Updating MUON code with the new class AliMUONTrackExtrap (Philippe Pillot)

[u/mrichter/AliRoot.git] / MUON / AliMUONTrackReconstructor.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 AliMUONTrackReconstructor
/// MUON track reconstructor using the original method
///
/// This class contains as data:
/// - the parameters for the track reconstruction
///
/// It contains as methods, among others:
/// - MakeTracks to build the tracks
///

#include <stdlib.h>
#include <Riostream.h>
#include <TMatrixD.h>

#include "AliMUONVTrackReconstructor.h"
#include "AliMUONTrackReconstructor.h"
#include "AliMUONData.h"
#include "AliMUONConstants.h"
#include "AliMUONRawCluster.h"
#include "AliMUONHitForRec.h"
#include "AliMUONSegment.h"
#include "AliMUONTrack.h"
#include "AliMUONTrackParam.h"
#include "AliMUONTrackExtrap.h"
#include "AliLog.h"
#include <TVirtualFitter.h>

// Functions to be minimized with Minuit
void TrackChi2(Int_t &NParam, Double_t *Gradient, Double_t &Chi2, Double_t *Param, Int_t Flag);
void TrackChi2MCS(Int_t &NParam, Double_t *Gradient, Double_t &Chi2, Double_t *Param, Int_t Flag);

void mnvertLocal(Double_t* a, Int_t l, Int_t m, Int_t n, Int_t& ifail);

Double_t MultipleScatteringAngle2(AliMUONTrackParam *param);

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

//************* Defaults parameters for reconstruction
const Double_t AliMUONTrackReconstructor::fgkDefaultMaxChi2 = 100.0;

TVirtualFitter* AliMUONTrackReconstructor::fgFitter = 0x0; 

//__________________________________________________________________________
AliMUONTrackReconstructor::AliMUONTrackReconstructor(AliMUONData* data)
  : AliMUONVTrackReconstructor(data),
    fMaxChi2(fgkDefaultMaxChi2)
{
  /// Constructor for class AliMUONTrackReconstructor
  
  // Memory allocation for the TClonesArray of reconstructed tracks
  fRecTracksPtr = new TClonesArray("AliMUONTrack", 10);
}

  //__________________________________________________________________________
AliMUONTrackReconstructor::~AliMUONTrackReconstructor(void)
{
  /// Destructor for class AliMUONTrackReconstructor
  delete fRecTracksPtr;
}

  //__________________________________________________________________________
void AliMUONTrackReconstructor::AddHitsForRecFromRawClusters()
{
  /// To add to the list of hits for reconstruction all the raw clusters
  TTree *TR = fMUONData->TreeR();
  AliMUONHitForRec *hitForRec;
  AliMUONRawCluster *clus;
  Int_t iclus, nclus, nTRentries;
  TClonesArray *rawclusters;
  AliDebug(1,"Enter AddHitsForRecFromRawClusters");
  
  fMUONData->SetTreeAddress("RC");
  nTRentries = Int_t(TR->GetEntries());
  if (nTRentries != 1) {
    AliError(Form("nTRentries = %d not equal to 1 ",nTRentries));
    exit(0);
  }
  fMUONData->GetRawClusters(); // only one entry  
  
  // Loop over tracking chambers
  for (Int_t ch = 0; ch < AliMUONConstants::NTrackingCh(); ch++) {
    // number of HitsForRec to 0 for the chamber
    fNHitsForRecPerChamber[ch] = 0;
    // index of first HitForRec for the chamber
    if (ch == 0) fIndexOfFirstHitForRecPerChamber[ch] = 0;
    else fIndexOfFirstHitForRecPerChamber[ch] = fNHitsForRec;
    rawclusters =fMUONData->RawClusters(ch);
    nclus = (Int_t) (rawclusters->GetEntries());
    // Loop over (cathode correlated) raw clusters
    for (iclus = 0; iclus < nclus; iclus++) {
      clus = (AliMUONRawCluster*) rawclusters->UncheckedAt(iclus);
      // new AliMUONHitForRec from raw cluster
      // and increment number of AliMUONHitForRec's (total and in chamber)
      hitForRec = new ((*fHitsForRecPtr)[fNHitsForRec]) AliMUONHitForRec(clus);
      fNHitsForRec++;
      (fNHitsForRecPerChamber[ch])++;
      // more information into HitForRec
      hitForRec->SetBendingReso2(clus->GetErrY() * clus->GetErrY());
      hitForRec->SetNonBendingReso2(clus->GetErrX() * clus->GetErrX());
      //  original raw cluster
      hitForRec->SetChamberNumber(ch);
      hitForRec->SetHitNumber(iclus);
      // Z coordinate of the raw cluster (cm)
      hitForRec->SetZ(clus->GetZ(0));
      
      StdoutToAliDebug(3,
                       cout << "Chamber " << ch <<
                       " raw cluster  " << iclus << " : " << endl;
                       clus->Print("full");
                       cout << "AliMUONHitForRec number (1...): " << fNHitsForRec << endl;
                       hitForRec->Print("full");
                       );
    } // end of cluster loop
  } // end of chamber loop
  SortHitsForRecWithIncreasingChamber(); 
  
  AliDebug(1,"End of AddHitsForRecFromRawClusters");
    if (AliLog::GetGlobalDebugLevel() > 0) {
      AliDebug(1, Form("NHitsForRec: %d",fNHitsForRec));
      for (Int_t ch = 0; ch < AliMUONConstants::NTrackingCh(); ch++) {
	AliDebug(1, Form("Chamber(0...): %d",ch));
	AliDebug(1, Form("NHitsForRec: %d", fNHitsForRecPerChamber[ch]));
	AliDebug(1, Form("Index(first HitForRec): %d", fIndexOfFirstHitForRecPerChamber[ch]));
	for (Int_t hit = fIndexOfFirstHitForRecPerChamber[ch];
	     hit < fIndexOfFirstHitForRecPerChamber[ch] + fNHitsForRecPerChamber[ch];
	     hit++) {
	  AliDebug(1, Form("HitForRec index(0...): %d",hit));
	  ((*fHitsForRecPtr)[hit])->Dump();
      }
    }
  }
  
  return;
}

  //__________________________________________________________________________
void AliMUONTrackReconstructor::MakeSegments(void)
{
  /// To make the list of segments in all stations,
  /// from the list of hits to be reconstructed
  AliDebug(1,"Enter MakeSegments");
  // Loop over stations
  for (Int_t st = 0; st < AliMUONConstants::NTrackingCh()/2; st++) MakeSegmentsPerStation(st); 
  
  StdoutToAliDebug(3,
    cout << "end of MakeSegments" << endl;
    for (Int_t st = 0; st < AliMUONConstants::NTrackingCh()/2; st++) 
    {
      cout << "station " << st
	    << "  has " << fNSegments[st] << " segments:"
	    << endl;
      for (Int_t seg = 0; seg < fNSegments[st]; seg++) 
      {
	      ((*fSegmentsPtr[st])[seg])->Print();
      }
    }
                   );
  return;
}

  //__________________________________________________________________________
void AliMUONTrackReconstructor::MakeTracks(void)
{
  /// To make the tracks from the list of segments and points in all stations
  AliDebug(1,"Enter MakeTracks");
  // Look for candidates from at least 3 aligned points in stations(1..) 4 and 5
  MakeTrackCandidates();
  // Follow tracks in stations(1..) 3, 2 and 1
  FollowTracks();
  // Remove double tracks
  RemoveDoubleTracks();
  UpdateHitForRecAtHit();
}

  //__________________________________________________________________________
void AliMUONTrackReconstructor::MakeTrackCandidates(void)
{
  /// To make track candidates
  /// with at least 3 aligned points in stations(1..) 4 and 5
  /// (two Segment's or one Segment and one HitForRec)
  Int_t begStation, iBegSegment, nbCan1Seg1Hit, nbCan2Seg;
  AliMUONSegment *begSegment;
  AliDebug(1,"Enter MakeTrackCandidates");
  // Loop over stations(1..) 5 and 4 for the beginning segment
  for (begStation = 4; begStation > 2; begStation--) {
    // Loop over segments in the beginning station
    for (iBegSegment = 0; iBegSegment < fNSegments[begStation]; iBegSegment++) {
      // pointer to segment
      begSegment = (AliMUONSegment*) ((*fSegmentsPtr[begStation])[iBegSegment]);
      AliDebug(2,Form("Look for TrackCandidate's with Segment %d  in Station(0..) %d", iBegSegment, begStation));
      // Look for track candidates with two segments,
      // "begSegment" and all compatible segments in other station.
      // Only for beginning station(1..) 5
      // because candidates with 2 segments have to looked for only once.
      if (begStation == 4)
	nbCan2Seg = MakeTrackCandidatesWithTwoSegments(begSegment);
      // Look for track candidates with one segment and one point,
      // "begSegment" and all compatible HitForRec's in other station.
      // Only if "begSegment" does not belong already to a track candidate.
      // Is that a too strong condition ????
      if (!(begSegment->GetInTrack()))
	nbCan1Seg1Hit = MakeTrackCandidatesWithOneSegmentAndOnePoint(begSegment);
    } // for (iBegSegment = 0;...
  } // for (begStation = 4;...
  return;
}

  //__________________________________________________________________________
Int_t AliMUONTrackReconstructor::MakeTrackCandidatesWithTwoSegments(AliMUONSegment *BegSegment)
{
  /// To make track candidates with two segments in stations(1..) 4 and 5,
  /// the first segment being pointed to by "BegSegment".
  /// Returns the number of such track candidates.
  Int_t endStation, iEndSegment, nbCan2Seg;
  AliMUONSegment *endSegment;
  AliMUONSegment *extrapSegment = NULL;
  AliMUONTrack *recTrack;
  Double_t mcsFactor;
  AliDebug(1,"Enter MakeTrackCandidatesWithTwoSegments");
  // Station for the end segment
  endStation = 7 - (BegSegment->GetHitForRec1())->GetChamberNumber() / 2;
  // multiple scattering factor corresponding to one chamber
  mcsFactor = 0.0136 /
    GetBendingMomentumFromImpactParam(BegSegment->GetBendingImpact());
  mcsFactor	= fChamberThicknessInX0 * mcsFactor * mcsFactor;
  // linear extrapolation to end station
  // number of candidates with 2 segments to 0
  nbCan2Seg = 0;
  // Loop over segments in the end station
  for (iEndSegment = 0; iEndSegment < fNSegments[endStation]; iEndSegment++) {
    // pointer to segment
    endSegment = (AliMUONSegment*) ((*fSegmentsPtr[endStation])[iEndSegment]);
    // test compatibility between current segment and "extrapSegment"
    // 4 because 4 quantities in chi2
    extrapSegment =
      BegSegment->CreateSegmentFromLinearExtrapToStation(endSegment->GetZ(), mcsFactor);
    if ((endSegment->
	 NormalizedChi2WithSegment(extrapSegment,
				   fMaxSigma2Distance)) <= 4.0) {
      // both segments compatible:
      // make track candidate from "begSegment" and "endSegment"
      AliDebug(2,Form("TrackCandidate with Segment %d in Station(0..) %d", iEndSegment, endStation));
      // flag for both segments in one track:
      // to be done in track constructor ????
      BegSegment->SetInTrack(kTRUE);
      endSegment->SetInTrack(kTRUE);
      recTrack = new ((*fRecTracksPtr)[fNRecTracks]) AliMUONTrack(BegSegment, endSegment);
      // Set track parameters at vertex from last stations 4 & 5
      CalcTrackParamAtVertex(recTrack);
      fNRecTracks++;
      if (AliLog::GetGlobalDebugLevel() > 1) recTrack->RecursiveDump();
      // increment number of track candidates with 2 segments
      nbCan2Seg++;
    }
    delete extrapSegment; // should not delete HitForRec's it points to !!!!
  } // for (iEndSegment = 0;...
  return nbCan2Seg;
}

  //__________________________________________________________________________
Int_t AliMUONTrackReconstructor::MakeTrackCandidatesWithOneSegmentAndOnePoint(AliMUONSegment *BegSegment)
{
  /// To make track candidates with one segment and one point
  /// in stations(1..) 4 and 5,
  /// the segment being pointed to by "BegSegment".
  Int_t ch, ch1, ch2, endStation, iHit, iHitMax, iHitMin, nbCan1Seg1Hit;
  AliMUONHitForRec *extrapHitForRec= NULL;
  AliMUONHitForRec *hit;
  AliMUONTrack *recTrack;
  Double_t mcsFactor;
  AliDebug(1,"Enter MakeTrackCandidatesWithOneSegmentAndOnePoint");
  // station for the end point
  endStation = 7 - (BegSegment->GetHitForRec1())->GetChamberNumber() / 2;
  // multiple scattering factor corresponding to one chamber
  mcsFactor = 0.0136 /
    GetBendingMomentumFromImpactParam(BegSegment->GetBendingImpact());
  mcsFactor	= fChamberThicknessInX0 * mcsFactor * mcsFactor;
  // first and second chambers(0..) in the end station
  ch1 = 2 * endStation;
  ch2 = ch1 + 1;
  // number of candidates to 0
  nbCan1Seg1Hit = 0;
  // Loop over chambers of the end station
  for (ch = ch2; ch >= ch1; ch--) {
    // limits for the hit index in the loop
    iHitMin = fIndexOfFirstHitForRecPerChamber[ch];
    iHitMax = iHitMin + fNHitsForRecPerChamber[ch];
    // Loop over HitForRec's in the chamber
    for (iHit = iHitMin; iHit < iHitMax; iHit++) {
      // pointer to HitForRec
      hit = (AliMUONHitForRec*) ((*fHitsForRecPtr)[iHit]);
      // test compatibility between current HitForRec and "extrapHitForRec"
      // 2 because 2 quantities in chi2
      // linear extrapolation to chamber
      extrapHitForRec =
	BegSegment->CreateHitForRecFromLinearExtrapToChamber( hit->GetZ(), mcsFactor);
      if ((hit->
	   NormalizedChi2WithHitForRec(extrapHitForRec,
				       fMaxSigma2Distance)) <= 2.0) {
	// both HitForRec's compatible:
	// make track candidate from begSegment and current HitForRec
	AliDebug(2, Form("TrackCandidate with HitForRec  %d in Chamber(0..) %d", iHit, ch));
	// flag for beginning segments in one track:
	// to be done in track constructor ????
	BegSegment->SetInTrack(kTRUE);
	recTrack = new ((*fRecTracksPtr)[fNRecTracks]) AliMUONTrack(BegSegment, hit);
        // Set track parameters at vertex from last stations 4 & 5
        CalcTrackParamAtVertex(recTrack);
	// the right place to eliminate "double counting" ???? how ????
	fNRecTracks++;
	if (AliLog::GetGlobalDebugLevel() > 1) recTrack->RecursiveDump();
	// increment number of track candidates
	nbCan1Seg1Hit++;
      }
      delete extrapHitForRec;
    } // for (iHit = iHitMin;...
  } // for (ch = ch2;...
  return nbCan1Seg1Hit;
}

  //__________________________________________________________________________
void AliMUONTrackReconstructor::CalcTrackParamAtVertex(AliMUONTrack *Track) const
{
  /// Set track parameters at vertex.
  /// TrackHit's are assumed to be only in stations(1..) 4 and 5,
  /// and sorted according to increasing Z.
  /// Parameters are calculated from information in HitForRec's
  /// of first and last TrackHit's.
  AliMUONTrackParam *trackParamVertex = Track->GetTrackParamAtVertex(); // pointer to track parameters at vertex
  // Pointer to HitForRec attached to first TrackParamAtHit
  AliMUONHitForRec *firstHit = ((AliMUONTrackParam*) (Track->GetTrackParamAtHit()->First()))->GetHitForRecPtr();
  // Pointer to HitForRec attached to last TrackParamAtHit
  AliMUONHitForRec *lastHit = ((AliMUONTrackParam*) (Track->GetTrackParamAtHit()->Last()))->GetHitForRecPtr();
  // Z difference between first and last hits
  Double_t deltaZ = firstHit->GetZ() - lastHit->GetZ();
  // bending slope in stations(1..) 4 and 5
  Double_t bendingSlope = (firstHit->GetBendingCoor() - lastHit->GetBendingCoor()) / deltaZ;
  trackParamVertex->SetBendingSlope(bendingSlope);
  // impact parameter
  Double_t impactParam = firstHit->GetBendingCoor() - bendingSlope * firstHit->GetZ();
  // signed bending momentum
  trackParamVertex->SetInverseBendingMomentum(1.0 / GetBendingMomentumFromImpactParam(impactParam));
  // bending slope at vertex
  trackParamVertex->SetBendingSlope(bendingSlope + impactParam / fSimpleBPosition);
  // non bending slope
  trackParamVertex->SetNonBendingSlope((firstHit->GetNonBendingCoor() - lastHit->GetNonBendingCoor()) / deltaZ);
  // vertex coordinates at (0,0,0)
  trackParamVertex->SetZ(0.0);
  trackParamVertex->SetBendingCoor(0.0);
  trackParamVertex->SetNonBendingCoor(0.0);
}

  //__________________________________________________________________________
void AliMUONTrackReconstructor::FollowTracks(void)
{
  /// Follow tracks in stations(1..) 3, 2 and 1
  // too long: should be made more modular !!!!
  AliMUONHitForRec *bestHit, *extrapHit, *hit;
  AliMUONSegment *bestSegment, *extrapSegment, *segment;
  AliMUONTrack *track, *nextTrack;
  AliMUONTrackParam *trackParam1, trackParam[2], trackParamVertex;
  // -1 to avoid compilation warnings
  Int_t ch = -1, chInStation, chBestHit = -1, iHit, iSegment, station, trackIndex; 
  Double_t bestChi2, chi2, dZ1, dZ2, dZ3, maxSigma2Distance, mcsFactor;
  Double_t bendingMomentum, chi2Norm = 0.;


  // local maxSigma2Distance, for easy increase in testing
  maxSigma2Distance = fMaxSigma2Distance;
  AliDebug(2,"Enter FollowTracks");
  // Loop over track candidates
  track = (AliMUONTrack*) fRecTracksPtr->First();
  trackIndex = -1;
  while (track) {
    trackIndex++;
    nextTrack = (AliMUONTrack*) fRecTracksPtr->After(track); // prepare next track
    AliDebug(2,Form("FollowTracks: track candidate(0..): %d", trackIndex));
    // Fit track candidate from parameters at vertex
    // -> with 3 parameters (X_vertex and Y_vertex are fixed)
    // without multiple Coulomb scattering
    Fit(track,0,0);
    if (AliLog::GetGlobalDebugLevel()> 2) {
      cout << "FollowTracks: track candidate(0..): " << trackIndex
	   << " after fit in stations(0..) 3 and 4" << endl;
      track->RecursiveDump();
    }
    // Loop over stations(1..) 3, 2 and 1
    // something SPECIAL for stations 2 and 1 for majority 3 coincidence ????
    // otherwise: majority coincidence 2 !!!!
    for (station = 2; station >= 0; station--) {
      // Track parameters at first track hit (smallest Z)
      trackParam1 = (AliMUONTrackParam*) (track->GetTrackParamAtHit()->First());
      // extrapolation to station
      AliMUONTrackExtrap::ExtrapToStation(trackParam1, station, trackParam);
      extrapSegment = new AliMUONSegment(); //  empty segment
      // multiple scattering factor corresponding to one chamber
      // and momentum in bending plane (not total)
      mcsFactor = 0.0136 * trackParam1->GetInverseBendingMomentum();
      mcsFactor	= fChamberThicknessInX0 * mcsFactor * mcsFactor;
      // Z difference from previous station
      dZ1 = AliMUONConstants::DefaultChamberZ(2 * station) -
	    AliMUONConstants::DefaultChamberZ(2 * station + 2);
      // Z difference between the two previous stations
      dZ2 = AliMUONConstants::DefaultChamberZ(2 * station + 2) -
	    AliMUONConstants::DefaultChamberZ(2 * station + 4);
      // Z difference between the two chambers in the previous station
      dZ3 = AliMUONConstants::DefaultChamberZ(2 * station) -
	    AliMUONConstants::DefaultChamberZ(2 * station + 1);
      extrapSegment->SetBendingCoorReso2(fBendingResolution * fBendingResolution);
      extrapSegment->SetNonBendingCoorReso2(fNonBendingResolution * fNonBendingResolution);
      extrapSegment->UpdateFromStationTrackParam(trackParam, mcsFactor, dZ1, dZ2, dZ3, station,
      						 trackParam1->GetInverseBendingMomentum());
      bestChi2 = 5.0;
      bestSegment = NULL;
      if (AliLog::GetGlobalDebugLevel() > 2) {
	cout << "FollowTracks: track candidate(0..): " << trackIndex
	     << " Look for segment in station(0..): " << station << endl;
      }

      // Loop over segments in station
      for (iSegment = 0; iSegment < fNSegments[station]; iSegment++) {
	// Look for best compatible Segment in station
	// should consider all possibilities ????
	// multiple scattering ????
	// separation in 2 functions: Segment and HitForRec ????
	segment = (AliMUONSegment*) ((*fSegmentsPtr[station])[iSegment]);
	// correction of corrected segment (fBendingCoor and fNonBendingCoor)
	// according to real Z value of "segment" and slopes of "extrapSegment"
	AliMUONTrackExtrap::ExtrapToZ(&(trackParam[0]), segment->GetZ());
	AliMUONTrackExtrap::ExtrapToZ(&(trackParam[1]), segment->GetZ()); // now same as trackParam[0] !?!?!?!?!?!
	extrapSegment->SetBendingCoor((&(trackParam[0]))->GetBendingCoor());
	extrapSegment->SetNonBendingCoor((&(trackParam[0]))->GetNonBendingCoor());
	extrapSegment->SetBendingSlope((&(trackParam[0]))->GetBendingSlope());
	extrapSegment->SetNonBendingSlope((&(trackParam[0]))->GetNonBendingSlope());
	chi2 = segment->NormalizedChi2WithSegment(extrapSegment, maxSigma2Distance);
	if (chi2 < bestChi2) {
	  // update best Chi2 and Segment if better found
	  bestSegment = segment;
	  bestChi2 = chi2;
	}
      }
      if (bestSegment) {
	// best segment found: add it to track candidate
	AliMUONTrackExtrap::ExtrapToZ(&(trackParam[0]), bestSegment->GetZ());
	track->AddTrackParamAtHit(&(trackParam[0]),bestSegment->GetHitForRec1());
	AliMUONTrackExtrap::ExtrapToZ(&(trackParam[1]), bestSegment->GetZ()); // now same as trackParam[0] !?!?!?!?!?!
	track->AddTrackParamAtHit(&(trackParam[1]),bestSegment->GetHitForRec2());
	AliDebug(3, Form("FollowTracks: track candidate(0..): %d  Added segment in station(0..): %d", trackIndex, station));
	if (AliLog::GetGlobalDebugLevel()>2) track->RecursiveDump();
      } else {
	// No best segment found:
	// Look for best compatible HitForRec in station:
	// should consider all possibilities ????
	// multiple scattering ???? do about like for extrapSegment !!!!
	extrapHit = new AliMUONHitForRec(); //  empty hit
	bestChi2 = 3.0;
	bestHit = NULL;
	AliDebug(3, Form("FollowTracks: track candidate(0..): %d Segment not found, look for hit in station(0..): %d ", 
			 trackIndex, station));
	
	// Loop over chambers of the station
	for (chInStation = 0; chInStation < 2; chInStation++) {
	  ch = 2 * station + chInStation;
	  for (iHit = fIndexOfFirstHitForRecPerChamber[ch]; iHit < fIndexOfFirstHitForRecPerChamber[ch]+fNHitsForRecPerChamber[ch]; iHit++) {
	    hit = (AliMUONHitForRec*) ((*fHitsForRecPtr)[iHit]);
	    // coordinates of extrapolated hit
	    AliMUONTrackExtrap::ExtrapToZ(&(trackParam[chInStation]), hit->GetZ());
	    extrapHit->SetBendingCoor((&(trackParam[chInStation]))->GetBendingCoor());
	    extrapHit->SetNonBendingCoor((&(trackParam[chInStation]))->GetNonBendingCoor());
	    // resolutions from "extrapSegment"
	    extrapHit->SetBendingReso2(extrapSegment->GetBendingCoorReso2());
	    extrapHit->SetNonBendingReso2(extrapSegment->GetNonBendingCoorReso2());
	    // Loop over hits in the chamber
	    // condition for hit not already in segment ????
	    chi2 = hit->NormalizedChi2WithHitForRec(extrapHit, maxSigma2Distance);
	    if (chi2 < bestChi2) {
	      // update best Chi2 and HitForRec if better found
	      bestHit = hit;
	      bestChi2 = chi2;
	      chBestHit = chInStation;
	    }
	  }
	}
	if (bestHit) {
	  // best hit found: add it to track candidate
	  AliMUONTrackExtrap::ExtrapToZ(&(trackParam[chBestHit]), bestHit->GetZ());
	  track->AddTrackParamAtHit(&(trackParam[chBestHit]),bestHit);
	  if (AliLog::GetGlobalDebugLevel() > 2) {
	    cout << "FollowTracks: track candidate(0..): " << trackIndex
		 << " Added hit in station(0..): " << station << endl;
	    track->RecursiveDump();
	  }
	} else {
	  // Remove current track candidate
	  // and corresponding TrackHit's, ...
	  fRecTracksPtr->Remove(track);
	  fNRecTracks--;
	  delete extrapSegment;
	  delete extrapHit;
	  break; // stop the search for this candidate:
	  // exit from the loop over station
	}
	delete extrapHit;
      }
      delete extrapSegment;
      // Sort TrackParamAtHit according to increasing Z
      track->GetTrackParamAtHit()->Sort();
      // Update track parameters at first track hit (smallest Z)
      trackParam1 = (AliMUONTrackParam*) (track->GetTrackParamAtHit()->First());
      bendingMomentum = 0.;
      if (TMath::Abs(trackParam1->GetInverseBendingMomentum()) > 0.)
	bendingMomentum = TMath::Abs(1/(trackParam1->GetInverseBendingMomentum()));
      // Track removed if bendingMomentum not in window [min, max]
      if ((bendingMomentum < fMinBendingMomentum) || (bendingMomentum > fMaxBendingMomentum)) {
	fRecTracksPtr->Remove(track);
	fNRecTracks--;
	break; // stop the search for this candidate:
	// exit from the loop over station 
      }
      // Track fit from parameters at first hit
      // -> with 5 parameters (momentum and position)
      // with multiple Coulomb scattering if all stations
      if (station == 0) Fit(track,1,1);
      // without multiple Coulomb scattering if not all stations
      else Fit(track,1,0);
      Double_t numberOfDegFree = (2.0 * track->GetNTrackHits() - 5);
      if (numberOfDegFree > 0) {
        chi2Norm =  track->GetFitFMin() / numberOfDegFree;
      } else {
	chi2Norm = 1.e10;
      }
      // Track removed if normalized chi2 too high
      if (chi2Norm > fMaxChi2) {
	fRecTracksPtr->Remove(track);
	fNRecTracks--;
	break; // stop the search for this candidate:
	// exit from the loop over station 
      }
      if (AliLog::GetGlobalDebugLevel() > 2) {
	cout << "FollowTracks: track candidate(0..): " << trackIndex
	     << " after fit from station(0..): " << station << " to 4" << endl;
	track->RecursiveDump();
      }
      // Track extrapolation to the vertex through the absorber (Branson)
      // after going through the first station
      if (station == 0) {
	trackParamVertex = *((AliMUONTrackParam*) (track->GetTrackParamAtHit()->First()));
	AliMUONTrackExtrap::ExtrapToVertex(&trackParamVertex, 0., 0., 0.);
	track->SetTrackParamAtVertex(&trackParamVertex);
	if (AliLog::GetGlobalDebugLevel() > 0) {
	  cout << "FollowTracks: track candidate(0..): " << trackIndex
	       << " after extrapolation to vertex" << endl;
	  track->RecursiveDump();
	}
      }
    } // for (station = 2;...
    // go really to next track
    track = nextTrack;
  } // while (track)
  // Compression of track array (necessary after Remove)
  fRecTracksPtr->Compress();
  return;
}

  //__________________________________________________________________________
void AliMUONTrackReconstructor::Fit(AliMUONTrack *Track, Int_t FitStart, Int_t FitMCS)
{
  /// Fit the track "Track",
  /// with or without multiple Coulomb scattering according to "FitMCS",
  /// starting, according to "FitStart",
  /// with track parameters at vertex or at the first TrackHit.
  
  if ((FitStart != 0) && (FitStart != 1)) {
    cout << "ERROR in AliMUONTrackReconstructor::Fit(...)" << endl;
    cout << "FitStart = " << FitStart << " is neither 0 nor 1" << endl;
    exit(0);
  }
  if ((FitMCS != 0) && (FitMCS != 1)) {
    cout << "ERROR in AliMUONTrackReconstructor::Fit(...)" << endl;
    cout << "FitMCS = " << FitMCS << " is neither 0 nor 1" << endl;
    exit(0);
  }
  
  Double_t arg[1], benC, errorParam, invBenP, lower, nonBenC, upper, x, y;
  char parName[50];
  AliMUONTrackParam *trackParam;
  // Check if Minuit is initialized...
  fgFitter = TVirtualFitter::Fitter(Track,5);
  fgFitter->Clear(); // necessary ???? probably yes
  // how to reset the printout number at every fit ????
  // is there any risk to leave it like that ????
  // how to go faster ???? choice of Minuit parameters like EDM ????
  // choice of function to be minimized according to fFitMCS
  if (FitMCS == 0) fgFitter->SetFCN(TrackChi2);
  else fgFitter->SetFCN(TrackChi2MCS);
  // Switch off printout
  arg[0] = -1;
  fgFitter->ExecuteCommand("SET PRINT", arg, 1); // More printing !!!!
  // No warnings
  fgFitter->ExecuteCommand("SET NOW", arg, 0);
  // Parameters according to "fFitStart"
  // (should be a function to be used at every place where needed ????)
  if (FitStart == 0) trackParam = Track->GetTrackParamAtVertex();
  else trackParam = (AliMUONTrackParam*) (Track->GetTrackParamAtHit()->First());
  // set first 3 Minuit parameters
  // could be tried with no limits for the search (min=max=0) ????
  fgFitter->SetParameter(0, "InvBenP",
			 trackParam->GetInverseBendingMomentum(),
			 0.003, -0.4, 0.4);
  fgFitter->SetParameter(1, "BenS",
			 trackParam->GetBendingSlope(),
			 0.001, -0.5, 0.5);
  fgFitter->SetParameter(2, "NonBenS",
			 trackParam->GetNonBendingSlope(),
			 0.001, -0.5, 0.5);
  if (FitStart == 1) {
    // set last 2 Minuit parameters when we start from first track hit
    // mandatory limits in Bending to avoid NaN values of parameters
    fgFitter->SetParameter(3, "X",
			   trackParam->GetNonBendingCoor(),
			   0.03, -500.0, 500.0);
    // mandatory limits in non Bending to avoid NaN values of parameters
    fgFitter->SetParameter(4, "Y",
			   trackParam->GetBendingCoor(),
			   0.10, -500.0, 500.0);
  }
  // search without gradient calculation in the function
  fgFitter->ExecuteCommand("SET NOGRADIENT", arg, 0);
  // minimization
  fgFitter->ExecuteCommand("MINIMIZE", arg, 0);
  // exit from Minuit
  //  fgFitter->ExecuteCommand("EXIT", arg, 0); // necessary ????
  // get results into "invBenP", "benC", "nonBenC" ("x", "y")
  fgFitter->GetParameter(0, parName, invBenP, errorParam, lower, upper);
  trackParam->SetInverseBendingMomentum(invBenP);
  fgFitter->GetParameter(1, parName, benC, errorParam, lower, upper);
  trackParam->SetBendingSlope(benC);
  fgFitter->GetParameter(2, parName, nonBenC, errorParam, lower, upper);
  trackParam->SetNonBendingSlope(nonBenC);
  if (FitStart == 1) {
    fgFitter->GetParameter(3, parName, x, errorParam, lower, upper);
    trackParam->SetNonBendingCoor(x);
    fgFitter->GetParameter(4, parName, y, errorParam, lower, upper);
    trackParam->SetBendingCoor(y);
  }
  // global result of the fit
  Double_t fedm, errdef, fitFMin;
  Int_t npari, nparx;
  fgFitter->GetStats(fitFMin, fedm, errdef, npari, nparx);
  Track->SetFitFMin(fitFMin);
}

  //__________________________________________________________________________
void TrackChi2(Int_t &NParam, Double_t * /*Gradient*/, Double_t &Chi2, Double_t *Param, Int_t /*Flag*/)
{
  /// Return the "Chi2" to be minimized with Minuit for track fitting,
  /// with "NParam" parameters
  /// and their current values in array pointed to by "Param".
  /// Assumes that the track hits are sorted according to increasing Z.
  /// Track parameters at each TrackHit are updated accordingly.
  /// Multiple Coulomb scattering is not taken into account
  AliMUONTrack *trackBeingFitted;
  AliMUONTrackParam param1;
  AliMUONTrackParam* trackParamAtHit;
  AliMUONHitForRec* hitForRec;
  Chi2 = 0.0; // initialize Chi2
  // copy of track parameters to be fitted
  trackBeingFitted = (AliMUONTrack*) AliMUONTrackReconstructor::Fitter()->GetObjectFit();
  // 3 parameters means fit track candidate from parameters at vertex (X_vertex and Y_vertex are fixed)
  if (NParam == 3) param1 = *(trackBeingFitted->GetTrackParamAtVertex());
  else param1 = *((AliMUONTrackParam*) (trackBeingFitted->GetTrackParamAtHit()->First()));
  // Minuit parameters to be fitted into this copy
  param1.SetInverseBendingMomentum(Param[0]);
  param1.SetBendingSlope(Param[1]);
  param1.SetNonBendingSlope(Param[2]);
  if (NParam == 5) {
    param1.SetNonBendingCoor(Param[3]);
    param1.SetBendingCoor(Param[4]);
  }
  // Follow track through all planes of track hits
  trackParamAtHit = (AliMUONTrackParam*) (trackBeingFitted->GetTrackParamAtHit()->First());
  while (trackParamAtHit) {
    hitForRec = trackParamAtHit->GetHitForRecPtr();
    // extrapolation to the plane of the hitForRec attached to the current trackParamAtHit
    AliMUONTrackExtrap::ExtrapToZ(&param1, hitForRec->GetZ());
    // update track parameters of the current hit
    trackParamAtHit->SetTrackParam(param1);
    // Increment Chi2
    // done hit per hit, with hit resolution,
    // and not with point and angle like in "reco_muon.F" !!!!
    // Needs to add multiple scattering contribution ????
    Double_t dX = hitForRec->GetNonBendingCoor() - param1.GetNonBendingCoor();
    Double_t dY = hitForRec->GetBendingCoor() - param1.GetBendingCoor();
    Chi2 = Chi2 + dX * dX / hitForRec->GetNonBendingReso2() + dY * dY / hitForRec->GetBendingReso2();
    trackParamAtHit = (AliMUONTrackParam*) (trackBeingFitted->GetTrackParamAtHit()->After(trackParamAtHit));
  }
}

  //__________________________________________________________________________
void TrackChi2MCS(Int_t &NParam, Double_t * /*Gradient*/, Double_t &Chi2, Double_t *Param, Int_t /*Flag*/)
{
  /// Return the "Chi2" to be minimized with Minuit for track fitting,
  /// with "NParam" parameters
  /// and their current values in array pointed to by "Param".
  /// Assumes that the track hits are sorted according to increasing Z.
  /// Track parameters at each TrackHit are updated accordingly.
  /// Multiple Coulomb scattering is taken into account with covariance matrix.
  AliMUONTrack *trackBeingFitted;
  AliMUONTrackParam param1;
  AliMUONTrackParam* trackParamAtHit;
  AliMUONHitForRec* hitForRec;
  Chi2 = 0.0; // initialize Chi2
  // copy of track parameters to be fitted
  trackBeingFitted = (AliMUONTrack*) AliMUONTrackReconstructor::Fitter()->GetObjectFit();
  // 3 parameters means fit track candidate from parameters at vertex (X_vertex and Y_vertex are fixed)
  if (NParam == 3) param1 = *(trackBeingFitted->GetTrackParamAtVertex());
  else param1 = *((AliMUONTrackParam*) (trackBeingFitted->GetTrackParamAtHit()->First()));
  // Minuit parameters to be fitted into this copy
  param1.SetInverseBendingMomentum(Param[0]);
  param1.SetBendingSlope(Param[1]);
  param1.SetNonBendingSlope(Param[2]);
  if (NParam == 5) {
    param1.SetNonBendingCoor(Param[3]);
    param1.SetBendingCoor(Param[4]);
  }

  Int_t chCurrent, chPrev = 0, hitNumber, hitNumber1, hitNumber2, hitNumber3;
  Double_t z1, z2, z3;
  AliMUONTrackParam *trackParamAtHit1, *trackParamAtHit2, *trackParamAtHit3;
  AliMUONHitForRec *hitForRec1, *hitForRec2;
  Double_t hbc1, hbc2, pbc1, pbc2;
  Double_t hnbc1, hnbc2, pnbc1, pnbc2;
  Int_t numberOfHit = trackBeingFitted->GetNTrackHits();
  TMatrixD *covBending = new TMatrixD(numberOfHit, numberOfHit);
  TMatrixD *covNonBending = new TMatrixD(numberOfHit, numberOfHit);
  Double_t *msa2 = new Double_t[numberOfHit];

  // Predicted coordinates and  multiple scattering angles are first calculated
  for (hitNumber = 0; hitNumber < numberOfHit; hitNumber++) {
    trackParamAtHit = (AliMUONTrackParam*) (trackBeingFitted->GetTrackParamAtHit()->UncheckedAt(hitNumber));
    hitForRec = trackParamAtHit->GetHitForRecPtr();
    // extrapolation to the plane of the hitForRec attached to the current trackParamAtHit
    AliMUONTrackExtrap::ExtrapToZ(&param1, hitForRec->GetZ());
    // update track parameters of the current hit
    trackParamAtHit->SetTrackParam(param1);
    // square of multiple scattering angle at current hit, with one chamber
    msa2[hitNumber] = MultipleScatteringAngle2(&param1);
    // correction for eventual missing hits or multiple hits in a chamber,
    // according to the number of chambers
    // between the current hit and the previous one
    chCurrent = hitForRec->GetChamberNumber();
    if (hitNumber > 0) msa2[hitNumber] = msa2[hitNumber] * (chCurrent - chPrev);
    chPrev = chCurrent;
  }

  // Calculates the covariance matrix
  for (hitNumber1 = 0; hitNumber1 < numberOfHit; hitNumber1++) { 
    trackParamAtHit1 = (AliMUONTrackParam*) (trackBeingFitted->GetTrackParamAtHit()->UncheckedAt(hitNumber1));
    hitForRec1 = trackParamAtHit1->GetHitForRecPtr();
    z1 = hitForRec1->GetZ();
    for (hitNumber2 = hitNumber1; hitNumber2 < numberOfHit; hitNumber2++) {
      trackParamAtHit2 = (AliMUONTrackParam*) (trackBeingFitted->GetTrackParamAtHit()->UncheckedAt(hitNumber2));
      z2 = trackParamAtHit2->GetHitForRecPtr()->GetZ();
      // initialization to 0 (diagonal plus upper triangular part)
      (*covBending)(hitNumber2, hitNumber1) = 0.0;
      // contribution from multiple scattering in bending plane:
      // loop over upstream hits
      for (hitNumber3 = 0; hitNumber3 < hitNumber1; hitNumber3++) { 	
        trackParamAtHit3 = (AliMUONTrackParam*) (trackBeingFitted->GetTrackParamAtHit()->UncheckedAt(hitNumber3));
	z3 = trackParamAtHit3->GetHitForRecPtr()->GetZ();
	(*covBending)(hitNumber2, hitNumber1) = (*covBending)(hitNumber2, hitNumber1) + ((z1 - z3) * (z2 - z3) * msa2[hitNumber3]); 
      }
      // equal contribution from multiple scattering in non bending plane
      (*covNonBending)(hitNumber2, hitNumber1) = (*covBending)(hitNumber2, hitNumber1);
      if (hitNumber1 == hitNumber2) {
	// Diagonal elements: add contribution from position measurements
	// in bending plane
	(*covBending)(hitNumber2, hitNumber1) = (*covBending)(hitNumber2, hitNumber1) + hitForRec1->GetBendingReso2();
	// and in non bending plane
	(*covNonBending)(hitNumber2, hitNumber1) = (*covNonBending)(hitNumber2, hitNumber1) + hitForRec1->GetNonBendingReso2();
      } else {
	// Non diagonal elements: symmetrization
	// for bending plane
	(*covBending)(hitNumber1, hitNumber2) = (*covBending)(hitNumber2, hitNumber1);
	// and non bending plane
	(*covNonBending)(hitNumber1, hitNumber2) = (*covNonBending)(hitNumber2, hitNumber1);
      }
    } // for (hitNumber2 = hitNumber1;...
  } // for (hitNumber1 = 0;...
    
  // Inversion of covariance matrices
  // with "mnvertLocal", local "mnvert" function of Minuit.
  // One cannot use directly "mnvert" since "TVirtualFitter" does not know it.
  // One will have to replace this local function by the right inversion function
  // from a specialized Root package for symmetric positive definite matrices,
  // when available!!!!
  Int_t ifailBending;
  mnvertLocal(&((*covBending)(0,0)), numberOfHit, numberOfHit, numberOfHit, ifailBending);
  Int_t ifailNonBending;
  mnvertLocal(&((*covNonBending)(0,0)), numberOfHit, numberOfHit, numberOfHit, ifailNonBending);

  // It would be worth trying to calculate the inverse of the covariance matrix
  // only once per fit, since it cannot change much in principle,
  // and it would save a lot of computing time !!!!
  
  // Calculates Chi2
  if ((ifailBending == 0) && (ifailNonBending == 0)) {
    // with Multiple Scattering if inversion correct
    for (hitNumber1 = 0; hitNumber1 < numberOfHit ; hitNumber1++) { 
      trackParamAtHit1 = (AliMUONTrackParam*) (trackBeingFitted->GetTrackParamAtHit()->UncheckedAt(hitNumber1));
      hitForRec1 = trackParamAtHit1->GetHitForRecPtr();
      hbc1 = hitForRec1->GetBendingCoor();
      pbc1 = trackParamAtHit1->GetBendingCoor();
      hnbc1 = hitForRec1->GetNonBendingCoor();
      pnbc1 = trackParamAtHit1->GetNonBendingCoor();
      for (hitNumber2 = 0; hitNumber2 < numberOfHit; hitNumber2++) {
	trackParamAtHit2 = (AliMUONTrackParam*) (trackBeingFitted->GetTrackParamAtHit()->UncheckedAt(hitNumber2));
        hitForRec2 = trackParamAtHit2->GetHitForRecPtr();
	hbc2 = hitForRec2->GetBendingCoor();
	pbc2 = trackParamAtHit2->GetBendingCoor();
	hnbc2 = hitForRec2->GetNonBendingCoor();
	pnbc2 = trackParamAtHit2->GetNonBendingCoor();
	Chi2 += ((*covBending)(hitNumber2, hitNumber1) * (hbc1 - pbc1) * (hbc2 - pbc2)) +
		((*covNonBending)(hitNumber2, hitNumber1) * (hnbc1 - pnbc1) * (hnbc2 - pnbc2));
      }
    }
  } else {
    // without Multiple Scattering if inversion impossible
    for (hitNumber1 = 0; hitNumber1 < numberOfHit ; hitNumber1++) { 
      trackParamAtHit1 = (AliMUONTrackParam*) (trackBeingFitted->GetTrackParamAtHit()->UncheckedAt(hitNumber1));
      hitForRec1 = trackParamAtHit1->GetHitForRecPtr();
      hbc1 = hitForRec1->GetBendingCoor();
      pbc1 = trackParamAtHit1->GetBendingCoor();
      hnbc1 = hitForRec1->GetNonBendingCoor();
      pnbc1 = trackParamAtHit1->GetNonBendingCoor();
      Chi2 += ((hbc1 - pbc1) * (hbc1 - pbc1) / hitForRec1->GetBendingReso2()) +
	      ((hnbc1 - pnbc1) * (hnbc1 - pnbc1) / hitForRec1->GetNonBendingReso2());
    }
  }
  
  delete covBending;
  delete covNonBending;
  delete [] msa2;
}

Double_t MultipleScatteringAngle2(AliMUONTrackParam *param)
{
  /// Returns square of multiple Coulomb scattering angle
  /// from TrackParamAtHit pointed to by "param"
  Double_t slopeBending, slopeNonBending, radiationLength, inverseBendingMomentum2, inverseTotalMomentum2;
  Double_t varMultipleScatteringAngle;
  // Better implementation in AliMUONTrack class ????
  slopeBending = param->GetBendingSlope();
  slopeNonBending = param->GetNonBendingSlope();
  // thickness in radiation length for the current track,
  // taking local angle into account
  radiationLength = AliMUONConstants::DefaultChamberThicknessInX0() *
		    TMath::Sqrt(1.0 + slopeBending*slopeBending + slopeNonBending*slopeNonBending);
  inverseBendingMomentum2 =  param->GetInverseBendingMomentum() * param->GetInverseBendingMomentum();
  inverseTotalMomentum2 = inverseBendingMomentum2 * (1.0 + slopeBending * slopeBending) /
			  (1.0 + slopeBending *slopeBending + slopeNonBending * slopeNonBending); 
  varMultipleScatteringAngle = 0.0136 * (1.0 + 0.038 * TMath::Log(radiationLength));
  // The velocity is assumed to be 1 !!!!
  varMultipleScatteringAngle = inverseTotalMomentum2 * radiationLength * varMultipleScatteringAngle * varMultipleScatteringAngle;
  return varMultipleScatteringAngle;
}

//______________________________________________________________________________
 void mnvertLocal(Double_t *a, Int_t l, Int_t, Int_t n, Int_t &ifail)
{
///*-*-*-*-*-*-*-*-*-*-*-*Inverts a symmetric matrix*-*-*-*-*-*-*-*-*-*-*-*-*
///*-*                    ==========================
///*-*        inverts a symmetric matrix.   matrix is first scaled to
///*-*        have all ones on the diagonal (equivalent to change of units)
///*-*        but no pivoting is done since matrix is positive-definite.
///*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

  // taken from TMinuit package of Root (l>=n)
  // fVERTs, fVERTq and fVERTpp changed to localVERTs, localVERTq and localVERTpp
  //  Double_t localVERTs[n], localVERTq[n], localVERTpp[n];
  Double_t * localVERTs = new Double_t[n];
  Double_t * localVERTq = new Double_t[n];
  Double_t * localVERTpp = new Double_t[n];
  // fMaxint changed to localMaxint
  Int_t localMaxint = n;

    /* System generated locals */
    Int_t aOffset;

    /* Local variables */
    Double_t si;
    Int_t i, j, k, kp1, km1;

    /* Parameter adjustments */
    aOffset = l + 1;
    a -= aOffset;

    /* Function Body */
    ifail = 0;
    if (n < 1) goto L100;
    if (n > localMaxint) goto L100;
//*-*-                  scale matrix by sqrt of diag elements
    for (i = 1; i <= n; ++i) {
        si = a[i + i*l];
        if (si <= 0) goto L100;
        localVERTs[i-1] = 1 / TMath::Sqrt(si);
    }
    for (i = 1; i <= n; ++i) {
        for (j = 1; j <= n; ++j) {
            a[i + j*l] = a[i + j*l]*localVERTs[i-1]*localVERTs[j-1];
        }
    }
//*-*-                                       . . . start main loop . . . .
    for (i = 1; i <= n; ++i) {
        k = i;
//*-*-                  preparation for elimination step1
        if (a[k + k*l] != 0) localVERTq[k-1] = 1 / a[k + k*l];
        else goto L100;
        localVERTpp[k-1] = 1;
        a[k + k*l] = 0;
        kp1 = k + 1;
        km1 = k - 1;
        if (km1 < 0) goto L100;
        else if (km1 == 0) goto L50;
        else               goto L40;
L40:
        for (j = 1; j <= km1; ++j) {
            localVERTpp[j-1] = a[j + k*l];
            localVERTq[j-1]  = a[j + k*l]*localVERTq[k-1];
            a[j + k*l]   = 0;
        }
L50:
        if (k - n < 0) goto L51;
        else if (k - n == 0) goto L60;
        else                goto L100;
L51:
        for (j = kp1; j <= n; ++j) {
            localVERTpp[j-1] = a[k + j*l];
            localVERTq[j-1]  = -a[k + j*l]*localVERTq[k-1];
            a[k + j*l]   = 0;
        }
//*-*-                  elimination proper
L60:
        for (j = 1; j <= n; ++j) {
            for (k = j; k <= n; ++k) { a[j + k*l] += localVERTpp[j-1]*localVERTq[k-1]; }
        }
    }
//*-*-                  elements of left diagonal and unscaling
    for (j = 1; j <= n; ++j) {
        for (k = 1; k <= j; ++k) {
            a[k + j*l] = a[k + j*l]*localVERTs[k-1]*localVERTs[j-1];
            a[j + k*l] = a[k + j*l];
        }
    }
    delete [] localVERTs;
    delete [] localVERTq;
    delete [] localVERTpp;
    return;
//*-*-                  failure return
L100:
    delete [] localVERTs;
    delete [] localVERTq;
    delete [] localVERTpp;
    ifail = 1;
} /* mnvertLocal */

  //__________________________________________________________________________
void AliMUONTrackReconstructor::RemoveDoubleTracks(void)
{
  /// To remove double tracks.
  /// Tracks are considered identical
  /// if they have at least half of their hits in common.
  /// Among two identical tracks, one keeps the track with the larger number of hits
  /// or, if these numbers are equal, the track with the minimum Chi2.
  AliMUONTrack *track1, *track2, *trackToRemove;
  Int_t hitsInCommon, nHits1, nHits2;
  Bool_t removedTrack1;
  // Loop over first track of the pair
  track1 = (AliMUONTrack*) fRecTracksPtr->First();
  while (track1) {
    removedTrack1 = kFALSE;
    nHits1 = track1->GetNTrackHits();
    // Loop over second track of the pair
    track2 = (AliMUONTrack*) fRecTracksPtr->After(track1);
    while (track2) {
      nHits2 = track2->GetNTrackHits();
      // number of hits in common between two tracks
      hitsInCommon = track1->HitsInCommon(track2);
      // check for identical tracks
      if ((4 * hitsInCommon) >= (nHits1 + nHits2)) {
        // decide which track to remove
        if ((nHits1 > nHits2) || ((nHits1 == nHits2) && (track1->GetFitFMin() < track2->GetFitFMin()))) {
	  // remove track2 and continue the second loop with the track next to track2
	  trackToRemove = track2;
	  track2 = (AliMUONTrack*) fRecTracksPtr->After(track2);
	  fRecTracksPtr->Remove(trackToRemove);
	  fNRecTracks--;
	  fRecTracksPtr->Compress(); // this is essential to retrieve the TClonesArray afterwards
        } else {
	  // else remove track1 and continue the first loop with the track next to track1
	  trackToRemove = track1;
	  track1 = (AliMUONTrack*) fRecTracksPtr->After(track1);
          fRecTracksPtr->Remove(trackToRemove);
	  fNRecTracks--;
	  fRecTracksPtr->Compress(); // this is essential to retrieve the TClonesArray afterwards
	  removedTrack1 = kTRUE;
	  break;
        }
      } else track2 = (AliMUONTrack*) fRecTracksPtr->After(track2);
    } // track2
    if (removedTrack1) continue;
    track1 = (AliMUONTrack*) fRecTracksPtr->After(track1);
  } // track1
  return;
}

  //__________________________________________________________________________
void AliMUONTrackReconstructor::UpdateHitForRecAtHit()
{
  /// Set cluster parameters after track fitting. Fill fHitForRecAtHit of AliMUONTrack's
  AliMUONTrack *track;
  AliMUONTrackParam *trackParamAtHit;
  track = (AliMUONTrack*) fRecTracksPtr->First();
  while (track) {
    trackParamAtHit = (AliMUONTrackParam*) (track->GetTrackParamAtHit()->First());
    while (trackParamAtHit) {
      track->AddHitForRecAtHit(trackParamAtHit->GetHitForRecPtr());
      trackParamAtHit = (AliMUONTrackParam*) (track->GetTrackParamAtHit()->After(trackParamAtHit)); 
    }
    track = (AliMUONTrack*) fRecTracksPtr->After(track);
  }
  return;
}

  //__________________________________________________________________________
void AliMUONTrackReconstructor::EventDump(void)
{
  /// Dump reconstructed event (track parameters at vertex and at first hit),
  /// and the particle parameters
  AliMUONTrack *track;
  AliMUONTrackParam *trackParam, *trackParam1;
  Double_t bendingSlope, nonBendingSlope, pYZ;
  Double_t pX, pY, pZ, x, y, z, c;
  Int_t trackIndex, nTrackHits;
 
  AliDebug(1,"****** enter EventDump ******");
  AliDebug(1, Form("Number of Reconstructed tracks : %d", fNRecTracks)); 
  
  fRecTracksPtr->Compress(); // for simple loop without "Next" since no hole
  // Loop over reconstructed tracks
  for (trackIndex = 0; trackIndex < fNRecTracks; trackIndex++) {
    AliDebug(1, Form("track number: %d", trackIndex));
    // function for each track for modularity ????
    track = (AliMUONTrack*) ((*fRecTracksPtr)[trackIndex]);
    nTrackHits = track->GetNTrackHits();
    AliDebug(1, Form("Number of track hits: %d ", nTrackHits));
    // track parameters at Vertex
    trackParam = track->GetTrackParamAtVertex();
    x = trackParam->GetNonBendingCoor();
    y = trackParam->GetBendingCoor();
    z = trackParam->GetZ();
    bendingSlope = trackParam->GetBendingSlope();
    nonBendingSlope = trackParam->GetNonBendingSlope();
    pYZ = 1/TMath::Abs(trackParam->GetInverseBendingMomentum());
    pZ = pYZ/TMath::Sqrt(1+bendingSlope*bendingSlope);
    pX = pZ * nonBendingSlope;
    pY = pZ * bendingSlope;
    c = TMath::Sign(1.0, trackParam->GetInverseBendingMomentum());
    AliDebug(1, Form("Track parameters at Vertex z= %f: X= %f Y= %f pX= %f pY= %f pZ= %f c= %f\n",
		     z, x, y, pX, pY, pZ, c));

    // track parameters at first hit
    trackParam1 = (AliMUONTrackParam*) track->GetTrackParamAtHit()->First();
    x = trackParam1->GetNonBendingCoor();
    y = trackParam1->GetBendingCoor();
    z = trackParam1->GetZ();
    bendingSlope = trackParam1->GetBendingSlope();
    nonBendingSlope = trackParam1->GetNonBendingSlope();
    pYZ = 1/TMath::Abs(trackParam1->GetInverseBendingMomentum());
    pZ = pYZ/TMath::Sqrt(1.0 + bendingSlope * bendingSlope);
    pX = pZ * nonBendingSlope;
    pY = pZ * bendingSlope;
    c = TMath::Sign(1.0, trackParam1->GetInverseBendingMomentum());
    AliDebug(1, Form("track parameters at z= %f: X= %f Y= %f pX= %f pY= %f pZ= %f c= %f\n",
		     z, x, y, pX, pY, pZ, c));
  }
  // informations about generated particles NO !!!!!!!!
  
//    for (Int_t iPart = 0; iPart < np; iPart++) {
//      p = gAlice->Particle(iPart);
//      printf(" particle %d: type= %d px= %f py= %f pz= %f pdg= %d\n",
//  	   iPart, p->GetPdgCode(), p->Px(), p->Py(), p->Pz(), p->GetPdgCode());    
//    }
  return;
}