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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18 Revision 1.1.2.4 2000/06/12 08:00:07 morsch
19 Dummy streamer to solve CINT compilation problem (to be investigated !)
21 Revision 1.1.2.3 2000/06/09 20:59:57 morsch
22 Make includes consistent with new file structure.
24 Revision 1.1.2.2 2000/06/09 12:58:05 gosset
25 Removed comment beginnings in Log sections of .cxx files
26 Suppressed most violations of coding rules
28 Revision 1.1.2.1 2000/06/07 14:44:53 gosset
29 Addition of files for track reconstruction in C++
32 //__________________________________________________________________________
34 // MUON event reconstructor in ALICE
36 // This class contains as data:
37 // * the parameters for the event reconstruction
38 // * a pointer to the array of hits to be reconstructed (the event)
39 // * a pointer to the array of segments made with these hits inside each station
40 // * a pointer to the array of reconstructed tracks
42 // It contains as methods, among others:
43 // * MakeEventToBeReconstructed to build the array of hits to be reconstructed
44 // * MakeSegments to build the segments
45 // * MakeTracks to build the tracks
46 //__________________________________________________________________________
53 #include "AliCallf77.h"
54 #include "AliMUONEventReconstructor.h"
56 #include "AliMUONHitForRec.h"
57 #include "AliMUONSegment.h"
58 #include "AliMUONHit.h"
59 #include "AliMUONRawCluster.h"
60 #include "AliMUONTrack.h"
61 #include "AliMUONChamber.h"
62 #include "AliMUONTrackHit.h"
66 # define initfield initfield_
67 # define reco_gufld reco_gufld_
69 # define initfield INITFIELD
70 # define reco_gufld RECO_GUFLD
75 void type_of_call initfield();
76 void type_of_call reco_gufld(Double_t *Coor, Double_t *Field);
79 //************* Defaults parameters for reconstruction
80 static const Double_t DefaultMinBendingMomentum = 3.0;
81 static const Double_t DefaultMaxSigma2Distance = 16.0;
82 static const Double_t DefaultBendingResolution = 0.01;
83 static const Double_t DefaultNonBendingResolution = 0.144;
84 static const Double_t DefaultChamberThicknessInX0 = 0.03;
85 // Simple magnetic field:
86 // Value taken from macro MUONtracking.C: 0.7 T, hence 7 kG
87 // Length and Position from reco_muon.F, with opposite sign:
88 // Length = ZMAGEND-ZCOIL
89 // Position = (ZMAGEND+ZCOIL)/2
90 // to be ajusted differently from real magnetic field ????
91 static const Double_t DefaultSimpleBValue = 7.0;
92 static const Double_t DefaultSimpleBLength = 428.0;
93 static const Double_t DefaultSimpleBPosition = 1019.0;
94 static const Int_t DefaultRecGeantHits = 0;
95 static const Double_t DefaultEfficiency = 0.95;
97 static const Int_t DefaultPrintLevel = 0;
99 ClassImp(AliMUONEventReconstructor) // Class implementation in ROOT context
101 //__________________________________________________________________________
102 AliMUONEventReconstructor::AliMUONEventReconstructor(void)
104 // Constructor for class AliMUONEventReconstructor
105 SetReconstructionParametersToDefaults();
106 // Memory allocation for the TClonesArray of hits for reconstruction
107 // Is 10000 the right size ????
108 fHitsForRecPtr = new TClonesArray("AliMUONHitForRec", 10000);
109 fNHitsForRec = 0; // really needed or GetEntriesFast sufficient ????
110 // Memory allocation for the TClonesArray's of segments in stations
111 // Is 2000 the right size ????
112 for (Int_t st = 0; st < MAX_MUON_TRACKING_STATIONS; st++) {
113 fSegmentsPtr[st] = new TClonesArray("AliMUONSegment", 2000);
114 fNSegments[st] = 0; // really needed or GetEntriesFast sufficient ????
116 // Memory allocation for the TClonesArray of reconstructed tracks
117 // Is 10 the right size ????
118 fRecTracksPtr = new TClonesArray("AliMUONTrack", 10);
119 fNRecTracks = 0; // really needed or GetEntriesFast sufficient ????
121 // Initialize magnetic field
122 // using Fortran subroutine INITFIELD in "reco_muon.F".
123 // Should rather use AliMagF ???? and remove prototyping ...
125 // Impression de quelques valeurs
126 Double_t coor[3], field[3];
130 reco_gufld(coor, field);
131 cout << "coor: " << coor[0] << ", " << coor[1] << ", " << coor[2] << endl;
132 cout << "field: " << field[0] << ", " << field[1] << ", " << field[2] << endl;
134 reco_gufld(coor, field);
135 cout << "coor: " << coor[0] << ", " << coor[1] << ", " << coor[2] << endl;
136 cout << "field: " << field[0] << ", " << field[1] << ", " << field[2] << endl;
139 if (fPrintLevel >= 0) {
140 cout << "AliMUONEventReconstructor constructed with defaults" << endl; Dump();}
144 //__________________________________________________________________________
145 AliMUONEventReconstructor::~AliMUONEventReconstructor(void)
147 // Destructor for class AliMUONEventReconstructor
148 delete fHitsForRecPtr; // Correct destruction of everything ???? or delete [] ????
149 for (Int_t st = 0; st < MAX_MUON_TRACKING_STATIONS; st++)
150 delete fSegmentsPtr[st]; // Correct destruction of everything ????
154 //__________________________________________________________________________
155 void AliMUONEventReconstructor::SetReconstructionParametersToDefaults(void)
157 // Set reconstruction parameters to default values
158 // Would be much more convenient with a structure (or class) ????
159 fMinBendingMomentum = DefaultMinBendingMomentum;
160 fMaxSigma2Distance = DefaultMaxSigma2Distance;
162 AliMUON *MUON = (AliMUON*) gAlice->GetModule("MUON");
163 // ******** Parameters for making HitsForRec
165 // like in TRACKF_STAT:
166 // 2 degrees for stations 1 and 2, or ch(0...) from 0 to 3;
167 // 30 cm for stations 3 to 5, or ch(0...) from 4 to 9
168 for (Int_t ch = 0; ch < MAX_MUON_TRACKING_CHAMBERS; ch++) {
169 if (ch < 4) fRMin[ch] = TMath::Abs((&(MUON->Chamber(ch)))->Z()) *
170 2.0 * TMath::Pi() / 180.0;
171 else fRMin[ch] = 30.0;
174 // like in TRACKF_STAT (10 degrees ????)
175 fRMax[0] = fRMax[1] = 91.5;
176 fRMax[2] = fRMax[3] = 122.5;
177 fRMax[4] = fRMax[5] = 158.3;
178 fRMax[6] = fRMax[7] = 260.0;
179 fRMax[8] = fRMax[9] = 260.0;
181 // ******** Parameters for making segments
182 // should be parametrized ????
183 // according to interval between chambers in a station ????
184 // Maximum distance in non bending plane
185 // 5 * 0.22 just to remember the way it was made in TRACKF_STAT
187 for (Int_t st = 0; st < MAX_MUON_TRACKING_STATIONS; st++)
188 fSegmentMaxDistNonBending[st] = 5. * 0.22;
189 // Maximum distance in bending plane
190 // values from TRACKF_STAT corresponding to (J psi 20cm)
191 fSegmentMaxDistBending[0] = 1.5;
192 fSegmentMaxDistBending[1] = 1.5;
193 fSegmentMaxDistBending[2] = 3.0;
194 fSegmentMaxDistBending[3] = 6.0;
195 fSegmentMaxDistBending[4] = 6.0;
197 fBendingResolution = DefaultBendingResolution;
198 fNonBendingResolution = DefaultNonBendingResolution;
199 fChamberThicknessInX0 = DefaultChamberThicknessInX0;
200 fSimpleBValue = DefaultSimpleBValue;
201 fSimpleBLength = DefaultSimpleBLength;
202 fSimpleBPosition = DefaultSimpleBPosition;
203 fRecGeantHits = DefaultRecGeantHits;
204 fEfficiency = DefaultEfficiency;
205 fPrintLevel = DefaultPrintLevel;
209 //__________________________________________________________________________
210 Double_t AliMUONEventReconstructor::GetImpactParamFromBendingMomentum(Double_t BendingMomentum)
212 // Returns impact parameter at vertex in bending plane (cm),
213 // from the signed bending momentum "BendingMomentum" in bending plane (GeV/c),
214 // using simple values for dipole magnetic field.
215 // The sign is the sign of the charge.
216 return (-0.0003 * fSimpleBValue * fSimpleBLength * fSimpleBPosition /
220 //__________________________________________________________________________
221 Double_t AliMUONEventReconstructor::GetBendingMomentumFromImpactParam(Double_t ImpactParam)
223 // Returns signed bending momentum in bending plane (GeV/c),
224 // from the impact parameter "ImpactParam" at vertex in bending plane (cm),
225 // using simple values for dipole magnetic field.
226 // The sign is the sign of the charge.
227 return (-0.0003 * fSimpleBValue * fSimpleBLength * fSimpleBPosition /
231 //__________________________________________________________________________
232 void AliMUONEventReconstructor::SetBkgGeantFile(Text_t *BkgGeantFileName)
234 // Set background file ... for GEANT hits
235 // Must be called after having loaded the firts signal event
236 if (fPrintLevel >= 0) {
237 cout << "Enter SetBkgGeantFile with BkgGeantFileName ``"
238 << BkgGeantFileName << "''" << endl;}
239 if (strlen(BkgGeantFileName)) {
240 // BkgGeantFileName not empty: try to open the file
241 if (fPrintLevel >= 2) {cout << "Before File(Bkg)" << endl; gDirectory->Dump();}
242 fBkgGeantFile = new TFile(BkgGeantFileName);
243 if (fPrintLevel >= 2) {cout << "After File(Bkg)" << endl; gDirectory->Dump();}
244 if (fBkgGeantFile-> IsOpen()) {
245 if (fPrintLevel >= 0) {
246 cout << "Background for GEANT hits in file: ``" << BkgGeantFileName
247 << "'' successfully opened" << endl;}
250 cout << "Background for GEANT hits in file: " << BkgGeantFileName << endl;
251 cout << "NOT FOUND: EXIT" << endl;
252 exit(0); // right instruction for exit ????
254 // Arrays for "particles" and "hits"
255 fBkgGeantParticles = new TClonesArray("TParticle", 200);
256 fBkgGeantHits = new TClonesArray("AliMUONHit", 2000);
257 // Event number to -1 for initialization
258 fBkgGeantEventNumber = -1;
259 // Back to the signal file:
260 // first signal event must have been loaded previously,
261 // otherwise, Segmentation violation at the next instruction
262 // How is it possible to do smething better ????
263 ((gAlice->TreeK())->GetCurrentFile())->cd();
264 if (fPrintLevel >= 2) {cout << "After cd(gAlice)" << endl; gDirectory->Dump();}
269 //__________________________________________________________________________
270 void AliMUONEventReconstructor::NextBkgGeantEvent(void)
272 // Get next event in background file for GEANT hits
273 // Goes back to event number 0 when end of file is reached
276 if (fPrintLevel >= 0) {
277 cout << "Enter NextBkgGeantEvent" << endl;}
278 // Clean previous event
279 if(fBkgGeantTK) delete fBkgGeantTK;
281 if(fBkgGeantParticles) fBkgGeantParticles->Clear();
282 if(fBkgGeantTH) delete fBkgGeantTH;
284 if(fBkgGeantHits) fBkgGeantHits->Clear();
285 // Increment event number
286 fBkgGeantEventNumber++;
287 // Get access to Particles and Hits for event from background file
288 if (fPrintLevel >= 2) {cout << "Before cd(Bkg)" << endl; gDirectory->Dump();}
290 if (fPrintLevel >= 2) {cout << "After cd(Bkg)" << endl; gDirectory->Dump();}
291 // Particles: TreeK for event and branch "Particles"
292 sprintf(treeName, "TreeK%d", fBkgGeantEventNumber);
293 fBkgGeantTK = (TTree*)gDirectory->Get(treeName);
295 if (fPrintLevel >= 0) {
296 cout << "Cannot find Kine Tree for background event: " <<
297 fBkgGeantEventNumber << endl;
298 cout << "Goes back to event 0" << endl;
300 fBkgGeantEventNumber = 0;
301 sprintf(treeName, "TreeK%d", fBkgGeantEventNumber);
302 fBkgGeantTK = (TTree*)gDirectory->Get(treeName);
304 cout << "ERROR: cannot find Kine Tree for background event: " <<
305 fBkgGeantEventNumber << endl;
310 fBkgGeantTK->SetBranchAddress("Particles", &fBkgGeantParticles);
311 fBkgGeantTK->GetEvent(0); // why event 0 ???? necessary ????
312 // Hits: TreeH for event and branch "MUON"
313 sprintf(treeName, "TreeH%d", fBkgGeantEventNumber);
314 fBkgGeantTH = (TTree*)gDirectory->Get(treeName);
316 cout << "ERROR: cannot find Hits Tree for background event: " <<
317 fBkgGeantEventNumber << endl;
320 if (fBkgGeantTH && fBkgGeantHits) {
321 branch = fBkgGeantTH->GetBranch("MUON");
322 if (branch) branch->SetAddress(&fBkgGeantHits);
324 fBkgGeantTH->GetEntries(); // necessary ????
325 // Back to the signal file
326 ((gAlice->TreeK())->GetCurrentFile())->cd();
327 if (fPrintLevel >= 2) {cout << "After cd(gAlice)" << endl; gDirectory->Dump();}
331 //__________________________________________________________________________
332 void AliMUONEventReconstructor::EventReconstruct(void)
334 // To reconstruct one event
335 if (fPrintLevel >= 1) cout << "enter EventReconstruct" << endl;
336 MakeEventToBeReconstructed();
342 //__________________________________________________________________________
343 void AliMUONEventReconstructor::ResetHitsForRec(void)
345 // To reset the array and the number of HitsForRec,
346 // and also the number of HitsForRec
347 // and the index of the first HitForRec per chamber
348 if (fHitsForRecPtr) fHitsForRecPtr->Clear();
350 for (Int_t ch = 0; ch < MAX_MUON_TRACKING_CHAMBERS; ch++)
351 fNHitsForRecPerChamber[ch] = fIndexOfFirstHitForRecPerChamber[ch] = 0;
355 //__________________________________________________________________________
356 void AliMUONEventReconstructor::ResetSegments(void)
358 // To reset the TClonesArray of segments and the number of Segments
360 for (Int_t st = 0; st < MAX_MUON_TRACKING_STATIONS; st++) {
361 if (fSegmentsPtr[st]) fSegmentsPtr[st]->Clear();
367 //__________________________________________________________________________
368 void AliMUONEventReconstructor::ResetTracks(void)
370 // To reset the TClonesArray of reconstructed tracks
371 if (fRecTracksPtr) fRecTracksPtr->Clear();
376 //__________________________________________________________________________
377 void AliMUONEventReconstructor::MakeEventToBeReconstructed(void)
379 // To make the list of hits to be reconstructed,
380 // either from the GEANT hits or from the raw clusters
381 // according to the parameter set for the reconstructor
382 if (fPrintLevel >= 1) cout << "enter MakeEventToBeReconstructed" << endl;
384 if (fRecGeantHits == 1) {
385 // Reconstruction from GEANT hits
386 // Back to the signal file
387 ((gAlice->TreeK())->GetCurrentFile())->cd();
389 // AliMUON *MUON = (AliMUON*) gAlice->GetModule("MUON"); // necessary ????
390 // Security on MUON ????
391 AddHitsForRecFromGEANT(gAlice->TreeH());
393 AddHitsForRecFromBkgGEANT(fBkgGeantTH, fBkgGeantHits);
394 // Sort HitsForRec in increasing order with respect to chamber number
395 SortHitsForRecWithIncreasingChamber();
398 // Reconstruction from raw clusters
399 // AliMUON *MUON = (AliMUON*) gAlice->GetModule("MUON"); // necessary ????
400 // Security on MUON ????
401 // TreeR assumed to be be "prepared" in calling function
402 // by "MUON->GetTreeR(nev)" ????
403 TTree *TR = gAlice->TreeR();
404 AddHitsForRecFromRawClusters(TR);
405 // No sorting: it is done automatically in the previous function
407 if (fPrintLevel >= 10) {
408 cout << "end of MakeEventToBeReconstructed" << endl;
409 cout << "NHitsForRec: " << fNHitsForRec << endl;
410 for (Int_t ch = 0; ch < MAX_MUON_TRACKING_CHAMBERS; ch++) {
411 cout << "chamber(0...): " << ch
412 << " NHitsForRec: " << fNHitsForRecPerChamber[ch]
413 << " index(first HitForRec): " << fIndexOfFirstHitForRecPerChamber[ch]
415 for (Int_t hit = fIndexOfFirstHitForRecPerChamber[ch];
416 hit < fIndexOfFirstHitForRecPerChamber[ch] + fNHitsForRecPerChamber[ch];
418 cout << "HitForRec index(0...): " << hit << endl;
419 ((*fHitsForRecPtr)[hit])->Dump();
426 //__________________________________________________________________________
427 void AliMUONEventReconstructor::AddHitsForRecFromGEANT(TTree *TH)
429 // To add to the list of hits for reconstruction
430 // the GEANT signal hits from a hit tree TH.
431 if (fPrintLevel >= 2)
432 cout << "enter AddHitsForRecFromGEANT with TH: " << TH << endl;
433 if (TH == NULL) return;
434 AliMUON *MUON = (AliMUON*) gAlice->GetModule("MUON"); // necessary ????
435 // Security on MUON ????
436 // See whether it could be the same for signal and background ????
437 // Loop over tracks in tree
438 Int_t ntracks = (Int_t) TH->GetEntries();
439 if (fPrintLevel >= 2)
440 cout << "ntracks: " << ntracks << endl;
441 for (Int_t track = 0; track < ntracks; track++) {
446 for (AliMUONHit* mHit = (AliMUONHit*) MUON->FirstHit(-1);
448 mHit = (AliMUONHit*) MUON->NextHit(), hit++) {
449 NewHitForRecFromGEANT(mHit,track, hit, 1);
451 } // end of track loop
455 //__________________________________________________________________________
456 void AliMUONEventReconstructor::AddHitsForRecFromBkgGEANT(TTree *TH, TClonesArray *Hits)
458 // To add to the list of hits for reconstruction
459 // the GEANT background hits from a hit tree TH and a pointer Hits to a hit list.
460 // How to have only one function "AddHitsForRecFromGEANT" ????
461 if (fPrintLevel >= 2)
462 cout << "enter AddHitsForRecFromBkgGEANT with TH: " << TH << endl;
463 if (TH == NULL) return;
464 // Loop over tracks in tree
465 Int_t ntracks = (Int_t) TH->GetEntries();
466 if (fPrintLevel >= 2)
467 cout << "ntracks: " << ntracks << endl;
468 for (Int_t track = 0; track < ntracks; track++) {
469 if (Hits) Hits->Clear();
472 for (Int_t hit = 0; hit < Hits->GetEntriesFast(); hit++) {
473 NewHitForRecFromGEANT((AliMUONHit*) (*Hits)[hit], track, hit, 0);
475 } // end of track loop
479 //__________________________________________________________________________
480 AliMUONHitForRec* AliMUONEventReconstructor::NewHitForRecFromGEANT(AliMUONHit* Hit, Int_t TrackNumber, Int_t HitNumber, Int_t Signal)
482 // To make a new hit for reconstruction from a GEANT hit pointed to by "Hit",
483 // with hit number "HitNumber" in the track numbered "TrackNumber",
484 // either from signal ("Signal" = 1) or background ("Signal" = 0) event.
485 // Selects hits in tracking (not trigger) chambers.
486 // Takes into account the efficiency (fEfficiency)
487 // and the smearing from resolution (fBendingResolution and fNonBendingResolution).
488 // Adds a condition on the radius between RMin and RMax
489 // to better simulate the real chambers.
490 // Returns the pointer to the new hit for reconstruction,
491 // or NULL in case of inefficiency or non tracking chamber or bad radius.
492 // No condition on at most 20 cm from a muon from a resonance
493 // like in Fortran TRACKF_STAT.
494 AliMUONHitForRec* hitForRec;
495 Double_t bendCoor, nonBendCoor, radius;
496 Int_t chamber = Hit->fChamber - 1; // chamber(0...)
497 // only in tracking chambers (fChamber starts at 1)
498 if (chamber >= MAX_MUON_TRACKING_CHAMBERS) return NULL;
499 // only if hit is efficient (keep track for checking ????)
500 if (gRandom->Rndm() > fEfficiency) return NULL;
501 // only if radius between RMin and RMax
503 nonBendCoor = Hit->fX;
504 radius = TMath::Sqrt((bendCoor * bendCoor) + (nonBendCoor * nonBendCoor));
505 if ((radius < fRMin[chamber]) || (radius > fRMax[chamber])) return NULL;
506 // new AliMUONHitForRec from GEANT hit and increment number of AliMUONHitForRec's
507 hitForRec = new ((*fHitsForRecPtr)[fNHitsForRec]) AliMUONHitForRec(Hit);
509 // add smearing from resolution
510 hitForRec->SetBendingCoor(bendCoor + gRandom->Gaus(0., fBendingResolution));
511 hitForRec->SetNonBendingCoor(nonBendCoor
512 + gRandom->Gaus(0., fNonBendingResolution));
513 // more information into HitForRec
514 // resolution: angular effect to be added here ????
515 hitForRec->SetBendingReso2(fBendingResolution * fBendingResolution);
516 hitForRec->SetNonBendingReso2(fNonBendingResolution * fNonBendingResolution);
518 hitForRec->SetHitNumber(HitNumber);
519 hitForRec->SetTHTrack(TrackNumber);
520 hitForRec->SetGeantSignal(Signal);
521 if (fPrintLevel >= 10) {
522 cout << "track: " << TrackNumber << " hit: " << HitNumber << endl;
524 cout << "AliMUONHitForRec number (1...): " << fNHitsForRec << endl;
529 //__________________________________________________________________________
530 void AliMUONEventReconstructor::SortHitsForRecWithIncreasingChamber()
532 // Sort HitsForRec's in increasing order with respect to chamber number.
533 // Uses the function "Compare".
534 // Update the information for HitsForRec per chamber too.
535 Int_t ch, nhits, prevch;
536 fHitsForRecPtr->Sort();
537 for (ch = 0; ch < MAX_MUON_TRACKING_CHAMBERS; ch++) {
538 fNHitsForRecPerChamber[ch] = 0;
539 fIndexOfFirstHitForRecPerChamber[ch] = 0;
541 prevch = 0; // previous chamber
542 nhits = 0; // number of hits in current chamber
543 // Loop over HitsForRec
544 for (Int_t hit = 0; hit < fNHitsForRec; hit++) {
545 // chamber number (0...)
546 ch = ((AliMUONHitForRec*) ((*fHitsForRecPtr)[hit]))->GetChamberNumber();
547 // increment number of hits in current chamber
548 (fNHitsForRecPerChamber[ch])++;
549 // update index of first HitForRec in current chamber
550 // if chamber number different from previous one
552 fIndexOfFirstHitForRecPerChamber[ch] = hit;
559 // //__________________________________________________________________________
560 // void AliMUONEventReconstructor::AddHitsForRecFromCathodeCorrelations(TTree* TC)
562 // // OLD VERSION WHEN ONE ONE WAS USING SO CALLED CATHODE CORRELATIONS
563 // // To add to the list of hits for reconstruction
564 // // the (cathode correlated) raw clusters
565 // // No condition added, like in Fortran TRACKF_STAT,
566 // // on the radius between RMin and RMax.
567 // AliMUONHitForRec *hitForRec;
568 // if (fPrintLevel >= 1) cout << "enter AddHitsForRecFromCathodeCorrelations" << endl;
569 // AliMUON *MUON = (AliMUON*) gAlice->GetModule("MUON"); // necessary ????
570 // // Security on MUON ????
571 // // Loop over tracking chambers
572 // for (Int_t ch = 0; ch < MAX_MUON_TRACKING_CHAMBERS; ch++) {
573 // // number of HitsForRec to 0 for the chamber
574 // fNHitsForRecPerChamber[ch] = 0;
575 // // index of first HitForRec for the chamber
576 // if (ch == 0) fIndexOfFirstHitForRecPerChamber[ch] = 0;
577 // else fIndexOfFirstHitForRecPerChamber[ch] = fNHitsForRec;
578 // TClonesArray *reconst_hits = MUON->ReconstHitsAddress(ch);
579 // MUON->ResetReconstHits();
581 // Int_t ncor = (Int_t)reconst_hits->GetEntries();
582 // // Loop over (cathode correlated) raw clusters
583 // for (Int_t cor = 0; cor < ncor; cor++) {
584 // AliMUONReconstHit * mCor =
585 // (AliMUONReconstHit*) reconst_hits->UncheckedAt(cor);
586 // // new AliMUONHitForRec from (cathode correlated) raw cluster
587 // // and increment number of AliMUONHitForRec's (total and in chamber)
588 // hitForRec = new ((*fHitsForRecPtr)[fNHitsForRec]) AliMUONHitForRec(mCor);
590 // (fNHitsForRecPerChamber[ch])++;
591 // // more information into HitForRec
592 // hitForRec->SetChamberNumber(ch);
593 // hitForRec->SetHitNumber(cor);
594 // // Z coordinate of the chamber (cm) with sign opposite to GEANT sign
595 // // could (should) be more exact from chamber geometry ????
596 // hitForRec->SetZ(-(&(MUON->Chamber(ch)))->Z());
597 // if (fPrintLevel >= 10) {
598 // cout << "chamber (0...): " << ch <<
599 // " cathcorrel (0...): " << cor << endl;
601 // cout << "AliMUONHitForRec number (1...): " << fNHitsForRec << endl;
602 // hitForRec->Dump();}
603 // } // end of cluster loop
604 // } // end of chamber loop
608 //__________________________________________________________________________
609 void AliMUONEventReconstructor::AddHitsForRecFromRawClusters(TTree* TR)
611 // To add to the list of hits for reconstruction all the raw clusters
612 // No condition added, like in Fortran TRACKF_STAT,
613 // on the radius between RMin and RMax.
614 AliMUONHitForRec *hitForRec;
615 AliMUONRawCluster *clus;
617 TClonesArray *rawclusters;
618 if (fPrintLevel >= 1) cout << "enter AddHitsForRecFromRawClusters" << endl;
619 AliMUON *MUON = (AliMUON*) gAlice->GetModule("MUON"); // necessary ????
620 // Security on MUON ????
621 // Loop over tracking chambers
622 for (Int_t ch = 0; ch < MAX_MUON_TRACKING_CHAMBERS; ch++) {
623 // number of HitsForRec to 0 for the chamber
624 fNHitsForRecPerChamber[ch] = 0;
625 // index of first HitForRec for the chamber
626 if (ch == 0) fIndexOfFirstHitForRecPerChamber[ch] = 0;
627 else fIndexOfFirstHitForRecPerChamber[ch] = fNHitsForRec;
628 rawclusters = MUON->RawClustAddress(ch);
629 MUON->ResetRawClusters();
630 TR->GetEvent((Int_t) (TR->GetEntries()) - 1); // to be checked ????
631 nclus = (Int_t) (rawclusters->GetEntries());
632 // Loop over (cathode correlated) raw clusters
633 for (iclus = 0; iclus < nclus; iclus++) {
634 clus = (AliMUONRawCluster*) rawclusters->UncheckedAt(iclus);
635 // new AliMUONHitForRec from raw cluster
636 // and increment number of AliMUONHitForRec's (total and in chamber)
637 hitForRec = new ((*fHitsForRecPtr)[fNHitsForRec]) AliMUONHitForRec(clus);
639 (fNHitsForRecPerChamber[ch])++;
640 // more information into HitForRec
641 // resolution: info should be already in raw cluster and taken from it ????
642 hitForRec->SetBendingReso2(fBendingResolution * fBendingResolution);
643 hitForRec->SetNonBendingReso2(fNonBendingResolution * fNonBendingResolution);
644 // original raw cluster
645 hitForRec->SetChamberNumber(ch);
646 hitForRec->SetHitNumber(iclus);
647 // Z coordinate of the chamber (cm) with sign opposite to GEANT sign
648 // could (should) be more exact from chamber geometry ????
649 hitForRec->SetZ(-(&(MUON->Chamber(ch)))->Z());
650 if (fPrintLevel >= 10) {
651 cout << "chamber (0...): " << ch <<
652 " raw cluster (0...): " << iclus << endl;
654 cout << "AliMUONHitForRec number (1...): " << fNHitsForRec << endl;
656 } // end of cluster loop
657 } // end of chamber loop
661 //__________________________________________________________________________
662 void AliMUONEventReconstructor::MakeSegments(void)
664 // To make the list of segments in all stations,
665 // from the list of hits to be reconstructed
666 if (fPrintLevel >= 1) cout << "enter MakeSegments" << endl;
668 // Loop over stations
669 for (Int_t st = 0; st < MAX_MUON_TRACKING_STATIONS; st++)
670 MakeSegmentsPerStation(st);
671 if (fPrintLevel >= 10) {
672 cout << "end of MakeSegments" << endl;
673 for (Int_t st = 0; st < MAX_MUON_TRACKING_STATIONS; st++) {
674 cout << "station(0...): " << st
675 << " Segments: " << fNSegments[st]
678 seg < fNSegments[st];
680 cout << "Segment index(0...): " << seg << endl;
681 ((*fSegmentsPtr[st])[seg])->Dump();
688 //__________________________________________________________________________
689 void AliMUONEventReconstructor::MakeSegmentsPerStation(Int_t Station)
691 // To make the list of segments in station number "Station" (0...)
692 // from the list of hits to be reconstructed.
693 // Updates "fNSegments"[Station].
694 // Segments in stations 4 and 5 are sorted
695 // according to increasing absolute value of "impact parameter"
696 AliMUONHitForRec *hit1Ptr, *hit2Ptr;
697 AliMUONSegment *segment;
699 Double_t bendingSlope, distBend, distNonBend, extBendCoor, extNonBendCoor,
700 impactParam, maxImpactParam;
701 AliMUON *MUON = (AliMUON*) gAlice->GetModule("MUON"); // necessary ????
702 if (fPrintLevel >= 1)
703 cout << "enter MakeSegmentsPerStation (0...) " << Station << endl;
704 // first and second chambers (0...) in the station
705 Int_t ch1 = 2 * Station;
707 // variable true for stations downstream of the dipole:
708 // Station(0..4) equal to 3 or 4
709 if ((Station == 3) || (Station == 4)) {
711 // maximum impact parameter (cm) according to fMinBendingMomentum...
713 TMath::Abs(GetImpactParamFromBendingMomentum(fMinBendingMomentum));
715 else last2st = kFALSE;
716 // extrapolation factor from Z of first chamber to Z of second chamber
717 // dZ to be changed to take into account fine structure of chambers ????
718 Double_t extrapFact =
719 (&(MUON->Chamber(ch2)))->Z() / (&(MUON->Chamber(ch1)))->Z();
720 // index for current segment
721 Int_t segmentIndex = 0;
722 // Loop over HitsForRec in the first chamber of the station
723 for (Int_t hit1 = fIndexOfFirstHitForRecPerChamber[ch1];
724 hit1 < fIndexOfFirstHitForRecPerChamber[ch1] + fNHitsForRecPerChamber[ch1];
726 // pointer to the HitForRec
727 hit1Ptr = (AliMUONHitForRec*) ((*fHitsForRecPtr)[hit1]);
729 // on the straight line joining the HitForRec to the vertex (0,0,0),
730 // to the Z of the second chamber of the station
731 extBendCoor = extrapFact * hit1Ptr->GetBendingCoor();
732 extNonBendCoor = extrapFact * hit1Ptr->GetNonBendingCoor();
733 // Loop over HitsForRec in the second chamber of the station
734 for (Int_t hit2 = fIndexOfFirstHitForRecPerChamber[ch2];
735 hit2 < fIndexOfFirstHitForRecPerChamber[ch2] + fNHitsForRecPerChamber[ch2];
737 // pointer to the HitForRec
738 hit2Ptr = (AliMUONHitForRec*) ((*fHitsForRecPtr)[hit2]);
739 // absolute values of distances, in bending and non bending planes,
740 // between the HitForRec in the second chamber
741 // and the previous extrapolation
742 distBend = TMath::Abs(hit2Ptr->GetBendingCoor() - extBendCoor);
743 distNonBend = TMath::Abs(hit2Ptr->GetNonBendingCoor() - extNonBendCoor);
746 bendingSlope = (hit1Ptr->GetBendingCoor() - hit2Ptr->GetBendingCoor()) /
747 (hit1Ptr->GetZ() - hit2Ptr->GetZ());
748 // absolute value of impact parameter
750 TMath::Abs(hit1Ptr->GetBendingCoor() - hit2Ptr->GetZ() * bendingSlope);
752 // check for distances not too large,
753 // and impact parameter not too big if stations downstream of the dipole.
754 // Conditions "distBend" and "impactParam" correlated for these stations ????
755 if ((distBend < fSegmentMaxDistBending[Station]) &&
756 (distNonBend < fSegmentMaxDistNonBending[Station]) &&
757 (!last2st || (impactParam < maxImpactParam))) {
759 segment = new ((*fSegmentsPtr[Station])[segmentIndex])
760 AliMUONSegment(hit1Ptr, hit2Ptr);
761 // update "link" to this segment from the hit in the first chamber
762 if (hit1Ptr->GetNSegments() == 0)
763 hit1Ptr->SetIndexOfFirstSegment(segmentIndex);
764 hit1Ptr->SetNSegments(hit1Ptr->GetNSegments() + 1);
765 if (fPrintLevel >= 10) {
766 cout << "segmentIndex(0...): " << segmentIndex
767 << " distBend: " << distBend
768 << " distNonBend: " << distNonBend
771 cout << "HitForRec in first chamber" << endl;
773 cout << "HitForRec in second chamber" << endl;
776 // increment index for current segment
780 } // for (Int_t hit1...
781 fNSegments[Station] = segmentIndex;
782 // Sorting according to "impact parameter" if station(1..5) 4 or 5,
783 // i.e. Station(0..4) 3 or 4, using the function "Compare".
784 // After this sorting, it is impossible to use
785 // the "fNSegments" and "fIndexOfFirstSegment"
786 // of the HitForRec in the first chamber to explore all segments formed with it.
787 // Is this sorting really needed ????
788 if ((Station == 3) || (Station == 4)) (fSegmentsPtr[Station])->Sort();
789 if (fPrintLevel >= 1) cout << "Station: " << Station << " NSegments: "
790 << fNSegments[Station] << endl;
794 //__________________________________________________________________________
795 void AliMUONEventReconstructor::MakeTracks(void)
797 // To make the tracks,
798 // from the list of segments and points in all stations
799 if (fPrintLevel >= 1) cout << "enter MakeTracks" << endl;
801 // Look for candidates from at least 3 aligned points in stations(1..) 4 and 5
802 MakeTrackCandidates();
803 // Follow tracks in stations(1..) 3, 2 and 1
808 //__________________________________________________________________________
809 Int_t AliMUONEventReconstructor::MakeTrackCandidatesWithTwoSegments(AliMUONSegment *BegSegment)
811 // To make track candidates with two segments in stations(1..) 4 and 5,
812 // the first segment being pointed to by "BegSegment".
813 // Returns the number of such track candidates.
814 Int_t endStation, iEndSegment, nbCan2Seg;
815 AliMUONSegment *endSegment, *extrapSegment;
816 AliMUONTrack *recTrack;
818 if (fPrintLevel >= 1) cout << "enter MakeTrackCandidatesWithTwoSegments" << endl;
819 // Station for the end segment
820 endStation = 7 - (BegSegment->GetHitForRec1())->GetChamberNumber() / 2;
821 // multiple scattering factor corresponding to one chamber
823 GetBendingMomentumFromImpactParam(BegSegment->GetBendingImpact());
824 mcsFactor = fChamberThicknessInX0 * mcsFactor * mcsFactor;
825 // linear extrapolation to end station
827 BegSegment->CreateSegmentFromLinearExtrapToStation(endStation, mcsFactor);
828 // number of candidates with 2 segments to 0
830 // Loop over segments in the end station
831 for (iEndSegment = 0; iEndSegment < fNSegments[endStation]; iEndSegment++) {
832 // pointer to segment
833 endSegment = (AliMUONSegment*) ((*fSegmentsPtr[endStation])[iEndSegment]);
834 // test compatibility between current segment and "extrapSegment"
836 NormalizedChi2WithSegment(extrapSegment,
837 fMaxSigma2Distance)) <= 4.0) {
838 // both segments compatible:
839 // make track candidate from "begSegment" and "endSegment"
840 if (fPrintLevel >= 2)
841 cout << "TrackCandidate with Segment " << iEndSegment <<
842 " in Station(0..) " << endStation << endl;
843 // flag for both segments in one track:
844 // to be done in track constructor ????
845 BegSegment->SetInTrack(kTRUE);
846 endSegment->SetInTrack(kTRUE);
847 recTrack = new ((*fRecTracksPtr)[fNRecTracks])
848 AliMUONTrack(BegSegment, endSegment, this);
850 if (fPrintLevel >= 10) recTrack->RecursiveDump();
851 // increment number of track candidates with 2 segments
854 } // for (iEndSegment = 0;...
855 delete extrapSegment; // should not delete HitForRec's it points to !!!!
859 //__________________________________________________________________________
860 Int_t AliMUONEventReconstructor::MakeTrackCandidatesWithOneSegmentAndOnePoint(AliMUONSegment *BegSegment)
862 // To make track candidates with one segment and one point
863 // in stations(1..) 4 and 5,
864 // the segment being pointed to by "BegSegment".
865 Int_t ch, ch1, ch2, endStation, iHit, iHitMax, iHitMin, nbCan1Seg1Hit;
866 AliMUONHitForRec *extrapHitForRec, *hit;
867 AliMUONTrack *recTrack;
869 if (fPrintLevel >= 1)
870 cout << "enter MakeTrackCandidatesWithOneSegmentAndOnePoint" << endl;
871 // station for the end point
872 endStation = 7 - (BegSegment->GetHitForRec1())->GetChamberNumber() / 2;
873 // multiple scattering factor corresponding to one chamber
875 GetBendingMomentumFromImpactParam(BegSegment->GetBendingImpact());
876 mcsFactor = fChamberThicknessInX0 * mcsFactor * mcsFactor;
877 // first and second chambers(0..) in the end station
878 ch1 = 2 * endStation;
880 // number of candidates to 0
882 // Loop over chambers of the end station
883 for (ch = ch2; ch >= ch1; ch--) {
884 // linear extrapolation to chamber
886 BegSegment->CreateHitForRecFromLinearExtrapToChamber(ch, mcsFactor);
887 // limits for the hit index in the loop
888 iHitMin = fIndexOfFirstHitForRecPerChamber[ch];
889 iHitMax = iHitMin + fNHitsForRecPerChamber[ch];
890 // Loop over HitForRec's in the chamber
891 for (iHit = iHitMin; iHit < iHitMax; iHit++) {
892 // pointer to HitForRec
893 hit = (AliMUONHitForRec*) ((*fHitsForRecPtr)[iHit]);
894 // test compatibility between current HitForRec and "extrapHitForRec"
896 NormalizedChi2WithHitForRec(extrapHitForRec,
897 fMaxSigma2Distance)) <= 2.0) {
898 // both HitForRec's compatible:
899 // make track candidate from begSegment and current HitForRec
900 if (fPrintLevel >= 2)
901 cout << "TrackCandidate with HitForRec " << iHit <<
902 " in Chamber(0..) " << ch << endl;
903 // flag for beginning segments in one track:
904 // to be done in track constructor ????
905 BegSegment->SetInTrack(kTRUE);
906 recTrack = new ((*fRecTracksPtr)[fNRecTracks])
907 AliMUONTrack(BegSegment, hit, this);
908 // the right place to eliminate "double counting" ???? how ????
910 if (fPrintLevel >= 10) recTrack->RecursiveDump();
911 // increment number of track candidates
914 } // for (iHit = iHitMin;...
915 delete extrapHitForRec;
916 } // for (ch = ch2;...
917 return nbCan1Seg1Hit;
920 //__________________________________________________________________________
921 void AliMUONEventReconstructor::MakeTrackCandidates(void)
923 // To make track candidates
924 // with at least 3 aligned points in stations(1..) 4 and 5
925 // (two Segment's or one Segment and one HitForRec)
926 Int_t begStation, iBegSegment, nbCan1Seg1Hit, nbCan2Seg;
927 AliMUONSegment *begSegment;
928 if (fPrintLevel >= 1) cout << "enter MakeTrackCandidates" << endl;
929 // Loop over stations(1..) 5 and 4 for the beginning segment
930 for (begStation = 4; begStation > 2; begStation--) {
931 // Loop over segments in the beginning station
932 for (iBegSegment = 0; iBegSegment < fNSegments[begStation]; iBegSegment++) {
933 // pointer to segment
934 begSegment = (AliMUONSegment*) ((*fSegmentsPtr[begStation])[iBegSegment]);
935 if (fPrintLevel >= 2)
936 cout << "look for TrackCandidate's with Segment " << iBegSegment <<
937 " in Station(0..) " << begStation << endl;
938 // Look for track candidates with two segments,
939 // "begSegment" and all compatible segments in other station.
940 // Only for beginning station(1..) 5
941 // because candidates with 2 segments have to looked for only once.
943 nbCan2Seg = MakeTrackCandidatesWithTwoSegments(begSegment);
944 // Look for track candidates with one segments and one point,
945 // "begSegment" and all compatible HitForRec's in other station.
946 // Only if "begSegment" does not belong already to a track candidate.
947 // Is that a too strong condition ????
948 if (!(begSegment->GetInTrack()))
949 nbCan1Seg1Hit = MakeTrackCandidatesWithOneSegmentAndOnePoint(begSegment);
950 } // for (iBegSegment = 0;...
951 } // for (begStation = 4;...
955 //__________________________________________________________________________
956 void AliMUONEventReconstructor::FollowTracks(void)
958 // Follow tracks in stations(1..) 3, 2 and 1
959 AliMUONHitForRec *bestHit, *extrapHit, *hit;
960 AliMUONSegment *bestSegment, *extrapSegment, *segment;
962 AliMUONTrackParam *trackParam1, trackParam[2];
963 Int_t ch, chBestHit, iHit, iSegment, station, trackIndex;
964 Double_t bestChi2, chi2, dZ1, dZ2, maxSigma2Distance, mcsFactor;
965 AliMUON *MUON = (AliMUON*) gAlice->GetModule("MUON"); // necessary ????
966 maxSigma2Distance = 4. * fMaxSigma2Distance; // sigma2cut increased by 4 !!!!
967 if (fPrintLevel >= 2)
968 cout << "enter FollowTracks" << endl;
969 // Loop over track candidates
970 for (trackIndex = 0; trackIndex < fNRecTracks; trackIndex++) {
971 if (fPrintLevel >= 2)
972 cout << "FollowTracks: track candidate(0..): " << trackIndex << endl;
973 // function for each track candidate ????
974 track = (AliMUONTrack*) ((*fRecTracksPtr)[trackIndex]);
975 // Fit track candidate from vertex at X = Y = 0
976 track->Fit(track->GetTrackParamAtVertex(), 3);
977 if (fPrintLevel >= 10) {
978 cout << "FollowTracks: track candidate(0..): " << trackIndex
979 << " after fit in stations(1..) 4 and 5" << endl;
980 track->RecursiveDump();
982 // Loop over stations(1..) 3, 2 and 1
983 // something SPECIAL for stations 2 and 1 for majority coincidence ????
984 for (station = 2; station >= 0; station--) {
985 // Track parameters at first track hit (smallest Z)
986 trackParam1 = ((AliMUONTrackHit*)
987 (track->GetTrackHitsPtr()->First()))->GetTrackParam();
988 // extrapolation to station
989 trackParam1->ExtrapToStation(station, trackParam);
990 extrapSegment = new AliMUONSegment::AliMUONSegment(); // empty segment
991 // multiple scattering factor corresponding to one chamber
992 // and momentum in bending plane (not total)
993 mcsFactor = 0.0136 * trackParam1->GetInverseBendingMomentum();
994 mcsFactor = fChamberThicknessInX0 * mcsFactor * mcsFactor;
995 // Z difference from previous station
996 dZ1 = (&(MUON->Chamber(2 * station)))->Z() -
997 (&(MUON->Chamber(2 * station + 2)))->Z();
998 // Z difference between the two previous stations
999 dZ2 = (&(MUON->Chamber(2 * station + 2)))->Z() -
1000 (&(MUON->Chamber(2 * station + 4)))->Z();
1001 extrapSegment->SetBendingCoorReso2(fBendingResolution);
1002 extrapSegment->SetNonBendingCoorReso2(fNonBendingResolution);
1003 extrapSegment->UpdateFromStationTrackParam(trackParam, mcsFactor, dZ1, dZ2);
1006 if (fPrintLevel >= 10) {
1007 cout << "FollowTracks: track candidate(0..): " << trackIndex
1008 << " Look for segment in station(0..): " << station << endl;
1010 // Loop over segments in station
1011 for (iSegment = 0; iSegment < fNSegments[station]; iSegment++) {
1012 // Look for best compatible Segment in station
1013 // should consider all possibilities ????
1014 // multiple scattering ????
1015 // separation in 2 functions: Segment and HitForRec ????
1016 segment = (AliMUONSegment*) ((*fSegmentsPtr[station])[iSegment]);
1017 chi2 = segment->NormalizedChi2WithSegment(extrapSegment, maxSigma2Distance);
1018 if (chi2 < bestChi2) {
1019 // update best Chi2 and Segment if better found
1020 bestSegment = segment;
1025 // best segment found: add it to track candidate
1026 track->AddSegment(bestSegment);
1027 // set track parameters at these two TrakHit's
1028 track->SetTrackParamAtHit(track->GetNTrackHits() - 2, &(trackParam[0]));
1029 track->SetTrackParamAtHit(track->GetNTrackHits() - 1, &(trackParam[1]));
1030 if (fPrintLevel >= 10) {
1031 cout << "FollowTracks: track candidate(0..): " << trackIndex
1032 << " Added segment in station(0..): " << station << endl;
1033 track->RecursiveDump();
1037 // No best segment found:
1038 // Look for best compatible HitForRec in station:
1039 // should consider all possibilities ????
1040 // multiple scattering ???? do about like for extrapSegment !!!!
1041 extrapHit = new AliMUONHitForRec::AliMUONHitForRec(); // empty hit
1044 if (fPrintLevel >= 10) {
1045 cout << "FollowTracks: track candidate(0..): " << trackIndex
1046 << " Segment not found, look for hit in station(0..): " << station
1049 // Loop over chambers of the station
1050 for (ch = 0; ch < 2; ch++) {
1051 // coordinates of extrapolated hit
1052 extrapHit->SetBendingCoor((&(trackParam[ch]))->GetBendingCoor());
1053 extrapHit->SetNonBendingCoor((&(trackParam[ch]))->GetNonBendingCoor());
1054 // resolutions from "extrapSegment"
1055 extrapHit->SetBendingReso2(extrapSegment->GetBendingCoorReso2());
1056 extrapHit->SetNonBendingReso2(extrapSegment->GetNonBendingCoorReso2());
1057 // Loop over hits in the chamber
1058 for (iHit = fIndexOfFirstHitForRecPerChamber[ch];
1059 iHit < fIndexOfFirstHitForRecPerChamber[ch] +
1060 fNHitsForRecPerChamber[ch];
1062 hit = (AliMUONHitForRec*) ((*fHitsForRecPtr)[iHit]);
1063 // condition for hit not already in segment ????
1064 chi2 = hit->NormalizedChi2WithHitForRec(extrapHit, maxSigma2Distance);
1065 if (chi2 < bestChi2) {
1066 // update best Chi2 and HitForRec if better found
1074 // best hit found: add it to track candidate
1075 track->AddHitForRec(bestHit);
1076 // set track parameters at these two TrakHit's
1077 track->SetTrackParamAtHit(track->GetNTrackHits() - 1,
1078 &(trackParam[chBestHit]));
1079 if (fPrintLevel >= 10) {
1080 cout << "FollowTracks: track candidate(0..): " << trackIndex
1081 << " Added hit in station(0..): " << station << endl;
1082 track->RecursiveDump();
1086 fRecTracksPtr->RemoveAt(trackIndex); // Remove candidate
1087 break; // stop the search for this candidate:
1088 // exit from the loop over station
1091 // Sort track hits according to increasing Z
1092 track->GetTrackHitsPtr()->Sort();
1093 // Update track parameters at first track hit (smallest Z)
1094 trackParam1 = ((AliMUONTrackHit*)
1095 (track->GetTrackHitsPtr()->First()))->GetTrackParam();
1096 // Track fit from first track hit varying X and Y
1097 track->Fit(trackParam1, 5);
1098 if (fPrintLevel >= 10) {
1099 cout << "FollowTracks: track candidate(0..): " << trackIndex
1100 << " after fit from station(0..): " << station << " to 4" << endl;
1101 track->RecursiveDump();
1103 delete extrapSegment;
1104 } // for (station = 2;...
1105 } // for (trackIndex = 0;...
1109 void AliMUONEventReconstructor::Streamer(TBuffer &R__b)