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[u/mrichter/AliRoot.git] / TRD / AliTRDtrack.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.                  *
 **************************************************************************/

/*
$Log$
Revision 1.8.8.4  2003/07/10 17:09:52  hristov
Merging to v3-10-00

Revision 1.20  2003/05/27 17:46:13  hristov
TRD PID included in the ESD schema (T.Kuhr)

Revision 1.19  2003/05/22 10:46:46  hristov
Using access methods instead of data members

Revision 1.18  2003/04/10 10:36:54  hristov
Code for unified TPC/TRD tracking (S.Radomski)

Revision 1.17  2003/02/19 09:02:28  hristov
Track time measurement (S.Radomski)

Revision 1.16  2003/02/10 14:06:10  cblume
Add tracking without tilted pads as option

Revision 1.15  2003/01/27 16:34:49  cblume
Update of tracking by Sergei and Chuncheng

Revision 1.14  2002/11/07 15:52:09  cblume
Update of tracking code for tilted pads

Revision 1.13  2002/10/22 15:53:08  alibrary
Introducing Riostream.h

Revision 1.12  2002/10/14 14:57:44  hristov
Merging the VirtualMC branch to the main development branch (HEAD)

Revision 1.8.10.2  2002/07/24 10:09:31  alibrary
Updating VirtualMC

RRevision 1.11  2002/06/13 12:09:58  hristov
Minor corrections

Revision 1.10  2002/06/12 09:54:35  cblume
Update of tracking code provided by Sergei

Revision 1.8  2001/05/30 12:17:47  hristov
Loop variables declared once

Revision 1.7  2001/05/28 17:07:58  hristov
Last minute changes; ExB correction in AliTRDclusterizerV1; taking into account of material in G10 TEC frames and material between TEC planes (C.Blume,S.Sedykh)

Revision 1.4  2000/12/08 16:07:02  cblume
Update of the tracking by Sergei

Revision 1.3  2000/10/15 23:40:01  cblume
Remove AliTRDconst

Revision 1.2  2000/10/06 16:49:46  cblume
Made Getters const

Revision 1.1.2.1  2000/09/22 14:47:52  cblume
Add the tracking code

*/                                                        

#include <Riostream.h>
#include <TObject.h>   

#include "AliTRDgeometry.h" 
#include "AliTRDcluster.h" 
#include "AliTRDtrack.h"
#include "../TPC/AliTPCtrack.h" 
#include "AliESDtrack.h" 


ClassImp(AliTRDtrack)


//_____________________________________________________________________________

AliTRDtrack::AliTRDtrack(const AliTRDcluster *c, UInt_t index, 
                         const Double_t xx[5], const Double_t cc[15], 
                         Double_t xref, Double_t alpha) : AliKalmanTrack() {
  //-----------------------------------------------------------------
  // This is the main track constructor.
  //-----------------------------------------------------------------

  fSeedLab = -1;

  fAlpha=alpha;
  if (fAlpha<-TMath::Pi()) fAlpha += 2*TMath::Pi();
  if (fAlpha>=TMath::Pi()) fAlpha -= 2*TMath::Pi();   

  fX=xref;

  fY=xx[0]; fZ=xx[1]; fE=xx[2]; fT=xx[3]; fC=xx[4];

  fCyy=cc[0];
  fCzy=cc[1];  fCzz=cc[2];
  fCey=cc[3];  fCez=cc[4];  fCee=cc[5];
  fCty=cc[6];  fCtz=cc[7];  fCte=cc[8];  fCtt=cc[9];
  fCcy=cc[10]; fCcz=cc[11]; fCce=cc[12]; fCct=cc[13]; fCcc=cc[14];  
  
  fIndex[0]=index;
  SetNumberOfClusters(1);

  fdEdx=0.;

  fLhElectron = 0.0;
  fNWrong = 0;
  fNRotate = 0;

  Double_t q = TMath::Abs(c->GetQ());
  Double_t s = fX*fC - fE, t=fT;
  if(s*s < 1) q *= TMath::Sqrt((1-s*s)/(1+t*t));

  fdQdl[0] = q;
  
  // initialisation [SR, GSI 18.02.2003] (i startd for 1)
  for(Int_t i=1; i<kMAX_CLUSTERS_PER_TRACK; i++) {
    fdQdl[i] = 0;
    fIndex[i] = 0;
  }
}                              
           
//_____________________________________________________________________________
AliTRDtrack::AliTRDtrack(const AliTRDtrack& t) : AliKalmanTrack(t) {
  //
  // Copy constructor.
  //
  
  SetLabel(t.GetLabel());
  fSeedLab=t.GetSeedLabel();

  SetChi2(t.GetChi2());
  fdEdx=t.fdEdx;

  fLhElectron = 0.0;
  fNWrong = t.fNWrong;
  fNRotate = t.fNRotate;

  fAlpha=t.fAlpha;
  fX=t.fX;

  fY=t.fY; fZ=t.fZ; fE=t.fE; fT=t.fT; fC=t.fC;

  fCyy=t.fCyy;
  fCzy=t.fCzy;  fCzz=t.fCzz;
  fCey=t.fCey;  fCez=t.fCez;  fCee=t.fCee;
  fCty=t.fCty;  fCtz=t.fCtz;  fCte=t.fCte;  fCtt=t.fCtt;
  fCcy=t.fCcy;  fCcz=t.fCcz;  fCce=t.fCce;  fCct=t.fCct;  fCcc=t.fCcc;  

  Int_t n=t.GetNumberOfClusters(); 
  SetNumberOfClusters(n);
  for (Int_t i=0; i<n; i++) {
    fIndex[i]=t.fIndex[i];
    fdQdl[i]=t.fdQdl[i];
  }

  // initialisation (i starts from n) [SR, GSI, 18.02.2003]
  for(Int_t i=n; i<kMAX_CLUSTERS_PER_TRACK; i++) {
    fdQdl[i] = 0;
    fIndex[i] = 0;
  }
}                                

//_____________________________________________________________________________
AliTRDtrack::AliTRDtrack(const AliKalmanTrack& t, Double_t alpha) 
           :AliKalmanTrack(t) {
  //
  // Constructor from AliTPCtrack or AliITStrack .
  //

  SetLabel(t.GetLabel());
  SetChi2(0.);
  SetMass(t.GetMass());
  SetNumberOfClusters(0);

  fdEdx=0;

  fLhElectron = 0.0;
  fNWrong = 0;
  fNRotate = 0;

  fAlpha = alpha;
  if      (fAlpha < -TMath::Pi()) fAlpha += 2*TMath::Pi();
  else if (fAlpha >= TMath::Pi()) fAlpha -= 2*TMath::Pi();

  Double_t x, p[5]; t.GetExternalParameters(x,p);

  fX=x;

  x = GetConvConst();  

  fY=p[0];
  fZ=p[1];
  fT=p[3];
  fC=p[4]/x;
  fE=fC*fX - p[2];   

  //Conversion of the covariance matrix
  Double_t c[15]; t.GetExternalCovariance(c);

  c[10]/=x; c[11]/=x; c[12]/=x; c[13]/=x; c[14]/=x*x;

  Double_t c22=fX*fX*c[14] - 2*fX*c[12] + c[5];
  Double_t c32=fX*c[13] - c[8];
  Double_t c20=fX*c[10] - c[3], c21=fX*c[11] - c[4], c42=fX*c[14] - c[12];

  fCyy=c[0 ];
  fCzy=c[1 ];   fCzz=c[2 ];
  fCey=c20;     fCez=c21;     fCee=c22;
  fCty=c[6 ];   fCtz=c[7 ];   fCte=c32;   fCtt=c[9 ];
  fCcy=c[10];   fCcz=c[11];   fCce=c42;   fCct=c[13]; fCcc=c[14];  

  // Initialization [SR, GSI, 18.02.2003]
  for(Int_t i=0; i<kMAX_CLUSTERS_PER_TRACK; i++) {
    fdQdl[i] = 0;
    fIndex[i] = 0;
  }
}              
//_____________________________________________________________________________
AliTRDtrack::AliTRDtrack(const AliESDtrack& t) 
           :AliKalmanTrack() {
  //
  // Constructor from AliESDtrack
  //

  SetLabel(t.GetLabel());
  SetChi2(0.);
  SetMass(t.GetMass());
  SetNumberOfClusters(0); 
  // WARNING: cluster indices are NOT copied !!!

  fdEdx=0;

  fLhElectron = 0.0;
  fNWrong = 0;
  fNRotate = 0;

  fAlpha = t.GetAlpha();
  if      (fAlpha < -TMath::Pi()) fAlpha += 2*TMath::Pi();
  else if (fAlpha >= TMath::Pi()) fAlpha -= 2*TMath::Pi();

  Double_t x, p[5]; t.GetExternalParameters(x,p);

  fX=x;

  x = GetConvConst();  

  fY=p[0];
  fZ=p[1];
  fT=p[3];
  fC=p[4]/x;
  fE=fC*fX - p[2];   

  //Conversion of the covariance matrix
  Double_t c[15]; t.GetExternalCovariance(c);

  c[10]/=x; c[11]/=x; c[12]/=x; c[13]/=x; c[14]/=x*x;

  Double_t c22=fX*fX*c[14] - 2*fX*c[12] + c[5];
  Double_t c32=fX*c[13] - c[8];
  Double_t c20=fX*c[10] - c[3], c21=fX*c[11] - c[4], c42=fX*c[14] - c[12];

  fCyy=c[0 ];
  fCzy=c[1 ];   fCzz=c[2 ];
  fCey=c20;     fCez=c21;     fCee=c22;
  fCty=c[6 ];   fCtz=c[7 ];   fCte=c32;   fCtt=c[9 ];
  fCcy=c[10];   fCcz=c[11];   fCce=c42;   fCct=c[13]; fCcc=c[14];  

  // Initialization [SR, GSI, 18.02.2003]
  for(Int_t i=0; i<kMAX_CLUSTERS_PER_TRACK; i++) {
    fdQdl[i] = 0;
    fIndex[i] = 0;
  }
}              
//_____________________________________________________________________________

void  AliTRDtrack::GetBarrelTrack(AliBarrelTrack *track) {
  //
  //
  //
  
  if (!track) return;
  Double_t xr, vec[5], cov[15];

  track->SetLabel(GetLabel());
  track->SetX(fX, fAlpha);
  track->SetNClusters(GetNumberOfClusters(), GetChi2());
  track->SetNWrongClusters(fNWrong);
  track->SetNRotate(fNRotate);
  Double_t times[10];
  GetIntegratedTimes(times);
  track->SetTime(times, GetIntegratedLength());

  track->SetMass(GetMass());
  track->SetdEdX(GetdEdx());

  GetExternalParameters(xr, vec);
  track->SetStateVector(vec);

  GetExternalCovariance(cov);
  track->SetCovarianceMatrix(cov);
}
//____________________________________________________________________________
void AliTRDtrack::GetExternalParameters(Double_t& xr, Double_t x[5]) const {
  //
  // This function returns external TRD track representation
  //
     xr=fX;
     x[0]=GetY();
     x[1]=GetZ();
     x[2]=GetSnp();
     x[3]=GetTgl();
     x[4]=Get1Pt();
}           

//_____________________________________________________________________________
void AliTRDtrack::GetExternalCovariance(Double_t cc[15]) const {
  //
  // This function returns external representation of the covriance matrix.
  //
  Double_t a=GetConvConst();

  Double_t c22=fX*fX*fCcc-2*fX*fCce+fCee;
  Double_t c32=fX*fCct-fCte;
  Double_t c20=fX*fCcy-fCey, c21=fX*fCcz-fCez, c42=fX*fCcc-fCce;

  cc[0 ]=fCyy;
  cc[1 ]=fCzy;   cc[2 ]=fCzz;
  cc[3 ]=c20;    cc[4 ]=c21;    cc[5 ]=c22;
  cc[6 ]=fCty;   cc[7 ]=fCtz;   cc[8 ]=c32;   cc[9 ]=fCtt;
  cc[10]=fCcy*a; cc[11]=fCcz*a; cc[12]=c42*a; cc[13]=fCct*a; cc[14]=fCcc*a*a; 
  
}               
                       

//_____________________________________________________________________________
void AliTRDtrack::GetCovariance(Double_t cc[15]) const {

  cc[0]=fCyy;
  cc[1]=fCzy;  cc[2]=fCzz;
  cc[3]=fCey;  cc[4]=fCez;  cc[5]=fCee;
  cc[6]=fCcy;  cc[7]=fCcz;  cc[8]=fCce;  cc[9]=fCcc;
  cc[10]=fCty; cc[11]=fCtz; cc[12]=fCte; cc[13]=fCct; cc[14]=fCtt;
  
}    

//_____________________________________________________________________________
Int_t AliTRDtrack::Compare(const TObject *o) const {

// Compares tracks according to their Y2 or curvature

  AliTRDtrack *t=(AliTRDtrack*)o;
  //  Double_t co=t->GetSigmaY2();
  //  Double_t c =GetSigmaY2();

  Double_t co=TMath::Abs(t->GetC());
  Double_t c =TMath::Abs(GetC());  

  if (c>co) return 1;
  else if (c<co) return -1;
  return 0;
}                

//_____________________________________________________________________________
void AliTRDtrack::CookdEdx(Double_t low, Double_t up) {
  //-----------------------------------------------------------------
  // Calculates dE/dX within the "low" and "up" cuts.
  //-----------------------------------------------------------------

  Int_t i;
  Int_t nc=GetNumberOfClusters(); 

  Float_t sorted[kMAX_CLUSTERS_PER_TRACK];
  for (i=0; i < nc; i++) {
    sorted[i]=fdQdl[i];
  }

  Int_t swap; 

  do {
    swap=0;
    for (i=0; i<nc-1; i++) {
      if (sorted[i]<=sorted[i+1]) continue;
      Float_t tmp=sorted[i];
      sorted[i]=sorted[i+1]; sorted[i+1]=tmp;
      swap++;
    }
  } while (swap);

  Int_t nl=Int_t(low*nc), nu=Int_t(up*nc);
  Float_t dedx=0;
  for (i=nl; i<=nu; i++) dedx += sorted[i];
  dedx /= (nu-nl+1);

  SetdEdx(dedx);
}                     


//_____________________________________________________________________________
Int_t AliTRDtrack::PropagateTo(Double_t xk,Double_t x0,Double_t rho)
{
  // Propagates a track of particle with mass=pm to a reference plane 
  // defined by x=xk through media of density=rho and radiationLength=x0

  if (xk == fX) return 1;

  if (TMath::Abs(fC*xk - fE) >= 0.99999) {
    Int_t n=GetNumberOfClusters();
    if (n>4) cerr << n << " AliTRDtrack: Propagation failed, \tPt = " 
                  << GetPt() << "\t" << GetLabel() << "\t" << GetMass() << endl;
    return 0;
  }

  // track Length measurement [SR, GSI, 17.02.2003]
  Double_t oldX = fX, oldY = fY, oldZ = fZ;  

  Double_t x1=fX, x2=x1+(xk-x1), dx=x2-x1, y1=fY, z1=fZ;
  Double_t c1=fC*x1 - fE;
  if((c1*c1) > 1) return 0;
  Double_t r1=sqrt(1.- c1*c1);
  Double_t c2=fC*x2 - fE; 
  if((c2*c2) > 1) return 0;
  Double_t r2=sqrt(1.- c2*c2);

  fY += dx*(c1+c2)/(r1+r2);
  fZ += dx*(c1+c2)/(c1*r2 + c2*r1)*fT;

  //f = F - 1
  Double_t rr=r1+r2, cc=c1+c2, xx=x1+x2;
  Double_t f02=-dx*(2*rr + cc*(c1/r1 + c2/r2))/(rr*rr);
  Double_t f04= dx*(rr*xx + cc*(c1*x1/r1+c2*x2/r2))/(rr*rr);
  Double_t cr=c1*r2+c2*r1;
  Double_t f12=-dx*fT*(2*cr + cc*(c2*c1/r1-r1 + c1*c2/r2-r2))/(cr*cr);
  Double_t f13= dx*cc/cr;
  Double_t f14=dx*fT*(cr*xx-cc*(r1*x2-c2*c1*x1/r1+r2*x1-c1*c2*x2/r2))/(cr*cr);

  //b = C*ft
  Double_t b00=f02*fCey + f04*fCcy, b01=f12*fCey + f14*fCcy + f13*fCty;
  Double_t b10=f02*fCez + f04*fCcz, b11=f12*fCez + f14*fCcz + f13*fCtz;
  Double_t b20=f02*fCee + f04*fCce, b21=f12*fCee + f14*fCce + f13*fCte;
  Double_t b30=f02*fCte + f04*fCct, b31=f12*fCte + f14*fCct + f13*fCtt;
  Double_t b40=f02*fCce + f04*fCcc, b41=f12*fCce + f14*fCcc + f13*fCct;

  //a = f*b = f*C*ft
  Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a11=f12*b21+f14*b41+f13*b31;

  //F*C*Ft = C + (a + b + bt)
  fCyy += a00 + 2*b00;
  fCzy += a01 + b01 + b10;
  fCey += b20;
  fCty += b30;
  fCcy += b40;
  fCzz += a11 + 2*b11;
  fCez += b21;
  fCtz += b31;
  fCcz += b41;

  fX=x2;                                                     

  //Multiple scattering  ******************
  Double_t d=sqrt((x1-fX)*(x1-fX)+(y1-fY)*(y1-fY)+(z1-fZ)*(z1-fZ));
  Double_t p2=(1.+ GetTgl()*GetTgl())/(Get1Pt()*Get1Pt());
  Double_t beta2=p2/(p2 + GetMass()*GetMass());
  Double_t theta2=14.1*14.1/(beta2*p2*1e6)*d/x0*rho;

  Double_t ey=fC*fX - fE, ez=fT;
  Double_t xz=fC*ez, zz1=ez*ez+1, xy=fE+ey;

  fCee += (2*ey*ez*ez*fE+1-ey*ey+ez*ez+fE*fE*ez*ez)*theta2;
  fCte += ez*zz1*xy*theta2;
  fCtt += zz1*zz1*theta2;
  fCce += xz*ez*xy*theta2;
  fCct += xz*zz1*theta2;
  fCcc += xz*xz*theta2;

  //Energy losses************************
  if((5940*beta2/(1-beta2+1e-10) - beta2) < 0) return 0;

  Double_t dE=0.153e-3/beta2*(log(5940*beta2/(1-beta2+1e-10)) - beta2)*d*rho;
  if (x1 < x2) dE=-dE;
  cc=fC;
  fC*=(1.- sqrt(p2+GetMass()*GetMass())/p2*dE);
  fE+=fX*(fC-cc);    

  // track time measurement [SR, GSI 17.02.2002]
  if (IsStartedTimeIntegral()) {
    Double_t l2 = (fX-oldX)*(fX-oldX) + (fY-oldY)*(fY-oldY) + (fZ-oldZ)*(fZ-oldZ);
    AddTimeStep(TMath::Sqrt(l2));
  }

  return 1;            
}     


//_____________________________________________________________________________
Int_t AliTRDtrack::Update(const AliTRDcluster *c, Double_t chisq, UInt_t index,                          Double_t h01)
{
  // Assignes found cluster to the track and updates track information

  Bool_t fNoTilt = kTRUE;
  if(TMath::Abs(h01) > 0.003) fNoTilt = kFALSE;

  Double_t r00=c->GetSigmaY2(), r01=0., r11=c->GetSigmaZ2();
  r00+=fCyy; r01+=fCzy; r11+=fCzz;
  Double_t det=r00*r11 - r01*r01;
  Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;

  Double_t k00=fCyy*r00+fCzy*r01, k01=fCyy*r01+fCzy*r11;
  Double_t k10=fCzy*r00+fCzz*r01, k11=fCzy*r01+fCzz*r11;
  Double_t k20=fCey*r00+fCez*r01, k21=fCey*r01+fCez*r11;
  Double_t k30=fCty*r00+fCtz*r01, k31=fCty*r01+fCtz*r11;
  Double_t k40=fCcy*r00+fCcz*r01, k41=fCcy*r01+fCcz*r11;

  Double_t dy=c->GetY() - fY, dz=c->GetZ() - fZ;
  Double_t cur=fC + k40*dy + k41*dz, eta=fE + k20*dy + k21*dz;

  Double_t c01=fCzy, c02=fCey, c03=fCty, c04=fCcy;
  Double_t c12=fCez, c13=fCtz, c14=fCcz;

  if(fNoTilt) {
    if (TMath::Abs(cur*fX-eta) >= 0.99999) {
      Int_t n=GetNumberOfClusters();
      if (n>4) cerr<<n<<" AliTRDtrack warning: Filtering failed !\n";
      return 0;
    }
    fY += k00*dy + k01*dz;
    fZ += k10*dy + k11*dz;
    fE  = eta;
    //fT += k30*dy + k31*dz;
    fC  = cur;
  }
  else {
    Double_t xu_factor = 100.;  // empirical factor set by C.Xu
                                // in the first tilt version      
    r00=c->GetSigmaY2(), r01=0., r11=c->GetSigmaZ2()*xu_factor; 
    r00+=(fCyy+2.0*h01*fCzy+h01*h01*fCzz);
    r01+=(fCzy+h01*fCzz);  
    det=r00*r11 - r01*r01;
    tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;

    k00=fCyy*r00+fCzy*(r01+h01*r00),k01=fCyy*r01+fCzy*(r11+h01*r01);
    k10=fCzy*r00+fCzz*(r01+h01*r00),k11=fCzy*r01+fCzz*(r11+h01*r01);
    k20=fCey*r00+fCez*(r01+h01*r00),k21=fCey*r01+fCez*(r11+h01*r01);
    k30=fCty*r00+fCtz*(r01+h01*r00),k31=fCty*r01+fCtz*(r11+h01*r01);
    k40=fCcy*r00+fCcz*(r01+h01*r00),k41=fCcy*r01+fCcz*(r11+h01*r01);  

    dy=c->GetY() - fY; dz=c->GetZ() - fZ; 
    dy=dy+h01*dz;

    cur=fC + k40*dy + k41*dz; eta=fE + k20*dy + k21*dz;
    if (TMath::Abs(cur*fX-eta) >= 0.99999) {
      Int_t n=GetNumberOfClusters();
      if (n>4) cerr<<n<<" AliTRDtrack warning: Filtering failed !\n";
      return 0;
    }                           
    fY += k00*dy + k01*dz;
    fZ += k10*dy + k11*dz;
    fE  = eta;
    //fT += k30*dy + k31*dz;
    fC  = cur;
    
    k01+=h01*k00;
    k11+=h01*k10;
    k21+=h01*k20;
    k31+=h01*k30;
    k41+=h01*k40;  
  }

  fCyy-=k00*fCyy+k01*fCzy; fCzy-=k00*c01+k01*fCzz;
  fCey-=k00*c02+k01*c12;   fCty-=k00*c03+k01*c13;
  fCcy-=k00*c04+k01*c14;
  
  fCzz-=k10*c01+k11*fCzz;
  fCez-=k10*c02+k11*c12;   fCtz-=k10*c03+k11*c13;
  fCcz-=k10*c04+k11*c14;
  
  fCee-=k20*c02+k21*c12;   fCte-=k20*c03+k21*c13;
  fCce-=k20*c04+k21*c14;
  
  fCtt-=k30*c03+k31*c13;
  fCct-=k40*c03+k41*c13;
  
  fCcc-=k40*c04+k41*c14;                 

  Int_t n=GetNumberOfClusters();
  fIndex[n]=index;
  SetNumberOfClusters(n+1);

  SetChi2(GetChi2()+chisq);
  //  cerr<<"in update: fIndex["<<fN<<"] = "<<index<<endl;

  return 1;     
}                     


//_____________________________________________________________________________
Int_t AliTRDtrack::Rotate(Double_t alpha)
{
  // Rotates track parameters in R*phi plane
  
  fNRotate++;

  fAlpha += alpha;
  if (fAlpha<-TMath::Pi()) fAlpha += 2*TMath::Pi();
  if (fAlpha>=TMath::Pi()) fAlpha -= 2*TMath::Pi();

  Double_t x1=fX, y1=fY;
  Double_t ca=cos(alpha), sa=sin(alpha);
  Double_t r1=fC*fX - fE;

  fX = x1*ca + y1*sa;
  fY =-x1*sa + y1*ca;
  if((r1*r1) > 1) return 0;
  fE=fE*ca + (fC*y1 + sqrt(1.- r1*r1))*sa;

  Double_t r2=fC*fX - fE;
  if (TMath::Abs(r2) >= 0.99999) {
    Int_t n=GetNumberOfClusters();
    if (n>4) cerr<<n<<" AliTRDtrack warning: Rotation failed !\n";
    return 0;
  }

  if((r2*r2) > 1) return 0;
  Double_t y0=fY + sqrt(1.- r2*r2)/fC;
  if ((fY-y0)*fC >= 0.) {
    Int_t n=GetNumberOfClusters();
    if (n>4) cerr<<n<<" AliTRDtrack warning: Rotation failed !!!\n";
    return 0;
  }

  //f = F - 1
  Double_t f00=ca-1,    f24=(y1 - r1*x1/sqrt(1.- r1*r1))*sa,
           f20=fC*sa,  f22=(ca + sa*r1/sqrt(1.- r1*r1))-1;

  //b = C*ft
  Double_t b00=fCyy*f00, b02=fCyy*f20+fCcy*f24+fCey*f22;
  Double_t b10=fCzy*f00, b12=fCzy*f20+fCcz*f24+fCez*f22;
  Double_t b20=fCey*f00, b22=fCey*f20+fCce*f24+fCee*f22;
  Double_t b30=fCty*f00, b32=fCty*f20+fCct*f24+fCte*f22;
  Double_t b40=fCcy*f00, b42=fCcy*f20+fCcc*f24+fCce*f22;

  //a = f*b = f*C*ft
  Double_t a00=f00*b00, a02=f00*b02, a22=f20*b02+f24*b42+f22*b22;

  //F*C*Ft = C + (a + b + bt)
  fCyy += a00 + 2*b00;
  fCzy += b10;
  fCey += a02+b20+b02;
  fCty += b30;
  fCcy += b40;
  fCez += b12;
  fCte += b32;
  fCee += a22 + 2*b22;
  fCce += b42;

  return 1;                            
}                         


//_____________________________________________________________________________
Double_t AliTRDtrack::GetPredictedChi2(const AliTRDcluster *c, Double_t h01) const
{
  
  Bool_t fNoTilt = kTRUE;
  if(TMath::Abs(h01) > 0.003) fNoTilt = kFALSE;
  Double_t chi2, dy, r00, r01, r11;

  if(fNoTilt) {
    dy=c->GetY() - fY;
    r00=c->GetSigmaY2();    
    chi2 = (dy*dy)/r00;    
  }
  else {
    r00=c->GetSigmaY2(); r01=0.; r11=c->GetSigmaZ2();
    r00+=fCyy; r01+=fCzy; r11+=fCzz;

    Double_t det=r00*r11 - r01*r01;
    if (TMath::Abs(det) < 1.e-10) {
      Int_t n=GetNumberOfClusters(); 
      if (n>4) cerr<<n<<" AliTRDtrack warning: Singular matrix !\n";
      return 1e10;
    }
    Double_t tmp=r00; r00=r11; r11=tmp; r01=-r01;
    Double_t dy=c->GetY() - fY, dz=c->GetZ() - fZ;
    dy=dy+h01*dz;

    chi2 = (dy*r00*dy + 2*r01*dy*dz + dz*r11*dz)/det; 
  }
  return chi2;
}      


//_________________________________________________________________________
void AliTRDtrack::GetPxPyPz(Double_t& px, Double_t& py, Double_t& pz) const
{
  // Returns reconstructed track momentum in the global system.

  Double_t pt=TMath::Abs(GetPt()); // GeV/c
  Double_t r=fC*fX-fE;

  Double_t y0; 
  if(r > 1) { py = pt; px = 0; }
  else if(r < -1) { py = -pt; px = 0; }
  else {
    y0=fY + sqrt(1.- r*r)/fC;  
    px=-pt*(fY-y0)*fC;    //cos(phi);
    py=-pt*(fE-fX*fC);   //sin(phi);
  }
  pz=pt*fT;
  Double_t tmp=px*TMath::Cos(fAlpha) - py*TMath::Sin(fAlpha);
  py=px*TMath::Sin(fAlpha) + py*TMath::Cos(fAlpha);
  px=tmp;            

}                                

//_________________________________________________________________________
void AliTRDtrack::GetGlobalXYZ(Double_t& x, Double_t& y, Double_t& z) const
{
  // Returns reconstructed track coordinates in the global system.

  x = fX; y = fY; z = fZ; 
  Double_t tmp=x*TMath::Cos(fAlpha) - y*TMath::Sin(fAlpha);
  y=x*TMath::Sin(fAlpha) + y*TMath::Cos(fAlpha);
  x=tmp;            

}                                

//_________________________________________________________________________
void AliTRDtrack::ResetCovariance() {
  //
  // Resets covariance matrix
  //

  fCyy*=10.;
  fCzy=0.;  fCzz*=10.;
  fCey=0.;  fCez=0.;  fCee*=10.;
  fCty=0.;  fCtz=0.;  fCte=0.;  fCtt*=10.;
  fCcy=0.;  fCcz=0.;  fCce=0.;  fCct=0.;  fCcc*=10.;  
}