+void AliKFParticleBase::ConstructGammaBz( const AliKFParticleBase &daughter1,
+ const AliKFParticleBase &daughter2, double Bz )
+{
+ //* Create gamma
+
+ const AliKFParticleBase *daughters[2] = { &daughter1, &daughter2};
+
+ double v0[3];
+
+ if( !fIsLinearized ){
+ Double_t ds, ds1;
+ Double_t m[8];
+ Double_t mCd[36];
+ daughter1.GetDStoParticle(daughter2, ds, ds1);
+ daughter1.Transport( ds, m, mCd );
+ fP[0] = m[0];
+ fP[1] = m[1];
+ fP[2] = m[2];
+ daughter2.Transport( ds1, m, mCd );
+ fP[0] = .5*( fP[0] + m[0] );
+ fP[1] = .5*( fP[1] + m[1] );
+ fP[2] = .5*( fP[2] + m[2] );
+ } else {
+ fP[0] = fVtxGuess[0];
+ fP[1] = fVtxGuess[1];
+ fP[2] = fVtxGuess[2];
+ }
+
+ double daughterP[2][8], daughterC[2][36];
+ double vtxMom[2][3];
+
+ int nIter = fIsLinearized ?1 :2;
+
+ for( int iter=0; iter<nIter; iter++){
+
+ v0[0] = fP[0];
+ v0[1] = fP[1];
+ v0[2] = fP[2];
+
+ fAtProductionVertex = 0;
+ fSFromDecay = 0;
+ fP[0] = v0[0];
+ fP[1] = v0[1];
+ fP[2] = v0[2];
+ fP[3] = 0;
+ fP[4] = 0;
+ fP[5] = 0;
+ fP[6] = 0;
+ fP[7] = 0;
+
+
+ // fit daughters to the vertex guess
+
+ {
+ for( int id=0; id<2; id++ ){
+
+ double *p = daughterP[id];
+ double *mC = daughterC[id];
+
+ daughters[id]->GetMeasurement( v0, p, mC );
+
+ Double_t mAi[6];
+ InvertSym3(mC, mAi );
+
+ Double_t mB[3][3];
+
+ mB[0][0] = mC[ 6]*mAi[0] + mC[ 7]*mAi[1] + mC[ 8]*mAi[3];
+ mB[0][1] = mC[ 6]*mAi[1] + mC[ 7]*mAi[2] + mC[ 8]*mAi[4];
+ mB[0][2] = mC[ 6]*mAi[3] + mC[ 7]*mAi[4] + mC[ 8]*mAi[5];
+
+ mB[1][0] = mC[10]*mAi[0] + mC[11]*mAi[1] + mC[12]*mAi[3];
+ mB[1][1] = mC[10]*mAi[1] + mC[11]*mAi[2] + mC[12]*mAi[4];
+ mB[1][2] = mC[10]*mAi[3] + mC[11]*mAi[4] + mC[12]*mAi[5];
+
+ mB[2][0] = mC[15]*mAi[0] + mC[16]*mAi[1] + mC[17]*mAi[3];
+ mB[2][1] = mC[15]*mAi[1] + mC[16]*mAi[2] + mC[17]*mAi[4];
+ mB[2][2] = mC[15]*mAi[3] + mC[16]*mAi[4] + mC[17]*mAi[5];
+
+ Double_t z[3] = { v0[0]-p[0], v0[1]-p[1], v0[2]-p[2] };
+
+ vtxMom[id][0] = p[3] + mB[0][0]*z[0] + mB[0][1]*z[1] + mB[0][2]*z[2];
+ vtxMom[id][1] = p[4] + mB[1][0]*z[0] + mB[1][1]*z[1] + mB[1][2]*z[2];
+ vtxMom[id][2] = p[5] + mB[2][0]*z[0] + mB[2][1]*z[1] + mB[2][2]*z[2];
+
+ daughters[id]->Transport( daughters[id]->GetDStoPoint(v0), p, mC );
+
+ }
+
+ } // fit daughters to guess
+
+
+ // fit new vertex
+ {
+
+ double mpx0 = vtxMom[0][0]+vtxMom[1][0];
+ double mpy0 = vtxMom[0][1]+vtxMom[1][1];
+ double mpt0 = TMath::Sqrt(mpx0*mpx0 + mpy0*mpy0);
+ // double a0 = TMath::ATan2(mpy0,mpx0);
+
+ double ca0 = mpx0/mpt0;
+ double sa0 = mpy0/mpt0;
+ double r[3] = { v0[0], v0[1], v0[2] };
+ double mC[3][3] = {{10000., 0 , 0 },
+ {0, 10000., 0 },
+ {0, 0, 10000. } };
+ double chi2=0;
+
+ for( int id=0; id<2; id++ ){
+ const Double_t kCLight = 0.000299792458;
+ Double_t q = Bz*daughters[id]->GetQ()*kCLight;
+ Double_t px0 = vtxMom[id][0];
+ Double_t py0 = vtxMom[id][1];
+ Double_t pz0 = vtxMom[id][2];
+ Double_t pt0 = TMath::Sqrt(px0*px0+py0*py0);
+ Double_t mG[3][6], mB[3], mH[3][3];
+ // r = {vx,vy,vz};
+ // m = {x,y,z,Px,Py,Pz};
+ // V = daughter.C
+ // G*m + B = H*r;
+ // q*x + Py - q*vx - sin(a)*Pt = 0
+ // q*y - Px - q*vy + cos(a)*Pt = 0
+ // (Px*cos(a) + Py*sin(a) ) (vz -z) - Pz( cos(a)*(vx-x) + sin(a)*(vy-y)) = 0
+
+ mG[0][0] = q;
+ mG[0][1] = 0;
+ mG[0][2] = 0;
+ mG[0][3] = -sa0*px0/pt0;
+ mG[0][4] = 1 -sa0*py0/pt0;
+ mG[0][5] = 0;
+ mH[0][0] = q;
+ mH[0][1] = 0;
+ mH[0][2] = 0;
+ mB[0] = py0 - sa0*pt0 - mG[0][3]*px0 - mG[0][4]*py0 ;
+
+ // q*y - Px - q*vy + cos(a)*Pt = 0
+
+ mG[1][0] = 0;
+ mG[1][1] = q;
+ mG[1][2] = 0;
+ mG[1][3] = -1 + ca0*px0/pt0;
+ mG[1][4] = + ca0*py0/pt0;
+ mG[1][5] = 0;
+ mH[1][0] = 0;
+ mH[1][1] = q;
+ mH[1][2] = 0;
+ mB[1] = -px0 + ca0*pt0 - mG[1][3]*px0 - mG[1][4]*py0 ;
+
+ // (Px*cos(a) + Py*sin(a) ) (z -vz) - Pz( cos(a)*(x-vx) + sin(a)*(y-vy)) = 0
+
+ mG[2][0] = -pz0*ca0;
+ mG[2][1] = -pz0*sa0;
+ mG[2][2] = px0*ca0 + py0*sa0;
+ mG[2][3] = 0;
+ mG[2][4] = 0;
+ mG[2][5] = 0;
+
+ mH[2][0] = mG[2][0];
+ mH[2][1] = mG[2][1];
+ mH[2][2] = mG[2][2];
+
+ mB[2] = 0;
+
+ // fit the vertex
+
+ // V = GVGt
+
+ double mGV[3][6];
+ double mV[6];
+ double m[3];
+ for( int i=0; i<3; i++ ){
+ m[i] = mB[i];
+ for( int k=0; k<6; k++ ) m[i]+=mG[i][k]*daughterP[id][k];
+ }
+ for( int i=0; i<3; i++ ){
+ for( int j=0; j<6; j++ ){
+ mGV[i][j] = 0;
+ for( int k=0; k<6; k++ ) mGV[i][j]+=mG[i][k]*daughterC[id][ IJ(k,j) ];
+ }
+ }
+ for( int i=0, k=0; i<3; i++ ){
+ for( int j=0; j<=i; j++,k++ ){
+ mV[k] = 0;
+ for( int l=0; l<6; l++ ) mV[k]+=mGV[i][l]*mG[j][l];
+ }
+ }
+
+
+ //* CHt
+
+ Double_t mCHt[3][3];
+ Double_t mHCHt[6];
+ Double_t mHr[3];
+ for( int i=0; i<3; i++ ){
+ mHr[i] = 0;
+ for( int k=0; k<3; k++ ) mHr[i]+= mH[i][k]*r[k];
+ }
+
+ for( int i=0; i<3; i++ ){
+ for( int j=0; j<3; j++){
+ mCHt[i][j] = 0;
+ for( int k=0; k<3; k++ ) mCHt[i][j]+= mC[i][k]*mH[j][k];
+ }
+ }
+
+ for( int i=0, k=0; i<3; i++ ){
+ for( int j=0; j<=i; j++, k++ ){
+ mHCHt[k] = 0;
+ for( int l=0; l<3; l++ ) mHCHt[k]+= mH[i][l]*mCHt[l][j];
+ }
+ }
+
+ Double_t mS[6] = { mHCHt[0]+mV[0],
+ mHCHt[1]+mV[1], mHCHt[2]+mV[2],
+ mHCHt[3]+mV[3], mHCHt[4]+mV[4], mHCHt[5]+mV[5] };
+
+
+ InvertSym3(mS,mS);
+
+ //* Residual (measured - estimated)
+
+ Double_t zeta[3] = { m[0]-mHr[0], m[1]-mHr[1], m[2]-mHr[2] };
+
+ //* Kalman gain K = mCH'*S
+
+ Double_t k[3][3];
+
+ for(Int_t i=0;i<3;++i){
+ k[i][0] = mCHt[i][0]*mS[0] + mCHt[i][1]*mS[1] + mCHt[i][2]*mS[3];
+ k[i][1] = mCHt[i][0]*mS[1] + mCHt[i][1]*mS[2] + mCHt[i][2]*mS[4];
+ k[i][2] = mCHt[i][0]*mS[3] + mCHt[i][1]*mS[4] + mCHt[i][2]*mS[5];
+ }
+
+ //* New estimation of the vertex position r += K*zeta
+
+ for(Int_t i=0;i<3;++i)
+ r[i] = r[i] + k[i][0]*zeta[0] + k[i][1]*zeta[1] + k[i][2]*zeta[2];
+
+ //* New covariance matrix C -= K*(mCH')'
+
+ for(Int_t i=0;i<3;++i){
+ for(Int_t j=0;j<=i;++j){
+ mC[i][j] = mC[i][j] - (k[i][0]*mCHt[j][0] + k[i][1]*mCHt[j][1] + k[i][2]*mCHt[j][2]);
+ mC[j][i] = mC[i][j];
+ }
+ }
+
+
+ //* Calculate Chi^2
+
+ chi2 += ( ( 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] );
+ }
+
+ // store vertex
+
+ fNDF = 2;
+ fChi2 = chi2;
+ for( int i=0; i<3; i++ ) fP[i] = r[i];
+ for( int i=0,k=0; i<3; i++ ){
+ for( int j=0; j<=i; j++,k++ ){
+ fC[k] = mC[i][j];
+ }
+ }
+ }
+
+ } // iterations
+
+ // now fit daughters to the vertex
+
+ fQ = 0;
+ fSFromDecay = 0;
+
+ for(Int_t i=3;i<8;++i) fP[i]=0.;
+ for(Int_t i=6;i<35;++i) fC[i]=0.;
+ fC[35] = 100.;
+
+ for( int id=0; id<2; id++ ){
+
+ double *p = daughterP[id];
+ double *mC = daughterC[id];
+ daughters[id]->GetMeasurement( v0, p, mC );
+
+ const Double_t *m = fP, *mV = fC;
+
+ Double_t mAi[6];
+ InvertSym3(mC, mAi );
+
+ Double_t mB[4][3];
+
+ mB[0][0] = mC[ 6]*mAi[0] + mC[ 7]*mAi[1] + mC[ 8]*mAi[3];
+ mB[0][1] = mC[ 6]*mAi[1] + mC[ 7]*mAi[2] + mC[ 8]*mAi[4];
+ mB[0][2] = mC[ 6]*mAi[3] + mC[ 7]*mAi[4] + mC[ 8]*mAi[5];
+
+ mB[1][0] = mC[10]*mAi[0] + mC[11]*mAi[1] + mC[12]*mAi[3];
+ mB[1][1] = mC[10]*mAi[1] + mC[11]*mAi[2] + mC[12]*mAi[4];
+ mB[1][2] = mC[10]*mAi[3] + mC[11]*mAi[4] + mC[12]*mAi[5];
+
+ mB[2][0] = mC[15]*mAi[0] + mC[16]*mAi[1] + mC[17]*mAi[3];
+ mB[2][1] = mC[15]*mAi[1] + mC[16]*mAi[2] + mC[17]*mAi[4];
+ mB[2][2] = mC[15]*mAi[3] + mC[16]*mAi[4] + mC[17]*mAi[5];
+
+ mB[3][0] = mC[21]*mAi[0] + mC[22]*mAi[1] + mC[23]*mAi[3];
+ mB[3][1] = mC[21]*mAi[1] + mC[22]*mAi[2] + mC[23]*mAi[4];
+ mB[3][2] = mC[21]*mAi[3] + mC[22]*mAi[4] + mC[23]*mAi[5];
+
+
+ Double_t z[3] = { m[0]-p[0], m[1]-p[1], m[2]-p[2] };
+
+ {
+ Double_t mAV[6] = { mC[0]-mV[0], mC[1]-mV[1], mC[2]-mV[2],
+ mC[3]-mV[3], mC[4]-mV[4], mC[5]-mV[5] };
+
+ Double_t mAVi[6];
+ if( !InvertSym3(mAV, mAVi) ){
+ Double_t dChi2 = ( +(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] );
+ fChi2+= TMath::Abs( dChi2 );
+ }
+ fNDF += 2;
+ }
+
+ //* Add the daughter momentum to the particle momentum
+
+ fP[3]+= p[3] + mB[0][0]*z[0] + mB[0][1]*z[1] + mB[0][2]*z[2];
+ fP[4]+= p[4] + mB[1][0]*z[0] + mB[1][1]*z[1] + mB[1][2]*z[2];
+ fP[5]+= p[5] + mB[2][0]*z[0] + mB[2][1]*z[1] + mB[2][2]*z[2];
+ fP[6]+= p[6] + mB[3][0]*z[0] + mB[3][1]*z[1] + mB[3][2]*z[2];
+
+ Double_t d0, d1, d2;
+
+ d0= mB[0][0]*mV[0] + mB[0][1]*mV[1] + mB[0][2]*mV[3] - mC[ 6];
+ d1= mB[0][0]*mV[1] + mB[0][1]*mV[2] + mB[0][2]*mV[4] - mC[ 7];
+ d2= mB[0][0]*mV[3] + mB[0][1]*mV[4] + mB[0][2]*mV[5] - mC[ 8];
+
+ //fC[6]+= mC[ 6] + d0;
+ //fC[7]+= mC[ 7] + d1;
+ //fC[8]+= mC[ 8] + d2;
+ fC[9]+= mC[ 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] - mC[10];
+ d1= mB[1][0]*mV[1] + mB[1][1]*mV[2] + mB[1][2]*mV[4] - mC[11];
+ d2= mB[1][0]*mV[3] + mB[1][1]*mV[4] + mB[1][2]*mV[5] - mC[12];
+
+ //fC[10]+= mC[10]+ d0;
+ //fC[11]+= mC[11]+ d1;
+ //fC[12]+= mC[12]+ d2;
+ fC[13]+= mC[13]+ d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2];
+ fC[14]+= mC[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] - mC[15];
+ d1= mB[2][0]*mV[1] + mB[2][1]*mV[2] + mB[2][2]*mV[4] - mC[16];
+ d2= mB[2][0]*mV[3] + mB[2][1]*mV[4] + mB[2][2]*mV[5] - mC[17];
+
+ //fC[15]+= mC[15]+ d0;
+ //fC[16]+= mC[16]+ d1;
+ //fC[17]+= mC[17]+ d2;
+ fC[18]+= mC[18]+ d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2];
+ fC[19]+= mC[19]+ d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2];
+ fC[20]+= mC[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] - mC[21];
+ d1= mB[3][0]*mV[1] + mB[3][1]*mV[2] + mB[3][2]*mV[4] - mC[22];
+ d2= mB[3][0]*mV[3] + mB[3][1]*mV[4] + mB[3][2]*mV[5] - mC[23];
+
+ //fC[21]+= mC[21] + d0;
+ //fC[22]+= mC[22] + d1;
+ //fC[23]+= mC[23] + d2;
+ fC[24]+= mC[24] + d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2];
+ fC[25]+= mC[25] + d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2];
+ fC[26]+= mC[26] + d0*mB[2][0] + d1*mB[2][1] + d2*mB[2][2];
+ fC[27]+= mC[27] + d0*mB[3][0] + d1*mB[3][1] + d2*mB[3][2];
+ }
+
+ SetMassConstraint(0,0);
+}
+
+Bool_t AliKFParticleBase::InvertSym3( const Double_t A[], Double_t Ai[] )
+{
+ //* Invert symmetric matric stored in low-triagonal form
+
+ bool ret = 0;
+ double a0 = A[0], a1 = A[1], a2 = A[2], a3 = A[3];
+
+ Ai[0] = a2*A[5] - A[4]*A[4];
+ Ai[1] = a3*A[4] - a1*A[5];
+ Ai[3] = a1*A[4] - a2*a3;
+ Double_t det = (a0*Ai[0] + a1*Ai[1] + a3*Ai[3]);
+ if( det>1.e-20 ) det = 1./det;
+ else{
+ det = 0;
+ ret = 1;
+ }
+ Ai[0] *= det;
+ Ai[1] *= det;
+ Ai[3] *= det;
+ Ai[2] = ( a0*A[5] - a3*a3 )*det;
+ Ai[4] = ( a1*a3 - a0*A[4] )*det;
+ Ai[5] = ( a0*a2 - a1*a1 )*det;
+ return ret;
+}
+