source: git/modules/VertexFinder4D.cc@ 8284b74

/** \class VertexFinder4D
 *
 *  Cluster vertices from tracks using deterministic annealing and timing information
 *
 *  \authors M. Selvaggi, L. Grey
 *
 */


#include "modules/VertexFinder4D.h"
#include "classes/DelphesClasses.h"
#include "classes/DelphesFactory.h"
#include "classes/DelphesFormula.h"
#include "classes/DelphesPileUpReader.h"

#include "ExRootAnalysis/ExRootResult.h"
#include "ExRootAnalysis/ExRootFilter.h"
#include "ExRootAnalysis/ExRootClassifier.h"

#include "TMath.h"
#include "TString.h"
#include "TFormula.h"
#include "TRandom3.h"
#include "TObjArray.h"
#include "TDatabasePDG.h"
#include "TLorentzVector.h"
#include "TMatrixT.h"
#include "TVector3.h"

static const Double_t mm  = 1.;
static const Double_t m = 1000.*mm;
static const Double_t ns  = 1.;
static const Double_t s = 1.e+9 *ns;
static const Double_t c_light   = 2.99792458e+8 * m/s;


namespace {
  constexpr double dtCutOff = 4.0;

  bool recTrackLessZ1(const VertexFinder4D::track_t & tk1,
                      const VertexFinder4D::track_t & tk2)
  {
    return tk1.z < tk2.z;
  }
}


//------------------------------------------------------------------------------

VertexFinder4D::VertexFinder4D() :
  fSigma(0), fMinPT(0), fMaxEta(0), fSeedMinPT(0), fMinNDF(0), fGrowSeeds(0)
{
}

//------------------------------------------------------------------------------

VertexFinder4D::~VertexFinder4D()
{
}

//------------------------------------------------------------------------------

void VertexFinder4D::Init()
{
  
  fVerbose = GetBool("Verbose", 1);
  fSigma = GetDouble("Sigma", 3.0);
  fMinPT = GetDouble("MinPT", 0.1);
  fMaxEta = GetDouble("MaxEta", 10.0);
  fSeedMinPT = GetDouble("SeedMinPT", 5.0);
  fMinNDF = GetInt("MinNDF", 4);
  fGrowSeeds = GetInt("GrowSeeds", 1);

  // setting everything in cm to be able to compare easily with Lindsey code
  useTc_=true;
  betamax_=0.1;
  betastop_  =1.0;
  coolingFactor_=0.8;
  maxIterations_=100;
  vertexSize_=0.05;  // 0.5 mm
  dzCutOff_=4.0;   // Adaptive Fitter uses 3.0 but that appears to be a bit tight here sometimes
  d0CutOff_=3.0; 
 
  fInputArray = ImportArray(GetString("InputArray", "TrackSmearing/tracks"));
  fItInputArray = fInputArray->MakeIterator();

  fOutputArray = ExportArray(GetString("OutputArray", "tracks"));
  fVertexOutputArray = ExportArray(GetString("VertexOutputArray", "vertices"));
}

//------------------------------------------------------------------------------

void VertexFinder4D::Finish()
{
  if(fItInputArray) delete fItInputArray;
}

//------------------------------------------------------------------------------

void VertexFinder4D::Process()
{
  Candidate *candidate, *track;
  TObjArray *ClusterArray;
  ClusterArray = new TObjArray;
  TIterator *ItClusterArray;
  Int_t ivtx = 0;

  // clusterize tracks in Z
  clusterize(*fInputArray, *ClusterArray);
 
  if (fVerbose){std::cout <<  " clustering returned  "<< ClusterArray->GetEntriesFast() << " clusters  from " << fInputArray->GetEntriesFast() << " selected tracks" <<std::endl;}

  
  //loop over vertex candidates
  ItClusterArray = ClusterArray->MakeIterator();
  ItClusterArray->Reset();
  while((candidate = static_cast<Candidate*>(ItClusterArray->Next())))
  {
     double meantime = 0.;
     double expv_x2 = 0.;
     double normw = 0.;      
     double errtime = 0;
     
     double meanpos = 0.;
     double meanerr2 = 0.;
     double normpos = 0.;      
     double errpos = 0.;
     
     double sumpt2 = 0.;
    
     int itr = 0;
     
     // loop over tracks belonging to this vertex
     TIter it1(candidate->GetCandidates());
     it1.Reset();
     while((track = static_cast<Candidate*>(it1.Next())))
     {
        
        itr++;
        // TBC: the time is in ns for now TBC 
        double t = track->Position.T()/c_light;
        double l = track->L/c_light;
        double dt = track->ErrorT/c_light;
        
        const double time = t-l;
        const double inverr = 1.0/dt;
        meantime += time*inverr;
        expv_x2  += time*time*inverr;
        normw    += inverr;
     
        // compute error position TBC
        const double pt = track->Momentum.Pt();
        const double z = track->DZ;
        const double err_pt = track->ErrorPT;
        const double err_z = track->ErrorDZ;
        
        const double wi = (pt/(err_pt*err_z))*(pt/(err_pt*err_z));
        meanpos += z*wi;
        
        meanerr2 += err_z*err_z*wi;
        normpos += wi;
        sumpt2 += pt*pt;
      
        // while we are here store cluster index in tracks
        track->ClusterIndex = ivtx; 
      
     }
     
     
     meantime = meantime/normw;
     expv_x2 = expv_x2/normw;
     errtime = TMath::Sqrt((expv_x2 - meantime*meantime)/itr); 

     meanpos = meanpos/normpos;
     meanerr2 = meanerr2/normpos;
     errpos = TMath::Sqrt(meanerr2/itr);
     
     candidate->Position.SetXYZT(0.0, 0.0, meanpos*10.0 , meantime*c_light);
     candidate->PositionError.SetXYZT(0.0, 0.0, errpos*10.0 , errtime*c_light);
     candidate->SumPT2 = sumpt2;
     candidate->ClusterNDF = itr;
     candidate->ClusterIndex = ivtx;

     ivtx++;
 
     if (fVerbose){
           std::cout << "x,y,z";
       std::cout << ",t";
       std::cout << "=" << candidate->Position.X()/10.0 <<" " << candidate->Position.Y()/10.0 << " " <<  candidate->Position.Z()/10.0;
       std::cout << " " << candidate->Position.T()/c_light;
       std::cout << std::endl;
     }
   }// end of cluster loop

    
    if(fVerbose){
      std::cout << "PrimaryVertexProducerAlgorithm::vertices  candidates =" << ClusterArray->GetEntriesFast() << std::endl;
    }

    //TBC maybe this can be done later  
    // sort vertices by pt**2  vertex (aka signal vertex tagging)
    /*if(pvs.size()>1){
      sort(pvs.begin(), pvs.end(), VertexHigherPtSquared());
    }
     */
        
  delete ClusterArray; 

}

//------------------------------------------------------------------------------


void VertexFinder4D::clusterize(const TObjArray & tracks, TObjArray & clusters)
{
  if(fVerbose) {
    cout << "###################################################" << endl;
    cout << "# VertexFinder4D::clusterize   nt="<<tracks.GetEntriesFast() << endl;
    cout << "###################################################" << endl;
  }

  Candidate *candidate;
  
  vector< Candidate > pv=vertices(tracks);

  cout<<"test"<<endl;
  if(fVerbose){ cout << "# VertexFinder4D::clusterize   pv.size="<<pv.size() << endl;  }
  if (pv.size()==0){ return;  }

  // convert into vector of candidates
  //TObjArray *ClusterArray = pv.begin()->GetCandidates();
  //Candidate *aCluster = static_cast<Candidate*>(&(pv.at(0)));
   Candidate *aCluster = &(pv.at(0));
   
  // fill into clusters and merge
   
  
  if( fVerbose ) { 
      std::cout << '\t' << 0;
      std::cout << ' ' << pv.begin()->Position.Z()/10.0 << ' ' << pv.begin()->Position.T()/c_light << std::endl; 
    }

  for(vector<Candidate>::iterator k=pv.begin()+1; k!=pv.end(); k++){
    if( fVerbose ) { 
      std::cout << '\t' << std::distance(pv.begin(),k);
      std::cout << ' ' << k->Position.Z() << ' ' << k->Position.T() << std::endl; 
    }
    
    
    // TBC - check units here
    if ( std::abs(k->Position.Z() - (k-1)->Position.Z())/10.0 > (2*vertexSize_) ||
         std::abs(k->Position.T() - (k-1)->Position.Z())/c_light > 2*0.010 ) {
      // close a cluster
      clusters.Add(aCluster);
      //aCluster.clear();
    }
    //for(unsigned int i=0; i<k->GetCandidates().GetEntriesFast(); i++){ 
      aCluster = &*k; 
    //}
    
  }
  clusters.Add(aCluster);
  
  if(fVerbose) { std::cout << "# VertexFinder4D::clusterize clusters.size="<<clusters.GetEntriesFast() << std::endl; }
 
}


//------------------------------------------------------------------------------

vector< Candidate >
VertexFinder4D::vertices(const TObjArray & tracks, const int verbosity) 
{
  Candidate *candidate;
  UInt_t clusterIndex = 0;
  vector< Candidate > clusters;
 
  vector<track_t> tks=fill(tracks);
   
  unsigned int nt=tks.size();
  double rho0=0.0;  // start with no outlier rejection

  if (tks.empty()) return clusters;

  vector<vertex_t> y; // the vertex prototypes

  // initialize:single vertex at infinite temperature
  vertex_t vstart;
  vstart.z=0.;
  vstart.t=0.;
  vstart.pk=1.;
  y.push_back(vstart);
  int niter=0;      // number of iterations
 
  // estimate first critical temperature
  double beta=beta0(betamax_, tks, y);
  niter=0; while((update(beta, tks,y)>1.e-6)  && (niter++ < maxIterations_)){ }

  // annealing loop, stop when T<Tmin  (i.e. beta>1/Tmin)
  while(beta<betamax_){ 

    if(useTc_){
      update(beta, tks,y);
      while(merge(y,beta)){update(beta, tks,y);}
      split(beta, tks,y, 1.);
      beta=beta/coolingFactor_;
    }else{
      beta=beta/coolingFactor_;
      splitAll(y);
    }


   // make sure we are not too far from equilibrium before cooling further
   niter=0; while((update(beta, tks,y)>1.e-6)  && (niter++ < maxIterations_)){ }

  }

  if(useTc_){
    // last round of splitting, make sure no critical clusters are left
    update(beta, tks,y);
    while(merge(y,beta)){update(beta, tks,y);}
    unsigned int ntry=0;
    while( split(beta, tks,y,1.) && (ntry++<10) ){
      niter=0; 
      while((update(beta, tks,y)>1.e-6)  && (niter++ < maxIterations_)){}
      merge(y,beta);
      update(beta, tks,y);
    }
  }else{
    // merge collapsed clusters 
    while(merge(y,beta)){update(beta, tks,y);}  
    if(fVerbose ){ cout << "dump after 1st merging " << endl;  dump(beta,y,tks,2);}
  }
 
  // switch on outlier rejection
  rho0=1./nt; for(vector<vertex_t>::iterator k=y.begin(); k!=y.end(); k++){ k->pk =1.; }  // democratic
  niter=0; while((update(beta, tks,y,rho0) > 1.e-8)  && (niter++ < maxIterations_)){  }
  if(fVerbose  ){ cout << "rho0=" << rho0 <<   " niter=" << niter <<  endl; dump(beta,y,tks,2);}

  
  // merge again  (some cluster split by outliers collapse here)
  while(merge(y,tks.size())){}  
  if(fVerbose  ){ cout << "dump after 2nd merging " << endl;  dump(beta,y,tks,2);}


  // continue from freeze-out to Tstop (=1) without splitting, eliminate insignificant vertices
  while(beta<=betastop_){
    while(purge(y,tks,rho0, beta)){
      niter=0; while((update(beta, tks, y, rho0) > 1.e-6)  && (niter++ < maxIterations_)){  }
    } 
    beta/=coolingFactor_;
    niter=0; while((update(beta, tks, y, rho0) > 1.e-6)  && (niter++ < maxIterations_)){  }
  }


//   // new, one last round of cleaning at T=Tstop
//   while(purge(y,tks,rho0, beta)){
//     niter=0; while((update(beta, tks,y,rho0) > 1.e-6)  && (niter++ < maxIterations_)){  }
//   } 


  if(fVerbose){
   cout << "Final result, rho0=" << rho0 << endl;
   dump(beta,y,tks,2);
  }


  // select significant tracks and use a TransientVertex as a container
  //GlobalError dummyError; 
  
  // ensure correct normalization of probabilities, should make double assginment reasonably impossible
  for(unsigned int i=0; i<nt; i++){  
    tks[i].Z=rho0*exp(-beta*( dzCutOff_*dzCutOff_));
    for(vector<vertex_t>::iterator k=y.begin(); k!=y.end(); k++){ 
      tks[i].Z += k->pk * exp(-beta*Eik(tks[i],*k));
    }
  }
  
  for(vector<vertex_t>::iterator k=y.begin(); k!=y.end(); k++){ 
    
    DelphesFactory *factory = GetFactory();
    candidate = factory->NewCandidate();
    
    //cout<<"new vertex"<<endl;
    //GlobalPoint pos(0, 0, k->z);
    double time = k->t;
    double z = k->z;
    //vector< reco::TransientTrack > vertexTracks;
    //double max_track_time_err2 = 0;
    double mean = 0.;
    double expv_x2 = 0.;
    double normw = 0.;
    for(unsigned int i=0; i<nt; i++){
      const double invdt = 1.0/std::sqrt(tks[i].dt2);
      if(tks[i].Z>0){
        double p = k->pk * exp(-beta*Eik(tks[i],*k)) / tks[i].Z;
        if( (tks[i].pi>0) && ( p > 0.5 ) ){ 
          //std::cout << "pushing back " << i << ' ' << tks[i].tt << std::endl;
          //vertexTracks.push_back(*(tks[i].tt)); tks[i].Z=0; 
          
          candidate->AddCandidate(tks[i].tt); tks[i].Z=0; 
         
          mean     += tks[i].t*invdt*p;
          expv_x2  += tks[i].t*tks[i].t*invdt*p;
          normw    += invdt*p;
        } // setting Z=0 excludes double assignment        
      }
    }
    
    mean = mean/normw;
    expv_x2 = expv_x2/normw;
    const double time_var = expv_x2 - mean*mean;    
    const double crappy_error_guess = std::sqrt(time_var);
    /*GlobalError dummyErrorWithTime(0,
                                   0,0,
                                   0,0,0,
                                   0,0,0,crappy_error_guess);*/
    //TransientVertex v(pos, time, dummyErrorWithTime, vertexTracks, 5);
   
    
    candidate->ClusterIndex = clusterIndex++;;
    //candidate->ClusterNDF = 5;
    //candidate->ClusterSigma = fSigma;
    //candidate->SumPT2 = cluster->second;
    
    // TBC units - set everything back in mm 
    
    //cout<<z<<","<<time<<endl;
    
    candidate->Position.SetXYZT(0.0, 0.0, z*10.0 , time*c_light);
    
    // TBC - fill error later ... 
    candidate->PositionError.SetXYZT(0.0, 0.0, 0.0 , crappy_error_guess*c_light);

    //fVertexOutputArray->Add(candidate);

    clusterIndex++;   
    clusters.push_back(*candidate);
  }
  

  return clusters;

}

//------------------------------------------------------------------------------

vector<VertexFinder4D::track_t> 
VertexFinder4D::fill( const TObjArray & tracks )const{
  
  Candidate *candidate;
  track_t tr;
  Double_t z, dz, t, l, dt, d0, d0error;
  
  
  // prepare track data for clustering
  vector< track_t > tks;
  
  // loop over input tracks
  fItInputArray->Reset();
  cout<<"new fill"<<endl;
  while((candidate = static_cast<Candidate*>(fItInputArray->Next())))
  {
     cout<<"new track"<<endl;
     //TBC everything in cm 
     z = candidate->DZ/10;
     tr.z = z;
     dz = candidate->ErrorDZ/10;
     tr.dz2 = dz*dz          // track error
   // TBC: beamspot size induced error, take 0 for now.        
   //   + (std::pow(beamspot.BeamWidthX()*cos(phi),2.)+std::pow(beamspot.BeamWidthY()*sin(phi),2.))/std::pow(tantheta,2.) // beam-width induced
      + vertexSize_*vertexSize_;                     // intrinsic vertex size, safer for outliers and short lived decays
    
    // TBC: the time is in ns for now TBC 
     t = candidate->Position.T()/c_light;
     l = candidate->L/c_light;
     
     tr.t = (t-l); // 
     tr.dtz = 0.;
     dt = candidate->ErrorT/c_light;
     tr.dt2 = dt*dt + 0.010*0.010;   // the ~injected~ timing error, need to add a small minimum vertex size in time
     //cout<<"t error: "<<dt<<endl;
    if (d0CutOff_>0){
    
      d0 = TMath::Abs(candidate->D0)/10.0;
      d0error = candidate->ErrorD0/10.0;
      
      tr.pi=1./(1.+exp((d0*d0)/(d0error*d0error) - d0CutOff_*d0CutOff_));  // reduce weight for high ip tracks  
     // cout<<"IP: "<<d0<<endl;
     // cout<<"IP error: "<<d0error<<endl;
    
    }else{
      tr.pi=1.;
    }
    tr.tt=&(*candidate);    
    tr.Z=1.;
    if( tr.pi > 1e-3 ) {
      tks.push_back(tr);
    }
 
   cout<<"dz2: "<<tr.dz2<<endl;
   cout<<"t: "<<tr.t<<endl;
   cout<<"z: "<<tr.z<<endl;
   cout<<"dt2: "<<tr.dt2<<endl;
   cout<<"pi: "<<tr.pi<<endl;

 
 
  }
  
  return tks;
}




//------------------------------------------------------------------------------

double VertexFinder4D::Eik(const track_t & t, const vertex_t &k ) const {
  return std::pow(t.z-k.z,2.)/t.dz2 + std::pow(t.t - k.t,2.)/t.dt2;
}
  
//--------------------------------------------------------------------------------  

void VertexFinder4D::dump(const double beta, const vector<vertex_t> & y, const vector<track_t> & tks0, int verbosity)const{

  // copy and sort for nicer printout
  vector<track_t> tks; 
  for(vector<track_t>::const_iterator t=tks0.begin(); t!=tks0.end(); t++){tks.push_back(*t); }
  std::stable_sort(tks.begin(), tks.end(), recTrackLessZ1);

  cout << "-----DAClusterizerInZT::dump ----" << endl;
  cout << " beta=" << beta << "   betamax= " << betamax_ << endl;
  cout << "                                                               z= ";
  cout.precision(4);
  for(vector<vertex_t>::const_iterator k=y.begin(); k!=y.end(); k++){
    cout  <<  setw(8) << fixed << k->z;
  }
  cout << endl << "                                                               t= ";
  for(vector<vertex_t>::const_iterator k=y.begin(); k!=y.end(); k++){
    cout  <<  setw(8) << fixed << k->t;
  }
  cout << endl << "T=" << setw(15) << 1./beta <<"                                             Tc= ";
  for(vector<vertex_t>::const_iterator k=y.begin(); k!=y.end(); k++){
    cout  <<  setw(8) << fixed << k->Tc ;
  }
 
  cout << endl << "                                                              pk=";
  double sumpk=0;
  for(vector<vertex_t>::const_iterator k=y.begin(); k!=y.end(); k++){
    cout <<  setw(8) <<  setprecision(3) <<  fixed << k->pk;
    sumpk+=k->pk;
  }
  cout  << endl;

  if(verbosity>0){
    double E=0, F=0;
    cout << endl;
    cout << "----       z +/- dz        t +/- dt        ip +/-dip       pt    phi  eta    weights  ----" << endl;
    cout.precision(4);
    for(unsigned int i=0; i<tks.size(); i++){
      if (tks[i].Z>0){  F-=log(tks[i].Z)/beta;}
      double tz= tks[i].z;
      double tt= tks[i].t;
      cout <<  setw (3)<< i << ")" <<  setw (8) << fixed << setprecision(4)<<  tz << " +/-" <<  setw (6)<< sqrt(tks[i].dz2) 
           << setw(8) << fixed << setprecision(4) << tt << " +/-" << setw(6) << std::sqrt(tks[i].dt2)  ;
      
      
      // TBC - see later if we want to keep these print outs 
      /*
      if(tks[i].tt->track().quality(reco::TrackBase::highPurity)){ cout << " *";}else{cout <<"  ";}
      if(tks[i].tt->track().hitPattern().hasValidHitInFirstPixelBarrel()){cout <<"+";}else{cout << "-";}
      
      cout << setw(1) << tks[i].tt->track().hitPattern().pixelBarrelLayersWithMeasurement(); // see DataFormats/TrackReco/interface/HitPattern.h
      cout << setw(1) << tks[i].tt->track().hitPattern().pixelEndcapLayersWithMeasurement(); 
      cout << setw(1) << hex << tks[i].tt->track().hitPattern().trackerLayersWithMeasurement()-tks[i].tt->track().hitPattern().pixelLayersWithMeasurement() <<dec; 
      cout << "=" << setw(1)<<hex <<tks[i].tt->track().trackerExpectedHitsOuter().numberOfHits() << dec;

      Measurement1D IP=tks[i].tt->stateAtBeamLine().transverseImpactParameter();
      cout << setw (8) << IP.value() << "+/-" << setw (6) << IP.error();
      cout << " " << setw(6) << setprecision(2)  << tks[i].tt->track().pt()*tks[i].tt->track().charge();
      cout << " " << setw(5) << setprecision(2) << tks[i].tt->track().phi() 
           << " "  << setw(5)  << setprecision(2)   << tks[i].tt->track().eta() ;
      */
      double sump=0.;
      for(vector<vertex_t>::const_iterator k=y.begin(); k!=y.end(); k++){
        if((tks[i].pi>0)&&(tks[i].Z>0)){
          //double p=pik(beta,tks[i],*k);
          double p=k->pk * std::exp(-beta*Eik(tks[i],*k)) / tks[i].Z; 
          if( p > 0.0001){
            cout <<  setw (8) <<  setprecision(3) << p;
          }else{
            cout << "    .   ";
          }
          E+=p*Eik(tks[i],*k);
          sump+=p;
        }else{
            cout << "        ";
        }
      }
      cout << endl;
    }
    cout << endl << "T=" << 1/beta  << " E=" << E << " n="<< y.size() << "  F= " << F <<  endl <<  "----------" << endl;
  }
}


  
  

//------------------------------------------------------------------------------


double VertexFinder4D::update( double beta,
                                  vector<track_t> & tks,
                                  vector<vertex_t> & y ) const {
  //update weights and vertex positions
  // mass constrained annealing without noise
  // returns the squared sum of changes of vertex positions

  unsigned int nt=tks.size();

  //initialize sums
  double sumpi=0;
  for(vector<vertex_t>::iterator k=y.begin(); k!=y.end(); ++k){
    k->sw=0.; k->swz=0.; k->swt = 0.; k->se=0.;
    k->swE=0.;  k->Tc=0.;
  }


  // loop over tracks
  for(unsigned int i=0; i<nt; i++){

    // update pik and Zi
    double Zi = 0.;
    for(vector<vertex_t>::iterator k=y.begin(); k!=y.end(); ++k){
      k->ei = std::exp(-beta*Eik(tks[i],*k));// cache exponential for one track at a time
      Zi   += k->pk * k->ei;      
    }
    tks[i].Z=Zi;

    // normalization for pk
    if (tks[i].Z>0){
      sumpi += tks[i].pi;
      // accumulate weighted z and weights for vertex update
      for(vector<vertex_t>::iterator k=y.begin(); k!=y.end(); ++k){
        k->se  += tks[i].pi* k->ei / Zi;
        const double w = k->pk * tks[i].pi* k->ei / ( Zi * ( tks[i].dz2 * tks[i].dt2 ) );
        k->sw  += w;
        k->swz += w * tks[i].z;
        k->swt += w * tks[i].t;
        k->swE += w * Eik(tks[i],*k);
      }
    }else{
      sumpi += tks[i].pi;
    }
    

  } // end of track loop


  // now update z and pk
  double delta=0;
  for(vector<vertex_t>::iterator k=y.begin(); k!=y.end(); k++){
    if ( k->sw > 0){
      const double znew = k->swz/k->sw; 
      const double tnew = k->swt/k->sw;
      delta += std::pow(k->z-znew,2.) + std::pow(k->t-tnew,2.);
      k->z  = znew;
      k->t  = tnew;
      k->Tc = 2.*k->swE/k->sw;
    }else{
      if(fVerbose){cout << " a cluster melted away ?  pk=" << k->pk <<  " sumw=" << k->sw <<  endl;}
      k->Tc=-1;
    }

    k->pk = k->pk * k->se / sumpi;
  }

  // return how much the prototypes moved
  return delta;
}

//------------------------------------------------------------------------------

double VertexFinder4D::update( double beta,
                                  vector<track_t> & tks,
                                  vector<vertex_t> & y,
                                  double & rho0 ) const {
  // MVF style, no more vertex weights, update tracks weights and vertex positions, with noise 
  // returns the squared sum of changes of vertex positions

  unsigned int nt=tks.size();

  //initialize sums
  for(vector<vertex_t>::iterator k=y.begin(); k!=y.end(); k++){
    k->sw = 0.;   k->swz = 0.; k->swt = 0.; k->se = 0.;    
    k->swE = 0.;  k->Tc=0.;
  }


  // loop over tracks
  for(unsigned int i=0; i<nt; i++){

    // update pik and Zi and Ti
    double Zi = rho0*std::exp(-beta*(dzCutOff_*dzCutOff_));// cut-off (eventually add finite size in time)
    //double Ti = 0.; // dt0*std::exp(-beta*dtCutOff_);
    for(vector<vertex_t>::iterator k=y.begin(); k!=y.end(); k++){
      k->ei = std::exp(-beta*Eik(tks[i],*k));// cache exponential for one track at a time
      Zi   += k->pk * k->ei;
    }
    tks[i].Z=Zi;
    
    // normalization
    if (tks[i].Z>0){
       // accumulate weighted z and weights for vertex update
      for(vector<vertex_t>::iterator k=y.begin(); k!=y.end(); k++){
        k->se += tks[i].pi* k->ei / Zi;
        double w = k->pk * tks[i].pi * k->ei /( Zi * ( tks[i].dz2 * tks[i].dt2 ) );
        k->sw  += w;
        k->swz += w * tks[i].z;
        k->swt += w * tks[i].t;
        k->swE += w * Eik(tks[i],*k);
      }
    }


  } // end of track loop


  // now update z
  double delta=0;
  for(vector<vertex_t>::iterator k=y.begin(); k!=y.end(); k++){
    if ( k->sw > 0){
      const double znew=k->swz/k->sw; 
      const double tnew=k->swt/k->sw;
      delta += std::pow(k->z-znew,2.) + std::pow(k->t-tnew,2.);
      k->z   = znew;
      k->t   = tnew;
      k->Tc  = 2*k->swE/k->sw;
    }else{
      if(fVerbose){cout << " a cluster melted away ?  pk=" << k->pk <<  " sumw=" << k->sw <<  endl;}
      k->Tc = 0;
    }

  }

  // return how much the prototypes moved
  return delta;
}

//------------------------------------------------------------------------------

bool VertexFinder4D::merge(vector<vertex_t> & y, int nt)const{
  // merge clusters that collapsed or never separated, return true if vertices were merged, false otherwise
  
  if(y.size()<2)  return false;
  
  for(vector<vertex_t>::iterator k=y.begin(); (k+1)!=y.end(); k++){
    if( std::abs( (k+1)->z - k->z ) < 1.e-3 &&
        std::abs( (k+1)->t - k->t ) < 1.e-3    ){  // with fabs if only called after freeze-out (splitAll() at highter T)
      double rho = k->pk + (k+1)->pk;
      if(rho>0){
        k->z = ( k->pk * k->z + (k+1)->z * (k+1)->pk)/rho;
        k->t = ( k->pk * k->t + (k+1)->t * (k+1)->pk)/rho;
      }else{
        k->z = 0.5*(k->z + (k+1)->z);
        k->t = 0.5*(k->t + (k+1)->t);
      }
      k->pk = rho;
      
      y.erase(k+1);
      return true;  
    }
  }
  
  return false;
}

//------------------------------------------------------------------------------

bool VertexFinder4D::merge(vector<vertex_t> & y, double & beta)const{
  // merge clusters that collapsed or never separated, 
  // only merge if the estimated critical temperature of the merged vertex is below the current temperature
  // return true if vertices were merged, false otherwise
  if(y.size()<2)  return false;

  for(vector<vertex_t>::iterator k=y.begin(); (k+1)!=y.end(); k++){
    if ( std::abs((k+1)->z - k->z) < 2.e-3 && 
         std::abs((k+1)->t - k->t) < 2.e-3    ) { 
      double rho=k->pk + (k+1)->pk;
      double swE=k->swE+(k+1)->swE - k->pk * (k+1)->pk / rho * ( std::pow((k+1)->z - k->z,2.) + 
                                                                 std::pow((k+1)->t - k->t,2.)   );
      double Tc=2*swE/(k->sw+(k+1)->sw);
      
      if(Tc*beta<1){
        if(rho>0){
          k->z = ( k->pk * k->z + (k+1)->z * (k+1)->pk)/rho;
          k->t = ( k->pk * k->t + (k+1)->t * (k+1)->pk)/rho;
        }else{
          k->z = 0.5*(k->z + (k+1)->z);
          k->t = 0.5*(k->t + (k+1)->t);
        }
        k->pk  = rho;
        k->sw += (k+1)->sw;
        k->swE = swE;
        k->Tc  = Tc;
        y.erase(k+1);
        return true; 
      }
    }
  }

  return false;
}

//------------------------------------------------------------------------------

bool VertexFinder4D::purge(vector<vertex_t> & y, vector<track_t> & tks, double & rho0, const double beta)const{
  // eliminate clusters with only one significant/unique track
  if(y.size()<2)  return false;
  
  unsigned int nt=tks.size();
  double sumpmin=nt;
  vector<vertex_t>::iterator k0=y.end();
  for(vector<vertex_t>::iterator k=y.begin(); k!=y.end(); k++){ 
    int nUnique=0;
    double sump=0;
    double pmax=k->pk/(k->pk+rho0*exp(-beta*dzCutOff_*dzCutOff_));
    for(unsigned int i=0; i<nt; i++){
      if(tks[i].Z > 0){
        double p = k->pk * std::exp(-beta*Eik(tks[i],*k)) / tks[i].Z ;
        sump+=p;
        if( (p > 0.9*pmax) && (tks[i].pi>0) ){ nUnique++; }
      }
    }

    if((nUnique<2)&&(sump<sumpmin)){
      sumpmin=sump;
      k0=k;
    }
  }
 
  if(k0!=y.end()){
    if(fVerbose){cout << "eliminating prototype at " << k0->z << "," << k0->t 
                      << " with sump=" << sumpmin << endl;}
    //rho0+=k0->pk;
    y.erase(k0);
    return true;
  }else{
    return false;
  }
}

//------------------------------------------------------------------------------

double VertexFinder4D::beta0( double betamax,
                                 vector<track_t> & tks,
                                 vector<vertex_t> & y ) const {
  
  double T0=0;  // max Tc for beta=0
  // estimate critical temperature from beta=0 (T=inf)
  unsigned int nt=tks.size();

  for(vector<vertex_t>::iterator k=y.begin(); k!=y.end(); k++){

    // vertex fit at T=inf 
    double sumwz=0.;
    double sumwt=0.;
    double sumw=0.;
    for(unsigned int i=0; i<nt; i++){
      double w = tks[i].pi/(tks[i].dz2 * tks[i].dt2);
      sumwz += w*tks[i].z;
      sumwt += w*tks[i].t;
      sumw  += w;
    }
    k->z = sumwz/sumw;
    k->t = sumwt/sumw;

    // estimate Tcrit, eventually do this in the same loop
    double a=0, b=0;
    for(unsigned int i=0; i<nt; i++){
      double dx = tks[i].z-(k->z);
      double dt = tks[i].t-(k->t);
      double w  = tks[i].pi/(tks[i].dz2 * tks[i].dt2);
      a += w*(std::pow(dx,2.)/tks[i].dz2 + std::pow(dt,2.)/tks[i].dt2);
      b += w;
    }
    double Tc= 2.*a/b;  // the critical temperature of this vertex
    if(Tc>T0) T0=Tc;
  }// vertex loop (normally there should be only one vertex at beta=0)
  
  if (T0>1./betamax){
    return betamax/pow(coolingFactor_, int(std::log(T0*betamax)/std::log(coolingFactor_))-1 );
  }else{
    // ensure at least one annealing step
    return betamax/coolingFactor_;
  }
}

//------------------------------------------------------------------------------

bool VertexFinder4D::split( double beta,
                               vector<track_t> & tks,
                               vector<vertex_t> & y,
                               double threshold ) const {
  // split only critical vertices (Tc >~ T=1/beta   <==>   beta*Tc>~1)
  // an update must have been made just before doing this (same beta, no merging)
  // returns true if at least one cluster was split

  constexpr double epsilon=1e-3;      // split all single vertices by 10 um 
  bool split=false;
  
  // avoid left-right biases by splitting highest Tc first
  
  std::vector<std::pair<double, unsigned int> > critical;
  for(unsigned int ik=0; ik<y.size(); ik++){
    if (beta*y[ik].Tc > 1.){
      critical.push_back( make_pair(y[ik].Tc, ik));
    }
  }
  std::stable_sort(critical.begin(), critical.end(), std::greater<std::pair<double, unsigned int> >() );

  for(unsigned int ic=0; ic<critical.size(); ic++){
    unsigned int ik=critical[ic].second;
    // estimate subcluster positions and weight
    double p1=0, z1=0, t1=0, w1=0;
    double p2=0, z2=0, t2=0, w2=0;
    //double sumpi=0;
    for(unsigned int i=0; i<tks.size(); i++){
      if(tks[i].Z>0){
        //sumpi+=tks[i].pi;
        double p=y[ik].pk * exp(-beta*Eik(tks[i],y[ik])) / tks[i].Z*tks[i].pi;
        double w=p/(tks[i].dz2 * tks[i].dt2);
        if(tks[i].z < y[ik].z){
          p1+=p; z1+=w*tks[i].z; t1+=w*tks[i].t; w1+=w;
        }else{
          p2+=p; z2+=w*tks[i].z; t2+=w*tks[i].t; w2+=w;
        }
      }
    }
    if(w1>0){  z1=z1/w1; t1=t1/w1;} else{ z1=y[ik].z-epsilon; t1=y[ik].t-epsilon; }
    if(w2>0){  z2=z2/w2; t2=t2/w2;} else{ z2=y[ik].z+epsilon; t2=y[ik].t+epsilon;}

    // reduce split size if there is not enough room
    if( ( ik   > 0       ) && ( y[ik-1].z>=z1 ) ){ z1=0.5*(y[ik].z+y[ik-1].z); t1=0.5*(y[ik].t+y[ik-1].t); }
    if( ( ik+1 < y.size()) && ( y[ik+1].z<=z2 ) ){ z2=0.5*(y[ik].z+y[ik+1].z); t2=0.5*(y[ik].t+y[ik+1].t); }

    // split if the new subclusters are significantly separated
    if( (z2-z1)>epsilon || std::abs(t2-t1) > epsilon){
      split=true;
      vertex_t vnew;
      vnew.pk = p1*y[ik].pk/(p1+p2);
      y[ik].pk= p2*y[ik].pk/(p1+p2);
      vnew.z  = z1;
      vnew.t  = t1;
      y[ik].z = z2;
      y[ik].t = t2;
      y.insert(y.begin()+ik, vnew);

     // adjust remaining pointers
      for(unsigned int jc=ic; jc<critical.size(); jc++){
        if (critical[jc].second>ik) {critical[jc].second++;}
      }
    }
  }

  //  stable_sort(y.begin(), y.end(), clusterLessZ);
  return split;
}

//------------------------------------------------------------------------------

void VertexFinder4D::splitAll( vector<vertex_t> & y ) const {


  constexpr double epsilon=1e-3;      // split all single vertices by 10 um 
  constexpr double zsep=2*epsilon;    // split vertices that are isolated by at least zsep (vertices that haven't collapsed)
  constexpr double tsep=2*epsilon;    // check t as well
  
  vector<vertex_t> y1;

  for(vector<vertex_t>::iterator k=y.begin(); k!=y.end(); k++){
    if ( ( (k==y.begin())|| (k-1)->z < k->z - zsep) && (((k+1)==y.end()  )|| (k+1)->z > k->z + zsep)) { 
      // isolated prototype, split
      vertex_t vnew;
      vnew.z  = k->z - epsilon;
      vnew.t  = k->t - epsilon;
      (*k).z  = k->z + epsilon;
      (*k).t  = k->t + epsilon;
      vnew.pk= 0.5* (*k).pk;
      (*k).pk= 0.5* (*k).pk;
      y1.push_back(vnew);
      y1.push_back(*k);

    }else if( y1.empty() || (y1.back().z < k->z -zsep) || (y1.back().t < k->t - tsep) ){
      y1.push_back(*k);
    }else{
      y1.back().z -= epsilon;
      y1.back().t -= epsilon;
      k->z += epsilon;
      k->t += epsilon;
      y1.push_back(*k);
    }
  }// vertex loop
  
  y=y1;
}