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 // The TRD offline tracklet
22 // The running horse of the TRD reconstruction. The following tasks are preformed:
23 // 1. Clusters attachment to tracks based on prior information stored at tracklet level (see AttachClusters)
24 // 2. Clusters position recalculation based on track information (see GetClusterXY and Fit)
25 // 3. Cluster error parametrization recalculation (see Fit)
26 // 4. Linear track approximation (Fit)
27 // 5. Optimal position (including z estimate for pad row cross tracklets) and covariance matrix of the track fit inside one TRD chamber (Fit)
28 // 6. Tilt pad correction and systematic effects (GetCovAt)
29 // 7. dEdx calculation (CookdEdx)
30 // 8. PID probabilities estimation (CookPID)
33 // Alex Bercuci <A.Bercuci@gsi.de> //
34 // Markus Fasel <M.Fasel@gsi.de> //
36 ////////////////////////////////////////////////////////////////////////////
39 #include <TTreeStream.h>
42 #include "AliMathBase.h"
43 #include "AliCDBManager.h"
44 #include "AliTracker.h"
46 #include "AliTRDpadPlane.h"
47 #include "AliTRDcluster.h"
48 #include "AliTRDseedV1.h"
49 #include "AliTRDtrackV1.h"
50 #include "AliTRDcalibDB.h"
51 #include "AliTRDchamberTimeBin.h"
52 #include "AliTRDtrackingChamber.h"
53 #include "AliTRDtrackerV1.h"
54 #include "AliTRDrecoParam.h"
55 #include "AliTRDCommonParam.h"
57 #include "Cal/AliTRDCalPID.h"
58 #include "Cal/AliTRDCalROC.h"
59 #include "Cal/AliTRDCalDet.h"
61 ClassImp(AliTRDseedV1)
63 //____________________________________________________________________
64 AliTRDseedV1::AliTRDseedV1(Int_t det)
66 ,fkReconstructor(NULL)
91 memset(fIndexes,0xFF,kNclusters*sizeof(fIndexes[0]));
92 memset(fClusters, 0, kNclusters*sizeof(AliTRDcluster*));
93 memset(fPad, 0, 3*sizeof(Float_t));
94 fYref[0] = 0.; fYref[1] = 0.;
95 fZref[0] = 0.; fZref[1] = 0.;
96 fYfit[0] = 0.; fYfit[1] = 0.;
97 fZfit[0] = 0.; fZfit[1] = 0.;
98 memset(fdEdx, 0, kNslices*sizeof(Float_t));
99 for(int ispec=0; ispec<AliPID::kSPECIES; ispec++) fProb[ispec] = -1.;
100 fLabels[0]=-1; fLabels[1]=-1; // most freq MC labels
101 fLabels[2]=0; // number of different labels for tracklet
102 memset(fRefCov, 0, 7*sizeof(Double_t));
103 // stand alone curvature
104 fC[0] = 0.; fC[1] = 0.;
105 // covariance matrix [diagonal]
106 // default sy = 200um and sz = 2.3 cm
107 fCov[0] = 4.e-4; fCov[1] = 0.; fCov[2] = 5.3;
108 SetStandAlone(kFALSE);
111 //____________________________________________________________________
112 AliTRDseedV1::AliTRDseedV1(const AliTRDseedV1 &ref)
113 :AliTRDtrackletBase((AliTRDtrackletBase&)ref)
114 ,fkReconstructor(NULL)
137 // Copy Constructor performing a deep copy
142 SetBit(kOwner, kFALSE);
143 SetStandAlone(ref.IsStandAlone());
147 //____________________________________________________________________
148 AliTRDseedV1& AliTRDseedV1::operator=(const AliTRDseedV1 &ref)
151 // Assignment Operator using the copy function
157 SetBit(kOwner, kFALSE);
162 //____________________________________________________________________
163 AliTRDseedV1::~AliTRDseedV1()
166 // Destructor. The RecoParam object belongs to the underlying tracker.
169 //printf("I-AliTRDseedV1::~AliTRDseedV1() : Owner[%s]\n", IsOwner()?"YES":"NO");
172 for(int itb=0; itb<kNclusters; itb++){
173 if(!fClusters[itb]) continue;
174 //AliInfo(Form("deleting c %p @ %d", fClusters[itb], itb));
175 delete fClusters[itb];
176 fClusters[itb] = NULL;
181 //____________________________________________________________________
182 void AliTRDseedV1::Copy(TObject &ref) const
189 AliTRDseedV1 &target = (AliTRDseedV1 &)ref;
191 target.fkReconstructor = fkReconstructor;
192 target.fClusterIter = NULL;
196 target.fS2PRF = fS2PRF;
197 target.fDiffL = fDiffL;
198 target.fDiffT = fDiffT;
199 target.fClusterIdx = 0;
200 target.fErrorMsg = fErrorMsg;
211 target.fChi2 = fChi2;
213 memcpy(target.fIndexes, fIndexes, kNclusters*sizeof(Int_t));
214 memcpy(target.fClusters, fClusters, kNclusters*sizeof(AliTRDcluster*));
215 memcpy(target.fPad, fPad, 3*sizeof(Float_t));
216 target.fYref[0] = fYref[0]; target.fYref[1] = fYref[1];
217 target.fZref[0] = fZref[0]; target.fZref[1] = fZref[1];
218 target.fYfit[0] = fYfit[0]; target.fYfit[1] = fYfit[1];
219 target.fZfit[0] = fZfit[0]; target.fZfit[1] = fZfit[1];
220 memcpy(target.fdEdx, fdEdx, kNslices*sizeof(Float_t));
221 memcpy(target.fProb, fProb, AliPID::kSPECIES*sizeof(Float_t));
222 memcpy(target.fLabels, fLabels, 3*sizeof(Int_t));
223 memcpy(target.fRefCov, fRefCov, 7*sizeof(Double_t));
224 target.fC[0] = fC[0]; target.fC[1] = fC[1];
225 memcpy(target.fCov, fCov, 3*sizeof(Double_t));
231 //____________________________________________________________
232 Bool_t AliTRDseedV1::Init(AliTRDtrackV1 *track)
234 // Initialize this tracklet using the track information
237 // track - the TRD track used to initialize the tracklet
239 // Detailed description
240 // The function sets the starting point and direction of the
241 // tracklet according to the information from the TRD track.
244 // The TRD track has to be propagated to the beginning of the
245 // chamber where the tracklet will be constructed
249 if(!track->GetProlongation(fX0, y, z)) return kFALSE;
255 //_____________________________________________________________________________
256 void AliTRDseedV1::Reset(Option_t *opt)
259 // Reset seed. If option opt="c" is given only cluster arrays are cleared.
261 for(Int_t ic=kNclusters; ic--;) fIndexes[ic] = -1;
262 memset(fClusters, 0, kNclusters*sizeof(AliTRDcluster*));
263 fN=0; SetBit(kRowCross, kFALSE);
264 if(strcmp(opt, "c")==0) return;
266 fExB=0.;fVD=0.;fT0=0.;fS2PRF=0.;
272 fdX=0.;fX0=0.; fX=0.; fY=0.; fZ=0.;
277 memset(fPad, 0, 3*sizeof(Float_t));
278 fYref[0] = 0.; fYref[1] = 0.;
279 fZref[0] = 0.; fZref[1] = 0.;
280 fYfit[0] = 0.; fYfit[1] = 0.;
281 fZfit[0] = 0.; fZfit[1] = 0.;
282 memset(fdEdx, 0, kNslices*sizeof(Float_t));
283 for(int ispec=0; ispec<AliPID::kSPECIES; ispec++) fProb[ispec] = -1.;
284 fLabels[0]=-1; fLabels[1]=-1; // most freq MC labels
285 fLabels[2]=0; // number of different labels for tracklet
286 memset(fRefCov, 0, 7*sizeof(Double_t));
287 // covariance matrix [diagonal]
288 // default sy = 200um and sz = 2.3 cm
289 fCov[0] = 4.e-4; fCov[1] = 0.; fCov[2] = 5.3;
292 //____________________________________________________________________
293 void AliTRDseedV1::Update(const AliTRDtrackV1 *trk)
295 // update tracklet reference position from the TRD track
297 Double_t fSnp = trk->GetSnp();
298 Double_t fTgl = trk->GetTgl();
300 Double_t norm =1./TMath::Sqrt((1.-fSnp)*(1.+fSnp));
301 fYref[1] = fSnp*norm;
302 fZref[1] = fTgl*norm;
303 SetCovRef(trk->GetCovariance());
305 Double_t dx = trk->GetX() - fX0;
306 fYref[0] = trk->GetY() - dx*fYref[1];
307 fZref[0] = trk->GetZ() - dx*fZref[1];
310 //_____________________________________________________________________________
311 void AliTRDseedV1::UpdateUsed()
314 // Calculate number of used clusers in the tracklet
317 Int_t nused = 0, nshared = 0;
318 for (Int_t i = kNclusters; i--; ) {
319 if (!fClusters[i]) continue;
320 if(fClusters[i]->IsUsed()){
322 } else if(fClusters[i]->IsShared()){
323 if(IsStandAlone()) nused++;
331 //_____________________________________________________________________________
332 void AliTRDseedV1::UseClusters()
337 // In stand alone mode:
338 // Clusters which are marked as used or shared from another track are
339 // removed from the tracklet
342 // - Clusters which are used by another track become shared
343 // - Clusters which are attached to a kink track become shared
345 AliTRDcluster **c = &fClusters[0];
346 for (Int_t ic=kNclusters; ic--; c++) {
349 if((*c)->IsShared() || (*c)->IsUsed()){
350 if((*c)->IsShared()) SetNShared(GetNShared()-1);
351 else SetNUsed(GetNUsed()-1);
358 if((*c)->IsUsed() || IsKink()){
369 //____________________________________________________________________
370 void AliTRDseedV1::CookdEdx(Int_t nslices)
372 // Calculates average dE/dx for all slices and store them in the internal array fdEdx.
375 // nslices : number of slices for which dE/dx should be calculated
377 // store results in the internal array fdEdx. This can be accessed with the method
378 // AliTRDseedV1::GetdEdx()
380 // Detailed description
381 // Calculates average dE/dx for all slices. Depending on the PID methode
382 // the number of slices can be 3 (LQ) or 8(NN).
383 // The calculation of dQ/dl are done using the tracklet fit results (see AliTRDseedV1::GetdQdl(Int_t))
385 // The following effects are included in the calculation:
386 // 1. calibration values for t0 and vdrift (using x coordinate to calculate slice)
387 // 2. cluster sharing (optional see AliTRDrecoParam::SetClusterSharing())
391 memset(fdEdx, 0, kNslices*sizeof(Float_t));
392 const Double_t kDriftLength = (.5 * AliTRDgeometry::AmThick() + AliTRDgeometry::DrThick());
394 AliTRDcluster *c(NULL);
395 for(int ic=0; ic<AliTRDtrackerV1::GetNTimeBins(); ic++){
396 if(!(c = fClusters[ic]) && !(c = fClusters[ic+kNtb])) continue;
397 Float_t dx = TMath::Abs(fX0 - c->GetX());
399 // Filter clusters for dE/dx calculation
401 // 1.consider calibration effects for slice determination
403 if(dx<kDriftLength){ // TODO should be replaced by c->IsInChamber()
404 slice = Int_t(dx * nslices / kDriftLength);
405 } else slice = c->GetX() < fX0 ? nslices-1 : 0;
408 // 2. take sharing into account
409 Float_t w = /*c->IsShared() ? .5 :*/ 1.;
411 // 3. take into account large clusters TODO
412 //w *= c->GetNPads() > 3 ? .8 : 1.;
415 fdEdx[slice] += w * GetdQdl(ic); //fdQdl[ic];
416 } // End of loop over clusters
419 //_____________________________________________________________________________
420 void AliTRDseedV1::CookLabels()
423 // Cook 2 labels for seed
429 for (Int_t i = 0; i < kNclusters; i++) {
430 if (!fClusters[i]) continue;
431 for (Int_t ilab = 0; ilab < 3; ilab++) {
432 if (fClusters[i]->GetLabel(ilab) >= 0) {
433 labels[nlab] = fClusters[i]->GetLabel(ilab);
439 fLabels[2] = AliMathBase::Freq(nlab,labels,out,kTRUE);
441 if ((fLabels[2] > 1) && (out[3] > 1)) fLabels[1] = out[2];
445 //____________________________________________________________________
446 Float_t AliTRDseedV1::GetdQdl(Int_t ic, Float_t *dl) const
448 // Using the linear approximation of the track inside one TRD chamber (TRD tracklet)
449 // the charge per unit length can be written as:
451 // #frac{dq}{dl} = #frac{q_{c}}{dx * #sqrt{1 + #(){#frac{dy}{dx}}^{2}_{fit} + #(){#frac{dz}{dx}}^{2}_{ref}}}
453 // where qc is the total charge collected in the current time bin and dx is the length
455 // The following correction are applied :
456 // - charge : pad row cross corrections
457 // [diffusion and TRF assymetry] TODO
458 // - dx : anisochronity, track inclination - see Fit and AliTRDcluster::GetXloc()
459 // and AliTRDcluster::GetYloc() for the effects taken into account
462 //<img src="TRD/trackletDQDT.gif">
464 // In the picture the energy loss measured on the tracklet as a function of drift time [left] and respectively
465 // drift length [right] for different particle species is displayed.
466 // Author : Alex Bercuci <A.Bercuci@gsi.de>
469 // check whether both clusters are inside the chamber
470 Bool_t hasClusterInChamber = kFALSE;
471 if(fClusters[ic] && fClusters[ic]->IsInChamber()){
472 hasClusterInChamber = kTRUE;
473 dq += TMath::Abs(fClusters[ic]->GetQ());
474 }else if(fClusters[ic+kNtb] && fClusters[ic+kNtb]->IsInChamber()){
475 hasClusterInChamber = kTRUE;
476 dq += TMath::Abs(fClusters[ic+kNtb]->GetQ());
478 if(!hasClusterInChamber) return 0.;
479 if(dq<1.e-3) return 0.;
482 if(ic-1>=0 && ic+1<kNtb){
483 Float_t x2(0.), x1(0.);
484 // try to estimate upper radial position (find the cluster which is inside the chamber)
485 if(fClusters[ic-1] && fClusters[ic-1]->IsInChamber()) x2 = fClusters[ic-1]->GetX();
486 else if(fClusters[ic-1+kNtb] && fClusters[ic-1+kNtb]->IsInChamber()) x2 = fClusters[ic-1+kNtb]->GetX();
487 else if(fClusters[ic] && fClusters[ic]->IsInChamber()) x2 = fClusters[ic]->GetX()+fdX;
488 else x2 = fClusters[ic+kNtb]->GetX()+fdX;
489 // try to estimate lower radial position (find the cluster which is inside the chamber)
490 if(fClusters[ic+1] && fClusters[ic+1]->IsInChamber()) x1 = fClusters[ic+1]->GetX();
491 else if(fClusters[ic+1+kNtb] && fClusters[ic+1+kNtb]->IsInChamber()) x1 = fClusters[ic+1+kNtb]->GetX();
492 else if(fClusters[ic] && fClusters[ic]->IsInChamber()) x1 = fClusters[ic]->GetX()-fdX;
493 else x1 = fClusters[ic+kNtb]->GetX()-fdX;
497 dx *= TMath::Sqrt(1. + fYfit[1]*fYfit[1] + fZref[1]*fZref[1]);
499 if(dx>1.e-9) return dq/dx;
503 //____________________________________________________________
504 Float_t AliTRDseedV1::GetMomentum(Float_t *err) const
506 // Returns momentum of the track after update with the current tracklet as:
508 // p=#frac{1}{1/p_{t}} #sqrt{1+tgl^{2}}
510 // and optionally the momentum error (if err is not null).
511 // The estimated variance of the momentum is given by:
513 // #sigma_{p}^{2} = (#frac{dp}{dp_{t}})^{2} #sigma_{p_{t}}^{2}+(#frac{dp}{dtgl})^{2} #sigma_{tgl}^{2}+2#frac{dp}{dp_{t}}#frac{dp}{dtgl} cov(tgl,1/p_{t})
515 // which can be simplified to
517 // #sigma_{p}^{2} = p^{2}p_{t}^{4}tgl^{2}#sigma_{tgl}^{2}-2p^{2}p_{t}^{3}tgl cov(tgl,1/p_{t})+p^{2}p_{t}^{2}#sigma_{1/p_{t}}^{2}
521 Double_t p = fPt*TMath::Sqrt(1.+fZref[1]*fZref[1]);
523 Double_t tgl2 = fZref[1]*fZref[1];
524 Double_t pt2 = fPt*fPt;
527 p2*tgl2*pt2*pt2*fRefCov[4]
528 -2.*p2*fZref[1]*fPt*pt2*fRefCov[5]
530 (*err) = TMath::Sqrt(s2);
535 //____________________________________________________________________
536 Float_t AliTRDseedV1::GetOccupancyTB() const
538 // Returns procentage of TB occupied by clusters
541 AliTRDcluster *c(NULL);
542 for(int ic=0; ic<AliTRDtrackerV1::GetNTimeBins(); ic++){
543 if(!(c = fClusters[ic]) && !(c = fClusters[ic+kNtb])) continue;
547 return Float_t(n)/AliTRDtrackerV1::GetNTimeBins();
550 //____________________________________________________________________
551 Float_t* AliTRDseedV1::GetProbability(Bool_t force)
553 if(!force) return &fProb[0];
554 if(!CookPID()) return NULL;
558 //____________________________________________________________
559 Bool_t AliTRDseedV1::CookPID()
561 // Fill probability array for tracklet from the DB.
566 // returns pointer to the probability array and NULL if missing DB access
568 // Retrieve PID probabilities for e+-, mu+-, K+-, pi+- and p+- from the DB according to tracklet information:
569 // - estimated momentum at tracklet reference point
570 // - dE/dx measurements
573 // According to the steering settings specified in the reconstruction one of the following methods are used
574 // - Neural Network [default] - option "nn"
575 // - 2D Likelihood - option "!nn"
577 AliTRDcalibDB *calibration = AliTRDcalibDB::Instance();
579 AliError("No access to calibration data");
583 if (!fkReconstructor) {
584 AliError("Reconstructor not set.");
588 // Retrieve the CDB container class with the parametric detector response
589 const AliTRDCalPID *pd = calibration->GetPIDObject(fkReconstructor->GetPIDMethod());
591 AliError("No access to AliTRDCalPID object");
595 // calculate tracklet length TO DO
596 Float_t length = (AliTRDgeometry::AmThick() + AliTRDgeometry::DrThick())/ TMath::Sqrt((1.0 - GetSnp()*GetSnp()) / (1.0 + GetTgl()*GetTgl()));
599 CookdEdx(AliTRDCalPID::kNSlicesNN);
600 AliDebug(4, Form("p=%6.4f[GeV/c] dEdx{%7.2f %7.2f %7.2f %7.2f %7.2f %7.2f %7.2f %7.2f} l=%4.2f[cm]", GetMomentum(), fdEdx[0], fdEdx[1], fdEdx[2], fdEdx[3], fdEdx[4], fdEdx[5], fdEdx[6], fdEdx[7], length));
602 // Sets the a priori probabilities
603 Bool_t kPIDNN(fkReconstructor->GetPIDMethod()==AliTRDpidUtil::kNN);
604 for(int ispec=0; ispec<AliPID::kSPECIES; ispec++)
605 fProb[ispec] = pd->GetProbability(ispec, GetMomentum(), &fdEdx[0], length, kPIDNN?GetPlane():fkReconstructor->GetRecoParam()->GetPIDLQslices());
610 //____________________________________________________________________
611 Float_t AliTRDseedV1::GetQuality(Bool_t kZcorr) const
614 // Returns a quality measurement of the current seed
617 Float_t zcorr = kZcorr ? GetTilt() * (fZfit[0] - fZref[0]) : 0.;
619 .5 * TMath::Abs(18.0 - GetN())
620 + 10.* TMath::Abs(fYfit[1] - fYref[1])
621 + 5. * TMath::Abs(fYfit[0] - fYref[0] + zcorr)
622 + 2. * TMath::Abs(fZfit[0] - fZref[0]) / GetPadLength();
625 //____________________________________________________________________
626 void AliTRDseedV1::GetCovAt(Double_t x, Double_t *cov) const
628 // Computes covariance in the y-z plane at radial point x (in tracking coordinates)
629 // and returns the results in the preallocated array cov[3] as :
636 // For the linear transformation
640 // The error propagation has the general form
642 // C_{Y} = T_{x} C_{X} T_{x}^{T}
644 // We apply this formula 2 times. First to calculate the covariance of the tracklet
645 // at point x we consider:
647 // T_{x} = (1 x); X=(y0 dy/dx); C_{X}=#(){#splitline{Var(y0) Cov(y0, dy/dx)}{Cov(y0, dy/dx) Var(dy/dx)}}
649 // and secondly to take into account the tilt angle
651 // T_{#alpha} = #(){#splitline{cos(#alpha) __ sin(#alpha)}{-sin(#alpha) __ cos(#alpha)}}; X=(y z); C_{X}=#(){#splitline{Var(y) 0}{0 Var(z)}}
654 // using simple trigonometrics one can write for this last case
656 // C_{Y}=#frac{1}{1+tg^{2}#alpha} #(){#splitline{(#sigma_{y}^{2}+tg^{2}#alpha#sigma_{z}^{2}) __ tg#alpha(#sigma_{z}^{2}-#sigma_{y}^{2})}{tg#alpha(#sigma_{z}^{2}-#sigma_{y}^{2}) __ (#sigma_{z}^{2}+tg^{2}#alpha#sigma_{y}^{2})}}
658 // which can be aproximated for small alphas (2 deg) with
660 // C_{Y}=#(){#splitline{#sigma_{y}^{2} __ (#sigma_{z}^{2}-#sigma_{y}^{2})tg#alpha}{((#sigma_{z}^{2}-#sigma_{y}^{2})tg#alpha __ #sigma_{z}^{2}}}
663 // before applying the tilt rotation we also apply systematic uncertainties to the tracklet
664 // position which can be tunned from outside via the AliTRDrecoParam::SetSysCovMatrix(). They might
665 // account for extra misalignment/miscalibration uncertainties.
668 // Alex Bercuci <A.Bercuci@gsi.de>
669 // Date : Jan 8th 2009
674 Double_t sy2 = fCov[0] +2.*xr*fCov[1] + xr*xr*fCov[2];
676 //GetPadLength()*GetPadLength()/12.;
678 // insert systematic uncertainties
680 Double_t sys[15]; memset(sys, 0, 15*sizeof(Double_t));
681 fkReconstructor->GetRecoParam()->GetSysCovMatrix(sys);
685 // rotate covariance matrix
686 Double_t t2 = GetTilt()*GetTilt();
687 Double_t correction = 1./(1. + t2);
688 cov[0] = (sy2+t2*sz2)*correction;
689 cov[1] = GetTilt()*(sz2 - sy2)*correction;
690 cov[2] = (t2*sy2+sz2)*correction;
692 //printf("C(%6.1f %+6.3f %6.1f) [%s]\n", 1.e4*TMath::Sqrt(cov[0]), cov[1], 1.e4*TMath::Sqrt(cov[2]), IsRowCross()?" RC ":"-");
695 //____________________________________________________________
696 Double_t AliTRDseedV1::GetCovSqrt(const Double_t * const c, Double_t *d)
698 // Helper function to calculate the square root of the covariance matrix.
699 // The input matrix is stored in the vector c and the result in the vector d.
700 // Both arrays have to be initialized by the user with at least 3 elements. Return negative in case of failure.
702 // For calculating the square root of the symmetric matrix c
703 // the following relation is used:
705 // C^{1/2} = VD^{1/2}V^{-1}
707 // with V being the matrix with the n eigenvectors as columns.
708 // In case C is symmetric the followings are true:
709 // - matrix D is diagonal with the diagonal given by the eigenvalues of C
712 // Author A.Bercuci <A.Bercuci@gsi.de>
715 Double_t l[2], // eigenvalues
716 v[3]; // eigenvectors
717 // the secular equation and its solution :
718 // (c[0]-L)(c[2]-L)-c[1]^2 = 0
719 // L^2 - L*Tr(c)+DET(c) = 0
720 // L12 = [Tr(c) +- sqrt(Tr(c)^2-4*DET(c))]/2
721 Double_t tr = c[0]+c[2], // trace
722 det = c[0]*c[2]-c[1]*c[1]; // determinant
723 if(TMath::Abs(det)<1.e-20) return -1.;
724 Double_t dd = TMath::Sqrt(tr*tr - 4*det);
727 if(l[0]<0. || l[1]<0.) return -1.;
732 Double_t tmp = (l[0]-c[0])/c[1];
733 v[0] = TMath::Sqrt(1./(tmp*tmp+1));
735 v[2] = v[1]*c[1]/(l[1]-c[2]);
737 l[0] = TMath::Sqrt(l[0]); l[1] = TMath::Sqrt(l[1]);
738 d[0] = v[0]*v[0]*l[0]+v[1]*v[1]*l[1];
739 d[1] = v[0]*v[1]*l[0]+v[1]*v[2]*l[1];
740 d[2] = v[1]*v[1]*l[0]+v[2]*v[2]*l[1];
745 //____________________________________________________________
746 Double_t AliTRDseedV1::GetCovInv(const Double_t * const c, Double_t *d)
748 // Helper function to calculate the inverse of the covariance matrix.
749 // The input matrix is stored in the vector c and the result in the vector d.
750 // Both arrays have to be initialized by the user with at least 3 elements
751 // The return value is the determinant or 0 in case of singularity.
753 // Author A.Bercuci <A.Bercuci@gsi.de>
756 Double_t det = c[0]*c[2] - c[1]*c[1];
757 if(TMath::Abs(det)<1.e-20) return 0.;
758 Double_t invDet = 1./det;
765 //____________________________________________________________________
766 UShort_t AliTRDseedV1::GetVolumeId() const
768 for(Int_t ic(0);ic<kNclusters; ic++){
769 if(fClusters[ic]) return fClusters[ic]->GetVolumeId();
775 //____________________________________________________________________
776 void AliTRDseedV1::Calibrate()
778 // Retrieve calibration and position parameters from OCDB.
779 // The following information are used
781 // - column and row position of first attached cluster. If no clusters are attached
782 // to the tracklet a random central chamber position (c=70, r=7) will be used.
784 // The following information is cached in the tracklet
785 // t0 (trigger delay)
788 // omega*tau = tg(a_L)
789 // diffusion coefficients (longitudinal and transversal)
792 // Alex Bercuci <A.Bercuci@gsi.de>
793 // Date : Jan 8th 2009
796 AliCDBManager *cdb = AliCDBManager::Instance();
797 if(cdb->GetRun() < 0){
798 AliError("OCDB manager not properly initialized");
802 AliTRDcalibDB *calib = AliTRDcalibDB::Instance();
803 AliTRDCalROC *vdROC = calib->GetVdriftROC(fDet),
804 *t0ROC = calib->GetT0ROC(fDet);;
805 const AliTRDCalDet *vdDet = calib->GetVdriftDet();
806 const AliTRDCalDet *t0Det = calib->GetT0Det();
808 Int_t col = 70, row = 7;
809 AliTRDcluster **c = &fClusters[0];
812 while (ic<kNclusters && !(*c)){ic++; c++;}
814 col = (*c)->GetPadCol();
815 row = (*c)->GetPadRow();
819 fT0 = (t0Det->GetValue(fDet) + t0ROC->GetValue(col,row)) / AliTRDCommonParam::Instance()->GetSamplingFrequency();
820 fVD = vdDet->GetValue(fDet) * vdROC->GetValue(col, row);
821 fS2PRF = calib->GetPRFWidth(fDet, col, row); fS2PRF *= fS2PRF;
822 fExB = AliTRDCommonParam::Instance()->GetOmegaTau(fVD);
823 AliTRDCommonParam::Instance()->GetDiffCoeff(fDiffL,
825 AliDebug(4, Form("Calibration params for Det[%3d] Col[%3d] Row[%2d]\n t0[%f] vd[%f] s2PRF[%f] ExB[%f] Dl[%f] Dt[%f]", fDet, col, row, fT0, fVD, fS2PRF, fExB, fDiffL, fDiffT));
828 SetBit(kCalib, kTRUE);
831 //____________________________________________________________________
832 void AliTRDseedV1::SetOwner()
834 //AliInfo(Form("own [%s] fOwner[%s]", own?"YES":"NO", fOwner?"YES":"NO"));
836 if(TestBit(kOwner)) return;
837 for(int ic=0; ic<kNclusters; ic++){
838 if(!fClusters[ic]) continue;
839 fClusters[ic] = new AliTRDcluster(*fClusters[ic]);
844 //____________________________________________________________
845 void AliTRDseedV1::SetPadPlane(AliTRDpadPlane *p)
847 // Shortcut method to initialize pad geometry.
849 SetTilt(TMath::Tan(TMath::DegToRad()*p->GetTiltingAngle()));
850 SetPadLength(p->GetLengthIPad());
851 SetPadWidth(p->GetWidthIPad());
855 //____________________________________________________________________
856 Bool_t AliTRDseedV1::AttachClusters(AliTRDtrackingChamber *const chamber, Bool_t tilt)
859 // Projective algorithm to attach clusters to seeding tracklets. The following steps are performed :
860 // 1. Collapse x coordinate for the full detector plane
861 // 2. truncated mean on y (r-phi) direction
863 // 4. truncated mean on z direction
867 // - chamber : pointer to tracking chamber container used to search the tracklet
868 // - tilt : switch for tilt correction during road building [default true]
870 // - true : if tracklet found successfully. Failure can happend because of the following:
872 // Detailed description
874 // We start up by defining the track direction in the xy plane and roads. The roads are calculated based
875 // on tracking information (variance in the r-phi direction) and estimated variance of the standard
876 // clusters (see AliTRDcluster::SetSigmaY2()) corrected for tilt (see GetCovAt()). From this the road is
878 // r_{y} = 3*#sqrt{12*(#sigma^{2}_{Trk}(y) + #frac{#sigma^{2}_{cl}(y) + tg^{2}(#alpha_{L})#sigma^{2}_{cl}(z)}{1+tg^{2}(#alpha_{L})})}
879 // r_{z} = 1.5*L_{pad}
882 // Author : Alexandru Bercuci <A.Bercuci@gsi.de>
885 const AliTRDrecoParam* const recoParam = fkReconstructor->GetRecoParam(); //the dynamic cast in GetRecoParam is slow, so caching the pointer to it
888 AliError("Tracklets can not be used without a valid RecoParam.");
891 // Initialize reco params for this tracklet
892 // 1. first time bin in the drift region
894 Int_t kClmin = Int_t(recoParam->GetFindableClusters()*AliTRDtrackerV1::GetNTimeBins());
896 Double_t sysCov[5]; recoParam->GetSysCovMatrix(sysCov);
897 Double_t s2yTrk= fRefCov[0],
899 s2zCl = GetPadLength()*GetPadLength()/12.,
900 syRef = TMath::Sqrt(s2yTrk),
901 t2 = GetTilt()*GetTilt();
903 Double_t kroady = 1., //recoParam->GetRoad1y();
904 kroadz = GetPadLength() * recoParam->GetRoadzMultiplicator() + 1.;
905 // define probing cluster (the perfect cluster) and default calibration
906 Short_t sig[] = {0, 0, 10, 30, 10, 0,0};
907 AliTRDcluster cp(fDet, 6, 75, 0, sig, 0);
908 if(fkReconstructor->IsHLT()) cp.SetRPhiMethod(AliTRDcluster::kCOG);
909 if(!IsCalibrated()) Calibrate();
912 AliDebug(4, Form("syKalman[%f] rY[%f] rZ[%f]", syRef, kroady, kroadz));
915 const Int_t kNrows = 16;
916 const Int_t kNcls = 3*kNclusters; // buffer size
917 AliTRDcluster *clst[kNrows][kNcls];
918 Bool_t blst[kNrows][kNcls];
919 Double_t cond[4], dx, dy, yt, zt, yres[kNrows][kNcls];
920 Int_t idxs[kNrows][kNcls], ncl[kNrows], ncls = 0;
921 memset(ncl, 0, kNrows*sizeof(Int_t));
922 memset(yres, 0, kNrows*kNcls*sizeof(Double_t));
923 memset(blst, 0, kNrows*kNcls*sizeof(Bool_t)); //this is 8 times faster to memset than "memset(clst, 0, kNrows*kNcls*sizeof(AliTRDcluster*))"
925 // Do cluster projection
926 AliTRDcluster *c = NULL;
927 AliTRDchamberTimeBin *layer = NULL;
928 Bool_t kBUFFER = kFALSE;
929 for (Int_t it = 0; it < kNtb; it++) {
930 if(!(layer = chamber->GetTB(it))) continue;
931 if(!Int_t(*layer)) continue;
932 // get track projection at layers position
933 dx = fX0 - layer->GetX();
934 yt = fYref[0] - fYref[1] * dx;
935 zt = fZref[0] - fZref[1] * dx;
936 // get standard cluster error corrected for tilt
937 cp.SetLocalTimeBin(it);
938 cp.SetSigmaY2(0.02, fDiffT, fExB, dx, -1./*zt*/, fYref[1]);
939 s2yCl = (cp.GetSigmaY2() + sysCov[0] + t2*s2zCl)/(1.+t2);
940 // get estimated road
941 kroady = 3.*TMath::Sqrt(12.*(s2yTrk + s2yCl));
943 AliDebug(5, Form(" %2d x[%f] yt[%f] zt[%f]", it, dx, yt, zt));
945 AliDebug(5, Form(" syTrk[um]=%6.2f syCl[um]=%6.2f syClTlt[um]=%6.2f Ry[mm]=%f", 1.e4*TMath::Sqrt(s2yTrk), 1.e4*TMath::Sqrt(cp.GetSigmaY2()), 1.e4*TMath::Sqrt(s2yCl), 1.e1*kroady));
948 cond[0] = yt; cond[2] = kroady;
949 cond[1] = zt; cond[3] = kroadz;
951 layer->GetClusters(cond, idx, n, 6);
952 for(Int_t ic = n; ic--;){
953 c = (*layer)[idx[ic]];
955 dy += tilt ? GetTilt() * (c->GetZ() - zt) : 0.;
956 // select clusters on a 3 sigmaKalman level
957 /* if(tilt && TMath::Abs(dy) > 3.*syRef){
958 printf("too large !!!\n");
961 Int_t r = c->GetPadRow();
962 AliDebug(5, Form(" -> dy[%f] yc[%f] r[%d]", TMath::Abs(dy), c->GetY(), r));
964 blst[r][ncl[r]] = kTRUE;
965 idxs[r][ncl[r]] = idx[ic];
966 yres[r][ncl[r]] = dy;
969 if(ncl[r] >= kNcls) {
970 AliWarning(Form("Cluster candidates row[%d] reached buffer limit[%d]. Some may be lost.", r, kNcls));
977 AliDebug(4, Form("Found %d clusters. Processing ...", ncls));
979 AliDebug(1, Form("CLUSTERS FOUND %d LESS THAN THRESHOLD %d.", ncls, kClmin));
980 SetErrorMsg(kAttachClFound);
984 // analyze each row individualy
985 Bool_t kRowSelection(kFALSE);
986 Double_t mean[]={1.e3, 1.e3, 1.3}, syDis[]={1.e3, 1.e3, 1.3};
987 Int_t nrow[] = {0, 0, 0}, rowId[] = {-1, -1, -1}, nr = 0, lr=-1;
989 for(Int_t ir=0; ir<kNrows; ir++){
990 if(!(ncl[ir])) continue;
991 if(lr>0 && ir-lr != 1){
992 AliDebug(2, "Rows attached not continuous. Turn on selection.");
996 AliDebug(5, Form(" r[%d] n[%d]", ir, ncl[ir]));
997 // Evaluate truncated mean on the y direction
998 if(ncl[ir] < 4) continue;
999 AliMathBase::EvaluateUni(ncl[ir], yres[ir], mean[nr], syDis[nr], Int_t(ncl[ir]*.8));
1001 // TODO check mean and sigma agains cluster resolution !!
1002 AliDebug(4, Form(" m_%d[%+5.3f (%5.3fs)] s[%f]", nr, mean[nr], TMath::Abs(mean[nr]/syDis[nr]), syDis[nr]));
1003 // remove outliers based on a 3 sigmaDistr level
1004 Bool_t kFOUND = kFALSE;
1005 for(Int_t ic = ncl[ir]; ic--;){
1006 if(yres[ir][ic] - mean[nr] > 3. * syDis[nr]){
1007 blst[ir][ic] = kFALSE; continue;
1009 nrow[nr]++; rowId[nr]=ir; kFOUND = kTRUE;
1012 vdy[nr].Use(nrow[nr], yres[ir]);
1015 lr = ir; if(nr>=3) break;
1017 if(recoParam->GetStreamLevel(AliTRDrecoParam::kTracker) > 3 && fkReconstructor->IsDebugStreaming()){
1018 TTreeSRedirector &cstreamer = *fkReconstructor->GetDebugStream(AliTRDrecoParam::kTracker);
1020 if(IsKink()) SETBIT(stat, 1);
1021 if(IsStandAlone()) SETBIT(stat, 2);
1022 cstreamer << "AttachClusters"
1027 << "r0=" << rowId[0]
1028 << "dy0=" << &vdy[0]
1030 << "s0=" << syDis[0]
1031 << "r1=" << rowId[1]
1032 << "dy1=" << &vdy[1]
1034 << "s1=" << syDis[1]
1035 << "r2=" << rowId[2]
1036 << "dy2=" << &vdy[2]
1038 << "s2=" << syDis[2]
1043 // analyze gap in rows attached
1045 SetErrorMsg(kAttachRowGap);
1046 Int_t rowRemove(-1);
1047 if(nr==2){ // select based on minimum distance to track projection
1048 if(TMath::Abs(mean[0])<TMath::Abs(mean[1])){
1049 if(nrow[1]>nrow[0]) AliDebug(2, Form("Conflicting mean[%f < %f] but ncl[%d < %d].", TMath::Abs(mean[0]), TMath::Abs(mean[1]), nrow[0], nrow[1]));
1051 if(nrow[1]<nrow[0]) AliDebug(2, Form("Conflicting mean[%f > %f] but ncl[%d > %d].", TMath::Abs(mean[0]), TMath::Abs(mean[1]), nrow[0], nrow[1]));
1052 Swap(nrow[0],nrow[1]); Swap(rowId[0],rowId[1]);
1053 Swap(mean[0],mean[1]); Swap(syDis[0],syDis[1]);
1056 } else if(nr==3){ // select based on 2 consecutive rows
1057 if(rowId[1]==rowId[0]+1 && rowId[1]!=rowId[2]-1){
1059 } else if(rowId[1]!=rowId[0]+1 && rowId[1]==rowId[2]-1){
1060 Swap(nrow[0],nrow[2]); Swap(rowId[0],rowId[2]);
1061 Swap(mean[0],mean[2]); Swap(syDis[0],syDis[2]);
1065 if(rowRemove>0){nrow[rowRemove]=0; rowId[rowRemove]=-1;}
1067 AliDebug(4, Form(" Ncl[%d[%d] + %d[%d] + %d[%d]]", nrow[0], rowId[0], nrow[1], rowId[1], nrow[2], rowId[2]));
1070 SetBit(kRowCross, kTRUE); // mark pad row crossing
1071 SetErrorMsg(kAttachRow);
1072 const Float_t am[]={TMath::Abs(mean[0]), TMath::Abs(mean[1]), TMath::Abs(mean[2])};
1073 AliDebug(4, Form("complex row configuration\n"
1074 " r[%d] n[%d] m[%6.3f] s[%6.3f]\n"
1075 " r[%d] n[%d] m[%6.3f] s[%6.3f]\n"
1076 " r[%d] n[%d] m[%6.3f] s[%6.3f]\n"
1077 , rowId[0], nrow[0], am[0], syDis[0]
1078 , rowId[1], nrow[1], am[1], syDis[1]
1079 , rowId[2], nrow[2], am[2], syDis[2]));
1080 Int_t id[]={0,1,2}; TMath::Sort(3, am, id, kFALSE);
1082 Int_t rnn[3]; memcpy(rnn, nrow, 3*sizeof(Int_t));
1083 Int_t rid[3]; memcpy(rid, rowId, 3*sizeof(Int_t));
1084 Double_t rm[3]; memcpy(rm, mean, 3*sizeof(Double_t));
1085 Double_t rs[3]; memcpy(rs, syDis, 3*sizeof(Double_t));
1086 nrow[0]=rnn[id[0]]; rowId[0]=rid[id[0]]; mean[0]=rm[id[0]]; syDis[0]=rs[id[0]];
1087 nrow[1]=rnn[id[1]]; rowId[1]=rid[id[1]]; mean[1]=rm[id[1]]; syDis[1]=rs[id[1]];
1088 nrow[2]=0; rowId[2]=-1; mean[2] = 1.e3; syDis[2] = 1.e3;
1089 AliDebug(4, Form("solved configuration\n"
1090 " r[%d] n[%d] m[%+6.3f] s[%6.3f]\n"
1091 " r[%d] n[%d] m[%+6.3f] s[%6.3f]\n"
1092 " r[%d] n[%d] m[%+6.3f] s[%6.3f]\n"
1093 , rowId[0], nrow[0], mean[0], syDis[0]
1094 , rowId[1], nrow[1], mean[1], syDis[1]
1095 , rowId[2], nrow[2], mean[2], syDis[2]));
1098 SetBit(kRowCross, kTRUE); // mark pad row crossing
1099 if(nrow[1] > nrow[0]){ // swap row order
1100 Swap(nrow[0],nrow[1]); Swap(rowId[0],rowId[1]);
1101 Swap(mean[0],mean[1]); Swap(syDis[0],syDis[1]);
1105 // Select and store clusters
1106 // We should consider here :
1107 // 1. How far is the chamber boundary
1108 // 2. How big is the mean
1109 Int_t n(0); Float_t dyc[kNclusters]; memset(dyc,0,kNclusters*sizeof(Float_t));
1110 for (Int_t ir = 0; ir < nr; ir++) {
1111 Int_t jr(rowId[ir]);
1112 AliDebug(4, Form(" Attaching Ncl[%d]=%d ...", jr, ncl[jr]));
1113 for (Int_t ic = 0; ic < ncl[jr]; ic++) {
1114 if(!blst[jr][ic])continue;
1116 Int_t it(c->GetPadTime());
1117 Int_t idx(it+kNtb*ir);
1119 AliDebug(4, Form("Many cluster candidates on row[%2d] tb[%2d].", jr, it));
1120 // TODO should save also the information on where the multiplicity happened and its size
1121 SetErrorMsg(kAttachMultipleCl);
1122 // TODO should also compare with mean and sigma for this row
1123 if(yres[jr][ic] > dyc[idx]) continue;
1126 // TODO proper indexing of clusters !!
1127 fIndexes[idx] = chamber->GetTB(it)->GetGlobalIndex(idxs[jr][ic]);
1129 dyc[idx] = yres[jr][ic];
1135 // number of minimum numbers of clusters expected for the tracklet
1136 if (GetN() < kClmin){
1137 AliDebug(1, Form("NOT ENOUGH CLUSTERS %d ATTACHED TO THE TRACKLET [min %d] FROM FOUND %d.", GetN(), kClmin, n));
1138 SetErrorMsg(kAttachClAttach);
1142 // Load calibration parameters for this tracklet
1145 // calculate dx for time bins in the drift region (calibration aware)
1146 Float_t x[2] = {0.,0.}; Int_t tb[2]={0,0};
1147 for (Int_t it = t0, irp=0; irp<2 && it < AliTRDtrackerV1::GetNTimeBins(); it++) {
1148 if(!fClusters[it]) continue;
1149 x[irp] = fClusters[it]->GetX();
1150 tb[irp] = fClusters[it]->GetLocalTimeBin();
1153 Int_t dtb = tb[1] - tb[0];
1154 fdX = dtb ? (x[0] - x[1]) / dtb : 0.15;
1158 //____________________________________________________________
1159 void AliTRDseedV1::Bootstrap(const AliTRDReconstructor *rec)
1161 // Fill in all derived information. It has to be called after recovery from file or HLT.
1162 // The primitive data are
1163 // - list of clusters
1164 // - detector (as the detector will be removed from clusters)
1165 // - position of anode wire (fX0) - temporary
1166 // - track reference position and direction
1167 // - momentum of the track
1168 // - time bin length [cm]
1170 // A.Bercuci <A.Bercuci@gsi.de> Oct 30th 2008
1172 fkReconstructor = rec;
1174 AliTRDpadPlane *pp = g.GetPadPlane(fDet);
1175 fPad[0] = pp->GetLengthIPad();
1176 fPad[1] = pp->GetWidthIPad();
1177 fPad[2] = TMath::Tan(TMath::DegToRad()*pp->GetTiltingAngle());
1178 //fSnp = fYref[1]/TMath::Sqrt(1+fYref[1]*fYref[1]);
1180 Int_t n = 0, nshare = 0, nused = 0;
1181 AliTRDcluster **cit = &fClusters[0];
1182 for(Int_t ic = kNclusters; ic--; cit++){
1185 if((*cit)->IsShared()) nshare++;
1186 if((*cit)->IsUsed()) nused++;
1188 SetN(n); SetNUsed(nused); SetNShared(nshare);
1195 //____________________________________________________________________
1196 Bool_t AliTRDseedV1::Fit(Bool_t tilt, Bool_t zcorr)
1199 // Linear fit of the clusters attached to the tracklet
1202 // - tilt : switch for tilt pad correction of cluster y position based on
1203 // the z, dzdx info from outside [default false].
1204 // - zcorr : switch for using z information to correct for anisochronity
1205 // and a finner error parameterization estimation [default false]
1207 // True if successful
1209 // Detailed description
1211 // Fit in the xy plane
1213 // The fit is performed to estimate the y position of the tracklet and the track
1214 // angle in the bending plane. The clusters are represented in the chamber coordinate
1215 // system (with respect to the anode wire - see AliTRDtrackerV1::FollowBackProlongation()
1216 // on how this is set). The x and y position of the cluster and also their variances
1217 // are known from clusterizer level (see AliTRDcluster::GetXloc(), AliTRDcluster::GetYloc(),
1218 // AliTRDcluster::GetSX() and AliTRDcluster::GetSY()).
1219 // If gaussian approximation is used to calculate y coordinate of the cluster the position
1220 // is recalculated taking into account the track angle. The general formula to calculate the
1221 // error of cluster position in the gaussian approximation taking into account diffusion and track
1222 // inclination is given for TRD by:
1224 // #sigma^{2}_{y} = #sigma^{2}_{PRF} + #frac{x#delta_{t}^{2}}{(1+tg(#alpha_{L}))^{2}} + #frac{x^{2}tg^{2}(#phi-#alpha_{L})tg^{2}(#alpha_{L})}{12}
1227 // Since errors are calculated only in the y directions, radial errors (x direction) are mapped to y
1228 // by projection i.e.
1230 // #sigma_{x|y} = tg(#phi) #sigma_{x}
1232 // and also by the lorentz angle correction
1234 // Fit in the xz plane
1236 // The "fit" is performed to estimate the radial position (x direction) where pad row cross happens.
1237 // If no pad row crossing the z position is taken from geometry and radial position is taken from the xy
1240 // There are two methods to estimate the radial position of the pad row cross:
1241 // 1. leading cluster radial position : Here the lower part of the tracklet is considered and the last
1242 // cluster registered (at radial x0) on this segment is chosen to mark the pad row crossing. The error
1243 // of the z estimate is given by :
1245 // #sigma_{z} = tg(#theta) #Delta x_{x_{0}}/12
1247 // The systematic errors for this estimation are generated by the following sources:
1248 // - no charge sharing between pad rows is considered (sharp cross)
1249 // - missing cluster at row cross (noise peak-up, under-threshold signal etc.).
1251 // 2. charge fit over the crossing point : Here the full energy deposit along the tracklet is considered
1252 // to estimate the position of the crossing by a fit in the qx plane. The errors in the q directions are
1253 // parameterized as s_q = q^2. The systematic errors for this estimation are generated by the following sources:
1254 // - no general model for the qx dependence
1255 // - physical fluctuations of the charge deposit
1256 // - gain calibration dependence
1258 // Estimation of the radial position of the tracklet
1260 // For pad row cross the radial position is taken from the xz fit (see above). Otherwise it is taken as the
1261 // interpolation point of the tracklet i.e. the point where the error in y of the fit is minimum. The error
1262 // in the y direction of the tracklet is (see AliTRDseedV1::GetCovAt()):
1264 // #sigma_{y} = #sigma^{2}_{y_{0}} + 2xcov(y_{0}, dy/dx) + #sigma^{2}_{dy/dx}
1266 // and thus the radial position is:
1268 // x = - cov(y_{0}, dy/dx)/#sigma^{2}_{dy/dx}
1271 // Estimation of tracklet position error
1273 // The error in y direction is the error of the linear fit at the radial position of the tracklet while in the z
1274 // direction is given by the cluster error or pad row cross error. In case of no pad row cross this is given by:
1276 // #sigma_{y} = #sigma^{2}_{y_{0}} - 2cov^{2}(y_{0}, dy/dx)/#sigma^{2}_{dy/dx} + #sigma^{2}_{dy/dx}
1277 // #sigma_{z} = Pad_{length}/12
1279 // For pad row cross the full error is calculated at the radial position of the crossing (see above) and the error
1280 // in z by the width of the crossing region - being a matter of parameterization.
1282 // #sigma_{z} = tg(#theta) #Delta x_{x_{0}}/12
1284 // In case of no tilt correction (default in the barrel tracking) the tilt is taken into account by the rotation of
1285 // the covariance matrix. See AliTRDseedV1::GetCovAt() for details.
1288 // A.Bercuci <A.Bercuci@gsi.de>
1290 if(!fkReconstructor){
1291 AliError("The tracklet needs the reconstruction setup. Please initialize by SetReconstructor().");
1294 if(!IsCalibrated()) Calibrate();
1296 const Int_t kClmin = 8;
1298 // get track direction
1299 Double_t y0 = fYref[0];
1300 Double_t dydx = fYref[1];
1301 Double_t z0 = fZref[0];
1302 Double_t dzdx = fZref[1];
1305 AliTRDtrackerV1::AliTRDLeastSquare fitterY;
1306 AliTRDtrackerV1::AliTRDLeastSquare fitterZ;
1308 // book cluster information
1309 Double_t qc[kNclusters], xc[kNclusters], yc[kNclusters], zc[kNclusters], sy[kNclusters];
1312 AliTRDcluster *c=NULL, **jc = &fClusters[0];
1313 const AliTRDrecoParam* const recoParam = fkReconstructor->GetRecoParam(); //the dynamic cast in GetRecoParam is slow, so caching the pointer to it
1314 for (Int_t ic=0; ic<kNtb; ic++, ++jc) {
1319 if(!(c = (*jc))) continue;
1320 if(!c->IsInChamber()) continue;
1323 if(c->GetNPads()>4) w = .5;
1324 if(c->GetNPads()>5) w = .2;
1327 qc[n] = TMath::Abs(c->GetQ());
1328 // pad row of leading
1330 // Radial cluster position
1331 //Int_t jc = TMath::Max(fN-3, 0);
1332 //xc[fN] = c->GetXloc(fT0, fVD, &qc[jc], &xc[jc]/*, z0 - c->GetX()*dzdx*/);
1333 xc[n] = fX0 - c->GetX();
1335 // extrapolated track to cluster position
1336 yt = y0 - xc[n]*dydx;
1337 zt = z0 - xc[n]*dzdx;
1339 // Recalculate cluster error based on tracking information
1340 c->SetSigmaY2(fS2PRF, fDiffT, fExB, xc[n], zcorr?zt:-1., dydx);
1341 sy[n] = TMath::Sqrt(c->GetSigmaY2());
1343 yc[n] = recoParam->UseGAUS() ?
1344 c->GetYloc(y0, sy[n], GetPadWidth()): c->GetY();
1346 //optional tilt correction
1347 if(tilt) yc[n] -= (GetTilt()*(zc[n] - zt));
1349 AliDebug(5, Form(" tb[%2d] dx[%6.3f] y[%6.2f+-%6.3f]", c->GetLocalTimeBin(), xc[n], yc[n], sy[n]));
1350 fitterY.AddPoint(&xc[n], yc[n], sy[n]);
1351 if(IsRowCross()) fitterZ.AddPoint(&xc[n], qc[n], 1.);
1356 if (n < kClmin) return kFALSE;
1359 if(!fitterY.Eval()){
1360 SetErrorMsg(kFitFailed);
1363 fYfit[0] = fitterY.GetFunctionParameter(0);
1364 fYfit[1] = -fitterY.GetFunctionParameter(1);
1367 fitterY.GetCovarianceMatrix(p);
1368 fCov[0] = p[1]; // variance of y0
1369 fCov[1] = p[2]; // covariance of y0, dydx
1370 fCov[2] = p[0]; // variance of dydx
1371 // the ref radial position is set at the minimum of
1372 // the y variance of the tracklet
1373 fX = -fCov[1]/fCov[2];
1374 Float_t xs=fX+.5*AliTRDgeometry::CamHght();
1375 if(xs < 0. || xs > AliTRDgeometry::CamHght()+AliTRDgeometry::CdrHght()){
1376 AliDebug(1, Form("Ref radial position ouside chamber x[%5.2f].", fX));
1377 SetErrorMsg(kFitOutside);
1381 // collect second row clusters
1384 /* // THE LEADING CLUSTER METHOD
1386 Int_t ic=n=kNclusters-1; jc = &fClusters[ic];
1387 AliTRDcluster *c0 =0x0, **kc = &fClusters[kNtb-1];
1388 for(; ic>kNtb; ic--, --jc, --kc){
1389 if((c0 = (*kc)) && c0->IsInChamber() && (xMin>c0->GetX())) xMin = c0->GetX();
1390 if(!(c = (*jc))) continue;
1391 if(!c->IsInChamber()) continue;
1392 zc[kNclusters-1] = c->GetZ();
1393 fX = fX0 - c->GetX();
1395 fZfit[0] = .5*(zc[0]+zc[kNclusters-1]); fZfit[1] = 0.;
1396 // Error parameterization
1397 fS2Z = fdX*fZref[1];
1398 fS2Z *= fS2Z; fS2Z *= 0.2887; // 1/sqrt(12)*/
1400 // THE FIT X-Q PLANE METHOD
1401 Int_t ic=n=kNclusters-1; jc = &fClusters[ic];
1402 for(; ic>kNtb; ic--, --jc){
1403 if(!(c = (*jc))) continue;
1404 if(!c->IsInChamber()) continue;
1405 qc[n] = TMath::Abs(c->GetQ());
1406 xc[n] = fX0 - c->GetX();
1408 fitterZ.AddPoint(&xc[n], -qc[n], 1.);
1413 if(m && IsRowCross()){
1415 if(fitterZ.GetFunctionParameter(1)!=0.){
1416 fX = -fitterZ.GetFunctionParameter(0)/fitterZ.GetFunctionParameter(1);
1418 Float_t dl = .5*AliTRDgeometry::CamHght()+AliTRDgeometry::CdrHght();
1420 fX-=.055; // TODO to be understood
1423 fZfit[0] = .5*(zc[0]+zc[kNclusters-1]); fZfit[1] = 0.;
1424 // temporary external error parameterization
1425 fS2Z = 0.05+0.4*TMath::Abs(fZref[1]); fS2Z *= fS2Z;
1426 // TODO correct formula
1427 //fS2Z = sigma_x*TMath::Abs(fZref[1]);
1429 if(IsRowCross() && !m){
1430 AliDebug(1, "Tracklet crossed row but no clusters found in neighbor row.");
1432 fZfit[0] = zc[0]; fZfit[1] = 0.;
1433 fS2Z = GetPadLength()*GetPadLength()/12.;
1435 fS2Y = fCov[0] +2.*fX*fCov[1] + fX*fX*fCov[2];
1441 //_____________________________________________________________________________
1442 void AliTRDseedV1::FitMI()
1446 // Marian Ivanov's version
1448 // linear fit on the y direction with respect to the reference direction.
1449 // The residuals for each x (x = xc - x0) are deduced from:
1451 // the tilting correction is written :
1452 // y = yc + h*(zc-zt) (2)
1453 // yt = y0+dy/dx*x (3)
1454 // zt = z0+dz/dx*x (4)
1455 // from (1),(2),(3) and (4)
1456 // dy = yc - y0 - (dy/dx + h*dz/dx)*x + h*(zc-z0)
1457 // the last term introduces the correction on y direction due to tilting pads. There are 2 ways to account for this:
1458 // 1. use tilting correction for calculating the y
1459 // 2. neglect tilting correction here and account for it in the error parametrization of the tracklet.
1460 const Float_t kRatio = 0.8;
1461 const Int_t kClmin = 5;
1462 const Float_t kmaxtan = 2;
1464 if (TMath::Abs(fYref[1]) > kmaxtan){
1465 //printf("Exit: Abs(fYref[1]) = %3.3f, kmaxtan = %3.3f\n", TMath::Abs(fYref[1]), kmaxtan);
1466 return; // Track inclined too much
1469 Float_t sigmaexp = 0.05 + TMath::Abs(fYref[1] * 0.25); // Expected r.m.s in y direction
1470 Float_t ycrosscor = GetPadLength() * GetTilt() * 0.5; // Y correction for crossing
1481 // Buffering: Leave it constant fot Performance issues
1482 Int_t zints[kNtb]; // Histograming of the z coordinate
1483 // Get 1 and second max probable coodinates in z
1484 Int_t zouts[2*kNtb];
1485 Float_t allowedz[kNtb]; // Allowed z for given time bin
1486 Float_t yres[kNtb]; // Residuals from reference
1487 //Float_t anglecor = GetTilt() * fZref[1]; // Correction to the angle
1489 Float_t pos[3*kNtb]; memset(pos, 0, 3*kNtb*sizeof(Float_t));
1490 Float_t *fX = &pos[0], *fY = &pos[kNtb], *fZ = &pos[2*kNtb];
1492 Int_t fN = 0; AliTRDcluster *c = 0x0;
1494 for (Int_t i = 0; i < AliTRDtrackerV1::GetNTimeBins(); i++) {
1496 if (!(c = fClusters[i])) continue;
1497 if(!c->IsInChamber()) continue;
1499 //yres[i] = fY[i] - fYref[0] - (fYref[1] + anglecor) * fX[i] + GetTilt()*(fZ[i] - fZref[0]);
1500 fX[i] = fX0 - c->GetX();
1503 yres[i] = fY[i] - GetTilt()*(fZ[i] - (fZref[0] - fX[i]*fZref[1]));
1504 zints[fN] = Int_t(fZ[i]);
1509 //printf("Exit fN < kClmin: fN = %d\n", fN);
1512 Int_t nz = AliTRDtrackerV1::Freq(fN, zints, zouts, kFALSE);
1513 Float_t fZProb = zouts[0];
1514 if (nz <= 1) zouts[3] = 0;
1515 if (zouts[1] + zouts[3] < kClmin) {
1516 //printf("Exit zouts[1] = %d, zouts[3] = %d\n",zouts[1],zouts[3]);
1520 // Z distance bigger than pad - length
1521 if (TMath::Abs(zouts[0]-zouts[2]) > 12.0) zouts[3] = 0;
1523 Int_t breaktime = -1;
1524 Bool_t mbefore = kFALSE;
1525 Int_t cumul[kNtb][2];
1526 Int_t counts[2] = { 0, 0 };
1528 if (zouts[3] >= 3) {
1531 // Find the break time allowing one chage on pad-rows
1532 // with maximal number of accepted clusters
1535 for (Int_t i = 0; i < AliTRDtrackerV1::GetNTimeBins(); i++) {
1536 cumul[i][0] = counts[0];
1537 cumul[i][1] = counts[1];
1538 if (TMath::Abs(fZ[i]-zouts[0]) < 2) counts[0]++;
1539 if (TMath::Abs(fZ[i]-zouts[2]) < 2) counts[1]++;
1542 for (Int_t i = 0; i < AliTRDtrackerV1::GetNTimeBins(); i++) {
1543 Int_t after = cumul[AliTRDtrackerV1::GetNTimeBins()][0] - cumul[i][0];
1544 Int_t before = cumul[i][1];
1545 if (after + before > maxcount) {
1546 maxcount = after + before;
1550 after = cumul[AliTRDtrackerV1::GetNTimeBins()-1][1] - cumul[i][1];
1551 before = cumul[i][0];
1552 if (after + before > maxcount) {
1553 maxcount = after + before;
1561 for (Int_t i = 0; i < AliTRDtrackerV1::GetNTimeBins()+1; i++) {
1562 if (i > breaktime) allowedz[i] = mbefore ? zouts[2] : zouts[0];
1563 if (i <= breaktime) allowedz[i] = (!mbefore) ? zouts[2] : zouts[0];
1566 if (((allowedz[0] > allowedz[AliTRDtrackerV1::GetNTimeBins()]) && (fZref[1] < 0)) ||
1567 ((allowedz[0] < allowedz[AliTRDtrackerV1::GetNTimeBins()]) && (fZref[1] > 0))) {
1569 // Tracklet z-direction not in correspondance with track z direction
1572 for (Int_t i = 0; i < AliTRDtrackerV1::GetNTimeBins()+1; i++) {
1573 allowedz[i] = zouts[0]; // Only longest taken
1579 // Cross pad -row tracklet - take the step change into account
1581 for (Int_t i = 0; i < AliTRDtrackerV1::GetNTimeBins()+1; i++) {
1582 if (!fClusters[i]) continue;
1583 if(!fClusters[i]->IsInChamber()) continue;
1584 if (TMath::Abs(fZ[i] - allowedz[i]) > 2) continue;
1586 //yres[i] = fY[i] - fYref[0] - (fYref[1] + anglecor) * fX[i] + GetTilt()*(fZ[i] - fZref[0]);
1587 yres[i] = fY[i] - GetTilt()*(fZ[i] - (fZref[0] - fX[i]*fZref[1]));
1588 // if (TMath::Abs(fZ[i] - fZProb) > 2) {
1589 // if (fZ[i] > fZProb) yres[i] += GetTilt() * GetPadLength();
1590 // if (fZ[i] < fZProb) yres[i] -= GetTilt() * GetPadLength();
1595 Double_t yres2[kNtb];
1598 for (Int_t i = 0; i < AliTRDtrackerV1::GetNTimeBins()+1; i++) {
1599 if (!fClusters[i]) continue;
1600 if(!fClusters[i]->IsInChamber()) continue;
1601 if (TMath::Abs(fZ[i] - allowedz[i]) > 2) continue;
1602 yres2[fN2] = yres[i];
1606 //printf("Exit fN2 < kClmin: fN2 = %d\n", fN2);
1610 AliMathBase::EvaluateUni(fN2,yres2,mean,sigma, Int_t(fN2*kRatio-2.));
1611 if (sigma < sigmaexp * 0.8) {
1614 //Float_t fSigmaY = sigma;
1629 for (Int_t i = 0; i < AliTRDtrackerV1::GetNTimeBins()+1; i++) {
1630 if (!fClusters[i]) continue;
1631 if (!fClusters[i]->IsInChamber()) continue;
1632 if (TMath::Abs(fZ[i] - allowedz[i]) > 2){fClusters[i] = 0x0; continue;}
1633 if (TMath::Abs(yres[i] - mean) > 4.0 * sigma){fClusters[i] = 0x0; continue;}
1636 fMPads += fClusters[i]->GetNPads();
1637 Float_t weight = 1.0;
1638 if (fClusters[i]->GetNPads() > 4) weight = 0.5;
1639 if (fClusters[i]->GetNPads() > 5) weight = 0.2;
1643 //printf("x = %7.3f dy = %7.3f fit %7.3f\n", x, yres[i], fY[i]-yres[i]);
1646 sumwx += x * weight;
1647 sumwx2 += x*x * weight;
1648 sumwy += weight * yres[i];
1649 sumwxy += weight * (yres[i]) * x;
1650 sumwz += weight * fZ[i];
1651 sumwxz += weight * fZ[i] * x;
1656 //printf("Exit fN2 < kClmin(2): fN2 = %d\n",fN2);
1660 fMeanz = sumwz / sumw;
1661 Float_t correction = 0;
1663 // Tracklet on boundary
1664 if (fMeanz < fZProb) correction = ycrosscor;
1665 if (fMeanz > fZProb) correction = -ycrosscor;
1668 Double_t det = sumw * sumwx2 - sumwx * sumwx;
1669 fYfit[0] = (sumwx2 * sumwy - sumwx * sumwxy) / det;
1670 fYfit[1] = (sumw * sumwxy - sumwx * sumwy) / det;
1673 for (Int_t i = 0; i < AliTRDtrackerV1::GetNTimeBins()+1; i++) {
1674 if (!TESTBIT(fUsable,i)) continue;
1675 Float_t delta = yres[i] - fYfit[0] - fYfit[1] * fX[i];
1676 fS2Y += delta*delta;
1678 fS2Y = TMath::Sqrt(fS2Y / Float_t(fN2-2));
1679 // TEMPORARY UNTIL covariance properly calculated
1680 fS2Y = TMath::Max(fS2Y, Float_t(.1));
1682 fZfit[0] = (sumwx2 * sumwz - sumwx * sumwxz) / det;
1683 fZfit[1] = (sumw * sumwxz - sumwx * sumwz) / det;
1684 // fYfitR[0] += fYref[0] + correction;
1685 // fYfitR[1] += fYref[1];
1686 // fYfit[0] = fYfitR[0];
1687 fYfit[1] = -fYfit[1];
1692 //___________________________________________________________________
1693 void AliTRDseedV1::Print(Option_t *o) const
1696 // Printing the seedstatus
1699 AliInfo(Form("Det[%3d] X0[%7.2f] Pad{L[%5.2f] W[%5.2f] Tilt[%+6.2f]}", fDet, fX0, GetPadLength(), GetPadWidth(), GetTilt()));
1700 AliInfo(Form("N[%2d] Nused[%2d] Nshared[%2d] [%d]", GetN(), GetNUsed(), GetNShared(), fN));
1701 AliInfo(Form("FLAGS : RC[%c] Kink[%c] SA[%c]", IsRowCross()?'y':'n', IsKink()?'y':'n', IsStandAlone()?'y':'n'));
1702 AliInfo(Form("CALIB PARAMS : T0[%5.2f] Vd[%5.2f] s2PRF[%5.2f] ExB[%5.2f] Dl[%5.2f] Dt[%5.2f]", fT0, fVD, fS2PRF, fExB, fDiffL, fDiffT));
1704 Double_t cov[3], x=GetX();
1706 AliInfo(" | x[cm] | y[cm] | z[cm] | dydx | dzdx |");
1707 AliInfo(Form("Fit | %7.2f | %7.2f+-%7.2f | %7.2f+-%7.2f| %5.2f | ----- |", x, GetY(), TMath::Sqrt(cov[0]), GetZ(), TMath::Sqrt(cov[2]), fYfit[1]));
1708 AliInfo(Form("Ref | %7.2f | %7.2f+-%7.2f | %7.2f+-%7.2f| %5.2f | %5.2f |", x, fYref[0]-fX*fYref[1], TMath::Sqrt(fRefCov[0]), fZref[0]-fX*fYref[1], TMath::Sqrt(fRefCov[2]), fYref[1], fZref[1]))
1709 AliInfo(Form("P / Pt [GeV/c] = %f / %f", GetMomentum(), fPt));
1710 if(IsStandAlone()) AliInfo(Form("C Rieman / Vertex [1/cm] = %f / %f", fC[0], fC[1]));
1711 AliInfo(Form("dEdx [a.u.] = %f / %f / %f / %f / %f/ %f / %f / %f", fdEdx[0], fdEdx[1], fdEdx[2], fdEdx[3], fdEdx[4], fdEdx[5], fdEdx[6], fdEdx[7]));
1712 AliInfo(Form("PID = %5.3f / %5.3f / %5.3f / %5.3f / %5.3f", fProb[0], fProb[1], fProb[2], fProb[3], fProb[4]));
1714 if(strcmp(o, "a")!=0) return;
1716 AliTRDcluster* const* jc = &fClusters[0];
1717 for(int ic=0; ic<kNclusters; ic++, jc++) {
1718 if(!(*jc)) continue;
1724 //___________________________________________________________________
1725 Bool_t AliTRDseedV1::IsEqual(const TObject *o) const
1727 // Checks if current instance of the class has the same essential members
1730 if(!o) return kFALSE;
1731 const AliTRDseedV1 *inTracklet = dynamic_cast<const AliTRDseedV1*>(o);
1732 if(!inTracklet) return kFALSE;
1734 for (Int_t i = 0; i < 2; i++){
1735 if ( fYref[i] != inTracklet->fYref[i] ) return kFALSE;
1736 if ( fZref[i] != inTracklet->fZref[i] ) return kFALSE;
1739 if ( fS2Y != inTracklet->fS2Y ) return kFALSE;
1740 if ( GetTilt() != inTracklet->GetTilt() ) return kFALSE;
1741 if ( GetPadLength() != inTracklet->GetPadLength() ) return kFALSE;
1743 for (Int_t i = 0; i < kNclusters; i++){
1744 // if ( fX[i] != inTracklet->GetX(i) ) return kFALSE;
1745 // if ( fY[i] != inTracklet->GetY(i) ) return kFALSE;
1746 // if ( fZ[i] != inTracklet->GetZ(i) ) return kFALSE;
1747 if ( fIndexes[i] != inTracklet->fIndexes[i] ) return kFALSE;
1749 // if ( fUsable != inTracklet->fUsable ) return kFALSE;
1751 for (Int_t i=0; i < 2; i++){
1752 if ( fYfit[i] != inTracklet->fYfit[i] ) return kFALSE;
1753 if ( fZfit[i] != inTracklet->fZfit[i] ) return kFALSE;
1754 if ( fLabels[i] != inTracklet->fLabels[i] ) return kFALSE;
1757 /* if ( fMeanz != inTracklet->GetMeanz() ) return kFALSE;
1758 if ( fZProb != inTracklet->GetZProb() ) return kFALSE;*/
1759 if ( fN != inTracklet->fN ) return kFALSE;
1760 //if ( fNUsed != inTracklet->fNUsed ) return kFALSE;
1761 //if ( fFreq != inTracklet->GetFreq() ) return kFALSE;
1762 //if ( fNChange != inTracklet->GetNChange() ) return kFALSE;
1764 if ( fC != inTracklet->fC ) return kFALSE;
1765 //if ( fCC != inTracklet->GetCC() ) return kFALSE;
1766 if ( fChi2 != inTracklet->fChi2 ) return kFALSE;
1767 // if ( fChi2Z != inTracklet->GetChi2Z() ) return kFALSE;
1769 if ( fDet != inTracklet->fDet ) return kFALSE;
1770 if ( fPt != inTracklet->fPt ) return kFALSE;
1771 if ( fdX != inTracklet->fdX ) return kFALSE;
1773 for (Int_t iCluster = 0; iCluster < kNclusters; iCluster++){
1774 AliTRDcluster *curCluster = fClusters[iCluster];
1775 AliTRDcluster *inCluster = inTracklet->fClusters[iCluster];
1776 if (curCluster && inCluster){
1777 if (! curCluster->IsEqual(inCluster) ) {
1778 curCluster->Print();
1783 // if one cluster exists, and corresponding
1784 // in other tracklet doesn't - return kFALSE
1785 if(curCluster || inCluster) return kFALSE;