/**************************************************************************
 * Copyright(c) 1998-2003, 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.                  *
 **************************************************************************/

//-----------------------------------------------------------------
//    Implementation of the vertexer from ESD tracks
//
// Origin: AliITSVertexerTracks
//         A.Dainese, Padova, 
//         andrea.dainese@pd.infn.it
//         M.Masera,  Torino, 
//         massimo.masera@to.infn.it
// Moved to STEER and adapted to ESD tracks: 
//          F.Prino,  Torino, prino@to.infn.it
//-----------------------------------------------------------------

//---- Root headers --------
#include <TTree.h>
#include <TMatrixD.h>
//---- AliRoot headers -----
#include "AliStrLine.h"
#include "AliVertexerTracks.h"
#include "AliESD.h"
#include "AliESDtrack.h"

ClassImp(AliVertexerTracks)


//----------------------------------------------------------------------------
AliVertexerTracks::AliVertexerTracks():
TObject(),
fVert(),
fCurrentVertex(0),
fMinTracks(2),
fMinITSClusters(5),
fTrkArray(),
fTrksToSkip(0),
fNTrksToSkip(0),
fDCAcut(0),
fAlgo(1),
fNSigma(3),
fDebug(0)
{
//
// Default constructor
//
  SetVtxStart();
  SetVtxStartSigma();
  SetMinTracks();
  SetMinITSClusters();
  SetNSigmad0(); 
}
//-----------------------------------------------------------------------------
AliVertexerTracks::AliVertexerTracks(Double_t xStart, Double_t yStart):
TObject(),
fVert(),
fCurrentVertex(0),
fMinTracks(2),
fMinITSClusters(5),
fTrkArray(),
fTrksToSkip(0),
fNTrksToSkip(0),
fDCAcut(0),
fAlgo(1),
fNSigma(3),
fDebug(0)
{
//
// Standard constructor
//
  SetVtxStart(xStart,yStart);
  SetVtxStartSigma();
  SetMinTracks();
  SetMinITSClusters();
  SetNSigmad0(); 
}
//-----------------------------------------------------------------------------
AliVertexerTracks::~AliVertexerTracks() {
  // Default Destructor
  // The objects pointed by the following pointer are not owned
  // by this class and are not deleted
  fCurrentVertex = 0;
  delete[] fTrksToSkip;
}
//---------------------------------------------------------------------------
void AliVertexerTracks::SetSkipTracks(Int_t n,Int_t *skipped) {
//
// Mark the tracks not ot be used in the vertex finding
//
  fNTrksToSkip = n;
  fTrksToSkip = new Int_t[n]; 
  for(Int_t i=0;i<n;i++) fTrksToSkip[i] = skipped[i]; 
  return; 
}
//----------------------------------------------------------------------------
Int_t AliVertexerTracks::PrepareTracks(TTree &trkTree, Int_t OptImpParCut) {
//
// Propagate tracks to initial vertex position and store them in a TObjArray
//
  Double_t maxd0rphi = 3.;  
  Int_t    nTrks    = 0;
  Double_t sigmaCurr[3],sigmaVtx[3],posVtx[3];
  Double_t covVtx[6],covVtxXY;
  Float_t  d0z0[2],covd0z0[3]; 
  Double_t momentum[3],postrk[3];
  Double_t pt,sigma,sigmavtxphi,phitrk;
  Double_t field=GetField();

  AliESDVertex *initVertex = new AliESDVertex(fNominalPos,fNominalSigma);

  Int_t    nEntries = (Int_t)trkTree.GetEntries();
  if(!fTrkArray.IsEmpty()) fTrkArray.Delete();
  // fTrkArray.Expand(nEntries);

  if(fDebug) {
    printf(" PrepareTracks()\n");
  }

  for(Int_t i=0; i<nEntries; i++) {
    AliESDtrack *track = new AliESDtrack; 
    trkTree.SetBranchAddress("tracks",&track);
    trkTree.GetEvent(i);



    // propagate track to vertex
    if(OptImpParCut==1) { // OptImpParCut==1
      track->RelateToVertex(initVertex,field,100.);
      initVertex->GetXYZ(posVtx);
      initVertex->GetSigmaXYZ(sigmaVtx);
      covVtxXY = 0.;
    } else {              // OptImpParCut==2
      fCurrentVertex->GetSigmaXYZ(sigmaCurr);
      if((sigmaCurr[0]+sigmaCurr[1])<(fNominalSigma[0]+fNominalSigma[1])) {
	track->RelateToVertex(fCurrentVertex,field,100.);
	fCurrentVertex->GetXYZ(posVtx);
	fCurrentVertex->GetSigmaXYZ(sigmaVtx);
	fCurrentVertex->GetCovMatrix(covVtx);
	covVtxXY = covVtx[1];
      } else {
	track->RelateToVertex(initVertex,field,100.);
	initVertex->GetXYZ(posVtx);
	initVertex->GetSigmaXYZ(sigmaVtx);
	covVtxXY = 0.;
      }
    }

    // select tracks with d0rphi < maxd0rphi
    track->GetImpactParameters(d0z0,covd0z0);

    track->GetXYZ(postrk);
    track->GetPxPyPz(momentum);
    pt = TMath::Sqrt(momentum[0]*momentum[0]+momentum[1]*momentum[1]);

    phitrk = TMath::ATan2(postrk[1]-posVtx[1],postrk[0]-posVtx[0]);
    sigmavtxphi = TMath::Sqrt(sigmaVtx[0]*sigmaVtx[0]*
			      TMath::Cos(phitrk)*TMath::Cos(phitrk)+
			      sigmaVtx[1]*sigmaVtx[1]*
			      TMath::Sin(phitrk)*TMath::Sin(phitrk)+
                              covVtxXY*
			      TMath::Cos(phitrk)*TMath::Sin(phitrk));
    sigma = TMath::Sqrt(Sigmad0rphi(pt)*Sigmad0rphi(pt)+
			sigmavtxphi*sigmavtxphi);
    maxd0rphi = fNSigma*sigma;
    if(OptImpParCut==1) maxd0rphi *= 5.;

    if(fDebug) printf("trk %d; lab %d; |d0| = %f;  cut = %f\n",i,track->GetLabel(),TMath::Abs(d0z0[0]),maxd0rphi);
    if(TMath::Abs(d0z0[0]) > maxd0rphi) { 
      if(fDebug) printf("     rejected\n");
      delete track; continue; 
    }

    fTrkArray.AddLast(track);
    nTrks++; 
  }

  delete initVertex;

  return nTrks;
} 
//----------------------------------------------------------------------------
Double_t AliVertexerTracks::Sigmad0rphi(Double_t pt) const {
//
// Impact parameter resolution in rphi [cm] vs pt [GeV/c]
//
  Double_t a_meas  = 11.6;
  Double_t a_scatt = 65.8;
  Double_t b       = 1.878;

  Double_t sigma = a_meas*a_meas+a_scatt*a_scatt/TMath::Power(pt,b);
  sigma = 0.0001*TMath::Sqrt(sigma);

  return sigma;
}
//----------------------------------------------------------------------------
AliVertex* AliVertexerTracks::VertexForSelectedTracks(TTree *trkTree) {
//
// Return vertex from tracks in trkTree
//

  // get tracks and propagate them to initial vertex position
  Int_t nTrks = PrepareTracks(*trkTree,1);
  if(nTrks < fMinTracks) {
    printf("TooFewTracks\n");
    Double_t vtx[3]={0,0,0};
    fVert.SetXYZ(vtx);
    fVert.SetDispersion(999);
    fVert.SetNContributors(-5);
    fTrkArray.Delete();
    return &fVert;
  }
 
  // Set initial vertex position from ESD
  if(fAlgo==1)  StrLinVertexFinderMinDist(1);
  if(fAlgo==2)  StrLinVertexFinderMinDist(0);
  if(fAlgo==3)  HelixVertexFinder();
  if(fAlgo==4)  VertexFinder(1);
  if(fAlgo==5)  VertexFinder(0);
  return &fVert;
}
//----------------------------------------------------------------------------
AliESDVertex* AliVertexerTracks::FindPrimaryVertex(const AliESD *esdEvent)
{
//
// Primary vertex for current ESD event
// (Two iterations: 
//  1st with 5*fNSigma*sigma(pt) cut w.r.t. to initial vertex; 
//  2nd with fNSigma*sigma(pt) cut w.r.t. to vertex found in 1st iteration) 
// All ESD tracks with inside the beam pipe are then propagated to found vertex
//
  fCurrentVertex = 0;

  Int_t entr = (Int_t)esdEvent->GetNumberOfTracks();
  TTree *trkTree = new TTree("TreeT","tracks");
  AliESDtrack *esdTrack = 0;
  trkTree->Branch("tracks","AliESDtrack",&esdTrack);

  Bool_t   skipThis;
  for(Int_t i=0; i<entr; i++) {
    // check tracks to skip
    skipThis = kFALSE;
    for(Int_t j=0; j<fNTrksToSkip; j++) { 
      if(i==fTrksToSkip[j]) {
	if(fDebug) printf("skipping track: %d\n",i);
	skipThis = kTRUE;
      }
    }
    if(skipThis) continue;
    AliESDtrack *et = esdEvent->GetTrack(i);
    esdTrack = new AliESDtrack(*et);
    if(!(esdTrack->GetStatus()&AliESDtrack::kITSin)) {delete esdTrack;continue;}
    if(!(esdTrack->GetStatus()&AliESDtrack::kITSrefit)) {delete esdTrack;continue;}
    Int_t nclus=esdTrack->GetNcls(0); // check number of clusters in ITS
    if(nclus<fMinITSClusters) {delete esdTrack;continue;}
    trkTree->Fill();
    delete esdTrack;
  }
  //  delete esdTrack;
 

  // ITERATION 1
  // propagate tracks to initVertex
  // preselect them  (reject for |d0|>5*fNSigma*sigma w.r.t. initVertex)
  Int_t nTrks;
  nTrks = PrepareTracks(*trkTree,1);
  if(fDebug) printf(" tracks prepared - step 1: %d\n",nTrks);
  if(nTrks < fMinTracks) {
    printf("TooFewTracks\n");
    TooFewTracks(esdEvent);
    if(fDebug) fCurrentVertex->PrintStatus();
    fTrkArray.Delete();
    delete trkTree;
    return fCurrentVertex; 
  }

  // vertex finder
  switch (fAlgo) {
    case 1: StrLinVertexFinderMinDist(1); break;
    case 2: StrLinVertexFinderMinDist(0); break;
    case 3: HelixVertexFinder();          break;
    case 4: VertexFinder(1);              break;
    case 5: VertexFinder(0);              break;
    default: printf("Wrong algorithm\n"); break;  
  }
  if(fDebug) printf(" vertex finding completed\n");

  // vertex fitter
  VertexFitter(kTRUE);
  if(fDebug) printf(" vertex fit completed\n");
  fTrkArray.Delete();
  // ITERATION 2
  // propagate tracks to best between initVertex and fCurrentVertex
  // preselect tracks (reject for |d0|>fNSigma*sigma w.r.t. best 
  //                   between initVertex and fCurrentVertex) 
  nTrks = PrepareTracks(*trkTree,2);
  delete trkTree;
  if(fDebug) printf(" tracks prepared - step 2: %d\n",nTrks);
  if(nTrks < fMinTracks) {
    printf("TooFewTracks\n");
    TooFewTracks(esdEvent);
    if(fDebug) fCurrentVertex->PrintStatus();
    fTrkArray.Delete();
    return fCurrentVertex; 
  }

  // vertex finder
  switch (fAlgo) {
    case 1: StrLinVertexFinderMinDist(1); break;
    case 2: StrLinVertexFinderMinDist(0); break;
    case 3: HelixVertexFinder();          break;
    case 4: VertexFinder(1);              break;
    case 5: VertexFinder(0);              break;
    default: printf("Wrong algorithm\n"); break;  
  }
  if(fDebug) printf(" vertex finding completed\n");

  // fitter
  VertexFitter(kTRUE);
  if(fDebug) printf(" vertex fit completed\n");


  fTrkArray.Delete();

  // take true pos from ESD
  Double_t tp[3];
  esdEvent->GetVertex()->GetTruePos(tp);
  fCurrentVertex->SetTruePos(tp);
  if(fNominalSigma[0]>1.) {
    fCurrentVertex->SetTitle("VertexerTracksNoConstraint");
  } else {
    fCurrentVertex->SetTitle("VertexerTracksWithConstraint");
  }

  if(fDebug) fCurrentVertex->PrintStatus();
  if(fTrksToSkip) delete [] fTrksToSkip;
  
  // propagate tracks to found vertex
  if(TMath::Sqrt(fCurrentVertex->GetXv()*fCurrentVertex->GetXv()+fCurrentVertex->GetYv()*fCurrentVertex->GetYv())<3.) {
    for(Int_t ii=0; ii<entr; ii++) {
      AliESDtrack *et = esdEvent->GetTrack(ii);
      if(!et->GetStatus()&AliESDtrack::kITSin) continue;
      if(et->GetX()>3.) continue;
      et->RelateToVertex(fCurrentVertex,GetField(),100.);
    }
  } else {
    AliWarning("Found vertex outside beam pipe!");
  }
 
  return fCurrentVertex;
}
//----------------------------------------------------------------------------
AliESDVertex* AliVertexerTracks::FindPrimaryVertexOld(const AliESD *esdEvent)
{
//
// Primary vertex for current ESD event (one iteration with |d0rphi|<3cm)
//
  fCurrentVertex = 0;

  Int_t entr = (Int_t)esdEvent->GetNumberOfTracks();
  TTree *trkTree = new TTree("TreeT","tracks");
  AliESDtrack *esdTrack = 0;
  trkTree->Branch("tracks","AliESDtrack",&esdTrack);

  for(Int_t i=0; i<entr; i++) {
    AliESDtrack *et = esdEvent->GetTrack(i);
    esdTrack = new AliESDtrack(*et);
    if(!(esdTrack->GetStatus()&AliESDtrack::kITSin)) {delete esdTrack;continue;}
    if(!(esdTrack->GetStatus()&AliESDtrack::kITSrefit)) {delete esdTrack;continue;}
    Int_t nclus=esdTrack->GetNcls(0); // check number of clusters in ITS
    if(nclus<fMinITSClusters) continue;

    trkTree->Fill();
    delete esdTrack;
  }
  //  delete esdTrack;

  // preselect tracks and propagate them to initial vertex position
  Int_t nTrks = PrepareTracks(*trkTree,1);
  delete trkTree;
  if(fDebug) printf(" tracks prepared: %d\n",nTrks);
  if(nTrks < fMinTracks) {
    printf("TooFewTracks\n");
    fCurrentVertex = new AliESDVertex(0.,0.,-1);
    fTrkArray.Delete();
    return fCurrentVertex; 
  }

  // VERTEX FINDER
  switch (fAlgo) {
    case 1: StrLinVertexFinderMinDist(1); break;
    case 2: StrLinVertexFinderMinDist(0); break;
    case 3: HelixVertexFinder();          break;
    case 4: VertexFinder(1);              break;
    case 5: VertexFinder(0);              break;
    default: printf("Wrong algorithm\n"); break;  
  }

  // VERTEX FITTER
  VertexFitter();
  if(fDebug) printf(" vertex fit completed\n");


  Double_t tp[3];
  esdEvent->GetVertex()->GetTruePos(tp);
  fCurrentVertex->SetTruePos(tp);
  fCurrentVertex->SetTitle("VertexerTracks");

  fTrkArray.Delete();
  return fCurrentVertex;
}
//----------------------------------------------------------------------------
AliVertex* AliVertexerTracks::VertexForSelectedTracks(TObjArray *trkArray) {
//
// Return vertex from array of tracks
//

  // get tracks and propagate them to initial vertex position
  Int_t nTrks = trkArray->GetEntriesFast();
  if(nTrks < fMinTracks) {
    printf("TooFewTracks\n");
    Double_t vtx[3]={0,0,0};
    fVert.SetXYZ(vtx);
    fVert.SetDispersion(999);
    fVert.SetNContributors(-5);
    fTrkArray.Delete();
    return &fVert;
  }
  TTree *trkTree = new TTree("TreeT","tracks");
  AliESDtrack *esdTrack = 0;
  trkTree->Branch("tracks","AliESDtrack",&esdTrack);
  for(Int_t i=0; i<nTrks; i++){
    esdTrack = (AliESDtrack*)trkArray->At(i);
    trkTree->Fill();
  }
    
  AliVertex *vtx =  VertexForSelectedTracks(trkTree);
  delete trkTree;
  return vtx;
}

//---------------------------------------------------------------------------
void AliVertexerTracks::VertexFinder(Int_t optUseWeights) {

  // Get estimate of vertex position in (x,y) from tracks DCA
 
  Double_t initPos[3];
  initPos[2] = 0.;
  for(Int_t i=0;i<2;i++)initPos[i]=fNominalPos[i];
  Int_t nacc = (Int_t)fTrkArray.GetEntriesFast();
  Double_t aver[3]={0.,0.,0.};
  Double_t aversq[3]={0.,0.,0.};
  Double_t sigmasq[3]={0.,0.,0.};
  Double_t sigma=0;
  Int_t ncombi = 0;
  AliESDtrack *track1;
  AliESDtrack *track2;
  Double_t pos[3],dir[3]; 
  Double_t alpha,mindist;
  Double_t field=GetField();

  for(Int_t i=0; i<nacc; i++){
    track1 = (AliESDtrack*)fTrkArray.At(i);
    alpha=track1->GetAlpha();
    mindist = TMath::Cos(alpha)*fNominalPos[0]+TMath::Sin(alpha)*fNominalPos[1];
    track1->GetXYZAt(mindist,field,pos);
    track1->GetPxPyPzAt(mindist,field,dir);
    AliStrLine *line1 = new AliStrLine(pos,dir); 

   //    AliStrLine *line1 = new AliStrLine();
   //    track1->ApproximateHelixWithLine(mindist,field,line1);
   
    for(Int_t j=i+1; j<nacc; j++){
      track2 = (AliESDtrack*)fTrkArray.At(j);
      alpha=track2->GetAlpha();
      mindist = TMath::Cos(alpha)*fNominalPos[0]+TMath::Sin(alpha)*fNominalPos[1];
      track2->GetXYZAt(mindist,field,pos);
      track2->GetPxPyPzAt(mindist,field,dir);
      AliStrLine *line2 = new AliStrLine(pos,dir); 
    //      AliStrLine *line2 = new AliStrLine();
    //  track2->ApproximateHelixWithLine(mindist,field,line2);
      Double_t distCA=line2->GetDCA(line1);
      if(fDCAcut<=0 || (fDCAcut>0&&distCA<fDCAcut)){
	Double_t pnt1[3],pnt2[3],crosspoint[3];

	if(optUseWeights<=0){
	  Int_t retcode = line2->Cross(line1,crosspoint);
	  if(retcode>=0){
	    ncombi++;
	    for(Int_t jj=0;jj<3;jj++)aver[jj]+=crosspoint[jj];
	    for(Int_t jj=0;jj<3;jj++)aversq[jj]+=(crosspoint[jj]*crosspoint[jj]);
	  }
	}
	if(optUseWeights>0){
	  Int_t retcode = line1->CrossPoints(line2,pnt1,pnt2);
	  if(retcode>=0){
	    Double_t alpha, cs, sn;
	    alpha=track1->GetAlpha();
	    cs=TMath::Cos(alpha); sn=TMath::Sin(alpha);	  
	    Double_t sx1=sn*sn*track1->GetSigmaY2(), sy1=cs*cs*track1->GetSigmaY2();
	    alpha=track2->GetAlpha();
	    cs=TMath::Cos(alpha); sn=TMath::Sin(alpha);
	    Double_t sx2=sn*sn*track2->GetSigmaY2(), sy2=cs*cs*track2->GetSigmaY2();
	    Double_t sz1=track1->GetSigmaZ2(), sz2=track2->GetSigmaZ2();
	    Double_t wx1=sx2/(sx1+sx2), wx2=1.- wx1;
	    Double_t wy1=sy2/(sy1+sy2), wy2=1.- wy1;
	    Double_t wz1=sz2/(sz1+sz2), wz2=1.- wz1;
	    crosspoint[0]=wx1*pnt1[0] + wx2*pnt2[0]; 
	    crosspoint[1]=wy1*pnt1[1] + wy2*pnt2[1]; 
	    crosspoint[2]=wz1*pnt1[2] + wz2*pnt2[2];
	  
	    ncombi++;
	    for(Int_t jj=0;jj<3;jj++)aver[jj]+=crosspoint[jj];
	    for(Int_t jj=0;jj<3;jj++)aversq[jj]+=(crosspoint[jj]*crosspoint[jj]);
	  }
	}
      }
      delete line2;
    }
    delete line1;
  }
  if(ncombi>0){
    for(Int_t jj=0;jj<3;jj++){
      initPos[jj] = aver[jj]/ncombi;
      aversq[jj]/=ncombi;
      sigmasq[jj]=aversq[jj]-initPos[jj]*initPos[jj];
      sigma+=sigmasq[jj];
    }
    sigma=TMath::Sqrt(TMath::Abs(sigma));
  }
  else {
    Warning("VertexFinder","Finder did not succed");
    sigma=999;
  }
  fVert.SetXYZ(initPos);
  fVert.SetDispersion(sigma);
  fVert.SetNContributors(ncombi);
}
//---------------------------------------------------------------------------
void AliVertexerTracks::HelixVertexFinder() {

  // Get estimate of vertex position in (x,y) from tracks DCA


  Double_t initPos[3];
  initPos[2] = 0.;
  for(Int_t i=0;i<2;i++)initPos[i]=fNominalPos[i];
  Double_t field=GetField();

  Int_t nacc = (Int_t)fTrkArray.GetEntriesFast();

  Double_t aver[3]={0.,0.,0.};
  Double_t averquad[3]={0.,0.,0.};
  Double_t sigmaquad[3]={0.,0.,0.};
  Double_t sigma=0;
  Int_t ncombi = 0;
  AliESDtrack *track1;
  AliESDtrack *track2;
  Double_t distCA;
  Double_t x, par[5];
  Double_t alpha, cs, sn;
  Double_t crosspoint[3];
  for(Int_t i=0; i<nacc; i++){
    track1 = (AliESDtrack*)fTrkArray.At(i);
    

    for(Int_t j=i+1; j<nacc; j++){
      track2 = (AliESDtrack*)fTrkArray.At(j);

      distCA=track2->PropagateToDCA(track1,field);

      if(fDCAcut<=0 ||(fDCAcut>0&&distCA<fDCAcut)){
	track1->GetExternalParameters(x,par);
	alpha=track1->GetAlpha();
	cs=TMath::Cos(alpha); sn=TMath::Sin(alpha);
	Double_t x1=x*cs - par[0]*sn;
	Double_t y1=x*sn + par[0]*cs;
	Double_t z1=par[1];
	Double_t sx1=sn*sn*track1->GetSigmaY2(), sy1=cs*cs*track1->GetSigmaY2(); 
	track2->GetExternalParameters(x,par);
	alpha=track2->GetAlpha();
	cs=TMath::Cos(alpha); sn=TMath::Sin(alpha);
	Double_t x2=x*cs - par[0]*sn;
	Double_t y2=x*sn + par[0]*cs;
	Double_t z2=par[1];
	Double_t sx2=sn*sn*track2->GetSigmaY2(), sy2=cs*cs*track2->GetSigmaY2();
	Double_t sz1=track1->GetSigmaZ2(), sz2=track2->GetSigmaZ2();
	Double_t wx1=sx2/(sx1+sx2), wx2=1.- wx1;
	Double_t wy1=sy2/(sy1+sy2), wy2=1.- wy1;
	Double_t wz1=sz2/(sz1+sz2), wz2=1.- wz1;
	crosspoint[0]=wx1*x1 + wx2*x2; 
	crosspoint[1]=wy1*y1 + wy2*y2; 
	crosspoint[2]=wz1*z1 + wz2*z2;

	ncombi++;
	for(Int_t jj=0;jj<3;jj++)aver[jj]+=crosspoint[jj];
	for(Int_t jj=0;jj<3;jj++)averquad[jj]+=(crosspoint[jj]*crosspoint[jj]);
      }
    }
      
  }
  if(ncombi>0){
    for(Int_t jj=0;jj<3;jj++){
      initPos[jj] = aver[jj]/ncombi;
      averquad[jj]/=ncombi;
      sigmaquad[jj]=averquad[jj]-initPos[jj]*initPos[jj];
      sigma+=sigmaquad[jj];
    }
    sigma=TMath::Sqrt(TMath::Abs(sigma));
  }
  else {
    Warning("HelixVertexFinder","Finder did not succed");
    sigma=999;
  }
  fVert.SetXYZ(initPos);
  fVert.SetDispersion(sigma);
  fVert.SetNContributors(ncombi);
}
//---------------------------------------------------------------------------
void AliVertexerTracks::StrLinVertexFinderMinDist(Int_t optUseWeights){

  // Calculate the point at minimum distance to prepared tracks 
  
  Double_t initPos[3];
  initPos[2] = 0.;
  Double_t sigma=0;
  for(Int_t i=0;i<2;i++)initPos[i]=fNominalPos[i];
  const Int_t knacc = (Int_t)fTrkArray.GetEntriesFast();
  Double_t field=GetField();

  AliESDtrack *track1;
  Double_t (*vectP0)[3]=new Double_t [knacc][3];
  Double_t (*vectP1)[3]=new Double_t [knacc][3];
  
  Double_t sum[3][3];
  Double_t dsum[3]={0,0,0};
  for(Int_t i=0;i<3;i++)
    for(Int_t j=0;j<3;j++)sum[i][j]=0;
  for(Int_t i=0; i<knacc; i++){
    track1 = (AliESDtrack*)fTrkArray.At(i);
    Double_t alpha=track1->GetAlpha();
    Double_t mindist = TMath::Cos(alpha)*fNominalPos[0]+TMath::Sin(alpha)*fNominalPos[1];
    Double_t pos[3],dir[3]; 
    track1->GetXYZAt(mindist,field,pos);
    track1->GetPxPyPzAt(mindist,field,dir);
    AliStrLine *line1 = new AliStrLine(pos,dir); 
    //    AliStrLine *line1 = new AliStrLine();
    //    track1->ApproximateHelixWithLine(mindist,field,line1);

    Double_t p0[3],cd[3];
    line1->GetP0(p0);
    line1->GetCd(cd);
    Double_t p1[3]={p0[0]+cd[0],p0[1]+cd[1],p0[2]+cd[2]};
    vectP0[i][0]=p0[0];
    vectP0[i][1]=p0[1];
    vectP0[i][2]=p0[2];
    vectP1[i][0]=p1[0];
    vectP1[i][1]=p1[1];
    vectP1[i][2]=p1[2];
    
    Double_t matr[3][3];
    Double_t dknow[3];
    if(optUseWeights==0)GetStrLinDerivMatrix(p0,p1,matr,dknow);
    if(optUseWeights==1){
      Double_t sigmasq[3];
      sigmasq[0]=track1->GetSigmaY2();
      sigmasq[1]=track1->GetSigmaY2();
      sigmasq[2]=track1->GetSigmaZ2();
      GetStrLinDerivMatrix(p0,p1,sigmasq,matr,dknow);
    }

    for(Int_t iii=0;iii<3;iii++){
      dsum[iii]+=dknow[iii]; 
      for(Int_t lj=0;lj<3;lj++) sum[iii][lj]+=matr[iii][lj];
    }
    delete line1;
  }
  
  Double_t vett[3][3];
  Double_t det=GetDeterminant3X3(sum);
  
   if(det!=0){
     for(Int_t zz=0;zz<3;zz++){
       for(Int_t ww=0;ww<3;ww++){
	 for(Int_t kk=0;kk<3;kk++) vett[ww][kk]=sum[ww][kk];
       }
       for(Int_t kk=0;kk<3;kk++) vett[kk][zz]=dsum[kk];
       initPos[zz]=GetDeterminant3X3(vett)/det;
     }


     for(Int_t i=0; i<knacc; i++){
       Double_t p0[3]={0,0,0},p1[3]={0,0,0};
       for(Int_t ii=0;ii<3;ii++){
	 p0[ii]=vectP0[i][ii];
	 p1[ii]=vectP1[i][ii];
       }
       sigma+=GetStrLinMinDist(p0,p1,initPos);
     }

     sigma=TMath::Sqrt(sigma);
   }else{
    Warning("StrLinVertexFinderMinDist","Finder did not succed");
    sigma=999;
  }
  delete vectP0;
  delete vectP1;
  fVert.SetXYZ(initPos);
  fVert.SetDispersion(sigma);
  fVert.SetNContributors(knacc);
}
//_______________________________________________________________________
Double_t AliVertexerTracks::GetDeterminant3X3(Double_t matr[][3]){
  //
  Double_t det=matr[0][0]*matr[1][1]*matr[2][2]-matr[0][0]*matr[1][2]*matr[2][1]-matr[0][1]*matr[1][0]*matr[2][2]+matr[0][1]*matr[1][2]*matr[2][0]+matr[0][2]*matr[1][0]*matr[2][1]-matr[0][2]*matr[1][1]*matr[2][0];
 return det;
}
//____________________________________________________________________________
void AliVertexerTracks::GetStrLinDerivMatrix(Double_t *p0,Double_t *p1,Double_t (*m)[3],Double_t *d){

  //
  Double_t x12=p0[0]-p1[0];
  Double_t y12=p0[1]-p1[1];
  Double_t z12=p0[2]-p1[2];
  Double_t kk=x12*x12+y12*y12+z12*z12;
  m[0][0]=2-2/kk*x12*x12;
  m[0][1]=-2/kk*x12*y12;
  m[0][2]=-2/kk*x12*z12;
  m[1][0]=-2/kk*x12*y12;
  m[1][1]=2-2/kk*y12*y12;
  m[1][2]=-2/kk*y12*z12;
  m[2][0]=-2/kk*x12*z12;
  m[2][1]=-2*y12*z12;
  m[2][2]=2-2/kk*z12*z12;
  d[0]=2*p0[0]-2/kk*p0[0]*x12*x12-2/kk*p0[2]*x12*z12-2/kk*p0[1]*x12*y12;
  d[1]=2*p0[1]-2/kk*p0[1]*y12*y12-2/kk*p0[0]*x12*y12-2/kk*p0[2]*z12*y12;
  d[2]=2*p0[2]-2/kk*p0[2]*z12*z12-2/kk*p0[0]*x12*z12-2/kk*p0[1]*z12*y12;

}
//____________________________________________________________________________
void AliVertexerTracks::GetStrLinDerivMatrix(Double_t *p0,Double_t *p1,Double_t *sigmasq,Double_t (*m)[3],Double_t *d){
  //
  Double_t x12=p1[0]-p0[0];
  Double_t y12=p1[1]-p0[1];
  Double_t z12=p1[2]-p0[2];

  Double_t den= x12*x12*sigmasq[1]*sigmasq[2]+y12*y12*sigmasq[0]*sigmasq[2]+z12*z12*sigmasq[0]*sigmasq[1];

  Double_t kk= 2*(x12*x12/sigmasq[0]+y12*y12/sigmasq[1]+z12*z12/sigmasq[2]);

  Double_t cc[3];
  cc[0]=-x12/sigmasq[0];
  cc[1]=-y12/sigmasq[1];
  cc[2]=-z12/sigmasq[2];

  Double_t ww=(-p0[0]*x12*sigmasq[1]*sigmasq[2]-p0[1]*y12*sigmasq[0]*sigmasq[2]-p0[2]*z12*sigmasq[0]*sigmasq[1])/den;

  Double_t ss= -p0[0]*cc[0]-p0[1]*cc[1]-p0[2]*cc[2];

  Double_t aa[3];
  aa[0]=x12*sigmasq[1]*sigmasq[2]/den;
  aa[1]=y12*sigmasq[0]*sigmasq[2]/den;
  aa[2]=z12*sigmasq[0]*sigmasq[1]/den;

  m[0][0]=aa[0]*(aa[0]*kk+2*cc[0])+2*cc[0]*aa[0]+2/sigmasq[0];
  m[0][1]=aa[1]*(aa[0]*kk+2*cc[0])+2*cc[1]*aa[0];
  m[0][2]=aa[2]*(aa[0]*kk+2*cc[0])+2*cc[2]*aa[0];

  m[1][0]=aa[0]*(aa[1]*kk+2*cc[1])+2*cc[0]*aa[1];
  m[1][1]=aa[1]*(aa[1]*kk+2*cc[1])+2*cc[1]*aa[1]+2/sigmasq[1];
  m[1][2]=aa[2]*(aa[1]*kk+2*cc[1])+2*cc[2]*aa[1];

  m[2][0]=aa[0]*(aa[2]*kk+2*cc[2])+2*cc[0]*aa[2];
  m[2][1]=aa[1]*(aa[2]*kk+2*cc[2])+2*cc[1]*aa[2];
  m[2][2]=aa[2]*(aa[2]*kk+2*cc[2])+2*cc[2]*aa[2]+2/sigmasq[2];

  d[0]=-ww*(aa[0]*kk+2*cc[0])-2*ss*aa[0]+2*p0[0]/sigmasq[0];
  d[1]=-ww*(aa[1]*kk+2*cc[1])-2*ss*aa[1]+2*p0[1]/sigmasq[1];
  d[2]=-ww*(aa[2]*kk+2*cc[2])-2*ss*aa[2]+2*p0[2]/sigmasq[2];

  }
//_____________________________________________________________________________
Double_t AliVertexerTracks::GetStrLinMinDist(Double_t *p0,Double_t *p1,Double_t *x0){
  //
  Double_t x12=p0[0]-p1[0];
  Double_t y12=p0[1]-p1[1];
  Double_t z12=p0[2]-p1[2];
  Double_t x10=p0[0]-x0[0];
  Double_t y10=p0[1]-x0[1];
  Double_t z10=p0[2]-x0[2];
  return ((x10*x10+y10*y10+z10*z10)*(x12*x12+y12*y12+z12*z12)-(x10*x12+y10*y12+z10*z12)*(x10*x12+y10*y12+z10*z12))/(x12*x12+y12*y12+z12*z12);
}
//---------------------------------------------------------------------------
void AliVertexerTracks::VertexFitter(Bool_t useNominalVtx) {
//
// The optimal estimate of the vertex position is given by a "weighted 
// average of tracks positions"
// Original method: CMS Note 97/0051
//
  Double_t initPos[3];
  fVert.GetXYZ(initPos);
  if(fDebug) { 
    printf(" VertexFitter(): start\n");
    printf(" Number of tracks in array: %d\n",(Int_t)fTrkArray.GetEntriesFast());
    printf(" Minimum # tracks required in fit: %d\n",fMinTracks);
    printf("Vertex position after finder: %f,%f,%f\n",initPos[0],initPos[1],initPos[2]);
    if(useNominalVtx) printf(" This vertex will be used in fit: (%f+-%f,%f+-%f)\n",fNominalPos[0],fNominalSigma[0],fNominalPos[1],fNominalSigma[1]); 
  }

  Int_t i,j,k,step=0;
  TMatrixD rv(3,1);
  TMatrixD vV(3,3);
  rv(0,0) = initPos[0];
  rv(1,0) = initPos[1];
  rv(2,0) = 0.;
  Double_t xlStart,alpha;
  Double_t rotAngle;
  Double_t cosRot,sinRot;
  Double_t cc[15];
  Int_t nUsedTrks;
  Double_t chi2,chi2i;
  Int_t arrEntries = (Int_t)fTrkArray.GetEntries();
  AliESDtrack *t = 0;
  Int_t failed = 0;

  // 2 steps:
  // 1st - estimate of vtx using all tracks
  // 2nd - estimate of global chi2
  for(step=0; step<2; step++) {
    if(fDebug) printf(" step = %d\n",step);
    chi2 = 0.;
    nUsedTrks = 0;

    TMatrixD sumWiri(3,1);
    TMatrixD sumWi(3,3);
    for(i=0; i<3; i++) {
      sumWiri(i,0) = 0.;
      for(j=0; j<3; j++) sumWi(j,i) = 0.;
    }

    if(useNominalVtx) {
      for(i=0; i<3; i++) {
	sumWiri(i,0) += fNominalPos[i]/fNominalSigma[i]/fNominalSigma[i];
	sumWi(i,i)   += 1./fNominalSigma[i]/fNominalSigma[i];
      }
    }


    // loop on tracks  
    for(k=0; k<arrEntries; k++) {
      // get track from track array
      t = (AliESDtrack*)fTrkArray.At(k);
      alpha = t->GetAlpha();
      xlStart = initPos[0]*TMath::Cos(alpha)+initPos[1]*TMath::Sin(alpha);
      t->AliExternalTrackParam::PropagateTo(xlStart,AliTracker::GetBz());   // to vtxSeed
      rotAngle = alpha;
      if(alpha<0.) rotAngle += 2.*TMath::Pi();
      cosRot = TMath::Cos(rotAngle);
      sinRot = TMath::Sin(rotAngle);
      
      // vector of track global coordinates
      TMatrixD ri(3,1);
      ri(0,0) = t->GetX()*cosRot-t->GetY()*sinRot;
      ri(1,0) = t->GetX()*sinRot+t->GetY()*cosRot;
      ri(2,0) = t->GetZ();

      // matrix to go from global (x,y,z) to local (y,z);
      TMatrixD qQi(2,3);
      qQi(0,0) = -sinRot;
      qQi(0,1) = cosRot;
      qQi(0,2) = 0.;
      qQi(1,0) = 0.;
      qQi(1,1) = 0.;
      qQi(1,2) = 1.;

      // covariance matrix of local (y,z) - inverted
      TMatrixD uUi(2,2);
      t->GetExternalCovariance(cc);
      uUi(0,0) = cc[0];
      uUi(0,1) = cc[1];
      uUi(1,0) = cc[1];
      uUi(1,1) = cc[2];

      // weights matrix: wWi = qQiT * uUiInv * qQi
      if(uUi.Determinant() <= 0.) continue;
      TMatrixD uUiInv(TMatrixD::kInverted,uUi);
      TMatrixD uUiInvQi(uUiInv,TMatrixD::kMult,qQi);
      TMatrixD wWi(qQi,TMatrixD::kTransposeMult,uUiInvQi);

      // track chi2
      TMatrixD deltar = rv; deltar -= ri;
      TMatrixD wWideltar(wWi,TMatrixD::kMult,deltar);
      chi2i = deltar(0,0)*wWideltar(0,0)+
              deltar(1,0)*wWideltar(1,0)+
	      deltar(2,0)*wWideltar(2,0);


      // add to total chi2
      chi2 += chi2i;

      TMatrixD wWiri(wWi,TMatrixD::kMult,ri); 

      sumWiri += wWiri;
      sumWi   += wWi;

      nUsedTrks++;
    } // end loop on tracks

    if(nUsedTrks < fMinTracks) {
      failed=1;
      continue;
    }

    Double_t determinant = sumWi.Determinant();
    //cerr<<" determinant: "<<determinant<<endl;
    if(determinant < 100.)  { 
      printf("det(V) = 0\n");       
      failed=1;
      continue;
    }

    // inverted of weights matrix
    TMatrixD invsumWi(TMatrixD::kInverted,sumWi);
    vV = invsumWi;
     
    // position of primary vertex
    rv.Mult(vV,sumWiri);

  } // end loop on the 2 steps

  // delete t;

  if(failed) { 
    printf("TooFewTracks\n");
    fCurrentVertex = new AliESDVertex(0.,0.,-1);
    return; 
  }

  Double_t position[3];
  position[0] = rv(0,0);
  position[1] = rv(1,0);
  position[2] = rv(2,0);
  Double_t covmatrix[6];
  covmatrix[0] = vV(0,0);
  covmatrix[1] = vV(0,1);
  covmatrix[2] = vV(1,1);
  covmatrix[3] = vV(0,2);
  covmatrix[4] = vV(1,2);
  covmatrix[5] = vV(2,2);
  
  // store data in the vertex object
  fCurrentVertex = new AliESDVertex(position,covmatrix,chi2,nUsedTrks);

  if(fDebug) {
    printf(" VertexFitter(): finish\n");
    printf(" rv = ( %f , %f , %f )\n\n",rv(0,0),rv(1,0),rv(2,0));
    fCurrentVertex->PrintStatus();
  }

  return;
}
//---------------------------------------------------------------------------
void AliVertexerTracks::TooFewTracks(const AliESD* esdEvent) {
//
// When the number of tracks is < fMinTracks
//

  // deal with vertices not found
  Double_t pos[3],err[3];
  Int_t    ncontr=0;
  pos[0] = fNominalPos[0];
  err[0] = fNominalSigma[0];
  pos[1] = fNominalPos[1];
  err[1] = fNominalSigma[1];
  pos[2] = esdEvent->GetVertex()->GetZv();
  err[2] = esdEvent->GetVertex()->GetZRes();
  if(err[0]>1. && esdEvent->GetVertex()->GetNContributors()<=0) 
    ncontr = -1; // (x,y,z) = (0,0,0) 
  if(err[0]>1. && esdEvent->GetVertex()->GetNContributors()>0) 
    ncontr = -2; // (x,y,z) = (0,0,z_fromSPD) 
  if(err[0]<1. && esdEvent->GetVertex()->GetNContributors()<=0) 
    ncontr = -3; // (x,y,z) = (x_mean,y_mean,0)
  if(err[0]<1. && esdEvent->GetVertex()->GetNContributors()>0) 
    ncontr = -4; // (x,y,z) = (x_mean,y_mean,z_fromSPD)
  fCurrentVertex = 0;
  fCurrentVertex = new AliESDVertex(pos,err);
  fCurrentVertex->SetNContributors(ncontr);

  Double_t tp[3];
  esdEvent->GetVertex()->GetTruePos(tp);
  fCurrentVertex->SetTruePos(tp);
  fCurrentVertex->SetTitle("VertexerTracksWithConstraint");
  if(ncontr==-1||ncontr==-2) 
    fCurrentVertex->SetTitle("VertexerTracksNoConstraint");

  return;
}