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 *
8 * documentation strictly for non-commercial purposes is hereby granted *
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11 * appear in the supporting documentation. The authors make no claims *
12 * about the suitability of this software for any purpose. It is *
13 * provided "as is" without express or implied warranty. *
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.GetLabel());
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);
97 // copy the module indices
99 for(i=0;i<2*AliITSgeomTGeo::kNLayers;i++) {
100 // printf(" %d\n",GetModuleIndex(i));
101 fESDtrack->SetITSModuleIndex(i,GetModuleIndex(i));
103 // copy the map of shared clusters
104 if(flags==AliESDtrack::kITSin) {
105 UChar_t itsSharedMap=0;
106 for(i=0;i<AliITSgeomTGeo::kNLayers;i++) {
107 if(fSharedWeight[i]>0) SETBIT(itsSharedMap,i);
110 fESDtrack->SetITSSharedMap(itsSharedMap);
113 // copy the 4 dedx samples
114 Double_t sdedx[4]={0.,0.,0.,0.};
115 for(i=0; i<4; i++) sdedx[i]=fdEdxSample[i];
116 fESDtrack->SetITSdEdxSamples(sdedx);
119 //____________________________________________________________________________
120 AliITStrackV2::AliITStrackV2(const AliITStrackV2& t) :
122 fCheckInvariant(t.fCheckInvariant),
124 fESDtrack(t.fESDtrack)
126 //------------------------------------------------------------------
128 //------------------------------------------------------------------
130 for (i=0; i<4; i++) fdEdxSample[i]=t.fdEdxSample[i];
131 for (i=0; i<2*AliITSgeomTGeo::GetNLayers(); i++) {
132 fIndex[i]=t.fIndex[i];
133 fModule[i]=t.fModule[i];
135 for (i=0; i<AliITSgeomTGeo::kNLayers; i++) {fSharedWeight[i]=t.fSharedWeight[i];}
138 //_____________________________________________________________________________
139 Int_t AliITStrackV2::Compare(const TObject *o) const {
140 //-----------------------------------------------------------------
141 // This function compares tracks according to the their curvature
142 //-----------------------------------------------------------------
143 AliITStrackV2 *t=(AliITStrackV2*)o;
144 //Double_t co=OneOverPt();
145 //Double_t c =OneOverPt();
146 Double_t co=t->GetSigmaY2()*t->GetSigmaZ2();
147 Double_t c =GetSigmaY2()*GetSigmaZ2();
149 else if (c<co) return -1;
153 //____________________________________________________________________________
155 AliITStrackV2::PropagateToVertex(const AliESDVertex *v,Double_t d,Double_t x0)
157 //------------------------------------------------------------------
158 //This function propagates a track to the minimal distance from the origin
159 //------------------------------------------------------------------
161 if (PropagateToDCA(v,bz,kVeryBig)) {
162 Double_t xOverX0,xTimesRho;
163 xOverX0 = d; xTimesRho = d*x0;
164 if (CorrectForMeanMaterial(xOverX0,xTimesRho,kTRUE)) return kTRUE;
169 //____________________________________________________________________________
170 Bool_t AliITStrackV2::
171 GetGlobalXYZat(Double_t xloc, Double_t &x, Double_t &y, Double_t &z) const {
172 //------------------------------------------------------------------
173 //This function returns a track position in the global system
174 //------------------------------------------------------------------
176 Bool_t rc=GetXYZAt(xloc, GetBz(), r);
177 x=r[0]; y=r[1]; z=r[2];
181 //_____________________________________________________________________________
182 Double_t AliITStrackV2::GetPredictedChi2(const AliCluster *c) const {
183 //-----------------------------------------------------------------
184 // This function calculates a predicted chi2 increment.
185 //-----------------------------------------------------------------
186 Double_t p[2]={c->GetY(), c->GetZ()};
187 Double_t cov[3]={c->GetSigmaY2(), 0., c->GetSigmaZ2()};
188 return AliExternalTrackParam::GetPredictedChi2(p,cov);
191 //____________________________________________________________________________
192 Bool_t AliITStrackV2::PropagateTo(Double_t xk, Double_t d, Double_t x0) {
193 //------------------------------------------------------------------
194 //This function propagates a track
195 //------------------------------------------------------------------
197 Double_t oldX=GetX(), oldY=GetY(), oldZ=GetZ();
199 //Double_t bz=GetBz();
200 //if (!AliExternalTrackParam::PropagateTo(xk,bz)) return kFALSE;
201 Double_t b[3]; GetBxByBz(b);
202 if (!AliExternalTrackParam::PropagateToBxByBz(xk,b)) return kFALSE;
203 Double_t xOverX0,xTimesRho;
204 xOverX0 = d; xTimesRho = d*x0;
205 if (!CorrectForMeanMaterial(xOverX0,xTimesRho,kTRUE)) return kFALSE;
207 Double_t x=GetX(), y=GetY(), z=GetZ();
208 if (IsStartedTimeIntegral() && x>oldX) {
209 Double_t l2 = (x-oldX)*(x-oldX) + (y-oldY)*(y-oldY) + (z-oldZ)*(z-oldZ);
210 AddTimeStep(TMath::Sqrt(l2));
216 //____________________________________________________________________________
217 Bool_t AliITStrackV2::PropagateToTGeo(Double_t xToGo, Int_t nstep, Double_t &xOverX0, Double_t &xTimesRho, Bool_t addTime) {
218 //-------------------------------------------------------------------
219 // Propagates the track to a reference plane x=xToGo in n steps.
220 // These n steps are only used to take into account the curvature.
221 // The material is calculated with TGeo. (L.Gaudichet)
222 //-------------------------------------------------------------------
224 Double_t startx = GetX(), starty = GetY(), startz = GetZ();
225 Double_t sign = (startx<xToGo) ? -1.:1.;
226 Double_t step = (xToGo-startx)/TMath::Abs(nstep);
228 Double_t start[3], end[3], mparam[7];
229 //Double_t bz = GetBz();
230 Double_t b[3]; GetBxByBz(b);
235 for (Int_t i=0; i<nstep; i++) {
237 GetXYZ(start); //starting global position
239 if (!GetXYZAt(x, bz, end)) return kFALSE;
240 //if (!AliExternalTrackParam::PropagateTo(x, bz)) return kFALSE;
241 if (!AliExternalTrackParam::PropagateToBxByBz(x, b)) return kFALSE;
242 AliTracker::MeanMaterialBudget(start, end, mparam);
243 xTimesRho = sign*mparam[4]*mparam[0];
245 if (mparam[1]<900000) {
246 if (!AliExternalTrackParam::CorrectForMeanMaterial(xOverX0,
247 xTimesRho,GetMass())) return kFALSE;
248 } else { // this happens when MeanMaterialBudget cannot cross a boundary
253 if (addTime && IsStartedTimeIntegral() && GetX()>startx) {
254 Double_t l2 = ( (GetX()-startx)*(GetX()-startx) +
255 (GetY()-starty)*(GetY()-starty) +
256 (GetZ()-startz)*(GetZ()-startz) );
257 AddTimeStep(TMath::Sqrt(l2));
263 //____________________________________________________________________________
264 Bool_t AliITStrackV2::Update(const AliCluster* c, Double_t chi2, Int_t index)
266 //------------------------------------------------------------------
267 //This function updates track parameters
268 //------------------------------------------------------------------
269 Double_t p[2]={c->GetY(), c->GetZ()};
270 Double_t cov[3]={c->GetSigmaY2(), c->GetSigmaYZ(), c->GetSigmaZ2()};
272 if (!AliExternalTrackParam::Update(p,cov)) return kFALSE;
274 Int_t n=GetNumberOfClusters();
276 if (n>fgkWARN) AliDebug(1,"Wrong invariant !");
280 if (chi2<0) return kTRUE;
282 // fill residuals for ITS+TPC tracks
284 if (fESDtrack->GetStatus()&AliESDtrack::kTPCin) {
285 AliTracker::FillResiduals(this,p,cov,c->GetVolumeId());
290 SetNumberOfClusters(n+1);
291 SetChi2(GetChi2()+chi2);
296 Bool_t AliITStrackV2::Invariant() const {
297 //------------------------------------------------------------------
298 // This function is for debugging purpose only
299 //------------------------------------------------------------------
300 if(!fCheckInvariant) return kTRUE;
302 Int_t n=GetNumberOfClusters();
303 static Float_t bz = GetBz();
304 // take into account the misalignment error
305 Float_t maxMisalErrY2=0,maxMisalErrZ2=0;
307 const AliITSRecoParam* recopar = AliITSReconstructor::GetRecoParam();
308 if (!recopar) recopar = AliITSRecoParam::GetHighFluxParam();
310 for (Int_t lay=0; lay<AliITSgeomTGeo::kNLayers; lay++) {
311 maxMisalErrY2 = TMath::Max(maxMisalErrY2,recopar->GetClusterMisalErrorY(lay,bz));
312 maxMisalErrZ2 = TMath::Max(maxMisalErrZ2,recopar->GetClusterMisalErrorZ(lay,bz));
314 maxMisalErrY2 *= maxMisalErrY2;
315 maxMisalErrZ2 *= maxMisalErrZ2;
316 // this is because when we reset before refitting, we multiply the
318 maxMisalErrY2 *= 10.;
319 maxMisalErrZ2 *= 10.;
321 Double_t sP2=GetParameter()[2];
322 if (TMath::Abs(sP2) >= kAlmost1){
323 if (n>fgkWARN) AliDebug(1,Form("fP2=%f\n",sP2));
326 Double_t sC00=GetCovariance()[0];
327 if (sC00<=0 || sC00>(9.+maxMisalErrY2)) {
328 if (n>fgkWARN) AliDebug(1,Form("fC00=%f\n",sC00));
331 Double_t sC11=GetCovariance()[2];
332 if (sC11<=0 || sC11>(9.+maxMisalErrZ2)) {
333 if (n>fgkWARN) AliDebug(1,Form("fC11=%f\n",sC11));
336 Double_t sC22=GetCovariance()[5];
337 if (sC22<=0 || sC22>1.) {
338 if (n>fgkWARN) AliDebug(1,Form("fC22=%f\n",sC22));
341 Double_t sC33=GetCovariance()[9];
342 if (sC33<=0 || sC33>1.) {
343 if (n>fgkWARN) AliDebug(1,Form("fC33=%f\n",sC33));
346 Double_t sC44=GetCovariance()[14];
347 if (sC44<=0 /*|| sC44>6e-5*/) {
348 if (n>fgkWARN) AliDebug(1,Form("fC44=%f\n",sC44));
355 //____________________________________________________________________________
356 Bool_t AliITStrackV2::Propagate(Double_t alp,Double_t xk) {
357 //------------------------------------------------------------------
358 //This function propagates a track
359 //------------------------------------------------------------------
360 //Double_t bz=GetBz();
361 //if (!AliExternalTrackParam::Propagate(alp,xk,bz)) return kFALSE;
362 Double_t b[3]; GetBxByBz(b);
363 if (!AliExternalTrackParam::PropagateBxByBz(alp,xk,b)) return kFALSE;
366 Int_t n=GetNumberOfClusters();
367 if (n>fgkWARN) AliDebug(1,"Wrong invariant !");
374 Bool_t AliITStrackV2::MeanBudgetToPrimVertex(Double_t xyz[3], Double_t step, Double_t &d) const {
376 //-------------------------------------------------------------------
377 // Get the mean material budget between the actual point and the
378 // primary vertex. (L.Gaudichet)
379 //-------------------------------------------------------------------
381 Double_t cs=TMath::Cos(GetAlpha()), sn=TMath::Sin(GetAlpha());
382 Double_t vertexX = xyz[0]*cs + xyz[1]*sn;
384 Int_t nstep = Int_t((GetX()-vertexX)/step);
385 if (nstep<1) nstep = 1;
386 step = (GetX()-vertexX)/nstep;
388 // Double_t mparam[7], densMean=0, radLength=0, length=0;
390 Double_t p1[3], p2[3], x = GetX(), bz = GetBz();
395 for (Int_t i=0; i<nstep; i++) {
397 if (!GetXYZAt(x, bz, p2)) return kFALSE;
398 AliTracker::MeanMaterialBudget(p1, p2, mparam);
399 if (mparam[1]>900000) return kFALSE;
410 Bool_t AliITStrackV2::Improve(Double_t x0,Double_t xyz[3],Double_t ers[3]) {
411 //------------------------------------------------------------------
412 //This function improves angular track parameters
413 //------------------------------------------------------------------
414 //Store the initail track parameters
417 Double_t alpha = GetAlpha();
418 Double_t par[] = {GetY(),GetZ(),GetSnp(),GetTgl(),GetSigned1Pt()};
438 Double_t cs=TMath::Cos(GetAlpha()), sn=TMath::Sin(GetAlpha());
439 Double_t xv = xyz[0]*cs + xyz[1]*sn; // vertex
440 Double_t yv =-xyz[0]*sn + xyz[1]*cs; // in the
441 Double_t zv = xyz[2]; // local frame
443 Double_t dx = x - xv, dy = par[0] - yv, dz = par[1] - zv;
444 Double_t r2=dx*dx + dy*dy;
445 Double_t p2=(1.+ GetTgl()*GetTgl())/(GetSigned1Pt()*GetSigned1Pt());
446 Double_t beta2=p2/(p2 + GetMass()*GetMass());
447 x0*=TMath::Sqrt((1.+ GetTgl()*GetTgl())/(1.- GetSnp()*GetSnp()));
448 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*x0;
449 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*x0*9.36*2.33;
452 Double_t cnv=bz*kB2C;
453 Double_t curv=GetC(bz);
455 Double_t dummy = 4/r2 - curv*curv;
456 if (dummy < 0) return kFALSE;
457 Double_t parp = 0.5*(curv*dx + dy*TMath::Sqrt(dummy));
458 Double_t sigma2p = theta2*(1.-GetSnp())*(1.+GetSnp())*(1. + GetTgl()*GetTgl());
459 Double_t ovSqr2 = 1./TMath::Sqrt(r2);
460 Double_t tfact = ovSqr2*(1.-dy*ovSqr2)*(1.+dy*ovSqr2);
461 sigma2p += cov[0]*tfact*tfact;
462 sigma2p += ers[1]*ers[1]/r2;
463 sigma2p += 0.25*cov[14]*cnv*cnv*dx*dx;
464 Double_t eps2p=sigma2p/(cov[5] + sigma2p);
465 par[0] += cov[3]/(cov[5] + sigma2p)*(parp - GetSnp());
466 par[2] = eps2p*GetSnp() + (1 - eps2p)*parp;
471 Double_t parl=0.5*curv*dz/TMath::ASin(0.5*curv*TMath::Sqrt(r2));
472 Double_t sigma2l=theta2;
473 sigma2l += cov[2]/r2 + cov[0]*dy*dy*dz*dz/(r2*r2*r2);
474 sigma2l += ers[2]*ers[2]/r2;
475 Double_t eps2l = sigma2l/(cov[9] + sigma2l);
476 par[1] += cov[7 ]/(cov[9] + sigma2l)*(parl - par[3]);
477 par[4] += cov[13]/(cov[9] + sigma2l)*(parl - par[3]);
478 par[3] = eps2l*par[3] + (1-eps2l)*parl;
484 Set(x,alpha,par,cov);
486 if (!Invariant()) return kFALSE;
491 void AliITStrackV2::CookdEdx(Double_t /*low*/, Double_t /*up*/) {
492 //-----------------------------------------------------------------
493 // This function calculates dE/dX within the "low" and "up" cuts.
494 // Origin: Boris Batyunya, JINR, Boris.Batiounia@cern.ch
495 // Updated: F. Prino 8-June-2009
496 //-----------------------------------------------------------------
497 // The cluster order is: SDD-1, SDD-2, SSD-1, SSD-2
501 for (Int_t il=0; il<4; il++) { // count good (>0) dE/dx values
502 if(fdEdxSample[il]>0.){
503 dedx[nc]= fdEdxSample[il];
512 Int_t swap; // sort in ascending order
515 for (Int_t i=0; i<nc-1; i++) {
516 if (dedx[i]<=dedx[i+1]) continue;
525 Double_t sumamp=0,sumweight=0;
526 Double_t weight[4]={1.,1.,0.,0.};
527 if(nc==3) weight[1]=0.5;
528 else if(nc<3) weight[1]=0.;
529 for (Int_t i=0; i<nc; i++) {
530 sumamp+= dedx[i]*weight[i];
531 sumweight+=weight[i];
533 SetdEdx(sumamp/sumweight);
536 //____________________________________________________________________________
537 Bool_t AliITStrackV2::
538 GetPhiZat(Double_t r, Double_t &phi, Double_t &z) const {
539 //------------------------------------------------------------------
540 // This function returns the global cylindrical (phi,z) of the track
541 // position estimated at the radius r.
542 // The track curvature is neglected.
543 //------------------------------------------------------------------
544 Double_t d=GetD(0.,0.);
545 if (TMath::Abs(d) > r) {
546 if (r>1e-1) return kFALSE;
550 Double_t rcurr=TMath::Sqrt(GetX()*GetX() + GetY()*GetY());
551 if (TMath::Abs(d) > rcurr) return kFALSE;
552 Double_t globXYZcurr[3]; GetXYZ(globXYZcurr);
553 Double_t phicurr=TMath::ATan2(globXYZcurr[1],globXYZcurr[0]);
556 phi=phicurr+TMath::ASin(d/r)-TMath::ASin(d/rcurr);
558 phi=phicurr+TMath::ASin(d/r)+TMath::ASin(d/rcurr)-TMath::Pi();
561 // return a phi in [0,2pi[
562 if (phi<0.) phi+=2.*TMath::Pi();
563 else if (phi>=2.*TMath::Pi()) phi-=2.*TMath::Pi();
564 z=GetZ()+GetTgl()*(TMath::Sqrt((r-d)*(r+d))-TMath::Sqrt((rcurr-d)*(rcurr+d)));
567 //____________________________________________________________________________
568 Bool_t AliITStrackV2::
569 GetLocalXat(Double_t r,Double_t &xloc) const {
570 //------------------------------------------------------------------
571 // This function returns the local x of the track
572 // position estimated at the radius r.
573 // The track curvature is neglected.
574 //------------------------------------------------------------------
575 Double_t d=GetD(0.,0.);
576 if (TMath::Abs(d) > r) {
577 if (r>1e-1) return kFALSE;
581 Double_t rcurr=TMath::Sqrt(GetX()*GetX() + GetY()*GetY());
582 Double_t globXYZcurr[3]; GetXYZ(globXYZcurr);
583 Double_t phicurr=TMath::ATan2(globXYZcurr[1],globXYZcurr[0]);
586 phi=phicurr+TMath::ASin(d/r)-TMath::ASin(d/rcurr);
588 phi=phicurr+TMath::ASin(d/r)+TMath::ASin(d/rcurr)-TMath::Pi();
591 xloc=r*(TMath::Cos(phi)*TMath::Cos(GetAlpha())
592 +TMath::Sin(phi)*TMath::Sin(GetAlpha()));
597 //____________________________________________________________________________
598 Bool_t AliITStrackV2::ImproveKalman(Double_t xyz[3],Double_t ers[3], const Double_t* xlMS, const Double_t* x2X0MS, Int_t nMS)
600 // Substitute the state of the track (p_{k|k},C_{k|k}) at the k-th measumerent by its
601 // smoothed value from the k-th measurement + measurement at the vertex.
602 // Account for the MS on nMS layers at x-postions xlMS with x/x0 = x2X0MS
603 // p_{k|kv} = p_{k|k} + C_{k|k}*D^Tr_{k+1} B^{-1}_{k+1} ( vtx - D_{k+1}*p_{k|k})
604 // C_{k|kv} = C_{k|k}*( I - D^Tr_{k+1} B^{-1}_{k+1} D_{k+1} C^Tr_{k|k})
606 // where D_{k} = H_{k} F_{k} with H being the matrix converting the tracks parameters
607 // to measurements m_{k} = H_{k} p_{k} and F_{k} the matrix propagating the track between the
608 // the point k-1 and k: p_{k|k-1} = F_{k} p_{k-1|k-1}
610 // 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
611 // at point k+1 (i.e. vertex), and C_{k+1|k} - error matrix extrapolated from k-th measurement to
612 // k+1 (vtx) and accounting for the MS inbetween
614 // H = {{1,0,0,0,0},{0,1,0,0,0}}
616 double covc[15], *cori = (double*) GetCovariance(),par[5] = {GetY(),GetZ(),GetSnp(),GetTgl(),GetSigned1Pt()},
618 &c01=cori[1],&c11=cori[2],
619 &c02=cori[3],&c12=cori[4],&c22=cori[5],
620 &c03=cori[6],&c13=cori[7],&c23=cori[8],&c33=cori[9],
621 &c04=cori[10],&c14=cori[11],&c24=cori[12],&c34=cori[13],&c44=cori[14],
622 // for smoothed cov matrix
624 &cov01=covc[1],&cov11=covc[2],
625 &cov02=covc[3],&cov12=covc[4],&cov22=covc[5],
626 &cov03=covc[6],&cov13=covc[7],&cov23=covc[8],&cov33=covc[9],
627 &cov04=covc[10],&cov14=covc[11],&cov24=covc[12],&cov34=covc[13],&cov44=covc[14];
629 double x = GetX(), alpha = GetAlpha();
630 // vertex in the track frame
631 double cs=TMath::Cos(alpha), sn=TMath::Sin(alpha);
632 double xv = xyz[0]*cs + xyz[1]*sn, yv =-xyz[0]*sn + xyz[1]*cs, zv = xyz[2];
633 double dx = xv - GetX();
634 if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
636 double cnv=GetBz()*kB2C, x2r=cnv*par[4]*dx, f1=par[2], f2=f1+x2r;
637 if (TMath::Abs(f1) >= kAlmost1 || TMath::Abs(f2) >= kAlmost1) {
638 AliInfo(Form("Fail: %+e %+e",f1,f2));
641 double r1=TMath::Sqrt((1.-f1)*(1.+f1)), r2=TMath::Sqrt((1.-f2)*(1.+f2)), dx2r=dx/(r1+r2);
642 // elements of matrix F_{k+1} (1s on diagonal)
643 double f02 = 2*dx2r, f04 = cnv*dx*dx2r, f13/*, f24 = cnv*dx*/;
644 if (TMath::Abs(x2r)<0.05) f13 = dx*r2+f2*(f1+f2)*dx2r; // see AliExternalTrackParam::PropagateTo
646 double dy2dx = (f1+f2)/(r1+r2);
647 f13 = 2*TMath::ASin(0.5*TMath::Sqrt(1+dy2dx*dy2dx)*x2r)/(cnv*par[4]);
649 // elements of matrix D_{k+1} = H_{k+1} * F_{k+1}
650 // double d00 = 1., d11 = 1.;
651 double &d02 = f02, &d04 = f04, &d13 = f13;
653 // elements of matrix DC = D_{k+1}*C_{kk}^T
654 double dc00 = c00+c02*d02+c04*d04, dc10 = c01+c03*d13;
655 double dc01 = c01+c12*d02+c14*d04, dc11 = c11+c13*d13;
656 double dc02 = c02+c22*d02+c24*d04, dc12 = c12+c23*d13;
657 double dc03 = c03+c23*d02+c34*d04, dc13 = c13+c33*d13;
658 double dc04 = c04+c24*d02+c44*d04, dc14 = c14+c34*d13;
660 // difference between the vertex and the the track extrapolated to vertex
661 yv -= par[0] + par[2]*d02 + par[4]*d04;
662 zv -= par[1] + par[3]*d13;
664 // y,z part of the cov.matrix extrapolated to vtx (w/o MS contribution)
665 // C_{k+1,k} = H F_{k+1} C_{k,k} F^Tr_{k+1} H^Tr = D C D^Tr
666 double cv00 = dc00+dc02*d02+dc04*d04, cv01 = dc01+dc03*d13, cv11 = dc11+dc13*d13;
668 // add MS contribution layer by layer
670 double p2Curr = par[2];
672 // precalculated factors of MS contribution matrix:
673 double ms22t = (1. + par[3]*par[3]);
674 double ms33t = ms22t*ms22t;
675 double p34 = par[3]*par[4];
676 double ms34t = p34*ms22t;
677 double ms44t = p34*p34;
679 double p2=(1.+ par[3]*par[3])/(par[4]*par[4]);
680 double beta2 = p2/(p2+GetMass()*GetMass());
681 double theta2t = 14.1*14.1/(beta2*p2*1e6) * (1. + par[3]*par[3]);
683 // account for the MS in the layers between the last measurement and the vertex
684 for (int il=0;il<nMS;il++) {
685 double dfx = xlMS[il] - xCurr;
687 p2Curr += dfx*cnv*par[4]; // p2 at the scattering layer
688 double dxL=xv - xCurr; // distance from scatering layer to vtx
689 double x2rL=cnv*par[4]*dxL, f1L=p2Curr, f2L=f1L+x2rL;
690 if (TMath::Abs(f1L) >= kAlmost1 || TMath::Abs(f2L) >= kAlmost1) {
691 AliInfo(Form("FailMS at step %d of %d: dfx:%e dxL:%e %e %e",il,nMS,dfx,dxL,f1L,f2L));
694 double r1L=TMath::Sqrt((1.-f1L)*(1.+f1L)), r2L=TMath::Sqrt((1.-f2L)*(1.+f2L)), dx2rL=dxL/(r1L+r2L);
695 // elements of matrix for propagation from scatering layer to vertex
696 double f02L = 2*dx2rL, f04L = cnv*dxL*dx2rL, f13L/*, f24L = cnv*dxL*/;
697 if (TMath::Abs(x2rL)<0.05) f13L = dxL*r2L+f2L*(f1L+f2L)*dx2rL; // see AliExternalTrackParam::PropagateTo
699 double dy2dxL = (f1L+f2L)/(r1L+r2L);
700 f13L = 2*TMath::ASin(0.5*TMath::Sqrt(1+dy2dxL*dy2dxL)*x2rL)/(cnv*par[4]);
702 // MS contribution matrix:
703 double theta2 = theta2t*TMath::Abs(x2X0MS[il]);
704 double ms22 = theta2*(1.-p2Curr)*(1.+p2Curr)*ms22t;
705 double ms33 = theta2*ms33t;
706 double ms34 = theta2*ms34t;
707 double ms44 = theta2*ms44t;
709 // add H F MS F^Tr H^Tr to cv
710 cv00 += f02L*f02L*ms22 + f04L*f04L*ms44;
711 cv01 += f04L*f13L*ms34;
712 cv11 += f13L*f13L*ms33;
715 // inverse of matrix B
716 double b11 = ers[1]*ers[1] + cv00;
717 double b00 = ers[2]*ers[2] + cv11;
718 double det = b11*b00 - cv01*cv01;
719 if (TMath::Abs(det)<kAlmost0) {
720 AliInfo(Form("Fail on det %e: %e %e %e",det,cv00,cv11,cv01));
724 b00 *= det; b11 *= det;
725 double b01 = -cv01*det;
727 // elements of matrix DC^Tr * B^-1
728 double dcb00 = b00*dc00+b01*dc10, dcb01 = b01*dc00+b11*dc10;
729 double dcb10 = b00*dc01+b01*dc11, dcb11 = b01*dc01+b11*dc11;
730 double dcb20 = b00*dc02+b01*dc12, dcb21 = b01*dc02+b11*dc12;
731 double dcb30 = b00*dc03+b01*dc13, dcb31 = b01*dc03+b11*dc13;
732 double dcb40 = b00*dc04+b01*dc14, dcb41 = b01*dc04+b11*dc14;
734 // 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})
735 par[0] += dcb00*yv + dcb01*zv;
736 par[1] += dcb10*yv + dcb11*zv;
737 par[2] += dcb20*yv + dcb21*zv;
738 par[3] += dcb30*yv + dcb31*zv;
739 par[4] += dcb40*yv + dcb41*zv;
741 // C_{k|kv} = C_{k|k} - C_{k|k} D^Tr_{k+1} B^{-1}_{k+1} D_{k+1} C^Tr_{k|k})
743 cov00 = c00 - (dc00*dcb00 + dc10*dcb01);
744 cov01 = c01 - (dc01*dcb00 + dc11*dcb01);
745 cov02 = c02 - (dc02*dcb00 + dc12*dcb01);
746 cov03 = c03 - (dc03*dcb00 + dc13*dcb01);
747 cov04 = c04 - (dc04*dcb00 + dc14*dcb01);
749 cov11 = c11 - (dc01*dcb10 + dc11*dcb11);
750 cov12 = c12 - (dc02*dcb10 + dc12*dcb11);
751 cov13 = c13 - (dc03*dcb10 + dc13*dcb11);
752 cov14 = c14 - (dc04*dcb10 + dc14*dcb11);
754 cov22 = c22 - (dc02*dcb20 + dc12*dcb21);
755 cov23 = c23 - (dc03*dcb20 + dc13*dcb21);
756 cov24 = c24 - (dc04*dcb20 + dc14*dcb21);
758 cov33 = c33 - (dc03*dcb30 + dc13*dcb31);
759 cov34 = c34 - (dc04*dcb30 + dc14*dcb31);
761 cov44 = c44 - (dc04*dcb40 + dc14*dcb41);
763 Set(x,alpha,par,covc);
765 AliInfo(Form("Fail on Invariant, X=%e",GetX()));