//--------------------------------------------------------------------------------- // Implementation of the AliKFParticleBase class // . // @author S.Gorbunov, I.Kisel // @version 1.0 // @since 13.05.07 // // Class to reconstruct and store the decayed particle parameters. // The method is described in CBM-SOFT note 2007-003, // ``Reconstruction of decayed particles based on the Kalman filter'', // http://www.gsi.de/documents/DOC-2007-May-14-1.pdf // // This class describes general mathematics which is used by AliKFParticle class // // -= Copyright © ALICE HLT Group =- //_________________________________________________________________________________ #include "AliKFParticleBase.h" #include "TMath.h" ClassImp(AliKFParticleBase) AliKFParticleBase::AliKFParticleBase() :fQ(0), fNDF(-3), fChi2(0), fSFromDecay(0), fAtProductionVertex(0), fIsLinearized(0) { //* Constructor Initialize(); } void AliKFParticleBase::Initialize() { //* Initialise covariance matrix and set current parameters to 0.0 for( Int_t i=0; i<8; i++) fP[i] = 0; for(Int_t i=0;i<36;++i) fC[i]=0.; fC[0] = fC[2] = fC[5] = 100.; fC[35] = 1.; fNDF = -3; fChi2 = 0.; fQ = 0; fSFromDecay = 0; fAtProductionVertex = 0; fVtxGuess[0]=fVtxGuess[1]=fVtxGuess[2]=0.; fIsLinearized = 0; } void AliKFParticleBase::SetVtxGuess( Double_t x, Double_t y, Double_t z ) { //* Set decay vertex parameters for linearisation fVtxGuess[0] = x; fVtxGuess[1] = y; fVtxGuess[2] = z; fIsLinearized = 1; } Int_t AliKFParticleBase::GetMomentum( Double_t &P, Double_t &Error ) const { //* Calculate particle momentum Double_t x = fP[3]; Double_t y = fP[4]; Double_t z = fP[5]; Double_t x2 = x*x; Double_t y2 = y*y; Double_t z2 = z*z; Double_t p2 = x2+y2+z2; P = TMath::Sqrt(p2); Error = (x2*fC[9]+y2*fC[14]+z2*fC[20] + 2*(x*y*fC[13]+x*z*fC[18]+y*z*fC[19]) ); if( Error>0 && P>1.e-4 ){ Error = TMath::Sqrt(Error)/P; return 0; } return 1; } Int_t AliKFParticleBase::GetMass( Double_t &M, Double_t &Error ) const { //* Calculate particle mass // s = sigma^2 of m2/2 Double_t s = ( fP[3]*fP[3]*fC[9] + fP[4]*fP[4]*fC[14] + fP[5]*fP[5]*fC[20] + fP[6]*fP[6]*fC[27] +2*( + fP[3]*fP[4]*fC[13] + fP[5]*(fP[3]*fC[18] + fP[4]*fC[19]) - fP[6]*( fP[3]*fC[24] + fP[4]*fC[25] + fP[5]*fC[26] ) ) ); Double_t m2 = fP[6]*fP[6] - fP[3]*fP[3] - fP[4]*fP[4] - fP[5]*fP[5]; M = 0; if( m2>1.e-20 ){ M = TMath::Sqrt(m2); if( s>=0 ){ Error = TMath::Sqrt(s/m2); return 0; } } Error = 1.e20; return 1; } Int_t AliKFParticleBase::GetDecayLength( Double_t &L, Double_t &Error ) const { //* Calculate particle decay length [cm] Double_t x = fP[3]; Double_t y = fP[4]; Double_t z = fP[5]; Double_t t = fP[7]; Double_t x2 = x*x; Double_t y2 = y*y; Double_t z2 = z*z; Double_t p2 = x2+y2+z2; L = t*TMath::Sqrt(p2); if( p2>1.e-4){ Error = p2*fC[35] + t*t/p2*(x2*fC[9]+y2*fC[14]+z2*fC[20] + 2*(x*y*fC[13]+x*z*fC[18]+y*z*fC[19]) ) + 2*t*(x*fC[31]+y*fC[32]+z*fC[33]); Error = TMath::Sqrt(TMath::Abs(Error)); return 0; } Error = 1.e20; return 1; } Int_t AliKFParticleBase::GetLifeTime( Double_t &TauC, Double_t &Error ) const { //* Calculate particle decay time [s] Double_t m, dm; GetMass( m, dm ); Double_t cTM = (-fP[3]*fC[31] - fP[4]*fC[32] - fP[5]*fC[33] + fP[6]*fC[34]); TauC = fP[7]*m; Error = m*m*fC[35] + 2*fP[7]*cTM + fP[7]*fP[7]*dm*dm; if( Error > 0 ){ Error = TMath::Sqrt( Error ); return 0; } Error = 1.e20; return 1; } void AliKFParticleBase::operator +=( const AliKFParticleBase &Daughter ) { //* Add daughter via operator+= AddDaughter( Daughter ); } void AliKFParticleBase::GetMeasurement( const Double_t XYZ[], Double_t m[], Double_t V[] ) const { Double_t b[3]; GetFieldValue( XYZ, b ); const Double_t kCLight = 0.000299792458; b[0]*=kCLight; b[1]*=kCLight; b[2]*=kCLight; Transport( GetDStoPoint(XYZ), m, V ); Double_t d[3] = { XYZ[0]-m[0], XYZ[1]-m[1], XYZ[2]-m[2] }; Double_t sigmaS = 1.+10.*TMath::Sqrt( (d[0]*d[0]+d[1]*d[1]+d[2]*d[2])/ (m[3]*m[3]+m[4]*m[4]+m[5]*m[5]) ); Double_t h[6]; h[0] = m[3]*sigmaS; h[1] = m[4]*sigmaS; h[2] = m[5]*sigmaS; h[3] = ( h[1]*b[2]-h[2]*b[1] )*GetQ(); h[4] = ( h[2]*b[0]-h[0]*b[2] )*GetQ(); h[5] = ( h[0]*b[1]-h[1]*b[0] )*GetQ(); //* Fit of momentum (Px,Py,Pz) to XYZ point if(0){ Double_t mVv[6] = { V[ 0] + h[0]*h[0], V[ 1] + h[0]*h[1], V[ 2] + h[1]*h[1], V[ 3] + h[0]*h[2], V[ 4] + h[1]*h[2], V[ 5] + h[2]*h[2] }; Double_t mVvp[9]= { V[ 6] + h[0]*h[3], V[ 7] + h[1]*h[3], V[ 8] + h[2]*h[3], V[10] + h[0]*h[4], V[11] + h[1]*h[4], V[12] + h[2]*h[4], V[15] + h[0]*h[5], V[16] + h[1]*h[5], V[17] + h[2]*h[5] }; Double_t mS[6] = { mVv[2]*mVv[5] - mVv[4]*mVv[4], mVv[3]*mVv[4] - mVv[1]*mVv[5], mVv[0]*mVv[5] - mVv[3]*mVv[3], mVv[1]*mVv[4] - mVv[2]*mVv[3], mVv[1]*mVv[3] - mVv[0]*mVv[4], mVv[0]*mVv[2] - mVv[1]*mVv[1] }; Double_t s = ( mVv[0]*mS[0] + mVv[1]*mS[1] + mVv[3]*mS[3] ); s = ( s > 1.E-20 ) ?1./s :0; Double_t mSz[3] = { mS[0]*d[0]+mS[1]*d[1]+mS[3]*d[2], mS[1]*d[0]+mS[2]*d[1]+mS[4]*d[2], mS[3]*d[0]+mS[4]*d[1]+mS[5]*d[2] }; Double_t px = m[3] + s*( mVvp[0]*mSz[0] + mVvp[1]*mSz[1] + mVvp[2]*mSz[2] ); Double_t py = m[4] + s*( mVvp[3]*mSz[0] + mVvp[4]*mSz[1] + mVvp[5]*mSz[2] ); Double_t pz = m[5] + s*( mVvp[6]*mSz[0] + mVvp[7]*mSz[1] + mVvp[8]*mSz[2] ); h[0] = px*sigmaS; h[1] = py*sigmaS; h[2] = pz*sigmaS; h[3] = ( h[1]*b[2]-h[2]*b[1] )*GetQ(); h[4] = ( h[2]*b[0]-h[0]*b[2] )*GetQ(); h[5] = ( h[0]*b[1]-h[1]*b[0] )*GetQ(); } V[ 0]+= h[0]*h[0]; V[ 1]+= h[1]*h[0]; V[ 2]+= h[1]*h[1]; V[ 3]+= h[2]*h[0]; V[ 4]+= h[2]*h[1]; V[ 5]+= h[2]*h[2]; V[ 6]+= h[3]*h[0]; V[ 7]+= h[3]*h[1]; V[ 8]+= h[3]*h[2]; V[ 9]+= h[3]*h[3]; V[10]+= h[4]*h[0]; V[11]+= h[4]*h[1]; V[12]+= h[4]*h[2]; V[13]+= h[4]*h[3]; V[14]+= h[4]*h[4]; V[15]+= h[5]*h[0]; V[16]+= h[5]*h[1]; V[17]+= h[5]*h[2]; V[18]+= h[5]*h[3]; V[19]+= h[5]*h[4]; V[20]+= h[5]*h[5]; } void AliKFParticleBase::AddDaughter( const AliKFParticleBase &Daughter ) { //* Add daughter if( fNDF<-1 ){ // first daughter -> just copy fNDF = -1; fQ = Daughter.GetQ(); for( Int_t i=0; i<7; i++) fP[i] = Daughter.fP[i]; for( Int_t i=0; i<28; i++) fC[i] = Daughter.fC[i]; fSFromDecay = 0; return; } TransportToDecayVertex(); Double_t b[3]; Int_t maxIter = 1; if( !fIsLinearized ){ if( fNDF==-1 ){ Double_t ds, ds1; GetDStoParticle(Daughter, ds, ds1); TransportToDS( ds ); Double_t m[8]; Double_t mCd[36]; Daughter.Transport( ds1, m, mCd ); fVtxGuess[0] = .5*( fP[0] + m[0] ); fVtxGuess[1] = .5*( fP[1] + m[1] ); fVtxGuess[2] = .5*( fP[2] + m[2] ); } else { fVtxGuess[0] = fP[0]; fVtxGuess[1] = fP[1]; fVtxGuess[2] = fP[2]; } maxIter = 3; } for( Int_t iter=0; iter 1.E-20 ) ?1./s :0; mS[0]*=s; mS[1]*=s; mS[2]*=s; mS[3]*=s; mS[4]*=s; mS[5]*=s; } //* Residual (measured - estimated) Double_t zeta[3] = { m[0]-ffP[0], m[1]-ffP[1], m[2]-ffP[2] }; //* CHt = CH' - D' Double_t mCHt0[7], mCHt1[7], mCHt2[7]; mCHt0[0]=ffC[ 0] ; mCHt1[0]=ffC[ 1] ; mCHt2[0]=ffC[ 3] ; mCHt0[1]=ffC[ 1] ; mCHt1[1]=ffC[ 2] ; mCHt2[1]=ffC[ 4] ; mCHt0[2]=ffC[ 3] ; mCHt1[2]=ffC[ 4] ; mCHt2[2]=ffC[ 5] ; mCHt0[3]=ffC[ 6]-mV[ 6]; mCHt1[3]=ffC[ 7]-mV[ 7]; mCHt2[3]=ffC[ 8]-mV[ 8]; mCHt0[4]=ffC[10]-mV[10]; mCHt1[4]=ffC[11]-mV[11]; mCHt2[4]=ffC[12]-mV[12]; mCHt0[5]=ffC[15]-mV[15]; mCHt1[5]=ffC[16]-mV[16]; mCHt2[5]=ffC[17]-mV[17]; mCHt0[6]=ffC[21]-mV[21]; mCHt1[6]=ffC[22]-mV[22]; mCHt2[6]=ffC[23]-mV[23]; //* Kalman gain K = mCH'*S Double_t k0[7], k1[7], k2[7]; for(Int_t i=0;i<7;++i){ k0[i] = mCHt0[i]*mS[0] + mCHt1[i]*mS[1] + mCHt2[i]*mS[3]; k1[i] = mCHt0[i]*mS[1] + mCHt1[i]*mS[2] + mCHt2[i]*mS[4]; k2[i] = mCHt0[i]*mS[3] + mCHt1[i]*mS[4] + mCHt2[i]*mS[5]; } //* New estimation of the vertex position if( iter update the particle //* Add the daughter momentum to the particle momentum ffP[ 3] += m[ 3]; ffP[ 4] += m[ 4]; ffP[ 5] += m[ 5]; ffP[ 6] += m[ 6]; ffC[ 9] += mV[ 9]; ffC[13] += mV[13]; ffC[14] += mV[14]; ffC[18] += mV[18]; ffC[19] += mV[19]; ffC[20] += mV[20]; ffC[24] += mV[24]; ffC[25] += mV[25]; ffC[26] += mV[26]; ffC[27] += mV[27]; //* New estimation of the vertex position r += K*zeta for(Int_t i=0;i<7;++i) fP[i] = ffP[i] + k0[i]*zeta[0] + k1[i]*zeta[1] + k2[i]*zeta[2]; //* New covariance matrix C -= K*(mCH')' for(Int_t i=0, k=0;i<7;++i){ for(Int_t j=0;j<=i;++j,++k) fC[k] = ffC[k] - (k0[i]*mCHt0[j] + k1[i]*mCHt1[j] + k2[i]*mCHt2[j] ); } //* Calculate Chi^2 fNDF += 2; fQ += Daughter.GetQ(); fSFromDecay = 0; fChi2 += (mS[0]*zeta[0] + mS[1]*zeta[1] + mS[3]*zeta[2])*zeta[0] + (mS[1]*zeta[0] + mS[2]*zeta[1] + mS[4]*zeta[2])*zeta[1] + (mS[3]*zeta[0] + mS[4]*zeta[1] + mS[5]*zeta[2])*zeta[2]; } } void AliKFParticleBase::SetProductionVertex( const AliKFParticleBase &Vtx ) { //* Set production vertex for the particle const Double_t *m = Vtx.fP, *mV = Vtx.fC; TransportToDS( GetDStoPoint( m ) ); fP[7] = -fSFromDecay; Convert(1); Double_t mAi[6]; mAi[0] = fC[4]*fC[4] - fC[2]*fC[5]; mAi[1] = fC[1]*fC[5] - fC[3]*fC[4]; mAi[3] = fC[2]*fC[3] - fC[1]*fC[4]; Double_t det = 1./(fC[0]*mAi[0] + fC[1]*mAi[1] + fC[3]*mAi[3]); mAi[0] *= det; mAi[1] *= det; mAi[3] *= det; mAi[2] = ( fC[3]*fC[3] - fC[0]*fC[5] )*det; mAi[4] = ( fC[0]*fC[4] - fC[1]*fC[3] )*det; mAi[5] = ( fC[1]*fC[1] - fC[0]*fC[2] )*det; Double_t mB[5][3]; mB[0][0] = fC[ 6]*mAi[0] + fC[ 7]*mAi[1] + fC[ 8]*mAi[3]; mB[0][1] = fC[ 6]*mAi[1] + fC[ 7]*mAi[2] + fC[ 8]*mAi[4]; mB[0][2] = fC[ 6]*mAi[3] + fC[ 7]*mAi[4] + fC[ 8]*mAi[5]; mB[1][0] = fC[10]*mAi[0] + fC[11]*mAi[1] + fC[12]*mAi[3]; mB[1][1] = fC[10]*mAi[1] + fC[11]*mAi[2] + fC[12]*mAi[4]; mB[1][2] = fC[10]*mAi[3] + fC[11]*mAi[4] + fC[12]*mAi[5]; mB[2][0] = fC[15]*mAi[0] + fC[16]*mAi[1] + fC[17]*mAi[3]; mB[2][1] = fC[15]*mAi[1] + fC[16]*mAi[2] + fC[17]*mAi[4]; mB[2][2] = fC[15]*mAi[3] + fC[16]*mAi[4] + fC[17]*mAi[5]; mB[3][0] = fC[21]*mAi[0] + fC[22]*mAi[1] + fC[23]*mAi[3]; mB[3][1] = fC[21]*mAi[1] + fC[22]*mAi[2] + fC[23]*mAi[4]; mB[3][2] = fC[21]*mAi[3] + fC[22]*mAi[4] + fC[23]*mAi[5]; mB[4][0] = fC[28]*mAi[0] + fC[29]*mAi[1] + fC[30]*mAi[3]; mB[4][1] = fC[28]*mAi[1] + fC[29]*mAi[2] + fC[30]*mAi[4]; mB[4][2] = fC[28]*mAi[3] + fC[29]*mAi[4] + fC[30]*mAi[5]; Double_t z[3] = { m[0]-fP[0], m[1]-fP[1], m[2]-fP[2] }; { Double_t mAV[6] = { fC[0]-mV[0], fC[1]-mV[1], fC[2]-mV[2], fC[3]-mV[3], fC[4]-mV[4], fC[5]-mV[5] }; Double_t mAVi[6]; mAVi[0] = mAV[4]*mAV[4] - mAV[2]*mAV[5]; mAVi[1] = mAV[1]*mAV[5] - mAV[3]*mAV[4]; mAVi[2] = mAV[3]*mAV[3] - mAV[0]*mAV[5] ; mAVi[3] = mAV[2]*mAV[3] - mAV[1]*mAV[4]; mAVi[4] = mAV[0]*mAV[4] - mAV[1]*mAV[3] ; mAVi[5] = mAV[1]*mAV[1] - mAV[0]*mAV[2] ; det = 1./( mAV[0]*mAVi[0] + mAV[1]*mAVi[1] + mAV[3]*mAVi[3] ); fNDF += 2; fChi2 += ( +(mAVi[0]*z[0] + mAVi[1]*z[1] + mAVi[3]*z[2])*z[0] +(mAVi[1]*z[0] + mAVi[2]*z[1] + mAVi[4]*z[2])*z[1] +(mAVi[3]*z[0] + mAVi[4]*z[1] + mAVi[5]*z[2])*z[2] )*det; } fP[0] = m[0]; fP[1] = m[1]; fP[2] = m[2]; fP[3]+= mB[0][0]*z[0] + mB[0][1]*z[1] + mB[0][2]*z[2]; fP[4]+= mB[1][0]*z[0] + mB[1][1]*z[1] + mB[1][2]*z[2]; fP[5]+= mB[2][0]*z[0] + mB[2][1]*z[1] + mB[2][2]*z[2]; fP[6]+= mB[3][0]*z[0] + mB[3][1]*z[1] + mB[3][2]*z[2]; fP[7]+= mB[4][0]*z[0] + mB[4][1]*z[1] + mB[4][2]*z[2]; Double_t d0, d1, d2; fC[0] = mV[0]; fC[1] = mV[1]; fC[2] = mV[2]; fC[3] = mV[3]; fC[4] = mV[4]; fC[5] = mV[5]; d0= mB[0][0]*mV[0] + mB[0][1]*mV[1] + mB[0][2]*mV[3] - fC[ 6]; d1= mB[0][0]*mV[1] + mB[0][1]*mV[2] + mB[0][2]*mV[4] - fC[ 7]; d2= mB[0][0]*mV[3] + mB[0][1]*mV[4] + mB[0][2]*mV[5] - fC[ 8]; fC[ 6]+= d0; fC[ 7]+= d1; fC[ 8]+= d2; fC[ 9]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2]; d0= mB[1][0]*mV[0] + mB[1][1]*mV[1] + mB[1][2]*mV[3] - fC[10]; d1= mB[1][0]*mV[1] + mB[1][1]*mV[2] + mB[1][2]*mV[4] - fC[11]; d2= mB[1][0]*mV[3] + mB[1][1]*mV[4] + mB[1][2]*mV[5] - fC[12]; fC[10]+= d0; fC[11]+= d1; fC[12]+= d2; fC[13]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2]; fC[14]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2]; d0= mB[2][0]*mV[0] + mB[2][1]*mV[1] + mB[2][2]*mV[3] - fC[15]; d1= mB[2][0]*mV[1] + mB[2][1]*mV[2] + mB[2][2]*mV[4] - fC[16]; d2= mB[2][0]*mV[3] + mB[2][1]*mV[4] + mB[2][2]*mV[5] - fC[17]; fC[15]+= d0; fC[16]+= d1; fC[17]+= d2; fC[18]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2]; fC[19]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2]; fC[20]+= d0*mB[2][0] + d1*mB[2][1] + d2*mB[2][2]; d0= mB[3][0]*mV[0] + mB[3][1]*mV[1] + mB[3][2]*mV[3] - fC[21]; d1= mB[3][0]*mV[1] + mB[3][1]*mV[2] + mB[3][2]*mV[4] - fC[22]; d2= mB[3][0]*mV[3] + mB[3][1]*mV[4] + mB[3][2]*mV[5] - fC[23]; fC[21]+= d0; fC[22]+= d1; fC[23]+= d2; fC[24]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2]; fC[25]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2]; fC[26]+= d0*mB[2][0] + d1*mB[2][1] + d2*mB[2][2]; fC[27]+= d0*mB[3][0] + d1*mB[3][1] + d2*mB[3][2]; d0= mB[4][0]*mV[0] + mB[4][1]*mV[1] + mB[4][2]*mV[3] - fC[28]; d1= mB[4][0]*mV[1] + mB[4][1]*mV[2] + mB[4][2]*mV[4] - fC[29]; d2= mB[4][0]*mV[3] + mB[4][1]*mV[4] + mB[4][2]*mV[5] - fC[30]; fC[28]+= d0; fC[29]+= d1; fC[30]+= d2; fC[31]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2]; fC[32]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2]; fC[33]+= d0*mB[2][0] + d1*mB[2][1] + d2*mB[2][2]; fC[34]+= d0*mB[3][0] + d1*mB[3][1] + d2*mB[3][2]; fC[35]+= d0*mB[4][0] + d1*mB[4][1] + d2*mB[4][2]; TransportToDS( fP[7] ); fSFromDecay = 0; Convert(0); } void AliKFParticleBase::SetMassConstraint( Double_t Mass ) { //* Set hard mass constraint Double_t mH[8]; mH[0] = mH[1] = mH[2] = 0.; mH[3] = -2*fP[3]; mH[4] = -2*fP[4]; mH[5] = -2*fP[5]; mH[6] = 2*fP[6]; mH[7] = 0; Double_t m2 = ( fP[6]*fP[6] - fP[3]*fP[3] - fP[4]*fP[4] - fP[5]*fP[5] ); Double_t zeta = Mass*Mass - m2; for(Int_t i=0;i<8;++i) zeta -= mH[i]*(fP[i]-fP[i]); Double_t s = 0.; Double_t mCHt[8]; for (Int_t i=0;i<8;++i ){ mCHt[i] = 0.0; for (Int_t j=0;j<8;++j) mCHt[i] += Cij(i,j)*mH[j]; s += mH[i]*mCHt[i]; } if( s<1.e-20 ) return; s = 1./s; fChi2 += zeta*zeta*s; fNDF += 1; for( Int_t i=0, ii=0; i<8; ++i ){ Double_t ki = mCHt[i]*s; fP[i]+= ki*zeta; for(Int_t j=0;j<=i;++j) fC[ii++] -= ki*mCHt[j]; } } void AliKFParticleBase::Construct( const AliKFParticleBase* vDaughters[], Int_t NDaughters, const AliKFParticleBase *Parent, Double_t Mass ) { //* Full reconstruction in one go Int_t maxIter = 1; bool wasLinearized = fIsLinearized; if( !fIsLinearized ){ //fVtxGuess[0] = fVtxGuess[1] = fVtxGuess[2] = 0; //!!!! fVtxGuess[0] = GetX(); fVtxGuess[1] = GetY(); fVtxGuess[2] = GetZ(); fIsLinearized = 1; maxIter = 3; } for( Int_t iter=0; iter=0 ) SetMassConstraint( Mass ); if( Parent ) SetProductionVertex( *Parent ); } void AliKFParticleBase::Convert( bool ToProduction ) { //* Tricky function - convert the particle error along its trajectory to //* the value which corresponds to its production/decay vertex //* It is done by combination of the error of decay length with the position errors Double_t fld[3]; { GetFieldValue( fP, fld ); const Double_t kCLight = fQ*0.000299792458; fld[0]*=kCLight; fld[1]*=kCLight; fld[2]*=kCLight; } Double_t h[6]; h[0] = fP[3]; h[1] = fP[4]; h[2] = fP[5]; if( ToProduction ){ h[0]=-h[0]; h[1]=-h[1]; h[2]=-h[2]; } h[3] = h[1]*fld[2]-h[2]*fld[1]; h[4] = h[2]*fld[0]-h[0]*fld[2]; h[5] = h[0]*fld[1]-h[1]*fld[0]; Double_t c; c = fC[28]+h[0]*fC[35]; fC[ 0]+= h[0]*(c+fC[28]); fC[28] = c; fC[ 1]+= h[1]*fC[28] + h[0]*fC[29]; c = fC[29]+h[1]*fC[35]; fC[ 2]+= h[1]*(c+fC[29]); fC[29] = c; fC[ 3]+= h[2]*fC[28] + h[0]*fC[30]; fC[ 4]+= h[2]*fC[29] + h[1]*fC[30]; c = fC[30]+h[2]*fC[35]; fC[ 5]+= h[2]*(c+fC[30]); fC[30] = c; fC[ 6]+= h[3]*fC[28] + h[0]*fC[31]; fC[ 7]+= h[3]*fC[29] + h[1]*fC[31]; fC[ 8]+= h[3]*fC[30] + h[2]*fC[31]; c = fC[31]+h[3]*fC[35]; fC[ 9]+= h[3]*(c+fC[31]); fC[31] = c; fC[10]+= h[4]*fC[28] + h[0]*fC[32]; fC[11]+= h[4]*fC[29] + h[1]*fC[32]; fC[12]+= h[4]*fC[30] + h[2]*fC[32]; fC[13]+= h[4]*fC[31] + h[3]*fC[32]; c = fC[32]+h[4]*fC[35]; fC[14]+= h[4]*(c+fC[32]); fC[32] = c; fC[15]+= h[5]*fC[28] + h[0]*fC[33]; fC[16]+= h[5]*fC[29] + h[1]*fC[33]; fC[17]+= h[5]*fC[30] + h[2]*fC[33]; fC[18]+= h[5]*fC[31] + h[3]*fC[33]; fC[19]+= h[5]*fC[32] + h[4]*fC[33]; c = fC[33]+h[5]*fC[35]; fC[20]+= h[5]*(c+fC[33]); fC[33] = c; fC[21]+= h[0]*fC[34]; fC[22]+= h[1]*fC[34]; fC[23]+= h[2]*fC[34]; fC[24]+= h[3]*fC[34]; fC[25]+= h[4]*fC[34]; fC[26]+= h[5]*fC[34]; } void AliKFParticleBase::TransportToDecayVertex() { //* Transport the particle to its decay vertex if( fSFromDecay != 0 ) TransportToDS( -fSFromDecay ); if( fAtProductionVertex ) Convert(0); fAtProductionVertex = 0; } void AliKFParticleBase::TransportToProductionVertex() { //* Transport the particle to its production vertex if( fSFromDecay != -fP[7] ) TransportToDS( -fSFromDecay-fP[7] ); if( !fAtProductionVertex ) Convert( 1 ); fAtProductionVertex = 1; } void AliKFParticleBase::TransportToDS( Double_t dS ) { //* Transport the particle on dS parameter (SignedPath/Momentum) Transport( dS, fP, fC ); fSFromDecay+= dS; } Double_t AliKFParticleBase::GetDStoPointLine( const Double_t xyz[] ) const { //* Get dS to a certain space point without field Double_t p2 = fP[3]*fP[3] + fP[4]*fP[4] + fP[5]*fP[5]; if( p2<1.e-4 ) p2 = 1; return ( fP[3]*(xyz[0]-fP[0]) + fP[4]*(xyz[1]-fP[1]) + fP[5]*(xyz[2]-fP[2]) )/p2; } Double_t AliKFParticleBase::GetDStoPointBz( Double_t B, const Double_t xyz[] ) const { //* Get dS to a certain space point for Bz field const Double_t kCLight = 0.000299792458; Double_t bq = B*fQ*kCLight; Double_t pt2 = fP[3]*fP[3] + fP[4]*fP[4]; if( pt2<1.e-4 ) return 0; Double_t dx = xyz[0] - fP[0]; Double_t dy = xyz[1] - fP[1]; Double_t a = dx*fP[3]+dy*fP[4]; if( TMath::Abs(bq)<1.e-8 ) return a/pt2; return TMath::ATan2( bq*a, pt2 + bq*(dy*fP[3] -dx*fP[4]) )/bq; } void AliKFParticleBase::GetDStoParticleBz( Double_t B, const AliKFParticleBase &p, Double_t &DS, Double_t &DS1 ) const { //* Get dS to another particle for Bz field Double_t px = fP[3]; Double_t py = fP[4]; Double_t pz = fP[5]; Double_t px1 = p.fP[3]; Double_t py1 = p.fP[4]; Double_t pz1 = p.fP[5]; const Double_t kCLight = 0.000299792458; Double_t bq = B*fQ*kCLight; Double_t bq1 = B*p.fQ*kCLight; Double_t s=0, ds=0, s1=0, ds1=0; if( TMath::Abs(bq)>1.e-8 || TMath::Abs(bq1)>1.e-8 ){ Double_t dx = (p.fP[0] - fP[0]); Double_t dy = (p.fP[1] - fP[1]); Double_t d2 = (dx*dx+dy*dy); Double_t p2 = (px *px + py *py); Double_t p21 = (px1*px1 + py1*py1); Double_t a = (px*py1 - py*px1); Double_t b = (px*px1 + py*py1); Double_t ldx = bq*bq1*dx - bq1*py + bq*py1 ; Double_t ldy = bq*bq1*dy + bq1*px - bq*px1 ; Double_t l2 = ldx*ldx + ldy*ldy; Double_t cS = bq1*p2 + bq*bq1*(dy* px - dx* py) - bq*b; Double_t cS1= bq*p21 - bq*bq1*(dy*px1 - dx*py1) - bq1*b; Double_t ca = bq*bq*bq1*d2 +2*( cS + bq*bq*(py1*dx-px1*dy)) ; Double_t ca1 = bq*bq1*bq1*d2 +2*( cS1 - bq1*bq1*(py*dx-px*dy)) ; Double_t sa = 4*l2*p2 - ca*ca; Double_t sa1 = 4*l2*p21 - ca1*ca1; if(sa<0) sa=0; if(sa1<0)sa1=0; if( TMath::Abs(bq)>1.e-8){ s = TMath::ATan2( bq*( bq1*(dx*px +dy*py) + a ) , cS )/bq; ds = TMath::ATan2(TMath::Sqrt(sa),ca)/bq; } else { s = ( (dx*px + dy*py) + (py*px1-px*py1)/bq1)/p2; ds = s*s - (d2-2*(px1*dy-py1*dx)/bq1)/p2; if( ds<0 ) ds = 0; ds = TMath::Sqrt(ds); } if( TMath::Abs(bq1)>1.e-8){ s1 = TMath::ATan2( -bq1*( bq*(dx*px1+dy*py1) + a), cS1 )/bq1; ds1 = TMath::ATan2(TMath::Sqrt(sa1),ca1)/bq1; } else { s1 = (-(dx*px1 + dy*py1) + (py*px1-px*py1)/bq)/p21; ds1 = s1*s1 - (d2+2*(px*dy-py*dx)/bq)/p21; if( ds1<0 ) ds1 = 0; ds1 = TMath::Sqrt(ds1); } } Double_t ss[2], ss1[2], g[2][5],g1[2][5]; ss[0] = s + ds; ss[1] = s - ds; ss1[0] = s1 + ds1; ss1[1] = s1 - ds1; for( Int_t i=0; i<2; i++){ Double_t bs = bq*ss[i]; Double_t c = TMath::Cos(bs), s = TMath::Sin(bs); Double_t cB,sB; if( TMath::Abs(bq)>1.e-8){ cB= (1-c)/bq; sB= s/bq; }else{ sB = (1. - bs*bs/6.)*ss[i]; cB = .5*sB*bs; } g[i][0] = fP[0] + sB*px + cB*py; g[i][1] = fP[1] - cB*px + sB*py; g[i][2] = fP[2] + ss[i]*pz; g[i][3] = + c*px + s*py; g[i][4] = - s*px + c*py; bs = bq1*ss1[i]; c = TMath::Cos(bs); s = TMath::Sin(bs); if( TMath::Abs(bq1)>1.e-8){ cB= (1-c)/bq1; sB= s/bq1; }else{ sB = (1. - bs*bs/6.)*ss1[i]; cB = .5*sB*bs; } g[i][0] = p.fP[0] + sB*px1 + cB*py1; g[i][1] = p.fP[1] - cB*px1 + sB*py1; g[i][2] = p.fP[2] + ss[i]*pz1; g[i][3] = + c*px1 + s*py1; g[i][4] = - s*px1 + c*py1; } Int_t i=0, i1=0; Double_t dMin = 1.e10; for( Int_t j=0; j<2; j++){ for( Int_t j1=0; j1<2; j1++){ Double_t xx = g[j][0]-g1[j1][0]; Double_t yy = g[j][1]-g1[j1][1]; Double_t zz = g[j][2]-g1[j1][2]; Double_t d = xx*xx + yy*yy + zz*zz; if( d1.e-8 ){ DS+=(a*b-pp21*c)/det; DS1+=(a*c-pp2*b)/det; } } void AliKFParticleBase::TransportCBM( Double_t dS, Double_t P[], Double_t C[] ) const { //* Transport the particle on dS, output to P[],C[], for CBM field if( fQ==0 ){ TransportLine( dS, P, C ); return; } const Double_t kCLight = 0.000299792458; Double_t c = fQ*kCLight; // construct coefficients Double_t px = fP[3], py = fP[4], pz = fP[5]; Double_t sx=0, sy=0, sz=0, syy=0, syz=0, syyy=0, ssx=0, ssy=0, ssz=0, ssyy=0, ssyz=0, ssyyy=0; { // get field integrals Double_t fld[3][3]; Double_t p0[3], p1[3], p2[3]; // line track approximation p0[0] = fP[0]; p0[1] = fP[1]; p0[2] = fP[2]; p2[0] = fP[0] + px*dS; p2[1] = fP[1] + py*dS; p2[2] = fP[2] + pz*dS; p1[0] = 0.5*(p0[0]+p2[0]); p1[1] = 0.5*(p0[1]+p2[1]); p1[2] = 0.5*(p0[2]+p2[2]); // first order track approximation { GetFieldValue( p0, fld[0] ); GetFieldValue( p1, fld[1] ); GetFieldValue( p2, fld[2] ); Double_t ssy1 = ( 7*fld[0][1] + 6*fld[1][1]-fld[2][1] )*c*dS*dS/96.; Double_t ssy2 = ( fld[0][1] + 2*fld[1][1] )*c*dS*dS/6.; p1[0] -= ssy1*pz; p1[2] += ssy1*px; p2[0] -= ssy2*pz; p2[2] += ssy2*px; } GetFieldValue( p0, fld[0] ); GetFieldValue( p1, fld[1] ); GetFieldValue( p2, fld[2] ); sx = c*( fld[0][0] + 4*fld[1][0] + fld[2][0] )*dS/6.; sy = c*( fld[0][1] + 4*fld[1][1] + fld[2][1] )*dS/6.; sz = c*( fld[0][2] + 4*fld[1][2] + fld[2][2] )*dS/6.; ssx = c*( fld[0][0] + 2*fld[1][0])*dS*dS/6.; ssy = c*( fld[0][1] + 2*fld[1][1])*dS*dS/6.; ssz = c*( fld[0][2] + 2*fld[1][2])*dS*dS/6.; Double_t c2[3][3] = { { 5, -4, -1},{ 44, 80, -4},{ 11, 44, 5} }; // /=360. Double_t cc2[3][3] = { { 38, 8, -4},{ 148, 208, -20},{ 3, 36, 3} }; // /=2520. for(Int_t n=0; n<3; n++) for(Int_t m=0; m<3; m++) { syz += c2[n][m]*fld[n][1]*fld[m][2]; ssyz += cc2[n][m]*fld[n][1]*fld[m][2]; } syz *= c*c*dS*dS/360.; ssyz *= c*c*dS*dS*dS/2520.; syy = c*( fld[0][1] + 4*fld[1][1] + fld[2][1] )*dS; syyy = syy*syy*syy / 1296; syy = syy*syy/72; ssyy = ( fld[0][1]*( 38*fld[0][1] + 156*fld[1][1] - fld[2][1] )+ fld[1][1]*( 208*fld[1][1] +16*fld[2][1] )+ fld[2][1]*( 3*fld[2][1] ) )*dS*dS*dS*c*c/2520.; ssyyy = ( fld[0][1]*( fld[0][1]*( 85*fld[0][1] + 526*fld[1][1] - 7*fld[2][1] )+ fld[1][1]*( 1376*fld[1][1] +84*fld[2][1] )+ fld[2][1]*( 19*fld[2][1] ) )+ fld[1][1]*( fld[1][1]*( 1376*fld[1][1] +256*fld[2][1] )+ fld[2][1]*( 62*fld[2][1] ) )+ fld[2][1]*fld[2][1] *( 3*fld[2][1] ) )*dS*dS*dS*dS*c*c*c/90720.; } Double_t mJ[8][8]; for( Int_t i=0; i<8; i++ ) for( Int_t j=0; j<8; j++) mJ[i][j]=0; mJ[0][0]=1; mJ[0][1]=0; mJ[0][2]=0; mJ[0][3]=dS-ssyy; mJ[0][4]=ssx; mJ[0][5]=ssyyy-ssy; mJ[1][0]=0; mJ[1][1]=1; mJ[1][2]=0; mJ[1][3]=-ssz; mJ[1][4]=dS; mJ[1][5]=ssx+ssyz; mJ[2][0]=0; mJ[2][1]=0; mJ[2][2]=1; mJ[2][3]=ssy-ssyyy; mJ[2][4]=-ssx; mJ[2][5]=dS-ssyy; mJ[3][0]=0; mJ[3][1]=0; mJ[3][2]=0; mJ[3][3]=1-syy; mJ[3][4]=sx; mJ[3][5]=syyy-sy; mJ[4][0]=0; mJ[4][1]=0; mJ[4][2]=0; mJ[4][3]=-sz; mJ[4][4]=1; mJ[4][5]=sx+syz; mJ[5][0]=0; mJ[5][1]=0; mJ[5][2]=0; mJ[5][3]=sy-syyy; mJ[5][4]=-sx; mJ[5][5]=1-syy; mJ[6][6] = mJ[7][7] = 1; P[0] = fP[0] + mJ[0][3]*px + mJ[0][4]*py + mJ[0][5]*pz; P[1] = fP[1] + mJ[1][3]*px + mJ[1][4]*py + mJ[1][5]*pz; P[2] = fP[2] + mJ[2][3]*px + mJ[2][4]*py + mJ[2][5]*pz; P[3] = mJ[3][3]*px + mJ[3][4]*py + mJ[3][5]*pz; P[4] = mJ[4][3]*px + mJ[4][4]*py + mJ[4][5]*pz; P[5] = mJ[5][3]*px + mJ[5][4]*py + mJ[5][5]*pz; P[6] = fP[6]; P[7] = fP[7]; MultQSQt( mJ[0], fC, C); } void AliKFParticleBase::TransportBz( Double_t B, Double_t S, Double_t P[], Double_t C[] ) const { //* Transport the particle on dS, output to P[],C[], for Bz field const Double_t kCLight = 0.000299792458; B = B*fQ*kCLight; Double_t bs= B*S; Double_t s = TMath::Sin(bs), c = TMath::Cos(bs); Double_t sB, cB; if( TMath::Abs(bs)>1.e-10){ sB= s/B; cB= (1-c)/B; }else{ sB = (1. - bs*bs/6.)*S; cB = .5*sB*bs; } Double_t px = fP[3]; Double_t py = fP[4]; Double_t pz = fP[5]; P[0] = fP[0] + sB*px + cB*py; P[1] = fP[1] - cB*px + sB*py; P[2] = fP[2] + S*pz; P[3] = c*px + s*py; P[4] = -s*px + c*py; P[5] = fP[5]; P[6] = fP[6]; P[7] = fP[7]; Double_t mJ[8][8] = { {1,0,0, sB, cB, 0, 0, 0 }, {0,1,0, -cB, sB, 0, 0, 0 }, {0,0,1, 0, 0, S, 0, 0 }, {0,0,0, c, s, 0, 0, 0 }, {0,0,0, -s, c, 0, 0, 0 }, {0,0,0, 0, 0, 1, 0, 0 }, {0,0,0, 0, 0, 0, 1, 0 }, {0,0,0, 0, 0, 0, 0, 1 } }; Double_t mA[8][8]; for( Int_t k=0,i=0; i<8; i++) for( Int_t j=0; j<=i; j++, k++ ) mA[i][j] = mA[j][i] = fC[k]; Double_t mJC[8][8]; for( Int_t i=0; i<8; i++ ) for( Int_t j=0; j<8; j++ ){ mJC[i][j]=0; for( Int_t k=0; k<8; k++ ) mJC[i][j]+=mJ[i][k]*mA[k][j]; } for( Int_t k=0,i=0; i<8; i++) for( Int_t j=0; j<=i; j++, k++ ){ C[k] = 0; for( Int_t l=0; l<8; l++ ) C[k]+=mJC[i][l]*mJ[j][l]; } return; /* Double_t cBC13 = cB*fC[13]; Double_t C17 = fC[17]; Double_t C18 = fC[18]; fC[ 0]+= 2*(sB*fC[ 6] + cB*fC[10]) + (sB*fC[ 9] + 2*cBC13)*sB + cB*cB*fC[14]; Double_t mJC13= fC[ 7] - cB*fC[ 9] + sB*fC[13]; Double_t mJC14= fC[11] - cBC13 + sB*fC[14]; fC[ 1]+= -cB*fC[ 6] + sB*fC[10] +mJC13*sB +mJC14*cB; fC[ 2]+= -cB*fC[ 7] + sB*fC[11] -mJC13*cB +mJC14*sB; Double_t mJC23= fC[ 8] + S*fC[18]; Double_t mJC24= fC[12] + S*fC[19]; fC[ 3]+= S*fC[15] +mJC23*sB +mJC24*cB; fC[ 4]+= S*fC[16] -mJC23*cB +mJC24*sB; fC[15]+= C18*sB + fC[19]*cB; fC[16]+= -C18*cB + fC[19]*sB; fC[17]+= fC[20]*S; fC[18] = C18*c + fC[19]*s; fC[19] = -C18*s + fC[19]*c; fC[ 5]+= (C17 + C17 + fC[17])*S; Double_t mJC33= c*fC[ 9] + s*fC[13]; Double_t mJC34= c*fC[13] + s*fC[14]; Double_t mJC43=-s*fC[ 9] + c*fC[13]; Double_t mJC44=-s*fC[13] + c*fC[14]; Double_t C6= fC[6], C7= fC[7], C8= fC[8]; fC[ 6]= c*C6 + s*fC[10] +mJC33*sB +mJC34*cB; fC[ 7]= c*C7 + s*fC[11] -mJC33*cB +mJC34*sB; fC[ 8]= c*C8 + s*fC[12] +fC[18]*S; fC[ 9]= mJC33*c +mJC34*s; fC[10]= -s*C6 + c*fC[10] +mJC43*sB +mJC44*cB; fC[11]= -s*C7 + c*fC[11] -mJC43*cB +mJC44*sB; fC[12]= -s*C8 + c*fC[12] +fC[19]*S; fC[13]= mJC43*c +mJC44*s; fC[14]=-mJC43*s +mJC44*c; */ } Double_t AliKFParticleBase::GetDistanceFromVertex( const AliKFParticleBase &Vtx ) const { //* Calculate distance from vertex [cm] return GetDistanceFromVertex( Vtx.fP ); } Double_t AliKFParticleBase::GetDistanceFromVertex( const Double_t vtx[] ) const { //* Calculate distance from vertex [cm] Double_t mP[8], mC[36]; Transport( GetDStoPoint(vtx), mP, mC ); Double_t d[3]={ vtx[0]-mP[0], vtx[1]-mP[1], vtx[2]-mP[2]}; return TMath::Sqrt( d[0]*d[0]+d[1]*d[1]+d[2]*d[2] ); } Double_t AliKFParticleBase::GetDistanceFromParticle( const AliKFParticleBase &p ) const { //* Calculate distance to other particle [cm] Double_t dS, dS1; GetDStoParticle( p, dS, dS1 ); Double_t mP[8], mC[36], mP1[8], mC1[36]; Transport( dS, mP, mC ); p.Transport( dS1, mP1, mC1 ); Double_t dx = mP[0]-mP1[0]; Double_t dy = mP[1]-mP1[1]; Double_t dz = mP[2]-mP1[2]; return TMath::Sqrt(dx*dx+dy*dy+dz*dz); } Double_t AliKFParticleBase::GetDeviationFromVertex( const AliKFParticleBase &Vtx ) const { //* Calculate sqrt(Chi2/ndf) deviation from vertex return GetDeviationFromVertex( Vtx.fP, Vtx.fC ); } Double_t AliKFParticleBase::GetDeviationFromVertex( const Double_t v[], const Double_t Cv[] ) const { //* Calculate sqrt(Chi2/ndf) deviation from vertex //* v = [xyz], Cv=[Cxx,Cxy,Cyy,Cxz,Cyz,Czz]-covariance matrix Double_t mP[8]; Double_t mC[36]; Transport( GetDStoPoint(v), mP, mC ); Double_t d[3]={ v[0]-mP[0], v[1]-mP[1], v[2]-mP[2]}; Double_t sigmaS = .1+10.*TMath::Sqrt( (d[0]*d[0]+d[1]*d[1]+d[2]*d[2])/ (mP[3]*mP[3]+mP[4]*mP[4]+mP[5]*mP[5]) ); Double_t h[3] = { mP[3]*sigmaS, mP[4]*sigmaS, mP[5]*sigmaS }; Double_t mSi[6] = { mC[0] +h[0]*h[0], mC[1] +h[1]*h[0], mC[2] +h[1]*h[1], mC[3] +h[2]*h[0], mC[4] +h[2]*h[1], mC[5] +h[2]*h[2] }; if( Cv ){ mSi[0]+=Cv[0]; mSi[1]+=Cv[1]; mSi[2]+=Cv[2]; mSi[3]+=Cv[3]; mSi[4]+=Cv[4]; mSi[5]+=Cv[5]; } Double_t mS[6]; mS[0] = mSi[2]*mSi[5] - mSi[4]*mSi[4]; mS[1] = mSi[3]*mSi[4] - mSi[1]*mSi[5]; mS[2] = mSi[0]*mSi[5] - mSi[3]*mSi[3]; mS[3] = mSi[1]*mSi[4] - mSi[2]*mSi[3]; mS[4] = mSi[1]*mSi[3] - mSi[0]*mSi[4]; mS[5] = mSi[0]*mSi[2] - mSi[1]*mSi[1]; Double_t s = ( mSi[0]*mS[0] + mSi[1]*mS[1] + mSi[3]*mS[3] ); s = ( s > 1.E-20 ) ?1./s :0; return TMath::Sqrt( TMath::Abs(s*( ( mS[0]*d[0] + mS[1]*d[1] + mS[3]*d[2])*d[0] +(mS[1]*d[0] + mS[2]*d[1] + mS[4]*d[2])*d[1] +(mS[3]*d[0] + mS[4]*d[1] + mS[5]*d[2])*d[2] ))/2); } Double_t AliKFParticleBase::GetDeviationFromParticle( const AliKFParticleBase &p ) const { //* Calculate sqrt(Chi2/ndf) deviation from other particle Double_t dS, dS1; GetDStoParticle( p, dS, dS1 ); Double_t mP1[8], mC1[36]; p.Transport( dS1, mP1, mC1 ); Double_t d[3]={ fP[0]-mP1[0], fP[1]-mP1[1], fP[2]-mP1[2]}; Double_t sigmaS = .1+10.*TMath::Sqrt( (d[0]*d[0]+d[1]*d[1]+d[2]*d[2])/ (mP1[3]*mP1[3]+mP1[4]*mP1[4]+mP1[5]*mP1[5]) ); Double_t h[3] = { mP1[3]*sigmaS, mP1[4]*sigmaS, mP1[5]*sigmaS }; mC1[0] +=h[0]*h[0]; mC1[1] +=h[1]*h[0]; mC1[2] +=h[1]*h[1]; mC1[3] +=h[2]*h[0]; mC1[4] +=h[2]*h[1]; mC1[5] +=h[2]*h[2]; return GetDeviationFromVertex( mP1, mC1 )*TMath::Sqrt(2./1.); } void AliKFParticleBase::SubtractFromVertex( Double_t v[], Double_t Cv[], Double_t &vChi2, Int_t vNDF ) const { //* Subtract the particle from the vertex Double_t fld[3]; { GetFieldValue( v, fld ); const Double_t kCLight = 0.000299792458; fld[0]*=kCLight; fld[1]*=kCLight; fld[2]*=kCLight; } Double_t m[8]; Double_t mCm[36]; Transport( GetDStoPoint(v), m, mCm ); Double_t d[3] = { v[0]-m[0], v[1]-m[1], v[2]-m[2] }; Double_t sigmaS = .1+10.*TMath::Sqrt( (d[0]*d[0]+d[1]*d[1]+d[2]*d[2])/ (m[3]*m[3]+m[4]*m[4]+m[5]*m[5]) ); Double_t h[6]; h[0] = m[3]*sigmaS; h[1] = m[4]*sigmaS; h[2] = m[5]*sigmaS; h[3] = ( h[1]*fld[2]-h[2]*fld[1] )*GetQ(); h[4] = ( h[2]*fld[0]-h[0]*fld[2] )*GetQ(); h[5] = ( h[0]*fld[1]-h[1]*fld[0] )*GetQ(); //* Fit of daughter momentum (Px,Py,Pz) to fVtxGuess vertex { Double_t zeta[3] = { v[0]-m[0], v[1]-m[1], v[2]-m[2] }; Double_t mVv[6] = { mCm[ 0] + h[0]*h[0], mCm[ 1] + h[1]*h[0], mCm[ 2] + h[1]*h[1], mCm[ 3] + h[2]*h[0], mCm[ 4] + h[2]*h[1], mCm[ 5] + h[2]*h[2] }; Double_t mVvp[9]= { mCm[ 6] + h[0]*h[3], mCm[ 7] + h[1]*h[3], mCm[ 8] + h[2]*h[3], mCm[10] + h[0]*h[4], mCm[11] + h[1]*h[4], mCm[12] + h[2]*h[4], mCm[15] + h[0]*h[5], mCm[16] + h[1]*h[5], mCm[17] + h[2]*h[5] }; Double_t mS[6] = { mVv[2]*mVv[5] - mVv[4]*mVv[4], mVv[3]*mVv[4] - mVv[1]*mVv[5], mVv[0]*mVv[5] - mVv[3]*mVv[3], mVv[1]*mVv[4] - mVv[2]*mVv[3], mVv[1]*mVv[3] - mVv[0]*mVv[4], mVv[0]*mVv[2] - mVv[1]*mVv[1] }; Double_t s = ( mVv[0]*mS[0] + mVv[1]*mS[1] + mVv[3]*mS[3] ); s = ( s > 1.E-20 ) ?1./s :0; mS[0]*=s; mS[1]*=s; mS[2]*=s; mS[3]*=s; mS[4]*=s; mS[5]*=s; Double_t mSz[3] = { (mS[0]*zeta[0]+mS[1]*zeta[1]+mS[3]*zeta[2]), (mS[1]*zeta[0]+mS[2]*zeta[1]+mS[4]*zeta[2]), (mS[3]*zeta[0]+mS[4]*zeta[1]+mS[5]*zeta[2]) }; Double_t px = m[3] + mVvp[0]*mSz[0] + mVvp[1]*mSz[1] + mVvp[2]*mSz[2]; Double_t py = m[4] + mVvp[3]*mSz[0] + mVvp[4]*mSz[1] + mVvp[5]*mSz[2]; Double_t pz = m[5] + mVvp[6]*mSz[0] + mVvp[7]*mSz[1] + mVvp[8]*mSz[2]; h[0] = px*sigmaS; h[1] = py*sigmaS; h[2] = pz*sigmaS; h[3] = ( h[1]*fld[2]-h[2]*fld[1] )*GetQ(); h[4] = ( h[2]*fld[0]-h[0]*fld[2] )*GetQ(); h[5] = ( h[0]*fld[1]-h[1]*fld[0] )*GetQ(); } Double_t mV[6]; mV[ 0] = mCm[ 0] + h[0]*h[0]; mV[ 1] = mCm[ 1] + h[1]*h[0]; mV[ 2] = mCm[ 2] + h[1]*h[1]; mV[ 3] = mCm[ 3] + h[2]*h[0]; mV[ 4] = mCm[ 4] + h[2]*h[1]; mV[ 5] = mCm[ 5] + h[2]*h[2]; //* Double_t mS[6]; { Double_t mSi[6] = { mV[0]-Cv[0], mV[1]-Cv[1], mV[2]-Cv[2], mV[3]-Cv[3], mV[4]-Cv[4], mV[5]-Cv[5] }; mS[0] = mSi[2]*mSi[5] - mSi[4]*mSi[4]; mS[1] = mSi[3]*mSi[4] - mSi[1]*mSi[5]; mS[2] = mSi[0]*mSi[5] - mSi[3]*mSi[3]; mS[3] = mSi[1]*mSi[4] - mSi[2]*mSi[3]; mS[4] = mSi[1]*mSi[3] - mSi[0]*mSi[4]; mS[5] = mSi[0]*mSi[2] - mSi[1]*mSi[1]; Double_t s = ( mSi[0]*mS[0] + mSi[1]*mS[1] + mSi[3]*mS[3] ); s = ( s > 1.E-20 ) ?1./s :0; mS[0]*=s; mS[1]*=s; mS[2]*=s; mS[3]*=s; mS[4]*=s; mS[5]*=s; } //* Residual (measured - estimated) Double_t zeta[3] = { m[0]-v[0], m[1]-v[1], m[2]-v[2] }; //* mCHt = mCH' - D' Double_t mCHt0[3], mCHt1[3], mCHt2[3]; mCHt0[0]=Cv[ 0] ; mCHt1[0]=Cv[ 1] ; mCHt2[0]=Cv[ 3] ; mCHt0[1]=Cv[ 1] ; mCHt1[1]=Cv[ 2] ; mCHt2[1]=Cv[ 4] ; mCHt0[2]=Cv[ 3] ; mCHt1[2]=Cv[ 4] ; mCHt2[2]=Cv[ 5] ; //* Kalman gain K = mCH'*S Double_t k0[3], k1[3], k2[3]; for(Int_t i=0;i<3;++i){ k0[i] = mCHt0[i]*mS[0] + mCHt1[i]*mS[1] + mCHt2[i]*mS[3]; k1[i] = mCHt0[i]*mS[1] + mCHt1[i]*mS[2] + mCHt2[i]*mS[4]; k2[i] = mCHt0[i]*mS[3] + mCHt1[i]*mS[4] + mCHt2[i]*mS[5]; } //* New estimation of the vertex position r += K*zeta for(Int_t i=0;i<3;++i) v[i] -= k0[i]*zeta[0] + k1[i]*zeta[1] + k2[i]*zeta[2]; //* New covariance matrix C -= K*(mCH')' for(Int_t i=0, k=0;i<3;++i){ for(Int_t j=0;j<=i;++j,++k) Cv[k] += k0[i]*mCHt0[j] + k1[i]*mCHt1[j] + k2[i]*mCHt2[j]; } //* Calculate Chi^2 vNDF -= 2; vChi2 -= (mS[0]*zeta[0] + mS[1]*zeta[1] + mS[3]*zeta[2])*zeta[0] + (mS[1]*zeta[0] + mS[2]*zeta[1] + mS[4]*zeta[2])*zeta[1] + (mS[3]*zeta[0] + mS[4]*zeta[1] + mS[5]*zeta[2])*zeta[2]; } void AliKFParticleBase::TransportLine( Double_t dS, Double_t P[], Double_t C[] ) const { //* Transport the particle as a straight line P[0] = fP[0] + dS*fP[3]; P[1] = fP[1] + dS*fP[4]; P[2] = fP[2] + dS*fP[5]; P[3] = fP[3]; P[4] = fP[4]; P[5] = fP[5]; P[6] = fP[6]; P[7] = fP[7]; Double_t c6 = fC[ 6] + dS*fC[ 9]; Double_t c11 = fC[11] + dS*fC[14]; Double_t c17 = fC[17] + dS*fC[20]; Double_t sc13 = dS*fC[13]; Double_t sc18 = dS*fC[18]; Double_t sc19 = dS*fC[19]; C[ 0] = fC[ 0] + dS*( fC[ 6] + c6 ); C[ 2] = fC[ 2] + dS*( fC[11] + c11 ); C[ 5] = fC[ 5] + dS*( fC[17] + c17 ); C[ 7] = fC[ 7] + sc13; C[ 8] = fC[ 8] + sc18; C[ 9] = fC[ 9]; C[12] = fC[12] + sc19; C[ 1] = fC[ 1] + dS*( fC[10] + C[ 7] ); C[ 3] = fC[ 3] + dS*( fC[15] + C[ 8] ); C[ 4] = fC[ 4] + dS*( fC[16] + C[12] ); C[ 6] = c6; C[10] = fC[10] + sc13; C[11] = c11; C[13] = fC[13]; C[14] = fC[14]; C[15] = fC[15] + sc18; C[16] = fC[16] + sc19; C[17] = c17; C[18] = fC[18]; C[19] = fC[19]; C[20] = fC[20]; C[21] = fC[21] + dS*fC[24]; C[22] = fC[22] + dS*fC[25]; C[23] = fC[23] + dS*fC[26]; C[24] = fC[24]; C[25] = fC[25]; C[26] = fC[26]; C[27] = fC[27]; C[28] = fC[28] + dS*fC[31]; C[29] = fC[29] + dS*fC[32]; C[30] = fC[30] + dS*fC[33]; C[31] = fC[31]; C[32] = fC[32]; C[33] = fC[33]; C[34] = fC[34]; C[35] = fC[35]; } void AliKFParticleBase::MultQSQt( const Double_t Q[], const Double_t S[], Double_t SOut[] ) { //* Matrix multiplication Q*S*Q^T, Q - square matrix, S - symmetric const Int_t kN= 8; Double_t mA[kN*kN]; for( Int_t i=0, ij=0; i