///////////////////////////////////////////////////////////////////////////////
// //
-// track parameters in "external" format //
-// //
-// The track parameters are: //
-// - local y coordinate //
-// - local z coordinate //
-// - sin of azimutal angle //
-// - tan of dip angle //
-// - charge/pt //
-// The parametrisation is given at the local x coordinate fX and the //
-// azimuthal angle fAlpha. //
-// //
-// The external parametrisation can be used to exchange track parameters //
-// between different detectors. //
+// Implementation of the external track parameterisation class. //
// //
+// This parameterisation is used to exchange tracks between the detectors. //
+// A set of functions returning the position and the momentum of tracks //
+// in the global coordinate system as well as the track impact parameters //
+// are implemented.
+// Origin: I.Belikov, CERN, Jouri.Belikov@cern.ch //
///////////////////////////////////////////////////////////////////////////////
-
-#include <TMath.h>
+#include <TMatrixDSym.h>
+#include <TPolyMarker3D.h>
#include <TVector3.h>
+#include <TMatrixD.h>
#include "AliExternalTrackParam.h"
-#include "AliKalmanTrack.h"
+#include "AliVVertex.h"
+#include "AliLog.h"
ClassImp(AliExternalTrackParam)
-
+Double32_t AliExternalTrackParam::fgMostProbablePt=kMostProbablePt;
+
//_____________________________________________________________________________
AliExternalTrackParam::AliExternalTrackParam() :
- AliTrackParam(),
+ AliVTrack(),
fX(0),
fAlpha(0)
{
//
// default constructor
//
- for (Int_t i = 0; i < 5; i++) fParam[i] = 0;
- for (Int_t i = 0; i < 15; i++) fCovar[i] = 0;
+ for (Int_t i = 0; i < 5; i++) fP[i] = 0;
+ for (Int_t i = 0; i < 15; i++) fC[i] = 0;
+}
+
+//_____________________________________________________________________________
+AliExternalTrackParam::AliExternalTrackParam(const AliExternalTrackParam &track):
+ AliVTrack(track),
+ fX(track.fX),
+ fAlpha(track.fAlpha)
+{
+ //
+ // copy constructor
+ //
+ for (Int_t i = 0; i < 5; i++) fP[i] = track.fP[i];
+ for (Int_t i = 0; i < 15; i++) fC[i] = track.fC[i];
+}
+
+//_____________________________________________________________________________
+AliExternalTrackParam& AliExternalTrackParam::operator=(const AliExternalTrackParam &trkPar)
+{
+ //
+ // assignment operator
+ //
+
+ if (this!=&trkPar) {
+ AliVTrack::operator=(trkPar);
+ fX = trkPar.fX;
+ fAlpha = trkPar.fAlpha;
+
+ for (Int_t i = 0; i < 5; i++) fP[i] = trkPar.fP[i];
+ for (Int_t i = 0; i < 15; i++) fC[i] = trkPar.fC[i];
+ }
+
+ return *this;
}
//_____________________________________________________________________________
AliExternalTrackParam::AliExternalTrackParam(Double_t x, Double_t alpha,
const Double_t param[5],
const Double_t covar[15]) :
- AliTrackParam(),
+ AliVTrack(),
fX(x),
fAlpha(alpha)
{
//
// create external track parameters from given arguments
//
- for (Int_t i = 0; i < 5; i++) fParam[i] = param[i];
- for (Int_t i = 0; i < 15; i++) fCovar[i] = covar[i];
+ for (Int_t i = 0; i < 5; i++) fP[i] = param[i];
+ for (Int_t i = 0; i < 15; i++) fC[i] = covar[i];
}
//_____________________________________________________________________________
-AliExternalTrackParam::AliExternalTrackParam(const AliKalmanTrack& track) :
- fX(0),
- fAlpha(track.GetAlpha())
+AliExternalTrackParam::AliExternalTrackParam(const AliVTrack *vTrack) :
+ AliVTrack(),
+ fX(0.),
+ fAlpha(0.)
{
//
+ // Constructor from virtual track,
+ // This is not a copy contructor !
//
- track.GetExternalParameters(fX,fParam);
- track.GetExternalCovariance(fCovar);
+
+ if (vTrack->InheritsFrom("AliExternalTrackParam")) {
+ AliError("This is not a copy constructor. Use AliExternalTrackParam(const AliExternalTrackParam &) !");
+ AliWarning("Calling the default constructor...");
+ AliExternalTrackParam();
+ return;
+ }
+
+ Double_t xyz[3],pxpypz[3],cv[21];
+ vTrack->GetXYZ(xyz);
+ pxpypz[0]=vTrack->Px();
+ pxpypz[1]=vTrack->Py();
+ pxpypz[2]=vTrack->Pz();
+ vTrack->GetCovarianceXYZPxPyPz(cv);
+ Short_t sign = (Short_t)vTrack->Charge();
+
+ Set(xyz,pxpypz,cv,sign);
}
//_____________________________________________________________________________
-const Double_t* AliExternalTrackParam::GetParameter() const
+AliExternalTrackParam::AliExternalTrackParam(Double_t xyz[3],Double_t pxpypz[3],
+ Double_t cv[21],Short_t sign) :
+ AliVTrack(),
+ fX(0.),
+ fAlpha(0.)
{
-// get a pointer to the array of track parameters
+ //
+ // constructor from the global parameters
+ //
- return fParam;
+ Set(xyz,pxpypz,cv,sign);
}
//_____________________________________________________________________________
-const Double_t* AliExternalTrackParam::GetCovariance() const
+void AliExternalTrackParam::Set(Double_t xyz[3],Double_t pxpypz[3],
+ Double_t cv[21],Short_t sign)
{
-// get a pointer to the array of the track parameter covariance matrix
+ //
+ // create external track parameters from the global parameters
+ // x,y,z,px,py,pz and their 6x6 covariance matrix
+ // A.Dainese 10.10.08
- return fCovar;
+ // Calculate alpha: the rotation angle of the corresponding local system.
+ //
+ // For global radial position inside the beam pipe, alpha is the
+ // azimuthal angle of the momentum projected on (x,y).
+ //
+ // For global radial position outside the ITS, alpha is the
+ // azimuthal angle of the centre of the TPC sector in which the point
+ // xyz lies
+ //
+ Double_t radPos2 = xyz[0]*xyz[0]+xyz[1]*xyz[1];
+ Double_t radMax = 45.; // approximately ITS outer radius
+ if (radPos2 < radMax*radMax) { // inside the ITS
+
+ fAlpha = TMath::ATan2(pxpypz[1],pxpypz[0]);
+ } else { // outside the ITS
+ Float_t phiPos = TMath::Pi()+TMath::ATan2(-xyz[1], -xyz[0]);
+ fAlpha =
+ TMath::DegToRad()*(20*((((Int_t)(phiPos*TMath::RadToDeg()))/20))+10);
+ }
+
+ // Get the vertex of origin and the momentum
+ TVector3 ver(xyz[0],xyz[1],xyz[2]);
+ TVector3 mom(pxpypz[0],pxpypz[1],pxpypz[2]);
+
+ // Rotate to the local coordinate system
+ ver.RotateZ(-fAlpha);
+ mom.RotateZ(-fAlpha);
+
+ // x of the reference plane
+ fX = ver.X();
+
+ Double_t charge = (Double_t)sign;
+
+ fP[0] = ver.Y();
+ fP[1] = ver.Z();
+ fP[2] = TMath::Sin(mom.Phi());
+ fP[3] = mom.Pz()/mom.Pt();
+ fP[4] = TMath::Sign(1/mom.Pt(),charge);
+
+ // Covariance matrix (formulas to be simplified)
+
+ Double_t pt=1./TMath::Abs(fP[4]);
+ Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
+ Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
+
+ Double_t m00=-sn;// m10=cs;
+ Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
+ Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
+ Double_t m35=pt, m45=-pt*pt*fP[3];
+
+ m43*=GetSign();
+ m44*=GetSign();
+ m45*=GetSign();
+
+ Double_t cv34 = TMath::Sqrt(cv[3 ]*cv[3 ]+cv[4 ]*cv[4 ]);
+ Double_t a1=cv[13]-cv[9]*(m23*m44+m43*m24)/m23/m43;
+ Double_t a2=m23*m24-m23*(m23*m44+m43*m24)/m43;
+ Double_t a3=m43*m44-m43*(m23*m44+m43*m24)/m23;
+ Double_t a4=cv[14]-2.*cv[9]*m24*m44/m23/m43;
+ Double_t a5=m24*m24-2.*m24*m44*m23/m43;
+ Double_t a6=m44*m44-2.*m24*m44*m43/m23;
+
+ fC[0 ] = cv[0 ]+cv[2 ];
+ fC[1 ] = TMath::Sign(cv34,cv[3 ]/m00);
+ fC[2 ] = cv[5 ];
+ fC[3 ] = (cv[10]/m44-cv[6]/m43)/(m24/m44-m23/m43)/m00;
+ fC[10] = (cv[6]/m00-fC[3 ]*m23)/m43;
+ fC[6 ] = (cv[15]/m00-fC[10]*m45)/m35;
+ fC[4 ] = (cv[12]-cv[8]*m44/m43)/(m24-m23*m44/m43);
+ fC[11] = (cv[8]-fC[4]*m23)/m43;
+ fC[7 ] = cv[17]/m35-fC[11]*m45/m35;
+ fC[5 ] = TMath::Abs((a4-a6*a1/a3)/(a5-a6*a2/a3));
+ fC[14] = TMath::Abs(a1/a3-a2*fC[5]/a3);
+ fC[12] = (cv[9]-fC[5]*m23*m23-fC[14]*m43*m43)/m23/m43;
+ Double_t b1=cv[18]-fC[12]*m23*m45-fC[14]*m43*m45;
+ Double_t b2=m23*m35;
+ Double_t b3=m43*m35;
+ Double_t b4=cv[19]-fC[12]*m24*m45-fC[14]*m44*m45;
+ Double_t b5=m24*m35;
+ Double_t b6=m44*m35;
+ fC[8 ] = (b4-b6*b1/b3)/(b5-b6*b2/b3);
+ fC[13] = b1/b3-b2*fC[8]/b3;
+ fC[9 ] = TMath::Abs((cv[20]-fC[14]*(m45*m45)-fC[13]*2.*m35*m45)/(m35*m35));
+
+ return;
}
//_____________________________________________________________________________
-AliExternalTrackParam* AliExternalTrackParam::CreateExternalParam() const
-{
-// copy this instance
-
- return new AliExternalTrackParam(fX, fAlpha, fParam, fCovar);
+void AliExternalTrackParam::Reset() {
+ //
+ // Resets all the parameters to 0
+ //
+ fX=fAlpha=0.;
+ for (Int_t i = 0; i < 5; i++) fP[i] = 0;
+ for (Int_t i = 0; i < 15; i++) fC[i] = 0;
}
//_____________________________________________________________________________
-void AliExternalTrackParam::ResetCovariance(Double_t factor,
- Bool_t clearOffDiagonal)
-{
-// reset the covariance matrix ("forget" track history)
-
- Int_t k = 0;
- for (Int_t i = 0; i < 5; i++) {
- for (Int_t j = 0; j < i; j++) { // off diagonal elements
- if (clearOffDiagonal) {
- fCovar[k++] = 0;
- } else {
- fCovar[k++] *= factor;
- }
- }
- fCovar[k++] *= factor; // diagonal elements
+void AliExternalTrackParam::AddCovariance(const Double_t c[15]) {
+ //
+ // Add "something" to the track covarince matrix.
+ // May be needed to account for unknown mis-calibration/mis-alignment
+ //
+ fC[0] +=c[0];
+ fC[1] +=c[1]; fC[2] +=c[2];
+ fC[3] +=c[3]; fC[4] +=c[4]; fC[5] +=c[5];
+ fC[6] +=c[6]; fC[7] +=c[7]; fC[8] +=c[8]; fC[9] +=c[9];
+ fC[10]+=c[10]; fC[11]+=c[11]; fC[12]+=c[12]; fC[13]+=c[13]; fC[14]+=c[14];
+}
+
+
+Double_t AliExternalTrackParam::GetP() const {
+ //---------------------------------------------------------------------
+ // This function returns the track momentum
+ // Results for (nearly) straight tracks are meaningless !
+ //---------------------------------------------------------------------
+ if (TMath::Abs(fP[4])<=kAlmost0) return kVeryBig;
+ return TMath::Sqrt(1.+ fP[3]*fP[3])/TMath::Abs(fP[4]);
+}
+
+Double_t AliExternalTrackParam::Get1P() const {
+ //---------------------------------------------------------------------
+ // This function returns the 1/(track momentum)
+ //---------------------------------------------------------------------
+ return TMath::Abs(fP[4])/TMath::Sqrt(1.+ fP[3]*fP[3]);
+}
+
+//_______________________________________________________________________
+Double_t AliExternalTrackParam::GetD(Double_t x,Double_t y,Double_t b) const {
+ //------------------------------------------------------------------
+ // This function calculates the transverse impact parameter
+ // with respect to a point with global coordinates (x,y)
+ // in the magnetic field "b" (kG)
+ //------------------------------------------------------------------
+ if (TMath::Abs(b) < kAlmost0Field) return GetLinearD(x,y);
+ Double_t rp4=GetC(b);
+
+ Double_t xt=fX, yt=fP[0];
+
+ Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
+ Double_t a = x*cs + y*sn;
+ y = -x*sn + y*cs; x=a;
+ xt-=x; yt-=y;
+
+ sn=rp4*xt - fP[2]; cs=rp4*yt + TMath::Sqrt(1.- fP[2]*fP[2]);
+ a=2*(xt*fP[2] - yt*TMath::Sqrt(1.- fP[2]*fP[2]))-rp4*(xt*xt + yt*yt);
+ return -a/(1 + TMath::Sqrt(sn*sn + cs*cs));
+}
+
+//_______________________________________________________________________
+void AliExternalTrackParam::
+GetDZ(Double_t x, Double_t y, Double_t z, Double_t b, Float_t dz[2]) const {
+ //------------------------------------------------------------------
+ // This function calculates the transverse and longitudinal impact parameters
+ // with respect to a point with global coordinates (x,y)
+ // in the magnetic field "b" (kG)
+ //------------------------------------------------------------------
+ Double_t f1 = fP[2], r1 = TMath::Sqrt(1. - f1*f1);
+ Double_t xt=fX, yt=fP[0];
+ Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
+ Double_t a = x*cs + y*sn;
+ y = -x*sn + y*cs; x=a;
+ xt-=x; yt-=y;
+
+ Double_t rp4=GetC(b);
+ if ((TMath::Abs(b) < kAlmost0Field) || (TMath::Abs(rp4) < kAlmost0)) {
+ dz[0] = -(xt*f1 - yt*r1);
+ dz[1] = fP[1] + (dz[0]*f1 - xt)/r1*fP[3] - z;
+ return;
}
+
+ sn=rp4*xt - f1; cs=rp4*yt + r1;
+ a=2*(xt*f1 - yt*r1)-rp4*(xt*xt + yt*yt);
+ Double_t rr=TMath::Sqrt(sn*sn + cs*cs);
+ dz[0] = -a/(1 + rr);
+ Double_t f2 = -sn/rr, r2 = TMath::Sqrt(1. - f2*f2);
+ dz[1] = fP[1] + fP[3]/rp4*TMath::ASin(f2*r1 - f1*r2) - z;
}
+//_______________________________________________________________________
+Double_t AliExternalTrackParam::GetLinearD(Double_t xv,Double_t yv) const {
+ //------------------------------------------------------------------
+ // This function calculates the transverse impact parameter
+ // with respect to a point with global coordinates (xv,yv)
+ // neglecting the track curvature.
+ //------------------------------------------------------------------
+ Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
+ Double_t x= xv*cs + yv*sn;
+ Double_t y=-xv*sn + yv*cs;
-//_____________________________________________________________________________
-Bool_t AliExternalTrackParam::PropagateTo(Double_t /*x*/, Double_t* /*length*/)
-{
-// Propagate the track parameters to the given x coordinate assuming vacuum.
-// If length is not NULL, the change of track length is added to it.
-//
-// NOT IMPLEMENTED for this class
+ Double_t d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt(1.- fP[2]*fP[2]);
- return kFALSE;
+ return -d;
}
-//_____________________________________________________________________________
-Bool_t AliExternalTrackParam::RotateTo(Double_t /*alpha*/)
-{
-// Rotate the reference axis for the parametrisation to the given angle.
-//
-// NOT IMPLEMENTED for this class
+Bool_t AliExternalTrackParam::CorrectForMeanMaterial
+(Double_t xOverX0, Double_t xTimesRho, Double_t mass, Bool_t anglecorr,
+ Double_t (*Bethe)(Double_t)) {
+ //------------------------------------------------------------------
+ // This function corrects the track parameters for the crossed material.
+ // "xOverX0" - X/X0, the thickness in units of the radiation length.
+ // "xTimesRho" - is the product length*density (g/cm^2).
+ // "mass" - the mass of this particle (GeV/c^2).
+ //------------------------------------------------------------------
+ Double_t &fP2=fP[2];
+ Double_t &fP3=fP[3];
+ Double_t &fP4=fP[4];
- return kFALSE;
+ Double_t &fC22=fC[5];
+ Double_t &fC33=fC[9];
+ Double_t &fC43=fC[13];
+ Double_t &fC44=fC[14];
+
+ //Apply angle correction, if requested
+ if(anglecorr) {
+ Double_t angle=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2));
+ xOverX0 *=angle;
+ xTimesRho *=angle;
+ }
+
+ Double_t p=GetP();
+ Double_t p2=p*p;
+ Double_t beta2=p2/(p2 + mass*mass);
+
+ //Calculating the multiple scattering corrections******************
+ Double_t cC22 = 0.;
+ Double_t cC33 = 0.;
+ Double_t cC43 = 0.;
+ Double_t cC44 = 0.;
+ if (xOverX0 != 0) {
+ Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(xOverX0);
+ //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
+ if(theta2>TMath::Pi()*TMath::Pi()) return kFALSE;
+ cC22 = theta2*(1.- fP2*fP2)*(1. + fP3*fP3);
+ cC33 = theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
+ cC43 = theta2*fP3*fP4*(1. + fP3*fP3);
+ cC44 = theta2*fP3*fP4*fP3*fP4;
+ }
+
+ //Calculating the energy loss corrections************************
+ Double_t cP4=1.;
+ if ((xTimesRho != 0.) && (beta2 < 1.)) {
+ Double_t dE=Bethe(p/mass)*xTimesRho;
+ Double_t e=TMath::Sqrt(p2 + mass*mass);
+ if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much!
+ cP4 = (1.- e/p2*dE);
+ if (TMath::Abs(fP4*cP4)>100.) return kFALSE; //Do not track below 10 MeV/c
+
+
+ // Approximate energy loss fluctuation (M.Ivanov)
+ const Double_t knst=0.07; // To be tuned.
+ Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE));
+ cC44 += ((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4));
+
+ }
+
+ //Applying the corrections*****************************
+ fC22 += cC22;
+ fC33 += cC33;
+ fC43 += cC43;
+ fC44 += cC44;
+ fP4 *= cP4;
+
+ return kTRUE;
}
-//_____________________________________________________________________________
-Bool_t AliExternalTrackParam::CorrectForMaterial(Double_t /*dAngle*/,
- Double_t /*dPrel*/)
-{
-// Take into account material effects assuming:
-// dAngle2: mean multiple scattering angle in rad squared
-// dPrel : mean relative momentum gain (if > 0) or loss (if < 0)
-//
-// NOT IMPLEMENTED for this class
+Bool_t AliExternalTrackParam::CorrectForMaterial
+(Double_t d, Double_t x0, Double_t mass, Double_t (*Bethe)(Double_t)) {
+ //------------------------------------------------------------------
+ // Deprecated function !
+ // Better use CorrectForMeanMaterial instead of it.
+ //
+ // This function corrects the track parameters for the crossed material
+ // "d" - the thickness (fraction of the radiation length)
+ // "x0" - the radiation length (g/cm^2)
+ // "mass" - the mass of this particle (GeV/c^2)
+ //------------------------------------------------------------------
+ Double_t &fP2=fP[2];
+ Double_t &fP3=fP[3];
+ Double_t &fP4=fP[4];
+
+ Double_t &fC22=fC[5];
+ Double_t &fC33=fC[9];
+ Double_t &fC43=fC[13];
+ Double_t &fC44=fC[14];
+
+ Double_t p=GetP();
+ Double_t p2=p*p;
+ Double_t beta2=p2/(p2 + mass*mass);
+ d*=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2));
+
+ //Multiple scattering******************
+ Double_t cC22 = 0.;
+ Double_t cC33 = 0.;
+ Double_t cC43 = 0.;
+ Double_t cC44 = 0.;
+ if (d!=0) {
+ Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(d);
+ //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
+ if(theta2>TMath::Pi()*TMath::Pi()) return kFALSE;
+ cC22 = theta2*(1.- fP2*fP2)*(1. + fP3*fP3);
+ cC33 = theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
+ cC43 = theta2*fP3*fP4*(1. + fP3*fP3);
+ cC44 = theta2*fP3*fP4*fP3*fP4;
+ }
+
+ //Energy losses************************
+ Double_t cP4=1.;
+ if (x0!=0. && beta2<1) {
+ d*=x0;
+ Double_t dE=Bethe(p/mass)*d;
+ Double_t e=TMath::Sqrt(p2 + mass*mass);
+ if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much!
+ cP4 = (1.- e/p2*dE);
+
+ // Approximate energy loss fluctuation (M.Ivanov)
+ const Double_t knst=0.07; // To be tuned.
+ Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE));
+ cC44 += ((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4));
+
+ }
+
+ fC22 += cC22;
+ fC33 += cC33;
+ fC43 += cC43;
+ fC44 += cC44;
+ fP4 *= cP4;
+
+ return kTRUE;
+}
+
+Double_t AliExternalTrackParam::BetheBlochAleph(Double_t bg,
+ Double_t kp1,
+ Double_t kp2,
+ Double_t kp3,
+ Double_t kp4,
+ Double_t kp5) {
+ //
+ // This is the empirical ALEPH parameterization of the Bethe-Bloch formula.
+ // It is normalized to 1 at the minimum.
+ //
+ // bg - beta*gamma
+ //
+ // The default values for the kp* parameters are for ALICE TPC.
+ // The returned value is in MIP units
+ //
+
+ Double_t beta = bg/TMath::Sqrt(1.+ bg*bg);
+
+ Double_t aa = TMath::Power(beta,kp4);
+ Double_t bb = TMath::Power(1./bg,kp5);
+
+ bb=TMath::Log(kp3+bb);
+
+ return (kp2-aa-bb)*kp1/aa;
+}
+
+Double_t AliExternalTrackParam::BetheBlochGeant(Double_t bg,
+ Double_t kp0,
+ Double_t kp1,
+ Double_t kp2,
+ Double_t kp3,
+ Double_t kp4) {
+ //
+ // This is the parameterization of the Bethe-Bloch formula inspired by Geant.
+ //
+ // bg - beta*gamma
+ // kp0 - density [g/cm^3]
+ // kp1 - density effect first junction point
+ // kp2 - density effect second junction point
+ // kp3 - mean excitation energy [GeV]
+ // kp4 - mean Z/A
+ //
+ // The default values for the kp* parameters are for silicon.
+ // The returned value is in [GeV/(g/cm^2)].
+ //
+
+ const Double_t mK = 0.307075e-3; // [GeV*cm^2/g]
+ const Double_t me = 0.511e-3; // [GeV/c^2]
+ const Double_t rho = kp0;
+ const Double_t x0 = kp1*2.303;
+ const Double_t x1 = kp2*2.303;
+ const Double_t mI = kp3;
+ const Double_t mZA = kp4;
+ const Double_t bg2 = bg*bg;
+ const Double_t maxT= 2*me*bg2; // neglecting the electron mass
+
+ //*** Density effect
+ Double_t d2=0.;
+ const Double_t x=TMath::Log(bg);
+ const Double_t lhwI=TMath::Log(28.816*1e-9*TMath::Sqrt(rho*mZA)/mI);
+ if (x > x1) {
+ d2 = lhwI + x - 0.5;
+ } else if (x > x0) {
+ const Double_t r=(x1-x)/(x1-x0);
+ d2 = lhwI + x - 0.5 + (0.5 - lhwI - x0)*r*r*r;
+ }
+
+ return mK*mZA*(1+bg2)/bg2*
+ (0.5*TMath::Log(2*me*bg2*maxT/(mI*mI)) - bg2/(1+bg2) - d2);
+}
+
+Double_t AliExternalTrackParam::BetheBlochSolid(Double_t bg) {
+ //------------------------------------------------------------------
+ // This is an approximation of the Bethe-Bloch formula,
+ // reasonable for solid materials.
+ // All the parameters are, in fact, for Si.
+ // The returned value is in [GeV/(g/cm^2)]
+ //------------------------------------------------------------------
+
+ return BetheBlochGeant(bg);
+}
+
+Double_t AliExternalTrackParam::BetheBlochGas(Double_t bg) {
+ //------------------------------------------------------------------
+ // This is an approximation of the Bethe-Bloch formula,
+ // reasonable for gas materials.
+ // All the parameters are, in fact, for Ne.
+ // The returned value is in [GeV/(g/cm^2)]
+ //------------------------------------------------------------------
+
+ const Double_t rho = 0.9e-3;
+ const Double_t x0 = 2.;
+ const Double_t x1 = 4.;
+ const Double_t mI = 140.e-9;
+ const Double_t mZA = 0.49555;
+
+ return BetheBlochGeant(bg,rho,x0,x1,mI,mZA);
+}
+
+Bool_t AliExternalTrackParam::Rotate(Double_t alpha) {
+ //------------------------------------------------------------------
+ // Transform this track to the local coord. system rotated
+ // by angle "alpha" (rad) with respect to the global coord. system.
+ //------------------------------------------------------------------
+ if (TMath::Abs(fP[2]) >= kAlmost1) {
+ AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2]));
+ return kFALSE;
+ }
+
+ if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi();
+ else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi();
+
+ Double_t &fP0=fP[0];
+ Double_t &fP2=fP[2];
+ Double_t &fC00=fC[0];
+ Double_t &fC10=fC[1];
+ Double_t &fC20=fC[3];
+ Double_t &fC21=fC[4];
+ Double_t &fC22=fC[5];
+ Double_t &fC30=fC[6];
+ Double_t &fC32=fC[8];
+ Double_t &fC40=fC[10];
+ Double_t &fC42=fC[12];
+
+ Double_t x=fX;
+ Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha);
+ Double_t sf=fP2, cf=TMath::Sqrt(1.- fP2*fP2);
+
+ Double_t tmp=sf*ca - cf*sa;
+ if (TMath::Abs(tmp) >= kAlmost1) {
+ AliError(Form("Rotation failed ! %.10e",tmp));
+ return kFALSE;
+ }
+
+ fAlpha = alpha;
+ fX = x*ca + fP0*sa;
+ fP0= -x*sa + fP0*ca;
+ fP2= tmp;
+
+ if (TMath::Abs(cf)<kAlmost0) {
+ AliError(Form("Too small cosine value %f",cf));
+ cf = kAlmost0;
+ }
+
+ Double_t rr=(ca+sf/cf*sa);
+
+ fC00 *= (ca*ca);
+ fC10 *= ca;
+ fC20 *= ca*rr;
+ fC21 *= rr;
+ fC22 *= rr*rr;
+ fC30 *= ca;
+ fC32 *= rr;
+ fC40 *= ca;
+ fC42 *= rr;
+
+ return kTRUE;
+}
+
+Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) {
+ //----------------------------------------------------------------
+ // Propagate this track to the plane X=xk (cm) in the field "b" (kG)
+ //----------------------------------------------------------------
+ Double_t dx=xk-fX;
+ if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
+
+ Double_t crv=GetC(b);
+ if (TMath::Abs(b) < kAlmost0Field) crv=0.;
+
+ Double_t f1=fP[2], f2=f1 + crv*dx;
+ if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
+ if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
+
+ Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
+ Double_t
+ &fC00=fC[0],
+ &fC10=fC[1], &fC11=fC[2],
+ &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
+ &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
+ &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
+
+ Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
+
+ fX=xk;
+ fP0 += dx*(f1+f2)/(r1+r2);
+ fP1 += dx*(r2 + f2*(f1+f2)/(r1+r2))*fP3; // Many thanks to P.Hristov !
+ fP2 += dx*crv;
+
+ //f = F - 1
+
+ Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4;
+ Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc;
+ Double_t f12= dx*fP3*f1/(r1*r1*r1);
+ Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc;
+ Double_t f13= dx/r1;
+ Double_t f24= dx; f24*=cc;
+
+ //b = C*ft
+ Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
+ Double_t b02=f24*fC40;
+ Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
+ Double_t b12=f24*fC41;
+ Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
+ Double_t b22=f24*fC42;
+ Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
+ Double_t b42=f24*fC44;
+ Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
+ Double_t b32=f24*fC43;
+
+ //a = f*b = f*C*ft
+ Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42;
+ Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32;
+ Double_t a22=f24*b42;
+
+ //F*C*Ft = C + (b + bt + a)
+ fC00 += b00 + b00 + a00;
+ fC10 += b10 + b01 + a01;
+ fC20 += b20 + b02 + a02;
+ fC30 += b30;
+ fC40 += b40;
+ fC11 += b11 + b11 + a11;
+ fC21 += b21 + b12 + a12;
+ fC31 += b31;
+ fC41 += b41;
+ fC22 += b22 + b22 + a22;
+ fC32 += b32;
+ fC42 += b42;
+
+ return kTRUE;
+}
+
+Bool_t
+AliExternalTrackParam::Propagate(Double_t alpha, Double_t x, Double_t b) {
+ //------------------------------------------------------------------
+ // Transform this track to the local coord. system rotated
+ // by angle "alpha" (rad) with respect to the global coord. system,
+ // and propagate this track to the plane X=xk (cm) in the field "b" (kG)
+ //------------------------------------------------------------------
+
+ //Save the parameters
+ Double_t as=fAlpha;
+ Double_t xs=fX;
+ Double_t ps[5], cs[15];
+ for (Int_t i=0; i<5; i++) ps[i]=fP[i];
+ for (Int_t i=0; i<15; i++) cs[i]=fC[i];
+
+ if (Rotate(alpha))
+ if (PropagateTo(x,b)) return kTRUE;
+
+ //Restore the parameters, if the operation failed
+ fAlpha=as;
+ fX=xs;
+ for (Int_t i=0; i<5; i++) fP[i]=ps[i];
+ for (Int_t i=0; i<15; i++) fC[i]=cs[i];
return kFALSE;
}
-//_____________________________________________________________________________
-Bool_t AliExternalTrackParam::GetProlongationAt(Double_t /*x*/,
- Double_t& /*y*/,
- Double_t& /*z*/) const
-{
-// Get the local y and z coordinates at the given x value
-//
-// NOT IMPLEMENTED for this class
+Bool_t AliExternalTrackParam::PropagateBxByBz
+(Double_t alpha, Double_t x, Double_t b[3]) {
+ //------------------------------------------------------------------
+ // Transform this track to the local coord. system rotated
+ // by angle "alpha" (rad) with respect to the global coord. system,
+ // and propagate this track to the plane X=xk (cm),
+ // taking into account all three components of the B field, "b[3]" (kG)
+ //------------------------------------------------------------------
+
+ //Save the parameters
+ Double_t as=fAlpha;
+ Double_t xs=fX;
+ Double_t ps[5], cs[15];
+ for (Int_t i=0; i<5; i++) ps[i]=fP[i];
+ for (Int_t i=0; i<15; i++) cs[i]=fC[i];
+ if (Rotate(alpha))
+ if (PropagateToBxByBz(x,b)) return kTRUE;
+
+ //Restore the parameters, if the operation failed
+ fAlpha=as;
+ fX=xs;
+ for (Int_t i=0; i<5; i++) fP[i]=ps[i];
+ for (Int_t i=0; i<15; i++) fC[i]=cs[i];
return kFALSE;
}
-//_____________________________________________________________________________
-Double_t AliExternalTrackParam::GetXAtVertex(Double_t /*x*/,
- Double_t /*y*/) const
-{
-// Get the x coordinate at the given vertex (x,y)
-//
-// NOT IMPLEMENTED for this class
- return 0;
+void AliExternalTrackParam::Propagate(Double_t len, Double_t x[3],
+Double_t p[3], Double_t bz) const {
+ //+++++++++++++++++++++++++++++++++++++++++
+ // Origin: K. Shileev (Kirill.Shileev@cern.ch)
+ // Extrapolate track along simple helix in magnetic field
+ // Arguments: len -distance alogn helix, [cm]
+ // bz - mag field, [kGaus]
+ // Returns: x and p contain extrapolated positon and momentum
+ // The momentum returned for straight-line tracks is meaningless !
+ //+++++++++++++++++++++++++++++++++++++++++
+ GetXYZ(x);
+
+ if (OneOverPt() < kAlmost0 || TMath::Abs(bz) < kAlmost0Field || GetC(bz) < kAlmost0){ //straight-line tracks
+ Double_t unit[3]; GetDirection(unit);
+ x[0]+=unit[0]*len;
+ x[1]+=unit[1]*len;
+ x[2]+=unit[2]*len;
+
+ p[0]=unit[0]/kAlmost0;
+ p[1]=unit[1]/kAlmost0;
+ p[2]=unit[2]/kAlmost0;
+ } else {
+ GetPxPyPz(p);
+ Double_t pp=GetP();
+ Double_t a = -kB2C*bz*GetSign();
+ Double_t rho = a/pp;
+ x[0] += p[0]*TMath::Sin(rho*len)/a - p[1]*(1-TMath::Cos(rho*len))/a;
+ x[1] += p[1]*TMath::Sin(rho*len)/a + p[0]*(1-TMath::Cos(rho*len))/a;
+ x[2] += p[2]*len/pp;
+
+ Double_t p0=p[0];
+ p[0] = p0 *TMath::Cos(rho*len) - p[1]*TMath::Sin(rho*len);
+ p[1] = p[1]*TMath::Cos(rho*len) + p0 *TMath::Sin(rho*len);
+ }
}
+Bool_t AliExternalTrackParam::Intersect(Double_t pnt[3], Double_t norm[3],
+Double_t bz) const {
+ //+++++++++++++++++++++++++++++++++++++++++
+ // Origin: K. Shileev (Kirill.Shileev@cern.ch)
+ // Finds point of intersection (if exists) of the helix with the plane.
+ // Stores result in fX and fP.
+ // Arguments: planePoint,planeNorm - the plane defined by any plane's point
+ // and vector, normal to the plane
+ // Returns: kTrue if helix intersects the plane, kFALSE otherwise.
+ //+++++++++++++++++++++++++++++++++++++++++
+ Double_t x0[3]; GetXYZ(x0); //get track position in MARS
+
+ //estimates initial helix length up to plane
+ Double_t s=
+ (pnt[0]-x0[0])*norm[0] + (pnt[1]-x0[1])*norm[1] + (pnt[2]-x0[2])*norm[2];
+ Double_t dist=99999,distPrev=dist;
+ Double_t x[3],p[3];
+ while(TMath::Abs(dist)>0.00001){
+ //calculates helix at the distance s from x0 ALONG the helix
+ Propagate(s,x,p,bz);
-//_____________________________________________________________________________
-Double_t AliExternalTrackParam::GetPredictedChi2(const AliCluster* /*cluster*/)
-{
-// calculate the chi2 contribution of the given cluster
-//
-// NOT IMPLEMENTED for this class
+ //distance between current helix position and plane
+ dist=(x[0]-pnt[0])*norm[0]+(x[1]-pnt[1])*norm[1]+(x[2]-pnt[2])*norm[2];
- return -1;
+ if(TMath::Abs(dist) >= TMath::Abs(distPrev)) {return kFALSE;}
+ distPrev=dist;
+ s-=dist;
+ }
+ //on exit pnt is intersection point,norm is track vector at that point,
+ //all in MARS
+ for (Int_t i=0; i<3; i++) {pnt[i]=x[i]; norm[i]=p[i];}
+ return kTRUE;
}
-//_____________________________________________________________________________
-Bool_t AliExternalTrackParam::Update(const AliCluster* /*cluster*/)
-{
-// update the track parameters using the position and error
-// of the given cluster
-//
-// NOT IMPLEMENTED for this class
+Double_t
+AliExternalTrackParam::GetPredictedChi2(Double_t p[2],Double_t cov[3]) const {
+ //----------------------------------------------------------------
+ // Estimate the chi2 of the space point "p" with the cov. matrix "cov"
+ //----------------------------------------------------------------
+ Double_t sdd = fC[0] + cov[0];
+ Double_t sdz = fC[1] + cov[1];
+ Double_t szz = fC[2] + cov[2];
+ Double_t det = sdd*szz - sdz*sdz;
- return kFALSE;
+ if (TMath::Abs(det) < kAlmost0) return kVeryBig;
+
+ Double_t d = fP[0] - p[0];
+ Double_t z = fP[1] - p[1];
+
+ return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det;
}
+Double_t AliExternalTrackParam::
+GetPredictedChi2(Double_t p[3],Double_t covyz[3],Double_t covxyz[3]) const {
+ //----------------------------------------------------------------
+ // Estimate the chi2 of the 3D space point "p" and
+ // the full covariance matrix "covyz" and "covxyz"
+ //
+ // Cov(x,x) ... : covxyz[0]
+ // Cov(y,x) ... : covxyz[1] covyz[0]
+ // Cov(z,x) ... : covxyz[2] covyz[1] covyz[2]
+ //----------------------------------------------------------------
-//_____________________________________________________________________________
-Double_t AliExternalTrackParam::SigmaPhi() const
-{
-// get the error of the azimuthal angle
+ Double_t res[3] = {
+ GetX() - p[0],
+ GetY() - p[1],
+ GetZ() - p[2]
+ };
+
+ Double_t f=GetSnp();
+ if (TMath::Abs(f) >= kAlmost1) return kVeryBig;
+ Double_t r=TMath::Sqrt(1.- f*f);
+ Double_t a=f/r, b=GetTgl()/r;
+
+ Double_t s2=333.*333.; //something reasonably big (cm^2)
+
+ TMatrixDSym v(3);
+ v(0,0)= s2; v(0,1)= a*s2; v(0,2)= b*s2;;
+ v(1,0)=a*s2; v(1,1)=a*a*s2 + GetSigmaY2(); v(1,2)=a*b*s2 + GetSigmaZY();
+ v(2,0)=b*s2; v(2,1)=a*b*s2 + GetSigmaZY(); v(2,2)=b*b*s2 + GetSigmaZ2();
+
+ v(0,0)+=covxyz[0]; v(0,1)+=covxyz[1]; v(0,2)+=covxyz[2];
+ v(1,0)+=covxyz[1]; v(1,1)+=covyz[0]; v(1,2)+=covyz[1];
+ v(2,0)+=covxyz[2]; v(2,1)+=covyz[1]; v(2,2)+=covyz[2];
- return TMath::Sqrt(TMath::Abs(fCovar[5] / (1. - fParam[2]*fParam[2])));
+ v.Invert();
+ if (!v.IsValid()) return kVeryBig;
+
+ Double_t chi2=0.;
+ for (Int_t i = 0; i < 3; i++)
+ for (Int_t j = 0; j < 3; j++) chi2 += res[i]*res[j]*v(i,j);
+
+ return chi2;
}
-//_____________________________________________________________________________
-Double_t AliExternalTrackParam::SigmaTheta() const
-{
-// get the error of the polar angle
+Double_t AliExternalTrackParam::
+GetPredictedChi2(const AliExternalTrackParam *t) const {
+ //----------------------------------------------------------------
+ // Estimate the chi2 (5 dof) of this track with respect to the track
+ // given by the argument.
+ // The two tracks must be in the same reference system
+ // and estimated at the same reference plane.
+ //----------------------------------------------------------------
+
+ if (TMath::Abs(1. - t->GetAlpha()/GetAlpha()) > FLT_EPSILON) {
+ AliError("The reference systems of the tracks differ !");
+ return kVeryBig;
+ }
+ if (TMath::Abs(1. - t->GetX()/GetX()) > FLT_EPSILON) {
+ AliError("The reference of the tracks planes differ !");
+ return kVeryBig;
+ }
- return TMath::Sqrt(TMath::Abs(fCovar[9])) / (1. + fParam[3]*fParam[3]);
+ TMatrixDSym c(5);
+ c(0,0)=GetSigmaY2();
+ c(1,0)=GetSigmaZY(); c(1,1)=GetSigmaZ2();
+ c(2,0)=GetSigmaSnpY(); c(2,1)=GetSigmaSnpZ(); c(2,2)=GetSigmaSnp2();
+ c(3,0)=GetSigmaTglY(); c(3,1)=GetSigmaTglZ(); c(3,2)=GetSigmaTglSnp(); c(3,3)=GetSigmaTgl2();
+ c(4,0)=GetSigma1PtY(); c(4,1)=GetSigma1PtZ(); c(4,2)=GetSigma1PtSnp(); c(4,3)=GetSigma1PtTgl(); c(4,4)=GetSigma1Pt2();
+
+ c(0,0)+=t->GetSigmaY2();
+ c(1,0)+=t->GetSigmaZY(); c(1,1)+=t->GetSigmaZ2();
+ c(2,0)+=t->GetSigmaSnpY();c(2,1)+=t->GetSigmaSnpZ();c(2,2)+=t->GetSigmaSnp2();
+ c(3,0)+=t->GetSigmaTglY();c(3,1)+=t->GetSigmaTglZ();c(3,2)+=t->GetSigmaTglSnp();c(3,3)+=t->GetSigmaTgl2();
+ c(4,0)+=t->GetSigma1PtY();c(4,1)+=t->GetSigma1PtZ();c(4,2)+=t->GetSigma1PtSnp();c(4,3)+=t->GetSigma1PtTgl();c(4,4)+=t->GetSigma1Pt2();
+ c(0,1)=c(1,0);
+ c(0,2)=c(2,0); c(1,2)=c(2,1);
+ c(0,3)=c(3,0); c(1,3)=c(3,1); c(2,3)=c(3,2);
+ c(0,4)=c(4,0); c(1,4)=c(4,1); c(2,4)=c(4,2); c(3,4)=c(4,3);
+
+ c.Invert();
+ if (!c.IsValid()) return kVeryBig;
+
+
+ Double_t res[5] = {
+ GetY() - t->GetY(),
+ GetZ() - t->GetZ(),
+ GetSnp() - t->GetSnp(),
+ GetTgl() - t->GetTgl(),
+ GetSigned1Pt() - t->GetSigned1Pt()
+ };
+
+ Double_t chi2=0.;
+ for (Int_t i = 0; i < 5; i++)
+ for (Int_t j = 0; j < 5; j++) chi2 += res[i]*res[j]*c(i,j);
+
+ return chi2;
}
-//_____________________________________________________________________________
-Double_t AliExternalTrackParam::SigmaPt() const
-{
-// get the error of the transversal component of the momentum
+Bool_t AliExternalTrackParam::
+PropagateTo(Double_t p[3],Double_t covyz[3],Double_t covxyz[3],Double_t bz) {
+ //----------------------------------------------------------------
+ // Propagate this track to the plane
+ // the 3D space point "p" (with the covariance matrix "covyz" and "covxyz")
+ // belongs to.
+ // The magnetic field is "bz" (kG)
+ //
+ // The track curvature and the change of the covariance matrix
+ // of the track parameters are negleted !
+ // (So the "step" should be small compared with 1/curvature)
+ //----------------------------------------------------------------
+
+ Double_t f=GetSnp();
+ if (TMath::Abs(f) >= kAlmost1) return kFALSE;
+ Double_t r=TMath::Sqrt(1.- f*f);
+ Double_t a=f/r, b=GetTgl()/r;
+
+ Double_t s2=333.*333.; //something reasonably big (cm^2)
+
+ TMatrixDSym tV(3);
+ tV(0,0)= s2; tV(0,1)= a*s2; tV(0,2)= b*s2;
+ tV(1,0)=a*s2; tV(1,1)=a*a*s2; tV(1,2)=a*b*s2;
+ tV(2,0)=b*s2; tV(2,1)=a*b*s2; tV(2,2)=b*b*s2;
+
+ TMatrixDSym pV(3);
+ pV(0,0)=covxyz[0]; pV(0,1)=covxyz[1]; pV(0,2)=covxyz[2];
+ pV(1,0)=covxyz[1]; pV(1,1)=covyz[0]; pV(1,2)=covyz[1];
+ pV(2,0)=covxyz[2]; pV(2,1)=covyz[1]; pV(2,2)=covyz[2];
+
+ TMatrixDSym tpV(tV);
+ tpV+=pV;
+ tpV.Invert();
+ if (!tpV.IsValid()) return kFALSE;
- return TMath::Sqrt(fCovar[14]) / TMath::Abs(fParam[4]);
+ TMatrixDSym pW(3),tW(3);
+ for (Int_t i=0; i<3; i++)
+ for (Int_t j=0; j<3; j++) {
+ pW(i,j)=tW(i,j)=0.;
+ for (Int_t k=0; k<3; k++) {
+ pW(i,j) += tV(i,k)*tpV(k,j);
+ tW(i,j) += pV(i,k)*tpV(k,j);
+ }
+ }
+
+ Double_t t[3] = {GetX(), GetY(), GetZ()};
+
+ Double_t x=0.;
+ for (Int_t i=0; i<3; i++) x += (tW(0,i)*t[i] + pW(0,i)*p[i]);
+ Double_t crv=GetC(bz);
+ if (TMath::Abs(b) < kAlmost0Field) crv=0.;
+ f += crv*(x-fX);
+ if (TMath::Abs(f) >= kAlmost1) return kFALSE;
+ fX=x;
+
+ fP[0]=0.;
+ for (Int_t i=0; i<3; i++) fP[0] += (tW(1,i)*t[i] + pW(1,i)*p[i]);
+ fP[1]=0.;
+ for (Int_t i=0; i<3; i++) fP[1] += (tW(2,i)*t[i] + pW(2,i)*p[i]);
+
+ return kTRUE;
}
-//_____________________________________________________________________________
-TVector3 AliExternalTrackParam::Momentum() const
-{
-// get the momentum vector
+Double_t *AliExternalTrackParam::GetResiduals(
+Double_t *p,Double_t *cov,Bool_t updated) const {
+ //------------------------------------------------------------------
+ // Returns the track residuals with the space point "p" having
+ // the covariance matrix "cov".
+ // If "updated" is kTRUE, the track parameters expected to be updated,
+ // otherwise they must be predicted.
+ //------------------------------------------------------------------
+ static Double_t res[2];
+
+ Double_t r00=cov[0], r01=cov[1], r11=cov[2];
+ if (updated) {
+ r00-=fC[0]; r01-=fC[1]; r11-=fC[2];
+ } else {
+ r00+=fC[0]; r01+=fC[1]; r11+=fC[2];
+ }
+ Double_t det=r00*r11 - r01*r01;
+
+ if (TMath::Abs(det) < kAlmost0) return 0;
+
+ Double_t tmp=r00; r00=r11/det; r11=tmp/det;
+
+ if (r00 < 0.) return 0;
+ if (r11 < 0.) return 0;
+
+ Double_t dy = fP[0] - p[0];
+ Double_t dz = fP[1] - p[1];
- Double_t phi = TMath::ASin(fParam[2]) + fAlpha;
- Double_t pt = 1. / TMath::Abs(fParam[4]);
- return TVector3(pt * TMath::Cos(phi),
- pt * TMath::Sin(phi),
- pt * fParam[3]);
+ res[0]=dy*TMath::Sqrt(r00);
+ res[1]=dz*TMath::Sqrt(r11);
+
+ return res;
}
-//_____________________________________________________________________________
-TVector3 AliExternalTrackParam::Position() const
+Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) {
+ //------------------------------------------------------------------
+ // Update the track parameters with the space point "p" having
+ // the covariance matrix "cov"
+ //------------------------------------------------------------------
+ Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
+ Double_t
+ &fC00=fC[0],
+ &fC10=fC[1], &fC11=fC[2],
+ &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
+ &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
+ &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
+
+ Double_t r00=cov[0], r01=cov[1], r11=cov[2];
+ r00+=fC00; r01+=fC10; r11+=fC11;
+ Double_t det=r00*r11 - r01*r01;
+
+ if (TMath::Abs(det) < kAlmost0) return kFALSE;
+
+
+ Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
+
+ Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11;
+ Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11;
+ Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11;
+ Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11;
+ Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11;
+
+ Double_t dy=p[0] - fP0, dz=p[1] - fP1;
+ Double_t sf=fP2 + k20*dy + k21*dz;
+ if (TMath::Abs(sf) > kAlmost1) return kFALSE;
+
+ fP0 += k00*dy + k01*dz;
+ fP1 += k10*dy + k11*dz;
+ fP2 = sf;
+ fP3 += k30*dy + k31*dz;
+ fP4 += k40*dy + k41*dz;
+
+ Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40;
+ Double_t c12=fC21, c13=fC31, c14=fC41;
+
+ fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11;
+ fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13;
+ fC40-=k00*c04+k01*c14;
+
+ fC11-=k10*c01+k11*fC11;
+ fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13;
+ fC41-=k10*c04+k11*c14;
+
+ fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13;
+ fC42-=k20*c04+k21*c14;
+
+ fC33-=k30*c03+k31*c13;
+ fC43-=k30*c04+k31*c14;
+
+ fC44-=k40*c04+k41*c14;
+
+ return kTRUE;
+}
+
+void
+AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const {
+ //--------------------------------------------------------------------
+ // External track parameters -> helix parameters
+ // "b" - magnetic field (kG)
+ //--------------------------------------------------------------------
+ Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
+
+ hlx[0]=fP[0]; hlx[1]=fP[1]; hlx[2]=fP[2]; hlx[3]=fP[3];
+
+ hlx[5]=fX*cs - hlx[0]*sn; // x0
+ hlx[0]=fX*sn + hlx[0]*cs; // y0
+//hlx[1]= // z0
+ hlx[2]=TMath::ASin(hlx[2]) + fAlpha; // phi0
+//hlx[3]= // tgl
+ hlx[4]=GetC(b); // 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
{
-// get the current spatial position in global coordinates
+ //--------------------------------------------------------------------
+ // 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];
+ r[1] = h[0];
+ if (TMath::Abs(h[4])>kAlmost0) {
+ r[0] += (sn - h[6])/h[4];
+ r[1] -= (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 AliExternalTrackParam::GetDCA(const AliExternalTrackParam *p,
+Double_t b, Double_t &xthis, Double_t &xp) const {
+ //------------------------------------------------------------
+ // Returns the (weighed !) distance of closest approach between
+ // this track and the track "p".
+ // 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;
+
+ Double_t p1[8]; GetHelixParameters(p1,b);
+ p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]);
+ Double_t p2[8]; p->GetHelixParameters(p2,b);
+ 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)
+ AliDebug(1," stopped at not a stationary point !");
+ Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det);
+ if (lmb < 0.)
+ AliDebug(1," stopped at not a minimum !");
+ 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) {
+ AliDebug(1," overshoot !"); break;
+ }
+ }
+ dm=dd;
+
+ t1+=dt1;
+ t2+=dt2;
+
+ }
+
+ if (max<=0) AliDebug(1," too many iterations !");
+
+ 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 AliExternalTrackParam::
+PropagateToDCA(AliExternalTrackParam *p, Double_t b) {
+ //--------------------------------------------------------------
+ // 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,b,xthis,xp);
+
+ if (!PropagateTo(xthis,b)) {
+ //AliWarning(" propagation failed !");
+ return 1e+33;
+ }
+
+ if (!p->PropagateTo(xp,b)) {
+ //AliWarning(" propagation failed !";
+ return 1e+33;
+ }
+
+ return dca;
+}
+
+
+Bool_t AliExternalTrackParam::PropagateToDCA(const AliVVertex *vtx,
+Double_t b, Double_t maxd, Double_t dz[2], Double_t covar[3]) {
+ //
+ // Propagate this track to the DCA to vertex "vtx",
+ // if the (rough) transverse impact parameter is not bigger then "maxd".
+ // Magnetic field is "b" (kG).
+ //
+ // a) The track gets extapolated to the DCA to the vertex.
+ // b) The impact parameters and their covariance matrix are calculated.
+ //
+ // In the case of success, the returned value is kTRUE
+ // (otherwise, it's kFALSE)
+ //
+ Double_t alpha=GetAlpha();
+ Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha);
+ Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2];
+ Double_t xv= vtx->GetX()*cs + vtx->GetY()*sn;
+ Double_t yv=-vtx->GetX()*sn + vtx->GetY()*cs, zv=vtx->GetZ();
+ x-=xv; y-=yv;
+
+ //Estimate the impact parameter neglecting the track curvature
+ Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt(1.- snp*snp));
+ if (d > maxd) return kFALSE;
+
+ //Propagate to the DCA
+ Double_t crv=GetC(b);
+ if (TMath::Abs(b) < kAlmost0Field) crv=0.;
+
+ Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt(1.-snp*snp));
+ sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt(1.- sn*sn);
+ if (TMath::Abs(tgfv)>0.) cs = sn/tgfv;
+ else cs=1.;
+
+ x = xv*cs + yv*sn;
+ yv=-xv*sn + yv*cs; xv=x;
+
+ if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE;
+
+ if (dz==0) return kTRUE;
+ dz[0] = GetParameter()[0] - yv;
+ dz[1] = GetParameter()[1] - zv;
+
+ if (covar==0) return kTRUE;
+ Double_t cov[6]; vtx->GetCovarianceMatrix(cov);
+
+ //***** Improvements by A.Dainese
+ alpha=GetAlpha(); sn=TMath::Sin(alpha); cs=TMath::Cos(alpha);
+ Double_t s2ylocvtx = cov[0]*sn*sn + cov[2]*cs*cs - 2.*cov[1]*cs*sn;
+ covar[0] = GetCovariance()[0] + s2ylocvtx; // neglecting correlations
+ covar[1] = GetCovariance()[1]; // between (x,y) and z
+ covar[2] = GetCovariance()[2] + cov[5]; // in vertex's covariance matrix
+ //*****
+
+ return kTRUE;
+}
+
+Bool_t AliExternalTrackParam::PropagateToDCABxByBz(const AliVVertex *vtx,
+Double_t b[3], Double_t maxd, Double_t dz[2], Double_t covar[3]) {
+ //
+ // Propagate this track to the DCA to vertex "vtx",
+ // if the (rough) transverse impact parameter is not bigger then "maxd".
+ //
+ // This function takes into account all three components of the magnetic
+ // field given by the b[3] arument (kG)
+ //
+ // a) The track gets extapolated to the DCA to the vertex.
+ // b) The impact parameters and their covariance matrix are calculated.
+ //
+ // In the case of success, the returned value is kTRUE
+ // (otherwise, it's kFALSE)
+ //
+ Double_t alpha=GetAlpha();
+ Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha);
+ Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2];
+ Double_t xv= vtx->GetX()*cs + vtx->GetY()*sn;
+ Double_t yv=-vtx->GetX()*sn + vtx->GetY()*cs, zv=vtx->GetZ();
+ x-=xv; y-=yv;
- return TVector3(fX * TMath::Cos(fAlpha) - fParam[0] * TMath::Sin(fAlpha),
- fX * TMath::Sin(fAlpha) + fParam[0] * TMath::Cos(fAlpha),
- fParam[1]);
+ //Estimate the impact parameter neglecting the track curvature
+ Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt(1.- snp*snp));
+ if (d > maxd) return kFALSE;
+
+ //Propagate to the DCA
+ Double_t crv=GetC(b[2]);
+ if (TMath::Abs(b[2]) < kAlmost0Field) crv=0.;
+
+ Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt(1.-snp*snp));
+ sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt(1.- sn*sn);
+ if (TMath::Abs(tgfv)>0.) cs = sn/tgfv;
+ else cs=1.;
+
+ x = xv*cs + yv*sn;
+ yv=-xv*sn + yv*cs; xv=x;
+
+ if (!PropagateBxByBz(alpha+TMath::ASin(sn),xv,b)) return kFALSE;
+
+ if (dz==0) return kTRUE;
+ dz[0] = GetParameter()[0] - yv;
+ dz[1] = GetParameter()[1] - zv;
+
+ if (covar==0) return kTRUE;
+ Double_t cov[6]; vtx->GetCovarianceMatrix(cov);
+
+ //***** Improvements by A.Dainese
+ alpha=GetAlpha(); sn=TMath::Sin(alpha); cs=TMath::Cos(alpha);
+ Double_t s2ylocvtx = cov[0]*sn*sn + cov[2]*cs*cs - 2.*cov[1]*cs*sn;
+ covar[0] = GetCovariance()[0] + s2ylocvtx; // neglecting correlations
+ covar[1] = GetCovariance()[1]; // between (x,y) and z
+ covar[2] = GetCovariance()[2] + cov[5]; // in vertex's covariance matrix
+ //*****
+
+ return kTRUE;
+}
+
+
+void AliExternalTrackParam::GetDirection(Double_t d[3]) const {
+ //----------------------------------------------------------------
+ // This function returns a unit vector along the track direction
+ // in the global coordinate system.
+ //----------------------------------------------------------------
+ Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
+ Double_t snp=fP[2];
+ Double_t csp =TMath::Sqrt((1.- snp)*(1.+snp));
+ Double_t norm=TMath::Sqrt(1.+ fP[3]*fP[3]);
+ d[0]=(csp*cs - snp*sn)/norm;
+ d[1]=(snp*cs + csp*sn)/norm;
+ d[2]=fP[3]/norm;
+}
+
+Bool_t AliExternalTrackParam::GetPxPyPz(Double_t p[3]) const {
+ //---------------------------------------------------------------------
+ // This function returns the global track momentum components
+ // Results for (nearly) straight tracks are meaningless !
+ //---------------------------------------------------------------------
+ p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3];
+ return Local2GlobalMomentum(p,fAlpha);
+}
+
+Double_t AliExternalTrackParam::Px() const {
+ //---------------------------------------------------------------------
+ // Returns x-component of momentum
+ // Result for (nearly) straight tracks is meaningless !
+ //---------------------------------------------------------------------
+
+ Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
+ GetPxPyPz(p);
+
+ return p[0];
+}
+
+Double_t AliExternalTrackParam::Py() const {
+ //---------------------------------------------------------------------
+ // Returns y-component of momentum
+ // Result for (nearly) straight tracks is meaningless !
+ //---------------------------------------------------------------------
+
+ Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
+ GetPxPyPz(p);
+
+ return p[1];
+}
+
+Double_t AliExternalTrackParam::Pz() const {
+ //---------------------------------------------------------------------
+ // Returns z-component of momentum
+ // Result for (nearly) straight tracks is meaningless !
+ //---------------------------------------------------------------------
+
+ Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
+ GetPxPyPz(p);
+
+ return p[2];
+}
+
+Double_t AliExternalTrackParam::Xv() const {
+ //---------------------------------------------------------------------
+ // Returns x-component of first track point
+ //---------------------------------------------------------------------
+
+ Double_t r[3]={0.,0.,0.};
+ GetXYZ(r);
+
+ return r[0];
}
+Double_t AliExternalTrackParam::Yv() const {
+ //---------------------------------------------------------------------
+ // Returns y-component of first track point
+ //---------------------------------------------------------------------
+
+ Double_t r[3]={0.,0.,0.};
+ GetXYZ(r);
+
+ return r[1];
+}
+
+Double_t AliExternalTrackParam::Zv() const {
+ //---------------------------------------------------------------------
+ // Returns z-component of first track point
+ //---------------------------------------------------------------------
+
+ Double_t r[3]={0.,0.,0.};
+ GetXYZ(r);
+
+ return r[2];
+}
+
+Double_t AliExternalTrackParam::Theta() const {
+ // return theta angle of momentum
+
+ return 0.5*TMath::Pi() - TMath::ATan(fP[3]);
+}
+
+Double_t AliExternalTrackParam::Phi() const {
+ //---------------------------------------------------------------------
+ // Returns the azimuthal angle of momentum
+ // 0 <= phi < 2*pi
+ //---------------------------------------------------------------------
+
+ Double_t phi=TMath::ASin(fP[2]) + fAlpha;
+ if (phi<0.) phi+=2.*TMath::Pi();
+ else if (phi>=2.*TMath::Pi()) phi-=2.*TMath::Pi();
+
+ return phi;
+}
+
+Double_t AliExternalTrackParam::M() const {
+ // return particle mass
+
+ // No mass information available so far.
+ // Redifine in derived class!
+
+ return -999.;
+}
+
+Double_t AliExternalTrackParam::E() const {
+ // return particle energy
+
+ // No PID information available so far.
+ // Redifine in derived class!
+
+ return -999.;
+}
+
+Double_t AliExternalTrackParam::Eta() const {
+ // return pseudorapidity
+
+ return -TMath::Log(TMath::Tan(0.5 * Theta()));
+}
+
+Double_t AliExternalTrackParam::Y() const {
+ // return rapidity
+
+ // No PID information available so far.
+ // Redifine in derived class!
+
+ return -999.;
+}
+
+Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const {
+ //---------------------------------------------------------------------
+ // This function returns the global track position
+ //---------------------------------------------------------------------
+ r[0]=fX; r[1]=fP[0]; r[2]=fP[1];
+ return Local2GlobalPosition(r,fAlpha);
+}
+
+Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const {
+ //---------------------------------------------------------------------
+ // This function returns the global covariance matrix of the track params
+ //
+ // Cov(x,x) ... : cv[0]
+ // Cov(y,x) ... : cv[1] cv[2]
+ // Cov(z,x) ... : cv[3] cv[4] cv[5]
+ // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9]
+ // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14]
+ // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20]
+ //
+ // Results for (nearly) straight tracks are meaningless !
+ //---------------------------------------------------------------------
+ if (TMath::Abs(fP[4])<=kAlmost0) {
+ for (Int_t i=0; i<21; i++) cv[i]=0.;
+ return kFALSE;
+ }
+ if (TMath::Abs(fP[2]) > kAlmost1) {
+ for (Int_t i=0; i<21; i++) cv[i]=0.;
+ return kFALSE;
+ }
+ Double_t pt=1./TMath::Abs(fP[4]);
+ Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
+ Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
+
+ Double_t m00=-sn, m10=cs;
+ Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
+ Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
+ Double_t m35=pt, m45=-pt*pt*fP[3];
+
+ m43*=GetSign();
+ m44*=GetSign();
+ m45*=GetSign();
+
+ cv[0 ] = fC[0]*m00*m00;
+ cv[1 ] = fC[0]*m00*m10;
+ cv[2 ] = fC[0]*m10*m10;
+ cv[3 ] = fC[1]*m00;
+ cv[4 ] = fC[1]*m10;
+ cv[5 ] = fC[2];
+ cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43);
+ cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43);
+ cv[8 ] = fC[4]*m23 + fC[11]*m43;
+ cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43);
+ cv[10] = m00*(fC[3]*m24 + fC[10]*m44);
+ cv[11] = m10*(fC[3]*m24 + fC[10]*m44);
+ cv[12] = fC[4]*m24 + fC[11]*m44;
+ cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44);
+ cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44);
+ cv[15] = m00*(fC[6]*m35 + fC[10]*m45);
+ cv[16] = m10*(fC[6]*m35 + fC[10]*m45);
+ cv[17] = fC[7]*m35 + fC[11]*m45;
+ cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45);
+ cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45);
+ cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45);
+
+ return kTRUE;
+}
+
+
+Bool_t
+AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const {
+ //---------------------------------------------------------------------
+ // This function returns the global track momentum extrapolated to
+ // the radial position "x" (cm) in the magnetic field "b" (kG)
+ //---------------------------------------------------------------------
+ p[0]=fP[4];
+ p[1]=fP[2]+(x-fX)*GetC(b);
+ p[2]=fP[3];
+ return Local2GlobalMomentum(p,fAlpha);
+}
+
+Bool_t
+AliExternalTrackParam::GetYAt(Double_t x, Double_t b, Double_t &y) const {
+ //---------------------------------------------------------------------
+ // This function returns the local Y-coordinate of the intersection
+ // point between this track and the reference plane "x" (cm).
+ // Magnetic field "b" (kG)
+ //---------------------------------------------------------------------
+ Double_t dx=x-fX;
+ if(TMath::Abs(dx)<=kAlmost0) {y=fP[0]; return kTRUE;}
+
+ Double_t f1=fP[2], f2=f1 + dx*GetC(b);
+
+ if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
+ if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
+
+ Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2));
+ y = fP[0] + dx*(f1+f2)/(r1+r2);
+ return kTRUE;
+}
+
+Bool_t
+AliExternalTrackParam::GetZAt(Double_t x, Double_t b, Double_t &z) const {
+ //---------------------------------------------------------------------
+ // This function returns the local Z-coordinate of the intersection
+ // point between this track and the reference plane "x" (cm).
+ // Magnetic field "b" (kG)
+ //---------------------------------------------------------------------
+ Double_t dx=x-fX;
+ if(TMath::Abs(dx)<=kAlmost0) {z=fP[1]; return kTRUE;}
+
+ Double_t f1=fP[2], f2=f1 + dx*GetC(b);
+
+ if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
+ if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
+
+ Double_t r1=sqrt((1.-f1)*(1.+f1)), r2=sqrt((1.-f2)*(1.+f2));
+ z = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3]; // Many thanks to P.Hristov !
+ return kTRUE;
+}
+
+Bool_t
+AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const {
+ //---------------------------------------------------------------------
+ // This function returns the global track position extrapolated to
+ // the radial position "x" (cm) in the magnetic field "b" (kG)
+ //---------------------------------------------------------------------
+ Double_t dx=x-fX;
+ if(TMath::Abs(dx)<=kAlmost0) return GetXYZ(r);
+
+ Double_t f1=fP[2], f2=f1 + dx*GetC(b);
+
+ if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
+ if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
+
+ Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2));
+ r[0] = x;
+ r[1] = fP[0] + dx*(f1+f2)/(r1+r2);
+ r[2] = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3];//Thanks to Andrea & Peter
+
+ return Local2GlobalPosition(r,fAlpha);
+}
//_____________________________________________________________________________
void AliExternalTrackParam::Print(Option_t* /*option*/) const
printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha);
printf(" parameters: %12g %12g %12g %12g %12g\n",
- fParam[0], fParam[1], fParam[2], fParam[3], fParam[4]);
- printf(" covariance: %12g\n", fCovar[0]);
- printf(" %12g %12g\n", fCovar[1], fCovar[2]);
- printf(" %12g %12g %12g\n", fCovar[3], fCovar[4], fCovar[5]);
+ fP[0], fP[1], fP[2], fP[3], fP[4]);
+ printf(" covariance: %12g\n", fC[0]);
+ printf(" %12g %12g\n", fC[1], fC[2]);
+ printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]);
printf(" %12g %12g %12g %12g\n",
- fCovar[6], fCovar[7], fCovar[8], fCovar[9]);
+ fC[6], fC[7], fC[8], fC[9]);
printf(" %12g %12g %12g %12g %12g\n",
- fCovar[10], fCovar[11], fCovar[12], fCovar[13], fCovar[14]);
+ fC[10], fC[11], fC[12], fC[13], fC[14]);
+}
+
+Double_t AliExternalTrackParam::GetSnpAt(Double_t x,Double_t b) const {
+ //
+ // Get sinus at given x
+ //
+ Double_t crv=GetC(b);
+ if (TMath::Abs(b) < kAlmost0Field) crv=0.;
+ Double_t dx = x-fX;
+ Double_t res = fP[2]+dx*crv;
+ return res;
+}
+
+Bool_t AliExternalTrackParam::GetDistance(AliExternalTrackParam *param2, Double_t x, Double_t dist[3], Double_t bz){
+ //------------------------------------------------------------------------
+ // Get the distance between two tracks at the local position x
+ // working in the local frame of this track.
+ // Origin : Marian.Ivanov@cern.ch
+ //-----------------------------------------------------------------------
+ Double_t xyz[3];
+ Double_t xyz2[3];
+ xyz[0]=x;
+ if (!GetYAt(x,bz,xyz[1])) return kFALSE;
+ if (!GetZAt(x,bz,xyz[2])) return kFALSE;
+ //
+ //
+ if (TMath::Abs(GetAlpha()-param2->GetAlpha())<kAlmost0){
+ xyz2[0]=x;
+ if (!param2->GetYAt(x,bz,xyz2[1])) return kFALSE;
+ if (!param2->GetZAt(x,bz,xyz2[2])) return kFALSE;
+ }else{
+ //
+ Double_t xyz1[3];
+ Double_t dfi = param2->GetAlpha()-GetAlpha();
+ Double_t ca = TMath::Cos(dfi), sa = TMath::Sin(dfi);
+ xyz2[0] = xyz[0]*ca+xyz[1]*sa;
+ xyz2[1] = -xyz[0]*sa+xyz[1]*ca;
+ //
+ xyz1[0]=xyz2[0];
+ if (!param2->GetYAt(xyz2[0],bz,xyz1[1])) return kFALSE;
+ if (!param2->GetZAt(xyz2[0],bz,xyz1[2])) return kFALSE;
+ //
+ xyz2[0] = xyz1[0]*ca-xyz1[1]*sa;
+ xyz2[1] = +xyz1[0]*sa+xyz1[1]*ca;
+ xyz2[2] = xyz1[2];
+ }
+ dist[0] = xyz[0]-xyz2[0];
+ dist[1] = xyz[1]-xyz2[1];
+ dist[2] = xyz[2]-xyz2[2];
+
+ return kTRUE;
+}
+
+
+//
+// Draw functionality.
+// Origin: Marian Ivanov, Marian.Ivanov@cern.ch
+//
+
+void AliExternalTrackParam::DrawTrack(Float_t magf, Float_t minR, Float_t maxR, Float_t stepR){
+ //
+ // Draw track line
+ //
+ if (minR>maxR) return ;
+ if (stepR<=0) return ;
+ Int_t npoints = TMath::Nint((maxR-minR)/stepR)+1;
+ if (npoints<1) return;
+ TPolyMarker3D *polymarker = new TPolyMarker3D(npoints);
+ FillPolymarker(polymarker, magf,minR,maxR,stepR);
+ polymarker->Draw();
+}
+
+//
+void AliExternalTrackParam::FillPolymarker(TPolyMarker3D *pol, Float_t magF, Float_t minR, Float_t maxR, Float_t stepR){
+ //
+ // Fill points in the polymarker
+ //
+ Int_t counter=0;
+ for (Double_t r=minR; r<maxR; r+=stepR){
+ Double_t point[3];
+ GetXYZAt(r,magF,point);
+ pol->SetPoint(counter,point[0],point[1], point[2]);
+ printf("xyz\t%f\t%f\t%f\n",point[0], point[1],point[2]);
+ counter++;
+ }
+}
+
+Int_t AliExternalTrackParam::GetIndex(Int_t i, Int_t j) const {
+ //
+ Int_t min = TMath::Min(i,j);
+ Int_t max = TMath::Max(i,j);
+
+ return min+(max+1)*max/2;
}
+
+
+void AliExternalTrackParam::g3helx3(Double_t qfield,
+ Double_t step,
+ Double_t vect[7]) {
+/******************************************************************
+ * *
+ * GEANT3 tracking routine in a constant field oriented *
+ * along axis 3 *
+ * Tracking is performed with a conventional *
+ * helix step method *
+ * *
+ * Authors R.Brun, M.Hansroul ********* *
+ * Rewritten V.Perevoztchikov *
+ * *
+ * Rewritten in C++ by I.Belikov *
+ * *
+ * qfield (kG) - particle charge times magnetic field *
+ * step (cm) - step length along the helix *
+ * vect[7](cm,GeV/c) - input/output x, y, z, px/p, py/p ,pz/p, p *
+ * *
+ ******************************************************************/
+ const Int_t ix=0, iy=1, iz=2, ipx=3, ipy=4, ipz=5, ipp=6;
+
+ Double_t cosx=vect[ipx], cosy=vect[ipy], cosz=vect[ipz];
+
+ Double_t rho = qfield*kB2C/vect[ipp];
+ Double_t tet = rho*step;
+
+ Double_t tsint, sintt, sint, cos1t;
+ if (TMath::Abs(tet) > 0.15) {
+ sint = TMath::Sin(tet);
+ sintt = sint/tet;
+ tsint = (tet - sint)/tet;
+ Double_t t=TMath::Sin(0.5*tet);
+ cos1t = 2*t*t/tet;
+ } else {
+ tsint = tet*tet/6.;
+ sintt = 1.- tsint;
+ sint = tet*sintt;
+ cos1t = 0.5*tet;
+ }
+
+ Double_t f1 = step*sintt;
+ Double_t f2 = step*cos1t;
+ Double_t f3 = step*tsint*cosz;
+ Double_t f4 = -tet*cos1t;
+ Double_t f5 = sint;
+
+ vect[ix] += f1*cosx - f2*cosy;
+ vect[iy] += f1*cosy + f2*cosx;
+ vect[iz] += f1*cosz + f3;
+
+ vect[ipx] += f4*cosx - f5*cosy;
+ vect[ipy] += f4*cosy + f5*cosx;
+
+}
+
+Bool_t AliExternalTrackParam::PropagateToBxByBz(Double_t xk, const Double_t b[3]) {
+ //----------------------------------------------------------------
+ // Extrapolate this track to the plane X=xk in the field b[].
+ //
+ // X [cm] is in the "tracking coordinate system" of this track.
+ // b[]={Bx,By,Bz} [kG] is in the Global coordidate system.
+ //----------------------------------------------------------------
+
+ Double_t dx=xk-fX;
+ if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
+
+ Double_t crv=GetC(b[2]);
+ if (TMath::Abs(b[2]) < kAlmost0Field) crv=0.;
+
+ Double_t f1=fP[2], f2=f1 + crv*dx;
+ if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
+ if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
+
+
+ // Estimate the covariance matrix
+ Double_t &fP3=fP[3], &fP4=fP[4];
+ Double_t
+ &fC00=fC[0],
+ &fC10=fC[1], &fC11=fC[2],
+ &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
+ &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
+ &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
+
+ Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
+
+ //f = F - 1
+ Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4;
+ Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc;
+ Double_t f12= dx*fP3*f1/(r1*r1*r1);
+ Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc;
+ Double_t f13= dx/r1;
+ Double_t f24= dx; f24*=cc;
+
+ //b = C*ft
+ Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
+ Double_t b02=f24*fC40;
+ Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
+ Double_t b12=f24*fC41;
+ Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
+ Double_t b22=f24*fC42;
+ Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
+ Double_t b42=f24*fC44;
+ Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
+ Double_t b32=f24*fC43;
+
+ //a = f*b = f*C*ft
+ Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42;
+ Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32;
+ Double_t a22=f24*b42;
+
+ //F*C*Ft = C + (b + bt + a)
+ fC00 += b00 + b00 + a00;
+ fC10 += b10 + b01 + a01;
+ fC20 += b20 + b02 + a02;
+ fC30 += b30;
+ fC40 += b40;
+ fC11 += b11 + b11 + a11;
+ fC21 += b21 + b12 + a12;
+ fC31 += b31;
+ fC41 += b41;
+ fC22 += b22 + b22 + a22;
+ fC32 += b32;
+ fC42 += b42;
+
+
+ // Appoximate step length
+ Double_t step=dx*TMath::Abs(r2 + f2*(f1+f2)/(r1+r2));
+ step *= TMath::Sqrt(1.+ GetTgl()*GetTgl());
+
+
+ // Get the track's (x,y,z) and (px,py,pz) in the Global System
+ Double_t r[3]; GetXYZ(r);
+ Double_t p[3]; GetPxPyPz(p);
+ Double_t pp=GetP();
+ p[0] /= pp;
+ p[1] /= pp;
+ p[2] /= pp;
+
+
+ // Rotate to the system where Bx=By=0.
+ Double_t bt=TMath::Sqrt(b[0]*b[0] + b[1]*b[1]);
+ Double_t cosphi=1., sinphi=0.;
+ if (bt > kAlmost0) {cosphi=b[0]/bt; sinphi=b[1]/bt;}
+ Double_t bb=TMath::Sqrt(b[0]*b[0] + b[1]*b[1] + b[2]*b[2]);
+ Double_t costet=1., sintet=0.;
+ if (bb > kAlmost0) {costet=b[2]/bb; sintet=bt/bb;}
+ Double_t vect[7];
+
+ vect[0] = costet*cosphi*r[0] + costet*sinphi*r[1] - sintet*r[2];
+ vect[1] = -sinphi*r[0] + cosphi*r[1];
+ vect[2] = sintet*cosphi*r[0] + sintet*sinphi*r[1] + costet*r[2];
+
+ vect[3] = costet*cosphi*p[0] + costet*sinphi*p[1] - sintet*p[2];
+ vect[4] = -sinphi*p[0] + cosphi*p[1];
+ vect[5] = sintet*cosphi*p[0] + sintet*sinphi*p[1] + costet*p[2];
+
+ vect[6] = pp;
+
+
+ // Do the helix step
+ g3helx3(GetSign()*bb,step,vect);
+
+
+ // Rotate back to the Global System
+ r[0] = cosphi*costet*vect[0] - sinphi*vect[1] + cosphi*sintet*vect[2];
+ r[1] = sinphi*costet*vect[0] + cosphi*vect[1] + sinphi*sintet*vect[2];
+ r[2] = -sintet*vect[0] + costet*vect[2];
+
+ p[0] = cosphi*costet*vect[3] - sinphi*vect[4] + cosphi*sintet*vect[5];
+ p[1] = sinphi*costet*vect[3] + cosphi*vect[4] + sinphi*sintet*vect[5];
+ p[2] = -sintet*vect[3] + costet*vect[5];
+
+
+ // Rotate back to the Tracking System
+ Double_t cosalp = TMath::Cos(fAlpha);
+ Double_t sinalp =-TMath::Sin(fAlpha);
+
+ Double_t
+ t = cosalp*r[0] - sinalp*r[1];
+ r[1] = sinalp*r[0] + cosalp*r[1];
+ r[0] = t;
+
+ t = cosalp*p[0] - sinalp*p[1];
+ p[1] = sinalp*p[0] + cosalp*p[1];
+ p[0] = t;
+
+
+ // Do the final correcting step to the target plane (linear approximation)
+ Double_t x=r[0], y=r[1], z=r[2];
+ if (TMath::Abs(dx) > kAlmost0) {
+ if (TMath::Abs(p[0]) < kAlmost0) return kFALSE;
+ dx = xk - r[0];
+ x += dx;
+ y += p[1]/p[0]*dx;
+ z += p[2]/p[0]*dx;
+ }
+
+
+ // Calculate the track parameters
+ t=TMath::Sqrt(p[0]*p[0] + p[1]*p[1]);
+ fX = x;
+ fP[0] = y;
+ fP[1] = z;
+ fP[2] = p[1]/t;
+ fP[3] = p[2]/t;
+ fP[4] = GetSign()/(t*pp);
+
+ return kTRUE;
+}
+
+Bool_t AliExternalTrackParam::Translate(Double_t *vTrasl,Double_t *covV){
+ //
+ //Translation: in the event mixing, the tracks can be shifted
+ //of the difference among primary vertices (vTrasl) and
+ //the covariance matrix is changed accordingly
+ //(covV = covariance of the primary vertex).
+ //Origin: "Romita, Rossella" <R.Romita@gsi.de>
+ //
+ TVector3 translation;
+ // vTrasl coordinates in the local system
+ translation.SetXYZ(vTrasl[0],vTrasl[1],vTrasl[2]);
+ translation.RotateZ(-fAlpha);
+ translation.GetXYZ(vTrasl);
+
+ //compute the new x,y,z of the track
+ Double_t newX=fX-vTrasl[0];
+ Double_t newY=fP[0]-vTrasl[1];
+ Double_t newZ=fP[1]-vTrasl[2];
+
+ //define the new parameters
+ Double_t newParam[5];
+ newParam[0]=newY;
+ newParam[1]=newZ;
+ newParam[2]=fP[2];
+ newParam[3]=fP[3];
+ newParam[4]=fP[4];
+
+ // recompute the covariance matrix:
+ // 1. covV in the local system
+ Double_t cosRot=TMath::Cos(fAlpha), sinRot=TMath::Sin(fAlpha);
+ TMatrixD qQi(3,3);
+ qQi(0,0) = cosRot;
+ qQi(0,1) = sinRot;
+ qQi(0,2) = 0.;
+ qQi(1,0) = -sinRot;
+ qQi(1,1) = cosRot;
+ qQi(1,2) = 0.;
+ qQi(2,0) = 0.;
+ qQi(2,1) = 0.;
+ qQi(2,2) = 1.;
+ TMatrixD uUi(3,3);
+ uUi(0,0) = covV[0];
+ uUi(0,0) = covV[0];
+ uUi(1,0) = covV[1];
+ uUi(0,1) = covV[1];
+ uUi(2,0) = covV[3];
+ uUi(0,2) = covV[3];
+ uUi(1,1) = covV[2];
+ uUi(2,2) = covV[5];
+ uUi(1,2) = covV[4];
+ if(uUi.Determinant() <= 0.) {return kFALSE;}
+ TMatrixD uUiQi(uUi,TMatrixD::kMult,qQi);
+ TMatrixD m(qQi,TMatrixD::kTransposeMult,uUiQi);
+
+ //2. compute the new covariance matrix of the track
+ Double_t sigmaXX=m(0,0);
+ Double_t sigmaXZ=m(2,0);
+ Double_t sigmaXY=m(1,0);
+ Double_t sigmaYY=GetSigmaY2()+m(1,1);
+ Double_t sigmaYZ=fC[1]+m(1,2);
+ Double_t sigmaZZ=fC[2]+m(2,2);
+ Double_t covarianceYY=sigmaYY + (-1.)*((sigmaXY*sigmaXY)/sigmaXX);
+ Double_t covarianceYZ=sigmaYZ-(sigmaXZ*sigmaXY/sigmaXX);
+ Double_t covarianceZZ=sigmaZZ-((sigmaXZ*sigmaXZ)/sigmaXX);
+
+ Double_t newCov[15];
+ newCov[0]=covarianceYY;
+ newCov[1]=covarianceYZ;
+ newCov[2]=covarianceZZ;
+ for(Int_t i=3;i<15;i++){
+ newCov[i]=fC[i];
+ }
+
+ // set the new parameters
+
+ Set(newX,fAlpha,newParam,newCov);
+
+ return kTRUE;
+ }
git://git.uio.no / u / mrichter / AliRoot.git / blobdiff