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d3da6dc4 1/**************************************************************************
2 * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
3 * *
4 * Author: The ALICE Off-line Project. *
5 * Contributors are mentioned in the code where appropriate. *
6 * *
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 **************************************************************************/
15
16//////////////////////////////////////////////////////////////////////////
17// //
18// AliHMPIDRecon //
19// //
20// HMPID class to perfom pattern recognition based on Hough transfrom //
21// for single chamber //
22//////////////////////////////////////////////////////////////////////////
23
a591e55f 24#include "AliHMPIDRecon.h" //class header
25#include "AliHMPIDParam.h" //CkovAngle()
d3da6dc4 26#include "AliHMPIDCluster.h" //CkovAngle()
43400d2d 27#include <TMinuit.h> //FitEllipse()
a591e55f 28#include <TRotation.h> //TracePhot()
29#include <TH1D.h> //HoughResponse()
30#include <TClonesArray.h> //CkovAngle()
31#include <AliESDtrack.h> //CkovAngle()
d3da6dc4 32
33const Double_t AliHMPIDRecon::fgkRadThick=1.5;
34const Double_t AliHMPIDRecon::fgkWinThick=0.5;
35const Double_t AliHMPIDRecon::fgkGapThick=8.0;
d3da6dc4 36const Double_t AliHMPIDRecon::fgkWinIdx =1.5787;
37const Double_t AliHMPIDRecon::fgkGapIdx =1.0005;
38
d3da6dc4 39//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
40AliHMPIDRecon::AliHMPIDRecon():TTask("RichRec","RichPat"),
abb5f786 41 fRadNmean(1.292),
d3da6dc4 42 fPhotCnt(-1),
43 fCkovSigma2(0),
44 fIsWEIGHT(kFALSE),
45 fDTheta(0.001),
46 fWindowWidth(0.045),
47 fTrkDir(TVector3(0,0,1)),fTrkPos(TVector2(30,40))
48{
49// main ctor
50 for (Int_t i=0; i<3000; i++) {
51 fPhotFlag[i] = 0;
52 fPhotCkov[i] = -1;
53 fPhotPhi [i] = -1;
54 fPhotWei [i] = 0;
55 }
611e810d 56//hidden algorithm
5b2b2013 57 fMipX=fMipY=fThTrkFit=fPhTrkFit=fCkovFit=fMipQ=fRadX=fRadY=-999;
611e810d 58 fIdxMip=fNClu=0;
5b2b2013 59 for (Int_t i=0; i<100; i++) {
611e810d 60 fXClu[i] = fYClu[i] = 0;
5b2b2013 61 fClCk[i] = kTRUE;
611e810d 62 }
d3da6dc4 63}
64//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
a591e55f 65void AliHMPIDRecon::CkovAngle(AliESDtrack *pTrk,TClonesArray *pCluLst,Double_t nmean)
d3da6dc4 66{
67// Pattern recognition method based on Hough transform
59280a5a 68// Arguments: pTrk - track for which Ckov angle is to be found
69// pCluLst - list of clusters for this chamber
70// Returns: - track ckov angle, [rad],
a591e55f 71
72 AliHMPIDParam *pParam=AliHMPIDParam::Instance();
d3da6dc4 73
a591e55f 74 if(pCluLst->GetEntries()>pParam->MultCut()) fIsWEIGHT = kTRUE; // offset to take into account bkg in reconstruction
75 else fIsWEIGHT = kFALSE;
d3da6dc4 76
611e810d 77 Float_t xRa,yRa,th,ph;
a591e55f 78 pTrk->GetHMPIDtrk(xRa,yRa,th,ph); //initialize this track: th and ph angles at middle of RAD
a591e55f 79 SetTrack(xRa,yRa,th,ph);
611e810d 80
abb5f786 81 fRadNmean=nmean;
d3da6dc4 82
59280a5a 83 Float_t dMin=999,mipX=-1,mipY=-1;Int_t chId=-1,mipId=-1,mipQ=-1;
d3da6dc4 84 fPhotCnt=0;
85 for (Int_t iClu=0; iClu<pCluLst->GetEntriesFast();iClu++){//clusters loop
86 AliHMPIDCluster *pClu=(AliHMPIDCluster*)pCluLst->UncheckedAt(iClu); //get pointer to current cluster
59280a5a 87 chId=pClu->Ch();
a591e55f 88 if(pClu->Q()>pParam->QCut()){ //charge compartible with MIP clusters
89 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
90 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
91 }else{ //charge compatible with photon cluster
92 Double_t thetaCer,phiCer;
93 if(FindPhotCkov(pClu->X(),pClu->Y(),thetaCer,phiCer)){ //find ckov angle for this photon candidate
94 fPhotCkov[fPhotCnt]=thetaCer; //actual theta Cerenkov (in TRS)
b4ad85e9 95 fPhotPhi [fPhotCnt]=phiCer; //actual phi Cerenkov (in TRS): -pi to come back to "unusual" ref system (X,Y,-Z)
a591e55f 96 fPhotCnt++; //increment counter of photon candidates
97 }
59280a5a 98 }
d3da6dc4 99 }//clusters loop
a591e55f 100 Int_t iNacc=FlagPhot(HoughResponse()); //flag photons according to individual theta ckov with respect to most probable
101 pTrk->SetHMPIDmip(mipX,mipY,mipQ,iNacc); //store mip info
59280a5a 102
a591e55f 103 if(mipId==-1) {pTrk->SetHMPIDsignal(kMipQdcCut); return;} //no clusters with QDC more the threshold at all
104 if(dMin>pParam->DistCut()) {pTrk->SetHMPIDsignal(kMipDistCut); return;} //closest cluster with enough charge is still too far from intersection
105 pTrk->SetHMPIDcluIdx(chId,mipId); //set index of cluster
106 if(iNacc<1) pTrk->SetHMPIDsignal(kNoPhotAccept); //no photon candidates is accepted
107 else pTrk->SetHMPIDsignal(FindRingCkov(pCluLst->GetEntries())); //find best Theta ckov for ring i.e. track
611e810d 108
a591e55f 109 pTrk->SetHMPIDchi2(fCkovSigma2); //errors squared
d3da6dc4 110
43400d2d 111}//CkovAngle()
d3da6dc4 112//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
a591e55f 113Bool_t AliHMPIDRecon::FindPhotCkov(Double_t cluX,Double_t cluY,Double_t &thetaCer,Double_t &phiCer)
d3da6dc4 114{
115// Finds Cerenkov angle for this photon candidate
116// Arguments: cluX,cluY - position of cadidate's cluster
a591e55f 117// Returns: Cerenkov angle
d3da6dc4 118
a591e55f 119 TVector3 dirCkov;
120
67a1c24c 121 Double_t zRad= -0.5*fgkRadThick-0.5*fgkWinThick; //z position of middle of RAD
122 TVector3 rad(fTrkPos.X(),fTrkPos.Y(),zRad); //impact point at middle of RAD
123 TVector3 pc(cluX,cluY,0.5*fgkWinThick+fgkGapIdx); //mip at PC
a591e55f 124 Double_t cluR = TMath::Sqrt((cluX-fTrkPos.X())*(cluX-fTrkPos.X())+
125 (cluY-fTrkPos.Y())*(cluY-fTrkPos.Y()));//ref. distance impact RAD-CLUSTER
67a1c24c 126 Double_t phi=(pc-rad).Phi(); //phi of photon
a591e55f 127
b4ad85e9 128 Double_t ckov1=0;
67a1c24c 129 Double_t ckov2=0.75+fTrkDir.Theta(); //start to find theta cerenkov in DRS
b4ad85e9 130 const Double_t kTol=0.01;
d3da6dc4 131 Int_t iIterCnt = 0;
132 while(1){
a591e55f 133 if(iIterCnt>=50) return kFALSE;
d3da6dc4 134 Double_t ckov=0.5*(ckov1+ckov2);
67a1c24c 135 dirCkov.SetMagThetaPhi(1,ckov,phi);
a591e55f 136 TVector2 posC=TraceForward(dirCkov); //trace photon with actual angles
137 Double_t dist=cluR-(posC-fTrkPos).Mod(); //get distance between trial point and cluster position
138 if(posC.X()==-999) dist = - 999; //total reflection problem
139 iIterCnt++; //counter step
b4ad85e9 140 if (dist> kTol) ckov1=ckov; //cluster @ larger ckov
d3da6dc4 141 else if(dist<-kTol) ckov2=ckov; //cluster @ smaller ckov
a591e55f 142 else{ //precision achived: ckov in DRS found
143 dirCkov.SetMagThetaPhi(1,ckov,phi); //
144 RecPhot(dirCkov,thetaCer,phiCer); //find ckov (in TRS:the effective Cherenkov angle!)
145 return kTRUE;
146 }
d3da6dc4 147 }
148}//FindPhotTheta()
149//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
a591e55f 150TVector2 AliHMPIDRecon::TraceForward(TVector3 dirCkov)const
d3da6dc4 151{
a591e55f 152 //Trace forward a photon from (x,y) up to PC
153 // Arguments: dirCkov photon vector in LORS
154 // Returns: pos of traced photon at PC
155 TVector2 pos(-999,-999);
67a1c24c 156 Double_t thetaCer = dirCkov.Theta();
157 if(thetaCer > TMath::ASin(1./fRadNmean)) return pos; //total refraction on WIN-GAP boundary
158 Double_t zRad= -0.5*fgkRadThick-0.5*fgkWinThick; //z position of middle of RAD
159 TVector3 posCkov(fTrkPos.X(),fTrkPos.Y(),zRad); //RAD: photon position is track position @ middle of RAD
160 Propagate(dirCkov,posCkov, -0.5*fgkWinThick); //go to RAD-WIN boundary
161 Refract (dirCkov, fRadNmean,fgkWinIdx); //RAD-WIN refraction
162 Propagate(dirCkov,posCkov, 0.5*fgkWinThick); //go to WIN-GAP boundary
163 Refract (dirCkov, fgkWinIdx,fgkGapIdx); //WIN-GAP refraction
164 Propagate(dirCkov,posCkov,0.5*fgkWinThick+fgkGapThick); //go to PC
a591e55f 165 pos.Set(posCkov.X(),posCkov.Y());
166 return pos;
167}//TraceForward()
168//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
169void AliHMPIDRecon::RecPhot(TVector3 dirCkov,Double_t &thetaCer,Double_t &phiCer)
170{
171 //Theta Cerenkov reconstruction
172 // Arguments: (x,y) of initial point in LORS, dirCkov photon vector in LORS
173 // Returns: thetaCer theta cerenkov reconstructed
174// TVector3 dirTrk;
175// dirTrk.SetMagThetaPhi(1,fTrkDir.Theta(),fTrkDir.Phi());
176// Double_t thetaCer = TMath::ACos(dirCkov*dirTrk);
177 TRotation mtheta; mtheta.RotateY(- fTrkDir.Theta());
178 TRotation mphi; mphi.RotateZ(- fTrkDir.Phi());
179 TRotation mrot=mtheta*mphi;
180 TVector3 dirCkovTRS;
181 dirCkovTRS=mrot*dirCkov;
182 phiCer = dirCkovTRS.Phi(); //actual value of the phi of the photon
183 thetaCer= dirCkovTRS.Theta(); //actual value of thetaCerenkov of the photon
d3da6dc4 184}
185//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
186Double_t AliHMPIDRecon::FindRingArea(Double_t ckovAng)const
187{
188// Find area inside the cerenkov ring which lays inside PCs
a591e55f 189// Arguments: ckovAng - cerenkov angle
d3da6dc4 190// Returns: area of the ring in cm^2 for given theta ckov
191
d3da6dc4 192 const Int_t kN=100;
193 Double_t area=0;
194 for(Int_t i=0;i<kN;i++){
a591e55f 195 TVector2 pos1=TracePhot(ckovAng,Double_t(TMath::TwoPi()*i /kN));//trace this photon
196 TVector2 pos2=TracePhot(ckovAng,Double_t(TMath::TwoPi()*(i+1)/kN));//trace the next photon
197 area+=(pos1-fTrkPos)*(pos2-fTrkPos); //add area of the triangle...
d3da6dc4 198 }
199 return area;
200}//FindRingArea()
201//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
202Double_t AliHMPIDRecon::FindRingCkov(Int_t)
203{
204// 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
205// collecting errors for all single Ckov candidates thetas. (Assuming they are independent)
206// Arguments: iNclus- total number of clusters in chamber for background estimation
207// Return: best estimation of track Theta ckov
208
209 Double_t wei = 0.;
210 Double_t weightThetaCerenkov = 0.;
211
212 Double_t ckovMin=9999.,ckovMax=0.;
213 Double_t sigma2 = 0; //to collect error squared for this ring
214
215 for(Int_t i=0;i<fPhotCnt;i++){//candidates loop
216 if(fPhotFlag[i] == 2){
a591e55f 217 if(fPhotCkov[i]<ckovMin) ckovMin=fPhotCkov[i]; //find max and min Theta ckov from all candidates within probable window
d3da6dc4 218 if(fPhotCkov[i]>ckovMax) ckovMax=fPhotCkov[i];
a591e55f 219 weightThetaCerenkov += fPhotCkov[i]*fPhotWei[i];
220 wei += fPhotWei[i]; //collect weight as sum of all candidate weghts
d3da6dc4 221
d3da6dc4 222 sigma2 += 1./Sigma2(fPhotCkov[i],fPhotPhi[i]);
223 }
224 }//candidates loop
225
226 if(sigma2>0) fCkovSigma2=1./sigma2;
227 else fCkovSigma2=1e10;
228
b4ad85e9 229 if(wei != 0.) weightThetaCerenkov /= wei; else weightThetaCerenkov = 0.;
d3da6dc4 230 return weightThetaCerenkov;
231}//FindCkovRing()
232//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
233Int_t AliHMPIDRecon::FlagPhot(Double_t ckov)
234{
235// Flag photon candidates if their individual ckov angle is inside the window around ckov angle returned by HoughResponse()
236// Arguments: ckov- value of most probable ckov angle for track as returned by HoughResponse()
237// Returns: number of photon candidates happened to be inside the window
238
a591e55f 239// Photon Flag: Flag = 0 initial set;
240// Flag = 1 good candidate (charge compatible with photon);
241// Flag = 2 photon used for the ring;
d3da6dc4 242
243 Int_t steps = (Int_t)((ckov )/ fDTheta); //how many times we need to have fDTheta to fill the distance between 0 and thetaCkovHough
244
245 Double_t tmin = (Double_t)(steps - 1)*fDTheta;
246 Double_t tmax = (Double_t)(steps)*fDTheta;
247 Double_t tavg = 0.5*(tmin+tmax);
248
249 tmin = tavg - 0.5*fWindowWidth; tmax = tavg + 0.5*fWindowWidth;
250
251 Int_t iInsideCnt = 0; //count photons which Theta ckov inside the window
252 for(Int_t i=0;i<fPhotCnt;i++){//photon candidates loop
253 if(fPhotCkov[i] >= tmin && fPhotCkov[i] <= tmax) {
254 fPhotFlag[i]=2;
255 iInsideCnt++;
256 }
257 }
258 return iInsideCnt;
259}//FlagPhot()
260//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
a591e55f 261TVector2 AliHMPIDRecon::TracePhot(Double_t ckovThe,Double_t ckovPhi)const
d3da6dc4 262{
263// Trace a single Ckov photon from emission point somewhere in radiator up to photocathode taking into account ref indexes of materials it travereses
a591e55f 264// Arguments: ckovThe,ckovPhi- photon ckov angles in DRS, [rad]
d3da6dc4 265// Returns: distance between photon point on PC and track projection
266 TRotation mtheta; mtheta.RotateY(fTrkDir.Theta());
267 TRotation mphi; mphi.RotateZ(fTrkDir.Phi());
268 TRotation mrot=mphi*mtheta;
a591e55f 269 TVector3 dirCkov,dirCkovTors;
270
271 dirCkovTors.SetMagThetaPhi(1,ckovThe,ckovPhi); //initially photon is directed according to requested ckov angle
272 dirCkov=mrot*dirCkovTors; //now we know photon direction in LORS
273 return TraceForward(dirCkov);
274}//TracePhot()
d3da6dc4 275//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
a591e55f 276void AliHMPIDRecon::Propagate(const TVector3 dir,TVector3 &pos,Double_t z)const
d3da6dc4 277{
278// Finds an intersection point between a line and XY plane shifted along Z.
279// Arguments: dir,pos - vector along the line and any point of the line
280// z - z coordinate of plain
281// Returns: none
282// On exit: pos is the position if this intesection if any
283 static TVector3 nrm(0,0,1);
284 TVector3 pnt(0,0,z);
285
286 TVector3 diff=pnt-pos;
287 Double_t sint=(nrm*diff)/(nrm*dir);
288 pos+=sint*dir;
289}//Propagate()
290//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
291void AliHMPIDRecon::Refract(TVector3 &dir,Double_t n1,Double_t n2)const
292{
293// Refract direction vector according to Snell law
294// Arguments:
295// n1 - ref idx of first substance
296// n2 - ref idx of second substance
297// Returns: none
298// On exit: dir is new direction
67a1c24c 299 Double_t sinref=(n1/n2)*TMath::Sin(dir.Theta());
d3da6dc4 300 if(sinref>1.) dir.SetXYZ(-999,-999,-999);
67a1c24c 301 else dir.SetTheta(TMath::ASin(sinref));
d3da6dc4 302}//Refract()
303//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
304Double_t AliHMPIDRecon::HoughResponse()
305{
306//
611e810d 307// fIdxMip = mipId;
308
d3da6dc4 309//
310 Double_t kThetaMax=0.75;
311 Int_t nChannels = (Int_t)(kThetaMax/fDTheta+0.5);
312 TH1D *phots = new TH1D("Rphot" ,"phots" ,nChannels,0,kThetaMax);
313 TH1D *photsw = new TH1D("RphotWeighted" ,"photsw" ,nChannels,0,kThetaMax);
314 TH1D *resultw = new TH1D("resultw","resultw" ,nChannels,0,kThetaMax);
315 Int_t nBin = (Int_t)(kThetaMax/fDTheta);
316 Int_t nCorrBand = (Int_t)(fWindowWidth/(2*fDTheta));
317
318 for (Int_t i=0; i< fPhotCnt; i++){//photon cadidates loop
319 Double_t angle = fPhotCkov[i]; if(angle<0||angle>kThetaMax) continue;
320 phots->Fill(angle);
321 Int_t bin = (Int_t)(0.5+angle/(fDTheta));
322 Double_t weight=1.;
323 if(fIsWEIGHT){
324 Double_t lowerlimit = ((Double_t)bin)*fDTheta - 0.5*fDTheta; Double_t upperlimit = ((Double_t)bin)*fDTheta + 0.5*fDTheta;
325 Double_t diffArea = FindRingArea(upperlimit)-FindRingArea(lowerlimit);
326 if(diffArea>0) weight = 1./diffArea;
327 }
328 photsw->Fill(angle,weight);
329 fPhotWei[i]=weight;
330 }//photon candidates loop
331
332 for (Int_t i=1; i<=nBin;i++){
333 Int_t bin1= i-nCorrBand;
334 Int_t bin2= i+nCorrBand;
335 if(bin1<1) bin1=1;
336 if(bin2>nBin)bin2=nBin;
337 Double_t sumPhots=phots->Integral(bin1,bin2);
338 if(sumPhots<3) continue; // if less then 3 photons don't trust to this ring
339 Double_t sumPhotsw=photsw->Integral(bin1,bin2);
340 resultw->Fill((Double_t)((i+0.5)*fDTheta),sumPhotsw);
341 }
342// evaluate the "BEST" theta ckov as the maximum value of histogramm
343 Double_t *pVec = resultw->GetArray();
344 Int_t locMax = TMath::LocMax(nBin,pVec);
345 phots->Delete();photsw->Delete();resultw->Delete(); // Reset and delete objects
346
347 return (Double_t)(locMax*fDTheta+0.5*fDTheta); //final most probable track theta ckov
348}//HoughResponse()
349//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
350Double_t AliHMPIDRecon::Sigma2(Double_t ckovTh, Double_t ckovPh)const
351{
352// Analithical calculation of total error (as a sum of localization, geometrical and chromatic errors) on Cerenkov angle for a given Cerenkov photon
353// created by a given MIP. Fromulae according to CERN-EP-2000-058
354// Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
355// dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
356// MIP beta
357// Returns: absolute error on Cerenkov angle, [radians]
358
359 TVector3 v(-999,-999,-999);
abb5f786 360 Double_t trkBeta = 1./(TMath::Cos(ckovTh)*fRadNmean);
d3da6dc4 361
362 v.SetX(SigLoc (ckovTh,ckovPh,trkBeta));
363 v.SetY(SigGeom(ckovTh,ckovPh,trkBeta));
364 v.SetZ(SigCrom(ckovTh,ckovPh,trkBeta));
365
366 return v.Mag2();
367}
368//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
369Double_t AliHMPIDRecon::SigLoc(Double_t thetaC, Double_t phiC,Double_t betaM)const
370{
371// Analithical calculation of localization error (due to finite segmentation of PC) on Cerenkov angle for a given Cerenkov photon
372// created by a given MIP. Fromulae according to CERN-EP-2000-058
373// Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
374// dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
375// MIP beta
376// Returns: absolute error on Cerenkov angle, [radians]
377 Double_t phiDelta = phiC - fTrkDir.Phi();
378
379 Double_t alpha =TMath::Cos(fTrkDir.Theta())-TMath::Tan(thetaC)*TMath::Cos(phiDelta)*TMath::Sin(fTrkDir.Theta());
abb5f786 380 Double_t k = 1.-fRadNmean*fRadNmean+alpha*alpha/(betaM*betaM);
d3da6dc4 381 if (k<0) return 1e10;
382
383 Double_t mu =TMath::Sin(fTrkDir.Theta())*TMath::Sin(fTrkDir.Phi())+TMath::Tan(thetaC)*(TMath::Cos(fTrkDir.Theta())*TMath::Cos(phiDelta)*TMath::Sin(fTrkDir.Phi())+TMath::Sin(phiDelta)*TMath::Cos(fTrkDir.Phi()));
384 Double_t e =TMath::Sin(fTrkDir.Theta())*TMath::Cos(fTrkDir.Phi())+TMath::Tan(thetaC)*(TMath::Cos(fTrkDir.Theta())*TMath::Cos(phiDelta)*TMath::Cos(fTrkDir.Phi())-TMath::Sin(phiDelta)*TMath::Sin(fTrkDir.Phi()));
385
386 Double_t kk = betaM*TMath::Sqrt(k)/(8*alpha);
387 Double_t dtdxc = kk*(k*(TMath::Cos(phiDelta)*TMath::Cos(fTrkDir.Phi())-TMath::Cos(fTrkDir.Theta())*TMath::Sin(phiDelta)*TMath::Sin(fTrkDir.Phi()))-(alpha*mu/(betaM*betaM))*TMath::Sin(fTrkDir.Theta())*TMath::Sin(phiDelta));
388 Double_t dtdyc = kk*(k*(TMath::Cos(phiDelta)*TMath::Sin(fTrkDir.Phi())+TMath::Cos(fTrkDir.Theta())*TMath::Sin(phiDelta)*TMath::Cos(fTrkDir.Phi()))+(alpha* e/(betaM*betaM))*TMath::Sin(fTrkDir.Theta())*TMath::Sin(phiDelta));
389
390 return TMath::Sqrt(0.2*0.2*dtdxc*dtdxc + 0.25*0.25*dtdyc*dtdyc);
391}
392//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
393Double_t AliHMPIDRecon::SigCrom(Double_t thetaC, Double_t phiC,Double_t betaM)const
394{
395// Analithical calculation of chromatic error (due to lack of knowledge of Cerenkov photon energy) on Cerenkov angle for a given Cerenkov photon
396// created by a given MIP. Fromulae according to CERN-EP-2000-058
397// Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
398// dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
399// MIP beta
400// Returns: absolute error on Cerenkov angle, [radians]
401 Double_t phiDelta = phiC - fTrkDir.Phi();
402 Double_t alpha =TMath::Cos(fTrkDir.Theta())-TMath::Tan(thetaC)*TMath::Cos(phiDelta)*TMath::Sin(fTrkDir.Theta());
403
abb5f786 404 Double_t dtdn = TMath::Cos(fTrkDir.Theta())*fRadNmean*betaM*betaM/(alpha*TMath::Tan(thetaC));
d3da6dc4 405
406 Double_t f = 0.00928*(7.75-5.635)/TMath::Sqrt(12.);
407
408 return f*dtdn;
409}//SigCrom()
410//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
411Double_t AliHMPIDRecon::SigGeom(Double_t thetaC, Double_t phiC,Double_t betaM)const
412{
413// Analithical calculation of geometric error (due to lack of knowledge of creation point in radiator) on Cerenkov angle for a given Cerenkov photon
414// created by a given MIP. Formulae according to CERN-EP-2000-058
415// Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
416// dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
417// MIP beta
418// Returns: absolute error on Cerenkov angle, [radians]
419
420 Double_t phiDelta = phiC - fTrkDir.Phi();
421 Double_t alpha =TMath::Cos(fTrkDir.Theta())-TMath::Tan(thetaC)*TMath::Cos(phiDelta)*TMath::Sin(fTrkDir.Theta());
422
abb5f786 423 Double_t k = 1.-fRadNmean*fRadNmean+alpha*alpha/(betaM*betaM);
d3da6dc4 424 if (k<0) return 1e10;
425
426 Double_t eTr = 0.5*1.5*betaM*TMath::Sqrt(k)/(8*alpha);
427 Double_t lambda = 1.-TMath::Sin(fTrkDir.Theta())*TMath::Sin(fTrkDir.Theta())*TMath::Sin(phiC)*TMath::Sin(phiC);
428
429 Double_t c = 1./(1.+ eTr*k/(alpha*alpha*TMath::Cos(thetaC)*TMath::Cos(thetaC)));
430 Double_t i = betaM*TMath::Tan(thetaC)*lambda*TMath::Power(k,1.5);
431 Double_t ii = 1.+eTr*betaM*i;
432
433 Double_t err = c * (i/(alpha*alpha*8) + ii*(1.-lambda) / ( alpha*alpha*8*betaM*(1.+eTr)) );
434 Double_t trErr = 1.5/(TMath::Sqrt(12.)*TMath::Cos(fTrkDir.Theta()));
435
436 return trErr*err;
437}//SigGeom()
438//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
43400d2d 439//
611e810d 440// From here HTA....
43400d2d 441//
442//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
5b2b2013 443Bool_t AliHMPIDRecon::CkovHiddenTrk(AliESDtrack *pTrk,TClonesArray *pCluLst,Double_t nmean)
43400d2d 444{
611e810d 445// Pattern recognition method without any infos from tracking:HTA (Hidden Track Algorithm)...
43400d2d 446// The method finds in the chmber the cluster with the highest charge
447// compatibile with a MIP, then the strategy is applied
611e810d 448// Arguments: pTrk - pointer to ESD track
449// pCluLs - list of clusters for a given chamber
450// nmean - mean freon ref. index
451// Returns: - 0=ok,1=not fitted
452
453 AliHMPIDParam *pParam=AliHMPIDParam::Instance();
43400d2d 454
455 fRadNmean=nmean;
456
457 Float_t mipX=-1,mipY=-1;Int_t mipId=-1,mipQ=-1;
43400d2d 458 Double_t qRef = 0;
5b2b2013 459 for (Int_t iClu=0;iClu<pCluLst->GetEntriesFast();iClu++){ //clusters loop
43400d2d 460 AliHMPIDCluster *pClu=(AliHMPIDCluster*)pCluLst->UncheckedAt(iClu); //get pointer to current cluster
461 fXClu[iClu] = pClu->X();fYClu[iClu] = pClu->Y(); //store x,y for fitting procedure
5b2b2013 462 fClCk[iClu] = kTRUE; //all cluster are accepted at this stage to be reconstructed
43400d2d 463 if(pClu->Q()>qRef){ //searching the highest charge to select a MIP
464 qRef = pClu->Q();
465 mipId=iClu; mipX=pClu->X();mipY=pClu->Y();mipQ=(Int_t)pClu->Q();
466 }
467 }//clusters loop
43400d2d 468
5b2b2013 469 fNClu = pCluLst->GetEntriesFast();
470 if(qRef>pParam->QCut()){ //charge compartible with MIP clusters
611e810d 471 fIdxMip = mipId;
5b2b2013 472 fClCk[mipId] = kFALSE;
611e810d 473 fMipX = mipX; fMipY=mipY; fMipQ = qRef;
5b2b2013 474 if(!DoRecHiddenTrk(pCluLst)) return kFALSE; //Do track and ring reconstruction,if problems returns 1
611e810d 475 pTrk->SetHMPIDtrk(fRadX,fRadY,fThTrkFit,fPhTrkFit); //store track intersection info
476 pTrk->SetHMPIDmip(fMipX,fMipY,(Int_t)fMipQ,fNClu); //store mip info
5b2b2013 477 pTrk->SetHMPIDcluIdx(pCluLst->GetEntriesFast(),fIdxMip); //set cham number and index of cluster
611e810d 478 pTrk->SetHMPIDsignal(fCkovFit); //find best Theta ckov for ring i.e. track
5b2b2013 479 Printf(" n clusters tot %i accepted %i",pCluLst->GetEntriesFast(),fNClu);
480 return kTRUE;
611e810d 481 }
5b2b2013 482 return kFALSE;
43400d2d 483}//CkovHiddenTrk()
484//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
5b2b2013 485Bool_t AliHMPIDRecon::DoRecHiddenTrk(TClonesArray *pCluLst)
43400d2d 486{
487// Pattern recognition method without any infos from tracking...
611e810d 488// First a preclustering filter to avoid part of the noise
43400d2d 489// Then only ellipsed-rings are fitted (no possibility,
611e810d 490// for the moment, to reconstruct very inclined tracks)
491// Finally a fitting with (th,ph) free, starting by very close values
43400d2d 492// previously evaluated.
493// Arguments: none
494// Returns: none
495 Double_t phiRec;
5b2b2013 496 if(!CluPreFilter(pCluLst)) {return kFALSE;}
611e810d 497 if(!FitEllipse(phiRec)) {return kFALSE;}
5b2b2013 498 Int_t nClTmp1 = pCluLst->GetEntriesFast()-1; //minus MIP...
499 Int_t nClTmp2 = 0;
500 while(nClTmp1 != nClTmp2){
501 SetNClu(pCluLst->GetEntriesFast());
502 if(!FitFree(phiRec)) {return kFALSE;}
503 nClTmp2 = NClu();
504 if(nClTmp2!=nClTmp1) {nClTmp1=nClTmp2;nClTmp2=0;}
505 }
506 fNClu = nClTmp2;
507 return kTRUE;
508}//DoRecHiddenTrk()
43400d2d 509//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
5b2b2013 510Bool_t AliHMPIDRecon::CluPreFilter(TClonesArray *pCluLst)
43400d2d 511{
512// Filter of bkg clusters
513// based on elliptical-shapes...
514//
5b2b2013 515 if(pCluLst->GetEntriesFast()>50||pCluLst->GetEntriesFast()<4) return kFALSE;
516 else return kTRUE;
43400d2d 517}
518//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
519Bool_t AliHMPIDRecon::FitEllipse(Double_t &phiRec)
520{
521//Fit a set of clusters with an analitical conical section function:
522 //
523 // Ax^2 + B*y^2 + 2Hxy + 2Gx + 2Fy + 1 = 0 ---> conical section
524 //
525 // H*H - A*B > 0 hyperbola
526 // < 0 ellipse
527 // = 0 parabola
528 //
529 // tan 2alfa = 2H/(A-B) alfa=angle of rotation
530 //
531 // coordinate of the centre of the conical section:
532 // x = x' + a
533 // y = y' + b
534 //
535 // HF - BG
536 // a = ---------
537 // AB - H^2
538 //
539 // HG - AF
540 // b = --------
541 // AB - H^2
43400d2d 542 Double_t cA,cB,cF,cG,cH;
611e810d 543 Double_t aArg=-1; Int_t iErrFlg; //tmp vars for TMinuit
43400d2d 544
611e810d 545 if(!gMinuit) gMinuit = new TMinuit(5); //init MINUIT with this number of parameters (5 params)
43400d2d 546 gMinuit->mncler(); // reset Minuit list of paramters
547 gMinuit->SetObjectFit((TObject*)this); gMinuit->SetFCN(AliHMPIDRecon::FunMinEl); //set fit function
548 gMinuit->mnexcm("SET PRI",&aArg,1,iErrFlg); //suspend all printout from TMinuit
549 gMinuit->mnexcm("SET NOW",&aArg,0,iErrFlg); //suspend all warning printout from TMinuit
550
551 Double_t d1,d2,d3;
552 TString sName;
553
611e810d 554 gMinuit->mnparm(0," A ",1,0.01,0,0,iErrFlg);
555 gMinuit->mnparm(1," B ",1,0.01,0,0,iErrFlg);
556 gMinuit->mnparm(2," H ",1,0.01,0,0,iErrFlg);
557 gMinuit->mnparm(3," G ",1,0.01,0,0,iErrFlg);
558 gMinuit->mnparm(4," F ",1,0.01,0,0,iErrFlg);
43400d2d 559
560 gMinuit->mnexcm("SIMPLEX" ,&aArg,0,iErrFlg);
561 gMinuit->mnexcm("MIGRAD" ,&aArg,0,iErrFlg);
562 gMinuit->mnpout(0,sName,cA,d1,d2,d3,iErrFlg);
563 gMinuit->mnpout(1,sName,cB,d1,d2,d3,iErrFlg);
564 gMinuit->mnpout(2,sName,cH,d1,d2,d3,iErrFlg);
565 gMinuit->mnpout(3,sName,cG,d1,d2,d3,iErrFlg);
566 gMinuit->mnpout(4,sName,cF,d1,d2,d3,iErrFlg);
567 delete gMinuit;
568
569 Double_t i2 = cA*cB-cH*cH; //quartic invariant : i2 > 0 ellipse, i2 < 0 hyperbola
096ddc3f 570 if(i2<=0) return kFALSE;
43400d2d 571 Double_t aX = (cH*cF-cB*cG)/i2; //x centre of the canonical section
572 Double_t bY = (cH*cG-cA*cF)/i2; //y centre of the canonical section
573 Double_t alfa1 = TMath::ATan(2*cH/(cA-cB)); //alpha = angle of rotation of the conical section
574 if(alfa1<0) alfa1+=TMath::Pi();
575 alfa1*=0.5;
576 Double_t alfa2 = alfa1+TMath::Pi();
577 Double_t phiref = TMath::ATan2(bY-fMipY,aX-fMipX); //evaluate in a unique way the angle of rotation comapring it
578 if(phiref<0) phiref+=TMath::TwoPi(); //with the vector that poinst to the centre from the mip
579 if(i2<0) phiref+=TMath::Pi();
580 if(phiref>TMath::TwoPi()) phiref-=TMath::TwoPi();
581
582// Printf(" alfa1 %f",alfa1*TMath::RadToDeg());
583// Printf(" alfa2 %f",alfa2*TMath::RadToDeg());
584// Printf(" firef %f",phiref*TMath::RadToDeg());
585 if(TMath::Abs(alfa1-phiref)<TMath::Abs(alfa2-phiref)) phiRec = alfa1; else phiRec = alfa2;
586
587// cout << " phi reconstructed " << phiRec*TMath::RadToDeg() << endl;
096ddc3f 588 return kTRUE;
43400d2d 589//
590}
591//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
611e810d 592Bool_t AliHMPIDRecon::FitFree(Double_t phiRec)
43400d2d 593{
594// Fit performed by minimizing RMS/sqrt(n) of the
595// photons reconstructed. First phi is fixed and theta
596// is fouond, then (th,ph) of the track
597// as free parameters
598// Arguments: PhiRec phi of the track
599// Returns: none
611e810d 600 Double_t aArg=-1; Int_t iErrFlg; //tmp vars for TMinuit
601 if(!gMinuit) gMinuit = new TMinuit(2); //init MINUIT with this number of parameters (5 params)
43400d2d 602 gMinuit->mncler(); // reset Minuit list of paramters
603 gMinuit->SetObjectFit((TObject*)this); gMinuit->SetFCN(AliHMPIDRecon::FunMinPhot); //set fit function
604 gMinuit->mnexcm("SET PRI",&aArg,1,iErrFlg); //suspend all printout from TMinuit
605 gMinuit->mnexcm("SET NOW",&aArg,0,iErrFlg); //suspend all warning printout from TMinuit
606
607 Double_t d1,d2,d3;
608 TString sName;
609 Double_t th,ph;
610
611e810d 611 gMinuit->mnparm(0," theta ", 0.01,0.01,0,TMath::PiOver2(),iErrFlg);
612 gMinuit->mnparm(1," phi ",phiRec,0.01,0,TMath::TwoPi() ,iErrFlg);
43400d2d 613
614 gMinuit->FixParameter(1);
615 gMinuit->mnexcm("SIMPLEX" ,&aArg,0,iErrFlg);
616 gMinuit->mnexcm("MIGRAD" ,&aArg,0,iErrFlg);
617 gMinuit->Release(1);
618 gMinuit->mnexcm("MIGRAD" ,&aArg,0,iErrFlg);
619
620 gMinuit->mnpout(0,sName,th,d1,d2,d3,iErrFlg);
621 gMinuit->mnpout(1,sName,ph,d1,d2,d3,iErrFlg);
611e810d 622
623 Double_t outPar[2] = {th,ph}; Double_t g; Double_t f;Int_t flag = 3;
624 gMinuit->Eval(2, &g, f, outPar,flag);
625
626 SetTrkFit(th,ph);
43400d2d 627
611e810d 628 return kTRUE;
43400d2d 629}
630//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
631Double_t AliHMPIDRecon::FunConSect(Double_t *c,Double_t x,Double_t y)
632{
633 return c[0]*x*x+c[1]*y*y+2*c[2]*x*y+2*c[3]*x+2*c[4]*y+1;
634}
635//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
636void AliHMPIDRecon::FunMinEl(Int_t &/* */,Double_t* /* */,Double_t &f,Double_t *par,Int_t /* */)
637{
638 AliHMPIDRecon *pRec=(AliHMPIDRecon*)gMinuit->GetObjectFit();
639 Double_t minFun = 0;
640 Int_t np = pRec->NClu();
641 for(Int_t i=0;i<np;i++) {
642 if(i==pRec->IdxMip()) continue;
643 Double_t el = pRec->FunConSect(par,pRec->XClu(i),pRec->YClu(i));
644 minFun +=el*el;
645 }
646 f = minFun;
647}
648//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
611e810d 649void AliHMPIDRecon::FunMinPhot(Int_t &/* */,Double_t* /* */,Double_t &f,Double_t *par,Int_t iflag)
43400d2d 650{
651 AliHMPIDRecon *pRec=(AliHMPIDRecon*)gMinuit->GetObjectFit();
611e810d 652 Double_t sizeCh = 0.5*fgkRadThick+fgkWinThick+fgkGapThick;
43400d2d 653 Double_t thTrk = par[0];
654 Double_t phTrk = par[1];
655 Double_t xrad = pRec->MipX() - sizeCh*TMath::Tan(thTrk)*TMath::Cos(phTrk);
656 Double_t yrad = pRec->MipY() - sizeCh*TMath::Tan(thTrk)*TMath::Sin(phTrk);
611e810d 657 pRec->SetRadXY(xrad,yrad);
43400d2d 658 pRec->SetTrack(xrad,yrad,thTrk,phTrk);
659
5b2b2013 660 Double_t meanCkov =0;
43400d2d 661 Double_t meanCkov2=0;
662 Double_t thetaCer,phiCer;
5b2b2013 663 Int_t nClAcc = 0;
664 Int_t nClTot=pRec->NClu();
665
666 for(Int_t i=0;i<nClTot;i++) {
667 if(!(pRec->ClCk(i))) continue;
43400d2d 668 pRec->FindPhotCkov(pRec->XClu(i),pRec->YClu(i),thetaCer,phiCer);
43400d2d 669 meanCkov += thetaCer;
670 meanCkov2 += thetaCer*thetaCer;
5b2b2013 671 nClAcc++;
43400d2d 672 }
096ddc3f 673 if(nClAcc==0) {f=999;return;}
5b2b2013 674 meanCkov/=nClAcc;
096ddc3f 675 Double_t rms = (meanCkov2 - meanCkov*meanCkov*nClAcc)/nClAcc;
676 if(rms<0) Printf(" rms2 = %f, strange!!!",rms);
677 rms = TMath::Sqrt(rms);
5b2b2013 678 f = rms/TMath::Sqrt(nClAcc);
611e810d 679
5b2b2013 680
681 if(iflag==3) {
682 Printf("FunMinPhot before: photons candidates %i used %i",nClTot,nClAcc);
683 nClAcc = 0;
684 Double_t meanCkov1=0;
685 for(Int_t i=0;i<nClTot;i++) {
686 if(!(pRec->ClCk(i))) continue;
687 pRec->FindPhotCkov(pRec->XClu(i),pRec->YClu(i),thetaCer,phiCer);
688 if(TMath::Abs(thetaCer-meanCkov)<2*rms) {
689 meanCkov1 += thetaCer;
690 nClAcc++;
691 } else pRec->SetClCk(i,kFALSE);
692 }
693 meanCkov1/=nClAcc;
694 Printf("FunMinPhot after: photons candidates %i used %i thetaCer %f",nClTot,nClAcc,meanCkov1);
695 pRec->SetCkovFit(meanCkov1);
696 pRec->SetNClu(nClAcc);
697 }
43400d2d 698}//FunMinPhot()
611e810d 699//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
700//
701// ended Hidden track algorithm....
702//
703//++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++