JETAN/AliDAJetFinder.cxx

   1
   2 //  **************************************************************************
   3 //  * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
   4 //  *                                                                        *
   5 //  * Author: The ALICE Off-line Project.                                    *
   6 //  * Contributors are mentioned in the code where appropriate.              *
   7 //  *                                                                        *
   8 //  * Permission to use, copy, modify and distribute this software and its   *
   9 //  * documentation strictly for non-commercial purposes is hereby granted   *
  10 //  * without fee, provided that the above copyright notice appears in all   *
  11 //  * copies and that both the copyright notice and this permission notice   *
  12 //  * appear in the supporting documentation. The authors make no claims     *
  13 //  * about the suitability of this software for any purpose. It is          *
  14 //  * provided "as is" without express or implied warranty.                  *
  15 //  **************************************************************************
  16
  17 //-----------------------------------------------------------------------------------
  18 // Jet finder based on Deterministic Annealing
  19 // For further informations about the DA working features see:
  20 // Phys.Lett. B601 (2004) 56-63 (http://arxiv.org/abs/hep-ph/0407214)
  21 // Author: Davide Perrino (davide.perrino@ba.infn.it, davide.perrino@cern.ch)
  22 //-----------------------------------------------------------------------------------
  23
  24 #include <TMath.h>
  25 #include <TRandom.h>
  26 #include <TClonesArray.h>
  27 #include "AliJetReader.h"
  28 #include "AliDAJetHeader.h"
  29 #include "AliDAJetFinder.h"
  30
  31
  32 ClassImp(AliDAJetFinder)
  33
  34
  35 //-----------------------------------------------------------------------------------
  36 AliDAJetFinder::AliDAJetFinder():
  37         fAlpha(1.01),
  38         fDelta(1e-8),
  39         fAvDist(1e-6),
  40         fEps(1e-4),
  41         fEpsMax(1e-2),
  42         fNloopMax(100),
  43         fBeta(0.1),
  44         fNclustMax(0),
  45         fPyx(0x0),
  46         fY(0x0),
  47         fPx(0x0),
  48         fPy(0x0),
  49         fXEta(0x0),
  50         fXPhi(0x0),
  51         fNin(0)
  52 {
  53         // Constructor
  54 }
  55
  56 //-----------------------------------------------------------------------------------
  57 AliDAJetFinder::~AliDAJetFinder()
  58 {
  59         // Destructor
  60         delete fPyx;
  61         delete fY;
  62         delete fPx;
  63         delete fPy;
  64         delete [] fXEta;
  65         delete [] fXPhi;
  66 }
  67
  68 //-----------------------------------------------------------------------------------
  69 void AliDAJetFinder::FindJets()
  70 {
  71 // Find the jets in current event
  72 //
  73         Float_t betaStop=100.;
  74
  75         Double_t dEtSum=0;
  76         InitDetAnn(dEtSum);
  77         if (!fNin) return;
  78
  79         Int_t nc=1,nk;
  80         DoubleClusters(nc,nk);
  81         do{                                     //loop over beta
  82                 fBeta*=fAlpha;
  83                 Annealing(nk);
  84                 NumCl(nc,nk);
  85         }while((fBeta<betaStop || nc<4) && nc<fNclustMax);
  86
  87         Int_t *xx=new Int_t[fNin];
  88         EndDetAnn(nk,xx,dEtSum);
  89         StoreJets(nk,xx);
  90         delete [] xx;
  91
  92 }
  93
  94 //-----------------------------------------------------------------------------------
  95 void AliDAJetFinder::InitDetAnn(Double_t &dEtSum)
  96 {
  97 //Initialise the variables used by the algorithm
  98         fBeta=0.1;
  99         TClonesArray *lvArray = fReader->GetMomentumArray();
 100         fNin = lvArray->GetEntries();
 101         fNclustMax= ((AliDAJetHeader*)fHeader)->GetFixedCl() ?
 102             ((AliDAJetHeader*)fHeader)->GetNclustMax()
 103             :
 104             TMath::Max((Int_t)TMath::Sqrt(fNin),5);
 105         fXEta=new Double_t[fNin]; fXPhi=new Double_t[fNin];
 106         fPx = new TVectorD(fNin);
 107         for (Int_t iIn=0; iIn<fNin; iIn++){
 108                 TLorentzVector *lv=(TLorentzVector*)lvArray->At(iIn);
 109                 fXEta[iIn] = lv->Eta();
 110                 fXPhi[iIn] = lv->Phi()<0 ? lv->Phi() + 2*TMath::Pi() : lv->Phi();
 111                 (*fPx)(iIn)=lv->Pt();
 112                 dEtSum+=(*fPx)(iIn);
 113         }
 114         for (Int_t iIn=0; iIn<fNin; iIn++) (*fPx)(iIn)=(*fPx)(iIn)/dEtSum;
 115
 116         Int_t njdim=2*fNclustMax+1;
 117         fPyx = new TMatrixD(fNin,njdim);
 118         fY = new TMatrixD(4,njdim);
 119         fPy= new TVectorD(njdim);
 120         fY->Zero();fPyx->Zero();fPy->Zero();
 121         (*fPy)(0)=1;
 122         TMatrixDColumn(*fPyx,0)=1;
 123         Double_t ypos=0,xpos=0;
 124         for (Int_t iIn=0; iIn<fNin; iIn++){
 125                 (*fY)(0,0)+=(*fPx)(iIn)*fXEta[iIn];
 126                 ypos+=(*fPx)(iIn)*TMath::Sin(fXPhi[iIn]);
 127                 xpos+=(*fPx)(iIn)*TMath::Cos(fXPhi[iIn]);
 128         }
 129         (*fY)(1,0)=(atan2(ypos,xpos)>0) ? atan2(ypos,xpos) : atan2(ypos,xpos)+2*TMath::Pi();
 130         lvArray->Delete();
 131 }
 132
 133 //-----------------------------------------------------------------------------------
 134 void AliDAJetFinder::DoubleClusters(Int_t nc,Int_t &nk)
 135 {
 136         for(Int_t iClust=0; iClust<nc; iClust++){
 137                 (*fPy)(iClust)=(*fPy)(iClust)/2;
 138                 (*fPy)(nc+iClust)=(*fPy)(iClust);
 139                 for(Int_t iComp=0; iComp<3; iComp++) (*fY)(iComp,nc+iClust)=(*fY)(iComp,iClust);
 140         }
 141         nk=2*nc;
 142 }
 143
 144 //-----------------------------------------------------------------------------------
 145 void AliDAJetFinder::Annealing(Int_t nk)
 146 {
 147 // Main part of the algorithm
 148         const Double_t pi=TMath::Pi();
 149         TVectorD *py = new TVectorD(nk);
 150         TVectorD *p  = new TVectorD(nk);
 151         TMatrixD *y  = new TMatrixD(4,nk);
 152         TMatrixD *y1 = new TMatrixD(4,nk);
 153         TMatrixD *ry = new TMatrixD(2,nk);
 154         Double_t Dist(TVectorD,TVectorD);
 155
 156         Double_t df[2]={((AliDAJetHeader*)fHeader)->GetEtaCut(),pi};
 157         TVectorD vPart(2);
 158         Double_t *m = new Double_t[nk];
 159         Double_t chi,chi1;
 160         do{
 161                 Int_t nloop=0;
 162                 for (Int_t iClust=0; iClust<nk; iClust++){
 163                         for (Int_t i=0; i<3; i++)(*y1)(i,iClust)=(*fY)(i,iClust);
 164                         (*py)(iClust)=(*fPy)(iClust);
 165                 }
 166         //perturbation of codevectors
 167                 Double_t seed=1000000*gRandom->Rndm(24);
 168                 ry->Randomize(-0.5,0.5,seed);
 169                 for (Int_t i=0; i<2; i++){
 170                         for (Int_t iClust=0; iClust<nk/2; iClust++)
 171                                 (*y1)(i,iClust)+=((*ry)(i,iClust)+TMath::Sign(0.5,(*ry)(i,iClust)))*fDelta*df[i];
 172                         for (Int_t iClust=nk/2; iClust<nk; iClust++)
 173                                 (*y1)(i,iClust)-=((*ry)(i,iClust-nk/2)+TMath::Sign(0.5,(*ry)(i,iClust-nk/2)))*fDelta*df[i];
 174                 }
 175                 do{
 176         //recalculate conditional probabilities
 177                         nloop++;
 178                         for (Int_t iIn=0; iIn<fNin; iIn++){
 179                                 vPart(0)=fXEta[iIn]; vPart(1)=fXPhi[iIn];
 180                                 for(Int_t iClust=0; iClust<nk; iClust++){
 181                                         (*fPyx)(iIn,iClust)=-log((*py)(iClust))+fBeta*Dist(vPart,TMatrixDColumn(*y1,iClust));
 182                                         m[iClust]=(*fPyx)(iIn,iClust);
 183                                 }
 184                                 Double_t pyxNorm=0;
 185                                 Double_t minPyx=TMath::MinElement(nk,m);
 186                                 for (Int_t iClust=0; iClust<nk; iClust++){
 187                                         (*fPyx)(iIn,iClust)-=minPyx;
 188                                         (*fPyx)(iIn,iClust)=exp(-(*fPyx)(iIn,iClust));
 189                                         pyxNorm+=(*fPyx)(iIn,iClust);
 190                                 }
 191                                 for (Int_t iClust=0; iClust<nk; iClust++) (*fPyx)(iIn,iClust)/=pyxNorm;
 192                         }
 193                         p->Zero();
 194                         y->Zero();
 195         //recalculate codevectors
 196                         for (Int_t iClust=0; iClust<nk; iClust++){
 197                                 Double_t xpos=0,ypos=0,pxy;
 198                                 for (Int_t iIn=0; iIn<fNin; iIn++) (*p)(iClust)+=(*fPx)(iIn)*(*fPyx)(iIn,iClust);
 199                                 for (Int_t iIn=0; iIn<fNin; iIn++){
 200                                         pxy=(*fPx)(iIn)*(*fPyx)(iIn,iClust)/(*p)(iClust);
 201                                         ypos+=pxy*TMath::Sin(fXPhi[iIn]);
 202                                         xpos+=pxy*TMath::Cos(fXPhi[iIn]);
 203                                         (*y)(0,iClust)+=pxy*fXEta[iIn];
 204                                 }
 205                                 (*y)(1,iClust)=(atan2(ypos,xpos)>0) ? atan2(ypos,xpos) : atan2(ypos,xpos)+2*pi;
 206                         }
 207         //verify codevectors' stability
 208                         chi=0;
 209                         for (Int_t iClust=0; iClust<nk; iClust++){
 210                                 chi1=TMath::CosH((*y1)(0,iClust)-(*y)(0,iClust))-TMath::Cos((*y1)(1,iClust)-(*y)(1,iClust));
 211                                 chi1/=(2*TMath::CosH((*y1)(0,iClust))*TMath::CosH((*y)(0,iClust)));
 212                                 chi1*=chi1;
 213                                 if (chi1>chi) chi=chi1;
 214                         }
 215                         chi=TMath::Sqrt(chi);
 216                         for (Int_t iClust=0; iClust<nk; iClust++){
 217                                 for (Int_t i=0; i<2; i++) (*y1)(i,iClust)=(*y)(i,iClust);
 218                                 (*py)(iClust)=(*p)(iClust);
 219                         }
 220                         if (nloop>fNloopMax){
 221                                 if (chi<fEpsMax || nloop>500) break;
 222                         }
 223                 }while (chi>fEps);
 224         }while (chi>fEpsMax);
 225         for (Int_t iClust=0; iClust<nk; iClust++){                              //set codevectors and probability equal to those calculated
 226                 for (Int_t i=0; i<2; i++) (*fY)(i,iClust)=(*y)(i,iClust);
 227                 (*fPy)(iClust)=(*p)(iClust);
 228         }
 229     delete py;
 230     delete p;
 231     delete y;
 232     delete y1;
 233     delete ry;
 234         delete [] m;
 235 }
 236
 237 //-----------------------------------------------------------------------------------
 238 void AliDAJetFinder::NumCl(Int_t &nc,Int_t &nk)
 239 {
 240         static Bool_t growcl=true;
 241
 242         if (nk==2) growcl=true;
 243         if (growcl){
 244 //verify if two codevectors are equal within fAvDist
 245                 Int_t *nSame = new Int_t[nk];
 246                 Int_t **iSame = new Int_t*[nk];
 247                 Int_t **cont = new Int_t*[nk];
 248                 for (Int_t iClust=0; iClust<nk; iClust++) cont[iClust]=new Int_t[nk],iSame[iClust]=new Int_t[nk];
 249                 for (Int_t iClust=0; iClust<nk; iClust++){
 250                         iSame[iClust][iClust]=1;
 251                         for (Int_t iClust1=iClust+1; iClust1<nk; iClust1++){
 252                                 Double_t eta  = (*fY)(0,iClust) ; Double_t phi  = (*fY)(1,iClust);
 253                                 Double_t eta1 = (*fY)(0,iClust1); Double_t phi1 = (*fY)(1,iClust1);
 254                                 Double_t distCl=(TMath::CosH(eta-eta1)-TMath::Cos(phi-phi1))/(2*TMath::CosH(eta)*TMath::CosH(eta1));
 255                                 if (distCl < fAvDist) iSame[iClust][iClust1]=iSame[iClust1][iClust]=1;
 256                         }
 257                 }
 258                 ReduceClusters(iSame,nk,nc,cont,nSame);
 259                 if (nc >= fNclustMax) growcl=false;
 260 //recalculate the nc distinct codevectors
 261                 TMatrixD *pyx = new TMatrixD(fNin,2*nc);
 262                 TVectorD *py = new TVectorD(nk);
 263                 TMatrixD *y1  = new TMatrixD(3,nk);
 264                 for (Int_t iClust=0; iClust<nc; iClust++){
 265                         for(Int_t j=0; j<nSame[iClust]; j++){
 266                                 Int_t iClust1 = cont[iClust][j];
 267                                 for (Int_t iIn=0; iIn<fNin; iIn++) (*pyx)(iIn,iClust)+=(*fPyx)(iIn,iClust1);
 268                                 (*py)(iClust)+=(*fPy)(iClust1);
 269                                 for (Int_t i=0; i<2; i++) (*y1)(i,iClust)+=(*fY)(i,iClust1);
 270                         }
 271                         for (Int_t i=0; i<2; i++) (*y1)(i,iClust)/=nSame[iClust];
 272                 }
 273                 if (nc > nk/2){
 274                         for (Int_t iClust=0; iClust<nc; iClust++){
 275                                 for (Int_t iIn=0; iIn<fNin; iIn++) (*fPyx)(iIn,iClust)=(*pyx)(iIn,iClust);
 276                                 for (Int_t iComp=0; iComp<2; iComp++) (*fY)(iComp,iClust)=(*y1)(iComp,iClust);
 277                                 (*fPy)(iClust)=(*py)(iClust);
 278                         }
 279                         nk=nc;
 280                         if (growcl) DoubleClusters(nc,nk);
 281                 }
 282                 delete [] nSame;
 283                 delete [] iSame;
 284                 delete [] cont;
 285                 delete pyx;
 286                 delete py;
 287                 delete y1;
 288         }
 289
 290 }
 291
 292 //-----------------------------------------------------------------------------------
 293 void AliDAJetFinder::ReduceClusters(Int_t **iSame,Int_t nc,Int_t &ncout,Int_t **cont,Int_t *nSameOut)
 294 {
 295         Int_t *nSame = new Int_t[nc];
 296         Int_t *iperm = new Int_t[nc];
 297         Int_t *go = new Int_t[nc];
 298         for (Int_t iCl=0; iCl<nc; iCl++){
 299                 nSame[iCl]=0;
 300                 for (Int_t jCl=0; jCl<nc; jCl++) nSame[iCl]+=iSame[iCl][jCl];
 301                 iperm[iCl]=iCl;
 302                 go[iCl]=1;
 303         }
 304         TMath::Sort(nc,nSame,iperm,true);
 305         Int_t l=0;
 306         for (Int_t iCl=0; iCl<nc; iCl++){
 307                 Int_t k=iperm[iCl];
 308                 if (go[k] == 1){
 309                         Int_t m=0;
 310                         for (Int_t jCl=0; jCl<nc; jCl++){
 311                                 if (iSame[k][jCl] == 1){
 312                                         cont[l][m]=jCl;
 313                                         go[jCl]=0;
 314                                         m++;
 315                                 }
 316                         }
 317                         nSameOut[l]=m;
 318                         l++;
 319                 }
 320         }
 321         ncout=l;
 322         delete [] nSame;
 323         delete [] iperm;
 324         delete [] go;
 325 }
 326
 327 //-----------------------------------------------------------------------------------
 328 void AliDAJetFinder::EndDetAnn(Int_t &nk,Int_t *xx,Double_t etx)
 329 {
 330 //now assign each particle to only one cluster
 331         Double_t *clusters=new Double_t[nk];
 332         for (Int_t iIn=0; iIn<fNin; iIn++){
 333                 for (Int_t iClust=0; iClust<nk; iClust++) clusters[iClust]=(*fPyx)(iIn,iClust);
 334                 xx[iIn]=TMath::LocMax(nk,clusters);
 335         }
 336     delete [] clusters;
 337
 338 //recalculate codevectors, having all p(y|x)=0 or 1
 339         fY->Zero();
 340         fPyx->Zero();
 341         fPy->Zero();
 342         for (Int_t iIn=0; iIn<fNin; iIn++){
 343                 Int_t iClust=xx[iIn];
 344                 (*fPyx)(iIn,iClust)=1;
 345                 (*fPy)(iClust)+=(*fPx)(iIn);
 346                 (*fY)(0,iClust)+=(*fPx)(iIn)*fXEta[iIn];
 347                 (*fY)(3,iClust)+=(*fPx)(iIn)*etx;
 348         }
 349         Int_t k=0;
 350         for (Int_t iClust=0; iClust<nk; iClust++){
 351                 if ((*fPy)(iClust)>0){
 352                         Double_t xpos=0,ypos=0,pxy;
 353                         for (Int_t iIn=0; iIn<fNin; iIn++){
 354                                 pxy=(*fPx)(iIn)*(*fPyx)(iIn,iClust)/(*fPy)(iClust);
 355                                 ypos+=pxy*TMath::Sin(fXPhi[iIn]);
 356                                 xpos+=pxy*TMath::Cos(fXPhi[iIn]);
 357                                 if (xx[iIn]==iClust) xx[iIn]=k;
 358                         }
 359                         (*fY)(0,k)=(*fY)(0,iClust)/(*fPy)(iClust);
 360                         (*fY)(1,k)=(atan2(ypos,xpos)>0) ? atan2(ypos,xpos) : atan2(ypos,xpos)+2*TMath::Pi();
 361                         (*fY)(3,k)=(*fY)(3,iClust);
 362                         k++;
 363                 }
 364         }
 365         nk=k;
 366 }
 367
 368 //-----------------------------------------------------------------------------------
 369 void AliDAJetFinder::StoreJets(Int_t nk,Int_t *xx)
 370 {
 371 //evaluate significant clusters properties
 372         const Double_t pi=TMath::Pi();
 373         Double_t dMeanDist=TMath::Sqrt(4*((AliDAJetHeader*)fHeader)->GetEtaCut()*pi/fNin);
 374         Bool_t   *isJet = new Bool_t[nk];
 375         Double_t *etNoBg= new Double_t[nk];
 376         Double_t *dDeltaEta=new Double_t[nk];
 377         Double_t *dDeltaPhi=new Double_t[nk];
 378         Double_t *surf  = new Double_t[nk];
 379         Double_t *etDens= new Double_t[nk];
 380         for (Int_t iClust=0; iClust<nk; iClust++){                                                                      //clusters loop
 381                 isJet[iClust]=false;
 382                 Double_t dEtaMin=10.,dEtaMax=-10.,dPhiMin=10.,dPhiMax=0.;
 383                 for (Int_t iIn=0; iIn<fNin; iIn++){
 384                         if (xx[iIn]!=iClust) continue;
 385                         if (fXEta[iIn] < dEtaMin) dEtaMin=fXEta[iIn];
 386                         if (fXEta[iIn] > dEtaMax) dEtaMax=fXEta[iIn];
 387                         Double_t dPhi=fXPhi[iIn]-(*fY)(1,iClust);
 388                         if      (dPhi > pi     ) dPhi-=2*pi;
 389                         else if (dPhi < (-1)*pi) dPhi+=2*pi;
 390                         if      (dPhi < dPhiMin) dPhiMin=dPhi;
 391                         else if (dPhi > dPhiMax) dPhiMax=dPhi;
 392                 }
 393                 dDeltaEta[iClust]=dEtaMax-dEtaMin+dMeanDist;
 394                 dDeltaPhi[iClust]=dPhiMax-dPhiMin+dMeanDist;
 395                 surf[iClust]=0.25*pi*dDeltaEta[iClust]*dDeltaPhi[iClust];
 396                 etDens[iClust]=(*fY)(3,iClust)/surf[iClust];
 397         }
 398
 399         if (((AliDAJetHeader*)fHeader)->GetSelJets()){
 400                 for (Int_t iClust=0; iClust<nk; iClust++){
 401                         if (!isJet[iClust]){
 402                                 Double_t etDensMed=0.;
 403                                 Double_t etDensSqr=0.;
 404                                 Int_t norm=0;
 405                                 for (Int_t iClust1=0; iClust1<nk; iClust1++){
 406                                         if(iClust1!=iClust){
 407                                                 etDensMed+=etDens[iClust1];
 408                                                 etDensSqr+=TMath::Power(etDens[iClust1],2);
 409                                                 norm++;
 410                                         }
 411                                 }
 412                                 etDensMed/=TMath::Max(norm,1);
 413                                 etDensSqr/=TMath::Max(norm,1);
 414                                 Double_t deltaEtDens=TMath::Sqrt(etDensSqr-TMath::Power(etDensMed,2));
 415                                 if ((*fY)(3,iClust) > (etDensMed+deltaEtDens)*surf[iClust]) isJet[iClust]=kTRUE;
 416                                 etNoBg[iClust]=(*fY)(3,iClust)-etDensMed*surf[iClust];
 417                         }
 418                 }
 419                 for (Int_t iClust=0; iClust<nk; iClust++){
 420                         if (isJet[iClust]){
 421                                 Double_t etDensMed=0;
 422                                 Double_t extSurf=4*((AliDAJetHeader*)fHeader)->GetEtaCut()*pi;
 423                                 for (Int_t iClust1=0; iClust1<nk; iClust1++){
 424                                         if (!isJet[iClust1]) etDensMed+=(*fY)(3,iClust1);
 425                                         else extSurf-=surf[iClust1];
 426                                 }
 427                                 etDensMed/=extSurf;
 428                                 etNoBg[iClust]=(*fY)(3,iClust)-etDensMed*surf[iClust];
 429                         }
 430                 }
 431         } else {
 432                 for (Int_t iClust=0; iClust<nk; iClust++) isJet[iClust]=true;
 433         }
 434         delete [] etDens;
 435         delete [] surf;
 436
 437 //now add selected jets to the list
 438         Int_t *inJet = new Int_t[fNin];
 439         TRefArray *refs = 0;
 440         Bool_t fromAod = !strcmp(fReader->ClassName(),"AliJetAODReader");
 441         if (fromAod) refs = fReader->GetReferences();
 442         for (Int_t iClust=0; iClust<nk; iClust++){                                                                      //clusters loop
 443                 if (isJet[iClust]){                                                                                                             //choose cluster
 444                         Float_t px,py,pz,en;
 445                         px = (*fY)(3,iClust)*TMath::Cos((*fY)(1,iClust));
 446                         py = (*fY)(3,iClust)*TMath::Sin((*fY)(1,iClust));
 447                         pz = (*fY)(3,iClust)/TMath::Tan(2.0 * TMath::ATan(TMath::Exp(-(*fY)(0,iClust))));
 448                         en = TMath::Sqrt(px * px + py * py + pz * pz);
 449                         AliAODJet jet(px, py, pz, en);
 450                         if (fromAod)
 451                             for (Int_t iIn=0; iIn<fNin; iIn++) if (xx[iIn]==iClust) jet.AddTrack(refs->At(iIn));
 452                         AddJet(jet);
 453                         printf("jet %d, Eta: %f, Phi: %f, Et: %f\n",iClust,jet.Eta(),jet.Phi(),jet.Pt());
 454                 }
 455         }
 456         delete [] dDeltaEta; delete [] dDeltaPhi;
 457         delete [] etNoBg;
 458         delete [] isJet;
 459         delete [] inJet;
 460 }
 461
 462 //-----------------------------------------------------------------------------------
 463 Double_t Dist(TVectorD x,TVectorD y)
 464 {
 465 // Squared distance
 466         const Double_t pi=TMath::Pi();
 467         Double_t dphi=TMath::Abs(x(1)-y(1));
 468         if (dphi > pi) dphi=2*pi-dphi;
 469         Double_t dist=pow(x(0)-y(0),2)+pow(dphi,2);
 470         return dist;
 471 }