// are implemented.
// Origin: I.Belikov, CERN, Jouri.Belikov@cern.ch //
///////////////////////////////////////////////////////////////////////////////
+#include <cassert>
+
+#include <TVectorD.h>
#include <TMatrixDSym.h>
#include <TPolyMarker3D.h>
#include <TVector3.h>
+#include <TMatrixD.h>
#include "AliExternalTrackParam.h"
#include "AliVVertex.h"
ClassImp(AliExternalTrackParam)
Double32_t AliExternalTrackParam::fgMostProbablePt=kMostProbablePt;
-
+Bool_t AliExternalTrackParam::fgUseLogTermMS = kFALSE;;
//_____________________________________________________________________________
AliExternalTrackParam::AliExternalTrackParam() :
AliVTrack(),
//
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];
+ CheckCovariance();
}
//_____________________________________________________________________________
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];
+ CheckCovariance();
}
return *this;
//
for (Int_t i = 0; i < 5; i++) fP[i] = param[i];
for (Int_t i = 0; i < 15; i++) fC[i] = covar[i];
+ CheckCovariance();
}
//_____________________________________________________________________________
// 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 beam pipe, alpha is the
+ // 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
//
+ const double kSafe = 1e-5;
Double_t radPos2 = xyz[0]*xyz[0]+xyz[1]*xyz[1];
- if (radPos2 < 3.*3.) { // inside beam pipe
+ Double_t radMax = 45.; // approximately ITS outer radius
+ if (radPos2 < radMax*radMax) { // inside the ITS
fAlpha = TMath::ATan2(pxpypz[1],pxpypz[0]);
- } else { // outside beam pipe
+ } 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);
}
-
+ //
+ Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
+ // protection: avoid alpha being too close to 0 or +-pi/2
+ if (TMath::Abs(sn)<kSafe) {
+ fAlpha = kSafe;
+ cs=TMath::Cos(fAlpha);
+ sn=TMath::Sin(fAlpha);
+ }
+ else if (cs<kSafe) {
+ fAlpha -= TMath::Sign(kSafe, fAlpha);
+ cs=TMath::Cos(fAlpha);
+ sn=TMath::Sin(fAlpha);
+ }
// Get the vertex of origin and the momentum
TVector3 ver(xyz[0],xyz[1],xyz[2]);
TVector3 mom(pxpypz[0],pxpypz[1],pxpypz[2]);
+ //
+ // avoid momenta along axis
+ if (TMath::Abs(mom[0])<kSafe) mom[0] = TMath::Sign(kSafe*TMath::Abs(mom[1]), mom[0]);
+ if (TMath::Abs(mom[1])<kSafe) mom[1] = TMath::Sign(kSafe*TMath::Abs(mom[0]), mom[1]);
// Rotate to the local coordinate system
ver.RotateZ(-fAlpha);
// Covariance matrix (formulas to be simplified)
+ if (TMath::Abs( 1-fP[2]) < kSafe) fP[2] = 1.- kSafe; //Protection
+ else if (TMath::Abs(-1-fP[2]) < kSafe) fP[2] =-1.+ kSafe; //Protection
+
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;
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));
+ CheckCovariance();
+
return;
}
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];
+ CheckCovariance();
}
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);
+ sn=rp4*xt - fP[2]; cs=rp4*yt + TMath::Sqrt((1.- fP[2])*(1.+fP[2]));
+ a=2*(xt*fP[2] - yt*TMath::Sqrt((1.-fP[2])*(1.+fP[2])))-rp4*(xt*xt + yt*yt);
return -a/(1 + TMath::Sqrt(sn*sn + cs*cs));
}
// 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 f1 = fP[2], r1 = TMath::Sqrt((1.-f1)*(1.+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;
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);
+ Double_t f2 = -sn/rr, r2 = TMath::Sqrt((1.-f2)*(1.+f2));
dz[1] = fP[1] + fP[3]/rp4*TMath::ASin(f2*r1 - f1*r2) - z;
}
Double_t x= xv*cs + yv*sn;
Double_t y=-xv*sn + yv*cs;
- Double_t d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt(1.- fP[2]*fP[2]);
+ Double_t d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
return -d;
}
-Bool_t AliExternalTrackParam::CorrectForMeanMaterial
-(Double_t xOverX0, Double_t xTimesRho, Double_t mass, Bool_t anglecorr,
- Double_t (*Bethe)(Double_t)) {
+Bool_t AliExternalTrackParam::CorrectForMeanMaterialdEdx
+(Double_t xOverX0, Double_t xTimesRho, Double_t mass,
+ Double_t dEdx,
+ Bool_t anglecorr) {
//------------------------------------------------------------------
// 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).
+ // "xTimesRho" - is the product length*density (g/cm^2).
+ // It should be passed as negative when propagating tracks
+ // from the intreaction point to the outside of the central barrel.
// "mass" - the mass of this particle (GeV/c^2).
+ // "dEdx" - mean enery loss (GeV/(g/cm^2)
+ // "anglecorr" - switch for the angular correction
//------------------------------------------------------------------
Double_t &fP2=fP[2];
Double_t &fP3=fP[3];
//Apply angle correction, if requested
if(anglecorr) {
- Double_t angle=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2));
+ Double_t angle=TMath::Sqrt((1.+ fP3*fP3)/((1-fP2)*(1.+fP2)));
xOverX0 *=angle;
xTimesRho *=angle;
}
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;
+ //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
+ Double_t theta2=0.0136*0.0136/(beta2*p2)*TMath::Abs(xOverX0);
+ if (GetUseLogTermMS()) {
+ double lt = 1+0.038*TMath::Log(TMath::Abs(xOverX0));
+ if (lt>0) theta2 *= lt*lt;
+ }
+ if(theta2>TMath::Pi()*TMath::Pi()) return kFALSE;
+ cC22 = theta2*((1.-fP2)*(1.+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 dE=dEdx*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);
+ //cP4 = (1.- e/p2*dE);
+ if ( (1.+ dE/p2*(dE + 2*e)) < 0. ) return kFALSE;
+ cP4 = 1./TMath::Sqrt(1.+ dE/p2*(dE + 2*e)); //A precise formula by Ruben !
if (TMath::Abs(fP4*cP4)>100.) return kFALSE; //Do not track below 10 MeV/c
fC44 += cC44;
fP4 *= cP4;
+ CheckCovariance();
+
return kTRUE;
}
+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).
+ // It should be passed as negative when propagating tracks
+ // from the intreaction point to the outside of the central barrel.
+ // "mass" - the mass of this particle (GeV/c^2).
+ // "anglecorr" - switch for the angular correction
+ // "Bethe" - function calculating the energy loss (GeV/(g/cm^2))
+ //------------------------------------------------------------------
+
+ Double_t bg=GetP()/mass;
+ Double_t dEdx=Bethe(bg);
+
+ return CorrectForMeanMaterialdEdx(xOverX0,xTimesRho,mass,dEdx,anglecorr);
+}
+
+Bool_t AliExternalTrackParam::CorrectForMeanMaterialZA
+(Double_t xOverX0, Double_t xTimesRho, Double_t mass,
+ Double_t zOverA,
+ Double_t density,
+ Double_t exEnergy,
+ Double_t jp1,
+ Double_t jp2,
+ Bool_t anglecorr) {
+ //------------------------------------------------------------------
+ // This function corrects the track parameters for the crossed material
+ // using the full Geant-like Bethe-Bloch formula parameterization
+ // "xOverX0" - X/X0, the thickness in units of the radiation length.
+ // "xTimesRho" - is the product length*density (g/cm^2).
+ // It should be passed as negative when propagating tracks
+ // from the intreaction point to the outside of the central barrel.
+ // "mass" - the mass of this particle (GeV/c^2).
+ // "density" - mean density (g/cm^3)
+ // "zOverA" - mean Z/A
+ // "exEnergy" - mean exitation energy (GeV)
+ // "jp1" - density effect first junction point
+ // "jp2" - density effect second junction point
+ // "anglecorr" - switch for the angular correction
+ //
+ // The default values of the parameters are for silicon
+ //
+ //------------------------------------------------------------------
+
+ Double_t bg=GetP()/mass;
+ Double_t dEdx=BetheBlochGeant(bg,density,jp1,jp2,exEnergy,zOverA);
+
+ return CorrectForMeanMaterialdEdx(xOverX0,xTimesRho,mass,dEdx,anglecorr);
+}
+
+
Bool_t AliExternalTrackParam::CorrectForMaterial
(Double_t d, Double_t x0, Double_t mass, Double_t (*Bethe)(Double_t)) {
//
// This function corrects the track parameters for the crossed material
// "d" - the thickness (fraction of the radiation length)
+ // It should be passed as negative when propagating tracks
+ // from the intreaction point to the outside of the central barrel.
// "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 CorrectForMeanMaterial(d,x0*d,mass,kTRUE,Bethe);
- return kTRUE;
}
Double_t AliExternalTrackParam::BetheBlochAleph(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]
+ // The returned value is in [GeV/(g/cm^2)]
//------------------------------------------------------------------
return BetheBlochGeant(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]
+ // The returned value is in [GeV/(g/cm^2)]
//------------------------------------------------------------------
const Double_t rho = 0.9e-3;
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 sf=fP2, cf=TMath::Sqrt((1.- fP2)*(1.+fP2)); // Improve precision
Double_t tmp=sf*ca - cf*sa;
if (TMath::Abs(tmp) >= kAlmost1) {
- AliError(Form("Rotation failed ! %.10e",tmp));
+ if (TMath::Abs(tmp) > 1.+ Double_t(FLT_EPSILON))
+ AliWarning(Form("Rotation failed ! %.10e",tmp));
return kFALSE;
}
fC40 *= ca;
fC42 *= rr;
+ CheckCovariance();
+
return kTRUE;
}
Double_t crv=GetC(b);
if (TMath::Abs(b) < kAlmost0Field) crv=0.;
- Double_t f1=fP[2], f2=f1 + crv*dx;
+ Double_t x2r = crv*dx;
+ Double_t f1=fP[2], f2=f1 + x2r;
if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
+ if (TMath::Abs(fP[4])< kAlmost0) return kFALSE;
Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
Double_t
&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);
+ Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2));
+ if (TMath::Abs(r1)<kAlmost0) return kFALSE;
+ if (TMath::Abs(r2)<kAlmost0) return kFALSE;
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;
+ double dy2dx = (f1+f2)/(r1+r2);
+ fP0 += dx*dy2dx;
+ if (TMath::Abs(x2r)<0.05) {
+ fP1 += dx*(r2 + f2*dy2dx)*fP3; // Many thanks to P.Hristov !
+ fP2 += x2r;
+ }
+ else {
+ // for small dx/R the linear apporximation of the arc by the segment is OK,
+ // but at large dx/R the error is very large and leads to incorrect Z propagation
+ // angle traversed delta = 2*asin(dist_start_end / R / 2), hence the arc is: R*deltaPhi
+ // The dist_start_end is obtained from sqrt(dx^2+dy^2) = x/(r1+r2)*sqrt(2+f1*f2+r1*r2)
+ // Similarly, the rotation angle in linear in dx only for dx<<R
+ double chord = dx*TMath::Sqrt(1+dy2dx*dy2dx); // distance from old position to new one
+ double rot = 2*TMath::ASin(0.5*chord*crv); // angular difference seen from the circle center
+ fP1 += rot/crv*fP3;
+ fP2 = TMath::Sin(rot + TMath::ASin(fP2));
+ }
//f = F - 1
fC32 += b32;
fC42 += b42;
+ CheckCovariance();
+
return kTRUE;
}
return kFALSE;
}
+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;
+}
+
void AliExternalTrackParam::Propagate(Double_t len, Double_t x[3],
Double_t p[3], Double_t bz) const {
Double_t f=GetSnp();
if (TMath::Abs(f) >= kAlmost1) return kVeryBig;
- Double_t r=TMath::Sqrt(1.- f*f);
+ Double_t r=TMath::Sqrt((1.-f)*(1.+f));
Double_t a=f/r, b=GetTgl()/r;
Double_t s2=333.*333.; //something reasonably big (cm^2)
for (Int_t j = 0; j < 3; j++) chi2 += res[i]*res[j]*v(i,j);
return chi2;
+}
+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;
+ }
+ 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;
}
Bool_t AliExternalTrackParam::
Double_t f=GetSnp();
if (TMath::Abs(f) >= kAlmost1) return kFALSE;
- Double_t r=TMath::Sqrt(1.- f*f);
+ Double_t r=TMath::Sqrt((1.-f)*(1.+f));
Double_t a=f/r, b=GetTgl()/r;
Double_t s2=333.*333.; //something reasonably big (cm^2)
fC44-=k40*c04+k41*c14;
+ CheckCovariance();
+
return kTRUE;
}
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));
+ Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt((1.-snp)*(1.+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);
+ Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt((1.-snp)*(1.+snp)));
+ sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt((1.-sn)*(1.+sn));
if (TMath::Abs(tgfv)>0.) cs = sn/tgfv;
else cs=1.;
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;
+
+ //Estimate the impact parameter neglecting the track curvature
+ Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt((1.-snp)*(1.+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)*(1.+snp)));
+ sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt((1.-sn)*(1.+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 {
//----------------------------------------------------------------
//----------------------------------------------------------------
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 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;
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
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 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;
+ const Double_t kOvSqSix=TMath::Sqrt(1./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) > 0.03) {
+ 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.-tet*kOvSqSix)*(1.+tet*kOvSqSix); // 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;
+ if (TMath::Abs(fP[4])<=kAlmost0) return kFALSE;
+ // Do not propagate tracks outside the ALICE detector
+ if (TMath::Abs(dx)>1e5 ||
+ TMath::Abs(GetY())>1e5 ||
+ TMath::Abs(GetZ())>1e5) {
+ AliWarning(Form("Anomalous track, target X:%f",xk));
+ Print();
+ return kFALSE;
+ }
+
+ Double_t crv=GetC(b[2]);
+ if (TMath::Abs(b[2]) < kAlmost0Field) crv=0.;
+
+ Double_t x2r = crv*dx;
+ Double_t f1=fP[2], f2=f1 + x2r;
+ 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)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+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;
+
+ CheckCovariance();
+
+ // Appoximate step length
+ double dy2dx = (f1+f2)/(r1+r2);
+ Double_t step = (TMath::Abs(x2r)<0.05) ? dx*TMath::Abs(r2 + f2*dy2dx) // chord
+ : 2.*TMath::ASin(0.5*dx*TMath::Sqrt(1.+dy2dx*dy2dx)*crv)/crv; // arc
+ 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;
+ }
+
+void AliExternalTrackParam::CheckCovariance() {
+
+ // This function forces the diagonal elements of the covariance matrix to be positive.
+ // In case the diagonal element is bigger than the maximal allowed value, it is set to
+ // the limit and the off-diagonal elements that correspond to it are set to zero.
+
+ fC[0] = TMath::Abs(fC[0]);
+ if (fC[0]>kC0max) {
+ fC[0] = kC0max;
+ fC[1] = 0;
+ fC[3] = 0;
+ fC[6] = 0;
+ fC[10] = 0;
+ }
+ fC[2] = TMath::Abs(fC[2]);
+ if (fC[2]>kC2max) {
+ fC[2] = kC2max;
+ fC[1] = 0;
+ fC[4] = 0;
+ fC[7] = 0;
+ fC[11] = 0;
+ }
+ fC[5] = TMath::Abs(fC[5]);
+ if (fC[5]>kC5max) {
+ fC[5] = kC5max;
+ fC[3] = 0;
+ fC[4] = 0;
+ fC[8] = 0;
+ fC[12] = 0;
+ }
+ fC[9] = TMath::Abs(fC[9]);
+ if (fC[9]>kC9max) {
+ fC[9] = kC9max;
+ fC[6] = 0;
+ fC[7] = 0;
+ fC[8] = 0;
+ fC[13] = 0;
+ }
+ fC[14] = TMath::Abs(fC[14]);
+ if (fC[14]>kC14max) {
+ fC[14] = kC14max;
+ fC[10] = 0;
+ fC[11] = 0;
+ fC[12] = 0;
+ fC[13] = 0;
+ }
+
+ // The part below is used for tests and normally is commented out
+// TMatrixDSym m(5);
+// TVectorD eig(5);
+
+// m(0,0)=fC[0];
+// m(1,0)=fC[1]; m(1,1)=fC[2];
+// m(2,0)=fC[3]; m(2,1)=fC[4]; m(2,2)=fC[5];
+// m(3,0)=fC[6]; m(3,1)=fC[7]; m(3,2)=fC[8]; m(3,3)=fC[9];
+// m(4,0)=fC[10]; m(4,1)=fC[11]; m(4,2)=fC[12]; m(4,3)=fC[13]; m(4,4)=fC[14];
+
+// m(0,1)=m(1,0);
+// m(0,2)=m(2,0); m(1,2)=m(2,1);
+// m(0,3)=m(3,0); m(1,3)=m(3,1); m(2,3)=m(3,2);
+// m(0,4)=m(4,0); m(1,4)=m(4,1); m(2,4)=m(4,2); m(3,4)=m(4,3);
+// m.EigenVectors(eig);
+
+// // assert(eig(0)>=0 && eig(1)>=0 && eig(2)>=0 && eig(3)>=0 && eig(4)>=0);
+// if (!(eig(0)>=0 && eig(1)>=0 && eig(2)>=0 && eig(3)>=0 && eig(4)>=0)) {
+// AliWarning("Negative eigenvalues of the covariance matrix!");
+// this->Print();
+// eig.Print();
+// }
+}
git://git.uio.no / u / mrichter / AliRoot.git / blobdiff