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