PWG2/FLOW/AliFlowAnalysisWithCumulants.cxx

   1 /*************************************************************************
   2 * Copyright(c) 1998-2008, ALICE Experiment at CERN, All rights reserved. *
   3 *                                                                        *
   4 * Author: The ALICE Off-line Project.                                    *
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  15
  16 /********************************
  17  * flow analysis with cumulants *
  18  *                              *
  19  * author: Ante Bilandzic       *
  20  *          (anteb@nikhef.nl)   *
  21  *******************************/
  22
  23 #define AliFlowAnalysisWithCumulants_cxx
  24
  25 #include "Riostream.h"
  26 #include "AliFlowCommonConstants.h"
  27 #include "AliFlowCommonHist.h"
  28 #include "AliFlowCommonHistResults.h"
  29 #include "TChain.h"
  30 #include "TFile.h"
  31 #include "TList.h" //NEW
  32 #include "TParticle.h"
  33 #include "TRandom3.h"
  34 #include "TProfile.h"
  35 #include "TProfile2D.h"
  36 #include "TProfile3D.h"
  37 #include "AliFlowEventSimple.h"
  38 #include "AliFlowTrackSimple.h"
  39 #include "AliFlowAnalysisWithCumulants.h"
  40 #include "AliFlowCumuConstants.h"
  41
  42 class TH1;
  43 class TGraph;
  44 class TPave;
  45 class TLatex;
  46 class TMarker;
  47 class TRandom3;
  48 class TObjArray;
  49 class TList;
  50 class TCanvas;
  51 class TSystem;
  52 class TROOT;
  53 class AliFlowVector;
  54 class TVector;
  55
  56 //================================================================================================================
  57
  58 ClassImp(AliFlowAnalysisWithCumulants)
  59
  60 AliFlowAnalysisWithCumulants::AliFlowAnalysisWithCumulants():
  61  fTrack(NULL),
  62  fHistList(NULL),
  63  fR0(0),
  64  fPtMax(0),
  65  fPtMin(0),
  66  fBinWidth(0),
  67  fAvQx(0),
  68  fAvQy(0),
  69  fAvQ2x(0),
  70  fAvQ2y(0),
  71  fAvMultIntFlow(NULL),
  72  fQVectorComponents(NULL),
  73  fIntFlowResults(NULL),
  74  fDiffFlowResults2(NULL),
  75  fDiffFlowResults4(NULL),
  76  fDiffFlowResults6(NULL),
  77  fDiffFlowResults8(NULL),
  78  fIntFlowGenFun(NULL),
  79  fDiffFlowGenFunRe(NULL),
  80  fDiffFlowGenFunIm(NULL),
  81  fDiffFlowGenFunRe0(NULL),
  82  fDiffFlowGenFunRe1(NULL),
  83  fDiffFlowGenFunRe2(NULL),
  84  fDiffFlowGenFunRe3(NULL),
  85  fDiffFlowGenFunRe4(NULL),
  86  fDiffFlowGenFunRe5(NULL),
  87  fDiffFlowGenFunRe6(NULL),
  88  fDiffFlowGenFunRe7(NULL),
  89  fDiffFlowGenFunIm0(NULL),
  90  fDiffFlowGenFunIm1(NULL),
  91  fDiffFlowGenFunIm2(NULL),
  92  fDiffFlowGenFunIm3(NULL),
  93  fDiffFlowGenFunIm4(NULL),
  94  fDiffFlowGenFunIm5(NULL),
  95  fDiffFlowGenFunIm6(NULL),
  96  fDiffFlowGenFunIm7(NULL),
  97  fCommonHists(NULL),
  98  fQDist(NULL)//q-distribution
  99 {
 100  //constructor
 101  fHistList = new TList();
 102  fR0=AliFlowCumuConstants::fgR0;
 103  fPtMax=AliFlowCommonConstants::GetPtMax();
 104  fPtMin=AliFlowCommonConstants::GetPtMin();
 105  fBinWidth=(fPtMax-fPtMin)/fgknBins;
 106 }
 107
 108 AliFlowAnalysisWithCumulants::~AliFlowAnalysisWithCumulants()
 109 {
 110  //desctructor
 111  delete fHistList;
 112 }
 113
 114 //================================================================================================================
 115
 116 void AliFlowAnalysisWithCumulants::CreateOutputObjects()
 117 {
 118  //various output histograms
 119
 120  //avarage multiplicity
 121  fAvMultIntFlow = new TProfile("fAvMultIntFlow","Avarage multiplicity of selected particles used for int. flow",1,0,1,0,100000);
 122  fAvMultIntFlow->SetXTitle("");
 123  fAvMultIntFlow->SetYTitle("<multiplicity>");
 124  fHistList->Add(fAvMultIntFlow);
 125
 126  //Q-vector stuff
 127  fQVectorComponents = new TProfile("fQVectorComponents","Avarage of Q-vector components",4,0.,4.);
 128  fQVectorComponents->SetXTitle("");
 129  fQVectorComponents->SetYTitle("< >");
 130  fHistList->Add(fQVectorComponents);
 131
 132  //final results for integrated flow (v_n{2}, v_n{4},..., v_n{16}) from cumulants (by default n=2)
 133  fIntFlowResults = new TH1D("fIntFlowResults","Integrated Flow From Cumulants",8,0,8);
 134  fIntFlowResults->SetXTitle("");
 135  fIntFlowResults->SetYTitle("Integrated Flow [%]");
 136  fHistList->Add(fIntFlowResults);
 137
 138  //final results for differential flow v_p/n{2} (by default p=n=2)
 139  fDiffFlowResults2 = new TH1D("fDiffFlowResults2","v'_2/2{2}",fgknBins,fPtMin,fPtMax);
 140  fDiffFlowResults2->SetXTitle("pt [GeV]");
 141  fDiffFlowResults2->SetYTitle("Differential Flow [%]");
 142  fHistList->Add(fDiffFlowResults2);
 143
 144  //final results for differential flow v_p/n{4} (by default p=n=2)
 145  fDiffFlowResults4 = new TH1D("fDiffFlowResults4","v'_2/2{4}",fgknBins,fPtMin,fPtMax);
 146  fDiffFlowResults4->SetXTitle("pt [GeV]");
 147  fDiffFlowResults4->SetYTitle("Differential Flow [%]");
 148  fHistList->Add(fDiffFlowResults4);
 149
 150  //final results for differential flow v_p/n{6} (by default p=n=2)
 151  fDiffFlowResults6 = new TH1D("fDiffFlowResults6","v'_2/2{6}",fgknBins,fPtMin,fPtMax);
 152  fDiffFlowResults6->SetXTitle("pt [GeV]");
 153  fDiffFlowResults6->SetYTitle("Differential Flow [%]");
 154  fHistList->Add(fDiffFlowResults6);
 155
 156  //final results for differential flow v_p/n{8} (by default p=n=2)
 157  fDiffFlowResults8 = new TH1D("fDiffFlowResults8","v'_2/2{8}",fgknBins,fPtMin,fPtMax);
 158  fDiffFlowResults8->SetXTitle("pt [GeV]");
 159  fDiffFlowResults8->SetYTitle("Differential Flow [%]");
 160  fHistList->Add(fDiffFlowResults8);
 161
 162  //avarage of the generating function for integrated flow <G[p][q]>
 163  fIntFlowGenFun = new TProfile2D("fIntFlowGenFun","<G[p][q]>",fgkPmax,0.,(Double_t)fgkPmax,fgkQmax,0.,(Double_t)fgkQmax);
 164  fIntFlowGenFun->SetXTitle("p");
 165  fIntFlowGenFun->SetYTitle("q");
 166  fHistList->Add(fIntFlowGenFun);
 167
 168  /*
 169  //avarage of the real part of generating function for differential flow <Re(D[b][p][q])>
 170  fDiffFlowGenFunRe = new TProfile3D("fDiffFlowGenFunRe","<Re(D[b][p][q])>",fgknBins,(Double_t)(fPtMin/fBinWidth),(Double_t)(fPtMax/fBinWidth),fgkPmax,0.,(Double_t)fgkPmax,fgkQmax,0.,(Double_t)fgkQmax);
 171  fDiffFlowGenFunRe->SetXTitle("b");
 172  fDiffFlowGenFunRe->SetYTitle("p");
 173  fDiffFlowGenFunRe->SetZTitle("q");
 174  fHistList->Add(fDiffFlowGenFunRe);
 175
 176  //avarage of the imaginary part of generating function for differential flow <Im(D[b][p][q])>
 177  fDiffFlowGenFunIm = new TProfile3D("fDiffFlowGenFunIm","<Im(D[b][p][q])>",fgknBins,(Double_t)(fPtMin/fBinWidth),(Double_t)(fPtMax/fBinWidth),fgkPmax,0.,(Double_t)fgkPmax,fgkQmax,0.,(Double_t)fgkQmax);
 178  fDiffFlowGenFunIm->SetXTitle("b");
 179  fDiffFlowGenFunIm->SetYTitle("p");
 180  fDiffFlowGenFunIm->SetZTitle("q");
 181  fHistList->Add(fDiffFlowGenFunIm);
 182  */
 183
 184  fDiffFlowGenFunRe0 = new TProfile2D("fDiffFlowGenFunRe0","Re(<D[b][0][q]>)",fgknBins,(Double_t)(fPtMin/fBinWidth),(Double_t)(fPtMax/fBinWidth),fgkQmax,0.,(Double_t)fgkQmax);
 185  fDiffFlowGenFunRe0->SetXTitle("b");
 186  fDiffFlowGenFunRe0->SetYTitle("q");
 187  fHistList->Add(fDiffFlowGenFunRe0);
 188
 189  fDiffFlowGenFunIm0 = new TProfile2D("fDiffFlowGenFunIm0","Im(<D[b][0][q]>)",fgknBins,(Double_t)(fPtMin/fBinWidth),(Double_t)(fPtMax/fBinWidth),fgkQmax,0.,(Double_t)fgkQmax);
 190  fDiffFlowGenFunIm0->SetXTitle("b");
 191  fDiffFlowGenFunIm0->SetYTitle("q");
 192  fHistList->Add(fDiffFlowGenFunIm0);
 193
 194  fDiffFlowGenFunRe1 = new TProfile2D("fDiffFlowGenFunRe1","Re(<D[b][1][q]>)",fgknBins,(Double_t)(fPtMin/fBinWidth),(Double_t)(fPtMax/fBinWidth),fgkQmax,0.,(Double_t)fgkQmax);
 195  fDiffFlowGenFunRe1->SetXTitle("b");
 196  fDiffFlowGenFunRe1->SetYTitle("q");
 197  fHistList->Add(fDiffFlowGenFunRe1);
 198
 199  fDiffFlowGenFunIm1 = new TProfile2D("fDiffFlowGenFunIm1","Im(<D[b][1][q]>)",fgknBins,(Double_t)(fPtMin/fBinWidth),(Double_t)(fPtMax/fBinWidth),fgkQmax,0.,(Double_t)fgkQmax);
 200  fDiffFlowGenFunIm1->SetXTitle("b");
 201  fDiffFlowGenFunIm1->SetYTitle("q");
 202  fHistList->Add(fDiffFlowGenFunIm1);
 203
 204  fDiffFlowGenFunRe2 = new TProfile2D("fDiffFlowGenFunRe2","Re(<D[b][2][q]>)",fgknBins,(Double_t)(fPtMin/fBinWidth),(Double_t)(fPtMax/fBinWidth),fgkQmax,0.,(Double_t)fgkQmax);
 205  fDiffFlowGenFunRe2->SetXTitle("b");
 206  fDiffFlowGenFunRe2->SetYTitle("q");
 207  fHistList->Add(fDiffFlowGenFunRe2);
 208
 209  fDiffFlowGenFunIm2 = new TProfile2D("fDiffFlowGenFunIm2","Im(<D[b][2][q]>)",fgknBins,(Double_t)(fPtMin/fBinWidth),(Double_t)(fPtMax/fBinWidth),fgkQmax,0.,(Double_t)fgkQmax);
 210  fDiffFlowGenFunIm2->SetXTitle("b");
 211  fDiffFlowGenFunIm2->SetYTitle("q");
 212  fHistList->Add(fDiffFlowGenFunIm2);
 213
 214  fDiffFlowGenFunRe3 = new TProfile2D("fDiffFlowGenFunRe3","Re(<D[b][3][q]>)",fgknBins,(Double_t)(fPtMin/fBinWidth),(Double_t)(fPtMax/fBinWidth),fgkQmax,0.,(Double_t)fgkQmax);
 215  fDiffFlowGenFunRe3->SetXTitle("b");
 216  fDiffFlowGenFunRe3->SetYTitle("q");
 217  fHistList->Add(fDiffFlowGenFunRe3);
 218
 219  fDiffFlowGenFunIm3 = new TProfile2D("fDiffFlowGenFunIm3","Im(<D[b][3][q]>)",fgknBins,(Double_t)(fPtMin/fBinWidth),(Double_t)(fPtMax/fBinWidth),fgkQmax,0.,(Double_t)fgkQmax);
 220  fDiffFlowGenFunIm3->SetXTitle("b");
 221  fDiffFlowGenFunIm3->SetYTitle("q");
 222  fHistList->Add(fDiffFlowGenFunIm3);
 223
 224  fDiffFlowGenFunRe4 = new TProfile2D("fDiffFlowGenFunRe4","Re(<D[b][4][q]>)",fgknBins,(Double_t)(fPtMin/fBinWidth),(Double_t)(fPtMax/fBinWidth),fgkQmax,0.,(Double_t)fgkQmax);
 225  fDiffFlowGenFunRe4->SetXTitle("b");
 226  fDiffFlowGenFunRe4->SetYTitle("q");
 227  fHistList->Add(fDiffFlowGenFunRe4);
 228
 229  fDiffFlowGenFunIm4 = new TProfile2D("fDiffFlowGenFunIm4","Im(<D[b][4][q]>)",fgknBins,(Double_t)(fPtMin/fBinWidth),(Double_t)(fPtMax/fBinWidth),fgkQmax,0.,(Double_t)fgkQmax);
 230  fDiffFlowGenFunIm4->SetXTitle("b");
 231  fDiffFlowGenFunIm4->SetYTitle("q");
 232  fHistList->Add(fDiffFlowGenFunIm4);
 233
 234  fDiffFlowGenFunRe5 = new TProfile2D("fDiffFlowGenFunRe5","Re(<D[b][5][q]>)",fgkQmax,0.,(Double_t)fgkQmax,fgknBins,(Double_t)(fPtMin/fBinWidth),(Double_t)(fPtMax/fBinWidth));
 235  fDiffFlowGenFunRe5->SetXTitle("b");
 236  fDiffFlowGenFunRe5->SetYTitle("q");
 237  fHistList->Add(fDiffFlowGenFunRe5);
 238
 239  fDiffFlowGenFunIm5 = new TProfile2D("fDiffFlowGenFunIm5","Im(<D[b][5][q]>)",fgknBins,(Double_t)(fPtMin/fBinWidth),(Double_t)(fPtMax/fBinWidth),fgkQmax,0.,(Double_t)fgkQmax);
 240  fDiffFlowGenFunIm5->SetXTitle("b");
 241  fDiffFlowGenFunIm5->SetYTitle("q");
 242  fHistList->Add(fDiffFlowGenFunIm5);
 243
 244  fDiffFlowGenFunRe6 = new TProfile2D("fDiffFlowGenFunRe6","Re(<D[b][6][q]>)",fgknBins,(Double_t)(fPtMin/fBinWidth),(Double_t)(fPtMax/fBinWidth),fgkQmax,0.,(Double_t)fgkQmax);
 245  fDiffFlowGenFunRe6->SetXTitle("b");
 246  fDiffFlowGenFunRe6->SetYTitle("q");
 247  fHistList->Add(fDiffFlowGenFunRe6);
 248
 249  fDiffFlowGenFunIm6 = new TProfile2D("fDiffFlowGenFunIm6","Im(<D[b][6][q]>)",fgknBins,(Double_t)(fPtMin/fBinWidth),(Double_t)(fPtMax/fBinWidth),fgkQmax,0.,(Double_t)fgkQmax);
 250  fDiffFlowGenFunIm6->SetXTitle("b");
 251  fDiffFlowGenFunIm6->SetYTitle("q");
 252  fHistList->Add(fDiffFlowGenFunIm6);
 253
 254  fDiffFlowGenFunRe7 = new TProfile2D("fDiffFlowGenFunRe7","Re(<D[b][7][q]>)",fgknBins,(Double_t)(fPtMin/fBinWidth),(Double_t)(fPtMax/fBinWidth),fgkQmax,0.,(Double_t)fgkQmax);
 255  fDiffFlowGenFunRe7->SetXTitle("b");
 256  fDiffFlowGenFunRe7->SetYTitle("q");
 257  fHistList->Add(fDiffFlowGenFunRe7);
 258
 259  fDiffFlowGenFunIm7 = new TProfile2D("fDiffFlowGenFunIm7","Im(<D[b][7][q]>)",fgknBins,(Double_t)(fPtMin/fBinWidth),(Double_t)(fPtMax/fBinWidth),fgkQmax,0.,(Double_t)fgkQmax);
 260  fDiffFlowGenFunIm7->SetXTitle("b");
 261  fDiffFlowGenFunIm7->SetYTitle("q");
 262  fHistList->Add(fDiffFlowGenFunIm7);
 263
 264  //common control histograms
 265  fCommonHists = new AliFlowCommonHist("Cumulants");
 266  fHistList->Add(fCommonHists->GetHistList());
 267
 268  //q-distribution
 269  fQDist = new TH1D("fQDist","q-distribution",100,0,10);
 270  fQDist->SetXTitle("q=Q/#sqrt{M}");
 271  fQDist->SetYTitle("dN_{event}/dq");
 272  fHistList->Add(fQDist);
 273
 274 }//end of CreateOutputObjects()
 275
 276 //================================================================================================================
 277
 278 void AliFlowAnalysisWithCumulants::Make(AliFlowEventSimple* anEvent)
 279 {
 280  //running over data
 281
 282  //fill the common control histograms
 283  fCommonHists->FillControlHistograms(anEvent);
 284
 285  //initializing the generating function G[p][q] for integrated flow
 286  Double_t G[fgkPmax][fgkQmax];
 287  for(Int_t p=0;p<fgkPmax;p++){
 288   for(Int_t q=0;q<fgkQmax;q++){
 289    G[p][q]=1.;
 290   }
 291  }
 292
 293  Int_t nPrim = anEvent->NumberOfTracks();//total multiplicity
 294  Int_t nEventNSelTracksIntFlow = anEvent->GetEventNSelTracksIntFlow();//selected multiplicity (parrticles used for int. flow)
 295  Int_t nSelTracksIntFlow = 0;//cross-checking the selected multiplicity
 296
 297  //first loop over data: evaluating the generating function G[p][q] for integrated flow
 298  for(Int_t i=0;i<nPrim;i++){
 299   fTrack=anEvent->GetTrack(i);
 300   if(fTrack&&fTrack->UseForIntegratedFlow()){
 301    nSelTracksIntFlow++;
 302    for(Int_t p=0;p<fgkPmax;p++){
 303     for(Int_t q=0;q<fgkQmax;q++){
 304      G[p][q]*=(1.+(2.*fR0*sqrt(p+1.)/nEventNSelTracksIntFlow)*cos(fgkFlow*fTrack->Phi()-2.*q*TMath::Pi()/fgkQmax));
 305     }
 306    }
 307   }
 308  }//ending the first loop over data
 309
 310  //storing the value of G[p][q] in 2D profile in order to get automatically the avarage <G[p][q]>
 311  for(Int_t p=0;p<fgkPmax;p++){
 312   for(Int_t q=0;q<fgkQmax;q++){
 313    fIntFlowGenFun->Fill((Double_t)p,(Double_t)q,G[p][q],1);
 314   }
 315  }
 316
 317  //storing the selected multiplicity (if fAvMultIntFlow is not filled here then you had wrongly selected the particles used for integrated flow)
 318  if(nSelTracksIntFlow==nEventNSelTracksIntFlow)
 319  {
 320   fAvMultIntFlow->Fill(0.,nSelTracksIntFlow,1);
 321  }
 322
 323  //calculating Q-vector of event (needed for errors)
 324  AliFlowVector fQVector;
 325  fQVector.Set(0.,0.);
 326  fQVector.SetMult(0);
 327  fQVector=anEvent->GetQ();                            //get the Q vector for this event
 328  fQVectorComponents->Fill(0.,fQVector.X(),1);         //in the 1st bin fill Q_x
 329  fQVectorComponents->Fill(1.,fQVector.Y(),1);         //in the 2nd bin fill Q_y
 330  fQVectorComponents->Fill(2.,pow(fQVector.X(),2.),1); //in the 3rd bin fill (Q_x)^2
 331  fQVectorComponents->Fill(3.,pow(fQVector.Y(),2.),1); //in the 4th bin fill (Q_y)^2
 332
 333  //q-distribution
 334  Double_t qDist = fQVector.Mod()/sqrt(fQVector.GetMult());
 335  fQDist->Fill(qDist,1);
 336
 337  /*
 338  //two 3D profiles for differential flow
 339  //second loop over data: evaluating the generating function D[b][p][q] for differential flow
 340  //remark 0: D[b][p][q] is a complex number => real and imaginary part are calculated separately
 341  //remark 1: note that below G[p][q] is needed, the value of generating function for integrated flow for the CURRENT event
 342  //remark 2: results are stored in two 3D profiles in order to automatically get <Re(D[b][p][q])> and <Im(D[b][p][q])>
 343  for(Int_t i=0;i<nPrim;i++){
 344   fTrack=anEvent->GetTrack(i);
 345   if (fTrack && fTrack->UseForDifferentialFlow()){
 346    for(Int_t p=0;p<fgkPmax;p++){
 347     for(Int_t q=0;q<fgkQmax;q++){
 348      //real part
 349      fDiffFlowGenFunRe->Fill(fTrack->Pt()/fBinWidth,(Double_t)p,(Double_t)q,G[p][q]*cos(fgkMltpl*fgkFlow*fTrack->Phi())/(1.+(2.*fR0*sqrt(p+1.)/nSelTracksIntFlow)*cos(fgkFlow*fTrack->Phi()-2.*q*TMath::Pi()/fgkQmax)),1.);
 350      //imaginary part
 351      fDiffFlowGenFunIm->Fill(fTrack->Pt()/fBinWidth,(Double_t)p,(Double_t)q,G[p][q]*sin(fgkMltpl*fgkFlow*fTrack->Phi())/(1.+(2.*fR0*sqrt(p+1.)/nSelTracksIntFlow)*cos(fgkFlow*fTrack->Phi()-2.*q*TMath::Pi()/fgkQmax)),1.);
 352     }
 353    }
 354   }
 355  }//ending the second loop over data
 356  */
 357
 358  //sixteen 2D profiles for differential flow
 359  for(Int_t i=0;i<nPrim;i++){
 360   fTrack=anEvent->GetTrack(i);
 361   if (fTrack && fTrack->UseForDifferentialFlow()){
 362    //for(Int_t p=0;p<fgkPmax;p++){
 363     for(Int_t q=0;q<fgkQmax;q++){
 364      //real part
 365      fDiffFlowGenFunRe0->Fill(fTrack->Pt()/fBinWidth,(Double_t)q,G[0][q]*cos(fgkMltpl*fgkFlow*fTrack->Phi())/(1.+(2.*fR0*sqrt(0.+1.)/nSelTracksIntFlow)*cos(fgkFlow*fTrack->Phi()-2.*q*TMath::Pi()/fgkQmax)),1.);
 366      //imaginary part
 367      fDiffFlowGenFunIm0->Fill(fTrack->Pt()/fBinWidth,(Double_t)q,G[0][q]*sin(fgkMltpl*fgkFlow*fTrack->Phi())/(1.+(2.*fR0*sqrt(0.+1.)/nSelTracksIntFlow)*cos(fgkFlow*fTrack->Phi()-2.*q*TMath::Pi()/fgkQmax)),1.);
 368      //-----------------------------------------------------------------------
 369      //real part
 370      fDiffFlowGenFunRe1->Fill(fTrack->Pt()/fBinWidth,(Double_t)q,G[1][q]*cos(fgkMltpl*fgkFlow*fTrack->Phi())/(1.+(2.*fR0*sqrt(1.+1.)/nSelTracksIntFlow)*cos(fgkFlow*fTrack->Phi()-2.*q*TMath::Pi()/fgkQmax)),1.);
 371      //imaginary part
 372      fDiffFlowGenFunIm1->Fill(fTrack->Pt()/fBinWidth,(Double_t)q,G[1][q]*sin(fgkMltpl*fgkFlow*fTrack->Phi())/(1.+(2.*fR0*sqrt(1.+1.)/nSelTracksIntFlow)*cos(fgkFlow*fTrack->Phi()-2.*q*TMath::Pi()/fgkQmax)),1.);
 373     //-----------------------------------------------------------------------
 374      //real part
 375      fDiffFlowGenFunRe2->Fill(fTrack->Pt()/fBinWidth,(Double_t)q,G[2][q]*cos(fgkMltpl*fgkFlow*fTrack->Phi())/(1.+(2.*fR0*sqrt(2.+1.)/nSelTracksIntFlow)*cos(fgkFlow*fTrack->Phi()-2.*q*TMath::Pi()/fgkQmax)),1.);
 376      //imaginary part
 377      fDiffFlowGenFunIm2->Fill(fTrack->Pt()/fBinWidth,(Double_t)q,G[2][q]*sin(fgkMltpl*fgkFlow*fTrack->Phi())/(1.+(2.*fR0*sqrt(2.+1.)/nSelTracksIntFlow)*cos(fgkFlow*fTrack->Phi()-2.*q*TMath::Pi()/fgkQmax)),1.);
 378      //-----------------------------------------------------------------------
 379      //real part
 380      fDiffFlowGenFunRe3->Fill(fTrack->Pt()/fBinWidth,(Double_t)q,G[3][q]*cos(fgkMltpl*fgkFlow*fTrack->Phi())/(1.+(2.*fR0*sqrt(3.+1.)/nSelTracksIntFlow)*cos(fgkFlow*fTrack->Phi()-2.*q*TMath::Pi()/fgkQmax)),1.);
 381      //imaginary part
 382      fDiffFlowGenFunIm3->Fill(fTrack->Pt()/fBinWidth,(Double_t)q,G[3][q]*sin(fgkMltpl*fgkFlow*fTrack->Phi())/(1.+(2.*fR0*sqrt(3.+1.)/nSelTracksIntFlow)*cos(fgkFlow*fTrack->Phi()-2.*q*TMath::Pi()/fgkQmax)),1.);
 383      //-----------------------------------------------------------------------
 384      //real part
 385      fDiffFlowGenFunRe4->Fill(fTrack->Pt()/fBinWidth,(Double_t)q,G[4][q]*cos(fgkMltpl*fgkFlow*fTrack->Phi())/(1.+(2.*fR0*sqrt(4.+1.)/nSelTracksIntFlow)*cos(fgkFlow*fTrack->Phi()-2.*q*TMath::Pi()/fgkQmax)),1.);
 386      //imaginary part
 387      fDiffFlowGenFunIm4->Fill(fTrack->Pt()/fBinWidth,(Double_t)q,G[4][q]*sin(fgkMltpl*fgkFlow*fTrack->Phi())/(1.+(2.*fR0*sqrt(4.+1.)/nSelTracksIntFlow)*cos(fgkFlow*fTrack->Phi()-2.*q*TMath::Pi()/fgkQmax)),1.);
 388      //-----------------------------------------------------------------------
 389      //real part
 390      fDiffFlowGenFunRe5->Fill(fTrack->Pt()/fBinWidth,(Double_t)q,G[5][q]*cos(fgkMltpl*fgkFlow*fTrack->Phi())/(1.+(2.*fR0*sqrt(5.+1.)/nSelTracksIntFlow)*cos(fgkFlow*fTrack->Phi()-2.*q*TMath::Pi()/fgkQmax)),1.);
 391      //imaginary part
 392      fDiffFlowGenFunIm5->Fill(fTrack->Pt()/fBinWidth,(Double_t)q,G[5][q]*sin(fgkMltpl*fgkFlow*fTrack->Phi())/(1.+(2.*fR0*sqrt(5.+1.)/nSelTracksIntFlow)*cos(fgkFlow*fTrack->Phi()-2.*q*TMath::Pi()/fgkQmax)),1.);
 393      //-----------------------------------------------------------------------
 394      //real part
 395      fDiffFlowGenFunRe6->Fill(fTrack->Pt()/fBinWidth,(Double_t)q,G[6][q]*cos(fgkMltpl*fgkFlow*fTrack->Phi())/(1.+(2.*fR0*sqrt(6.+1.)/nSelTracksIntFlow)*cos(fgkFlow*fTrack->Phi()-2.*q*TMath::Pi()/fgkQmax)),1.);
 396      //imaginary part
 397      fDiffFlowGenFunIm6->Fill(fTrack->Pt()/fBinWidth,(Double_t)q,G[6][q]*sin(fgkMltpl*fgkFlow*fTrack->Phi())/(1.+(2.*fR0*sqrt(6.+1.)/nSelTracksIntFlow)*cos(fgkFlow*fTrack->Phi()-2.*q*TMath::Pi()/fgkQmax)),1.);
 398      //-----------------------------------------------------------------------
 399      //real part
 400      fDiffFlowGenFunRe7->Fill(fTrack->Pt()/fBinWidth,(Double_t)q,G[7][q]*cos(fgkMltpl*fgkFlow*fTrack->Phi())/(1.+(2.*fR0*sqrt(7.+1.)/nSelTracksIntFlow)*cos(fgkFlow*fTrack->Phi()-2.*q*TMath::Pi()/fgkQmax)),1.);
 401      //imaginary part
 402      fDiffFlowGenFunIm7->Fill(fTrack->Pt()/fBinWidth,(Double_t)q,G[7][q]*sin(fgkMltpl*fgkFlow*fTrack->Phi())/(1.+(2.*fR0*sqrt(7.+1.)/nSelTracksIntFlow)*cos(fgkFlow*fTrack->Phi()-2.*q*TMath::Pi()/fgkQmax)),1.);
 403    }
 404    //}
 405   }
 406  }//ending the second loop over data
 407
 408 }//end of Make()
 409
 410 //================================================================================================================
 411
 412 void AliFlowAnalysisWithCumulants::Finish()
 413 {
 414  //not needed for the time being...
 415 }
 416
 417
 418
 419