#include <cassert>
#include <TVectorD.h>
#include <TMatrixDSym.h>
#include <TPolyMarker3D.h>
#include <TVector3.h>
#include <TMatrixD.h>
#include "AliExternalTrackParam.h"
#include "AliVVertex.h"
#include "AliLog.h"
ClassImp(AliExternalTrackParam)
Double32_t AliExternalTrackParam::fgMostProbablePt=kMostProbablePt;
Bool_t AliExternalTrackParam::fgUseLogTermMS = kFALSE;;
AliExternalTrackParam::AliExternalTrackParam() :
AliVTrack(),
fX(0),
fAlpha(0)
{
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):
AliVTrack(track),
fX(track.fX),
fAlpha(track.fAlpha)
{
for (Int_t i = 0; i < 5; i++) fP[i] = track.fP[i];
for (Int_t i = 0; i < 15; i++) fC[i] = track.fC[i];
CheckCovariance();
}
AliExternalTrackParam& AliExternalTrackParam::operator=(const AliExternalTrackParam &trkPar)
{
if (this!=&trkPar) {
AliVTrack::operator=(trkPar);
fX = trkPar.fX;
fAlpha = trkPar.fAlpha;
for (Int_t i = 0; i < 5; i++) fP[i] = trkPar.fP[i];
for (Int_t i = 0; i < 15; i++) fC[i] = trkPar.fC[i];
CheckCovariance();
}
return *this;
}
AliExternalTrackParam::AliExternalTrackParam(Double_t x, Double_t alpha,
const Double_t param[5],
const Double_t covar[15]) :
AliVTrack(),
fX(x),
fAlpha(alpha)
{
for (Int_t i = 0; i < 5; i++) fP[i] = param[i];
for (Int_t i = 0; i < 15; i++) fC[i] = covar[i];
CheckCovariance();
}
void AliExternalTrackParam::CopyFromVTrack(const AliVTrack *vTrack)
{
if (!vTrack) {
AliError("Source VTrack is NULL");
return;
}
if (this==vTrack) {
AliError("Copy of itself is requested");
return;
}
if (vTrack->InheritsFrom(AliExternalTrackParam::Class())) {
AliDebug(1,"Source itself is AliExternalTrackParam, using assignment operator");
*this = *(AliExternalTrackParam*)vTrack;
return;
}
AliVTrack::operator=( *vTrack );
Double_t xyz[3],pxpypz[3],cv[21];
vTrack->GetXYZ(xyz);
pxpypz[0]=vTrack->Px();
pxpypz[1]=vTrack->Py();
pxpypz[2]=vTrack->Pz();
vTrack->GetCovarianceXYZPxPyPz(cv);
Short_t sign = (Short_t)vTrack->Charge();
Set(xyz,pxpypz,cv,sign);
}
AliExternalTrackParam::AliExternalTrackParam(const AliVTrack *vTrack) :
AliVTrack(),
fX(0.),
fAlpha(0.)
{
if (vTrack->InheritsFrom("AliExternalTrackParam")) {
AliError("This is not a copy constructor. Use AliExternalTrackParam(const AliExternalTrackParam &) !");
AliWarning("Calling the default constructor...");
AliExternalTrackParam();
return;
}
Double_t xyz[3],pxpypz[3],cv[21];
vTrack->GetXYZ(xyz);
pxpypz[0]=vTrack->Px();
pxpypz[1]=vTrack->Py();
pxpypz[2]=vTrack->Pz();
vTrack->GetCovarianceXYZPxPyPz(cv);
Short_t sign = (Short_t)vTrack->Charge();
Set(xyz,pxpypz,cv,sign);
}
AliExternalTrackParam::AliExternalTrackParam(Double_t xyz[3],Double_t pxpypz[3],
Double_t cv[21],Short_t sign) :
AliVTrack(),
fX(0.),
fAlpha(0.)
{
Set(xyz,pxpypz,cv,sign);
}
void AliExternalTrackParam::Set(Double_t xyz[3],Double_t pxpypz[3],
Double_t cv[21],Short_t sign)
{
const double kSafe = 1e-5;
Double_t radPos2 = xyz[0]*xyz[0]+xyz[1]*xyz[1];
Double_t radMax = 45.;
if (radPos2 < radMax*radMax) {
fAlpha = TMath::ATan2(pxpypz[1],pxpypz[0]);
} else {
Float_t phiPos = TMath::Pi()+TMath::ATan2(-xyz[1], -xyz[0]);
fAlpha =
TMath::DegToRad()*(20*((((Int_t)(phiPos*TMath::RadToDeg()))/20))+10);
}
Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
if (TMath::Abs(sn)<2*kSafe) {
if (fAlpha>0) fAlpha += fAlpha< TMath::Pi()/2. ? 2*kSafe : -2*kSafe;
else fAlpha += fAlpha>-TMath::Pi()/2. ? -2*kSafe : 2*kSafe;
cs=TMath::Cos(fAlpha);
sn=TMath::Sin(fAlpha);
}
else if (TMath::Abs(cs)<2*kSafe) {
if (fAlpha>0) fAlpha += fAlpha> TMath::Pi()/2. ? 2*kSafe : -2*kSafe;
else fAlpha += fAlpha>-TMath::Pi()/2. ? 2*kSafe : -2*kSafe;
cs=TMath::Cos(fAlpha);
sn=TMath::Sin(fAlpha);
}
TVector3 ver(xyz[0],xyz[1],xyz[2]);
TVector3 mom(pxpypz[0],pxpypz[1],pxpypz[2]);
ver.RotateZ(-fAlpha);
mom.RotateZ(-fAlpha);
fX = ver.X();
Double_t charge = (Double_t)sign;
fP[0] = ver.Y();
fP[1] = ver.Z();
fP[2] = TMath::Sin(mom.Phi());
fP[3] = mom.Pz()/mom.Pt();
fP[4] = TMath::Sign(1/mom.Pt(),charge);
if (TMath::Abs( 1-fP[2]) < kSafe) fP[2] = 1.- kSafe;
else if (TMath::Abs(-1-fP[2]) < kSafe) fP[2] =-1.+ kSafe;
Double_t pt=1./TMath::Abs(fP[4]);
Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
Double_t cv34 = TMath::Sqrt(cv[3 ]*cv[3 ]+cv[4 ]*cv[4 ]);
Int_t special = 0;
double sgcheck = r*sn + fP[2]*cs;
if (TMath::Abs(sgcheck)>=1-kSafe) {
special = 1;
sgcheck = TMath::Sign(1.0,sgcheck);
}
else if (TMath::Abs(sgcheck)<kSafe) {
sgcheck = TMath::Sign(1.0,cs);
special = 2;
}
fC[0 ] = cv[0 ]+cv[2 ];
fC[1 ] = TMath::Sign(cv34,-cv[3 ]*sn);
fC[2 ] = cv[5 ];
if (special==1) {
double pti = 1./pt;
double pti2 = pti*pti;
int q = GetSign();
fC[3 ] = cv[6]*pti;
fC[4 ] = -sgcheck*cv[8]*r*pti;
fC[5 ] = TMath::Abs(cv[9]*r*r*pti2);
fC[6 ] = (cv[10]*fP[3]-sgcheck*cv[15])*pti/r;
fC[7 ] = (cv[17]-sgcheck*cv[12]*fP[3])*pti;
fC[8 ] = (-sgcheck*cv[18]+cv[13]*fP[3])*r*pti2;
fC[9 ] = TMath::Abs( cv[20]-2*sgcheck*cv[19]*fP[3]+cv[14]*fP[3]*fP[3])*pti2;
fC[10] = cv[10]*pti2/r*q;
fC[11] = -sgcheck*cv[12]*pti2*q;
fC[12] = cv[13]*r*pti*pti2*q;
fC[13] = (-sgcheck*cv[19]+cv[14]*fP[3])*r*pti2*pti;
fC[14] = TMath::Abs(cv[14]*pti2*pti2);
} else if (special==2) {
double pti = 1./pt;
double pti2 = pti*pti;
int q = GetSign();
fC[3 ] = -cv[10]*pti*cs/sn;
fC[4 ] = cv[12]*cs*pti;
fC[5 ] = TMath::Abs(cv[14]*cs*cs*pti2);
fC[6 ] = (sgcheck*cv[6]*fP[3]-cv[15])*pti/sn;
fC[7 ] = (cv[17]-sgcheck*cv[8]*fP[3])*pti;
fC[8 ] = (cv[19]-sgcheck*cv[13]*fP[3])*cs*pti2;
fC[9 ] = TMath::Abs( cv[20]-2*sgcheck*cv[18]*fP[3]+cv[9]*fP[3]*fP[3])*pti2;
fC[10] = sgcheck*cv[6]*pti2/sn*q;
fC[11] = -sgcheck*cv[8]*pti2*q;
fC[12] = -sgcheck*cv[13]*cs*pti*pti2*q;
fC[13] = (-sgcheck*cv[18]+cv[9]*fP[3])*pti2*pti*q;
fC[14] = TMath::Abs(cv[9]*pti2*pti2);
}
else {
Double_t m00=-sn;
Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
Double_t m35=pt, m45=-pt*pt*fP[3];
m43*=GetSign();
m44*=GetSign();
m45*=GetSign();
Double_t a1=cv[13]-cv[9]*(m23*m44+m43*m24)/m23/m43;
Double_t a2=m23*m24-m23*(m23*m44+m43*m24)/m43;
Double_t a3=m43*m44-m43*(m23*m44+m43*m24)/m23;
Double_t a4=cv[14]+2.*cv[9];
Double_t a5=m24*m24-2.*m24*m44*m23/m43;
Double_t a6=m44*m44-2.*m24*m44*m43/m23;
fC[3 ] = (cv[10]*m43-cv[6]*m44)/(m24*m43-m23*m44)/m00;
fC[10] = (cv[6]/m00-fC[3 ]*m23)/m43;
fC[6 ] = (cv[15]/m00-fC[10]*m45)/m35;
fC[4 ] = (cv[12]*m43-cv[8]*m44)/(m24*m43-m23*m44);
fC[11] = (cv[8]-fC[4]*m23)/m43;
fC[7 ] = cv[17]/m35-fC[11]*m45/m35;
fC[5 ] = TMath::Abs((a4*a3-a6*a1)/(a5*a3-a6*a2));
fC[14] = TMath::Abs((a1-a2*fC[5])/a3);
fC[12] = (cv[9]-fC[5]*m23*m23-fC[14]*m43*m43)/m23/m43;
Double_t b1=cv[18]-fC[12]*m23*m45-fC[14]*m43*m45;
Double_t b2=m23*m35;
Double_t b3=m43*m35;
Double_t b4=cv[19]-fC[12]*m24*m45-fC[14]*m44*m45;
Double_t b5=m24*m35;
Double_t b6=m44*m35;
fC[8 ] = (b4-b6*b1/b3)/(b5-b6*b2/b3);
fC[13] = b1/b3-b2*fC[8]/b3;
fC[9 ] = TMath::Abs((cv[20]-fC[14]*(m45*m45)-fC[13]*2.*m35*m45)/(m35*m35));
}
CheckCovariance();
return;
}
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;
}
void AliExternalTrackParam::AddCovariance(const Double_t c[15]) {
fC[0] +=c[0];
fC[1] +=c[1]; fC[2] +=c[2];
fC[3] +=c[3]; fC[4] +=c[4]; fC[5] +=c[5];
fC[6] +=c[6]; fC[7] +=c[7]; fC[8] +=c[8]; fC[9] +=c[9];
fC[10]+=c[10]; fC[11]+=c[11]; fC[12]+=c[12]; fC[13]+=c[13]; fC[14]+=c[14];
CheckCovariance();
}
Double_t AliExternalTrackParam::GetP() const {
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 {
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 {
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])*(1.+fP[2]));
a=2*(xt*fP[2] - yt*TMath::Sqrt((1.-fP[2])*(1.+fP[2])))-rp4*(xt*xt + yt*yt);
return -a/(1 + TMath::Sqrt(sn*sn + cs*cs));
}
void AliExternalTrackParam::
GetDZ(Double_t x, Double_t y, Double_t z, Double_t b, Float_t dz[2]) const {
Double_t f1 = fP[2], r1 = TMath::Sqrt((1.-f1)*(1.+f1));
Double_t xt=fX, yt=fP[0];
Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
Double_t a = x*cs + y*sn;
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)*(1.+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 {
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])*(1.+fP[2]));
return -d;
}
Bool_t AliExternalTrackParam::CorrectForMeanMaterialdEdx
(Double_t xOverX0, Double_t xTimesRho, Double_t mass,
Double_t dEdx,
Bool_t anglecorr) {
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];
if(anglecorr) {
Double_t angle=TMath::Sqrt((1.+ fP3*fP3)/((1-fP2)*(1.+fP2)));
xOverX0 *=angle;
xTimesRho *=angle;
}
Double_t p=GetP();
if (mass<0) p += p;
Double_t p2=p*p;
Double_t beta2=p2/(p2 + mass*mass);
Double_t cC22 = 0.;
Double_t cC33 = 0.;
Double_t cC43 = 0.;
Double_t cC44 = 0.;
if (xOverX0 != 0) {
Double_t theta2=0.0136*0.0136/(beta2*p2)*TMath::Abs(xOverX0);
if (GetUseLogTermMS()) {
double lt = 1+0.038*TMath::Log(TMath::Abs(xOverX0));
if (lt>0) theta2 *= lt*lt;
}
if (mass<0) theta2 *= 4;
if(theta2>TMath::Pi()*TMath::Pi()) return kFALSE;
cC22 = theta2*((1.-fP2)*(1.+fP2))*(1. + fP3*fP3);
cC33 = theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
cC43 = theta2*fP3*fP4*(1. + fP3*fP3);
cC44 = theta2*fP3*fP4*fP3*fP4;
}
Double_t cP4=1.;
if ((xTimesRho != 0.) && (beta2 < 1.)) {
Double_t dE=dEdx*xTimesRho;
Double_t e=TMath::Sqrt(p2 + mass*mass);
if ( TMath::Abs(dE) > 0.3*e ) return kFALSE;
if ( (1.+ dE/p2*(dE + 2*e)) < 0. ) return kFALSE;
cP4 = 1./TMath::Sqrt(1.+ dE/p2*(dE + 2*e));
if (TMath::Abs(fP4*cP4)>100.) return kFALSE;
const Double_t knst=0.07;
Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE));
cC44 += ((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4));
}
fC22 += cC22;
fC33 += cC33;
fC43 += cC43;
fC44 += cC44;
fP4 *= cP4;
CheckCovariance();
return kTRUE;
}
Bool_t AliExternalTrackParam::CorrectForMeanMaterial
(Double_t xOverX0, Double_t xTimesRho, Double_t mass,
Bool_t anglecorr,
Double_t (*Bethe)(Double_t)) {
Double_t bg=GetP()/mass;
if (mass<0) {
if (mass<-990) {
AliDebug(2,Form("Mass %f corresponds to unknown PID particle",mass));
return kFALSE;
}
bg = -2*bg;
}
Double_t dEdx=Bethe(bg);
if (mass<0) dEdx *= 4;
return CorrectForMeanMaterialdEdx(xOverX0,xTimesRho,mass,dEdx,anglecorr);
}
Bool_t AliExternalTrackParam::CorrectForMeanMaterialZA
(Double_t xOverX0, Double_t xTimesRho, Double_t mass,
Double_t zOverA,
Double_t density,
Double_t exEnergy,
Double_t jp1,
Double_t jp2,
Bool_t anglecorr) {
Double_t bg=GetP()/mass;
if (mass<0) {
if (mass<-990) {
AliDebug(2,Form("Mass %f corresponds to unknown PID particle",mass));
return kFALSE;
}
bg = -2*bg;
}
Double_t dEdx=BetheBlochGeant(bg,density,jp1,jp2,exEnergy,zOverA);
if (mass<0) dEdx *= 4;
return CorrectForMeanMaterialdEdx(xOverX0,xTimesRho,mass,dEdx,anglecorr);
}
Bool_t AliExternalTrackParam::CorrectForMaterial
(Double_t d, Double_t x0, Double_t mass, Double_t (*Bethe)(Double_t)) {
return CorrectForMeanMaterial(d,x0*d,mass,kTRUE,Bethe);
}
Double_t AliExternalTrackParam::BetheBlochAleph(Double_t bg,
Double_t kp1,
Double_t kp2,
Double_t kp3,
Double_t kp4,
Double_t kp5) {
Double_t beta = bg/TMath::Sqrt(1.+ bg*bg);
Double_t aa = TMath::Power(beta,kp4);
Double_t bb = TMath::Power(1./bg,kp5);
bb=TMath::Log(kp3+bb);
return (kp2-aa-bb)*kp1/aa;
}
Double_t AliExternalTrackParam::BetheBlochGeant(Double_t bg,
Double_t kp0,
Double_t kp1,
Double_t kp2,
Double_t kp3,
Double_t kp4) {
const Double_t mK = 0.307075e-3;
const Double_t me = 0.511e-3;
const Double_t rho = kp0;
const Double_t x0 = kp1*2.303;
const Double_t x1 = kp2*2.303;
const Double_t mI = kp3;
const Double_t mZA = kp4;
const Double_t bg2 = bg*bg;
const Double_t maxT= 2*me*bg2;
Double_t d2=0.;
const Double_t x=TMath::Log(bg);
const Double_t lhwI=TMath::Log(28.816*1e-9*TMath::Sqrt(rho*mZA)/mI);
if (x > x1) {
d2 = lhwI + x - 0.5;
} else if (x > x0) {
const Double_t r=(x1-x)/(x1-x0);
d2 = lhwI + x - 0.5 + (0.5 - lhwI - x0)*r*r*r;
}
return mK*mZA*(1+bg2)/bg2*
(0.5*TMath::Log(2*me*bg2*maxT/(mI*mI)) - bg2/(1+bg2) - d2);
}
Double_t AliExternalTrackParam::BetheBlochSolid(Double_t bg) {
return BetheBlochGeant(bg);
}
Double_t AliExternalTrackParam::BetheBlochGas(Double_t bg) {
const Double_t rho = 0.9e-3;
const Double_t x0 = 2.;
const Double_t x1 = 4.;
const Double_t mI = 140.e-9;
const Double_t mZA = 0.49555;
return BetheBlochGeant(bg,rho,x0,x1,mI,mZA);
}
Bool_t AliExternalTrackParam::Rotate(Double_t alpha) {
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)*(1.+fP2));
if ((cf*ca+sf*sa)<0) {
AliDebug(1,Form("Rotation failed: local cos(phi) would become %.2f",cf*ca+sf*sa));
return kFALSE;
}
Double_t tmp=sf*ca - cf*sa;
if (TMath::Abs(tmp) >= kAlmost1) {
if (TMath::Abs(tmp) > 1.+ Double_t(FLT_EPSILON))
AliWarning(Form("Rotation failed ! %.10e",tmp));
return kFALSE;
}
fAlpha = alpha;
fX = x*ca + fP0*sa;
fP0= -x*sa + fP0*ca;
fP2= tmp;
if (TMath::Abs(cf)<kAlmost0) {
AliError(Form("Too small cosine value %f",cf));
cf = kAlmost0;
}
Double_t rr=(ca+sf/cf*sa);
fC00 *= (ca*ca);
fC10 *= ca;
fC20 *= ca*rr;
fC21 *= rr;
fC22 *= rr*rr;
fC30 *= ca;
fC32 *= rr;
fC40 *= ca;
fC42 *= rr;
CheckCovariance();
return kTRUE;
}
Bool_t AliExternalTrackParam::RotateParamOnly(Double_t alpha)
{
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 x=fX;
Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha);
Double_t sf=fP2, cf=TMath::Sqrt((1.- fP2)*(1.+fP2));
if ((cf*ca+sf*sa)<0) {
AliDebug(1,Form("Rotation failed: local cos(phi) would become %.2f",cf*ca+sf*sa));
return kFALSE;
}
Double_t tmp=sf*ca - cf*sa;
if (TMath::Abs(tmp) >= kAlmost1) {
if (TMath::Abs(tmp) > 1.+ Double_t(FLT_EPSILON))
AliWarning(Form("Rotation failed ! %.10e",tmp));
return kFALSE;
}
fAlpha = alpha;
fX = x*ca + fP0*sa;
fP0= -x*sa + fP0*ca;
fP2= tmp;
return kTRUE;
}
Bool_t AliExternalTrackParam::Invert() {
fX = -fX;
fAlpha += TMath::Pi();
while (fAlpha < -TMath::Pi()) fAlpha += 2*TMath::Pi();
while (fAlpha >= TMath::Pi()) fAlpha -= 2*TMath::Pi();
fP[0] = -fP[0];
fP[3] = -fP[3];
fP[4] = -fP[4];
fC[1] = -fC[1];
fC[3] = -fC[3];
fC[7] = -fC[7];
fC[8] = -fC[8];
fC[11] = -fC[11];
fC[12] = -fC[12];
return kTRUE;
}
Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) {
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 x2r = crv*dx;
Double_t f1=fP[2], f2=f1 + x2r;
if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
if (TMath::Abs(fP[4])< kAlmost0) return kFALSE;
Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
Double_t
&fC00=fC[0],
&fC10=fC[1], &fC11=fC[2],
&fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
&fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
&fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2));
if (TMath::Abs(r1)<kAlmost0) return kFALSE;
if (TMath::Abs(r2)<kAlmost0) return kFALSE;
fX=xk;
double dy2dx = (f1+f2)/(r1+r2);
fP0 += dx*dy2dx;
fP2 += x2r;
if (TMath::Abs(x2r)<0.05) fP1 += dx*(r2 + f2*dy2dx)*fP3;
else {
double rot = TMath::ASin(r1*f2 - r2*f1);
if (f1*f1+f2*f2>1 && f1*f2<0) {
if (f2>0) rot = TMath::Pi() - rot;
else rot = -TMath::Pi() - rot;
}
fP1 += fP3/crv*rot;
}
Double_t rinv = 1./r1;
Double_t r3inv = rinv*rinv*rinv;
Double_t f24= x2r/fP4;
Double_t f02= dx*r3inv;
Double_t f04=0.5*f24*f02;
Double_t f12= f02*fP3*f1;
Double_t f14=0.5*f24*f02*fP3*f1;
Double_t f13= dx*rinv;
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;
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;
fC00 += b00 + b00 + a00;
fC10 += b10 + b01 + a01;
fC20 += b20 + b02 + a02;
fC30 += b30;
fC40 += b40;
fC11 += b11 + b11 + a11;
fC21 += b21 + b12 + a12;
fC31 += b31;
fC41 += b41;
fC22 += b22 + b22 + a22;
fC32 += b32;
fC42 += b42;
CheckCovariance();
return kTRUE;
}
Bool_t AliExternalTrackParam::PropagateParamOnlyTo(Double_t xk, Double_t b) {
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 x2r = crv*dx;
Double_t f1=fP[2], f2=f1 + x2r;
if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
if (TMath::Abs(fP[4])< kAlmost0) return kFALSE;
Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2));
if (TMath::Abs(r1)<kAlmost0) return kFALSE;
if (TMath::Abs(r2)<kAlmost0) return kFALSE;
fX=xk;
double dy2dx = (f1+f2)/(r1+r2);
fP[0] += dx*dy2dx;
fP[2] += x2r;
if (TMath::Abs(x2r)<0.05) fP[1] += dx*(r2 + f2*dy2dx)*fP[3];
else {
double rot = TMath::ASin(r1*f2 - r2*f1);
if (f1*f1+f2*f2>1 && f1*f2<0) {
if (f2>0) rot = TMath::Pi() - rot;
else rot = -TMath::Pi() - rot;
}
fP[1] += fP[3]/crv*rot;
}
return kTRUE;
}
Bool_t
AliExternalTrackParam::Propagate(Double_t alpha, Double_t x, Double_t b) {
Double_t as=fAlpha;
Double_t xs=fX;
Double_t ps[5], cs[15];
for (Int_t i=0; i<5; i++) ps[i]=fP[i];
for (Int_t i=0; i<15; i++) cs[i]=fC[i];
if (Rotate(alpha))
if (PropagateTo(x,b)) return kTRUE;
fAlpha=as;
fX=xs;
for (Int_t i=0; i<5; i++) fP[i]=ps[i];
for (Int_t i=0; i<15; i++) fC[i]=cs[i];
return kFALSE;
}
Bool_t AliExternalTrackParam::PropagateBxByBz
(Double_t alpha, Double_t x, Double_t b[3]) {
Double_t as=fAlpha;
Double_t xs=fX;
Double_t ps[5], cs[15];
for (Int_t i=0; i<5; i++) ps[i]=fP[i];
for (Int_t i=0; i<15; i++) cs[i]=fC[i];
if (Rotate(alpha))
if (PropagateToBxByBz(x,b)) return kTRUE;
fAlpha=as;
fX=xs;
for (Int_t i=0; i<5; i++) fP[i]=ps[i];
for (Int_t i=0; i<15; i++) fC[i]=cs[i];
return kFALSE;
}
void AliExternalTrackParam::Propagate(Double_t len, Double_t x[3],
Double_t p[3], Double_t bz) const {
GetXYZ(x);
if (OneOverPt() < kAlmost0 || TMath::Abs(bz) < kAlmost0Field || GetC(bz) < kAlmost0){
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 {
Double_t x0[3]; GetXYZ(x0);
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){
Propagate(s,x,p,bz);
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;
}
for (Int_t i=0; i<3; i++) {pnt[i]=x[i]; norm[i]=p[i];}
return kTRUE;
}
Double_t
AliExternalTrackParam::GetPredictedChi2(const Double_t p[2],const Double_t cov[3]) const {
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;
}
Double_t AliExternalTrackParam::
GetPredictedChi2(const Double_t p[3],const Double_t covyz[3],const Double_t covxyz[3]) const {
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)*(1.+f));
Double_t a=f/r, b=GetTgl()/r;
Double_t s2=333.*333.;
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;
}
Double_t AliExternalTrackParam::
GetPredictedChi2(const AliExternalTrackParam *t) const {
if (TMath::Abs(t->GetAlpha()-GetAlpha()) > FLT_EPSILON) {
AliError("The reference systems of the tracks differ !");
return kVeryBig;
}
if (TMath::Abs(t->GetX()-GetX()) > FLT_EPSILON) {
AliError("The reference of the tracks planes differ !");
return kVeryBig;
}
TMatrixDSym c(5);
c(0,0)=GetSigmaY2();
c(1,0)=GetSigmaZY(); c(1,1)=GetSigmaZ2();
c(2,0)=GetSigmaSnpY(); c(2,1)=GetSigmaSnpZ(); c(2,2)=GetSigmaSnp2();
c(3,0)=GetSigmaTglY(); c(3,1)=GetSigmaTglZ(); c(3,2)=GetSigmaTglSnp(); c(3,3)=GetSigmaTgl2();
c(4,0)=GetSigma1PtY(); c(4,1)=GetSigma1PtZ(); c(4,2)=GetSigma1PtSnp(); c(4,3)=GetSigma1PtTgl(); c(4,4)=GetSigma1Pt2();
c(0,0)+=t->GetSigmaY2();
c(1,0)+=t->GetSigmaZY(); c(1,1)+=t->GetSigmaZ2();
c(2,0)+=t->GetSigmaSnpY();c(2,1)+=t->GetSigmaSnpZ();c(2,2)+=t->GetSigmaSnp2();
c(3,0)+=t->GetSigmaTglY();c(3,1)+=t->GetSigmaTglZ();c(3,2)+=t->GetSigmaTglSnp();c(3,3)+=t->GetSigmaTgl2();
c(4,0)+=t->GetSigma1PtY();c(4,1)+=t->GetSigma1PtZ();c(4,2)+=t->GetSigma1PtSnp();c(4,3)+=t->GetSigma1PtTgl();c(4,4)+=t->GetSigma1Pt2();
c(0,1)=c(1,0);
c(0,2)=c(2,0); c(1,2)=c(2,1);
c(0,3)=c(3,0); c(1,3)=c(3,1); c(2,3)=c(3,2);
c(0,4)=c(4,0); c(1,4)=c(4,1); c(2,4)=c(4,2); c(3,4)=c(4,3);
c.Invert();
if (!c.IsValid()) return kVeryBig;
Double_t res[5] = {
GetY() - t->GetY(),
GetZ() - t->GetZ(),
GetSnp() - t->GetSnp(),
GetTgl() - t->GetTgl(),
GetSigned1Pt() - t->GetSigned1Pt()
};
Double_t chi2=0.;
for (Int_t i = 0; i < 5; i++)
for (Int_t j = 0; j < 5; j++) chi2 += res[i]*res[j]*c(i,j);
return chi2;
}
Bool_t AliExternalTrackParam::
PropagateTo(Double_t p[3],Double_t covyz[3],Double_t covxyz[3],Double_t bz) {
Double_t f=GetSnp();
if (TMath::Abs(f) >= kAlmost1) return kFALSE;
Double_t r=TMath::Sqrt((1.-f)*(1.+f));
Double_t a=f/r, b=GetTgl()/r;
Double_t s2=333.*333.;
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 {
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(const Double_t p[2], const Double_t cov[3]) {
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;
CheckCovariance();
return kTRUE;
}
void
AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const {
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;
hlx[0]=fX*sn + hlx[0]*cs;
hlx[2]=TMath::ASin(hlx[2]) + fAlpha;
hlx[4]=GetC(b);
}
static void Evaluate(const Double_t *h, Double_t t,
Double_t r[3],
Double_t g[3],
Double_t gg[3])
{
Double_t phase=h[4]*t+h[2];
Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase);
r[0] = h[5];
r[1] = h[0];
if (TMath::Abs(h[4])>kAlmost0) {
r[0] += (sn - h[6])/h[4];
r[1] -= (cs - h[7])/h[4];
}
r[2] = h[1] + h[3]*t;
g[0] = cs; g[1]=sn; g[2]=h[3];
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 {
Double_t dy2=GetSigmaY2() + p->GetSigmaY2();
Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2();
Double_t dx2=dy2;
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) {
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;}
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)
AliDebug(1," stopped at not a stationary point !");
Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det);
if (lmb < 0.)
AliDebug(1," 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) {
AliDebug(1," overshoot !"); break;
}
}
dm=dd;
t1+=dt1;
t2+=dt2;
}
if (max<=0) AliDebug(1," 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) {
Double_t xthis,xp;
Double_t dca=GetDCA(p,b,xthis,xp);
if (!PropagateTo(xthis,b)) {
return 1e+33;
}
if (!p->PropagateTo(xp,b)) {
return 1e+33;
}
return dca;
}
Bool_t AliExternalTrackParam::PropagateToDCA(const AliVVertex *vtx,
Double_t b, Double_t maxd, Double_t dz[2], Double_t covar[3]) {
Double_t alpha=GetAlpha();
Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha);
Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2];
Double_t xv= vtx->GetX()*cs + vtx->GetY()*sn;
Double_t yv=-vtx->GetX()*sn + vtx->GetY()*cs, zv=vtx->GetZ();
x-=xv; y-=yv;
Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt((1.-snp)*(1.+snp)));
if (d > maxd) return kFALSE;
Double_t crv=GetC(b);
if (TMath::Abs(b) < kAlmost0Field) crv=0.;
Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt((1.-snp)*(1.+snp)));
sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt((1.-sn)*(1.+sn));
if (TMath::Abs(tgfv)>0.) cs = sn/tgfv;
else cs=1.;
x = xv*cs + yv*sn;
yv=-xv*sn + yv*cs; xv=x;
if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE;
if (dz==0) return kTRUE;
dz[0] = GetParameter()[0] - yv;
dz[1] = GetParameter()[1] - zv;
if (covar==0) return kTRUE;
Double_t cov[6]; vtx->GetCovarianceMatrix(cov);
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;
covar[1] = GetCovariance()[1];
covar[2] = GetCovariance()[2] + cov[5];
return kTRUE;
}
Bool_t AliExternalTrackParam::PropagateToDCABxByBz(const AliVVertex *vtx,
Double_t b[3], Double_t maxd, Double_t dz[2], Double_t covar[3]) {
Double_t alpha=GetAlpha();
Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha);
Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2];
Double_t xv= vtx->GetX()*cs + vtx->GetY()*sn;
Double_t yv=-vtx->GetX()*sn + vtx->GetY()*cs, zv=vtx->GetZ();
x-=xv; y-=yv;
Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt((1.-snp)*(1.+snp)));
if (d > maxd) return kFALSE;
Double_t crv=GetC(b[2]);
if (TMath::Abs(b[2]) < kAlmost0Field) crv=0.;
Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt((1.-snp)*(1.+snp)));
sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt((1.-sn)*(1.+sn));
if (TMath::Abs(tgfv)>0.) cs = sn/tgfv;
else cs=1.;
x = xv*cs + yv*sn;
yv=-xv*sn + yv*cs; xv=x;
if (!PropagateBxByBz(alpha+TMath::ASin(sn),xv,b)) return kFALSE;
if (dz==0) return kTRUE;
dz[0] = GetParameter()[0] - yv;
dz[1] = GetParameter()[1] - zv;
if (covar==0) return kTRUE;
Double_t cov[6]; vtx->GetCovarianceMatrix(cov);
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;
covar[1] = GetCovariance()[1];
covar[2] = GetCovariance()[2] + cov[5];
return kTRUE;
}
void AliExternalTrackParam::GetDirection(Double_t d[3]) const {
Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
Double_t snp=fP[2];
Double_t csp =TMath::Sqrt((1.-snp)*(1.+snp));
Double_t 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[3]) const {
p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3];
return Local2GlobalMomentum(p,fAlpha);
}
Double_t AliExternalTrackParam::Px() const {
Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
GetPxPyPz(p);
return p[0];
}
Double_t AliExternalTrackParam::Py() const {
Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
GetPxPyPz(p);
return p[1];
}
Double_t AliExternalTrackParam::Xv() const {
Double_t r[3]={0.,0.,0.};
GetXYZ(r);
return r[0];
}
Double_t AliExternalTrackParam::Yv() const {
Double_t r[3]={0.,0.,0.};
GetXYZ(r);
return r[1];
}
Double_t AliExternalTrackParam::Theta() const {
return 0.5*TMath::Pi() - TMath::ATan(fP[3]);
}
Double_t AliExternalTrackParam::Phi() const {
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::PhiPos() const {
Double_t r[3]={0.,0.,0.};
GetXYZ(r);
Double_t phi=TMath::ATan2(r[1],r[0]);
if (phi<0.) phi+=2.*TMath::Pi();
return phi;
}
Double_t AliExternalTrackParam::M() const {
return -999.;
}
Double_t AliExternalTrackParam::E() const {
return -999.;
}
Double_t AliExternalTrackParam::Eta() const {
return -TMath::Log(TMath::Tan(0.5 * Theta()));
}
Double_t AliExternalTrackParam::Y() const {
return -999.;
}
Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const {
r[0]=fX; r[1]=fP[0]; r[2]=fP[1];
return Local2GlobalPosition(r,fAlpha);
}
Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const {
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];
m43*=GetSign();
m44*=GetSign();
m45*=GetSign();
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 {
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 {
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)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+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 {
Double_t dx=x-fX;
if(TMath::Abs(dx)<=kAlmost0) {z=fP[1]; return kTRUE;}
Double_t crv=GetC(b);
Double_t x2r = crv*dx;
Double_t f1=fP[2], f2=f1 + x2r;
if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
Double_t r1=sqrt((1.-f1)*(1.+f1)), r2=sqrt((1.-f2)*(1.+f2));
double dy2dx = (f1+f2)/(r1+r2);
if (TMath::Abs(x2r)<0.05) {
z = fP[1] + dx*(r2 + f2*dy2dx)*fP[3];
}
else {
double chord = dx*TMath::Sqrt(1+dy2dx*dy2dx);
double rot = 2*TMath::ASin(0.5*chord*crv);
z = fP[1] + rot/crv*fP[3];
}
return kTRUE;
}
Bool_t
AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const {
Double_t dx=x-fX;
if(TMath::Abs(dx)<=kAlmost0) return GetXYZ(r);
Double_t crv=GetC(b);
Double_t x2r = crv*dx;
Double_t f1=fP[2], f2=f1 + dx*crv;
if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2));
double dy2dx = (f1+f2)/(r1+r2);
r[0] = x;
r[1] = fP[0] + dx*dy2dx;
if (TMath::Abs(x2r)<0.05) {
r[2] = fP[1] + dx*(r2 + f2*dy2dx)*fP[3];
}
else {
double chord = dx*TMath::Sqrt(1+dy2dx*dy2dx);
double rot = 2*TMath::ASin(0.5*chord*crv);
r[2] = fP[1] + rot/crv*fP[3];
}
return Local2GlobalPosition(r,fAlpha);
}
void AliExternalTrackParam::Print(Option_t* ) const
{
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 {
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){
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;
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;
}
void AliExternalTrackParam::DrawTrack(Float_t magf, Float_t minR, Float_t maxR, Float_t stepR){
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){
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]);
counter++;
}
}
Int_t AliExternalTrackParam::GetIndex(Int_t i, Int_t j) const {
Int_t min = TMath::Min(i,j);
Int_t max = TMath::Max(i,j);
return min+(max+1)*max/2;
}
void AliExternalTrackParam::g3helx3(Double_t qfield,
Double_t step,
Double_t vect[7]) {
const Int_t ix=0, iy=1, iz=2, ipx=3, ipy=4, ipz=5, ipp=6;
const Double_t kOvSqSix=TMath::Sqrt(1./6.);
Double_t cosx=vect[ipx], cosy=vect[ipy], cosz=vect[ipz];
Double_t rho = qfield*kB2C/vect[ipp];
Double_t tet = rho*step;
Double_t tsint, sintt, sint, cos1t;
if (TMath::Abs(tet) > 0.03) {
sint = TMath::Sin(tet);
sintt = sint/tet;
tsint = (tet - sint)/tet;
Double_t t=TMath::Sin(0.5*tet);
cos1t = 2*t*t/tet;
} else {
tsint = tet*tet/6.;
sintt = (1.-tet*kOvSqSix)*(1.+tet*kOvSqSix);
sint = tet*sintt;
cos1t = 0.5*tet;
}
Double_t f1 = step*sintt;
Double_t f2 = step*cos1t;
Double_t f3 = step*tsint*cosz;
Double_t f4 = -tet*cos1t;
Double_t f5 = sint;
vect[ix] += f1*cosx - f2*cosy;
vect[iy] += f1*cosy + f2*cosx;
vect[iz] += f1*cosz + f3;
vect[ipx] += f4*cosx - f5*cosy;
vect[ipy] += f4*cosy + f5*cosx;
}
Bool_t AliExternalTrackParam::PropagateToBxByBz(Double_t xk, const Double_t b[3]) {
Double_t dx=xk-fX;
if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
if (TMath::Abs(fP[4])<=kAlmost0) return kFALSE;
if (TMath::Abs(dx)>1e5 ||
TMath::Abs(GetY())>1e5 ||
TMath::Abs(GetZ())>1e5) {
AliWarning(Form("Anomalous track, target X:%f",xk));
Print();
return kFALSE;
}
Double_t crv=GetC(b[2]);
if (TMath::Abs(b[2]) < kAlmost0Field) crv=0.;
Double_t x2r = crv*dx;
Double_t f1=fP[2], f2=f1 + x2r;
if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
Double_t &fP3=fP[3], &fP4=fP[4];
Double_t
&fC00=fC[0],
&fC10=fC[1], &fC11=fC[2],
&fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
&fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
&fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2));
Double_t rinv = 1./r1;
Double_t r3inv = rinv*rinv*rinv;
Double_t f24= x2r/fP4;
Double_t f02= dx*r3inv;
Double_t f04=0.5*f24*f02;
Double_t f12= f02*fP3*f1;
Double_t f14=0.5*f24*f02*fP3*f1;
Double_t f13= dx*rinv;
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;
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;
fC00 += b00 + b00 + a00;
fC10 += b10 + b01 + a01;
fC20 += b20 + b02 + a02;
fC30 += b30;
fC40 += b40;
fC11 += b11 + b11 + a11;
fC21 += b21 + b12 + a12;
fC31 += b31;
fC41 += b41;
fC22 += b22 + b22 + a22;
fC32 += b32;
fC42 += b42;
CheckCovariance();
double dy2dx = (f1+f2)/(r1+r2);
Double_t step = (TMath::Abs(x2r)<0.05) ? dx*TMath::Abs(r2 + f2*dy2dx)
: 2.*TMath::ASin(0.5*dx*TMath::Sqrt(1.+dy2dx*dy2dx)*crv)/crv;
step *= TMath::Sqrt(1.+ GetTgl()*GetTgl());
Double_t r[3]; GetXYZ(r);
Double_t p[3]; GetPxPyPz(p);
Double_t pp=GetP();
p[0] /= pp;
p[1] /= pp;
p[2] /= pp;
Double_t bt=TMath::Sqrt(b[0]*b[0] + b[1]*b[1]);
Double_t cosphi=1., sinphi=0.;
if (bt > kAlmost0) {cosphi=b[0]/bt; sinphi=b[1]/bt;}
Double_t bb=TMath::Sqrt(b[0]*b[0] + b[1]*b[1] + b[2]*b[2]);
Double_t costet=1., sintet=0.;
if (bb > kAlmost0) {costet=b[2]/bb; sintet=bt/bb;}
Double_t vect[7];
vect[0] = costet*cosphi*r[0] + costet*sinphi*r[1] - sintet*r[2];
vect[1] = -sinphi*r[0] + cosphi*r[1];
vect[2] = sintet*cosphi*r[0] + sintet*sinphi*r[1] + costet*r[2];
vect[3] = costet*cosphi*p[0] + costet*sinphi*p[1] - sintet*p[2];
vect[4] = -sinphi*p[0] + cosphi*p[1];
vect[5] = sintet*cosphi*p[0] + sintet*sinphi*p[1] + costet*p[2];
vect[6] = pp;
g3helx3(GetSign()*bb,step,vect);
r[0] = cosphi*costet*vect[0] - sinphi*vect[1] + cosphi*sintet*vect[2];
r[1] = sinphi*costet*vect[0] + cosphi*vect[1] + sinphi*sintet*vect[2];
r[2] = -sintet*vect[0] + costet*vect[2];
p[0] = cosphi*costet*vect[3] - sinphi*vect[4] + cosphi*sintet*vect[5];
p[1] = sinphi*costet*vect[3] + cosphi*vect[4] + sinphi*sintet*vect[5];
p[2] = -sintet*vect[3] + costet*vect[5];
Double_t cosalp = TMath::Cos(fAlpha);
Double_t sinalp =-TMath::Sin(fAlpha);
Double_t
t = cosalp*r[0] - sinalp*r[1];
r[1] = sinalp*r[0] + cosalp*r[1];
r[0] = t;
t = cosalp*p[0] - sinalp*p[1];
p[1] = sinalp*p[0] + cosalp*p[1];
p[0] = t;
Double_t x=r[0], y=r[1], z=r[2];
if (TMath::Abs(dx) > kAlmost0) {
if (TMath::Abs(p[0]) < kAlmost0) return kFALSE;
dx = xk - r[0];
x += dx;
y += p[1]/p[0]*dx;
z += p[2]/p[0]*dx;
}
t=TMath::Sqrt(p[0]*p[0] + p[1]*p[1]);
fX = x;
fP[0] = y;
fP[1] = z;
fP[2] = p[1]/t;
fP[3] = p[2]/t;
fP[4] = GetSign()/(t*pp);
return kTRUE;
}
Bool_t AliExternalTrackParam::PropagateParamOnlyBxByBzTo(Double_t xk, const Double_t b[3]) {
Double_t dx=xk-fX;
if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
if (TMath::Abs(fP[4])<=kAlmost0) return kFALSE;
if (TMath::Abs(dx)>1e5 ||
TMath::Abs(GetY())>1e5 ||
TMath::Abs(GetZ())>1e5) {
AliWarning(Form("Anomalous track, target X:%f",xk));
Print();
return kFALSE;
}
Double_t crv=GetC(b[2]);
if (TMath::Abs(b[2]) < kAlmost0Field) crv=0.;
Double_t x2r = crv*dx;
Double_t f1=fP[2], f2=f1 + x2r;
if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
Double_t r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2));
double dy2dx = (f1+f2)/(r1+r2);
Double_t step = (TMath::Abs(x2r)<0.05) ? dx*TMath::Abs(r2 + f2*dy2dx)
: 2.*TMath::ASin(0.5*dx*TMath::Sqrt(1.+dy2dx*dy2dx)*crv)/crv;
step *= TMath::Sqrt(1.+ GetTgl()*GetTgl());
Double_t r[3]; GetXYZ(r);
Double_t p[3]; GetPxPyPz(p);
Double_t pp=GetP();
p[0] /= pp;
p[1] /= pp;
p[2] /= pp;
Double_t bt=TMath::Sqrt(b[0]*b[0] + b[1]*b[1]);
Double_t cosphi=1., sinphi=0.;
if (bt > kAlmost0) {cosphi=b[0]/bt; sinphi=b[1]/bt;}
Double_t bb=TMath::Sqrt(b[0]*b[0] + b[1]*b[1] + b[2]*b[2]);
Double_t costet=1., sintet=0.;
if (bb > kAlmost0) {costet=b[2]/bb; sintet=bt/bb;}
Double_t vect[7];
vect[0] = costet*cosphi*r[0] + costet*sinphi*r[1] - sintet*r[2];
vect[1] = -sinphi*r[0] + cosphi*r[1];
vect[2] = sintet*cosphi*r[0] + sintet*sinphi*r[1] + costet*r[2];
vect[3] = costet*cosphi*p[0] + costet*sinphi*p[1] - sintet*p[2];
vect[4] = -sinphi*p[0] + cosphi*p[1];
vect[5] = sintet*cosphi*p[0] + sintet*sinphi*p[1] + costet*p[2];
vect[6] = pp;
g3helx3(GetSign()*bb,step,vect);
r[0] = cosphi*costet*vect[0] - sinphi*vect[1] + cosphi*sintet*vect[2];
r[1] = sinphi*costet*vect[0] + cosphi*vect[1] + sinphi*sintet*vect[2];
r[2] = -sintet*vect[0] + costet*vect[2];
p[0] = cosphi*costet*vect[3] - sinphi*vect[4] + cosphi*sintet*vect[5];
p[1] = sinphi*costet*vect[3] + cosphi*vect[4] + sinphi*sintet*vect[5];
p[2] = -sintet*vect[3] + costet*vect[5];
Double_t cosalp = TMath::Cos(fAlpha);
Double_t sinalp =-TMath::Sin(fAlpha);
Double_t
t = cosalp*r[0] - sinalp*r[1];
r[1] = sinalp*r[0] + cosalp*r[1];
r[0] = t;
t = cosalp*p[0] - sinalp*p[1];
p[1] = sinalp*p[0] + cosalp*p[1];
p[0] = t;
Double_t x=r[0], y=r[1], z=r[2];
if (TMath::Abs(dx) > kAlmost0) {
if (TMath::Abs(p[0]) < kAlmost0) return kFALSE;
dx = xk - r[0];
x += dx;
y += p[1]/p[0]*dx;
z += p[2]/p[0]*dx;
}
t=TMath::Sqrt(p[0]*p[0] + p[1]*p[1]);
fX = x;
fP[0] = y;
fP[1] = z;
fP[2] = p[1]/t;
fP[3] = p[2]/t;
fP[4] = GetSign()/(t*pp);
return kTRUE;
}
Bool_t AliExternalTrackParam::Translate(Double_t *vTrasl,Double_t *covV){
TVector3 translation;
translation.SetXYZ(vTrasl[0],vTrasl[1],vTrasl[2]);
translation.RotateZ(-fAlpha);
translation.GetXYZ(vTrasl);
Double_t newX=fX-vTrasl[0];
Double_t newY=fP[0]-vTrasl[1];
Double_t newZ=fP[1]-vTrasl[2];
Double_t newParam[5];
newParam[0]=newY;
newParam[1]=newZ;
newParam[2]=fP[2];
newParam[3]=fP[3];
newParam[4]=fP[4];
Double_t cosRot=TMath::Cos(fAlpha), sinRot=TMath::Sin(fAlpha);
TMatrixD qQi(3,3);
qQi(0,0) = cosRot;
qQi(0,1) = sinRot;
qQi(0,2) = 0.;
qQi(1,0) = -sinRot;
qQi(1,1) = cosRot;
qQi(1,2) = 0.;
qQi(2,0) = 0.;
qQi(2,1) = 0.;
qQi(2,2) = 1.;
TMatrixD uUi(3,3);
uUi(0,0) = covV[0];
uUi(0,0) = covV[0];
uUi(1,0) = covV[1];
uUi(0,1) = covV[1];
uUi(2,0) = covV[3];
uUi(0,2) = covV[3];
uUi(1,1) = covV[2];
uUi(2,2) = covV[5];
uUi(1,2) = covV[4];
if(uUi.Determinant() <= 0.) {return kFALSE;}
TMatrixD uUiQi(uUi,TMatrixD::kMult,qQi);
TMatrixD m(qQi,TMatrixD::kTransposeMult,uUiQi);
Double_t sigmaXX=m(0,0);
Double_t sigmaXZ=m(2,0);
Double_t sigmaXY=m(1,0);
Double_t sigmaYY=GetSigmaY2()+m(1,1);
Double_t sigmaYZ=fC[1]+m(1,2);
Double_t sigmaZZ=fC[2]+m(2,2);
Double_t covarianceYY=sigmaYY + (-1.)*((sigmaXY*sigmaXY)/sigmaXX);
Double_t covarianceYZ=sigmaYZ-(sigmaXZ*sigmaXY/sigmaXX);
Double_t covarianceZZ=sigmaZZ-((sigmaXZ*sigmaXZ)/sigmaXX);
Double_t newCov[15];
newCov[0]=covarianceYY;
newCov[1]=covarianceYZ;
newCov[2]=covarianceZZ;
for(Int_t i=3;i<15;i++){
newCov[i]=fC[i];
}
Set(newX,fAlpha,newParam,newCov);
return kTRUE;
}
void AliExternalTrackParam::CheckCovariance() {
fC[0] = TMath::Abs(fC[0]);
if (fC[0]>kC0max) {
double scl = TMath::Sqrt(kC0max/fC[0]);
fC[0] = kC0max;
fC[1] *= scl;
fC[3] *= scl;
fC[6] *= scl;
fC[10] *= scl;
}
fC[2] = TMath::Abs(fC[2]);
if (fC[2]>kC2max) {
double scl = TMath::Sqrt(kC2max/fC[2]);
fC[2] = kC2max;
fC[1] *= scl;
fC[4] *= scl;
fC[7] *= scl;
fC[11] *= scl;
}
fC[5] = TMath::Abs(fC[5]);
if (fC[5]>kC5max) {
double scl = TMath::Sqrt(kC5max/fC[5]);
fC[5] = kC5max;
fC[3] *= scl;
fC[4] *= scl;
fC[8] *= scl;
fC[12] *= scl;
}
fC[9] = TMath::Abs(fC[9]);
if (fC[9]>kC9max) {
double scl = TMath::Sqrt(kC9max/fC[9]);
fC[9] = kC9max;
fC[6] *= scl;
fC[7] *= scl;
fC[8] *= scl;
fC[13] *= scl;
}
fC[14] = TMath::Abs(fC[14]);
if (fC[14]>kC14max) {
double scl = TMath::Sqrt(kC14max/fC[14]);
fC[14] = kC14max;
fC[10] *= scl;
fC[11] *= scl;
fC[12] *= scl;
fC[13] *= scl;
}
}
Bool_t AliExternalTrackParam::ConstrainToVertex(const AliVVertex* vtx, Double_t b[3])
{
if (!vtx)
return kFALSE;
Double_t dz[2], cov[3];
if (!PropagateToDCABxByBz(vtx, b, 3, dz, cov))
return kFALSE;
Double_t covar[6];
vtx->GetCovarianceMatrix(covar);
Double_t p[2]= { fP[0] - dz[0], fP[1] - dz[1] };
Double_t c[3]= { covar[2], 0., covar[5] };
Double_t chi2C = GetPredictedChi2(p,c);
if (chi2C>kVeryBig)
return kFALSE;
if (!Update(p,c))
return kFALSE;
return kTRUE;
}
Bool_t AliExternalTrackParam::GetXatLabR(Double_t r,Double_t &x, Double_t bz, Int_t dir) const
{
const Double_t &fy=fP[0], &sn = fP[2];
const double kEps = 1.e-6;
double crv = GetC(bz);
if (TMath::Abs(crv)>kAlmost0) {
double tR = 1./crv;
double cs = TMath::Sqrt((1-sn)*(1+sn));
double x0 = fX - sn*tR;
double y0 = fy + cs*tR;
double r0 = TMath::Sqrt(x0*x0+y0*y0);
if (r0<=kAlmost0) return kFALSE;
tR = TMath::Abs(tR);
double tR2r0=1.,g=0,tmp=0;
if (TMath::Abs(tR-r0)>kEps) {
tR2r0 = tR/r0;
g = 0.5*(r*r/(r0*tR) - tR2r0 - 1./tR2r0);
tmp = 1.+g*tR2r0;
}
else {
tR2r0 = 1.0;
g = 0.5*r*r/(r0*tR) - 1;
tmp = 0.5*r*r/(r0*r0);
}
double det = (1.-g)*(1.+g);
if (det<0) return kFALSE;
det = TMath::Sqrt(det);
x = x0*tmp;
double y = y0*tmp;
if (TMath::Abs(y0)>kAlmost0) {
double dfx = tR2r0*TMath::Abs(y0)*det;
double dfy = tR2r0*x0*TMath::Sign(det,y0);
if (dir==0) {
double delta = (x-fX)*dfx-(y-fy)*dfy;
if (delta<0) x += dfx;
else x -= dfx;
}
else if (dir>0) {
x -= dfx;
double dfeps = fX-x;
if (dfeps<-kEps) return kTRUE;
if (TMath::Abs(dfeps)<kEps &&
TMath::Abs(fX*fX+fy*fy - r*r)<kEps) return fX;
x += dfx+dfx;
if (x-fX>0) return kTRUE;
if (x-fX<-kEps) return kFALSE;
x = fX;
}
else {
x += dfx;
double dfeps = x-fX;
if (dfeps<-kEps) return kTRUE;
if (TMath::Abs(dfeps)<kEps &&
TMath::Abs(fX*fX+fy*fy - r*r)<kEps) return fX;
x-=dfx+dfx;
if (x-fX<0) return kTRUE;
if (x-fX>kEps) return kFALSE;
x = fX;
}
}
else {
if ( (dir>0&&x<fX) || (dir<0&&x>fX) ) return kFALSE;
}
}
else {
if (TMath::Abs(sn)>=kAlmost1) {
double det = (r-fX)*(r+fX);
if (det<0) return kFALSE;
x = fX;
if (dir==0) return kTRUE;
det = TMath::Sqrt(det);
if (dir>0) {
if (sn>0) {if (fy>det) return kFALSE;}
else {if (fy<-det) return kFALSE;}
}
else if(dir>0) {
if (sn>0) {if (fy<-det) return kFALSE;}
else if (fy>det) return kFALSE;
}
}
else if (TMath::Abs(sn)<=kAlmost0) {
double det = (r-fy)*(r+fy);
if (det<0) return kFALSE;
det = TMath::Sqrt(det);
if (!dir) {
x = fX>0 ? det : -det;
return kTRUE;
}
else if (dir>0) {
if (fX > det) return kFALSE;
else if (fX <-det) x = -det;
else x = det;
}
else {
if (fX <-det) return kFALSE;
else if (fX > det) x = det;
else x = -det;
}
}
else {
double cs = TMath::Sqrt((1-sn)*(1+sn));
double xsyc = fX*sn-fy*cs;
double det = (r-xsyc)*(r+xsyc);
if (det<0) return kFALSE;
det = TMath::Sqrt(det);
double xcys = fX*cs+fy*sn;
double t = -xcys;
if (dir==0) t += t>0 ? -det:det;
else if (dir>0) {
if (t>=-det) t += -det;
else return kFALSE;
}
else {
if (t<det) t -= det;
else return kFALSE;
}
x = fX + cs*t;
}
}
return kTRUE;
}
Bool_t AliExternalTrackParam::GetXYZatR(Double_t xr,Double_t bz, Double_t *xyz, Double_t* alpSect) const
{
double crv = GetC(bz);
if ( (TMath::Abs(bz))<kAlmost0Field ) crv=0.;
const double &fy = fP[0];
const double &fz = fP[1];
const double &sn = fP[2];
const double &tgl = fP[3];
double tR = 1./crv;
double cs = TMath::Sqrt((1-sn)*(1+sn));
double x0 = fX - sn*tR;
double y0 = fy + cs*tR;
double phi0 = TMath::ATan2(y0,x0);
if (tR<0) phi0 += TMath::Pi();
if (phi0 > TMath::Pi()) phi0 -= 2.*TMath::Pi();
else if (phi0 <-TMath::Pi()) phi0 += 2.*TMath::Pi();
double cs0 = TMath::Cos(phi0);
double sn0 = TMath::Sin(phi0);
double r0 = x0*cs0 + y0*sn0 - tR;
double r2R = 1.+r0/tR;
if (r2R<kAlmost0) return kFALSE;
if (!xyz && !alpSect) return kTRUE;
double xr2R = xr/tR;
double r2Ri = 1./r2R;
double cosT = 0.5*(r2R + (1-xr2R*xr2R)*r2Ri);
if ( TMath::Abs(cosT)>kAlmost1 ) {
return kFALSE;
}
double t = TMath::ACos(cosT);
if (tR<0) t = -t;
double xyzi[3];
xyzi[0] = x0 - tR*TMath::Cos(t+phi0);
xyzi[1] = y0 - tR*TMath::Sin(t+phi0);
if (xyz) {
double t0 = TMath::ATan2(cs,-sn) - phi0;
double z0 = fz - t0*tR*tgl;
xyzi[2] = z0 + tR*t*tgl;
}
else xyzi[2] = 0;
Local2GlobalPosition(xyzi,fAlpha);
if (xyz) {
xyz[0] = xyzi[0];
xyz[1] = xyzi[1];
xyz[2] = xyzi[2];
}
if (alpSect) {
double &alp = *alpSect;
double phiPos = TMath::Pi()+TMath::ATan2(-xyzi[1],-xyzi[0]);
int sect = ((Int_t)(phiPos*TMath::RadToDeg()))/20;
alp = TMath::DegToRad()*(20*sect+10);
double x2r,f1,f2,r1,r2,dx,dy2dx,yloc=0, ylocMax = xr*TMath::Tan(TMath::Pi()/18);
while(1) {
Double_t ca=TMath::Cos(alp-fAlpha), sa=TMath::Sin(alp-fAlpha);
if ((cs*ca+sn*sa)<0) {
AliDebug(1,Form("Rotation to target sector impossible: local cos(phi) would become %.2f",cs*ca+sn*sa));
return kFALSE;
}
f1 = sn*ca - cs*sa;
if (TMath::Abs(f1) >= kAlmost1) {
AliDebug(1,Form("Rotation to target sector impossible: local sin(phi) would become %.2f",f1));
return kFALSE;
}
double tmpX = fX*ca + fy*sa;
double tmpY = -fX*sa + fy*ca;
dx=xr-tmpX;
x2r = crv*dx;
f2=f1 + x2r;
if (TMath::Abs(f2) >= kAlmost1) {
AliDebug(1,Form("Propagation in target sector failed ! %.10e",f2));
return kFALSE;
}
r1 = TMath::Sqrt((1.-f1)*(1.+f1));
r2 = TMath::Sqrt((1.-f2)*(1.+f2));
dy2dx = (f1+f2)/(r1+r2);
yloc = tmpY + dx*dy2dx;
if (yloc>ylocMax) {alp += 2*TMath::Pi()/18; sect++;}
else if (yloc<-ylocMax) {alp -= 2*TMath::Pi()/18; sect--;}
else break;
if (alp >= TMath::Pi()) alp -= 2*TMath::Pi();
else if (alp < -TMath::Pi()) alp += 2*TMath::Pi();
}
if (xyz) {
xyz[0] = xr;
xyz[1] = yloc;
if (TMath::Abs(x2r)<0.05) xyz[2] = fz + dx*(r2 + f2*dy2dx)*tgl;
else {
double chord = dx*TMath::Sqrt(1+dy2dx*dy2dx);
double rot = 2*TMath::ASin(0.5*chord*crv);
xyz[2] = fz + rot/crv*tgl;
}
Local2GlobalPosition(xyz,alp);
}
}
return kTRUE;
}
Double_t AliExternalTrackParam::GetParameterAtRadius(Double_t r, Double_t bz, Int_t parType) const
{
if (parType<0) {
parType=-1;
return 0;
}
Double_t xyz[3];
Double_t pxyz[3];
Double_t localX=0;
Bool_t res = GetXatLabR(r,localX,bz,1);
if (!res) {
parType=-1;
return 0;
}
GetXYZAt(localX,bz,xyz);
if (parType<3) {
return xyz[parType];
}
if (parType==6) return TMath::Sqrt(xyz[0]*xyz[0]+xyz[1]*xyz[1]);
if (parType==7) return TMath::ATan2(xyz[1],xyz[0]);
GetPxPyPzAt(localX,bz,pxyz);
if (parType==8) return TMath::ATan2(pxyz[1],pxyz[0]);
if (parType==9) {
Double_t diff = TMath::ATan2(pxyz[1],pxyz[0])-TMath::ATan2(xyz[1],xyz[0]);
if (diff>TMath::Pi()) diff-=TMath::TwoPi();
if (diff<-TMath::Pi()) diff+=TMath::TwoPi();
return diff;
}
if (parType>=3&&parType<6) {
return pxyz[parType%3];
}
return 0;
}
AliExternalTrackParam.cxx:1 AliExternalTrackParam.cxx:2 AliExternalTrackParam.cxx:3 AliExternalTrackParam.cxx:4 AliExternalTrackParam.cxx:5 AliExternalTrackParam.cxx:6 AliExternalTrackParam.cxx:7 AliExternalTrackParam.cxx:8 AliExternalTrackParam.cxx:9 AliExternalTrackParam.cxx:10 AliExternalTrackParam.cxx:11 AliExternalTrackParam.cxx:12 AliExternalTrackParam.cxx:13 AliExternalTrackParam.cxx:14 AliExternalTrackParam.cxx:15 AliExternalTrackParam.cxx:16 AliExternalTrackParam.cxx:17 AliExternalTrackParam.cxx:18 AliExternalTrackParam.cxx:19 AliExternalTrackParam.cxx:20 AliExternalTrackParam.cxx:21 AliExternalTrackParam.cxx:22 AliExternalTrackParam.cxx:23 AliExternalTrackParam.cxx:24 AliExternalTrackParam.cxx:25 AliExternalTrackParam.cxx:26 AliExternalTrackParam.cxx:27 AliExternalTrackParam.cxx:28 AliExternalTrackParam.cxx:29 AliExternalTrackParam.cxx:30 AliExternalTrackParam.cxx:31 AliExternalTrackParam.cxx:32 AliExternalTrackParam.cxx:33 AliExternalTrackParam.cxx:34 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