// are implemented.
// Origin: I.Belikov, CERN, Jouri.Belikov@cern.ch //
///////////////////////////////////////////////////////////////////////////////
+#include <TMatrixDSym.h>
#include "AliExternalTrackParam.h"
-#include "AliKalmanTrack.h"
+#include "AliESDVertex.h"
+#include "AliLog.h"
ClassImp(AliExternalTrackParam)
+Double32_t AliExternalTrackParam::fgMostProbablePt=kMostProbablePt;
+
//_____________________________________________________________________________
AliExternalTrackParam::AliExternalTrackParam() :
+ TObject(),
fX(0),
fAlpha(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)
{
}
//_____________________________________________________________________________
-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 b,Double_t x,Double_t y) const {
+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)
//------------------------------------------------------------------
- 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::CorrectForMeanMaterial
+(Double_t xOverX0, Double_t xTimesRho, Double_t mass,
+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];
+
+ Double_t p=GetP();
+ Double_t p2=p*p;
+ Double_t beta2=p2/(p2 + mass*mass);
+ xOverX0*=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2));
+
+ //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)
+ // "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 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-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 crv=kB2C*b*fP[4];
Double_t dx=xk-fX;
+ if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
+
+ Double_t crv=GetC(b);
+ if (TMath::Abs(b) < kAlmost0Field) crv=0.;
+
Double_t f1=fP[2], f2=f1 + crv*dx;
+ if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
fX=xk;
fP0 += dx*(f1+f2)/(r1+r2);
- fP1 += dx*(f1+f2)/(f1*r2 + f2*r1)*fP3;
+ fP1 += dx*(r2 + f2*(f1+f2)/(r1+r2))*fP3; // Many thanks to P.Hristov !
fP2 += dx*crv;
//f = F - 1
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 {
//----------------------------------------------------------------
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;
+}
+
Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) {
//------------------------------------------------------------------
// Update the track parameters with the space point "p" having
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 (dd<dm) break;
+ dt1*=0.5; dt2*=0.5;
+ if (div>512) {
+ 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
// p[2] = pz
// Results for (nearly) straight tracks are meaningless !
//----------------------------------------------------------------
- if (TMath::Abs(p[0])<=0) return kFALSE;
+ if (TMath::Abs(p[0])<=kAlmost0) return kFALSE;
if (TMath::Abs(p[1])> kAlmost1) return kFALSE;
Double_t pt=1./TMath::Abs(p[0]);
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 !
//---------------------------------------------------------------------
- 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::Print(Option_t* /*option*/) const
{
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;
+}
git://git.uio.no / u / mrichter / AliRoot.git / blobdiff