1 /**************************************************************************
2 * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
4 * Author: The ALICE Off-line Project. *
5 * Contributors are mentioned in the code where appropriate. *
7 * Permission to use, copy, modify and distribute this software and its *
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12 * about the suitability of this software for any purpose. It is *
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14 **************************************************************************/
18 ///////////////////////////////////////////////////////////////////////////
19 // Implementation of the ITS track class
21 // Origin: Iouri Belikov, CERN, Jouri.Belikov@cern.ch
22 // dEdx analysis by: Boris Batyunya, JINR, Boris.Batiounia@cern.ch
23 ///////////////////////////////////////////////////////////////////////////
26 #include "AliCluster.h"
27 #include "AliESDVertex.h"
28 #include "AliITSReconstructor.h"
29 #include "AliITStrackV2.h"
30 #include "AliTracker.h"
33 const Int_t AliITStrackV2::fgkWARN = 5;
35 ClassImp(AliITStrackV2)
38 //____________________________________________________________________________
39 AliITStrackV2::AliITStrackV2() : AliKalmanTrack(),
40 fCheckInvariant(kTRUE),
44 for(Int_t i=0; i<2*AliITSgeomTGeo::kNLayers; i++) {fIndex[i]=-1; fModule[i]=-1;}
45 for(Int_t i=0; i<AliITSgeomTGeo::kNLayers; i++) {fSharedWeight[i]=0;}
46 for(Int_t i=0; i<4; i++) fdEdxSample[i]=0;
50 //____________________________________________________________________________
51 AliITStrackV2::AliITStrackV2(AliESDtrack& t,Bool_t c):
53 fCheckInvariant(kTRUE),
54 fdEdx(t.GetITSsignal()),
57 //------------------------------------------------------------------
58 // Conversion ESD track -> ITS track.
59 // If c==kTRUE, create the ITS track out of the constrained params.
60 //------------------------------------------------------------------
61 const AliExternalTrackParam *par=&t;
63 par=t.GetConstrainedParam();
64 if (!par) AliError("AliITStrackV2: conversion failed !\n");
66 Set(par->GetX(),par->GetAlpha(),par->GetParameter(),par->GetCovariance());
68 SetLabel(t.GetITSLabel());
69 SetMass(t.GetMassForTracking());
70 SetNumberOfClusters(t.GetITSclusters(fIndex));
72 if (t.GetStatus()&AliESDtrack::kTIME) {
74 Double_t times[10]; t.GetIntegratedTimes(times); SetIntegratedTimes(times);
75 SetIntegratedLength(t.GetIntegratedLength());
78 for(Int_t i=0; i<AliITSgeomTGeo::kNLayers; i++) {fSharedWeight[i]=0;}
79 for(Int_t i=0; i<4; i++) fdEdxSample[i]=0;
82 //____________________________________________________________________________
83 void AliITStrackV2::ResetClusters() {
84 //------------------------------------------------------------------
85 // Reset the array of attached clusters.
86 //------------------------------------------------------------------
87 for (Int_t i=0; i<2*AliITSgeomTGeo::kNLayers; i++) fIndex[i]=-1;
88 for (Int_t i=0; i<AliITSgeomTGeo::kNLayers; i++) {fSharedWeight[i]=0;}
90 SetNumberOfClusters(0);
93 //____________________________________________________________________________
94 void AliITStrackV2::UpdateESDtrack(ULong_t flags) const {
95 // Update track params
96 fESDtrack->UpdateTrackParams(this,flags);
98 // set correctly the global label
99 if (fESDtrack->IsOn(AliESDtrack::kTPCin)) {
100 // for global track the GetLabel should be negative if
102 // 2) this->GetLabel()<0
103 // 3) GetTPCLabel() != this->GetLabel()
104 int label = fESDtrack->GetTPCLabel();
105 int itsLabel = GetLabel();
106 if (label<0 || itsLabel<0 || itsLabel!=label) label = -TMath::Abs(label);
107 fESDtrack->SetLabel(label);
110 // copy the module indices
112 for(i=0;i<2*AliITSgeomTGeo::kNLayers;i++) {
113 // printf(" %d\n",GetModuleIndex(i));
114 fESDtrack->SetITSModuleIndex(i,GetModuleIndex(i));
116 // copy the map of shared clusters
117 if(flags==AliESDtrack::kITSin) {
118 UChar_t itsSharedMap=0;
119 for(i=0;i<AliITSgeomTGeo::kNLayers;i++) {
120 if(fSharedWeight[i]>0) SETBIT(itsSharedMap,i);
123 fESDtrack->SetITSSharedMap(itsSharedMap);
126 // copy the 4 dedx samples
127 Double_t sdedx[4]={0.,0.,0.,0.};
128 for(i=0; i<4; i++) sdedx[i]=fdEdxSample[i];
129 fESDtrack->SetITSdEdxSamples(sdedx);
132 //____________________________________________________________________________
133 AliITStrackV2::AliITStrackV2(const AliITStrackV2& t) :
135 fCheckInvariant(t.fCheckInvariant),
137 fESDtrack(t.fESDtrack)
139 //------------------------------------------------------------------
141 //------------------------------------------------------------------
143 for (i=0; i<4; i++) fdEdxSample[i]=t.fdEdxSample[i];
144 for (i=0; i<2*AliITSgeomTGeo::GetNLayers(); i++) {
145 fIndex[i]=t.fIndex[i];
146 fModule[i]=t.fModule[i];
148 for (i=0; i<AliITSgeomTGeo::kNLayers; i++) {fSharedWeight[i]=t.fSharedWeight[i];}
151 //_____________________________________________________________________________
152 Int_t AliITStrackV2::Compare(const TObject *o) const {
153 //-----------------------------------------------------------------
154 // This function compares tracks according to the their curvature
155 //-----------------------------------------------------------------
156 AliITStrackV2 *t=(AliITStrackV2*)o;
157 //Double_t co=OneOverPt();
158 //Double_t c =OneOverPt();
159 Double_t co=t->GetSigmaY2()*t->GetSigmaZ2();
160 Double_t c =GetSigmaY2()*GetSigmaZ2();
162 else if (c<co) return -1;
166 //____________________________________________________________________________
168 AliITStrackV2::PropagateToVertex(const AliESDVertex *v,Double_t d,Double_t x0)
170 //------------------------------------------------------------------
171 //This function propagates a track to the minimal distance from the origin
172 //------------------------------------------------------------------
174 if (PropagateToDCA(v,bz,kVeryBig)) {
175 Double_t xOverX0,xTimesRho;
176 xOverX0 = d; xTimesRho = d*x0;
177 if (CorrectForMeanMaterial(xOverX0,xTimesRho,kTRUE)) return kTRUE;
182 //____________________________________________________________________________
183 Bool_t AliITStrackV2::
184 GetGlobalXYZat(Double_t xloc, Double_t &x, Double_t &y, Double_t &z) const {
185 //------------------------------------------------------------------
186 //This function returns a track position in the global system
187 //------------------------------------------------------------------
189 Bool_t rc=GetXYZAt(xloc, GetBz(), r);
190 x=r[0]; y=r[1]; z=r[2];
194 //_____________________________________________________________________________
195 Double_t AliITStrackV2::GetPredictedChi2(const AliCluster *c) const {
196 //-----------------------------------------------------------------
197 // This function calculates a predicted chi2 increment.
198 //-----------------------------------------------------------------
199 Double_t p[2]={c->GetY(), c->GetZ()};
200 Double_t cov[3]={c->GetSigmaY2(), 0., c->GetSigmaZ2()};
201 return AliExternalTrackParam::GetPredictedChi2(p,cov);
204 //____________________________________________________________________________
205 Bool_t AliITStrackV2::PropagateTo(Double_t xk, Double_t d, Double_t x0) {
206 //------------------------------------------------------------------
207 //This function propagates a track
208 //------------------------------------------------------------------
210 Double_t oldX=GetX(), oldY=GetY(), oldZ=GetZ();
212 //Double_t bz=GetBz();
213 //if (!AliExternalTrackParam::PropagateTo(xk,bz)) return kFALSE;
214 Double_t b[3]; GetBxByBz(b);
215 if (!AliExternalTrackParam::PropagateToBxByBz(xk,b)) return kFALSE;
216 Double_t xOverX0,xTimesRho;
217 xOverX0 = d; xTimesRho = d*x0;
218 if (!CorrectForMeanMaterial(xOverX0,xTimesRho,kTRUE)) return kFALSE;
220 Double_t x=GetX(), y=GetY(), z=GetZ();
221 if (IsStartedTimeIntegral() && x>oldX) {
222 Double_t l2 = (x-oldX)*(x-oldX) + (y-oldY)*(y-oldY) + (z-oldZ)*(z-oldZ);
223 AddTimeStep(TMath::Sqrt(l2));
229 //____________________________________________________________________________
230 Bool_t AliITStrackV2::PropagateToTGeo(Double_t xToGo, Int_t nstep, Double_t &xOverX0, Double_t &xTimesRho, Bool_t addTime) {
231 //-------------------------------------------------------------------
232 // Propagates the track to a reference plane x=xToGo in n steps.
233 // These n steps are only used to take into account the curvature.
234 // The material is calculated with TGeo. (L.Gaudichet)
235 //-------------------------------------------------------------------
237 Double_t startx = GetX(), starty = GetY(), startz = GetZ();
238 Double_t sign = (startx<xToGo) ? -1.:1.;
239 Double_t step = (xToGo-startx)/TMath::Abs(nstep);
241 Double_t start[3], end[3], mparam[7];
242 //Double_t bz = GetBz();
243 Double_t b[3]; GetBxByBz(b);
248 for (Int_t i=0; i<nstep; i++) {
250 GetXYZ(start); //starting global position
252 if (!GetXYZAt(x, bz, end)) return kFALSE;
253 //if (!AliExternalTrackParam::PropagateTo(x, bz)) return kFALSE;
254 if (!AliExternalTrackParam::PropagateToBxByBz(x, b)) return kFALSE;
255 AliTracker::MeanMaterialBudget(start, end, mparam);
256 xTimesRho = sign*mparam[4]*mparam[0];
258 if (mparam[1]<900000) {
259 if (!AliExternalTrackParam::CorrectForMeanMaterial(xOverX0,
260 xTimesRho,GetMass())) return kFALSE;
261 } else { // this happens when MeanMaterialBudget cannot cross a boundary
266 if (addTime && IsStartedTimeIntegral() && GetX()>startx) {
267 Double_t l2 = ( (GetX()-startx)*(GetX()-startx) +
268 (GetY()-starty)*(GetY()-starty) +
269 (GetZ()-startz)*(GetZ()-startz) );
270 AddTimeStep(TMath::Sqrt(l2));
276 //____________________________________________________________________________
277 Bool_t AliITStrackV2::Update(const AliCluster* c, Double_t chi2, Int_t index)
279 //------------------------------------------------------------------
280 //This function updates track parameters
281 //------------------------------------------------------------------
282 Double_t p[2]={c->GetY(), c->GetZ()};
283 Double_t cov[3]={c->GetSigmaY2(), c->GetSigmaYZ(), c->GetSigmaZ2()};
285 if (!AliExternalTrackParam::Update(p,cov)) return kFALSE;
287 Int_t n=GetNumberOfClusters();
289 if (n>fgkWARN) AliDebug(1,"Wrong invariant !");
293 if (chi2<0) return kTRUE;
295 // fill residuals for ITS+TPC tracks
297 if (fESDtrack->GetStatus()&AliESDtrack::kTPCin) {
298 AliTracker::FillResiduals(this,p,cov,c->GetVolumeId());
303 SetNumberOfClusters(n+1);
304 SetChi2(GetChi2()+chi2);
309 Bool_t AliITStrackV2::Invariant() const {
310 //------------------------------------------------------------------
311 // This function is for debugging purpose only
312 //------------------------------------------------------------------
313 if(!fCheckInvariant) return kTRUE;
315 Int_t n=GetNumberOfClusters();
316 static Float_t bz = GetBz();
317 // take into account the misalignment error
318 Float_t maxMisalErrY2=0,maxMisalErrZ2=0;
320 const AliITSRecoParam* recopar = AliITSReconstructor::GetRecoParam();
321 if (!recopar) recopar = AliITSRecoParam::GetHighFluxParam();
323 for (Int_t lay=0; lay<AliITSgeomTGeo::kNLayers; lay++) {
324 maxMisalErrY2 = TMath::Max(maxMisalErrY2,recopar->GetClusterMisalErrorY(lay,bz));
325 maxMisalErrZ2 = TMath::Max(maxMisalErrZ2,recopar->GetClusterMisalErrorZ(lay,bz));
327 maxMisalErrY2 *= maxMisalErrY2;
328 maxMisalErrZ2 *= maxMisalErrZ2;
329 // this is because when we reset before refitting, we multiply the
331 maxMisalErrY2 *= 10.;
332 maxMisalErrZ2 *= 10.;
334 Double_t sP2=GetParameter()[2];
335 if (TMath::Abs(sP2) >= kAlmost1){
336 if (n>fgkWARN) AliDebug(1,Form("fP2=%f\n",sP2));
339 Double_t sC00=GetCovariance()[0];
340 if (sC00<=0 || sC00>(9.+maxMisalErrY2)) {
341 if (n>fgkWARN) AliDebug(1,Form("fC00=%f\n",sC00));
344 Double_t sC11=GetCovariance()[2];
345 if (sC11<=0 || sC11>(9.+maxMisalErrZ2)) {
346 if (n>fgkWARN) AliDebug(1,Form("fC11=%f\n",sC11));
349 Double_t sC22=GetCovariance()[5];
350 if (sC22<=0 || sC22>1.) {
351 if (n>fgkWARN) AliDebug(1,Form("fC22=%f\n",sC22));
354 Double_t sC33=GetCovariance()[9];
355 if (sC33<=0 || sC33>1.) {
356 if (n>fgkWARN) AliDebug(1,Form("fC33=%f\n",sC33));
359 Double_t sC44=GetCovariance()[14];
360 if (sC44<=0 /*|| sC44>6e-5*/) {
361 if (n>fgkWARN) AliDebug(1,Form("fC44=%f\n",sC44));
368 //____________________________________________________________________________
369 Bool_t AliITStrackV2::Propagate(Double_t alp,Double_t xk) {
370 //------------------------------------------------------------------
371 //This function propagates a track
372 //------------------------------------------------------------------
373 //Double_t bz=GetBz();
374 //if (!AliExternalTrackParam::Propagate(alp,xk,bz)) return kFALSE;
375 Double_t b[3]; GetBxByBz(b);
376 if (!AliExternalTrackParam::PropagateBxByBz(alp,xk,b)) return kFALSE;
379 Int_t n=GetNumberOfClusters();
380 if (n>fgkWARN) AliDebug(1,"Wrong invariant !");
387 Bool_t AliITStrackV2::MeanBudgetToPrimVertex(Double_t xyz[3], Double_t step, Double_t &d) const {
389 //-------------------------------------------------------------------
390 // Get the mean material budget between the actual point and the
391 // primary vertex. (L.Gaudichet)
392 //-------------------------------------------------------------------
394 Double_t cs=TMath::Cos(GetAlpha()), sn=TMath::Sin(GetAlpha());
395 Double_t vertexX = xyz[0]*cs + xyz[1]*sn;
397 Int_t nstep = Int_t((GetX()-vertexX)/step);
398 if (nstep<1) nstep = 1;
399 step = (GetX()-vertexX)/nstep;
401 // Double_t mparam[7], densMean=0, radLength=0, length=0;
403 Double_t p1[3], p2[3], x = GetX(), bz = GetBz();
408 for (Int_t i=0; i<nstep; i++) {
410 if (!GetXYZAt(x, bz, p2)) return kFALSE;
411 AliTracker::MeanMaterialBudget(p1, p2, mparam);
412 if (mparam[1]>900000) return kFALSE;
423 Bool_t AliITStrackV2::Improve(Double_t x0,Double_t xyz[3],Double_t ers[3]) {
424 //------------------------------------------------------------------
425 //This function improves angular track parameters
426 //------------------------------------------------------------------
427 //Store the initail track parameters
430 Double_t alpha = GetAlpha();
431 Double_t par[] = {GetY(),GetZ(),GetSnp(),GetTgl(),GetSigned1Pt()};
451 Double_t cs=TMath::Cos(GetAlpha()), sn=TMath::Sin(GetAlpha());
452 Double_t xv = xyz[0]*cs + xyz[1]*sn; // vertex
453 Double_t yv =-xyz[0]*sn + xyz[1]*cs; // in the
454 Double_t zv = xyz[2]; // local frame
456 Double_t dx = x - xv, dy = par[0] - yv, dz = par[1] - zv;
457 Double_t r2=dx*dx + dy*dy;
458 Double_t p2=(1.+ GetTgl()*GetTgl())/(GetSigned1Pt()*GetSigned1Pt());
459 if (GetMass()<0) p2 *= 4; // q=2
460 Double_t beta2=p2/(p2 + GetMass()*GetMass());
461 x0*=TMath::Sqrt((1.+ GetTgl()*GetTgl())/(1.- GetSnp()*GetSnp()));
462 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*x0;
463 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*x0*9.36*2.33;
466 Double_t cnv=bz*kB2C;
467 Double_t curv=GetC(bz);
469 Double_t dummy = 4/r2 - curv*curv;
470 if (dummy < 0) return kFALSE;
471 Double_t parp = 0.5*(curv*dx + dy*TMath::Sqrt(dummy));
472 Double_t sigma2p = theta2*(1.-GetSnp())*(1.+GetSnp())*(1. + GetTgl()*GetTgl());
473 Double_t ovSqr2 = 1./TMath::Sqrt(r2);
474 Double_t tfact = ovSqr2*(1.-dy*ovSqr2)*(1.+dy*ovSqr2);
475 sigma2p += cov[0]*tfact*tfact;
476 sigma2p += ers[1]*ers[1]/r2;
477 sigma2p += 0.25*cov[14]*cnv*cnv*dx*dx;
478 Double_t eps2p=sigma2p/(cov[5] + sigma2p);
479 par[0] += cov[3]/(cov[5] + sigma2p)*(parp - GetSnp());
480 par[2] = eps2p*GetSnp() + (1 - eps2p)*parp;
485 Double_t parl=0.5*curv*dz/TMath::ASin(0.5*curv*TMath::Sqrt(r2));
486 Double_t sigma2l=theta2;
487 sigma2l += cov[2]/r2 + cov[0]*dy*dy*dz*dz/(r2*r2*r2);
488 sigma2l += ers[2]*ers[2]/r2;
489 Double_t eps2l = sigma2l/(cov[9] + sigma2l);
490 par[1] += cov[7 ]/(cov[9] + sigma2l)*(parl - par[3]);
491 par[4] += cov[13]/(cov[9] + sigma2l)*(parl - par[3]);
492 par[3] = eps2l*par[3] + (1-eps2l)*parl;
498 Set(x,alpha,par,cov);
500 if (!Invariant()) return kFALSE;
505 void AliITStrackV2::CookdEdx(Double_t /*low*/, Double_t /*up*/) {
506 //-----------------------------------------------------------------
507 // This function calculates dE/dX within the "low" and "up" cuts.
508 // Origin: Boris Batyunya, JINR, Boris.Batiounia@cern.ch
509 // Updated: F. Prino 8-June-2009
510 //-----------------------------------------------------------------
511 // The cluster order is: SDD-1, SDD-2, SSD-1, SSD-2
515 for (Int_t il=0; il<4; il++) { // count good (>0) dE/dx values
516 if(fdEdxSample[il]>0.){
517 dedx[nc]= fdEdxSample[il];
526 Int_t swap; // sort in ascending order
529 for (Int_t i=0; i<nc-1; i++) {
530 if (dedx[i]<=dedx[i+1]) continue;
539 Double_t sumamp=0,sumweight=0;
540 Double_t weight[4]={1.,1.,0.,0.};
541 if(nc==3) weight[1]=0.5;
542 else if(nc<3) weight[1]=0.;
543 for (Int_t i=0; i<nc; i++) {
544 sumamp+= dedx[i]*weight[i];
545 sumweight+=weight[i];
547 SetdEdx(sumamp/sumweight);
550 //____________________________________________________________________________
551 Bool_t AliITStrackV2::
552 GetPhiZat(Double_t r, Double_t &phi, Double_t &z) const {
553 //------------------------------------------------------------------
554 // This function returns the global cylindrical (phi,z) of the track
555 // position estimated at the radius r.
556 // The track curvature is neglected.
557 //------------------------------------------------------------------
558 Double_t d=GetD(0.,0.);
559 if (TMath::Abs(d) > r) {
560 if (r>1e-1) return kFALSE;
564 Double_t rcurr=TMath::Sqrt(GetX()*GetX() + GetY()*GetY());
565 if (TMath::Abs(d) > rcurr) return kFALSE;
566 Double_t globXYZcurr[3]; GetXYZ(globXYZcurr);
567 Double_t phicurr=TMath::ATan2(globXYZcurr[1],globXYZcurr[0]);
570 phi=phicurr+TMath::ASin(d/r)-TMath::ASin(d/rcurr);
572 phi=phicurr+TMath::ASin(d/r)+TMath::ASin(d/rcurr)-TMath::Pi();
575 // return a phi in [0,2pi[
576 if (phi<0.) phi+=2.*TMath::Pi();
577 else if (phi>=2.*TMath::Pi()) phi-=2.*TMath::Pi();
578 z=GetZ()+GetTgl()*(TMath::Sqrt((r-d)*(r+d))-TMath::Sqrt((rcurr-d)*(rcurr+d)));
581 //____________________________________________________________________________
582 Bool_t AliITStrackV2::
583 GetLocalXat(Double_t r,Double_t &xloc) const {
584 //------------------------------------------------------------------
585 // This function returns the local x of the track
586 // position estimated at the radius r.
587 // The track curvature is neglected.
588 //------------------------------------------------------------------
589 Double_t d=GetD(0.,0.);
590 if (TMath::Abs(d) > r) {
591 if (r>1e-1) return kFALSE;
595 Double_t rcurr=TMath::Sqrt(GetX()*GetX() + GetY()*GetY());
596 Double_t globXYZcurr[3]; GetXYZ(globXYZcurr);
597 Double_t phicurr=TMath::ATan2(globXYZcurr[1],globXYZcurr[0]);
600 phi=phicurr+TMath::ASin(d/r)-TMath::ASin(d/rcurr);
602 phi=phicurr+TMath::ASin(d/r)+TMath::ASin(d/rcurr)-TMath::Pi();
605 xloc=r*(TMath::Cos(phi)*TMath::Cos(GetAlpha())
606 +TMath::Sin(phi)*TMath::Sin(GetAlpha()));
611 //____________________________________________________________________________
612 Bool_t AliITStrackV2::ImproveKalman(Double_t xyz[3],Double_t ers[3], const Double_t* xlMS, const Double_t* x2X0MS, Int_t nMS)
614 // Substitute the state of the track (p_{k|k},C_{k|k}) at the k-th measumerent by its
615 // smoothed value from the k-th measurement + measurement at the vertex.
616 // Account for the MS on nMS layers at x-postions xlMS with x/x0 = x2X0MS
617 // p_{k|kv} = p_{k|k} + C_{k|k}*D^Tr_{k+1} B^{-1}_{k+1} ( vtx - D_{k+1}*p_{k|k})
618 // C_{k|kv} = C_{k|k}*( I - D^Tr_{k+1} B^{-1}_{k+1} D_{k+1} C^Tr_{k|k})
620 // where D_{k} = H_{k} F_{k} with H being the matrix converting the tracks parameters
621 // to measurements m_{k} = H_{k} p_{k} and F_{k} the matrix propagating the track between the
622 // the point k-1 and k: p_{k|k-1} = F_{k} p_{k-1|k-1}
624 // B_{k+1} = V_{k+1} + H_{k+1} C_{k+1|k} H^Tr_{k+1} with V_{k+1} being the error of the measurment
625 // at point k+1 (i.e. vertex), and C_{k+1|k} - error matrix extrapolated from k-th measurement to
626 // k+1 (vtx) and accounting for the MS inbetween
628 // H = {{1,0,0,0,0},{0,1,0,0,0}}
630 double covc[15], *cori = (double*) GetCovariance(),par[5] = {GetY(),GetZ(),GetSnp(),GetTgl(),GetSigned1Pt()},
632 &c01=cori[1],&c11=cori[2],
633 &c02=cori[3],&c12=cori[4],&c22=cori[5],
634 &c03=cori[6],&c13=cori[7],&c23=cori[8],&c33=cori[9],
635 &c04=cori[10],&c14=cori[11],&c24=cori[12],&c34=cori[13],&c44=cori[14],
636 // for smoothed cov matrix
638 &cov01=covc[1],&cov11=covc[2],
639 &cov02=covc[3],&cov12=covc[4],&cov22=covc[5],
640 &cov03=covc[6],&cov13=covc[7],&cov23=covc[8],&cov33=covc[9],
641 &cov04=covc[10],&cov14=covc[11],&cov24=covc[12],&cov34=covc[13],&cov44=covc[14];
643 double x = GetX(), alpha = GetAlpha();
644 // vertex in the track frame
645 double cs=TMath::Cos(alpha), sn=TMath::Sin(alpha);
646 double xv = xyz[0]*cs + xyz[1]*sn, yv =-xyz[0]*sn + xyz[1]*cs, zv = xyz[2];
647 double dx = xv - GetX();
648 if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
650 double cnv=GetBz()*kB2C, x2r=cnv*par[4]*dx, f1=par[2], f2=f1+x2r;
651 if (TMath::Abs(f1) >= kAlmost1 || TMath::Abs(f2) >= kAlmost1) {
652 AliInfo(Form("Fail: %+e %+e",f1,f2));
655 double r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2)), dx2r=dx/(r1+r2);
656 // elements of matrix F_{k+1} (1s on diagonal)
657 double f02 = 2*dx2r, f04 = cnv*dx*dx2r, f13/*, f24 = cnv*dx*/;
658 if (TMath::Abs(x2r)<0.05) f13 = dx*r2+f2*(f1+f2)*dx2r; // see AliExternalTrackParam::PropagateTo
660 double dy2dx = (f1+f2)/(r1+r2);
661 f13 = 2*TMath::ASin(0.5*TMath::Sqrt(1+dy2dx*dy2dx)*x2r)/(cnv*par[4]);
663 // elements of matrix D_{k+1} = H_{k+1} * F_{k+1}
664 // double d00 = 1., d11 = 1.;
665 double &d02 = f02, &d04 = f04, &d13 = f13;
667 // elements of matrix DC = D_{k+1}*C_{kk}^T
668 double dc00 = c00+c02*d02+c04*d04, dc10 = c01+c03*d13;
669 double dc01 = c01+c12*d02+c14*d04, dc11 = c11+c13*d13;
670 double dc02 = c02+c22*d02+c24*d04, dc12 = c12+c23*d13;
671 double dc03 = c03+c23*d02+c34*d04, dc13 = c13+c33*d13;
672 double dc04 = c04+c24*d02+c44*d04, dc14 = c14+c34*d13;
674 // difference between the vertex and the the track extrapolated to vertex
675 yv -= par[0] + par[2]*d02 + par[4]*d04;
676 zv -= par[1] + par[3]*d13;
678 // y,z part of the cov.matrix extrapolated to vtx (w/o MS contribution)
679 // C_{k+1,k} = H F_{k+1} C_{k,k} F^Tr_{k+1} H^Tr = D C D^Tr
680 double cv00 = dc00+dc02*d02+dc04*d04, cv01 = dc01+dc03*d13, cv11 = dc11+dc13*d13;
682 // add MS contribution layer by layer
684 double p2Curr = par[2];
686 // precalculated factors of MS contribution matrix:
687 double ms22t = (1. + par[3]*par[3]);
688 double ms33t = ms22t*ms22t;
689 double p34 = par[3]*par[4];
690 double ms34t = p34*ms22t;
691 double ms44t = p34*p34;
693 double p2=(1.+ par[3]*par[3])/(par[4]*par[4]);
694 if (GetMass()<0) p2 *= 4; // q=2
695 double beta2 = p2/(p2+GetMass()*GetMass());
696 double theta2t = 14.1*14.1/(beta2*p2*1e6) * (1. + par[3]*par[3]);
698 // account for the MS in the layers between the last measurement and the vertex
699 for (int il=0;il<nMS;il++) {
700 double dfx = xlMS[il] - xCurr;
702 p2Curr += dfx*cnv*par[4]; // p2 at the scattering layer
703 double dxL=xv - xCurr; // distance from scatering layer to vtx
704 double x2rL=cnv*par[4]*dxL, f1L=p2Curr, f2L=f1L+x2rL;
705 if (TMath::Abs(f1L) >= kAlmost1 || TMath::Abs(f2L) >= kAlmost1) {
706 AliInfo(Form("FailMS at step %d of %d: dfx:%e dxL:%e %e %e",il,nMS,dfx,dxL,f1L,f2L));
709 double r1L=TMath::Sqrt((1.-f1L)*(1.+f1L)), r2L=TMath::Sqrt((1.-f2L)*(1.+f2L)), dx2rL=dxL/(r1L+r2L);
710 // elements of matrix for propagation from scatering layer to vertex
711 double f02L = 2*dx2rL, f04L = cnv*dxL*dx2rL, f13L/*, f24L = cnv*dxL*/;
712 if (TMath::Abs(x2rL)<0.05) f13L = dxL*r2L+f2L*(f1L+f2L)*dx2rL; // see AliExternalTrackParam::PropagateTo
714 double dy2dxL = (f1L+f2L)/(r1L+r2L);
715 f13L = 2*TMath::ASin(0.5*TMath::Sqrt(1+dy2dxL*dy2dxL)*x2rL)/(cnv*par[4]);
717 // MS contribution matrix:
718 double theta2 = theta2t*TMath::Abs(x2X0MS[il]);
719 double ms22 = theta2*(1.-p2Curr)*(1.+p2Curr)*ms22t;
720 double ms33 = theta2*ms33t;
721 double ms34 = theta2*ms34t;
722 double ms44 = theta2*ms44t;
724 // add H F MS F^Tr H^Tr to cv
725 cv00 += f02L*f02L*ms22 + f04L*f04L*ms44;
726 cv01 += f04L*f13L*ms34;
727 cv11 += f13L*f13L*ms33;
730 // inverse of matrix B
731 double b11 = ers[1]*ers[1] + cv00;
732 double b00 = ers[2]*ers[2] + cv11;
733 double det = b11*b00 - cv01*cv01;
734 if (TMath::Abs(det)<kAlmost0) {
735 AliInfo(Form("Fail on det %e: %e %e %e",det,cv00,cv11,cv01));
739 b00 *= det; b11 *= det;
740 double b01 = -cv01*det;
742 // elements of matrix DC^Tr * B^-1
743 double dcb00 = b00*dc00+b01*dc10, dcb01 = b01*dc00+b11*dc10;
744 double dcb10 = b00*dc01+b01*dc11, dcb11 = b01*dc01+b11*dc11;
745 double dcb20 = b00*dc02+b01*dc12, dcb21 = b01*dc02+b11*dc12;
746 double dcb30 = b00*dc03+b01*dc13, dcb31 = b01*dc03+b11*dc13;
747 double dcb40 = b00*dc04+b01*dc14, dcb41 = b01*dc04+b11*dc14;
749 // p_{k|k+1} = p_{k|k} + C_{k|k}*D^Tr_{k+1} B^{-1}_{k+1} ( vtx - D_{k+1}*p_{k|k})
750 par[0] += dcb00*yv + dcb01*zv;
751 par[1] += dcb10*yv + dcb11*zv;
752 par[2] += dcb20*yv + dcb21*zv;
753 par[3] += dcb30*yv + dcb31*zv;
754 par[4] += dcb40*yv + dcb41*zv;
756 // C_{k|kv} = C_{k|k} - C_{k|k} D^Tr_{k+1} B^{-1}_{k+1} D_{k+1} C^Tr_{k|k})
758 cov00 = c00 - (dc00*dcb00 + dc10*dcb01);
759 cov01 = c01 - (dc01*dcb00 + dc11*dcb01);
760 cov02 = c02 - (dc02*dcb00 + dc12*dcb01);
761 cov03 = c03 - (dc03*dcb00 + dc13*dcb01);
762 cov04 = c04 - (dc04*dcb00 + dc14*dcb01);
764 cov11 = c11 - (dc01*dcb10 + dc11*dcb11);
765 cov12 = c12 - (dc02*dcb10 + dc12*dcb11);
766 cov13 = c13 - (dc03*dcb10 + dc13*dcb11);
767 cov14 = c14 - (dc04*dcb10 + dc14*dcb11);
769 cov22 = c22 - (dc02*dcb20 + dc12*dcb21);
770 cov23 = c23 - (dc03*dcb20 + dc13*dcb21);
771 cov24 = c24 - (dc04*dcb20 + dc14*dcb21);
773 cov33 = c33 - (dc03*dcb30 + dc13*dcb31);
774 cov34 = c34 - (dc04*dcb30 + dc14*dcb31);
776 cov44 = c44 - (dc04*dcb40 + dc14*dcb41);
778 Set(x,alpha,par,covc);
780 AliInfo(Form("Fail on Invariant, X=%e",GetX()));