/************************************************************************** * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. * * * * Author: The ALICE Off-line Project. * * Contributors are mentioned in the code where appropriate. * * * * Permission to use, copy, modify and distribute this software and its * * documentation strictly for non-commercial purposes is hereby granted * * without fee, provided that the above copyright notice appears in all * * copies and that both the copyright notice and this permission notice * * appear in the supporting documentation. The authors make no claims * * about the suitability of this software for any purpose. It is * * provided "as is" without express or implied warranty. * **************************************************************************/ /* $Id$ */ /////////////////////////////////////////////////////////////////////////////// // // // 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 "AliExternalTrackParam.h" #include "AliESDVertex.h" #include "AliLog.h" ClassImp(AliExternalTrackParam) //_____________________________________________________________________________ AliExternalTrackParam::AliExternalTrackParam() : TObject(), fX(0), fAlpha(0) { // // default constructor // 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): TObject(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(Double_t x, Double_t alpha, const Double_t param[5], const Double_t covar[15]) : TObject(), fX(x), fAlpha(alpha) { // // create external track parameters from given arguments // for (Int_t i = 0; i < 5; i++) fP[i] = param[i]; for (Int_t i = 0; i < 15; i++) fC[i] = covar[i]; } //_____________________________________________________________________________ void AliExternalTrackParam::Set(Double_t x, Double_t alpha, const Double_t p[5], const Double_t cov[15]) { // // Sets the parameters // 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]; } //_____________________________________________________________________________ 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; } 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; Double_t d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt(1.- fP[2]*fP[2]); return -d; } 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) // "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****************** 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; 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; } //Energy losses************************ if (x0!=0. && beta2<1) { d*=x0; Double_t dE=Bethe(beta2)*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); // Approximate energy loss fluctuation (M.Ivanov) const Double_t cnst=0.07; // To be tuned. Double_t sigmadE=cnst*TMath::Sqrt(TMath::Abs(dE)); fC44+=((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4)); } return kTRUE; } Double_t ApproximateBetheBloch(Double_t beta2) { //------------------------------------------------------------------ // 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) //------------------------------------------------------------------ if (beta2/(1-beta2)>3.5*3.5) return 0.153e-3/beta2*(log(3.5*5940)+0.5*log(beta2/(1-beta2)) - beta2); return 0.153e-3/beta2*(log(5940*beta2/(1-beta2)) - beta2); } 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) return kFALSE; fAlpha = alpha; fX = x*ca + fP0*sa; fP0= -x*sa + fP0*ca; fP2= tmp; if (TMath::Abs(cf)= 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; } 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 (TMath::Abs(Get1Pt()) < kAlmost0 || TMath::Abs(bz) < kAlmost0Field ){ //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); //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]; 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; } 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; 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; } 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 { //-------------------------------------------------------------------- // Calculate position of a point on a track and some derivatives //-------------------------------------------------------------------- Double_t phase=h[4]*t+h[2]; Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase); r[0] = h[5] + (sn - h[6])/h[4]; r[1] = h[0] - (cs - h[7])/h[4]; r[2] = h[1] + h[3]*t; g[0] = cs; g[1]=sn; g[2]=h[3]; gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.; } Double_t 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; //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); 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) AliWarning(" stopped at not a stationary point !"); Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det); if (lmb < 0.) AliWarning(" 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 (dd512) { AliWarning(" overshoot !"); break; } } dm=dd; t1+=dt1; t2+=dt2; } if (max<=0) AliWarning(" 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 AliESDVertex *vtx, Double_t b, Double_t maxd){ // // Try to relate this track to the 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->GetXv()*cs + vtx->GetYv()*sn; Double_t yv=-vtx->GetXv()*sn + vtx->GetYv()*cs; 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=0.299792458e-3*b*GetParameter()[4]; 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); x = xv*cs + yv*sn; yv=-xv*sn + yv*cs; xv=x; if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE; return kTRUE; } Bool_t Local2GlobalMomentum(Double_t p[3],Double_t alpha) { //---------------------------------------------------------------- // This function performs local->global transformation of the // track momentum. // When called, the arguments are: // p[0] = 1/pt of the track; // p[1] = sine of local azim. angle of the track momentum; // p[2] = tangent of the track momentum dip angle; // alpha - rotation angle. // The result is returned as: // p[0] = px // p[1] = py // p[2] = pz // Results for (nearly) straight tracks are meaningless ! //---------------------------------------------------------------- if (TMath::Abs(p[0])<=kAlmost0) return kFALSE; if (TMath::Abs(p[1])> kAlmost1) return kFALSE; Double_t pt=1./TMath::Abs(p[0]); Double_t cs=TMath::Cos(alpha), sn=TMath::Sin(alpha); Double_t r=TMath::Sqrt(1 - p[1]*p[1]); p[0]=pt*(r*cs - p[1]*sn); p[1]=pt*(p[1]*cs + r*sn); p[2]=pt*p[2]; return kTRUE; } Bool_t Local2GlobalPosition(Double_t r[3],Double_t alpha) { //---------------------------------------------------------------- // This function performs local->global transformation of the // track position. // When called, the arguments are: // r[0] = local x // r[1] = local y // r[2] = local z // alpha - rotation angle. // The result is returned as: // r[0] = global x // r[1] = global y // r[2] = global z //---------------------------------------------------------------- Double_t cs=TMath::Cos(alpha), sn=TMath::Sin(alpha), x=r[0]; r[0]=x*cs - r[1]*sn; r[1]=x*sn + r[1]*cs; 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) 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); } 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]; 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*f1), r2=TMath::Sqrt(1.- f2*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*fP[4]*b*kB2C; 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); 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*f1), r2=TMath::Sqrt(1.- f2*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]; return Local2GlobalPosition(r,fAlpha); } //_____________________________________________________________________________ void AliExternalTrackParam::Print(Option_t* /*option*/) const { // print the parameters and the covariance matrix printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha); printf(" parameters: %12g %12g %12g %12g %12g\n", 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", fC[6], fC[7], fC[8], fC[9]); printf(" %12g %12g %12g %12g %12g\n", 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; }