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 *
9 * without fee, provided that the above copyright notice appears in all *
10 * copies and that both the copyright notice and this permission notice *
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 ///////////////////////////////////////////////////
20 // Reconstructed track
26 ///////////////////////////////////////////////////
28 #include <Riostream.h> // for cout
29 #include <stdlib.h> // for exit()
31 #include <TClonesArray.h>
34 #include <TObjArray.h>
35 #include <TVirtualFitter.h>
37 #include "AliMUONEventReconstructor.h"
38 #include "AliMUONHitForRec.h"
39 #include "AliMUONSegment.h"
40 #include "AliMUONTrack.h"
41 #include "AliMUONTrackHit.h"
43 // Functions to be minimized with Minuit
44 void TrackChi2(Int_t &NParam, Double_t *Gradient, Double_t &Chi2, Double_t *Param, Int_t Flag);
45 void TrackChi2MCS(Int_t &NParam, Double_t *Gradient, Double_t &Chi2, Double_t *Param, Int_t Flag);
47 void mnvertLocal(Double_t* a, Int_t l, Int_t m, Int_t n, Int_t& ifail);
49 Double_t MultipleScatteringAngle2(AliMUONTrackHit *TrackHit);
51 ClassImp(AliMUONTrack) // Class implementation in ROOT context
53 TVirtualFitter* AliMUONTrack::fgFitter = NULL;
55 //__________________________________________________________________________
56 AliMUONTrack::AliMUONTrack(AliMUONSegment* BegSegment, AliMUONSegment* EndSegment, AliMUONEventReconstructor* EventReconstructor)
58 // Constructor from two Segment's
59 fEventReconstructor = EventReconstructor; // link back to EventReconstructor
60 // memory allocation for the TObjArray of pointers to reconstructed TrackHit's
61 fTrackHitsPtr = new TObjArray(10);
63 AddSegment(BegSegment); // add hits from BegSegment
64 AddSegment(EndSegment); // add hits from EndSegment
65 fTrackHitsPtr->Sort(); // sort TrackHits according to increasing Z
66 SetTrackParamAtVertex(); // set track parameters at vertex
67 // set fit conditions...
75 //__________________________________________________________________________
76 AliMUONTrack::AliMUONTrack(AliMUONSegment* Segment, AliMUONHitForRec* HitForRec, AliMUONEventReconstructor* EventReconstructor)
78 // Constructor from one Segment and one HitForRec
79 fEventReconstructor = EventReconstructor; // link back to EventReconstructor
80 // memory allocation for the TObjArray of pointers to reconstructed TrackHit's
81 fTrackHitsPtr = new TObjArray(10);
83 AddSegment(Segment); // add hits from Segment
84 AddHitForRec(HitForRec); // add HitForRec
85 fTrackHitsPtr->Sort(); // sort TrackHits according to increasing Z
86 SetTrackParamAtVertex(); // set track parameters at vertex
87 // set fit conditions...
95 //__________________________________________________________________________
96 AliMUONTrack::~AliMUONTrack()
100 delete fTrackHitsPtr; // delete the TObjArray of pointers to TrackHit's
101 fTrackHitsPtr = NULL;
105 //__________________________________________________________________________
106 AliMUONTrack::AliMUONTrack (const AliMUONTrack& MUONTrack):TObject(MUONTrack)
108 fEventReconstructor = new AliMUONEventReconstructor(*MUONTrack.fEventReconstructor);
109 fTrackParamAtVertex = MUONTrack.fTrackParamAtVertex;
110 fTrackHitsPtr = new TObjArray(*MUONTrack.fTrackHitsPtr);
111 fNTrackHits = MUONTrack.fNTrackHits;
112 fFitMCS = MUONTrack.fFitMCS;
113 fFitNParam = MUONTrack.fFitNParam;
114 fFitFMin = MUONTrack.fFitFMin;
115 fFitStart = MUONTrack.fFitStart;
118 //__________________________________________________________________________
119 AliMUONTrack & AliMUONTrack::operator=(const AliMUONTrack& MUONTrack)
121 if (this == &MUONTrack)
124 fEventReconstructor = new AliMUONEventReconstructor(*MUONTrack.fEventReconstructor);
125 fTrackParamAtVertex = MUONTrack.fTrackParamAtVertex;
126 fTrackHitsPtr = new TObjArray(*MUONTrack.fTrackHitsPtr);
127 fNTrackHits = MUONTrack.fNTrackHits;
128 fFitMCS = MUONTrack.fFitMCS;
129 fFitNParam = MUONTrack.fFitNParam;
130 fFitFMin = MUONTrack.fFitFMin;
131 fFitStart = MUONTrack.fFitStart;
135 //__________________________________________________________________________
136 void AliMUONTrack::Remove()
138 // Remove current track from array of tracks,
139 // and corresponding track hits from array of track hits.
140 // Compress the TClonesArray it belongs to.
141 AliMUONTrackHit *nextTrackHit;
142 AliMUONEventReconstructor *eventRec = this->fEventReconstructor;
143 TClonesArray *trackHitsPtr = eventRec->GetRecTrackHitsPtr();
144 // Loop over all track hits of track
145 AliMUONTrackHit *trackHit = (AliMUONTrackHit*) fTrackHitsPtr->First();
147 nextTrackHit = (AliMUONTrackHit*) fTrackHitsPtr->After(trackHit);
148 // Remove TrackHit from event TClonesArray.
149 // Destructor is called,
150 // hence links between HitForRec's and TrackHit's are updated
151 trackHitsPtr->Remove(trackHit);
152 trackHit = nextTrackHit;
154 // Remove the track from event TClonesArray
155 // Destructor is called,
156 // hence space for TObjArray of pointers to TrackHit's is freed
157 eventRec->GetRecTracksPtr()->Remove(this);
158 // Number of tracks decreased by 1
159 eventRec->SetNRecTracks(eventRec->GetNRecTracks() - 1);
160 // Compress event TClonesArray of Track's:
161 // this is essential to retrieve the TClonesArray afterwards
162 eventRec->GetRecTracksPtr()->Compress();
163 // Compress event TClonesArray of TrackHit's:
164 // this is probably also essential to retrieve the TClonesArray afterwards
165 trackHitsPtr->Compress();
168 //__________________________________________________________________________
169 void AliMUONTrack::SetFitMCS(Int_t FitMCS)
171 // Set multiple Coulomb scattering option for track fit "fFitMCS"
172 // from "FitMCS" argument: 0 without, 1 with
173 if ((FitMCS == 0) || (FitMCS == 1)) fFitMCS = FitMCS;
174 // better implementation with enum(with, without) ????
176 cout << "ERROR in AliMUONTrack::SetFitMCS(FitMCS)" << endl;
177 cout << "FitMCS = " << FitMCS << " is neither 0 nor 1" << endl;
183 //__________________________________________________________________________
184 void AliMUONTrack::SetFitNParam(Int_t FitNParam)
186 // Set number of parameters for track fit "fFitNParam" from "FitNParam":
187 // 3 for momentum, 5 for momentum and position
188 if ((FitNParam == 3) || (FitNParam == 5)) fFitNParam = FitNParam;
190 cout << "ERROR in AliMUONTrack::SetFitNParam(FitNParam)" << endl;
191 cout << "FitNParam = " << FitNParam << " is neither 3 nor 5" << endl;
197 //__________________________________________________________________________
198 void AliMUONTrack::SetFitStart(Int_t FitStart)
200 // Set multiple Coulomb scattering option for track fit "fFitStart"
201 // from "FitStart" argument: 0 without, 1 with
202 if ((FitStart == 0) || (FitStart == 1)) fFitStart = FitStart;
203 // better implementation with enum(vertex, firstHit) ????
205 cout << "ERROR in AliMUONTrack::SetFitStart(FitStart)" << endl;
206 cout << "FitStart = " << FitStart << " is neither 0 nor 1" << endl;
212 //__________________________________________________________________________
213 AliMUONTrackParam* AliMUONTrack::GetTrackParamAtFirstHit(void) const {
214 // Get pointer to TrackParamAtFirstHit
215 return ((AliMUONTrackHit*) (fTrackHitsPtr->First()))->GetTrackParam();}
217 //__________________________________________________________________________
218 void AliMUONTrack::RecursiveDump(void) const
220 // Recursive dump of AliMUONTrack, i.e. with dump of TrackHit's and HitForRec's
221 AliMUONTrackHit *trackHit;
222 AliMUONHitForRec *hitForRec;
223 cout << "Recursive dump of Track: " << this << endl;
226 for (Int_t trackHitIndex = 0; trackHitIndex < fNTrackHits; trackHitIndex++) {
227 trackHit = (AliMUONTrackHit*) ((*fTrackHitsPtr)[trackHitIndex]);
229 cout << "TrackHit: " << trackHit << " (index: " << trackHitIndex << ")" << endl;
231 hitForRec = trackHit->GetHitForRecPtr();
233 cout << "HitForRec: " << hitForRec << endl;
239 //__________________________________________________________________________
240 Int_t AliMUONTrack::HitsInCommon(AliMUONTrack* Track)
242 // Returns the number of hits in common
243 // between the current track ("this")
244 // and the track pointed to by "Track".
245 Int_t hitsInCommon = 0;
246 AliMUONTrackHit *trackHit1, *trackHit2;
247 // Loop over hits of first track
248 trackHit1 = (AliMUONTrackHit*) this->GetTrackHitsPtr()->First();
250 // Loop over hits of second track
251 trackHit2 = (AliMUONTrackHit*) Track->GetTrackHitsPtr()->First();
253 // Increment "hitsInCommon" if both TrackHits point to the same HitForRec
254 if ( (trackHit1->GetHitForRecPtr()) ==
255 (trackHit2->GetHitForRecPtr()) ) hitsInCommon++;
256 trackHit2 = (AliMUONTrackHit*) Track->GetTrackHitsPtr()->After(trackHit2);
258 trackHit1 = (AliMUONTrackHit*) this->GetTrackHitsPtr()->After(trackHit1);
263 //__________________________________________________________________________
264 void AliMUONTrack::Fit()
266 // Fit the current track ("this"),
267 // with or without multiple Coulomb scattering according to "fFitMCS",
268 // with the number of parameters given by "fFitNParam"
269 // (3 if one keeps X and Y fixed in "TrackParam", 5 if one lets them vary),
270 // starting, according to "fFitStart",
271 // with track parameters at vertex or at the first TrackHit.
272 // "fFitMCS", "fFitNParam" and "fFitStart" have to be set before
273 // by calling the corresponding Set methods.
274 Double_t arg[1], benC, errorParam, invBenP, lower, nonBenC, upper, x, y;
276 AliMUONTrackParam *trackParam;
277 // Check if Minuit is initialized...
278 fgFitter = TVirtualFitter::Fitter(this); // add 3 or 5 for the maximum number of parameters ???
279 fgFitter->Clear(); // necessary ???? probably yes
280 // how to reset the printout number at every fit ????
281 // is there any risk to leave it like that ????
282 // how to go faster ???? choice of Minuit parameters like EDM ????
283 // choice of function to be minimized according to fFitMCS
284 if (fFitMCS == 0) fgFitter->SetFCN(TrackChi2);
285 else fgFitter->SetFCN(TrackChi2MCS);
286 // Switch off printout
288 fgFitter->ExecuteCommand("SET PRINT", arg, 1); // More printing !!!!
290 fgFitter->ExecuteCommand("SET NOW", arg, 0);
291 // Parameters according to "fFitStart"
292 // (should be a function to be used at every place where needed ????)
293 if (fFitStart == 0) trackParam = &fTrackParamAtVertex;
294 else trackParam = this->GetTrackParamAtFirstHit();
295 // set first 3 Minuit parameters
296 // could be tried with no limits for the search (min=max=0) ????
297 fgFitter->SetParameter(0, "InvBenP",
298 trackParam->GetInverseBendingMomentum(),
300 fgFitter->SetParameter(1, "BenS",
301 trackParam->GetBendingSlope(),
303 fgFitter->SetParameter(2, "NonBenS",
304 trackParam->GetNonBendingSlope(),
306 if (fFitNParam == 5) {
307 // set last 2 Minuit parameters
308 // mandatory limits in Bending to avoid NaN values of parameters
309 fgFitter->SetParameter(3, "X",
310 trackParam->GetNonBendingCoor(),
311 0.03, -500.0, 500.0);
312 // mandatory limits in non Bending to avoid NaN values of parameters
313 fgFitter->SetParameter(4, "Y",
314 trackParam->GetBendingCoor(),
315 0.10, -500.0, 500.0);
317 // search without gradient calculation in the function
318 fgFitter->ExecuteCommand("SET NOGRADIENT", arg, 0);
320 fgFitter->ExecuteCommand("MINIMIZE", arg, 0);
322 fgFitter->ExecuteCommand("EXIT", arg, 0); // necessary ????
323 // get results into "invBenP", "benC", "nonBenC" ("x", "y")
324 fgFitter->GetParameter(0, parName, invBenP, errorParam, lower, upper);
325 fgFitter->GetParameter(1, parName, benC, errorParam, lower, upper);
326 fgFitter->GetParameter(2, parName, nonBenC, errorParam, lower, upper);
327 if (fFitNParam == 5) {
328 fgFitter->GetParameter(3, parName, x, errorParam, lower, upper);
329 fgFitter->GetParameter(4, parName, y, errorParam, lower, upper);
331 // result of the fit into track parameters
332 trackParam->SetInverseBendingMomentum(invBenP);
333 trackParam->SetBendingSlope(benC);
334 trackParam->SetNonBendingSlope(nonBenC);
335 if (fFitNParam == 5) {
336 trackParam->SetNonBendingCoor(x);
337 trackParam->SetBendingCoor(y);
339 // global result of the fit
340 Double_t fedm, errdef;
342 fgFitter->GetStats(fFitFMin, fedm, errdef, npari, nparx);
345 //__________________________________________________________________________
346 void AliMUONTrack::AddSegment(AliMUONSegment* Segment)
348 // Add Segment to the track
349 AddHitForRec(Segment->GetHitForRec1()); // 1st hit
350 AddHitForRec(Segment->GetHitForRec2()); // 2nd hit
353 //__________________________________________________________________________
354 void AliMUONTrack::AddHitForRec(AliMUONHitForRec* HitForRec)
356 // Add HitForRec to the track:
357 // actual TrackHit into TClonesArray of TrackHit's for the event;
358 // pointer to actual TrackHit in TObjArray of pointers to TrackHit's for the track
359 TClonesArray *recTrackHitsPtr = this->fEventReconstructor->GetRecTrackHitsPtr();
360 Int_t eventTrackHits = this->fEventReconstructor->GetNRecTrackHits();
362 AliMUONTrackHit* trackHit =
363 new ((*recTrackHitsPtr)[eventTrackHits]) AliMUONTrackHit(HitForRec);
364 this->fEventReconstructor->SetNRecTrackHits(eventTrackHits + 1);
366 fTrackHitsPtr->Add(trackHit);
370 //__________________________________________________________________________
371 void AliMUONTrack::SetTrackParamAtHit(Int_t indexHit, AliMUONTrackParam *TrackParam) const
373 // Set track parameters at TrackHit with index "indexHit"
374 // from the track parameters pointed to by "TrackParam".
375 //PH AliMUONTrackHit* trackHit = (AliMUONTrackHit*) ((*fTrackHitsPtr)[indexHit]);
376 AliMUONTrackHit* trackHit = (AliMUONTrackHit*) (fTrackHitsPtr->At(indexHit));
377 trackHit->SetTrackParam(TrackParam);
380 //__________________________________________________________________________
381 void AliMUONTrack::SetTrackParamAtVertex()
383 // Set track parameters at vertex.
384 // TrackHit's are assumed to be only in stations(1..) 4 and 5,
385 // and sorted according to increasing Z..
386 // Parameters are calculated from information in HitForRec's
387 // of first and last TrackHit's.
388 AliMUONTrackParam *trackParam =
389 &fTrackParamAtVertex; // pointer to track parameters
390 // Pointer to HitForRec of first TrackHit
391 AliMUONHitForRec *firstHit =
392 ((AliMUONTrackHit*) (fTrackHitsPtr->First()))->GetHitForRecPtr();
393 // Pointer to HitForRec of last TrackHit
394 AliMUONHitForRec *lastHit =
395 ((AliMUONTrackHit*) (fTrackHitsPtr->Last()))->GetHitForRecPtr();
396 // Z difference between first and last hits
397 Double_t deltaZ = firstHit->GetZ() - lastHit->GetZ();
398 // bending slope in stations(1..) 4 and 5
399 Double_t bendingSlope =
400 (firstHit->GetBendingCoor() - lastHit->GetBendingCoor()) / deltaZ;
401 trackParam->SetBendingSlope(bendingSlope);
403 Double_t impactParam =
404 firstHit->GetBendingCoor() - bendingSlope * firstHit->GetZ(); // same if from firstHit and lastHit ????
405 // signed bending momentum
406 Double_t signedBendingMomentum =
407 fEventReconstructor->GetBendingMomentumFromImpactParam(impactParam);
408 trackParam->SetInverseBendingMomentum(1.0 / signedBendingMomentum);
409 // bending slope at vertex
411 SetBendingSlope(bendingSlope +
412 impactParam / fEventReconstructor->GetSimpleBPosition());
414 Double_t nonBendingSlope =
415 (firstHit->GetNonBendingCoor() - lastHit->GetNonBendingCoor()) / deltaZ;
416 trackParam->SetNonBendingSlope(nonBendingSlope);
417 // vertex coordinates at (0,0,0)
418 trackParam->SetZ(0.0);
419 trackParam->SetBendingCoor(0.0);
420 trackParam->SetNonBendingCoor(0.0);
423 //__________________________________________________________________________
424 void TrackChi2(Int_t &NParam, Double_t * /*Gradient*/, Double_t &Chi2, Double_t *Param, Int_t /*Flag*/)
426 // Return the "Chi2" to be minimized with Minuit for track fitting,
427 // with "NParam" parameters
428 // and their current values in array pointed to by "Param".
429 // Assumes that the track hits are sorted according to increasing Z.
430 // Track parameters at each TrackHit are updated accordingly.
431 // Multiple Coulomb scattering is not taken into account
432 AliMUONTrack *trackBeingFitted;
433 AliMUONTrackHit* hit;
434 AliMUONTrackParam param1;
437 Chi2 = 0.0; // initialize Chi2
438 // copy of track parameters to be fitted
439 trackBeingFitted = (AliMUONTrack*) AliMUONTrack::Fitter()->GetObjectFit();
440 if (trackBeingFitted->GetFitStart() == 0)
441 param1 = *(trackBeingFitted->GetTrackParamAtVertex());
442 else param1 = *(trackBeingFitted->GetTrackParamAtFirstHit());
443 // Minuit parameters to be fitted into this copy
444 param1.SetInverseBendingMomentum(Param[0]);
445 param1.SetBendingSlope(Param[1]);
446 param1.SetNonBendingSlope(Param[2]);
448 param1.SetNonBendingCoor(Param[3]);
449 param1.SetBendingCoor(Param[4]);
451 // Follow track through all planes of track hits
452 for (hitNumber = 0; hitNumber < trackBeingFitted->GetNTrackHits(); hitNumber++) {
453 hit = (AliMUONTrackHit*) (*(trackBeingFitted->GetTrackHitsPtr()))[hitNumber];
454 zHit = hit->GetHitForRecPtr()->GetZ();
455 // do something special if 2 hits with same Z ????
456 // security against infinite loop ????
457 (¶m1)->ExtrapToZ(zHit); // extrapolation
458 hit->SetTrackParam(¶m1);
460 // done hit per hit, with hit resolution,
461 // and not with point and angle like in "reco_muon.F" !!!!
462 // Needs to add multiple scattering contribution ????
464 hit->GetHitForRecPtr()->GetNonBendingCoor() - (¶m1)->GetNonBendingCoor();
466 hit->GetHitForRecPtr()->GetBendingCoor() - (¶m1)->GetBendingCoor();
469 dX * dX / hit->GetHitForRecPtr()->GetNonBendingReso2() +
470 dY * dY / hit->GetHitForRecPtr()->GetBendingReso2();
474 //__________________________________________________________________________
475 void TrackChi2MCS(Int_t &NParam, Double_t * /*Gradient*/, Double_t &Chi2, Double_t *Param, Int_t /*Flag*/)
477 // Return the "Chi2" to be minimized with Minuit for track fitting,
478 // with "NParam" parameters
479 // and their current values in array pointed to by "Param".
480 // Assumes that the track hits are sorted according to increasing Z.
481 // Track parameters at each TrackHit are updated accordingly.
482 // Multiple Coulomb scattering is taken into account with covariance matrix.
483 AliMUONTrack *trackBeingFitted;
484 AliMUONTrackParam param1;
485 Chi2 = 0.0; // initialize Chi2
486 // copy of track parameters to be fitted
487 trackBeingFitted = (AliMUONTrack*) AliMUONTrack::Fitter()->GetObjectFit();
488 if (trackBeingFitted->GetFitStart() == 0)
489 param1 = *(trackBeingFitted->GetTrackParamAtVertex());
490 else param1 = *(trackBeingFitted->GetTrackParamAtFirstHit());
491 // Minuit parameters to be fitted into this copy
492 param1.SetInverseBendingMomentum(Param[0]);
493 param1.SetBendingSlope(Param[1]);
494 param1.SetNonBendingSlope(Param[2]);
496 param1.SetNonBendingCoor(Param[3]);
497 param1.SetBendingCoor(Param[4]);
500 AliMUONTrackHit *hit;
501 Int_t chCurrent, chPrev = 0, hitNumber, hitNumber1, hitNumber2, hitNumber3;
502 Double_t z, z1, z2, z3;
503 AliMUONTrackHit *hit1, *hit2, *hit3;
504 Double_t hbc1, hbc2, pbc1, pbc2;
505 Double_t hnbc1, hnbc2, pnbc1, pnbc2;
506 Int_t numberOfHit = trackBeingFitted->GetNTrackHits();
507 TMatrixD *covBending = new TMatrixD(numberOfHit, numberOfHit);
508 TMatrixD *covNonBending = new TMatrixD(numberOfHit, numberOfHit);
509 Double_t *msa2 = new Double_t[numberOfHit];
511 // Predicted coordinates and multiple scattering angles are first calculated
512 for (hitNumber = 0; hitNumber < numberOfHit; hitNumber++) {
513 hit = (AliMUONTrackHit*) (*(trackBeingFitted->GetTrackHitsPtr()))[hitNumber];
514 z = hit->GetHitForRecPtr()->GetZ();
515 // do something special if 2 hits with same Z ????
516 // security against infinite loop ????
517 (¶m1)->ExtrapToZ(z); // extrapolation
518 hit->SetTrackParam(¶m1);
519 // square of multiple scattering angle at current hit, with one chamber
520 msa2[hitNumber] = MultipleScatteringAngle2(hit);
521 // correction for eventual missing hits or multiple hits in a chamber,
522 // according to the number of chambers
523 // between the current hit and the previous one
524 chCurrent = hit->GetHitForRecPtr()->GetChamberNumber();
525 if (hitNumber > 0) msa2[hitNumber] = msa2[hitNumber] * (chCurrent - chPrev);
529 // Calculates the covariance matrix
530 for (hitNumber1 = 0; hitNumber1 < numberOfHit; hitNumber1++) {
531 hit1 = (AliMUONTrackHit*) (*(trackBeingFitted->GetTrackHitsPtr()))[hitNumber1];
532 z1 = hit1->GetHitForRecPtr()->GetZ();
533 for (hitNumber2 = hitNumber1; hitNumber2 < numberOfHit; hitNumber2++) {
534 hit2 = (AliMUONTrackHit*) (*(trackBeingFitted->GetTrackHitsPtr()))[hitNumber2];
535 z2 = hit2->GetHitForRecPtr()->GetZ();
536 // initialization to 0 (diagonal plus upper triangular part)
537 (*covBending)(hitNumber2, hitNumber1) = 0.0;
538 // contribution from multiple scattering in bending plane:
539 // loop over upstream hits
540 for (hitNumber3 = 0; hitNumber3 < hitNumber1; hitNumber3++) {
541 hit3 = (AliMUONTrackHit*)
542 (*(trackBeingFitted->GetTrackHitsPtr()))[hitNumber3];
543 z3 = hit3->GetHitForRecPtr()->GetZ();
544 (*covBending)(hitNumber2, hitNumber1) =
545 (*covBending)(hitNumber2, hitNumber1) +
546 ((z1 - z3) * (z2 - z3) * msa2[hitNumber3]);
548 // equal contribution from multiple scattering in non bending plane
549 (*covNonBending)(hitNumber2, hitNumber1) =
550 (*covBending)(hitNumber2, hitNumber1);
551 if (hitNumber1 == hitNumber2) {
552 // Diagonal elements: add contribution from position measurements
554 (*covBending)(hitNumber2, hitNumber1) =
555 (*covBending)(hitNumber2, hitNumber1) +
556 hit1->GetHitForRecPtr()->GetBendingReso2();
557 // and in non bending plane
558 (*covNonBending)(hitNumber2, hitNumber1) =
559 (*covNonBending)(hitNumber2, hitNumber1) +
560 hit1->GetHitForRecPtr()->GetNonBendingReso2();
563 // Non diagonal elements: symmetrization
565 (*covBending)(hitNumber1, hitNumber2) =
566 (*covBending)(hitNumber2, hitNumber1);
567 // and non bending plane
568 (*covNonBending)(hitNumber1, hitNumber2) =
569 (*covNonBending)(hitNumber2, hitNumber1);
571 } // for (hitNumber2 = hitNumber1;...
572 } // for (hitNumber1 = 0;...
574 // Inversion of covariance matrices
575 // with "mnvertLocal", local "mnvert" function of Minuit.
576 // One cannot use directly "mnvert" since "TVirtualFitter" does not know it.
577 // One will have to replace this local function by the right inversion function
578 // from a specialized Root package for symmetric positive definite matrices,
579 // when available!!!!
581 mnvertLocal(&((*covBending)(0,0)), numberOfHit, numberOfHit, numberOfHit,
583 Int_t ifailNonBending;
584 mnvertLocal(&((*covNonBending)(0,0)), numberOfHit, numberOfHit, numberOfHit,
587 // It would be worth trying to calculate the inverse of the covariance matrix
588 // only once per fit, since it cannot change much in principle,
589 // and it would save a lot of computing time !!!!
592 if ((ifailBending == 0) && (ifailNonBending == 0)) {
593 // with Multiple Scattering if inversion correct
594 for (hitNumber1 = 0; hitNumber1 < numberOfHit ; hitNumber1++) {
595 hit1 = (AliMUONTrackHit*) (*(trackBeingFitted->GetTrackHitsPtr()))[hitNumber1];
596 hbc1 = hit1->GetHitForRecPtr()->GetBendingCoor();
597 pbc1 = hit1->GetTrackParam()->GetBendingCoor();
598 hnbc1 = hit1->GetHitForRecPtr()->GetNonBendingCoor();
599 pnbc1 = hit1->GetTrackParam()->GetNonBendingCoor();
600 for (hitNumber2 = 0; hitNumber2 < numberOfHit; hitNumber2++) {
601 hit2 = (AliMUONTrackHit*)
602 (*(trackBeingFitted->GetTrackHitsPtr()))[hitNumber2];
603 hbc2 = hit2->GetHitForRecPtr()->GetBendingCoor();
604 pbc2 = hit2->GetTrackParam()->GetBendingCoor();
605 hnbc2 = hit2->GetHitForRecPtr()->GetNonBendingCoor();
606 pnbc2 = hit2->GetTrackParam()->GetNonBendingCoor();
608 ((*covBending)(hitNumber2, hitNumber1) *
609 (hbc1 - pbc1) * (hbc2 - pbc2)) +
610 ((*covNonBending)(hitNumber2, hitNumber1) *
611 (hnbc1 - pnbc1) * (hnbc2 - pnbc2));
615 // without Multiple Scattering if inversion impossible
616 for (hitNumber1 = 0; hitNumber1 < numberOfHit ; hitNumber1++) {
617 hit1 = (AliMUONTrackHit*) (*(trackBeingFitted->GetTrackHitsPtr()))[hitNumber1];
618 hbc1 = hit1->GetHitForRecPtr()->GetBendingCoor();
619 pbc1 = hit1->GetTrackParam()->GetBendingCoor();
620 hnbc1 = hit1->GetHitForRecPtr()->GetNonBendingCoor();
621 pnbc1 = hit1->GetTrackParam()->GetNonBendingCoor();
623 ((hbc1 - pbc1) * (hbc1 - pbc1) /
624 hit1->GetHitForRecPtr()->GetBendingReso2()) +
625 ((hnbc1 - pnbc1) * (hnbc1 - pnbc1) /
626 hit1->GetHitForRecPtr()->GetNonBendingReso2());
631 delete covNonBending;
635 Double_t MultipleScatteringAngle2(AliMUONTrackHit *TrackHit)
637 // Returns square of multiple Coulomb scattering angle
638 // at TrackHit pointed to by "TrackHit"
639 Double_t slopeBending, slopeNonBending, radiationLength, inverseBendingMomentum2, inverseTotalMomentum2;
640 Double_t varMultipleScatteringAngle;
641 AliMUONTrack *trackBeingFitted = (AliMUONTrack*) AliMUONTrack::Fitter()->GetObjectFit();
642 AliMUONTrackParam *param = TrackHit->GetTrackParam();
643 // Better implementation in AliMUONTrack class ????
644 slopeBending = param->GetBendingSlope();
645 slopeNonBending = param->GetNonBendingSlope();
646 // thickness in radiation length for the current track,
647 // taking local angle into account
649 trackBeingFitted->GetEventReconstructor()->GetChamberThicknessInX0() *
651 slopeBending * slopeBending + slopeNonBending * slopeNonBending);
652 inverseBendingMomentum2 =
653 param->GetInverseBendingMomentum() * param->GetInverseBendingMomentum();
654 inverseTotalMomentum2 =
655 inverseBendingMomentum2 * (1.0 + slopeBending * slopeBending) /
656 (1.0 + slopeBending *slopeBending + slopeNonBending * slopeNonBending);
657 varMultipleScatteringAngle = 0.0136 * (1.0 + 0.038 * TMath::Log(radiationLength));
658 // The velocity is assumed to be 1 !!!!
659 varMultipleScatteringAngle = inverseTotalMomentum2 * radiationLength *
660 varMultipleScatteringAngle * varMultipleScatteringAngle;
661 return varMultipleScatteringAngle;
664 //______________________________________________________________________________
665 void mnvertLocal(Double_t *a, Int_t l, Int_t, Int_t n, Int_t &ifail)
667 //*-*-*-*-*-*-*-*-*-*-*-*Inverts a symmetric matrix*-*-*-*-*-*-*-*-*-*-*-*-*
668 //*-* ==========================
669 //*-* inverts a symmetric matrix. matrix is first scaled to
670 //*-* have all ones on the diagonal (equivalent to change of units)
671 //*-* but no pivoting is done since matrix is positive-definite.
672 //*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
674 // taken from TMinuit package of Root (l>=n)
675 // fVERTs, fVERTq and fVERTpp changed to localVERTs, localVERTq and localVERTpp
676 // Double_t localVERTs[n], localVERTq[n], localVERTpp[n];
677 Double_t * localVERTs = new Double_t[n];
678 Double_t * localVERTq = new Double_t[n];
679 Double_t * localVERTpp = new Double_t[n];
680 // fMaxint changed to localMaxint
681 Int_t localMaxint = n;
683 /* System generated locals */
686 /* Local variables */
688 Int_t i, j, k, kp1, km1;
690 /* Parameter adjustments */
696 if (n < 1) goto L100;
697 if (n > localMaxint) goto L100;
698 //*-*- scale matrix by sqrt of diag elements
699 for (i = 1; i <= n; ++i) {
701 if (si <= 0) goto L100;
702 localVERTs[i-1] = 1 / TMath::Sqrt(si);
704 for (i = 1; i <= n; ++i) {
705 for (j = 1; j <= n; ++j) {
706 a[i + j*l] = a[i + j*l]*localVERTs[i-1]*localVERTs[j-1];
709 //*-*- . . . start main loop . . . .
710 for (i = 1; i <= n; ++i) {
712 //*-*- preparation for elimination step1
713 if (a[k + k*l] != 0) localVERTq[k-1] = 1 / a[k + k*l];
715 localVERTpp[k-1] = 1;
719 if (km1 < 0) goto L100;
720 else if (km1 == 0) goto L50;
723 for (j = 1; j <= km1; ++j) {
724 localVERTpp[j-1] = a[j + k*l];
725 localVERTq[j-1] = a[j + k*l]*localVERTq[k-1];
729 if (k - n < 0) goto L51;
730 else if (k - n == 0) goto L60;
733 for (j = kp1; j <= n; ++j) {
734 localVERTpp[j-1] = a[k + j*l];
735 localVERTq[j-1] = -a[k + j*l]*localVERTq[k-1];
738 //*-*- elimination proper
740 for (j = 1; j <= n; ++j) {
741 for (k = j; k <= n; ++k) { a[j + k*l] += localVERTpp[j-1]*localVERTq[k-1]; }
744 //*-*- elements of left diagonal and unscaling
745 for (j = 1; j <= n; ++j) {
746 for (k = 1; k <= j; ++k) {
747 a[k + j*l] = a[k + j*l]*localVERTs[k-1]*localVERTs[j-1];
748 a[j + k*l] = a[k + j*l];
755 //*-*- failure return