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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12 * about the suitability of this software for any purpose. It is *
13 * provided "as is" without express or implied warranty. *
14 **************************************************************************/
16 //////////////////////////////////////////////////////////////////////////
20 // HMPID class to perfom pattern recognition based on Hough transfrom //
21 // for single chamber //
22 //////////////////////////////////////////////////////////////////////////
24 #include "AliHMPIDRecon.h" //class header
25 #include "AliHMPIDParam.h" //CkovAngle()
26 #include "AliHMPIDCluster.h" //CkovAngle()
27 #include <TMinuit.h> //FitEllipse()
28 #include <TRotation.h> //TracePhot()
29 #include <TH1D.h> //HoughResponse()
30 #include <TClonesArray.h> //CkovAngle()
31 #include <AliESDtrack.h> //CkovAngle()
33 const Double_t AliHMPIDRecon::fgkRadThick=1.5;
34 const Double_t AliHMPIDRecon::fgkWinThick=0.5;
35 const Double_t AliHMPIDRecon::fgkGapThick=8.0;
36 const Double_t AliHMPIDRecon::fgkWinIdx =1.5787;
37 const Double_t AliHMPIDRecon::fgkGapIdx =1.0005;
39 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
40 AliHMPIDRecon::AliHMPIDRecon():TTask("RichRec","RichPat"),
47 fTrkDir(TVector3(0,0,1)),fTrkPos(TVector2(30,40))
50 for (Int_t i=0; i<3000; i++) {
57 fMipX=fMipY=fThTrkFit=fPhTrkFit=fCkovFit=fMipQ=fRadX=fRadY=-999;
60 for (Int_t i=0; i<100; i++) {
61 fXClu[i] = fYClu[i] = 0;
65 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
66 void AliHMPIDRecon::CkovAngle(AliESDtrack *pTrk,TClonesArray *pCluLst,Double_t nmean)
68 // Pattern recognition method based on Hough transform
69 // Arguments: pTrk - track for which Ckov angle is to be found
70 // pCluLst - list of clusters for this chamber
71 // Returns: - track ckov angle, [rad],
73 AliHMPIDParam *pParam=AliHMPIDParam::Instance();
75 if(pCluLst->GetEntries()>pParam->MultCut()) fIsWEIGHT = kTRUE; // offset to take into account bkg in reconstruction
76 else fIsWEIGHT = kFALSE;
78 Float_t xRa,yRa,th,ph;
79 pTrk->GetHMPIDtrk(xRa,yRa,th,ph); //initialize this track: th and ph angles at middle of RAD
80 SetTrack(xRa,yRa,th,ph);
84 Float_t dMin=999,mipX=-1,mipY=-1;Int_t chId=-1,mipId=-1,mipQ=-1;
86 for (Int_t iClu=0; iClu<pCluLst->GetEntriesFast();iClu++){//clusters loop
87 AliHMPIDCluster *pClu=(AliHMPIDCluster*)pCluLst->UncheckedAt(iClu); //get pointer to current cluster
89 if(pClu->Q()>pParam->QCut()){ //charge compartible with MIP clusters
90 Float_t dX=fPc.X()-pClu->X(),dY=fPc.Y()-pClu->Y(),d =TMath::Sqrt(dX*dX+dY*dY); //distance between current cluster and intersection point
91 if( d < dMin) {mipId=iClu; dMin=d;mipX=pClu->X();mipY=pClu->Y();mipQ=(Int_t)pClu->Q();} //current cluster is closer, overwrite data for min cluster
92 }else{ //charge compatible with photon cluster
93 Double_t thetaCer,phiCer;
94 if(FindPhotCkov(pClu->X(),pClu->Y(),thetaCer,phiCer)){ //find ckov angle for this photon candidate
95 fPhotCkov[fPhotCnt]=thetaCer; //actual theta Cerenkov (in TRS)
96 fPhotPhi [fPhotCnt]=phiCer; //actual phi Cerenkov (in TRS): -pi to come back to "unusual" ref system (X,Y,-Z)
97 fPhotCnt++; //increment counter of photon candidates
101 Int_t iNacc=FlagPhot(HoughResponse()); //flag photons according to individual theta ckov with respect to most probable
102 pTrk->SetHMPIDmip(mipX,mipY,mipQ,iNacc); //store mip info
104 if(mipId==-1) {pTrk->SetHMPIDsignal(kMipQdcCut); return;} //no clusters with QDC more the threshold at all
105 if(dMin>pParam->DistCut()) {pTrk->SetHMPIDsignal(kMipDistCut); return;} //closest cluster with enough charge is still too far from intersection
106 pTrk->SetHMPIDcluIdx(chId,mipId); //set index of cluster
107 if(iNacc<1) pTrk->SetHMPIDsignal(kNoPhotAccept); //no photon candidates is accepted
108 else pTrk->SetHMPIDsignal(FindRingCkov(pCluLst->GetEntries())); //find best Theta ckov for ring i.e. track
110 pTrk->SetHMPIDchi2(fCkovSigma2); //errors squared
113 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
114 Bool_t AliHMPIDRecon::FindPhotCkov(Double_t cluX,Double_t cluY,Double_t &thetaCer,Double_t &phiCer)
116 // Finds Cerenkov angle for this photon candidate
117 // Arguments: cluX,cluY - position of cadidate's cluster
118 // Returns: Cerenkov angle
122 Double_t zRad= -0.5*fgkRadThick-0.5*fgkWinThick; //z position of middle of RAD
123 TVector3 rad(fTrkPos.X(),fTrkPos.Y(),zRad); //impact point at middle of RAD
124 TVector3 pc(cluX,cluY,0.5*fgkWinThick+fgkGapIdx); //mip at PC
125 Double_t cluR = TMath::Sqrt((cluX-fTrkPos.X())*(cluX-fTrkPos.X())+
126 (cluY-fTrkPos.Y())*(cluY-fTrkPos.Y()));//ref. distance impact RAD-CLUSTER
127 Double_t phi=(pc-rad).Phi(); //phi of photon
130 Double_t ckov2=0.75+fTrkDir.Theta(); //start to find theta cerenkov in DRS
131 const Double_t kTol=0.01;
134 if(iIterCnt>=50) return kFALSE;
135 Double_t ckov=0.5*(ckov1+ckov2);
136 dirCkov.SetMagThetaPhi(1,ckov,phi);
137 TVector2 posC=TraceForward(dirCkov); //trace photon with actual angles
138 Double_t dist=cluR-(posC-fTrkPos).Mod(); //get distance between trial point and cluster position
139 if(posC.X()==-999) dist = - 999; //total reflection problem
140 iIterCnt++; //counter step
141 if (dist> kTol) ckov1=ckov; //cluster @ larger ckov
142 else if(dist<-kTol) ckov2=ckov; //cluster @ smaller ckov
143 else{ //precision achived: ckov in DRS found
144 dirCkov.SetMagThetaPhi(1,ckov,phi); //
145 RecPhot(dirCkov,thetaCer,phiCer); //find ckov (in TRS:the effective Cherenkov angle!)
150 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
151 TVector2 AliHMPIDRecon::TraceForward(TVector3 dirCkov)const
153 //Trace forward a photon from (x,y) up to PC
154 // Arguments: dirCkov photon vector in LORS
155 // Returns: pos of traced photon at PC
156 TVector2 pos(-999,-999);
157 Double_t thetaCer = dirCkov.Theta();
158 if(thetaCer > TMath::ASin(1./fRadNmean)) return pos; //total refraction on WIN-GAP boundary
159 Double_t zRad= -0.5*fgkRadThick-0.5*fgkWinThick; //z position of middle of RAD
160 TVector3 posCkov(fTrkPos.X(),fTrkPos.Y(),zRad); //RAD: photon position is track position @ middle of RAD
161 Propagate(dirCkov,posCkov, -0.5*fgkWinThick); //go to RAD-WIN boundary
162 Refract (dirCkov, fRadNmean,fgkWinIdx); //RAD-WIN refraction
163 Propagate(dirCkov,posCkov, 0.5*fgkWinThick); //go to WIN-GAP boundary
164 Refract (dirCkov, fgkWinIdx,fgkGapIdx); //WIN-GAP refraction
165 Propagate(dirCkov,posCkov,0.5*fgkWinThick+fgkGapThick); //go to PC
166 pos.Set(posCkov.X(),posCkov.Y());
169 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
170 void AliHMPIDRecon::RecPhot(TVector3 dirCkov,Double_t &thetaCer,Double_t &phiCer)
172 //Theta Cerenkov reconstruction
173 // Arguments: (x,y) of initial point in LORS, dirCkov photon vector in LORS
174 // Returns: thetaCer theta cerenkov reconstructed
176 // dirTrk.SetMagThetaPhi(1,fTrkDir.Theta(),fTrkDir.Phi());
177 // Double_t thetaCer = TMath::ACos(dirCkov*dirTrk);
178 TRotation mtheta; mtheta.RotateY(- fTrkDir.Theta());
179 TRotation mphi; mphi.RotateZ(- fTrkDir.Phi());
180 TRotation mrot=mtheta*mphi;
182 dirCkovTRS=mrot*dirCkov;
183 phiCer = dirCkovTRS.Phi(); //actual value of the phi of the photon
184 thetaCer= dirCkovTRS.Theta(); //actual value of thetaCerenkov of the photon
186 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
187 Double_t AliHMPIDRecon::FindRingArea(Double_t ckovAng)const
189 // Find area inside the cerenkov ring which lays inside PCs
190 // Arguments: ckovAng - cerenkov angle
191 // Returns: area of the ring in cm^2 for given theta ckov
195 for(Int_t i=0;i<kN;i++){
196 TVector2 pos1=TracePhot(ckovAng,Double_t(TMath::TwoPi()*i /kN));//trace this photon
197 TVector2 pos2=TracePhot(ckovAng,Double_t(TMath::TwoPi()*(i+1)/kN));//trace the next photon
198 area+=(pos1-fTrkPos)*(pos2-fTrkPos); //add area of the triangle...
202 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
203 Double_t AliHMPIDRecon::FindRingCkov(Int_t)
205 // Loops on all Ckov candidates and estimates the best Theta Ckov for a ring formed by those candidates. Also estimates an error for that Theat Ckov
206 // collecting errors for all single Ckov candidates thetas. (Assuming they are independent)
207 // Arguments: iNclus- total number of clusters in chamber for background estimation
208 // Return: best estimation of track Theta ckov
211 Double_t weightThetaCerenkov = 0.;
213 Double_t ckovMin=9999.,ckovMax=0.;
214 Double_t sigma2 = 0; //to collect error squared for this ring
216 for(Int_t i=0;i<fPhotCnt;i++){//candidates loop
217 if(fPhotFlag[i] == 2){
218 if(fPhotCkov[i]<ckovMin) ckovMin=fPhotCkov[i]; //find max and min Theta ckov from all candidates within probable window
219 if(fPhotCkov[i]>ckovMax) ckovMax=fPhotCkov[i];
220 weightThetaCerenkov += fPhotCkov[i]*fPhotWei[i];
221 wei += fPhotWei[i]; //collect weight as sum of all candidate weghts
223 sigma2 += 1./Sigma2(fPhotCkov[i],fPhotPhi[i]);
227 if(sigma2>0) fCkovSigma2=1./sigma2;
228 else fCkovSigma2=1e10;
230 if(wei != 0.) weightThetaCerenkov /= wei; else weightThetaCerenkov = 0.;
231 return weightThetaCerenkov;
233 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
234 Int_t AliHMPIDRecon::FlagPhot(Double_t ckov)
236 // Flag photon candidates if their individual ckov angle is inside the window around ckov angle returned by HoughResponse()
237 // Arguments: ckov- value of most probable ckov angle for track as returned by HoughResponse()
238 // Returns: number of photon candidates happened to be inside the window
240 // Photon Flag: Flag = 0 initial set;
241 // Flag = 1 good candidate (charge compatible with photon);
242 // Flag = 2 photon used for the ring;
244 Int_t steps = (Int_t)((ckov )/ fDTheta); //how many times we need to have fDTheta to fill the distance between 0 and thetaCkovHough
246 Double_t tmin = (Double_t)(steps - 1)*fDTheta;
247 Double_t tmax = (Double_t)(steps)*fDTheta;
248 Double_t tavg = 0.5*(tmin+tmax);
250 tmin = tavg - 0.5*fWindowWidth; tmax = tavg + 0.5*fWindowWidth;
252 Int_t iInsideCnt = 0; //count photons which Theta ckov inside the window
253 for(Int_t i=0;i<fPhotCnt;i++){//photon candidates loop
254 if(fPhotCkov[i] >= tmin && fPhotCkov[i] <= tmax) {
261 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
262 TVector2 AliHMPIDRecon::TracePhot(Double_t ckovThe,Double_t ckovPhi)const
264 // Trace a single Ckov photon from emission point somewhere in radiator up to photocathode taking into account ref indexes of materials it travereses
265 // Arguments: ckovThe,ckovPhi- photon ckov angles in DRS, [rad]
266 // Returns: distance between photon point on PC and track projection
267 TRotation mtheta; mtheta.RotateY(fTrkDir.Theta());
268 TRotation mphi; mphi.RotateZ(fTrkDir.Phi());
269 TRotation mrot=mphi*mtheta;
270 TVector3 dirCkov,dirCkovTors;
272 dirCkovTors.SetMagThetaPhi(1,ckovThe,ckovPhi); //initially photon is directed according to requested ckov angle
273 dirCkov=mrot*dirCkovTors; //now we know photon direction in LORS
274 return TraceForward(dirCkov);
276 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
277 void AliHMPIDRecon::Propagate(const TVector3 dir,TVector3 &pos,Double_t z)const
279 // Finds an intersection point between a line and XY plane shifted along Z.
280 // Arguments: dir,pos - vector along the line and any point of the line
281 // z - z coordinate of plain
283 // On exit: pos is the position if this intesection if any
284 static TVector3 nrm(0,0,1);
287 TVector3 diff=pnt-pos;
288 Double_t sint=(nrm*diff)/(nrm*dir);
291 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
292 void AliHMPIDRecon::Refract(TVector3 &dir,Double_t n1,Double_t n2)const
294 // Refract direction vector according to Snell law
296 // n1 - ref idx of first substance
297 // n2 - ref idx of second substance
299 // On exit: dir is new direction
300 Double_t sinref=(n1/n2)*TMath::Sin(dir.Theta());
301 if(sinref>1.) dir.SetXYZ(-999,-999,-999);
302 else dir.SetTheta(TMath::ASin(sinref));
304 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
305 Double_t AliHMPIDRecon::HoughResponse()
311 Double_t kThetaMax=0.75;
312 Int_t nChannels = (Int_t)(kThetaMax/fDTheta+0.5);
313 TH1D *phots = new TH1D("Rphot" ,"phots" ,nChannels,0,kThetaMax);
314 TH1D *photsw = new TH1D("RphotWeighted" ,"photsw" ,nChannels,0,kThetaMax);
315 TH1D *resultw = new TH1D("resultw","resultw" ,nChannels,0,kThetaMax);
316 Int_t nBin = (Int_t)(kThetaMax/fDTheta);
317 Int_t nCorrBand = (Int_t)(fWindowWidth/(2*fDTheta));
319 for (Int_t i=0; i< fPhotCnt; i++){//photon cadidates loop
320 Double_t angle = fPhotCkov[i]; if(angle<0||angle>kThetaMax) continue;
322 Int_t bin = (Int_t)(0.5+angle/(fDTheta));
325 Double_t lowerlimit = ((Double_t)bin)*fDTheta - 0.5*fDTheta; Double_t upperlimit = ((Double_t)bin)*fDTheta + 0.5*fDTheta;
326 Double_t diffArea = FindRingArea(upperlimit)-FindRingArea(lowerlimit);
327 if(diffArea>0) weight = 1./diffArea;
329 photsw->Fill(angle,weight);
331 }//photon candidates loop
333 for (Int_t i=1; i<=nBin;i++){
334 Int_t bin1= i-nCorrBand;
335 Int_t bin2= i+nCorrBand;
337 if(bin2>nBin)bin2=nBin;
338 Double_t sumPhots=phots->Integral(bin1,bin2);
339 if(sumPhots<3) continue; // if less then 3 photons don't trust to this ring
340 Double_t sumPhotsw=photsw->Integral(bin1,bin2);
341 resultw->Fill((Double_t)((i+0.5)*fDTheta),sumPhotsw);
343 // evaluate the "BEST" theta ckov as the maximum value of histogramm
344 Double_t *pVec = resultw->GetArray();
345 Int_t locMax = TMath::LocMax(nBin,pVec);
346 phots->Delete();photsw->Delete();resultw->Delete(); // Reset and delete objects
348 return (Double_t)(locMax*fDTheta+0.5*fDTheta); //final most probable track theta ckov
350 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
351 Double_t AliHMPIDRecon::Sigma2(Double_t ckovTh, Double_t ckovPh)const
353 // Analithical calculation of total error (as a sum of localization, geometrical and chromatic errors) on Cerenkov angle for a given Cerenkov photon
354 // created by a given MIP. Fromulae according to CERN-EP-2000-058
355 // Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
356 // dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
358 // Returns: absolute error on Cerenkov angle, [radians]
360 TVector3 v(-999,-999,-999);
361 Double_t trkBeta = 1./(TMath::Cos(ckovTh)*fRadNmean);
363 if(trkBeta > 1) trkBeta = 1; //protection against bad measured thetaCer
364 if(trkBeta < 0) trkBeta = 0.0001; //
366 v.SetX(SigLoc (ckovTh,ckovPh,trkBeta));
367 v.SetY(SigGeom(ckovTh,ckovPh,trkBeta));
368 v.SetZ(SigCrom(ckovTh,ckovPh,trkBeta));
372 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
373 Double_t AliHMPIDRecon::SigLoc(Double_t thetaC, Double_t phiC,Double_t betaM)const
375 // Analithical calculation of localization error (due to finite segmentation of PC) on Cerenkov angle for a given Cerenkov photon
376 // created by a given MIP. Fromulae according to CERN-EP-2000-058
377 // Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
378 // dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
380 // Returns: absolute error on Cerenkov angle, [radians]
382 Double_t phiDelta = phiC - fTrkDir.Phi();
384 Double_t sint = TMath::Sin(fTrkDir.Theta());
385 Double_t cost = TMath::Cos(fTrkDir.Theta());
386 Double_t sinf = TMath::Sin(fTrkDir.Phi());
387 Double_t cosf = TMath::Cos(fTrkDir.Phi());
388 Double_t sinfd = TMath::Sin(phiDelta);
389 Double_t cosfd = TMath::Cos(phiDelta);
390 Double_t tantheta = TMath::Tan(thetaC);
392 Double_t alpha =cost-tantheta*cosfd*sint; // formula (11)
393 Double_t k = 1.-fRadNmean*fRadNmean+alpha*alpha/(betaM*betaM); // formula (after 8 in the text)
394 if (k<0) return 1e10;
395 Double_t mu =sint*sinf+tantheta*(cost*cosfd*sinf+sinfd*cosf); // formula (10)
396 Double_t e =sint*cosf+tantheta*(cost*cosfd*cosf-sinfd*sinf); // formula (9)
398 Double_t kk = betaM*TMath::Sqrt(k)/(fgkGapThick*alpha); // formula (6) and (7)
399 Double_t dtdxc = kk*(k*(cosfd*cosf-cost*sinfd*sinf)-(alpha*mu/(betaM*betaM))*sint*sinfd); // formula (6)
400 Double_t dtdyc = kk*(k*(cosfd*sinf+cost*sinfd*cosf)+(alpha* e/(betaM*betaM))*sint*sinfd); // formula (7) pag.4
402 Double_t errX = 0.2,errY=0.25; //end of page 7
403 return TMath::Sqrt(errX*errX*dtdxc*dtdxc + errY*errY*dtdyc*dtdyc);
405 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
406 Double_t AliHMPIDRecon::SigCrom(Double_t thetaC, Double_t phiC,Double_t betaM)const
408 // Analithical calculation of chromatic error (due to lack of knowledge of Cerenkov photon energy) on Cerenkov angle for a given Cerenkov photon
409 // created by a given MIP. Fromulae according to CERN-EP-2000-058
410 // Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
411 // dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
413 // Returns: absolute error on Cerenkov angle, [radians]
415 Double_t phiDelta = phiC - fTrkDir.Phi();
417 Double_t sint = TMath::Sin(fTrkDir.Theta());
418 Double_t cost = TMath::Cos(fTrkDir.Theta());
419 Double_t cosfd = TMath::Cos(phiDelta);
420 Double_t tantheta = TMath::Tan(thetaC);
422 Double_t alpha =cost-tantheta*cosfd*sint; // formula (11)
423 Double_t dtdn = cost*fRadNmean*betaM*betaM/(alpha*tantheta); // formula (12)
425 // Double_t f = 0.00928*(7.75-5.635)/TMath::Sqrt(12.);
426 Double_t f = 0.0172*(7.75-5.635)/TMath::Sqrt(24.);
430 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
431 Double_t AliHMPIDRecon::SigGeom(Double_t thetaC, Double_t phiC,Double_t betaM)const
433 // Analithical calculation of geometric error (due to lack of knowledge of creation point in radiator) on Cerenkov angle for a given Cerenkov photon
434 // created by a given MIP. Formulae according to CERN-EP-2000-058
435 // Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
436 // dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
438 // Returns: absolute error on Cerenkov angle, [radians]
440 Double_t phiDelta = phiC - fTrkDir.Phi();
442 Double_t sint = TMath::Sin(fTrkDir.Theta());
443 Double_t cost = TMath::Cos(fTrkDir.Theta());
444 Double_t sinf = TMath::Sin(fTrkDir.Phi());
445 Double_t cosfd = TMath::Cos(phiDelta);
446 Double_t costheta = TMath::Cos(thetaC);
447 Double_t tantheta = TMath::Tan(thetaC);
449 Double_t alpha =cost-tantheta*cosfd*sint; // formula (11)
451 Double_t k = 1.-fRadNmean*fRadNmean+alpha*alpha/(betaM*betaM); // formula (after 8 in the text)
452 if (k<0) return 1e10;
454 Double_t eTr = 0.5*fgkRadThick*betaM*TMath::Sqrt(k)/(fgkGapThick*alpha); // formula (14)
455 Double_t lambda = 1.-sint*sint*sinf*sinf; // formula (15)
457 Double_t c1 = 1./(1.+ eTr*k/(alpha*alpha*costheta*costheta)); // formula (13.a)
458 Double_t c2 = betaM*TMath::Power(k,1.5)*tantheta*lambda/(fgkGapThick*alpha*alpha); // formula (13.b)
459 Double_t c3 = (1.+eTr*k*betaM*betaM)/((1+eTr)*alpha*alpha); // formula (13.c)
460 Double_t c4 = TMath::Sqrt(k)*tantheta*(1-lambda)/(fgkGapThick*betaM); // formula (13.d)
461 Double_t dtdT = c1 * (c2+c3*c4);
462 Double_t trErr = fgkRadThick/(TMath::Sqrt(12.)*cost);
466 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
470 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
471 Bool_t AliHMPIDRecon::CkovHiddenTrk(AliESDtrack *pTrk,TClonesArray *pCluLst,Double_t nmean)
473 // Pattern recognition method without any infos from tracking:HTA (Hidden Track Algorithm)...
474 // The method finds in the chmber the cluster with the highest charge
475 // compatibile with a MIP, then the strategy is applied
476 // Arguments: pTrk - pointer to ESD track
477 // pCluLs - list of clusters for a given chamber
478 // nmean - mean freon ref. index
479 // Returns: - 0=ok,1=not fitted
481 AliHMPIDParam *pParam=AliHMPIDParam::Instance();
485 if(pCluLst->GetEntriesFast()>100) return kFALSE; //boundary check for CluX,CluY...
486 Float_t mipX=-1,mipY=-1;Int_t mipId=-1,mipQ=-1;
489 for (Int_t iClu=0;iClu<pCluLst->GetEntriesFast();iClu++){ //clusters loop
490 AliHMPIDCluster *pClu=(AliHMPIDCluster*)pCluLst->UncheckedAt(iClu); //get pointer to current cluster
492 fXClu[iClu] = pClu->X();fYClu[iClu] = pClu->Y(); //store x,y for fitting procedure
493 fClCk[iClu] = kTRUE; //all cluster are accepted at this stage to be reconstructed
494 if(pClu->Q()>qRef){ //searching the highest charge to select a MIP
496 mipId=iClu; mipX=pClu->X();mipY=pClu->Y();mipQ=(Int_t)pClu->Q();
500 fNClu = pCluLst->GetEntriesFast();
501 if(qRef>pParam->QCut()){ //charge compartible with MIP clusters
503 fClCk[mipId] = kFALSE;
504 fMipX = mipX; fMipY=mipY; fMipQ = qRef;
505 if(!DoRecHiddenTrk(pCluLst)) {
506 pTrk->SetHMPIDsignal(kNoPhotAccept);
508 } //Do track and ring reconstruction,if problems returns 1
509 pTrk->SetHMPIDtrk(fRadX,fRadY,fThTrkFit,fPhTrkFit); //store track intersection info
510 pTrk->SetHMPIDmip(fMipX,fMipY,(Int_t)fMipQ,fNClu); //store mip info
511 pTrk->SetHMPIDcluIdx(nCh,fIdxMip); //set cham number and index of cluster
512 pTrk->SetHMPIDsignal(fCkovFit); //find best Theta ckov for ring i.e. track
513 pTrk->SetHMPIDchi2(fCkovSig2); //errors squared
514 // Printf(" n clusters tot %i accepted %i",pCluLst->GetEntriesFast(),fNClu);
520 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
521 Bool_t AliHMPIDRecon::DoRecHiddenTrk(TClonesArray *pCluLst)
523 // Pattern recognition method without any infos from tracking...
524 // First a preclustering filter to avoid part of the noise
525 // Then only ellipsed-rings are fitted (no possibility,
526 // for the moment, to reconstruct very inclined tracks)
527 // Finally a fitting with (th,ph) free, starting by very close values
528 // previously evaluated.
532 if(!CluPreFilter(pCluLst)) {return kFALSE;}
533 if(!FitEllipse(phiRec)) {return kFALSE;}
534 Int_t nClTmp1 = pCluLst->GetEntriesFast()-1; //minus MIP...
536 while(nClTmp1 != nClTmp2){
537 SetNClu(pCluLst->GetEntriesFast());
538 if(!FitFree(phiRec)) {return kFALSE;}
540 if(nClTmp2!=nClTmp1) {nClTmp1=nClTmp2;nClTmp2=0;}
545 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
546 Bool_t AliHMPIDRecon::CluPreFilter(TClonesArray *pCluLst)
548 // Filter of bkg clusters
549 // based on elliptical-shapes...
551 if(pCluLst->GetEntriesFast()>50||pCluLst->GetEntriesFast()<4) return kFALSE;
554 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
555 Bool_t AliHMPIDRecon::FitEllipse(Double_t &phiRec)
557 //Fit a set of clusters with an analitical conical section function:
559 // Ax^2 + B*y^2 + 2Hxy + 2Gx + 2Fy + 1 = 0 ---> conical section
561 // H*H - A*B > 0 hyperbola
565 // tan 2alfa = 2H/(A-B) alfa=angle of rotation
567 // coordinate of the centre of the conical section:
578 Double_t cA,cB,cF,cG,cH;
579 Double_t aArg=-1; Int_t iErrFlg; //tmp vars for TMinuit
581 if(!gMinuit) gMinuit = new TMinuit(5); //init MINUIT with this number of parameters (5 params)
582 gMinuit->mncler(); // reset Minuit list of paramters
583 gMinuit->SetObjectFit((TObject*)this); gMinuit->SetFCN(AliHMPIDRecon::FunMinEl); //set fit function
584 gMinuit->mnexcm("SET PRI",&aArg,1,iErrFlg); //suspend all printout from TMinuit
585 gMinuit->mnexcm("SET NOW",&aArg,0,iErrFlg); //suspend all warning printout from TMinuit
590 gMinuit->mnparm(0," A ",1,0.01,0,0,iErrFlg);
591 gMinuit->mnparm(1," B ",1,0.01,0,0,iErrFlg);
592 gMinuit->mnparm(2," H ",1,0.01,0,0,iErrFlg);
593 gMinuit->mnparm(3," G ",1,0.01,0,0,iErrFlg);
594 gMinuit->mnparm(4," F ",1,0.01,0,0,iErrFlg);
596 gMinuit->mnexcm("SIMPLEX",&aArg,0,iErrFlg);
597 gMinuit->mnexcm("MIGRAD" ,&aArg,0,iErrFlg);
598 gMinuit->mnpout(0,sName,cA,d1,d2,d3,iErrFlg);
599 gMinuit->mnpout(1,sName,cB,d1,d2,d3,iErrFlg);
600 gMinuit->mnpout(2,sName,cH,d1,d2,d3,iErrFlg);
601 gMinuit->mnpout(3,sName,cG,d1,d2,d3,iErrFlg);
602 gMinuit->mnpout(4,sName,cF,d1,d2,d3,iErrFlg);
605 Double_t i2 = cA*cB-cH*cH; //quartic invariant : i2 > 0 ellipse, i2 < 0 hyperbola
606 if(i2<=0) return kFALSE;
607 Double_t aX = (cH*cF-cB*cG)/i2; //x centre of the canonical section
608 Double_t bY = (cH*cG-cA*cF)/i2; //y centre of the canonical section
609 Double_t alfa1 = TMath::ATan(2*cH/(cA-cB)); //alpha = angle of rotation of the conical section
610 if(alfa1<0) alfa1+=TMath::Pi();
612 // Double_t alfa2 = alfa1+TMath::Pi();
613 Double_t phiref = TMath::ATan2(bY-fMipY,aX-fMipX); //evaluate in a unique way the angle of rotation comparing it
614 if(phiref<0) phiref+=TMath::TwoPi(); //with the vector that points to the centre from the mip
615 if(i2<0) phiref+=TMath::Pi();
616 if(phiref>TMath::TwoPi()) phiref-=TMath::TwoPi();
618 // Printf(" alfa1 %f",alfa1*TMath::RadToDeg());
619 // Printf(" alfa2 %f",alfa2*TMath::RadToDeg());
620 // Printf(" firef %f",phiref*TMath::RadToDeg());
621 // if(TMath::Abs(alfa1-phiref)<TMath::Abs(alfa2-phiref)) phiRec = alfa1; else phiRec = alfa2;
623 // Printf("FitEllipse: phi reconstructed %f",phiRec*TMath::RadToDeg());
628 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
629 Bool_t AliHMPIDRecon::FitFree(Double_t phiRec)
631 // Fit performed by minimizing RMS/sqrt(n) of the
632 // photons reconstructed. First phi is fixed and theta
633 // is fouond, then (th,ph) of the track
634 // as free parameters
635 // Arguments: PhiRec phi of the track
637 Double_t aArg=-1; Int_t iErrFlg; //tmp vars for TMinuit
638 if(!gMinuit) gMinuit = new TMinuit(2); //init MINUIT with this number of parameters (5 params)
639 gMinuit->mncler(); // reset Minuit list of paramters
640 gMinuit->SetObjectFit((TObject*)this); gMinuit->SetFCN(AliHMPIDRecon::FunMinPhot); //set fit function
641 gMinuit->mnexcm("SET PRI",&aArg,1,iErrFlg); //suspend all printout from TMinuit
642 gMinuit->mnexcm("SET NOW",&aArg,0,iErrFlg); //suspend all warning printout from TMinuit
648 gMinuit->mnparm(0," theta ", 0.01,0.01,0,TMath::PiOver2(),iErrFlg);
649 gMinuit->mnparm(1," phi ",phiRec,0.01,0,TMath::TwoPi() ,iErrFlg);
651 gMinuit->FixParameter(1);
652 gMinuit->mnexcm("SIMPLEX" ,&aArg,0,iErrFlg);
653 gMinuit->mnexcm("MIGRAD" ,&aArg,0,iErrFlg);
655 gMinuit->mnexcm("MIGRAD" ,&aArg,0,iErrFlg);
657 gMinuit->mnpout(0,sName,th,d1,d2,d3,iErrFlg);
658 gMinuit->mnpout(1,sName,ph,d1,d2,d3,iErrFlg);
660 Double_t outPar[2] = {th,ph}; Double_t g; Double_t f;Int_t flag = 3;
661 gMinuit->Eval(2, &g, f, outPar,flag);
667 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
668 Double_t AliHMPIDRecon::FunConSect(Double_t *c,Double_t x,Double_t y)
670 return c[0]*x*x+c[1]*y*y+2*c[2]*x*y+2*c[3]*x+2*c[4]*y+1;
672 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
673 void AliHMPIDRecon::FunMinEl(Int_t &/* */,Double_t* /* */,Double_t &f,Double_t *par,Int_t /* */)
675 AliHMPIDRecon *pRec=(AliHMPIDRecon*)gMinuit->GetObjectFit();
677 Int_t np = pRec->NClu();
678 for(Int_t i=0;i<np;i++) {
679 if(i==pRec->IdxMip()) continue;
680 Double_t el = pRec->FunConSect(par,pRec->XClu(i),pRec->YClu(i));
685 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
686 void AliHMPIDRecon::FunMinPhot(Int_t &/* */,Double_t* /* */,Double_t &f,Double_t *par,Int_t iflag)
688 AliHMPIDRecon *pRec=(AliHMPIDRecon*)gMinuit->GetObjectFit();
689 Double_t sizeCh = 0.5*fgkRadThick+fgkWinThick+fgkGapThick;
690 Double_t thTrk = par[0];
691 Double_t phTrk = par[1];
692 Double_t xrad = pRec->MipX() - sizeCh*TMath::Tan(thTrk)*TMath::Cos(phTrk);
693 Double_t yrad = pRec->MipY() - sizeCh*TMath::Tan(thTrk)*TMath::Sin(phTrk);
694 pRec->SetRadXY(xrad,yrad);
695 pRec->SetTrack(xrad,yrad,thTrk,phTrk);
697 Double_t meanCkov =0;
698 Double_t meanCkov2=0;
699 Double_t thetaCer,phiCer;
701 Int_t nClTot=pRec->NClu();
703 for(Int_t i=0;i<nClTot;i++) {
704 if(!(pRec->ClCk(i))) continue;
705 pRec->FindPhotCkov(pRec->XClu(i),pRec->YClu(i),thetaCer,phiCer);
706 meanCkov += thetaCer;
707 meanCkov2 += thetaCer*thetaCer;
710 if(nClAcc==0) {f=999;return;}
712 Double_t rms = (meanCkov2 - meanCkov*meanCkov*nClAcc)/nClAcc;
713 if(rms<0) Printf(" rms2 = %f, strange!!!",rms);
714 rms = TMath::Sqrt(rms);
715 f = rms/TMath::Sqrt(nClAcc);
719 Printf("FunMinPhot before: photons candidates %i used %i",nClTot,nClAcc);
721 Double_t meanCkov1=0;
722 Double_t meanCkov2=0;
723 for(Int_t i=0;i<nClTot;i++) {
724 if(!(pRec->ClCk(i))) continue;
725 pRec->FindPhotCkov(pRec->XClu(i),pRec->YClu(i),thetaCer,phiCer);
726 if(TMath::Abs(thetaCer-meanCkov)<2*rms) {
727 meanCkov1 += thetaCer;
728 meanCkov2 += thetaCer*thetaCer;
730 } else pRec->SetClCk(i,kFALSE);
733 Double_t rms2 = (meanCkov2 - meanCkov*meanCkov*nClAcc)/nClAcc;
734 Printf("FunMinPhot after: photons candidates %i used %i thetaCer %f",nClTot,nClAcc,meanCkov1);
735 pRec->SetCkovFit(meanCkov1);
736 pRec->SetCkovSig2(rms2);
737 pRec->SetNClu(nClAcc);
740 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
742 // ended Hidden track algorithm....
744 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++