Getting the trigger descriptors from CDB
[u/mrichter/AliRoot.git] / HMPID / AliHMPIDRecon.cxx
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15
16 //////////////////////////////////////////////////////////////////////////
17 //                                                                      //
18 // AliHMPIDRecon                                                         //
19 //                                                                      //
20 // HMPID class to perfom pattern recognition based on Hough transfrom    //
21 // for single chamber                                                   //
22 //////////////////////////////////////////////////////////////////////////
23
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()
32
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;
38
39 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
40 AliHMPIDRecon::AliHMPIDRecon():TTask("RichRec","RichPat"),
41   fRadNmean(1.292),  
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   }
56 //hidden algorithm
57   fMipX=fMipY=fThTrkFit=fPhTrkFit=fCkovFit=fMipQ=fRadX=fRadY=-999;
58   fIdxMip=fNClu=0;
59   fCkovSig2=0;
60   for (Int_t i=0; i<100; i++) {
61     fXClu[i] = fYClu[i] = 0;
62     fClCk[i] = kTRUE;
63   }
64 }
65 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
66 void AliHMPIDRecon::CkovAngle(AliESDtrack *pTrk,TClonesArray *pCluLst,Double_t nmean)
67 {
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], 
72     
73   AliHMPIDParam *pParam=AliHMPIDParam::Instance();
74   
75   if(pCluLst->GetEntries()>pParam->MultCut()) fIsWEIGHT = kTRUE; // offset to take into account bkg in reconstruction
76   else                                        fIsWEIGHT = kFALSE;
77
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);
81
82   fRadNmean=nmean;
83
84   Float_t dMin=999,mipX=-1,mipY=-1;Int_t chId=-1,mipId=-1,mipQ=-1;                                                                           
85   fPhotCnt=0;                                                      
86   for (Int_t iClu=0; iClu<pCluLst->GetEntriesFast();iClu++){//clusters loop
87     AliHMPIDCluster *pClu=(AliHMPIDCluster*)pCluLst->UncheckedAt(iClu);                       //get pointer to current cluster    
88     chId=pClu->Ch();
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
98       }
99     }
100   }//clusters loop
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 
103
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
109
110   pTrk->SetHMPIDchi2(fCkovSigma2);                                                            //errors squared 
111
112 }//CkovAngle()
113 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
114 Bool_t AliHMPIDRecon::FindPhotCkov(Double_t cluX,Double_t cluY,Double_t &thetaCer,Double_t &phiCer)
115 {
116 // Finds Cerenkov angle  for this photon candidate
117 // Arguments: cluX,cluY - position of cadidate's cluster  
118 // Returns: Cerenkov angle 
119
120   TVector3 dirCkov;
121   
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
128     
129   Double_t ckov1=0;
130   Double_t ckov2=0.75+fTrkDir.Theta();                        //start to find theta cerenkov in DRS
131   const Double_t kTol=0.01;
132   Int_t iIterCnt = 0;
133   while(1){
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!)
146       return kTRUE;
147     }
148   }
149 }//FindPhotTheta()
150 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
151 TVector2 AliHMPIDRecon::TraceForward(TVector3 dirCkov)const
152 {
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());
167   return pos;
168 }//TraceForward()
169 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
170 void AliHMPIDRecon::RecPhot(TVector3 dirCkov,Double_t &thetaCer,Double_t &phiCer)
171 {
172   //Theta Cerenkov reconstruction 
173   // Arguments: (x,y) of initial point in LORS, dirCkov photon vector in LORS
174   //   Returns: thetaCer theta cerenkov reconstructed
175 //  TVector3 dirTrk;
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;
181   TVector3 dirCkovTRS;
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
185 }
186 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
187 Double_t AliHMPIDRecon::FindRingArea(Double_t ckovAng)const
188 {
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
192    
193   const Int_t kN=100;
194   Double_t area=0;
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... 
199   }
200   return area;
201 }//FindRingArea()
202 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
203 Double_t AliHMPIDRecon::FindRingCkov(Int_t)
204 {
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
209
210   Double_t wei = 0.;
211   Double_t weightThetaCerenkov = 0.;
212
213   Double_t ckovMin=9999.,ckovMax=0.;
214   Double_t sigma2 = 0;   //to collect error squared for this ring
215   
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   
222       
223       sigma2 += 1./Sigma2(fPhotCkov[i],fPhotPhi[i]);
224     }
225   }//candidates loop
226   
227   if(sigma2>0) fCkovSigma2=1./sigma2;
228   else         fCkovSigma2=1e10;  
229   
230   if(wei != 0.) weightThetaCerenkov /= wei; else weightThetaCerenkov = 0.;
231   return weightThetaCerenkov;
232 }//FindCkovRing()
233 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
234 Int_t AliHMPIDRecon::FlagPhot(Double_t ckov)
235 {
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
239
240 // Photon Flag:  Flag = 0 initial set; 
241 //               Flag = 1 good candidate (charge compatible with photon); 
242 //               Flag = 2 photon used for the ring;
243   
244   Int_t steps = (Int_t)((ckov )/ fDTheta); //how many times we need to have fDTheta to fill the distance between 0  and thetaCkovHough
245
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);
249
250   tmin = tavg - 0.5*fWindowWidth;  tmax = tavg + 0.5*fWindowWidth;
251
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)    { 
255       fPhotFlag[i]=2;     
256       iInsideCnt++;
257     }
258   }
259   return iInsideCnt;
260 }//FlagPhot()
261 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
262 TVector2 AliHMPIDRecon::TracePhot(Double_t ckovThe,Double_t ckovPhi)const
263 {
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;   
271
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);
275 }//TracePhot()
276 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
277 void AliHMPIDRecon::Propagate(const TVector3 dir,TVector3 &pos,Double_t z)const
278 {
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 
282 //   Returns:  none
283 //   On exit:  pos is the position if this intesection if any
284   static TVector3 nrm(0,0,1); 
285          TVector3 pnt(0,0,z);
286   
287   TVector3 diff=pnt-pos;
288   Double_t sint=(nrm*diff)/(nrm*dir);
289   pos+=sint*dir;
290 }//Propagate()
291 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
292 void AliHMPIDRecon::Refract(TVector3 &dir,Double_t n1,Double_t n2)const
293 {
294 // Refract direction vector according to Snell law
295 // Arguments: 
296 //            n1 - ref idx of first substance
297 //            n2 - ref idx of second substance
298 //   Returns: none
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));
303 }//Refract()
304 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
305 Double_t AliHMPIDRecon::HoughResponse()
306 {
307 //
308 //    fIdxMip = mipId;
309
310 //       
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));
318   
319   for (Int_t i=0; i< fPhotCnt; i++){//photon cadidates loop
320     Double_t angle = fPhotCkov[i];  if(angle<0||angle>kThetaMax) continue;
321     phots->Fill(angle);
322     Int_t bin = (Int_t)(0.5+angle/(fDTheta));
323     Double_t weight=1.;
324     if(fIsWEIGHT){
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;
328     }
329     photsw->Fill(angle,weight);
330     fPhotWei[i]=weight;
331   }//photon candidates loop 
332    
333   for (Int_t i=1; i<=nBin;i++){
334     Int_t bin1= i-nCorrBand;
335     Int_t bin2= i+nCorrBand;
336     if(bin1<1) bin1=1;
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);
342   } 
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   delete phots;delete photsw;delete resultw; // Reset and delete objects
347   
348   return (Double_t)(locMax*fDTheta+0.5*fDTheta); //final most probable track theta ckov   
349 }//HoughResponse()
350 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
351 Double_t AliHMPIDRecon::Sigma2(Double_t ckovTh, Double_t ckovPh)const
352 {
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]        
357 //            MIP beta
358 //   Returns: absolute error on Cerenkov angle, [radians]    
359   
360   TVector3 v(-999,-999,-999);
361   Double_t trkBeta = 1./(TMath::Cos(ckovTh)*fRadNmean);
362   
363   if(trkBeta > 1) trkBeta = 1;                 //protection against bad measured thetaCer  
364   if(trkBeta < 0) trkBeta = 0.0001;            //
365
366   v.SetX(SigLoc (ckovTh,ckovPh,trkBeta));
367   v.SetY(SigGeom(ckovTh,ckovPh,trkBeta));
368   v.SetZ(SigCrom(ckovTh,ckovPh,trkBeta));
369
370   return v.Mag2();
371 }
372 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
373 Double_t AliHMPIDRecon::SigLoc(Double_t thetaC, Double_t phiC,Double_t betaM)const
374 {
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]        
379 //            MIP beta
380 //   Returns: absolute error on Cerenkov angle, [radians]    
381   
382   Double_t phiDelta = phiC - fTrkDir.Phi();
383
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);
391   
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)
397
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
401
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);
404 }
405 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
406 Double_t AliHMPIDRecon::SigCrom(Double_t thetaC, Double_t phiC,Double_t betaM)const
407 {
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]        
412 //            MIP beta
413 //   Returns: absolute error on Cerenkov angle, [radians]    
414   
415   Double_t phiDelta = phiC - fTrkDir.Phi();
416
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);
421   
422   Double_t alpha =cost-tantheta*cosfd*sint;                                                 // formula (11)
423   Double_t dtdn = cost*fRadNmean*betaM*betaM/(alpha*tantheta);                              // formula (12)
424             
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.);
427
428   return f*dtdn;
429 }//SigCrom()
430 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
431 Double_t AliHMPIDRecon::SigGeom(Double_t thetaC, Double_t phiC,Double_t betaM)const
432 {
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]        
437 //            MIP beta
438 //   Returns: absolute error on Cerenkov angle, [radians]    
439
440   Double_t phiDelta = phiC - fTrkDir.Phi();
441
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);
448   
449   Double_t alpha =cost-tantheta*cosfd*sint;                                                  // formula (11)
450   
451   Double_t k = 1.-fRadNmean*fRadNmean+alpha*alpha/(betaM*betaM);                             // formula (after 8 in the text)
452   if (k<0) return 1e10;
453
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)
456
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);
463
464   return trErr*dtdT;
465 }//SigGeom()
466 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
467 //
468 // From here HTA....
469 //
470 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
471 Bool_t AliHMPIDRecon::CkovHiddenTrk(AliESDtrack *pTrk,TClonesArray *pCluLst,Double_t nmean)
472 {
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 
480   
481   AliHMPIDParam *pParam=AliHMPIDParam::Instance();
482     
483   fRadNmean=nmean;
484
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;                                                                           
487   Double_t qRef = 0;
488   Int_t nCh=0;
489   for (Int_t iClu=0;iClu<pCluLst->GetEntriesFast();iClu++){                                   //clusters loop
490     AliHMPIDCluster *pClu=(AliHMPIDCluster*)pCluLst->UncheckedAt(iClu);                       //get pointer to current cluster    
491     nCh = pClu->Ch();
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      
495       qRef = pClu->Q();
496       mipId=iClu; mipX=pClu->X();mipY=pClu->Y();mipQ=(Int_t)pClu->Q();
497     }                                                                                    
498   }//clusters loop
499
500   fNClu = pCluLst->GetEntriesFast();
501   if(qRef>pParam->QCut()){                                                                     //charge compartible with MIP clusters
502     fIdxMip = mipId;
503     fClCk[mipId] = kFALSE;
504     fMipX = mipX; fMipY=mipY; fMipQ = qRef;
505     if(!DoRecHiddenTrk(pCluLst)) {
506       pTrk->SetHMPIDsignal(kNoPhotAccept);
507       return kFALSE;
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);
515     return kTRUE;
516   }
517   
518   return kFALSE;
519 }//CkovHiddenTrk()
520 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
521 Bool_t AliHMPIDRecon::DoRecHiddenTrk(TClonesArray *pCluLst)
522 {
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.
529 // Arguments:   none
530 //   Returns:   none
531   Double_t phiRec;
532   if(!CluPreFilter(pCluLst)) {return kFALSE;}
533   if(!FitEllipse(phiRec)) {return kFALSE;}
534   Int_t nClTmp1 = pCluLst->GetEntriesFast()-1;  //minus MIP...
535   Int_t nClTmp2 = 0;
536   while(nClTmp1 != nClTmp2){
537     SetNClu(pCluLst->GetEntriesFast());
538     if(!FitFree(phiRec)) {return kFALSE;}
539     nClTmp2 = NClu();
540     if(nClTmp2!=nClTmp1) {nClTmp1=nClTmp2;nClTmp2=0;}
541   }
542   fNClu = nClTmp2;
543   return kTRUE;
544 }//DoRecHiddenTrk()
545 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
546 Bool_t AliHMPIDRecon::CluPreFilter(TClonesArray *pCluLst)
547 {
548 // Filter of bkg clusters
549 // based on elliptical-shapes...
550 //
551   if(pCluLst->GetEntriesFast()>50||pCluLst->GetEntriesFast()<4) return kFALSE; 
552   else return kTRUE;
553 }
554 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
555 Bool_t AliHMPIDRecon::FitEllipse(Double_t &phiRec)
556 {
557 //Fit a set of clusters with an analitical conical section function:
558   //
559   // Ax^2 + B*y^2 + 2Hxy + 2Gx + 2Fy + 1 = 0   ---> conical section
560   //
561   //  H*H - A*B > 0 hyperbola
562   //            < 0 ellipse
563   //            = 0 parabola
564   //
565   // tan 2alfa = 2H/(A-B)  alfa=angle of rotation
566   //
567   // coordinate of the centre of the conical section:
568   //   x = x' + a
569   //   y = y' + b
570   //
571   //       HF - BG
572   //  a = ---------
573   //       AB - H^2
574   //
575   //       HG - AF
576   //  b = --------
577   //       AB - H^2
578   Double_t cA,cB,cF,cG,cH;
579   Double_t aArg=-1;      Int_t iErrFlg;                                                //tmp vars for TMinuit
580
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
586   
587   Double_t d1,d2,d3;
588   TString sName;
589
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);
595
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);
603   delete gMinuit;
604
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(); 
611   alfa1*=0.5;
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();
617
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;  
622   
623 //  Printf("FitEllipse: phi reconstructed %f",phiRec*TMath::RadToDeg());
624   phiRec=phiref;
625   return kTRUE;
626 //
627 }
628 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
629 Bool_t AliHMPIDRecon::FitFree(Double_t phiRec)
630 {
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
636 //   Returns:    none
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
643   
644   Double_t d1,d2,d3;
645   TString sName;
646   Double_t th,ph;
647   
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);
650   
651   gMinuit->FixParameter(1);
652   gMinuit->mnexcm("SIMPLEX" ,&aArg,0,iErrFlg);   
653   gMinuit->mnexcm("MIGRAD"  ,&aArg,0,iErrFlg);
654   gMinuit->Release(1);  
655   gMinuit->mnexcm("MIGRAD"  ,&aArg,0,iErrFlg);
656   
657   gMinuit->mnpout(0,sName,th,d1,d2,d3,iErrFlg);
658   gMinuit->mnpout(1,sName,ph,d1,d2,d3,iErrFlg);   
659
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);  
662
663   SetTrkFit(th,ph);
664   
665   return kTRUE;
666 }
667 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
668 Double_t AliHMPIDRecon::FunConSect(Double_t *c,Double_t x,Double_t y)
669 {
670   return c[0]*x*x+c[1]*y*y+2*c[2]*x*y+2*c[3]*x+2*c[4]*y+1;
671 }
672 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
673 void AliHMPIDRecon::FunMinEl(Int_t &/* */,Double_t* /* */,Double_t &f,Double_t *par,Int_t /* */)
674 {
675   AliHMPIDRecon *pRec=(AliHMPIDRecon*)gMinuit->GetObjectFit();
676   Double_t minFun = 0;
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));
681     minFun +=el*el;
682   }
683   f = minFun;
684 }
685 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
686 void AliHMPIDRecon::FunMinPhot(Int_t &/* */,Double_t* /* */,Double_t &f,Double_t *par,Int_t iflag)
687 {
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);
696
697   Double_t meanCkov =0;
698   Double_t meanCkov2=0;
699   Double_t thetaCer,phiCer;
700   Int_t nClAcc = 0;
701   Int_t nClTot=pRec->NClu();
702     
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;
708     nClAcc++;
709   }
710   if(nClAcc==0) {f=999;return;}
711   meanCkov/=nClAcc;
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);
716   
717   
718   if(iflag==3) {
719     Printf("FunMinPhot before: photons candidates %i used %i",nClTot,nClAcc);
720     nClAcc = 0;
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;
729         nClAcc++;
730       } else pRec->SetClCk(i,kFALSE);
731     }
732     meanCkov1/=nClAcc;
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);
738   }
739 }//FunMinPhot()
740 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
741 //
742 // ended Hidden track algorithm....
743 //
744 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++