X-Git-Url: http://git.uio.no/git/?a=blobdiff_plain;f=STEER%2FAliExternalTrackParam.cxx;h=f0f7b484c467ef8d201429b0984c56bb44b4575f;hb=40cfa14d48c5cedd0a34b12c1c1854301534acf5;hp=e60bd30ef4cb64ce88c97c4db8682bac7b2dd264;hpb=9a53dcc68889060334e60dfb58b945342bd53a21;p=u%2Fmrichter%2FAliRoot.git diff --git a/STEER/AliExternalTrackParam.cxx b/STEER/AliExternalTrackParam.cxx index e60bd30ef4c..f0f7b484c46 100644 --- a/STEER/AliExternalTrackParam.cxx +++ b/STEER/AliExternalTrackParam.cxx @@ -25,10 +25,16 @@ // are implemented. // Origin: I.Belikov, CERN, Jouri.Belikov@cern.ch // /////////////////////////////////////////////////////////////////////////////// +#include + +#include #include +#include +#include +#include + #include "AliExternalTrackParam.h" -#include "AliESDVertex.h" -#include "TPolyMarker3D.h" +#include "AliVVertex.h" #include "AliLog.h" ClassImp(AliExternalTrackParam) @@ -37,7 +43,7 @@ Double32_t AliExternalTrackParam::fgMostProbablePt=kMostProbablePt; //_____________________________________________________________________________ AliExternalTrackParam::AliExternalTrackParam() : - AliVParticle(), + AliVTrack(), fX(0), fAlpha(0) { @@ -50,7 +56,7 @@ AliExternalTrackParam::AliExternalTrackParam() : //_____________________________________________________________________________ AliExternalTrackParam::AliExternalTrackParam(const AliExternalTrackParam &track): - AliVParticle(track), + AliVTrack(track), fX(track.fX), fAlpha(track.fAlpha) { @@ -59,6 +65,7 @@ AliExternalTrackParam::AliExternalTrackParam(const AliExternalTrackParam &track) // 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(); } //_____________________________________________________________________________ @@ -69,12 +76,13 @@ AliExternalTrackParam& AliExternalTrackParam::operator=(const AliExternalTrackPa // if (this!=&trkPar) { - AliVParticle::operator=(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]; + CheckCovariance(); } return *this; @@ -84,7 +92,7 @@ AliExternalTrackParam& AliExternalTrackParam::operator=(const AliExternalTrackPa AliExternalTrackParam::AliExternalTrackParam(Double_t x, Double_t alpha, const Double_t param[5], const Double_t covar[15]) : - AliVParticle(), + AliVTrack(), fX(x), fAlpha(alpha) { @@ -93,18 +101,148 @@ AliExternalTrackParam::AliExternalTrackParam(Double_t x, Double_t alpha, // 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(); } //_____________________________________________________________________________ -void AliExternalTrackParam::Set(Double_t x, Double_t alpha, - const Double_t p[5], const Double_t cov[15]) { +AliExternalTrackParam::AliExternalTrackParam(const AliVTrack *vTrack) : + AliVTrack(), + fX(0.), + fAlpha(0.) +{ // - // Sets the parameters + // Constructor from virtual track, + // This is not a copy contructor ! // - fX=x; - fAlpha=alpha; - for (Int_t i = 0; i < 5; i++) fP[i] = p[i]; - for (Int_t i = 0; i < 15; i++) fC[i] = cov[i]; + + 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); +} + +//_____________________________________________________________________________ +AliExternalTrackParam::AliExternalTrackParam(Double_t xyz[3],Double_t pxpypz[3], + Double_t cv[21],Short_t sign) : + AliVTrack(), + fX(0.), + fAlpha(0.) +{ + // + // constructor from the global parameters + // + + Set(xyz,pxpypz,cv,sign); +} + +//_____________________________________________________________________________ +void AliExternalTrackParam::Set(Double_t xyz[3],Double_t pxpypz[3], + Double_t cv[21],Short_t sign) +{ + // + // create external track parameters from the global parameters + // x,y,z,px,py,pz and their 6x6 covariance matrix + // A.Dainese 10.10.08 + + // 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)); + + CheckCovariance(); + + return; } //_____________________________________________________________________________ @@ -128,6 +266,7 @@ void AliExternalTrackParam::AddCovariance(const Double_t c[15]) { 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(); } @@ -164,8 +303,8 @@ Double_t AliExternalTrackParam::GetD(Double_t x,Double_t y,Double_t b) const { 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)); } @@ -177,7 +316,7 @@ GetDZ(Double_t x, Double_t y, Double_t z, Double_t b, Float_t dz[2]) const { // 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; @@ -195,7 +334,7 @@ GetDZ(Double_t x, Double_t y, Double_t z, Double_t b, Float_t dz[2]) const { 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; } @@ -210,7 +349,7 @@ Double_t AliExternalTrackParam::GetLinearD(Double_t xv,Double_t yv) const { 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; } @@ -235,7 +374,7 @@ Bool_t AliExternalTrackParam::CorrectForMeanMaterial //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; } @@ -244,33 +383,47 @@ Bool_t AliExternalTrackParam::CorrectForMeanMaterial Double_t p2=p*p; Double_t beta2=p2/(p2 + mass*mass); - //Multiple scattering****************** + //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); - if(theta2>TMath::Pi()*TMath::Pi()) return kFALSE; //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33; - fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3); - fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3); - fC43 += theta2*fP3*fP4*(1. + fP3*fP3); - fC44 += theta2*fP3*fP4*fP3*fP4; + 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; } - //Energy losses************************ + //Calculating the energy loss corrections************************ + Double_t cP4=1.; if ((xTimesRho != 0.) && (beta2 < 1.)) { - Double_t dE=Bethe(beta2)*xTimesRho; + 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! - fP4*=(1.- e/p2*dE); - if (TMath::Abs(fP4)>100.) return kFALSE; // Do not track below 10 MeV/c + 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)); - fC44+=((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4)); + cC44 += ((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4)); } + //Applying the corrections***************************** + fC22 += cC22; + fC33 += cC33; + fC43 += cC43; + fC44 += cC44; + fP4 *= cP4; + + CheckCovariance(); + return kTRUE; } @@ -298,49 +451,147 @@ Bool_t AliExternalTrackParam::CorrectForMaterial 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)); + d*=TMath::Sqrt((1.+ fP3*fP3)/((1.-fP2)*(1.+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); - if(theta2>TMath::Pi()*TMath::Pi()) return kFALSE; //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33; - fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3); - fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3); - fC43 += theta2*fP3*fP4*(1. + fP3*fP3); - fC44 += theta2*fP3*fP4*fP3*fP4; + 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; } //Energy losses************************ + Double_t cP4=1.; if (x0!=0. && beta2<1) { d*=x0; - Double_t dE=Bethe(beta2)*d; + 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! - fP4*=(1.- e/p2*dE); + 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)); - fC44+=((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4)); + cC44 += ((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4)); } + fC22 += cC22; + fC33 += cC33; + fC43 += cC43; + fC44 += cC44; + fP4 *= cP4; + + CheckCovariance(); + return kTRUE; } -Double_t ApproximateBetheBloch(Double_t beta2) { +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 with - // the density effect taken into account at beta*gamma > 3.5 - // (the approximation is reasonable only for solid materials) + // 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)] //------------------------------------------------------------------ - if (beta2 >= 1) return kVeryBig; - if (beta2/(1-beta2)>3.5*3.5) - return 0.153e-3/beta2*(log(3.5*5940)+0.5*log(beta2/(1-beta2)) - beta2); + 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 0.153e-3/beta2*(log(5940*beta2/(1-beta2)) - beta2); + return BetheBlochGeant(bg,rho,x0,x1,mI,mZA); } Bool_t AliExternalTrackParam::Rotate(Double_t alpha) { @@ -370,10 +621,14 @@ Bool_t AliExternalTrackParam::Rotate(Double_t alpha) { 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) return kFALSE; + if (TMath::Abs(tmp) >= kAlmost1) { + if (TMath::Abs(tmp) > 1.+ Double_t(FLT_EPSILON)) + AliWarning(Form("Rotation failed ! %.10e",tmp)); + return kFALSE; + } fAlpha = alpha; fX = x*ca + fP0*sa; @@ -397,6 +652,8 @@ Bool_t AliExternalTrackParam::Rotate(Double_t alpha) { fC40 *= ca; fC42 *= rr; + CheckCovariance(); + return kTRUE; } @@ -422,7 +679,7 @@ Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) { &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)); fX=xk; fP0 += dx*(f1+f2)/(r1+r2); @@ -469,9 +726,65 @@ Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) { fC32 += b32; fC42 += b42; + CheckCovariance(); + 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::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 { //+++++++++++++++++++++++++++++++++++++++++ @@ -484,7 +797,7 @@ Double_t p[3], Double_t bz) const { //+++++++++++++++++++++++++++++++++++++++++ GetXYZ(x); - if (OneOverPt() < kAlmost0 || TMath::Abs(bz) < kAlmost0Field ){ //straight-line tracks + 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; @@ -579,7 +892,7 @@ GetPredictedChi2(Double_t p[3],Double_t covyz[3],Double_t covxyz[3]) 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) @@ -601,8 +914,60 @@ GetPredictedChi2(Double_t p[3],Double_t covyz[3],Double_t covxyz[3]) const { 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:: @@ -620,7 +985,7 @@ PropagateTo(Double_t p[3],Double_t covyz[3],Double_t covxyz[3],Double_t bz) { 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) @@ -759,6 +1124,8 @@ Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) { fC44-=k40*c04+k41*c14; + CheckCovariance(); + return kTRUE; } @@ -792,8 +1159,12 @@ static void Evaluate(const Double_t *h, Double_t t, Double_t phase=h[4]*t+h[2]; Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase); - r[0] = h[5] + (sn - h[6])/h[4]; - r[1] = h[0] - (cs - h[7])/h[4]; + r[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]; @@ -813,8 +1184,6 @@ Double_t b, Double_t &xthis, Double_t &xp) const { Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2(); Double_t dx2=dy2; - //dx2=dy2=dz2=1.; - 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); @@ -923,7 +1292,7 @@ PropagateToDCA(AliExternalTrackParam *p, Double_t b) { } -Bool_t AliExternalTrackParam::PropagateToDCA(const AliESDVertex *vtx, +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", @@ -939,20 +1308,20 @@ Double_t b, Double_t maxd, Double_t dz[2], Double_t covar[3]) { 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->GetXv()*cs + vtx->GetYv()*sn; - Double_t yv=-vtx->GetXv()*sn + vtx->GetYv()*cs, zv=vtx->GetZv(); + 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)); + 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=kB2C*b*GetParameter()[4]; + 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.; @@ -966,7 +1335,7 @@ Double_t b, Double_t maxd, Double_t dz[2], Double_t covar[3]) { dz[1] = GetParameter()[1] - zv; if (covar==0) return kTRUE; - Double_t cov[6]; vtx->GetCovMatrix(cov); + Double_t cov[6]; vtx->GetCovarianceMatrix(cov); //***** Improvements by A.Dainese alpha=GetAlpha(); sn=TMath::Sin(alpha); cs=TMath::Cos(alpha); @@ -979,6 +1348,63 @@ Double_t b, Double_t maxd, Double_t dz[2], Double_t covar[3]) { 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 { //---------------------------------------------------------------- @@ -987,7 +1413,7 @@ 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; @@ -1027,18 +1453,6 @@ Double_t AliExternalTrackParam::Py() const { 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 @@ -1061,17 +1475,6 @@ Double_t AliExternalTrackParam::Yv() const { 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 @@ -1219,7 +1622,7 @@ AliExternalTrackParam::GetYAt(Double_t x, Double_t b, Double_t &y) const { if (TMath::Abs(f1) >= kAlmost1) return kFALSE; if (TMath::Abs(f2) >= kAlmost1) return kFALSE; - 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)); y = fP[0] + dx*(f1+f2)/(r1+r2); return kTRUE; } @@ -1234,12 +1637,12 @@ AliExternalTrackParam::GetZAt(Double_t x, Double_t b, Double_t &z) const { Double_t dx=x-fX; if(TMath::Abs(dx)<=kAlmost0) {z=fP[1]; return kTRUE;} - Double_t f1=fP[2], f2=f1 + dx*fP[4]*b*kB2C; + 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*f1), r2=sqrt(1.- f2*f2); + 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; } @@ -1258,10 +1661,11 @@ AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const { if (TMath::Abs(f1) >= kAlmost1) return kFALSE; if (TMath::Abs(f2) >= kAlmost1) return kFALSE; - 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)); r[0] = x; r[1] = fP[0] + dx*(f1+f2)/(r1+r2); - r[2] = fP[1] + dx*(f1+f2)/(f1*r2 + f2*r1)*fP[3]; + r[2] = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3];//Thanks to Andrea & Peter + return Local2GlobalPosition(r,fAlpha); } @@ -1366,3 +1770,376 @@ void AliExternalTrackParam::FillPolymarker(TPolyMarker3D *pol, Float_t magF, Flo 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; + 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) > 0.15) { + 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.-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; + + 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)*(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_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" + // + 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(); +// } +}