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[u/mrichter/AliRoot.git] / MUON / AliMUONTrack.cxx

/**************************************************************************
 * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
 *                                                                        *
 * Author: The ALICE Off-line Project.                                    *
 * Contributors are mentioned in the code where appropriate.              *
 *                                                                        *
 * Permission to use, copy, modify and distribute this software and its   *
 * documentation strictly for non-commercial purposes is hereby granted   *
 * without fee, provided that the above copyright notice appears in all   *
 * copies and that both the copyright notice and this permission notice   *
 * appear in the supporting documentation. The authors make no claims     *
 * about the suitability of this software for any purpose. It is          *
 * provided "as is" without express or implied warranty.                  *
 **************************************************************************/

/* $Id$ */

//-----------------------------------------------------------------------------
// Class AliMUONTrack
//-------------------
// Reconstructed track in ALICE dimuon spectrometer
//-----------------------------------------------------------------------------

#include "AliMUONTrack.h"

#include "AliMUONTrackParam.h" 
#include "AliMUONVCluster.h" 
#include "AliMUONObjectPair.h" 
#include "AliMUONConstants.h"
#include "AliMUONTrackExtrap.h" 

#include "AliLog.h"

#include <TMath.h>
#include <TMatrixD.h>

#include <Riostream.h>

/// \cond CLASSIMP
ClassImp(AliMUONTrack) // Class implementation in ROOT context
/// \endcond

//__________________________________________________________________________
AliMUONTrack::AliMUONTrack()
  : TObject(),
    fTrackParamAtCluster(new TClonesArray("AliMUONTrackParam",10)),
    fFitWithVertex(kFALSE),
    fVertexErrXY2(),
    fFitWithMCS(kFALSE),
    fClusterWeightsNonBending(0x0),
    fClusterWeightsBending(0x0),
    fGlobalChi2(-1.),
    fImproved(kFALSE),
    fMatchTrigger(-1),
    floTrgNum(-1),
    fChi2MatchTrigger(0.),
    fTrackID(0),
    fTrackParamAtVertex(0x0),
    fHitsPatternInTrigCh(0),
    fLocalTrigger(0)
{
  /// Default constructor
  fTrackParamAtCluster->SetOwner(kTRUE);
  fVertexErrXY2[0] = 0.;
  fVertexErrXY2[1] = 0.;
}

  //__________________________________________________________________________
AliMUONTrack::AliMUONTrack(AliMUONObjectPair *segment)
  : TObject(),
    fTrackParamAtCluster(new TClonesArray("AliMUONTrackParam",10)),
    fFitWithVertex(kFALSE),
    fVertexErrXY2(),
    fFitWithMCS(kFALSE),
    fClusterWeightsNonBending(0x0),
    fClusterWeightsBending(0x0),
    fGlobalChi2(0.),
    fImproved(kFALSE),
    fMatchTrigger(-1),
    floTrgNum(-1),    
    fChi2MatchTrigger(0.),
    fTrackID(0),
    fTrackParamAtVertex(0x0),
    fHitsPatternInTrigCh(0),
    fLocalTrigger(0)
{
  /// Constructor from two clusters
  fTrackParamAtCluster->SetOwner(kTRUE);
  
  fVertexErrXY2[0] = 0.;
  fVertexErrXY2[1] = 0.;
  
  // Pointers to clusters from the segment
  AliMUONVCluster* cluster1 = (AliMUONVCluster*) segment->First();
  AliMUONVCluster* cluster2 = (AliMUONVCluster*) segment->Second();
  
  // check sorting in -Z (spectro z<0)
  if (cluster1->GetZ() < cluster2->GetZ()) {
    cluster1 = cluster2;
    cluster2 = (AliMUONVCluster*) segment->First();
  }
  
  // order the clusters into the track according to the station the segment belong to
  //(the cluster first attached is the one from which we will start the tracking procedure)
  AliMUONVCluster *firstCluster, *lastCluster;
  if (cluster1->GetChamberId() == 8) {
    firstCluster = cluster1;
    lastCluster = cluster2;
  } else {
    firstCluster = cluster2;
    lastCluster = cluster1;
  }
  
  // Compute track parameters
  Double_t z1 = firstCluster->GetZ();
  Double_t z2 = lastCluster->GetZ();
  Double_t dZ = z1 - z2;
  // Non bending plane
  Double_t nonBendingCoor1 = firstCluster->GetX();
  Double_t nonBendingCoor2 = lastCluster->GetX();
  Double_t nonBendingSlope = (nonBendingCoor1 - nonBendingCoor2) / dZ;
  // Bending plane
  Double_t bendingCoor1 = firstCluster->GetY();
  Double_t bendingCoor2 = lastCluster->GetY();
  Double_t bendingSlope = (bendingCoor1 - bendingCoor2) / dZ;
  // Inverse bending momentum
  Double_t bendingImpact = bendingCoor1 - z1 * bendingSlope;
  Double_t inverseBendingMomentum = 1. / AliMUONTrackExtrap::GetBendingMomentumFromImpactParam(bendingImpact);
  
  
  // Set track parameters at first cluster
  AliMUONTrackParam trackParamAtFirstCluster;
  trackParamAtFirstCluster.SetZ(z1);
  trackParamAtFirstCluster.SetNonBendingCoor(nonBendingCoor1);
  trackParamAtFirstCluster.SetNonBendingSlope(nonBendingSlope);
  trackParamAtFirstCluster.SetBendingCoor(bendingCoor1);
  trackParamAtFirstCluster.SetBendingSlope(bendingSlope);
  trackParamAtFirstCluster.SetInverseBendingMomentum(inverseBendingMomentum);
  
  
  // Set track parameters at last cluster
  AliMUONTrackParam trackParamAtLastCluster;
  trackParamAtLastCluster.SetZ(z2);
  trackParamAtLastCluster.SetNonBendingCoor(nonBendingCoor2);
  trackParamAtLastCluster.SetNonBendingSlope(nonBendingSlope);
  trackParamAtLastCluster.SetBendingCoor(bendingCoor2);
  trackParamAtLastCluster.SetBendingSlope(bendingSlope);
  trackParamAtLastCluster.SetInverseBendingMomentum(inverseBendingMomentum);
  
  
  // Compute and set track parameters covariances at first cluster
  TMatrixD paramCov1(5,5);
  paramCov1.Zero();
  // Non bending plane
  paramCov1(0,0) = firstCluster->GetErrX2();
  paramCov1(0,1) = firstCluster->GetErrX2() / dZ;
  paramCov1(1,0) = paramCov1(0,1);
  paramCov1(1,1) = ( firstCluster->GetErrX2() + lastCluster->GetErrX2() ) / dZ / dZ;
  // Bending plane
  paramCov1(2,2) = firstCluster->GetErrY2();
  paramCov1(2,3) = firstCluster->GetErrY2() / dZ;
  paramCov1(3,2) = paramCov1(2,3);
  paramCov1(3,3) = ( firstCluster->GetErrY2() + lastCluster->GetErrY2() ) / dZ / dZ;
  // Inverse bending momentum (50% error)
  paramCov1(4,4) = 0.5*inverseBendingMomentum * 0.5*inverseBendingMomentum;
  // Set covariances
  trackParamAtFirstCluster.SetCovariances(paramCov1);
  
  
  // Compute and set track parameters covariances at last cluster (as if the first cluster did not exist)
  TMatrixD paramCov2(5,5);
  paramCov2.Zero();
  // Non bending plane
  paramCov2(0,0) = paramCov1(0,0);
  paramCov2(1,1) = 100.*paramCov1(1,1);
  // Bending plane
  paramCov2(2,2) = paramCov1(2,2);
  paramCov2(3,3) = 100.*paramCov1(3,3);
  // Inverse bending momentum
  paramCov2(4,4) = paramCov1(4,4);
  // Set covariances
  trackParamAtLastCluster.SetCovariances(paramCov2);
  
  // Flag clusters as being removable
  trackParamAtFirstCluster.SetRemovable(kTRUE);
  trackParamAtLastCluster.SetRemovable(kTRUE);
  
  // Add track parameters at clusters
  AddTrackParamAtCluster(trackParamAtFirstCluster,*firstCluster);
  AddTrackParamAtCluster(trackParamAtLastCluster,*lastCluster);
  
}

  //__________________________________________________________________________
AliMUONTrack::AliMUONTrack(const AliMUONTrack& track)
  : TObject(track),
    fTrackParamAtCluster(new TClonesArray("AliMUONTrackParam",10)),
    fFitWithVertex(track.fFitWithVertex),
    fVertexErrXY2(),
    fFitWithMCS(track.fFitWithMCS),
    fClusterWeightsNonBending(0x0),
    fClusterWeightsBending(0x0),
    fGlobalChi2(track.fGlobalChi2),
    fImproved(track.fImproved),
    fMatchTrigger(track.fMatchTrigger),
    floTrgNum(track.floTrgNum),    
    fChi2MatchTrigger(track.fChi2MatchTrigger),
    fTrackID(track.fTrackID),
    fTrackParamAtVertex(0x0),
    fHitsPatternInTrigCh(track.fHitsPatternInTrigCh),
    fLocalTrigger(track.fLocalTrigger)
{
  ///copy constructor
  
  // necessary to make a copy of the objects and not only the pointers in TClonesArray.
  AliMUONTrackParam *trackParamAtCluster = (AliMUONTrackParam*) track.fTrackParamAtCluster->First();
  while (trackParamAtCluster) {
    new ((*fTrackParamAtCluster)[GetNClusters()]) AliMUONTrackParam(*trackParamAtCluster);
    trackParamAtCluster = (AliMUONTrackParam*) track.fTrackParamAtCluster->After(trackParamAtCluster);
  }
  
  // copy vertex resolution square used during the tracking procedure
  fVertexErrXY2[0] = track.fVertexErrXY2[0];
  fVertexErrXY2[1] = track.fVertexErrXY2[1];
  
  // copy cluster weights matrices if any
  if (track.fClusterWeightsNonBending) fClusterWeightsNonBending = new TMatrixD(*(track.fClusterWeightsNonBending));
  if (track.fClusterWeightsBending) fClusterWeightsBending = new TMatrixD(*(track.fClusterWeightsBending));
  
  // copy track parameters at vertex if any
  if (track.fTrackParamAtVertex) fTrackParamAtVertex = new AliMUONTrackParam(*(track.fTrackParamAtVertex));
  
}

  //__________________________________________________________________________
AliMUONTrack & AliMUONTrack::operator=(const AliMUONTrack& track)
{
  /// Asignment operator
  // check assignement to self
  if (this == &track)
    return *this;

  // base class assignement
  TObject::operator=(track);

  // necessary to make a copy of the objects and not only the pointers in TClonesArray.
  fTrackParamAtCluster = new TClonesArray("AliMUONTrackParam",10);
  AliMUONTrackParam *trackParamAtCluster = (AliMUONTrackParam*) track.fTrackParamAtCluster->First();
  while (trackParamAtCluster) {
    new ((*fTrackParamAtCluster)[GetNClusters()]) AliMUONTrackParam(*trackParamAtCluster);
    trackParamAtCluster = (AliMUONTrackParam*) track.fTrackParamAtCluster->After(trackParamAtCluster);
  }
  
  // copy cluster weights matrix if any
  if (track.fClusterWeightsNonBending) {
    if (fClusterWeightsNonBending) {
      fClusterWeightsNonBending->ResizeTo(*(track.fClusterWeightsNonBending));
      *fClusterWeightsNonBending = *(track.fClusterWeightsNonBending);
    } else fClusterWeightsNonBending = new TMatrixD(*(track.fClusterWeightsNonBending));
  } else if (fClusterWeightsNonBending) {
    delete fClusterWeightsNonBending;
    fClusterWeightsNonBending = 0x0;
  }
  
  // copy cluster weights matrix if any
  if (track.fClusterWeightsBending) {
    if (fClusterWeightsBending) {
      fClusterWeightsBending->ResizeTo(*(track.fClusterWeightsBending));
      *fClusterWeightsBending = *(track.fClusterWeightsBending);
    } else fClusterWeightsBending = new TMatrixD(*(track.fClusterWeightsBending));
  } else if (fClusterWeightsBending) {
    delete fClusterWeightsBending;
    fClusterWeightsBending = 0x0;
  }
  
  // copy track parameters at vertex if any
  if (track.fTrackParamAtVertex) {
    if (fTrackParamAtVertex) *fTrackParamAtVertex = *(track.fTrackParamAtVertex);
    else fTrackParamAtVertex = new AliMUONTrackParam(*(track.fTrackParamAtVertex));
  } else if (fTrackParamAtVertex) {
    delete fTrackParamAtVertex;
    fTrackParamAtVertex = 0x0;
  }
  
  fFitWithVertex      =  track.fFitWithVertex;
  fVertexErrXY2[0]    =  track.fVertexErrXY2[0];
  fVertexErrXY2[1]    =  track.fVertexErrXY2[1];
  fFitWithMCS         =  track.fFitWithMCS;
  fGlobalChi2         =  track.fGlobalChi2;
  fImproved           =  track.fImproved;
  fMatchTrigger       =  track.fMatchTrigger;
  floTrgNum           =  track.floTrgNum;
  fChi2MatchTrigger   =  track.fChi2MatchTrigger;
  fTrackID            =  track.fTrackID; 
  fHitsPatternInTrigCh = track.fHitsPatternInTrigCh;
  fLocalTrigger        = track.fLocalTrigger;

  return *this;
}

  //__________________________________________________________________________
AliMUONTrack::~AliMUONTrack()
{
  /// Destructor
  delete fTrackParamAtCluster;
  delete fClusterWeightsNonBending;
  delete fClusterWeightsBending;
  delete fTrackParamAtVertex;
}

  //__________________________________________________________________________
void AliMUONTrack::Clear(Option_t* opt)
{
  /// Clear arrays
  fTrackParamAtCluster->Clear(opt);
  delete fClusterWeightsNonBending; fClusterWeightsNonBending = 0x0;
  delete fClusterWeightsBending; fClusterWeightsBending = 0x0;
  delete fTrackParamAtVertex; fTrackParamAtVertex = 0x0;
}

  //__________________________________________________________________________
void AliMUONTrack::AddTrackParamAtCluster(const AliMUONTrackParam &trackParam, AliMUONVCluster &cluster, Bool_t copy)
{
  /// Copy given track parameters into a new TrackParamAtCluster
  /// Link parameters with the associated cluster
  /// If copy=kTRUE: the cluster is copied then passed the trackParam which become its owner 
  ///     otherwise: make sure to do not delete the cluster until it is used by the track
  
  // check chamber ID of the associated cluster
  if (cluster.GetChamberId() < 0 || cluster.GetChamberId() > AliMUONConstants::NTrackingCh()) {
    AliError(Form("Chamber ID of the associated cluster is not valid (ChamberId=%d)",cluster.GetChamberId()));
    return;
  }
  
  // check whether track parameters are given at the correct cluster z position
  if (cluster.GetZ() != trackParam.GetZ()) {
    AliError("track parameters are given at a different z position than the one of the associated cluster");
    return;
  }
  
  // add parameters to the array of track parameters
  AliMUONTrackParam* trackParamAtCluster = new ((*fTrackParamAtCluster)[GetNClusters()]) AliMUONTrackParam(trackParam);
  
  // link parameters with the associated cluster or its copy
  if (copy) {
    AliMUONVCluster *clusterCopy = static_cast<AliMUONVCluster*>(cluster.Clone());
    trackParamAtCluster->SetClusterPtr(clusterCopy, kTRUE);
  } else trackParamAtCluster->SetClusterPtr(&cluster);
}

  //__________________________________________________________________________
void AliMUONTrack::RemoveTrackParamAtCluster(AliMUONTrackParam *trackParam)
{
  /// Remove trackParam from the array of TrackParamAtCluster
  if (!fTrackParamAtCluster->Remove(trackParam)) {
    AliWarning("object to remove does not exist in array fTrackParamAtCluster");
    return;
  }
  
  fTrackParamAtCluster->Compress();
}

  //__________________________________________________________________________
void AliMUONTrack::UpdateTrackParamAtCluster()
{
  /// Update track parameters at each attached cluster
  
  if (GetNClusters() == 0) {
    AliWarning("no cluster attached to the track");
    return;
  }
  
  AliMUONTrackParam* startingTrackParam = (AliMUONTrackParam*) fTrackParamAtCluster->First();
  AliMUONTrackParam* trackParamAtCluster = (AliMUONTrackParam*) fTrackParamAtCluster->After(startingTrackParam);
  while (trackParamAtCluster) {
    
    // reset track parameters and their covariances
    trackParamAtCluster->SetParameters(startingTrackParam->GetParameters());
    trackParamAtCluster->SetZ(startingTrackParam->GetZ());
    
    // extrapolation to the given z
    AliMUONTrackExtrap::ExtrapToZ(trackParamAtCluster, trackParamAtCluster->GetClusterPtr()->GetZ());
    
    // prepare next step
    startingTrackParam = trackParamAtCluster;
    trackParamAtCluster = (AliMUONTrackParam*) (fTrackParamAtCluster->After(trackParamAtCluster));
  }

}

  //__________________________________________________________________________
void AliMUONTrack::UpdateCovTrackParamAtCluster()
{
  /// Update track parameters and their covariances at each attached cluster
  /// Include effects of multiple scattering in chambers
  
  if (GetNClusters() == 0) {
    AliWarning("no cluster attached to the track");
    return;
  }
  
  AliMUONTrackParam* startingTrackParam = (AliMUONTrackParam*) fTrackParamAtCluster->First();
  AliMUONTrackParam* trackParamAtCluster = (AliMUONTrackParam*) fTrackParamAtCluster->After(startingTrackParam);
  Int_t expectedChamber = startingTrackParam->GetClusterPtr()->GetChamberId() + 1;
  Int_t currentChamber;
  while (trackParamAtCluster) {
    
    // reset track parameters and their covariances
    trackParamAtCluster->SetParameters(startingTrackParam->GetParameters());
    trackParamAtCluster->SetZ(startingTrackParam->GetZ());
    trackParamAtCluster->SetCovariances(startingTrackParam->GetCovariances());
    
    // add MCS effect
    AliMUONTrackExtrap::AddMCSEffect(trackParamAtCluster,AliMUONConstants::ChamberThicknessInX0(),1.);
    
    // add MCS in missing chambers if any
    currentChamber = trackParamAtCluster->GetClusterPtr()->GetChamberId();
    while (currentChamber > expectedChamber) {
      // extrapolation to the missing chamber
      AliMUONTrackExtrap::ExtrapToZCov(trackParamAtCluster, AliMUONConstants::DefaultChamberZ(expectedChamber));
      // add MCS effect
      AliMUONTrackExtrap::AddMCSEffect(trackParamAtCluster,AliMUONConstants::ChamberThicknessInX0(),1.);
      expectedChamber++;
    }
    
    // extrapolation to the z of the current cluster
    AliMUONTrackExtrap::ExtrapToZCov(trackParamAtCluster, trackParamAtCluster->GetClusterPtr()->GetZ());
    
    // prepare next step
    expectedChamber = currentChamber + 1;
    startingTrackParam = trackParamAtCluster;
    trackParamAtCluster = (AliMUONTrackParam*) (fTrackParamAtCluster->After(trackParamAtCluster));
  }
  
}

  //__________________________________________________________________________
Bool_t AliMUONTrack::ComputeLocalChi2(Bool_t accountForMCS)
{
  /// Compute each cluster contribution to the chi2 of the track
  /// accounting for multiple scattering or not according to the flag
  /// - Also recompute the weight matrices of the attached clusters if accountForMCS=kTRUE
  /// - Assume that track parameters at each cluster are corrects
  /// - Return kFALSE if computation failed
  
  if (accountForMCS) { // Compute local chi2 taking into account multiple scattering effects
      
    // Compute MCS covariance matrix only once
    Int_t nClusters = GetNClusters();
    TMatrixD mcsCovariances(nClusters,nClusters);
    ComputeMCSCovariances(mcsCovariances);
    
    // Make sure cluster weights are consistent with following calculations
    if (!ComputeClusterWeights(&mcsCovariances)) {
      AliWarning("cannot take into account the multiple scattering effects");
      return ComputeLocalChi2(kFALSE);
    }
    
    // Compute chi2 of the track
    Double_t globalChi2 = ComputeGlobalChi2(kTRUE);
    if (globalChi2 < 0.) return kFALSE;
    
    // Loop over removable clusters and compute their local chi2
    AliMUONTrackParam* trackParamAtCluster1;
    AliMUONVCluster *cluster, *discardedCluster;
    Int_t iCluster1, iCluster2, iCurrentCluster1, iCurrentCluster2;
    TMatrixD ClusterWeightsNB(nClusters-1,nClusters-1);
    TMatrixD ClusterWeightsB(nClusters-1,nClusters-1);
    Double_t *dX = new Double_t[nClusters-1];
    Double_t *dY = new Double_t[nClusters-1];
    Double_t globalChi2b;
    AliMUONTrackParam* trackParamAtCluster = (AliMUONTrackParam*) fTrackParamAtCluster->First();
    while (trackParamAtCluster) {
      
      discardedCluster = trackParamAtCluster->GetClusterPtr();
      
      // Recompute cluster weights without the current cluster
      if (!ComputeClusterWeights(ClusterWeightsNB, ClusterWeightsB, &mcsCovariances, discardedCluster)) {
  	AliWarning("cannot take into account the multiple scattering effects");
	delete [] dX;
	delete [] dY;
	return ComputeLocalChi2(kFALSE);
      }
      
      // Compute track chi2 without the current cluster
      globalChi2b = 0.;
      iCurrentCluster1 = 0;
      for (iCluster1 = 0; iCluster1 < nClusters ; iCluster1++) { 
    	trackParamAtCluster1 = (AliMUONTrackParam*) fTrackParamAtCluster->UncheckedAt(iCluster1);
    	cluster = trackParamAtCluster1->GetClusterPtr();
        
        if (cluster == discardedCluster) continue;
        
        // Compute and save residuals
    	dX[iCurrentCluster1] = cluster->GetX() - trackParamAtCluster1->GetNonBendingCoor();
    	dY[iCurrentCluster1] = cluster->GetY() - trackParamAtCluster1->GetBendingCoor();
        
        iCurrentCluster2 = 0;
    	for (iCluster2 = 0; iCluster2 < iCluster1; iCluster2++) {
    	  cluster = ((AliMUONTrackParam*) fTrackParamAtCluster->UncheckedAt(iCluster2))->GetClusterPtr();
          
          if (cluster == discardedCluster) continue;
          
          // Add contribution from covariances
          globalChi2b += (ClusterWeightsNB(iCurrentCluster1, iCurrentCluster2) +
        		  ClusterWeightsNB(iCurrentCluster2, iCurrentCluster1)) * dX[iCurrentCluster1] * dX[iCurrentCluster2] +
        		 (ClusterWeightsB(iCurrentCluster1, iCurrentCluster2) +
        		  ClusterWeightsB(iCurrentCluster2, iCurrentCluster1)) * dY[iCurrentCluster1] * dY[iCurrentCluster2];
          
          iCurrentCluster2++;
    	}
        
        // Add contribution from variances
    	globalChi2b += ClusterWeightsNB(iCurrentCluster1, iCurrentCluster1) * dX[iCurrentCluster1] * dX[iCurrentCluster1] +
        	       ClusterWeightsB(iCurrentCluster1, iCurrentCluster1) * dY[iCurrentCluster1] * dY[iCurrentCluster1];
    	
        iCurrentCluster1++;
      }

      // Set local chi2
      trackParamAtCluster->SetLocalChi2(globalChi2 - globalChi2b);
      
      trackParamAtCluster = (AliMUONTrackParam*) fTrackParamAtCluster->After(trackParamAtCluster);
    }
    
    delete [] dX;
    delete [] dY;
    
  } else { // without multiple scattering effects
    
    AliMUONVCluster *discardedCluster;
    Double_t dX, dY;
    AliMUONTrackParam* trackParamAtCluster = (AliMUONTrackParam*) fTrackParamAtCluster->First();
    while (trackParamAtCluster) {
      
      discardedCluster = trackParamAtCluster->GetClusterPtr();
      
      // Compute residuals
      dX = discardedCluster->GetX() - trackParamAtCluster->GetNonBendingCoor();
      dY = discardedCluster->GetY() - trackParamAtCluster->GetBendingCoor();
      
      // Set local chi2
      trackParamAtCluster->SetLocalChi2(dX * dX / discardedCluster->GetErrX2() + dY * dY / discardedCluster->GetErrY2());
    
      trackParamAtCluster = (AliMUONTrackParam*) fTrackParamAtCluster->After(trackParamAtCluster);
    }
  
  }
  
  return kTRUE;
  
}

  //__________________________________________________________________________
Double_t AliMUONTrack::ComputeGlobalChi2(Bool_t accountForMCS)
{
  /// Compute the chi2 of the track accounting for multiple scattering or not according to the flag
  /// - Assume that track parameters at each cluster are corrects
  /// - Assume the cluster weights matrices are corrects
  /// - Return negative value if chi2 computation failed
  
  Double_t chi2 = 0.;
  
  if (accountForMCS) {
    
    // Check the weight matrices. If weight matrices are not available compute chi2 without MCS
    if (!fClusterWeightsNonBending || !fClusterWeightsBending) {
      AliWarning("cluster weights including multiple scattering effects are not available\n\t\t --> compute chi2 WITHOUT multiple scattering");
      return ComputeGlobalChi2(kFALSE);
    }
    Int_t nClusters = GetNClusters();
    if (fClusterWeightsNonBending->GetNrows() != nClusters || fClusterWeightsBending->GetNcols() != nClusters) {
      AliWarning("cluster weights including multiple scattering effects are not available\n\t\t --> compute chi2 WITHOUT multiple scattering");
      return ComputeGlobalChi2(kFALSE);
    }
    
    // Compute chi2
    AliMUONVCluster *cluster;
    Double_t *dX = new Double_t[nClusters];
    Double_t *dY = new Double_t[nClusters];
    AliMUONTrackParam* trackParamAtCluster;
    for (Int_t iCluster1 = 0; iCluster1 < nClusters; iCluster1++) { 
      trackParamAtCluster = (AliMUONTrackParam*) fTrackParamAtCluster->UncheckedAt(iCluster1);
      cluster = trackParamAtCluster->GetClusterPtr();
      dX[iCluster1] = cluster->GetX() - trackParamAtCluster->GetNonBendingCoor();
      dY[iCluster1] = cluster->GetY() - trackParamAtCluster->GetBendingCoor();
      for (Int_t iCluster2 = 0; iCluster2 < iCluster1; iCluster2++) {
        chi2 += ((*fClusterWeightsNonBending)(iCluster1, iCluster2) + (*fClusterWeightsNonBending)(iCluster2, iCluster1)) * dX[iCluster1] * dX[iCluster2] +
		((*fClusterWeightsBending)(iCluster1, iCluster2) + (*fClusterWeightsBending)(iCluster2, iCluster1)) * dY[iCluster1] * dY[iCluster2];
      }
      chi2 += ((*fClusterWeightsNonBending)(iCluster1, iCluster1) * dX[iCluster1] * dX[iCluster1]) +
	      ((*fClusterWeightsBending)(iCluster1, iCluster1) * dY[iCluster1] * dY[iCluster1]);
    }
    delete [] dX;
    delete [] dY;
    
  } else {
    
    AliMUONVCluster *cluster;
    Double_t dX, dY;
    AliMUONTrackParam* trackParamAtCluster;
    Int_t nClusters = GetNClusters();
    for (Int_t iCluster = 0; iCluster < nClusters ; iCluster++) { 
      trackParamAtCluster = (AliMUONTrackParam*) fTrackParamAtCluster->UncheckedAt(iCluster);
      cluster = trackParamAtCluster->GetClusterPtr();
      dX = cluster->GetX() - trackParamAtCluster->GetNonBendingCoor();
      dY = cluster->GetY() - trackParamAtCluster->GetBendingCoor();
      chi2 += dX * dX / cluster->GetErrX2() + dY * dY / cluster->GetErrY2();
    }
    
  }
  
  return chi2;
  
}

  //__________________________________________________________________________
Bool_t AliMUONTrack::ComputeClusterWeights(TMatrixD* mcsCovariances)
{
  /// Compute the weight matrices of the attached clusters, in non bending and bending direction,
  /// accounting for multiple scattering correlations and cluster resolution
  /// - Use the provided MCS covariance matrix if any (otherwise build it temporarily)
  /// - Assume that track parameters at each cluster are corrects
  /// - Return kFALSE if computation failed
  
  // Alocate memory
  Int_t nClusters = GetNClusters();
  if (!fClusterWeightsNonBending) fClusterWeightsNonBending = new TMatrixD(nClusters,nClusters);
  if (!fClusterWeightsBending) fClusterWeightsBending = new TMatrixD(nClusters,nClusters);
  
  // Compute weights matrices
  if (!ComputeClusterWeights(*fClusterWeightsNonBending, *fClusterWeightsBending, mcsCovariances)) return kFALSE;
  
  return kTRUE;
  
}

  //__________________________________________________________________________
Bool_t AliMUONTrack::ComputeClusterWeights(TMatrixD& ClusterWeightsNB, TMatrixD& ClusterWeightsB,
					   TMatrixD* mcsCovariances, AliMUONVCluster* discardedCluster) const
{
  /// Compute the weight matrices, in non bending and bending direction,
  /// of the other attached clusters assuming the discarded one does not exist
  /// accounting for multiple scattering correlations and cluster resolution
  /// - Use the provided MCS covariance matrix if any (otherwise build it temporarily)
  /// - Return kFALSE if computation failed
  
  // Check MCS covariance matrix and recompute it if need
  Int_t nClusters = GetNClusters();
  Bool_t deleteMCSCov = kFALSE;
  if (!mcsCovariances) {
    mcsCovariances = new TMatrixD(nClusters,nClusters);
    deleteMCSCov = kTRUE;
    ComputeMCSCovariances(*mcsCovariances);
  }
  
  // Resize the weights matrices; alocate memory
  if (discardedCluster) {
    ClusterWeightsNB.ResizeTo(nClusters-1,nClusters-1);
    ClusterWeightsB.ResizeTo(nClusters-1,nClusters-1);
  } else {
    ClusterWeightsNB.ResizeTo(nClusters,nClusters);
    ClusterWeightsB.ResizeTo(nClusters,nClusters);
  }
  
  // Define variables
  AliMUONVCluster *cluster1, *cluster2;
  Int_t iCurrentCluster1, iCurrentCluster2;
  
  // Compute the covariance matrices
  iCurrentCluster1 = 0;
  for (Int_t iCluster1 = 0; iCluster1 < nClusters; iCluster1++) { 
    cluster1 = ((AliMUONTrackParam*) fTrackParamAtCluster->UncheckedAt(iCluster1))->GetClusterPtr();
    
    if (cluster1 == discardedCluster) continue;
    
    // Loop over next clusters
    iCurrentCluster2 = iCurrentCluster1;
    for (Int_t iCluster2 = iCluster1; iCluster2 < nClusters; iCluster2++) {
      cluster2 = ((AliMUONTrackParam*) fTrackParamAtCluster->UncheckedAt(iCluster2))->GetClusterPtr();
      
      if (cluster2 == discardedCluster) continue;
      
      // Fill with MCS covariances
      ClusterWeightsNB(iCurrentCluster1, iCurrentCluster2) = (*mcsCovariances)(iCluster1,iCluster2);
      
      // Equal contribution from multiple scattering in non bending and bending directions
      ClusterWeightsB(iCurrentCluster1, iCurrentCluster2) = ClusterWeightsNB(iCurrentCluster1, iCurrentCluster2);
      
      // Add contribution from cluster resolution to diagonal element and symmetrize the matrix
      if (iCurrentCluster1 == iCurrentCluster2) {
	
	// In non bending plane
        ClusterWeightsNB(iCurrentCluster1, iCurrentCluster1) += cluster1->GetErrX2();
	// In bending plane
	ClusterWeightsB(iCurrentCluster1, iCurrentCluster1) += cluster1->GetErrY2();
	
      } else {
	
	// In non bending plane
	ClusterWeightsNB(iCurrentCluster2, iCurrentCluster1) = ClusterWeightsNB(iCurrentCluster1, iCurrentCluster2);
	// In bending plane
	ClusterWeightsB(iCurrentCluster2, iCurrentCluster1) = ClusterWeightsB(iCurrentCluster1, iCurrentCluster2);
	
      }
      
      iCurrentCluster2++;
    }
    
    iCurrentCluster1++;
  }
    
  // Inversion of covariance matrices to get the weights
  if (ClusterWeightsNB.Determinant() != 0 && ClusterWeightsB.Determinant() != 0) {
    ClusterWeightsNB.Invert();
    ClusterWeightsB.Invert();
  } else {
    AliWarning(" Determinant = 0");
    ClusterWeightsNB.ResizeTo(0,0);
    ClusterWeightsB.ResizeTo(0,0);
    if(deleteMCSCov) delete mcsCovariances;
    return kFALSE;
  }
  
  if(deleteMCSCov) delete mcsCovariances;
  
  return kTRUE;
  
}

  //__________________________________________________________________________
void AliMUONTrack::ComputeMCSCovariances(TMatrixD& mcsCovariances) const
{
  /// Compute the multiple scattering covariance matrix
  /// (assume that track parameters at each cluster are corrects)
  
  // Reset the size of the covariance matrix if needed
  Int_t nClusters = GetNClusters();
  if (mcsCovariances.GetNrows() != nClusters) mcsCovariances.ResizeTo(nClusters,nClusters);
  
  // Define variables
  Int_t nChambers = AliMUONConstants::NTrackingCh();
  AliMUONTrackParam* trackParamAtCluster;
  AliMUONTrackParam extrapTrackParam;
  Int_t currentChamber = 0, expectedChamber = 0, size = 0;
  Double_t *mcsAngle2 = new Double_t[2*nChambers];
  Double_t *zMCS = new Double_t[2*nChambers];
  Int_t *indices = new Int_t[2*nClusters];
  
  // Compute multiple scattering dispersion angle at each chamber
  // and save the z position where it is calculated
  for (Int_t iCluster = 0; iCluster < nClusters; iCluster++) {
    trackParamAtCluster = (AliMUONTrackParam*) fTrackParamAtCluster->UncheckedAt(iCluster);
    
    // look for missing chambers if any
    currentChamber = trackParamAtCluster->GetClusterPtr()->GetChamberId();
    while (currentChamber > expectedChamber) {
      
      // Save the z position where MCS dispersion is calculated
      zMCS[size] = AliMUONConstants::DefaultChamberZ(expectedChamber);
      
      // Do not take into account MCS in chambers prior the first cluster
      if (iCluster > 0) {
        
        // Get track parameters at missing chamber z
        extrapTrackParam = *trackParamAtCluster;
        AliMUONTrackExtrap::ExtrapToZ(&extrapTrackParam, zMCS[size]);
        
        // Save multiple scattering dispersion angle in missing chamber
        mcsAngle2[size] = AliMUONTrackExtrap::GetMCSAngle2(extrapTrackParam,AliMUONConstants::ChamberThicknessInX0(),1.);
        
      } else mcsAngle2[size] = 0.;
      
      expectedChamber++;
      size++;
    }
    
    // Save z position where MCS dispersion is calculated
    zMCS[size] = trackParamAtCluster->GetZ();
    
    // Save multiple scattering dispersion angle in current chamber
    mcsAngle2[size] = AliMUONTrackExtrap::GetMCSAngle2(*trackParamAtCluster,AliMUONConstants::ChamberThicknessInX0(),1.);
    
    // Save indice in zMCS array corresponding to the current cluster
    indices[iCluster] = size;
    
    expectedChamber = currentChamber + 1;
    size++;
  }
  
  // complete array of z if last cluster is on the last but one chamber
  if (currentChamber != nChambers-1) zMCS[size++] = AliMUONConstants::DefaultChamberZ(nChambers-1);
  
  // Compute the covariance matrix
  for (Int_t iCluster1 = 0; iCluster1 < nClusters; iCluster1++) { 
    
    for (Int_t iCluster2 = iCluster1; iCluster2 < nClusters; iCluster2++) {
      
      // Initialization to 0 (diagonal plus upper triangular part)
      mcsCovariances(iCluster1,iCluster2) = 0.;
      
      // Compute contribution from multiple scattering in upstream chambers
      for (Int_t k = 0; k < indices[iCluster1]; k++) { 	
	mcsCovariances(iCluster1,iCluster2) += (zMCS[indices[iCluster1]] - zMCS[k]) * (zMCS[indices[iCluster2]] - zMCS[k]) * mcsAngle2[k];
      }
      
      // Symetrize the matrix
      mcsCovariances(iCluster2,iCluster1) = mcsCovariances(iCluster1,iCluster2);
    }
    
  }
    
  delete [] mcsAngle2;
  delete [] zMCS;
  delete [] indices;
  
}

  //__________________________________________________________________________
Int_t AliMUONTrack::ClustersInCommon(AliMUONTrack* track) const
{
  /// Returns the number of clusters in common between the current track ("this")
  /// and the track pointed to by "track".
  Int_t clustersInCommon = 0;
  AliMUONTrackParam *trackParamAtCluster1, *trackParamAtCluster2;
  // Loop over clusters of first track
  trackParamAtCluster1 = (AliMUONTrackParam*) this->fTrackParamAtCluster->First();
  while (trackParamAtCluster1) {
    // Loop over clusters of second track
    trackParamAtCluster2 = (AliMUONTrackParam*) track->fTrackParamAtCluster->First();
    while (trackParamAtCluster2) {
      // Increment "clustersInCommon" if both trackParamAtCluster1 & 2 point to the same cluster
      if ((trackParamAtCluster1->GetClusterPtr()) == (trackParamAtCluster2->GetClusterPtr())) {
        clustersInCommon++;
	break;
      }
      trackParamAtCluster2 = (AliMUONTrackParam*) track->fTrackParamAtCluster->After(trackParamAtCluster2);
    } // trackParamAtCluster2
    trackParamAtCluster1 = (AliMUONTrackParam*) this->fTrackParamAtCluster->After(trackParamAtCluster1);
  } // trackParamAtCluster1
  return clustersInCommon;
}

  //__________________________________________________________________________
Double_t AliMUONTrack::GetNormalizedChi2() const
{
  /// return the chi2 value divided by the number of degrees of freedom (or 1.e10 if ndf < 0)
  
  Double_t numberOfDegFree = (2. * GetNClusters() - 5.);
  if (numberOfDegFree > 0.) return fGlobalChi2 / numberOfDegFree;
  else return 1.e10;
}

  //__________________________________________________________________________
Bool_t* AliMUONTrack::CompatibleTrack(AliMUONTrack *track, Double_t sigma2Cut) const
{
  /// for each chamber: return kTRUE (kFALSE) if clusters are compatible (not compatible)
  AliMUONTrackParam *trackParamAtCluster1, *trackParamAtCluster2;
  AliMUONVCluster *cluster1, *cluster2;
  Double_t chi2, dX, dY, dZ;
  Double_t chi2Max = sigma2Cut * sigma2Cut;
  Double_t dZMax = 1.; // 1 cm
  
  Bool_t *compatibleCluster = new Bool_t[AliMUONConstants::NTrackingCh()]; 
  for ( Int_t ch = 0; ch < AliMUONConstants::NTrackingCh(); ch++) compatibleCluster[ch] = kFALSE;

  // Loop over clusters of first track
  trackParamAtCluster1 = (AliMUONTrackParam*) this->fTrackParamAtCluster->First();
  while (trackParamAtCluster1) {
    
    cluster1 = trackParamAtCluster1->GetClusterPtr();
    
    // Loop over clusters of second track
    trackParamAtCluster2 = (AliMUONTrackParam*) track->fTrackParamAtCluster->First();
    while (trackParamAtCluster2) {
      
      cluster2 = trackParamAtCluster2->GetClusterPtr();
      
      //prepare next step
      trackParamAtCluster2 = (AliMUONTrackParam*) track->fTrackParamAtCluster->After(trackParamAtCluster2);
      
      // z direction
      dZ = cluster1->GetZ() - cluster2->GetZ();
      if (dZ > dZMax) continue;
      
      // non bending direction
      dX = cluster1->GetX() - cluster2->GetX();
      chi2 = dX * dX / (cluster1->GetErrX2() + cluster2->GetErrX2());
      if (chi2 > chi2Max) continue;
      
      // bending direction
      dY = cluster1->GetY() - cluster2->GetY();
      chi2 = dY * dY / (cluster1->GetErrY2() + cluster2->GetErrY2());
      if (chi2 > chi2Max) continue;
      
      compatibleCluster[cluster1->GetChamberId()] = kTRUE;
      break;
    }
    
    trackParamAtCluster1 = (AliMUONTrackParam*) this->fTrackParamAtCluster->After(trackParamAtCluster1);
  }
  
  return compatibleCluster;
}

//__________________________________________________________________________
AliMUONTrackParam* AliMUONTrack::GetTrackParamAtVertex()
{
  /// return reference to track parameters at vertex (create it before if needed)
  if (!fTrackParamAtVertex) fTrackParamAtVertex = new AliMUONTrackParam();
  return fTrackParamAtVertex;
}

//__________________________________________________________________________
void AliMUONTrack::SetTrackParamAtVertex(const AliMUONTrackParam* trackParam)
{
  /// set track parameters at vertex
  if (trackParam == 0x0) return;
  if (fTrackParamAtVertex) *fTrackParamAtVertex = *trackParam;
  else fTrackParamAtVertex = new AliMUONTrackParam(*trackParam);
}

//__________________________________________________________________________
void AliMUONTrack::RecursiveDump() const
{
  /// Recursive dump of AliMUONTrack, i.e. with dump of trackParamAtCluster and attached clusters
  AliMUONTrackParam *trackParamAtCluster;
  AliMUONVCluster *cluster;
  cout << "Recursive dump of Track: " << this << endl;
  // Track
  this->Dump();
  for (Int_t iCluster = 0; iCluster < GetNClusters(); iCluster++) {
    trackParamAtCluster = (AliMUONTrackParam*) ((*fTrackParamAtCluster)[iCluster]);
    // trackParamAtCluster
    cout << "trackParamAtCluster: " << trackParamAtCluster << " (index: " << iCluster << ")" << endl;
    trackParamAtCluster->Dump();
    cluster = trackParamAtCluster->GetClusterPtr();
    // cluster
    cout << "cluster: " << cluster << endl;
    cluster->Print();
  }
  return;
}
  
//_____________________________________________-
void AliMUONTrack::Print(Option_t*) const
{
  /// Printing Track information 

  cout << "<AliMUONTrack> No.Clusters=" << setw(2)   << GetNClusters() << 
      ", Match2Trig=" << setw(1) << GetMatchTrigger()  << 
      ", LoTrgNum=" << setw(3) << GetLoTrgNum()  << 
    ", Chi2-tracking-trigger=" << setw(8) << setprecision(5) <<  GetChi2MatchTrigger();
  cout << Form(" HitTriggerPattern %x",fHitsPatternInTrigCh) << endl;
  fTrackParamAtCluster->First()->Print("FULL");
}

//__________________________________________________________________________
void AliMUONTrack::SetLocalTrigger(Int_t loCirc, Int_t loStripX, Int_t loStripY, Int_t loDev, Int_t loLpt, Int_t loHpt)
{
  /// pack the local trigger information and store

  if (loCirc < 0) return;

  fLocalTrigger = 0;
  fLocalTrigger += loCirc;
  fLocalTrigger += loStripX << 8;
  fLocalTrigger += loStripY << 13;
  fLocalTrigger += loDev    << 17;
  fLocalTrigger += loLpt    << 22;
  fLocalTrigger += loHpt    << 24;

}