PWG2/FLOW/AliFlowAnalysisWithCumulants.cxx

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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 #include "AliCumulantsFunctions.h"
  42
  43 class TH1;
  44 class TGraph;
  45 class TPave;
  46 class TLatex;
  47 class TMarker;
  48 class TRandom3;
  49 class TObjArray;
  50 class TList;
  51 class TCanvas;
  52 class TSystem;
  53 class TROOT;
  54 class AliFlowVector;
  55 class TVector;
  56
  57 //================================================================================================================
  58
  59 ClassImp(AliFlowAnalysisWithCumulants)
  60
  61 AliFlowAnalysisWithCumulants::AliFlowAnalysisWithCumulants():
  62  fTrack(NULL),
  63  fHistList(NULL),
  64  fR0(0),
  65  fPtMax(0),
  66  fPtMin(0),
  67  fBinWidthPt(0),
  68  fgknBinsPt(0),
  69  fEtaMax(0),
  70  fEtaMin(0),
  71  fBinWidthEta(0),
  72  fgknBinsEta(0),
  73  fAvQx(0),
  74  fAvQy(0),
  75  fAvQ2x(0),
  76  fAvQ2y(0),
  77  fAvMultIntFlowGFC(NULL),
  78  fQVectorComponentsGFC(NULL),
  79  fIntFlowResultsGFC(NULL),
  80  fDiffFlowResults2ndOrderGFC(NULL),
  81  fDiffFlowResults4thOrderGFC(NULL),
  82  fDiffFlowResults6thOrderGFC(NULL),
  83  fDiffFlowResults8thOrderGFC(NULL),
  84  fCommonHistsResults2nd(NULL),
  85  fCommonHistsResults4th(NULL),
  86  fCommonHistsResults6th(NULL),
  87  fCommonHistsResults8th(NULL),
  88  fIntFlowGenFun(NULL),
  89  fIntFlowGenFun4(NULL),//(only for other system of Eq.)
  90  fIntFlowGenFun6(NULL),//(only for other system of Eq.)
  91  fIntFlowGenFun8(NULL),//(only for other system of Eq.)
  92  fIntFlowGenFun16(NULL),//(only for other system of Eq.)
  93  fAvMultIntFlow4GFC(NULL),//(only for other system of Eq.)
  94  fAvMultIntFlow6GFC(NULL),//(only for other system of Eq.)
  95  fAvMultIntFlow8GFC(NULL),//(only for other system of Eq.)
  96  fAvMultIntFlow16GFC(NULL),//(only for other system of Eq.)
  97  fDiffFlowPtRPGenFunRe(NULL),
  98  fDiffFlowPtRPGenFunIm(NULL),
  99  fPtBinRPNoOfParticles(NULL),
 100  fDiffFlowEtaRPGenFunRe(NULL),
 101  fDiffFlowEtaRPGenFunIm(NULL),
 102  fEtaBinRPNoOfParticles(NULL),
 103  fDiffFlowPtPOIGenFunRe(NULL),
 104  fDiffFlowPtPOIGenFunIm(NULL),
 105  fPtBinPOINoOfParticles(NULL),
 106  fDiffFlowEtaPOIGenFunRe(NULL),
 107  fDiffFlowEtaPOIGenFunIm(NULL),
 108  fEtaBinPOINoOfParticles(NULL),
 109  /*
 110  fDiffFlowGenFunRe0(NULL),
 111  fDiffFlowGenFunRe1(NULL),
 112  fDiffFlowGenFunRe2(NULL),
 113  fDiffFlowGenFunRe3(NULL),
 114  fDiffFlowGenFunRe4(NULL),
 115  fDiffFlowGenFunRe5(NULL),
 116  fDiffFlowGenFunRe6(NULL),
 117  fDiffFlowGenFunRe7(NULL),
 118  fDiffFlowGenFunIm0(NULL),
 119  fDiffFlowGenFunIm1(NULL),
 120  fDiffFlowGenFunIm2(NULL),
 121  fDiffFlowGenFunIm3(NULL),
 122  fDiffFlowGenFunIm4(NULL),
 123  fDiffFlowGenFunIm5(NULL),
 124  fDiffFlowGenFunIm6(NULL),
 125  fDiffFlowGenFunIm7(NULL),
 126  */
 127  fCommonHists(NULL),
 128  fOtherEquations(kFALSE)
 129 {
 130  //constructor
 131  fHistList = new TList();
 132  fR0=AliFlowCumuConstants::fgR0;
 133  //Pt:
 134  fPtMax=AliFlowCommonConstants::GetPtMax();
 135  fPtMin=AliFlowCommonConstants::GetPtMin();
 136  fgknBinsPt=AliFlowCommonConstants::GetNbinsPt();
 137  if(fgknBinsPt)
 138  {
 139   fBinWidthPt=(fPtMax-fPtMin)/fgknBinsPt;
 140  }
 141  //Eta:
 142  fEtaMax=AliFlowCommonConstants::GetEtaMax();
 143  fEtaMin=AliFlowCommonConstants::GetEtaMin();
 144  fgknBinsEta=AliFlowCommonConstants::GetNbinsEta();
 145  if(fgknBinsEta)
 146  {
 147   fBinWidthEta=(fEtaMax-fEtaMin)/fgknBinsEta;
 148  }
 149
 150  fOtherEquations=AliFlowCumuConstants::fgOtherEquations;
 151 }
 152
 153 AliFlowAnalysisWithCumulants::~AliFlowAnalysisWithCumulants()
 154 {
 155  //desctructor
 156  delete fHistList;
 157 }
 158
 159 //================================================================================================================
 160
 161 void AliFlowAnalysisWithCumulants::CreateOutputObjects()
 162 {
 163  //various output histograms
 164
 165  //average multiplicity
 166  fAvMultIntFlowGFC = new TProfile("fAvMultIntFlowGFC","Average Multiplicity",1,0,1,"s");
 167  fAvMultIntFlowGFC->SetXTitle("");
 168  fAvMultIntFlowGFC->SetYTitle("");
 169  fAvMultIntFlowGFC->SetLabelSize(0.06);
 170  fAvMultIntFlowGFC->SetMarkerStyle(25);
 171  fAvMultIntFlowGFC->SetLabelOffset(0.01);
 172  (fAvMultIntFlowGFC->GetXaxis())->SetBinLabel(1,"Average Multiplicity");
 173  fHistList->Add(fAvMultIntFlowGFC);
 174
 175  //averages of Q-vector components (1st bin: <Q_x>, 2nd bin: <Q_y>, 3rd bin: <(Q_x)^2>, 4th bin: <(Q_y)^2>)
 176  fQVectorComponentsGFC = new TProfile("fQVectorComponentsGFC","Average of Q-vector components",4,0.,4.);
 177  fQVectorComponentsGFC->SetXTitle("");
 178  fQVectorComponentsGFC->SetYTitle("");
 179  fQVectorComponentsGFC->SetLabelSize(0.06);
 180  fQVectorComponentsGFC->SetMarkerStyle(25);
 181  (fQVectorComponentsGFC->GetXaxis())->SetBinLabel(1,"<Q_{x}>");
 182  (fQVectorComponentsGFC->GetXaxis())->SetBinLabel(2,"<Q_{y}>");
 183  (fQVectorComponentsGFC->GetXaxis())->SetBinLabel(3,"<Q_{x}^{2}>");
 184  (fQVectorComponentsGFC->GetXaxis())->SetBinLabel(4,"<Q_{y}^{2}>");
 185  fHistList->Add(fQVectorComponentsGFC);
 186
 187  //final results for integrated flow (v_n{2}, v_n{4},..., v_n{16}) from cumulants (by default n=2)
 188  fIntFlowResultsGFC = new TH1D("fIntFlowResultsGFC","Integrated Flow From Cumulants (Generating Function)",4,0,4);
 189  fIntFlowResultsGFC->SetXTitle("");
 190  fIntFlowResultsGFC->SetYTitle("");
 191  fIntFlowResultsGFC->SetLabelSize(0.06);
 192  //fIntFlowResultsGFC->SetTickLength(1);
 193  fIntFlowResultsGFC->SetMarkerStyle(25);
 194  (fIntFlowResultsGFC->GetXaxis())->SetBinLabel(1,"v_{n}{2}");
 195  (fIntFlowResultsGFC->GetXaxis())->SetBinLabel(2,"v_{n}{4}");
 196  (fIntFlowResultsGFC->GetXaxis())->SetBinLabel(3,"v_{n}{6}");
 197  (fIntFlowResultsGFC->GetXaxis())->SetBinLabel(4,"v_{n}{8}");
 198  fHistList->Add(fIntFlowResultsGFC);
 199
 200  //final results for differential flow v_p/n{2} (by default p=n=2)
 201  fDiffFlowResults2ndOrderGFC = new TH1D("fDiffFlowResults2ndOrderGFC","v'_2/2{2}",fgknBinsPt,fPtMin,fPtMax);
 202  fDiffFlowResults2ndOrderGFC->SetXTitle("pt [GeV]");
 203  fDiffFlowResults2ndOrderGFC->SetYTitle("");
 204  fHistList->Add(fDiffFlowResults2ndOrderGFC);
 205
 206  //final results for differential flow v_p/n{4} (by default p=n=2)
 207  fDiffFlowResults4thOrderGFC = new TH1D("fDiffFlowResults4thOrderGFC","v'_2/2{4}",fgknBinsPt,fPtMin,fPtMax);
 208  fDiffFlowResults4thOrderGFC->SetXTitle("pt [GeV]");
 209  fDiffFlowResults4thOrderGFC->SetYTitle("");
 210  fHistList->Add(fDiffFlowResults4thOrderGFC);
 211
 212  //final results for differential flow v_p/n{6} (by default p=n=2)
 213  fDiffFlowResults6thOrderGFC = new TH1D("fDiffFlowResults6thOrderGFC","v'_2/2{6}",fgknBinsPt,fPtMin,fPtMax);
 214  fDiffFlowResults6thOrderGFC->SetXTitle("pt [GeV]");
 215  fDiffFlowResults6thOrderGFC->SetYTitle("");
 216  fHistList->Add(fDiffFlowResults6thOrderGFC);
 217
 218  //final results for differential flow v_p/n{8} (by default p=n=2)
 219  fDiffFlowResults8thOrderGFC = new TH1D("fDiffFlowResults8thOrderGFC","v'_2/2{8}",fgknBinsPt,fPtMin,fPtMax);
 220  fDiffFlowResults8thOrderGFC->SetXTitle("pt [GeV]");
 221  fDiffFlowResults8thOrderGFC->SetYTitle("");
 222  fHistList->Add(fDiffFlowResults8thOrderGFC);
 223
 224  //avarage of the generating function for integrated flow <G[p][q]>
 225  fIntFlowGenFun = new TProfile2D("fIntFlowGenFun","<G[p][q]>",fgkPmax,0.,(Double_t)fgkPmax,fgkQmax,0.,(Double_t)fgkQmax);
 226  fIntFlowGenFun->SetXTitle("p");
 227  fIntFlowGenFun->SetYTitle("q");
 228  fHistList->Add(fIntFlowGenFun);
 229
 230  if(fOtherEquations)
 231  {
 232   //avarage of the generating function for integrated flow <G[p][q]> (only for other system of Eq. - up to 4th order)
 233   fIntFlowGenFun4 = new TProfile2D("fIntFlowGenFun4","<G4[p4][q4]>",fgkPmax4,0.,(Double_t)fgkPmax4,fgkQmax4,0.,(Double_t)fgkQmax4);
 234   fIntFlowGenFun4->SetXTitle("p4");
 235   fIntFlowGenFun4->SetYTitle("q4");
 236   fHistList->Add(fIntFlowGenFun4);
 237
 238   //avarage of the generating function for integrated flow <G[p][q]> (only for other system of Eq. - up to 6th order)
 239   fIntFlowGenFun6 = new TProfile2D("fIntFlowGenFun6","<G6[p6][q6]>",fgkPmax6,0.,(Double_t)fgkPmax6,fgkQmax6,0.,(Double_t)fgkQmax6);
 240   fIntFlowGenFun6->SetXTitle("p6");
 241   fIntFlowGenFun6->SetYTitle("q6");
 242   fHistList->Add(fIntFlowGenFun6);
 243
 244   //avarage of the generating function for integrated flow <G[p][q]> (only for other system of Eq. - up to 8th order)
 245   fIntFlowGenFun8 = new TProfile2D("fIntFlowGenFun8","<G8[p8][q8]>",fgkPmax8,0.,(Double_t)fgkPmax8,fgkQmax8,0.,(Double_t)fgkQmax8);
 246   fIntFlowGenFun8->SetXTitle("p8");
 247   fIntFlowGenFun8->SetYTitle("q8");
 248   fHistList->Add(fIntFlowGenFun8);
 249
 250   //avarage of the generating function for integrated flow <G[p][q]> (only for other system of Eq. - up to 16th order)
 251   fIntFlowGenFun16 = new TProfile2D("fIntFlowGenFun16","<G16[p16][q16]>",fgkPmax16,0.,(Double_t)fgkPmax16,fgkQmax16,0.,(Double_t)fgkQmax16);
 252   fIntFlowGenFun16->SetXTitle("p16");
 253   fIntFlowGenFun16->SetYTitle("q16");
 254   fHistList->Add(fIntFlowGenFun16);
 255
 256   //average multiplicity (only for other system of Eq. - up to 4th order)
 257   fAvMultIntFlow4GFC = new TProfile("fAvMultIntFlow4GFC","Average Multiplicity",1,0,1,"s");
 258   fAvMultIntFlow4GFC->SetXTitle("");
 259   fAvMultIntFlow4GFC->SetYTitle("");
 260   fAvMultIntFlow4GFC->SetLabelSize(0.06);
 261   fAvMultIntFlow4GFC->SetMarkerStyle(25);
 262   fAvMultIntFlow4GFC->SetLabelOffset(0.01);
 263   (fAvMultIntFlow4GFC->GetXaxis())->SetBinLabel(1,"Average Multiplicity");
 264   fHistList->Add(fAvMultIntFlow4GFC);
 265
 266   //average multiplicity (only for other system of Eq. - up to 6th order)
 267   fAvMultIntFlow6GFC = new TProfile("fAvMultIntFlow6GFC","Average Multiplicity",1,0,1,"s");
 268   fAvMultIntFlow6GFC->SetXTitle("");
 269   fAvMultIntFlow6GFC->SetYTitle("");
 270   fAvMultIntFlow6GFC->SetLabelSize(0.06);
 271   fAvMultIntFlow6GFC->SetMarkerStyle(25);
 272   fAvMultIntFlow6GFC->SetLabelOffset(0.01);
 273   (fAvMultIntFlow6GFC->GetXaxis())->SetBinLabel(1,"Average Multiplicity");
 274   fHistList->Add(fAvMultIntFlow6GFC);
 275
 276   //average multiplicity (only for other system of Eq. - up to 8th order)
 277   fAvMultIntFlow8GFC = new TProfile("fAvMultIntFlow8GFC","Average Multiplicity",1,0,1,"s");
 278   fAvMultIntFlow8GFC->SetXTitle("");
 279   fAvMultIntFlow8GFC->SetYTitle("");
 280   fAvMultIntFlow8GFC->SetLabelSize(0.06);
 281   fAvMultIntFlow8GFC->SetMarkerStyle(25);
 282   fAvMultIntFlow8GFC->SetLabelOffset(0.01);
 283   (fAvMultIntFlow8GFC->GetXaxis())->SetBinLabel(1,"Average Multiplicity");
 284   fHistList->Add(fAvMultIntFlow8GFC);
 285
 286   //average multiplicity (only for other system of Eq. - up to 16th order)
 287   fAvMultIntFlow16GFC = new TProfile("fAvMultIntFlow16GFC","Average Multiplicity",1,0,1,"s");
 288   fAvMultIntFlow16GFC->SetXTitle("");
 289   fAvMultIntFlow16GFC->SetYTitle("");
 290   fAvMultIntFlow16GFC->SetLabelSize(0.06);
 291   fAvMultIntFlow16GFC->SetMarkerStyle(25);
 292   fAvMultIntFlow16GFC->SetLabelOffset(0.01);
 293   (fAvMultIntFlow16GFC->GetXaxis())->SetBinLabel(1,"Average Multiplicity");
 294   fHistList->Add(fAvMultIntFlow16GFC);
 295  }
 296
 297  //avarage of the real part of generating function for differential flow in Pt <Re(D[b][p][q])>
 298  fDiffFlowPtRPGenFunRe = new TProfile3D("fDiffFlowPtRPGenFunRe","<Re(D[b][p][q])>",fgknBinsPt,(Double_t)(fPtMin/fBinWidthPt),(Double_t)(fPtMax/fBinWidthPt),fgkPmax,0.,(Double_t)fgkPmax,fgkQmax,0.,(Double_t)fgkQmax);
 299  fDiffFlowPtRPGenFunRe->SetXTitle("b");
 300  fDiffFlowPtRPGenFunRe->SetYTitle("p");
 301  fDiffFlowPtRPGenFunRe->SetZTitle("q");
 302  fDiffFlowPtRPGenFunRe->SetTitleOffset(1.44,"X");
 303  fDiffFlowPtRPGenFunRe->SetTitleOffset(1.44,"Y");
 304  fHistList->Add(fDiffFlowPtRPGenFunRe);
 305
 306  //avarage of the imaginary part of generating function for differential flow in Pt <Im(D[b][p][q])>
 307  fDiffFlowPtRPGenFunIm = new TProfile3D("fDiffFlowPtRPGenFunIm","<Im(D[b][p][q])>",fgknBinsPt,(Double_t)(fPtMin/fBinWidthPt),(Double_t)(fPtMax/fBinWidthPt),fgkPmax,0.,(Double_t)fgkPmax,fgkQmax,0.,(Double_t)fgkQmax);
 308  fDiffFlowPtRPGenFunIm->SetXTitle("b");
 309  fDiffFlowPtRPGenFunIm->SetYTitle("p");
 310  fDiffFlowPtRPGenFunIm->SetZTitle("q");
 311  fDiffFlowPtRPGenFunIm->SetTitleOffset(1.44,"X");
 312  fDiffFlowPtRPGenFunIm->SetTitleOffset(1.44,"Y");
 313  fHistList->Add(fDiffFlowPtRPGenFunIm);
 314
 315  //number of particles per pt bin
 316  fPtBinRPNoOfParticles = new TProfile("fPtBinRPNoOfParticles","Number of particles per #p_{t} bin",fgknBinsPt,fPtMin,fPtMax);
 317  fPtBinRPNoOfParticles->SetXTitle("pt [GeV]");
 318  fPtBinRPNoOfParticles->SetYTitle("");
 319  fHistList->Add(fPtBinRPNoOfParticles);
 320
 321  //avarage of the real part of generating function for differential flow in Eta <Re(D[b][p][q])>
 322  fDiffFlowEtaRPGenFunRe = new TProfile3D("fDiffFlowEtaRPGenFunRe","<Re(D[b][p][q])>",fgknBinsEta,(Double_t)(fEtaMin/fBinWidthEta),(Double_t)(fEtaMax/fBinWidthEta),fgkPmax,0.,(Double_t)fgkPmax,fgkQmax,0.,(Double_t)fgkQmax);
 323  fDiffFlowEtaRPGenFunRe->SetXTitle("b");
 324  fDiffFlowEtaRPGenFunRe->SetYTitle("p");
 325  fDiffFlowEtaRPGenFunRe->SetZTitle("q");
 326  fDiffFlowEtaRPGenFunRe->SetTitleOffset(1.44,"X");
 327  fDiffFlowEtaRPGenFunRe->SetTitleOffset(1.44,"Y");
 328  fHistList->Add(fDiffFlowEtaRPGenFunRe);
 329
 330  //avarage of the imaginary part of generating function for differential flow in Eta <Im(D[b][p][q])>
 331  fDiffFlowEtaRPGenFunIm = new TProfile3D("fDiffFlowEtaRPGenFunIm","<Im(D[b][p][q])>",fgknBinsEta,(Double_t)(fEtaMin/fBinWidthEta),(Double_t)(fEtaMax/fBinWidthEta),fgkPmax,0.,(Double_t)fgkPmax,fgkQmax,0.,(Double_t)fgkQmax);
 332  fDiffFlowEtaRPGenFunIm->SetXTitle("b");
 333  fDiffFlowEtaRPGenFunIm->SetYTitle("p");
 334  fDiffFlowEtaRPGenFunIm->SetZTitle("q");
 335  fDiffFlowEtaRPGenFunIm->SetTitleOffset(1.44,"X");
 336  fDiffFlowEtaRPGenFunIm->SetTitleOffset(1.44,"Y");
 337  fHistList->Add(fDiffFlowEtaRPGenFunIm);
 338
 339  //number of particles per eta bin
 340  fEtaBinRPNoOfParticles = new TProfile("fEtaBinRPNoOfParticles","Number of particles per #eta bin",fgknBinsEta,fEtaMin,fEtaMax);
 341  fEtaBinRPNoOfParticles->SetXTitle("#eta");
 342  fEtaBinRPNoOfParticles->SetYTitle("");
 343  fHistList->Add(fEtaBinRPNoOfParticles);
 344
 345  //avarage of the real part of generating function for differential flow in Pt <Re(D[b][p][q])>
 346  fDiffFlowPtPOIGenFunRe = new TProfile3D("fDiffFlowPtPOIGenFunRe","<Re(D[b][p][q])>",fgknBinsPt,(Double_t)(fPtMin/fBinWidthPt),(Double_t)(fPtMax/fBinWidthPt),fgkPmax,0.,(Double_t)fgkPmax,fgkQmax,0.,(Double_t)fgkQmax);
 347  fDiffFlowPtPOIGenFunRe->SetXTitle("b");
 348  fDiffFlowPtPOIGenFunRe->SetYTitle("p");
 349  fDiffFlowPtPOIGenFunRe->SetZTitle("q");
 350  fDiffFlowPtPOIGenFunRe->SetTitleOffset(1.44,"X");
 351  fDiffFlowPtPOIGenFunRe->SetTitleOffset(1.44,"Y");
 352  fHistList->Add(fDiffFlowPtPOIGenFunRe);
 353
 354  //avarage of the imaginary part of generating function for differential flow in Pt <Im(D[b][p][q])>
 355  fDiffFlowPtPOIGenFunIm = new TProfile3D("fDiffFlowPtPOIGenFunIm","<Im(D[b][p][q])>",fgknBinsPt,(Double_t)(fPtMin/fBinWidthPt),(Double_t)(fPtMax/fBinWidthPt),fgkPmax,0.,(Double_t)fgkPmax,fgkQmax,0.,(Double_t)fgkQmax);
 356  fDiffFlowPtPOIGenFunIm->SetXTitle("b");
 357  fDiffFlowPtPOIGenFunIm->SetYTitle("p");
 358  fDiffFlowPtPOIGenFunIm->SetZTitle("q");
 359  fDiffFlowPtPOIGenFunIm->SetTitleOffset(1.44,"X");
 360  fDiffFlowPtPOIGenFunIm->SetTitleOffset(1.44,"Y");
 361  fHistList->Add(fDiffFlowPtPOIGenFunIm);
 362
 363  //number of particles per pt bin
 364  fPtBinPOINoOfParticles = new TProfile("fPtBinPOINoOfParticles","Number of particles per #p_{t} bin",fgknBinsPt,fPtMin,fPtMax);
 365  fPtBinPOINoOfParticles->SetXTitle("pt [GeV]");
 366  fPtBinPOINoOfParticles->SetYTitle("");
 367  fHistList->Add(fPtBinPOINoOfParticles);
 368
 369  //avarage of the real part of generating function for differential flow in Eta <Re(D[b][p][q])>
 370  fDiffFlowEtaPOIGenFunRe = new TProfile3D("fDiffFlowEtaPOIGenFunRe","<Re(D[b][p][q])>",fgknBinsEta,(Double_t)(fEtaMin/fBinWidthEta),(Double_t)(fEtaMax/fBinWidthEta),fgkPmax,0.,(Double_t)fgkPmax,fgkQmax,0.,(Double_t)fgkQmax);
 371  fDiffFlowEtaPOIGenFunRe->SetXTitle("b");
 372  fDiffFlowEtaPOIGenFunRe->SetYTitle("p");
 373  fDiffFlowEtaPOIGenFunRe->SetZTitle("q");
 374  fDiffFlowEtaPOIGenFunRe->SetTitleOffset(1.44,"X");
 375  fDiffFlowEtaPOIGenFunRe->SetTitleOffset(1.44,"Y");
 376  fHistList->Add(fDiffFlowEtaPOIGenFunRe);
 377
 378  //avarage of the imaginary part of generating function for differential flow in Eta <Im(D[b][p][q])>
 379  fDiffFlowEtaPOIGenFunIm = new TProfile3D("fDiffFlowEtaPOIGenFunIm","<Im(D[b][p][q])>",fgknBinsEta,(Double_t)(fEtaMin/fBinWidthEta),(Double_t)(fEtaMax/fBinWidthEta),fgkPmax,0.,(Double_t)fgkPmax,fgkQmax,0.,(Double_t)fgkQmax);
 380  fDiffFlowEtaPOIGenFunIm->SetXTitle("b");
 381  fDiffFlowEtaPOIGenFunIm->SetYTitle("p");
 382  fDiffFlowEtaPOIGenFunIm->SetZTitle("q");
 383  fDiffFlowEtaPOIGenFunIm->SetTitleOffset(1.44,"X");
 384  fDiffFlowEtaPOIGenFunIm->SetTitleOffset(1.44,"Y");
 385  fHistList->Add(fDiffFlowEtaPOIGenFunIm);
 386
 387  //number of particles per eta bin
 388  fEtaBinPOINoOfParticles = new TProfile("fEtaBinPOINoOfParticles","Number of particles per #eta bin",fgknBinsEta,fEtaMin,fEtaMax);
 389  fEtaBinPOINoOfParticles->SetXTitle("#eta");
 390  fEtaBinPOINoOfParticles->SetYTitle("");
 391  fHistList->Add(fEtaBinPOINoOfParticles);
 392
 393  /*
 394  fDiffFlowGenFunRe0 = new TProfile2D("fDiffFlowGenFunRe0","Re(<D[b][0][q]>)",fgknBins,(Double_t)(fPtMin/fBinWidth),(Double_t)(fPtMax/fBinWidth),fgkQmax,0.,(Double_t)fgkQmax);
 395  fDiffFlowGenFunRe0->SetXTitle("b");
 396  fDiffFlowGenFunRe0->SetYTitle("q");
 397  fHistList->Add(fDiffFlowGenFunRe0);
 398
 399  fDiffFlowGenFunIm0 = new TProfile2D("fDiffFlowGcout<<"HEY M1"<<endl;enFunIm0","Im(<D[b][0][q]>)",fgknBins,(Double_t)(fPtMin/fBinWidth),(Double_t)(fPtMax/fBinWidth),fgkQmax,0.,(Double_t)fgkQmax);
 400  fDiffFlowGenFunIm0->SetXTitle("b");
 401  fDiffFlowGenFunIm0->SetYTitle("q");
 402  fHistList->Add(fDiffFlowGenFunIm0);
 403
 404  fDiffFlowGenFunRe1 = new TProfile2D("fDiffFlowGenFunRe1","Re(<D[b][1][q]>)",fgknBins,(Double_t)(fPtMin/fBinWidth),(Double_t)(fPtMax/fBinWidth),fgkQmax,0.,(Double_t)fgkQmax);
 405  fDiffFlowGenFunRe1->SetXTitle("b");
 406  fDiffFlowGenFunRe1->SetYTitle("q");
 407  fHistList->Add(fDiffFlowGenFunRe1);
 408
 409  fDiffFlowGenFunIm1 = new TProfile2D("fDiffFlowGenFunIm1","Im(<D[b][1][q]>)",fgknBins,(Double_t)(fPtMin/fBinWidth),(Double_t)(fPtMax/fBinWidth),fgkQmax,0.,(Double_t)fgkQmax);
 410  fDiffFlowGenFunIm1->SetXTitle("b");
 411  fDiffFlowGenFunIm1->SetYTitle("q");
 412  fHistList->Add(fDiffFlowGenFunIm1);
 413
 414  fDiffFlowGenFunRe2 = new TProfile2D("fDiffFlowGenFunRe2","Re(<D[b][2][q]>)",fgknBins,(Double_t)(fPtMin/fBinWidth),(Double_t)(fPtMax/fBinWidth),fgkQmax,0.,(Double_t)fgkQmax);
 415  fDiffFlowGenFunRe2->SetXTitle("b");
 416  fDiffFlowGenFunRe2->SetYTitle("q");
 417  fHistList->Add(fDiffFlowGenFunRe2);
 418
 419  fDiffFlowGenFunIm2 = new TProfile2D("fDiffFlowGenFunIm2","Im(<D[b][2][q]>)",fgknBins,(Double_t)(fPtMin/fBinWidth),(Double_t)(fPtMax/fBinWidth),fgkQmax,0.,(Double_t)fgkQmax);
 420  fDiffFlowGenFunIm2->SetXTitle("b");
 421  fDiffFlowGenFunIm2->SetYTitle("q");
 422  fHistList->Add(fDiffFlowGenFunIm2);
 423
 424  fDiffFlowGenFunRe3 = new TProfile2D("fDiffFlowGenFunRe3","Re(<D[b][3][q]>)",fgknBins,(Double_t)(fPtMin/fBinWidth),(Double_t)(fPtMax/fBinWidth),fgkQmax,0.,(Double_t)fgkQmax);
 425  fDiffFlowGenFunRe3->SetXTitle("b");
 426  fDiffFlowGenFunRe3->SetYTitle("q");
 427  fHistList->Add(fDiffFlowGenFunRe3);
 428
 429  fDiffFlowGenFunIm3 = new TProfile2D("fDiffFlowGenFunIm3","Im(<D[b][3][q]>)",fgknBins,(Double_t)(fPtMin/fBinWidth),(Double_t)(fPtMax/fBinWidth),fgkQmax,0.,(Double_t)fgkQmax);
 430  fDiffFlowGenFunIm3->SetXTitle("b");
 431  fDiffFlowGenFunIm3->SetYTitle("q");
 432  fHistList->Add(fDiffFlowGenFunIm3);
 433
 434  fDiffFlowGenFunRe4 = new TProfile2D("fDiffFlowGenFunRe4","Re(<D[b][4][q]>)",fgknBins,(Double_t)(fPtMin/fBinWidth),(Double_t)(fPtMax/fBinWidth),fgkQmax,0.,(Double_t)fgkQmax);
 435  fDiffFlowGenFunRe4->SetXTitle("b");
 436  fDiffFlowGenFunRe4->SetYTitle("q");
 437  fHistList->Add(fDiffFlowGenFunRe4);
 438
 439  fDiffFlowGenFunIm4 = new TProfile2D("fDiffFlowGenFunIm4","Im(<D[b][4][q]>)",fgknBins,(Double_t)(fPtMin/fBinWidth),(Double_t)(fPtMax/fBinWidth),fgkQmax,0.,(Double_t)fgkQmax);
 440  fDiffFlowGenFunIm4->SetXTitle("b");
 441  fDiffFlowGenFunIm4->SetYTitle("q");
 442  fHistList->Add(fDiffFlowGenFunIm4);
 443
 444  fDiffFlowGenFunRe5 = new TProfile2D("fDiffFlowGenFunRe5","Re(<D[b][5][q]>)",fgkQmax,0.,(Double_t)fgkQmax,fgknBins,(Double_t)(fPtMin/fBinWidth),(Double_t)(fPtMax/fBinWidth));
 445  fDiffFlowGenFunRe5->SetXTitle("b");
 446  fDiffFlowGenFunRe5->SetYTitle("q");
 447  fHistList->Add(fDiffFlowGenFunRe5);
 448
 449  fDiffFlowGenFunIm5 = new TProfile2D("fDiffFlowGenFunIm5","Im(<D[b][5][q]>)",fgknBins,(Double_t)(fPtMin/fBinWidth),(Double_t)(fPtMax/fBinWidth),fgkQmax,0.,(Double_t)fgkQmax);
 450  fDiffFlowGenFunIm5->SetXTitle("b");
 451  fDiffFlowGenFunIm5->SetYTitle("q");
 452  fHistList->Add(fDiffFlowGenFunIm5);
 453
 454  fDiffFlowGenFunRe6 = new TProfile2D("fDiffFlowGenFunRe6","Re(<D[b][6][q]>)",fgknBins,(Double_t)(fPtMin/fBinWidth),(Double_t)(fPtMax/fBinWidth),fgkQmax,0.,(Double_t)fgkQmax);
 455  fDiffFlowGenFunRe6->SetXTitle("b");
 456  fDiffFlowGenFunRe6->SetYTitle("q");
 457  fHistList->Add(fDiffFlowGenFunRe6);
 458
 459  fDiffFlowGenFunIm6 = new TProfile2D("fDiffFlowGenFunIm6","Im(<D[b][6][q]>)",fgknBins,(Double_t)(fPtMin/fBinWidth),(Double_t)(fPtMax/fBinWidth),fgkQmax,0.,(Double_t)fgkQmax);
 460  fDiffFlowGenFunIm6->SetXTitle("b");
 461  fDiffFlowGenFunIm6->SetYTitle("q");
 462  fHistList->Add(fDiffFlowGenFunIm6);
 463
 464  fDiffFlowGenFunRe7 = new TProfile2D("fDiffFlowGenFunRe7","Re(<D[b][7][q]>)",fgknBins,(Double_t)(fPtMin/fBinWidth),(Double_t)(fPtMax/fBinWidth),fgkQmax,0.,(Double_t)fgkQmax);
 465  fDiffFlowGenFunRe7->SetXTitle("b");
 466  fDiffFlowGenFunRe7->SetYTitle("q");
 467  fHistList->Add(fDiffFlowGenFunRe7);
 468
 469  fDiffFlowGenFunIm7 = new TProfile2D("fDiffFlowGenFunIm7","Im(<D[b][7][q]>)",fgknBins,(Double_t)(fPtMin/fBinWidth),(Double_t)(fPtMax/fBinWidth),fgkQmax,0.,(Double_t)fgkQmax);
 470  fDiffFlowGenFunIm7->SetXTitle("b");
 471  fDiffFlowGenFunIm7->SetYTitle("q");
 472  fHistList->Add(fDiffFlowGenFunIm7);
 473  */
 474
 475  //common control histograms
 476  fCommonHists = new AliFlowCommonHist("AliFlowCommonHistGFC");
 477  fHistList->Add(fCommonHists);
 478
 479  //common histograms for final results (2nd order)
 480  fCommonHistsResults2nd = new AliFlowCommonHistResults("AliFlowCommonHistResults2ndOrderGFC");
 481  fHistList->Add(fCommonHistsResults2nd);
 482
 483  //common histograms for final results (4th order)
 484  fCommonHistsResults4th = new AliFlowCommonHistResults("AliFlowCommonHistResults4thOrderGFC");
 485  fHistList->Add(fCommonHistsResults4th);
 486
 487  //common histograms for final results (6th order)
 488  fCommonHistsResults6th = new AliFlowCommonHistResults("AliFlowCommonHistResults6thOrderGFC");
 489  fHistList->Add(fCommonHistsResults6th);
 490
 491  //common histograms for final results (8th order)
 492  fCommonHistsResults8th = new AliFlowCommonHistResults("AliFlowCommonHistResults8thOrderGFC");
 493  fHistList->Add(fCommonHistsResults8th);
 494
 495 }//end of CreateOutputObjects()
 496
 497 //================================================================================================================
 498
 499 void AliFlowAnalysisWithCumulants::Make(AliFlowEventSimple* anEvent)
 500 {
 501  //running over data:
 502  Int_t nPrim = anEvent->NumberOfTracks(); //total multiplicity
 503
 504  Int_t nEventNSelTracksIntFlow = anEvent->GetEventNSelTracksIntFlow(); //selected multiplicity (particles used for int. flow)
 505
 506  if(nEventNSelTracksIntFlow>9) //generating function formalism applied here make sense only for selected multiplicity >= 10
 507  {
 508  //fill the common control histograms
 509  fCommonHists->FillControlHistograms(anEvent);
 510
 511  //initializing the generating function G[p][q] for integrated flow
 512  Double_t G[fgkPmax][fgkQmax];
 513
 514  for(Int_t p=0;p<fgkPmax;p++)
 515   {
 516    for(Int_t q=0;q<fgkQmax;q++)
 517    {
 518     G[p][q]=1.;
 519    }
 520   }
 521
 522  Int_t nSelTracksIntFlow = 0; //cross-checking the selected multiplicity
 523
 524  for(Int_t i=0;i<nPrim;i++)
 525  {
 526   fTrack=anEvent->GetTrack(i);
 527   if(fTrack && fTrack->UseForIntegratedFlow())
 528   {
 529    nSelTracksIntFlow++;
 530    for(Int_t p=0;p<fgkPmax;p++)
 531    {
 532     for(Int_t q=0;q<fgkQmax;q++)
 533     {
 534      G[p][q]*=(1.+(2.*fR0*sqrt(p+1.)/nEventNSelTracksIntFlow)*cos(fgkFlow*fTrack->Phi()-2.*q*TMath::Pi()/fgkQmax));
 535     }
 536    }
 537   }
 538  }
 539
 540  //storing the value of G[p][q] in 2D profile in order to get automatically the avarage <G[p][q]>
 541  for(Int_t p=0;p<fgkPmax;p++)
 542  {
 543   for(Int_t q=0;q<fgkQmax;q++)
 544   {
 545    fIntFlowGenFun->Fill((Double_t)p,(Double_t)q,G[p][q],1);
 546   }
 547  }
 548
 549  //storing the selected multiplicity (if fAvMultIntFlow is not filled here then you had wrongly selected the particles used for integrated flow)
 550  if(nSelTracksIntFlow==nEventNSelTracksIntFlow)
 551  {
 552   fAvMultIntFlowGFC->Fill(0.,nSelTracksIntFlow,1);
 553  }
 554
 555  //calculating Q-vector of event (needed for errors)
 556  AliFlowVector fQVector;
 557  fQVector.Set(0.,0.);
 558  fQVector.SetMult(0);
 559  fQVector=anEvent->GetQ();                               //get the Q vector for this event
 560  fQVectorComponentsGFC->Fill(0.,fQVector.X(),1);         //in the 1st bin fill Q_x
 561  fQVectorComponentsGFC->Fill(1.,fQVector.Y(),1);         //in the 2nd bin fill Q_y
 562  fQVectorComponentsGFC->Fill(2.,pow(fQVector.X(),2.),1); //in the 3rd bin fill (Q_x)^2
 563  fQVectorComponentsGFC->Fill(3.,pow(fQVector.Y(),2.),1); //in the 4th bin fill (Q_y)^2
 564
 565  //3D profiles for differential flow in pt and eta
 566  //second loop over data: evaluating the generating function D[b][p][q] for differential flow
 567  //remark 0: D[b][p][q] is a complex number => real and imaginary part are calculated separately
 568  //remark 1: note that bellow G[p][q] is needed, the value of generating function for integrated flow for the CURRENT event
 569  //remark 2: results are stored in 3D profiles in order to automatically get <Re(D[b][p][q])> and <Im(D[b][p][q])>
 570  for(Int_t i=0;i<nPrim;i++)
 571  {
 572   fTrack=anEvent->GetTrack(i);
 573   if(fTrack)
 574   {
 575    if(fTrack->UseForIntegratedFlow() && fTrack->UseForDifferentialFlow())
 576    {
 577     fPtBinPOINoOfParticles->Fill(fTrack->Pt(),fTrack->Pt(),1.);
 578     fEtaBinPOINoOfParticles->Fill(fTrack->Eta(),fTrack->Eta(),1.);
 579     for(Int_t p=0;p<fgkPmax;p++)
 580     {
 581      for(Int_t q=0;q<fgkQmax;q++)
 582      {
 583       //real part (Pt)
 584       fDiffFlowPtPOIGenFunRe->Fill(fTrack->Pt()/fBinWidthPt,(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.);
 585       //imaginary part (Pt)
 586       fDiffFlowPtPOIGenFunIm->Fill(fTrack->Pt()/fBinWidthPt,(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.);
 587       //real part (Eta)
 588       fDiffFlowEtaPOIGenFunRe->Fill(fTrack->Eta()/fBinWidthEta,(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.);
 589       //imaginary part (Eta)
 590       fDiffFlowEtaPOIGenFunIm->Fill(fTrack->Eta()/fBinWidthEta,(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.);
 591      }
 592     }
 593    }
 594    else if(fTrack->UseForDifferentialFlow() && !(fTrack->UseForIntegratedFlow()))
 595    {
 596     fPtBinPOINoOfParticles->Fill(fTrack->Pt(),fTrack->Pt(),1.);
 597     fEtaBinPOINoOfParticles->Fill(fTrack->Eta(),fTrack->Eta(),1.);
 598     for(Int_t p=0;p<fgkPmax;p++)
 599     {
 600      for(Int_t q=0;q<fgkQmax;q++)
 601      {
 602       //real part (Pt)
 603       fDiffFlowPtPOIGenFunRe->Fill(fTrack->Pt()/fBinWidthPt,(Double_t)p,(Double_t)q,G[p][q]*cos(fgkMltpl*fgkFlow*fTrack->Phi()),1.);
 604       //imaginary part (Pt)
 605       fDiffFlowPtPOIGenFunIm->Fill(fTrack->Pt()/fBinWidthPt,(Double_t)p,(Double_t)q,G[p][q]*sin(fgkMltpl*fgkFlow*fTrack->Phi()),1.);
 606       //real part (Eta)
 607       fDiffFlowEtaPOIGenFunRe->Fill(fTrack->Eta()/fBinWidthEta,(Double_t)p,(Double_t)q,G[p][q]*cos(fgkMltpl*fgkFlow*fTrack->Phi()),1.);
 608       //imaginary part (Eta)
 609       fDiffFlowEtaPOIGenFunIm->Fill(fTrack->Eta()/fBinWidthEta,(Double_t)p,(Double_t)q,G[p][q]*sin(fgkMltpl*fgkFlow*fTrack->Phi()),1.);
 610      }
 611     }
 612    }
 613    //RP:
 614    if(fTrack->UseForIntegratedFlow())
 615    {
 616     fPtBinRPNoOfParticles->Fill(fTrack->Pt(),fTrack->Pt(),1.);
 617     fEtaBinRPNoOfParticles->Fill(fTrack->Eta(),fTrack->Eta(),1.);
 618     for(Int_t p=0;p<fgkPmax;p++)
 619     {
 620      for(Int_t q=0;q<fgkQmax;q++)
 621      {
 622       //real part (Pt)
 623       fDiffFlowPtRPGenFunRe->Fill(fTrack->Pt()/fBinWidthPt,(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.);
 624       //imaginary part (Pt)
 625       fDiffFlowPtRPGenFunIm->Fill(fTrack->Pt()/fBinWidthPt,(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.);
 626       //real part (Eta)
 627       fDiffFlowEtaRPGenFunRe->Fill(fTrack->Eta()/fBinWidthEta,(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.);
 628       //imaginary part (Eta)
 629       fDiffFlowEtaRPGenFunIm->Fill(fTrack->Eta()/fBinWidthEta,(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.);
 630      }
 631     }
 632    }//end of if(fTrack->UseForIntegratedFlow())
 633   }//end of if(fTrack)
 634  }//ending the second loop over data
 635
 636
 637
 638  /*
 639  //sixteen 2D profiles for differential flow
 640  for(Int_t i=0;i<nPrim;i++){
 641   fTrack=anEvent->GetTrack(i);
 642   if (fTrack && fTrack->UseForDifferentialFlow()){
 643    //for(Int_t p=0;p<fgkPmax;p++){
 644     for(Int_t q=0;q<fgkQmax;q++){
 645      //real part
 646      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.);
 647      //imaginary part
 648      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.);
 649      //-----------------------------------------------------------------------
 650      //real part
 651      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.);
 652      //imaginary part
 653      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.);
 654     //-----------------------------------------------------------------------
 655      //real part
 656      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.);
 657      //imaginary part
 658      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.);
 659      //-----------------------------------------------------------------------
 660      //real part
 661      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.);
 662      //imaginary part
 663      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.);
 664      //-----------------------------------------------------------------------
 665      //real part
 666      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.);
 667      //imaginary part
 668      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.);
 669      //-----------------------------------------------------------------------
 670      //real part
 671      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.);
 672      //imaginary part
 673      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.);
 674      //-----------------------------------------------------------------------
 675      //real part
 676      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.);
 677      //imaginary part
 678      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.);
 679      //-----------------------------------------------------------------------
 680      //real part
 681      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.);
 682      //imaginary part
 683      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.);
 684    }
 685    //}
 686   }
 687  }//ending the second loop over data
 688  */
 689
 690  }//end of if(nEventNSelTracksIntFlow>9)
 691
 692
 693
 694
 695
 696
 697
 698
 699
 700
 701
 702
 703
 704  //off the record: numerical equations for cumulants solved up to different highest order
 705  if(fOtherEquations)
 706  {
 707   //running over data
 708   Int_t nPrimOE = anEvent->NumberOfTracks();//total multiplicity
 709
 710   Int_t nEventNSelTracksIntFlowOE = anEvent->GetEventNSelTracksIntFlow();
 711
 712   Double_t G4[fgkPmax4][fgkQmax4];
 713   Double_t G6[fgkPmax6][fgkQmax6];
 714   Double_t G8[fgkPmax8][fgkQmax8];
 715   Double_t G16[fgkPmax16][fgkQmax16];
 716   for(Int_t p=0;p<fgkPmax16;p++)
 717   {
 718    for(Int_t q=0;q<fgkQmax16;q++)
 719    {
 720     G16[p][q]=1.;
 721     if(p<fgkPmax8 && q<fgkQmax8)
 722     {
 723      G8[p][q]=1.;
 724      if(p<fgkPmax6 && q<fgkQmax6)
 725      {
 726       G6[p][q]=1.;
 727       if(p<fgkPmax4 && q<fgkQmax4)
 728       {
 729        G4[p][q]=1.;
 730       }
 731      }
 732     }
 733    }
 734   }
 735
 736   //multiplicities:
 737   if(nEventNSelTracksIntFlowOE>15) fAvMultIntFlow16GFC->Fill(0.,nEventNSelTracksIntFlowOE,1);
 738   if(nEventNSelTracksIntFlowOE>7) fAvMultIntFlow8GFC->Fill(0.,nEventNSelTracksIntFlowOE,1);
 739   if(nEventNSelTracksIntFlowOE>5) fAvMultIntFlow6GFC->Fill(0.,nEventNSelTracksIntFlowOE,1);
 740   if(nEventNSelTracksIntFlowOE>3) fAvMultIntFlow4GFC->Fill(0.,nEventNSelTracksIntFlowOE,1);
 741
 742   //first loop over data: evaluating the generating function G[p][q] for integrated flow
 743   for(Int_t i=0;i<nPrimOE;i++)
 744   {
 745    fTrack=anEvent->GetTrack(i);
 746    if(fTrack && fTrack->UseForIntegratedFlow())
 747    {
 748     for(Int_t p=0;p<fgkPmax16;p++)
 749     {
 750      for(Int_t q=0;q<fgkQmax16;q++)
 751      {
 752       if(nEventNSelTracksIntFlowOE>15)
 753       {
 754        G16[p][q]*=(1.+(2.*fR0*sqrt(p+1.)/nEventNSelTracksIntFlowOE)*cos(fgkFlow*fTrack->Phi()-2.*q*TMath::Pi()/fgkQmax16));
 755       }
 756       if(p<fgkPmax8 && q<fgkQmax8)
 757       {
 758        if(nEventNSelTracksIntFlowOE>7)
 759        {
 760         G8[p][q]*=(1.+(2.*fR0*sqrt(p+1.)/nEventNSelTracksIntFlowOE)*cos(fgkFlow*fTrack->Phi()-2.*q*TMath::Pi()/fgkQmax8));
 761        }
 762        if(p<fgkPmax6 && q<fgkQmax6)
 763        {
 764         if(nEventNSelTracksIntFlowOE>5)
 765         {
 766          G6[p][q]*=(1.+(2.*fR0*sqrt(p+1.)/nEventNSelTracksIntFlowOE)*cos(fgkFlow*fTrack->Phi()-2.*q*TMath::Pi()/fgkQmax6));
 767         }
 768         if(p<fgkPmax4 && q<fgkQmax4)
 769         {
 770          if(nEventNSelTracksIntFlowOE>3)
 771          {
 772           G4[p][q]*=(1.+(2.*fR0*sqrt(p+1.)/nEventNSelTracksIntFlowOE)*cos(fgkFlow*fTrack->Phi()-2.*q*TMath::Pi()/fgkQmax4));
 773          }
 774         }
 775        }
 776       }
 777      }
 778     }
 779    }//end of if(fTrack && fTrack->UseForIntegratedFlow())
 780   }//ending the loop over data
 781
 782  //storing the value of G[p][q] in 2D profile in order to get automatically the avarage <G[p][q]>
 783  for(Int_t p=0;p<fgkPmax16;p++)
 784  {
 785   for(Int_t q=0;q<fgkQmax16;q++)
 786   {
 787    if(nEventNSelTracksIntFlowOE>15) fIntFlowGenFun16->Fill((Double_t)p,(Double_t)q,G16[p][q],1);
 788    if(p<fgkPmax8 && q<fgkQmax8)
 789    {
 790     if(nEventNSelTracksIntFlowOE>7) fIntFlowGenFun8->Fill((Double_t)p,(Double_t)q,G8[p][q],1);
 791     if(p<fgkPmax6 && q<fgkQmax6)
 792     {
 793      if(nEventNSelTracksIntFlowOE>5) fIntFlowGenFun6->Fill((Double_t)p,(Double_t)q,G6[p][q],1);
 794      if(p<fgkPmax4 && q<fgkQmax4)
 795      {
 796       if(nEventNSelTracksIntFlowOE>3) fIntFlowGenFun4->Fill((Double_t)p,(Double_t)q,G4[p][q],1);
 797      }
 798     }
 799    }
 800   }
 801  }
 802 }//end of if(fOtherEquations)
 803
 804 }//end of Make()
 805
 806 //================================================================================================================
 807
 808 void AliFlowAnalysisWithCumulants::Finish()
 809 {
 810  //calculate the final results
 811  //AliCumulantsFunctions finalResults(fIntFlowGenFun,NULL,NULL, fIntFlowResults,fDiffFlowResults2,fDiffFlowResults4,fDiffFlowResults6,fDiffFlowResults8,fAvMultIntFlow,fQVectorComponents,  fQDist,fDiffFlowGenFunRe0,fDiffFlowGenFunRe1,fDiffFlowGenFunRe2, fDiffFlowGenFunRe3,fDiffFlowGenFunRe4,fDiffFlowGenFunRe5,fDiffFlowGenFunRe6,fDiffFlowGenFunRe7,fDiffFlowGenFunIm0,fDiffFlowGenFunIm1, fDiffFlowGenFunIm2,fDiffFlowGenFunIm3,fDiffFlowGenFunIm4,fDiffFlowGenFunIm5,fDiffFlowGenFunIm6,fDiffFlowGenFunIm7);
 812
 813  AliCumulantsFunctions finalResults(fIntFlowGenFun,fIntFlowGenFun4,fIntFlowGenFun6,fIntFlowGenFun8,fIntFlowGenFun16,fAvMultIntFlow4GFC, fAvMultIntFlow6GFC,fAvMultIntFlow8GFC,fAvMultIntFlow16GFC,fDiffFlowPtRPGenFunRe,fDiffFlowPtRPGenFunIm,fPtBinRPNoOfParticles, fDiffFlowEtaRPGenFunRe,fDiffFlowEtaRPGenFunIm,fEtaBinRPNoOfParticles,fDiffFlowPtPOIGenFunRe,fDiffFlowPtPOIGenFunIm,fPtBinPOINoOfParticles, fDiffFlowEtaPOIGenFunRe,fDiffFlowEtaPOIGenFunIm,fEtaBinPOINoOfParticles,fIntFlowResultsGFC,fDiffFlowResults2ndOrderGFC,fDiffFlowResults4thOrderGFC,fDiffFlowResults6thOrderGFC,fDiffFlowResults8thOrderGFC, fAvMultIntFlowGFC,fQVectorComponentsGFC,fCommonHistsResults2nd, fCommonHistsResults4th,fCommonHistsResults6th,fCommonHistsResults8th,fCommonHists);
 814
 815  finalResults.Calculate();
 816 }
 817
 818 //================================================================================================================
 819
 820 void AliFlowAnalysisWithCumulants::WriteHistograms(TString* outputFileName)
 821 {
 822  //store the final results in output .root file
 823  TFile *output = new TFile(outputFileName->Data(),"RECREATE");
 824  output->WriteObject(fHistList, "cobjGFC","SingleKey");
 825  delete output;
 826 }
 827
 828 //================================================================================================================
 829
 830
 831
 832