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         //PH        Printf("photon n. %i reconstructed theta = %f",fPhotCnt,fPhotCkov[fPhotCnt]);
  98         fPhotCnt++;                                                                           //increment counter of photon candidates
  99       }
 100     }
 101   }//clusters loop
 102   if(fPhotCnt<=3) pTrk->SetHMPIDsignal(kNoPhotAccept);                                        //no reconstruction with <=3 photon candidates
 103   Int_t iNacc=FlagPhot(HoughResponse());                                                      //flag photons according to individual theta ckov with respect to most probable
 104   pTrk->SetHMPIDmip(mipX,mipY,mipQ,iNacc);                                                    //store mip info
 105
 106   if(mipId==-1)              {pTrk->SetHMPIDsignal(kMipQdcCut);  return;}                     //no clusters with QDC more the threshold at all
 107   if(dMin>pParam->DistCut()) {pTrk->SetHMPIDsignal(kMipDistCut); return;}                     //closest cluster with enough charge is still too far from intersection
 108   pTrk->SetHMPIDcluIdx(chId,mipId);                                                           //set index of cluster
 109   if(iNacc<1){
 110     pTrk->SetHMPIDsignal(kNoPhotAccept);                                                      //no photon candidates is accepted
 111   }
 112   else {
 113     pTrk->SetHMPIDsignal(FindRingCkov(pCluLst->GetEntries()));                                //find best Theta ckov for ring i.e. track
 114     pTrk->SetHMPIDchi2(fCkovSigma2);                                                          //errors squared
 115   }
 116
 117 }//CkovAngle()
 118 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 119 Bool_t AliHMPIDRecon::FindPhotCkov(Double_t cluX,Double_t cluY,Double_t &thetaCer,Double_t &phiCer)
 120 {
 121 // Finds Cerenkov angle  for this photon candidate
 122 // Arguments: cluX,cluY - position of cadidate's cluster
 123 // Returns: Cerenkov angle
 124
 125   TVector3 dirCkov;
 126
 127   Double_t zRad= -0.5*fgkRadThick-0.5*fgkWinThick;                   //z position of middle of RAD
 128   TVector3 rad(fTrkPos.X(),fTrkPos.Y(),zRad);                        //impact point at middle of RAD
 129   TVector3  pc(cluX,cluY,0.5*fgkWinThick+fgkGapIdx);                 //mip at PC
 130   Double_t cluR = TMath::Sqrt((cluX-fTrkPos.X())*(cluX-fTrkPos.X())+
 131                               (cluY-fTrkPos.Y())*(cluY-fTrkPos.Y()));//ref. distance impact RAD-CLUSTER
 132   Double_t phi=(pc-rad).Phi();                                       //phi of photon
 133
 134   Double_t ckov1=0;
 135   Double_t ckov2=0.75+fTrkDir.Theta();                        //start to find theta cerenkov in DRS
 136   const Double_t kTol=0.01;
 137   Int_t iIterCnt = 0;
 138   while(1){
 139     if(iIterCnt>=50) return kFALSE;
 140     Double_t ckov=0.5*(ckov1+ckov2);
 141     dirCkov.SetMagThetaPhi(1,ckov,phi);
 142     TVector2 posC=TraceForward(dirCkov);                      //trace photon with actual angles
 143     Double_t dist=cluR-(posC-fTrkPos).Mod();                  //get distance between trial point and cluster position
 144     if(posC.X()==-999) dist = - 999;                          //total reflection problem
 145     iIterCnt++;                                               //counter step
 146     if     (dist> kTol) ckov1=ckov;                           //cluster @ larger ckov
 147     else if(dist<-kTol) ckov2=ckov;                           //cluster @ smaller ckov
 148     else{                                                     //precision achived: ckov in DRS found
 149       dirCkov.SetMagThetaPhi(1,ckov,phi);                     //
 150       RecPhot(dirCkov,thetaCer,phiCer);                       //find ckov (in TRS:the effective Cherenkov angle!)
 151       return kTRUE;
 152     }
 153   }
 154 }//FindPhotTheta()
 155 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 156 TVector2 AliHMPIDRecon::TraceForward(TVector3 dirCkov)const
 157 {
 158   //Trace forward a photon from (x,y) up to PC
 159   // Arguments: dirCkov photon vector in LORS
 160   //   Returns: pos of traced photon at PC
 161   TVector2 pos(-999,-999);
 162   Double_t thetaCer = dirCkov.Theta();
 163   if(thetaCer > TMath::ASin(1./fRadNmean))  return pos;         //total refraction on WIN-GAP boundary
 164   Double_t zRad= -0.5*fgkRadThick-0.5*fgkWinThick;              //z position of middle of RAD
 165   TVector3  posCkov(fTrkPos.X(),fTrkPos.Y(),zRad);              //RAD: photon position is track position @ middle of RAD
 166   Propagate(dirCkov,posCkov,           -0.5*fgkWinThick);       //go to RAD-WIN boundary
 167   Refract  (dirCkov,         fRadNmean,fgkWinIdx);              //RAD-WIN refraction
 168   Propagate(dirCkov,posCkov,            0.5*fgkWinThick);       //go to WIN-GAP boundary
 169   Refract  (dirCkov,         fgkWinIdx,fgkGapIdx);              //WIN-GAP refraction
 170   Propagate(dirCkov,posCkov,0.5*fgkWinThick+fgkGapThick);       //go to PC
 171   pos.Set(posCkov.X(),posCkov.Y());
 172   return pos;
 173 }//TraceForward()
 174 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 175 void AliHMPIDRecon::RecPhot(TVector3 dirCkov,Double_t &thetaCer,Double_t &phiCer)
 176 {
 177   //Theta Cerenkov reconstruction
 178   // Arguments: (x,y) of initial point in LORS, dirCkov photon vector in LORS
 179   //   Returns: thetaCer theta cerenkov reconstructed
 180 //  TVector3 dirTrk;
 181 //  dirTrk.SetMagThetaPhi(1,fTrkDir.Theta(),fTrkDir.Phi());
 182 //  Double_t thetaCer = TMath::ACos(dirCkov*dirTrk);
 183   TRotation mtheta;   mtheta.RotateY(- fTrkDir.Theta());
 184   TRotation mphi;       mphi.RotateZ(- fTrkDir.Phi());
 185   TRotation mrot=mtheta*mphi;
 186   TVector3 dirCkovTRS;
 187   dirCkovTRS=mrot*dirCkov;
 188   phiCer  = dirCkovTRS.Phi();                                          //actual value of the phi of the photon
 189   thetaCer= dirCkovTRS.Theta();                                        //actual value of thetaCerenkov of the photon
 190 }
 191 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 192 Double_t AliHMPIDRecon::FindRingArea(Double_t ckovAng)const
 193 {
 194 // Find area inside the cerenkov ring which lays inside PCs
 195 // Arguments: ckovAng - cerenkov angle
 196 //   Returns: area of the ring in cm^2 for given theta ckov
 197
 198   const Int_t kN=100;
 199   Double_t area=0;
 200   for(Int_t i=0;i<kN;i++){
 201     TVector2 pos1=TracePhot(ckovAng,Double_t(TMath::TwoPi()*i    /kN));//trace this photon
 202     TVector2 pos2=TracePhot(ckovAng,Double_t(TMath::TwoPi()*(i+1)/kN));//trace the next photon
 203     area+=(pos1-fTrkPos)*(pos2-fTrkPos);                               //add area of the triangle...
 204   }
 205   return area;
 206 }//FindRingArea()
 207 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 208 Double_t AliHMPIDRecon::FindRingCkov(Int_t)
 209 {
 210 // 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
 211 // collecting errors for all single Ckov candidates thetas. (Assuming they are independent)
 212 // Arguments: iNclus- total number of clusters in chamber for background estimation
 213 //    Return: best estimation of track Theta ckov
 214
 215   Double_t wei = 0.;
 216   Double_t weightThetaCerenkov = 0.;
 217
 218   Double_t ckovMin=9999.,ckovMax=0.;
 219   Double_t sigma2 = 0;   //to collect error squared for this ring
 220
 221   for(Int_t i=0;i<fPhotCnt;i++){//candidates loop
 222     if(fPhotFlag[i] == 2){
 223       if(fPhotCkov[i]<ckovMin) ckovMin=fPhotCkov[i];                         //find max and min Theta ckov from all candidates within probable window
 224       if(fPhotCkov[i]>ckovMax) ckovMax=fPhotCkov[i];
 225       weightThetaCerenkov += fPhotCkov[i]*fPhotWei[i];
 226       wei += fPhotWei[i];                                                    //collect weight as sum of all candidate weghts
 227
 228       sigma2 += 1./Sigma2(fPhotCkov[i],fPhotPhi[i]);
 229     }
 230   }//candidates loop
 231
 232   if(sigma2>0) fCkovSigma2=1./sigma2;
 233   else         fCkovSigma2=1e10;
 234
 235   if(wei != 0.) weightThetaCerenkov /= wei; else weightThetaCerenkov = 0.;
 236   return weightThetaCerenkov;
 237 }//FindCkovRing()
 238 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 239 Int_t AliHMPIDRecon::FlagPhot(Double_t ckov)
 240 {
 241 // Flag photon candidates if their individual ckov angle is inside the window around ckov angle returned by  HoughResponse()
 242 // Arguments: ckov- value of most probable ckov angle for track as returned by HoughResponse()
 243 //   Returns: number of photon candidates happened to be inside the window
 244
 245 // Photon Flag:  Flag = 0 initial set;
 246 //               Flag = 1 good candidate (charge compatible with photon);
 247 //               Flag = 2 photon used for the ring;
 248
 249   Int_t steps = (Int_t)((ckov )/ fDTheta); //how many times we need to have fDTheta to fill the distance between 0  and thetaCkovHough
 250
 251   Double_t tmin = (Double_t)(steps - 1)*fDTheta;
 252   Double_t tmax = (Double_t)(steps)*fDTheta;
 253   Double_t tavg = 0.5*(tmin+tmax);
 254
 255   tmin = tavg - 0.5*fWindowWidth;  tmax = tavg + 0.5*fWindowWidth;
 256
 257   Int_t iInsideCnt = 0; //count photons which Theta ckov inside the window
 258   for(Int_t i=0;i<fPhotCnt;i++){//photon candidates loop
 259     if(fPhotCkov[i] >= tmin && fPhotCkov[i] <= tmax)    {
 260       fPhotFlag[i]=2;
 261       iInsideCnt++;
 262     }
 263   }
 264   return iInsideCnt;
 265 }//FlagPhot()
 266 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 267 TVector2 AliHMPIDRecon::TracePhot(Double_t ckovThe,Double_t ckovPhi)const
 268 {
 269 // Trace a single Ckov photon from emission point somewhere in radiator up to photocathode taking into account ref indexes of materials it travereses
 270 // Arguments: ckovThe,ckovPhi- photon ckov angles in DRS, [rad]
 271 //   Returns: distance between photon point on PC and track projection
 272   TRotation mtheta;   mtheta.RotateY(fTrkDir.Theta());
 273   TRotation mphi;       mphi.RotateZ(fTrkDir.Phi());
 274   TRotation mrot=mphi*mtheta;
 275   TVector3  dirCkov,dirCkovTors;
 276
 277   dirCkovTors.SetMagThetaPhi(1,ckovThe,ckovPhi);                    //initially photon is directed according to requested ckov angle
 278   dirCkov=mrot*dirCkovTors;                                         //now we know photon direction in LORS
 279   return TraceForward(dirCkov);
 280 }//TracePhot()
 281 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 282 void AliHMPIDRecon::Propagate(const TVector3 dir,TVector3 &pos,Double_t z)const
 283 {
 284 // Finds an intersection point between a line and XY plane shifted along Z.
 285 // Arguments:  dir,pos   - vector along the line and any point of the line
 286 //             z         - z coordinate of plain
 287 //   Returns:  none
 288 //   On exit:  pos is the position if this intesection if any
 289   static TVector3 nrm(0,0,1);
 290          TVector3 pnt(0,0,z);
 291
 292   TVector3 diff=pnt-pos;
 293   Double_t sint=(nrm*diff)/(nrm*dir);
 294   pos+=sint*dir;
 295 }//Propagate()
 296 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 297 void AliHMPIDRecon::Refract(TVector3 &dir,Double_t n1,Double_t n2)const
 298 {
 299 // Refract direction vector according to Snell law
 300 // Arguments:
 301 //            n1 - ref idx of first substance
 302 //            n2 - ref idx of second substance
 303 //   Returns: none
 304 //   On exit: dir is new direction
 305   Double_t sinref=(n1/n2)*TMath::Sin(dir.Theta());
 306   if(TMath::Abs(sinref)>1.) dir.SetXYZ(-999,-999,-999);
 307   else             dir.SetTheta(TMath::ASin(sinref));
 308 }//Refract()
 309 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 310 Double_t AliHMPIDRecon::HoughResponse()
 311 {
 312 //
 313 //    fIdxMip = mipId;
 314
 315 //
 316   Double_t kThetaMax=0.75;
 317   Int_t nChannels = (Int_t)(kThetaMax/fDTheta+0.5);
 318   TH1D *phots   = new TH1D("Rphot"  ,"phots"         ,nChannels,0,kThetaMax);
 319   TH1D *photsw  = new TH1D("RphotWeighted" ,"photsw" ,nChannels,0,kThetaMax);
 320   TH1D *resultw = new TH1D("resultw","resultw"       ,nChannels,0,kThetaMax);
 321   Int_t nBin = (Int_t)(kThetaMax/fDTheta);
 322   Int_t nCorrBand = (Int_t)(fWindowWidth/(2*fDTheta));
 323
 324   for (Int_t i=0; i< fPhotCnt; i++){//photon cadidates loop
 325     Double_t angle = fPhotCkov[i];  if(angle<0||angle>kThetaMax) continue;
 326     phots->Fill(angle);
 327     Int_t bin = (Int_t)(0.5+angle/(fDTheta));
 328     Double_t weight=1.;
 329     if(fIsWEIGHT){
 330       Double_t lowerlimit = ((Double_t)bin)*fDTheta - 0.5*fDTheta;  Double_t upperlimit = ((Double_t)bin)*fDTheta + 0.5*fDTheta;
 331       Double_t diffArea = FindRingArea(upperlimit)-FindRingArea(lowerlimit);
 332       if(diffArea>0) weight = 1./diffArea;
 333     }
 334     photsw->Fill(angle,weight);
 335     fPhotWei[i]=weight;
 336   }//photon candidates loop
 337
 338   for (Int_t i=1; i<=nBin;i++){
 339     Int_t bin1= i-nCorrBand;
 340     Int_t bin2= i+nCorrBand;
 341     if(bin1<1) bin1=1;
 342     if(bin2>nBin)bin2=nBin;
 343     Double_t sumPhots=phots->Integral(bin1,bin2);
 344     if(sumPhots<3) continue;                            // if less then 3 photons don't trust to this ring
 345     Double_t sumPhotsw=photsw->Integral(bin1,bin2);
 346     resultw->Fill((Double_t)((i+0.5)*fDTheta),sumPhotsw);
 347   }
 348 // evaluate the "BEST" theta ckov as the maximum value of histogramm
 349   Double_t *pVec = resultw->GetArray();
 350   Int_t locMax = TMath::LocMax(nBin,pVec);
 351   delete phots;delete photsw;delete resultw; // Reset and delete objects
 352
 353   return (Double_t)(locMax*fDTheta+0.5*fDTheta); //final most probable track theta ckov
 354 }//HoughResponse()
 355 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 356 Double_t AliHMPIDRecon::Sigma2(Double_t ckovTh, Double_t ckovPh)const
 357 {
 358 // Analithical calculation of total error (as a sum of localization, geometrical and chromatic errors) on Cerenkov angle for a given Cerenkov photon
 359 // created by a given MIP. Fromulae according to CERN-EP-2000-058
 360 // Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
 361 //            dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
 362 //            MIP beta
 363 //   Returns: absolute error on Cerenkov angle, [radians]
 364
 365   TVector3 v(-999,-999,-999);
 366   Double_t trkBeta = 1./(TMath::Cos(ckovTh)*fRadNmean);
 367
 368   if(trkBeta > 1) trkBeta = 1;                 //protection against bad measured thetaCer
 369   if(trkBeta < 0) trkBeta = 0.0001;            //
 370
 371   v.SetX(SigLoc (ckovTh,ckovPh,trkBeta));
 372   v.SetY(SigGeom(ckovTh,ckovPh,trkBeta));
 373   v.SetZ(SigCrom(ckovTh,ckovPh,trkBeta));
 374
 375   return v.Mag2();
 376 }
 377 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 378 Double_t AliHMPIDRecon::SigLoc(Double_t thetaC, Double_t phiC,Double_t betaM)const
 379 {
 380 // Analithical calculation of localization error (due to finite segmentation of PC) on Cerenkov angle for a given Cerenkov photon
 381 // created by a given MIP. Fromulae according to CERN-EP-2000-058
 382 // Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
 383 //            dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
 384 //            MIP beta
 385 //   Returns: absolute error on Cerenkov angle, [radians]
 386
 387   Double_t phiDelta = phiC - fTrkDir.Phi();
 388
 389   Double_t sint     = TMath::Sin(fTrkDir.Theta());
 390   Double_t cost     = TMath::Cos(fTrkDir.Theta());
 391   Double_t sinf     = TMath::Sin(fTrkDir.Phi());
 392   Double_t cosf     = TMath::Cos(fTrkDir.Phi());
 393   Double_t sinfd    = TMath::Sin(phiDelta);
 394   Double_t cosfd    = TMath::Cos(phiDelta);
 395   Double_t tantheta = TMath::Tan(thetaC);
 396
 397   Double_t alpha =cost-tantheta*cosfd*sint;                                                 // formula (11)
 398   Double_t k = 1.-fRadNmean*fRadNmean+alpha*alpha/(betaM*betaM);                            // formula (after 8 in the text)
 399   if (k<0) return 1e10;
 400   Double_t mu =sint*sinf+tantheta*(cost*cosfd*sinf+sinfd*cosf);                             // formula (10)
 401   Double_t e  =sint*cosf+tantheta*(cost*cosfd*cosf-sinfd*sinf);                             // formula (9)
 402
 403   Double_t kk = betaM*TMath::Sqrt(k)/(fgkGapThick*alpha);                                   // formula (6) and (7)
 404   Double_t dtdxc = kk*(k*(cosfd*cosf-cost*sinfd*sinf)-(alpha*mu/(betaM*betaM))*sint*sinfd); // formula (6)
 405   Double_t dtdyc = kk*(k*(cosfd*sinf+cost*sinfd*cosf)+(alpha* e/(betaM*betaM))*sint*sinfd); // formula (7)            pag.4
 406
 407   Double_t errX = 0.2,errY=0.25;                                                            //end of page 7
 408   return  TMath::Sqrt(errX*errX*dtdxc*dtdxc + errY*errY*dtdyc*dtdyc);
 409 }
 410 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 411 Double_t AliHMPIDRecon::SigCrom(Double_t thetaC, Double_t phiC,Double_t betaM)const
 412 {
 413 // Analithical calculation of chromatic error (due to lack of knowledge of Cerenkov photon energy) on Cerenkov angle for a given Cerenkov photon
 414 // created by a given MIP. Fromulae 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
 422   Double_t sint     = TMath::Sin(fTrkDir.Theta());
 423   Double_t cost     = TMath::Cos(fTrkDir.Theta());
 424   Double_t cosfd    = TMath::Cos(phiDelta);
 425   Double_t tantheta = TMath::Tan(thetaC);
 426
 427   Double_t alpha =cost-tantheta*cosfd*sint;                                                 // formula (11)
 428   Double_t dtdn = cost*fRadNmean*betaM*betaM/(alpha*tantheta);                              // formula (12)
 429
 430 //  Double_t f = 0.00928*(7.75-5.635)/TMath::Sqrt(12.);
 431   Double_t f = 0.0172*(7.75-5.635)/TMath::Sqrt(24.);
 432
 433   return f*dtdn;
 434 }//SigCrom()
 435 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 436 Double_t AliHMPIDRecon::SigGeom(Double_t thetaC, Double_t phiC,Double_t betaM)const
 437 {
 438 // Analithical calculation of geometric error (due to lack of knowledge of creation point in radiator) on Cerenkov angle for a given Cerenkov photon
 439 // created by a given MIP. Formulae according to CERN-EP-2000-058
 440 // Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
 441 //            dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
 442 //            MIP beta
 443 //   Returns: absolute error on Cerenkov angle, [radians]
 444
 445   Double_t phiDelta = phiC - fTrkDir.Phi();
 446
 447   Double_t sint     = TMath::Sin(fTrkDir.Theta());
 448   Double_t cost     = TMath::Cos(fTrkDir.Theta());
 449   Double_t sinf     = TMath::Sin(fTrkDir.Phi());
 450   Double_t cosfd    = TMath::Cos(phiDelta);
 451   Double_t costheta = TMath::Cos(thetaC);
 452   Double_t tantheta = TMath::Tan(thetaC);
 453
 454   Double_t alpha =cost-tantheta*cosfd*sint;                                                  // formula (11)
 455
 456   Double_t k = 1.-fRadNmean*fRadNmean+alpha*alpha/(betaM*betaM);                             // formula (after 8 in the text)
 457   if (k<0) return 1e10;
 458
 459   Double_t eTr = 0.5*fgkRadThick*betaM*TMath::Sqrt(k)/(fgkGapThick*alpha);                   // formula (14)
 460   Double_t lambda = 1.-sint*sint*sinf*sinf;                                                  // formula (15)
 461
 462   Double_t c1 = 1./(1.+ eTr*k/(alpha*alpha*costheta*costheta));                              // formula (13.a)
 463   Double_t c2 = betaM*TMath::Power(k,1.5)*tantheta*lambda/(fgkGapThick*alpha*alpha);         // formula (13.b)
 464   Double_t c3 = (1.+eTr*k*betaM*betaM)/((1+eTr)*alpha*alpha);                                // formula (13.c)
 465   Double_t c4 = TMath::Sqrt(k)*tantheta*(1-lambda)/(fgkGapThick*betaM);                      // formula (13.d)
 466   Double_t dtdT = c1 * (c2+c3*c4);
 467   Double_t trErr = fgkRadThick/(TMath::Sqrt(12.)*cost);
 468
 469   return trErr*dtdT;
 470 }//SigGeom()
 471 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 472 //
 473 // From here HTA....
 474 //
 475 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 476 Bool_t AliHMPIDRecon::CkovHiddenTrk(AliESDtrack *pTrk,TClonesArray *pCluLst,Double_t nmean)
 477 {
 478 // Pattern recognition method without any infos from tracking:HTA (Hidden Track Algorithm)...
 479 // The method finds in the chmber the cluster with the highest charge
 480 // compatibile with a MIP, then the strategy is applied
 481 // Arguments:  pTrk     - pointer to ESD track
 482 //             pCluLs   - list of clusters for a given chamber
 483 //             nmean    - mean freon ref. index
 484 //   Returns:           - 0=ok,1=not fitted
 485
 486   AliHMPIDParam *pParam=AliHMPIDParam::Instance();
 487
 488   fRadNmean=nmean;
 489
 490   if(pCluLst->GetEntriesFast()>100) return kFALSE;                                            //boundary check for CluX,CluY...
 491   Float_t mipX=-1,mipY=-1;Int_t mipId=-1,mipQ=-1;
 492   Double_t qRef = 0;
 493   Int_t nCh=0;
 494   for (Int_t iClu=0;iClu<pCluLst->GetEntriesFast();iClu++){                                   //clusters loop
 495     AliHMPIDCluster *pClu=(AliHMPIDCluster*)pCluLst->UncheckedAt(iClu);                       //get pointer to current cluster
 496     nCh = pClu->Ch();
 497     fXClu[iClu] = pClu->X();fYClu[iClu] = pClu->Y();                                          //store x,y for fitting procedure
 498     fClCk[iClu] = kTRUE;                                                                      //all cluster are accepted at this stage to be reconstructed
 499     if(pClu->Q()>qRef){                                                                       //searching the highest charge to select a MIP
 500       qRef = pClu->Q();
 501       mipId=iClu; mipX=pClu->X();mipY=pClu->Y();mipQ=(Int_t)pClu->Q();
 502     }
 503   }//clusters loop
 504
 505   fNClu = pCluLst->GetEntriesFast();
 506   if(qRef>pParam->QCut()){                                                                     //charge compartible with MIP clusters
 507     fIdxMip = mipId;
 508     fClCk[mipId] = kFALSE;
 509     fMipX = mipX; fMipY=mipY; fMipQ = qRef;
 510     if(!DoRecHiddenTrk(pCluLst)) {
 511       pTrk->SetHMPIDsignal(kNoPhotAccept);
 512       return kFALSE;
 513     }                                                                           //Do track and ring reconstruction,if problems returns 1
 514     pTrk->SetHMPIDtrk(fRadX,fRadY,fThTrkFit,fPhTrkFit);                                        //store track intersection info
 515     pTrk->SetHMPIDmip(fMipX,fMipY,(Int_t)fMipQ,fNClu);                                         //store mip info
 516     pTrk->SetHMPIDcluIdx(nCh,fIdxMip);                                                         //set cham number and index of cluster
 517     pTrk->SetHMPIDsignal(fCkovFit);                                                            //find best Theta ckov for ring i.e. track
 518     pTrk->SetHMPIDchi2(fCkovSig2);                                                             //errors squared
 519 //    Printf(" n clusters tot %i accepted %i",pCluLst->GetEntriesFast(),fNClu);
 520     return kTRUE;
 521   }
 522
 523   return kFALSE;
 524 }//CkovHiddenTrk()
 525 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 526 Bool_t AliHMPIDRecon::DoRecHiddenTrk(TClonesArray *pCluLst)
 527 {
 528 // Pattern recognition method without any infos from tracking...
 529 // First a preclustering filter to avoid part of the noise
 530 // Then only ellipsed-rings are fitted (no possibility,
 531 // for the moment, to reconstruct very inclined tracks)
 532 // Finally a fitting with (th,ph) free, starting by very close values
 533 // previously evaluated.
 534 // Arguments:   none
 535 //   Returns:   none
 536   Double_t phiRec;
 537   if(!CluPreFilter(pCluLst)) {return kFALSE;}
 538   if(!FitEllipse(phiRec)) {return kFALSE;}
 539   Int_t nClTmp1 = pCluLst->GetEntriesFast()-1;  //minus MIP...
 540   Int_t nClTmp2 = 0;
 541   while(nClTmp1 != nClTmp2){
 542     SetNClu(pCluLst->GetEntriesFast());
 543     if(!FitFree(phiRec)) {return kFALSE;}
 544     nClTmp2 = NClu();
 545     if(nClTmp2!=nClTmp1) {nClTmp1=nClTmp2;nClTmp2=0;}
 546   }
 547   fNClu = nClTmp2;
 548   return kTRUE;
 549 }//DoRecHiddenTrk()
 550 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 551 Bool_t AliHMPIDRecon::CluPreFilter(TClonesArray *pCluLst)
 552 {
 553 // Filter of bkg clusters
 554 // based on elliptical-shapes...
 555 //
 556   if(pCluLst->GetEntriesFast()>50||pCluLst->GetEntriesFast()<4) return kFALSE;
 557   else return kTRUE;
 558 }
 559 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 560 Bool_t AliHMPIDRecon::FitEllipse(Double_t &phiRec)
 561 {
 562 //Fit a set of clusters with an analitical conical section function:
 563   //
 564   // Ax^2 + B*y^2 + 2Hxy + 2Gx + 2Fy + 1 = 0   ---> conical section
 565   //
 566   //  H*H - A*B > 0 hyperbola
 567   //            < 0 ellipse
 568   //            = 0 parabola
 569   //
 570   // tan 2alfa = 2H/(A-B)  alfa=angle of rotation
 571   //
 572   // coordinate of the centre of the conical section:
 573   //   x = x' + a
 574   //   y = y' + b
 575   //
 576   //       HF - BG
 577   //  a = ---------
 578   //       AB - H^2
 579   //
 580   //       HG - AF
 581   //  b = --------
 582   //       AB - H^2
 583   Double_t cA,cB,cF,cG,cH;
 584   Double_t aArg=-1;      Int_t iErrFlg;                                                //tmp vars for TMinuit
 585
 586   if(!gMinuit) gMinuit = new TMinuit(5);                                               //init MINUIT with this number of parameters (5 params)
 587   gMinuit->mncler();                                                                   // reset Minuit list of paramters
 588   gMinuit->SetObjectFit((TObject*)this);  gMinuit->SetFCN(AliHMPIDRecon::FunMinEl);    //set fit function
 589   gMinuit->mnexcm("SET PRI",&aArg,1,iErrFlg);                                          //suspend all printout from TMinuit
 590   gMinuit->mnexcm("SET NOW",&aArg,0,iErrFlg);                                          //suspend all warning printout from TMinuit
 591
 592   Double_t d1,d2,d3;
 593   TString sName;
 594
 595   gMinuit->mnparm(0," A ",1,0.01,0,0,iErrFlg);
 596   gMinuit->mnparm(1," B ",1,0.01,0,0,iErrFlg);
 597   gMinuit->mnparm(2," H ",1,0.01,0,0,iErrFlg);
 598   gMinuit->mnparm(3," G ",1,0.01,0,0,iErrFlg);
 599   gMinuit->mnparm(4," F ",1,0.01,0,0,iErrFlg);
 600
 601   gMinuit->mnexcm("SIMPLEX",&aArg,0,iErrFlg);
 602   gMinuit->mnexcm("MIGRAD" ,&aArg,0,iErrFlg);
 603   gMinuit->mnpout(0,sName,cA,d1,d2,d3,iErrFlg);
 604   gMinuit->mnpout(1,sName,cB,d1,d2,d3,iErrFlg);
 605   gMinuit->mnpout(2,sName,cH,d1,d2,d3,iErrFlg);
 606   gMinuit->mnpout(3,sName,cG,d1,d2,d3,iErrFlg);
 607   gMinuit->mnpout(4,sName,cF,d1,d2,d3,iErrFlg);
 608   delete gMinuit;
 609
 610   Double_t i2 = cA*cB-cH*cH;                                       //quartic invariant : i2 > 0  ellipse, i2 < 0 hyperbola
 611   if(i2<=0) return kFALSE;
 612   Double_t aX = (cH*cF-cB*cG)/i2;                                  //x centre of the canonical section
 613   Double_t bY = (cH*cG-cA*cF)/i2;                                  //y centre of the canonical section
 614   Double_t alfa1 = TMath::ATan(2*cH/(cA-cB));                      //alpha = angle of rotation of the conical section
 615   if(alfa1<0) alfa1+=TMath::Pi();
 616   alfa1*=0.5;
 617 //  Double_t alfa2 = alfa1+TMath::Pi();
 618   Double_t phiref = TMath::ATan2(bY-fMipY,aX-fMipX);               //evaluate in a unique way the angle of rotation comparing it
 619   if(phiref<0) phiref+=TMath::TwoPi();                             //with the vector that points to the centre from the mip
 620   if(i2<0) phiref+=TMath::Pi();
 621   if(phiref>TMath::TwoPi()) phiref-=TMath::TwoPi();
 622
 623 //  Printf(" alfa1 %f",alfa1*TMath::RadToDeg());
 624 //  Printf(" alfa2 %f",alfa2*TMath::RadToDeg());
 625 //  Printf(" firef %f",phiref*TMath::RadToDeg());
 626 //  if(TMath::Abs(alfa1-phiref)<TMath::Abs(alfa2-phiref)) phiRec = alfa1; else phiRec = alfa2;
 627
 628 //  Printf("FitEllipse: phi reconstructed %f",phiRec*TMath::RadToDeg());
 629   phiRec=phiref;
 630   return kTRUE;
 631 //
 632 }
 633 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 634 Bool_t AliHMPIDRecon::FitFree(Double_t phiRec)
 635 {
 636 // Fit performed by minimizing RMS/sqrt(n) of the
 637 // photons reconstructed. First phi is fixed and theta
 638 // is fouond, then (th,ph) of the track
 639 // as free parameters
 640 // Arguments:    PhiRec phi of the track
 641 //   Returns:    none
 642   Double_t aArg=-1;  Int_t iErrFlg;                                                    //tmp vars for TMinuit
 643   if(!gMinuit) gMinuit = new TMinuit(2);                                               //init MINUIT with this number of parameters (5 params)
 644   gMinuit->mncler();                                                                   // reset Minuit list of paramters
 645   gMinuit->SetObjectFit((TObject*)this);  gMinuit->SetFCN(AliHMPIDRecon::FunMinPhot);  //set fit function
 646   gMinuit->mnexcm("SET PRI",&aArg,1,iErrFlg);                                          //suspend all printout from TMinuit
 647   gMinuit->mnexcm("SET NOW",&aArg,0,iErrFlg);                                          //suspend all warning printout from TMinuit
 648
 649   Double_t d1,d2,d3;
 650   TString sName;
 651   Double_t th,ph;
 652
 653   gMinuit->mnparm(0," theta ",  0.01,0.01,0,TMath::PiOver2(),iErrFlg);
 654   gMinuit->mnparm(1," phi   ",phiRec,0.01,0,TMath::TwoPi()  ,iErrFlg);
 655
 656   gMinuit->FixParameter(1);
 657   gMinuit->mnexcm("SIMPLEX" ,&aArg,0,iErrFlg);
 658   gMinuit->mnexcm("MIGRAD"  ,&aArg,0,iErrFlg);
 659   gMinuit->Release(1);
 660   gMinuit->mnexcm("MIGRAD"  ,&aArg,0,iErrFlg);
 661
 662   gMinuit->mnpout(0,sName,th,d1,d2,d3,iErrFlg);
 663   gMinuit->mnpout(1,sName,ph,d1,d2,d3,iErrFlg);
 664
 665   Double_t outPar[2] = {th,ph}; Double_t g; Double_t f;Int_t flag = 3;
 666   gMinuit->Eval(2, &g, f, outPar,flag);
 667
 668   SetTrkFit(th,ph);
 669
 670   return kTRUE;
 671 }
 672 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 673 Double_t AliHMPIDRecon::FunConSect(Double_t *c,Double_t x,Double_t y)
 674 {
 675   return c[0]*x*x+c[1]*y*y+2*c[2]*x*y+2*c[3]*x+2*c[4]*y+1;
 676 }
 677 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 678 void AliHMPIDRecon::FunMinEl(Int_t &/* */,Double_t* /* */,Double_t &f,Double_t *par,Int_t /* */)
 679 {
 680   AliHMPIDRecon *pRec=(AliHMPIDRecon*)gMinuit->GetObjectFit();
 681   Double_t minFun = 0;
 682   Int_t np = pRec->NClu();
 683   for(Int_t i=0;i<np;i++) {
 684     if(i==pRec->IdxMip()) continue;
 685     Double_t el = pRec->FunConSect(par,pRec->XClu(i),pRec->YClu(i));
 686     minFun +=el*el;
 687   }
 688   f = minFun;
 689 }
 690 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 691 void AliHMPIDRecon::FunMinPhot(Int_t &/* */,Double_t* /* */,Double_t &f,Double_t *par,Int_t iflag)
 692 {
 693   AliHMPIDRecon *pRec=(AliHMPIDRecon*)gMinuit->GetObjectFit();
 694   Double_t sizeCh = 0.5*fgkRadThick+fgkWinThick+fgkGapThick;
 695   Double_t thTrk = par[0];
 696   Double_t phTrk = par[1];
 697   Double_t xrad = pRec->MipX() - sizeCh*TMath::Tan(thTrk)*TMath::Cos(phTrk);
 698   Double_t yrad = pRec->MipY() - sizeCh*TMath::Tan(thTrk)*TMath::Sin(phTrk);
 699   pRec->SetRadXY(xrad,yrad);
 700   pRec->SetTrack(xrad,yrad,thTrk,phTrk);
 701
 702   Double_t meanCkov =0;
 703   Double_t meanCkov2=0;
 704   Double_t thetaCer,phiCer;
 705   Int_t nClAcc = 0;
 706   Int_t nClTot=pRec->NClu();
 707
 708   for(Int_t i=0;i<nClTot;i++) {
 709     if(!(pRec->ClCk(i))) continue;
 710     pRec->FindPhotCkov(pRec->XClu(i),pRec->YClu(i),thetaCer,phiCer);
 711     meanCkov  += thetaCer;
 712     meanCkov2 += thetaCer*thetaCer;
 713     nClAcc++;
 714   }
 715   if(nClAcc==0) {f=999;return;}
 716   meanCkov/=nClAcc;
 717   Double_t rms = (meanCkov2 - meanCkov*meanCkov*nClAcc)/nClAcc;
 718   if(rms<0) Printf(" rms2 = %f, strange!!!",rms);
 719   rms = TMath::Sqrt(rms);
 720   f = rms/TMath::Sqrt(nClAcc);
 721
 722
 723   if(iflag==3) {
 724     Printf("FunMinPhot before: photons candidates %i used %i",nClTot,nClAcc);
 725     nClAcc = 0;
 726     Double_t meanCkov1=0;
 727     Double_t meanCkov2=0;
 728     for(Int_t i=0;i<nClTot;i++) {
 729       if(!(pRec->ClCk(i))) continue;
 730       pRec->FindPhotCkov(pRec->XClu(i),pRec->YClu(i),thetaCer,phiCer);
 731       if(TMath::Abs(thetaCer-meanCkov)<2*rms) {
 732         meanCkov1 += thetaCer;
 733         meanCkov2 += thetaCer*thetaCer;
 734         nClAcc++;
 735       } else pRec->SetClCk(i,kFALSE);
 736     }
 737     meanCkov1/=nClAcc;
 738     Double_t rms2 = (meanCkov2 - meanCkov*meanCkov*nClAcc)/nClAcc;
 739     Printf("FunMinPhot after: photons candidates %i used %i thetaCer %f",nClTot,nClAcc,meanCkov1);
 740     pRec->SetCkovFit(meanCkov1);
 741     pRec->SetCkovSig2(rms2);
 742     pRec->SetNClu(nClAcc);
 743   }
 744 }//FunMinPhot()
 745 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 746 //
 747 // ended Hidden track algorithm....
 748 //
 749 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++