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( const Double_t Param[], const Double_t Cov[], Int_t Charge, Double_t Mass )
34 // Constructor from "cartesian" track, particle mass hypothesis should be provided
36 // Param[6] = { X, Y, Z, Px, Py, Pz } - position and momentum
37 // Cov [21] = lower-triangular part of the covariance matrix:
41 // Cov. matrix = ( 3 4 5 . . . ) - numbering of covariance elements in Cov[]
43 // ( 10 11 12 13 14 . )
44 // ( 15 16 17 18 19 20 )
47 for( Int_t i=0; i<6 ; i++ ) fP[i] = Param[i];
48 for( Int_t i=0; i<21; i++ ) fC[i] = Cov[i];
50 Double_t energy = TMath::Sqrt( Mass*Mass + fP[3]*fP[3] + fP[4]*fP[4] + fP[5]*fP[5]);
56 fAtProductionVertex = 0;
60 Double_t energyInv = 1./energy;
66 fC[21] = h0*fC[ 6] + h1*fC[10] + h2*fC[15];
67 fC[22] = h0*fC[ 7] + h1*fC[11] + h2*fC[16];
68 fC[23] = h0*fC[ 8] + h1*fC[12] + h2*fC[17];
69 fC[24] = h0*fC[ 9] + h1*fC[13] + h2*fC[18];
70 fC[25] = h0*fC[13] + h1*fC[14] + h2*fC[19];
71 fC[26] = h0*fC[18] + h1*fC[19] + h2*fC[20];
72 fC[27] = ( h0*h0*fC[ 9] + h1*h1*fC[14] + h2*h2*fC[20]
73 + 2*(h0*h1*fC[13] + h0*h2*fC[18] + h1*h2*fC[19] ) );
74 for( Int_t i=28; i<36; i++ ) fC[i] = 0;
78 void AliKFParticleBase::Initialize()
80 //* Initialise covariance matrix and set current parameters to 0.0
82 for( Int_t i=0; i<8; i++) fP[i] = 0;
83 for(Int_t i=0;i<36;++i) fC[i]=0.;
84 fC[0] = fC[2] = fC[5] = 100.;
90 fAtProductionVertex = 0;
91 fVtxGuess[0]=fVtxGuess[1]=fVtxGuess[2]=0.;
95 void AliKFParticleBase::SetVtxGuess( Double_t x, Double_t y, Double_t z )
97 //* Set decay vertex parameters for linearisation
106 Int_t AliKFParticleBase::GetMomentum( Double_t &p, Double_t &error ) const
108 //* Calculate particle momentum
116 Double_t p2 = x2+y2+z2;
118 error = (x2*fC[9]+y2*fC[14]+z2*fC[20] + 2*(x*y*fC[13]+x*z*fC[18]+y*z*fC[19]) );
119 if( error>0 && p>1.e-4 ){
120 error = TMath::Sqrt(error)/p;
126 Int_t AliKFParticleBase::GetPt( Double_t &pt, Double_t &error ) const
128 //* Calculate particle transverse momentum
132 Double_t px2 = px*px;
133 Double_t py2 = py*py;
134 Double_t pt2 = px2+py2;
135 pt = TMath::Sqrt(pt2);
136 error = (px2*fC[9] + py2*fC[14] + 2*px*py*fC[13] );
137 if( error>0 && pt>1.e-4 ){
138 error = TMath::Sqrt(error)/pt;
145 Int_t AliKFParticleBase::GetEta( Double_t &eta, Double_t &error ) const
147 //* Calculate particle pseudorapidity
152 Double_t pt2 = px*px + py*py;
153 Double_t p2 = pt2 + pz*pz;
154 Double_t p = TMath::Sqrt(p2);
160 if( c>1.e-8 ) eta = 0.5*TMath::Log(a/b);
162 Double_t h3 = -px*pz;
163 Double_t h4 = -py*pz;
164 Double_t p2pt2 = p2*pt2;
166 error = (h3*h3*fC[9] + h4*h4*fC[14] + pt2*fC[20] +
167 2*( h3*(h4*fC[13] + fC[18]) + h4*fC[19] )
170 if( error>0 && p2pt2>1.e-4 ){
171 error = TMath::Sqrt(error/p2pt2);
178 Int_t AliKFParticleBase::GetPhi( Double_t &phi, Double_t &error ) const
180 //* Calculate particle polar angle
184 Double_t px2 = px*px;
185 Double_t py2 = py*py;
186 Double_t pt2 = px2 + py2;
187 phi = TMath::ATan2(py,px);
188 error = (py2*fC[9] + px2*fC[14] - 2*px*py*fC[13] );
189 if( error>0 && pt2>1.e-4 ){
190 error = TMath::Sqrt(error)/pt2;
197 Int_t AliKFParticleBase::GetR( Double_t &r, Double_t &error ) const
199 //* Calculate distance to the origin
205 r = TMath::Sqrt(x2 + y2);
206 error = (x2*fC[0] + y2*fC[2] - 2*x*y*fC[1] );
207 if( error>0 && r>1.e-4 ){
208 error = TMath::Sqrt(error)/r;
215 Int_t AliKFParticleBase::GetMass( Double_t &m, Double_t &error ) const
217 //* Calculate particle mass
219 // s = sigma^2 of m2/2
221 Double_t s = ( fP[3]*fP[3]*fC[9] + fP[4]*fP[4]*fC[14] + fP[5]*fP[5]*fC[20]
223 +2*( + fP[3]*fP[4]*fC[13] + fP[5]*(fP[3]*fC[18] + fP[4]*fC[19])
224 - fP[6]*( fP[3]*fC[24] + fP[4]*fC[25] + fP[5]*fC[26] ) )
226 Double_t m2 = TMath::Abs(fP[6]*fP[6] - fP[3]*fP[3] - fP[4]*fP[4] - fP[5]*fP[5]);
230 error = TMath::Sqrt(s)/m;
239 Int_t AliKFParticleBase::GetDecayLength( Double_t &l, Double_t &error ) const
241 //* Calculate particle decay length [cm]
250 Double_t p2 = x2+y2+z2;
251 l = t*TMath::Sqrt(p2);
253 error = p2*fC[35] + t*t/p2*(x2*fC[9]+y2*fC[14]+z2*fC[20]
254 + 2*(x*y*fC[13]+x*z*fC[18]+y*z*fC[19]) )
255 + 2*t*(x*fC[31]+y*fC[32]+z*fC[33]);
256 error = TMath::Sqrt(TMath::Abs(error));
263 Int_t AliKFParticleBase::GetLifeTime( Double_t &tauC, Double_t &error ) const
265 //* Calculate particle decay time [s]
269 Double_t cTM = (-fP[3]*fC[31] - fP[4]*fC[32] - fP[5]*fC[33] + fP[6]*fC[34]);
271 error = m*m*fC[35] + 2*fP[7]*cTM + fP[7]*fP[7]*dm*dm;
273 error = TMath::Sqrt( error );
281 void AliKFParticleBase::operator +=( const AliKFParticleBase &Daughter )
283 //* Add daughter via operator+=
285 AddDaughter( Daughter );
288 Double_t AliKFParticleBase::GetSCorrection( const Double_t Part[], const Double_t XYZ[] )
290 //* Get big enough correction for S error to let the particle Part be fitted to XYZ point
292 Double_t d[3] = { XYZ[0]-Part[0], XYZ[1]-Part[1], XYZ[2]-Part[2] };
293 Double_t p2 = Part[3]*Part[3]+Part[4]*Part[4]+Part[5]*Part[5];
294 Double_t sigmaS = (p2>1.e-4) ? ( .1+3.*TMath::Sqrt( d[0]*d[0]+d[1]*d[1]+d[2]*d[2]) )/TMath::Sqrt(p2) : 1.;
298 void AliKFParticleBase::GetMeasurement( const Double_t XYZ[], Double_t m[], Double_t V[] ) const
300 //* Get additional covariances V used during measurement
303 GetFieldValue( XYZ, b );
304 const Double_t kCLight = 0.000299792458;
305 b[0]*=kCLight; b[1]*=kCLight; b[2]*=kCLight;
307 Transport( GetDStoPoint(XYZ), m, V );
309 Double_t sigmaS = GetSCorrection( m, XYZ );
316 h[3] = ( h[1]*b[2]-h[2]*b[1] )*GetQ();
317 h[4] = ( h[2]*b[0]-h[0]*b[2] )*GetQ();
318 h[5] = ( h[0]*b[1]-h[1]*b[0] )*GetQ();
347 void AliKFParticleBase::AddDaughter( const AliKFParticleBase &Daughter )
351 if( fNDF<-1 ){ // first daughter -> just copy
353 fQ = Daughter.GetQ();
354 for( Int_t i=0; i<7; i++) fP[i] = Daughter.fP[i];
355 for( Int_t i=0; i<28; i++) fC[i] = Daughter.fC[i];
360 TransportToDecayVertex();
365 if( !fIsLinearized ){
368 GetDStoParticle(Daughter, ds, ds1);
372 Daughter.Transport( ds1, m, mCd );
373 fVtxGuess[0] = .5*( fP[0] + m[0] );
374 fVtxGuess[1] = .5*( fP[1] + m[1] );
375 fVtxGuess[2] = .5*( fP[2] + m[2] );
377 fVtxGuess[0] = fP[0];
378 fVtxGuess[1] = fP[1];
379 fVtxGuess[2] = fP[2];
384 for( Int_t iter=0; iter<maxIter; iter++ ){
387 GetFieldValue( fVtxGuess, b );
388 const Double_t kCLight = 0.000299792458;
389 b[0]*=kCLight; b[1]*=kCLight; b[2]*=kCLight;
392 Double_t *ffP = fP, *ffC = fC, tmpP[8], tmpC[36];
394 GetMeasurement( fVtxGuess, tmpP, tmpC );
399 Double_t m[8], mV[36];
401 if( Daughter.fC[35]>0 ){
402 Daughter.GetMeasurement( fVtxGuess, m, mV );
404 for( Int_t i=0; i<8; i++ ) m[i] = Daughter.fP[i];
405 for( Int_t i=0; i<36; i++ ) mV[i] = Daughter.fC[i];
412 Double_t mSi[6] = { ffC[0]+mV[0],
413 ffC[1]+mV[1], ffC[2]+mV[2],
414 ffC[3]+mV[3], ffC[4]+mV[4], ffC[5]+mV[5] };
416 mS[0] = mSi[2]*mSi[5] - mSi[4]*mSi[4];
417 mS[1] = mSi[3]*mSi[4] - mSi[1]*mSi[5];
418 mS[2] = mSi[0]*mSi[5] - mSi[3]*mSi[3];
419 mS[3] = mSi[1]*mSi[4] - mSi[2]*mSi[3];
420 mS[4] = mSi[1]*mSi[3] - mSi[0]*mSi[4];
421 mS[5] = mSi[0]*mSi[2] - mSi[1]*mSi[1];
423 Double_t s = ( mSi[0]*mS[0] + mSi[1]*mS[1] + mSi[3]*mS[3] );
425 s = ( s > 1.E-20 ) ?1./s :0;
434 //* Residual (measured - estimated)
436 Double_t zeta[3] = { m[0]-ffP[0], m[1]-ffP[1], m[2]-ffP[2] };
441 Double_t mCHt0[7], mCHt1[7], mCHt2[7];
443 mCHt0[0]=ffC[ 0] ; mCHt1[0]=ffC[ 1] ; mCHt2[0]=ffC[ 3] ;
444 mCHt0[1]=ffC[ 1] ; mCHt1[1]=ffC[ 2] ; mCHt2[1]=ffC[ 4] ;
445 mCHt0[2]=ffC[ 3] ; mCHt1[2]=ffC[ 4] ; mCHt2[2]=ffC[ 5] ;
446 mCHt0[3]=ffC[ 6]-mV[ 6]; mCHt1[3]=ffC[ 7]-mV[ 7]; mCHt2[3]=ffC[ 8]-mV[ 8];
447 mCHt0[4]=ffC[10]-mV[10]; mCHt1[4]=ffC[11]-mV[11]; mCHt2[4]=ffC[12]-mV[12];
448 mCHt0[5]=ffC[15]-mV[15]; mCHt1[5]=ffC[16]-mV[16]; mCHt2[5]=ffC[17]-mV[17];
449 mCHt0[6]=ffC[21]-mV[21]; mCHt1[6]=ffC[22]-mV[22]; mCHt2[6]=ffC[23]-mV[23];
451 //* Kalman gain K = mCH'*S
453 Double_t k0[7], k1[7], k2[7];
455 for(Int_t i=0;i<7;++i){
456 k0[i] = mCHt0[i]*mS[0] + mCHt1[i]*mS[1] + mCHt2[i]*mS[3];
457 k1[i] = mCHt0[i]*mS[1] + mCHt1[i]*mS[2] + mCHt2[i]*mS[4];
458 k2[i] = mCHt0[i]*mS[3] + mCHt1[i]*mS[4] + mCHt2[i]*mS[5];
461 //* New estimation of the vertex position
463 if( iter<maxIter-1 ){
464 for(Int_t i=0; i<3; ++i)
465 fVtxGuess[i]= ffP[i] + k0[i]*zeta[0]+k1[i]*zeta[1]+k2[i]*zeta[2];
469 // last itearation -> update the particle
471 //* Add the daughter momentum to the particle momentum
490 //* New estimation of the vertex position r += K*zeta
492 for(Int_t i=0;i<7;++i)
493 fP[i] = ffP[i] + k0[i]*zeta[0] + k1[i]*zeta[1] + k2[i]*zeta[2];
495 //* New covariance matrix C -= K*(mCH')'
497 for(Int_t i=0, k=0;i<7;++i){
498 for(Int_t j=0;j<=i;++j,++k){
499 fC[k] = ffC[k] - (k0[i]*mCHt0[j] + k1[i]*mCHt1[j] + k2[i]*mCHt2[j] );
506 fQ += Daughter.GetQ();
508 fChi2 += (mS[0]*zeta[0] + mS[1]*zeta[1] + mS[3]*zeta[2])*zeta[0]
509 + (mS[1]*zeta[0] + mS[2]*zeta[1] + mS[4]*zeta[2])*zeta[1]
510 + (mS[3]*zeta[0] + mS[4]*zeta[1] + mS[5]*zeta[2])*zeta[2];
516 void AliKFParticleBase::SetProductionVertex( const AliKFParticleBase &Vtx )
518 //* Set production vertex for the particle, when the particle was not used in the vertex fit
520 const Double_t *m = Vtx.fP, *mV = Vtx.fC;
522 Bool_t noS = ( fC[35]<=0 ); // no decay length allowed
525 TransportToDecayVertex();
527 fC[28] = fC[29] = fC[30] = fC[31] = fC[32] = fC[33] = fC[35] = fC[35] = 0;
529 TransportToDS( GetDStoPoint( m ) );
530 fP[7] = -fSFromDecay;
535 mAi[0] = fC[2]*fC[5] - fC[4]*fC[4];
536 mAi[1] = fC[3]*fC[4] - fC[1]*fC[5];
537 mAi[3] = fC[1]*fC[4] - fC[2]*fC[3];
538 Double_t det = (fC[0]*mAi[0] + fC[1]*mAi[1] + fC[3]*mAi[3]);
539 if( det>1.e-20 ) det = 1./det;
545 mAi[2] = ( fC[0]*fC[5] - fC[3]*fC[3] )*det;
546 mAi[4] = ( fC[1]*fC[3] - fC[0]*fC[4] )*det;
547 mAi[5] = ( fC[0]*fC[2] - fC[1]*fC[1] )*det;
551 mB[0][0] = fC[ 6]*mAi[0] + fC[ 7]*mAi[1] + fC[ 8]*mAi[3];
552 mB[0][1] = fC[ 6]*mAi[1] + fC[ 7]*mAi[2] + fC[ 8]*mAi[4];
553 mB[0][2] = fC[ 6]*mAi[3] + fC[ 7]*mAi[4] + fC[ 8]*mAi[5];
555 mB[1][0] = fC[10]*mAi[0] + fC[11]*mAi[1] + fC[12]*mAi[3];
556 mB[1][1] = fC[10]*mAi[1] + fC[11]*mAi[2] + fC[12]*mAi[4];
557 mB[1][2] = fC[10]*mAi[3] + fC[11]*mAi[4] + fC[12]*mAi[5];
559 mB[2][0] = fC[15]*mAi[0] + fC[16]*mAi[1] + fC[17]*mAi[3];
560 mB[2][1] = fC[15]*mAi[1] + fC[16]*mAi[2] + fC[17]*mAi[4];
561 mB[2][2] = fC[15]*mAi[3] + fC[16]*mAi[4] + fC[17]*mAi[5];
563 mB[3][0] = fC[21]*mAi[0] + fC[22]*mAi[1] + fC[23]*mAi[3];
564 mB[3][1] = fC[21]*mAi[1] + fC[22]*mAi[2] + fC[23]*mAi[4];
565 mB[3][2] = fC[21]*mAi[3] + fC[22]*mAi[4] + fC[23]*mAi[5];
567 mB[4][0] = fC[28]*mAi[0] + fC[29]*mAi[1] + fC[30]*mAi[3];
568 mB[4][1] = fC[28]*mAi[1] + fC[29]*mAi[2] + fC[30]*mAi[4];
569 mB[4][2] = fC[28]*mAi[3] + fC[29]*mAi[4] + fC[30]*mAi[5];
571 Double_t z[3] = { m[0]-fP[0], m[1]-fP[1], m[2]-fP[2] };
574 Double_t mAV[6] = { fC[0]-mV[0], fC[1]-mV[1], fC[2]-mV[2],
575 fC[3]-mV[3], fC[4]-mV[4], fC[5]-mV[5] };
578 mAVi[0] = mAV[2]*mAV[5] - mAV[4]*mAV[4];
579 mAVi[1] = mAV[3]*mAV[4] - mAV[1]*mAV[5];
580 mAVi[2] = mAV[0]*mAV[5] - mAV[3]*mAV[3];
581 mAVi[3] = mAV[1]*mAV[4] - mAV[2]*mAV[3];
582 mAVi[4] = mAV[1]*mAV[3] - mAV[0]*mAV[4];
583 mAVi[5] = mAV[0]*mAV[2] - mAV[1]*mAV[1];
585 det = ( mAV[0]*mAVi[0] + mAV[1]*mAVi[1] + mAV[3]*mAVi[3] );
587 if( TMath::Abs(det) > 1.E-20 ){
589 Double_t dChi2 = ( +(mAVi[0]*z[0] + mAVi[1]*z[1] + mAVi[3]*z[2])*z[0]
590 +(mAVi[1]*z[0] + mAVi[2]*z[1] + mAVi[4]*z[2])*z[1]
591 +(mAVi[3]*z[0] + mAVi[4]*z[1] + mAVi[5]*z[2])*z[2] )/det ;
593 // Take Abs(dChi2) here. Negative value of 'det' or 'dChi2' shows that the particle
594 // was not used in the production vertex fit
596 fChi2+= TMath::Abs( dChi2 );
604 fP[3]+= mB[0][0]*z[0] + mB[0][1]*z[1] + mB[0][2]*z[2];
605 fP[4]+= mB[1][0]*z[0] + mB[1][1]*z[1] + mB[1][2]*z[2];
606 fP[5]+= mB[2][0]*z[0] + mB[2][1]*z[1] + mB[2][2]*z[2];
607 fP[6]+= mB[3][0]*z[0] + mB[3][1]*z[1] + mB[3][2]*z[2];
608 fP[7]+= mB[4][0]*z[0] + mB[4][1]*z[1] + mB[4][2]*z[2];
619 d0= mB[0][0]*mV[0] + mB[0][1]*mV[1] + mB[0][2]*mV[3] - fC[ 6];
620 d1= mB[0][0]*mV[1] + mB[0][1]*mV[2] + mB[0][2]*mV[4] - fC[ 7];
621 d2= mB[0][0]*mV[3] + mB[0][1]*mV[4] + mB[0][2]*mV[5] - fC[ 8];
626 fC[ 9]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2];
628 d0= mB[1][0]*mV[0] + mB[1][1]*mV[1] + mB[1][2]*mV[3] - fC[10];
629 d1= mB[1][0]*mV[1] + mB[1][1]*mV[2] + mB[1][2]*mV[4] - fC[11];
630 d2= mB[1][0]*mV[3] + mB[1][1]*mV[4] + mB[1][2]*mV[5] - fC[12];
635 fC[13]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2];
636 fC[14]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2];
638 d0= mB[2][0]*mV[0] + mB[2][1]*mV[1] + mB[2][2]*mV[3] - fC[15];
639 d1= mB[2][0]*mV[1] + mB[2][1]*mV[2] + mB[2][2]*mV[4] - fC[16];
640 d2= mB[2][0]*mV[3] + mB[2][1]*mV[4] + mB[2][2]*mV[5] - fC[17];
645 fC[18]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2];
646 fC[19]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2];
647 fC[20]+= d0*mB[2][0] + d1*mB[2][1] + d2*mB[2][2];
649 d0= mB[3][0]*mV[0] + mB[3][1]*mV[1] + mB[3][2]*mV[3] - fC[21];
650 d1= mB[3][0]*mV[1] + mB[3][1]*mV[2] + mB[3][2]*mV[4] - fC[22];
651 d2= mB[3][0]*mV[3] + mB[3][1]*mV[4] + mB[3][2]*mV[5] - fC[23];
656 fC[24]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2];
657 fC[25]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2];
658 fC[26]+= d0*mB[2][0] + d1*mB[2][1] + d2*mB[2][2];
659 fC[27]+= d0*mB[3][0] + d1*mB[3][1] + d2*mB[3][2];
661 d0= mB[4][0]*mV[0] + mB[4][1]*mV[1] + mB[4][2]*mV[3] - fC[28];
662 d1= mB[4][0]*mV[1] + mB[4][1]*mV[2] + mB[4][2]*mV[4] - fC[29];
663 d2= mB[4][0]*mV[3] + mB[4][1]*mV[4] + mB[4][2]*mV[5] - fC[30];
668 fC[31]+= d0*mB[0][0] + d1*mB[0][1] + d2*mB[0][2];
669 fC[32]+= d0*mB[1][0] + d1*mB[1][1] + d2*mB[1][2];
670 fC[33]+= d0*mB[2][0] + d1*mB[2][1] + d2*mB[2][2];
671 fC[34]+= d0*mB[3][0] + d1*mB[3][1] + d2*mB[3][2];
672 fC[35]+= d0*mB[4][0] + d1*mB[4][1] + d2*mB[4][2];
676 fC[28] = fC[29] = fC[30] = fC[31] = fC[32] = fC[33] = fC[35] = fC[35] = 0;
678 TransportToDS( fP[7] );
687 void AliKFParticleBase::SetMassConstraint( Double_t Mass, Double_t SigmaMass )
689 //* Set hard( SigmaMass=0 ) or soft (SigmaMass>0) mass constraint
691 Double_t m2 = Mass*Mass; // measurement, weighted by Mass
692 Double_t s2 = m2*SigmaMass*SigmaMass; // sigma^2
694 Double_t p2 = fP[3]*fP[3] + fP[4]*fP[4] + fP[5]*fP[5];
695 Double_t e0 = TMath::Sqrt(m2+p2);
698 mH[0] = mH[1] = mH[2] = 0.;
702 mH[6] = 2*fP[6];//e0;
705 Double_t zeta = e0*e0 - e0*fP[6];
706 zeta = m2 - (fP[6]*fP[6]-p2);
708 Double_t mCHt[8], s2_est=0;
709 for( Int_t i=0; i<8; ++i ){
711 for (Int_t j=0;j<8;++j) mCHt[i] += Cij(i,j)*mH[j];
712 s2_est += mH[i]*mCHt[i];
715 if( s2_est<1.e-20 ) return; // calculated mass error is already 0,
716 // the particle can not be constrained on mass
718 Double_t w2 = 1./( s2 + s2_est );
719 fChi2 += zeta*zeta*w2;
721 for( Int_t i=0, ii=0; i<8; ++i ){
722 Double_t ki = mCHt[i]*w2;
724 for(Int_t j=0;j<=i;++j) fC[ii++] -= ki*mCHt[j];
729 void AliKFParticleBase::SetNoDecayLength()
731 //* Set no decay length for resonances
733 TransportToDecayVertex();
736 h[0] = h[1] = h[2] = h[3] = h[4] = h[5] = h[6] = 0;
739 Double_t zeta = 0 - fP[7];
740 for(Int_t i=0;i<8;++i) zeta -= h[i]*(fP[i]-fP[i]);
745 fChi2 += zeta*zeta*s;
747 for( Int_t i=0, ii=0; i<7; ++i ){
748 Double_t ki = fC[28+i]*s;
750 for(Int_t j=0;j<=i;++j) fC[ii++] -= ki*fC[28+j];
754 fC[28] = fC[29] = fC[30] = fC[31] = fC[32] = fC[33] = fC[35] = fC[35] = 0;
758 void AliKFParticleBase::Construct( const AliKFParticleBase* vDaughters[], Int_t NDaughters,
759 const AliKFParticleBase *Parent, Double_t Mass, Bool_t IsConstrained )
761 //* Full reconstruction in one go
764 bool wasLinearized = fIsLinearized;
765 if( !fIsLinearized || IsConstrained ){
766 //fVtxGuess[0] = fVtxGuess[1] = fVtxGuess[2] = 0; //!!!!
767 fVtxGuess[0] = GetX();
768 fVtxGuess[1] = GetY();
769 fVtxGuess[2] = GetZ();
774 Double_t constraintC[6];
777 for(Int_t i=0;i<6;++i) constraintC[i]=fC[i];
779 for(Int_t i=0;i<6;++i) constraintC[i]=0.;
780 constraintC[0] = constraintC[2] = constraintC[5] = 100.;
784 for( Int_t iter=0; iter<maxIter; iter++ ){
785 fAtProductionVertex = 0;
787 fP[0] = fVtxGuess[0];
788 fP[1] = fVtxGuess[1];
789 fP[2] = fVtxGuess[2];
796 for(Int_t i=0;i<6; ++i) fC[i]=constraintC[i];
797 for(Int_t i=6;i<36;++i) fC[i]=0.;
800 fNDF = IsConstrained ?0 :-3;
804 for( Int_t itr =0; itr<NDaughters; itr++ ){
805 AddDaughter( *vDaughters[itr] );
808 for( Int_t i=0; i<3; i++ ) fVtxGuess[i] = fP[i];
811 fIsLinearized = wasLinearized;
813 if( Mass>=0 ) SetMassConstraint( Mass );
814 if( Parent ) SetProductionVertex( *Parent );
818 void AliKFParticleBase::Convert( bool ToProduction )
820 //* Tricky function - convert the particle error along its trajectory to
821 //* the value which corresponds to its production/decay vertex
822 //* It is done by combination of the error of decay length with the position errors
826 GetFieldValue( fP, fld );
827 const Double_t kCLight = fQ*0.000299792458;
828 fld[0]*=kCLight; fld[1]*=kCLight; fld[2]*=kCLight;
836 if( ToProduction ){ h[0]=-h[0]; h[1]=-h[1]; h[2]=-h[2]; }
837 h[3] = h[1]*fld[2]-h[2]*fld[1];
838 h[4] = h[2]*fld[0]-h[0]*fld[2];
839 h[5] = h[0]*fld[1]-h[1]*fld[0];
843 c = fC[28]+h[0]*fC[35];
844 fC[ 0]+= h[0]*(c+fC[28]);
847 fC[ 1]+= h[1]*fC[28] + h[0]*fC[29];
848 c = fC[29]+h[1]*fC[35];
849 fC[ 2]+= h[1]*(c+fC[29]);
852 fC[ 3]+= h[2]*fC[28] + h[0]*fC[30];
853 fC[ 4]+= h[2]*fC[29] + h[1]*fC[30];
854 c = fC[30]+h[2]*fC[35];
855 fC[ 5]+= h[2]*(c+fC[30]);
858 fC[ 6]+= h[3]*fC[28] + h[0]*fC[31];
859 fC[ 7]+= h[3]*fC[29] + h[1]*fC[31];
860 fC[ 8]+= h[3]*fC[30] + h[2]*fC[31];
861 c = fC[31]+h[3]*fC[35];
862 fC[ 9]+= h[3]*(c+fC[31]);
865 fC[10]+= h[4]*fC[28] + h[0]*fC[32];
866 fC[11]+= h[4]*fC[29] + h[1]*fC[32];
867 fC[12]+= h[4]*fC[30] + h[2]*fC[32];
868 fC[13]+= h[4]*fC[31] + h[3]*fC[32];
869 c = fC[32]+h[4]*fC[35];
870 fC[14]+= h[4]*(c+fC[32]);
873 fC[15]+= h[5]*fC[28] + h[0]*fC[33];
874 fC[16]+= h[5]*fC[29] + h[1]*fC[33];
875 fC[17]+= h[5]*fC[30] + h[2]*fC[33];
876 fC[18]+= h[5]*fC[31] + h[3]*fC[33];
877 fC[19]+= h[5]*fC[32] + h[4]*fC[33];
878 c = fC[33]+h[5]*fC[35];
879 fC[20]+= h[5]*(c+fC[33]);
882 fC[21]+= h[0]*fC[34];
883 fC[22]+= h[1]*fC[34];
884 fC[23]+= h[2]*fC[34];
885 fC[24]+= h[3]*fC[34];
886 fC[25]+= h[4]*fC[34];
887 fC[26]+= h[5]*fC[34];
891 void AliKFParticleBase::TransportToDecayVertex()
893 //* Transport the particle to its decay vertex
895 if( fSFromDecay != 0 ) TransportToDS( -fSFromDecay );
896 if( fAtProductionVertex ) Convert(0);
897 fAtProductionVertex = 0;
900 void AliKFParticleBase::TransportToProductionVertex()
902 //* Transport the particle to its production vertex
904 if( fSFromDecay != -fP[7] ) TransportToDS( -fSFromDecay-fP[7] );
905 if( !fAtProductionVertex ) Convert( 1 );
906 fAtProductionVertex = 1;
910 void AliKFParticleBase::TransportToDS( Double_t dS )
912 //* Transport the particle on dS parameter (SignedPath/Momentum)
914 Transport( dS, fP, fC );
919 Double_t AliKFParticleBase::GetDStoPointLine( const Double_t xyz[] ) const
921 //* Get dS to a certain space point without field
923 Double_t p2 = fP[3]*fP[3] + fP[4]*fP[4] + fP[5]*fP[5];
924 if( p2<1.e-4 ) p2 = 1;
925 return ( fP[3]*(xyz[0]-fP[0]) + fP[4]*(xyz[1]-fP[1]) + fP[5]*(xyz[2]-fP[2]) )/p2;
929 Double_t AliKFParticleBase::GetDStoPointBz( Double_t B, const Double_t xyz[] )
933 //* Get dS to a certain space point for Bz field
934 const Double_t kCLight = 0.000299792458;
935 Double_t bq = B*fQ*kCLight;
936 Double_t pt2 = fP[3]*fP[3] + fP[4]*fP[4];
937 if( pt2<1.e-4 ) return 0;
938 Double_t dx = xyz[0] - fP[0];
939 Double_t dy = xyz[1] - fP[1];
940 Double_t a = dx*fP[3]+dy*fP[4];
943 if( TMath::Abs(bq)<1.e-8 ) dS = a/pt2;
944 else dS = TMath::ATan2( bq*a, pt2 + bq*(dy*fP[3] -dx*fP[4]) )/bq;
951 Double_t ss[2], g[2][5];
955 for( Int_t i=0; i<2; i++){
956 Double_t bs = bq*ss[i];
957 Double_t c = TMath::Cos(bs), s = TMath::Sin(bs);
959 if( TMath::Abs(bq)>1.e-8){
963 const Double_t kOvSqr6 = 1./TMath::Sqrt(6.);
964 sB = (1.-bs*kOvSqr6)*(1.+bs*kOvSqr6)*ss[i];
967 g[i][0] = fP[0] + sB*px + cB*py;
968 g[i][1] = fP[1] - cB*px + sB*py;
969 g[i][2] = fP[2] + ss[i]*pz;
970 g[i][3] = + c*px + s*py;
971 g[i][4] = - s*px + c*py;
976 Double_t dMin = 1.e10;
977 for( Int_t j=0; j<2; j++){
978 Double_t xx = g[j][0]-xyz[0];
979 Double_t yy = g[j][1]-xyz[1];
980 Double_t zz = g[j][2]-xyz[2];
981 Double_t d = xx*xx + yy*yy + zz*zz;
990 Double_t x= g[i][0], y= g[i][1], z= g[i][2], ppx= g[i][3], ppy= g[i][4];
991 Double_t ddx = x-xyz[0];
992 Double_t ddy = y-xyz[1];
993 Double_t ddz = z-xyz[2];
994 Double_t c = ddx*ppx + ddy*ppy + ddz*pz ;
995 Double_t pp2 = ppx*ppx + ppy*ppy + pz*pz;
996 if( TMath::Abs(pp2)>1.e-8 ){
1004 void AliKFParticleBase::GetDStoParticleBz( Double_t B, const AliKFParticleBase &p,
1005 Double_t &DS, Double_t &DS1 )
1008 //* Get dS to another particle for Bz field
1009 Double_t px = fP[3];
1010 Double_t py = fP[4];
1011 Double_t pz = fP[5];
1013 Double_t px1 = p.fP[3];
1014 Double_t py1 = p.fP[4];
1015 Double_t pz1 = p.fP[5];
1017 const Double_t kCLight = 0.000299792458;
1019 Double_t bq = B*fQ*kCLight;
1020 Double_t bq1 = B*p.fQ*kCLight;
1021 Double_t s=0, ds=0, s1=0, ds1=0;
1023 if( TMath::Abs(bq)>1.e-8 || TMath::Abs(bq1)>1.e-8 ){
1025 Double_t dx = (p.fP[0] - fP[0]);
1026 Double_t dy = (p.fP[1] - fP[1]);
1027 Double_t d2 = (dx*dx+dy*dy);
1029 Double_t p2 = (px *px + py *py);
1030 Double_t p21 = (px1*px1 + py1*py1);
1032 Double_t a = (px*py1 - py*px1);
1033 Double_t b = (px*px1 + py*py1);
1035 Double_t ldx = bq*bq1*dx - bq1*py + bq*py1 ;
1036 Double_t ldy = bq*bq1*dy + bq1*px - bq*px1 ;
1037 Double_t l2 = ldx*ldx + ldy*ldy;
1039 Double_t cS = bq1*p2 + bq*bq1*(dy* px - dx* py) - bq*b;
1040 Double_t cS1= bq*p21 - bq*bq1*(dy*px1 - dx*py1) - bq1*b;
1042 Double_t ca = bq*bq*bq1*d2 +2*( cS + bq*bq*(py1*dx-px1*dy)) ;
1043 Double_t ca1 = bq*bq1*bq1*d2 +2*( cS1 - bq1*bq1*(py*dx-px*dy)) ;
1045 Double_t sa = 4*l2*p2 - ca*ca;
1046 Double_t sa1 = 4*l2*p21 - ca1*ca1;
1051 if( TMath::Abs(bq)>1.e-8){
1052 s = TMath::ATan2( bq*( bq1*(dx*px +dy*py) + a ) , cS )/bq;
1053 ds = TMath::ATan2(TMath::Sqrt(sa),ca)/bq;
1055 s = ( (dx*px + dy*py) + (py*px1-px*py1)/bq1)/p2;
1056 ds = s*s - (d2-2*(px1*dy-py1*dx)/bq1)/p2;
1058 ds = TMath::Sqrt(ds);
1061 if( TMath::Abs(bq1)>1.e-8){
1062 s1 = TMath::ATan2( -bq1*( bq*(dx*px1+dy*py1) + a), cS1 )/bq1;
1063 ds1 = TMath::ATan2(TMath::Sqrt(sa1),ca1)/bq1;
1065 s1 = (-(dx*px1 + dy*py1) + (py*px1-px*py1)/bq)/p21;
1066 ds1 = s1*s1 - (d2+2*(px*dy-py*dx)/bq)/p21;
1067 if( ds1<0 ) ds1 = 0;
1068 ds1 = TMath::Sqrt(ds1);
1072 Double_t ss[2], ss1[2], g[2][5],g1[2][5];
1078 for( Int_t i=0; i<2; i++){
1079 Double_t bs = bq*ss[i];
1080 Double_t c = TMath::Cos(bs), sss = TMath::Sin(bs);
1082 if( TMath::Abs(bq)>1.e-8){
1086 const Double_t kOvSqr6 = 1./TMath::Sqrt(6.);
1087 sB = (1.-bs*kOvSqr6)*(1.+bs*kOvSqr6)*ss[i];
1090 g[i][0] = fP[0] + sB*px + cB*py;
1091 g[i][1] = fP[1] - cB*px + sB*py;
1092 g[i][2] = fP[2] + ss[i]*pz;
1093 g[i][3] = + c*px + sss*py;
1094 g[i][4] = - sss*px + c*py;
1097 c = TMath::Cos(bs); sss = TMath::Sin(bs);
1098 if( TMath::Abs(bq1)>1.e-8){
1102 const Double_t kOvSqr6 = 1./TMath::Sqrt(6.);
1103 sB = (1.-bs*kOvSqr6)*(1.+bs*kOvSqr6)*ss1[i];
1107 g1[i][0] = p.fP[0] + sB*px1 + cB*py1;
1108 g1[i][1] = p.fP[1] - cB*px1 + sB*py1;
1109 g1[i][2] = p.fP[2] + ss[i]*pz1;
1110 g1[i][3] = + c*px1 + sss*py1;
1111 g1[i][4] = - sss*px1 + c*py1;
1116 Double_t dMin = 1.e10;
1117 for( Int_t j=0; j<2; j++){
1118 for( Int_t j1=0; j1<2; j1++){
1119 Double_t xx = g[j][0]-g1[j1][0];
1120 Double_t yy = g[j][1]-g1[j1][1];
1121 Double_t zz = g[j][2]-g1[j1][2];
1122 Double_t d = xx*xx + yy*yy + zz*zz;
1134 Double_t x= g[i][0], y= g[i][1], z= g[i][2], ppx= g[i][3], ppy= g[i][4];
1135 Double_t x1=g1[i1][0], y1= g1[i1][1], z1= g1[i1][2], ppx1= g1[i1][3], ppy1= g1[i1][4];
1139 Double_t a = ppx*ppx1 + ppy*ppy1 + pz*pz1;
1140 Double_t b = dx*ppx1 + dy*ppy1 + dz*pz1;
1141 Double_t c = dx*ppx + dy*ppy + dz*pz ;
1142 Double_t pp2 = ppx*ppx + ppy*ppy + pz*pz;
1143 Double_t pp21= ppx1*ppx1 + ppy1*ppy1 + pz1*pz1;
1144 Double_t det = pp2*pp21 - a*a;
1145 if( TMath::Abs(det)>1.e-8 ){
1146 DS+=(a*b-pp21*c)/det;
1147 DS1+=(a*c-pp2*b)/det;
1154 void AliKFParticleBase::TransportCBM( Double_t dS,
1155 Double_t P[], Double_t C[] ) const
1157 //* Transport the particle on dS, output to P[],C[], for CBM field
1160 TransportLine( dS, P, C );
1164 const Double_t kCLight = 0.000299792458;
1166 Double_t c = fQ*kCLight;
1168 // construct coefficients
1175 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;
1177 { // get field integrals
1180 Double_t p0[3], p1[3], p2[3];
1182 // line track approximation
1188 p2[0] = fP[0] + px*dS;
1189 p2[1] = fP[1] + py*dS;
1190 p2[2] = fP[2] + pz*dS;
1192 p1[0] = 0.5*(p0[0]+p2[0]);
1193 p1[1] = 0.5*(p0[1]+p2[1]);
1194 p1[2] = 0.5*(p0[2]+p2[2]);
1196 // first order track approximation
1198 GetFieldValue( p0, fld[0] );
1199 GetFieldValue( p1, fld[1] );
1200 GetFieldValue( p2, fld[2] );
1202 Double_t ssy1 = ( 7*fld[0][1] + 6*fld[1][1]-fld[2][1] )*c*dS*dS/96.;
1203 Double_t ssy2 = ( fld[0][1] + 2*fld[1][1] )*c*dS*dS/6.;
1211 GetFieldValue( p0, fld[0] );
1212 GetFieldValue( p1, fld[1] );
1213 GetFieldValue( p2, fld[2] );
1215 sx = c*( fld[0][0] + 4*fld[1][0] + fld[2][0] )*dS/6.;
1216 sy = c*( fld[0][1] + 4*fld[1][1] + fld[2][1] )*dS/6.;
1217 sz = c*( fld[0][2] + 4*fld[1][2] + fld[2][2] )*dS/6.;
1219 ssx = c*( fld[0][0] + 2*fld[1][0])*dS*dS/6.;
1220 ssy = c*( fld[0][1] + 2*fld[1][1])*dS*dS/6.;
1221 ssz = c*( fld[0][2] + 2*fld[1][2])*dS*dS/6.;
1223 Double_t c2[3][3] = { { 5, -4, -1},{ 44, 80, -4},{ 11, 44, 5} }; // /=360.
1224 Double_t cc2[3][3] = { { 38, 8, -4},{ 148, 208, -20},{ 3, 36, 3} }; // /=2520.
1225 for(Int_t n=0; n<3; n++)
1226 for(Int_t m=0; m<3; m++)
1228 syz += c2[n][m]*fld[n][1]*fld[m][2];
1229 ssyz += cc2[n][m]*fld[n][1]*fld[m][2];
1232 syz *= c*c*dS*dS/360.;
1233 ssyz *= c*c*dS*dS*dS/2520.;
1235 syy = c*( fld[0][1] + 4*fld[1][1] + fld[2][1] )*dS;
1236 syyy = syy*syy*syy / 1296;
1239 ssyy = ( fld[0][1]*( 38*fld[0][1] + 156*fld[1][1] - fld[2][1] )+
1240 fld[1][1]*( 208*fld[1][1] +16*fld[2][1] )+
1241 fld[2][1]*( 3*fld[2][1] )
1242 )*dS*dS*dS*c*c/2520.;
1245 fld[0][1]*( fld[0][1]*( 85*fld[0][1] + 526*fld[1][1] - 7*fld[2][1] )+
1246 fld[1][1]*( 1376*fld[1][1] +84*fld[2][1] )+
1247 fld[2][1]*( 19*fld[2][1] ) )+
1248 fld[1][1]*( fld[1][1]*( 1376*fld[1][1] +256*fld[2][1] )+
1249 fld[2][1]*( 62*fld[2][1] ) )+
1250 fld[2][1]*fld[2][1] *( 3*fld[2][1] )
1251 )*dS*dS*dS*dS*c*c*c/90720.;
1256 for( Int_t i=0; i<8; i++ ) for( Int_t j=0; j<8; j++) mJ[i][j]=0;
1258 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;
1259 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;
1260 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;
1262 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;
1263 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;
1264 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;
1265 mJ[6][6] = mJ[7][7] = 1;
1267 P[0] = fP[0] + mJ[0][3]*px + mJ[0][4]*py + mJ[0][5]*pz;
1268 P[1] = fP[1] + mJ[1][3]*px + mJ[1][4]*py + mJ[1][5]*pz;
1269 P[2] = fP[2] + mJ[2][3]*px + mJ[2][4]*py + mJ[2][5]*pz;
1270 P[3] = mJ[3][3]*px + mJ[3][4]*py + mJ[3][5]*pz;
1271 P[4] = mJ[4][3]*px + mJ[4][4]*py + mJ[4][5]*pz;
1272 P[5] = mJ[5][3]*px + mJ[5][4]*py + mJ[5][5]*pz;
1276 MultQSQt( mJ[0], fC, C);
1281 void AliKFParticleBase::TransportBz( Double_t b, Double_t ss,
1282 Double_t p[], Double_t cc[] ) const
1284 //* Transport the particle on dS, output to P[],C[], for Bz field
1286 const Double_t kCLight = 0.000299792458;
1289 Double_t s = TMath::Sin(bs), c = TMath::Cos(bs);
1291 if( TMath::Abs(bs)>1.e-10){
1295 const Double_t kOvSqr6 = 1./TMath::Sqrt(6.);
1296 sB = (1.-bs*kOvSqr6)*(1.+bs*kOvSqr6)*ss;
1300 Double_t px = fP[3];
1301 Double_t py = fP[4];
1302 Double_t pz = fP[5];
1304 p[0] = fP[0] + sB*px + cB*py;
1305 p[1] = fP[1] - cB*px + sB*py;
1306 p[2] = fP[2] + ss*pz;
1308 p[4] = -s*px + c*py;
1313 Double_t mJ[8][8] = { {1,0,0, sB, cB, 0, 0, 0 },
1314 {0,1,0, -cB, sB, 0, 0, 0 },
1315 {0,0,1, 0, 0, ss, 0, 0 },
1316 {0,0,0, c, s, 0, 0, 0 },
1317 {0,0,0, -s, c, 0, 0, 0 },
1318 {0,0,0, 0, 0, 1, 0, 0 },
1319 {0,0,0, 0, 0, 0, 1, 0 },
1320 {0,0,0, 0, 0, 0, 0, 1 } };
1322 for( Int_t k=0,i=0; i<8; i++)
1323 for( Int_t j=0; j<=i; j++, k++ ) mA[i][j] = mA[j][i] = fC[k];
1326 for( Int_t i=0; i<8; i++ )
1327 for( Int_t j=0; j<8; j++ ){
1329 for( Int_t k=0; k<8; k++ ) mJC[i][j]+=mJ[i][k]*mA[k][j];
1332 for( Int_t k=0,i=0; i<8; i++)
1333 for( Int_t j=0; j<=i; j++, k++ ){
1335 for( Int_t l=0; l<8; l++ ) cc[k]+=mJC[i][l]*mJ[j][l];
1340 Double_t cBC13 = cB*fC[13];
1341 Double_t C17 = fC[17];
1342 Double_t C18 = fC[18];
1343 fC[ 0]+= 2*(sB*fC[ 6] + cB*fC[10]) + (sB*fC[ 9] + 2*cBC13)*sB + cB*cB*fC[14];
1345 Double_t mJC13= fC[ 7] - cB*fC[ 9] + sB*fC[13];
1346 Double_t mJC14= fC[11] - cBC13 + sB*fC[14];
1348 fC[ 1]+= -cB*fC[ 6] + sB*fC[10] +mJC13*sB +mJC14*cB;
1349 fC[ 2]+= -cB*fC[ 7] + sB*fC[11] -mJC13*cB +mJC14*sB;
1351 Double_t mJC23= fC[ 8] + S*fC[18];
1352 Double_t mJC24= fC[12] + S*fC[19];
1353 fC[ 3]+= S*fC[15] +mJC23*sB +mJC24*cB;
1354 fC[ 4]+= S*fC[16] -mJC23*cB +mJC24*sB;
1356 fC[15]+= C18*sB + fC[19]*cB;
1357 fC[16]+= -C18*cB + fC[19]*sB;
1359 fC[18] = C18*c + fC[19]*s;
1360 fC[19] = -C18*s + fC[19]*c;
1362 fC[ 5]+= (C17 + C17 + fC[17])*S;
1364 Double_t mJC33= c*fC[ 9] + s*fC[13]; Double_t mJC34= c*fC[13] + s*fC[14];
1365 Double_t mJC43=-s*fC[ 9] + c*fC[13]; Double_t mJC44=-s*fC[13] + c*fC[14];
1366 Double_t C6= fC[6], C7= fC[7], C8= fC[8];
1368 fC[ 6]= c*C6 + s*fC[10] +mJC33*sB +mJC34*cB;
1369 fC[ 7]= c*C7 + s*fC[11] -mJC33*cB +mJC34*sB;
1370 fC[ 8]= c*C8 + s*fC[12] +fC[18]*S;
1371 fC[ 9]= mJC33*c +mJC34*s;
1373 fC[10]= -s*C6 + c*fC[10] +mJC43*sB +mJC44*cB;
1374 fC[11]= -s*C7 + c*fC[11] -mJC43*cB +mJC44*sB;
1375 fC[12]= -s*C8 + c*fC[12] +fC[19]*S;
1376 fC[13]= mJC43*c +mJC44*s;
1377 fC[14]=-mJC43*s +mJC44*c;
1382 Double_t AliKFParticleBase::GetDistanceFromVertex( const AliKFParticleBase &Vtx ) const
1384 //* Calculate distance from vertex [cm]
1386 return GetDistanceFromVertex( Vtx.fP );
1389 Double_t AliKFParticleBase::GetDistanceFromVertex( const Double_t vtx[] ) const
1391 //* Calculate distance from vertex [cm]
1393 Double_t mP[8], mC[36];
1394 Transport( GetDStoPoint(vtx), mP, mC );
1395 Double_t d[3]={ vtx[0]-mP[0], vtx[1]-mP[1], vtx[2]-mP[2]};
1396 return TMath::Sqrt( d[0]*d[0]+d[1]*d[1]+d[2]*d[2] );
1399 Double_t AliKFParticleBase::GetDistanceFromParticle( const AliKFParticleBase &p )
1402 //* Calculate distance to other particle [cm]
1405 GetDStoParticle( p, dS, dS1 );
1406 Double_t mP[8], mC[36], mP1[8], mC1[36];
1407 Transport( dS, mP, mC );
1408 p.Transport( dS1, mP1, mC1 );
1409 Double_t dx = mP[0]-mP1[0];
1410 Double_t dy = mP[1]-mP1[1];
1411 Double_t dz = mP[2]-mP1[2];
1412 return TMath::Sqrt(dx*dx+dy*dy+dz*dz);
1415 Double_t AliKFParticleBase::GetDeviationFromVertex( const AliKFParticleBase &Vtx ) const
1417 //* Calculate sqrt(Chi2/ndf) deviation from vertex
1419 return GetDeviationFromVertex( Vtx.fP, Vtx.fC );
1423 Double_t AliKFParticleBase::GetDeviationFromVertex( const Double_t v[], const Double_t Cv[] ) const
1425 //* Calculate sqrt(Chi2/ndf) deviation from vertex
1426 //* v = [xyz], Cv=[Cxx,Cxy,Cyy,Cxz,Cyz,Czz]-covariance matrix
1431 Transport( GetDStoPoint(v), mP, mC );
1433 Double_t d[3]={ v[0]-mP[0], v[1]-mP[1], v[2]-mP[2]};
1435 Double_t sigmaS = .1+10.*TMath::Sqrt( (d[0]*d[0]+d[1]*d[1]+d[2]*d[2])/
1436 (mP[3]*mP[3]+mP[4]*mP[4]+mP[5]*mP[5]) );
1439 Double_t h[3] = { mP[3]*sigmaS, mP[4]*sigmaS, mP[5]*sigmaS };
1443 mC[1] +h[1]*h[0], mC[2] +h[1]*h[1],
1444 mC[3] +h[2]*h[0], mC[4] +h[2]*h[1], mC[5] +h[2]*h[2] };
1457 mS[0] = mSi[2]*mSi[5] - mSi[4]*mSi[4];
1458 mS[1] = mSi[3]*mSi[4] - mSi[1]*mSi[5];
1459 mS[2] = mSi[0]*mSi[5] - mSi[3]*mSi[3];
1460 mS[3] = mSi[1]*mSi[4] - mSi[2]*mSi[3];
1461 mS[4] = mSi[1]*mSi[3] - mSi[0]*mSi[4];
1462 mS[5] = mSi[0]*mSi[2] - mSi[1]*mSi[1];
1464 Double_t s = ( mSi[0]*mS[0] + mSi[1]*mS[1] + mSi[3]*mS[3] );
1465 s = ( s > 1.E-20 ) ?1./s :0;
1467 return TMath::Sqrt( TMath::Abs(s*( ( mS[0]*d[0] + mS[1]*d[1] + mS[3]*d[2])*d[0]
1468 +(mS[1]*d[0] + mS[2]*d[1] + mS[4]*d[2])*d[1]
1469 +(mS[3]*d[0] + mS[4]*d[1] + mS[5]*d[2])*d[2] ))/2);
1473 Double_t AliKFParticleBase::GetDeviationFromParticle( const AliKFParticleBase &p )
1476 //* Calculate sqrt(Chi2/ndf) deviation from other particle
1479 GetDStoParticle( p, dS, dS1 );
1480 Double_t mP1[8], mC1[36];
1481 p.Transport( dS1, mP1, mC1 );
1483 Double_t d[3]={ fP[0]-mP1[0], fP[1]-mP1[1], fP[2]-mP1[2]};
1485 Double_t sigmaS = .1+10.*TMath::Sqrt( (d[0]*d[0]+d[1]*d[1]+d[2]*d[2])/
1486 (mP1[3]*mP1[3]+mP1[4]*mP1[4]+mP1[5]*mP1[5]) );
1488 Double_t h[3] = { mP1[3]*sigmaS, mP1[4]*sigmaS, mP1[5]*sigmaS };
1497 return GetDeviationFromVertex( mP1, mC1 )*TMath::Sqrt(2./1.);
1502 void AliKFParticleBase::SubtractFromVertex( AliKFParticleBase &Vtx ) const
1504 //* Subtract the particle from the vertex
1508 GetFieldValue( Vtx.fP, fld );
1509 const Double_t kCLight = 0.000299792458;
1510 fld[0]*=kCLight; fld[1]*=kCLight; fld[2]*=kCLight;
1516 if( Vtx.fIsLinearized ){
1517 GetMeasurement( Vtx.fVtxGuess, m, mCm );
1519 GetMeasurement( Vtx.fP, m, mCm );
1535 Double_t mSi[6] = { mV[0]-Vtx.fC[0],
1536 mV[1]-Vtx.fC[1], mV[2]-Vtx.fC[2],
1537 mV[3]-Vtx.fC[3], mV[4]-Vtx.fC[4], mV[5]-Vtx.fC[5] };
1539 mS[0] = mSi[2]*mSi[5] - mSi[4]*mSi[4];
1540 mS[1] = mSi[3]*mSi[4] - mSi[1]*mSi[5];
1541 mS[2] = mSi[0]*mSi[5] - mSi[3]*mSi[3];
1542 mS[3] = mSi[1]*mSi[4] - mSi[2]*mSi[3];
1543 mS[4] = mSi[1]*mSi[3] - mSi[0]*mSi[4];
1544 mS[5] = mSi[0]*mSi[2] - mSi[1]*mSi[1];
1546 Double_t s = ( mSi[0]*mS[0] + mSi[1]*mS[1] + mSi[3]*mS[3] );
1547 s = ( s > 1.E-20 ) ?1./s :0;
1556 //* Residual (measured - estimated)
1558 Double_t zeta[3] = { m[0]-Vtx.fP[0], m[1]-Vtx.fP[1], m[2]-Vtx.fP[2] };
1560 //* mCHt = mCH' - D'
1562 Double_t mCHt0[3], mCHt1[3], mCHt2[3];
1564 mCHt0[0]=Vtx.fC[ 0] ; mCHt1[0]=Vtx.fC[ 1] ; mCHt2[0]=Vtx.fC[ 3] ;
1565 mCHt0[1]=Vtx.fC[ 1] ; mCHt1[1]=Vtx.fC[ 2] ; mCHt2[1]=Vtx.fC[ 4] ;
1566 mCHt0[2]=Vtx.fC[ 3] ; mCHt1[2]=Vtx.fC[ 4] ; mCHt2[2]=Vtx.fC[ 5] ;
1568 //* Kalman gain K = mCH'*S
1570 Double_t k0[3], k1[3], k2[3];
1572 for(Int_t i=0;i<3;++i){
1573 k0[i] = mCHt0[i]*mS[0] + mCHt1[i]*mS[1] + mCHt2[i]*mS[3];
1574 k1[i] = mCHt0[i]*mS[1] + mCHt1[i]*mS[2] + mCHt2[i]*mS[4];
1575 k2[i] = mCHt0[i]*mS[3] + mCHt1[i]*mS[4] + mCHt2[i]*mS[5];
1578 //* New estimation of the vertex position r += K*zeta
1580 Double_t dChi2 = -(mS[0]*zeta[0] + mS[1]*zeta[1] + mS[3]*zeta[2])*zeta[0]
1581 + (mS[1]*zeta[0] + mS[2]*zeta[1] + mS[4]*zeta[2])*zeta[1]
1582 + (mS[3]*zeta[0] + mS[4]*zeta[1] + mS[5]*zeta[2])*zeta[2];
1584 if( Vtx.fChi2 - dChi2 < 0 ) return;
1586 for(Int_t i=0;i<3;++i)
1587 Vtx.fP[i] -= k0[i]*zeta[0] + k1[i]*zeta[1] + k2[i]*zeta[2];
1589 //* New covariance matrix C -= K*(mCH')'
1591 for(Int_t i=0, k=0;i<3;++i){
1592 for(Int_t j=0;j<=i;++j,++k)
1593 Vtx.fC[k] += k0[i]*mCHt0[j] + k1[i]*mCHt1[j] + k2[i]*mCHt2[j];
1604 void AliKFParticleBase::TransportLine( Double_t dS,
1605 Double_t P[], Double_t C[] ) const
1607 //* Transport the particle as a straight line
1609 P[0] = fP[0] + dS*fP[3];
1610 P[1] = fP[1] + dS*fP[4];
1611 P[2] = fP[2] + dS*fP[5];
1618 Double_t c6 = fC[ 6] + dS*fC[ 9];
1619 Double_t c11 = fC[11] + dS*fC[14];
1620 Double_t c17 = fC[17] + dS*fC[20];
1621 Double_t sc13 = dS*fC[13];
1622 Double_t sc18 = dS*fC[18];
1623 Double_t sc19 = dS*fC[19];
1625 C[ 0] = fC[ 0] + dS*( fC[ 6] + c6 );
1626 C[ 2] = fC[ 2] + dS*( fC[11] + c11 );
1627 C[ 5] = fC[ 5] + dS*( fC[17] + c17 );
1629 C[ 7] = fC[ 7] + sc13;
1630 C[ 8] = fC[ 8] + sc18;
1633 C[12] = fC[12] + sc19;
1635 C[ 1] = fC[ 1] + dS*( fC[10] + C[ 7] );
1636 C[ 3] = fC[ 3] + dS*( fC[15] + C[ 8] );
1637 C[ 4] = fC[ 4] + dS*( fC[16] + C[12] );
1640 C[10] = fC[10] + sc13;
1645 C[15] = fC[15] + sc18;
1646 C[16] = fC[16] + sc19;
1652 C[21] = fC[21] + dS*fC[24];
1653 C[22] = fC[22] + dS*fC[25];
1654 C[23] = fC[23] + dS*fC[26];
1660 C[28] = fC[28] + dS*fC[31];
1661 C[29] = fC[29] + dS*fC[32];
1662 C[30] = fC[30] + dS*fC[33];
1672 void AliKFParticleBase::MultQSQt( const Double_t Q[], const Double_t S[], Double_t SOut[] )
1674 //* Matrix multiplication Q*S*Q^T, Q - square matrix, S - symmetric
1679 for( Int_t i=0, ij=0; i<kN; i++ ){
1680 for( Int_t j=0; j<kN; j++, ++ij ){
1682 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];
1686 for( Int_t i=0; i<kN; i++ ){
1687 for( Int_t j=0; j<=i; j++ ){
1688 Int_t ij = ( j<=i ) ? i*(i+1)/2+j :j*(j+1)/2+i;
1690 for( Int_t k=0; k<kN; k++ ) SOut[ij] += Q[ i*kN+k ] * mA[ k*kN+j ];
1696 // 72-charachters line to define the printer border
1697 //3456789012345678901234567890123456789012345678901234567890123456789012