// are implemented.
// Origin: I.Belikov, CERN, Jouri.Belikov@cern.ch //
///////////////////////////////////////////////////////////////////////////////
+#include <TMatrixDSym.h>
#include "AliExternalTrackParam.h"
-#include "AliKalmanTrack.h"
-#include "AliTracker.h"
-#include "AliStrLine.h"
#include "AliESDVertex.h"
-
+#include "TPolyMarker3D.h"
+#include "AliLog.h"
ClassImp(AliExternalTrackParam)
+Double32_t AliExternalTrackParam::fgMostProbablePt=kMostProbablePt;
+
//_____________________________________________________________________________
AliExternalTrackParam::AliExternalTrackParam() :
+ AliVParticle(),
fX(0),
fAlpha(0)
{
for (Int_t i = 0; i < 15; i++) fC[i] = 0;
}
+//_____________________________________________________________________________
+AliExternalTrackParam::AliExternalTrackParam(const AliExternalTrackParam &track):
+ AliVParticle(track),
+ fX(track.fX),
+ fAlpha(track.fAlpha)
+{
+ //
+ // copy constructor
+ //
+ for (Int_t i = 0; i < 5; i++) fP[i] = track.fP[i];
+ for (Int_t i = 0; i < 15; i++) fC[i] = track.fC[i];
+}
+
+//_____________________________________________________________________________
+AliExternalTrackParam& AliExternalTrackParam::operator=(const AliExternalTrackParam &trkPar)
+{
+ //
+ // assignment operator
+ //
+
+ if (this!=&trkPar) {
+ AliVParticle::operator=(trkPar);
+ fX = trkPar.fX;
+ fAlpha = trkPar.fAlpha;
+
+ for (Int_t i = 0; i < 5; i++) fP[i] = trkPar.fP[i];
+ for (Int_t i = 0; i < 15; i++) fC[i] = trkPar.fC[i];
+ }
+
+ return *this;
+}
+
//_____________________________________________________________________________
AliExternalTrackParam::AliExternalTrackParam(Double_t x, Double_t alpha,
const Double_t param[5],
const Double_t covar[15]) :
+ AliVParticle(),
fX(x),
fAlpha(alpha)
{
}
//_____________________________________________________________________________
-AliExternalTrackParam::AliExternalTrackParam(const AliKalmanTrack& track) :
- fAlpha(track.GetAlpha())
-{
+void AliExternalTrackParam::Set(Double_t x, Double_t alpha,
+ const Double_t p[5], const Double_t cov[15]) {
//
+ // Sets the parameters
//
- track.GetExternalParameters(fX,fP);
- track.GetExternalCovariance(fC);
+ 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::Set(const AliKalmanTrack& track) {
+void AliExternalTrackParam::Reset() {
//
+ // Resets all the parameters to 0
//
- fAlpha=track.GetAlpha();
- track.GetExternalParameters(fX,fP);
- track.GetExternalCovariance(fC);
-}
-
-//_____________________________________________________________________________
-void AliExternalTrackParam::Reset() {
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;
// This function returns the track momentum
// Results for (nearly) straight tracks are meaningless !
//---------------------------------------------------------------------
- if (TMath::Abs(fP[4])<=0) return 0;
+ 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 {
//------------------------------------------------------------------
// with respect to a point with global coordinates (x,y)
// in the magnetic field "b" (kG)
//------------------------------------------------------------------
- Double_t rp4=kB2C*b*fP[4];
+ if (TMath::Abs(b) < kAlmost0Field) return GetLinearD(x,y);
+ Double_t rp4=GetC(b);
Double_t xt=fX, yt=fP[0];
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);
- if (rp4<0) a=-a;
- return a/(1 + TMath::Sqrt(sn*sn + cs*cs));
+ 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 d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt(1.- fP[2]*fP[2]);
- return d;
+ return -d;
}
-Bool_t AliExternalTrackParam::
-CorrectForMaterial(Double_t d, Double_t x0, Double_t mass) {
+Bool_t AliExternalTrackParam::CorrectForMeanMaterial
+(Double_t xOverX0, Double_t xTimesRho, Double_t mass, Bool_t anglecorr,
+ Double_t (*Bethe)(Double_t)) {
//------------------------------------------------------------------
+ // This function corrects the track parameters for the crossed material.
+ // "xOverX0" - X/X0, the thickness in units of the radiation length.
+ // "xTimesRho" - is the product length*density (g/cm^2).
+ // "mass" - the mass of this particle (GeV/c^2).
+ //------------------------------------------------------------------
+ Double_t &fP2=fP[2];
+ Double_t &fP3=fP[3];
+ Double_t &fP4=fP[4];
+
+ Double_t &fC22=fC[5];
+ Double_t &fC33=fC[9];
+ Double_t &fC43=fC[13];
+ Double_t &fC44=fC[14];
+
+ //Apply angle correction, if requested
+ if(anglecorr) {
+ Double_t angle=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2));
+ xOverX0 *=angle;
+ xTimesRho *=angle;
+ }
+
+ Double_t p=GetP();
+ Double_t p2=p*p;
+ Double_t beta2=p2/(p2 + mass*mass);
+
+ //Multiple scattering******************
+ 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;
+ 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 ((xTimesRho != 0.) && (beta2 < 1.)) {
+ Double_t dE=Bethe(beta2)*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);
+
+ // 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));
+
+ }
+
+ return kTRUE;
+}
+
+
+Bool_t AliExternalTrackParam::CorrectForMaterial
+(Double_t d, Double_t x0, Double_t mass, Double_t (*Bethe)(Double_t)) {
+ //------------------------------------------------------------------
+ // Deprecated function !
+ // Better use CorrectForMeanMaterial instead of it.
+ //
// This function corrects the track parameters for the crossed material
// "d" - the thickness (fraction of the radiation length)
// "x0" - the radiation length (g/cm^2)
Double_t &fC43=fC[13];
Double_t &fC44=fC[14];
- Double_t p2=(1.+ fP3*fP3)/(fP4*fP4);
+ 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));
}
//Energy losses************************
- if (x0!=0.) {
+ if (x0!=0. && beta2<1) {
d*=x0;
- Double_t dE=0.153e-3/beta2*(log(5940*beta2/(1-beta2)) - beta2)*d;
- if (beta2/(1-beta2)>3.5*3.5)
- dE=0.153e-3/beta2*(log(3.5*5940)+0.5*log(beta2/(1-beta2)) - beta2)*d;
-
- fP4*=(1.- TMath::Sqrt(p2 + mass*mass)/p2*dE);
+ 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 knst=0.07; // To be tuned.
+ Double_t sigmadE=knst*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) 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);
+
+ 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 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= sf*ca - cf*sa;
+ fP2= tmp;
+
+ if (TMath::Abs(cf)<kAlmost0) {
+ AliError(Form("Too small cosine value %f",cf));
+ cf = kAlmost0;
+ }
Double_t rr=(ca+sf/cf*sa);
// Propagate this track to the plane X=xk (cm) in the field "b" (kG)
//----------------------------------------------------------------
Double_t dx=xk-fX;
- if (TMath::Abs(dx)<=0) return kTRUE;
+ if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
+
+ Double_t crv=GetC(b);
+ if (TMath::Abs(b) < kAlmost0Field) crv=0.;
- Double_t crv=kB2C*b*fP[4];
Double_t f1=fP[2], f2=f1 + crv*dx;
if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
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 (OneOverPt() < 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 {
//----------------------------------------------------------------
return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det;
}
+Double_t AliExternalTrackParam::
+GetPredictedChi2(Double_t p[3],Double_t covyz[3],Double_t covxyz[3]) const {
+ //----------------------------------------------------------------
+ // Estimate the chi2 of the 3D space point "p" and
+ // the full covariance matrix "covyz" and "covxyz"
+ //
+ // Cov(x,x) ... : covxyz[0]
+ // Cov(y,x) ... : covxyz[1] covyz[0]
+ // Cov(z,x) ... : covxyz[2] covyz[1] covyz[2]
+ //----------------------------------------------------------------
+
+ Double_t res[3] = {
+ GetX() - p[0],
+ GetY() - p[1],
+ GetZ() - p[2]
+ };
+
+ Double_t f=GetSnp();
+ if (TMath::Abs(f) >= kAlmost1) return kVeryBig;
+ Double_t r=TMath::Sqrt(1.- f*f);
+ Double_t a=f/r, b=GetTgl()/r;
+
+ Double_t s2=333.*333.; //something reasonably big (cm^2)
+
+ TMatrixDSym v(3);
+ v(0,0)= s2; v(0,1)= a*s2; v(0,2)= b*s2;;
+ v(1,0)=a*s2; v(1,1)=a*a*s2 + GetSigmaY2(); v(1,2)=a*b*s2 + GetSigmaZY();
+ v(2,0)=b*s2; v(2,1)=a*b*s2 + GetSigmaZY(); v(2,2)=b*b*s2 + GetSigmaZ2();
+
+ v(0,0)+=covxyz[0]; v(0,1)+=covxyz[1]; v(0,2)+=covxyz[2];
+ v(1,0)+=covxyz[1]; v(1,1)+=covyz[0]; v(1,2)+=covyz[1];
+ v(2,0)+=covxyz[2]; v(2,1)+=covyz[1]; v(2,2)+=covyz[2];
+
+ v.Invert();
+ if (!v.IsValid()) return kVeryBig;
+
+ Double_t chi2=0.;
+ for (Int_t i = 0; i < 3; i++)
+ for (Int_t j = 0; j < 3; j++) chi2 += res[i]*res[j]*v(i,j);
+
+ return chi2;
+
+
+}
+
+Bool_t AliExternalTrackParam::
+PropagateTo(Double_t p[3],Double_t covyz[3],Double_t covxyz[3],Double_t bz) {
+ //----------------------------------------------------------------
+ // Propagate this track to the plane
+ // the 3D space point "p" (with the covariance matrix "covyz" and "covxyz")
+ // belongs to.
+ // The magnetic field is "bz" (kG)
+ //
+ // The track curvature and the change of the covariance matrix
+ // of the track parameters are negleted !
+ // (So the "step" should be small compared with 1/curvature)
+ //----------------------------------------------------------------
+
+ Double_t f=GetSnp();
+ if (TMath::Abs(f) >= kAlmost1) return kFALSE;
+ Double_t r=TMath::Sqrt(1.- f*f);
+ Double_t a=f/r, b=GetTgl()/r;
+
+ Double_t s2=333.*333.; //something reasonably big (cm^2)
+
+ TMatrixDSym tV(3);
+ tV(0,0)= s2; tV(0,1)= a*s2; tV(0,2)= b*s2;
+ tV(1,0)=a*s2; tV(1,1)=a*a*s2; tV(1,2)=a*b*s2;
+ tV(2,0)=b*s2; tV(2,1)=a*b*s2; tV(2,2)=b*b*s2;
+
+ TMatrixDSym pV(3);
+ pV(0,0)=covxyz[0]; pV(0,1)=covxyz[1]; pV(0,2)=covxyz[2];
+ pV(1,0)=covxyz[1]; pV(1,1)=covyz[0]; pV(1,2)=covyz[1];
+ pV(2,0)=covxyz[2]; pV(2,1)=covyz[1]; pV(2,2)=covyz[2];
+
+ TMatrixDSym tpV(tV);
+ tpV+=pV;
+ tpV.Invert();
+ if (!tpV.IsValid()) return kFALSE;
+
+ TMatrixDSym pW(3),tW(3);
+ for (Int_t i=0; i<3; i++)
+ for (Int_t j=0; j<3; j++) {
+ pW(i,j)=tW(i,j)=0.;
+ for (Int_t k=0; k<3; k++) {
+ pW(i,j) += tV(i,k)*tpV(k,j);
+ tW(i,j) += pV(i,k)*tpV(k,j);
+ }
+ }
+
+ Double_t t[3] = {GetX(), GetY(), GetZ()};
+
+ Double_t x=0.;
+ for (Int_t i=0; i<3; i++) x += (tW(0,i)*t[i] + pW(0,i)*p[i]);
+ Double_t crv=GetC(bz);
+ if (TMath::Abs(b) < kAlmost0Field) crv=0.;
+ f += crv*(x-fX);
+ if (TMath::Abs(f) >= kAlmost1) return kFALSE;
+ fX=x;
+
+ fP[0]=0.;
+ for (Int_t i=0; i<3; i++) fP[0] += (tW(1,i)*t[i] + pW(1,i)*p[i]);
+ fP[1]=0.;
+ for (Int_t i=0; i<3; i++) fP[1] += (tW(2,i)*t[i] + pW(2,i)*p[i]);
+
+ return kTRUE;
+}
+
+Double_t *AliExternalTrackParam::GetResiduals(
+Double_t *p,Double_t *cov,Bool_t updated) const {
+ //------------------------------------------------------------------
+ // Returns the track residuals with the space point "p" having
+ // the covariance matrix "cov".
+ // If "updated" is kTRUE, the track parameters expected to be updated,
+ // otherwise they must be predicted.
+ //------------------------------------------------------------------
+ static Double_t res[2];
+
+ Double_t r00=cov[0], r01=cov[1], r11=cov[2];
+ if (updated) {
+ r00-=fC[0]; r01-=fC[1]; r11-=fC[2];
+ } else {
+ r00+=fC[0]; r01+=fC[1]; r11+=fC[2];
+ }
+ Double_t det=r00*r11 - r01*r01;
+
+ if (TMath::Abs(det) < kAlmost0) return 0;
+
+ Double_t tmp=r00; r00=r11/det; r11=tmp/det;
+
+ if (r00 < 0.) return 0;
+ if (r11 < 0.) return 0;
+
+ Double_t dy = fP[0] - p[0];
+ Double_t dz = fP[1] - p[1];
+
+ res[0]=dy*TMath::Sqrt(r00);
+ res[1]=dz*TMath::Sqrt(r11);
+
+ return res;
+}
+
Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) {
//------------------------------------------------------------------
// Update the track parameters with the space point "p" having
//--------------------------------------------------------------------
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[4]=fP[4];
+ 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]=hlx[4]*kB2C*b; // C
+ hlx[4]=GetC(b); // C
}
}
-
-
-Bool_t AliExternalTrackParam::PropagateToDCA(const AliESDVertex *vtx, Double_t b, Double_t maxd){
+Bool_t AliExternalTrackParam::PropagateToDCA(const AliESDVertex *vtx,
+Double_t b, Double_t maxd, Double_t dz[2], Double_t covar[3]) {
//
- // Try to relate this track to the vertex "vtx",
+ // Propagate this track to the DCA to vertex "vtx",
// if the (rough) transverse impact parameter is not bigger then "maxd".
// Magnetic field is "b" (kG).
//
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;
+ Double_t yv=-vtx->GetXv()*sn + vtx->GetYv()*cs, zv=vtx->GetZv();
x-=xv; y-=yv;
//Estimate the impact parameter neglecting the track curvature
if (d > maxd) return kFALSE;
//Propagate to the DCA
- Double_t crv=0.299792458e-3*b*GetParameter()[4];
+ Double_t crv=kB2C*b*GetParameter()[4];
+ if (TMath::Abs(b) < kAlmost0Field) crv=0.;
+
Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt(1.-snp*snp));
sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt(1.- sn*sn);
+ if (TMath::Abs(tgfv)>0.) cs = sn/tgfv;
+ else cs=1.;
x = xv*cs + yv*sn;
yv=-xv*sn + yv*cs; xv=x;
if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE;
- return kTRUE;
-}
+ 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->GetCovMatrix(cov);
-
-
-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])<=0) 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];
+ //***** Improvements by A.Dainese
+ alpha=GetAlpha(); sn=TMath::Sin(alpha); cs=TMath::Cos(alpha);
+ Double_t s2ylocvtx = cov[0]*sn*sn + cov[2]*cs*cs - 2.*cov[1]*cs*sn;
+ covar[0] = GetCovariance()[0] + s2ylocvtx; // neglecting correlations
+ covar[1] = GetCovariance()[1]; // between (x,y) and z
+ covar[2] = GetCovariance()[2] + cov[5]; // in vertex's covariance matrix
+ //*****
return kTRUE;
}
-Bool_t Local2GlobalPosition(Double_t r[3],Double_t alpha) {
+
+void AliExternalTrackParam::GetDirection(Double_t d[3]) const {
//----------------------------------------------------------------
- // 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
+ // This function returns a unit vector along the track direction
+ // in the global coordinate system.
//----------------------------------------------------------------
- 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;
+ 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 {
+Bool_t AliExternalTrackParam::GetPxPyPz(Double_t p[3]) const {
//---------------------------------------------------------------------
// This function returns the global track momentum components
// Results for (nearly) straight tracks are meaningless !
return Local2GlobalMomentum(p,fAlpha);
}
+Double_t AliExternalTrackParam::Px() const {
+ //---------------------------------------------------------------------
+ // Returns x-component of momentum
+ // Result for (nearly) straight tracks is meaningless !
+ //---------------------------------------------------------------------
+
+ Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
+ GetPxPyPz(p);
+
+ return p[0];
+}
+
+Double_t AliExternalTrackParam::Py() const {
+ //---------------------------------------------------------------------
+ // Returns y-component of momentum
+ // Result for (nearly) straight tracks is meaningless !
+ //---------------------------------------------------------------------
+
+ Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
+ GetPxPyPz(p);
+
+ return p[1];
+}
+
+Double_t AliExternalTrackParam::Pz() const {
+ //---------------------------------------------------------------------
+ // Returns z-component of momentum
+ // Result for (nearly) straight tracks is meaningless !
+ //---------------------------------------------------------------------
+
+ Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
+ GetPxPyPz(p);
+
+ return p[2];
+}
+
+Double_t AliExternalTrackParam::Xv() const {
+ //---------------------------------------------------------------------
+ // Returns x-component of first track point
+ //---------------------------------------------------------------------
+
+ Double_t r[3]={0.,0.,0.};
+ GetXYZ(r);
+
+ return r[0];
+}
+
+Double_t AliExternalTrackParam::Yv() const {
+ //---------------------------------------------------------------------
+ // Returns y-component of first track point
+ //---------------------------------------------------------------------
+
+ Double_t r[3]={0.,0.,0.};
+ GetXYZ(r);
+
+ return r[1];
+}
+
+Double_t AliExternalTrackParam::Zv() const {
+ //---------------------------------------------------------------------
+ // Returns z-component of first track point
+ //---------------------------------------------------------------------
+
+ Double_t r[3]={0.,0.,0.};
+ GetXYZ(r);
+
+ return r[2];
+}
+
+Double_t AliExternalTrackParam::Theta() const {
+ // return theta angle of momentum
+
+ return 0.5*TMath::Pi() - TMath::ATan(fP[3]);
+}
+
+Double_t AliExternalTrackParam::Phi() const {
+ //---------------------------------------------------------------------
+ // Returns the azimuthal angle of momentum
+ // 0 <= phi < 2*pi
+ //---------------------------------------------------------------------
+
+ Double_t phi=TMath::ASin(fP[2]) + fAlpha;
+ if (phi<0.) phi+=2.*TMath::Pi();
+ else if (phi>=2.*TMath::Pi()) phi-=2.*TMath::Pi();
+
+ return phi;
+}
+
+Double_t AliExternalTrackParam::M() const {
+ // return particle mass
+
+ // No mass information available so far.
+ // Redifine in derived class!
+
+ return -999.;
+}
+
+Double_t AliExternalTrackParam::E() const {
+ // return particle energy
+
+ // No PID information available so far.
+ // Redifine in derived class!
+
+ return -999.;
+}
+
+Double_t AliExternalTrackParam::Eta() const {
+ // return pseudorapidity
+
+ return -TMath::Log(TMath::Tan(0.5 * Theta()));
+}
+
+Double_t AliExternalTrackParam::Y() const {
+ // return rapidity
+
+ // No PID information available so far.
+ // Redifine in derived class!
+
+ return -999.;
+}
+
Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const {
//---------------------------------------------------------------------
// This function returns the global track position
//
// Results for (nearly) straight tracks are meaningless !
//---------------------------------------------------------------------
- if (TMath::Abs(fP[4])<=0) {
+ if (TMath::Abs(fP[4])<=kAlmost0) {
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]*fP[2]);
+ Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
Double_t m00=-sn, m10=cs;
Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
Double_t m35=pt, m45=-pt*pt*fP[3];
+ m43*=GetSign();
+ m44*=GetSign();
+ m45*=GetSign();
+
cv[0 ] = fC[0]*m00*m00;
cv[1 ] = fC[0]*m00*m10;
cv[2 ] = fC[0]*m10*m10;
// the radial position "x" (cm) in the magnetic field "b" (kG)
//---------------------------------------------------------------------
p[0]=fP[4];
- p[1]=fP[2]+(x-fX)*fP[4]*b*kB2C;
+ 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 {
//---------------------------------------------------------------------
// the radial position "x" (cm) in the magnetic field "b" (kG)
//---------------------------------------------------------------------
Double_t dx=x-fX;
- Double_t f1=fP[2], f2=f1 + dx*fP[4]*b*kB2C;
+ 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);
return Local2GlobalPosition(r,fAlpha);
}
-
-//_____________________________________________________________________________
-void AliExternalTrackParam::ApproximateHelixWithLine(Double_t xk, Double_t b, AliStrLine *line)
-{
- //------------------------------------------------------------
- // Approximate the track (helix) with a straight line tangent to the
- // helix in the point defined by r (F. Prino, prino@to.infn.it)
- //------------------------------------------------------------
- Double_t mom[3];
- Double_t azim = TMath::ASin(fP[2])+fAlpha;
- Double_t theta = TMath::Pi()/2. - TMath::ATan(fP[3]);
- mom[0] = TMath::Sin(theta)*TMath::Cos(azim);
- mom[1] = TMath::Sin(theta)*TMath::Sin(azim);
- mom[2] = TMath::Cos(theta);
- Double_t pos[3];
- GetXYZAt(xk,b,pos);
- line->SetP0(pos);
- line->SetCd(mom);
-}
//_____________________________________________________________________________
void AliExternalTrackParam::Print(Option_t* /*option*/) const
{
fC[10], fC[11], fC[12], fC[13], fC[14]);
}
-
-Bool_t AliExternalTrackParam::PropagateTo(Double_t xToGo, Double_t mass, Double_t maxStep, Bool_t rotateTo){
- //----------------------------------------------------------------
- // Propagate this track to the plane X=xk (cm)
- // correction for unhomogenity of the magnetic field and the
- // the correction for the material is included
+Double_t AliExternalTrackParam::GetSnpAt(Double_t x,Double_t b) const {
//
- // Require acces to magnetic field and geomanager
+ // Get sinus at given x
//
- // mass - mass used in propagation - used for energy loss correction
- // maxStep - maximal step for propagation
- //----------------------------------------------------------------
- const Double_t kEpsilon = 0.00001;
- Double_t xpos = GetX();
- Double_t dir = (xpos<xToGo) ? 1.:-1.;
+ Double_t crv=GetC(b);
+ if (TMath::Abs(b) < kAlmost0Field) crv=0.;
+ Double_t dx = x-fX;
+ Double_t res = fP[2]+dx*crv;
+ return res;
+}
+
+Bool_t AliExternalTrackParam::GetDistance(AliExternalTrackParam *param2, Double_t x, Double_t dist[3], Double_t bz){
+ //------------------------------------------------------------------------
+ // Get the distance between two tracks at the local position x
+ // working in the local frame of this track.
+ // Origin : Marian.Ivanov@cern.ch
+ //-----------------------------------------------------------------------
+ Double_t xyz[3];
+ Double_t xyz2[3];
+ xyz[0]=x;
+ if (!GetYAt(x,bz,xyz[1])) return kFALSE;
+ if (!GetZAt(x,bz,xyz[2])) return kFALSE;
+ //
//
- while ( (xToGo-xpos)*dir > kEpsilon){
- Double_t step = dir*TMath::Min(TMath::Abs(xToGo-xpos), maxStep);
- Double_t x = xpos+step;
- Double_t xyz0[3],xyz1[3],param[7];
- GetXYZ(xyz0); //starting global position
- Float_t pos0[3] = {xyz0[0],xyz0[1],xyz0[2]};
- Double_t magZ = AliTracker::GetBz(pos0);
- if (!GetXYZAt(x,magZ,xyz1)) return kFALSE; // no prolongation
- AliKalmanTrack::MeanMaterialBudget(xyz0,xyz1,param);
- if (!PropagateTo(x,magZ)) return kFALSE;
- Double_t distance = param[4];
- if (!CorrectForMaterial(distance,param[1],param[0],mass)) return kFALSE;
- if (rotateTo){
- GetXYZ(xyz0); // global position
- Double_t alphan = TMath::ATan2(xyz0[1], xyz0[0]);
- if (!Rotate(alphan)) return kFALSE;
- }
- xpos = GetX();
+ if (TMath::Abs(GetAlpha()-param2->GetAlpha())<kAlmost0){
+ xyz2[0]=x;
+ if (!param2->GetYAt(x,bz,xyz2[1])) return kFALSE;
+ if (!param2->GetZAt(x,bz,xyz2[2])) return kFALSE;
+ }else{
+ //
+ Double_t xyz1[3];
+ Double_t dfi = param2->GetAlpha()-GetAlpha();
+ Double_t ca = TMath::Cos(dfi), sa = TMath::Sin(dfi);
+ xyz2[0] = xyz[0]*ca+xyz[1]*sa;
+ xyz2[1] = -xyz[0]*sa+xyz[1]*ca;
+ //
+ xyz1[0]=xyz2[0];
+ if (!param2->GetYAt(xyz2[0],bz,xyz1[1])) return kFALSE;
+ if (!param2->GetZAt(xyz2[0],bz,xyz1[2])) return kFALSE;
+ //
+ xyz2[0] = xyz1[0]*ca-xyz1[1]*sa;
+ xyz2[1] = +xyz1[0]*sa+xyz1[1]*ca;
+ xyz2[2] = xyz1[2];
}
+ dist[0] = xyz[0]-xyz2[0];
+ dist[1] = xyz[1]-xyz2[1];
+ dist[2] = xyz[2]-xyz2[2];
+
return kTRUE;
}
-//_____________________________________________________________________________
-Bool_t AliExternalTrackParam::CorrectForMaterial(Double_t d, Double_t x0, Double_t rho, Double_t mass)
-{
- //
- // Take into account material effects assuming:
- // x0 - mean rad length
- // rho - mean density
+//
+// Draw functionality.
+// Origin: Marian Ivanov, Marian.Ivanov@cern.ch
+//
+
+void AliExternalTrackParam::DrawTrack(Float_t magf, Float_t minR, Float_t maxR, Float_t stepR){
//
- // multiple scattering
+ // Draw track line
//
- if (mass<=0) {
- AliError("Non-positive mass");
- return kFALSE;
- }
- Double_t p2=(1.+ fP[3]*fP[3])/(fP[4]*fP[4]);
- Double_t beta2=p2/(p2 + mass*mass);
- Double_t theta2=14.1*14.1/(beta2*p2*1e6)*d/x0*rho;
- //
- fC[5] += theta2*(1.- fP[2]*fP[2])*(1. + fP[3]*fP[3]);
- fC[9] += theta2*(1. + fP[3]*fP[3])*(1. + fP[3]*fP[3]);
- fC[13] += theta2*fP[3]*fP[4]*(1. + fP[3]*fP[3]);
- fC[14] += theta2*fP[3]*fP[4]*fP[3]*fP[4];
+ if (minR>maxR) return ;
+ if (stepR<=0) return ;
+ Int_t npoints = TMath::Nint((maxR-minR)/stepR)+1;
+ if (npoints<1) return;
+ TPolyMarker3D *polymarker = new TPolyMarker3D(npoints);
+ FillPolymarker(polymarker, magf,minR,maxR,stepR);
+ polymarker->Draw();
+}
+
+//
+void AliExternalTrackParam::FillPolymarker(TPolyMarker3D *pol, Float_t magF, Float_t minR, Float_t maxR, Float_t stepR){
//
- Double_t dE=0.153e-3/beta2*(log(5940*beta2/(1-beta2+1e-10)) - beta2)*d*rho;
- fP[4] *=(1.- TMath::Sqrt(p2+mass*mass)/p2*dE);
+ // Fill points in the polymarker
//
- Double_t sigmade = 0.02*TMath::Sqrt(TMath::Abs(dE)); // energy loss fluctuation
- Double_t sigmac2 = sigmade*sigmade*fP[4]*fP[4]*(p2+mass*mass)/(p2*p2);
- fC[14] += sigmac2;
- return kTRUE;
+ Int_t counter=0;
+ for (Double_t r=minR; r<maxR; r+=stepR){
+ Double_t point[3];
+ GetXYZAt(r,magF,point);
+ pol->SetPoint(counter,point[0],point[1], point[2]);
+ printf("xyz\t%f\t%f\t%f\n",point[0], point[1],point[2]);
+ counter++;
+ }
}
-
-
git://git.uio.no / u / mrichter / AliRoot.git / blobdiff