ensure jetB < jetA, that way if
      // the larger of them == newtail then that ends up being jetA and 
      // the new jet that is added as jetB is inserted in a position that
      // has a future!
      if (jetA < jetB) {std::swap(jetA,jetB);}

      int nn; // new jet index
      _cs.plugin_record_ij_recombination(jetA->_jets_index, jetB->_jets_index, diJ_min, nn);
      
      // what was jetB will now become the new jet
      _bj_remove_from_tiles(jetA);
      oldB = * jetB;  // take a copy because we will need it...
      _bj_remove_from_tiles(jetB);
      _tj_set_jetinfo(jetB, nn); // cause jetB to become _jets[nn]
                                 // (also registers the jet in the tiling)
    } else {
      // jet-beam recombination
      // get the hist_index
      _cs.plugin_record_iB_recombination(jetA->_jets_index, diJ_min);
      _bj_remove_from_tiles(jetA);
    }

    // remove the minheap entry for jetA
    minheap.remove(jetA-head);

    int n_near_tiles = 0;

    // Initialise jetB's NN distance as well as updating it for other
    // particles. While doing so, examine whether jetA or old jetB was
    // some other particle's NN.
    if (jetB != NULL) {
      Tile2 & jetB_tile = _tiles[jetB->tile_index];
      for (Tile2 ** near_tile  = jetB_tile.begin_tiles; 
                   near_tile != jetB_tile.end_tiles; near_tile++) {

        double dist_to_tile = _distance_to_tile(jetB, *near_tile);
        // use <= in next line so that on first tile, relevant_for_jetB is 
        // set to true
        bool relevant_for_jetB  = dist_to_tile <= jetB->NN_dist;
        bool relevant_for_near_tile = dist_to_tile <= (*near_tile)->max_NN_dist;
        bool relevant = relevant_for_jetB || relevant_for_near_tile;
        if (! relevant) continue;
        // now label this tile as having been considered (so that we 
        // don't go over it again later)
        tile_union[n_near_tiles] = *near_tile - & _tiles[0];
        (*near_tile)->tagged = true;
        n_near_tiles++;
        
        // if going over the neighbouring tile's jets, check anyway
        // whether A or B were nearest neighbours, since it comes at a
        // modest cost relative to the distance computation (and we would
        // in most cases have to do it again later anyway).
        for (TiledJet * jetI = (*near_tile)->head; jetI != NULL; jetI = jetI->next) {
          if (jetI->NN == jetA || jetI->NN == jetB) _set_NN(jetI, jets_for_minheap);
          _update_jetX_jetI_NN(jetB, jetI, jets_for_minheap);
        }
      }
    }

    // first establish the set of tiles over which we are going to
    // have to run searches for updated and new nearest-neighbours --
    // basically a combination of vicinity of the tiles of the two old
    // and one new jet.
    int n_done_tiles = n_near_tiles;
    _add_untagged_neighbours_to_tile_union_using_max_info(jetA, 
                                           tile_union, n_near_tiles);
    if (jetB != NULL) {
        _add_untagged_neighbours_to_tile_union_using_max_info(&oldB,
                                                              tile_union,n_near_tiles);
      jetB->label_minheap_update_needed();
      jets_for_minheap.push_back(jetB);
    }


    // first untag the tiles we have already dealt with
    for (int itile = 0; itile < n_done_tiles; itile++) {
      _tiles[tile_union[itile]].tagged = false;
    }
    // now run over the tiles that were tagged earlier and that we haven't yet
    // had a change to visit.
    for (int itile = n_done_tiles; itile < n_near_tiles; itile++) {
      Tile2 * tile_ptr = &_tiles[tile_union[itile]];
      tile_ptr->tagged = false;
      // run over all jets in the current tile
      for (TiledJet * jetI = tile_ptr->head; jetI != NULL; jetI = jetI->next) {
        // see if jetI had jetA or jetB as a NN -- if so recalculate the NN
        if (jetI->NN == jetA || (jetI->NN == jetB && jetB != NULL)) {
          _set_NN(jetI, jets_for_minheap);
        }
      }
    }

    // deal with jets whose minheap entry needs updating
    //if (verbose) cout << "  jets whose NN was modified: " << endl;
    while (jets_for_minheap.size() > 0) {
      TiledJet * jetI = jets_for_minheap.back(); 
      jets_for_minheap.pop_back();
      minheap.update(jetI-head, _bj_diJ(jetI));
      jetI->label_minheap_update_done();
      // handle max_NN_dist update for all jets that might have
      // seen a change (increase) of distance
      Tile2 & tile_I = _tiles[jetI->tile_index];
      if (tile_I.max_NN_dist < jetI->NN_dist) tile_I.max_NN_dist = jetI->NN_dist;
    }
    n--;
  }

  // final cleaning up;
  delete[] briefjets;
#ifdef INSTRUMENT2
  cout << "ncall, dtt = " << _ncall << " " << _ncall_dtt << endl; // GPS tmp
#endif // INSTRUMENT2

}

FASTJET_END_NAMESPACE