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   for (Int_t i=0; i<100; i++) {
  60     fXClu[i] = fYClu[i] = 0;
  61     fClCk[i] = kTRUE;
  62   }
  63 }
  64 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
  65 void AliHMPIDRecon::CkovAngle(AliESDtrack *pTrk,TClonesArray *pCluLst,Double_t nmean)
  66 {
  67 // Pattern recognition method based on Hough transform
  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],
  71
  72   AliHMPIDParam *pParam=AliHMPIDParam::Instance();
  73
  74   if(pCluLst->GetEntries()>pParam->MultCut()) fIsWEIGHT = kTRUE; // offset to take into account bkg in reconstruction
  75   else                                        fIsWEIGHT = kFALSE;
  76
  77   Float_t xRa,yRa,th,ph;
  78   pTrk->GetHMPIDtrk(xRa,yRa,th,ph);        //initialize this track: th and ph angles at middle of RAD
  79   SetTrack(xRa,yRa,th,ph);
  80
  81   fRadNmean=nmean;
  82
  83   Float_t dMin=999,mipX=-1,mipY=-1;Int_t chId=-1,mipId=-1,mipQ=-1;
  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
  87     chId=pClu->Ch();
  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)
  95         fPhotPhi [fPhotCnt]=phiCer;                                                           //actual phi   Cerenkov (in TRS): -pi to come back to "unusual" ref system (X,Y,-Z)
  96         fPhotCnt++;                                                                           //increment counter of photon candidates
  97       }
  98     }
  99   }//clusters loop
 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
 102
 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
 108
 109   pTrk->SetHMPIDchi2(fCkovSigma2);                                                            //errors squared
 110
 111 }//CkovAngle()
 112 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 113 Bool_t AliHMPIDRecon::FindPhotCkov(Double_t cluX,Double_t cluY,Double_t &thetaCer,Double_t &phiCer)
 114 {
 115 // Finds Cerenkov angle  for this photon candidate
 116 // Arguments: cluX,cluY - position of cadidate's cluster
 117 // Returns: Cerenkov angle
 118
 119   TVector3 dirCkov;
 120
 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
 124   Double_t cluR = TMath::Sqrt((cluX-fTrkPos.X())*(cluX-fTrkPos.X())+
 125                               (cluY-fTrkPos.Y())*(cluY-fTrkPos.Y()));//ref. distance impact RAD-CLUSTER
 126   Double_t phi=(pc-rad).Phi();                                       //phi of photon
 127
 128   Double_t ckov1=0;
 129   Double_t ckov2=0.75+fTrkDir.Theta();                        //start to find theta cerenkov in DRS
 130   const Double_t kTol=0.01;
 131   Int_t iIterCnt = 0;
 132   while(1){
 133     if(iIterCnt>=50) return kFALSE;
 134     Double_t ckov=0.5*(ckov1+ckov2);
 135     dirCkov.SetMagThetaPhi(1,ckov,phi);
 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
 140     if     (dist> kTol) ckov1=ckov;                           //cluster @ larger ckov
 141     else if(dist<-kTol) ckov2=ckov;                           //cluster @ smaller ckov
 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     }
 147   }
 148 }//FindPhotTheta()
 149 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 150 TVector2 AliHMPIDRecon::TraceForward(TVector3 dirCkov)const
 151 {
 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);
 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
 165   pos.Set(posCkov.X(),posCkov.Y());
 166   return pos;
 167 }//TraceForward()
 168 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 169 void 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
 184 }
 185 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 186 Double_t AliHMPIDRecon::FindRingArea(Double_t ckovAng)const
 187 {
 188 // Find area inside the cerenkov ring which lays inside PCs
 189 // Arguments: ckovAng - cerenkov angle
 190 //   Returns: area of the ring in cm^2 for given theta ckov
 191
 192   const Int_t kN=100;
 193   Double_t area=0;
 194   for(Int_t i=0;i<kN;i++){
 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...
 198   }
 199   return area;
 200 }//FindRingArea()
 201 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 202 Double_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){
 217       if(fPhotCkov[i]<ckovMin) ckovMin=fPhotCkov[i];                         //find max and min Theta ckov from all candidates within probable window
 218       if(fPhotCkov[i]>ckovMax) ckovMax=fPhotCkov[i];
 219       weightThetaCerenkov += fPhotCkov[i]*fPhotWei[i];
 220       wei += fPhotWei[i];                                                    //collect weight as sum of all candidate weghts
 221
 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
 229   if(wei != 0.) weightThetaCerenkov /= wei; else weightThetaCerenkov = 0.;
 230   return weightThetaCerenkov;
 231 }//FindCkovRing()
 232 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 233 Int_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
 239 // Photon Flag:  Flag = 0 initial set;
 240 //               Flag = 1 good candidate (charge compatible with photon);
 241 //               Flag = 2 photon used for the ring;
 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 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 261 TVector2 AliHMPIDRecon::TracePhot(Double_t ckovThe,Double_t ckovPhi)const
 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
 264 // Arguments: ckovThe,ckovPhi- photon ckov angles in DRS, [rad]
 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;
 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()
 275 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 276 void AliHMPIDRecon::Propagate(const TVector3 dir,TVector3 &pos,Double_t z)const
 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 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 291 void 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
 299   Double_t sinref=(n1/n2)*TMath::Sin(dir.Theta());
 300   if(sinref>1.)    dir.SetXYZ(-999,-999,-999);
 301   else             dir.SetTheta(TMath::ASin(sinref));
 302 }//Refract()
 303 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 304 Double_t AliHMPIDRecon::HoughResponse()
 305 {
 306 //
 307 //    fIdxMip = mipId;
 308
 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 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 350 Double_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);
 360   Double_t trkBeta = 1./(TMath::Cos(ckovTh)*fRadNmean);
 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 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 369 Double_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());
 380   Double_t k = 1.-fRadNmean*fRadNmean+alpha*alpha/(betaM*betaM);
 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 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 393 Double_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
 404   Double_t dtdn = TMath::Cos(fTrkDir.Theta())*fRadNmean*betaM*betaM/(alpha*TMath::Tan(thetaC));
 405
 406   Double_t f = 0.00928*(7.75-5.635)/TMath::Sqrt(12.);
 407
 408   return f*dtdn;
 409 }//SigCrom()
 410 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 411 Double_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
 423   Double_t k = 1.-fRadNmean*fRadNmean+alpha*alpha/(betaM*betaM);
 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 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 439 //
 440 // From here HTA....
 441 //
 442 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 443 Bool_t AliHMPIDRecon::CkovHiddenTrk(AliESDtrack *pTrk,TClonesArray *pCluLst,Double_t nmean)
 444 {
 445 // Pattern recognition method without any infos from tracking:HTA (Hidden Track Algorithm)...
 446 // The method finds in the chmber the cluster with the highest charge
 447 // compatibile with a MIP, then the strategy is applied
 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();
 454
 455   fRadNmean=nmean;
 456
 457   Float_t mipX=-1,mipY=-1;Int_t mipId=-1,mipQ=-1;
 458   Double_t qRef = 0;
 459   for (Int_t iClu=0;iClu<pCluLst->GetEntriesFast();iClu++){                                   //clusters loop
 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
 462     fClCk[iClu] = kTRUE;                                                                      //all cluster are accepted at this stage to be reconstructed
 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
 468
 469   fNClu = pCluLst->GetEntriesFast();
 470   if(qRef>pParam->QCut()){                                                                       //charge compartible with MIP clusters
 471     fIdxMip = mipId;
 472     fClCk[mipId] = kFALSE;
 473     fMipX = mipX; fMipY=mipY; fMipQ = qRef;
 474     if(!DoRecHiddenTrk(pCluLst)) return kFALSE;                                                  //Do track and ring reconstruction,if problems returns 1
 475     pTrk->SetHMPIDtrk(fRadX,fRadY,fThTrkFit,fPhTrkFit);                                          //store track intersection info
 476     pTrk->SetHMPIDmip(fMipX,fMipY,(Int_t)fMipQ,fNClu);                                           //store mip info
 477     pTrk->SetHMPIDcluIdx(pCluLst->GetEntriesFast(),fIdxMip);                                     //set cham number and index of cluster
 478     pTrk->SetHMPIDsignal(fCkovFit);                                                              //find best Theta ckov for ring i.e. track
 479     Printf(" n clusters tot %i accepted %i",pCluLst->GetEntriesFast(),fNClu);
 480     return kTRUE;
 481   }
 482   return kFALSE;
 483 }//CkovHiddenTrk()
 484 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 485 Bool_t AliHMPIDRecon::DoRecHiddenTrk(TClonesArray *pCluLst)
 486 {
 487 // Pattern recognition method without any infos from tracking...
 488 // First a preclustering filter to avoid part of the noise
 489 // Then only ellipsed-rings are fitted (no possibility,
 490 // for the moment, to reconstruct very inclined tracks)
 491 // Finally a fitting with (th,ph) free, starting by very close values
 492 // previously evaluated.
 493 // Arguments:   none
 494 //   Returns:   none
 495   Double_t phiRec;
 496   if(!CluPreFilter(pCluLst)) {return kFALSE;}
 497   if(!FitEllipse(phiRec)) {return kFALSE;}
 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()
 509 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 510 Bool_t AliHMPIDRecon::CluPreFilter(TClonesArray *pCluLst)
 511 {
 512 // Filter of bkg clusters
 513 // based on elliptical-shapes...
 514 //
 515   if(pCluLst->GetEntriesFast()>50||pCluLst->GetEntriesFast()<4) return kFALSE;
 516   else return kTRUE;
 517 }
 518 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 519 Bool_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
 542   Double_t cA,cB,cF,cG,cH;
 543   Double_t aArg=-1;      Int_t iErrFlg;                                                //tmp vars for TMinuit
 544
 545   if(!gMinuit) gMinuit = new TMinuit(5);                                               //init MINUIT with this number of parameters (5 params)
 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
 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);
 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
 570   Double_t aX = (cH*cF-cB*cG)/i2;                                  //x centre of the canonical section
 571   Double_t bY = (cH*cG-cA*cF)/i2;                                  //y centre of the canonical section
 572   Double_t alfa1 = TMath::ATan(2*cH/(cA-cB));                      //alpha = angle of rotation of the conical section
 573   if(alfa1<0) alfa1+=TMath::Pi();
 574   alfa1*=0.5;
 575   Double_t alfa2 = alfa1+TMath::Pi();
 576   Double_t phiref = TMath::ATan2(bY-fMipY,aX-fMipX);               //evaluate in a unique way the angle of rotation comapring it
 577   if(phiref<0) phiref+=TMath::TwoPi();                             //with the vector that poinst to the centre from the mip
 578   if(i2<0) phiref+=TMath::Pi();
 579   if(phiref>TMath::TwoPi()) phiref-=TMath::TwoPi();
 580
 581 //  Printf(" alfa1 %f",alfa1*TMath::RadToDeg());
 582 //  Printf(" alfa2 %f",alfa2*TMath::RadToDeg());
 583 //  Printf(" firef %f",phiref*TMath::RadToDeg());
 584   if(TMath::Abs(alfa1-phiref)<TMath::Abs(alfa2-phiref)) phiRec = alfa1; else phiRec = alfa2;
 585
 586 //  cout << " phi reconstructed " << phiRec*TMath::RadToDeg() << endl;
 587   return (i2>0);
 588 //
 589 }
 590 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 591 Bool_t AliHMPIDRecon::FitFree(Double_t phiRec)
 592 {
 593 // Fit performed by minimizing RMS/sqrt(n) of the
 594 // photons reconstructed. First phi is fixed and theta
 595 // is fouond, then (th,ph) of the track
 596 // as free parameters
 597 // Arguments:    PhiRec phi of the track
 598 //   Returns:    none
 599   Double_t aArg=-1;  Int_t iErrFlg;                                                    //tmp vars for TMinuit
 600   if(!gMinuit) gMinuit = new TMinuit(2);                                               //init MINUIT with this number of parameters (5 params)
 601   gMinuit->mncler();                                                                   // reset Minuit list of paramters
 602   gMinuit->SetObjectFit((TObject*)this);  gMinuit->SetFCN(AliHMPIDRecon::FunMinPhot);  //set fit function
 603   gMinuit->mnexcm("SET PRI",&aArg,1,iErrFlg);                                          //suspend all printout from TMinuit
 604   gMinuit->mnexcm("SET NOW",&aArg,0,iErrFlg);                                          //suspend all warning printout from TMinuit
 605
 606   Double_t d1,d2,d3;
 607   TString sName;
 608   Double_t th,ph;
 609
 610   gMinuit->mnparm(0," theta ",  0.01,0.01,0,TMath::PiOver2(),iErrFlg);
 611   gMinuit->mnparm(1," phi   ",phiRec,0.01,0,TMath::TwoPi()  ,iErrFlg);
 612
 613   gMinuit->FixParameter(1);
 614   gMinuit->mnexcm("SIMPLEX" ,&aArg,0,iErrFlg);
 615   gMinuit->mnexcm("MIGRAD"  ,&aArg,0,iErrFlg);
 616   gMinuit->Release(1);
 617   gMinuit->mnexcm("MIGRAD"  ,&aArg,0,iErrFlg);
 618
 619   gMinuit->mnpout(0,sName,th,d1,d2,d3,iErrFlg);
 620   gMinuit->mnpout(1,sName,ph,d1,d2,d3,iErrFlg);
 621
 622   Double_t outPar[2] = {th,ph}; Double_t g; Double_t f;Int_t flag = 3;
 623   gMinuit->Eval(2, &g, f, outPar,flag);
 624
 625   SetTrkFit(th,ph);
 626
 627   return kTRUE;
 628 }
 629 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 630 Double_t AliHMPIDRecon::FunConSect(Double_t *c,Double_t x,Double_t y)
 631 {
 632   return c[0]*x*x+c[1]*y*y+2*c[2]*x*y+2*c[3]*x+2*c[4]*y+1;
 633 }
 634 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 635 void AliHMPIDRecon::FunMinEl(Int_t &/* */,Double_t* /* */,Double_t &f,Double_t *par,Int_t /* */)
 636 {
 637   AliHMPIDRecon *pRec=(AliHMPIDRecon*)gMinuit->GetObjectFit();
 638   Double_t minFun = 0;
 639   Int_t np = pRec->NClu();
 640   for(Int_t i=0;i<np;i++) {
 641     if(i==pRec->IdxMip()) continue;
 642     Double_t el = pRec->FunConSect(par,pRec->XClu(i),pRec->YClu(i));
 643     minFun +=el*el;
 644   }
 645   f = minFun;
 646 }
 647 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 648 void AliHMPIDRecon::FunMinPhot(Int_t &/* */,Double_t* /* */,Double_t &f,Double_t *par,Int_t iflag)
 649 {
 650   AliHMPIDRecon *pRec=(AliHMPIDRecon*)gMinuit->GetObjectFit();
 651   Double_t sizeCh = 0.5*fgkRadThick+fgkWinThick+fgkGapThick;
 652   Double_t thTrk = par[0];
 653   Double_t phTrk = par[1];
 654   Double_t xrad = pRec->MipX() - sizeCh*TMath::Tan(thTrk)*TMath::Cos(phTrk);
 655   Double_t yrad = pRec->MipY() - sizeCh*TMath::Tan(thTrk)*TMath::Sin(phTrk);
 656   pRec->SetRadXY(xrad,yrad);
 657   pRec->SetTrack(xrad,yrad,thTrk,phTrk);
 658
 659   Double_t meanCkov =0;
 660   Double_t meanCkov2=0;
 661   Double_t thetaCer,phiCer;
 662   Int_t nClAcc = 0;
 663   Int_t nClTot=pRec->NClu();
 664
 665   for(Int_t i=0;i<nClTot;i++) {
 666     if(!(pRec->ClCk(i))) continue;
 667     pRec->FindPhotCkov(pRec->XClu(i),pRec->YClu(i),thetaCer,phiCer);
 668     meanCkov  += thetaCer;
 669     meanCkov2 += thetaCer*thetaCer;
 670     nClAcc++;
 671   }
 672   if(nClAcc==0) {f=0;return;}
 673   meanCkov/=nClAcc;
 674   Double_t rms = TMath::Sqrt(meanCkov2/nClAcc - meanCkov*meanCkov);
 675   f = rms/TMath::Sqrt(nClAcc);
 676
 677
 678   if(iflag==3) {
 679     Printf("FunMinPhot before: photons candidates %i used %i",nClTot,nClAcc);
 680     nClAcc = 0;
 681     Double_t meanCkov1=0;
 682     for(Int_t i=0;i<nClTot;i++) {
 683       if(!(pRec->ClCk(i))) continue;
 684       pRec->FindPhotCkov(pRec->XClu(i),pRec->YClu(i),thetaCer,phiCer);
 685       if(TMath::Abs(thetaCer-meanCkov)<2*rms) {
 686         meanCkov1  += thetaCer;
 687         nClAcc++;
 688       } else pRec->SetClCk(i,kFALSE);
 689     }
 690     meanCkov1/=nClAcc;
 691     Printf("FunMinPhot after: photons candidates %i used %i thetaCer %f",nClTot,nClAcc,meanCkov1);
 692     pRec->SetCkovFit(meanCkov1);
 693     pRec->SetNClu(nClAcc);
 694   }
 695 }//FunMinPhot()
 696 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 697 //
 698 // ended Hidden track algorithm....
 699 //
 700 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++