1 //---------------------------------------------------------------------------------
2 // Implementation of the AliKFParticleBase class
4 // @author S.Gorbunov, I.Kisel
8 // Class to reconstruct and store the decayed particle parameters.
9 // The method is described in CBM-SOFT note 2007-003,
10 // ``Reconstruction of decayed particles based on the Kalman filter'',
11 // http://www.gsi.de/documents/DOC-2007-May-14-1.pdf
13 // This class describes general mathematics which is used by AliKFParticle class
15 // -= Copyright © ALICE HLT Group =-
16 //_________________________________________________________________________________
19 #include "AliKFParticleBase.h"
22 ClassImp(AliKFParticleBase)
25 AliKFParticleBase::AliKFParticleBase() :fQ(0), fNDF(-3), fChi2(0), fSFromDecay(0), fAtProductionVertex(0), fIsLinearized(0)
32 void AliKFParticleBase::Initialize()
34 //* Initialise covariance matrix and set current parameters to 0.0
36 for( Int_t i=0; i<8; i++) fP[i] = 0;
37 for(Int_t i=0;i<36;++i) fC[i]=0.;
38 fC[0] = fC[2] = fC[5] = 100.;
44 fAtProductionVertex = 0;
45 fVtxGuess[0]=fVtxGuess[1]=fVtxGuess[2]=0.;
49 void AliKFParticleBase::SetVtxGuess( Double_t x, Double_t y, Double_t z )
51 //* Set decay vertex parameters for linearisation
60 Int_t AliKFParticleBase::GetMomentum( Double_t &P, Double_t &Error ) const
62 //* Calculate particle momentum
70 Double_t p2 = x2+y2+z2;
72 Error = (x2*fC[9]+y2*fC[14]+z2*fC[20] + 2*(x*y*fC[13]+x*z*fC[18]+y*z*fC[19]) );
73 if( Error>0 && P>1.e-4 ){
74 Error = TMath::Sqrt(Error)/P;
80 Int_t AliKFParticleBase::GetMass( Double_t &M, Double_t &Error ) const
82 //* Calculate particle mass
84 // s = sigma^2 of m2/2
86 Double_t s = ( fP[3]*fP[3]*fC[9] + fP[4]*fP[4]*fC[14] + fP[5]*fP[5]*fC[20]
88 +2*( + fP[3]*fP[4]*fC[13] + fP[5]*(fP[3]*fC[18] + fP[4]*fC[19])
89 - fP[6]*( fP[3]*fC[24] + fP[4]*fC[25] + fP[5]*fC[26] ) )
91 Double_t m2 = fP[6]*fP[6] - fP[3]*fP[3] - fP[4]*fP[4] - fP[5]*fP[5];
96 Error = TMath::Sqrt(s/m2);
105 Int_t AliKFParticleBase::GetDecayLength( Double_t &L, Double_t &Error ) const
107 //* Calculate particle decay length [cm]
116 Double_t p2 = x2+y2+z2;
117 L = t*TMath::Sqrt(p2);
119 Error = p2*fC[35] + t*t/p2*(x2*fC[9]+y2*fC[14]+z2*fC[20]
120 + 2*(x*y*fC[13]+x*z*fC[18]+y*z*fC[19]) )
121 + 2*t*(x*fC[31]+y*fC[32]+z*fC[33]);
122 Error = TMath::Sqrt(TMath::Abs(Error));
129 Int_t AliKFParticleBase::GetLifeTime( Double_t &TauC, Double_t &Error ) const
131 //* Calculate particle decay time [s]
135 Double_t cTM = (-fP[3]*fC[31] - fP[4]*fC[32] - fP[5]*fC[33] + fP[6]*fC[34]);
137 Error = m*m*fC[35] + 2*fP[7]*cTM + fP[7]*fP[7]*dm*dm;
139 Error = TMath::Sqrt( Error );
147 void AliKFParticleBase::operator +=( const AliKFParticleBase &Daughter )
149 //* Add daughter via operator+=
151 AddDaughter( Daughter );
155 void AliKFParticleBase::GetMeasurement( const Double_t XYZ[], Double_t m[], Double_t V[] ) const
158 GetFieldValue( XYZ, b );
159 const Double_t kCLight = 0.000299792458;
160 b[0]*=kCLight; b[1]*=kCLight; b[2]*=kCLight;
162 Transport( GetDStoPoint(XYZ), m, V );
164 Double_t d[3] = { XYZ[0]-m[0], XYZ[1]-m[1], XYZ[2]-m[2] };
165 Double_t sigmaS = 1.+10.*TMath::Sqrt( (d[0]*d[0]+d[1]*d[1]+d[2]*d[2])/
166 (m[3]*m[3]+m[4]*m[4]+m[5]*m[5]) );
173 h[3] = ( h[1]*b[2]-h[2]*b[1] )*GetQ();
174 h[4] = ( h[2]*b[0]-h[0]*b[2] )*GetQ();
175 h[5] = ( h[0]*b[1]-h[1]*b[0] )*GetQ();
177 //* Fit of momentum (Px,Py,Pz) to XYZ point
181 V[ 1] + h[0]*h[1], V[ 2] + h[1]*h[1],
182 V[ 3] + h[0]*h[2], V[ 4] + h[1]*h[2], V[ 5] + h[2]*h[2] };
185 { V[ 6] + h[0]*h[3], V[ 7] + h[1]*h[3], V[ 8] + h[2]*h[3],
186 V[10] + h[0]*h[4], V[11] + h[1]*h[4], V[12] + h[2]*h[4],
187 V[15] + h[0]*h[5], V[16] + h[1]*h[5], V[17] + h[2]*h[5] };
190 { mVv[2]*mVv[5] - mVv[4]*mVv[4],
191 mVv[3]*mVv[4] - mVv[1]*mVv[5], mVv[0]*mVv[5] - mVv[3]*mVv[3],
192 mVv[1]*mVv[4] - mVv[2]*mVv[3], mVv[1]*mVv[3] - mVv[0]*mVv[4],
193 mVv[0]*mVv[2] - mVv[1]*mVv[1] };
195 Double_t s = ( mVv[0]*mS[0] + mVv[1]*mS[1] + mVv[3]*mS[3] );
196 s = ( s > 1.E-20 ) ?1./s :0;
198 Double_t mSz[3] = { mS[0]*d[0]+mS[1]*d[1]+mS[3]*d[2],
199 mS[1]*d[0]+mS[2]*d[1]+mS[4]*d[2],
200 mS[3]*d[0]+mS[4]*d[1]+mS[5]*d[2] };
202 Double_t px = m[3] + s*( mVvp[0]*mSz[0] + mVvp[1]*mSz[1] + mVvp[2]*mSz[2] );
203 Double_t py = m[4] + s*( mVvp[3]*mSz[0] + mVvp[4]*mSz[1] + mVvp[5]*mSz[2] );
204 Double_t pz = m[5] + s*( mVvp[6]*mSz[0] + mVvp[7]*mSz[1] + mVvp[8]*mSz[2] );
209 h[3] = ( h[1]*b[2]-h[2]*b[1] )*GetQ();
210 h[4] = ( h[2]*b[0]-h[0]*b[2] )*GetQ();
211 h[5] = ( h[0]*b[1]-h[1]*b[0] )*GetQ();
242 void AliKFParticleBase::AddDaughter( const AliKFParticleBase &Daughter )
246 if( fNDF<-1 ){ // first daughter -> just copy
248 fQ = Daughter.GetQ();
249 for( Int_t i=0; i<7; i++) fP[i] = Daughter.fP[i];
250 for( Int_t i=0; i<28; i++) fC[i] = Daughter.fC[i];
255 TransportToDecayVertex();
260 if( !fIsLinearized ){
263 GetDStoParticle(Daughter, ds, ds1);
267 Daughter.Transport( ds1, m, mCd );
268 fVtxGuess[0] = .5*( fP[0] + m[0] );
269 fVtxGuess[1] = .5*( fP[1] + m[1] );
270 fVtxGuess[2] = .5*( fP[2] + m[2] );
272 fVtxGuess[0] = fP[0];
273 fVtxGuess[1] = fP[1];
274 fVtxGuess[2] = fP[2];
279 for( Int_t iter=0; iter<maxIter; iter++ ){
282 GetFieldValue( fVtxGuess, b );
283 const Double_t kCLight = 0.000299792458;
284 b[0]*=kCLight; b[1]*=kCLight; b[2]*=kCLight;
287 Double_t *ffP = fP, *ffC = fC, tmpP[8], tmpC[36];
289 GetMeasurement( fVtxGuess, tmpP, tmpC );
294 Double_t m[8], mV[36];
295 Daughter.GetMeasurement( fVtxGuess, m, mV );
301 Double_t mSi[6] = { ffC[0]+mV[0],
302 ffC[1]+mV[1], ffC[2]+mV[2],
303 ffC[3]+mV[3], ffC[4]+mV[4], ffC[5]+mV[5] };
305 mS[0] = mSi[2]*mSi[5] - mSi[4]*mSi[4];
306 mS[1] = mSi[3]*mSi[4] - mSi[1]*mSi[5];
307 mS[2] = mSi[0]*mSi[5] - mSi[3]*mSi[3];
308 mS[3] = mSi[1]*mSi[4] - mSi[2]*mSi[3];
309 mS[4] = mSi[1]*mSi[3] - mSi[0]*mSi[4];
310 mS[5] = mSi[0]*mSi[2] - mSi[1]*mSi[1];
312 Double_t s = ( mSi[0]*mS[0] + mSi[1]*mS[1] + mSi[3]*mS[3] );
313 s = ( s > 1.E-20 ) ?1./s :0;
322 //* Residual (measured - estimated)
324 Double_t zeta[3] = { m[0]-ffP[0], m[1]-ffP[1], m[2]-ffP[2] };
328 Double_t mCHt0[7], mCHt1[7], mCHt2[7];
330 mCHt0[0]=ffC[ 0] ; mCHt1[0]=ffC[ 1] ; mCHt2[0]=ffC[ 3] ;
331 mCHt0[1]=ffC[ 1] ; mCHt1[1]=ffC[ 2] ; mCHt2[1]=ffC[ 4] ;
332 mCHt0[2]=ffC[ 3] ; mCHt1[2]=ffC[ 4] ; mCHt2[2]=ffC[ 5] ;
333 mCHt0[3]=ffC[ 6]-mV[ 6]; mCHt1[3]=ffC[ 7]-mV[ 7]; mCHt2[3]=ffC[ 8]-mV[ 8];
334 mCHt0[4]=ffC[10]-mV[10]; mCHt1[4]=ffC[11]-mV[11]; mCHt2[4]=ffC[12]-mV[12];
335 mCHt0[5]=ffC[15]-mV[15]; mCHt1[5]=ffC[16]-mV[16]; mCHt2[5]=ffC[17]-mV[17];
336 mCHt0[6]=ffC[21]-mV[21]; mCHt1[6]=ffC[22]-mV[22]; mCHt2[6]=ffC[23]-mV[23];
338 //* Kalman gain K = mCH'*S
340 Double_t k0[7], k1[7], k2[7];
342 for(Int_t i=0;i<7;++i){
343 k0[i] = mCHt0[i]*mS[0] + mCHt1[i]*mS[1] + mCHt2[i]*mS[3];
344 k1[i] = mCHt0[i]*mS[1] + mCHt1[i]*mS[2] + mCHt2[i]*mS[4];
345 k2[i] = mCHt0[i]*mS[3] + mCHt1[i]*mS[4] + mCHt2[i]*mS[5];
348 //* New estimation of the vertex position
350 if( iter<maxIter-1 ){
351 for(Int_t i=0; i<3; ++i)
352 fVtxGuess[i]= ffP[i] + k0[i]*zeta[0]+k1[i]*zeta[1]+k2[i]*zeta[2];
356 // last itearation -> update the particle
358 //* Add the daughter momentum to the particle momentum
376 //* New estimation of the vertex position r += K*zeta
378 for(Int_t i=0;i<7;++i)
379 fP[i] = ffP[i] + k0[i]*zeta[0] + k1[i]*zeta[1] + k2[i]*zeta[2];
381 //* New covariance matrix C -= K*(mCH')'
383 for(Int_t i=0, k=0;i<7;++i){
384 for(Int_t j=0;j<=i;++j,++k)
385 fC[k] = ffC[k] - (k0[i]*mCHt0[j] + k1[i]*mCHt1[j] + k2[i]*mCHt2[j] );
391 fQ += Daughter.GetQ();
393 fChi2 += (mS[0]*zeta[0] + mS[1]*zeta[1] + mS[3]*zeta[2])*zeta[0]
394 + (mS[1]*zeta[0] + mS[2]*zeta[1] + mS[4]*zeta[2])*zeta[1]
395 + (mS[3]*zeta[0] + mS[4]*zeta[1] + mS[5]*zeta[2])*zeta[2];
400 void AliKFParticleBase::SetProductionVertex( const AliKFParticleBase &Vtx )
402 //* Set production vertex for the particle
404 const Double_t *m = Vtx.fP, *mV = Vtx.fC;
406 TransportToDS( GetDStoPoint( m ) );
407 fP[7] = -fSFromDecay;
411 mAi[0] = fC[4]*fC[4] - fC[2]*fC[5];
412 mAi[1] = fC[1]*fC[5] - fC[3]*fC[4];
413 mAi[3] = fC[2]*fC[3] - fC[1]*fC[4];
414 Double_t det = 1./(fC[0]*mAi[0] + fC[1]*mAi[1] + fC[3]*mAi[3]);
418 mAi[2] = ( fC[3]*fC[3] - fC[0]*fC[5] )*det;
419 mAi[4] = ( fC[0]*fC[4] - fC[1]*fC[3] )*det;
420 mAi[5] = ( fC[1]*fC[1] - fC[0]*fC[2] )*det;
424 mB[0][0] = fC[ 6]*mAi[0] + fC[ 7]*mAi[1] + fC[ 8]*mAi[3];
425 mB[0][1] = fC[ 6]*mAi[1] + fC[ 7]*mAi[2] + fC[ 8]*mAi[4];
426 mB[0][2] = fC[ 6]*mAi[3] + fC[ 7]*mAi[4] + fC[ 8]*mAi[5];
428 mB[1][0] = fC[10]*mAi[0] + fC[11]*mAi[1] + fC[12]*mAi[3];
429 mB[1][1] = fC[10]*mAi[1] + fC[11]*mAi[2] + fC[12]*mAi[4];
430 mB[1][2] = fC[10]*mAi[3] + fC[11]*mAi[4] + fC[12]*mAi[5];
432 mB[2][0] = fC[15]*mAi[0] + fC[16]*mAi[1] + fC[17]*mAi[3];
433 mB[2][1] = fC[15]*mAi[1] + fC[16]*mAi[2] + fC[17]*mAi[4];
434 mB[2][2] = fC[15]*mAi[3] + fC[16]*mAi[4] + fC[17]*mAi[5];
436 mB[3][0] = fC[21]*mAi[0] + fC[22]*mAi[1] + fC[23]*mAi[3];
437 mB[3][1] = fC[21]*mAi[1] + fC[22]*mAi[2] + fC[23]*mAi[4];
438 mB[3][2] = fC[21]*mAi[3] + fC[22]*mAi[4] + fC[23]*mAi[5];
440 mB[4][0] = fC[28]*mAi[0] + fC[29]*mAi[1] + fC[30]*mAi[3];
441 mB[4][1] = fC[28]*mAi[1] + fC[29]*mAi[2] + fC[30]*mAi[4];
442 mB[4][2] = fC[28]*mAi[3] + fC[29]*mAi[4] + fC[30]*mAi[5];
444 Double_t z[3] = { m[0]-fP[0], m[1]-fP[1], m[2]-fP[2] };
447 Double_t mAV[6] = { fC[0]-mV[0], fC[1]-mV[1], fC[2]-mV[2],
448 fC[3]-mV[3], fC[4]-mV[4], fC[5]-mV[5] };
450 mAVi[0] = mAV[4]*mAV[4] - mAV[2]*mAV[5];
451 mAVi[1] = mAV[1]*mAV[5] - mAV[3]*mAV[4];
452 mAVi[2] = mAV[3]*mAV[3] - mAV[0]*mAV[5] ;
453 mAVi[3] = mAV[2]*mAV[3] - mAV[1]*mAV[4];
454 mAVi[4] = mAV[0]*mAV[4] - mAV[1]*mAV[3] ;
455 mAVi[5] = mAV[1]*mAV[1] - mAV[0]*mAV[2] ;
457 det = 1./( mAV[0]*mAVi[0] + mAV[1]*mAVi[1] + mAV[3]*mAVi[3] );
461 ( +(mAVi[0]*z[0] + mAVi[1]*z[1] + mAVi[3]*z[2])*z[0]
462 +(mAVi[1]*z[0] + mAVi[2]*z[1] + mAVi[4]*z[2])*z[1]
463 +(mAVi[3]*z[0] + mAVi[4]*z[1] + mAVi[5]*z[2])*z[2] )*det;
469 fP[3]+= mB[0][0]*z[0] + mB[0][1]*z[1] + mB[0][2]*z[2];
470 fP[4]+= mB[1][0]*z[0] + mB[1][1]*z[1] + mB[1][2]*z[2];
471 fP[5]+= mB[2][0]*z[0] + mB[2][1]*z[1] + mB[2][2]*z[2];
472 fP[6]+= mB[3][0]*z[0] + mB[3][1]*z[1] + mB[3][2]*z[2];
473 fP[7]+= mB[4][0]*z[0] + mB[4][1]*z[1] + mB[4][2]*z[2];
484 d0= mB[0][0]*mV[0] + mB[0][1]*mV[1] + mB[0][2]*mV[3] - fC[ 6];
485 d1= mB[0][0]*mV[1] + mB[0][1]*mV[2] + mB[0][2]*mV[4] - fC[ 7];
486 d2= mB[0][0]*mV[3] + mB[0][1]*mV[4] + mB[0][2]*mV[5] - fC[ 8];
491 fC[ 9]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2];
493 d0= mB[1][0]*mV[0] + mB[1][1]*mV[1] + mB[1][2]*mV[3] - fC[10];
494 d1= mB[1][0]*mV[1] + mB[1][1]*mV[2] + mB[1][2]*mV[4] - fC[11];
495 d2= mB[1][0]*mV[3] + mB[1][1]*mV[4] + mB[1][2]*mV[5] - fC[12];
500 fC[13]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2];
501 fC[14]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2];
503 d0= mB[2][0]*mV[0] + mB[2][1]*mV[1] + mB[2][2]*mV[3] - fC[15];
504 d1= mB[2][0]*mV[1] + mB[2][1]*mV[2] + mB[2][2]*mV[4] - fC[16];
505 d2= mB[2][0]*mV[3] + mB[2][1]*mV[4] + mB[2][2]*mV[5] - fC[17];
510 fC[18]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2];
511 fC[19]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2];
512 fC[20]+= d0*mB[2][0] + d1*mB[2][1] + d2*mB[2][2];
514 d0= mB[3][0]*mV[0] + mB[3][1]*mV[1] + mB[3][2]*mV[3] - fC[21];
515 d1= mB[3][0]*mV[1] + mB[3][1]*mV[2] + mB[3][2]*mV[4] - fC[22];
516 d2= mB[3][0]*mV[3] + mB[3][1]*mV[4] + mB[3][2]*mV[5] - fC[23];
521 fC[24]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2];
522 fC[25]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2];
523 fC[26]+= d0*mB[2][0] + d1*mB[2][1] + d2*mB[2][2];
524 fC[27]+= d0*mB[3][0] + d1*mB[3][1] + d2*mB[3][2];
526 d0= mB[4][0]*mV[0] + mB[4][1]*mV[1] + mB[4][2]*mV[3] - fC[28];
527 d1= mB[4][0]*mV[1] + mB[4][1]*mV[2] + mB[4][2]*mV[4] - fC[29];
528 d2= mB[4][0]*mV[3] + mB[4][1]*mV[4] + mB[4][2]*mV[5] - fC[30];
533 fC[31]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2];
534 fC[32]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2];
535 fC[33]+= d0*mB[2][0] + d1*mB[2][1] + d2*mB[2][2];
536 fC[34]+= d0*mB[3][0] + d1*mB[3][1] + d2*mB[3][2];
537 fC[35]+= d0*mB[4][0] + d1*mB[4][1] + d2*mB[4][2];
539 TransportToDS( fP[7] );
547 void AliKFParticleBase::SetMassConstraint( Double_t Mass )
549 //* Set hard mass constraint
552 mH[0] = mH[1] = mH[2] = 0.;
558 Double_t m2 = ( fP[6]*fP[6]
559 - fP[3]*fP[3] - fP[4]*fP[4] - fP[5]*fP[5] );
561 Double_t zeta = Mass*Mass - m2;
562 for(Int_t i=0;i<8;++i) zeta -= mH[i]*(fP[i]-fP[i]);
566 for (Int_t i=0;i<8;++i ){
568 for (Int_t j=0;j<8;++j) mCHt[i] += Cij(i,j)*mH[j];
572 if( s<1.e-20 ) return;
574 fChi2 += zeta*zeta*s;
576 for( Int_t i=0, ii=0; i<8; ++i ){
577 Double_t ki = mCHt[i]*s;
579 for(Int_t j=0;j<=i;++j) fC[ii++] -= ki*mCHt[j];
584 void AliKFParticleBase::Construct( const AliKFParticleBase* vDaughters[], Int_t NDaughters,
585 const AliKFParticleBase *Parent, Double_t Mass )
587 //* Full reconstruction in one go
590 bool wasLinearized = fIsLinearized;
591 if( !fIsLinearized ){
592 //fVtxGuess[0] = fVtxGuess[1] = fVtxGuess[2] = 0; //!!!!
593 fVtxGuess[0] = GetX();
594 fVtxGuess[1] = GetY();
595 fVtxGuess[2] = GetZ();
600 for( Int_t iter=0; iter<maxIter; iter++ ){
601 fAtProductionVertex = 0;
603 fP[0] = fVtxGuess[0];
604 fP[1] = fVtxGuess[1];
605 fP[2] = fVtxGuess[2];
612 for(Int_t i=0;i<36;++i) fC[i]=0.;
614 fC[0] = fC[2] = fC[5] = 100.;
621 for( Int_t itr =0; itr<NDaughters; itr++ ){
622 AddDaughter( *vDaughters[itr] );
625 for( Int_t i=0; i<3; i++ ) fVtxGuess[i] = fP[i];
628 fIsLinearized = wasLinearized;
630 if( Mass>=0 ) SetMassConstraint( Mass );
631 if( Parent ) SetProductionVertex( *Parent );
635 void AliKFParticleBase::Convert( bool ToProduction )
637 //* Tricky function - convert the particle error along its trajectory to
638 //* the value which corresponds to its production/decay vertex
639 //* It is done by combination of the error of decay length with the position errors
643 GetFieldValue( fP, fld );
644 const Double_t kCLight = fQ*0.000299792458;
645 fld[0]*=kCLight; fld[1]*=kCLight; fld[2]*=kCLight;
653 if( ToProduction ){ h[0]=-h[0]; h[1]=-h[1]; h[2]=-h[2]; }
654 h[3] = h[1]*fld[2]-h[2]*fld[1];
655 h[4] = h[2]*fld[0]-h[0]*fld[2];
656 h[5] = h[0]*fld[1]-h[1]*fld[0];
660 c = fC[28]+h[0]*fC[35];
661 fC[ 0]+= h[0]*(c+fC[28]);
664 fC[ 1]+= h[1]*fC[28] + h[0]*fC[29];
665 c = fC[29]+h[1]*fC[35];
666 fC[ 2]+= h[1]*(c+fC[29]);
669 fC[ 3]+= h[2]*fC[28] + h[0]*fC[30];
670 fC[ 4]+= h[2]*fC[29] + h[1]*fC[30];
671 c = fC[30]+h[2]*fC[35];
672 fC[ 5]+= h[2]*(c+fC[30]);
675 fC[ 6]+= h[3]*fC[28] + h[0]*fC[31];
676 fC[ 7]+= h[3]*fC[29] + h[1]*fC[31];
677 fC[ 8]+= h[3]*fC[30] + h[2]*fC[31];
678 c = fC[31]+h[3]*fC[35];
679 fC[ 9]+= h[3]*(c+fC[31]);
682 fC[10]+= h[4]*fC[28] + h[0]*fC[32];
683 fC[11]+= h[4]*fC[29] + h[1]*fC[32];
684 fC[12]+= h[4]*fC[30] + h[2]*fC[32];
685 fC[13]+= h[4]*fC[31] + h[3]*fC[32];
686 c = fC[32]+h[4]*fC[35];
687 fC[14]+= h[4]*(c+fC[32]);
690 fC[15]+= h[5]*fC[28] + h[0]*fC[33];
691 fC[16]+= h[5]*fC[29] + h[1]*fC[33];
692 fC[17]+= h[5]*fC[30] + h[2]*fC[33];
693 fC[18]+= h[5]*fC[31] + h[3]*fC[33];
694 fC[19]+= h[5]*fC[32] + h[4]*fC[33];
695 c = fC[33]+h[5]*fC[35];
696 fC[20]+= h[5]*(c+fC[33]);
699 fC[21]+= h[0]*fC[34];
700 fC[22]+= h[1]*fC[34];
701 fC[23]+= h[2]*fC[34];
702 fC[24]+= h[3]*fC[34];
703 fC[25]+= h[4]*fC[34];
704 fC[26]+= h[5]*fC[34];
708 void AliKFParticleBase::TransportToDecayVertex()
710 //* Transport the particle to its decay vertex
712 if( fSFromDecay != 0 ) TransportToDS( -fSFromDecay );
713 if( fAtProductionVertex ) Convert(0);
714 fAtProductionVertex = 0;
717 void AliKFParticleBase::TransportToProductionVertex()
719 //* Transport the particle to its production vertex
721 if( fSFromDecay != -fP[7] ) TransportToDS( -fSFromDecay-fP[7] );
722 if( !fAtProductionVertex ) Convert( 1 );
723 fAtProductionVertex = 1;
727 void AliKFParticleBase::TransportToDS( Double_t dS )
729 //* Transport the particle on dS parameter (SignedPath/Momentum)
731 Transport( dS, fP, fC );
736 Double_t AliKFParticleBase::GetDStoPointLine( const Double_t xyz[] ) const
738 //* Get dS to a certain space point without field
740 Double_t p2 = fP[3]*fP[3] + fP[4]*fP[4] + fP[5]*fP[5];
741 if( p2<1.e-4 ) p2 = 1;
742 return ( fP[3]*(xyz[0]-fP[0]) + fP[4]*(xyz[1]-fP[1]) + fP[5]*(xyz[2]-fP[2]) )/p2;
746 Double_t AliKFParticleBase::GetDStoPointBz( Double_t B, const Double_t xyz[] )
750 //* Get dS to a certain space point for Bz field
751 const Double_t kCLight = 0.000299792458;
752 Double_t bq = B*fQ*kCLight;
753 Double_t pt2 = fP[3]*fP[3] + fP[4]*fP[4];
754 if( pt2<1.e-4 ) return 0;
755 Double_t dx = xyz[0] - fP[0];
756 Double_t dy = xyz[1] - fP[1];
757 Double_t a = dx*fP[3]+dy*fP[4];
758 if( TMath::Abs(bq)<1.e-8 ) return a/pt2;
759 return TMath::ATan2( bq*a, pt2 + bq*(dy*fP[3] -dx*fP[4]) )/bq;
763 void AliKFParticleBase::GetDStoParticleBz( Double_t B, const AliKFParticleBase &p,
764 Double_t &DS, Double_t &DS1 )
767 //* Get dS to another particle for Bz field
772 Double_t px1 = p.fP[3];
773 Double_t py1 = p.fP[4];
774 Double_t pz1 = p.fP[5];
776 const Double_t kCLight = 0.000299792458;
778 Double_t bq = B*fQ*kCLight;
779 Double_t bq1 = B*p.fQ*kCLight;
780 Double_t s=0, ds=0, s1=0, ds1=0;
782 if( TMath::Abs(bq)>1.e-8 || TMath::Abs(bq1)>1.e-8 ){
784 Double_t dx = (p.fP[0] - fP[0]);
785 Double_t dy = (p.fP[1] - fP[1]);
786 Double_t d2 = (dx*dx+dy*dy);
788 Double_t p2 = (px *px + py *py);
789 Double_t p21 = (px1*px1 + py1*py1);
791 Double_t a = (px*py1 - py*px1);
792 Double_t b = (px*px1 + py*py1);
794 Double_t ldx = bq*bq1*dx - bq1*py + bq*py1 ;
795 Double_t ldy = bq*bq1*dy + bq1*px - bq*px1 ;
796 Double_t l2 = ldx*ldx + ldy*ldy;
798 Double_t cS = bq1*p2 + bq*bq1*(dy* px - dx* py) - bq*b;
799 Double_t cS1= bq*p21 - bq*bq1*(dy*px1 - dx*py1) - bq1*b;
801 Double_t ca = bq*bq*bq1*d2 +2*( cS + bq*bq*(py1*dx-px1*dy)) ;
802 Double_t ca1 = bq*bq1*bq1*d2 +2*( cS1 - bq1*bq1*(py*dx-px*dy)) ;
804 Double_t sa = 4*l2*p2 - ca*ca;
805 Double_t sa1 = 4*l2*p21 - ca1*ca1;
809 if( TMath::Abs(bq)>1.e-8){
810 s = TMath::ATan2( bq*( bq1*(dx*px +dy*py) + a ) , cS )/bq;
811 ds = TMath::ATan2(TMath::Sqrt(sa),ca)/bq;
813 s = ( (dx*px + dy*py) + (py*px1-px*py1)/bq1)/p2;
814 ds = s*s - (d2-2*(px1*dy-py1*dx)/bq1)/p2;
816 ds = TMath::Sqrt(ds);
819 if( TMath::Abs(bq1)>1.e-8){
820 s1 = TMath::ATan2( -bq1*( bq*(dx*px1+dy*py1) + a), cS1 )/bq1;
821 ds1 = TMath::ATan2(TMath::Sqrt(sa1),ca1)/bq1;
823 s1 = (-(dx*px1 + dy*py1) + (py*px1-px*py1)/bq)/p21;
824 ds1 = s1*s1 - (d2+2*(px*dy-py*dx)/bq)/p21;
826 ds1 = TMath::Sqrt(ds1);
830 Double_t ss[2], ss1[2], g[2][5],g1[2][5];
836 for( Int_t i=0; i<2; i++){
837 Double_t bs = bq*ss[i];
838 Double_t c = TMath::Cos(bs), s = TMath::Sin(bs);
840 if( TMath::Abs(bq)>1.e-8){
844 sB = (1. - bs*bs/6.)*ss[i];
847 g[i][0] = fP[0] + sB*px + cB*py;
848 g[i][1] = fP[1] - cB*px + sB*py;
849 g[i][2] = fP[2] + ss[i]*pz;
850 g[i][3] = + c*px + s*py;
851 g[i][4] = - s*px + c*py;
854 c = TMath::Cos(bs); s = TMath::Sin(bs);
855 if( TMath::Abs(bq1)>1.e-8){
859 sB = (1. - bs*bs/6.)*ss1[i];
863 g[i][0] = p.fP[0] + sB*px1 + cB*py1;
864 g[i][1] = p.fP[1] - cB*px1 + sB*py1;
865 g[i][2] = p.fP[2] + ss[i]*pz1;
866 g[i][3] = + c*px1 + s*py1;
867 g[i][4] = - s*px1 + c*py1;
872 Double_t dMin = 1.e10;
873 for( Int_t j=0; j<2; j++){
874 for( Int_t j1=0; j1<2; j1++){
875 Double_t xx = g[j][0]-g1[j1][0];
876 Double_t yy = g[j][1]-g1[j1][1];
877 Double_t zz = g[j][2]-g1[j1][2];
878 Double_t d = xx*xx + yy*yy + zz*zz;
890 Double_t x= g[i][0], y= g[i][1], z= g[i][2], ppx= g[i][3], ppy= g[i][4];
891 Double_t x1=g[i1][0], y1= g[i1][1], z1= g[i1][2], ppx1= g[i1][3], ppy1= g[i1][4];
895 Double_t a = ppx*ppx1 + ppy*ppy1 + pz*pz1;
896 Double_t b = dx*ppx1 + dy*ppy1 + dz*pz1;
897 Double_t c = dx*ppx + dy*ppy + dz*pz ;
898 Double_t pp2 = ppx*ppx + ppy*ppy + pz*pz;
899 Double_t pp21= ppx1*ppx1 + ppy1*ppy1 + pz1*pz1;
900 Double_t det = pp2*pp21 - a*a;
901 if( TMath::Abs(det)>1.e-8 ){
902 DS+=(a*b-pp21*c)/det;
903 DS1+=(a*c-pp2*b)/det;
909 void AliKFParticleBase::TransportCBM( Double_t dS,
910 Double_t P[], Double_t C[] ) const
912 //* Transport the particle on dS, output to P[],C[], for CBM field
915 TransportLine( dS, P, C );
919 const Double_t kCLight = 0.000299792458;
921 Double_t c = fQ*kCLight;
923 // construct coefficients
930 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;
932 { // get field integrals
935 Double_t p0[3], p1[3], p2[3];
937 // line track approximation
943 p2[0] = fP[0] + px*dS;
944 p2[1] = fP[1] + py*dS;
945 p2[2] = fP[2] + pz*dS;
947 p1[0] = 0.5*(p0[0]+p2[0]);
948 p1[1] = 0.5*(p0[1]+p2[1]);
949 p1[2] = 0.5*(p0[2]+p2[2]);
951 // first order track approximation
953 GetFieldValue( p0, fld[0] );
954 GetFieldValue( p1, fld[1] );
955 GetFieldValue( p2, fld[2] );
957 Double_t ssy1 = ( 7*fld[0][1] + 6*fld[1][1]-fld[2][1] )*c*dS*dS/96.;
958 Double_t ssy2 = ( fld[0][1] + 2*fld[1][1] )*c*dS*dS/6.;
966 GetFieldValue( p0, fld[0] );
967 GetFieldValue( p1, fld[1] );
968 GetFieldValue( p2, fld[2] );
970 sx = c*( fld[0][0] + 4*fld[1][0] + fld[2][0] )*dS/6.;
971 sy = c*( fld[0][1] + 4*fld[1][1] + fld[2][1] )*dS/6.;
972 sz = c*( fld[0][2] + 4*fld[1][2] + fld[2][2] )*dS/6.;
974 ssx = c*( fld[0][0] + 2*fld[1][0])*dS*dS/6.;
975 ssy = c*( fld[0][1] + 2*fld[1][1])*dS*dS/6.;
976 ssz = c*( fld[0][2] + 2*fld[1][2])*dS*dS/6.;
978 Double_t c2[3][3] = { { 5, -4, -1},{ 44, 80, -4},{ 11, 44, 5} }; // /=360.
979 Double_t cc2[3][3] = { { 38, 8, -4},{ 148, 208, -20},{ 3, 36, 3} }; // /=2520.
980 for(Int_t n=0; n<3; n++)
981 for(Int_t m=0; m<3; m++)
983 syz += c2[n][m]*fld[n][1]*fld[m][2];
984 ssyz += cc2[n][m]*fld[n][1]*fld[m][2];
987 syz *= c*c*dS*dS/360.;
988 ssyz *= c*c*dS*dS*dS/2520.;
990 syy = c*( fld[0][1] + 4*fld[1][1] + fld[2][1] )*dS;
991 syyy = syy*syy*syy / 1296;
994 ssyy = ( fld[0][1]*( 38*fld[0][1] + 156*fld[1][1] - fld[2][1] )+
995 fld[1][1]*( 208*fld[1][1] +16*fld[2][1] )+
996 fld[2][1]*( 3*fld[2][1] )
997 )*dS*dS*dS*c*c/2520.;
1000 fld[0][1]*( fld[0][1]*( 85*fld[0][1] + 526*fld[1][1] - 7*fld[2][1] )+
1001 fld[1][1]*( 1376*fld[1][1] +84*fld[2][1] )+
1002 fld[2][1]*( 19*fld[2][1] ) )+
1003 fld[1][1]*( fld[1][1]*( 1376*fld[1][1] +256*fld[2][1] )+
1004 fld[2][1]*( 62*fld[2][1] ) )+
1005 fld[2][1]*fld[2][1] *( 3*fld[2][1] )
1006 )*dS*dS*dS*dS*c*c*c/90720.;
1011 for( Int_t i=0; i<8; i++ ) for( Int_t j=0; j<8; j++) mJ[i][j]=0;
1013 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;
1014 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;
1015 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;
1017 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;
1018 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;
1019 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;
1020 mJ[6][6] = mJ[7][7] = 1;
1022 P[0] = fP[0] + mJ[0][3]*px + mJ[0][4]*py + mJ[0][5]*pz;
1023 P[1] = fP[1] + mJ[1][3]*px + mJ[1][4]*py + mJ[1][5]*pz;
1024 P[2] = fP[2] + mJ[2][3]*px + mJ[2][4]*py + mJ[2][5]*pz;
1025 P[3] = mJ[3][3]*px + mJ[3][4]*py + mJ[3][5]*pz;
1026 P[4] = mJ[4][3]*px + mJ[4][4]*py + mJ[4][5]*pz;
1027 P[5] = mJ[5][3]*px + mJ[5][4]*py + mJ[5][5]*pz;
1031 MultQSQt( mJ[0], fC, C);
1036 void AliKFParticleBase::TransportBz( Double_t B, Double_t S,
1037 Double_t P[], Double_t C[] ) const
1039 //* Transport the particle on dS, output to P[],C[], for Bz field
1041 const Double_t kCLight = 0.000299792458;
1044 Double_t s = TMath::Sin(bs), c = TMath::Cos(bs);
1046 if( TMath::Abs(bs)>1.e-10){
1050 sB = (1. - bs*bs/6.)*S;
1054 Double_t px = fP[3];
1055 Double_t py = fP[4];
1056 Double_t pz = fP[5];
1058 P[0] = fP[0] + sB*px + cB*py;
1059 P[1] = fP[1] - cB*px + sB*py;
1060 P[2] = fP[2] + S*pz;
1062 P[4] = -s*px + c*py;
1067 Double_t mJ[8][8] = { {1,0,0, sB, cB, 0, 0, 0 },
1068 {0,1,0, -cB, sB, 0, 0, 0 },
1069 {0,0,1, 0, 0, S, 0, 0 },
1070 {0,0,0, c, s, 0, 0, 0 },
1071 {0,0,0, -s, c, 0, 0, 0 },
1072 {0,0,0, 0, 0, 1, 0, 0 },
1073 {0,0,0, 0, 0, 0, 1, 0 },
1074 {0,0,0, 0, 0, 0, 0, 1 } };
1076 for( Int_t k=0,i=0; i<8; i++)
1077 for( Int_t j=0; j<=i; j++, k++ ) mA[i][j] = mA[j][i] = fC[k];
1080 for( Int_t i=0; i<8; i++ )
1081 for( Int_t j=0; j<8; j++ ){
1083 for( Int_t k=0; k<8; k++ ) mJC[i][j]+=mJ[i][k]*mA[k][j];
1086 for( Int_t k=0,i=0; i<8; i++)
1087 for( Int_t j=0; j<=i; j++, k++ ){
1089 for( Int_t l=0; l<8; l++ ) C[k]+=mJC[i][l]*mJ[j][l];
1094 Double_t cBC13 = cB*fC[13];
1095 Double_t C17 = fC[17];
1096 Double_t C18 = fC[18];
1097 fC[ 0]+= 2*(sB*fC[ 6] + cB*fC[10]) + (sB*fC[ 9] + 2*cBC13)*sB + cB*cB*fC[14];
1099 Double_t mJC13= fC[ 7] - cB*fC[ 9] + sB*fC[13];
1100 Double_t mJC14= fC[11] - cBC13 + sB*fC[14];
1102 fC[ 1]+= -cB*fC[ 6] + sB*fC[10] +mJC13*sB +mJC14*cB;
1103 fC[ 2]+= -cB*fC[ 7] + sB*fC[11] -mJC13*cB +mJC14*sB;
1105 Double_t mJC23= fC[ 8] + S*fC[18];
1106 Double_t mJC24= fC[12] + S*fC[19];
1107 fC[ 3]+= S*fC[15] +mJC23*sB +mJC24*cB;
1108 fC[ 4]+= S*fC[16] -mJC23*cB +mJC24*sB;
1110 fC[15]+= C18*sB + fC[19]*cB;
1111 fC[16]+= -C18*cB + fC[19]*sB;
1113 fC[18] = C18*c + fC[19]*s;
1114 fC[19] = -C18*s + fC[19]*c;
1116 fC[ 5]+= (C17 + C17 + fC[17])*S;
1118 Double_t mJC33= c*fC[ 9] + s*fC[13]; Double_t mJC34= c*fC[13] + s*fC[14];
1119 Double_t mJC43=-s*fC[ 9] + c*fC[13]; Double_t mJC44=-s*fC[13] + c*fC[14];
1120 Double_t C6= fC[6], C7= fC[7], C8= fC[8];
1122 fC[ 6]= c*C6 + s*fC[10] +mJC33*sB +mJC34*cB;
1123 fC[ 7]= c*C7 + s*fC[11] -mJC33*cB +mJC34*sB;
1124 fC[ 8]= c*C8 + s*fC[12] +fC[18]*S;
1125 fC[ 9]= mJC33*c +mJC34*s;
1127 fC[10]= -s*C6 + c*fC[10] +mJC43*sB +mJC44*cB;
1128 fC[11]= -s*C7 + c*fC[11] -mJC43*cB +mJC44*sB;
1129 fC[12]= -s*C8 + c*fC[12] +fC[19]*S;
1130 fC[13]= mJC43*c +mJC44*s;
1131 fC[14]=-mJC43*s +mJC44*c;
1136 Double_t AliKFParticleBase::GetDistanceFromVertex( const AliKFParticleBase &Vtx ) const
1138 //* Calculate distance from vertex [cm]
1140 return GetDistanceFromVertex( Vtx.fP );
1143 Double_t AliKFParticleBase::GetDistanceFromVertex( const Double_t vtx[] ) const
1145 //* Calculate distance from vertex [cm]
1147 Double_t mP[8], mC[36];
1148 Transport( GetDStoPoint(vtx), mP, mC );
1149 Double_t d[3]={ vtx[0]-mP[0], vtx[1]-mP[1], vtx[2]-mP[2]};
1150 return TMath::Sqrt( d[0]*d[0]+d[1]*d[1]+d[2]*d[2] );
1153 Double_t AliKFParticleBase::GetDistanceFromParticle( const AliKFParticleBase &p )
1156 //* Calculate distance to other particle [cm]
1159 GetDStoParticle( p, dS, dS1 );
1160 Double_t mP[8], mC[36], mP1[8], mC1[36];
1161 Transport( dS, mP, mC );
1162 p.Transport( dS1, mP1, mC1 );
1163 Double_t dx = mP[0]-mP1[0];
1164 Double_t dy = mP[1]-mP1[1];
1165 Double_t dz = mP[2]-mP1[2];
1166 return TMath::Sqrt(dx*dx+dy*dy+dz*dz);
1169 Double_t AliKFParticleBase::GetDeviationFromVertex( const AliKFParticleBase &Vtx ) const
1171 //* Calculate sqrt(Chi2/ndf) deviation from vertex
1173 return GetDeviationFromVertex( Vtx.fP, Vtx.fC );
1177 Double_t AliKFParticleBase::GetDeviationFromVertex( const Double_t v[], const Double_t Cv[] ) const
1179 //* Calculate sqrt(Chi2/ndf) deviation from vertex
1180 //* v = [xyz], Cv=[Cxx,Cxy,Cyy,Cxz,Cyz,Czz]-covariance matrix
1185 Transport( GetDStoPoint(v), mP, mC );
1187 Double_t d[3]={ v[0]-mP[0], v[1]-mP[1], v[2]-mP[2]};
1189 Double_t sigmaS = .1+10.*TMath::Sqrt( (d[0]*d[0]+d[1]*d[1]+d[2]*d[2])/
1190 (mP[3]*mP[3]+mP[4]*mP[4]+mP[5]*mP[5]) );
1193 Double_t h[3] = { mP[3]*sigmaS, mP[4]*sigmaS, mP[5]*sigmaS };
1197 mC[1] +h[1]*h[0], mC[2] +h[1]*h[1],
1198 mC[3] +h[2]*h[0], mC[4] +h[2]*h[1], mC[5] +h[2]*h[2] };
1211 mS[0] = mSi[2]*mSi[5] - mSi[4]*mSi[4];
1212 mS[1] = mSi[3]*mSi[4] - mSi[1]*mSi[5];
1213 mS[2] = mSi[0]*mSi[5] - mSi[3]*mSi[3];
1214 mS[3] = mSi[1]*mSi[4] - mSi[2]*mSi[3];
1215 mS[4] = mSi[1]*mSi[3] - mSi[0]*mSi[4];
1216 mS[5] = mSi[0]*mSi[2] - mSi[1]*mSi[1];
1218 Double_t s = ( mSi[0]*mS[0] + mSi[1]*mS[1] + mSi[3]*mS[3] );
1219 s = ( s > 1.E-20 ) ?1./s :0;
1221 return TMath::Sqrt( TMath::Abs(s*( ( mS[0]*d[0] + mS[1]*d[1] + mS[3]*d[2])*d[0]
1222 +(mS[1]*d[0] + mS[2]*d[1] + mS[4]*d[2])*d[1]
1223 +(mS[3]*d[0] + mS[4]*d[1] + mS[5]*d[2])*d[2] ))/2);
1227 Double_t AliKFParticleBase::GetDeviationFromParticle( const AliKFParticleBase &p )
1230 //* Calculate sqrt(Chi2/ndf) deviation from other particle
1233 GetDStoParticle( p, dS, dS1 );
1234 Double_t mP1[8], mC1[36];
1235 p.Transport( dS1, mP1, mC1 );
1237 Double_t d[3]={ fP[0]-mP1[0], fP[1]-mP1[1], fP[2]-mP1[2]};
1239 Double_t sigmaS = .1+10.*TMath::Sqrt( (d[0]*d[0]+d[1]*d[1]+d[2]*d[2])/
1240 (mP1[3]*mP1[3]+mP1[4]*mP1[4]+mP1[5]*mP1[5]) );
1242 Double_t h[3] = { mP1[3]*sigmaS, mP1[4]*sigmaS, mP1[5]*sigmaS };
1251 return GetDeviationFromVertex( mP1, mC1 )*TMath::Sqrt(2./1.);
1256 void AliKFParticleBase::SubtractFromVertex( Double_t v[], Double_t Cv[],
1257 Double_t &vChi2, Int_t vNDF ) const
1259 //* Subtract the particle from the vertex
1263 GetFieldValue( v, fld );
1264 const Double_t kCLight = 0.000299792458;
1265 fld[0]*=kCLight; fld[1]*=kCLight; fld[2]*=kCLight;
1271 Transport( GetDStoPoint(v), m, mCm );
1273 Double_t d[3] = { v[0]-m[0], v[1]-m[1], v[2]-m[2] };
1274 Double_t sigmaS = .1+10.*TMath::Sqrt( (d[0]*d[0]+d[1]*d[1]+d[2]*d[2])/
1275 (m[3]*m[3]+m[4]*m[4]+m[5]*m[5]) );
1282 h[3] = ( h[1]*fld[2]-h[2]*fld[1] )*GetQ();
1283 h[4] = ( h[2]*fld[0]-h[0]*fld[2] )*GetQ();
1284 h[5] = ( h[0]*fld[1]-h[1]*fld[0] )*GetQ();
1286 //* Fit of daughter momentum (Px,Py,Pz) to fVtxGuess vertex
1288 Double_t zeta[3] = { v[0]-m[0], v[1]-m[1], v[2]-m[2] };
1291 { mCm[ 0] + h[0]*h[0],
1292 mCm[ 1] + h[1]*h[0], mCm[ 2] + h[1]*h[1],
1293 mCm[ 3] + h[2]*h[0], mCm[ 4] + h[2]*h[1], mCm[ 5] + h[2]*h[2] };
1296 { mCm[ 6] + h[0]*h[3], mCm[ 7] + h[1]*h[3], mCm[ 8] + h[2]*h[3],
1297 mCm[10] + h[0]*h[4], mCm[11] + h[1]*h[4], mCm[12] + h[2]*h[4],
1298 mCm[15] + h[0]*h[5], mCm[16] + h[1]*h[5], mCm[17] + h[2]*h[5] };
1301 { mVv[2]*mVv[5] - mVv[4]*mVv[4],
1302 mVv[3]*mVv[4] - mVv[1]*mVv[5], mVv[0]*mVv[5] - mVv[3]*mVv[3],
1303 mVv[1]*mVv[4] - mVv[2]*mVv[3], mVv[1]*mVv[3] - mVv[0]*mVv[4],
1304 mVv[0]*mVv[2] - mVv[1]*mVv[1] };
1306 Double_t s = ( mVv[0]*mS[0] + mVv[1]*mS[1] + mVv[3]*mS[3] );
1307 s = ( s > 1.E-20 ) ?1./s :0;
1309 mS[0]*=s; mS[1]*=s; mS[2]*=s; mS[3]*=s; mS[4]*=s; mS[5]*=s;
1311 Double_t mSz[3] = { (mS[0]*zeta[0]+mS[1]*zeta[1]+mS[3]*zeta[2]),
1312 (mS[1]*zeta[0]+mS[2]*zeta[1]+mS[4]*zeta[2]),
1313 (mS[3]*zeta[0]+mS[4]*zeta[1]+mS[5]*zeta[2]) };
1315 Double_t px = m[3] + mVvp[0]*mSz[0] + mVvp[1]*mSz[1] + mVvp[2]*mSz[2];
1316 Double_t py = m[4] + mVvp[3]*mSz[0] + mVvp[4]*mSz[1] + mVvp[5]*mSz[2];
1317 Double_t pz = m[5] + mVvp[6]*mSz[0] + mVvp[7]*mSz[1] + mVvp[8]*mSz[2];
1322 h[3] = ( h[1]*fld[2]-h[2]*fld[1] )*GetQ();
1323 h[4] = ( h[2]*fld[0]-h[0]*fld[2] )*GetQ();
1324 h[5] = ( h[0]*fld[1]-h[1]*fld[0] )*GetQ();
1329 mV[ 0] = mCm[ 0] + h[0]*h[0];
1330 mV[ 1] = mCm[ 1] + h[1]*h[0];
1331 mV[ 2] = mCm[ 2] + h[1]*h[1];
1332 mV[ 3] = mCm[ 3] + h[2]*h[0];
1333 mV[ 4] = mCm[ 4] + h[2]*h[1];
1334 mV[ 5] = mCm[ 5] + h[2]*h[2];
1340 Double_t mSi[6] = { mV[0]-Cv[0],
1341 mV[1]-Cv[1], mV[2]-Cv[2],
1342 mV[3]-Cv[3], mV[4]-Cv[4], mV[5]-Cv[5] };
1344 mS[0] = mSi[2]*mSi[5] - mSi[4]*mSi[4];
1345 mS[1] = mSi[3]*mSi[4] - mSi[1]*mSi[5];
1346 mS[2] = mSi[0]*mSi[5] - mSi[3]*mSi[3];
1347 mS[3] = mSi[1]*mSi[4] - mSi[2]*mSi[3];
1348 mS[4] = mSi[1]*mSi[3] - mSi[0]*mSi[4];
1349 mS[5] = mSi[0]*mSi[2] - mSi[1]*mSi[1];
1351 Double_t s = ( mSi[0]*mS[0] + mSi[1]*mS[1] + mSi[3]*mS[3] );
1352 s = ( s > 1.E-20 ) ?1./s :0;
1361 //* Residual (measured - estimated)
1363 Double_t zeta[3] = { m[0]-v[0], m[1]-v[1], m[2]-v[2] };
1365 //* mCHt = mCH' - D'
1367 Double_t mCHt0[3], mCHt1[3], mCHt2[3];
1369 mCHt0[0]=Cv[ 0] ; mCHt1[0]=Cv[ 1] ; mCHt2[0]=Cv[ 3] ;
1370 mCHt0[1]=Cv[ 1] ; mCHt1[1]=Cv[ 2] ; mCHt2[1]=Cv[ 4] ;
1371 mCHt0[2]=Cv[ 3] ; mCHt1[2]=Cv[ 4] ; mCHt2[2]=Cv[ 5] ;
1373 //* Kalman gain K = mCH'*S
1375 Double_t k0[3], k1[3], k2[3];
1377 for(Int_t i=0;i<3;++i){
1378 k0[i] = mCHt0[i]*mS[0] + mCHt1[i]*mS[1] + mCHt2[i]*mS[3];
1379 k1[i] = mCHt0[i]*mS[1] + mCHt1[i]*mS[2] + mCHt2[i]*mS[4];
1380 k2[i] = mCHt0[i]*mS[3] + mCHt1[i]*mS[4] + mCHt2[i]*mS[5];
1383 //* New estimation of the vertex position r += K*zeta
1385 for(Int_t i=0;i<3;++i)
1386 v[i] -= k0[i]*zeta[0] + k1[i]*zeta[1] + k2[i]*zeta[2];
1388 //* New covariance matrix C -= K*(mCH')'
1390 for(Int_t i=0, k=0;i<3;++i){
1391 for(Int_t j=0;j<=i;++j,++k)
1392 Cv[k] += k0[i]*mCHt0[j] + k1[i]*mCHt1[j] + k2[i]*mCHt2[j];
1398 vChi2 -= (mS[0]*zeta[0] + mS[1]*zeta[1] + mS[3]*zeta[2])*zeta[0]
1399 + (mS[1]*zeta[0] + mS[2]*zeta[1] + mS[4]*zeta[2])*zeta[1]
1400 + (mS[3]*zeta[0] + mS[4]*zeta[1] + mS[5]*zeta[2])*zeta[2];
1405 void AliKFParticleBase::TransportLine( Double_t dS,
1406 Double_t P[], Double_t C[] ) const
1408 //* Transport the particle as a straight line
1410 P[0] = fP[0] + dS*fP[3];
1411 P[1] = fP[1] + dS*fP[4];
1412 P[2] = fP[2] + dS*fP[5];
1419 Double_t c6 = fC[ 6] + dS*fC[ 9];
1420 Double_t c11 = fC[11] + dS*fC[14];
1421 Double_t c17 = fC[17] + dS*fC[20];
1422 Double_t sc13 = dS*fC[13];
1423 Double_t sc18 = dS*fC[18];
1424 Double_t sc19 = dS*fC[19];
1426 C[ 0] = fC[ 0] + dS*( fC[ 6] + c6 );
1427 C[ 2] = fC[ 2] + dS*( fC[11] + c11 );
1428 C[ 5] = fC[ 5] + dS*( fC[17] + c17 );
1430 C[ 7] = fC[ 7] + sc13;
1431 C[ 8] = fC[ 8] + sc18;
1434 C[12] = fC[12] + sc19;
1436 C[ 1] = fC[ 1] + dS*( fC[10] + C[ 7] );
1437 C[ 3] = fC[ 3] + dS*( fC[15] + C[ 8] );
1438 C[ 4] = fC[ 4] + dS*( fC[16] + C[12] );
1441 C[10] = fC[10] + sc13;
1446 C[15] = fC[15] + sc18;
1447 C[16] = fC[16] + sc19;
1453 C[21] = fC[21] + dS*fC[24];
1454 C[22] = fC[22] + dS*fC[25];
1455 C[23] = fC[23] + dS*fC[26];
1461 C[28] = fC[28] + dS*fC[31];
1462 C[29] = fC[29] + dS*fC[32];
1463 C[30] = fC[30] + dS*fC[33];
1473 void AliKFParticleBase::MultQSQt( const Double_t Q[], const Double_t S[], Double_t SOut[] )
1475 //* Matrix multiplication Q*S*Q^T, Q - square matrix, S - symmetric
1480 for( Int_t i=0, ij=0; i<kN; i++ ){
1481 for( Int_t j=0; j<kN; j++, ++ij ){
1483 for( Int_t k=0; k<kN; ++k ) mA[ij]+= S[( k<=i ) ? i*(i+1)/2+k :k*(k+1)/2+i] * Q[ j*kN+k];
1487 for( Int_t i=0; i<kN; i++ ){
1488 for( Int_t j=0; j<=i; j++ ){
1489 Int_t ij = ( j<=i ) ? i*(i+1)/2+j :j*(j+1)/2+i;
1491 for( Int_t k=0; k<kN; k++ ) SOut[ij] += Q[ i*kN+k ] * mA[ k*kN+j ];
1497 // 72-charachters line to define the printer border
1498 //3456789012345678901234567890123456789012345678901234567890123456789012