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 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++