* provided "as is" without express or implied warranty. *
**************************************************************************/
+/* $Id$ */
+
//-------------------------------------------------------------------------
// Implementation of the AliKalmanTrack class
-//
+// that is the base for AliTPCtrack, AliITStrackV2 and AliTRDtrack
// Origin: Iouri Belikov, CERN, Jouri.Belikov@cern.ch
//-------------------------------------------------------------------------
#include "AliKalmanTrack.h"
+#include "AliPDG.h"
+#include "TPDGCode.h"
+#include "TDatabasePDG.h"
ClassImp(AliKalmanTrack)
-Double_t AliKalmanTrack::fConvConst;
+Double_t AliKalmanTrack::fgConvConst;
+
+//_______________________________________________________________________
+AliKalmanTrack::AliKalmanTrack():
+ fLab(-3141593),
+ fChi2(0),
+ fMass(0.13957),
+ fN(0)
+{
+ //
+ // Default constructor
+ //
+ if (fgConvConst==0) {
+ Fatal("AliKalmanTrack()", "The magnetic field has not been set!");
+ }
+
+ fStartTimeIntegral = kFALSE;
+ fIntegratedLength = 0;
+ for(Int_t i=0; i<5; i++) fIntegratedTime[i] = 0;
+}
+
+//_______________________________________________________________________
+AliKalmanTrack::AliKalmanTrack(const AliKalmanTrack &t):
+ TObject(t),
+ fLab(t.fLab),
+ fFakeRatio(t.fFakeRatio),
+ fChi2(t.fChi2),
+ fMass(t.fMass),
+ fN(t.fN)
+{
+ //
+ // Copy constructor
+ //
+ if (fgConvConst==0) {
+ Fatal("AliKalmanTrack(const AliKalmanTrack&)",
+ "The magnetic field has not been set!");
+ }
+
+ fStartTimeIntegral = t.fStartTimeIntegral;
+ fIntegratedLength = t.fIntegratedLength;
+
+ for (Int_t i=0; i<5; i++)
+ fIntegratedTime[i] = t.fIntegratedTime[i];
+}
+
+//_______________________________________________________________________
+Double_t AliKalmanTrack::GetX() const
+{
+ // Returns the X coordinate of the current track position
+ Warning("GetX()","Method must be overloaded !\n");
+ return 0.;
+}
+//_______________________________________________________________________
+Double_t AliKalmanTrack::GetdEdx() const
+{
+ // Returns the dE/dx of the track
+ Warning("GetdEdx()","Method must be overloaded !\n");
+ return 0.;
+}
+
+//_______________________________________________________________________
+Double_t AliKalmanTrack::GetY() const
+{
+ // Returns the Y coordinate of the current track position
+ Double_t par[5];
+ Double_t localX = GetX();
+ GetExternalParameters(localX, par);
+ return par[0];
+}
+//_______________________________________________________________________
+Double_t AliKalmanTrack::GetZ() const
+{
+ // Returns the Z coordinate of the current track position
+ Double_t par[5];
+ Double_t localX = GetX();
+ GetExternalParameters(localX, par);
+ return par[1];
+}
+//_______________________________________________________________________
+Double_t AliKalmanTrack::GetSnp() const
+{
+ // Returns the Sin(phi), where phi is the angle between the transverse
+ // momentum (in xOy plane) and the X axis
+ Double_t par[5];
+ Double_t localX = GetX();
+ GetExternalParameters(localX, par);
+ return par[2];
+}
+//_______________________________________________________________________
+Double_t AliKalmanTrack::GetTgl() const
+{
+ // Returns the Tan(lambda), where lambda is the dip angle (between
+ // the bending plane (xOy) and the momentum of the track
+ Double_t par[5];
+ Double_t localX = GetX();
+ GetExternalParameters(localX, par);
+ return par[3];
+}
+//_______________________________________________________________________
+Double_t AliKalmanTrack::Get1Pt() const
+{
+ // Returns 1/pT
+ Double_t par[5];
+ Double_t localX = GetX();
+ GetExternalParameters(localX, par);
+ return par[4];
+}
+
+//_______________________________________________________________________
+Double_t AliKalmanTrack::Phi() const
+{
+// return global phi of track
+
+ Double_t par[5];
+ Double_t localX = GetX();
+ GetExternalParameters(localX, par);
+ if (par[2] > 1.) par[2] = 1.;
+ if (par[2] < -1.) par[2] = -1.;
+ Double_t phi = TMath::ASin(par[2]) + GetAlpha();
+ while (phi < 0) phi += TMath::TwoPi();
+ while (phi > TMath::TwoPi()) phi -= TMath::TwoPi();
+ return phi;
+}
+//_______________________________________________________________________
+Double_t AliKalmanTrack::SigmaPhi() const
+{
+// return error of global phi of track
+
+ Double_t par[5];
+ Double_t cov[15];
+ Double_t localX = GetX();
+ GetExternalParameters(localX, par);
+ GetExternalCovariance(cov);
+ return TMath::Sqrt(TMath::Abs(cov[5] / (1. - par[2]*par[2])));
+}
+//_______________________________________________________________________
+Double_t AliKalmanTrack::Theta() const
+{
+// return global theta of track
+
+ Double_t par[5];
+ Double_t localX = GetX();
+ GetExternalParameters(localX, par);
+ return TMath::Pi()/2. - TMath::ATan(par[3]);
+}
+//_______________________________________________________________________
+Double_t AliKalmanTrack::SigmaTheta() const
+{
+// return error of global theta of track
+
+ Double_t par[5];
+ Double_t cov[15];
+ Double_t localX = GetX();
+ GetExternalParameters(localX, par);
+ GetExternalCovariance(cov);
+ return TMath::Sqrt(TMath::Abs(cov[5])) / (1. + par[3]*par[3]);
+}
+//_______________________________________________________________________
+Double_t AliKalmanTrack::Eta() const
+{
+// return global eta of track
+
+ return -TMath::Log(TMath::Tan(Theta()/2.));
+}
+//_______________________________________________________________________
+Double_t AliKalmanTrack::Px() const
+{
+// return x component of track momentum
+
+ Double_t par[5];
+ Double_t localX = GetX();
+ GetExternalParameters(localX, par);
+ Double_t phi = TMath::ASin(par[2]) + GetAlpha();
+ return TMath::Cos(phi) / TMath::Abs(par[4]);
+}
+//_______________________________________________________________________
+Double_t AliKalmanTrack::Py() const
+{
+// return y component of track momentum
+
+ Double_t par[5];
+ Double_t localX = GetX();
+ GetExternalParameters(localX, par);
+ Double_t phi = TMath::ASin(par[2]) + GetAlpha();
+ return TMath::Sin(phi) / TMath::Abs(par[4]);
+}
+//_______________________________________________________________________
+Double_t AliKalmanTrack::Pz() const
+{
+// return z component of track momentum
+
+ Double_t par[5];
+ Double_t localX = GetX();
+ GetExternalParameters(localX, par);
+ return par[3] / TMath::Abs(par[4]);
+}
+//_______________________________________________________________________
+Double_t AliKalmanTrack::Pt() const
+{
+// return transverse component of track momentum
+
+ Double_t par[5];
+ Double_t localX = GetX();
+ GetExternalParameters(localX, par);
+ return 1. / TMath::Abs(par[4]);
+}
+//_______________________________________________________________________
+Double_t AliKalmanTrack::SigmaPt() const
+{
+// return error of transverse component of track momentum
+
+ Double_t par[5];
+ Double_t cov[15];
+ Double_t localX = GetX();
+ GetExternalParameters(localX, par);
+ GetExternalCovariance(cov);
+ return TMath::Sqrt(cov[14]) / TMath::Abs(par[4]);
+}
+//_______________________________________________________________________
+Double_t AliKalmanTrack::P() const
+{
+// return total track momentum
+
+ Double_t par[5];
+ Double_t localX = GetX();
+ GetExternalParameters(localX, par);
+ return 1. / TMath::Abs(par[4] * TMath::Cos(TMath::ATan(par[3])));
+}
+//_______________________________________________________________________
+void AliKalmanTrack::StartTimeIntegral()
+{
+ // Sylwester Radomski, GSI
+ // S.Radomski@gsi.de
+ //
+ // Start time integration
+ // To be called at Vertex by ITS tracker
+ //
+
+ //if (fStartTimeIntegral)
+ // Warning("StartTimeIntegral", "Reseting Recorded Time.");
+
+ fStartTimeIntegral = kTRUE;
+ for(Int_t i=0; i<fgkTypes; i++) fIntegratedTime[i] = 0;
+ fIntegratedLength = 0;
+}
+//_______________________________________________________________________
+void AliKalmanTrack:: AddTimeStep(Double_t length)
+{
+ //
+ // Add step to integrated time
+ // this method should be called by a sublasses at the end
+ // of the PropagateTo function or by a tracker
+ // each time step is made.
+ //
+ // If integration not started function does nothing
+ //
+ // Formula
+ // dt = dl * sqrt(p^2 + m^2) / p
+ // p = pT * (1 + tg^2 (lambda) )
+ //
+ // pt = 1/external parameter [4]
+ // tg lambda = external parameter [3]
+ //
+ //
+ // Sylwester Radomski, GSI
+ // S.Radomski@gsi.de
+ //
+
+ static const Double_t kcc = 2.99792458e-2;
+
+ if (!fStartTimeIntegral) return;
+
+ fIntegratedLength += length;
+
+ static Int_t pdgCode[fgkTypes] = {kElectron, kMuonMinus, kPiPlus, kKPlus, kProton};
+ TDatabasePDG *db = TDatabasePDG::Instance();
+
+ Double_t xr, param[5];
+ Double_t pt, tgl;
+
+ GetExternalParameters(xr, param);
+ pt = 1/param[4] ;
+ tgl = param[3];
+
+ Double_t p = TMath::Abs(pt * TMath::Sqrt(1+tgl*tgl));
+
+ if (length > 100) return;
+
+ for (Int_t i=0; i<fgkTypes; i++) {
+
+ Double_t mass = db->GetParticle(pdgCode[i])->Mass();
+ Double_t correction = TMath::Sqrt( pt*pt * (1 + tgl*tgl) + mass * mass ) / p;
+ Double_t time = length * correction / kcc;
+
+ fIntegratedTime[i] += time;
+ }
+}
+
+//_______________________________________________________________________
+
+Double_t AliKalmanTrack::GetIntegratedTime(Int_t pdg) const
+{
+ // Sylwester Radomski, GSI
+ // S.Radomski@gsi.de
+ //
+ // Return integrated time hypothesis for a given particle
+ // type assumption.
+ //
+ // Input parameter:
+ // pdg - Pdg code of a particle type
+ //
+
+
+ if (!fStartTimeIntegral) {
+ Warning("GetIntegratedTime","Time integration not started");
+ return 0.;
+ }
+
+ static Int_t pdgCode[fgkTypes] = {kElectron, kMuonMinus, kPiPlus, kKPlus, kProton};
+
+ for (Int_t i=0; i<fgkTypes; i++)
+ if (pdgCode[i] == TMath::Abs(pdg)) return fIntegratedTime[i];
+
+ Warning(":GetIntegratedTime","Particle type [%d] not found", pdg);
+ return 0;
+}
+
+void AliKalmanTrack::GetIntegratedTimes(Double_t *times) const {
+ for (Int_t i=0; i<fgkTypes; i++) times[i]=fIntegratedTime[i];
+}
+
+void AliKalmanTrack::SetIntegratedTimes(const Double_t *times) {
+ for (Int_t i=0; i<fgkTypes; i++) fIntegratedTime[i]=times[i];
+}
+
+//_______________________________________________________________________
+
+void AliKalmanTrack::PrintTime() const
+{
+ // Sylwester Radomski, GSI
+ // S.Radomski@gsi.de
+ //
+ // For testing
+ // Prints time for all hypothesis
+ //
+
+ static Int_t pdgCode[fgkTypes] = {kElectron, kMuonMinus, kPiPlus, kKPlus, kProton};
+
+ for (Int_t i=0; i<fgkTypes; i++)
+ printf("%d: %.2f ", pdgCode[i], fIntegratedTime[i]);
+ printf("\n");
+}
+
+static void External2Helix(const AliKalmanTrack *t, Double_t helix[6]) {
+ //--------------------------------------------------------------------
+ // External track parameters -> helix parameters
+ //--------------------------------------------------------------------
+ Double_t alpha,x,cs,sn;
+ t->GetExternalParameters(x,helix); alpha=t->GetAlpha();
+
+ cs=TMath::Cos(alpha); sn=TMath::Sin(alpha);
+ helix[5]=x*cs - helix[0]*sn; // x0
+ helix[0]=x*sn + helix[0]*cs; // y0
+//helix[1]= // z0
+ helix[2]=TMath::ASin(helix[2]) + alpha; // phi0
+//helix[3]= // tgl
+ helix[4]=helix[4]/t->GetConvConst(); // C
+}
+
+static void Evaluate(const Double_t *h, Double_t t,
+ Double_t r[3], //radius vector
+ Double_t g[3], //first defivatives
+ Double_t gg[3]) //second derivatives
+{
+ //--------------------------------------------------------------------
+ // Calculate position of a point on a track and some derivatives
+ //--------------------------------------------------------------------
+ Double_t phase=h[4]*t+h[2];
+ Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase);
+
+ r[0] = h[5] + (sn - h[6])/h[4];
+ r[1] = h[0] - (cs - h[7])/h[4];
+ r[2] = h[1] + h[3]*t;
+
+ g[0] = cs; g[1]=sn; g[2]=h[3];
+
+ gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.;
+}
+
+Double_t AliKalmanTrack::
+GetDCA(const AliKalmanTrack *p, Double_t &xthis, Double_t &xp) const {
+ //------------------------------------------------------------
+ // Returns the (weighed !) distance of closest approach between
+ // this track and the track passed as the argument.
+ // Other returned values:
+ // xthis, xt - coordinates of tracks' reference planes at the DCA
+ //-----------------------------------------------------------
+ Double_t dy2=GetSigmaY2() + p->GetSigmaY2();
+ Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2();
+ Double_t dx2=dy2;
+
+ //dx2=dy2=dz2=1.;
+
+ Double_t p1[8]; External2Helix(this,p1);
+ p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]);
+ Double_t p2[8]; External2Helix(p,p2);
+ p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]);
+
+
+ Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.;
+ Evaluate(p1,t1,r1,g1,gg1);
+ Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.;
+ Evaluate(p2,t2,r2,g2,gg2);
+
+ Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2];
+ Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
+
+ Int_t max=27;
+ while (max--) {
+ Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2);
+ Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2);
+ Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 +
+ (g1[1]*g1[1] - dy*gg1[1])/dy2 +
+ (g1[2]*g1[2] - dz*gg1[2])/dz2;
+ Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 +
+ (g2[1]*g2[1] + dy*gg2[1])/dy2 +
+ (g2[2]*g2[2] + dz*gg2[2])/dz2;
+ Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2);
+
+ Double_t det=h11*h22-h12*h12;
+
+ Double_t dt1,dt2;
+ if (TMath::Abs(det)<1.e-33) {
+ //(quasi)singular Hessian
+ dt1=-gt1; dt2=-gt2;
+ } else {
+ dt1=-(gt1*h22 - gt2*h12)/det;
+ dt2=-(h11*gt2 - h12*gt1)/det;
+ }
+
+ if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;}
+
+ //check delta(phase1) ?
+ //check delta(phase2) ?
+
+ if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4)
+ if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) {
+ if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2)
+ Warning("GetDCA"," stopped at not a stationary point !\n");
+ Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det);
+ if (lmb < 0.)
+ Warning("GetDCA"," stopped at not a minimum !\n");
+ break;
+ }
+
+ Double_t dd=dm;
+ for (Int_t div=1 ; ; div*=2) {
+ Evaluate(p1,t1+dt1,r1,g1,gg1);
+ Evaluate(p2,t2+dt2,r2,g2,gg2);
+ dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2];
+ dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
+ if (dd<dm) break;
+ dt1*=0.5; dt2*=0.5;
+ if (div>512) {
+ Warning("GetDCA"," overshoot !\n"); break;
+ }
+ }
+ dm=dd;
+
+ t1+=dt1;
+ t2+=dt2;
+
+ }
+
+ if (max<=0) Warning("GetDCA"," too many iterations !\n");
+
+ Double_t cs=TMath::Cos(GetAlpha());
+ Double_t sn=TMath::Sin(GetAlpha());
+ xthis=r1[0]*cs + r1[1]*sn;
+
+ cs=TMath::Cos(p->GetAlpha());
+ sn=TMath::Sin(p->GetAlpha());
+ xp=r2[0]*cs + r2[1]*sn;
+
+ return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2));
+}
+
+Double_t AliKalmanTrack::
+PropagateToDCA(AliKalmanTrack *p, Double_t d, Double_t x0) {
+ //--------------------------------------------------------------
+ // Propagates this track and the argument track to the position of the
+ // distance of closest approach.
+ // Returns the (weighed !) distance of closest approach.
+ //--------------------------------------------------------------
+ Double_t xthis,xp;
+ Double_t dca=GetDCA(p,xthis,xp);
+
+ if (!PropagateTo(xthis,d,x0)) {
+ //Warning("PropagateToDCA"," propagation failed !\n");
+ return 1e+33;
+ }
+
+ if (!p->PropagateTo(xp,d,x0)) {
+ //Warning("PropagateToDCA"," propagation failed !\n";
+ return 1e+33;
+ }
+ return dca;
+}
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