[u/mrichter/AliRoot.git] / PWG2 / FLOW / AliFlowCommon / AliFlowAnalysisWithQCumulants.cxx

/*************************************************************************\r
* Copyright(c) 1998-2008, ALICE Experiment at CERN, All rights reserved. *\r
*                                                                        *\r
* Author: The ALICE Off-line Project.                                    *\r
* Contributors are mentioned in the code where appropriate.              *\r
*                                                                        *\r
* Permission to use, copy, modify and distribute this software and its   *\r
* documentation strictly for non-commercial purposes is hereby granted   *\r
* without fee, provided that the above copyright notice appears in all   *\r
* copies and that both the copyright notice and this permission notice   *\r
* appear in the supporting documentation. The authors make no claims     *\r
* about the suitability of this software for any purpose. It is          *\r
* provided "as is" without express or implied warranty.                  * \r
**************************************************************************/\r
\r
/********************************** \r
 * flow analysis with Q-cumulants * \r
 *                                * \r
 * author:  Ante Bilandzic        * \r
 *           (anteb@nikhef.nl)    *\r
 *********************************/ \r
\r
#define AliFlowAnalysisWithQCumulants_cxx\r
\r
#include "Riostream.h"\r
#include "AliFlowCommonConstants.h"\r
#include "AliFlowCommonHist.h"\r
#include "AliFlowCommonHistResults.h"\r
#include "TChain.h"\r
\r
#include "TFile.h"\r
#include "TList.h"\r
#include "TGraph.h"\r
#include "TParticle.h"\r
#include "TRandom3.h"\r
#include "TStyle.h"\r
#include "TProfile.h"\r
#include "TProfile2D.h" \r
#include "TProfile3D.h"\r
#include "TMath.h"\r
#include "TArrow.h"\r
#include "TPaveLabel.h"\r
#include "TCanvas.h"\r
#include "AliFlowEventSimple.h"\r
#include "AliFlowTrackSimple.h"\r
#include "AliFlowAnalysisWithQCumulants.h"\r
#include "TArrayD.h"\r
#include "TRandom.h"\r
#include "TF1.h"\r
\r
class TH1;\r
class TH2;\r
class TGraph;\r
class TPave;\r
class TLatex;\r
class TMarker;\r
class TRandom3;\r
class TObjArray;\r
class TList;\r
class TCanvas;\r
class TSystem;\r
class TROOT;\r
class AliFlowVector;\r
class TVector;\r
\r
\r
//================================================================================================================\r
\r
\r
ClassImp(AliFlowAnalysisWithQCumulants)\r
\r
AliFlowAnalysisWithQCumulants::AliFlowAnalysisWithQCumulants(): \r
 // 0.) base:\r
 fHistList(NULL),\r
 // 1.) common:\r
 fCommonHists(NULL),\r
 fCommonHists2nd(NULL), \r
 fCommonHists4th(NULL),\r
 fCommonHists6th(NULL),\r
 fCommonHists8th(NULL),\r
 fCommonHistsResults2nd(NULL),\r
 fCommonHistsResults4th(NULL),\r
 fCommonHistsResults6th(NULL),\r
 fCommonHistsResults8th(NULL),\r
 fnBinsPhi(0),\r
 fPhiMin(0),\r
 fPhiMax(0),\r
 fPhiBinWidth(0),\r
 fnBinsPt(0),\r
 fPtMin(0),\r
 fPtMax(0),\r
 fPtBinWidth(0),\r
 fnBinsEta(0),\r
 fEtaMin(0),\r
 fEtaMax(0),\r
 fEtaBinWidth(0),\r
 fHarmonic(2),\r
 fAnalysisLabel(NULL),\r
 // 2a.) particle weights:\r
 fWeightsList(NULL),\r
 fUsePhiWeights(kFALSE),\r
 fUsePtWeights(kFALSE),\r
 fUseEtaWeights(kFALSE),\r
 fUseParticleWeights(NULL),\r
 fPhiWeights(NULL),\r
 fPtWeights(NULL),\r
 fEtaWeights(NULL),\r
 // 2b.) event weights:\r
 fMultiplicityWeight(NULL),\r
 // 3.) integrated flow:\r
 fIntFlowList(NULL), \r
 fIntFlowProfiles(NULL),\r
 fIntFlowResults(NULL),\r
 fIntFlowFlags(NULL),\r
 fApplyCorrectionForNUA(kTRUE), \r
 fReQ(NULL),\r
 fImQ(NULL),\r
 fSMpk(NULL),\r
 fIntFlowCorrelationsEBE(NULL),\r
 fIntFlowEventWeightsForCorrelationsEBE(NULL),\r
 fIntFlowCorrelationsAllEBE(NULL),\r
 fAvMultiplicity(NULL),\r
 fIntFlowCorrelationsPro(NULL),\r
 fIntFlowCorrelationsAllPro(NULL),\r
 fIntFlowExtraCorrelationsPro(NULL),\r
 fIntFlowProductOfCorrelationsPro(NULL),\r
 fIntFlowCorrelationsHist(NULL),\r
 fIntFlowCorrelationsAllHist(NULL),\r
 fIntFlowCovariances(NULL),\r
 fIntFlowSumOfProductOfEventWeights(NULL),\r
 fIntFlowQcumulants(NULL),\r
 fIntFlow(NULL),\r
 // 4.) differential flow:\r
 fDiffFlowList(NULL),\r
 fDiffFlowProfiles(NULL),\r
 fDiffFlowResults(NULL),\r
 fDiffFlowFlags(NULL),\r
 fCalculate2DFlow(kFALSE),\r
 // 5.) distributions:\r
 fDistributionsList(NULL),
 fDistributionsFlags(NULL),
 fStoreDistributions(kFALSE),\r
 // x.) debugging and cross-checking:\r
 fNestedLoopsList(NULL),\r
 fEvaluateIntFlowNestedLoops(kFALSE),\r
 fEvaluateDiffFlowNestedLoops(kFALSE),\r
 fMaxAllowedMultiplicity(10),\r
 fEvaluateNestedLoops(NULL),\r
 fIntFlowDirectCorrelations(NULL),\r
 fIntFlowExtraDirectCorrelations(NULL),\r
 fCrossCheckInPtBinNo(10),\r
 fCrossCheckInEtaBinNo(20),
 fNoOfParticlesInBin(NULL)\r
 {\r
  // constructor  \r
  \r
  // base list to hold all output objects:\r
  fHistList = new TList();\r
  fHistList->SetName("cobjQC");\r
  fHistList->SetOwner(kTRUE);\r
  \r
  // list to hold histograms with phi, pt and eta weights:      \r
  fWeightsList = new TList();\r
  \r
  // multiplicity weight:\r
  fMultiplicityWeight = new TString("combinations");\r
    \r
  // analysis label;\r
  fAnalysisLabel = new TString();\r
      \r
  // initialize all arrays:  \r
  this->InitializeArraysForIntFlow();\r
  this->InitializeArraysForDiffFlow();\r
  this->InitializeArraysForDistributions();\r
  this->InitializeArraysForNestedLoops();\r
  \r
 } // end of constructor\r
 \r
\r
//================================================================================================================  \r
\r
\r
AliFlowAnalysisWithQCumulants::~AliFlowAnalysisWithQCumulants()\r
{\r
 // destructor\r
 \r
 delete fHistList;\r
\r
} // end of AliFlowAnalysisWithQCumulants::~AliFlowAnalysisWithQCumulants()\r
\r
\r
//================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::Init()\r
{\r
 // a) Cross check if the settings make sense before starting the QC adventure;
 // b) Access all common constants;\r
 // c) Book all objects;\r
 // d) Store flags for integrated and differential flow;
 // e) Store flags for distributions of corelations;\r
 // f) Store harmonic which will be estimated.\r
  
 // a) Cross check if the settings make sense before starting the QC adventure; 
 this->CrossCheckSettings();\r
 // b) Access all common constants:\r
 this->AccessConstants();\r
 // c) Book all objects:\r
 this->BookAndFillWeightsHistograms();\r
 this->BookAndNestAllLists();\r
 this->BookCommonHistograms();\r
 this->BookEverythingForIntegratedFlow(); \r
 this->BookEverythingForDifferentialFlow(); \r
 this->BookEverythingForDistributions();\r
 this->BookEverythingForNestedLoops();\r
 // d) Store flags for integrated and differential flow:\r
 this->StoreIntFlowFlags();\r
 this->StoreDiffFlowFlags();
 // e) Store flags for distributions of corelations:\r
 this->StoreFlagsForDistributions();\r
 // f) Store harmonic which will be estimated:\r
 this->StoreHarmonic();\r
 \r
} // end of void AliFlowAnalysisWithQCumulants::Init()\r
\r
\r
//================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::Make(AliFlowEventSimple* anEvent)\r
{\r
 // Running over data only in this method.\r
 \r
 //  a) Fill the common control histograms and call the method to fill fAvMultiplicity;\r
 //  b) Loop over data and calculate e-b-e quantities;\r
 //  c) Call all the methods;\r
 //  d) Debugging and cross-checking (evaluate nested loops);\r
 //  e) Reset all event by event quantities. \r
 \r
 Double_t dPhi = 0.; // azimuthal angle in the laboratory frame\r
 Double_t dPt  = 0.; // transverse momentum\r
 Double_t dEta = 0.; // pseudorapidity\r
\r
 Double_t wPhi = 1.; // phi weight\r
 Double_t wPt  = 1.; // pt weight\r
 Double_t wEta = 1.; // eta weight\r
 \r
 Int_t nRP = anEvent->GetEventNSelTracksRP(); // number of RPs (i.e. number of particles used to determine the reaction plane)\r
 \r
 // a) Fill the common control histograms and call the method to fill fAvMultiplicity:\r
 this->FillCommonControlHistograms(anEvent);                                                               \r
 this->FillAverageMultiplicities(nRP);                                                                  \r
                                                                                                                                                                                                                                                                                        \r
 // b) Loop over data and calculate e-b-e quantities:\r
 Int_t nPrim = anEvent->NumberOfTracks();  // nPrim = total number of primary tracks, i.e. nPrim = nRP + nPOI + rest, where:\r
                                           // nRP   = # of particles used to determine the reaction plane;\r
                                           // nPOI  = # of particles of interest for a detailed flow analysis;\r
                                           // rest  = # of particles which are not niether RPs nor POIs.  \r
 \r
 AliFlowTrackSimple *aftsTrack = NULL;\r
 \r
 for(Int_t i=0;i<nPrim;i++) \r
 { \r
  aftsTrack=anEvent->GetTrack(i);\r
  if(aftsTrack)\r
  {\r
   if(!(aftsTrack->InRPSelection() || aftsTrack->InPOISelection())) continue; // consider only tracks which are RPs or POIs\r
   Int_t n = fHarmonic; // shortcut for the harmonic\r
   if(aftsTrack->InRPSelection()) // RP condition:\r
   {    \r
    dPhi = aftsTrack->Phi();\r
    dPt  = aftsTrack->Pt();\r
    dEta = aftsTrack->Eta();\r
    if(fUsePhiWeights && fPhiWeights && fnBinsPhi) // determine phi weight for this particle:\r
    {\r
     wPhi = fPhiWeights->GetBinContent(1+(Int_t)(TMath::Floor(dPhi*fnBinsPhi/TMath::TwoPi())));\r
    }\r
    if(fUsePtWeights && fPtWeights && fnBinsPt) // determine pt weight for this particle:\r
    {\r
     wPt = fPtWeights->GetBinContent(1+(Int_t)(TMath::Floor((dPt-fPtMin)/fPtBinWidth))); \r
    }              \r
    if(fUseEtaWeights && fEtaWeights && fEtaBinWidth) // determine eta weight for this particle: \r
    {\r
     wEta = fEtaWeights->GetBinContent(1+(Int_t)(TMath::Floor((dEta-fEtaMin)/fEtaBinWidth))); \r
    } \r
      \r
    // integrated flow: \r
    // calculate Re[Q_{m*n,k}] and Im[Q_{m*n,k}], m = 1,2,3,4, for this event:\r
    for(Int_t m=0;m<4;m++)\r
    {\r
     for(Int_t k=0;k<9;k++)\r
     {\r
      (*fReQ)(m,k)+=pow(wPhi*wPt*wEta,k)*TMath::Cos((m+1)*n*dPhi); \r
      (*fImQ)(m,k)+=pow(wPhi*wPt*wEta,k)*TMath::Sin((m+1)*n*dPhi); \r
     } \r
    }\r
    // calculate S^{M}_{p,k} for this event \r
    // Remark: final calculation of S^{M}_{p,k} follows after the loop over data bellow:\r
    for(Int_t p=0;p<8;p++)\r
    {\r
     for(Int_t k=0;k<9;k++)\r
     {     \r
      (*fSMpk)(p,k)+=pow(wPhi*wPt*wEta,k);\r
     }\r
    } \r
    \r
    // differential flow:\r
    // 1D (pt):\r
    // (r_{m*m,k}(pt)): \r
    for(Int_t m=0;m<4;m++)\r
    {\r
     for(Int_t k=0;k<9;k++)\r
     {\r
      fReRPQ1dEBE[0][0][m][k]->Fill(dPt,pow(wPhi*wPt*wEta,k)*TMath::Cos((m+1.)*n*dPhi),1.);\r
      fImRPQ1dEBE[0][0][m][k]->Fill(dPt,pow(wPhi*wPt*wEta,k)*TMath::Sin((m+1.)*n*dPhi),1.);\r
     }\r
    }\r
           \r
    // s_{k}(pt) for RPs // to be improved (clarified)\r
    // Remark: final calculation of s_{p,k}(pt) follows after the loop over data bellow:\r
    for(Int_t k=0;k<9;k++)\r
    {\r
     fs1dEBE[0][0][k]->Fill(dPt,pow(wPhi*wPt*wEta,k),1.);\r
    }\r
    // 1D (eta):\r
    // (r_{m*m,k}(eta)): \r
    for(Int_t m=0;m<4;m++)\r
    {\r
     for(Int_t k=0;k<9;k++)\r
     {\r
      fReRPQ1dEBE[0][1][m][k]->Fill(dEta,pow(wPhi*wPt*wEta,k)*TMath::Cos((m+1.)*n*dPhi),1.);\r
      fImRPQ1dEBE[0][1][m][k]->Fill(dEta,pow(wPhi*wPt*wEta,k)*TMath::Sin((m+1.)*n*dPhi),1.);\r
     }\r
    }   \r
    // s_{k}(eta) for RPs // to be improved (clarified)\r
    // Remark: final calculation of s_{p,k}(eta) follows after the loop over data bellow:\r
    for(Int_t k=0;k<9;k++)\r
    {\r
     fs1dEBE[0][1][k]->Fill(dEta,pow(wPhi*wPt*wEta,k),1.);\r
    }\r
    \r
    \r
    \r
    /*\r
    // 2D (pt,eta):\r
    if(fCalculate2DFlow)\r
    {\r
     // (r_{m*m,k}(pt,eta)): \r
     for(Int_t m=0;m<4;m++)\r
     {\r
      for(Int_t k=0;k<9;k++)\r
      {\r
       fReRPQ2dEBE[0][m][k]->Fill(dPt,dEta,pow(wPhi*wPt*wEta,k)*TMath::Cos((m+1.)*n*dPhi),1.);\r
       fImRPQ2dEBE[0][m][k]->Fill(dPt,dEta,pow(wPhi*wPt*wEta,k)*TMath::Sin((m+1.)*n*dPhi),1.);\r
      }\r
     }    \r
     // s_{k}(pt,eta) for RPs // to be improved (clarified)\r
     // Remark: final calculation of s_{p,k}(pt,eta) follows after the loop over data bellow:\r
     for(Int_t k=0;k<9;k++)\r
     {\r
      fs2dEBE[0][k]->Fill(dPt,dEta,pow(wPhi*wPt*wEta,k),1.);\r
     }\r
    } // end of if(fCalculate2DFlow)  \r
    */ \r
    \r
      \r
     \r
    if(aftsTrack->InPOISelection())\r
    {\r
     // 1D (pt): \r
     // (q_{m*m,k}(pt)): \r
     for(Int_t m=0;m<4;m++)\r
     {\r
      for(Int_t k=0;k<9;k++)\r
      {\r
       fReRPQ1dEBE[2][0][m][k]->Fill(dPt,pow(wPhi*wPt*wEta,k)*TMath::Cos((m+1.)*n*dPhi),1.);\r
       fImRPQ1dEBE[2][0][m][k]->Fill(dPt,pow(wPhi*wPt*wEta,k)*TMath::Sin((m+1.)*n*dPhi),1.);\r
      }\r
     } \r
     // s_{k}(pt) for RP&&POIs // to be improved (clarified)\r
     // Remark: final calculation of s_{p,k}(pt,eta) follows after the loop over data bellow:\r
     for(Int_t k=0;k<9;k++)\r
     {\r
      fs1dEBE[2][0][k]->Fill(dPt,pow(wPhi*wPt*wEta,k),1.);\r
     }\r
     // 1D (eta): \r
     // (q_{m*m,k}(eta)): \r
     for(Int_t m=0;m<4;m++)\r
     {\r
      for(Int_t k=0;k<9;k++)\r
      {\r
       fReRPQ1dEBE[2][1][m][k]->Fill(dEta,pow(wPhi*wPt*wEta,k)*TMath::Cos((m+1.)*n*dPhi),1.);\r
       fImRPQ1dEBE[2][1][m][k]->Fill(dEta,pow(wPhi*wPt*wEta,k)*TMath::Sin((m+1.)*n*dPhi),1.);\r
      }\r
     } \r
     // s_{k}(eta) for RP&&POIs // to be improved (clarified)\r
     // Remark: final calculation of s_{p,k}(pt,eta) follows after the loop over data bellow:\r
     for(Int_t k=0;k<9;k++)\r
     {\r
      fs1dEBE[2][1][k]->Fill(dEta,pow(wPhi*wPt*wEta,k),1.);\r
     }\r
     \r
     /*\r
     // 2D (pt,eta) \r
     if(fCalculate2DFlow)\r
     {\r
      // (q_{m*m,k}(pt,eta)): \r
      for(Int_t m=0;m<4;m++)\r
      {\r
       for(Int_t k=0;k<9;k++)\r
       {\r
        fReRPQ2dEBE[2][m][k]->Fill(dPt,dEta,pow(wPhi*wPt*wEta,k)*TMath::Cos((m+1.)*n*dPhi),1.);\r
        fImRPQ2dEBE[2][m][k]->Fill(dPt,dEta,pow(wPhi*wPt*wEta,k)*TMath::Sin((m+1.)*n*dPhi),1.);\r
       }\r
      } \r
      // s_{k}(pt,eta) for RP&&POIs // to be improved (clarified)\r
      // Remark: final calculation of s_{p,k}(pt,eta) follows after the loop over data bellow:\r
      for(Int_t k=0;k<9;k++)\r
      {\r
       fs2dEBE[2][k]->Fill(dPt,dEta,pow(wPhi*wPt*wEta,k),1.);\r
      }\r
     } // end of if(fCalculate2DFlow) \r
     */\r
      \r
    } // end of if(aftsTrack->InPOISelection())\r
    \r
\r
     \r
   } // end of if(pTrack->InRPSelection())\r
\r
  \r
  \r
   if(aftsTrack->InPOISelection())\r
   {\r
    dPhi = aftsTrack->Phi();\r
    dPt  = aftsTrack->Pt();\r
    dEta = aftsTrack->Eta();\r
    \r
    // 1D (pt)\r
    // p_n(m*n,0):   \r
    for(Int_t m=0;m<4;m++)\r
    {\r
     fReRPQ1dEBE[1][0][m][0]->Fill(dPt,TMath::Cos((m+1.)*n*dPhi),1.);\r
     fImRPQ1dEBE[1][0][m][0]->Fill(dPt,TMath::Sin((m+1.)*n*dPhi),1.);\r
    }\r
    // 1D (eta)\r
    // p_n(m*n,0):   \r
    for(Int_t m=0;m<4;m++)\r
    {\r
     fReRPQ1dEBE[1][1][m][0]->Fill(dEta,TMath::Cos((m+1.)*n*dPhi),1.);\r
     fImRPQ1dEBE[1][1][m][0]->Fill(dEta,TMath::Sin((m+1.)*n*dPhi),1.);\r
    }\r
    \r
    \r
    /*\r
    // 2D (pt,eta):\r
    if(fCalculate2DFlow)\r
    {      \r
     // p_n(m*n,0):   \r
     for(Int_t m=0;m<4;m++)\r
     {\r
      fReRPQ2dEBE[1][m][0]->Fill(dPt,dEta,TMath::Cos((m+1.)*n*dPhi),1.);\r
      fImRPQ2dEBE[1][m][0]->Fill(dPt,dEta,TMath::Sin((m+1.)*n*dPhi),1.);\r
     }\r
    } // end of if(fCalculate2DFlow)  \r
    */\r
    \r
    \r
   } // end of if(pTrack->InPOISelection() )   \r
 \r
  \r
  } else // to if(aftsTrack)\r
    {\r
     cout<<endl;\r
     cout<<" WARNING: no particle! (i.e. aftsTrack is a NULL pointer in AFAWQC::Make().)"<<endl;\r
     cout<<endl;       \r
    }\r
 } // end of for(Int_t i=0;i<nPrim;i++) \r
\r
 // calculate the final expressions for S^{M}_{p,k}:\r
 for(Int_t p=0;p<8;p++)\r
 {\r
  for(Int_t k=0;k<9;k++)\r
  {\r
   (*fSMpk)(p,k)=pow((*fSMpk)(p,k),p+1);\r
  }  \r
 } \r
 \r
 // *****************************\r
 // **** CALL THE METHODS *******\r
 // *****************************\r
 // integrated flow:\r
 if(!fEvaluateIntFlowNestedLoops)\r
 {\r
  if(!(fUsePhiWeights||fUsePtWeights||fUseEtaWeights))\r
  {\r
   if(nRP>1) this->CalculateIntFlowCorrelations(); // without using particle weights\r
  } else \r
    {\r
     if(nRP>1) this->CalculateIntFlowCorrelationsUsingParticleWeights(); // with using particle weights   \r
    } \r
       \r
  if(nRP>3) this->CalculateIntFlowProductOfCorrelations();\r
  if(nRP>1) this->CalculateIntFlowSumOfEventWeights();\r
  if(nRP>1) this->CalculateIntFlowSumOfProductOfEventWeights();\r
  if(fApplyCorrectionForNUA)\r
  {\r
   if(!(fUsePhiWeights||fUsePtWeights||fUseEtaWeights))
   {
    if(nRP>0) this->CalculateIntFlowCorrectionsForNUASinTerms();\r
    if(nRP>0) this->CalculateIntFlowCorrectionsForNUACosTerms();\r
   } else // to if(!(fUsePhiWeights||fUsePtWeights||fUseEtaWeights))
     {
      if(nRP>0) this->CalculateIntFlowCorrectionsForNUASinTermsUsingParticleWeights();\r
      if(nRP>0) this->CalculateIntFlowCorrectionsForNUACosTermsUsingParticleWeights();     
     }  
  } // end of if(fApplyCorrectionForNUA)\r
 } // end of if(!fEvaluateIntFlowNestedLoops)\r
\r
 // differential flow:\r
 if(!fEvaluateDiffFlowNestedLoops)\r
 {\r
  if(!(fUsePhiWeights||fUsePtWeights||fUseEtaWeights))\r
  {\r
   // without using particle weights:\r
   this->CalculateDiffFlowCorrelations("RP","Pt"); \r
   this->CalculateDiffFlowCorrelations("RP","Eta");\r
   this->CalculateDiffFlowCorrelations("POI","Pt");\r
   this->CalculateDiffFlowCorrelations("POI","Eta");
   if(fApplyCorrectionForNUA)
   {
    this->CalculateDiffFlowCorrectionsForNUASinTerms("RP","Pt");\r
    this->CalculateDiffFlowCorrectionsForNUASinTerms("RP","Eta");\r
    this->CalculateDiffFlowCorrectionsForNUASinTerms("POI","Pt");\r
    this->CalculateDiffFlowCorrectionsForNUASinTerms("POI","Eta");\r
    this->CalculateDiffFlowCorrectionsForNUACosTerms("RP","Pt");\r
    this->CalculateDiffFlowCorrectionsForNUACosTerms("RP","Eta");\r
    this->CalculateDiffFlowCorrectionsForNUACosTerms("POI","Pt");\r
    this->CalculateDiffFlowCorrectionsForNUACosTerms("POI","Eta");   
   } // end of if(fApplyCorrectionForNUA)  \r
  } else // to if(!(fUsePhiWeights||fUsePtWeights||fUseEtaWeights))\r
    {\r
     // with using particle weights:   \r
     this->CalculateDiffFlowCorrelationsUsingParticleWeights("RP","Pt"); \r
     this->CalculateDiffFlowCorrelationsUsingParticleWeights("RP","Eta"); \r
     this->CalculateDiffFlowCorrelationsUsingParticleWeights("POI","Pt"); \r
     this->CalculateDiffFlowCorrelationsUsingParticleWeights("POI","Eta"); \r
     if(fApplyCorrectionForNUA)
     {
      this->CalculateDiffFlowCorrectionsForNUASinTermsUsingParticleWeights("RP","Pt");\r
      this->CalculateDiffFlowCorrectionsForNUASinTermsUsingParticleWeights("RP","Eta");\r
      this->CalculateDiffFlowCorrectionsForNUASinTermsUsingParticleWeights("POI","Pt");\r
      this->CalculateDiffFlowCorrectionsForNUASinTermsUsingParticleWeights("POI","Eta");\r
      this->CalculateDiffFlowCorrectionsForNUACosTermsUsingParticleWeights("RP","Pt");\r
      this->CalculateDiffFlowCorrectionsForNUACosTermsUsingParticleWeights("RP","Eta");\r
      this->CalculateDiffFlowCorrectionsForNUACosTermsUsingParticleWeights("POI","Pt");\r
      this->CalculateDiffFlowCorrectionsForNUACosTermsUsingParticleWeights("POI","Eta");   
     } // end of if(fApplyCorrectionForNUA)  \r
    } \r
    
  // whether or not using particle weights the following is calculated in the same way:  \r
  this->CalculateDiffFlowProductOfCorrelations("RP","Pt");\r
  this->CalculateDiffFlowProductOfCorrelations("RP","Eta");\r
  this->CalculateDiffFlowProductOfCorrelations("POI","Pt");\r
  this->CalculateDiffFlowProductOfCorrelations("POI","Eta");\r
  this->CalculateDiffFlowSumOfEventWeights("RP","Pt");\r
  this->CalculateDiffFlowSumOfEventWeights("RP","Eta");\r
  this->CalculateDiffFlowSumOfEventWeights("POI","Pt");\r
  this->CalculateDiffFlowSumOfEventWeights("POI","Eta");\r
  this->CalculateDiffFlowSumOfProductOfEventWeights("RP","Pt");\r
  this->CalculateDiffFlowSumOfProductOfEventWeights("RP","Eta");\r
  this->CalculateDiffFlowSumOfProductOfEventWeights("POI","Pt");\r
  this->CalculateDiffFlowSumOfProductOfEventWeights("POI","Eta");   \r
 } // end of if(!fEvaluateDiffFlowNestedLoops)\r
\r
\r
   \r
  // with weights:\r
  // ... \r
  \r
  /*\r
  // 2D differential flow\r
  if(fCalculate2DFlow)\r
  {\r
   // without weights:\r
   if(nRP>1) this->CalculateCorrelationsForDifferentialFlow2D("RP");\r
   if(nRP>1) this->CalculateCorrelationsForDifferentialFlow2D("POI");\r
  \r
   // with weights:\r
   if(fUsePhiWeights||fUsePtWeights||fUseEtaWeights)\r
   {\r
    if(nRP>1) this->CalculateWeightedCorrelationsForDifferentialFlow2D("RP");\r
    if(nRP>1) this->CalculateWeightedCorrelationsForDifferentialFlow2D("POI");\r
   } \r
  } // end of if(fCalculate2DFlow)\r
  */\r
  
 // distributions of correlations:
 if(fStoreDistributions)
 {
  this->StoreDistributionsOfCorrelations();
 }
  \r
 // d) Debugging and cross-checking (evaluate nested loops):\r
 //  d1) cross-checking results for integrated flow:\r
 if(fEvaluateIntFlowNestedLoops)\r
 {\r
  if(nPrim>0 && nPrim<=fMaxAllowedMultiplicity) // by default fMaxAllowedMultiplicity = 10 \r
  {\r
   // without using particle weights:\r
   if(!(fUsePhiWeights||fUsePtWeights||fUseEtaWeights))\r
   {\r
    // correlations:\r
    this->CalculateIntFlowCorrelations(); // from Q-vectors\r
    this->EvaluateIntFlowCorrelationsWithNestedLoops(anEvent); // from nested loops (to be improved: do I have to pass here anEvent or not?)\r
    // correction for non-uniform acceptance:\r
    this->CalculateIntFlowCorrectionsForNUASinTerms(); // from Q-vectors (sin terms)\r
    this->CalculateIntFlowCorrectionsForNUACosTerms(); // from Q-vectors (cos terms)\r
    this->EvaluateIntFlowCorrectionsForNUAWithNestedLoops(anEvent); // from nested loops (both sin and cos terms)\r
   }\r
   // using particle weights:\r
   if(fUsePhiWeights||fUsePtWeights||fUseEtaWeights)\r
   {\r
    // correlations:\r
    this->CalculateIntFlowCorrelationsUsingParticleWeights(); // from Q-vectors\r
    this->EvaluateIntFlowCorrelationsWithNestedLoopsUsingParticleWeights(anEvent); // from nested loops (to be improved: do I have to pass here anEvent or not?)\r
    // correction for non-uniform acceptance:\r
    this->CalculateIntFlowCorrectionsForNUASinTermsUsingParticleWeights(); // from Q-vectors (sin terms)\r
    this->CalculateIntFlowCorrectionsForNUACosTermsUsingParticleWeights(); // from Q-vectors (cos terms)\r
    this->EvaluateIntFlowCorrectionsForNUAWithNestedLoopsUsingParticleWeights(anEvent); // from nested loops (both sin and cos terms)   
   }\r
  } else if (nPrim>fMaxAllowedMultiplicity) // to if(nPrim>0 && nPrim<=fMaxAllowedMultiplicity)\r
    {\r
     cout<<endl;\r
     cout<<"Skipping the event because multiplicity is "<<nPrim<<". Too high to evaluate nested loops!"<<endl;\r
    } else\r
      {\r
       cout<<endl;\r
       cout<<"Skipping the event because multiplicity is "<<nPrim<<"."<<endl;      \r
      } \r
 } // end of if(fEvaluateIntFlowNestedLoops) \r
 \r
 //  d2) cross-checking results for differential flow:\r
 if(fEvaluateDiffFlowNestedLoops)\r
 {\r
  if(nPrim>0 && nPrim<=fMaxAllowedMultiplicity) // by default fMaxAllowedMultiplicity = 10\r
  {\r
   // without using particle weights:\r
   if(!(fUsePhiWeights||fUsePtWeights||fUseEtaWeights))\r
   {\r
    // reduced correlations:\r
    // Q-vectors:\r
    this->CalculateDiffFlowCorrelations("RP","Pt");\r
    this->CalculateDiffFlowCorrelations("RP","Eta");\r
    this->CalculateDiffFlowCorrelations("POI","Pt");\r
    this->CalculateDiffFlowCorrelations("POI","Eta");\r
    // nested loops:\r
    this->EvaluateDiffFlowCorrelationsWithNestedLoops(anEvent,"RP","Pt"); \r
    this->EvaluateDiffFlowCorrelationsWithNestedLoops(anEvent,"RP","Eta"); \r
    this->EvaluateDiffFlowCorrelationsWithNestedLoops(anEvent,"POI","Pt"); \r
    this->EvaluateDiffFlowCorrelationsWithNestedLoops(anEvent,"POI","Eta"); \r
    // reduced corrections for non-uniform acceptance:\r
    // Q-vectors:\r
    this->CalculateDiffFlowCorrectionsForNUASinTerms("RP","Pt");\r
    this->CalculateDiffFlowCorrectionsForNUASinTerms("RP","Eta");\r
    this->CalculateDiffFlowCorrectionsForNUASinTerms("POI","Pt");\r
    this->CalculateDiffFlowCorrectionsForNUASinTerms("POI","Eta");\r
    this->CalculateDiffFlowCorrectionsForNUACosTerms("RP","Pt");\r
    this->CalculateDiffFlowCorrectionsForNUACosTerms("RP","Eta");\r
    this->CalculateDiffFlowCorrectionsForNUACosTerms("POI","Pt");\r
    this->CalculateDiffFlowCorrectionsForNUACosTerms("POI","Eta");\r
    // nested loops:\r
    this->EvaluateDiffFlowCorrectionTermsForNUAWithNestedLoops(anEvent,"RP","Pt");\r
    this->EvaluateDiffFlowCorrectionTermsForNUAWithNestedLoops(anEvent,"RP","Eta");\r
    this->EvaluateDiffFlowCorrectionTermsForNUAWithNestedLoops(anEvent,"POI","Pt"); \r
    this->EvaluateDiffFlowCorrectionTermsForNUAWithNestedLoops(anEvent,"POI","Eta"); \r
   } // end of if(!(fUsePhiWeights||fUsePtWeights||fUseEtaWeights))\r
   // using particle weights:\r
   if(fUsePhiWeights||fUsePtWeights||fUseEtaWeights)\r
   {\r
    this->CalculateDiffFlowCorrelationsUsingParticleWeights("RP","Pt"); \r
    this->CalculateDiffFlowCorrelationsUsingParticleWeights("RP","Eta"); \r
    this->CalculateDiffFlowCorrelationsUsingParticleWeights("POI","Pt"); \r
    this->CalculateDiffFlowCorrelationsUsingParticleWeights("POI","Eta"); \r
    this->CalculateDiffFlowCorrectionsForNUASinTermsUsingParticleWeights("RP","Pt");\r
    this->CalculateDiffFlowCorrectionsForNUASinTermsUsingParticleWeights("RP","Eta");\r
    this->CalculateDiffFlowCorrectionsForNUASinTermsUsingParticleWeights("POI","Pt");\r
    this->CalculateDiffFlowCorrectionsForNUASinTermsUsingParticleWeights("POI","Eta");\r
    this->CalculateDiffFlowCorrectionsForNUACosTermsUsingParticleWeights("RP","Pt");\r
    this->CalculateDiffFlowCorrectionsForNUACosTermsUsingParticleWeights("RP","Eta");\r
    this->CalculateDiffFlowCorrectionsForNUACosTermsUsingParticleWeights("POI","Pt");\r
    this->CalculateDiffFlowCorrectionsForNUACosTermsUsingParticleWeights("POI","Eta");\r
    this->EvaluateDiffFlowCorrelationsWithNestedLoopsUsingParticleWeights(anEvent,"RP","Pt"); \r
    this->EvaluateDiffFlowCorrelationsWithNestedLoopsUsingParticleWeights(anEvent,"RP","Eta");\r
    this->EvaluateDiffFlowCorrelationsWithNestedLoopsUsingParticleWeights(anEvent,"POI","Pt"); \r
    this->EvaluateDiffFlowCorrelationsWithNestedLoopsUsingParticleWeights(anEvent,"POI","Eta");   
    this->EvaluateDiffFlowCorrectionTermsForNUAWithNestedLoopsUsingParticleWeights(anEvent,"RP","Pt"); \r
    this->EvaluateDiffFlowCorrectionTermsForNUAWithNestedLoopsUsingParticleWeights(anEvent,"RP","Eta"); \r
    this->EvaluateDiffFlowCorrectionTermsForNUAWithNestedLoopsUsingParticleWeights(anEvent,"POI","Pt"); \r
    this->EvaluateDiffFlowCorrectionTermsForNUAWithNestedLoopsUsingParticleWeights(anEvent,"POI","Eta"); \r
   } // end of if(fUsePhiWeights||fUsePtWeights||fUseEtaWeights)\r
  } // end of if(nPrim>0 && nPrim<=fMaxAllowedMultiplicity) // by default fMaxAllowedMultiplicity = 10\r
 } // end of if(fEvaluateDiffFlowNestedLoops) \r
 \r
 // e) Reset all event by event quantities: \r
 this->ResetEventByEventQuantities();\r
 \r
} // end of AliFlowAnalysisWithQCumulants::Make(AliFlowEventSimple* anEvent)\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::Finish()\r
{\r
 // Calculate the final results.\r
 //  a) acces the constants;\r
 //  b) access the flags;\r
 //  c) calculate the final results for integrated flow (without and with weights);\r
 //  d) store in AliFlowCommonHistResults and print the final results for integrated flow;\r
 //  e) calculate the final results for differential flow (without and with weights);\r
 //  f) print the final results for integrated flow obtained from differential flow (to be improved (terminology));\r
 //  g) cross-check the results: results from Q-vectors vs results from nested loops\r
 \r
 // ******************************\r
 // **** ACCESS THE CONSTANTS ****\r
 // ******************************\r
 \r
 this->AccessConstants();          \r
 \r
 if(fCommonHists && fCommonHists->GetHarmonic())\r
 {\r
  fHarmonic = (Int_t)(fCommonHists->GetHarmonic())->GetBinContent(1); // to be improved (moved somewhere else)\r
 } \r
\r
 // **************************\r
 // **** ACCESS THE FLAGS ****\r
 // **************************    \r
 fUsePhiWeights = (Int_t)fUseParticleWeights->GetBinContent(1); \r
 fUsePtWeights = (Int_t)fUseParticleWeights->GetBinContent(2); \r
 fUseEtaWeights = (Int_t)fUseParticleWeights->GetBinContent(3);  \r
 fApplyCorrectionForNUA = (Int_t)fIntFlowFlags->GetBinContent(3); 
 fPrintFinalResults[0] = (Int_t)fIntFlowFlags->GetBinContent(4);\r
 fPrintFinalResults[1] = (Int_t)fIntFlowFlags->GetBinContent(5);\r
 fPrintFinalResults[2] = (Int_t)fIntFlowFlags->GetBinContent(6);\r
 fEvaluateIntFlowNestedLoops = (Int_t)fEvaluateNestedLoops->GetBinContent(1);\r
 fEvaluateDiffFlowNestedLoops = (Int_t)fEvaluateNestedLoops->GetBinContent(2); \r
 fCrossCheckInPtBinNo = (Int_t)fEvaluateNestedLoops->GetBinContent(3);\r
 fCrossCheckInEtaBinNo = (Int_t)fEvaluateNestedLoops->GetBinContent(4); \r
    \r
 // *********************************************************\r
 // **** CALCULATE THE FINAL RESULTS FOR INTEGRATED FLOW ****\r
 // *********************************************************     \r
 \r
 this->FinalizeCorrelationsIntFlow();\r
 this->CalculateCovariancesIntFlow();\r
 this->CalculateCumulantsIntFlow();\r
 this->CalculateIntFlow(); \r
\r
 if(fApplyCorrectionForNUA) // to be improved (reorganized, etc)\r
 {\r
  this->FinalizeCorrectionTermsForNUAIntFlow();\r
  this->CalculateQcumulantsCorrectedForNUAIntFlow();   \r
  this->CalculateIntFlowCorrectedForNUA(); \r
 }\r
  \r
 // ***************************************************************\r
 // **** STORE AND PRINT THE FINAL RESULTS FOR INTEGRATED FLOW ****\r
 // ***************************************************************\r
 \r
 this->FillCommonHistResultsIntFlow();  \r
  \r
 if(fPrintFinalResults[0])
 {
  this->PrintFinalResultsForIntegratedFlow("NONAME"); // to be improved (name)\r
 }
 \r
 // ***********************************************************\r
 // **** CALCULATE THE FINAL RESULTS FOR DIFFERENTIAL FLOW ****\r
 // ***********************************************************    \r
 \r
 this->FinalizeReducedCorrelations("RP","Pt"); \r
 this->FinalizeReducedCorrelations("RP","Eta"); \r
 this->FinalizeReducedCorrelations("POI","Pt"); \r
 this->FinalizeReducedCorrelations("POI","Eta");\r
 this->CalculateDiffFlowCovariances("RP","Pt");\r
 this->CalculateDiffFlowCovariances("RP","Eta");\r
 this->CalculateDiffFlowCovariances("POI","Pt");\r
 this->CalculateDiffFlowCovariances("POI","Eta");\r
 this->CalculateDiffFlowCumulants("RP","Pt");\r
 this->CalculateDiffFlowCumulants("RP","Eta");\r
 this->CalculateDiffFlowCumulants("POI","Pt");\r
 this->CalculateDiffFlowCumulants("POI","Eta");\r
 this->CalculateDiffFlow("RP","Pt");\r
 this->CalculateDiffFlow("RP","Eta");\r
 this->CalculateDiffFlow("POI","Pt");\r
 this->CalculateDiffFlow("POI","Eta");\r
 \r
 if(fApplyCorrectionForNUA) // to be improved (reorganized, etc)\r
 {\r
  this->FinalizeCorrectionTermsForNUADiffFlow("RP","Pt");\r
  this->FinalizeCorrectionTermsForNUADiffFlow("RP","Eta");\r
  this->FinalizeCorrectionTermsForNUADiffFlow("POI","Pt");\r
  this->FinalizeCorrectionTermsForNUADiffFlow("POI","Eta");      \r
  this->CalculateDiffFlowCumulantsCorrectedForNUA("RP","Pt");   \r
  this->CalculateDiffFlowCumulantsCorrectedForNUA("RP","Eta");   \r
  this->CalculateDiffFlowCumulantsCorrectedForNUA("POI","Pt");   \r
  this->CalculateDiffFlowCumulantsCorrectedForNUA("POI","Eta");  \r
  this->CalculateDiffFlowCorrectedForNUA("RP","Pt"); \r
  this->CalculateDiffFlowCorrectedForNUA("RP","Eta"); \r
  this->CalculateDiffFlowCorrectedForNUA("POI","Pt"); \r
  this->CalculateDiffFlowCorrectedForNUA("POI","Eta"); \r
 }\r
 \r
 this->CalculateFinalResultsForRPandPOIIntegratedFlow("RP");\r
 this->CalculateFinalResultsForRPandPOIIntegratedFlow("POI");\r
\r
 // *****************************************************************\r
 // **** STORE AND PRINT THE FINAL RESULTS FOR DIFFERENTIAL FLOW ****\r
 // *****************************************************************\r
 this->FillCommonHistResultsDiffFlow("RP");\r
 this->FillCommonHistResultsDiffFlow("POI");\r
\r
 if(fPrintFinalResults[1])
 {
  this->PrintFinalResultsForIntegratedFlow("RP"); \r
 } 
 if(fPrintFinalResults[2])
 {
  this->PrintFinalResultsForIntegratedFlow("POI"); \r
 } \r
 // g) cross-check the results: results from Q-vectors vs results from nested loops\r
 
 //  g1) integrated flow:\r
 if(fEvaluateIntFlowNestedLoops)\r
 {\r
  this->CrossCheckIntFlowCorrelations();\r
  this->CrossCheckIntFlowCorrectionTermsForNUA(); \r
  if(fUsePhiWeights||fUsePtWeights||fUseEtaWeights) this->CrossCheckIntFlowExtraCorrelations();     \r
 } // end of if(fEvaluateIntFlowNestedLoops)  \r
 
 //  g2) differential flow: \r
 if(fEvaluateDiffFlowNestedLoops) \r
 {\r
  // correlations:
  this->PrintNumberOfParticlesInSelectedBin();\r
  this->CrossCheckDiffFlowCorrelations("RP","Pt");  \r
  this->CrossCheckDiffFlowCorrelations("RP","Eta"); \r
  this->CrossCheckDiffFlowCorrelations("POI","Pt");  \r
  this->CrossCheckDiffFlowCorrelations("POI","Eta");\r
  // correction terms for non-uniform acceptance:\r
  this->CrossCheckDiffFlowCorrectionTermsForNUA("RP","Pt");      \r
  this->CrossCheckDiffFlowCorrectionTermsForNUA("RP","Eta");       \r
  this->CrossCheckDiffFlowCorrectionTermsForNUA("POI","Pt");      \r
  this->CrossCheckDiffFlowCorrectionTermsForNUA("POI","Eta");       \r
 } // end of if(fEvaluateDiffFlowNestedLoops)\r
                                                                                                                                                                                                                                                                                                                                   \r
} // end of AliFlowAnalysisWithQCumulants::Finish()\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::CalculateIntFlowCorrectionsForNUACosTerms()\r
{\r
 // calculate corrections for non-uniform acceptance of the detector for no-name integrated flow (cos terms)\r
 \r
 // multiplicity:\r
 Double_t dMult = (*fSMpk)(0,0);\r
 \r
 // real and imaginary parts of non-weighted Q-vectors evaluated in harmonics n, 2n, 3n and 4n: \r
 Double_t dReQ1n = (*fReQ)(0,0);\r
 Double_t dReQ2n = (*fReQ)(1,0);\r
 //Double_t dReQ3n = (*fReQ)(2,0);\r
 //Double_t dReQ4n = (*fReQ)(3,0);\r
 Double_t dImQ1n = (*fImQ)(0,0);\r
 Double_t dImQ2n = (*fImQ)(1,0);\r
 //Double_t dImQ3n = (*fImQ)(2,0);\r
 //Double_t dImQ4n = (*fImQ)(3,0);\r
        \r
 //                                  *************************************************************\r
 //                                  **** corrections for non-uniform acceptance (cos terms): ****\r
 //                                  *************************************************************\r
 //\r
 // Remark 1: corrections for non-uniform acceptance (cos terms) calculated with non-weighted Q-vectors \r
 //           are stored in 1D profile fQCorrectionsCos.\r
 // Remark 2: binning of fIntFlowCorrectionTermsForNUAPro[1] is organized as follows:\r
 // --------------------------------------------------------------------------------------------------------------------\r
 // 1st bin: <<cos(n*(phi1))>> = cosP1n\r
 // 2nd bin: <<cos(n*(phi1+phi2))>> = cosP1nP1n\r
 // 3rd bin: <<cos(n*(phi1-phi2-phi3))>> = cosP1nM1nM1n\r
 // 4th bin: <<cos(n*(2phi1-phi2))>> = cosP2nM1n\r
 // --------------------------------------------------------------------------------------------------------------------\r
  \r
 // 1-particle:\r
 Double_t cosP1n = 0.; // <<cos(n*(phi1))>>\r
   \r
 if(dMult>0)\r
 {\r
  cosP1n = dReQ1n/dMult; \r
  \r
  // average non-weighted 1-particle correction (cos terms) for non-uniform acceptance for single event:\r
  fIntFlowCorrectionTermsForNUAEBE[1]->SetBinContent(1,cosP1n);\r
  \r
  // final average non-weighted 1-particle correction (cos terms) for non-uniform acceptance for all events:\r
  fIntFlowCorrectionTermsForNUAPro[1]->Fill(0.5,cosP1n,dMult);  \r
 } \r
 \r
 // 2-particle:\r
 Double_t cosP1nP1n = 0.; // <<cos(n*(phi1+phi2))>>
 Double_t cosP2nM1n = 0.; // <<cos(n*(2phi1-phi2))>>\r
 \r
 if(dMult>1)\r
 {\r
  cosP1nP1n = (pow(dReQ1n,2)-pow(dImQ1n,2)-dReQ2n)/(dMult*(dMult-1)); \r
  cosP2nM1n = (dReQ2n*dReQ1n+dImQ2n*dImQ1n-dReQ1n)/(dMult*(dMult-1)); \r
  \r
  // average non-weighted 2-particle correction (cos terms) for non-uniform acceptance for single event:\r
  fIntFlowCorrectionTermsForNUAEBE[1]->SetBinContent(2,cosP1nP1n);
  fIntFlowCorrectionTermsForNUAEBE[1]->SetBinContent(4,cosP2nM1n);\r
  \r
  // final average non-weighted 2-particle correction (cos terms) for non-uniform acceptance for all events:\r
  fIntFlowCorrectionTermsForNUAPro[1]->Fill(1.5,cosP1nP1n,dMult*(dMult-1));  
  fIntFlowCorrectionTermsForNUAPro[1]->Fill(3.5,cosP2nM1n,dMult*(dMult-1));\r
 } \r
 \r
 // 3-particle:\r
 Double_t cosP1nM1nM1n = 0.; // <<cos(n*(phi1-phi2-phi3))>>\r
 \r
 if(dMult>2)\r
 {\r
  cosP1nM1nM1n = (dReQ1n*(pow(dReQ1n,2)+pow(dImQ1n,2))-dReQ1n*dReQ2n-dImQ1n*dImQ2n-2.*(dMult-1)*dReQ1n)\r
               / (dMult*(dMult-1)*(dMult-2)); \r
  \r
  // average non-weighted 3-particle correction (cos terms) for non-uniform acceptance for single event:\r
  fIntFlowCorrectionTermsForNUAEBE[1]->SetBinContent(3,cosP1nM1nM1n);\r
  \r
  // final average non-weighted 3-particle correction (cos terms) for non-uniform acceptance for all events:\r
  fIntFlowCorrectionTermsForNUAPro[1]->Fill(2.5,cosP1nM1nM1n,dMult*(dMult-1)*(dMult-2));  \r
 } \r
 \r
} // end of AliFlowAnalysisWithQCumulants::CalculateIntFlowCorrectionsForNUACosTerms()\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::CalculateIntFlowCorrectionsForNUASinTerms()\r
{\r
 // calculate corrections for non-uniform acceptance of the detector for no-name integrated flow (sin terms)\r
 \r
 // multiplicity:\r
 Double_t dMult = (*fSMpk)(0,0);\r
 \r
 // real and imaginary parts of non-weighted Q-vectors evaluated in harmonics n, 2n, 3n and 4n: \r
 Double_t dReQ1n = (*fReQ)(0,0);\r
 Double_t dReQ2n = (*fReQ)(1,0);\r
 //Double_t dReQ3n = (*fReQ)(2,0);\r
 //Double_t dReQ4n = (*fReQ)(3,0);\r
 Double_t dImQ1n = (*fImQ)(0,0);\r
 Double_t dImQ2n = (*fImQ)(1,0);\r
 //Double_t dImQ3n = (*fImQ)(2,0);\r
 //Double_t dImQ4n = (*fImQ)(3,0);\r
        \r
 //                                  *************************************************************\r
 //                                  **** corrections for non-uniform acceptance (sin terms): ****\r
 //                                  *************************************************************\r
 //\r
 // Remark 1: corrections for non-uniform acceptance (sin terms) calculated with non-weighted Q-vectors \r
 //           are stored in 1D profile fQCorrectionsSin.\r
 // Remark 2: binning of fIntFlowCorrectionTermsForNUAPro[0] is organized as follows:\r
 // --------------------------------------------------------------------------------------------------------------------\r
 // 1st bin: <<sin(n*(phi1))>> = sinP1n\r
 // 2nd bin: <<sin(n*(phi1+phi2))>> = sinP1nP1n\r
 // 3rd bin: <<sin(n*(phi1-phi2-phi3))>> = sinP1nM1nM1n\r
 // 4th bin: <<sin(n*(2phi1-phi2))>> = sinP2nM1n\r
 // --------------------------------------------------------------------------------------------------------------------\r
 \r
 // 1-particle:\r
 Double_t sinP1n = 0.; // <sin(n*(phi1))>\r
 \r
 if(dMult>0)\r
 {\r
  sinP1n = dImQ1n/dMult; \r
     \r
  // average non-weighted 1-particle correction (sin terms) for non-uniform acceptance for single event:\r
  fIntFlowCorrectionTermsForNUAEBE[0]->SetBinContent(1,sinP1n);\r
  \r
  // final average non-weighted 1-particle correction (sin terms) for non-uniform acceptance for all events:   \r
  fIntFlowCorrectionTermsForNUAPro[0]->Fill(0.5,sinP1n,dMult);  \r
 } \r
 \r
 // 2-particle:\r
 Double_t sinP1nP1n = 0.; // <<sin(n*(phi1+phi2))>>\r
 Double_t sinP2nM1n = 0.; // <<sin(n*(2phi1-phi2))>>\r
 if(dMult>1)\r
 {\r
  sinP1nP1n = (2.*dReQ1n*dImQ1n-dImQ2n)/(dMult*(dMult-1)); 
  sinP2nM1n = (dImQ2n*dReQ1n-dReQ2n*dImQ1n-dImQ1n)/(dMult*(dMult-1)); \r
     \r
  // average non-weighted 2-particle correction (sin terms) for non-uniform acceptance for single event:\r
  fIntFlowCorrectionTermsForNUAEBE[0]->SetBinContent(2,sinP1nP1n);\r
  fIntFlowCorrectionTermsForNUAEBE[0]->SetBinContent(4,sinP2nM1n);
  \r
  // final average non-weighted 1-particle correction (sin terms) for non-uniform acceptance for all events:      \r
  fIntFlowCorrectionTermsForNUAPro[0]->Fill(1.5,sinP1nP1n,dMult*(dMult-1));  \r
  fIntFlowCorrectionTermsForNUAPro[0]->Fill(3.5,sinP2nM1n,dMult*(dMult-1));  \r
 } \r
 \r
 // 3-particle:\r
 Double_t sinP1nM1nM1n = 0.; // <<sin(n*(phi1-phi2-phi3))>>\r
 \r
 if(dMult>2)\r
 {\r
  sinP1nM1nM1n = (-dImQ1n*(pow(dReQ1n,2)+pow(dImQ1n,2))+dReQ1n*dImQ2n-dImQ1n*dReQ2n+2.*(dMult-1)*dImQ1n)\r
               / (dMult*(dMult-1)*(dMult-2)); \r
  \r
  // average non-weighted 3-particle correction (sin terms) for non-uniform acceptance for single event:\r
  fIntFlowCorrectionTermsForNUAEBE[0]->SetBinContent(3,sinP1nM1nM1n);\r
  \r
  // final average non-weighted 3-particle correction (sin terms) for non-uniform acceptance for all events:  \r
  fIntFlowCorrectionTermsForNUAPro[0]->Fill(2.5,sinP1nM1nM1n,dMult*(dMult-1)*(dMult-2));  \r
 } \r
 \r
} // end of AliFlowAnalysisWithQCumulants::CalculateIntFlowCorrectionsForNUASinTerms()\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::GetOutputHistograms(TList *outputListHistos)\r
{\r
 // a) Get pointers for common control and common result histograms and profiles.\r
 // b) Get pointers for histograms with particle weights.\r
 // c) Get pointers for histograms and profiles relevant for integrated flow.\r
 // d) Get pointers for histograms and profiles relevant for differental flow.\r
 // e) Get pointers for histograms and profiles holding results obtained with nested loops.\r
 \r
 if(outputListHistos)\r
 {	
  this->SetHistList(outputListHistos);
  if(!fHistList)
  {
   cout<<endl;
   cout<<" WARNING (QC): fHistList is NULL in AFAWQC::GOH() !!!!"<<endl;
   cout<<endl;
   exit(0);
  }\r
  this->GetPointersForCommonHistograms(); \r
  this->GetPointersForParticleWeightsHistograms(); \r
  this->GetPointersForIntFlowHistograms();\r
  this->GetPointersForDiffFlowHistograms(); \r
  this->GetPointersForNestedLoopsHistograms(); \r
 } else 
   {
    cout<<endl;
    cout<<" WARNING (QC): outputListHistos is NULL in AFAWQC::GOH() !!!!"<<endl;
    cout<<endl;
    exit(0);
   }\r
   \r
} // end of void AliFlowAnalysisWithQCumulants::GetOutputHistograms(TList *outputListHistos)\r
\r
\r
//================================================================================================================================\r
\r
\r
TProfile* AliFlowAnalysisWithQCumulants::MakePtProjection(TProfile2D *profilePtEta) const\r
{\r
 // project 2D profile onto pt axis to get 1D profile\r
 \r
 Int_t nBinsPt   = profilePtEta->GetNbinsX();\r
 Double_t dPtMin = (profilePtEta->GetXaxis())->GetXmin();\r
 Double_t dPtMax = (profilePtEta->GetXaxis())->GetXmax();\r
 \r
 Int_t nBinsEta   = profilePtEta->GetNbinsY();\r
 \r
 TProfile *profilePt = new TProfile("","",nBinsPt,dPtMin,dPtMax); \r
 \r
 for(Int_t p=1;p<=nBinsPt;p++)\r
 {\r
  Double_t contentPt = 0.;\r
  Double_t entryPt = 0.;\r
  Double_t spreadPt = 0.;\r
  Double_t sum1 = 0.;\r
  Double_t sum2 = 0.;\r
  Double_t sum3 = 0.;\r
  for(Int_t e=1;e<=nBinsEta;e++)\r
  {\r
   contentPt += (profilePtEta->GetBinContent(profilePtEta->GetBin(p,e)))\r
              * (profilePtEta->GetBinEntries(profilePtEta->GetBin(p,e)));\r
   entryPt   += (profilePtEta->GetBinEntries(profilePtEta->GetBin(p,e)));\r
   \r
   sum1 += (profilePtEta->GetBinEntries(profilePtEta->GetBin(p,e)))\r
         * (pow(profilePtEta->GetBinError(profilePtEta->GetBin(p,e)),2.)\r
            + pow(profilePtEta->GetBinContent(profilePtEta->GetBin(p,e)),2.)); \r
   sum2 += (profilePtEta->GetBinEntries(profilePtEta->GetBin(p,e)));\r
   sum3 += (profilePtEta->GetBinEntries(profilePtEta->GetBin(p,e)))\r
         * (profilePtEta->GetBinContent(profilePtEta->GetBin(p,e)));            \r
  }\r
  if(sum2>0. && sum1/sum2-pow(sum3/sum2,2.) > 0.)\r
  {\r
   spreadPt = pow(sum1/sum2-pow(sum3/sum2,2.),0.5);\r
  }\r
  profilePt->SetBinContent(p,contentPt);\r
  profilePt->SetBinEntries(p,entryPt);\r
  {\r
   profilePt->SetBinError(p,spreadPt);\r
  }\r
  \r
 }\r
 \r
 return profilePt;\r
 \r
} // end of TProfile* AliFlowAnalysisWithQCumulants::MakePtProjection(TProfile2D *profilePtEta)\r
\r
\r
//================================================================================================================================\r
\r
\r
TProfile* AliFlowAnalysisWithQCumulants::MakeEtaProjection(TProfile2D *profilePtEta) const\r
{\r
 // project 2D profile onto eta axis to get 1D profile\r
 \r
 Int_t nBinsEta   = profilePtEta->GetNbinsY();\r
 Double_t dEtaMin = (profilePtEta->GetYaxis())->GetXmin();\r
 Double_t dEtaMax = (profilePtEta->GetYaxis())->GetXmax();\r
 \r
 Int_t nBinsPt = profilePtEta->GetNbinsX();\r
 \r
 TProfile *profileEta = new TProfile("","",nBinsEta,dEtaMin,dEtaMax); \r
 \r
 for(Int_t e=1;e<=nBinsEta;e++)\r
 {\r
  Double_t contentEta = 0.;\r
  Double_t entryEta = 0.;\r
  for(Int_t p=1;p<=nBinsPt;p++)\r
  {\r
   contentEta += (profilePtEta->GetBinContent(profilePtEta->GetBin(p,e)))\r
              * (profilePtEta->GetBinEntries(profilePtEta->GetBin(p,e)));\r
   entryEta   += (profilePtEta->GetBinEntries(profilePtEta->GetBin(p,e)));\r
  }\r
  profileEta->SetBinContent(e,contentEta);\r
  profileEta->SetBinEntries(e,entryEta);\r
 }\r
 \r
 return profileEta;\r
 \r
} // end of TProfile* AliFlowAnalysisWithQCumulants::MakeEtaProjection(TProfile2D *profilePtEta)\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::PrintFinalResultsForIntegratedFlow(TString type)\r
{\r
 // printing on the screen the final results for integrated flow (NONAME, POI and RP) // to be improved (NONAME) \r
 \r
 Int_t n = fHarmonic; \r
 \r
 if(type == "NONAME" || type == "RP" || type == "POI")\r
 {\r
  if(!(fCommonHistsResults2nd && fCommonHistsResults4th && fCommonHistsResults6th && fCommonHistsResults8th))\r
  {\r
   cout<<"WARNING: fCommonHistsResults2nd && fCommonHistsResults4th && fCommonHistsResults6th && fCommonHistsResults8th"<<endl;\r
   cout<<"         is NULL in AFAWQC::PFRFIF() !!!!"<<endl;\r
  }\r
 } else\r
   {\r
    cout<<"WARNING: type in not from {NONAME, RP, POI} in AFAWQC::PFRFIF() !!!!"<<endl;\r
    exit(0);\r
   }\r
 \r
 Double_t dVn[4] = {0.}; // array to hold Vn{2}, Vn{4}, Vn{6} and Vn{8}   \r
 Double_t dVnErr[4] = {0.}; // array to hold errors of Vn{2}, Vn{4}, Vn{6} and Vn{8}   \r
 \r
 if(type == "NONAME")\r
 {\r
  dVn[0] = (fCommonHistsResults2nd->GetHistIntFlow())->GetBinContent(1); \r
  dVnErr[0] = (fCommonHistsResults2nd->GetHistIntFlow())->GetBinError(1); \r
  dVn[1] = (fCommonHistsResults4th->GetHistIntFlow())->GetBinContent(1); \r
  dVnErr[1] = (fCommonHistsResults4th->GetHistIntFlow())->GetBinError(1); \r
  dVn[2] = (fCommonHistsResults6th->GetHistIntFlow())->GetBinContent(1); \r
  dVnErr[2] = (fCommonHistsResults6th->GetHistIntFlow())->GetBinError(1); \r
  dVn[3] = (fCommonHistsResults8th->GetHistIntFlow())->GetBinContent(1); \r
  dVnErr[3] = (fCommonHistsResults8th->GetHistIntFlow())->GetBinError(1); \r
 } else if(type == "RP")\r
   {\r
    dVn[0] = (fCommonHistsResults2nd->GetHistIntFlowRP())->GetBinContent(1); \r
    dVnErr[0] = (fCommonHistsResults2nd->GetHistIntFlowRP())->GetBinError(1); \r
    dVn[1] = (fCommonHistsResults4th->GetHistIntFlowRP())->GetBinContent(1); \r
    dVnErr[1] = (fCommonHistsResults4th->GetHistIntFlowRP())->GetBinError(1); \r
    dVn[2] = (fCommonHistsResults6th->GetHistIntFlowRP())->GetBinContent(1); \r
    dVnErr[2] = (fCommonHistsResults6th->GetHistIntFlowRP())->GetBinError(1); \r
    dVn[3] = (fCommonHistsResults8th->GetHistIntFlowRP())->GetBinContent(1); \r
    dVnErr[3] = (fCommonHistsResults8th->GetHistIntFlowRP())->GetBinError(1); \r
   } else if(type == "POI")\r
     {\r
      dVn[0] = (fCommonHistsResults2nd->GetHistIntFlowPOI())->GetBinContent(1); \r
      dVnErr[0] = (fCommonHistsResults2nd->GetHistIntFlowPOI())->GetBinError(1); \r
      dVn[1] = (fCommonHistsResults4th->GetHistIntFlowPOI())->GetBinContent(1); \r
      dVnErr[1] = (fCommonHistsResults4th->GetHistIntFlowPOI())->GetBinError(1); \r
      dVn[2] = (fCommonHistsResults6th->GetHistIntFlowPOI())->GetBinContent(1); \r
      dVnErr[2] = (fCommonHistsResults6th->GetHistIntFlowPOI())->GetBinError(1); \r
      dVn[3] = (fCommonHistsResults8th->GetHistIntFlowPOI())->GetBinContent(1); \r
      dVnErr[3] = (fCommonHistsResults8th->GetHistIntFlowPOI())->GetBinError(1); \r
     }\r
 \r
 TString title = " flow estimates from Q-cumulants"; \r
 TString subtitle = "    ("; \r
 \r
 if(!(fUsePhiWeights||fUsePtWeights||fUseEtaWeights))\r
 {\r
  subtitle.Append(type);\r
  subtitle.Append(", without weights)");\r
 } else  \r
   {\r
    subtitle.Append(type);\r
    subtitle.Append(", with weights)");\r
   }\r
  \r
 cout<<endl;\r
 cout<<"*************************************"<<endl;\r
 cout<<"*************************************"<<endl;\r
 cout<<title.Data()<<endl; \r
 cout<<subtitle.Data()<<endl; \r
 cout<<endl;\r
  \r
 for(Int_t i=0;i<4;i++)\r
 {\r
  if(dVn[i]>=0.)\r
  {\r
   cout<<"  v_"<<n<<"{"<<2*(i+1)<<"} = "<<dVn[i]<<" +/- "<<dVnErr[i]<<endl;\r
  }\r
  else\r
  {\r
   cout<<"  v_"<<n<<"{"<<2*(i+1)<<"} = Im"<<endl;\r
  }  \r
 }\r
\r
 cout<<endl;\r
 /*\r
 if(type == "NONAME")\r
 {\r
  cout<<"     nEvts = "<<nEvtsNoName<<", AvM = "<<dMultNoName<<endl; // to be improved\r
 }\r
 else if (type == "RP")\r
 {\r
  cout<<"     nEvts = "<<nEvtsRP<<", AvM = "<<dMultRP<<endl; // to be improved  \r
 } \r
 else if (type == "POI")\r
 {\r
  cout<<"     nEvts = "<<nEvtsPOI<<", AvM = "<<dMultPOI<<endl; // to be improved  \r
 } \r
 */\r
 cout<<"*************************************"<<endl;\r
 cout<<"*************************************"<<endl;\r
 cout<<endl; \r
  \r
}// end of AliFlowAnalysisWithQCumulants::PrintFinalResultsForIntegratedFlow(TString type="NONAME");\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::WriteHistograms(TString outputFileName)\r
{\r
 //store the final results in output .root file\r
 TFile *output = new TFile(outputFileName.Data(),"RECREATE");\r
 //output->WriteObject(fHistList, "cobjQC","SingleKey");\r
 fHistList->Write(fHistList->GetName(), TObject::kSingleKey);\r
 delete output;\r
}\r
\r
\r
//================================================================================================================================\r


void AliFlowAnalysisWithQCumulants::WriteHistograms(TDirectoryFile *outputFileName)
{
 //store the final results in output .root file
 fHistList->SetName("cobjQC");
 fHistList->SetOwner(kTRUE);
 outputFileName->Add(fHistList);
 outputFileName->Write(outputFileName->GetName(), TObject::kSingleKey);
}
\r

//================================================================================================================================\r

\r
void AliFlowAnalysisWithQCumulants::BookCommonHistograms()\r
{\r
 // Book common control histograms and common histograms for final results.\r
 // common control histogram (ALL events)\r
 TString commonHistsName = "AliFlowCommonHistQC";\r
 commonHistsName += fAnalysisLabel->Data();\r
 fCommonHists = new AliFlowCommonHist(commonHistsName.Data());\r
 fHistList->Add(fCommonHists);  \r
 // common control histogram (for events with 2 and more particles)\r
 TString commonHists2ndOrderName = "AliFlowCommonHist2ndOrderQC";\r
 commonHists2ndOrderName += fAnalysisLabel->Data();\r
 fCommonHists2nd = new AliFlowCommonHist(commonHists2ndOrderName.Data());\r
 fHistList->Add(fCommonHists2nd);  \r
 // common control histogram (for events with 4 and more particles)\r
 TString commonHists4thOrderName = "AliFlowCommonHist4thOrderQC";\r
 commonHists4thOrderName += fAnalysisLabel->Data();\r
 fCommonHists4th = new AliFlowCommonHist(commonHists4thOrderName.Data());\r
 fHistList->Add(fCommonHists4th);  \r
 // common control histogram (for events with 6 and more particles)\r
 TString commonHists6thOrderName = "AliFlowCommonHist6thOrderQC";\r
 commonHists6thOrderName += fAnalysisLabel->Data();\r
 fCommonHists6th = new AliFlowCommonHist(commonHists6thOrderName.Data());\r
 fHistList->Add(fCommonHists6th);  \r
 // common control histogram (for events with 8 and more particles)\r
 TString commonHists8thOrderName = "AliFlowCommonHist8thOrderQC";\r
 commonHists8thOrderName += fAnalysisLabel->Data();\r
 fCommonHists8th = new AliFlowCommonHist(commonHists8thOrderName.Data());\r
 fHistList->Add(fCommonHists8th);    \r
 // common histograms for final results (calculated for events with 2 and more particles)\r
 TString commonHistResults2ndOrderName = "AliFlowCommonHistResults2ndOrderQC";\r
 commonHistResults2ndOrderName += fAnalysisLabel->Data();\r
 fCommonHistsResults2nd = new AliFlowCommonHistResults(commonHistResults2ndOrderName.Data());\r
 fHistList->Add(fCommonHistsResults2nd);  \r
 // common histograms for final results (calculated for events with 4 and more particles)\r
 TString commonHistResults4thOrderName = "AliFlowCommonHistResults4thOrderQC";\r
 commonHistResults4thOrderName += fAnalysisLabel->Data();\r
 fCommonHistsResults4th = new AliFlowCommonHistResults(commonHistResults4thOrderName.Data());\r
 fHistList->Add(fCommonHistsResults4th); \r
 // common histograms for final results (calculated for events with 6 and more particles)\r
 TString commonHistResults6thOrderName = "AliFlowCommonHistResults6thOrderQC";\r
 commonHistResults6thOrderName += fAnalysisLabel->Data();\r
 fCommonHistsResults6th = new AliFlowCommonHistResults(commonHistResults6thOrderName.Data());\r
 fHistList->Add(fCommonHistsResults6th);  \r
 // common histograms for final results (calculated for events with 8 and more particles)\r
 TString commonHistResults8thOrderName = "AliFlowCommonHistResults8thOrderQC";\r
 commonHistResults8thOrderName += fAnalysisLabel->Data();\r
 fCommonHistsResults8th = new AliFlowCommonHistResults(commonHistResults8thOrderName.Data());\r
 fHistList->Add(fCommonHistsResults8th); \r
 \r
} // end of void AliFlowAnalysisWithQCumulants::BookCommonHistograms()\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::BookAndFillWeightsHistograms()\r
{\r
 // book and fill histograms which hold phi, pt and eta weights\r
\r
 if(!fWeightsList)\r
 {\r
  cout<<"WARNING: fWeightsList is NULL in AFAWQC::BAFWH() !!!!"<<endl;\r
  exit(0);  \r
 }\r
    \r
 TString fUseParticleWeightsName = "fUseParticleWeightsQC";\r
 fUseParticleWeightsName += fAnalysisLabel->Data();\r
 fUseParticleWeights = new TProfile(fUseParticleWeightsName.Data(),"0 = particle weight not used, 1 = particle weight used ",3,0,3);\r
 fUseParticleWeights->SetLabelSize(0.06);\r
 (fUseParticleWeights->GetXaxis())->SetBinLabel(1,"w_{#phi}");\r
 (fUseParticleWeights->GetXaxis())->SetBinLabel(2,"w_{p_{T}}");\r
 (fUseParticleWeights->GetXaxis())->SetBinLabel(3,"w_{#eta}");\r
 fUseParticleWeights->Fill(0.5,(Int_t)fUsePhiWeights);\r
 fUseParticleWeights->Fill(1.5,(Int_t)fUsePtWeights);\r
 fUseParticleWeights->Fill(2.5,(Int_t)fUseEtaWeights);\r
 fWeightsList->Add(fUseParticleWeights); \r
  \r
 if(fUsePhiWeights)\r
 {\r
  if(fWeightsList->FindObject("phi_weights"))\r
  {\r
   fPhiWeights = dynamic_cast<TH1F*>(fWeightsList->FindObject("phi_weights"));\r
   if(TMath::Abs(fPhiWeights->GetBinWidth(1)-fPhiBinWidth)>pow(10.,-6.))\r
   {\r
    cout<<endl;
    cout<<"WARNING (QC): Inconsistent binning in histograms for phi-weights throughout the code."<<endl;\r
    cout<<endl;\r
    exit(0);\r
   }\r
  } else \r
    {\r
     cout<<"WARNING: fWeightsList->FindObject(\"phi_weights\") is NULL in AFAWQC::BAFWH() !!!!"<<endl;\r
     exit(0);\r
    }\r
 } // end of if(fUsePhiWeights)\r
 \r
 if(fUsePtWeights) \r
 {\r
  if(fWeightsList->FindObject("pt_weights"))\r
  {\r
   fPtWeights = dynamic_cast<TH1D*>(fWeightsList->FindObject("pt_weights"));\r
   if(TMath::Abs(fPtWeights->GetBinWidth(1)-fPtBinWidth)>pow(10.,-6.))\r
   {\r
    cout<<endl;
    cout<<"WARNING (QC): Inconsistent binning in histograms for pt-weights throughout the code."<<endl;\r
    cout<<endl;\r
    exit(0);\r
   }\r
  } else \r
    {\r
     cout<<"WARNING: fWeightsList->FindObject(\"pt_weights\") is NULL in AFAWQC::BAFWH() !!!!"<<endl;\r
     exit(0);\r
    }\r
 } // end of if(fUsePtWeights)    \r
\r
 if(fUseEtaWeights) \r
 {\r
  if(fWeightsList->FindObject("eta_weights"))\r
  {\r
   fEtaWeights = dynamic_cast<TH1D*>(fWeightsList->FindObject("eta_weights"));\r
   if(TMath::Abs(fEtaWeights->GetBinWidth(1)-fEtaBinWidth)>pow(10.,-6.))\r
   {\r
    cout<<endl;
    cout<<"WARNING (QC): Inconsistent binning in histograms for eta-weights throughout the code."<<endl;\r
    cout<<endl;\r
    exit(0);\r
   }\r
  } else \r
    {\r
     cout<<"WARNING: fUseEtaWeights && fWeightsList->FindObject(\"eta_weights\") is NULL in AFAWQC::BAFWH() !!!!"<<endl;\r
     exit(0);\r
    }\r
 } // end of if(fUseEtaWeights)\r
 \r
} // end of AliFlowAnalysisWithQCumulants::BookAndFillWeightsHistograms()\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::BookEverythingForIntegratedFlow()\r
{\r
 // Book all objects for integrated flow:\r
 //  a) Book profile to hold all flags for integrated flow.\r
 //  b) Book event-by-event quantities.\r
 //  c) Book profiles. // to be improved (comment)\r
 //  d) Book histograms holding the final results.\r
 \r
 TString sinCosFlag[2] = {"sin","cos"}; // to be improved (should I promote this to data members?)\r
 TString powerFlag[2] = {"linear","quadratic"}; // to be improved (should I promote this to data members?)\r
 \r
 // a) Book profile to hold all flags for integrated flow:\r
 TString intFlowFlagsName = "fIntFlowFlags";\r
 intFlowFlagsName += fAnalysisLabel->Data();\r
 fIntFlowFlags = new TProfile(intFlowFlagsName.Data(),"Flags for Integrated Flow",6,0,6);\r
 fIntFlowFlags->SetTickLength(-0.01,"Y");\r
 fIntFlowFlags->SetMarkerStyle(25);\r
 fIntFlowFlags->SetLabelSize(0.05);\r
 fIntFlowFlags->SetLabelOffset(0.02,"Y");\r
 fIntFlowFlags->GetXaxis()->SetBinLabel(1,"Particle Weights");\r
 fIntFlowFlags->GetXaxis()->SetBinLabel(2,"Event Weights");\r
 fIntFlowFlags->GetXaxis()->SetBinLabel(3,"Corrected for NUA?");
 fIntFlowFlags->GetXaxis()->SetBinLabel(4,"Print NONAME results");\r
 fIntFlowFlags->GetXaxis()->SetBinLabel(5,"Print RP results");\r
 fIntFlowFlags->GetXaxis()->SetBinLabel(6,"Print POI results");
 fIntFlowList->Add(fIntFlowFlags);\r
\r
 // b) Book event-by-event quantities:\r
 // Re[Q_{m*n,k}], Im[Q_{m*n,k}] and S_{p,k}^M: \r
 fReQ  = new TMatrixD(4,9);\r
 fImQ  = new TMatrixD(4,9);\r
 fSMpk = new TMatrixD(8,9);\r
 // average correlations <2>, <4>, <6> and <8> for single event (bining is the same as in fIntFlowCorrelationsPro and fIntFlowCorrelationsHist):\r
 TString intFlowCorrelationsEBEName = "fIntFlowCorrelationsEBE";\r
 intFlowCorrelationsEBEName += fAnalysisLabel->Data();\r
 fIntFlowCorrelationsEBE = new TH1D(intFlowCorrelationsEBEName.Data(),intFlowCorrelationsEBEName.Data(),4,0,4);\r
 // weights for average correlations <2>, <4>, <6> and <8> for single event:\r
 TString intFlowEventWeightsForCorrelationsEBEName = "fIntFlowEventWeightsForCorrelationsEBE";\r
 intFlowEventWeightsForCorrelationsEBEName += fAnalysisLabel->Data();\r
 fIntFlowEventWeightsForCorrelationsEBE = new TH1D(intFlowEventWeightsForCorrelationsEBEName.Data(),intFlowEventWeightsForCorrelationsEBEName.Data(),4,0,4);\r
 // average all correlations for single event (bining is the same as in fIntFlowCorrelationsAllPro and fIntFlowCorrelationsAllHist):\r
 TString intFlowCorrelationsAllEBEName = "fIntFlowCorrelationsAllEBE";\r
 intFlowCorrelationsAllEBEName += fAnalysisLabel->Data();\r
 fIntFlowCorrelationsAllEBE = new TH1D(intFlowCorrelationsAllEBEName.Data(),intFlowCorrelationsAllEBEName.Data(),32,0,32);\r
 // average correction terms for non-uniform acceptance for single event \r
 // (binning is the same as in fIntFlowCorrectionTermsForNUAPro[2] and fIntFlowCorrectionTermsForNUAHist[2]):\r
 TString fIntFlowCorrectionTermsForNUAEBEName = "fIntFlowCorrectionTermsForNUAEBE";\r
 fIntFlowCorrectionTermsForNUAEBEName += fAnalysisLabel->Data();\r
 for(Int_t sc=0;sc<2;sc++) // sin or cos terms\r
 {\r
  fIntFlowCorrectionTermsForNUAEBE[sc] = new TH1D(Form("%s: %s terms",fIntFlowCorrectionTermsForNUAEBEName.Data(),sinCosFlag[sc].Data()),Form("Correction terms for non-uniform acceptance (%s terms)",sinCosFlag[sc].Data()),10,0,10);  \r
 }\r
 \r
 // c) Book profiles: // to be improved (comment)\r
 // profile to hold average multiplicities and number of events for events with nRP>=0, nRP>=1, ... , and nRP>=8:\r
 TString avMultiplicityName = "fAvMultiplicity";\r
 avMultiplicityName += fAnalysisLabel->Data();\r
 fAvMultiplicity = new TProfile(avMultiplicityName.Data(),"Average Multiplicities of RPs",9,0,9);\r
 fAvMultiplicity->SetTickLength(-0.01,"Y");\r
 fAvMultiplicity->SetMarkerStyle(25);\r
 fAvMultiplicity->SetLabelSize(0.05);\r
 fAvMultiplicity->SetLabelOffset(0.02,"Y");\r
 fAvMultiplicity->SetYTitle("Average Multiplicity");\r
 (fAvMultiplicity->GetXaxis())->SetBinLabel(1,"all evts");\r
 (fAvMultiplicity->GetXaxis())->SetBinLabel(2,"n_{RP} #geq 1");\r
 (fAvMultiplicity->GetXaxis())->SetBinLabel(3,"n_{RP} #geq 2");\r
 (fAvMultiplicity->GetXaxis())->SetBinLabel(4,"n_{RP} #geq 3");\r
 (fAvMultiplicity->GetXaxis())->SetBinLabel(5,"n_{RP} #geq 4");\r
 (fAvMultiplicity->GetXaxis())->SetBinLabel(6,"n_{RP} #geq 5");\r
 (fAvMultiplicity->GetXaxis())->SetBinLabel(7,"n_{RP} #geq 6");\r
 (fAvMultiplicity->GetXaxis())->SetBinLabel(8,"n_{RP} #geq 7");\r
 (fAvMultiplicity->GetXaxis())->SetBinLabel(9,"n_{RP} #geq 8");\r
 fIntFlowProfiles->Add(fAvMultiplicity);\r
 // average correlations <<2>>, <<4>>, <<6>> and <<8>> for all events (with wrong errors!):\r
 TString intFlowCorrelationsProName = "fIntFlowCorrelationsPro";\r
 intFlowCorrelationsProName += fAnalysisLabel->Data();\r
 fIntFlowCorrelationsPro = new TProfile(intFlowCorrelationsProName.Data(),"Average correlations for all events",4,0,4,"s");\r
 fIntFlowCorrelationsPro->SetTickLength(-0.01,"Y");\r
 fIntFlowCorrelationsPro->SetMarkerStyle(25);\r
 fIntFlowCorrelationsPro->SetLabelSize(0.06);\r
 fIntFlowCorrelationsPro->SetLabelOffset(0.01,"Y");\r
 (fIntFlowCorrelationsPro->GetXaxis())->SetBinLabel(1,"<<2>>");\r
 (fIntFlowCorrelationsPro->GetXaxis())->SetBinLabel(2,"<<4>>");\r
 (fIntFlowCorrelationsPro->GetXaxis())->SetBinLabel(3,"<<6>>");\r
 (fIntFlowCorrelationsPro->GetXaxis())->SetBinLabel(4,"<<8>>");\r
 fIntFlowProfiles->Add(fIntFlowCorrelationsPro);\r
 // averaged all correlations for all events (with wrong errors!):\r
 TString intFlowCorrelationsAllProName = "fIntFlowCorrelationsAllPro";\r
 intFlowCorrelationsAllProName += fAnalysisLabel->Data();\r
 fIntFlowCorrelationsAllPro = new TProfile(intFlowCorrelationsAllProName.Data(),"Average correlations for all events",32,0,32,"s");\r
 fIntFlowCorrelationsAllPro->SetTickLength(-0.01,"Y");\r
 fIntFlowCorrelationsAllPro->SetMarkerStyle(25);\r
 fIntFlowCorrelationsAllPro->SetLabelSize(0.03);\r
 fIntFlowCorrelationsAllPro->SetLabelOffset(0.01,"Y");\r
 // 2-p correlations:\r
 (fIntFlowCorrelationsAllPro->GetXaxis())->SetBinLabel(1,"<<2>>_{n|n}");\r
 (fIntFlowCorrelationsAllPro->GetXaxis())->SetBinLabel(2,"<<2>>_{2n|2n}");\r
 (fIntFlowCorrelationsAllPro->GetXaxis())->SetBinLabel(3,"<<2>>_{3n|3n}");\r
 (fIntFlowCorrelationsAllPro->GetXaxis())->SetBinLabel(4,"<<2>>_{4n|4n}");\r
 // 3-p correlations:\r
 (fIntFlowCorrelationsAllPro->GetXaxis())->SetBinLabel(6,"<<3>>_{2n|n,n}");\r
 (fIntFlowCorrelationsAllPro->GetXaxis())->SetBinLabel(7,"<<3>>_{3n|2n,n}");\r
 (fIntFlowCorrelationsAllPro->GetXaxis())->SetBinLabel(8,"<<3>>_{4n|2n,2n}");\r
 (fIntFlowCorrelationsAllPro->GetXaxis())->SetBinLabel(9,"<<3>>_{4n|3n,n}");\r
 // 4-p correlations:\r
 (fIntFlowCorrelationsAllPro->GetXaxis())->SetBinLabel(11,"<<4>>_{n,n|n,n}"); \r
 (fIntFlowCorrelationsAllPro->GetXaxis())->SetBinLabel(12,"<<4>>_{2n,n|2n,n}");\r
 (fIntFlowCorrelationsAllPro->GetXaxis())->SetBinLabel(13,"<<4>>_{2n,2n|2n,2n}");\r
 (fIntFlowCorrelationsAllPro->GetXaxis())->SetBinLabel(14,"<<4>>_{3n|n,n,n}");\r
 (fIntFlowCorrelationsAllPro->GetXaxis())->SetBinLabel(15,"<<4>>_{3n,n|3n,n}");\r
 (fIntFlowCorrelationsAllPro->GetXaxis())->SetBinLabel(16,"<<4>>_{3n,n|2n,2n}"); \r
 (fIntFlowCorrelationsAllPro->GetXaxis())->SetBinLabel(17,"<<4>>_{4n|2n,n,n}");\r
 // 5-p correlations:\r
 (fIntFlowCorrelationsAllPro->GetXaxis())->SetBinLabel(19,"<<5>>_{2n|n,n,n,n}"); \r
 (fIntFlowCorrelationsAllPro->GetXaxis())->SetBinLabel(20,"<<5>>_{2n,2n|2n,n,n}");\r
 (fIntFlowCorrelationsAllPro->GetXaxis())->SetBinLabel(21,"<<5>>_{3n,n|2n,n,n}");\r
 (fIntFlowCorrelationsAllPro->GetXaxis())->SetBinLabel(22,"<<5>>_{4n|n,n,n,n}");\r
 // 6-p correlations:\r
 (fIntFlowCorrelationsAllPro->GetXaxis())->SetBinLabel(24,"<<6>>_{n,n,n|n,n,n}");\r
 (fIntFlowCorrelationsAllPro->GetXaxis())->SetBinLabel(25,"<<6>>_{2n,n,n|2n,n,n}");\r
 (fIntFlowCorrelationsAllPro->GetXaxis())->SetBinLabel(26,"<<6>>_{2n,2n|n,n,n,n}");\r
 (fIntFlowCorrelationsAllPro->GetXaxis())->SetBinLabel(27,"<<6>>_{3n,n|n,n,n,n}");\r
 // 7-p correlations:  \r
 (fIntFlowCorrelationsAllPro->GetXaxis())->SetBinLabel(29,"<<7>>_{2n,n,n|n,n,n,n}");\r
 // 8-p correlations:\r
 (fIntFlowCorrelationsAllPro->GetXaxis())->SetBinLabel(31,"<<8>>_{n,n,n,n|n,n,n,n}");\r
 fIntFlowProfiles->Add(fIntFlowCorrelationsAllPro);\r
 // when particle weights are used some extra correlations appear:\r
 if(fUsePhiWeights||fUsePtWeights||fUseEtaWeights) \r
 {\r
  TString intFlowExtraCorrelationsProName = "fIntFlowExtraCorrelationsPro";\r
  intFlowExtraCorrelationsProName += fAnalysisLabel->Data();\r
  fIntFlowExtraCorrelationsPro = new TProfile(intFlowExtraCorrelationsProName.Data(),"Average extra correlations for all events",100,0,100,"s");\r
  fIntFlowExtraCorrelationsPro->SetTickLength(-0.01,"Y");\r
  fIntFlowExtraCorrelationsPro->SetMarkerStyle(25);\r
  fIntFlowExtraCorrelationsPro->SetLabelSize(0.03);\r
  fIntFlowExtraCorrelationsPro->SetLabelOffset(0.01,"Y");\r
  // extra 2-p correlations:\r
  (fIntFlowExtraCorrelationsPro->GetXaxis())->SetBinLabel(1,"<<w1^3 w2 cos(n*(phi1-phi2))>>");\r
  (fIntFlowExtraCorrelationsPro->GetXaxis())->SetBinLabel(2,"<<w1 w2 w3^2 cos(n*(phi1-phi2))>>");\r
  fIntFlowProfiles->Add(fIntFlowExtraCorrelationsPro);\r
 } // end of if(fUsePhiWeights||fUsePtWeights||fUseEtaWeights)\r
 // average product of correlations <2>, <4>, <6> and <8>:  \r
 TString intFlowProductOfCorrelationsProName = "fIntFlowProductOfCorrelationsPro";\r
 intFlowProductOfCorrelationsProName += fAnalysisLabel->Data();\r
 fIntFlowProductOfCorrelationsPro = new TProfile(intFlowProductOfCorrelationsProName.Data(),"Average products of correlations",6,0,6);\r
 fIntFlowProductOfCorrelationsPro->SetTickLength(-0.01,"Y");\r
 fIntFlowProductOfCorrelationsPro->SetMarkerStyle(25); \r
 fIntFlowProductOfCorrelationsPro->SetLabelSize(0.05);\r
 fIntFlowProductOfCorrelationsPro->SetLabelOffset(0.01,"Y");\r
 (fIntFlowProductOfCorrelationsPro->GetXaxis())->SetBinLabel(1,"<<2><4>>");\r
 (fIntFlowProductOfCorrelationsPro->GetXaxis())->SetBinLabel(2,"<<2><6>>");\r
 (fIntFlowProductOfCorrelationsPro->GetXaxis())->SetBinLabel(3,"<<2><8>>");\r
 (fIntFlowProductOfCorrelationsPro->GetXaxis())->SetBinLabel(4,"<<4><6>>");\r
 (fIntFlowProductOfCorrelationsPro->GetXaxis())->SetBinLabel(5,"<<4><8>>");\r
 (fIntFlowProductOfCorrelationsPro->GetXaxis())->SetBinLabel(6,"<<6><8>>");\r
 fIntFlowProfiles->Add(fIntFlowProductOfCorrelationsPro);\r
 // average correction terms for non-uniform acceptance (with wrong errors!):\r
 for(Int_t sc=0;sc<2;sc++) // sin or cos terms\r
 {\r
  TString intFlowCorrectionTermsForNUAProName = "fIntFlowCorrectionTermsForNUAPro";\r
  intFlowCorrectionTermsForNUAProName += fAnalysisLabel->Data();\r
  fIntFlowCorrectionTermsForNUAPro[sc] = new TProfile(Form("%s: %s terms",intFlowCorrectionTermsForNUAProName.Data(),sinCosFlag[sc].Data()),Form("Correction terms for non-uniform acceptance (%s terms)",sinCosFlag[sc].Data()),10,0,10,"s");\r
  fIntFlowCorrectionTermsForNUAPro[sc]->SetTickLength(-0.01,"Y");\r
  fIntFlowCorrectionTermsForNUAPro[sc]->SetMarkerStyle(25);\r
  fIntFlowCorrectionTermsForNUAPro[sc]->SetLabelSize(0.03);\r
  fIntFlowCorrectionTermsForNUAPro[sc]->SetLabelOffset(0.01,"Y");\r
  (fIntFlowCorrectionTermsForNUAPro[sc]->GetXaxis())->SetBinLabel(1,Form("<<%s(n(phi1))>>",sinCosFlag[sc].Data()));\r
  (fIntFlowCorrectionTermsForNUAPro[sc]->GetXaxis())->SetBinLabel(2,Form("<<%s(n(phi1+phi2))>>",sinCosFlag[sc].Data()));  \r
  (fIntFlowCorrectionTermsForNUAPro[sc]->GetXaxis())->SetBinLabel(3,Form("<<%s(n(phi1-phi2-phi3))>>",sinCosFlag[sc].Data()));  \r
  (fIntFlowCorrectionTermsForNUAPro[sc]->GetXaxis())->SetBinLabel(4,Form("<<%s(n(2phi1-phi2))>>",sinCosFlag[sc].Data()));  \r
  fIntFlowProfiles->Add(fIntFlowCorrectionTermsForNUAPro[sc]);\r
 } // end of for(Int_t sc=0;sc<2;sc++) \r
 \r
 // d) Book histograms holding the final results:\r
 // average correlations <<2>>, <<4>>, <<6>> and <<8>> for all events (with correct errors!):\r
 TString intFlowCorrelationsHistName = "fIntFlowCorrelationsHist";\r
 intFlowCorrelationsHistName += fAnalysisLabel->Data();\r
 fIntFlowCorrelationsHist = new TH1D(intFlowCorrelationsHistName.Data(),"Average correlations for all events",4,0,4);\r
 fIntFlowCorrelationsHist->SetTickLength(-0.01,"Y");\r
 fIntFlowCorrelationsHist->SetMarkerStyle(25);\r
 fIntFlowCorrelationsHist->SetLabelSize(0.06);\r
 fIntFlowCorrelationsHist->SetLabelOffset(0.01,"Y");\r
 (fIntFlowCorrelationsHist->GetXaxis())->SetBinLabel(1,"<<2>>");\r
 (fIntFlowCorrelationsHist->GetXaxis())->SetBinLabel(2,"<<4>>");\r
 (fIntFlowCorrelationsHist->GetXaxis())->SetBinLabel(3,"<<6>>");\r
 (fIntFlowCorrelationsHist->GetXaxis())->SetBinLabel(4,"<<8>>");\r
 fIntFlowResults->Add(fIntFlowCorrelationsHist);\r
 // average all correlations for all events (with correct errors!):\r
 TString intFlowCorrelationsAllHistName = "fIntFlowCorrelationsAllHist";\r
 intFlowCorrelationsAllHistName += fAnalysisLabel->Data();\r
 fIntFlowCorrelationsAllHist = new TH1D(intFlowCorrelationsAllHistName.Data(),"Average correlations for all events",32,0,32);\r
 fIntFlowCorrelationsAllHist->SetTickLength(-0.01,"Y");\r
 fIntFlowCorrelationsAllHist->SetMarkerStyle(25);\r
 fIntFlowCorrelationsAllHist->SetLabelSize(0.03);\r
 fIntFlowCorrelationsAllHist->SetLabelOffset(0.01,"Y");\r
 // 2-p correlations:\r
 (fIntFlowCorrelationsAllHist->GetXaxis())->SetBinLabel(1,"<<2>>_{n|n}");\r
 (fIntFlowCorrelationsAllHist->GetXaxis())->SetBinLabel(2,"<<2>>_{2n|2n}");\r
 (fIntFlowCorrelationsAllHist->GetXaxis())->SetBinLabel(3,"<<2>>_{3n|3n}");\r
 (fIntFlowCorrelationsAllHist->GetXaxis())->SetBinLabel(4,"<<2>>_{4n|4n}");\r
 // 3-p correlations:\r
 (fIntFlowCorrelationsAllHist->GetXaxis())->SetBinLabel(6,"<<3>>_{2n|n,n}");\r
 (fIntFlowCorrelationsAllHist->GetXaxis())->SetBinLabel(7,"<<3>>_{3n|2n,n}");\r
 (fIntFlowCorrelationsAllHist->GetXaxis())->SetBinLabel(8,"<<3>>_{4n|2n,2n}");\r
 (fIntFlowCorrelationsAllHist->GetXaxis())->SetBinLabel(9,"<<3>>_{4n|3n,n}");\r
 // 4-p correlations:\r
 (fIntFlowCorrelationsAllHist->GetXaxis())->SetBinLabel(11,"<<4>>_{n,n|n,n}"); \r
 (fIntFlowCorrelationsAllHist->GetXaxis())->SetBinLabel(12,"<<4>>_{2n,n|2n,n}");\r
 (fIntFlowCorrelationsAllHist->GetXaxis())->SetBinLabel(13,"<<4>>_{2n,2n|2n,2n}");\r
 (fIntFlowCorrelationsAllHist->GetXaxis())->SetBinLabel(14,"<<4>>_{3n|n,n,n}");\r
 (fIntFlowCorrelationsAllHist->GetXaxis())->SetBinLabel(15,"<<4>>_{3n,n|3n,n}");\r
 (fIntFlowCorrelationsAllHist->GetXaxis())->SetBinLabel(16,"<<4>>_{3n,n|2n,2n}"); \r
 (fIntFlowCorrelationsAllHist->GetXaxis())->SetBinLabel(17,"<<4>>_{4n|2n,n,n}");\r
 // 5-p correlations:\r
 (fIntFlowCorrelationsAllHist->GetXaxis())->SetBinLabel(19,"<<5>>_{2n|n,n,n,n}"); \r
 (fIntFlowCorrelationsAllHist->GetXaxis())->SetBinLabel(20,"<<5>>_{2n,2n|2n,n,n}");\r
 (fIntFlowCorrelationsAllHist->GetXaxis())->SetBinLabel(21,"<<5>>_{3n,n|2n,n,n}");\r
 (fIntFlowCorrelationsAllHist->GetXaxis())->SetBinLabel(22,"<<5>>_{4n|n,n,n,n}");\r
 // 6-p correlations:\r
 (fIntFlowCorrelationsAllHist->GetXaxis())->SetBinLabel(24,"<<6>>_{n,n,n|n,n,n}");\r
 (fIntFlowCorrelationsAllHist->GetXaxis())->SetBinLabel(25,"<<6>>_{2n,n,n|2n,n,n}");\r
 (fIntFlowCorrelationsAllHist->GetXaxis())->SetBinLabel(26,"<<6>>_{2n,2n|n,n,n,n}");\r
 (fIntFlowCorrelationsAllHist->GetXaxis())->SetBinLabel(27,"<<6>>_{3n,n|n,n,n,n}");\r
 // 7-p correlations:  \r
 (fIntFlowCorrelationsAllHist->GetXaxis())->SetBinLabel(29,"<<7>>_{2n,n,n|n,n,n,n}");\r
 // 8-p correlations:\r
 (fIntFlowCorrelationsAllHist->GetXaxis())->SetBinLabel(31,"<<8>>_{n,n,n,n|n,n,n,n}");\r
 fIntFlowResults->Add(fIntFlowCorrelationsAllHist);\r
 // average correction terms for non-uniform acceptance (with correct errors!):\r
 for(Int_t sc=0;sc<2;sc++) // sin or cos terms\r
 {\r
  TString intFlowCorrectionTermsForNUAHistName = "fIntFlowCorrectionTermsForNUAHist";\r
  intFlowCorrectionTermsForNUAHistName += fAnalysisLabel->Data();\r
  fIntFlowCorrectionTermsForNUAHist[sc] = new TH1D(Form("%s: %s terms",intFlowCorrectionTermsForNUAHistName.Data(),sinCosFlag[sc].Data()),Form("Correction terms for non-uniform acceptance (%s terms)",sinCosFlag[sc].Data()),10,0,10);\r
  fIntFlowCorrectionTermsForNUAHist[sc]->SetTickLength(-0.01,"Y");\r
  fIntFlowCorrectionTermsForNUAHist[sc]->SetMarkerStyle(25);\r
  fIntFlowCorrectionTermsForNUAHist[sc]->SetLabelSize(0.03);\r
  fIntFlowCorrectionTermsForNUAHist[sc]->SetLabelOffset(0.01,"Y");\r
  // ......................................................................... \r
  // 1-p terms:\r
  (fIntFlowCorrectionTermsForNUAHist[sc]->GetXaxis())->SetBinLabel(1,Form("%s(n(#phi_{1}))>",sinCosFlag[sc].Data()));\r
  // 2-p terms:\r
  // 3-p terms:\r
  // ...\r
  // ......................................................................... \r
  fIntFlowResults->Add(fIntFlowCorrectionTermsForNUAHist[sc]);\r
 } // end of for(Int_t sc=0;sc<2;sc++) \r
 // covariances (multiplied with weight dependent prefactor):\r
 TString intFlowCovariancesName = "fIntFlowCovariances";\r
 intFlowCovariancesName += fAnalysisLabel->Data();\r
 fIntFlowCovariances = new TH1D(intFlowCovariancesName.Data(),"Covariances (multiplied with weight dependent prefactor)",6,0,6);\r
 fIntFlowCovariances->SetLabelSize(0.04);\r
 fIntFlowCovariances->SetMarkerStyle(25);\r
 (fIntFlowCovariances->GetXaxis())->SetBinLabel(1,"Cov(<2>,<4>)");\r
 (fIntFlowCovariances->GetXaxis())->SetBinLabel(2,"Cov(<2>,<6>)");\r
 (fIntFlowCovariances->GetXaxis())->SetBinLabel(3,"Cov(<2>,<8>)");\r
 (fIntFlowCovariances->GetXaxis())->SetBinLabel(4,"Cov(<4>,<6>)");\r
 (fIntFlowCovariances->GetXaxis())->SetBinLabel(5,"Cov(<4>,<8>)");\r
 (fIntFlowCovariances->GetXaxis())->SetBinLabel(6,"Cov(<6>,<8>)");  \r
 fIntFlowResults->Add(fIntFlowCovariances);\r
 // sum of linear and quadratic event weights for <2>, <4>, <6> and <8>:\r
 TString intFlowSumOfEventWeightsName = "fIntFlowSumOfEventWeights";\r
 intFlowSumOfEventWeightsName += fAnalysisLabel->Data();\r
 for(Int_t power=0;power<2;power++)\r
 {\r
  fIntFlowSumOfEventWeights[power] = new TH1D(Form("%s: %s",intFlowSumOfEventWeightsName.Data(),powerFlag[power].Data()),Form("Sum of %s event weights for correlations",powerFlag[power].Data()),4,0,4);\r
  fIntFlowSumOfEventWeights[power]->SetLabelSize(0.05);\r
  fIntFlowSumOfEventWeights[power]->SetMarkerStyle(25);\r
  if(power == 0)\r
  {\r
   (fIntFlowSumOfEventWeights[power]->GetXaxis())->SetBinLabel(1,"#sum_{i=1}^{N} w_{<2>}");\r
   (fIntFlowSumOfEventWeights[power]->GetXaxis())->SetBinLabel(2,"#sum_{i=1}^{N} w_{<4>}");\r
   (fIntFlowSumOfEventWeights[power]->GetXaxis())->SetBinLabel(3,"#sum_{i=1}^{N} w_{<6>}");\r
   (fIntFlowSumOfEventWeights[power]->GetXaxis())->SetBinLabel(4,"#sum_{i=1}^{N} w_{<8>}");\r
  } else if (power == 1) \r
    {\r
     (fIntFlowSumOfEventWeights[power]->GetXaxis())->SetBinLabel(1,"#sum_{i=1}^{N} w_{<2>}^{2}");\r
     (fIntFlowSumOfEventWeights[power]->GetXaxis())->SetBinLabel(2,"#sum_{i=1}^{N} w_{<4>}^{2}");\r
     (fIntFlowSumOfEventWeights[power]->GetXaxis())->SetBinLabel(3,"#sum_{i=1}^{N} w_{<6>}^{2}");\r
     (fIntFlowSumOfEventWeights[power]->GetXaxis())->SetBinLabel(4,"#sum_{i=1}^{N} w_{<8>}^{2}");\r
    }\r
  fIntFlowResults->Add(fIntFlowSumOfEventWeights[power]);\r
 } \r
 // sum of products of event weights for correlations <2>, <4>, <6> and <8>:  \r
 TString intFlowSumOfProductOfEventWeightsName = "fIntFlowSumOfProductOfEventWeights";\r
 intFlowSumOfProductOfEventWeightsName += fAnalysisLabel->Data();\r
 fIntFlowSumOfProductOfEventWeights = new TH1D(intFlowSumOfProductOfEventWeightsName.Data(),"Sum of product of event weights for correlations",6,0,6);\r
 fIntFlowSumOfProductOfEventWeights->SetLabelSize(0.05);\r
 fIntFlowSumOfProductOfEventWeights->SetMarkerStyle(25);\r
 (fIntFlowSumOfProductOfEventWeights->GetXaxis())->SetBinLabel(1,"#sum_{i=1}^{N} w_{<2>} w_{<4>}");\r
 (fIntFlowSumOfProductOfEventWeights->GetXaxis())->SetBinLabel(2,"#sum_{i=1}^{N} w_{<2>} w_{<6>}");\r
 (fIntFlowSumOfProductOfEventWeights->GetXaxis())->SetBinLabel(3,"#sum_{i=1}^{N} w_{<2>} w_{<8>}");\r
 (fIntFlowSumOfProductOfEventWeights->GetXaxis())->SetBinLabel(4,"#sum_{i=1}^{N} w_{<4>} w_{<6>}");\r
 (fIntFlowSumOfProductOfEventWeights->GetXaxis())->SetBinLabel(5,"#sum_{i=1}^{N} w_{<4>} w_{<8>}");\r
 (fIntFlowSumOfProductOfEventWeights->GetXaxis())->SetBinLabel(6,"#sum_{i=1}^{N} w_{<6>} w_{<8>}");\r
 fIntFlowResults->Add(fIntFlowSumOfProductOfEventWeights);\r
 // final results for integrated Q-cumulants:\r
 TString intFlowQcumulantsName = "fIntFlowQcumulants";\r
 intFlowQcumulantsName += fAnalysisLabel->Data();\r
 fIntFlowQcumulants = new TH1D(intFlowQcumulantsName.Data(),"Integrated Q-cumulants",4,0,4);\r
 fIntFlowQcumulants->SetLabelSize(0.05);\r
 fIntFlowQcumulants->SetMarkerStyle(25);\r
 (fIntFlowQcumulants->GetXaxis())->SetBinLabel(1,"QC{2}");\r
 (fIntFlowQcumulants->GetXaxis())->SetBinLabel(2,"QC{4}");\r
 (fIntFlowQcumulants->GetXaxis())->SetBinLabel(3,"QC{6}");\r
 (fIntFlowQcumulants->GetXaxis())->SetBinLabel(4,"QC{8}");\r
 fIntFlowResults->Add(fIntFlowQcumulants);\r
 // final integrated flow estimates from Q-cumulants:\r
 TString intFlowName = "fIntFlow";\r
 intFlowName += fAnalysisLabel->Data();  \r
 // integrated flow from Q-cumulants:\r
 fIntFlow = new TH1D(intFlowName.Data(),"Integrated flow estimates from Q-cumulants",4,0,4);\r
 fIntFlow->SetLabelSize(0.05);\r
 fIntFlow->SetMarkerStyle(25);\r
 (fIntFlow->GetXaxis())->SetBinLabel(1,"v_{2}{2,QC}");\r
 (fIntFlow->GetXaxis())->SetBinLabel(2,"v_{2}{4,QC}");\r
 (fIntFlow->GetXaxis())->SetBinLabel(3,"v_{2}{6,QC}");\r
 (fIntFlow->GetXaxis())->SetBinLabel(4,"v_{2}{8,QC}");\r
 fIntFlowResults->Add(fIntFlow);\r
\r
 /* // to be improved (removed):\r
  // final average weighted multi-particle correlations for all events calculated from Q-vectors\r
  fQCorrelations[1] = new TProfile("Weighted correlations","final average multi-particle correlations from weighted Q-vectors",200,0,200,"s");\r
  fQCorrelations[1]->SetTickLength(-0.01,"Y");\r
  fQCorrelations[1]->SetMarkerStyle(25);\r
  fQCorrelations[1]->SetLabelSize(0.03);\r
  fQCorrelations[1]->SetLabelOffset(0.01,"Y");\r
  // 2-particle correlations:\r
  (fQCorrelations[1]->GetXaxis())->SetBinLabel(1,"<w_{1}w_{2}cos(n(#phi_{1}-#phi_{2}))>");\r
  (fQCorrelations[1]->GetXaxis())->SetBinLabel(2,"<w_{1}^{2}w_{2}^{2}cos(2n(#phi_{1}-#phi_{2}))>");\r
  (fQCorrelations[1]->GetXaxis())->SetBinLabel(3,"<w_{1}^{3}w_{2}^{3}cos(3n(#phi_{1}-#phi_{2}))>");\r
  (fQCorrelations[1]->GetXaxis())->SetBinLabel(4,"<w_{1}^{4}w_{2}^{4}cos(4n(#phi_{1}-#phi_{2}))>");\r
  (fQCorrelations[1]->GetXaxis())->SetBinLabel(5,"<w_{1}^{3}w_{2}cos(n(#phi_{1}-#phi_{2}))>");\r
  (fQCorrelations[1]->GetXaxis())->SetBinLabel(6,"<w_{1}^{2}w_{2}w_{3}cos(n(#phi_{1}-#phi_{2}))>");\r
  // 3-particle correlations:\r
  (fQCorrelations[1]->GetXaxis())->SetBinLabel(21,"<w_{1}w_{2}w_{3}^{2}cos(n(2#phi_{1}-#phi_{2}-#phi_{3}))>");\r
  // 4-particle correlations:\r
  (fQCorrelations[1]->GetXaxis())->SetBinLabel(41,"<w_{1}w_{2}w_{3}w_{4}cos(n(#phi_{1}+#phi_{2}-#phi_{3}-#phi_{4}))>");\r
  // add fQCorrelations[1] to the list fIntFlowList:\r
  fIntFlowList->Add(fQCorrelations[1]); \r
 */\r
  \r
} // end of AliFlowAnalysisWithQCumulants::BookEverythingForIntegratedFlow()\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::InitializeArraysForNestedLoops()\r
{\r
 // Initialize arrays of all objects relevant for calculations with nested loops.\r
 \r
 // integrated flow:\r
 for(Int_t sc=0;sc<2;sc++) // sin or cos terms\r
 {\r
  fIntFlowDirectCorrectionTermsForNUA[sc] = NULL;\r
 } \r
\r
 // differential flow:  \r
 // correlations:\r
 for(Int_t t=0;t<2;t++) // type: RP or POI\r
 { \r
  for(Int_t pe=0;pe<2;pe++) // pt or eta\r
  {\r
   for(Int_t ci=0;ci<4;ci++) // correlation index\r
   {\r
    fDiffFlowDirectCorrelations[t][pe][ci] = NULL;\r
   } // end of for(Int_t ci=0;ci<4;ci++) // correlation index  \r
  } // end of for(Int_t pe=0;pe<2;pe++) // pt or eta\r
 } // end of for(Int_t t=0;t<2;t++) // type: RP or POI\r
 // correction terms for non-uniform acceptance:\r
 for(Int_t t=0;t<2;t++) // type: RP or POI\r
 { \r
  for(Int_t pe=0;pe<2;pe++) // pt or eta\r
  {\r
   for(Int_t sc=0;sc<2;sc++) // sin or cos terms\r
   {\r
    for(Int_t cti=0;cti<9;cti++) // correction term index\r
    {\r
     fDiffFlowDirectCorrectionTermsForNUA[t][pe][sc][cti] = NULL;\r
    }   \r
   }\r
  } // end of for(Int_t pe=0;pe<2;pe++) // pt or eta\r
 } // end of for(Int_t t=0;t<2;t++) // type: RP or POI\r
\r
\r
} // end of void AliFlowAnalysisWithQCumulants::InitializeArraysForNestedLoops()\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::BookEverythingForNestedLoops()\r
{\r
 // Book all objects relevant for calculations with nested loops.\r
 \r
 TString sinCosFlag[2] = {"sin","cos"}; // to be improved (should I promote this to data members?)\r
 TString typeFlag[2] = {"RP","POI"}; // to be improved (should I promote this to data members?)\r
 TString ptEtaFlag[2] = {"p_{T}","#eta"}; // to be improved (should I promote this to data members?)\r
 TString reducedCorrelationIndex[4] = {"<2'>","<4'>","<6'>","<8'>"}; // to be improved (should I promote this to data members?)\r
 Double_t lowerPtEtaEdge[2] = {fPtMin+(fCrossCheckInPtBinNo-1)*fPtBinWidth,fEtaMin+(fCrossCheckInEtaBinNo-1)*fEtaBinWidth};\r
 Double_t upperPtEtaEdge[2] = {fPtMin+fCrossCheckInPtBinNo*fPtBinWidth,fEtaMin+fCrossCheckInEtaBinNo*fEtaBinWidth};\r
\r
 TString evaluateNestedLoopsName = "fEvaluateNestedLoops";\r
 evaluateNestedLoopsName += fAnalysisLabel->Data();\r
 fEvaluateNestedLoops = new TProfile(evaluateNestedLoopsName.Data(),"Flags for nested loops",4,0,4);\r
 fEvaluateNestedLoops->SetLabelSize(0.03);\r
 (fEvaluateNestedLoops->GetXaxis())->SetBinLabel(1,"fEvaluateIntFlowNestedLoops");\r
 (fEvaluateNestedLoops->GetXaxis())->SetBinLabel(2,"fEvaluateDiffFlowNestedLoops");\r
 (fEvaluateNestedLoops->GetXaxis())->SetBinLabel(3,"fCrossCheckInPtBinNo");\r
 (fEvaluateNestedLoops->GetXaxis())->SetBinLabel(4,"fCrossCheckInEtaBinNo");\r
 fEvaluateNestedLoops->Fill(0.5,(Int_t)fEvaluateIntFlowNestedLoops);\r
 fEvaluateNestedLoops->Fill(1.5,(Int_t)fEvaluateDiffFlowNestedLoops);\r
 fEvaluateNestedLoops->Fill(2.5,fCrossCheckInPtBinNo);\r
 fEvaluateNestedLoops->Fill(3.5,fCrossCheckInEtaBinNo);\r
 fNestedLoopsList->Add(fEvaluateNestedLoops);\r
 // nested loops for integrated flow:\r
 if(fEvaluateIntFlowNestedLoops)\r
 {\r
  // correlations:\r
  TString intFlowDirectCorrelationsName = "fIntFlowDirectCorrelations";\r
  intFlowDirectCorrelationsName += fAnalysisLabel->Data();\r
  fIntFlowDirectCorrelations = new TProfile(intFlowDirectCorrelationsName.Data(),"Multiparticle correlations calculated with nested loops (for int. flow)",32,0,32,"s");\r
  fNestedLoopsList->Add(fIntFlowDirectCorrelations);\r
  if(fUsePhiWeights||fUsePtWeights||fUseEtaWeights)\r
  {\r
   TString intFlowExtraDirectCorrelationsName = "fIntFlowExtraDirectCorrelations";\r
   intFlowExtraDirectCorrelationsName += fAnalysisLabel->Data();\r
   fIntFlowExtraDirectCorrelations = new TProfile(intFlowExtraDirectCorrelationsName.Data(),"Extra multiparticle correlations calculated with nested loops (for int. flow)",100,0,100,"s");\r
   fNestedLoopsList->Add(fIntFlowExtraDirectCorrelations);  \r
  } // end of if(fUsePhiWeights||fUsePtWeights||fUseEtaWeights)\r
  // correction terms for non-uniform acceptance:\r
  for(Int_t sc=0;sc<2;sc++) // sin or cos terms\r
  {\r
   TString intFlowDirectCorrectionTermsForNUAName = "fIntFlowDirectCorrectionTermsForNUA";\r
   intFlowDirectCorrectionTermsForNUAName += fAnalysisLabel->Data();\r
   fIntFlowDirectCorrectionTermsForNUA[sc] = new TProfile(Form("%s: %s terms",intFlowDirectCorrectionTermsForNUAName.Data(),sinCosFlag[sc].Data()),Form("Correction terms for non-uniform acceptance (%s terms)",sinCosFlag[sc].Data()),10,0,10,"s");\r
   fNestedLoopsList->Add(fIntFlowDirectCorrectionTermsForNUA[sc]);\r
  } // end of for(Int_t sc=0;sc<2;sc++) \r
 } // end of if(fEvaluateIntFlowNestedLoops)\r
 \r
 // nested loops for differential flow: \r
 if(fEvaluateDiffFlowNestedLoops)\r
 {\r
  // reduced correlations:\r
  TString diffFlowDirectCorrelationsName = "fDiffFlowDirectCorrelations";\r
  diffFlowDirectCorrelationsName += fAnalysisLabel->Data();\r
  for(Int_t t=0;t<2;t++) // type: RP or POI\r
  { \r
   for(Int_t pe=0;pe<2;pe++) // pt or eta\r
   {\r
    for(Int_t rci=0;rci<4;rci++) // reduced correlation index\r
    {\r
     // reduced correlations:\r
     fDiffFlowDirectCorrelations[t][pe][rci] = new TProfile(Form("%s, %s, %s, %s",diffFlowDirectCorrelationsName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),reducedCorrelationIndex[rci].Data()),Form("%s, %s, %s, %s",diffFlowDirectCorrelationsName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),reducedCorrelationIndex[rci].Data()),1,lowerPtEtaEdge[pe],upperPtEtaEdge[pe],"s");\r
     fDiffFlowDirectCorrelations[t][pe][rci]->SetXTitle(ptEtaFlag[pe].Data());\r
     fNestedLoopsList->Add(fDiffFlowDirectCorrelations[t][pe][rci]); // to be improved (add dedicated list to hold reduced correlations)\r
    } // end of for(Int_t rci=0;rci<4;rci++) // correlation index\r
   } // end of for(Int_t pe=0;pe<2;pe++) // pt or eta \r
  } // end of for(Int_t t=0;t<2;t++) // type: RP or POI \r
  // correction terms for non-uniform acceptance:\r
  TString diffFlowDirectCorrectionTermsForNUAName = "fDiffFlowDirectCorrectionTermsForNUA";\r
  diffFlowDirectCorrectionTermsForNUAName += fAnalysisLabel->Data();\r
  for(Int_t t=0;t<2;t++) // typeFlag (0 = RP, 1 = POI)\r
  { \r
   for(Int_t pe=0;pe<2;pe++) // pt or eta\r
   {\r
    for(Int_t sc=0;sc<2;sc++) // sin or cos\r
    {\r
     for(Int_t cti=0;cti<9;cti++) // correction term index\r
     {\r
      fDiffFlowDirectCorrectionTermsForNUA[t][pe][sc][cti] = new TProfile(Form("%s, %s, %s, %s, cti = %d",diffFlowDirectCorrectionTermsForNUAName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),sinCosFlag[sc].Data(),cti+1),Form("%s, %s, %s, %s, cti = %d",diffFlowDirectCorrectionTermsForNUAName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),sinCosFlag[sc].Data(),cti+1),1,lowerPtEtaEdge[pe],upperPtEtaEdge[pe],"s"); \r
      fNestedLoopsList->Add(fDiffFlowDirectCorrectionTermsForNUA[t][pe][sc][cti]);\r
     }\r
    }\r
   }\r
  } 
  // number of RPs and POIs in selected pt and eta bins for cross-checkings:
  TString noOfParticlesInBinName = "fNoOfParticlesInBin";
  fNoOfParticlesInBin = new TH1D(noOfParticlesInBinName.Data(),"Number of RPs and POIs in selected p_{T} and #eta bin",4,0,4);
  fNoOfParticlesInBin->GetXaxis()->SetBinLabel(1,"# of RPs in p_{T} bin");\r
  fNoOfParticlesInBin->GetXaxis()->SetBinLabel(2,"# of RPs in #eta bin");\r
  fNoOfParticlesInBin->GetXaxis()->SetBinLabel(3,"# of POIs in p_{T} bin");\r
  fNoOfParticlesInBin->GetXaxis()->SetBinLabel(4,"# of POIs in #eta bin");
  fNestedLoopsList->Add(fNoOfParticlesInBin);\r
 } // end of if(fEvaluateDiffFlowNestedLoops)\r
\r
} // end of AliFlowAnalysisWithQCumulants::BookEverythingForNestedLoops()\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::CalculateIntFlowCorrelations()\r
{\r
 // calculate all correlations needed for integrated flow\r
 \r
 // multiplicity:\r
 Double_t dMult = (*fSMpk)(0,0);\r
 \r
 // real and imaginary parts of non-weighted Q-vectors evaluated in harmonics n, 2n, 3n and 4n: \r
 Double_t dReQ1n = (*fReQ)(0,0);\r
 Double_t dReQ2n = (*fReQ)(1,0);\r
 Double_t dReQ3n = (*fReQ)(2,0);\r
 Double_t dReQ4n = (*fReQ)(3,0);\r
 Double_t dImQ1n = (*fImQ)(0,0);\r
 Double_t dImQ2n = (*fImQ)(1,0);\r
 Double_t dImQ3n = (*fImQ)(2,0);\r
 Double_t dImQ4n = (*fImQ)(3,0);\r
  \r
 // real and imaginary parts of some expressions involving various combinations of Q-vectors evaluated in harmonics n, 2n, 3n and 4n:\r
 // (these expression appear in the Eqs. for the multi-particle correlations bellow)\r
 \r
 // Re[Q_{2n} Q_{n}^* Q_{n}^*]\r
 Double_t reQ2nQ1nstarQ1nstar = pow(dReQ1n,2.)*dReQ2n + 2.*dReQ1n*dImQ1n*dImQ2n - pow(dImQ1n,2.)*dReQ2n; \r
 \r
 // Im[Q_{2n} Q_{n}^* Q_{n}^*]\r
 //Double_t imQ2nQ1nstarQ1nstar = pow(dReQ1n,2.)*dImQ2n-2.*dReQ1n*dImQ1n*dReQ2n-pow(dImQ1n,2.)*dImQ2n; \r
 \r
 // Re[Q_{n} Q_{n} Q_{2n}^*] = Re[Q_{2n} Q_{n}^* Q_{n}^*]\r
 Double_t reQ1nQ1nQ2nstar = reQ2nQ1nstarQ1nstar; \r
 \r
 // Re[Q_{3n} Q_{n} Q_{2n}^* Q_{2n}^*]\r
 Double_t reQ3nQ1nQ2nstarQ2nstar = (pow(dReQ2n,2.)-pow(dImQ2n,2.))*(dReQ3n*dReQ1n-dImQ3n*dImQ1n) \r
                                 + 2.*dReQ2n*dImQ2n*(dReQ3n*dImQ1n+dImQ3n*dReQ1n);\r
\r
 // Im[Q_{3n} Q_{n} Q_{2n}^* Q_{2n}^*]                                                                  \r
 //Double_t imQ3nQ1nQ2nstarQ2nstar = calculate and implement this (deleteMe)\r
  \r
 // Re[Q_{2n} Q_{2n} Q_{3n}^* Q_{1n}^*] = Re[Q_{3n} Q_{n} Q_{2n}^* Q_{2n}^*]\r
 Double_t reQ2nQ2nQ3nstarQ1nstar = reQ3nQ1nQ2nstarQ2nstar;\r
  \r
 // Re[Q_{4n} Q_{2n}^* Q_{2n}^*]\r
 Double_t reQ4nQ2nstarQ2nstar = pow(dReQ2n,2.)*dReQ4n+2.*dReQ2n*dImQ2n*dImQ4n-pow(dImQ2n,2.)*dReQ4n;\r
\r
 // Im[Q_{4n} Q_{2n}^* Q_{2n}^*]\r
 //Double_t imQ4nQ2nstarQ2nstar = calculate and implement this (deleteMe)\r
 \r
 // Re[Q_{2n} Q_{2n} Q_{4n}^*] =  Re[Q_{4n} Q_{2n}^* Q_{2n}^*]\r
 Double_t reQ2nQ2nQ4nstar = reQ4nQ2nstarQ2nstar;\r
 \r
 // Re[Q_{4n} Q_{3n}^* Q_{n}^*]\r
 Double_t reQ4nQ3nstarQ1nstar = dReQ4n*(dReQ3n*dReQ1n-dImQ3n*dImQ1n)+dImQ4n*(dReQ3n*dImQ1n+dImQ3n*dReQ1n);\r
 \r
 // Re[Q_{3n} Q_{n} Q_{4n}^*] = Re[Q_{4n} Q_{3n}^* Q_{n}^*]\r
 Double_t reQ3nQ1nQ4nstar = reQ4nQ3nstarQ1nstar;\r
 \r
 // Im[Q_{4n} Q_{3n}^* Q_{n}^*]\r
 //Double_t imQ4nQ3nstarQ1nstar = calculate and implement this (deleteMe)\r
\r
 // Re[Q_{3n} Q_{2n}^* Q_{n}^*]\r
 Double_t reQ3nQ2nstarQ1nstar = dReQ3n*dReQ2n*dReQ1n-dReQ3n*dImQ2n*dImQ1n+dImQ3n*dReQ2n*dImQ1n\r
                              + dImQ3n*dImQ2n*dReQ1n;\r
                              \r
 // Re[Q_{2n} Q_{n} Q_{3n}^*] = Re[Q_{3n} Q_{2n}^* Q_{n}^*]\r
 Double_t reQ2nQ1nQ3nstar = reQ3nQ2nstarQ1nstar;\r
 \r
 // Im[Q_{3n} Q_{2n}^* Q_{n}^*]\r
 //Double_t imQ3nQ2nstarQ1nstar; //calculate and implement this (deleteMe)\r
 \r
 // Re[Q_{3n} Q_{n}^* Q_{n}^* Q_{n}^*]\r
 Double_t reQ3nQ1nstarQ1nstarQ1nstar = dReQ3n*pow(dReQ1n,3)-3.*dReQ1n*dReQ3n*pow(dImQ1n,2)\r
                                     + 3.*dImQ1n*dImQ3n*pow(dReQ1n,2)-dImQ3n*pow(dImQ1n,3);\r
\r
 // Im[Q_{3n} Q_{n}^* Q_{n}^* Q_{n}^*]\r
 //Double_t imQ3nQ1nstarQ1nstarQ1nstar; //calculate and implement this (deleteMe)\r
 \r
 // |Q_{2n}|^2 |Q_{n}|^2\r
 Double_t dQ2nQ1nQ2nstarQ1nstar = (pow(dReQ2n,2.)+pow(dImQ2n,2.))*(pow(dReQ1n,2.)+pow(dImQ1n,2.));\r
 \r
 // Re[Q_{4n} Q_{2n}^* Q_{n}^* Q_{n}^*]\r
 Double_t reQ4nQ2nstarQ1nstarQ1nstar = (dReQ4n*dReQ2n+dImQ4n*dImQ2n)*(pow(dReQ1n,2)-pow(dImQ1n,2))\r
                                     + 2.*dReQ1n*dImQ1n*(dImQ4n*dReQ2n-dReQ4n*dImQ2n); \r
 \r
 // Im[Q_{4n} Q_{2n}^* Q_{n}^* Q_{n}^*]\r
 //Double_t imQ4nQ2nstarQ1nstarQ1nstar; //calculate and implement this (deleteMe)\r
 \r
 // Re[Q_{2n} Q_{n} Q_{n}^* Q_{n}^* Q_{n}^*]\r
 Double_t reQ2nQ1nQ1nstarQ1nstarQ1nstar = (dReQ2n*dReQ1n-dImQ2n*dImQ1n)*(pow(dReQ1n,3)-3.*dReQ1n*pow(dImQ1n,2))\r
                                        + (dReQ2n*dImQ1n+dReQ1n*dImQ2n)*(3.*dImQ1n*pow(dReQ1n,2)-pow(dImQ1n,3));\r
\r
 // Im[Q_{2n} Q_{n} Q_{n}^* Q_{n}^* Q_{n}^*] \r
 //Double_t imQ2nQ1nQ1nstarQ1nstarQ1nstar; //calculate and implement this (deleteMe)\r
 \r
 // Re[Q_{2n} Q_{2n} Q_{2n}^* Q_{n}^* Q_{n}^*]\r
 Double_t reQ2nQ2nQ2nstarQ1nstarQ1nstar = (pow(dReQ2n,2.)+pow(dImQ2n,2.))\r
                                        * (dReQ2n*(pow(dReQ1n,2.)-pow(dImQ1n,2.)) + 2.*dImQ2n*dReQ1n*dImQ1n);\r
\r
 // Im[Q_{2n} Q_{2n} Q_{2n}^* Q_{n}^* Q_{n}^*]\r
 //Double_t imQ2nQ2nQ2nstarQ1nstarQ1nstar = (pow(dReQ2n,2.)+pow(dImQ2n,2.))\r
 //                                       * (dImQ2n*(pow(dReQ1n,2.)-pow(dImQ1n,2.)) - 2.*dReQ2n*dReQ1n*dImQ1n);\r
 \r
 // Re[Q_{4n} Q_{n}^* Q_{n}^* Q_{n}^* Q_{n}^*]\r
 Double_t reQ4nQ1nstarQ1nstarQ1nstarQ1nstar = pow(dReQ1n,4.)*dReQ4n-6.*pow(dReQ1n,2.)*dReQ4n*pow(dImQ1n,2.)\r
                                            + pow(dImQ1n,4.)*dReQ4n+4.*pow(dReQ1n,3.)*dImQ1n*dImQ4n\r
                                            - 4.*pow(dImQ1n,3.)*dReQ1n*dImQ4n;\r
                                            \r
 // Im[Q_{4n} Q_{n}^* Q_{n}^* Q_{n}^* Q_{n}^*]\r
 //Double_t imQ4nQ1nstarQ1nstarQ1nstarQ1nstar = pow(dReQ1n,4.)*dImQ4n-6.*pow(dReQ1n,2.)*dImQ4n*pow(dImQ1n,2.)\r
 //                                           + pow(dImQ1n,4.)*dImQ4n+4.*pow(dImQ1n,3.)*dReQ1n*dReQ4n\r
 //                                           - 4.*pow(dReQ1n,3.)*dImQ1n*dReQ4n;\r
 \r
 // Re[Q_{3n} Q_{n} Q_{2n}^* Q_{n}^* Q_{n}^*]\r
 Double_t reQ3nQ1nQ2nstarQ1nstarQ1nstar = (pow(dReQ1n,2.)+pow(dImQ1n,2.))\r
                                        * (dReQ1n*dReQ2n*dReQ3n-dReQ3n*dImQ1n*dImQ2n+dReQ2n*dImQ1n*dImQ3n+dReQ1n*dImQ2n*dImQ3n);\r
 \r
 // Im[Q_{3n} Q_{n} Q_{2n}^* Q_{n}^* Q_{n}^*]\r
 //Double_t imQ3nQ1nQ2nstarQ1nstarQ1nstar = (pow(dReQ1n,2.)+pow(dImQ1n,2.))\r
 //                                       * (-dReQ2n*dReQ3n*dImQ1n-dReQ1n*dReQ3n*dImQ2n+dReQ1n*dReQ2n*dImQ3n-dImQ1n*dImQ2n*dImQ3n);\r
 \r
 \r
 // Re[Q_{2n} Q_{2n} Q_{n}^* Q_{n}^* Q_{n}^* Q_{n}^*]\r
 Double_t reQ2nQ2nQ1nstarQ1nstarQ1nstarQ1nstar = (pow(dReQ1n,2.)*dReQ2n-2.*dReQ1n*dReQ2n*dImQ1n-dReQ2n*pow(dImQ1n,2.)\r
                                               + dImQ2n*pow(dReQ1n,2.)+2.*dReQ1n*dImQ1n*dImQ2n-pow(dImQ1n,2.)*dImQ2n)\r
                                               * (pow(dReQ1n,2.)*dReQ2n+2.*dReQ1n*dReQ2n*dImQ1n-dReQ2n*pow(dImQ1n,2.)\r
                                               - dImQ2n*pow(dReQ1n,2.)+2.*dReQ1n*dImQ1n*dImQ2n+pow(dImQ1n,2.)*dImQ2n);\r
 \r
 // Im[Q_{2n} Q_{2n} Q_{n}^* Q_{n}^* Q_{n}^* Q_{n}^*]\r
 //Double_t imQ2nQ2nQ1nstarQ1nstarQ1nstarQ1nstar = 2.*(pow(dReQ1n,2.)*dReQ2n-dReQ2n*pow(dImQ1n,2.)\r
 //                                              + 2.*dReQ1n*dImQ1n*dImQ2n)*(pow(dReQ1n,2.)*dImQ2n\r
 //                                              - 2.*dReQ1n*dImQ1n*dReQ2n-pow(dImQ1n,2.)*dImQ2n);\r
 \r
 // Re[Q_{3n} Q_{n} Q_{n}^* Q_{n}^* Q_{n}^* Q_{n}^*]\r
 Double_t reQ3nQ1nQ1nstarQ1nstarQ1nstarQ1nstar = (pow(dReQ1n,2.)+pow(dImQ1n,2.))\r
                                               * (pow(dReQ1n,3.)*dReQ3n-3.*dReQ1n*dReQ3n*pow(dImQ1n,2.)\r
                                               + 3.*pow(dReQ1n,2.)*dImQ1n*dImQ3n-pow(dImQ1n,3.)*dImQ3n);\r
  \r
 // Im[Q_{3n} Q_{n} Q_{n}^* Q_{n}^* Q_{n}^* Q_{n}^*]                                                                                           \r
 //Double_t imQ3nQ1nQ1nstarQ1nstarQ1nstarQ1nstar = (pow(dReQ1n,2.)+pow(dImQ1n,2.))\r
 //                                              * (pow(dImQ1n,3.)*dReQ3n-3.*dImQ1n*dReQ3n*pow(dReQ1n,2.)\r
 //                                              - 3.*pow(dImQ1n,2.)*dReQ1n*dImQ3n+pow(dReQ1n,3.)*dImQ3n);\r
 \r
 // |Q_{2n}|^2 |Q_{n}|^4\r
 Double_t dQ2nQ1nQ1nQ2nstarQ1nstarQ1nstar = (pow(dReQ2n,2.)+pow(dImQ2n,2.))*pow((pow(dReQ1n,2.)+pow(dImQ1n,2.)),2.);\r
 \r
 // Re[Q_{2n} Q_{n} Q_{n} Q_{n}^* Q_{n}^* Q_{n}^* Q_{n}^*]\r
 Double_t reQ2nQ1nQ1nQ1nstarQ1nstarQ1nstarQ1nstar = pow((pow(dReQ1n,2.)+pow(dImQ1n,2.)),2.)\r
                                                  * (pow(dReQ1n,2.)*dReQ2n-dReQ2n*pow(dImQ1n,2.)\r
                                                  + 2.*dReQ1n*dImQ1n*dImQ2n);\r
                                                  \r
 // Im[Q_{2n} Q_{n} Q_{n} Q_{n}^* Q_{n}^* Q_{n}^* Q_{n}^*]                                                  \r
 //Double_t imQ2nQ1nQ1nQ1nstarQ1nstarQ1nstarQ1nstar = pow((pow(dReQ1n,2.)+pow(dImQ1n,2.)),2.)\r
 //                                                 * (pow(dReQ1n,2.)*dImQ2n-dImQ2n*pow(dImQ1n,2.)\r
 //                                                 - 2.*dReQ1n*dReQ2n*dImQ1n);\r
 \r
  \r
 \r
       \r
 //                                        **************************************\r
 //                                        **** multi-particle correlations: ****\r
 //                                        **************************************\r
 //\r
 // Remark 1: multi-particle correlations calculated with non-weighted Q-vectors are stored in 1D profile fQCorrelations[0]. // to be improved (wrong profiles)\r
 // Remark 2: binning of fQCorrelations[0] is organized as follows: // to be improved (wrong profiles)\r
 // --------------------------------------------------------------------------------------------------------------------\r
 //  1st bin: <2>_{1n|1n} = two1n1n = cos(n*(phi1-phi2))>\r
 //  2nd bin: <2>_{2n|2n} = two2n2n = cos(2n*(phi1-phi2))>\r
 //  3rd bin: <2>_{3n|3n} = two3n3n = cos(3n*(phi1-phi2))> \r
 //  4th bin: <2>_{4n|4n} = two4n4n = cos(4n*(phi1-phi2))>\r
 //  5th bin:           ----  EMPTY ----\r
 //  6th bin: <3>_{2n|1n,1n} = three2n1n1n = <cos(n*(2.*phi1-phi2-phi3))>\r
 //  7th bin: <3>_{3n|2n,1n} = three3n2n1n = <cos(n*(3.*phi1-2.*phi2-phi3))>\r
 //  8th bin: <3>_{4n|2n,2n} = three4n2n2n = <cos(n*(4.*phi1-2.*phi2-2.*phi3))>\r
 //  9th bin: <3>_{4n|3n,1n} = three4n3n1n = <cos(n*(4.*phi1-3.*phi2-phi3))>\r
 // 10th bin:           ----  EMPTY ----\r
 // 11th bin: <4>_{1n,1n|1n,1n} = four1n1n1n1n = <cos(n*(phi1+phi2-phi3-phi4))>\r
 // 12th bin: <4>_{2n,1n|2n,1n} = four2n1n2n1n = <cos(2.*n*(phi1+phi2-phi3-phi4))>\r
 // 13th bin: <4>_{2n,2n|2n,2n} = four2n2n2n2n = <cos(n*(2.*phi1+phi2-2.*phi3-phi4))>\r
 // 14th bin: <4>_{3n|1n,1n,1n} = four3n1n1n1n = <cos(n*(3.*phi1-phi2-phi3-phi4))> \r
 // 15th bin: <4>_{3n,1n|3n,1n} = four3n1n3n1n = <cos(n*(4.*phi1-2.*phi2-phi3-phi4))>\r
 // 16th bin: <4>_{3n,1n|2n,2n} = four3n1n2n2n = <cos(n*(3.*phi1+phi2-2.*phi3-2.*phi4))>\r
 // 17th bin: <4>_{4n|2n,1n,1n} = four4n2n1n1n = <cos(n*(3.*phi1+phi2-3.*phi3-phi4))> \r
 // 18th bin:           ----  EMPTY ----\r
 // 19th bin: <5>_{2n|1n,1n,1n,1n} = five2n1n1n1n1n = <cos(n*(2.*phi1+phi2-phi3-phi4-phi5))>\r
 // 20th bin: <5>_{2n,2n|2n,1n,1n} = five2n2n2n1n1n = <cos(n*(2.*phi1+2.*phi2-2.*phi3-phi4-phi5))>\r
 // 21st bin: <5>_{3n,1n|2n,1n,1n} = five3n1n2n1n1n = <cos(n*(3.*phi1+phi2-2.*phi3-phi4-phi5))>\r
 // 22nd bin: <5>_{4n|1n,1n,1n,1n} = five4n1n1n1n1n = <cos(n*(4.*phi1-phi2-phi3-phi4-phi5))>\r
 // 23rd bin:           ----  EMPTY ----\r
 // 24th bin: <6>_{1n,1n,1n|1n,1n,1n} = six1n1n1n1n1n1n = <cos(n*(phi1+phi2+phi3-phi4-phi5-phi6))>\r
 // 25th bin: <6>_{2n,1n,1n|2n,1n,1n} = six2n1n1n2n1n1n = <cos(n*(2.*phi1+2.*phi2-phi3-phi4-phi5-phi6))>\r
 // 26th bin: <6>_{2n,2n|1n,1n,1n,1n} = six2n2n1n1n1n1n = <cos(n*(3.*phi1+phi2-phi3-phi4-phi5-phi6))>\r
 // 27th bin: <6>_{3n,1n|1n,1n,1n,1n} = six3n1n1n1n1n1n = <cos(n*(2.*phi1+phi2+phi3-2.*phi4-phi5-phi6))>\r
 // 28th bin:           ----  EMPTY ----\r
 // 29th bin: <7>_{2n,1n,1n|1n,1n,1n,1n} = seven2n1n1n1n1n1n1n =  <cos(n*(2.*phi1+phi2+phi3-phi4-phi5-phi6-phi7))>\r
 // 30th bin:           ----  EMPTY ----\r
 // 31st bin: <8>_{1n,1n,1n,1n|1n,1n,1n,1n} = eight1n1n1n1n1n1n1n1n = <cos(n*(phi1+phi2+phi3+phi4-phi5-phi6-phi7-phi8))>\r
 // --------------------------------------------------------------------------------------------------------------------\r
    \r
 // 2-particle:\r
 Double_t two1n1n = 0.; // <cos(n*(phi1-phi2))>\r
 Double_t two2n2n = 0.; // <cos(2n*(phi1-phi2))>\r
 Double_t two3n3n = 0.; // <cos(3n*(phi1-phi2))>\r
 Double_t two4n4n = 0.; // <cos(4n*(phi1-phi2))>\r
 \r
 if(dMult>1)\r
 {\r
  two1n1n = (pow(dReQ1n,2.)+pow(dImQ1n,2.)-dMult)/(dMult*(dMult-1.)); \r
  two2n2n = (pow(dReQ2n,2.)+pow(dImQ2n,2.)-dMult)/(dMult*(dMult-1.)); \r
  two3n3n = (pow(dReQ3n,2.)+pow(dImQ3n,2.)-dMult)/(dMult*(dMult-1.)); \r
  two4n4n = (pow(dReQ4n,2.)+pow(dImQ4n,2.)-dMult)/(dMult*(dMult-1.)); \r
  \r
  // average 2-particle correlations for single event: \r
  fIntFlowCorrelationsAllEBE->SetBinContent(1,two1n1n);\r
  fIntFlowCorrelationsAllEBE->SetBinContent(2,two2n2n);\r
  fIntFlowCorrelationsAllEBE->SetBinContent(3,two3n3n);\r
  fIntFlowCorrelationsAllEBE->SetBinContent(4,two4n4n);\r
          \r
  // average 2-particle correlations for all events:      \r
  fIntFlowCorrelationsAllPro->Fill(0.5,two1n1n,dMult*(dMult-1.));  \r
  fIntFlowCorrelationsAllPro->Fill(1.5,two2n2n,dMult*(dMult-1.)); \r
  fIntFlowCorrelationsAllPro->Fill(2.5,two3n3n,dMult*(dMult-1.)); \r
  fIntFlowCorrelationsAllPro->Fill(3.5,two4n4n,dMult*(dMult-1.)); \r
  \r
  // store separetately <2> (to be improved: do I really need this?)\r
  fIntFlowCorrelationsEBE->SetBinContent(1,two1n1n); // <2>\r
  \r
  // to be improved (this can be implemented better):\r
  Double_t mWeight2p = 0.;\r
  if(!strcmp(fMultiplicityWeight->Data(),"combinations"))\r
  {\r
   mWeight2p = dMult*(dMult-1.);\r
  } else if(!strcmp(fMultiplicityWeight->Data(),"unit"))\r
    {\r
     mWeight2p = 1.;    \r
    } else if(!strcmp(fMultiplicityWeight->Data(),"multiplicity"))\r
      {\r
       mWeight2p = dMult;           \r
      }\r
            \r
  fIntFlowEventWeightsForCorrelationsEBE->SetBinContent(1,mWeight2p); // eW_<2>\r
  fIntFlowCorrelationsPro->Fill(0.5,two1n1n,mWeight2p);\r
    \r
  // distribution of <cos(n*(phi1-phi2))>:\r
  //f2pDistribution->Fill(two1n1n,dMult*(dMult-1.)); \r
 } // end of if(dMult>1)\r
 \r
 // 3-particle:\r
 Double_t three2n1n1n = 0.; // <cos(n*(2.*phi1-phi2-phi3))>\r
 Double_t three3n2n1n = 0.; // <cos(n*(3.*phi1-2.*phi2-phi3))>\r
 Double_t three4n2n2n = 0.; // <cos(n*(4.*phi1-2.*phi2-2.*phi3))>\r
 Double_t three4n3n1n = 0.; // <cos(n*(4.*phi1-3.*phi2-phi3))>\r
 \r
 if(dMult>2)\r
 {\r
  three2n1n1n = (reQ2nQ1nstarQ1nstar-2.*(pow(dReQ1n,2.)+pow(dImQ1n,2.))\r
              - (pow(dReQ2n,2.)+pow(dImQ2n,2.))+2.*dMult)\r
              / (dMult*(dMult-1.)*(dMult-2.));                     \r
  three3n2n1n = (reQ3nQ2nstarQ1nstar-(pow(dReQ3n,2.)+pow(dImQ3n,2.))\r
              - (pow(dReQ2n,2.)+pow(dImQ2n,2.))\r
              - (pow(dReQ1n,2.)+pow(dImQ1n,2.))+2.*dMult)\r
              / (dMult*(dMult-1.)*(dMult-2.));\r
  three4n2n2n = (reQ4nQ2nstarQ2nstar-2.*(pow(dReQ2n,2.)+pow(dImQ2n,2.))\r
              - (pow(dReQ4n,2.)+pow(dImQ4n,2.))+2.*dMult)\r
              / (dMult*(dMult-1.)*(dMult-2.)); \r
  three4n3n1n = (reQ4nQ3nstarQ1nstar-(pow(dReQ4n,2.)+pow(dImQ4n,2.))\r
              - (pow(dReQ3n,2.)+pow(dImQ3n,2.))\r
              - (pow(dReQ1n,2.)+pow(dImQ1n,2.))+2.*dMult)\r
              / (dMult*(dMult-1.)*(dMult-2.)); \r
              \r
  // average 3-particle correlations for single event: \r
  fIntFlowCorrelationsAllEBE->SetBinContent(6,three2n1n1n);\r
  fIntFlowCorrelationsAllEBE->SetBinContent(7,three3n2n1n);\r
  fIntFlowCorrelationsAllEBE->SetBinContent(8,three4n2n2n);\r
  fIntFlowCorrelationsAllEBE->SetBinContent(9,three4n3n1n);\r
        \r
  // average 3-particle correlations for all events:                \r
  fIntFlowCorrelationsAllPro->Fill(5.5,three2n1n1n,dMult*(dMult-1.)*(dMult-2.)); \r
  fIntFlowCorrelationsAllPro->Fill(6.5,three3n2n1n,dMult*(dMult-1.)*(dMult-2.));\r
  fIntFlowCorrelationsAllPro->Fill(7.5,three4n2n2n,dMult*(dMult-1.)*(dMult-2.)); \r
  fIntFlowCorrelationsAllPro->Fill(8.5,three4n3n1n,dMult*(dMult-1.)*(dMult-2.));    \r
 } // end of if(dMult>2)\r
 \r
 // 4-particle:\r
 Double_t four1n1n1n1n = 0.; // <cos(n*(phi1+phi2-phi3-phi4))>\r
 Double_t four2n2n2n2n = 0.; // <cos(2.*n*(phi1+phi2-phi3-phi4))>\r
 Double_t four2n1n2n1n = 0.; // <cos(n*(2.*phi1+phi2-2.*phi3-phi4))> \r
 Double_t four3n1n1n1n = 0.; // <cos(n*(3.*phi1-phi2-phi3-phi4))> \r
 Double_t four4n2n1n1n = 0.; // <cos(n*(4.*phi1-2.*phi2-phi3-phi4))> \r
 Double_t four3n1n2n2n = 0.; // <cos(n*(3.*phi1+phi2-2.*phi3-2.*phi4))> \r
 Double_t four3n1n3n1n = 0.; // <cos(n*(3.*phi1+phi2-3.*phi3-phi4))>   \r
 \r
 if(dMult>3)\r
 {\r
  four1n1n1n1n = (2.*dMult*(dMult-3.)+pow((pow(dReQ1n,2.)+pow(dImQ1n,2.)),2.)-4.*(dMult-2.)*(pow(dReQ1n,2.)\r
               + pow(dImQ1n,2.))-2.*reQ2nQ1nstarQ1nstar+(pow(dReQ2n,2.)+pow(dImQ2n,2.)))\r
               / (dMult*(dMult-1)*(dMult-2.)*(dMult-3.));     \r
  four2n2n2n2n = (2.*dMult*(dMult-3.)+pow((pow(dReQ2n,2.)+pow(dImQ2n,2.)),2.)-4.*(dMult-2.)*(pow(dReQ2n,2.)\r
               + pow(dImQ2n,2.))-2.*reQ4nQ2nstarQ2nstar+(pow(dReQ4n,2.)+pow(dImQ4n,2.)))\r
               / (dMult*(dMult-1)*(dMult-2.)*(dMult-3.));\r
  four2n1n2n1n = (dQ2nQ1nQ2nstarQ1nstar-2.*reQ3nQ2nstarQ1nstar-2.*reQ2nQ1nstarQ1nstar)\r
               / (dMult*(dMult-1.)*(dMult-2.)*(dMult-3.))\r
               - ((dMult-5.)*(pow(dReQ1n,2.)+pow(dImQ1n,2.))\r
               + (dMult-4.)*(pow(dReQ2n,2.)+pow(dImQ2n,2.))-(pow(dReQ3n,2.)+pow(dImQ3n,2.)))\r
               / (dMult*(dMult-1.)*(dMult-2.)*(dMult-3.))\r
               + (dMult-6.)/((dMult-1.)*(dMult-2.)*(dMult-3.));\r
  four3n1n1n1n = (reQ3nQ1nstarQ1nstarQ1nstar-3.*reQ3nQ2nstarQ1nstar-3.*reQ2nQ1nstarQ1nstar)\r
               / (dMult*(dMult-1.)*(dMult-2.)*(dMult-3.))\r
               + (2.*(pow(dReQ3n,2.)+pow(dImQ3n,2.))+3.*(pow(dReQ2n,2.)+pow(dImQ2n,2.))\r
               + 6.*(pow(dReQ1n,2.)+pow(dImQ1n,2.))-6.*dMult)\r
               / (dMult*(dMult-1.)*(dMult-2.)*(dMult-3.));\r
  four4n2n1n1n = (reQ4nQ2nstarQ1nstarQ1nstar-2.*reQ4nQ3nstarQ1nstar-reQ4nQ2nstarQ2nstar-2.*reQ3nQ2nstarQ1nstar)\r
               / (dMult*(dMult-1.)*(dMult-2.)*(dMult-3.))\r
               - (reQ2nQ1nstarQ1nstar-2.*(pow(dReQ4n,2.)+pow(dImQ4n,2.))-2.*(pow(dReQ3n,2.)+pow(dImQ3n,2.))\r
               - 3.*(pow(dReQ2n,2.)+pow(dImQ2n,2.))-4.*(pow(dReQ1n,2.)+pow(dImQ1n,2.)))\r
               / (dMult*(dMult-1.)*(dMult-2.)*(dMult-3.))\r
               - 6./((dMult-1.)*(dMult-2.)*(dMult-3.));\r
  four3n1n2n2n = (reQ3nQ1nQ2nstarQ2nstar-reQ4nQ2nstarQ2nstar-reQ3nQ1nQ4nstar-2.*reQ3nQ2nstarQ1nstar)\r
               / (dMult*(dMult-1.)*(dMult-2.)*(dMult-3.))\r
               - (2.*reQ1nQ1nQ2nstar-(pow(dReQ4n,2.)+pow(dImQ4n,2.))-2.*(pow(dReQ3n,2.)+pow(dImQ3n,2.))\r
               - 4.*(pow(dReQ2n,2.)+pow(dImQ2n,2.))-4.*(pow(dReQ1n,2.)+pow(dImQ1n,2.)))\r
               / (dMult*(dMult-1.)*(dMult-2.)*(dMult-3.))\r
               - 6./((dMult-1.)*(dMult-2.)*(dMult-3.)); \r
  four3n1n3n1n = ((pow(dReQ3n,2.)+pow(dImQ3n,2.))*(pow(dReQ1n,2.)+pow(dImQ1n,2.))\r
               - 2.*reQ4nQ3nstarQ1nstar-2.*reQ3nQ2nstarQ1nstar)\r
               / (dMult*(dMult-1.)*(dMult-2.)*(dMult-3.))\r
               + ((pow(dReQ4n,2.)+pow(dImQ4n,2.))-(dMult-4.)*(pow(dReQ3n,2.)+pow(dImQ3n,2.))\r
               + (pow(dReQ2n,2.)+pow(dImQ2n,2.))-(dMult-4.)*(pow(dReQ1n,2.)+pow(dImQ1n,2.)))\r
               / (dMult*(dMult-1.)*(dMult-2.)*(dMult-3.))\r
               + (dMult-6.)/((dMult-1.)*(dMult-2.)*(dMult-3.));\r
               \r
  // average 4-particle correlations for single event: \r
  fIntFlowCorrelationsAllEBE->SetBinContent(11,four1n1n1n1n);\r
  fIntFlowCorrelationsAllEBE->SetBinContent(12,four2n1n2n1n);\r
  fIntFlowCorrelationsAllEBE->SetBinContent(13,four2n2n2n2n);\r
  fIntFlowCorrelationsAllEBE->SetBinContent(14,four3n1n1n1n);\r
  fIntFlowCorrelationsAllEBE->SetBinContent(15,four3n1n3n1n);\r
  fIntFlowCorrelationsAllEBE->SetBinContent(16,four3n1n2n2n);\r
  fIntFlowCorrelationsAllEBE->SetBinContent(17,four4n2n1n1n);\r
        \r
  // average 4-particle correlations for all events:                \r
  fIntFlowCorrelationsAllPro->Fill(10.5,four1n1n1n1n,dMult*(dMult-1.)*(dMult-2.)*(dMult-3.));\r
  fIntFlowCorrelationsAllPro->Fill(11.5,four2n1n2n1n,dMult*(dMult-1.)*(dMult-2.)*(dMult-3.));\r
  fIntFlowCorrelationsAllPro->Fill(12.5,four2n2n2n2n,dMult*(dMult-1.)*(dMult-2.)*(dMult-3.));\r
  fIntFlowCorrelationsAllPro->Fill(13.5,four3n1n1n1n,dMult*(dMult-1.)*(dMult-2.)*(dMult-3.));\r
  fIntFlowCorrelationsAllPro->Fill(14.5,four3n1n3n1n,dMult*(dMult-1.)*(dMult-2.)*(dMult-3.));\r
  fIntFlowCorrelationsAllPro->Fill(15.5,four3n1n2n2n,dMult*(dMult-1.)*(dMult-2.)*(dMult-3.));  \r
  fIntFlowCorrelationsAllPro->Fill(16.5,four4n2n1n1n,dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)); \r
  \r
  // store separetately <4> (to be improved: do I really need this?)\r
  fIntFlowCorrelationsEBE->SetBinContent(2,four1n1n1n1n); // <4>\r
  \r
  // to be improved (this can be implemented better):\r
  Double_t mWeight4p = 0.;\r
  if(!strcmp(fMultiplicityWeight->Data(),"combinations"))\r
  {\r
   mWeight4p = dMult*(dMult-1.)*(dMult-2.)*(dMult-3.);\r
  } else if(!strcmp(fMultiplicityWeight->Data(),"unit"))\r
    {\r
     mWeight4p = 1.;    \r
    } else if(!strcmp(fMultiplicityWeight->Data(),"multiplicity"))\r
      {\r
       mWeight4p = dMult;           \r
      }\r
      \r
  fIntFlowEventWeightsForCorrelationsEBE->SetBinContent(2,mWeight4p); // eW_<4>\r
  fIntFlowCorrelationsPro->Fill(1.5,four1n1n1n1n,mWeight4p);\r
  \r
  // distribution of <cos(n*(phi1+phi2-phi3-phi4))>\r
  //f4pDistribution->Fill(four1n1n1n1n,dMult*(dMult-1.)*(dMult-2.)*(dMult-3.));\r
  \r
 } // end of if(dMult>3)\r
\r
 // 5-particle:\r
 Double_t five2n1n1n1n1n = 0.; // <cos(n*(2.*phi1+phi2-phi3-phi4-phi5))>\r
 Double_t five2n2n2n1n1n = 0.; // <cos(n*(2.*phi1+2.*phi2-2.*phi3-phi4-phi5))>\r
 Double_t five3n1n2n1n1n = 0.; // <cos(n*(3.*phi1+phi2-2.*phi3-phi4-phi5))>\r
 Double_t five4n1n1n1n1n = 0.; // <cos(n*(4.*phi1-phi2-phi3-phi4-phi5))>\r
 \r
 if(dMult>4)\r
 {\r
  five2n1n1n1n1n = (reQ2nQ1nQ1nstarQ1nstarQ1nstar-reQ3nQ1nstarQ1nstarQ1nstar+6.*reQ3nQ2nstarQ1nstar)\r
                 / (dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.))\r
                 - (reQ2nQ1nQ3nstar+3.*(dMult-6.)*reQ2nQ1nstarQ1nstar+3.*reQ1nQ1nQ2nstar)\r
                 / (dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.))\r
                 - (2.*(pow(dReQ3n,2.)+pow(dImQ3n,2.))\r
                 + 3.*(pow(dReQ1n,2.)+pow(dImQ1n,2.))*(pow(dReQ2n,2.)+pow(dImQ2n,2.))     \r
                 - 3.*(dMult-4.)*(pow(dReQ2n,2.)+pow(dImQ2n,2.)))\r
                 / (dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.))\r
                 - 3.*(pow((pow(dReQ1n,2.)+pow(dImQ1n,2.)),2.)\r
                 - 2.*(2*dMult-5.)*(pow(dReQ1n,2.)+pow(dImQ1n,2.))+2.*dMult*(dMult-4.))\r
                 / (dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.));\r
                 \r
  five2n2n2n1n1n = (reQ2nQ2nQ2nstarQ1nstarQ1nstar-reQ4nQ2nstarQ1nstarQ1nstar-2.*reQ2nQ2nQ3nstarQ1nstar)\r
                 / (dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.))\r
                 + 2.*(reQ4nQ2nstarQ2nstar+4.*reQ3nQ2nstarQ1nstar+reQ3nQ1nQ4nstar)\r
                 / (dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.))\r
                 + (reQ2nQ2nQ4nstar-2.*(dMult-5.)*reQ2nQ1nstarQ1nstar+2.*reQ1nQ1nQ2nstar)\r
                 / (dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.))\r
                 - (2.*(pow(dReQ4n,2.)+pow(dImQ4n,2.))+4.*(pow(dReQ3n,2.)+pow(dImQ3n,2.))\r
                 + 1.*pow((pow(dReQ2n,2.)+pow(dImQ2n,2.)),2.)\r
                 - 2.*(3.*dMult-10.)*(pow(dReQ2n,2.)+pow(dImQ2n,2.)))\r
                 / (dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.))\r
                 - (4.*(pow(dReQ1n,2.)+pow(dImQ1n,2.))*(pow(dReQ2n,2.)+pow(dImQ2n,2.))\r
                 - 4.*(dMult-5.)*(pow(dReQ1n,2.)+pow(dImQ1n,2.))+4.*dMult*(dMult-6.))\r
                 / (dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.)); \r
\r
  five4n1n1n1n1n = (reQ4nQ1nstarQ1nstarQ1nstarQ1nstar-6.*reQ4nQ2nstarQ1nstarQ1nstar-4.*reQ3nQ1nstarQ1nstarQ1nstar)\r
                 / (dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.))\r
                 + (8.*reQ4nQ3nstarQ1nstar+3.*reQ4nQ2nstarQ2nstar+12.*reQ3nQ2nstarQ1nstar+12.*reQ2nQ1nstarQ1nstar)\r
                 / (dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.))\r
                 - (6.*(pow(dReQ4n,2.)+pow(dImQ4n,2.))+8.*(pow(dReQ3n,2.)+pow(dImQ3n,2.))\r
                 + 12.*(pow(dReQ2n,2.)+pow(dImQ2n,2.))+24.*(pow(dReQ1n,2.)+pow(dImQ1n,2.))-24.*dMult)\r
                 / (dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.));\r
  \r
  five3n1n2n1n1n = (reQ3nQ1nQ2nstarQ1nstarQ1nstar-reQ4nQ2nstarQ1nstarQ1nstar-reQ3nQ1nstarQ1nstarQ1nstar)\r
                 / (dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.))\r
                 - (reQ3nQ1nQ2nstarQ2nstar-3.*reQ4nQ3nstarQ1nstar-reQ4nQ2nstarQ2nstar)\r
                 / (dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.))\r
                 - ((2.*dMult-13.)*reQ3nQ2nstarQ1nstar-reQ3nQ1nQ4nstar-9.*reQ2nQ1nstarQ1nstar)\r
                 / (dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.))\r
                 - (2.*reQ1nQ1nQ2nstar+2.*(pow(dReQ4n,2.)+pow(dImQ4n,2.))\r
                 - 2.*(dMult-5.)*(pow(dReQ3n,2.)+pow(dImQ3n,2.))+2.*(pow(dReQ3n,2.)\r
                 + pow(dImQ3n,2.))*(pow(dReQ1n,2.)+pow(dImQ1n,2.)))\r
                 / (dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.))\r
                 + (2.*(dMult-6.)*(pow(dReQ2n,2.)+pow(dImQ2n,2.))\r
                 - 2.*(pow(dReQ2n,2.)+pow(dImQ2n,2.))*(pow(dReQ1n,2.)+pow(dImQ1n,2.))\r
                 - pow((pow(dReQ1n,2.)+pow(dImQ1n,2.)),2.)\r
                 + 2.*(3.*dMult-11.)*(pow(dReQ1n,2.)+pow(dImQ1n,2.)))\r
                 / (dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.))\r
                 - 4.*(dMult-6.)/((dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.));\r
                 \r
  // average 5-particle correlations for single event: \r
  fIntFlowCorrelationsAllEBE->SetBinContent(19,five2n1n1n1n1n);\r
  fIntFlowCorrelationsAllEBE->SetBinContent(20,five2n2n2n1n1n);\r
  fIntFlowCorrelationsAllEBE->SetBinContent(21,five3n1n2n1n1n);\r
  fIntFlowCorrelationsAllEBE->SetBinContent(22,five4n1n1n1n1n);\r
        \r
  // average 5-particle correlations for all events:                         \r
  fIntFlowCorrelationsAllPro->Fill(18.5,five2n1n1n1n1n,dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.)); \r
  fIntFlowCorrelationsAllPro->Fill(19.5,five2n2n2n1n1n,dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.));\r
  fIntFlowCorrelationsAllPro->Fill(20.5,five3n1n2n1n1n,dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.));\r
  fIntFlowCorrelationsAllPro->Fill(21.5,five4n1n1n1n1n,dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.));\r
 } // end of if(dMult>4)\r
    \r
 // 6-particle:\r
 Double_t six1n1n1n1n1n1n = 0.; // <cos(n*(phi1+phi2+phi3-phi4-phi5-phi6))>\r
 Double_t six2n2n1n1n1n1n = 0.; // <cos(n*(2.*phi1+2.*phi2-phi3-phi4-phi5-phi6))>\r
 Double_t six3n1n1n1n1n1n = 0.; // <cos(n*(3.*phi1+phi2-phi3-phi4-phi5-phi6))>\r
 Double_t six2n1n1n2n1n1n = 0.; // <cos(n*(2.*phi1+phi2+phi3-2.*phi4-phi5-phi6))>\r
 \r
 if(dMult>5)\r
 {\r
  six1n1n1n1n1n1n = (pow(pow(dReQ1n,2.)+pow(dImQ1n,2.),3.)+9.*dQ2nQ1nQ2nstarQ1nstar-6.*reQ2nQ1nQ1nstarQ1nstarQ1nstar)\r
                  / (dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.)*(dMult-5.))\r
                  + 4.*(reQ3nQ1nstarQ1nstarQ1nstar-3.*reQ3nQ2nstarQ1nstar)\r
                  / (dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.)*(dMult-5.))\r
                  + 2.*(9.*(dMult-4.)*reQ2nQ1nstarQ1nstar+2.*(pow(dReQ3n,2.)+pow(dImQ3n,2.)))\r
                  / (dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.)*(dMult-5.))\r
                  - 9.*(pow((pow(dReQ1n,2.)+pow(dImQ1n,2.)),2.)+(pow(dReQ2n,2.)+pow(dImQ2n,2.)))\r
                  / (dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-5.))\r
                  + (18.*(pow(dReQ1n,2.)+pow(dImQ1n,2.)))\r
                  / (dMult*(dMult-1)*(dMult-3)*(dMult-4))\r
                  - 6./((dMult-1.)*(dMult-2.)*(dMult-3.));\r
                  \r
  six2n1n1n2n1n1n = (dQ2nQ1nQ1nQ2nstarQ1nstarQ1nstar-dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.)\r
                  * (2.*five2n2n2n1n1n+4.*five2n1n1n1n1n+4.*five3n1n2n1n1n+4.*four2n1n2n1n+1.*four1n1n1n1n)\r
                  - dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(4.*four1n1n1n1n+4.*two1n1n\r
                  + 2.*three2n1n1n+2.*three2n1n1n+4.*four3n1n1n1n+8.*three2n1n1n+2.*four4n2n1n1n\r
                  + 4.*four2n1n2n1n+2.*two2n2n+8.*four2n1n2n1n+4.*four3n1n3n1n+8.*three3n2n1n\r
                  + 4.*four3n1n2n2n+4.*four1n1n1n1n+4.*four2n1n2n1n+1.*four2n2n2n2n)\r
                  - dMult*(dMult-1.)*(dMult-2.)*(2.*three2n1n1n+8.*two1n1n+4.*two1n1n+2.\r
                  + 4.*two1n1n+4.*three2n1n1n+2.*two2n2n+4.*three2n1n1n+8.*three3n2n1n\r
                  + 8.*two2n2n+4.*three4n3n1n+4.*two3n3n+4.*three3n2n1n+4.*two1n1n\r
                  + 8.*three2n1n1n+4.*two1n1n+4.*three3n2n1n+4.*three2n1n1n+2.*two2n2n\r
                  + 4.*three3n2n1n+2.*three4n2n2n)-dMult*(dMult-1.)\r
                  * (4.*two1n1n+4.+4.*two1n1n+2.*two2n2n+1.+4.*two1n1n+4.*two2n2n+4.*two3n3n\r
                  + 1.+2.*two2n2n+1.*two4n4n)-dMult)\r
                  / (dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.)*(dMult-5.)); // to be improved (direct formula needed)\r
 \r
  six2n2n1n1n1n1n = (reQ2nQ2nQ1nstarQ1nstarQ1nstarQ1nstar-dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.)\r
                  * (five4n1n1n1n1n+8.*five2n1n1n1n1n+6.*five2n2n2n1n1n)-dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)\r
                  * (4.*four3n1n1n1n+6.*four4n2n1n1n+12.*three2n1n1n+12.*four1n1n1n1n+24.*four2n1n2n1n\r
                  + 4.*four3n1n2n2n+3.*four2n2n2n2n)-dMult*(dMult-1.)*(dMult-2.)*(6.*three2n1n1n+12.*three3n2n1n\r
                  + 4.*three4n3n1n+3.*three4n2n2n+8.*three2n1n1n+24.*two1n1n+12.*two2n2n+12.*three2n1n1n+8.*three3n2n1n\r
                  + 1.*three4n2n2n)-dMult*(dMult-1.)*(4.*two1n1n+6.*two2n2n+4.*two3n3n+1.*two4n4n+2.*two2n2n+8.*two1n1n+6.)-dMult)\r
                  / (dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.)*(dMult-5.)); // to be improved (direct formula needed)\r
   \r
  six3n1n1n1n1n1n = (reQ3nQ1nQ1nstarQ1nstarQ1nstarQ1nstar-dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.)\r
                  * (five4n1n1n1n1n+4.*five2n1n1n1n1n+6.*five3n1n2n1n1n+4.*four3n1n1n1n)\r
                  - dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(4.*four3n1n1n1n+6.*four4n2n1n1n+6.*four1n1n1n1n\r
                  + 12.*three2n1n1n+12.*four2n1n2n1n+6.*four3n1n1n1n+12.*three3n2n1n+4.*four3n1n3n1n+3.*four3n1n2n2n)\r
                  - dMult*(dMult-1.)*(dMult-2.)*(6.*three2n1n1n+12.*three3n2n1n+4.*three4n3n1n+3.*three4n2n2n+4.*two1n1n\r
                  + 12.*two1n1n+6.*three2n1n1n+12.*three2n1n1n+4.*three3n2n1n+12.*two2n2n+4.*three3n2n1n+4.*two3n3n+1.*three4n3n1n\r
                  + 6.*three3n2n1n)-dMult*(dMult-1.)*(4.*two1n1n+6.*two2n2n+4.*two3n3n+1.*two4n4n+1.*two1n1n+4.+6.*two1n1n+4.*two2n2n\r
                  + 1.*two3n3n)-dMult)/(dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.)*(dMult-5.)); // to be improved (direct formula needed)\r
                                 \r
  // average 6-particle correlations for single event: \r
  fIntFlowCorrelationsAllEBE->SetBinContent(24,six1n1n1n1n1n1n);\r
  fIntFlowCorrelationsAllEBE->SetBinContent(25,six2n1n1n2n1n1n);\r
  fIntFlowCorrelationsAllEBE->SetBinContent(26,six2n2n1n1n1n1n);\r
  fIntFlowCorrelationsAllEBE->SetBinContent(27,six3n1n1n1n1n1n);\r
        \r
  // average 6-particle correlations for all events:         \r
  fIntFlowCorrelationsAllPro->Fill(23.5,six1n1n1n1n1n1n,dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.)*(dMult-5.)); \r
  fIntFlowCorrelationsAllPro->Fill(24.5,six2n1n1n2n1n1n,dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.)*(dMult-5.)); \r
  fIntFlowCorrelationsAllPro->Fill(25.5,six2n2n1n1n1n1n,dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.)*(dMult-5.));\r
  fIntFlowCorrelationsAllPro->Fill(26.5,six3n1n1n1n1n1n,dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.)*(dMult-5.)); \r
\r
  // store separetately <6> (to be improved: do I really need this?)\r
  fIntFlowCorrelationsEBE->SetBinContent(3,six1n1n1n1n1n1n); // <6>\r
  \r
  // to be improved (this can be implemented better):\r
  Double_t mWeight6p = 0.;\r
  if(!strcmp(fMultiplicityWeight->Data(),"combinations"))\r
  {\r
   mWeight6p = dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.)*(dMult-5.);\r
  } else if(!strcmp(fMultiplicityWeight->Data(),"unit"))\r
    {\r
     mWeight6p = 1.;    \r
    } else if(!strcmp(fMultiplicityWeight->Data(),"multiplicity"))\r
      {\r
       mWeight6p = dMult;           \r
      }\r
      \r
  fIntFlowEventWeightsForCorrelationsEBE->SetBinContent(3,mWeight6p); // eW_<6>\r
  fIntFlowCorrelationsPro->Fill(2.5,six1n1n1n1n1n1n,mWeight6p);\r
 \r
  // distribution of <cos(n*(phi1+phi2+phi3-phi4-phi5-phi6))>\r
  //f6pDistribution->Fill(six1n1n1n1n1n1n,dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.)*(dMult-5.)); \r
 } // end of if(dMult>5)\r
 \r
 // 7-particle:\r
 Double_t seven2n1n1n1n1n1n1n = 0.; // <cos(n*(2.*phi1+phi2+phi3-phi4-phi5-phi6-phi7))>\r
 \r
 if(dMult>6)\r
 {\r
  seven2n1n1n1n1n1n1n = (reQ2nQ1nQ1nQ1nstarQ1nstarQ1nstarQ1nstar-dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.)*(dMult-5.)\r
                      * (2.*six3n1n1n1n1n1n+4.*six1n1n1n1n1n1n+1.*six2n2n1n1n1n1n+6.*six2n1n1n2n1n1n+8.*five2n1n1n1n1n)\r
                      - dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.)*(1.*five4n1n1n1n1n +8.*five2n1n1n1n1n+8.*four3n1n1n1n\r
                      + 12.*five3n1n2n1n1n+4.*five2n1n1n1n1n+3.*five2n2n2n1n1n+6.*five2n2n2n1n1n+6.*four1n1n1n1n+24.*four1n1n1n1n\r
                      + 12.*five2n1n1n1n1n+12.*five2n1n1n1n1n+12.*three2n1n1n+24.*four2n1n2n1n+4.*five3n1n2n1n1n+4.*five2n1n1n1n1n)\r
                      - dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(4.*four3n1n1n1n+6.*four4n2n1n1n+12.*four1n1n1n1n+24.*three2n1n1n\r
                      + 24.*four2n1n2n1n+12.*four3n1n1n1n+24.*three3n2n1n+8.*four3n1n3n1n+6.*four3n1n2n2n+6.*three2n1n1n+12.*four1n1n1n1n\r
                      + 12.*four2n1n2n1n+6.*three2n1n1n+12.*four2n1n2n1n+4.*four3n1n2n2n+3.*four2n2n2n2n+4.*four1n1n1n1n+6.*three2n1n1n\r
                      + 24.*two1n1n+24.*four1n1n1n1n+4.*four3n1n1n1n+24.*two1n1n+24.*three2n1n1n+12.*two2n2n+24.*three2n1n1n+12.*four2n1n2n1n\r
                      + 8.*three3n2n1n+8.*four2n1n2n1n+1.*four4n2n1n1n)-dMult*(dMult-1.)*(dMult-2.)*(6.*three2n1n1n+1.*three2n1n1n+8.*two1n1n\r
                      + 12.*three3n2n1n+24.*two1n1n+12.*three2n1n1n+4.*three2n1n1n+8.*two1n1n+4.*three4n3n1n+24.*three2n1n1n+8.*three3n2n1n\r
                      + 12.*two1n1n+12.*two1n1n+3.*three4n2n2n+24.*two2n2n+6.*two2n2n+12.+12.*three3n2n1n+8.*two3n3n+12.*three2n1n1n+24.*two1n1n\r
                      + 4.*three3n2n1n+8.*three3n2n1n+2.*three4n3n1n+12.*two1n1n+8.*three2n1n1n+4.*three2n1n1n+2.*three3n2n1n+6.*two2n2n+8.*two2n2n\r
                      + 1.*three4n2n2n+4.*three3n2n1n+6.*three2n1n1n)-dMult*(dMult-1.)*(4.*two1n1n+2.*two1n1n+6.*two2n2n+8.+1.*two2n2n+4.*two3n3n\r
                      + 12.*two1n1n+4.*two1n1n+1.*two4n4n+8.*two2n2n+6.+2.*two3n3n+4.*two1n1n+1.*two2n2n)-dMult)\r
                      / (dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.)*(dMult-5.)*(dMult-6.)); // to be improved (direct formula needed)\r
        \r
  // average 7-particle correlations for single event: \r
  fIntFlowCorrelationsAllEBE->SetBinContent(29,seven2n1n1n1n1n1n1n);\r
       \r
  // average 7-particle correlations for all events:                      \r
  fIntFlowCorrelationsAllPro->Fill(28.5,seven2n1n1n1n1n1n1n,dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.)*(dMult-5.)*(dMult-6.));\r
 } // end of if(dMult>6)\r
 \r
 // 8-particle:\r
 Double_t eight1n1n1n1n1n1n1n1n = 0.; // <cos(n*(phi1+phi2+phi3+phi4-phi5-phi6-phi7-phi8))>\r
 if(dMult>7)\r
 {\r
  eight1n1n1n1n1n1n1n1n = (pow(pow(dReQ1n,2.)+pow(dImQ1n,2.),4.)-dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.)*(dMult-5.)*(dMult-6.)\r
                        * (12.*seven2n1n1n1n1n1n1n+16.*six1n1n1n1n1n1n)-dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.)*(dMult-5.)\r
                        * (8.*six3n1n1n1n1n1n+48.*six1n1n1n1n1n1n+6.*six2n2n1n1n1n1n+96.*five2n1n1n1n1n+72.*four1n1n1n1n+36.*six2n1n1n2n1n1n)\r
                        - dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.)*(2.*five4n1n1n1n1n+32.*five2n1n1n1n1n+36.*four1n1n1n1n\r
                        + 32.*four3n1n1n1n+48.*five2n1n1n1n1n+48.*five3n1n2n1n1n+144.*five2n1n1n1n1n+288.*four1n1n1n1n+36.*five2n2n2n1n1n\r
                        + 144.*three2n1n1n+96.*two1n1n+144.*four2n1n2n1n)-dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)\r
                        * (8.*four3n1n1n1n+48.*four1n1n1n1n+12.*four4n2n1n1n+96.*four2n1n2n1n+96.*three2n1n1n+72.*three2n1n1n+144.*two1n1n\r
                        + 16.*four3n1n3n1n+48.*four3n1n1n1n+144.*four1n1n1n1n+72.*four1n1n1n1n+96.*three3n2n1n+24.*four3n1n2n2n+144.*four2n1n2n1n\r
                        + 288.*two1n1n+288.*three2n1n1n+9.*four2n2n2n2n+72.*two2n2n+24.)-dMult*(dMult-1.)*(dMult-2.)*(12.*three2n1n1n+16.*two1n1n\r
                        + 24.*three3n2n1n+48.*three2n1n1n+96.*two1n1n+8.*three4n3n1n+32.*three3n2n1n+96.*three2n1n1n+144.*two1n1n+6.*three4n2n2n\r
                        + 96.*two2n2n+36.*two2n2n+72.+48.*three3n2n1n+16.*two3n3n+72.*three2n1n1n+144.*two1n1n)-dMult*(dMult-1.)*(8.*two1n1n\r
                        + 12.*two2n2n+16.+8.*two3n3n+48.*two1n1n+1.*two4n4n+16.*two2n2n+18.)-dMult)\r
                        / (dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.)*(dMult-5.)*(dMult-6.)*(dMult-7.)); // to be improved (direct formula needed)\r
  \r
  // average 8-particle correlations for single event: \r
  fIntFlowCorrelationsAllEBE->SetBinContent(31,eight1n1n1n1n1n1n1n1n);\r
       \r
  // average 8-particle correlations for all events:                       \r
  fIntFlowCorrelationsAllPro->Fill(30.5,eight1n1n1n1n1n1n1n1n,dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.)*(dMult-5.)*(dMult-6.)*(dMult-7.));\r
 \r
  // store separetately <8> (to be improved: do I really need this?)\r
  fIntFlowCorrelationsEBE->SetBinContent(4,eight1n1n1n1n1n1n1n1n); // <8>\r
  \r
  // to be improved (this can be implemented better):\r
  Double_t mWeight8p = 0.;\r
  if(!strcmp(fMultiplicityWeight->Data(),"combinations"))\r
  {\r
   mWeight8p = dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.)*(dMult-5.)*(dMult-6.)*(dMult-7.);\r
  } else if(!strcmp(fMultiplicityWeight->Data(),"unit"))\r
    {\r
     mWeight8p = 1.;    \r
    } else if(!strcmp(fMultiplicityWeight->Data(),"multiplicity"))\r
      {\r
       mWeight8p = dMult;           \r
      }\r
        \r
  fIntFlowEventWeightsForCorrelationsEBE->SetBinContent(4,mWeight8p); // eW_<8>\r
  fIntFlowCorrelationsPro->Fill(3.5,eight1n1n1n1n1n1n1n1n,mWeight8p);  \r
  \r
  // distribution of <cos(n*(phi1+phi2+phi3+phi4-phi5-phi6-phi7-phi8))>\r
  //f8pDistribution->Fill(eight1n1n1n1n1n1n1n1n,dMult*(dMult-1.)*(dMult-2.)*(dMult-3.)*(dMult-4.)*(dMult-5.)*(dMult-6.)*(dMult-7.));\r
 } // end of if(dMult>7) \r
 \r
} // end of AliFlowAnalysisWithQCumulants::CalculateIntFlowCorrelations()\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::CalculateIntFlowProductOfCorrelations()\r
{\r
 // Calculate averages of products of correlations for integrated flow  // to be improved (this method can be implemented better)\r
 \r
 // a) Binning of fIntFlowProductOfCorrelationsPro is organized as follows:\r
 //     1st bin: <<2><4>> \r
 //     2nd bin: <<2><6>>\r
 //     3rd bin: <<2><8>>\r
 //     4th bin: <<4><6>>\r
 //     5th bin: <<4><8>>\r
 //     6th bin: <<6><8>>\r
\r
 /*\r
 Double_t dMult = (*fSMpk)(0,0); // multiplicity \r
\r
 Double_t twoEBE = fIntFlowCorrelationsEBE->GetBinContent(1); // <2>\r
 Double_t fourEBE = fIntFlowCorrelationsEBE->GetBinContent(2); // <4>\r
 Double_t sixEBE = fIntFlowCorrelationsEBE->GetBinContent(3); // <6>\r
 Double_t eightEBE = fIntFlowCorrelationsEBE->GetBinContent(4); // <8>\r
 \r
 Double_t eW2 = 0.; // event weight for <2>\r
 Double_t eW4 = 0.; // event weight for <4>\r
 Double_t eW6 = 0.; // event weight for <6>\r
 Double_t eW8 = 0.; // event weight for <8>\r
 \r
 if(!(fUsePhiWeights||fUsePtWeights||fUseEtaWeights))\r
 {\r
  eW2 = dMult*(dMult-1);\r
  eW4 = dMult*(dMult-1)*(dMult-2)*(dMult-3);\r
  eW6 = dMult*(dMult-1)*(dMult-2)*(dMult-3)*(dMult-4)*(dMult-5);\r
  eW8 = dMult*(dMult-1)*(dMult-2)*(dMult-3)*(dMult-4)*(dMult-5)*(dMult-6)*(dMult-7);\r
 } else \r
   {\r
    eW2 = (*fSMpk)(1,1)-(*fSMpk)(0,2); // dM11 = sum_{i,j=1,i!=j}^M w_i w_j;\r
    eW4 = (*fSMpk)(3,1)-6.*(*fSMpk)(0,2)*(*fSMpk)(1,1)  \r
        + 8.*(*fSMpk)(0,3)*(*fSMpk)(0,1)\r
        + 3.*(*fSMpk)(1,2)-6.*(*fSMpk)(0,4); // dM1111 = sum_{i,j,k,l=1,i!=j!=k!=l}^M w_i w_j w_k w_l\r
   }\r
  \r
 fIntFlowProductOfCorrelationsPro->Fill(0.5,twoEBE*fourEBE,eW2*eW4); // <<2><4>> \r
 fIntFlowProductOfCorrelationsPro->Fill(1.5,twoEBE*sixEBE,eW2*eW6); // <<2><6>>\r
 fIntFlowProductOfCorrelationsPro->Fill(2.5,twoEBE*eightEBE,eW2*eW8); // <<2><8>>\r
 fIntFlowProductOfCorrelationsPro->Fill(3.5,fourEBE*sixEBE,eW4*eW6); // <<4><6>>\r
 fIntFlowProductOfCorrelationsPro->Fill(4.5,fourEBE*eightEBE,eW4*eW8); // <<4><8>>\r
 fIntFlowProductOfCorrelationsPro->Fill(5.5,sixEBE*eightEBE,eW6*eW8); // <<6><8>>\r
 */\r
 \r
 \r
 Int_t counter = 0;\r
 \r
 for(Int_t ci1=1;ci1<4;ci1++)\r
 {\r
  for(Int_t ci2=ci1+1;ci2<=4;ci2++)\r
  {\r
   fIntFlowProductOfCorrelationsPro->Fill(0.5+counter++,\r
                                          fIntFlowCorrelationsEBE->GetBinContent(ci1)*fIntFlowCorrelationsEBE->GetBinContent(ci2),\r
                                          fIntFlowEventWeightsForCorrelationsEBE->GetBinContent(ci1)*fIntFlowEventWeightsForCorrelationsEBE->GetBinContent(ci2));\r
  }\r
 }\r
 \r
} // end of AliFlowAnalysisWithQCumulants::CalculateIntFlowProductOfCorrelations()\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::CalculateCovariancesIntFlow()\r
{\r
 // a) Calculate unbiased estimators Cov(<2>,<4>), Cov(<2>,<6>), Cov(<2>,<8>), Cov(<4>,<6>), Cov(<4>,<8>) and Cov(<6>,<8>)\r
 //    for covariances V_(<2>,<4>), V_(<2>,<6>), V_(<2>,<8>), V_(<4>,<6>), V_(<4>,<8>) and V_(<6>,<8>).\r
 // b) Store in histogram fIntFlowCovariances for instance the following: \r
 //\r
 //             Cov(<2>,<4>) * (sum_{i=1}^{N} w_{<2>}_i w_{<4>}_i )/[(sum_{i=1}^{N} w_{<2>}_i) * (sum_{j=1}^{N} w_{<4>}_j)]\r
 // \r
 //    where N is the number of events, w_{<2>} is event weight for <2> and w_{<4>} is event weight for <4>.\r
 // c) Binning of fIntFlowCovariances is organized as follows:\r
 // \r
 //     1st bin: Cov(<2>,<4>) * (sum_{i=1}^{N} w_{<2>}_i w_{<4>}_i )/[(sum_{i=1}^{N} w_{<2>}_i) * (sum_{j=1}^{N} w_{<4>}_j)] \r
 //     2nd bin: Cov(<2>,<6>) * (sum_{i=1}^{N} w_{<2>}_i w_{<6>}_i )/[(sum_{i=1}^{N} w_{<2>}_i) * (sum_{j=1}^{N} w_{<6>}_j)]\r
 //     3rd bin: Cov(<2>,<8>) * (sum_{i=1}^{N} w_{<2>}_i w_{<8>}_i )/[(sum_{i=1}^{N} w_{<2>}_i) * (sum_{j=1}^{N} w_{<8>}_j)]\r
 //     4th bin: Cov(<4>,<6>) * (sum_{i=1}^{N} w_{<4>}_i w_{<6>}_i )/[(sum_{i=1}^{N} w_{<4>}_i) * (sum_{j=1}^{N} w_{<6>}_j)]\r
 //     5th bin: Cov(<4>,<8>) * (sum_{i=1}^{N} w_{<4>}_i w_{<8>}_i )/[(sum_{i=1}^{N} w_{<4>}_i) * (sum_{j=1}^{N} w_{<8>}_j)]\r
 //     6th bin: Cov(<6>,<8>) * (sum_{i=1}^{N} w_{<6>}_i w_{<8>}_i )/[(sum_{i=1}^{N} w_{<6>}_i) * (sum_{j=1}^{N} w_{<8>}_j)]\r
    \r
 for(Int_t power=0;power<2;power++)\r
 { \r
  if(!(fIntFlowCorrelationsPro && fIntFlowProductOfCorrelationsPro \r
       && fIntFlowSumOfEventWeights[power] && fIntFlowSumOfProductOfEventWeights\r
       && fIntFlowCovariances)) \r
  {\r
   cout<<"WARNING: fIntFlowCorrelationsPro && fIntFlowProductOfCorrelationsPro "<<endl;\r
   cout<<"         && fIntFlowSumOfEventWeights[power] && fIntFlowSumOfProductOfEventWeights"<<endl;\r
   cout<<"         && fIntFlowCovariances is NULL in AFAWQC::FCIF() !!!!"<<endl;\r
   cout<<"power = "<<power<<endl;\r
   exit(0);\r
  }\r
 }\r
   \r
 // average 2-, 4-, 6- and 8-particle correlations for all events:\r
 Double_t correlation[4] = {0.};\r
 for(Int_t ci=0;ci<4;ci++)\r
 {\r
  correlation[ci] = fIntFlowCorrelationsPro->GetBinContent(ci+1);\r
 } \r
 // average products of 2-, 4-, 6- and 8-particle correlations: \r
 Double_t productOfCorrelations[4][4] = {{0.}};\r
 Int_t productOfCorrelationsLabel = 1;\r
 // denominators in the expressions for the unbiased estimator for covariance:\r
 Double_t denominator[4][4] = {{0.}};\r
 Int_t sumOfProductOfEventWeightsLabel1 = 1;\r
 // weight dependent prefactor which multiply unbiased estimators for covariances:\r
 Double_t wPrefactor[4][4] = {{0.}}; \r
 Int_t sumOfProductOfEventWeightsLabel2 = 1;\r
 for(Int_t c1=0;c1<4;c1++)\r
 {\r
  for(Int_t c2=c1+1;c2<4;c2++)\r
  {\r
   productOfCorrelations[c1][c2] = fIntFlowProductOfCorrelationsPro->GetBinContent(productOfCorrelationsLabel);\r
   if(fIntFlowSumOfEventWeights[0]->GetBinContent(c1+1) && fIntFlowSumOfEventWeights[0]->GetBinContent(c2+1))\r
   {\r
    denominator[c1][c2] = 1.-(fIntFlowSumOfProductOfEventWeights->GetBinContent(sumOfProductOfEventWeightsLabel1))/\r
                             (fIntFlowSumOfEventWeights[0]->GetBinContent(c1+1) \r
                              * fIntFlowSumOfEventWeights[0]->GetBinContent(c2+1));\r
                              \r
    wPrefactor[c1][c2] =  fIntFlowSumOfProductOfEventWeights->GetBinContent(sumOfProductOfEventWeightsLabel2)/ \r
                          (fIntFlowSumOfEventWeights[0]->GetBinContent(c1+1)\r
                            * fIntFlowSumOfEventWeights[0]->GetBinContent(c2+1));\r
                          \r
                              \r
   }\r
   productOfCorrelationsLabel++;\r
   sumOfProductOfEventWeightsLabel1++;\r
   sumOfProductOfEventWeightsLabel2++;  \r
  }\r
 }\r
 \r
 // covariance label:\r
 Int_t covarianceLabel = 1;\r
 for(Int_t c1=0;c1<4;c1++)\r
 {\r
  for(Int_t c2=c1+1;c2<4;c2++)\r
  {\r
   if(denominator[c1][c2])\r
   {\r
    // covariances:\r
    Double_t cov = (productOfCorrelations[c1][c2]-correlation[c1]*correlation[c2])/denominator[c1][c2]; \r
    // covarianced multiplied with weight dependent prefactor:\r
    Double_t wCov = cov * wPrefactor[c1][c2];\r
    fIntFlowCovariances->SetBinContent(covarianceLabel,wCov);\r
   }\r
   covarianceLabel++;\r
  }\r
 }\r
 \r
} // end of AliFlowAnalysisWithQCumulants::CalculateCovariancesIntFlow()\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::FinalizeCorrelationsIntFlow() \r
{\r
 // From profile fIntFlowCorrelationsPro access measured correlations and spread, \r
 // correctly calculate the statistical errors and store the final results and \r
 // statistical errors for correlations in histogram fIntFlowCorrelationsHist.\r
 //\r
 // Remark: Statistical error of correlation is calculated as:\r
 //\r
 //          statistical error = termA * spread * termB:\r
 //          termA = sqrt{sum_{i=1}^{N} w^2}/(sum_{i=1}^{N} w)\r
 //          termB = 1/sqrt(1-termA^2)   \r
 \r
 for(Int_t power=0;power<2;power++)\r
 { \r
  if(!(fIntFlowCorrelationsHist && fIntFlowCorrelationsPro && fIntFlowSumOfEventWeights[power])) \r
  {\r
   cout<<"WARNING: fIntFlowCorrelationsHist && fIntFlowCorrelationsPro && fIntFlowSumOfEventWeights[power] is NULL in AFAWQC::FCIF() !!!!"<<endl;\r
   cout<<"power = "<<power<<endl;\r
   exit(0);\r
  }\r
 }\r
  \r
 for(Int_t ci=1;ci<=4;ci++) // correlation index\r
 {\r
  Double_t correlation = fIntFlowCorrelationsPro->GetBinContent(ci);\r
  Double_t spread = fIntFlowCorrelationsPro->GetBinError(ci);\r
  Double_t sumOfLinearEventWeights = fIntFlowSumOfEventWeights[0]->GetBinContent(ci);\r
  Double_t sumOfQuadraticEventWeights = fIntFlowSumOfEventWeights[1]->GetBinContent(ci);\r
  Double_t termA = 0.;\r
  Double_t termB = 0.;\r
  if(sumOfLinearEventWeights)\r
  {\r
   termA = pow(sumOfQuadraticEventWeights,0.5)/sumOfLinearEventWeights;\r
  } else\r
    {\r
     cout<<"WARNING: sumOfLinearEventWeights == 0 in AFAWQC::FCIF() !!!!"<<endl;\r
     cout<<"         (for "<<2*ci<<"-particle correlation)"<<endl;\r
    }\r
  if(1.-pow(termA,2.) > 0.)\r
  {\r
   termB = 1./pow(1-pow(termA,2.),0.5);\r
  } else\r
    {\r
     cout<<"WARNING: 1.-pow(termA,2.) <= 0 in AFAWQC::FCIF() !!!!"<<endl;   \r
     cout<<"         (for "<<2*ci<<"-particle correlation)"<<endl;\r
    }     \r
  Double_t statisticalError = termA * spread * termB;\r
  fIntFlowCorrelationsHist->SetBinContent(ci,correlation);\r
  fIntFlowCorrelationsHist->SetBinError(ci,statisticalError);\r
 } // end of for(Int_t ci=1;ci<=4;ci++) // correlation index                                                                \r
                                                                                                                              \r
} // end of AliFlowAnalysisWithQCumulants::FinalizeCorrelationsIntFlow()\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::FillAverageMultiplicities(Int_t nRP)\r
{\r
 // Fill profile fAverageMultiplicity to hold average multiplicities and number of events for events with nRP>=0, nRP>=1, ... , and nRP>=8\r
 \r
 // Binning of fAverageMultiplicity is organized as follows:\r
 //  1st bin: all events (including the empty ones)\r
 //  2nd bin: event with # of RPs greater or equal to 1\r
 //  3rd bin: event with # of RPs greater or equal to 2\r
 //  4th bin: event with # of RPs greater or equal to 3\r
 //  5th bin: event with # of RPs greater or equal to 4\r
 //  6th bin: event with # of RPs greater or equal to 5\r
 //  7th bin: event with # of RPs greater or equal to 6\r
 //  8th bin: event with # of RPs greater or equal to 7\r
 //  9th bin: event with # of RPs greater or equal to 8\r
 \r
 if(!fAvMultiplicity)\r
 {\r
  cout<<"WARNING: fAvMultiplicity is NULL in AFAWQC::FAM() !!!!"<<endl;\r
  exit(0);\r
 }\r
 \r
 if(nRP<0)\r
 {\r
  cout<<"WARNING: nRP<0 in in AFAWQC::FAM() !!!!"<<endl;\r
  exit(0);\r
 }\r
 \r
 for(Int_t i=0;i<9;i++)\r
 {\r
  if(nRP>=i) fAvMultiplicity->Fill(i+0.5,nRP,1);\r
 }\r
 \r
} // end of AliFlowAnalysisWithQCumulants::FillAverageMultiplicities(nRP)\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::CalculateCumulantsIntFlow()\r
{\r
 // a) Calculate Q-cumulants from the measured multiparticle correlations.\r
 // b) Propagate the statistical errors of measured multiparticle correlations to statistical errors of Q-cumulants.  \r
 // c) REMARK: Q-cumulants calculated in this method are biased by non-uniform acceptance of detector !!!! \r
 //            Method ApplyCorrectionForNonUniformAcceptance* (to be improved: finalize the name here)\r
 //            is called afterwards to correct for this bias.   \r
 // d) Store the results and statistical error of Q-cumulants in histogram fCumulants.\r
 //    Binning of fCumulants is organized as follows:\r
 //\r
 //     1st bin: QC{2}\r
 //     2nd bin: QC{4}\r
 //     3rd bin: QC{6}\r
 //     4th bin: QC{8}\r
 \r
 if(!(fIntFlowCorrelationsHist && fIntFlowCovariances && fIntFlowQcumulants))\r
 {\r
  cout<<"WARNING: fIntFlowCorrelationsHist && fIntFlowCovariances && fIntFlowQcumulants is NULL in AFAWQC::CCIF() !!!!"<<endl;\r
  exit(0);\r
 }\r
 \r
 // correlations:\r
 Double_t two = fIntFlowCorrelationsHist->GetBinContent(1); // <<2>> \r
 Double_t four = fIntFlowCorrelationsHist->GetBinContent(2); // <<4>>  \r
 Double_t six = fIntFlowCorrelationsHist->GetBinContent(3); // <<6>> \r
 Double_t eight = fIntFlowCorrelationsHist->GetBinContent(4); // <<8>>  \r
 \r
 // statistical errors of average 2-, 4-, 6- and 8-particle azimuthal correlations:\r
 Double_t twoError = fIntFlowCorrelationsHist->GetBinError(1); // statistical error of <2>  \r
 Double_t fourError = fIntFlowCorrelationsHist->GetBinError(2); // statistical error of <4>   \r
 Double_t sixError = fIntFlowCorrelationsHist->GetBinError(3); // statistical error of <6> \r
 Double_t eightError = fIntFlowCorrelationsHist->GetBinError(4); // statistical error of <8> \r
 \r
 // covariances (multiplied by prefactor depending on weights - see comments in CalculateCovariancesIntFlow()):\r
 Double_t wCov24 = fIntFlowCovariances->GetBinContent(1); // Cov(<2>,<4>) * prefactor(w_<2>,w_<4>)\r
 Double_t wCov26 = fIntFlowCovariances->GetBinContent(2); // Cov(<2>,<6>) * prefactor(w_<2>,w_<6>)\r
 Double_t wCov28 = fIntFlowCovariances->GetBinContent(3); // Cov(<2>,<8>) * prefactor(w_<2>,w_<8>)\r
 Double_t wCov46 = fIntFlowCovariances->GetBinContent(4); // Cov(<4>,<6>) * prefactor(w_<4>,w_<6>)\r
 Double_t wCov48 = fIntFlowCovariances->GetBinContent(5); // Cov(<4>,<8>) * prefactor(w_<4>,w_<8>)\r
 Double_t wCov68 = fIntFlowCovariances->GetBinContent(6); // Cov(<6>,<8>) * prefactor(w_<6>,w_<8>)\r
 \r
 // Q-cumulants: \r
 Double_t qc2 = 0.; // QC{2}\r
 Double_t qc4 = 0.; // QC{4}\r
 Double_t qc6 = 0.; // QC{6}\r
 Double_t qc8 = 0.; // QC{8}\r
 if(two) qc2 = two; \r
 if(four) qc4 = four-2.*pow(two,2.); \r
 if(six) qc6 = six-9.*two*four+12.*pow(two,3.); \r
 if(eight) qc8 = eight-16.*two*six-18.*pow(four,2.)+144.*pow(two,2.)*four-144.*pow(two,4.); \r
 \r
 // statistical errors of Q-cumulants:       \r
 Double_t qc2Error = 0.;\r
 Double_t qc4Error = 0.;\r
 Double_t qc6Error = 0.;\r
 Double_t qc8Error = 0.;\r
 \r
 // squared statistical errors of Q-cumulants:       \r
 //Double_t qc2ErrorSquared = 0.;\r
 Double_t qc4ErrorSquared = 0.;\r
 Double_t qc6ErrorSquared = 0.;\r
 Double_t qc8ErrorSquared = 0.;\r
        \r
 // statistical error of QC{2}:              \r
 qc2Error = twoError;                     \r
                             \r
 // statistical error of QC{4}:              \r
 qc4ErrorSquared = 16.*pow(two,2.)*pow(twoError,2)+pow(fourError,2.)\r
                 - 8.*two*wCov24;                     \r
 if(qc4ErrorSquared>0.)\r
 {\r
  qc4Error = pow(qc4ErrorSquared,0.5);\r
 } else \r
   {\r
    cout<<"WARNING: Statistical error of QC{4} is imaginary !!!!"<<endl;\r
   }\r
                                           \r
 // statistical error of QC{6}:              \r
 qc6ErrorSquared = 81.*pow(4.*pow(two,2.)-four,2.)*pow(twoError,2.)\r
                 + 81.*pow(two,2.)*pow(fourError,2.)\r
                 + pow(sixError,2.)\r
                 - 162.*two*(4.*pow(two,2.)-four)*wCov24\r
                 + 18.*(4.*pow(two,2.)-four)*wCov26\r
                 - 18.*two*wCov46; \r
                    \r
 if(qc6ErrorSquared>0.)\r
 {\r
  qc6Error = pow(qc6ErrorSquared,0.5);\r
 } else \r
   {\r
    cout<<"WARNING: Statistical error of QC{6} is imaginary !!!!"<<endl;\r
   }\r
                            \r
 // statistical error of QC{8}:              \r
 qc8ErrorSquared = 256.*pow(36.*pow(two,3.)-18.*four*two+six,2.)*pow(twoError,2.)\r
                 + 1296.*pow(4.*pow(two,2.)-four,2.)*pow(fourError,2.)\r
                 + 256.*pow(two,2.)*pow(sixError,2.)\r
                 + pow(eightError,2.)\r
                 - 1152.*(36.*pow(two,3.)-18.*four*two+six)*(4.*pow(two,2.)-four)*wCov24\r
                 + 512.*two*(36.*pow(two,3.)-18.*four*two+six)*wCov26\r
                 - 32.*(36.*pow(two,3.)-18.*four*two+six)*wCov28\r
                 - 1152.*two*(4.*pow(two,2.)-four)*wCov46\r
                 + 72.*(4.*pow(two,2.)-four)*wCov48\r
                 - 32.*two*wCov68;      \r
 if(qc8ErrorSquared>0.)\r
 {\r
  qc8Error = pow(qc8ErrorSquared,0.5);\r
 } else \r
   {\r
    cout<<"WARNING: Statistical error of QC{8} is imaginary !!!!"<<endl;\r
   }\r
\r
 // store the results and statistical errors for Q-cumulants:\r
 fIntFlowQcumulants->SetBinContent(1,qc2);\r
 fIntFlowQcumulants->SetBinError(1,qc2Error);\r
 fIntFlowQcumulants->SetBinContent(2,qc4);\r
 fIntFlowQcumulants->SetBinError(2,qc4Error);\r
 fIntFlowQcumulants->SetBinContent(3,qc6);\r
 fIntFlowQcumulants->SetBinError(3,qc6Error);\r
 fIntFlowQcumulants->SetBinContent(4,qc8); \r
 fIntFlowQcumulants->SetBinError(4,qc8Error); \r
  \r
} // end of AliFlowAnalysisWithQCumulants::CalculateCumulantsIntFlow()\r
\r
\r
//================================================================================================================================ \r
\r
\r
void AliFlowAnalysisWithQCumulants::CalculateIntFlow()\r
{\r
 // a) Calculate the final results for integrated flow estimates from Q-cumulants.\r
 // b) Propagate the statistical errors of measured multiparticle correlations to statistical errors of integrated flow estimates.  \r
 // c) Store the results and statistical errors of integrated flow estimates in histogram fIntFlow.\r
 //    Binning of fIntFlow is organized as follows:\r
 //\r
 //     1st bin: v{2,QC}\r
 //     2nd bin: v{4,QC}\r
 //     3rd bin: v{6,QC}\r
 //     4th bin: v{8,QC}\r
 \r
 if(!(fIntFlowCorrelationsHist && fIntFlowCovariances && fIntFlowQcumulants && fIntFlow))\r
 {\r
  cout<<"WARNING: fIntFlowCorrelationsHist && fIntFlowCovariances && fIntFlowQcumulants && fIntFlow is NULL in AFAWQC::CCIF() !!!!"<<endl;\r
  exit(0);\r
 }\r
   \r
 // Q-cumulants:\r
 Double_t qc2 = fIntFlowQcumulants->GetBinContent(1); // QC{2}  \r
 Double_t qc4 = fIntFlowQcumulants->GetBinContent(2); // QC{4}  \r
 Double_t qc6 = fIntFlowQcumulants->GetBinContent(3); // QC{6}  \r
 Double_t qc8 = fIntFlowQcumulants->GetBinContent(4); // QC{8}\r
  \r
 // correlations:\r
 Double_t two = fIntFlowCorrelationsHist->GetBinContent(1); // <<2>> \r
 Double_t four = fIntFlowCorrelationsHist->GetBinContent(2); // <<4>>  \r
 Double_t six = fIntFlowCorrelationsHist->GetBinContent(3); // <<6>> \r
 Double_t eight = fIntFlowCorrelationsHist->GetBinContent(4); // <<8>>  \r
 \r
 // statistical errors of average 2-, 4-, 6- and 8-particle azimuthal correlations:\r
 Double_t twoError = fIntFlowCorrelationsHist->GetBinError(1); // statistical error of <2>  \r
 Double_t fourError = fIntFlowCorrelationsHist->GetBinError(2); // statistical error of <4>   \r
 Double_t sixError = fIntFlowCorrelationsHist->GetBinError(3); // statistical error of <6> \r
 Double_t eightError = fIntFlowCorrelationsHist->GetBinError(4); // statistical error of <8> \r
 \r
 // covariances (multiplied by prefactor depending on weights - see comments in CalculateCovariancesIntFlow()):\r
 Double_t wCov24 = fIntFlowCovariances->GetBinContent(1); // Cov(<2>,<4>) * prefactor(w_<2>,w_<4>)\r
 Double_t wCov26 = fIntFlowCovariances->GetBinContent(2); // Cov(<2>,<6>) * prefactor(w_<2>,w_<6>)\r
 Double_t wCov28 = fIntFlowCovariances->GetBinContent(3); // Cov(<2>,<8>) * prefactor(w_<2>,w_<8>)\r
 Double_t wCov46 = fIntFlowCovariances->GetBinContent(4); // Cov(<4>,<6>) * prefactor(w_<4>,w_<6>)\r
 Double_t wCov48 = fIntFlowCovariances->GetBinContent(5); // Cov(<4>,<8>) * prefactor(w_<4>,w_<8>)\r
 Double_t wCov68 = fIntFlowCovariances->GetBinContent(6); // Cov(<6>,<8>) * prefactor(w_<6>,w_<8>)\r
  \r
 // integrated flow estimates:\r
 Double_t v2 = 0.; // v{2,QC}  \r
 Double_t v4 = 0.; // v{4,QC}  \r
 Double_t v6 = 0.; // v{6,QC}  \r
 Double_t v8 = 0.; // v{8,QC}\r
 \r
 // calculate integrated flow estimates from Q-cumulants: \r
 if(qc2>=0.) v2 = pow(qc2,1./2.); \r
 if(qc4<=0.) v4 = pow(-1.*qc4,1./4.); \r
 if(qc6>=0.) v6 = pow((1./4.)*qc6,1./6.); \r
 if(qc8<=0.) v8 = pow((-1./33.)*qc8,1./8.); \r
   \r
 // statistical errors of integrated flow estimates:\r
 Double_t v2Error = 0.; // statistical error of v{2,QC}  \r
 Double_t v4Error = 0.; // statistical error of v{4,QC}  \r
 Double_t v6Error = 0.; // statistical error of v{6,QC}  \r
 Double_t v8Error = 0.; // statistical error of v{8,QC}\r
   \r
 // squares of statistical errors of integrated flow estimates:\r
 Double_t v2ErrorSquared = 0.; // squared statistical error of v{2,QC} \r
 Double_t v4ErrorSquared = 0.; // squared statistical error of v{4,QC}   \r
 Double_t v6ErrorSquared = 0.; // squared statistical error of v{6,QC}   \r
 Double_t v8ErrorSquared = 0.; // squared statistical error of v{8,QC} \r
 \r
 // calculate squared statistical errors of integrated flow estimates:\r
 if(two > 0.) \r
 { \r
  v2ErrorSquared = (1./(4.*two))*pow(twoError,2.);\r
 } \r
 if(2.*pow(two,2.)-four > 0.)\r
 {\r
  v4ErrorSquared = (1./pow(2.*pow(two,2.)-four,3./2.))*\r
                   (pow(two,2.)*pow(twoError,2.)+(1./16.)*pow(fourError,2.)-(1./2.)*two*wCov24);\r
 }\r
 if(six-9.*four*two+12.*pow(two,3.) > 0.) \r
 {\r
  v6ErrorSquared = ((1./2.)*(1./pow(2.,2./3.))*(1./pow(six-9.*four*two+12.*pow(two,3.),5./3.)))*\r
                   ((9./2.)*pow(4.*pow(two,2.)-four,2.)*pow(twoError,2.) \r
                    + (9./2.)*pow(two,2.)*pow(fourError,2.)+(1./18.)*pow(sixError,2.)\r
                    - 9.*two*(4.*pow(two,2.)-four)*wCov24+(4.*pow(two,2.)-four)*wCov26-two*wCov46); \r
 }\r
 if(-1.*eight+16.*six*two+18.*pow(four,2.)-144.*four*pow(two,2.)+144.*pow(two,4.) > 0.) \r
 {\r
  v8ErrorSquared = (4./pow(33,1./4.))*(1./pow(-1.*eight+16.*six*two+18.*pow(four,2.)-144.*four*pow(two,2.)+144.*pow(two,4.),7./4.))*\r
                   (pow(36.*pow(two,3.)-18.*four*two+six,2.)*pow(twoError,2.)\r
                    + (81./16.)*pow(4.*pow(two,2.)-four,2.)*pow(fourError,2.)\r
                    + pow(two,2.)*pow(sixError,2.)\r
                    + (1./256.)*pow(eightError,2.)\r
                    - (9./2.)*(36.*pow(two,3.)-18.*four*two+six)*(4.*pow(two,2.)-four)*wCov24\r
                    + 2.*two*(36.*pow(two,3.)-18.*four*two+six)*wCov26\r
                    - (1./8.)*(36.*pow(two,3.)-18.*four*two+six)*wCov28                    \r
                    - (9./2.)*two*(4.*pow(two,2.)-four)*wCov46                   \r
                    + (9./32.)*(4.*pow(two,2.)-four)*wCov48                    \r
                    - (1./8.)*two*wCov68);\r
 } \r
\r
 // calculate statistical errors of integrated flow estimates: \r
 if(v2ErrorSquared > 0.)\r
 {\r
  v2Error = pow(v2ErrorSquared,0.5);\r
 } else\r
   {\r
    cout<<"WARNING: Statistical error of v{2,QC} is imaginary !!!!"<<endl;\r
   }    \r
 if(v4ErrorSquared > 0.)\r
 {\r
  v4Error = pow(v4ErrorSquared,0.5);\r
 } else\r
   {\r
    cout<<"WARNING: Statistical error of v{4,QC} is imaginary !!!!"<<endl;\r
   }     \r
 if(v6ErrorSquared > 0.)\r
 {\r
  v6Error = pow(v6ErrorSquared,0.5);\r
 } else\r
   {\r
    cout<<"WARNING: Statistical error of v{6,QC} is imaginary !!!!"<<endl;\r
   }     \r
 if(v8ErrorSquared > 0.)\r
 {\r
  v8Error = pow(v8ErrorSquared,0.5);\r
 } else\r
   {\r
    cout<<"WARNING: Statistical error of v{8,QC} is imaginary !!!!"<<endl;\r
   }    \r
                     \r
 // store the results and statistical errors of integrated flow estimates:\r
 fIntFlow->SetBinContent(1,v2);\r
 fIntFlow->SetBinError(1,v2Error);\r
 fIntFlow->SetBinContent(2,v4);\r
 fIntFlow->SetBinError(2,v4Error);\r
 fIntFlow->SetBinContent(3,v6);\r
 fIntFlow->SetBinError(3,v6Error);\r
 fIntFlow->SetBinContent(4,v8);\r
 fIntFlow->SetBinError(4,v8Error);\r
       \r
} // end of AliFlowAnalysisWithQCumulants::CalculateIntFlow()\r
\r
\r
//================================================================================================================================ \r
\r
\r
void AliFlowAnalysisWithQCumulants::FillCommonHistResultsIntFlow()\r
{\r
 // Fill in AliFlowCommonHistResults histograms relevant for 'NONAME' integrated flow (to be improved (name))\r
 \r
 if(!fIntFlow)\r
 {\r
  cout<<"WARNING: fIntFlow is NULL in AFAWQC::FCHRIF() !!!!"<<endl;\r
  exit(0); \r
 }  \r
    \r
 if(!(fCommonHistsResults2nd && fCommonHistsResults4th && fCommonHistsResults6th && fCommonHistsResults8th))\r
 {\r
  cout<<"WARNING: fCommonHistsResults2nd && fCommonHistsResults4th && fCommonHistsResults6th && fCommonHistsResults8th"<<endl; \r
  cout<<"         is NULL in AFAWQC::FCHRIF() !!!!"<<endl;\r
  exit(0);\r
 }\r
 \r
 Double_t v2 = fIntFlow->GetBinContent(1);\r
 Double_t v4 = fIntFlow->GetBinContent(2);\r
 Double_t v6 = fIntFlow->GetBinContent(3);\r
 Double_t v8 = fIntFlow->GetBinContent(4);\r
  \r
 Double_t v2Error = fIntFlow->GetBinError(1);\r
 Double_t v4Error = fIntFlow->GetBinError(2);\r
 Double_t v6Error = fIntFlow->GetBinError(3);\r
 Double_t v8Error = fIntFlow->GetBinError(4);\r
 \r
 fCommonHistsResults2nd->FillIntegratedFlow(v2,v2Error); // to be improved (hardwired 2nd in the name)  \r
 fCommonHistsResults4th->FillIntegratedFlow(v4,v4Error); // to be improved (hardwired 4th in the name)\r
 if(!(fUsePhiWeights||fUsePtWeights||fUseEtaWeights)) // to be improved (calculate also 6th and 8th order)\r
 {\r
  fCommonHistsResults6th->FillIntegratedFlow(v6,v6Error); // to be improved (hardwired 6th in the name)\r
  fCommonHistsResults8th->FillIntegratedFlow(v8,v8Error); // to be improved (hardwired 8th in the name) \r
 }\r
 \r
} // end of AliFlowAnalysisWithQCumulants::FillCommonHistResultsIntFlow()\r
\r
\r
//================================================================================================================================ \r
\r
\r
/*\r
void AliFlowAnalysisWithQCumulants::ApplyCorrectionForNonUniformAcceptanceToCumulantsForIntFlow(Bool_t useParticleWeights, TString eventWeights)\r
{\r
 // apply correction for non-uniform acceptance to cumulants for integrated flow \r
 // (Remark: non-corrected cumulants are accessed from fCumulants[pW][0], corrected cumulants are stored in fCumulants[pW][1])\r
 \r
 // shortcuts for the flags:\r
 Int_t pW = (Int_t)(useParticleWeights); // 0=pWeights not used, 1=pWeights used\r
 Int_t eW = -1;\r
 \r
 if(eventWeights == "exact")\r
 {\r
  eW = 0;\r
 }\r
 \r
 if(!(fCumulants[pW][eW][0] && fCumulants[pW][eW][1] && fCorrections[pW][eW]))\r
 {\r
  cout<<"WARNING: fCumulants[pW][eW][0] && fCumulants[pW][eW][1] && fCorrections[pW][eW] is NULL in AFAWQC::ACFNUATCFIF() !!!!"<<endl;\r
  cout<<"pW = "<<pW<<endl;\r
  cout<<"eW = "<<eW<<endl;\r
  exit(0);\r
 } \r
  \r
 // non-corrected cumulants:\r
 Double_t qc2 = fCumulants[pW][eW][0]->GetBinContent(1); \r
 Double_t qc4 = fCumulants[pW][eW][0]->GetBinContent(2); \r
 Double_t qc6 = fCumulants[pW][eW][0]->GetBinContent(3); \r
 Double_t qc8 = fCumulants[pW][eW][0]->GetBinContent(4); \r
 // statistical error of non-corrected cumulants:  \r
 Double_t qc2Error = fCumulants[pW][eW][0]->GetBinError(1); \r
 Double_t qc4Error = fCumulants[pW][eW][0]->GetBinError(2); \r
 Double_t qc6Error = fCumulants[pW][eW][0]->GetBinError(3); \r
 Double_t qc8Error = fCumulants[pW][eW][0]->GetBinError(4); \r
 // corrections for non-uniform acceptance:\r
 Double_t qc2Correction = fCorrections[pW][eW]->GetBinContent(1); \r
 Double_t qc4Correction = fCorrections[pW][eW]->GetBinContent(2); \r
 Double_t qc6Correction = fCorrections[pW][eW]->GetBinContent(3); \r
 Double_t qc8Correction = fCorrections[pW][eW]->GetBinContent(4); \r
 // corrected cumulants:\r
 Double_t qc2Corrected = qc2 + qc2Correction;\r
 Double_t qc4Corrected = qc4 + qc4Correction;\r
 Double_t qc6Corrected = qc6 + qc6Correction;\r
 Double_t qc8Corrected = qc8 + qc8Correction;\r
  \r
 // ... to be improved (I need here also to correct error of QCs for NUA. \r
 // For simplicity sake I assume at the moment that this correction is negliglible, but it will be added eventually...)\r
 \r
 // store corrected results and statistical errors for cumulants:   \r
 fCumulants[pW][eW][1]->SetBinContent(1,qc2Corrected);\r
 fCumulants[pW][eW][1]->SetBinContent(2,qc4Corrected);\r
 fCumulants[pW][eW][1]->SetBinContent(3,qc6Corrected);\r
 fCumulants[pW][eW][1]->SetBinContent(4,qc8Corrected);\r
 fCumulants[pW][eW][1]->SetBinError(1,qc2Error); // to be improved (correct also qc2Error for NUA)\r
 fCumulants[pW][eW][1]->SetBinError(2,qc4Error); // to be improved (correct also qc4Error for NUA)\r
 fCumulants[pW][eW][1]->SetBinError(3,qc6Error); // to be improved (correct also qc6Error for NUA)\r
 fCumulants[pW][eW][1]->SetBinError(4,qc8Error); // to be improved (correct also qc8Error for NUA)  \r
  \r
} // end of AliFlowAnalysisWithQCumulants::ApplyCorrectionForNonUniformAcceptanceToCumulantsForIntFlow(Bool_t useParticleWeights, TString eventWeights)\r
*/\r
\r
\r
//================================================================================================================================\r
\r
\r
/*  \r
void AliFlowAnalysisWithQCumulants::PrintQuantifyingCorrectionsForNonUniformAcceptance(Bool_t useParticleWeights, TString eventWeights)\r
{\r
 // print on the screen QC{n,biased}/QC{n,corrected}\r
 \r
 // shortcuts for the flags:\r
 Int_t pW = (Int_t)(useParticleWeights); // 0=pWeights not used, 1=pWeights used\r
 \r
 Int_t eW = -1;\r
 \r
 if(eventWeights == "exact")\r
 {\r
  eW = 0;\r
 } \r
 \r
 if(!(fCumulants[pW][eW][0] && fCumulants[pW][eW][1]))\r
 {\r
  cout<<"WARNING: fCumulants[pW][eW][0] && fCumulants[pW][eW][1] is NULL in AFAWQC::PQCFNUA() !!!!"<<endl;\r
  cout<<"pW = "<<pW<<endl;\r
  cout<<"eW = "<<eW<<endl;\r
  exit(0);\r
 }\r
   \r
 cout<<endl;\r
 cout<<" Quantifying the bias to Q-cumulants from"<<endl;\r
 cout<<"  non-uniform acceptance of the detector:"<<endl;\r
 cout<<endl;\r
  \r
 if(fCumulants[pW][eW][1]->GetBinContent(1)) \r
 { \r
  cout<<"  QC{2,biased}/QC{2,corrected} = "<<(fCumulants[pW][eW][0]->GetBinContent(1))/(fCumulants[pW][eW][1]->GetBinContent(1))<<endl;   \r
 }\r
 if(fCumulants[pW][eW][1]->GetBinContent(2)) \r
 { \r
  cout<<"  QC{4,biased}/QC{4,corrected} = "<<fCumulants[pW][eW][0]->GetBinContent(2)/fCumulants[pW][eW][1]->GetBinContent(2)<<endl;   \r
 }\r
 \r
 cout<<endl;\r
            \r
} // end of AliFlowAnalysisWithQCumulants::PrintQuantifyingCorrectionsForNonUniformAcceptance(Bool_t useParticleWeights, TString eventWeights)\r
*/\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::CalculateIntFlowCorrelationsUsingParticleWeights()\r
{\r
 // Calculate all correlations needed for integrated flow using particle weights.\r
  \r
 // Remark 1: When particle weights are used the binning of fIntFlowCorrelationAllPro is organized as follows:\r
 //\r
 //  1st bin: <2>_{1n|1n} = two1n1nW1W1 = <w1 w2 cos(n*(phi1-phi2))>\r
 //  2nd bin: <2>_{2n|2n} = two2n2nW2W2 = <w1^2 w2^2 cos(2n*(phi1-phi2))>\r
 //  3rd bin: <2>_{3n|3n} = two3n3nW3W3 = <w1^3 w2^3 cos(3n*(phi1-phi2))> \r
 //  4th bin: <2>_{4n|4n} = two4n4nW4W4 = <w1^4 w2^4 cos(4n*(phi1-phi2))>\r
 //  5th bin:           ----  EMPTY ----\r
 //  6th bin: <3>_{2n|1n,1n} = three2n1n1nW2W1W1 = <w1^2 w2 w3 cos(n*(2phi1-phi2-phi3))>\r
 //  7th bin: <3>_{3n|2n,1n} = ...\r
 //  8th bin: <3>_{4n|2n,2n} = ...\r
 //  9th bin: <3>_{4n|3n,1n} = ...\r
 // 10th bin:           ----  EMPTY ----\r
 // 11th bin: <4>_{1n,1n|1n,1n} = four1n1n1n1nW1W1W1W1 = <w1 w2 w3 w4 cos(n*(phi1+phi2-phi3-phi4))>\r
 // 12th bin: <4>_{2n,1n|2n,1n} = ...\r
 // 13th bin: <4>_{2n,2n|2n,2n} = ...\r
 // 14th bin: <4>_{3n|1n,1n,1n} = ... \r
 // 15th bin: <4>_{3n,1n|3n,1n} = ...\r
 // 16th bin: <4>_{3n,1n|2n,2n} = ...\r
 // 17th bin: <4>_{4n|2n,1n,1n} = ... \r
 // 18th bin:           ----  EMPTY ----\r
 // 19th bin: <5>_{2n|1n,1n,1n,1n} = ...\r
 // 20th bin: <5>_{2n,2n|2n,1n,1n} = ...\r
 // 21st bin: <5>_{3n,1n|2n,1n,1n} = ...\r
 // 22nd bin: <5>_{4n|1n,1n,1n,1n} = ...\r
 // 23rd bin:           ----  EMPTY ----\r
 // 24th bin: <6>_{1n,1n,1n|1n,1n,1n} = ...\r
 // 25th bin: <6>_{2n,1n,1n|2n,1n,1n} = ...\r
 // 26th bin: <6>_{2n,2n|1n,1n,1n,1n} = ...\r
 // 27th bin: <6>_{3n,1n|1n,1n,1n,1n} = ...\r
 // 28th bin:           ----  EMPTY ----\r
 // 29th bin: <7>_{2n,1n,1n|1n,1n,1n,1n} = ...\r
 // 30th bin:           ----  EMPTY ----\r
 // 31st bin: <8>_{1n,1n,1n,1n|1n,1n,1n,1n} = ...\r
 \r
 // Remark 2: When particle weights are used there are some extra correlations. They are stored in \r
 // fIntFlowExtraCorrelationsPro binning of which is organized as follows:\r
 \r
 // 1st bin: two1n1nW3W1 = <w1^3 w2 cos(n*(phi1-phi2))>\r
 // 2nd bin: two1n1nW1W1W2 = <w1 w2 w3^2 cos(n*(phi1-phi2))>  \r
 
 // multiplicity (number of particles used to determine the reaction plane)\r
 Double_t dMult = (*fSMpk)(0,0);\r
 \r
 // real and imaginary parts of weighted Q-vectors evaluated in harmonics n, 2n, 3n and 4n: \r
 Double_t dReQ1n1k = (*fReQ)(0,1);\r
 Double_t dReQ2n2k = (*fReQ)(1,2);\r
 Double_t dReQ3n3k = (*fReQ)(2,3);\r
 Double_t dReQ4n4k = (*fReQ)(3,4);\r
 Double_t dReQ1n3k = (*fReQ)(0,3);\r
 Double_t dImQ1n1k = (*fImQ)(0,1);\r
 Double_t dImQ2n2k = (*fImQ)(1,2);\r
 Double_t dImQ3n3k = (*fImQ)(2,3);\r
 Double_t dImQ4n4k = (*fImQ)(3,4);\r
 Double_t dImQ1n3k = (*fImQ)(0,3);\r
\r
 // dMs are variables introduced in order to simplify some Eqs. bellow:\r
 //..............................................................................................\r
 Double_t dM11 = (*fSMpk)(1,1)-(*fSMpk)(0,2); // dM11 = sum_{i,j=1,i!=j}^M w_i w_j\r
 Double_t dM22 = (*fSMpk)(1,2)-(*fSMpk)(0,4); // dM22 = sum_{i,j=1,i!=j}^M w_i^2 w_j^2\r
 Double_t dM33 = (*fSMpk)(1,3)-(*fSMpk)(0,6); // dM33 = sum_{i,j=1,i!=j}^M w_i^3 w_j^3\r
 Double_t dM44 = (*fSMpk)(1,4)-(*fSMpk)(0,8); // dM44 = sum_{i,j=1,i!=j}^M w_i^4 w_j^4\r
 Double_t dM31 = (*fSMpk)(0,3)*(*fSMpk)(0,1)-(*fSMpk)(0,4); // dM31 = sum_{i,j=1,i!=j}^M w_i^3 w_j\r
 Double_t dM211 = (*fSMpk)(0,2)*(*fSMpk)(1,1)-2.*(*fSMpk)(0,3)*(*fSMpk)(0,1)\r
                - (*fSMpk)(1,2)+2.*(*fSMpk)(0,4); // dM211 = sum_{i,j,k=1,i!=j!=k}^M w_i^2 w_j w_k\r
 Double_t dM1111 = (*fSMpk)(3,1)-6.*(*fSMpk)(0,2)*(*fSMpk)(1,1)  \r
                 + 8.*(*fSMpk)(0,3)*(*fSMpk)(0,1)\r
                 + 3.*(*fSMpk)(1,2)-6.*(*fSMpk)(0,4); // dM1111 = sum_{i,j,k,l=1,i!=j!=k!=l}^M w_i w_j w_k w_l\r
 //..............................................................................................\r
\r
 // 2-particle correlations:\r
 Double_t two1n1nW1W1 = 0.; // <w1 w2 cos(n*(phi1-phi2))>\r
 Double_t two2n2nW2W2 = 0.; // <w1^2 w2^2 cos(2n*(phi1-phi2))>\r
 Double_t two3n3nW3W3 = 0.; // <w1^3 w2^3 cos(3n*(phi1-phi2))>\r
 Double_t two4n4nW4W4 = 0.; // <w1^4 w2^4 cos(4n*(phi1-phi2))>\r
 if(dMult>1) \r
 { \r
  if(dM11)\r
  {\r
   two1n1nW1W1 = (pow(dReQ1n1k,2)+pow(dImQ1n1k,2)-(*fSMpk)(0,2))/dM11;    \r
   // average correlation <w1 w2 cos(n*(phi1-phi2))> for single event: \r
   fIntFlowCorrelationsEBE->SetBinContent(1,two1n1nW1W1);\r
   fIntFlowEventWeightsForCorrelationsEBE->SetBinContent(1,dM11);\r
   // average correlation <w1 w2 cos(n*(phi1-phi2))> for all events:\r
   fIntFlowCorrelationsPro->Fill(0.5,two1n1nW1W1,dM11);   \r
   fIntFlowCorrelationsAllPro->Fill(0.5,two1n1nW1W1,dM11);   \r
  }\r
  if(dM22)\r
  {\r
   two2n2nW2W2 = (pow(dReQ2n2k,2)+pow(dImQ2n2k,2)-(*fSMpk)(0,4))/dM22; \r
   // ...\r
   // average correlation <w1^2 w2^2 cos(2n*(phi1-phi2))> for all events:\r
   fIntFlowCorrelationsAllPro->Fill(1.5,two2n2nW2W2,dM22);   \r
  }\r
  if(dM33)\r
  {\r
   two3n3nW3W3 = (pow(dReQ3n3k,2)+pow(dImQ3n3k,2)-(*fSMpk)(0,6))/dM33;\r
   // ...\r
   // average correlation <w1^3 w2^3 cos(3n*(phi1-phi2))> for all events:\r
   fIntFlowCorrelationsAllPro->Fill(2.5,two3n3nW3W3,dM33);   \r
  }\r
  if(dM44)\r
  {\r
   two4n4nW4W4 = (pow(dReQ4n4k,2)+pow(dImQ4n4k,2)-(*fSMpk)(0,8))/dM44; \r
   // ...\r
   // average correlation <w1^4 w2^4 cos(4n*(phi1-phi2))> for all events:\r
   fIntFlowCorrelationsAllPro->Fill(3.5,two4n4nW4W4,dM44);      \r
  }\r
 } // end of if(dMult>1) \r
\r
 // extra 2-particle correlations:\r
 Double_t two1n1nW3W1 = 0.; // <w1^3 w2 cos(n*(phi1-phi2))>\r
 Double_t two1n1nW1W1W2 = 0.; // <w1 w2 w3^2 cos(n*(phi1-phi2))> \r
 if(dMult>1) \r
 {    \r
  if(dM31)\r
  {\r
   two1n1nW3W1 = (dReQ1n3k*dReQ1n1k+dImQ1n3k*dImQ1n1k-(*fSMpk)(0,4))/dM31; \r
   fIntFlowExtraCorrelationsPro->Fill(0.5,two1n1nW3W1,dM31);  \r
  } \r
  if(dM211)\r
  {\r
   two1n1nW1W1W2 = ((*fSMpk)(0,2)*(pow(dReQ1n1k,2)+pow(dImQ1n1k,2)-(*fSMpk)(0,2))\r
                 - 2.*(dReQ1n3k*dReQ1n1k+dImQ1n3k*dImQ1n1k\r
                 - (*fSMpk)(0,4)))/dM211;\r
   fIntFlowExtraCorrelationsPro->Fill(1.5,two1n1nW1W1W2,dM211);  \r
  }  \r
 } // end of if(dMult>1)\r
 //..............................................................................................\r
 \r
 //..............................................................................................\r
 // 3-particle correlations:\r
 Double_t three2n1n1nW2W1W1 = 0.; // <w1^2 w2 w3 cos(n*(2phi1-phi2-phi3))>\r
 \r
 if(dMult>2) \r
 { \r
  if(dM211)\r
  {                                                       \r
   three2n1n1nW2W1W1 = (pow(dReQ1n1k,2.)*dReQ2n2k+2.*dReQ1n1k*dImQ1n1k*dImQ2n2k-pow(dImQ1n1k,2.)*dReQ2n2k\r
                     - 2.*(dReQ1n3k*dReQ1n1k+dImQ1n3k*dImQ1n1k)\r
                     - pow(dReQ2n2k,2)-pow(dImQ2n2k,2)\r
                     + 2.*(*fSMpk)(0,4))/dM211;                                                                               \r
   fIntFlowCorrelationsAllPro->Fill(5.5,three2n1n1nW2W1W1,dM211);\r
  } \r
 } // end of if(dMult>2) \r
 //..............................................................................................\r
 \r
 //..............................................................................................\r
 // 4-particle correlations:\r
 Double_t four1n1n1n1nW1W1W1W1 = 0.; // <w1 w2 w3 w4 cos(n*(phi1+phi2-phi3-phi4))>\r
 if(dMult>3) \r
 { \r
  if(dM1111)\r
  {      \r
   four1n1n1n1nW1W1W1W1 = (pow(pow(dReQ1n1k,2.)+pow(dImQ1n1k,2.),2)\r
                        - 2.*(pow(dReQ1n1k,2.)*dReQ2n2k+2.*dReQ1n1k*dImQ1n1k*dImQ2n2k-pow(dImQ1n1k,2.)*dReQ2n2k)\r
                        + 8.*(dReQ1n3k*dReQ1n1k+dImQ1n3k*dImQ1n1k)\r
                        + (pow(dReQ2n2k,2)+pow(dImQ2n2k,2))\r
                        - 4.*(*fSMpk)(0,2)*(pow(dReQ1n1k,2)+pow(dImQ1n1k,2))\r
                        - 6.*(*fSMpk)(0,4)+2.*(*fSMpk)(1,2))/dM1111;  \r
                          \r
   // average correlation <w1 w2 w3 w4 cos(n*(phi1+phi2-phi3-phi4))> for single event: \r
   fIntFlowCorrelationsEBE->SetBinContent(2,four1n1n1n1nW1W1W1W1);\r
   fIntFlowEventWeightsForCorrelationsEBE->SetBinContent(2,dM1111);\r
   // average correlation <w1 w2 w3 w4 cos(n*(phi1+phi2-phi3-phi4))> for all events:\r
   fIntFlowCorrelationsPro->Fill(1.5,four1n1n1n1nW1W1W1W1,dM1111);   \r
   fIntFlowCorrelationsAllPro->Fill(10.5,four1n1n1n1nW1W1W1W1,dM1111);   \r
  } \r
 } // end of if(dMult>3) \r
 //..............................................................................................\r
 \r
} // end of AliFlowAnalysisWithQCumulants::CalculateIntFlowCorrelationsUsingParticleWeights()\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::CalculateWeightedQProductsForIntFlow() // to be improved (completed)\r
{\r
 // calculate averages like <<2><4>>, <<2><6>>, <<4><6>>, etc. which are needed to calculate covariances \r
 // Remark: here we take weighted correlations!\r
 \r
 /*\r
 \r
 // binning of fQProductsW is organized as follows:\r
 // \r
 // 1st bin: <2><4> \r
 // 2nd bin: <2><6>\r
 // 3rd bin: <2><8>\r
 // 4th bin: <4><6>\r
 // 5th bin: <4><8>\r
 // 6th bin: <6><8>\r
 \r
 Double_t dMult = (*fSMpk)(0,0); // multiplicity (number of particles used to determine the reaction plane)\r
\r
 Double_t dM11 = (*fSMpk)(1,1)-(*fSMpk)(0,2); // dM11 = sum_{i,j=1,i!=j}^M w_i w_j\r
 Double_t dM1111 = (*fSMpk)(3,1)-6.*(*fSMpk)(0,2)*(*fSMpk)(1,1)  \r
                 + 8.*(*fSMpk)(0,3)*(*fSMpk)(0,1)\r
                 + 3.*(*fSMpk)(1,2)-6.*(*fSMpk)(0,4); // dM1111 = sum_{i,j,k,l=1,i!=j!=k!=l}^M w_i w_j w_k w_l\r
\r
 Double_t twoEBEW = 0.; // <2>\r
 Double_t fourEBEW = 0.; // <4>\r
 \r
 twoEBEW = fQCorrelationsEBE[1]->GetBinContent(1);\r
 fourEBEW = fQCorrelationsEBE[1]->GetBinContent(11);\r
 \r
 // <2><4>\r
 if(dMult>3)\r
 {\r
  fQProducts[1][0]->Fill(0.5,twoEBEW*fourEBEW,dM11*dM1111);\r
 }\r
 \r
 */\r
 \r
} // end of AliFlowAnalysisWithQCumulants::CalculateWeightedQProductsForIntFlow()  \r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::InitializeArraysForIntFlow()\r
{\r
 // Initialize all arrays used to calculate integrated flow.\r
 \r
 for(Int_t sc=0;sc<2;sc++) // sin or cos terms\r
 {\r
  fIntFlowCorrectionTermsForNUAEBE[sc] = NULL;\r
  fIntFlowCorrectionTermsForNUAPro[sc] = NULL;\r
  fIntFlowCorrectionTermsForNUAHist[sc] = NULL;\r
 }\r
 for(Int_t power=0;power<2;power++) // linear or quadratic \r
 {\r
  fIntFlowSumOfEventWeights[power] = NULL;    \r
 }
 for(Int_t i=0;i<3;i++) // print on the screen the final results (0=NONAME, 1=RP, 2=POI)
 {
  fPrintFinalResults[i] = kTRUE;
 }
 \r
} // end of void AliFlowAnalysisWithQCumulants::InitializeArraysForIntFlow()\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::InitializeArraysForDiffFlow()\r
{\r
 // Initialize all arrays needed to calculate differential flow.\r
 //  a) Initialize lists holding profiles;\r
 //  b) Initialize lists holding histograms;\r
 //  c) Initialize event-by-event quantities;\r
 //  d) Initialize profiles;\r
 //  e) Initialize histograms holding final results.\r
 \r
 // a) Initialize lists holding profiles;\r
 for(Int_t t=0;t<2;t++) // type (RP, POI)\r
 {\r
  for(Int_t pe=0;pe<2;pe++) // pt or eta\r
  {\r
   fDiffFlowCorrelationsProList[t][pe] = NULL;\r
   fDiffFlowProductOfCorrelationsProList[t][pe] = NULL;\r
   fDiffFlowCorrectionsProList[t][pe] = NULL;\r
  }\r
 }  \r
 \r
 // b) Initialize lists holding histograms;\r
 for(Int_t t=0;t<2;t++) // type (RP, POI)\r
 {\r
  for(Int_t pe=0;pe<2;pe++) // pt or eta\r
  {\r
   fDiffFlowCorrelationsHistList[t][pe] = NULL;\r
   for(Int_t power=0;power<2;power++)\r
   {\r
    fDiffFlowSumOfEventWeightsHistList[t][pe][power] = NULL;\r
   } // end of for(Int_t power=0;power<2;power++)  \r
   fDiffFlowSumOfProductOfEventWeightsHistList[t][pe] = NULL;\r
   fDiffFlowCorrectionsHistList[t][pe] = NULL;\r
   fDiffFlowCovariancesHistList[t][pe] = NULL;\r
   fDiffFlowCumulantsHistList[t][pe] = NULL;\r
   fDiffFlowHistList[t][pe] = NULL;\r
  } // end of for(Int_t pe=0;pe<2;pe++) // pt or eta\r
 } // enf of for(Int_t t=0;t<2;t++) // type (RP, POI) \r
 \r
 // c) Initialize event-by-event quantities:\r
 // 1D:\r
 for(Int_t t=0;t<3;t++) // type (RP, POI, POI&&RP)\r
 {\r
  for(Int_t pe=0;pe<2;pe++) // pt or eta\r
  { \r
   for(Int_t m=0;m<4;m++) // multiple of harmonic\r
   {\r
    for(Int_t k=0;k<9;k++) // power of weight\r
    {\r
     fReRPQ1dEBE[t][pe][m][k] = NULL;\r
     fImRPQ1dEBE[t][pe][m][k] = NULL;\r
     fs1dEBE[t][pe][k] = NULL; // to be improved (this doesn't need to be within loop over m)\r
    }   \r
   }\r
  }\r
 }\r
 // 1D:\r
 for(Int_t t=0;t<2;t++) // type (RP or POI)\r
 {\r
  for(Int_t pe=0;pe<2;pe++) // pt or eta\r
  { \r
   for(Int_t sc=0;sc<2;sc++) // sin or cos terms\r
   {\r
    for(Int_t cti=0;cti<9;cti++) // correction term index\r
    {\r
     fDiffFlowCorrectionTermsForNUAEBE[t][pe][sc][cti] = NULL;\r
    }   \r
   }\r
  }\r
 }\r
 // 2D:  \r
 for(Int_t t=0;t<3;t++) // type (RP, POI, POI&&RP)\r
 {\r
  for(Int_t m=0;m<4;m++) // multiple of harmonic\r
  {\r
   for(Int_t k=0;k<9;k++) // power of weight\r
   {\r
    fReRPQ2dEBE[t][m][k] = NULL;\r
    fImRPQ2dEBE[t][m][k] = NULL;\r
    fs2dEBE[t][k] = NULL; // to be improved (this doesn't need to be within loop over m)\r
   }   \r
  }\r
 }\r
 \r
 // d) Initialize profiles:\r
 for(Int_t t=0;t<2;t++) // type: RP or POI\r
 { \r
  for(Int_t pe=0;pe<2;pe++) // pt or eta\r
  {\r
   for(Int_t ci=0;ci<4;ci++) // correlation index\r
   {\r
    fDiffFlowCorrelationsPro[t][pe][ci] = NULL;\r
   } // end of for(Int_t ci=0;ci<4;ci++)   \r
   for(Int_t mci1=0;mci1<8;mci1++) // mixed correlation index\r
   {\r
    for(Int_t mci2=0;mci2<8;mci2++) // mixed correlation index\r
    {\r
     fDiffFlowProductOfCorrelationsPro[t][pe][mci1][mci2] = NULL;\r
    } // end of for(Int_t mci2=0;mci2<8;mci2++) // mixed correlation index\r
   } // end of for(Int_t mci1=0;mci1<8;mci1++) // mixed correlation index  \r
   // correction terms for nua:\r
   for(Int_t sc=0;sc<2;sc++) // sin or cos terms\r
   {\r
    for(Int_t cti=0;cti<9;cti++) // correction term index\r
    {\r
     fDiffFlowCorrectionTermsForNUAPro[t][pe][sc][cti] = NULL;\r
    }   \r
   }\r
  } // end of for(Int_t pe=0;pe<2;pe++) // pt or eta\r
 } // end of for(Int_t t=0;t<2;t++) // type: RP or POI\r
  \r
 // e) Initialize histograms holding final results.\r
 for(Int_t t=0;t<2;t++) // type: RP or POI\r
 { \r
  for(Int_t pe=0;pe<2;pe++) // pt or eta\r
  {\r
   for(Int_t ci=0;ci<4;ci++) // correlation index\r
   {\r
    fDiffFlowCorrelationsHist[t][pe][ci] = NULL;\r
    fDiffFlowCumulants[t][pe][ci] = NULL;\r
    fDiffFlow[t][pe][ci] = NULL;\r
   } // end of for(Int_t ci=0;ci<4;ci++)    \r
   for(Int_t covarianceIndex=0;covarianceIndex<5;covarianceIndex++) \r
   {\r
    fDiffFlowCovariances[t][pe][covarianceIndex] = NULL;     \r
   } // end of for(Int_t covarianceIndex=0;covarianceIndex<5;covarianceIndex++) \r
   // correction terms for nua:\r
   for(Int_t sc=0;sc<2;sc++) // sin or cos terms\r
   {\r
    for(Int_t cti=0;cti<9;cti++) // correction term index\r
    {\r
     fDiffFlowCorrectionTermsForNUAHist[t][pe][sc][cti] = NULL;\r
    }   \r
   }\r
  } // end of for(Int_t pe=0;pe<2;pe++) // pt or eta\r
 } // end of for(Int_t t=0;t<2;t++) // type: RP or POI\r
 \r
 // sum of event weights for reduced correlations:\r
 for(Int_t t=0;t<2;t++) // type = RP or POI\r
 {\r
  for(Int_t pe=0;pe<2;pe++) // pt or eta\r
  {\r
   for(Int_t p=0;p<2;p++) // power of weight is 1 or 2\r
   {\r
    for(Int_t ew=0;ew<4;ew++) // event weight index for reduced correlations\r
    {\r
     fDiffFlowSumOfEventWeights[t][pe][p][ew] = NULL;\r
    } \r
   }   \r
  }\r
 }\r
 // product of event weights for both types of correlations:\r
 for(Int_t t=0;t<2;t++) // type = RP or POI\r
 {\r
  for(Int_t pe=0;pe<2;pe++) // pt or eta\r
  {\r
   for(Int_t mci1=0;mci1<8;mci1++) // mixed correlation index\r
   {\r
    for(Int_t mci2=0;mci2<8;mci2++) // mixed correlation index\r
    {\r
     fDiffFlowSumOfProductOfEventWeights[t][pe][mci1][mci2] = NULL;\r
    } \r
   }   \r
  }\r
 }\r
\r
 \r
 \r
 \r
 /*\r
 \r
 // nested lists in fDiffFlowProfiles:\r
 for(Int_t t=0;t<2;t++)\r
 {\r
  fDFPType[t] = NULL;\r
  for(Int_t pW=0;pW<2;pW++) // particle weights not used (0) or used (1)\r
  {\r
   fDFPParticleWeights[t][pW] = NULL;\r
   for(Int_t eW=0;eW<2;eW++)\r
   {   \r
    fDFPEventWeights[t][pW][eW] = NULL;\r
    fDiffFlowCorrelations[t][pW][eW] = NULL;\r
    fDiffFlowProductsOfCorrelations[t][pW][eW] = NULL;\r
    for(Int_t sc=0;sc<2;sc++)\r
    {\r
     fDiffFlowCorrectionTerms[t][pW][eW][sc] = NULL;\r
    }\r
   } \r
  }\r
 }  \r
 \r
 \r
 */\r
 \r
  \r
  \r
  /*\r
  for(Int_t pW=0;pW<2;pW++) // particle weights not used (0) or used (1)\r
  {\r
   for(Int_t eW=0;eW<2;eW++)\r
   {\r
    // correlations:\r
    for(Int_t correlationIndex=0;correlationIndex<4;correlationIndex++)\r
    {\r
     fCorrelationsPro[t][pW][eW][correlationIndex] = NULL;\r
    }\r
    // products of correlations:\r
    for(Int_t productOfCorrelationsIndex=0;productOfCorrelationsIndex<6;productOfCorrelationsIndex++)\r
    {\r
     fProductsOfCorrelationsPro[t][pW][eW][productOfCorrelationsIndex] = NULL;\r
    }\r
    // correction terms:\r
    for(Int_t sc=0;sc<2;sc++)\r
    {\r
     for(Int_t correctionsIndex=0;correctionsIndex<2;correctionsIndex++)\r
     {\r
      fCorrectionTermsPro[t][pW][eW][sc][correctionsIndex] = NULL;\r
     } \r
    } \r
   }\r
  } \r
  */\r
    \r
} // end of AliFlowAnalysisWithQCumulants::InitializeArraysForDiffFlow()\r
\r
\r
//================================================================================================================================\r
 /*\r
\r
\r
void AliFlowAnalysisWithQCumulants::CalculateCorrelationsForDifferentialFlow2D(TString type)\r
{\r
 // calculate all reduced correlations needed for differential flow for each (pt,eta) bin: \r
 \r
 if(type == "RP") // to be improved (removed)\r
 {\r
  cout<<endl;\r
 }\r
 // ... \r
 \r
 \r
 Int_t typeFlag = -1; \r
  \r
 // reduced correlations ares stored in fCorrelationsPro[t][pW][index] and are indexed as follows:\r
 // index:\r
 // 0: <2'>\r
 // 1: <4'>\r
\r
 // multiplicity:\r
 Double_t dMult = (*fSMpk)(0,0);\r
 \r
 // real and imaginary parts of non-weighted Q-vectors evaluated in harmonics n, 2n, 3n and 4n: \r
 Double_t dReQ1n = (*fReQ)(0,0);\r
 Double_t dReQ2n = (*fReQ)(1,0);\r
 //Double_t dReQ3n = (*fReQ)(2,0);\r
 //Double_t dReQ4n = (*fReQ)(3,0);\r
 Double_t dImQ1n = (*fImQ)(0,0);\r
 Double_t dImQ2n = (*fImQ)(1,0);\r
 //Double_t dImQ3n = (*fImQ)(2,0);\r
 //Double_t dImQ4n = (*fImQ)(3,0);\r
\r
 // looping over all (pt,eta) bins and calculating correlations needed for differential flow: \r
 for(Int_t p=1;p<=fnBinsPt;p++)\r
 {\r
  for(Int_t e=1;e<=fnBinsEta;e++)\r
  {\r
   // real and imaginary parts of p_{m*n,0} (non-weighted Q-vector evaluated for POIs in particular (pt,eta) bin): \r
   Double_t p1n0kRe = 0.;\r
   Double_t p1n0kIm = 0.;\r
\r
   // number of POIs in particular (pt,eta) bin:\r
   Double_t mp = 0.;\r
\r
   // real and imaginary parts of q_{m*n,0} (non-weighted Q-vector evaluated for particles which are both RPs and POIs in particular (pt,eta) bin):\r
   Double_t q1n0kRe = 0.;\r
   Double_t q1n0kIm = 0.;\r
   Double_t q2n0kRe = 0.;\r
   Double_t q2n0kIm = 0.;\r
\r
   // number of particles which are both RPs and POIs in particular (pt,eta) bin:\r
   Double_t mq = 0.;\r
   \r
   // q_{m*n,0}:\r
   q1n0kRe = fReEBE2D[2][0][0]->GetBinContent(fReEBE2D[2][0][0]->GetBin(p,e))\r
           * fReEBE2D[2][0][0]->GetBinEntries(fReEBE2D[2][0][0]->GetBin(p,e));\r
   q1n0kIm = fImEBE2D[2][0][0]->GetBinContent(fImEBE2D[2][0][0]->GetBin(p,e))\r
           * fImEBE2D[2][0][0]->GetBinEntries(fImEBE2D[2][0][0]->GetBin(p,e));\r
   q2n0kRe = fReEBE2D[2][1][0]->GetBinContent(fReEBE2D[2][1][0]->GetBin(p,e))\r
           * fReEBE2D[2][1][0]->GetBinEntries(fReEBE2D[2][1][0]->GetBin(p,e));\r
   q2n0kIm = fImEBE2D[2][1][0]->GetBinContent(fImEBE2D[2][1][0]->GetBin(p,e))\r
           * fImEBE2D[2][1][0]->GetBinEntries(fImEBE2D[2][1][0]->GetBin(p,e));\r
           \r
   mq = fReEBE2D[2][0][0]->GetBinEntries(fReEBE2D[2][0][0]->GetBin(p,e)); // to be improved (cross-checked by accessing other profiles here)\r
   \r
   if(type == "POI")\r
   {\r
    // p_{m*n,0}:\r
    p1n0kRe = fReEBE2D[1][0][0]->GetBinContent(fReEBE2D[1][0][0]->GetBin(p,e))\r
            * fReEBE2D[1][0][0]->GetBinEntries(fReEBE2D[1][0][0]->GetBin(p,e));\r
    p1n0kIm = fImEBE2D[1][0][0]->GetBinContent(fImEBE2D[1][0][0]->GetBin(p,e))  \r
            * fImEBE2D[1][0][0]->GetBinEntries(fImEBE2D[1][0][0]->GetBin(p,e));\r
            \r
    mp = fReEBE2D[1][0][0]->GetBinEntries(fReEBE2D[1][0][0]->GetBin(p,e)); // to be improved (cross-checked by accessing other profiles here)\r
    \r
    typeFlag = 1;\r
   }\r
   else if(type == "RP")\r
   {\r
    // p_{m*n,0} = q_{m*n,0}:\r
    p1n0kRe = q1n0kRe; \r
    p1n0kIm = q1n0kIm; \r
    mp = mq; \r
    \r
    typeFlag = 0;\r
   }\r
   \r
   // count events with non-empty (pt,eta) bin:\r
   if(mp>0)\r
   {\r
    fNonEmptyBins2D[typeFlag]->Fill(fPtMin+(p-1)*fPtBinWidth,fEtaMin+(e-1)*fEtaBinWidth,1);\r
   }\r
   \r
   // 2'-particle correlation for particular (pt,eta) bin:\r
   Double_t two1n1nPtEta = 0.;\r
   if(mp*dMult-mq)\r
   {\r
    two1n1nPtEta = (p1n0kRe*dReQ1n+p1n0kIm*dImQ1n-mq)\r
                 / (mp*dMult-mq);\r
   \r
    // fill the 2D profile to get the average correlation for each (pt,eta) bin:\r
    if(type == "POI")\r
    { \r
     //f2pPtEtaPOI->Fill(fPtMin+(p-1)*fPtBinWidth,fEtaMin+(e-1)*fEtaBinWidth,two1n1nPtEta,mp*dMult-mq);\r
     \r
     fCorrelationsPro[1][0][0][0]->Fill(fPtMin+(p-1)*fPtBinWidth,fEtaMin+(e-1)*fEtaBinWidth,two1n1nPtEta,mp*dMult-mq);\r
    }\r
    else if(type == "RP")\r
    {\r
     //f2pPtEtaRP->Fill(fPtMin+(p-1)*fPtBinWidth,fEtaMin+(e-1)*fEtaBinWidth,two1n1nPtEta,mp*dMult-mq);   \r
     fCorrelationsPro[0][0][0][0]->Fill(fPtMin+(p-1)*fPtBinWidth,fEtaMin+(e-1)*fEtaBinWidth,two1n1nPtEta,mp*dMult-mq);\r
    }\r
   } // end of if(mp*dMult-mq)\r
  \r
   // 4'-particle correlation:\r
   Double_t four1n1n1n1nPtEta = 0.;\r
   if((mp-mq)*dMult*(dMult-1.)*(dMult-2.)\r
       + mq*(dMult-1.)*(dMult-2.)*(dMult-3.)) // to be improved (introduce a new variable for this expression)\r
   {\r
    four1n1n1n1nPtEta = ((pow(dReQ1n,2.)+pow(dImQ1n,2.))*(p1n0kRe*dReQ1n+p1n0kIm*dImQ1n)\r
                      - q2n0kRe*(pow(dReQ1n,2.)-pow(dImQ1n,2.))\r
                      - 2.*q2n0kIm*dReQ1n*dImQ1n\r
                      - p1n0kRe*(dReQ1n*dReQ2n+dImQ1n*dImQ2n)\r
                      + p1n0kIm*(dImQ1n*dReQ2n-dReQ1n*dImQ2n)\r
                      - 2.*dMult*(p1n0kRe*dReQ1n+p1n0kIm*dImQ1n)\r
                      - 2.*(pow(dReQ1n,2.)+pow(dImQ1n,2.))*mq                      \r
                      + 6.*(q1n0kRe*dReQ1n+q1n0kIm*dImQ1n)                                            \r
                      + 1.*(q2n0kRe*dReQ2n+q2n0kIm*dImQ2n)                      \r
                      + 2.*(p1n0kRe*dReQ1n+p1n0kIm*dImQ1n)                       \r
                      + 2.*mq*dMult                      \r
                      - 6.*mq)        \r
                      / ((mp-mq)*dMult*(dMult-1.)*(dMult-2.)\r
                          + mq*(dMult-1.)*(dMult-2.)*(dMult-3.)); \r
    \r
    // fill the 2D profile to get the average correlation for each (pt, eta) bin:\r
    if(type == "POI")\r
    {\r
     //f4pPtEtaPOI->Fill(fPtMin+(p-1)*fPtBinWidth,fEtaMin+(e-1)*fEtaBinWidth,four1n1n1n1nPtEta,\r
     //                  (mp-mq)*dMult*(dMult-1.)*(dMult-2.)\r
     //                   + mq*(dMult-1.)*(dMult-2.)*(dMult-3.));\r
     \r
     fCorrelationsPro[1][0][0][1]->Fill(fPtMin+(p-1)*fPtBinWidth,fEtaMin+(e-1)*fEtaBinWidth,four1n1n1n1nPtEta,\r
                                     (mp-mq)*dMult*(dMult-1.)*(dMult-2.)\r
                                     + mq*(dMult-1.)*(dMult-2.)*(dMult-3.));\r
    }\r
    else if(type == "RP")\r
    {\r
     //f4pPtEtaRP->Fill(fPtMin+(p-1)*fPtBinWidth,fEtaMin+(e-1)*fEtaBinWidth,four1n1n1n1nPtEta,\r
     //                 (mp-mq)*dMult*(dMult-1.)*(dMult-2.)\r
     //                  + mq*(dMult-1.)*(dMult-2.)*(dMult-3.));   \r
                       \r
     fCorrelationsPro[0][0][0][1]->Fill(fPtMin+(p-1)*fPtBinWidth,fEtaMin+(e-1)*fEtaBinWidth,four1n1n1n1nPtEta,\r
                                       (mp-mq)*dMult*(dMult-1.)*(dMult-2.)\r
                                       + mq*(dMult-1.)*(dMult-2.)*(dMult-3.));                   \r
    }\r
   } // end of if((mp-mq)*dMult*(dMult-1.)*(dMult-2.)\r
     //            +mq*(dMult-1.)*(dMult-2.)*(dMult-3.))\r
   \r
  } // end of for(Int_t e=1;e<=fnBinsEta;e++)\r
 } // end of for(Int_t p=1;p<=fnBinsPt;p++)\r
\r
 \r
   \r
    \r
      \r
} // end of AliFlowAnalysisWithQCumulants::CalculateCorrelationsForDifferentialFlow2D()\r
\r
\r
\r
 \r
 \r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::CalculateWeightedCorrelationsForDifferentialFlow2D(TString type)\r
{\r
 // calculate all weighted correlations needed for differential flow \r
 \r
  if(type == "RP") // to be improved (removed)\r
 {\r
  cout<<endl;\r
 }\r
 // ... \r
 \r
 \r
 \r
 \r
 // real and imaginary parts of weighted Q-vectors evaluated in harmonics n, 2n, 3n and 4n: \r
 Double_t dReQ1n1k = (*fReQ)(0,1);\r
 Double_t dReQ2n2k = (*fReQ)(1,2);\r
 Double_t dReQ1n3k = (*fReQ)(0,3);\r
 //Double_t dReQ4n4k = (*fReQ)(3,4);\r
 Double_t dImQ1n1k = (*fImQ)(0,1);\r
 Double_t dImQ2n2k = (*fImQ)(1,2);\r
 Double_t dImQ1n3k = (*fImQ)(0,3);\r
 //Double_t dImQ4n4k = (*fImQ)(3,4);\r
 \r
 // S^M_{p,k} (see .h file for the definition of fSMpk):\r
 Double_t dSM1p1k = (*fSMpk)(0,1);\r
 Double_t dSM1p2k = (*fSMpk)(0,2);\r
 Double_t dSM1p3k = (*fSMpk)(0,3);\r
 Double_t dSM2p1k = (*fSMpk)(1,1);\r
 Double_t dSM3p1k = (*fSMpk)(2,1);\r
 \r
 // looping over all (pt,eta) bins and calculating weighted correlations needed for differential flow: \r
 for(Int_t p=1;p<=fnBinsPt;p++)\r
 {\r
  for(Int_t e=1;e<=fnBinsEta;e++)\r
  {\r
   // real and imaginary parts of p_{m*n,0} (non-weighted Q-vector evaluated for POIs in particular (pt,eta) bin):  \r
   Double_t p1n0kRe = 0.;\r
   Double_t p1n0kIm = 0.;\r
\r
   // number of POIs in particular (pt,eta) bin):\r
   Double_t mp = 0.;\r
\r
   // real and imaginary parts of q_{m*n,k}: \r
   // (weighted Q-vector evaluated for particles which are both RPs and POIs in particular (pt,eta) bin)\r
   Double_t q1n2kRe = 0.;\r
   Double_t q1n2kIm = 0.;\r
   Double_t q2n1kRe = 0.;\r
   Double_t q2n1kIm = 0.;\r
\r
   // s_{1,1}, s_{1,2} and s_{1,3} // to be improved (add explanation)  \r
   Double_t s1p1k = 0.; \r
   Double_t s1p2k = 0.; \r
   Double_t s1p3k = 0.; \r
   \r
   // M0111 from Eq. (118) in QC2c (to be improved (notation))\r
   Double_t dM0111 = 0.;\r
 \r
   if(type == "POI")\r
   {\r
    // p_{m*n,0}:\r
    p1n0kRe = fReEBE2D[1][0][0]->GetBinContent(fReEBE2D[1][0][0]->GetBin(p,e))\r
            * fReEBE2D[1][0][0]->GetBinEntries(fReEBE2D[1][0][0]->GetBin(p,e));\r
    p1n0kIm = fImEBE2D[1][0][0]->GetBinContent(fImEBE2D[1][0][0]->GetBin(p,e))\r
            * fImEBE2D[1][0][0]->GetBinEntries(fImEBE2D[1][0][0]->GetBin(p,e)); \r
            \r
    mp = fReEBE2D[1][0][0]->GetBinEntries(fReEBE2D[1][0][0]->GetBin(p,e));\r
    \r
    // q_{m*n,k}: \r
    q1n2kRe = fReEBE2D[2][0][2]->GetBinContent(fReEBE2D[2][0][2]->GetBin(p,e))\r
            * fReEBE2D[2][0][2]->GetBinEntries(fReEBE2D[2][0][2]->GetBin(p,e));\r
    q1n2kIm = fImEBE2D[2][0][2]->GetBinContent(fImEBE2D[2][0][2]->GetBin(p,e))\r
            * fImEBE2D[2][0][2]->GetBinEntries(fImEBE2D[2][0][2]->GetBin(p,e));\r
    q2n1kRe = fReEBE2D[2][1][1]->GetBinContent(fReEBE2D[2][1][1]->GetBin(p,e))\r
            * fReEBE2D[2][1][1]->GetBinEntries(fReEBE2D[2][1][1]->GetBin(p,e)); \r
    q2n1kIm = fImEBE2D[2][1][1]->GetBinContent(fImEBE2D[2][1][1]->GetBin(p,e))\r
            * fImEBE2D[2][1][1]->GetBinEntries(fImEBE2D[2][1][1]->GetBin(p,e));\r
       \r
    // s_{1,1}, s_{1,2} and s_{1,3} // to be improved (add explanation)  \r
    s1p1k = pow(fs2D[2][1]->GetBinContent(fs2D[2][1]->GetBin(p,e)),1.); \r
    s1p2k = pow(fs2D[2][2]->GetBinContent(fs2D[2][2]->GetBin(p,e)),1.); \r
    s1p3k = pow(fs2D[2][3]->GetBinContent(fs2D[2][3]->GetBin(p,e)),1.); \r
   \r
    // M0111 from Eq. (118) in QC2c (to be improved (notation)):\r
    dM0111 = mp*(dSM3p1k-3.*dSM1p1k*dSM1p2k+2.*dSM1p3k)\r
           - 3.*(s1p1k*(dSM2p1k-dSM1p2k)\r
           + 2.*(s1p3k-s1p2k*dSM1p1k));\r
   }\r
   else if(type == "RP")\r
   {\r
    p1n0kRe = fReEBE2D[0][0][0]->GetBinContent(fReEBE2D[0][0][0]->GetBin(p,e))\r
            * fReEBE2D[0][0][0]->GetBinEntries(fReEBE2D[0][0][0]->GetBin(p,e));\r
    p1n0kIm = fImEBE2D[0][0][0]->GetBinContent(fImEBE2D[0][0][0]->GetBin(p,e))\r
            * fImEBE2D[0][0][0]->GetBinEntries(fImEBE2D[0][0][0]->GetBin(p,e));\r
            \r
    mp = fReEBE2D[0][0][0]->GetBinEntries(fReEBE2D[0][0][0]->GetBin(p,e));\r
    \r
    // q_{m*n,k}: \r
    q1n2kRe = fReEBE2D[0][0][2]->GetBinContent(fReEBE2D[0][0][2]->GetBin(p,e))\r
            * fReEBE2D[0][0][2]->GetBinEntries(fReEBE2D[0][0][2]->GetBin(p,e));\r
    q1n2kIm = fImEBE2D[0][0][2]->GetBinContent(fImEBE2D[0][0][2]->GetBin(p,e))\r
            * fImEBE2D[0][0][2]->GetBinEntries(fImEBE2D[0][0][2]->GetBin(p,e));\r
    q2n1kRe = fReEBE2D[0][1][1]->GetBinContent(fReEBE2D[0][1][1]->GetBin(p,e))\r
            * fReEBE2D[0][1][1]->GetBinEntries(fReEBE2D[0][1][1]->GetBin(p,e));\r
    q2n1kIm = fImEBE2D[0][1][1]->GetBinContent(fImEBE2D[0][1][1]->GetBin(p,e))\r
            * fImEBE2D[0][1][1]->GetBinEntries(fImEBE2D[0][1][1]->GetBin(p,e));\r
   \r
    // s_{1,1}, s_{1,2} and s_{1,3} // to be improved (add explanation)  \r
    s1p1k = pow(fs2D[0][1]->GetBinContent(fs2D[0][1]->GetBin(p,e)),1.); \r
    s1p2k = pow(fs2D[0][2]->GetBinContent(fs2D[0][2]->GetBin(p,e)),1.); \r
    s1p3k = pow(fs2D[0][3]->GetBinContent(fs2D[0][3]->GetBin(p,e)),1.); \r
   \r
    // M0111 from Eq. (118) in QC2c (to be improved (notation)):\r
    dM0111 = mp*(dSM3p1k-3.*dSM1p1k*dSM1p2k+2.*dSM1p3k)\r
           - 3.*(s1p1k*(dSM2p1k-dSM1p2k)\r
           + 2.*(s1p3k-s1p2k*dSM1p1k));\r
    //...............................................................................................   \r
   }\r
   \r
   // 2'-particle correlation:\r
   Double_t two1n1nW0W1PtEta = 0.;\r
   if(mp*dSM1p1k-s1p1k)\r
   {\r
    two1n1nW0W1PtEta = (p1n0kRe*dReQ1n1k+p1n0kIm*dImQ1n1k-s1p1k)\r
                 / (mp*dSM1p1k-s1p1k);\r
   \r
    // fill the 2D profile to get the average correlation for each (pt, eta) bin:\r
    if(type == "POI")\r
    {\r
     //f2pPtEtaPOIW->Fill(fPtMin+(p-1)*fPtBinWidth,fEtaMin+(e-1)*fEtaBinWidth,two1n1nW0W1PtEta,\r
     //                   mp*dSM1p1k-s1p1k);\r
     fCorrelationsPro[1][1][0][0]->Fill(fPtMin+(p-1)*fPtBinWidth,fEtaMin+(e-1)*fEtaBinWidth,two1n1nW0W1PtEta,mp*dSM1p1k-s1p1k);\r
    }\r
    else if(type == "RP")\r
    {\r
     //f2pPtEtaRPW->Fill(fPtMin+(p-1)*fPtBinWidth,fEtaMin+(e-1)*fEtaBinWidth,two1n1nW0W1PtEta,\r
     //                  mp*dSM1p1k-s1p1k); \r
     fCorrelationsPro[0][1][0][0]->Fill(fPtMin+(p-1)*fPtBinWidth,fEtaMin+(e-1)*fEtaBinWidth,two1n1nW0W1PtEta,mp*dSM1p1k-s1p1k);  \r
    }\r
   } // end of if(mp*dMult-dmPrimePrimePtEta)\r
   \r
   // 4'-particle correlation:\r
   Double_t four1n1n1n1nW0W1W1W1PtEta = 0.;\r
   if(dM0111)\r
   {\r
    four1n1n1n1nW0W1W1W1PtEta = ((pow(dReQ1n1k,2.)+pow(dImQ1n1k,2.))*(p1n0kRe*dReQ1n1k+p1n0kIm*dImQ1n1k)\r
                      - q2n1kRe*(pow(dReQ1n1k,2.)-pow(dImQ1n1k,2.))\r
                      - 2.*q2n1kIm*dReQ1n1k*dImQ1n1k\r
                      - p1n0kRe*(dReQ1n1k*dReQ2n2k+dImQ1n1k*dImQ2n2k)\r
                      + p1n0kIm*(dImQ1n1k*dReQ2n2k-dReQ1n1k*dImQ2n2k)\r
                      - 2.*dSM1p2k*(p1n0kRe*dReQ1n1k+p1n0kIm*dImQ1n1k)\r
                      - 2.*(pow(dReQ1n1k,2.)+pow(dImQ1n1k,2.))*s1p1k                                            \r
                      + 6.*(q1n2kRe*dReQ1n1k+q1n2kIm*dImQ1n1k)                                           \r
                      + 1.*(q2n1kRe*dReQ2n2k+q2n1kIm*dImQ2n2k)                         \r
                      + 2.*(p1n0kRe*dReQ1n3k+p1n0kIm*dImQ1n3k)                      \r
                      + 2.*s1p1k*dSM1p2k                                      \r
                      - 6.*s1p3k)        \r
                      / dM0111; // to be imropoved (notation of dM0111)\r
   \r
    // fill the 2D profile to get the average correlation for each (pt, eta) bin:\r
    if(type == "POI")\r
    {\r
     //f4pPtEtaPOIW->Fill(fPtMin+(p-1)*fPtBinWidth,fEtaMin+(e-1)*fEtaBinWidth,four1n1n1n1nW0W1W1W1PtEta,dM0111);\r
     fCorrelationsPro[1][1][0][1]->Fill(fPtMin+(p-1)*fPtBinWidth,fEtaMin+(e-1)*fEtaBinWidth,four1n1n1n1nW0W1W1W1PtEta,dM0111);\r
    }\r
    else if(type == "RP")\r
    {\r
     //f4pPtEtaRPW->Fill(fPtMin+(p-1)*fPtBinWidth,fEtaMin+(e-1)*fEtaBinWidth,four1n1n1n1nW0W1W1W1PtEta,dM0111); \r
     fCorrelationsPro[0][1][0][1]->Fill(fPtMin+(p-1)*fPtBinWidth,fEtaMin+(e-1)*fEtaBinWidth,four1n1n1n1nW0W1W1W1PtEta,dM0111); \r
    }\r
   } // end of if(dM0111)\r
  \r
  } // end of for(Int_t e=1;e<=fnBinsEta;e++)\r
 } // end of for(Int_t p=1;p<=fnBinsPt;p++)\r
 \r
  \r
    \r
      \r
} // end of AliFlowAnalysisWithQCumulants::CalculateWeightedCorrelationsForDifferentialFlow2D(TString type)\r
\r
\r
//================================================================================================================================\r
\r
 */  \r
\r
/*\r
void AliFlowAnalysisWithQCumulants::FinalizeCorrelationsForDiffFlow(TString type, Bool_t useParticleWeights, TString eventWeights)\r
{\r
 // 1.) Access average for 2D correlations from profiles and store them in 2D final results histograms;\r
 // 2.) Access spread for 2D correlations from profiles, calculate error and store it in 2D final results histograms;\r
 // 3.) Make projections along pt and eta axis and store results and errors in 1D final results histograms. \r
 \r
 Int_t typeFlag = -1;\r
 Int_t pWeightsFlag = -1;\r
 Int_t eWeightsFlag = -1;\r
\r
 if(type == "RP")\r
 {\r
  typeFlag = 0;\r
 } else if(type == "POI")\r
   {\r
    typeFlag = 1;\r
   } else \r
     {\r
      cout<<"WARNING: type must be either RP or POI in AFAWQC::FCFDF() !!!!"<<endl;\r
      exit(0);\r
     }\r
     \r
 if(!useParticleWeights)\r
 {\r
  pWeightsFlag = 0;\r
 } else \r
   {\r
    pWeightsFlag = 1;   \r
   }   \r
   \r
 if(eventWeights == "exact")\r
 {\r
  eWeightsFlag = 0;\r
 }          \r
  \r
 // shortcuts:\r
 Int_t t = typeFlag;\r
 Int_t pW = pWeightsFlag;\r
 Int_t eW = eWeightsFlag;\r
 \r
 // from 2D histogram fNonEmptyBins2D make two 1D histograms fNonEmptyBins1D in pt and eta (to be improved (i.e. moved somewhere else))  \r
 // pt:\r
 for(Int_t p=1;p<fnBinsPt;p++)\r
 {\r
  Double_t contentPt = 0.;\r
  for(Int_t e=1;e<=fnBinsEta;e++)\r
  {\r
   contentPt += (fNonEmptyBins2D[t]->GetBinContent(fNonEmptyBins2D[t]->GetBin(p,e)));          \r
  }\r
  fNonEmptyBins1D[t][0]->SetBinContent(p,contentPt);\r
 }\r
 // eta:\r
 for(Int_t e=1;e<fnBinsEta;e++)\r
 {\r
  Double_t contentEta = 0.;\r
  for(Int_t p=1;p<=fnBinsPt;p++)\r
  {\r
   contentEta += (fNonEmptyBins2D[t]->GetBinContent(fNonEmptyBins2D[t]->GetBin(p,e)));          \r
  }\r
  fNonEmptyBins1D[t][1]->SetBinContent(e,contentEta);\r
 }\r
 \r
 // from 2D profile in (pt,eta) make two 1D profiles in (pt) and (eta):\r
 TProfile *profile[2][4]; // [0=pt,1=eta][correlation index] // to be improved (do not hardwire the correlation index)\r
 \r
 for(Int_t pe=0;pe<2;pe++) // pt or eta\r
 {\r
  for(Int_t ci=0;ci<4;ci++) // correlation index\r
  {\r
   if(pe==0) profile[pe][ci] = this->MakePtProjection(fCorrelationsPro[t][pW][eW][ci]);\r
   if(pe==1) profile[pe][ci] = this->MakeEtaProjection(fCorrelationsPro[t][pW][eW][ci]);\r
  }\r
 }\r
  \r
 // transfer 2D profile into 2D histogram:\r
 // to be improved (see in documentation if there is a method to transfer values from 2D profile into 2D histogram)    \r
 for(Int_t ci=0;ci<4;ci++)\r
 {\r
  for(Int_t p=1;p<=fnBinsPt;p++)\r
  {\r
   for(Int_t e=1;e<=fnBinsEta;e++)\r
   {\r
    Double_t correlation = fCorrelationsPro[t][pW][eW][ci]->GetBinContent(fCorrelationsPro[t][pW][eW][ci]->GetBin(p,e)); \r
    Double_t spread = fCorrelationsPro[t][pW][eW][ci]->GetBinError(fCorrelationsPro[t][pW][eW][ci]->GetBin(p,e));\r
    Double_t nEvts = fNonEmptyBins2D[t]->GetBinContent(fNonEmptyBins2D[t]->GetBin(p,e));\r
    Double_t error = 0.;\r
    fFinalCorrelations2D[t][pW][eW][ci]->SetBinContent(fFinalCorrelations2D[t][pW][eW][ci]->GetBin(p,e),correlation);          \r
    if(nEvts>0)\r
    {\r
     error = spread/pow(nEvts,0.5);\r
     fFinalCorrelations2D[t][pW][eW][ci]->SetBinError(fFinalCorrelations2D[t][pW][eW][ci]->GetBin(p,e),error);\r
    }\r
   } // end of for(Int_t e=1;e<=fnBinsEta;e++)\r
  } // end of for(Int_t p=1;p<=fnBinsPt;p++)\r
 } // end of for(Int_t ci=0;ci<4;ci++)\r
 \r
 // transfer 1D profile into 1D histogram (pt):\r
 // to be improved (see in documentation if there is a method to transfer values from 1D profile into 1D histogram)    \r
 for(Int_t ci=0;ci<4;ci++)\r
 {\r
  for(Int_t p=1;p<=fnBinsPt;p++)\r
  {\r
   if(profile[0][ci])\r
   {\r
    Double_t correlation = profile[0][ci]->GetBinContent(p); \r
    Double_t spread = profile[0][ci]->GetBinError(p);\r
    Double_t nEvts = fNonEmptyBins1D[t][0]->GetBinContent(p);\r
    Double_t error = 0.;\r
    fFinalCorrelations1D[t][pW][eW][0][ci]->SetBinContent(p,correlation); \r
    if(nEvts>0)\r
    {\r
     error = spread/pow(nEvts,0.5);\r
     fFinalCorrelations1D[t][pW][eW][0][ci]->SetBinError(p,error);\r
    }  \r
   }   \r
  } // end of for(Int_t p=1;p<=fnBinsPt;p++)\r
 } // end of for(Int_t ci=0;ci<4;ci++)\r
 \r
 // transfer 1D profile into 1D histogram (eta):\r
 // to be improved (see in documentation if there is a method to transfer values from 1D profile into 1D histogram)    \r
 for(Int_t ci=0;ci<4;ci++)\r
 {\r
  for(Int_t e=1;e<=fnBinsEta;e++)\r
  {\r
   if(profile[1][ci])\r
   {\r
    Double_t correlation = profile[1][ci]->GetBinContent(e); \r
    fFinalCorrelations1D[t][pW][eW][1][ci]->SetBinContent(e,correlation);      \r
   }    \r
  } // end of for(Int_t e=1;e<=fnBinsEta;e++)\r
 } // end of for(Int_t ci=0;ci<4;ci++)\r
        \r
} // end of void AliFlowAnalysisWithQCumulants::FinalizeCorrelationsForDiffFlow(TString type, Bool_t useParticleWeights, TString eventWeights)\r
*/\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::CalculateDiffFlowCumulants(TString type, TString ptOrEta)\r
{\r
 // calcualate cumulants for differential flow from measured correlations\r
 // Remark: cumulants calculated here are NOT corrected for non-uniform acceptance. This correction is applied in the method ...\r
 // to be improved (description) \r
 \r
 Int_t typeFlag = -1;\r
 Int_t ptEtaFlag = -1;\r
\r
 if(type == "RP")\r
 {\r
  typeFlag = 0;\r
 } else if(type == "POI")\r
   {\r
    typeFlag = 1;\r
   } \r
     \r
 if(ptOrEta == "Pt")\r
 {\r
  ptEtaFlag = 0;\r
 } else if(ptOrEta == "Eta")\r
   {\r
    ptEtaFlag = 1;\r
   } \r
  \r
 // shortcuts:\r
 Int_t t = typeFlag;\r
 Int_t pe = ptEtaFlag;\r
     \r
 // common:\r
 Int_t nBinsPtEta[2] = {fnBinsPt,fnBinsEta};\r
 \r
 // correlation <<2>>: \r
 Double_t two = fIntFlowCorrelationsHist->GetBinContent(1);\r
 \r
 // 1D:\r
 for(Int_t b=1;b<=nBinsPtEta[pe];b++)\r
 {\r
  // reduced correlations:   \r
  Double_t twoPrime = fDiffFlowCorrelationsHist[t][pe][0]->GetBinContent(b); // <<2'>>(pt)\r
  Double_t fourPrime = fDiffFlowCorrelationsHist[t][pe][1]->GetBinContent(b); // <<4'>>(pt)\r
  // final statistical error of reduced correlations:\r
  //Double_t twoPrimeError = fFinalCorrelations1D[t][pW][eW][0][0]->GetBinError(p); \r
  // QC{2'}:\r
  Double_t qc2Prime = twoPrime; // QC{2'}\r
  //Double_t qc2PrimeError = twoPrimeError; // final stat. error of QC{2'}\r
  fDiffFlowCumulants[t][pe][0]->SetBinContent(b,qc2Prime); \r
  //fFinalCumulantsPt[t][pW][eW][nua][0]->SetBinError(p,qc2PrimeError);   \r
  // QC{4'}:\r
  Double_t qc4Prime = fourPrime - 2.*twoPrime*two; // QC{4'} = <<4'>> - 2*<<2'>><<2>>\r
  fDiffFlowCumulants[t][pe][1]->SetBinContent(b,qc4Prime); \r
 } // end of for(Int_t p=1;p<=fnBinsPt;p++)\r
 \r
    \r
 /* \r
 // 2D (pt,eta):\r
 // to be improved (see documentation if I can do all this without looping)\r
 for(Int_t p=1;p<=fnBinsPt;p++)\r
 {\r
  for(Int_t e=1;e<=fnBinsEta;e++) \r
  {  \r
   // reduced correlations:   \r
   Double_t twoPrime = fFinalCorrelations2D[t][pW][eW][0]->GetBinContent(fFinalCorrelations2D[t][pW][eW][0]->GetBin(p,e)); // <<2'>>(pt,eta)\r
   Double_t fourPrime = fFinalCorrelations2D[t][pW][eW][1]->GetBinContent(fFinalCorrelations2D[t][pW][eW][1]->GetBin(p,e)); // <<4'>>(pt,eta)\r
   for(Int_t nua=0;nua<2;nua++)\r
   {\r
    // QC{2'}:\r
    Double_t qc2Prime = twoPrime; // QC{2'} = <<2'>>\r
    fFinalCumulants2D[t][pW][eW][nua][0]->SetBinContent(fFinalCumulants2D[t][pW][eW][nua][0]->GetBin(p,e),qc2Prime);    \r
    // QC{4'}:\r
    Double_t qc4Prime = fourPrime - 2.*twoPrime*two; // QC{4'} = <<4'>> - 2*<<2'>><<2>>\r
    fFinalCumulants2D[t][pW][eW][nua][1]->SetBinContent(fFinalCumulants2D[t][pW][eW][nua][1]->GetBin(p,e),qc4Prime);   \r
   } // end of for(Int_t nua=0;nua<2;nua++)   \r
  } // end of for(Int_t e=1;e<=fnBinsEta;e++)\r
 } // end of for(Int_t p=1;p<=fnBinsPt;p++)\r
 */\r
   \r
} // end of void AliFlowAnalysisWithQCumulants::CalculateDiffFlowCumulants(TString type, Bool_t useParticleWeights, TString eventWeights); \r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::CalculateFinalResultsForRPandPOIIntegratedFlow(TString type)\r
{\r
 // calculate final results for integrated flow of RPs and POIs \r
  \r
 Int_t typeFlag = -1;\r
\r
 if(type == "RP")\r
 {\r
  typeFlag = 0;\r
 } else if(type == "POI")\r
   {\r
    typeFlag = 1;\r
   } else \r
     {\r
      cout<<"WARNING: type must be either RP or POI in AFAWQC::CDF() !!!!"<<endl;\r
      exit(0);\r
     }\r
     \r
 // shortcuts:\r
 Int_t t = typeFlag;\r
  \r
 // pt yield:    \r
 TH1F *yield2ndPt = NULL;\r
 TH1F *yield4thPt = NULL;\r
 TH1F *yield6thPt = NULL;\r
 TH1F *yield8thPt = NULL;\r
 \r
 if(type == "POI")\r
 {\r
  yield2ndPt = (TH1F*)(fCommonHists2nd->GetHistPtPOI())->Clone();\r
  yield4thPt = (TH1F*)(fCommonHists4th->GetHistPtPOI())->Clone();\r
  yield6thPt = (TH1F*)(fCommonHists6th->GetHistPtPOI())->Clone();\r
  yield8thPt = (TH1F*)(fCommonHists8th->GetHistPtPOI())->Clone();  \r
 } \r
 else if(type == "RP")\r
 {\r
  yield2ndPt = (TH1F*)(fCommonHists2nd->GetHistPtRP())->Clone();\r
  yield4thPt = (TH1F*)(fCommonHists4th->GetHistPtRP())->Clone();\r
  yield6thPt = (TH1F*)(fCommonHists6th->GetHistPtRP())->Clone();\r
  yield8thPt = (TH1F*)(fCommonHists8th->GetHistPtRP())->Clone();  \r
 } \r
 \r
 Int_t nBinsPt = yield2ndPt->GetNbinsX();\r
 \r
 TH1D *flow2ndPt = NULL;\r
 TH1D *flow4thPt = NULL;\r
 TH1D *flow6thPt = NULL;\r
 TH1D *flow8thPt = NULL;\r
 \r
 // to be improved (hardwired pt index)\r
 flow2ndPt = (TH1D*)fDiffFlow[t][0][0]->Clone();\r
 flow4thPt = (TH1D*)fDiffFlow[t][0][1]->Clone();\r
 flow6thPt = (TH1D*)fDiffFlow[t][0][2]->Clone();\r
 flow8thPt = (TH1D*)fDiffFlow[t][0][3]->Clone(); \r
   \r
 Double_t dvn2nd = 0., dvn4th = 0., dvn6th = 0., dvn8th = 0.; // differential flow\r
 Double_t dErrvn2nd = 0., dErrvn4th = 0., dErrvn6th = 0., dErrvn8th = 0.; // error on differential flow\r
 \r
 Double_t dVn2nd = 0., dVn4th = 0., dVn6th = 0., dVn8th = 0.; // integrated flow \r
 Double_t dErrVn2nd = 0., dErrVn4th = 0., dErrVn6th = 0., dErrVn8th = 0.; // error on integrated flow\r
\r
 Double_t dYield2nd = 0., dYield4th = 0., dYield6th = 0., dYield8th = 0.; // pt yield \r
 Double_t dSum2nd = 0., dSum4th = 0., dSum6th = 0., dSum8th = 0.; // needed for normalizing integrated flow\r
 \r
 // looping over pt bins:\r
 for(Int_t p=1;p<nBinsPt+1;p++)\r
 {\r
  dvn2nd = flow2ndPt->GetBinContent(p);\r
  dvn4th = flow4thPt->GetBinContent(p);\r
  dvn6th = flow6thPt->GetBinContent(p);\r
  dvn8th = flow8thPt->GetBinContent(p);\r
  \r
  dErrvn2nd = flow2ndPt->GetBinError(p);\r
  dErrvn4th = flow4thPt->GetBinError(p);\r
  dErrvn6th = flow6thPt->GetBinError(p);\r
  dErrvn8th = flow8thPt->GetBinError(p);\r
\r
  dYield2nd = yield2ndPt->GetBinContent(p);  \r
  dYield4th = yield4thPt->GetBinContent(p);\r
  dYield6th = yield6thPt->GetBinContent(p);\r
  dYield8th = yield8thPt->GetBinContent(p);\r
  \r
  dVn2nd += dvn2nd*dYield2nd;\r
  dVn4th += dvn4th*dYield4th;\r
  dVn6th += dvn6th*dYield6th;\r
  dVn8th += dvn8th*dYield8th;\r
  \r
  dSum2nd += dYield2nd;\r
  dSum4th += dYield4th;\r
  dSum6th += dYield6th;\r
  dSum8th += dYield8th;\r
  \r
  dErrVn2nd += dYield2nd*dYield2nd*dErrvn2nd*dErrvn2nd; // ro be improved (check this relation)\r
  dErrVn4th += dYield4th*dYield4th*dErrvn4th*dErrvn4th;\r
  dErrVn6th += dYield6th*dYield6th*dErrvn6th*dErrvn6th;\r
  dErrVn8th += dYield8th*dYield8th*dErrvn8th*dErrvn8th;\r
    \r
 } // end of for(Int_t p=1;p<nBinsPt+1;p++)\r
\r
 // normalizing the results for integrated flow:\r
 if(dSum2nd) \r
 {\r
  dVn2nd /= dSum2nd;\r
  dErrVn2nd /= (dSum2nd*dSum2nd);\r
  dErrVn2nd = TMath::Sqrt(dErrVn2nd);\r
 } \r
 if(dSum4th) \r
 {\r
  dVn4th /= dSum4th;\r
  dErrVn4th /= (dSum4th*dSum4th);\r
  dErrVn4th = TMath::Sqrt(dErrVn4th);\r
 } \r
 //if(dSum6th) dVn6th/=dSum6th;\r
 //if(dSum8th) dVn8th/=dSum8th;\r
  \r
 // storing the results for integrated flow in common histos: (to be improved: new method for this?)\r
 if(type == "POI")\r
 {\r
  fCommonHistsResults2nd->FillIntegratedFlowPOI(dVn2nd,dErrVn2nd); \r
  fCommonHistsResults4th->FillIntegratedFlowPOI(dVn4th,dErrVn4th); \r
  fCommonHistsResults6th->FillIntegratedFlowPOI(dVn6th,0.); // to be improved (errors)\r
  fCommonHistsResults8th->FillIntegratedFlowPOI(dVn8th,0.); // to be improved (errors)\r
 }\r
 else if (type == "RP")\r
 {\r
  fCommonHistsResults2nd->FillIntegratedFlowRP(dVn2nd,dErrVn2nd); \r
  fCommonHistsResults4th->FillIntegratedFlowRP(dVn4th,dErrVn4th);\r
  fCommonHistsResults6th->FillIntegratedFlowRP(dVn6th,0.); // to be improved (errors)\r
  fCommonHistsResults8th->FillIntegratedFlowRP(dVn8th,0.); // to be improved (errors)\r
 }\r
 \r
 delete flow2ndPt;\r
 delete flow4thPt;\r
 //delete flow6thPt;\r
 //delete flow8thPt;\r
 \r
 delete yield2ndPt;\r
 delete yield4thPt;\r
 delete yield6thPt;\r
 delete yield8thPt;\r
           \r
} // end of AliFlowAnalysisWithQCumulants::CalculateFinalResultsForRPandPOIIntegratedFlow(TString type)\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::InitializeArraysForDistributions()\r
{\r
 // Initialize all arrays used for distributions.
 
 // a) Initialize arrays of histograms used to hold distributions of correlations; 
 // b) Initialize array to hold min and max values of correlations.
 
 // a) Initialize arrays of histograms used to hold distributions of correlations:
 for(Int_t di=0;di<4;di++) // distribution index\r
 {\r
  fDistributions[di] = NULL;\r
 }\r
 
 // b) Initialize default min and max values of correlations:
 //    (Remark: The default values bellow were chosen for v2=5% and M=500)
 fMinValueOfCorrelation[0] = -0.01; // <2>_min 
 fMaxValueOfCorrelation[0] = 0.04; // <2>_max 
 fMinValueOfCorrelation[1] = -0.00002; // <4>_min 
 fMaxValueOfCorrelation[1] = 0.00015; // <4>_max  
 fMinValueOfCorrelation[2] = -0.0000003; // <6>_min 
 fMaxValueOfCorrelation[2] = 0.0000006; // <6>_max  
 fMinValueOfCorrelation[3] = -0.000000006; // <8>_min 
 fMaxValueOfCorrelation[3] = 0.000000003; // <8>_max 
 \r
} // end of void AliFlowAnalysisWithQCumulants::InitializeArraysForDistributions()\r
\r

//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::BookEverythingForDistributions()\r
{\r
 // a) Book profile to hold all flags for distributions of correlations;
 // b) Book all histograms to hold distributions of correlations.
 
 TString correlationIndex[4] = {"<2>","<4>","<6>","<8>"}; // to be improved (should I promote this to data members?)
  
 // a) Book profile to hold all flags for distributions of correlations:
 TString distributionsFlagsName = "fDistributionsFlags";\r
 distributionsFlagsName += fAnalysisLabel->Data();\r
 fDistributionsFlags = new TProfile(distributionsFlagsName.Data(),"Flags for Distributions of Correlations",9,0,9);\r
 fDistributionsFlags->SetTickLength(-0.01,"Y");\r
 fDistributionsFlags->SetMarkerStyle(25);\r
 fDistributionsFlags->SetLabelSize(0.05);\r
 fDistributionsFlags->SetLabelOffset(0.02,"Y");\r
 fDistributionsFlags->GetXaxis()->SetBinLabel(1,"Store or not?");\r
 fDistributionsFlags->GetXaxis()->SetBinLabel(2,"<2>_{min}");\r
 fDistributionsFlags->GetXaxis()->SetBinLabel(3,"<2>_{max}");\r
 fDistributionsFlags->GetXaxis()->SetBinLabel(4,"<4>_{min}");\r
 fDistributionsFlags->GetXaxis()->SetBinLabel(5,"<4>_{max}");\r
 fDistributionsFlags->GetXaxis()->SetBinLabel(6,"<6>_{min}");\r
 fDistributionsFlags->GetXaxis()->SetBinLabel(7,"<6>_{max}");\r
 fDistributionsFlags->GetXaxis()->SetBinLabel(8,"<8>_{min}");\r
 fDistributionsFlags->GetXaxis()->SetBinLabel(9,"<8>_{max}");\r
 fDistributionsList->Add(fDistributionsFlags);\r
 
 // b) Book all histograms to hold distributions of correlations.
 if(fStoreDistributions)
 { 
  TString distributionsName = "fDistributions";\r
  distributionsName += fAnalysisLabel->Data();\r
  for(Int_t di=0;di<4;di++) // distribution index\r
  {
   fDistributions[di] = new TH1D(Form("Distribution of %s",correlationIndex[di].Data()),Form("Distribution of %s",correlationIndex[di].Data()),10000,fMinValueOfCorrelation[di],fMaxValueOfCorrelation[di]); \r
   fDistributions[di]->SetXTitle(correlationIndex[di].Data());\r
   fDistributionsList->Add(fDistributions[di]);\r
  } // end of for(Int_t di=0;di<4;di++) // distribution index
 } // end of if(fStoreDistributions)
 
} // end of void AliFlowAnalysisWithQCumulants::BookEverythingForDistributions()\r
\r
\r
//================================================================================================================================\r
\r

void AliFlowAnalysisWithQCumulants::StoreFlagsForDistributions()\r
{\r
 // Store all flags for distributiuons of correlations in profile fDistributionsFlags.\r
 \r
 if(!fDistributionsFlags)\r
 {\r
  cout<<"WARNING: fDistributionsFlags is NULL in AFAWQC::SDF() !!!!"<<endl;\r
  exit(0);\r
 } \r
\r
 fDistributionsFlags->Fill(0.5,(Int_t)fStoreDistributions); // histos with distributions of correlations stored or not in the output file
 // store min and max values of correlations:
 for(Int_t di=0;di<4;di++) // distribution index\r
 {\r
  fDistributionsFlags->Fill(1.5+2.*(Double_t)di,fMinValueOfCorrelation[di]);
  fDistributionsFlags->Fill(2.5+2.*(Double_t)di,fMaxValueOfCorrelation[di]);
 }\r
     \r
} // end of void AliFlowAnalysisWithQCumulants::StoreFlagsForDistributions()\r
\r

//================================================================================================================================\r


void AliFlowAnalysisWithQCumulants::StoreDistributionsOfCorrelations()
{
 // Store distributions of correlations.
 
 if(!(fIntFlowCorrelationsEBE && fIntFlowEventWeightsForCorrelationsEBE))\r
 {\r
  cout<<"WARNING: fIntFlowCorrelationsEBE && fIntFlowEventWeightsForCorrelationsEBE"<<endl; \r
  cout<<"         is NULL in AFAWQC::SDOC() !!!!"<<endl;\r
  exit(0);\r
 }\r

 for(Int_t di=0;di<4;di++) // distribution index\r
 {
  if(!fDistributions[di])\r
  { \r
   cout<<"WARNING: fDistributions[di] is NULL in AFAWQC::SDOC() !!!!"<<endl;\r
   cout<<"di = "<<di<<endl;\r
   exit(0);\r
  } else 
    {
     fDistributions[di]->Fill(fIntFlowCorrelationsEBE->GetBinContent(di+1),fIntFlowEventWeightsForCorrelationsEBE->GetBinContent(di+1)); 
    } \r
 } // end of for(Int_t di=0;di<4;di++) // distribution index\r

} // end of void AliFlowAnalysisWithQCumulants::StoreDistributionsOfCorrelations()


//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::BookAndNestAllLists()\r
{\r
 // Book and nest all lists nested in the base list fHistList.\r
 //  a) Book and nest lists for integrated flow;\r
 //  b) Book and nest lists for differential flow;\r
 //  c) Book and nest list for particle weights;\r
 //  d) Book and nest list for distributions;\r
 //  e) Book and nest list for nested loops;\r
 \r
 // a) Book and nest all lists for integrated flow:\r
 // base list for integrated flow:\r
 fIntFlowList = new TList();\r
 fIntFlowList->SetName("Integrated Flow");\r
 fIntFlowList->SetOwner(kTRUE);\r
 fHistList->Add(fIntFlowList);\r
 // list holding profiles: \r
 fIntFlowProfiles = new TList();\r
 fIntFlowProfiles->SetName("Profiles");\r
 fIntFlowProfiles->SetOwner(kTRUE);\r
 fIntFlowList->Add(fIntFlowProfiles);\r
 // list holding histograms with results:\r
 fIntFlowResults = new TList();\r
 fIntFlowResults->SetName("Results");\r
 fIntFlowResults->SetOwner(kTRUE);\r
 fIntFlowList->Add(fIntFlowResults);\r
 \r
 // b) Book and nest lists for differential flow;\r
 fDiffFlowList = new TList();\r
 fDiffFlowList->SetName("Differential Flow");\r
 fDiffFlowList->SetOwner(kTRUE); \r
 fHistList->Add(fDiffFlowList);\r
 // list holding profiles: \r
 fDiffFlowProfiles = new TList(); \r
 fDiffFlowProfiles->SetName("Profiles");\r
 fDiffFlowProfiles->SetOwner(kTRUE);\r
 fDiffFlowList->Add(fDiffFlowProfiles);\r
 // list holding histograms with results: \r
 fDiffFlowResults = new TList();\r
 fDiffFlowResults->SetName("Results");\r
 fDiffFlowResults->SetOwner(kTRUE);\r
 fDiffFlowList->Add(fDiffFlowResults);\r
 // flags used for naming nested lists in list fDiffFlowProfiles and fDiffFlowResults:  \r
 TList list;\r
 list.SetOwner(kTRUE);\r
 TString typeFlag[2] = {"RP","POI"};  \r
 TString ptEtaFlag[2] = {"p_{T}","#eta"}; \r
 TString powerFlag[2] = {"linear","quadratic"};   \r
 // nested lists in fDiffFlowProfiles (~/Differential Flow/Profiles):\r
 for(Int_t t=0;t<2;t++) // type: RP or POI\r
 {\r
  for(Int_t pe=0;pe<2;pe++) // pt or eta\r
  {\r
   // list holding profiles with correlations:\r
   fDiffFlowCorrelationsProList[t][pe] = (TList*)list.Clone();\r
   fDiffFlowCorrelationsProList[t][pe]->SetName(Form("Profiles with correlations (%s, %s)",typeFlag[t].Data(),ptEtaFlag[pe].Data()));\r
   fDiffFlowProfiles->Add(fDiffFlowCorrelationsProList[t][pe]);\r
   // list holding profiles with products of correlations:\r
   fDiffFlowProductOfCorrelationsProList[t][pe] = (TList*)list.Clone();\r
   fDiffFlowProductOfCorrelationsProList[t][pe]->SetName(Form("Profiles with products of correlations (%s, %s)",typeFlag[t].Data(),ptEtaFlag[pe].Data()));\r
   fDiffFlowProfiles->Add(fDiffFlowProductOfCorrelationsProList[t][pe]);\r
   // list holding profiles with corrections:\r
   fDiffFlowCorrectionsProList[t][pe] = (TList*)list.Clone();\r
   fDiffFlowCorrectionsProList[t][pe]->SetName(Form("Profiles with correction terms for NUA (%s, %s)",typeFlag[t].Data(),ptEtaFlag[pe].Data()));\r
   fDiffFlowProfiles->Add(fDiffFlowCorrectionsProList[t][pe]);   \r
  } // end of for(Int_t pe=0;pe<2;pe++) // pt or eta \r
 } // end of for(Int_t t=0;t<2;t++) // type: RP or POI   \r
 // nested lists in fDiffFlowResults (~/Differential Flow/Results):\r
 for(Int_t t=0;t<2;t++) // type: RP or POI\r
 {\r
  for(Int_t pe=0;pe<2;pe++) // pt or eta\r
  {\r
   // list holding histograms with correlations:\r
   fDiffFlowCorrelationsHistList[t][pe] = (TList*)list.Clone();\r
   fDiffFlowCorrelationsHistList[t][pe]->SetName(Form("Correlations (%s, %s)",typeFlag[t].Data(),ptEtaFlag[pe].Data()));\r
   fDiffFlowResults->Add(fDiffFlowCorrelationsHistList[t][pe]);\r
   // list holding histograms with corrections:\r
   fDiffFlowCorrectionsHistList[t][pe] = (TList*)list.Clone();\r
   fDiffFlowCorrectionsHistList[t][pe]->SetName(Form("Histograms with correction terms for NUA (%s, %s)",typeFlag[t].Data(),ptEtaFlag[pe].Data()));\r
   fDiffFlowResults->Add(fDiffFlowCorrectionsHistList[t][pe]);   \r
   for(Int_t power=0;power<2;power++)\r
   {\r
    // list holding histograms with sums of event weights:\r
    fDiffFlowSumOfEventWeightsHistList[t][pe][power] = (TList*)list.Clone();\r
    fDiffFlowSumOfEventWeightsHistList[t][pe][power]->SetName(Form("Sum of %s event weights (%s, %s)",powerFlag[power].Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data()));\r
    fDiffFlowResults->Add(fDiffFlowSumOfEventWeightsHistList[t][pe][power]);    \r
   } // end of for(Int_t power=0;power<2;power++)\r
   // list holding histograms with sums of products of event weights:\r
   fDiffFlowSumOfProductOfEventWeightsHistList[t][pe] = (TList*)list.Clone();\r
   fDiffFlowSumOfProductOfEventWeightsHistList[t][pe]->SetName(Form("Sum of products of event weights (%s, %s)",typeFlag[t].Data(),ptEtaFlag[pe].Data()));\r
   fDiffFlowResults->Add(fDiffFlowSumOfProductOfEventWeightsHistList[t][pe]);\r
   // list holding histograms with covariances of correlations:\r
   fDiffFlowCovariancesHistList[t][pe] = (TList*)list.Clone();\r
   fDiffFlowCovariancesHistList[t][pe]->SetName(Form("Covariances of correlations (%s, %s)",typeFlag[t].Data(),ptEtaFlag[pe].Data()));\r
   fDiffFlowResults->Add(fDiffFlowCovariancesHistList[t][pe]);\r
   // list holding histograms with differential Q-cumulants:\r
   fDiffFlowCumulantsHistList[t][pe] = (TList*)list.Clone();\r
   fDiffFlowCumulantsHistList[t][pe]->SetName(Form("Differential Q-cumulants (%s, %s)",typeFlag[t].Data(),ptEtaFlag[pe].Data()));\r
   fDiffFlowResults->Add(fDiffFlowCumulantsHistList[t][pe]);   \r
   // list holding histograms with differential flow estimates from Q-cumulants:\r
   fDiffFlowHistList[t][pe] = (TList*)list.Clone();\r
   fDiffFlowHistList[t][pe]->SetName(Form("Differential flow (%s, %s)",typeFlag[t].Data(),ptEtaFlag[pe].Data()));\r
   fDiffFlowResults->Add(fDiffFlowHistList[t][pe]);      \r
  } // end of for(Int_t pe=0;pe<2;pe++) // pt or eta\r
 } // end of for(Int_t t=0;t<2;t++) // type: RP or POI\r
  \r
 // c) Book and nest list for particle weights:\r
 fWeightsList->SetName("Weights");\r
 fWeightsList->SetOwner(kTRUE);   \r
 fHistList->Add(fWeightsList); \r
\r
 // d) Book and nest list for distributions:\r
 fDistributionsList = new TList();\r
 fDistributionsList->SetName("Distributions");\r
 fDistributionsList->SetOwner(kTRUE);\r
 fHistList->Add(fDistributionsList);\r
 \r
 // e) Book and nest list for nested loops:\r
 fNestedLoopsList = new TList();\r
 fNestedLoopsList->SetName("Nested Loops");\r
 fNestedLoopsList->SetOwner(kTRUE);\r
 fHistList->Add(fNestedLoopsList);\r
 \r
} // end of void AliFlowAnalysisWithQCumulants::BookAndNestAllLists()\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::FillCommonHistResultsDiffFlow(TString type)\r
{\r
 // fill common result histograms for differential flow\r
 \r
 Int_t typeFlag = -1;\r
 //Int_t ptEtaFlag = -1;\r
\r
 if(type == "RP")\r
 {\r
  typeFlag = 0;\r
 } else if(type == "POI")\r
   {\r
    typeFlag = 1;\r
   } \r
  \r
 // shortcuts:\r
 Int_t t = typeFlag;\r
 //Int_t pe = ptEtaFlag;\r
\r
 // to be improved (implement protection here)\r
     \r
 if(!(fCommonHistsResults2nd && fCommonHistsResults4th && fCommonHistsResults6th && fCommonHistsResults8th))\r
 {\r
  cout<<"WARNING: fCommonHistsResults2nd && fCommonHistsResults4th && fCommonHistsResults6th && fCommonHistsResults8th"<<endl; \r
  cout<<"         is NULL in AFAWQC::FCHRIF() !!!!"<<endl;\r
  exit(0);\r
 }\r
 \r
 // pt:\r
 for(Int_t p=1;p<=fnBinsPt;p++)\r
 {\r
  Double_t v2 = fDiffFlow[t][0][0]->GetBinContent(p);\r
  Double_t v4 = fDiffFlow[t][0][1]->GetBinContent(p);\r
  Double_t v6 = fDiffFlow[t][0][2]->GetBinContent(p);\r
  Double_t v8 = fDiffFlow[t][0][3]->GetBinContent(p);\r
  \r
  Double_t v2Error = fDiffFlow[t][0][0]->GetBinError(p);\r
  Double_t v4Error = fDiffFlow[t][0][1]->GetBinError(p);\r
  //Double_t v6Error = fFinalFlow1D[t][pW][nua][0][2]->GetBinError(p);\r
  //Double_t v8Error = fFinalFlow1D[t][pW][nua][0][3]->GetBinError(p);\r
 \r
  if(type == "RP")\r
  {\r
   fCommonHistsResults2nd->FillDifferentialFlowPtRP(p,v2,v2Error);\r
   fCommonHistsResults4th->FillDifferentialFlowPtRP(p,v4,v4Error);\r
   fCommonHistsResults6th->FillDifferentialFlowPtRP(p,v6,0.);\r
   fCommonHistsResults8th->FillDifferentialFlowPtRP(p,v8,0.);\r
  } else if(type == "POI")\r
    {\r
     fCommonHistsResults2nd->FillDifferentialFlowPtPOI(p,v2,v2Error);\r
     fCommonHistsResults4th->FillDifferentialFlowPtPOI(p,v4,v4Error);\r
     fCommonHistsResults6th->FillDifferentialFlowPtPOI(p,v6,0.);\r
     fCommonHistsResults8th->FillDifferentialFlowPtPOI(p,v8,0.);\r
    }\r
 } // end of for(Int_t p=1;p<=fnBinsPt;p++)   \r
 \r
 // eta:\r
 for(Int_t e=1;e<=fnBinsEta;e++)\r
 {\r
  Double_t v2 = fDiffFlow[t][1][0]->GetBinContent(e);\r
  Double_t v4 = fDiffFlow[t][1][1]->GetBinContent(e);\r
  Double_t v6 = fDiffFlow[t][1][2]->GetBinContent(e);\r
  Double_t v8 = fDiffFlow[t][1][3]->GetBinContent(e);\r
  \r
  Double_t v2Error = fDiffFlow[t][1][0]->GetBinError(e);\r
  Double_t v4Error = fDiffFlow[t][1][1]->GetBinError(e);\r
  //Double_t v6Error = fDiffFlow[t][1][2]->GetBinError(e);\r
  //Double_t v8Error = fDiffFlow[t][1][3]->GetBinError(e);\r
 \r
  if(type == "RP")\r
  {\r
   fCommonHistsResults2nd->FillDifferentialFlowEtaRP(e,v2,v2Error);\r
   fCommonHistsResults4th->FillDifferentialFlowEtaRP(e,v4,v4Error);\r
   fCommonHistsResults6th->FillDifferentialFlowEtaRP(e,v6,0.);\r
   fCommonHistsResults8th->FillDifferentialFlowEtaRP(e,v8,0.);\r
  } else if(type == "POI")\r
    {\r
     fCommonHistsResults2nd->FillDifferentialFlowEtaPOI(e,v2,v2Error);\r
     fCommonHistsResults4th->FillDifferentialFlowEtaPOI(e,v4,v4Error);\r
     fCommonHistsResults6th->FillDifferentialFlowEtaPOI(e,v6,0.);\r
     fCommonHistsResults8th->FillDifferentialFlowEtaPOI(e,v8,0.);\r
    }\r
 } // end of for(Int_t e=1;e<=fnBinsEta;e++)    \r
 \r
} // end of void AliFlowAnalysisWithQCumulants::FillCommonHistResultsDiffFlow(TString type, Bool_t useParticleWeights, TString eventWeights, Bool_t correctedForNUA)\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::AccessConstants()\r
{\r
 // Access needed common constants from AliFlowCommonConstants\r
 \r
 fnBinsPhi = AliFlowCommonConstants::GetMaster()->GetNbinsPhi();\r
 fPhiMin = AliFlowCommonConstants::GetMaster()->GetPhiMin();	     \r
 fPhiMax = AliFlowCommonConstants::GetMaster()->GetPhiMax();\r
 if(fnBinsPhi) fPhiBinWidth = (fPhiMax-fPhiMin)/fnBinsPhi;  \r
 fnBinsPt = AliFlowCommonConstants::GetMaster()->GetNbinsPt();\r
 fPtMin = AliFlowCommonConstants::GetMaster()->GetPtMin();	     \r
 fPtMax = AliFlowCommonConstants::GetMaster()->GetPtMax();\r
 if(fnBinsPt) fPtBinWidth = (fPtMax-fPtMin)/fnBinsPt;  \r
 fnBinsEta = AliFlowCommonConstants::GetMaster()->GetNbinsEta();\r
 fEtaMin = AliFlowCommonConstants::GetMaster()->GetEtaMin();	     \r
 fEtaMax = AliFlowCommonConstants::GetMaster()->GetEtaMax();\r
 if(fnBinsEta) fEtaBinWidth = (fEtaMax-fEtaMin)/fnBinsEta;  \r
 \r
} // end of void AliFlowAnalysisWithQCumulants::AccessConstants()


//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::CrossCheckSettings()\r
{\r
 // a) Cross check if the choice for multiplicity weights make sense;\r
 \r
 // a) Cross check if the choice for multiplicity weights make sense:
 if(strcmp(fMultiplicityWeight->Data(),"combinations") && 
    strcmp(fMultiplicityWeight->Data(),"unit") &&
    strcmp(fMultiplicityWeight->Data(),"multiplicity"))
 {
  cout<<"WARNING (QC): Multiplicity weight can be either \"combinations\", \"unit\""<<endl;
  cout<<"              or \"multiplicity\". Certainly not \""<<fMultiplicityWeight->Data()<<"\"."<<endl;
  exit(0);
 }   \r
 \r
} // end of void AliFlowAnalysisWithQCumulants::CrossCheckSettings()\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::CalculateIntFlowSumOfEventWeights()\r
{\r
 // Calculate sum of linear and quadratic event weights for correlations\r
 \r
 \r
 /*\r
 Double_t dMult = (*fSMpk)(0,0); // multiplicity \r
\r
 Double_t eventWeight[4] = {0}; \r
 \r
 if(!(fUsePhiWeights||fUsePtWeights||fUseEtaWeights))\r
 {\r
  eventWeight[0] = dMult*(dMult-1); // event weight for <2> \r
  eventWeight[1] = dMult*(dMult-1)*(dMult-2)*(dMult-3); // event weight for <4> \r
  eventWeight[2] = dMult*(dMult-1)*(dMult-2)*(dMult-3)*(dMult-4)*(dMult-5); // event weight for <6> \r
  eventWeight[3] = dMult*(dMult-1)*(dMult-2)*(dMult-3)*(dMult-4)*(dMult-5)*(dMult-6)*(dMult-7); // event weight for <8> \r
 } else\r
   {\r
    eventWeight[0] = (*fSMpk)(1,1)-(*fSMpk)(0,2); // dM11 = sum_{i,j=1,i!=j}^M w_i w_j;\r
    eventWeight[1] = (*fSMpk)(3,1)-6.*(*fSMpk)(0,2)*(*fSMpk)(1,1)  \r
                   + 8.*(*fSMpk)(0,3)*(*fSMpk)(0,1)\r
                   + 3.*(*fSMpk)(1,2)-6.*(*fSMpk)(0,4); // dM1111 = sum_{i,j,k,l=1,i!=j!=k!=l}^M w_i w_j w_k w_l\r
    //eventWeight[2] = ... // to be improved (calculated)               \r
    //eventWeight[3] = ... // to be improved (calculated)              \r
   }\r
 */\r
        \r
                      \r
 for(Int_t p=0;p<2;p++) // power-1\r
 {\r
  for(Int_t ci=0;ci<4;ci++) // correlation index\r
  { \r
   fIntFlowSumOfEventWeights[p]->Fill(ci+0.5,pow(fIntFlowEventWeightsForCorrelationsEBE->GetBinContent(ci+1),p+1)); \r
  }\r
 }\r
  \r
} // end of void AliFlowAnalysisWithQCumulants::CalculateIntFlowSumOfEventWeights()\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::CalculateIntFlowSumOfProductOfEventWeights()\r
{\r
 // Calculate sum of product of event weights for correlations\r
 \r
 \r
 /*\r
 Double_t dMult = (*fSMpk)(0,0); // multiplicity \r
\r
 Double_t eventWeight[4] = {0}; \r
 \r
 if(!(fUsePhiWeights||fUsePtWeights||fUseEtaWeights))\r
 {\r
  eventWeight[0] = dMult*(dMult-1); // event weight for <2> \r
  eventWeight[1] = dMult*(dMult-1)*(dMult-2)*(dMult-3); // event weight for <4> \r
  eventWeight[2] = dMult*(dMult-1)*(dMult-2)*(dMult-3)*(dMult-4)*(dMult-5); // event weight for <6> \r
  eventWeight[3] = dMult*(dMult-1)*(dMult-2)*(dMult-3)*(dMult-4)*(dMult-5)*(dMult-6)*(dMult-7); // event weight for <8> \r
 } else\r
   {\r
    eventWeight[0] = (*fSMpk)(1,1)-(*fSMpk)(0,2); // dM11 = sum_{i,j=1,i!=j}^M w_i w_j;\r
    eventWeight[1] = (*fSMpk)(3,1)-6.*(*fSMpk)(0,2)*(*fSMpk)(1,1)  \r
                   + 8.*(*fSMpk)(0,3)*(*fSMpk)(0,1)\r
                   + 3.*(*fSMpk)(1,2)-6.*(*fSMpk)(0,4); // dM1111 = sum_{i,j,k,l=1,i!=j!=k!=l}^M w_i w_j w_k w_l\r
    //eventWeight[2] = ... // to be improved (calculated)               \r
    //eventWeight[3] = ... // to be improved (calculated)              \r
   }\r
\r
 fIntFlowSumOfProductOfEventWeights->Fill(0.5,eventWeight[0]*eventWeight[1]); \r
 fIntFlowSumOfProductOfEventWeights->Fill(1.5,eventWeight[0]*eventWeight[2]); \r
 fIntFlowSumOfProductOfEventWeights->Fill(2.5,eventWeight[0]*eventWeight[3]); \r
 fIntFlowSumOfProductOfEventWeights->Fill(3.5,eventWeight[1]*eventWeight[2]); \r
 fIntFlowSumOfProductOfEventWeights->Fill(4.5,eventWeight[1]*eventWeight[3]); \r
 fIntFlowSumOfProductOfEventWeights->Fill(5.5,eventWeight[2]*eventWeight[3]); \r
 */\r
  \r
 \r
 Int_t counter = 0;\r
 \r
 for(Int_t ci1=1;ci1<4;ci1++)\r
 {\r
  for(Int_t ci2=ci1+1;ci2<=4;ci2++)\r
  {\r
   fIntFlowSumOfProductOfEventWeights->Fill(0.5+counter++,\r
                                            fIntFlowEventWeightsForCorrelationsEBE->GetBinContent(ci1)*fIntFlowEventWeightsForCorrelationsEBE->GetBinContent(ci2));\r
  }\r
 }\r
\r
 \r
\r
} // end of void AliFlowAnalysisWithQCumulants::CalculateIntFlowIntFlowSumOfProductOfEventWeights()\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::CalculateDiffFlowCorrelations(TString type, TString ptOrEta)\r
{\r
 // calculate reduced correlations for RPs or POIs in pt or eta bins\r
\r
 // multiplicity:\r
 Double_t dMult = (*fSMpk)(0,0);\r
 \r
 // real and imaginary parts of non-weighted Q-vectors evaluated in harmonics n, 2n, 3n and 4n: \r
 Double_t dReQ1n = (*fReQ)(0,0);\r
 Double_t dReQ2n = (*fReQ)(1,0);\r
 //Double_t dReQ3n = (*fReQ)(2,0);\r
 //Double_t dReQ4n = (*fReQ)(3,0);\r
 Double_t dImQ1n = (*fImQ)(0,0);\r
 Double_t dImQ2n = (*fImQ)(1,0);\r
 //Double_t dImQ3n = (*fImQ)(2,0);\r
 //Double_t dImQ4n = (*fImQ)(3,0);\r
\r
 // reduced correlations are stored in fDiffFlowCorrelationsPro[0=RP,1=POI][0=pt,1=eta][correlation index]. Correlation index runs as follows:\r
 // \r
 // 0: <<2'>>\r
 // 1: <<4'>>\r
 // 2: <<6'>>\r
 // 3: <<8'>>\r
 \r
 Int_t t = -1; // type flag \r
 Int_t pe = -1; // ptEta flag\r
 \r
 if(type == "RP")\r
 {\r
  t = 0;\r
 } else if(type == "POI")\r
   {\r
    t = 1;\r
   }\r
\r
 if(ptOrEta == "Pt")\r
 {\r
  pe = 0;\r
 } else if(ptOrEta == "Eta")\r
   {\r
    pe = 1;\r
   }\r
    \r
 Int_t nBinsPtEta[2] = {fnBinsPt,fnBinsEta};\r
 Double_t minPtEta[2] = {fPtMin,fEtaMin};\r
 //Double_t maxPtEta[2] = {fPtMax,fEtaMax};\r
 Double_t binWidthPtEta[2] = {fPtBinWidth,fEtaBinWidth};\r
\r
 // looping over all bins and calculating reduced correlations: \r
 for(Int_t b=1;b<=nBinsPtEta[pe];b++)\r
 {\r
  // real and imaginary parts of p_{m*n,0} (non-weighted Q-vector evaluated for POIs in particular pt or eta bin): \r
  Double_t p1n0kRe = 0.;\r
  Double_t p1n0kIm = 0.;\r
\r
  // number of POIs in particular pt or eta bin:\r
  Double_t mp = 0.;\r
\r
  // real and imaginary parts of q_{m*n,0} (non-weighted Q-vector evaluated for particles which are both RPs and POIs in particular pt or eta bin):\r
  Double_t q1n0kRe = 0.;\r
  Double_t q1n0kIm = 0.;\r
  Double_t q2n0kRe = 0.;\r
  Double_t q2n0kIm = 0.;\r
\r
  // number of particles which are both RPs and POIs in particular pt or eta bin:\r
  Double_t mq = 0.;\r
   \r
  if(type == "POI")\r
  {\r
   // q_{m*n,0}:\r
   q1n0kRe = fReRPQ1dEBE[2][pe][0][0]->GetBinContent(fReRPQ1dEBE[2][pe][0][0]->GetBin(b))\r
           * fReRPQ1dEBE[2][pe][0][0]->GetBinEntries(fReRPQ1dEBE[2][pe][0][0]->GetBin(b));\r
   q1n0kIm = fImRPQ1dEBE[2][pe][0][0]->GetBinContent(fImRPQ1dEBE[2][pe][0][0]->GetBin(b))\r
           * fImRPQ1dEBE[2][pe][0][0]->GetBinEntries(fImRPQ1dEBE[2][pe][0][0]->GetBin(b));\r
   q2n0kRe = fReRPQ1dEBE[2][pe][1][0]->GetBinContent(fReRPQ1dEBE[2][pe][1][0]->GetBin(b))\r
           * fReRPQ1dEBE[2][pe][1][0]->GetBinEntries(fReRPQ1dEBE[2][pe][1][0]->GetBin(b));\r
   q2n0kIm = fImRPQ1dEBE[2][pe][1][0]->GetBinContent(fImRPQ1dEBE[2][pe][1][0]->GetBin(b))\r
           * fImRPQ1dEBE[2][pe][1][0]->GetBinEntries(fImRPQ1dEBE[2][pe][1][0]->GetBin(b));         \r
                 \r
   mq = fReRPQ1dEBE[2][pe][0][0]->GetBinEntries(fReRPQ1dEBE[2][pe][0][0]->GetBin(b)); // to be improved (cross-checked by accessing other profiles here)\r
  } \r
  else if(type == "RP")\r
  {\r
   // q_{m*n,0}:\r
   q1n0kRe = fReRPQ1dEBE[0][pe][0][0]->GetBinContent(fReRPQ1dEBE[0][pe][0][0]->GetBin(b))\r
           * fReRPQ1dEBE[0][pe][0][0]->GetBinEntries(fReRPQ1dEBE[0][pe][0][0]->GetBin(b));\r
   q1n0kIm = fImRPQ1dEBE[0][pe][0][0]->GetBinContent(fImRPQ1dEBE[0][pe][0][0]->GetBin(b))\r
           * fImRPQ1dEBE[0][pe][0][0]->GetBinEntries(fImRPQ1dEBE[0][pe][0][0]->GetBin(b));\r
   q2n0kRe = fReRPQ1dEBE[0][pe][1][0]->GetBinContent(fReRPQ1dEBE[0][pe][1][0]->GetBin(b))\r
           * fReRPQ1dEBE[0][pe][1][0]->GetBinEntries(fReRPQ1dEBE[0][pe][1][0]->GetBin(b));\r
   q2n0kIm = fImRPQ1dEBE[0][pe][1][0]->GetBinContent(fImRPQ1dEBE[0][pe][1][0]->GetBin(b))\r
           * fImRPQ1dEBE[0][pe][1][0]->GetBinEntries(fImRPQ1dEBE[0][pe][1][0]->GetBin(b));         \r
                 \r
   mq = fReRPQ1dEBE[0][pe][0][0]->GetBinEntries(fReRPQ1dEBE[0][pe][0][0]->GetBin(b)); // to be improved (cross-checked by accessing other profiles here)  \r
  }\r
      \r
   if(type == "POI")\r
   {\r
    // p_{m*n,0}:\r
    p1n0kRe = fReRPQ1dEBE[1][pe][0][0]->GetBinContent(fReRPQ1dEBE[1][pe][0][0]->GetBin(b))\r
            * fReRPQ1dEBE[1][pe][0][0]->GetBinEntries(fReRPQ1dEBE[1][pe][0][0]->GetBin(b));\r
    p1n0kIm = fImRPQ1dEBE[1][pe][0][0]->GetBinContent(fImRPQ1dEBE[1][pe][0][0]->GetBin(b))  \r
            * fImRPQ1dEBE[1][pe][0][0]->GetBinEntries(fImRPQ1dEBE[1][pe][0][0]->GetBin(b));\r
            \r
    mp = fReRPQ1dEBE[1][pe][0][0]->GetBinEntries(fReRPQ1dEBE[1][pe][0][0]->GetBin(b)); // to be improved (cross-checked by accessing other profiles here)\r
    \r
    t = 1; // typeFlag = RP or POI\r
   }\r
   else if(type == "RP")\r
   {\r
    // p_{m*n,0} = q_{m*n,0}:\r
    p1n0kRe = q1n0kRe; \r
    p1n0kIm = q1n0kIm; \r
            \r
    mp = mq; \r
    \r
    t = 0; // typeFlag = RP or POI\r
   }\r
      \r
   // 2'-particle correlation for particular (pt,eta) bin:\r
   Double_t two1n1nPtEta = 0.;\r
   if(mp*dMult-mq)\r
   {\r
    two1n1nPtEta = (p1n0kRe*dReQ1n+p1n0kIm*dImQ1n-mq)\r
                 / (mp*dMult-mq);\r
   \r
    if(type == "POI") // to be improved (I do not this if)\r
    { \r
     // fill profile to get <<2'>> for POIs\r
     fDiffFlowCorrelationsPro[1][pe][0]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],two1n1nPtEta,mp*dMult-mq);\r
     // histogram to store <2'> for POIs e-b-e (needed in some other methods):\r
     fDiffFlowCorrelationsEBE[1][pe][0]->SetBinContent(b,two1n1nPtEta);      \r
     fDiffFlowEventWeightsForCorrelationsEBE[1][pe][0]->SetBinContent(b,mp*dMult-mq);      \r
    }\r
    else if(type == "RP") // to be improved (I do not this if)\r
    {\r
     // profile to get <<2'>> for RPs:\r
     fDiffFlowCorrelationsPro[0][pe][0]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],two1n1nPtEta,mp*dMult-mq);\r
     // histogram to store <2'> for RPs e-b-e (needed in some other methods):\r
     fDiffFlowCorrelationsEBE[0][pe][0]->SetBinContent(b,two1n1nPtEta); \r
     fDiffFlowEventWeightsForCorrelationsEBE[0][pe][0]->SetBinContent(b,mp*dMult-mq); \r
    }\r
   } // end of if(mp*dMult-mq)\r
  \r
   // 4'-particle correlation:\r
   Double_t four1n1n1n1nPtEta = 0.;\r
   if((mp-mq)*dMult*(dMult-1.)*(dMult-2.)\r
       + mq*(dMult-1.)*(dMult-2.)*(dMult-3.)) // to be improved (introduce a new variable for this expression)\r
   {\r
    four1n1n1n1nPtEta = ((pow(dReQ1n,2.)+pow(dImQ1n,2.))*(p1n0kRe*dReQ1n+p1n0kIm*dImQ1n)\r
                      - q2n0kRe*(pow(dReQ1n,2.)-pow(dImQ1n,2.))\r
                      - 2.*q2n0kIm*dReQ1n*dImQ1n\r
                      - p1n0kRe*(dReQ1n*dReQ2n+dImQ1n*dImQ2n)\r
                      + p1n0kIm*(dImQ1n*dReQ2n-dReQ1n*dImQ2n)\r
                      - 2.*dMult*(p1n0kRe*dReQ1n+p1n0kIm*dImQ1n)\r
                      - 2.*(pow(dReQ1n,2.)+pow(dImQ1n,2.))*mq                      \r
                      + 6.*(q1n0kRe*dReQ1n+q1n0kIm*dImQ1n)                                            \r
                      + 1.*(q2n0kRe*dReQ2n+q2n0kIm*dImQ2n)                      \r
                      + 2.*(p1n0kRe*dReQ1n+p1n0kIm*dImQ1n)                       \r
                      + 2.*mq*dMult                      \r
                      - 6.*mq)        \r
                      / ((mp-mq)*dMult*(dMult-1.)*(dMult-2.)\r
                          + mq*(dMult-1.)*(dMult-2.)*(dMult-3.)); \r
    \r
    if(type == "POI")\r
    {\r
     // profile to get <<4'>> for POIs:\r
     fDiffFlowCorrelationsPro[1][pe][1]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],four1n1n1n1nPtEta,\r
                                     (mp-mq)*dMult*(dMult-1.)*(dMult-2.)\r
                                     + mq*(dMult-1.)*(dMult-2.)*(dMult-3.)); \r
     // histogram to store <4'> for POIs e-b-e (needed in some other methods):\r
     fDiffFlowCorrelationsEBE[1][pe][1]->SetBinContent(b,four1n1n1n1nPtEta);                               \r
     fDiffFlowEventWeightsForCorrelationsEBE[1][pe][1]->SetBinContent(b,(mp-mq)*dMult*(dMult-1.)*(dMult-2.)\r
                                                                        + mq*(dMult-1.)*(dMult-2.)*(dMult-3.));                               \r
    }\r
    else if(type == "RP")\r
    {\r
     // profile to get <<4'>> for RPs:\r
     fDiffFlowCorrelationsPro[0][pe][1]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],four1n1n1n1nPtEta,\r
                                       (mp-mq)*dMult*(dMult-1.)*(dMult-2.)\r
                                       + mq*(dMult-1.)*(dMult-2.)*(dMult-3.));                   \r
     // histogram to store <4'> for RPs e-b-e (needed in some other methods):\r
     fDiffFlowCorrelationsEBE[0][pe][1]->SetBinContent(b,four1n1n1n1nPtEta);                   \r
     fDiffFlowEventWeightsForCorrelationsEBE[0][pe][1]->SetBinContent(b,(mp-mq)*dMult*(dMult-1.)*(dMult-2.)\r
                                                                        + mq*(dMult-1.)*(dMult-2.)*(dMult-3.));                   \r
    }\r
   } // end of if((mp-mq)*dMult*(dMult-1.)*(dMult-2.)\r
     //            +mq*(dMult-1.)*(dMult-2.)*(dMult-3.))\r
   \r
 } // end of for(Int_t b=1;b<=nBinsPtEta[pe];b++)\r
 \r
   \r
} // end of void AliFlowAnalysisWithQCumulants::CalculateDiffFlowCorrelations(TString type, TString ptOrEta);\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::CalculateDiffFlowSumOfEventWeights(TString type, TString ptOrEta)\r
{\r
 // Calculate sums of various event weights for reduced correlations. \r
 // (These quantitites are needed in expressions for unbiased estimators relevant for the statistical errors.)\r
\r
 Int_t typeFlag = -1;\r
 Int_t ptEtaFlag = -1;\r
\r
 if(type == "RP")\r
 {\r
  typeFlag = 0;\r
 } else if(type == "POI")\r
   {\r
    typeFlag = 1;\r
   } \r
     \r
 if(ptOrEta == "Pt")\r
 {\r
  ptEtaFlag = 0;\r
 } else if(ptOrEta == "Eta")\r
   {\r
    ptEtaFlag = 1;\r
   } \r
   \r
 // shortcuts:\r
 Int_t t = typeFlag;\r
 Int_t pe = ptEtaFlag;\r
 \r
 // binning:\r
 Int_t nBinsPtEta[2] = {fnBinsPt,fnBinsEta};\r
 Double_t minPtEta[2] = {fPtMin,fEtaMin};\r
 //Double_t maxPtEta[2] = {fPtMax,fEtaMax};\r
 Double_t binWidthPtEta[2] = {fPtBinWidth,fEtaBinWidth};\r
 \r
 for(Int_t rpq=0;rpq<3;rpq++)\r
 {\r
  for(Int_t m=0;m<4;m++)\r
  {\r
   for(Int_t k=0;k<9;k++)\r
   {\r
    if(!fReRPQ1dEBE[rpq][pe][m][k])\r
    {\r
     cout<<"WARNING: fReRPQ1dEBE[rpq][pe][m][k] is NULL in AFAWQC::CSAPOEWFDF() !!!!"<<endl;\r
     cout<<"pe  = "<<pe<<endl;\r
     cout<<"rpq = "<<rpq<<endl;\r
     cout<<"m   = "<<m<<endl;\r
     cout<<"k   = "<<k<<endl;\r
     exit(0); \r
    }\r
   }\r
  }\r
 }  \r
\r
 // multiplicities:\r
 Double_t dMult = (*fSMpk)(0,0); // total event multiplicity\r
 //Double_t mr = 0.; // number of RPs in particular pt or eta bin\r
 Double_t mp = 0.; // number of POIs in particular pt or eta bin \r
 Double_t mq = 0.; // number of particles which are both RPs and POIs in particular pt or eta bin\r
 \r
 // event weights for reduced correlations:\r
 Double_t dw2 = 0.; // event weight for <2'>\r
 Double_t dw4 = 0.; // event weight for <4'>\r
 //Double_t dw6 = 0.; // event weight for <6'>\r
 //Double_t dw8 = 0.; // event weight for <8'>\r
\r
 // looping over bins:\r
 for(Int_t b=1;b<=nBinsPtEta[pe];b++)\r
 {\r
  if(type == "RP")\r
  {\r
   mq = fReRPQ1dEBE[0][pe][0][0]->GetBinEntries(b);\r
   mp = mq; // trick to use the very same Eqs. bellow both for RP's and POI's diff. flow\r
  } else if(type == "POI")\r
    {\r
     mp = fReRPQ1dEBE[1][pe][0][0]->GetBinEntries(b);\r
     mq = fReRPQ1dEBE[2][pe][0][0]->GetBinEntries(b);    \r
    }\r
  \r
  // event weight for <2'>:\r
  dw2 = mp*dMult-mq;  \r
  fDiffFlowSumOfEventWeights[t][pe][0][0]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],dw2);\r
  fDiffFlowSumOfEventWeights[t][pe][1][0]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],pow(dw2,2.));\r
  \r
  // event weight for <4'>:\r
  dw4 = (mp-mq)*dMult*(dMult-1.)*(dMult-2.)\r
     + mq*(dMult-1.)*(dMult-2.)*(dMult-3.);  \r
  fDiffFlowSumOfEventWeights[t][pe][0][1]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],dw4);\r
  fDiffFlowSumOfEventWeights[t][pe][1][1]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],pow(dw4,2.));\r
  \r
  // event weight for <6'>:\r
  //dw6 = ...;  \r
  //fDiffFlowSumOfEventWeights[t][pe][0][2]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],dw6);\r
  //fDiffFlowSumOfEventWeights[t][pe][t][1][2]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],pow(dw6,2.));\r
  \r
  // event weight for <8'>:\r
  //dw8 = ...;  \r
  //fDiffFlowSumOfEventWeights[t][pe][0][3]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],dw8);\r
  //fDiffFlowSumOfEventWeights[t][pe][1][3]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],pow(dw8,2.));   \r
 } // end of for(Int_t b=1;b<=nBinsPtEta[pe];b++) \r
 \r
} // end of void AliFlowAnalysisWithQCumulants::CalculateDiffFlowSumOfEventWeights()\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::CalculateDiffFlowSumOfProductOfEventWeights(TString type, TString ptOrEta)\r
{\r
 // Calculate sum of products of various event weights for both types of correlations (the ones for int. and diff. flow). \r
 // (These quantitites are needed in expressions for unbiased estimators relevant for the statistical errors.)\r
 //\r
 // Important: To fill fDiffFlowSumOfProductOfEventWeights[][][][] use bellow table (i,j) with following constraints: \r
 // 1.) i<j  \r
 // 2.) do not store terms which DO NOT include reduced correlations;\r
 // Table:\r
 // [0=<2>,1=<2'>,2=<4>,3=<4'>,4=<6>,5=<6'>,6=<8>,7=<8'>] x [0=<2>,1=<2'>,2=<4>,3=<4'>,4=<6>,5=<6'>,6=<8>,7=<8'>]\r
  \r
 Int_t typeFlag = -1;\r
 Int_t ptEtaFlag = -1;\r
\r
 if(type == "RP")\r
 {\r
  typeFlag = 0;\r
 } else if(type == "POI")\r
   {\r
    typeFlag = 1;\r
   } \r
     \r
 if(ptOrEta == "Pt")\r
 {\r
  ptEtaFlag = 0;\r
 } else if(ptOrEta == "Eta")\r
   {\r
    ptEtaFlag = 1;\r
   } \r
     \r
 // shortcuts:\r
 Int_t t = typeFlag;\r
 Int_t pe = ptEtaFlag;\r
  \r
 // binning:\r
 Int_t nBinsPtEta[2] = {fnBinsPt,fnBinsEta};\r
 Double_t minPtEta[2] = {fPtMin,fEtaMin};\r
 //Double_t maxPtEta[2] = {fPtMax,fEtaMax};\r
 Double_t binWidthPtEta[2] = {fPtBinWidth,fEtaBinWidth};\r
 \r
 // protection:\r
 for(Int_t rpq=0;rpq<3;rpq++)\r
 {\r
  for(Int_t m=0;m<4;m++)\r
  {\r
   for(Int_t k=0;k<9;k++)\r
   {\r
    if(!fReRPQ1dEBE[rpq][pe][m][k])\r
    {\r
     cout<<"WARNING: fReRPQ1dEBE[rpq][pe][m][k] is NULL in AFAWQC::CSAPOEWFDF() !!!!"<<endl;\r
     cout<<"pe  = "<<pe<<endl;\r
     cout<<"rpq = "<<rpq<<endl;\r
     cout<<"m   = "<<m<<endl;\r
     cout<<"k   = "<<k<<endl;\r
     exit(0); \r
    }\r
   }\r
  }\r
 }  \r
 \r
 // multiplicities:\r
 Double_t dMult = (*fSMpk)(0,0); // total event multiplicity\r
 //Double_t mr = 0.; // number of RPs in particular pt or eta bin\r
 Double_t mp = 0.; // number of POIs in particular pt or eta bin \r
 Double_t mq = 0.; // number of particles which are both RPs and POIs in particular pt or eta bin\r
 \r
 // event weights for correlations:\r
 Double_t dW2 = dMult*(dMult-1); // event weight for <2> \r
 Double_t dW4 = dMult*(dMult-1)*(dMult-2)*(dMult-3); // event weight for <4> \r
 Double_t dW6 = dMult*(dMult-1)*(dMult-2)*(dMult-3)*(dMult-4)*(dMult-5); // event weight for <6> \r
 Double_t dW8 = dMult*(dMult-1)*(dMult-2)*(dMult-3)*(dMult-4)*(dMult-5)*(dMult-6)*(dMult-7); // event weight for <8> \r
\r
 // event weights for reduced correlations:\r
 Double_t dw2 = 0.; // event weight for <2'>\r
 Double_t dw4 = 0.; // event weight for <4'>\r
 //Double_t dw6 = 0.; // event weight for <6'>\r
 //Double_t dw8 = 0.; // event weight for <8'>\r
 \r
 // looping over bins:\r
 for(Int_t b=1;b<=nBinsPtEta[pe];b++)\r
 {\r
  if(type == "RP")\r
  {\r
   mq = fReRPQ1dEBE[0][pe][0][0]->GetBinEntries(b);\r
   mp = mq; // trick to use the very same Eqs. bellow both for RP's and POI's diff. flow\r
  } else if(type == "POI")\r
    {\r
     mp = fReRPQ1dEBE[1][pe][0][0]->GetBinEntries(b);\r
     mq = fReRPQ1dEBE[2][pe][0][0]->GetBinEntries(b);    \r
    }\r
  \r
  // event weight for <2'>:\r
  dw2 = mp*dMult-mq;  \r
  fDiffFlowSumOfProductOfEventWeights[t][pe][0][1]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],dW2*dw2); // storing product of even weights for <2> and <2'>\r
  fDiffFlowSumOfProductOfEventWeights[t][pe][1][2]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],dw2*dW4); // storing product of even weights for <4> and <2'>\r
  fDiffFlowSumOfProductOfEventWeights[t][pe][1][4]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],dw2*dW6); // storing product of even weights for <6> and <2'>\r
  fDiffFlowSumOfProductOfEventWeights[t][pe][1][6]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],dw2*dW8); // storing product of even weights for <8> and <2'>\r
  \r
  // event weight for <4'>:\r
  dw4 = (mp-mq)*dMult*(dMult-1.)*(dMult-2.)\r
     + mq*(dMult-1.)*(dMult-2.)*(dMult-3.);  \r
  fDiffFlowSumOfProductOfEventWeights[t][pe][0][3]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],dW2*dw4); // storing product of even weights for <2> and <4'>\r
  fDiffFlowSumOfProductOfEventWeights[t][pe][1][3]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],dw2*dw4); // storing product of even weights for <2'> and <4'>\r
  fDiffFlowSumOfProductOfEventWeights[t][pe][2][3]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],dW4*dw4); // storing product of even weights for <4> and <4'>\r
  fDiffFlowSumOfProductOfEventWeights[t][pe][3][4]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],dw4*dW6); // storing product of even weights for <6> and <4'> \r
  fDiffFlowSumOfProductOfEventWeights[t][pe][3][6]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],dw4*dW8); // storing product of even weights for <8> and <4'>\r
\r
  // event weight for <6'>:\r
  //dw6 = ...;  \r
  //fDiffFlowSumOfProductOfEventWeights[t][pe][0][5]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],dW2*dw6); // storing product of even weights for <2> and <6'>\r
  //fDiffFlowSumOfProductOfEventWeights[t][pe][1][5]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],dw2*dw6); // storing product of even weights for <2'> and <6'>\r
  //fDiffFlowSumOfProductOfEventWeights[t][pe][2][5]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],dW4*dw6); // storing product of even weights for <4> and <6'>\r
  //fDiffFlowSumOfProductOfEventWeights[t][pe][3][5]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],dw4*dw6); // storing product of even weights for <4'> and <6'> \r
  //fDiffFlowSumOfProductOfEventWeights[t][pe][4][5]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],dW6*dw6); // storing product of even weights for <6> and <6'>\r
  //fDiffFlowSumOfProductOfEventWeights[t][pe][5][6]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],dw6*dW8); // storing product of even weights for <6'> and <8>\r
  //fDiffFlowSumOfProductOfEventWeights[t][pe][5][7]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],dw6*dw8); // storing product of even weights for <6'> and <8'>\r
\r
  // event weight for <8'>:\r
  //dw8 = ...;  \r
  //fDiffFlowSumOfProductOfEventWeights[t][pe][0][7]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],dW2*dw8); // storing product of even weights for <2> and <8'>\r
  //fDiffFlowSumOfProductOfEventWeights[t][pe][1][7]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],dw2*dw8); // storing product of even weights for <2'> and <8'>\r
  //fDiffFlowSumOfProductOfEventWeights[t][pe][2][7]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],dW4*dw8); // storing product of even weights for <4> and <8'>\r
  //fDiffFlowSumOfProductOfEventWeights[t][pe][3][7]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],dw4*dw8); // storing product of even weights for <4'> and <8'> \r
  //fDiffFlowSumOfProductOfEventWeights[t][pe][4][7]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],dW6*dw8); // storing product of even weights for <6> and <8'>\r
  //fDiffFlowSumOfProductOfEventWeights[t][pe][5][7]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],dw6*dw8); // storing product of even weights for <6'> and <8'>\r
  //fDiffFlowSumOfProductOfEventWeights[t][pe][6][7]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],dW8*dw8); // storing product of even weights for <8> and <8'>\r
  \r
  // Table:\r
  // [0=<2>,1=<2'>,2=<4>,3=<4'>,4=<6>,5=<6'>,6=<8>,7=<8'>] x [0=<2>,1=<2'>,2=<4>,3=<4'>,4=<6>,5=<6'>,6=<8>,7=<8'>]\r
   \r
 } // end of for(Int_t b=1;b<=nBinsPtEta[pe];b++)\r
 \r
\r
\r
} // end of void AliFlowAnalysisWithQCumulants::CalculateDiffFlowSumOfProductOfEventWeights(TString type, TString ptOrEta)\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::FinalizeReducedCorrelations(TString type, TString ptOrEta)\r
{\r
 // Transfer profiles into histograms and calculate statistical errors correctly.\r
\r
 Int_t typeFlag = -1;\r
 Int_t ptEtaFlag = -1;\r
\r
 if(type == "RP")\r
 {\r
  typeFlag = 0;\r
 } else if(type == "POI")\r
   {\r
    typeFlag = 1;\r
   } \r
     \r
 if(ptOrEta == "Pt")\r
 {\r
  ptEtaFlag = 0;\r
 } else if(ptOrEta == "Eta")\r
   {\r
    ptEtaFlag = 1;\r
   } \r
  \r
 // shortcuts:\r
 Int_t t = typeFlag;\r
 Int_t pe = ptEtaFlag;\r
             \r
 for(Int_t rci=0;rci<4;rci++)\r
 {\r
  if(!fDiffFlowCorrelationsPro[t][pe][rci])\r
  {\r
   cout<<"WARNING: fDiffFlowCorrelationsPro[t][pe][rci] is NULL in AFAWQC::FRC() !!!!"<<endl;\r
   cout<<"t   = "<<t<<endl; \r
   cout<<"pe  = "<<pe<<endl; \r
   cout<<"rci = "<<rci<<endl;\r
   exit(0); \r
  }\r
  for(Int_t power=0;power<2;power++)\r
  {\r
   if(!fDiffFlowSumOfEventWeights[t][pe][power][rci])\r
   {\r
    cout<<"WARNING: fDiffFlowSumOfEventWeights[t][pe][power][rci] is NULL in AFAWQC::FRC() !!!!"<<endl;\r
    cout<<"t     = "<<t<<endl; \r
    cout<<"pe    = "<<pe<<endl;\r
    cout<<"power = "<<power<<endl; \r
    cout<<"rci   = "<<rci<<endl;\r
    exit(0); \r
   }   \r
  } // end of for(Int_t power=0;power<2;power++)\r
 } // end of for(Int_t rci=0;rci<4;rci++)\r
    \r
 // common:\r
 Int_t nBinsPtEta[2] = {fnBinsPt,fnBinsEta};\r
 \r
 // transfer 1D profile into 1D histogram:\r
 Double_t correlation = 0.;\r
 Double_t spread = 0.;\r
 Double_t sumOfWeights = 0.; // sum of weights for particular reduced correlations for particular pt or eta bin\r
 Double_t sumOfSquaredWeights = 0.; // sum of squared weights for particular reduced correlations for particular pt or eta bin\r
 Double_t error = 0.; // error = termA * spread * termB\r
                      // termA = (sqrt(sumOfSquaredWeights)/sumOfWeights) \r
                      // termB = 1/pow(1-termA^2,0.5)\r
 Double_t termA = 0.;                      \r
 Double_t termB = 0.;                      \r
 for(Int_t rci=0;rci<4;rci++) // index of reduced correlation\r
 {\r
  for(Int_t b=1;b<=nBinsPtEta[pe];b++) // number of pt or eta bins\r
  {\r
   correlation = fDiffFlowCorrelationsPro[t][pe][rci]->GetBinContent(b); \r
   spread = fDiffFlowCorrelationsPro[t][pe][rci]->GetBinError(b);\r
   sumOfWeights = fDiffFlowSumOfEventWeights[t][pe][0][rci]->GetBinContent(b);\r
   sumOfSquaredWeights = fDiffFlowSumOfEventWeights[t][pe][1][rci]->GetBinContent(b);\r
   if(sumOfWeights) termA = (pow(sumOfSquaredWeights,0.5)/sumOfWeights);\r
   if(1.-pow(termA,2.)>0.) termB = 1./pow(1.-pow(termA,2.),0.5); \r
   error = termA*spread*termB; // final error (unbiased estimator for standard deviation)\r
   fDiffFlowCorrelationsHist[t][pe][rci]->SetBinContent(b,correlation); \r
   fDiffFlowCorrelationsHist[t][pe][rci]->SetBinError(b,error); \r
  } // end of for(Int_t b=1;b<=nBinsPtEta[pe];b++)\r
 } // end of for(Int_t rci=0;rci<4;rci++)\r
 \r
} // end of void AliFlowAnalysisWithQCumulants::FinalizeReducedCorrelations(TString type, TString ptOrEta)\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::CalculateDiffFlowProductOfCorrelations(TString type, TString ptOrEta)\r
{\r
 // store products: <2><2'>, <2><4'>, <2><6'>, <2><8'>, <2'><4>, \r
 //                 <2'><4'>, <2'><6>, <2'><6'>, <2'><8>, <2'><8'>,\r
 //                 <4><4'>, <4><6'>, <4><8'>, <4'><6>, <4'><6'>, \r
 //                 <4'><8>, <4'><8'>, <6><6'>, <6><8'>, <6'><8>, \r
 //                 <6'><8'>, <8><8'>.\r
  \r
 Int_t typeFlag = -1;\r
 Int_t ptEtaFlag = -1;\r
\r
 if(type == "RP")\r
 {\r
  typeFlag = 0;\r
 } else if(type == "POI")\r
   {\r
    typeFlag = 1;\r
   } \r
     \r
 if(ptOrEta == "Pt")\r
 {\r
  ptEtaFlag = 0;\r
 } else if(ptOrEta == "Eta")\r
   {\r
    ptEtaFlag = 1;\r
   } \r
  \r
 // shortcuts:\r
 Int_t t = typeFlag;\r
 Int_t pe = ptEtaFlag;\r
     \r
 // common:\r
 Int_t nBinsPtEta[2] = {fnBinsPt,fnBinsEta};\r
 Double_t minPtEta[2] = {fPtMin,fEtaMin};\r
 Double_t binWidthPtEta[2] = {fPtBinWidth,fEtaBinWidth};\r
   \r
 // protections // to be improved (add protection for all pointers in this method)\r
 if(!fIntFlowCorrelationsEBE)\r
 {\r
  cout<<"WARNING: fIntFlowCorrelationsEBE is NULL in AFAWQC::CDFPOC() !!!!"<<endl;\r
  exit(0);\r
 } \r
 \r
 /*    \r
 Double_t dMult = (*fSMpk)(0,0); // multiplicity (number of particles used to determine the reaction plane)\r
 //Double_t mr = 0.; // number of RPs in particular pt or eta bin\r
 Double_t mp = 0.; // number of POIs in particular pt or eta bin \r
 Double_t mq = 0.; // number of particles which are both RPs and POIs in particular pt or eta bin\r
 */\r
\r
 // e-b-e correlations:\r
 Double_t twoEBE = fIntFlowCorrelationsEBE->GetBinContent(1); // <2>\r
 Double_t fourEBE = fIntFlowCorrelationsEBE->GetBinContent(2); // <4>\r
 Double_t sixEBE = fIntFlowCorrelationsEBE->GetBinContent(3); // <6>\r
 Double_t eightEBE = fIntFlowCorrelationsEBE->GetBinContent(4); // <8>\r
 \r
 // event weights for correlations:\r
 Double_t dW2 = fIntFlowEventWeightsForCorrelationsEBE->GetBinContent(1); // event weight for <2> \r
 Double_t dW4 = fIntFlowEventWeightsForCorrelationsEBE->GetBinContent(2); // event weight for <4> \r
 Double_t dW6 = fIntFlowEventWeightsForCorrelationsEBE->GetBinContent(3); // event weight for <6> \r
 Double_t dW8 = fIntFlowEventWeightsForCorrelationsEBE->GetBinContent(4); // event weight for <8> \r
  \r
 // e-b-e reduced correlations:\r
 Double_t twoReducedEBE = 0.; // <2'>\r
 Double_t fourReducedEBE = 0.; // <4'>\r
 Double_t sixReducedEBE = 0.; // <6'>\r
 Double_t eightReducedEBE = 0.; // <8'> \r
 \r
 // event weights for reduced correlations:\r
 Double_t dw2 = 0.; // event weight for <2'>\r
 Double_t dw4 = 0.; // event weight for <4'>\r
 //Double_t dw6 = 0.; // event weight for <6'>\r
 //Double_t dw8 = 0.; // event weight for <8'>\r
\r
 // looping over bins:\r
 for(Int_t b=1;b<=nBinsPtEta[pe];b++)\r
 {\r
  // e-b-e reduced correlations:\r
  twoReducedEBE = fDiffFlowCorrelationsEBE[t][pe][0]->GetBinContent(b);\r
  fourReducedEBE = fDiffFlowCorrelationsEBE[t][pe][1]->GetBinContent(b);\r
  sixReducedEBE = fDiffFlowCorrelationsEBE[t][pe][2]->GetBinContent(b);\r
  eightReducedEBE = fDiffFlowCorrelationsEBE[t][pe][3]->GetBinContent(b);\r
  \r
  /*\r
  // to be improved (I should not do this here again)\r
  if(type == "RP")\r
  {\r
   mq = fReRPQ1dEBE[0][pe][0][0]->GetBinEntries(b);\r
   mp = mq; // trick to use the very same Eqs. bellow both for RP's and POI's diff. flow\r
  } else if(type == "POI")\r
    {\r
     mp = fReRPQ1dEBE[1][pe][0][0]->GetBinEntries(b);\r
     mq = fReRPQ1dEBE[2][pe][0][0]->GetBinEntries(b);    \r
    }\r
  \r
  // event weights for reduced correlations:\r
  dw2 = mp*dMult-mq; // weight for <2'> \r
  dw4 = (mp-mq)*dMult*(dMult-1.)*(dMult-2.)\r
     + mq*(dMult-1.)*(dMult-2.)*(dMult-3.); // weight for <4'>\r
  //dw6 = ...     \r
  //dw8 = ...     \r
  \r
  */\r
  \r
  dw2 = fDiffFlowEventWeightsForCorrelationsEBE[t][pe][0]->GetBinContent(b);\r
  dw4 = fDiffFlowEventWeightsForCorrelationsEBE[t][pe][1]->GetBinContent(b);\r
 \r
  // storing all products:\r
  fDiffFlowProductOfCorrelationsPro[t][pe][0][1]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],twoEBE*twoReducedEBE,dW2*dw2); // storing <2><2'>\r
  fDiffFlowProductOfCorrelationsPro[t][pe][1][2]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],fourEBE*twoReducedEBE,dW4*dw2); // storing <4><2'>\r
  fDiffFlowProductOfCorrelationsPro[t][pe][1][4]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],sixEBE*twoReducedEBE,dW6*dw2); // storing <6><2'>\r
  fDiffFlowProductOfCorrelationsPro[t][pe][1][6]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],eightEBE*twoReducedEBE,dW8*dw2); // storing <8><2'>\r
  \r
  // event weight for <4'>:\r
  fDiffFlowProductOfCorrelationsPro[t][pe][0][3]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],twoEBE*fourReducedEBE,dW2*dw4); // storing <2><4'>\r
  fDiffFlowProductOfCorrelationsPro[t][pe][1][3]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],twoReducedEBE*fourReducedEBE,dw2*dw4); // storing <2'><4'>\r
  fDiffFlowProductOfCorrelationsPro[t][pe][2][3]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],fourEBE*fourReducedEBE,dW4*dw4); // storing <4><4'>\r
  fDiffFlowProductOfCorrelationsPro[t][pe][3][4]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],sixEBE*fourReducedEBE,dW6*dw4); // storing <6><4'> \r
  fDiffFlowProductOfCorrelationsPro[t][pe][3][6]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],eightEBE*fourReducedEBE,dW8*dw4); // storing <8><4'>\r
\r
  // event weight for <6'>:\r
  //dw6 = ...;  \r
  //fDiffFlowProductOfCorrelationsPro[t][pe][0][5]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],twoEBE*sixReducedEBE,dW2*dw6); // storing <2><6'>\r
  //fDiffFlowProductOfCorrelationsPro[t][pe][1][5]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],twoReducedEBE*sixReducedEBE,dw2*dw6); // storing <2'><6'>\r
  //fDiffFlowProductOfCorrelationsPro[t][pe][2][5]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],fourEBE*sixReducedEBE,dW4*dw6); // storing <4><6'>\r
  //fDiffFlowProductOfCorrelationsPro[t][pe][3][5]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],fourReducedEBE*sixReducedEBE,dw4*dw6); // storing <4'><6'> \r
  //fDiffFlowProductOfCorrelationsPro[t][pe][4][5]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],sixEBE*sixReducedEBE,dW6*dw6); // storing <6><6'>\r
  //fDiffFlowProductOfCorrelationsPro[t][pe][5][6]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],sixReducedEBE*eightEBE,dw6*dW8); // storing <6'><8>\r
  //fDiffFlowProductOfCorrelationsPro[t][pe][5][7]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],sixReducedEBE*eightReducedEBE,dw6*dw8); // storing <6'><8'>\r
\r
  // event weight for <8'>:\r
  //dw8 = ...;  \r
  //fDiffFlowProductOfCorrelationsPro[t][pe][0][7]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],twoEBE*eightReducedEBE,dW2*dw8); // storing <2><8'>\r
  //fDiffFlowProductOfCorrelationsPro[t][pe][1][7]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],twoReducedEBE*eightReducedEBE,dw2*dw8); // storing <2'><8'>\r
  //fDiffFlowProductOfCorrelationsPro[t][pe][2][7]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],fourEBE*eightReducedEBE,dW4*dw8); // storing <4><8'>\r
  //fDiffFlowProductOfCorrelationsPro[t][pe][3][7]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],fourReducedEBE*eightReducedEBE,dw4*dw8); // storing <4'><8'> \r
  //fDiffFlowProductOfCorrelationsPro[t][pe][4][7]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],sixEBE*eightReducedEBE,dW6*dw8); // storing <6><8'>\r
  //fDiffFlowProductOfCorrelationsPro[t][pe][5][7]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],sixReducedEBE*eightReducedEBE,dw6*dw8); // storing <6'><8'>\r
  //fDiffFlowProductOfCorrelationsPro[t][pe][6][7]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],eightEBE*eightReducedEBE,dW8*dw8); // storing <8><8'> \r
 } // end of for(Int_t b=1;b<=nBinsPtEta[pe];b++       \r
     \r
} // end of void AliFlowAnalysisWithQCumulants::CalculateDiffFlowProductOfCorrelations(TString type, TString ptOrEta)\r
\r
\r
//================================================================================================================================\r
    \r
    \r
void AliFlowAnalysisWithQCumulants::CalculateDiffFlowCovariances(TString type, TString ptOrEta) // to be improved (reimplemented)\r
{\r
 // a) Calculate unbiased estimators Cov(<2>,<2'>), Cov(<2>,<4'>), Cov(<4>,<2'>), Cov(<4>,<4'>) and Cov(<2'>,<4'>)\r
 //    for covariances V(<2>,<2'>), V(<2>,<4'>), V(<4>,<2'>), V(<4>,<4'>) and V(<2'>,<4'>).  \r
 // b) Store in histogram fDiffFlowCovariances[t][pe][index] for instance the following: \r
 //\r
 //             Cov(<2>,<2'>) * (sum_{i=1}^{N} w_{<2>}_i w_{<2'>}_i )/[(sum_{i=1}^{N} w_{<2>}_i) * (sum_{j=1}^{N} w_{<2'>}_j)]\r
 // \r
 //     where N is the number of events, w_{<2>} is event weight for <2> and w_{<2'>} is event weight for <2'>.\r
 // c) Binning of fDiffFlowCovariances[t][pe][index] is organized as follows:\r
 // \r
 //     1st bin: Cov(<2>,<2'>) * (sum_{i=1}^{N} w_{<2>}_i w_{<2'>}_i )/[(sum_{i=1}^{N} w_{<2>}_i) * (sum_{j=1}^{N} w_{<2'>}_j)] \r
 //     2nd bin: Cov(<2>,<4'>) * (sum_{i=1}^{N} w_{<2>}_i w_{<4'>}_i )/[(sum_{i=1}^{N} w_{<2>}_i) * (sum_{j=1}^{N} w_{<4'>}_j)] \r
 //     3rd bin: Cov(<4>,<2'>) * (sum_{i=1}^{N} w_{<4>}_i w_{<2'>}_i )/[(sum_{i=1}^{N} w_{<4>}_i) * (sum_{j=1}^{N} w_{<2'>}_j)] \r
 //     4th bin: Cov(<4>,<4'>) * (sum_{i=1}^{N} w_{<4>}_i w_{<4'>}_i )/[(sum_{i=1}^{N} w_{<4>}_i) * (sum_{j=1}^{N} w_{<4'>}_j)] \r
 //     5th bin: Cov(<2'>,<4'>) * (sum_{i=1}^{N} w_{<2'>}_i w_{<4'>}_i )/[(sum_{i=1}^{N} w_{<2'>}_i) * (sum_{j=1}^{N} w_{<4'>}_j)] \r
 //     ...\r
  \r
 Int_t typeFlag = -1;\r
 Int_t ptEtaFlag = -1;\r
\r
 if(type == "RP")\r
 {\r
  typeFlag = 0;\r
 } else if(type == "POI")\r
   {\r
    typeFlag = 1;\r
   } \r
     \r
 if(ptOrEta == "Pt")\r
 {\r
  ptEtaFlag = 0;\r
 } else if(ptOrEta == "Eta")\r
   {\r
    ptEtaFlag = 1;\r
   } \r
  \r
 // shortcuts:\r
 Int_t t = typeFlag;\r
 Int_t pe = ptEtaFlag;\r
     \r
 // common:\r
 Int_t nBinsPtEta[2] = {fnBinsPt,fnBinsEta};\r
 //Double_t minPtEta[2] = {fPtMin,fEtaMin};\r
 //Double_t maxPtEta[2] = {fPtMax,fEtaMax};\r
 //Double_t binWidthPtEta[2] = {fPtBinWidth,fEtaBinWidth};\r
 \r
 // average correlations:\r
 Double_t two = fIntFlowCorrelationsHist->GetBinContent(1); // <<2>>\r
 Double_t four = fIntFlowCorrelationsHist->GetBinContent(2); // <<4>>\r
 //Double_t six = fIntFlowCorrelationsHist->GetBinContent(3); // <<6>>\r
 //Double_t eight = fIntFlowCorrelationsHist->GetBinContent(4); // <<8>>\r
 \r
 // sum of weights for correlation:\r
 Double_t sumOfWeightsForTwo = fIntFlowSumOfEventWeights[0]->GetBinContent(1); // sum_{i=1}^{N} w_{<2>}\r
 Double_t sumOfWeightsForFour = fIntFlowSumOfEventWeights[0]->GetBinContent(2); // sum_{i=1}^{N} w_{<4>}\r
 //Double_t sumOfWeightsForSix = fIntFlowSumOfEventWeights[0]->GetBinContent(3); // sum_{i=1}^{N} w_{<6>}\r
 //Double_t sumOfWeightsForEight = fIntFlowSumOfEventWeights[0]->GetBinContent(4); // sum_{i=1}^{N} w_{<8>}\r
 \r
 // average reduced correlations:\r
 Double_t twoReduced = 0.; // <<2'>> \r
 Double_t fourReduced = 0.; // <<4'>>\r
 //Double_t sixReduced = 0.; // <<6'>>\r
 //Double_t eightReduced = 0.; // <<8'>>\r
\r
 // sum of weights for reduced correlation:\r
 Double_t sumOfWeightsForTwoReduced = 0.; // sum_{i=1}^{N} w_{<2'>}\r
 Double_t sumOfWeightsForFourReduced = 0.; // sum_{i=1}^{N} w_{<4'>}\r
 //Double_t sumOfWeightsForSixReduced = 0.; // sum_{i=1}^{N} w_{<6'>}\r
 //Double_t sumOfWeightsForEightReduced = 0.; // sum_{i=1}^{N} w_{<8'>}\r
  \r
 // product of weights for reduced correlation:\r
 Double_t productOfWeightsForTwoTwoReduced = 0.; // sum_{i=1}^{N} w_{<2>}w_{<2'>}\r
 Double_t productOfWeightsForTwoFourReduced = 0.; // sum_{i=1}^{N} w_{<2>}w_{<4'>}\r
 Double_t productOfWeightsForFourTwoReduced = 0.; // sum_{i=1}^{N} w_{<4>}w_{<2'>}\r
 Double_t productOfWeightsForFourFourReduced = 0.; // sum_{i=1}^{N} w_{<4>}w_{<4'>}\r
 Double_t productOfWeightsForTwoReducedFourReduced = 0.; // sum_{i=1}^{N} w_{<2'>}w_{<4'>}\r
 // ...\r
 \r
 // products for differential flow:\r
 Double_t twoTwoReduced = 0; // <<2><2'>> \r
 Double_t twoFourReduced = 0; // <<2><4'>> \r
 Double_t fourTwoReduced = 0; // <<4><2'>> \r
 Double_t fourFourReduced = 0; // <<4><4'>> \r
 Double_t twoReducedFourReduced = 0; // <<2'><4'>> \r
\r
 // denominators in the expressions for the unbiased estimators for covariances:\r
 // denominator = 1 - term1/(term2*term3)\r
 // prefactor = term1/(term2*term3)\r
 Double_t denominator = 0.; \r
 Double_t prefactor = 0.;\r
 Double_t term1 = 0.; \r
 Double_t term2 = 0.; \r
 Double_t term3 = 0.; \r
 \r
 // unbiased estimators for covariances for differential flow:\r
 Double_t covTwoTwoReduced = 0.; // Cov(<2>,<2'>)\r
 Double_t wCovTwoTwoReduced = 0.; // Cov(<2>,<2'>) * prefactor(w_{<2>},w_{<2'>})\r
 Double_t covTwoFourReduced = 0.; // Cov(<2>,<4'>)\r
 Double_t wCovTwoFourReduced = 0.; // Cov(<2>,<4'>) * prefactor(w_{<2>},w_{<4'>})\r
 Double_t covFourTwoReduced = 0.; // Cov(<4>,<2'>)\r
 Double_t wCovFourTwoReduced = 0.; // Cov(<4>,<2'>) * prefactor(w_{<4>},w_{<2'>})\r
 Double_t covFourFourReduced = 0.; // Cov(<4>,<4'>)\r
 Double_t wCovFourFourReduced = 0.; // Cov(<4>,<4'>) * prefactor(w_{<4>},w_{<4'>})\r
 Double_t covTwoReducedFourReduced = 0.; // Cov(<2'>,<4'>)\r
 Double_t wCovTwoReducedFourReduced = 0.; // Cov(<2'>,<4'>) * prefactor(w_{<2'>},w_{<4'>})\r
 \r
 for(Int_t b=1;b<=nBinsPtEta[pe];b++)\r
 {\r
  // average reduced corelations:\r
  twoReduced = fDiffFlowCorrelationsHist[t][pe][0]->GetBinContent(b);\r
  fourReduced = fDiffFlowCorrelationsHist[t][pe][1]->GetBinContent(b);\r
  // average products:\r
  twoTwoReduced = fDiffFlowProductOfCorrelationsPro[t][pe][0][1]->GetBinContent(b);\r
  twoFourReduced = fDiffFlowProductOfCorrelationsPro[t][pe][0][3]->GetBinContent(b);\r
  fourTwoReduced = fDiffFlowProductOfCorrelationsPro[t][pe][1][2]->GetBinContent(b);\r
  fourFourReduced = fDiffFlowProductOfCorrelationsPro[t][pe][2][3]->GetBinContent(b);\r
  twoReducedFourReduced = fDiffFlowProductOfCorrelationsPro[t][pe][1][3]->GetBinContent(b);  \r
  // sum of weights for reduced correlations:\r
  sumOfWeightsForTwoReduced = fDiffFlowSumOfEventWeights[t][pe][0][0]->GetBinContent(b);\r
  sumOfWeightsForFourReduced = fDiffFlowSumOfEventWeights[t][pe][0][1]->GetBinContent(b);\r
  // products of weights for correlations:\r
  productOfWeightsForTwoTwoReduced = fDiffFlowSumOfProductOfEventWeights[t][pe][0][1]->GetBinContent(b); \r
  productOfWeightsForTwoFourReduced = fDiffFlowSumOfProductOfEventWeights[t][pe][0][3]->GetBinContent(b);\r
  productOfWeightsForFourTwoReduced = fDiffFlowSumOfProductOfEventWeights[t][pe][1][2]->GetBinContent(b);\r
  productOfWeightsForFourFourReduced = fDiffFlowSumOfProductOfEventWeights[t][pe][2][3]->GetBinContent(b);\r
  productOfWeightsForTwoReducedFourReduced = fDiffFlowSumOfProductOfEventWeights[t][pe][1][3]->GetBinContent(b);\r
  // denominator for the unbiased estimator for covariances: 1 - term1/(term2*term3) \r
  // prefactor (multiplies Cov's) = term1/(term2*term3)       \r
  // <2>,<2'>:\r
  term1 = productOfWeightsForTwoTwoReduced;      \r
  term2 = sumOfWeightsForTwo;\r
  term3 = sumOfWeightsForTwoReduced;        \r
  if(term2*term3>0.)\r
  {\r
   denominator = 1.-term1/(term2*term3);\r
   prefactor = term1/(term2*term3);\r
   if(denominator!=0)\r
   {\r
    covTwoTwoReduced = (twoTwoReduced-two*twoReduced)/denominator;            \r
    wCovTwoTwoReduced = covTwoTwoReduced*prefactor; \r
    fDiffFlowCovariances[t][pe][0]->SetBinContent(b,wCovTwoTwoReduced);\r
   }\r
  }\r
  // <2>,<4'>:\r
  term1 = productOfWeightsForTwoFourReduced;      \r
  term2 = sumOfWeightsForTwo;\r
  term3 = sumOfWeightsForFourReduced;        \r
  if(term2*term3>0.)\r
  {\r
   denominator = 1.-term1/(term2*term3);\r
   prefactor = term1/(term2*term3);\r
   if(denominator!=0)\r
   {\r
    covTwoFourReduced = (twoFourReduced-two*fourReduced)/denominator;            \r
    wCovTwoFourReduced = covTwoFourReduced*prefactor; \r
    fDiffFlowCovariances[t][pe][1]->SetBinContent(b,wCovTwoFourReduced);\r
   }\r
  }\r
  // <4>,<2'>:\r
  term1 = productOfWeightsForFourTwoReduced;      \r
  term2 = sumOfWeightsForFour;\r
  term3 = sumOfWeightsForTwoReduced;        \r
  if(term2*term3>0.)\r
  {\r
   denominator = 1.-term1/(term2*term3);\r
   prefactor = term1/(term2*term3);\r
   if(denominator!=0)\r
   {\r
    covFourTwoReduced = (fourTwoReduced-four*twoReduced)/denominator;            \r
    wCovFourTwoReduced = covFourTwoReduced*prefactor; \r
    fDiffFlowCovariances[t][pe][2]->SetBinContent(b,wCovFourTwoReduced);\r
   }\r
  }\r
  // <4>,<4'>:\r
  term1 = productOfWeightsForFourFourReduced;      \r
  term2 = sumOfWeightsForFour;\r
  term3 = sumOfWeightsForFourReduced;        \r
  if(term2*term3>0.)\r
  {\r
   denominator = 1.-term1/(term2*term3);\r
   prefactor = term1/(term2*term3);\r
   if(denominator!=0)\r
   {\r
    covFourFourReduced = (fourFourReduced-four*fourReduced)/denominator;            \r
    wCovFourFourReduced = covFourFourReduced*prefactor; \r
    fDiffFlowCovariances[t][pe][3]->SetBinContent(b,wCovFourFourReduced);\r
   }\r
  }\r
  // <2'>,<4'>:\r
  term1 = productOfWeightsForTwoReducedFourReduced;      \r
  term2 = sumOfWeightsForTwoReduced;\r
  term3 = sumOfWeightsForFourReduced;        \r
  if(term2*term3>0.)\r
  {\r
   denominator = 1.-term1/(term2*term3);\r
   prefactor = term1/(term2*term3);\r
   if(denominator!=0)\r
   {\r
    covTwoReducedFourReduced = (twoReducedFourReduced-twoReduced*fourReduced)/denominator;            \r
    wCovTwoReducedFourReduced = covTwoReducedFourReduced*prefactor; \r
    fDiffFlowCovariances[t][pe][4]->SetBinContent(b,wCovTwoReducedFourReduced);\r
   }\r
  }   \r
 } // end of for(Int_t b=1;b<=nBinsPtEta[pe];b++)\r
  \r
} // end of void AliFlowAnalysisWithQCumulants::CalculateDiffFlowCovariances(TString type, TString ptOrEta)\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::CalculateDiffFlow(TString type, TString ptOrEta)\r
{\r
 // calculate differential flow from differential cumulants and previously obtained integrated flow: (to be improved: description)\r
 \r
 Int_t typeFlag = -1;\r
 Int_t ptEtaFlag = -1;\r
\r
 if(type == "RP")\r
 {\r
  typeFlag = 0;\r
 } else if(type == "POI")\r
   {\r
    typeFlag = 1;\r
   } \r
     \r
 if(ptOrEta == "Pt")\r
 {\r
  ptEtaFlag = 0;\r
 } else if(ptOrEta == "Eta")\r
   {\r
    ptEtaFlag = 1;\r
   } \r
  \r
 // shortcuts:\r
 Int_t t = typeFlag;\r
 Int_t pe = ptEtaFlag;\r
     \r
 // common:\r
 Int_t nBinsPtEta[2] = {fnBinsPt,fnBinsEta};\r
   \r
 // correlations:\r
 Double_t two = fIntFlowCorrelationsHist->GetBinContent(1); // <<2>>\r
 Double_t four = fIntFlowCorrelationsHist->GetBinContent(2); // <<4>>\r
 \r
 // statistical errors of correlations:\r
 Double_t twoError = fIntFlowCorrelationsHist->GetBinError(1);\r
 Double_t fourError = fIntFlowCorrelationsHist->GetBinError(2);   \r
    \r
 // reduced correlations:\r
 Double_t twoReduced = 0.; // <<2'>>\r
 Double_t fourReduced = 0.; // <<4'>>\r
 \r
 // statistical errors of reduced correlations:\r
 Double_t twoReducedError = 0.; \r
 Double_t fourReducedError = 0.; \r
\r
 // covariances:\r
 Double_t wCovTwoFour = fIntFlowCovariances->GetBinContent(1);// // Cov(<2>,<4>) * prefactor(<2>,<4>)\r
 Double_t wCovTwoTwoReduced = 0.; // Cov(<2>,<2'>) * prefactor(<2>,<2'>)\r
 Double_t wCovTwoFourReduced = 0.; // Cov(<2>,<4'>) * prefactor(<2>,<4'>)\r
 Double_t wCovFourTwoReduced = 0.; // Cov(<4>,<2'>) * prefactor(<4>,<2'>)\r
 Double_t wCovFourFourReduced = 0.; // Cov(<4>,<4'>) * prefactor(<4>,<4'>)\r
 Double_t wCovTwoReducedFourReduced = 0.; // Cov(<2'>,<4'>) * prefactor(<2'>,<4'>)\r
 \r
 // differential flow:\r
 Double_t v2Prime = 0.; // v'{2}                   \r
 Double_t v4Prime = 0.; // v'{4}\r
 \r
 // statistical error of differential flow:\r
 Double_t v2PrimeError = 0.;                    \r
 Double_t v4PrimeError = 0.; \r
 \r
 // squared statistical error of differential flow:\r
 Double_t v2PrimeErrorSquared = 0.;                    \r
 Double_t v4PrimeErrorSquared = 0.; \r
 \r
 // loop over pt or eta bins:\r
 for(Int_t b=1;b<=nBinsPtEta[pe];b++)\r
 {\r
  // reduced correlations and statistical errors:\r
  twoReduced = fDiffFlowCorrelationsHist[t][pe][0]->GetBinContent(b);\r
  twoReducedError = fDiffFlowCorrelationsHist[t][pe][0]->GetBinError(b);\r
  fourReduced = fDiffFlowCorrelationsHist[t][pe][1]->GetBinContent(b);\r
  fourReducedError = fDiffFlowCorrelationsHist[t][pe][1]->GetBinError(b);\r
  // covariances:\r
  wCovTwoTwoReduced = fDiffFlowCovariances[t][pe][0]->GetBinContent(b);\r
  wCovTwoFourReduced = fDiffFlowCovariances[t][pe][1]->GetBinContent(b);\r
  wCovFourTwoReduced = fDiffFlowCovariances[t][pe][2]->GetBinContent(b);\r
  wCovFourFourReduced = fDiffFlowCovariances[t][pe][3]->GetBinContent(b);\r
  wCovTwoReducedFourReduced = fDiffFlowCovariances[t][pe][4]->GetBinContent(b);\r
  // differential flow:\r
  // v'{2}:\r
  if(two>0.) \r
  {\r
   v2Prime = twoReduced/pow(two,0.5);\r
   v2PrimeErrorSquared = (1./4.)*pow(two,-3.)*\r
                         (pow(twoReduced,2.)*pow(twoError,2.)\r
                          + 4.*pow(two,2.)*pow(twoReducedError,2.)\r
                          - 4.*two*twoReduced*wCovTwoTwoReduced);\r
     \r
                                                            \r
   if(v2PrimeErrorSquared>0.) v2PrimeError = pow(v2PrimeErrorSquared,0.5);\r
   fDiffFlow[t][pe][0]->SetBinContent(b,v2Prime); \r
   fDiffFlow[t][pe][0]->SetBinError(b,v2PrimeError);     \r
  }\r
  // differential flow:\r
  // v'{4}\r
  if(2.*pow(two,2.)-four > 0.) \r
  {\r
   v4Prime = (2.*two*twoReduced-fourReduced)/pow(2.*pow(two,2.)-four,3./4.);\r
   v4PrimeErrorSquared = pow(2.*pow(two,2.)-four,-7./2.)*\r
                         (pow(2.*pow(two,2.)*twoReduced-3.*two*fourReduced+2.*four*twoReduced,2.)*pow(twoError,2.)\r
                          + (9./16.)*pow(2.*two*twoReduced-fourReduced,2.)*pow(fourError,2.)\r
                          + 4.*pow(two,2.)*pow(2.*pow(two,2.)-four,2.)*pow(twoReducedError,2.)\r
                          + pow(2.*pow(two,2.)-four,2.)*pow(fourReducedError,2.)                          \r
                          - (3./2.)*(2.*two*twoReduced-fourReduced)\r
                          * (2.*pow(two,2.)*twoReduced-3.*two*fourReduced+2.*four*twoReduced)*wCovTwoFour\r
                          - 4.*two*(2.*pow(two,2.)-four)\r
                          * (2.*pow(two,2.)*twoReduced-3.*two*fourReduced+2.*four*twoReduced)*wCovTwoTwoReduced\r
                          + 2.*(2.*pow(two,2.)-four)\r
                          * (2.*pow(two,2.)*twoReduced-3.*two*fourReduced+2.*four*twoReduced)*wCovTwoFourReduced\r
                          + 3.*two*(2.*pow(two,2.)-four)*(2.*two*twoReduced-fourReduced)*wCovFourTwoReduced\r
                          - (3./2.)*(2.*pow(two,2.)-four)*(2.*two*twoReduced-fourReduced)*wCovFourFourReduced \r
                          - 4.*two*pow(2.*pow(two,2.)-four,2.)*wCovTwoReducedFourReduced);  \r
   if(v4PrimeErrorSquared>0.) v4PrimeError = pow(v4PrimeErrorSquared,0.5);        \r
   fDiffFlow[t][pe][1]->SetBinContent(b,v4Prime);\r
   fDiffFlow[t][pe][1]->SetBinError(b,v4PrimeError);     \r
  }\r
  \r
 } // end of for(Int_t b=1;b<=fnBinsPtEta[pe];b++)\r
 \r
   \r
 \r
 \r
 /*\r
 // 2D:\r
 for(Int_t nua=0;nua<2;nua++)\r
 {\r
  for(Int_t p=1;p<=fnBinsPt;p++)\r
  {\r
   for(Int_t e=1;e<=fnBinsEta;e++) \r
   { \r
    // differential cumulants:\r
    Double_t qc2Prime = fFinalCumulants2D[t][pW][eW][nua][0]->GetBinContent(fFinalCumulants2D[t][pW][eW][nua][0]->GetBin(p,e)); // QC{2'}                    \r
    Double_t qc4Prime = fFinalCumulants2D[t][pW][eW][nua][1]->GetBinContent(fFinalCumulants2D[t][pW][eW][nua][1]->GetBin(p,e)); // QC{4'}\r
    // differential flow:\r
    Double_t v2Prime = 0.;                    \r
    Double_t v4Prime = 0.; \r
    if(v2) \r
    {\r
     v2Prime = qc2Prime/v2;\r
     fFinalFlow2D[t][pW][eW][nua][0]->SetBinContent(fFinalFlow2D[t][pW][eW][nua][0]->GetBin(p,e),v2Prime);  \r
    }                   \r
    if(v4)\r
    {\r
     v4Prime = -qc4Prime/pow(v4,3.); \r
     fFinalFlow2D[t][pW][eW][nua][1]->SetBinContent(fFinalFlow2D[t][pW][eW][nua][1]->GetBin(p,e),v4Prime);  \r
    }                    \r
   } // end of for(Int_t e=1;e<=fnBinsEta;e++)\r
  } // end of for(Int_t p=1;p<=fnBinsPt;p++)\r
 } // end of for(Int_t nua=0;nua<2;nua++)\r
 */\r
\r
} // end of AliFlowAnalysisWithQCumulants::CalculateDiffFlow(TString type, Bool_t useParticleWeights)\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::StoreIntFlowFlags()\r
{\r
 // a) Store all flags for integrated flow in profile fIntFlowFlags.\r
 \r
 if(!fIntFlowFlags)\r
 {\r
  cout<<"WARNING: fIntFlowFlags is NULL in AFAWQC::SFFIF() !!!!"<<endl;\r
  exit(0);\r
 } \r

 // particle weights used or not:\r
 fIntFlowFlags->Fill(0.5,(Int_t)fUsePhiWeights||fUsePtWeights||fUseEtaWeights);\r
 // which event weights were used:
 if(strcmp(fMultiplicityWeight->Data(),"combinations"))
 {
  fIntFlowFlags->Fill(1.5,0); // 0 = "combinations" (default)\r
 } else if(strcmp(fMultiplicityWeight->Data(),"unit"))
   {
    fIntFlowFlags->Fill(1.5,1); // 1 = "unit"   
   } else if(strcmp(fMultiplicityWeight->Data(),"multiplicity"))
     {
      fIntFlowFlags->Fill(1.5,2); // 2 = "multiplicity"        
     } 
 // corrected for non-uniform acceptance or not:
 fIntFlowFlags->Fill(2.5,(Int_t)fApplyCorrectionForNUA);
 fIntFlowFlags->Fill(3.5,(Int_t)fPrintFinalResults[0]);\r
 fIntFlowFlags->Fill(4.5,(Int_t)fPrintFinalResults[1]);\r
 fIntFlowFlags->Fill(5.5,(Int_t)fPrintFinalResults[2]);\r
  \r
} // end of void AliFlowAnalysisWithQCumulants::StoreIntFlowFlags()\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::StoreDiffFlowFlags()\r
{\r
 // Store all flags for differential flow in the profile fDiffFlowFlags.\r
  \r
 if(!fDiffFlowFlags)\r
 {\r
  cout<<"WARNING: fDiffFlowFlags is NULL in AFAWQC::SFFDF() !!!!"<<endl;\r
  exit(0);\r
 } \r
 \r
 fDiffFlowFlags->Fill(0.5,fUsePhiWeights||fUsePtWeights||fUseEtaWeights); // particle weights used or not\r
 //fDiffFlowFlags->Fill(1.5,""); // which event weight was used? // to be improved\r
 fDiffFlowFlags->Fill(2.5,fApplyCorrectionForNUA); // corrected for non-uniform acceptance or not\r
 fDiffFlowFlags->Fill(3.5,fCalculate2DFlow); // calculate also 2D differential flow in (pt,eta) or not\r
    \r
} // end of void AliFlowAnalysisWithQCumulants::StoreDiffFlowFlags()\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::GetPointersForCommonHistograms() \r
{\r
 // Access all pointers to common control and common result histograms and profiles.\r
 \r
 TString commonHistsName = "AliFlowCommonHistQC";\r
 commonHistsName += fAnalysisLabel->Data();\r
 AliFlowCommonHist *commonHist = dynamic_cast<AliFlowCommonHist*>(fHistList->FindObject(commonHistsName.Data()));\r
 if(commonHist) this->SetCommonHists(commonHist); \r
 TString commonHists2ndOrderName = "AliFlowCommonHist2ndOrderQC";\r
 commonHists2ndOrderName += fAnalysisLabel->Data();\r
 AliFlowCommonHist *commonHist2nd = dynamic_cast<AliFlowCommonHist*>(fHistList->FindObject(commonHists2ndOrderName.Data()));\r
 if(commonHist2nd) this->SetCommonHists2nd(commonHist2nd);   \r
 TString commonHists4thOrderName = "AliFlowCommonHist4thOrderQC";\r
 commonHists4thOrderName += fAnalysisLabel->Data();\r
 AliFlowCommonHist *commonHist4th = dynamic_cast<AliFlowCommonHist*>(fHistList->FindObject(commonHists4thOrderName.Data()));\r
 if(commonHist4th) this->SetCommonHists4th(commonHist4th);  \r
 TString commonHists6thOrderName = "AliFlowCommonHist6thOrderQC";\r
 commonHists6thOrderName += fAnalysisLabel->Data();\r
 AliFlowCommonHist *commonHist6th = dynamic_cast<AliFlowCommonHist*>(fHistList->FindObject(commonHists6thOrderName.Data()));\r
 if(commonHist6th) this->SetCommonHists6th(commonHist6th);  \r
 TString commonHists8thOrderName = "AliFlowCommonHist8thOrderQC";\r
 commonHists8thOrderName += fAnalysisLabel->Data();\r
 AliFlowCommonHist *commonHist8th = dynamic_cast<AliFlowCommonHist*>(fHistList->FindObject(commonHists8thOrderName.Data()));\r
 if(commonHist8th) this->SetCommonHists8th(commonHist8th);  \r
 TString commonHistResults2ndOrderName = "AliFlowCommonHistResults2ndOrderQC"; \r
 commonHistResults2ndOrderName += fAnalysisLabel->Data(); \r
 AliFlowCommonHistResults *commonHistRes2nd = dynamic_cast<AliFlowCommonHistResults*>\r                                              (fHistList->FindObject(commonHistResults2ndOrderName.Data()));\r
 if(commonHistRes2nd) this->SetCommonHistsResults2nd(commonHistRes2nd);   \r
 TString commonHistResults4thOrderName = "AliFlowCommonHistResults4thOrderQC";\r
 commonHistResults4thOrderName += fAnalysisLabel->Data();\r
 AliFlowCommonHistResults *commonHistRes4th = dynamic_cast<AliFlowCommonHistResults*>\r
                                              (fHistList->FindObject(commonHistResults4thOrderName.Data()));\r
 if(commonHistRes4th) this->SetCommonHistsResults4th(commonHistRes4th);  \r
 TString commonHistResults6thOrderName = "AliFlowCommonHistResults6thOrderQC";\r
 commonHistResults6thOrderName += fAnalysisLabel->Data();\r
 AliFlowCommonHistResults *commonHistRes6th = dynamic_cast<AliFlowCommonHistResults*>\r
                                              (fHistList->FindObject(commonHistResults6thOrderName.Data()));\r
 if(commonHistRes6th) this->SetCommonHistsResults6th(commonHistRes6th);  \r
 TString commonHistResults8thOrderName = "AliFlowCommonHistResults8thOrderQC";\r
 commonHistResults8thOrderName += fAnalysisLabel->Data();\r
 AliFlowCommonHistResults *commonHistRes8th = dynamic_cast<AliFlowCommonHistResults*>\r
                                              (fHistList->FindObject(commonHistResults8thOrderName.Data()));  \r
 if(commonHistRes8th) this->SetCommonHistsResults8th(commonHistRes8th);
       \r
} // end of void AliFlowAnalysisWithQCumulants::GetPointersForCommonHistograms() \r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::GetPointersForParticleWeightsHistograms() \r
{\r
 // Get pointers for histograms with particle weights.\r
\r
 TList *weightsList = dynamic_cast<TList*>(fHistList->FindObject("Weights"));\r
 if(weightsList) this->SetWeightsList(weightsList);\r
 TString fUseParticleWeightsName = "fUseParticleWeightsQC"; // to be improved (hirdwired label QC)\r
 fUseParticleWeightsName += fAnalysisLabel->Data();\r
 TProfile *useParticleWeights = dynamic_cast<TProfile*>(weightsList->FindObject(fUseParticleWeightsName.Data()));\r
 if(useParticleWeights)\r
 {\r
  this->SetUseParticleWeights(useParticleWeights);  \r
  fUsePhiWeights = (Int_t)fUseParticleWeights->GetBinContent(1); \r
  fUsePtWeights = (Int_t)fUseParticleWeights->GetBinContent(2); \r
  fUseEtaWeights = (Int_t)fUseParticleWeights->GetBinContent(3);  \r
 }\r\r
} // end of void AliFlowAnalysisWithQCumulants::GetPointersForParticleWeightsHistograms(); \r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::GetPointersForIntFlowHistograms() \r
{\r
 // Get pointers for histograms and profiles relevant for integrated flow:\r
 //  a) Get pointer to base list for integrated flow holding profile fIntFlowFlags and lists fIntFlowProfiles and fIntFlowResults.\r
 //  b) Get pointer to profile fIntFlowFlags holding all flags for integrated flow.\r
 //  c) Get pointer to list fIntFlowProfiles and pointers to all objects that she holds. \r
 //  d) Get pointer to list fIntFlowResults and pointers to all objects that she holds. \r
  \r
 TString sinCosFlag[2] = {"sin","cos"}; // to be improved (should I promote this to data member?)\r
 TString powerFlag[2] = {"linear","quadratic"}; // to be improved (should I promote this to data member?)\r
 \r
 // a) Get pointer to base list for integrated flow holding profile fIntFlowFlags and lists fIntFlowProfiles and fIntFlowResults:\r
 TList *intFlowList = NULL;\r
 intFlowList = dynamic_cast<TList*>(fHistList->FindObject("Integrated Flow"));\r
 if(!intFlowList) \r
 {\r
  cout<<"WARNING: intFlowList is NULL in AFAWQC::GPFIFH() !!!!"<<endl;\r
  exit(0); \r
 }  \r
  \r
  // b) Get pointer to profile fIntFlowFlags holding all flags for integrated flow:\r
  TString intFlowFlagsName = "fIntFlowFlags";\r
  intFlowFlagsName += fAnalysisLabel->Data();\r
  TProfile *intFlowFlags = dynamic_cast<TProfile*>(intFlowList->FindObject(intFlowFlagsName.Data()));\r
  Bool_t bApplyCorrectionForNUA = kFALSE;\r
  if(intFlowFlags)\r
  {\r
   this->SetIntFlowFlags(intFlowFlags);  \r
   bApplyCorrectionForNUA = (Int_t)intFlowFlags->GetBinContent(3); \r
   this->SetApplyCorrectionForNUA(bApplyCorrectionForNUA);      \r
  } else \r
    {\r
     cout<<"WARNING: intFlowFlags is NULL in FAWQC::GPFIFH() !!!!"<<endl;\r
    }\r
  \r
  // c) Get pointer to list fIntFlowProfiles and pointers to all objects that she holds:\r
  TList *intFlowProfiles = NULL;\r
  intFlowProfiles = dynamic_cast<TList*>(intFlowList->FindObject("Profiles"));\r
  if(intFlowProfiles)  \r
  {\r
   // average multiplicities:\r
   TString avMultiplicityName = "fAvMultiplicity";\r
   avMultiplicityName += fAnalysisLabel->Data();\r
   TProfile *avMultiplicity = dynamic_cast<TProfile*>(intFlowProfiles->FindObject(avMultiplicityName.Data()));\r
   if(avMultiplicity) \r
   {\r
    this->SetAvMultiplicity(avMultiplicity);\r
   } else \r
     {\r
      cout<<"WARNING: avMultiplicity is NULL in AFAWQC::GPFIFH() !!!!"<<endl;\r
     }\r
   // average correlations <<2>>, <<4>>, <<6>> and <<8>> (with wrong errors!):\r
   TString intFlowCorrelationsProName = "fIntFlowCorrelationsPro";\r
   intFlowCorrelationsProName += fAnalysisLabel->Data();\r
   TProfile *intFlowCorrelationsPro = dynamic_cast<TProfile*>(intFlowProfiles->FindObject(intFlowCorrelationsProName.Data()));\r
   if(intFlowCorrelationsPro) \r
   {\r
    this->SetIntFlowCorrelationsPro(intFlowCorrelationsPro);\r
   } else \r
     {\r
      cout<<"WARNING: intFlowCorrelationsPro is NULL in AFAWQC::GPFIFH() !!!!"<<endl;\r
     } \r
   // average all correlations for integrated flow (with wrong errors!):\r
   TString intFlowCorrelationsAllProName = "fIntFlowCorrelationsAllPro";\r
   intFlowCorrelationsAllProName += fAnalysisLabel->Data();\r
   TProfile *intFlowCorrelationsAllPro = dynamic_cast<TProfile*>(intFlowProfiles->FindObject(intFlowCorrelationsAllProName.Data()));\r
   if(intFlowCorrelationsAllPro) \r
   {\r
    this->SetIntFlowCorrelationsAllPro(intFlowCorrelationsAllPro);\r
   } else \r
     {\r
      cout<<"WARNING: intFlowCorrelationsAllPro is NULL in AFAWQC::GPFIFH() !!!!"<<endl;\r
     }     \r
   // average extra correlations for integrated flow (which appear only when particle weights are used):\r
   // (to be improved: Weak point in implementation, I am assuming here that method GetPointersForParticleWeightsHistograms() was called)\r
   if(fUsePhiWeights||fUsePtWeights||fUseEtaWeights)\r
   {\r
    TString intFlowExtraCorrelationsProName = "fIntFlowExtraCorrelationsPro";\r
    intFlowExtraCorrelationsProName += fAnalysisLabel->Data();\r
    TProfile *intFlowExtraCorrelationsPro = dynamic_cast<TProfile*>(intFlowProfiles->FindObject(intFlowExtraCorrelationsProName.Data()));\r
    if(intFlowExtraCorrelationsPro) \r
    {\r
     this->SetIntFlowExtraCorrelationsPro(intFlowExtraCorrelationsPro);\r
    } else \r
      {\r
       cout<<"WARNING: intFlowExtraCorrelationsPro is NULL in AFAWQC::GPFIFH() !!!!"<<endl;\r
      }\r
   } // end of if(fUsePhiWeights||fUsePtWeights||fUseEtaWeights)        \r
   // average products of correlations <2>, <4>, <6> and <8>:  \r
   TString intFlowProductOfCorrelationsProName = "fIntFlowProductOfCorrelationsPro";\r
   intFlowProductOfCorrelationsProName += fAnalysisLabel->Data();\r
   TProfile *intFlowProductOfCorrelationsPro = dynamic_cast<TProfile*>(intFlowProfiles->FindObject(intFlowProductOfCorrelationsProName.Data()));\r
   if(intFlowProductOfCorrelationsPro) \r
   {\r
    this->SetIntFlowProductOfCorrelationsPro(intFlowProductOfCorrelationsPro);\r
   } else \r
     {\r
      cout<<"WARNING: intFlowProductOfCorrelationsPro is NULL in AFAWQC::GPFIFH() !!!!"<<endl;\r
     }     \r
   // average correction terms for non-uniform acceptance (with wrong errors!):\r
   for(Int_t sc=0;sc<2;sc++)\r
   {\r
    TString intFlowCorrectionTermsForNUAProName = "fIntFlowCorrectionTermsForNUAPro";\r
    intFlowCorrectionTermsForNUAProName += fAnalysisLabel->Data();\r
    TProfile *intFlowCorrectionTermsForNUAPro = dynamic_cast<TProfile*>(intFlowProfiles->FindObject((Form("%s: %s terms",intFlowCorrectionTermsForNUAProName.Data(),sinCosFlag[sc].Data()))));\r
    if(intFlowCorrectionTermsForNUAPro) \r
    {\r
     this->SetIntFlowCorrectionTermsForNUAPro(intFlowCorrectionTermsForNUAPro,sc);\r
    } else \r
      {\r
       cout<<"WARNING: intFlowCorrectionTermsForNUAPro is NULL in AFAWQC::GPFIFH() !!!!"<<endl;\r
       cout<<"sc = "<<sc<<endl;\r
      } \r
   } // end of for(Int_t sc=0;sc<2;sc++)           \r
  } else // to if(intFlowProfiles)  \r
    {\r
     cout<<"WARNING: intFlowProfiles is NULL in AFAWQC::GPFIFH() !!!!"<<endl;\r
    }\r
   \r
  //  d) Get pointer to list fIntFlowResults and pointers to all objects that she holds. \r
  TList *intFlowResults = NULL;\r
  intFlowResults = dynamic_cast<TList*>(intFlowList->FindObject("Results"));\r
  if(intFlowResults)\r
  {\r
   // average correlations <<2>>, <<4>>, <<6>> and <<8>> (with correct errors!):\r
   TString intFlowCorrelationsHistName = "fIntFlowCorrelationsHist";\r
   intFlowCorrelationsHistName += fAnalysisLabel->Data();\r
   TH1D *intFlowCorrelationsHist = dynamic_cast<TH1D*>(intFlowResults->FindObject(intFlowCorrelationsHistName.Data()));\r
   if(intFlowCorrelationsHist) \r
   {\r
    this->SetIntFlowCorrelationsHist(intFlowCorrelationsHist);\r
   } else \r
     {\r
      cout<<"WARNING: intFlowCorrelationsHist is NULL in AFAWQC::GPFIFH() !!!!"<<endl;\r
     } \r
   // average all correlations for integrated flow (with correct errors!):\r
   TString intFlowCorrelationsAllHistName = "fIntFlowCorrelationsAllHist";\r
   intFlowCorrelationsAllHistName += fAnalysisLabel->Data();\r
   TH1D *intFlowCorrelationsAllHist = dynamic_cast<TH1D*>(intFlowResults->FindObject(intFlowCorrelationsAllHistName.Data()));\r
   if(intFlowCorrelationsAllHist) \r
   {\r
    this->SetIntFlowCorrelationsAllHist(intFlowCorrelationsAllHist);\r
   } else \r
     {\r
      cout<<"WARNING: intFlowCorrelationsAllHist is NULL in AFAWQC::GPFIFH() !!!!"<<endl;\r
     }  \r
   // average correction terms for non-uniform acceptance (with correct errors!):\r
   TString intFlowCorrectionTermsForNUAHistName = "fIntFlowCorrectionTermsForNUAHist";\r
   intFlowCorrectionTermsForNUAHistName += fAnalysisLabel->Data();\r
   for(Int_t sc=0;sc<2;sc++)\r
   {\r
    TH1D *intFlowCorrectionTermsForNUAHist = dynamic_cast<TH1D*>(intFlowResults->FindObject((Form("%s: %s terms",intFlowCorrectionTermsForNUAHistName.Data(),sinCosFlag[sc].Data()))));\r
    if(intFlowCorrectionTermsForNUAHist) \r
    {\r
     this->SetIntFlowCorrectionTermsForNUAHist(intFlowCorrectionTermsForNUAHist,sc);\r
    } else \r
      {\r
       cout<<"WARNING: intFlowCorrectionTermsForNUAHist is NULL in AFAWQC::GPFIFH() !!!!"<<endl;\r
       cout<<"sc = "<<sc<<endl;\r
      } \r
   } // end of for(Int_t sc=0;sc<2;sc++)           \r
   // covariances (multiplied with weight dependent prefactor):\r
   TString intFlowCovariancesName = "fIntFlowCovariances";\r
   intFlowCovariancesName += fAnalysisLabel->Data();\r
   TH1D *intFlowCovariances = dynamic_cast<TH1D*>(intFlowResults->FindObject(intFlowCovariancesName.Data()));\r
   if(intFlowCovariances) \r
   {\r
    this->SetIntFlowCovariances(intFlowCovariances); \r
   } else \r
     {\r
      cout<<"WARNING: intFlowCovariances is NULL in AFAWQC::GPFIFH() !!!!"<<endl;\r
     } \r
   // sum of linear and quadratic event weights for <2>, <4>, <6> and <8>:\r
   TString intFlowSumOfEventWeightsName = "fIntFlowSumOfEventWeights";\r
   intFlowSumOfEventWeightsName += fAnalysisLabel->Data();\r
   for(Int_t power=0;power<2;power++)\r
   {\r
    TH1D *intFlowSumOfEventWeights = dynamic_cast<TH1D*>(intFlowResults->FindObject(Form("%s: %s",intFlowSumOfEventWeightsName.Data(),powerFlag[power].Data())));\r
    if(intFlowSumOfEventWeights) \r
    {\r
     this->SetIntFlowSumOfEventWeights(intFlowSumOfEventWeights,power);\r
    } else \r
      {\r
       cout<<"WARNING: intFlowSumOfEventWeights is NULL in AFAWQC::GPFIFH() !!!!"<<endl;\r
       cout<<"power = "<<power<<endl;\r
      }                                   \r
   } // end of for(Int_t power=0;power<2;power++)                                                                  \r
   // sum of products of event weights for correlations <2>, <4>, <6> and <8>:  \r
   TString intFlowSumOfProductOfEventWeightsName = "fIntFlowSumOfProductOfEventWeights";\r
   intFlowSumOfProductOfEventWeightsName += fAnalysisLabel->Data();\r
   TH1D *intFlowSumOfProductOfEventWeights = dynamic_cast<TH1D*>(intFlowResults->FindObject(intFlowSumOfProductOfEventWeightsName.Data()));\r
   if(intFlowSumOfProductOfEventWeights) \r
   {\r
    this->SetIntFlowSumOfProductOfEventWeights(intFlowSumOfProductOfEventWeights);\r
   } else \r
     {\r
      cout<<"WARNING: intFlowSumOfProductOfEventWeights is NULL in AFAWQC::GPFIFH() !!!!"<<endl;\r
     } \r
   // final results for integrated Q-cumulants:\r
   TString intFlowQcumulantsName = "fIntFlowQcumulants";\r
   intFlowQcumulantsName += fAnalysisLabel->Data();\r
   TH1D *intFlowQcumulants = dynamic_cast<TH1D*>(intFlowResults->FindObject(intFlowQcumulantsName.Data()));\r
   if(intFlowQcumulants) \r
   {\r
    this->SetIntFlowQcumulants(intFlowQcumulants);\r
   } else \r
     {\r
      cout<<"WARNING: intFlowQcumulants is NULL in AFAWQC::GPFIFH() !!!!"<<endl;\r
     }  \r
   // final integrated flow estimates from Q-cumulants:\r
   TString intFlowName = "fIntFlow";\r
   intFlowName += fAnalysisLabel->Data();\r
   TH1D *intFlow = dynamic_cast<TH1D*>(intFlowResults->FindObject(intFlowName.Data()));\r
   if(intFlow) \r
   {\r
    this->SetIntFlow(intFlow);\r
   } else \r
     {\r
      cout<<"WARNING: intFlow is NULL in AFAWQC::GPFIFH() !!!!"<<endl; \r
     }   \r
  } else // to if(intFlowResults)\r
    {\r
     cout<<"WARNING: intFlowResults is NULL in AFAWQC::GPFIFH() !!!!"<<endl;\r
    }\r
\r
} // end of void AliFlowAnalysisWithQCumulants::GetPointersForIntFlowHistograms()\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::GetPointersForDiffFlowHistograms()\r
{\r
 // Get pointer to all objects relevant for differential flow.\r
 //  a) Define flags locally (to be improved: should I promote flags to data members?);\r
 //  b) Get pointer to base list for differential flow fDiffFlowList and nested lists fDiffFlowListProfiles and fDiffFlowListResults;\r
 //  c) Get pointer to profile fDiffFlowFlags holding all flags for differential flow;\r
 //  d) Get pointers to all nested lists in fDiffFlowListProfiles and to profiles which they hold;\r
 //  e) Get pointers to all nested lists in fDiffFlowListResults and to histograms which they hold.\r
 \r
 // a) Define flags locally (to be improved: should I promote flags to data members?): \r
 TString typeFlag[2] = {"RP","POI"}; \r
 TString ptEtaFlag[2] = {"p_{T}","#eta"};\r
 TString powerFlag[2] = {"linear","quadratic"};\r
 TString sinCosFlag[2] = {"sin","cos"};\r
 TString differentialCumulantIndex[4] = {"QC{2'}","QC{4'}","QC{6'}","QC{8'}"};  \r
 TString differentialFlowIndex[4] = {"v'{2}","v'{4}","v'{6}","v'{8}"};  \r
 TString reducedCorrelationIndex[4] = {"<2'>","<4'>","<6'>","<8'>"};\r
 TString mixedCorrelationIndex[8] = {"<2>","<2'>","<4>","<4'>","<6>","<6'>","<8>","<8'>"};\r
 TString covarianceName[5] = {"Cov(<2>,<2'>)","Cov(<2>,<4'>)","Cov(<4>,<2'>)","Cov(<4>,<4'>)","Cov(<2'>,<4'>)"}; \r
  \r
 // b) Get pointer to base list for differential flow fDiffFlowList and nested lists fDiffFlowListProfiles and fDiffFlowListResults:\r
 TList *diffFlowList = NULL;\r
 diffFlowList = dynamic_cast<TList*>(fHistList->FindObject("Differential Flow"));  \r
 if(!diffFlowList)\r
 { \r
  cout<<"WARNING: diffFlowList is NULL in AFAWQC::GPFDFH() !!!!"<<endl;\r
  exit(0);\r
 }\r
 // list holding nested lists containing profiles:\r
 TList *diffFlowListProfiles = NULL;\r
 diffFlowListProfiles = dynamic_cast<TList*>(diffFlowList->FindObject("Profiles"));\r
 if(!diffFlowListProfiles)\r
 { \r
  cout<<"WARNING: diffFlowListProfiles is NULL in AFAWQC::GPFDFH() !!!!"<<endl;\r
  exit(0);\r
 }\r
 // list holding nested lists containing 2D and 1D histograms with final results:\r
 TList *diffFlowListResults = NULL;\r
 diffFlowListResults = dynamic_cast<TList*>(diffFlowList->FindObject("Results"));\r
 if(!diffFlowListResults)\r
 { \r
  cout<<"WARNING: diffFlowListResults is NULL in AFAWQC::GPFDFH() !!!!"<<endl;\r
  exit(0);\r
 }\r
 \r
 // c) Get pointer to profile holding all flags for differential flow;\r
 TString diffFlowFlagsName = "fDiffFlowFlags";\r
 diffFlowFlagsName += fAnalysisLabel->Data();\r
 TProfile *diffFlowFlags = dynamic_cast<TProfile*>(diffFlowList->FindObject(diffFlowFlagsName.Data()));\r
 Bool_t bCalculate2DFlow = kFALSE;\r
 if(diffFlowFlags)\r
 {\r
  this->SetDiffFlowFlags(diffFlowFlags);  \r
  bCalculate2DFlow = (Int_t)diffFlowFlags->GetBinContent(4);\r
  this->SetCalculate2DFlow(bCalculate2DFlow); // to be improved (shoul I call this setter somewhere else?)     \r
 }\r
  \r
 // d) Get pointers to all nested lists in fDiffFlowListProfiles and to profiles which they hold;\r
 // correlations:\r
 TList *diffFlowCorrelationsProList[2][2] = {{NULL}};\r
 TString diffFlowCorrelationsProName = "fDiffFlowCorrelationsPro";\r
 diffFlowCorrelationsProName += fAnalysisLabel->Data();\r
 TProfile *diffFlowCorrelationsPro[2][2][4] = {{{NULL}}};   \r
 // products of correlations:\r
 TList *diffFlowProductOfCorrelationsProList[2][2] = {{NULL}};\r
 TString diffFlowProductOfCorrelationsProName = "fDiffFlowProductOfCorrelationsPro";\r
 diffFlowProductOfCorrelationsProName += fAnalysisLabel->Data();  \r
 TProfile *diffFlowProductOfCorrelationsPro[2][2][8][8] = {{{{NULL}}}};   \r
 // corrections:\r
 TList *diffFlowCorrectionsProList[2][2] = {{NULL}};\r
 TString diffFlowCorrectionTermsForNUAProName = "fDiffFlowCorrectionTermsForNUAPro";\r
 diffFlowCorrectionTermsForNUAProName += fAnalysisLabel->Data();  \r
 TProfile *diffFlowCorrectionTermsForNUAPro[2][2][2][10] = {{{{NULL}}}};   \r
 for(Int_t t=0;t<2;t++)\r
 {\r
  for(Int_t pe=0;pe<2;pe++)\r
  {\r
   diffFlowCorrelationsProList[t][pe] = dynamic_cast<TList*>(diffFlowListProfiles->FindObject(Form("Profiles with correlations (%s, %s)",typeFlag[t].Data(),ptEtaFlag[pe].Data())));\r
   if(!diffFlowCorrelationsProList[t][pe])\r
   { \r
    cout<<"WARNING: diffFlowCorrelationsProList[t][pe] is NULL in AFAWQC::GPFDFH() !!!!"<<endl;\r
    cout<<"t = "<<t<<endl;\r
    cout<<"pe = "<<pe<<endl;\r
    exit(0);\r
   }\r
   for(Int_t ci=0;ci<4;ci++) // correlation index\r
   {\r
    diffFlowCorrelationsPro[t][pe][ci] = dynamic_cast<TProfile*>(diffFlowCorrelationsProList[t][pe]->FindObject(Form("%s, %s, %s, %s",diffFlowCorrelationsProName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),reducedCorrelationIndex[ci].Data())));\r
    if(diffFlowCorrelationsPro[t][pe][ci])\r
    {\r
     this->SetDiffFlowCorrelationsPro(diffFlowCorrelationsPro[t][pe][ci],t,pe,ci);\r
    } else\r
      {\r
       cout<<"WARNING: diffFlowCorrelationsPro[t][pe][ci] is NULL in AFAWQC::GPFDFH() !!!!"<<endl;\r
       cout<<"t  = "<<t<<endl;\r
       cout<<"pe = "<<pe<<endl;   \r
       cout<<"ci = "<<ci<<endl;\r
      }     \r
   } // end of for(Int_t ci=0;ci<4;ci++) // correlation index  \r
   // products of correlations:    \r
   diffFlowProductOfCorrelationsProList[t][pe] = dynamic_cast<TList*>(diffFlowListProfiles->FindObject(Form("Profiles with products of correlations (%s, %s)",typeFlag[t].Data(),ptEtaFlag[pe].Data()))); \r
   if(!diffFlowProductOfCorrelationsProList[t][pe])\r
   { \r
    cout<<"WARNING: ddiffFlowProductOfCorrelationsProList[t][pe] is NULL in AFAWQC::GPFDFH() !!!!"<<endl;\r
    cout<<"t = "<<t<<endl;\r
    cout<<"pe = "<<pe<<endl;\r
    exit(0);\r
   }\r
   for(Int_t mci1=0;mci1<8;mci1++) // mixed correlation index\r
   {\r
    for(Int_t mci2=mci1+1;mci2<8;mci2++) // mixed correlation index\r
    {\r
     diffFlowProductOfCorrelationsPro[t][pe][mci1][mci2] = dynamic_cast<TProfile*>(diffFlowProductOfCorrelationsProList[t][pe]->FindObject(Form("%s, %s, %s, %s, %s",diffFlowProductOfCorrelationsProName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),mixedCorrelationIndex[mci1].Data(),mixedCorrelationIndex[mci2].Data())));\r
     if(diffFlowProductOfCorrelationsPro[t][pe][mci1][mci2])\r
     {\r
      this->SetDiffFlowProductOfCorrelationsPro(diffFlowProductOfCorrelationsPro[t][pe][mci1][mci2],t,pe,mci1,mci2);\r
     } else\r
       {\r
        cout<<"WARNING: diffFlowCorrelationsPro[t][pe][ci] is NULL in AFAWQC::GPFDFH() !!!!"<<endl;\r
        cout<<"t    = "<<t<<endl;\r
        cout<<"pe   = "<<pe<<endl;   \r
        cout<<"mci1 = "<<mci1<<endl;\r
        cout<<"mci2 = "<<mci2<<endl;\r
       }\r
     if(mci1%2 == 0) mci2++; // products which DO NOT include reduced correlations are not stored here\r
    } // end of for(Int_t mci2=mci1+1;mci2<8;mci2++) // mixed correlation index\r
   } // end of for(Int_t mci1=0;mci1<8;mci1++) // mixed correlation index    \r
   // corrections:\r
   diffFlowCorrectionsProList[t][pe] = dynamic_cast<TList*>(diffFlowListProfiles->FindObject(Form("Profiles with correction terms for NUA (%s, %s)",typeFlag[t].Data(),ptEtaFlag[pe].Data())));\r
   if(!diffFlowCorrectionsProList[t][pe])\r
   { \r
    cout<<"WARNING: diffFlowCorrectionsProList[t][pe] is NULL in AFAWQC::GPFDFH() !!!!"<<endl;\r
    cout<<"t = "<<t<<endl;\r
    cout<<"pe = "<<pe<<endl;\r
    exit(0);\r
   }\r
   // correction terms for NUA:\r
   for(Int_t sc=0;sc<2;sc++) // sin or cos\r
   {\r
    for(Int_t cti=0;cti<9;cti++) // correction term index\r
    {\r
     diffFlowCorrectionTermsForNUAPro[t][pe][sc][cti] = dynamic_cast<TProfile*>(diffFlowCorrectionsProList[t][pe]->FindObject(Form("%s, %s, %s, %s, cti = %d",diffFlowCorrectionTermsForNUAProName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),sinCosFlag[sc].Data(),cti+1)));\r
     if(diffFlowCorrectionTermsForNUAPro[t][pe][sc][cti])\r
     {\r
      this->SetDiffFlowCorrectionTermsForNUAPro(diffFlowCorrectionTermsForNUAPro[t][pe][sc][cti],t,pe,sc,cti);\r
     } else\r
       {\r
        cout<<"WARNING: diffFlowCorrectionTermsForNUAPro[t][pe][sc][cti] is NULL in AFAWQC::GPFDFH() !!!!"<<endl;\r
        cout<<"t   = "<<t<<endl;\r
        cout<<"pe  = "<<pe<<endl;   \r
        cout<<"sc  = "<<sc<<endl;\r
        cout<<"cti = "<<cti<<endl;\r
       }    \r
    } // end of for(Int_t cti=0;cti<9;cti++) // correction term index\r
   } // end of for(Int_t sc=0;sc<2;sc++) // sin or cos\r
   // ...\r
  } // end of for(Int_t pe=0;pe<2;pe++)\r
 } // end of for(Int_t t=0;t<2;t++)\r
  \r
 // e) Get pointers to all nested lists in fDiffFlowListResults and to histograms which they hold.\r
 // reduced correlations:\r
 TList *diffFlowCorrelationsHistList[2][2] = {{NULL}};\r
 TString diffFlowCorrelationsHistName = "fDiffFlowCorrelationsHist";\r
 diffFlowCorrelationsHistName += fAnalysisLabel->Data();  \r
 TH1D *diffFlowCorrelationsHist[2][2][4] = {{{NULL}}};\r
 // corrections for NUA:\r
 TList *diffFlowCorrectionsHistList[2][2] = {{NULL}};\r
 TString diffFlowCorrectionTermsForNUAHistName = "fDiffFlowCorrectionTermsForNUAHist";\r
 diffFlowCorrectionTermsForNUAHistName += fAnalysisLabel->Data();  \r
 TH1D *diffFlowCorrectionTermsForNUAHist[2][2][2][10] = {{{{NULL}}}};\r
 // differential Q-cumulants:\r
 TList *diffFlowCumulantsHistList[2][2] = {{NULL}};\r
 TString diffFlowCumulantsName = "fDiffFlowCumulants";\r
 diffFlowCumulantsName += fAnalysisLabel->Data();  \r
 TH1D *diffFlowCumulants[2][2][4] = {{{NULL}}};\r
 // differential flow estimates from Q-cumulants:\r
 TList *diffFlowHistList[2][2] = {{NULL}};\r
 TString diffFlowName = "fDiffFlow";\r
 diffFlowName += fAnalysisLabel->Data();  \r
 TH1D *diffFlow[2][2][4] = {{{NULL}}};\r
 // differential covariances:\r
 TList *diffFlowCovariancesHistList[2][2] = {{NULL}};\r
 TString diffFlowCovariancesName = "fDiffFlowCovariances";\r
 diffFlowCovariancesName += fAnalysisLabel->Data();  \r
 TH1D *diffFlowCovariances[2][2][5] = {{{NULL}}};\r
 for(Int_t t=0;t<2;t++) // type: RP or POI\r
 { \r
  for(Int_t pe=0;pe<2;pe++) // pt or eta\r
  {\r
   // reduced correlations:\r
   diffFlowCorrelationsHistList[t][pe] = dynamic_cast<TList*>(diffFlowListResults->FindObject(Form("Correlations (%s, %s)",typeFlag[t].Data(),ptEtaFlag[pe].Data())));\r
   if(!diffFlowCorrelationsHistList[t][pe])\r
   { \r
    cout<<"WARNING: diffFlowCorrelationsHistList[t][pe] is NULL in AFAWQC::GPFDFH() !!!!"<<endl;\r
    cout<<"t = "<<t<<endl;\r
    cout<<"pe = "<<pe<<endl;\r
    exit(0);\r
   }\r
   for(Int_t index=0;index<4;index++) \r
   {\r
    diffFlowCorrelationsHist[t][pe][index] = dynamic_cast<TH1D*>(diffFlowCorrelationsHistList[t][pe]->FindObject(Form("%s, %s, %s, %s",diffFlowCorrelationsHistName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),reducedCorrelationIndex[index].Data())));\r
    if(diffFlowCorrelationsHist[t][pe][index])\r
    {\r
     this->SetDiffFlowCorrelationsHist(diffFlowCorrelationsHist[t][pe][index],t,pe,index);\r
    } else \r
      {\r
       cout<<"WARNING: diffFlowCorrelationsHist[t][pe][index] is NULL in AFAWQC::GPFDFH() !!!!"<<endl;\r
       cout<<"t     = "<<t<<endl;\r
       cout<<"pe    = "<<pe<<endl;\r
       cout<<"index = "<<index<<endl;\r
       exit(0);       \r
      } \r
   } // end of for(Int_t index=0;index<4;index++)\r
   // corrections:\r
   diffFlowCorrectionsHistList[t][pe] = dynamic_cast<TList*>(diffFlowListResults->FindObject(Form("Histograms with correction terms for NUA (%s, %s)",typeFlag[t].Data(),ptEtaFlag[pe].Data())));\r
   if(!diffFlowCorrectionsHistList[t][pe])\r
   { \r
    cout<<"WARNING: diffFlowCorrectionsHistList[t][pe] is NULL in AFAWQC::GPFDFH() !!!!"<<endl;\r
    cout<<"t = "<<t<<endl;\r
    cout<<"pe = "<<pe<<endl;\r
    exit(0);\r
   }\r
   // correction terms for NUA:\r
   for(Int_t sc=0;sc<2;sc++) // sin or cos\r
   {\r
    for(Int_t cti=0;cti<9;cti++) // correction term index\r
    {\r
     diffFlowCorrectionTermsForNUAHist[t][pe][sc][cti] = dynamic_cast<TH1D*>(diffFlowCorrectionsHistList[t][pe]->FindObject(Form("%s, %s, %s, %s, cti = %d",diffFlowCorrectionTermsForNUAHistName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),sinCosFlag[sc].Data(),cti+1)));\r
     if(diffFlowCorrectionTermsForNUAHist[t][pe][sc][cti])\r
     {\r
      this->SetDiffFlowCorrectionTermsForNUAHist(diffFlowCorrectionTermsForNUAHist[t][pe][sc][cti],t,pe,sc,cti);\r
     } else\r
       {\r
        cout<<"WARNING: diffFlowCorrectionTermsForNUAHist[t][pe][sc][cti] is NULL in AFAWQC::GPFDFH() !!!!"<<endl;\r
        cout<<"t   = "<<t<<endl;\r
        cout<<"pe  = "<<pe<<endl;   \r
        cout<<"sc  = "<<sc<<endl;\r
        cout<<"cti = "<<cti<<endl;\r
       }    \r
    } // end of for(Int_t cti=0;cti<9;cti++) // correction term index\r
   } // end of for(Int_t sc=0;sc<2;sc++) // sin or cos\r
   // ...\r
   // differential Q-cumulants:\r
   diffFlowCumulantsHistList[t][pe] = dynamic_cast<TList*>(diffFlowListResults->FindObject(Form("Differential Q-cumulants (%s, %s)",typeFlag[t].Data(),ptEtaFlag[pe].Data())));\r
   if(!diffFlowCumulantsHistList[t][pe])\r
   { \r
    cout<<"WARNING: diffFlowCumulantsHistList[t][pe] is NULL in AFAWQC::GPFDFH() !!!!"<<endl;\r
    cout<<"t  = "<<t<<endl;\r
    cout<<"pe = "<<pe<<endl;\r
    exit(0);\r
   }\r
   for(Int_t index=0;index<4;index++) \r
   {\r
    diffFlowCumulants[t][pe][index] = dynamic_cast<TH1D*>(diffFlowCumulantsHistList[t][pe]->FindObject(Form("%s, %s, %s, %s",diffFlowCumulantsName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),differentialCumulantIndex[index].Data())));\r
    if(diffFlowCumulants[t][pe][index])\r
    {\r
     this->SetDiffFlowCumulants(diffFlowCumulants[t][pe][index],t,pe,index);\r
    } else \r
      {\r
       cout<<"WARNING: diffFlowCumulants[t][pe][index] is NULL in AFAWQC::GPFDFH() !!!!"<<endl;\r
       cout<<"t     = "<<t<<endl;\r
       cout<<"pe    = "<<pe<<endl;\r
       cout<<"index = "<<index<<endl;\r
       exit(0);       \r
      } \r
   } // end of for(Int_t index=0;index<4;index++)\r
   // differential flow estimates from Q-cumulants:\r
   diffFlowHistList[t][pe] = dynamic_cast<TList*>(diffFlowListResults->FindObject(Form("Differential flow (%s, %s)",typeFlag[t].Data(),ptEtaFlag[pe].Data())));\r
   if(!diffFlowHistList[t][pe])\r
   { \r
    cout<<"WARNING: diffFlowHistList[t][pe] is NULL in AFAWQC::GPFDFH() !!!!"<<endl;\r
    cout<<"t  = "<<t<<endl;\r
    cout<<"pe = "<<pe<<endl;\r
    exit(0);\r
   }\r
   for(Int_t index=0;index<4;index++) \r
   {\r
    diffFlow[t][pe][index] = dynamic_cast<TH1D*>(diffFlowHistList[t][pe]->FindObject(Form("%s, %s, %s, %s",diffFlowName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),differentialFlowIndex[index].Data())));\r
    if(diffFlow[t][pe][index])\r
    {\r
     this->SetDiffFlow(diffFlow[t][pe][index],t,pe,index);\r
    } else \r
      {\r
       cout<<"WARNING: diffFlow[t][pe][index] is NULL in AFAWQC::GPFDFH() !!!!"<<endl;\r
       cout<<"t     = "<<t<<endl;\r
       cout<<"pe    = "<<pe<<endl;\r
       cout<<"index = "<<index<<endl;\r
       exit(0);       \r
      } \r
   } // end of for(Int_t index=0;index<4;index++)\r
   // differential covariances:\r
   diffFlowCovariancesHistList[t][pe] = dynamic_cast<TList*>(diffFlowListResults->FindObject(Form("Covariances of correlations (%s, %s)",typeFlag[t].Data(),ptEtaFlag[pe].Data())));\r
   if(!diffFlowCovariancesHistList[t][pe])\r
   { \r
    cout<<"WARNING: diffFlowCovariancesHistList[t][pe] is NULL in AFAWQC::GPFDFH() !!!!"<<endl;\r
    cout<<"t  = "<<t<<endl;\r
    cout<<"pe = "<<pe<<endl;\r
    exit(0);\r
   }\r
   for(Int_t covIndex=0;covIndex<5;covIndex++) \r
   {\r
    diffFlowCovariances[t][pe][covIndex] = dynamic_cast<TH1D*>(diffFlowCovariancesHistList[t][pe]->FindObject(Form("%s, %s, %s, %s",diffFlowCovariancesName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),covarianceName[covIndex].Data())));\r
    if(diffFlowCovariances[t][pe][covIndex])\r
    {\r
     this->SetDiffFlowCovariances(diffFlowCovariances[t][pe][covIndex],t,pe,covIndex);\r
    } else \r
      {\r
       cout<<"WARNING: diffFlowCovariances[t][pe][covIndex] is NULL in AFAWQC::GPFDFH() !!!!"<<endl;\r
       cout<<"t        = "<<t<<endl;\r
       cout<<"pe       = "<<pe<<endl;\r
       cout<<"covIndex = "<<covIndex<<endl;\r
       exit(0);       \r
      } \r
   } // end of for(Int_t covIndex=0;covIndex<5;covIndex++) // covariance index    \r
  } // end of for(Int_t pe=0;pe<2;pe++) // pt or eta\r
 } // end of for(Int_t t=0;t<2;t++) // type: RP or POI \r
 // sum of event weights for reduced correlations:\r
 TList *diffFlowSumOfEventWeightsHistList[2][2][2] = {{{NULL}}};\r
 TString diffFlowSumOfEventWeightsName = "fDiffFlowSumOfEventWeights";\r
 diffFlowSumOfEventWeightsName += fAnalysisLabel->Data();  \r
 TH1D *diffFlowSumOfEventWeights[2][2][2][4] = {{{{NULL}}}};\r
 for(Int_t t=0;t<2;t++) // type is RP or POI\r
 { \r
  for(Int_t pe=0;pe<2;pe++) // pt or eta\r
  { \r
   for(Int_t p=0;p<2;p++) // power of event weights is either 1 or 2\r
   {\r
    diffFlowSumOfEventWeightsHistList[t][pe][p] = dynamic_cast<TList*>(diffFlowListResults->FindObject(Form("Sum of %s event weights (%s, %s)",powerFlag[p].Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data())));\r
    if(!diffFlowSumOfEventWeightsHistList[t][pe][p])\r
    { \r
     cout<<"WARNING: diffFlowSumOfEventWeightsHistList[t][pe][p] is NULL in AFAWQC::GPFDFH() !!!!"<<endl;\r
     cout<<"t     = "<<t<<endl;\r
     cout<<"pe    = "<<pe<<endl;\r
     cout<<"power = "<<p<<endl;\r
     exit(0);\r
    }\r
    for(Int_t ew=0;ew<4;ew++) // index of reduced correlation\r
    {\r
     diffFlowSumOfEventWeights[t][pe][p][ew] = dynamic_cast<TH1D*>(diffFlowSumOfEventWeightsHistList[t][pe][p]->FindObject(Form("%s, %s, %s, %s, %s",diffFlowSumOfEventWeightsName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),powerFlag[p].Data(),reducedCorrelationIndex[ew].Data())));    \r
     if(diffFlowSumOfEventWeights[t][pe][p][ew])\r
     {\r
      this->SetDiffFlowSumOfEventWeights(diffFlowSumOfEventWeights[t][pe][p][ew],t,pe,p,ew);\r
     } else \r
       {\r
        cout<<"WARNING: diffFlowSumOfEventWeights[t][pe][p][ew] is NULL in AFAWQC::GPFDFH() !!!!"<<endl;\r
        cout<<"t     = "<<t<<endl;\r
        cout<<"pe    = "<<pe<<endl;\r
        cout<<"power = "<<p<<endl;\r
        cout<<"ew    = "<<ew<<endl;\r
        exit(0);       \r
       } \r
    }\r
   } // end of for(Int_t p=0;p<2;p++) // power of event weights is either 1 or 2\r
  } // end of for(Int_t pe=0;pe<2;pe++) // pt or eta\r
 } // end of for(Int_t t=0;t<2;t++) // type is RP or POI\r
 //  \r
 TList *diffFlowSumOfProductOfEventWeightsHistList[2][2] = {{NULL}};\r
 TString diffFlowSumOfProductOfEventWeightsName = "fDiffFlowSumOfProductOfEventWeights";\r
 diffFlowSumOfProductOfEventWeightsName += fAnalysisLabel->Data();  \r
 TH1D *diffFlowSumOfProductOfEventWeights[2][2][8][8] = {{{{NULL}}}};\r
 for(Int_t t=0;t<2;t++) // type is RP or POI\r
 { \r
  for(Int_t pe=0;pe<2;pe++) // pt or eta\r
  { \r
   diffFlowSumOfProductOfEventWeightsHistList[t][pe] = dynamic_cast<TList*>(diffFlowListResults->FindObject(Form("Sum of products of event weights (%s, %s)",typeFlag[t].Data(),ptEtaFlag[pe].Data())));\r
   if(!diffFlowSumOfProductOfEventWeightsHistList[t][pe])\r
   { \r
    cout<<"WARNING: diffFlowSumOfProductOfEventWeightsHistList[t][pe] is NULL in AFAWQC::GPFDFH() !!!!"<<endl;\r
    cout<<"t     = "<<t<<endl;\r
    cout<<"pe    = "<<pe<<endl;\r
    exit(0);\r
   }\r
   for(Int_t mci1=0;mci1<8;mci1++) // mixed correlation index\r
   {\r
    for(Int_t mci2=mci1+1;mci2<8;mci2++) // mixed correlation index\r
    {\r
     diffFlowSumOfProductOfEventWeights[t][pe][mci1][mci2] = dynamic_cast<TH1D*>(diffFlowSumOfProductOfEventWeightsHistList[t][pe]->FindObject(Form("%s, %s, %s, %s, %s",diffFlowSumOfProductOfEventWeightsName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),mixedCorrelationIndex[mci1].Data(),mixedCorrelationIndex[mci2].Data())));    \r
      if(diffFlowSumOfProductOfEventWeights[t][pe][mci1][mci2])\r
      {\r
       this->SetDiffFlowSumOfProductOfEventWeights(diffFlowSumOfProductOfEventWeights[t][pe][mci1][mci2],t,pe,mci1,mci2);\r
      } else \r
        {\r
         cout<<"WARNING: diffFlowSumOfProductOfEventWeights[t][pe][mci1][mci2] is NULL in AFAWQC::GPFDFH() !!!!"<<endl;\r
         cout<<"t    = "<<t<<endl;\r
         cout<<"pe   = "<<pe<<endl;\r
         cout<<"mci1 = "<<mci1<<endl;\r
         cout<<"mci2 = "<<mci2<<endl;\r
         exit(0);       \r
        } \r
     if(mci1%2 == 0) mci2++; // products which DO NOT include reduced correlations are not stored here\r
    } // end of for(Int_t mci2=mci1+1;mci2<8;mci2++) // mixed correlation index\r
   } // end of for(Int_t mci1=0;mci1<8;mci1++) // mixed correlation index\r
  } // end of for(Int_t pe=0;pe<2;pe++) // pt or eta\r
 } // end of for(Int_t t=0;t<2;t++) // type is RP or POI\r
\r
} // end void AliFlowAnalysisWithQCumulants::GetPointersForDiffFlowHistograms()\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::BookEverythingForDifferentialFlow()\r
{\r
 // Book all histograms and profiles needed for differential flow.\r
 //  a) Define flags locally (to be improved: should I promote flags to data members?);\r
 //  b) Book profile to hold all flags for differential flow;\r
 //  c) Book e-b-e quantities;\r
 //  d) Book profiles;\r
 //  e) Book histograms holding final results. \r
 \r
 // a) Define flags locally (to be improved: should I promote flags to data members?): \r
 TString typeFlag[2] = {"RP","POI"}; \r
 TString ptEtaFlag[2] = {"p_{T}","#eta"};\r
 TString powerFlag[2] = {"linear","quadratic"};\r
 TString sinCosFlag[2] = {"sin","cos"};\r
 TString differentialCumulantIndex[4] = {"QC{2'}","QC{4'}","QC{6'}","QC{8'}"};  \r
 TString differentialFlowIndex[4] = {"v'{2}","v'{4}","v'{6}","v'{8}"};  \r
 TString reducedCorrelationIndex[4] = {"<2'>","<4'>","<6'>","<8'>"};\r
 TString mixedCorrelationIndex[8] = {"<2>","<2'>","<4>","<4'>","<6>","<6'>","<8>","<8'>"};\r
 TString covarianceName[5] = {"Cov(<2>,<2'>)","Cov(<2>,<4'>)","Cov(<4>,<2'>)","Cov(<4>,<4'>)","Cov(<2'>,<4'>)"}; \r
 Int_t nBinsPtEta[2] = {fnBinsPt,fnBinsEta};\r
 Double_t minPtEta[2] = {fPtMin,fEtaMin};\r
 Double_t maxPtEta[2] = {fPtMax,fEtaMax};\r
  \r
 // b) Book profile to hold all flags for differential flow:\r
 TString diffFlowFlagsName = "fDiffFlowFlags";\r
 diffFlowFlagsName += fAnalysisLabel->Data();\r
 fDiffFlowFlags = new TProfile(diffFlowFlagsName.Data(),"Flags for Differential Flow",4,0,4);\r
 fDiffFlowFlags->SetTickLength(-0.01,"Y");\r
 fDiffFlowFlags->SetMarkerStyle(25);\r
 fDiffFlowFlags->SetLabelSize(0.05);\r
 fDiffFlowFlags->SetLabelOffset(0.02,"Y");\r
 (fDiffFlowFlags->GetXaxis())->SetBinLabel(1,"Particle Weights");\r
 (fDiffFlowFlags->GetXaxis())->SetBinLabel(2,"Event Weights");\r
 (fDiffFlowFlags->GetXaxis())->SetBinLabel(3,"Corrected for NUA?");\r
 (fDiffFlowFlags->GetXaxis())->SetBinLabel(4,"Calculated 2D flow?");\r
 fDiffFlowList->Add(fDiffFlowFlags);\r
\r
 // c) Book e-b-e quantities:\r
 // Event-by-event r_{m*n,k}(pt,eta), p_{m*n,k}(pt,eta) and q_{m*n,k}(pt,eta)\r
 // Explanantion of notation:\r
 //  1.) n is harmonic, m is multiple of harmonic;\r
 //  2.) k is power of particle weight;\r
 //  3.) r_{m*n,k}(pt,eta) = Q-vector evaluated in harmonic m*n for RPs in particular (pt,eta) bin (i-th RP is weighted with w_i^k);   \r
 //  4.) p_{m*n,k}(pt,eta) = Q-vector evaluated in harmonic m*n for POIs in particular (pt,eta) bin \r
 //                          (if i-th POI is also RP, than it is weighted with w_i^k);   \r
 //  5.) q_{m*n,k}(pt,eta) = Q-vector evaluated in harmonic m*n for particles which are both RPs and POIs in particular (pt,eta) bin \r
 //                          (i-th RP&&POI is weighted with w_i^k)            \r
  \r
 // 1D:\r
 for(Int_t t=0;t<3;t++) // typeFlag (0 = RP, 1 = POI, 2 = RP && POI )\r
 { \r
  for(Int_t pe=0;pe<2;pe++) // pt or eta\r
  {\r
   for(Int_t m=0;m<4;m++) // multiple of harmonic\r
   {\r
    for(Int_t k=0;k<9;k++) // power of particle weight\r
    {\r
     fReRPQ1dEBE[t][pe][m][k] = new TProfile(Form("TypeFlag%dpteta%dmultiple%dpower%dRe",t,pe,m,k),\r
                                             Form("TypeFlag%dpteta%dmultiple%dpower%dRe",t,pe,m,k),nBinsPtEta[pe],minPtEta[pe],maxPtEta[pe]); \r
     fImRPQ1dEBE[t][pe][m][k] = new TProfile(Form("TypeFlag%dpteta%dmultiple%dpower%dIm",t,pe,m,k),\r
                                             Form("TypeFlag%dpteta%dmultiple%dpower%dIm",t,pe,m,k),nBinsPtEta[pe],minPtEta[pe],maxPtEta[pe]); \r
    }\r
   }\r
  }\r
 } \r
 // to be improved (add explanation of fs1dEBE[t][pe][k]):   \r
 for(Int_t t=0;t<3;t++) // typeFlag (0 = RP, 1 = POI, 2 = RP&&POI )\r
 { \r
  for(Int_t pe=0;pe<2;pe++) // pt or eta\r
  {\r
   for(Int_t k=0;k<9;k++) // power of particle weight\r
   {\r
    fs1dEBE[t][pe][k] = new TProfile(Form("TypeFlag%dpteta%dmultiple%d",t,pe,k),\r
                                     Form("TypeFlag%dpteta%dmultiple%d",t,pe,k),nBinsPtEta[pe],minPtEta[pe],maxPtEta[pe]); \r
   }\r
  }\r
 }\r
 // correction terms for nua:\r
 for(Int_t t=0;t<2;t++) // typeFlag (0 = RP, 1 = POI)\r
 { \r
  for(Int_t pe=0;pe<2;pe++) // pt or eta\r
  {\r
   for(Int_t sc=0;sc<2;sc++) // sin or cos\r
   {\r
    for(Int_t cti=0;cti<9;cti++) // correction term index\r
    {\r
     fDiffFlowCorrectionTermsForNUAEBE[t][pe][sc][cti] = new TH1D(Form("typeFlag%d pteta%d sincos%d cti%d",t,pe,sc,cti),\r
                                             Form("typeFlag%d pteta%d sincos%d cti%d",t,pe,sc,cti),nBinsPtEta[pe],minPtEta[pe],maxPtEta[pe]); \r
    }\r
   }\r
  }\r
 } \r
 // 2D:\r
 TProfile2D styleRe("typeMultiplePowerRe","typeMultiplePowerRe",fnBinsPt,fPtMin,fPtMax,fnBinsEta,fEtaMin,fEtaMax);\r
 TProfile2D styleIm("typeMultiplePowerIm","typeMultiplePowerIm",fnBinsPt,fPtMin,fPtMax,fnBinsEta,fEtaMin,fEtaMax);\r
 for(Int_t t=0;t<3;t++) // typeFlag (0 = RP, 1 = POI, 2 = RP&&POI )\r
 { \r
  for(Int_t m=0;m<4;m++)\r
  {\r
   for(Int_t k=0;k<9;k++)\r
   {\r
    fReRPQ2dEBE[t][m][k] = (TProfile2D*)styleRe.Clone(Form("typeFlag%dmultiple%dpower%dRe",t,m,k)); \r
    fImRPQ2dEBE[t][m][k] = (TProfile2D*)styleIm.Clone(Form("typeFlag%dmultiple%dpower%dIm",t,m,k));\r
   }\r
  } \r
 } \r
 TProfile2D styleS("typePower","typePower",fnBinsPt,fPtMin,fPtMax,fnBinsEta,fEtaMin,fEtaMax);\r
 for(Int_t t=0;t<3;t++) // typeFlag (0 = RP, 1 = POI, 2 = RP&&POI )\r
 { \r
  for(Int_t k=0;k<9;k++)\r
  {\r
   fs2dEBE[t][k] = (TProfile2D*)styleS.Clone(Form("typeFlag%dpower%d",t,k));\r
  }\r
 }\r
 // reduced correlations e-b-e:\r
 TString diffFlowCorrelationsEBEName = "fDiffFlowCorrelationsEBE";\r
 diffFlowCorrelationsEBEName += fAnalysisLabel->Data();\r
 for(Int_t t=0;t<2;t++) // type: RP or POI\r
 { \r
  for(Int_t pe=0;pe<2;pe++) // pt or eta\r
  {\r
   for(Int_t rci=0;rci<4;rci++) // reduced correlation index\r
   {\r
    fDiffFlowCorrelationsEBE[t][pe][rci] = new TH1D(Form("%s, %s, %s, %s",diffFlowCorrelationsEBEName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),reducedCorrelationIndex[rci].Data()),Form("%s, %s, %s, %s",diffFlowCorrelationsEBEName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),reducedCorrelationIndex[rci].Data()),nBinsPtEta[pe],minPtEta[pe],maxPtEta[pe]);\r
   } // end of for(Int_t ci=0;ci<4;ci++) // correlation index\r
  } // end of for(Int_t pe=0;pe<2;pe++) // pt or eta \r
 } // end of for(Int_t t=0;t<2;t++) // type: RP or POI\r
 // event weights for reduced correlations e-b-e:\r
 TString diffFlowEventWeightsForCorrelationsEBEName = "fDiffFlowEventWeightsForCorrelationsEBE";\r
 diffFlowEventWeightsForCorrelationsEBEName += fAnalysisLabel->Data();\r
 for(Int_t t=0;t<2;t++) // type: RP or POI\r
 { \r
  for(Int_t pe=0;pe<2;pe++) // pt or eta\r
  {\r
   for(Int_t rci=0;rci<4;rci++) // event weight for reduced correlation index\r
   {\r
    fDiffFlowEventWeightsForCorrelationsEBE[t][pe][rci] = new TH1D(Form("%s, %s, %s, eW for %s",diffFlowEventWeightsForCorrelationsEBEName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),reducedCorrelationIndex[rci].Data()),Form("%s, %s, %s, eW for %s",diffFlowEventWeightsForCorrelationsEBEName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),reducedCorrelationIndex[rci].Data()),nBinsPtEta[pe],minPtEta[pe],maxPtEta[pe]);\r
   } // end of for(Int_t ci=0;ci<4;ci++) // correlation index\r
  } // end of for(Int_t pe=0;pe<2;pe++) // pt or eta \r
 } // end of for(Int_t t=0;t<2;t++) // type: RP or POI\r
      \r
 // d) Book profiles;\r
 // reduced correlations:\r
 TString diffFlowCorrelationsProName = "fDiffFlowCorrelationsPro";\r
 diffFlowCorrelationsProName += fAnalysisLabel->Data();\r
 // corrections terms:\r
 TString diffFlowCorrectionTermsForNUAProName = "fDiffFlowCorrectionTermsForNUAPro";\r
 diffFlowCorrectionTermsForNUAProName += fAnalysisLabel->Data();\r
 for(Int_t t=0;t<2;t++) // type: RP or POI\r
 { \r
  for(Int_t pe=0;pe<2;pe++) // pt or eta\r
  {\r
   for(Int_t rci=0;rci<4;rci++) // reduced correlation index\r
   {\r
    // reduced correlations:\r
    fDiffFlowCorrelationsPro[t][pe][rci] = new TProfile(Form("%s, %s, %s, %s",diffFlowCorrelationsProName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),reducedCorrelationIndex[rci].Data()),Form("%s, %s, %s, %s",diffFlowCorrelationsProName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),reducedCorrelationIndex[rci].Data()),nBinsPtEta[pe],minPtEta[pe],maxPtEta[pe],"s");\r
    fDiffFlowCorrelationsPro[t][pe][rci]->SetXTitle(ptEtaFlag[pe].Data());\r
    fDiffFlowCorrelationsProList[t][pe]->Add(fDiffFlowCorrelationsPro[t][pe][rci]); // to be improved (add dedicated list to hold reduced correlations)\r
   } // end of for(Int_t rci=0;rci<4;rci++) // correlation index\r
  } // end of for(Int_t pe=0;pe<2;pe++) // pt or eta \r
 } // end of for(Int_t t=0;t<2;t++) // type: RP or POI\r
 // correction terms for nua:\r
 for(Int_t t=0;t<2;t++) // typeFlag (0 = RP, 1 = POI)\r
 { \r
  for(Int_t pe=0;pe<2;pe++) // pt or eta\r
  {\r
   for(Int_t sc=0;sc<2;sc++) // sin or cos\r
   {\r
    for(Int_t cti=0;cti<9;cti++) // correction term index\r
    {\r
     fDiffFlowCorrectionTermsForNUAPro[t][pe][sc][cti] = new TProfile(Form("%s, %s, %s, %s, cti = %d",diffFlowCorrectionTermsForNUAProName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),sinCosFlag[sc].Data(),cti+1),Form("%s, %s, %s, %s, cti = %d",diffFlowCorrectionTermsForNUAProName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),sinCosFlag[sc].Data(),cti+1),nBinsPtEta[pe],minPtEta[pe],maxPtEta[pe]); \r
     fDiffFlowCorrectionsProList[t][pe]->Add(fDiffFlowCorrectionTermsForNUAPro[t][pe][sc][cti]);\r
    }\r
   }\r
  }\r
 } \r
 // e) Book histograms holding final results. \r
 // reduced correlations:\r
 TString diffFlowCorrelationsHistName = "fDiffFlowCorrelationsHist";\r
 diffFlowCorrelationsHistName += fAnalysisLabel->Data();\r
 // corrections terms:\r
 TString diffFlowCorrectionTermsForNUAHistName = "fDiffFlowCorrectionTermsForNUAHist";\r
 diffFlowCorrectionTermsForNUAHistName += fAnalysisLabel->Data();\r
 // differential covariances:\r
 TString diffFlowCovariancesName = "fDiffFlowCovariances";\r
 diffFlowCovariancesName += fAnalysisLabel->Data();\r
 // differential Q-cumulants:\r
 TString diffFlowCumulantsName = "fDiffFlowCumulants";\r
 diffFlowCumulantsName += fAnalysisLabel->Data();\r
 // differential flow:\r
 TString diffFlowName = "fDiffFlow";\r
 diffFlowName += fAnalysisLabel->Data();\r
 for(Int_t t=0;t<2;t++) // type: RP or POI\r
 { \r
  for(Int_t pe=0;pe<2;pe++) // pt or eta\r
  {\r
   for(Int_t index=0;index<4;index++) \r
   {\r
    // reduced correlations:\r
    fDiffFlowCorrelationsHist[t][pe][index] = new TH1D(Form("%s, %s, %s, %s",diffFlowCorrelationsHistName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),reducedCorrelationIndex[index].Data()),Form("%s, %s, %s, %s",diffFlowCorrelationsHistName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),reducedCorrelationIndex[index].Data()),nBinsPtEta[pe],minPtEta[pe],maxPtEta[pe]);\r
    fDiffFlowCorrelationsHist[t][pe][index]->SetXTitle(ptEtaFlag[pe].Data());\r
    fDiffFlowCorrelationsHistList[t][pe]->Add(fDiffFlowCorrelationsHist[t][pe][index]); \r
    // differential Q-cumulants:\r
    fDiffFlowCumulants[t][pe][index] = new TH1D(Form("%s, %s, %s, %s",diffFlowCumulantsName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),differentialCumulantIndex[index].Data()),Form("%s, %s, %s, %s",diffFlowCumulantsName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),differentialCumulantIndex[index].Data()),nBinsPtEta[pe],minPtEta[pe],maxPtEta[pe]);\r
    fDiffFlowCumulants[t][pe][index]->SetXTitle(ptEtaFlag[pe].Data());\r
    fDiffFlowCumulantsHistList[t][pe]->Add(fDiffFlowCumulants[t][pe][index]); \r
    // differential flow estimates from Q-cumulants:\r
    fDiffFlow[t][pe][index] = new TH1D(Form("%s, %s, %s, %s",diffFlowName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),differentialFlowIndex[index].Data()),Form("%s, %s, %s, %s",diffFlowName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),differentialFlowIndex[index].Data()),nBinsPtEta[pe],minPtEta[pe],maxPtEta[pe]);\r
    fDiffFlow[t][pe][index]->SetXTitle(ptEtaFlag[pe].Data());\r
    fDiffFlowHistList[t][pe]->Add(fDiffFlow[t][pe][index]); \r
   } // end of for(Int_t index=0;index<4;index++) \r
   for(Int_t covIndex=0;covIndex<5;covIndex++) // covariance index \r
   {\r
    // differential covariances:\r
    fDiffFlowCovariances[t][pe][covIndex] = new TH1D(Form("%s, %s, %s, %s",diffFlowCovariancesName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),covarianceName[covIndex].Data()),Form("%s, %s, %s, %s",diffFlowCovariancesName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),covarianceName[covIndex].Data()),nBinsPtEta[pe],minPtEta[pe],maxPtEta[pe]);\r
    fDiffFlowCovariances[t][pe][covIndex]->SetXTitle(ptEtaFlag[pe].Data());\r
    fDiffFlowCovariancesHistList[t][pe]->Add(fDiffFlowCovariances[t][pe][covIndex]); \r
   } // end of for(Int_t covIndex=0;covIndex<5;covIndex++) // covariance index\r
   // products of both types of correlations: \r
   TString diffFlowProductOfCorrelationsProName = "fDiffFlowProductOfCorrelationsPro";\r
   diffFlowProductOfCorrelationsProName += fAnalysisLabel->Data();  \r
   for(Int_t mci1=0;mci1<8;mci1++) // mixed correlation index\r
   {\r
    for(Int_t mci2=mci1+1;mci2<8;mci2++) // mixed correlation index\r
    {\r
     fDiffFlowProductOfCorrelationsPro[t][pe][mci1][mci2] = new TProfile(Form("%s, %s, %s, %s, %s",diffFlowProductOfCorrelationsProName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),mixedCorrelationIndex[mci1].Data(),mixedCorrelationIndex[mci2].Data()),Form("%s, %s, %s, %s #times %s",diffFlowProductOfCorrelationsProName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),mixedCorrelationIndex[mci1].Data(),mixedCorrelationIndex[mci2].Data()),nBinsPtEta[pe],minPtEta[pe],maxPtEta[pe]); \r
     fDiffFlowProductOfCorrelationsPro[t][pe][mci1][mci2]->SetXTitle(ptEtaFlag[pe].Data());\r
     fDiffFlowProductOfCorrelationsProList[t][pe]->Add(fDiffFlowProductOfCorrelationsPro[t][pe][mci1][mci2]); \r
     if(mci1%2 == 0) mci2++; // products which DO NOT include reduced correlations are not stored here\r
    } // end of for(Int_t mci2=mci1+1;mci2<8;mci2++) // mixed correlation index\r
   } // end of for(Int_t mci1=0;mci1<8;mci1++) // mixed correlation index    \r
  } // end of for(Int_t pe=0;pe<2;pe++) // pt or eta \r
 } // end of for(Int_t t=0;t<2;t++) // type: RP or POI\r
 // sums of event weights for reduced correlations: \r
 TString diffFlowSumOfEventWeightsName = "fDiffFlowSumOfEventWeights";\r
 diffFlowSumOfEventWeightsName += fAnalysisLabel->Data();  \r
 for(Int_t t=0;t<2;t++) // type is RP or POI\r
 { \r
  for(Int_t pe=0;pe<2;pe++) // pt or eta\r
  { \r
   for(Int_t p=0;p<2;p++) // power of weights is either 1 or 2\r
   {\r
    for(Int_t ew=0;ew<4;ew++) // index of reduced correlation\r
    {\r
     fDiffFlowSumOfEventWeights[t][pe][p][ew] = new TH1D(Form("%s, %s, %s, %s, %s",diffFlowSumOfEventWeightsName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),powerFlag[p].Data(),reducedCorrelationIndex[ew].Data()),Form("%s, %s, %s, power = %s, %s",diffFlowSumOfEventWeightsName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),powerFlag[p].Data(),reducedCorrelationIndex[ew].Data()),nBinsPtEta[pe],minPtEta[pe],maxPtEta[pe]); \r
     fDiffFlowSumOfEventWeights[t][pe][p][ew]->SetXTitle(ptEtaFlag[pe].Data());\r
     fDiffFlowSumOfEventWeightsHistList[t][pe][p]->Add(fDiffFlowSumOfEventWeights[t][pe][p][ew]); // to be improved (add dedicated list to hold all this)\r
    }\r
   }\r
  }\r
 } \r
 // sum of products of event weights for both types of correlations: \r
 TString diffFlowSumOfProductOfEventWeightsName = "fDiffFlowSumOfProductOfEventWeights";\r
 diffFlowSumOfProductOfEventWeightsName += fAnalysisLabel->Data();  \r
 for(Int_t t=0;t<2;t++) // type is RP or POI\r
 {\r
  for(Int_t pe=0;pe<2;pe++) // pt or eta\r
  { \r
   for(Int_t mci1=0;mci1<8;mci1++) // mixed correlation index\r
   {\r
    for(Int_t mci2=mci1+1;mci2<8;mci2++) // mixed correlation index\r
    {\r
     fDiffFlowSumOfProductOfEventWeights[t][pe][mci1][mci2] = new TH1D(Form("%s, %s, %s, %s, %s",diffFlowSumOfProductOfEventWeightsName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),mixedCorrelationIndex[mci1].Data(),mixedCorrelationIndex[mci2].Data()),Form("%s, %s, %s, %s #times %s",diffFlowSumOfProductOfEventWeightsName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),mixedCorrelationIndex[mci1].Data(),mixedCorrelationIndex[mci2].Data()),nBinsPtEta[pe],minPtEta[pe],maxPtEta[pe]); \r
     fDiffFlowSumOfProductOfEventWeights[t][pe][mci1][mci2]->SetXTitle(ptEtaFlag[pe].Data());\r
     fDiffFlowSumOfProductOfEventWeightsHistList[t][pe]->Add(fDiffFlowSumOfProductOfEventWeights[t][pe][mci1][mci2]); \r
     if(mci1%2 == 0) mci2++; // products which DO NOT include reduced correlations are not stored here\r
    }\r
   }\r
  }\r
 } \r
 // correction terms for nua:\r
 for(Int_t t=0;t<2;t++) // typeFlag (0 = RP, 1 = POI)\r
 { \r
  for(Int_t pe=0;pe<2;pe++) // pt or eta\r
  {\r
   for(Int_t sc=0;sc<2;sc++) // sin or cos\r
   {\r
    for(Int_t cti=0;cti<9;cti++) // correction term index\r
    {\r
     fDiffFlowCorrectionTermsForNUAHist[t][pe][sc][cti] = new TH1D(Form("%s, %s, %s, %s, cti = %d",diffFlowCorrectionTermsForNUAHistName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),sinCosFlag[sc].Data(),cti+1),Form("%s, %s, %s, %s, cti = %d",diffFlowCorrectionTermsForNUAHistName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),sinCosFlag[sc].Data(),cti+1),nBinsPtEta[pe],minPtEta[pe],maxPtEta[pe]); \r
     fDiffFlowCorrectionsHistList[t][pe]->Add(fDiffFlowCorrectionTermsForNUAHist[t][pe][sc][cti]);\r
    }\r
   }\r
  }\r
 } \r
          \r
} // end of AliFlowAnalysisWithQCumulants::BookEverythingForDifferentialFlow()\r
\r
\r
//================================================================================================================================\r
\r
/*\r
void AliFlowAnalysisWithQCumulants::CalculateCorrectionsForNUAForIntQcumulants() // to be improved (do I really need this method?)\r
{\r
 // Calculate final corrections for non-uniform acceptance for Q-cumulants.\r
  \r
 // Corrections for non-uniform acceptance are stored in histogram fCorrectionsForNUA,\r
 // binning of fCorrectionsForNUA is organized as follows:\r
 //\r
 // 1st bin: correction to QC{2}\r
 // 2nd bin: correction to QC{4}\r
 // 3rd bin: correction to QC{6}\r
 // 4th bin: correction to QC{8}\r
  \r
 // shortcuts flags:\r
 Int_t pW = (Int_t)(useParticleWeights);\r
 \r
 Int_t eW = -1;\r
 \r
 if(eventWeights == "exact")\r
 {\r
  eW = 0;\r
 }\r
\r
 for(Int_t sc=0;sc<2;sc++) // sin or cos terms flag\r
 {\r
  if(!(fQCorrelations[pW][eW] && fQCorrections[pW][eW][sc] && fCorrections[pW][eW]))\r
  {\r
   cout<<"WARNING: fQCorrelations[pW][eW] && fQCorrections[pW][eW][sc] && fCorrections[pW][eW] is NULL in AFAWQC::CFCFNUAFIF() !!!!"<<endl;\r
   cout<<"pW = "<<pW<<endl;\r
   cout<<"eW = "<<eW<<endl;\r
   cout<<"sc = "<<sc<<endl;\r
   exit(0);\r
  }\r
 }  \r
\r
 // measured 2-, 4-, 6- and 8-particle azimuthal correlations (biased with non-uniform acceptance!):\r
 Double_t two = fQCorrelations[pW][eW]->GetBinContent(1); // <<2>>\r
 //Double_t four = fQCorrelations[pW][eW]->GetBinContent(11); // <<4>>\r
 //Double_t six = fQCorrelations[pW][eW]->GetBinContent(24); // <<6>>\r
 //Double_t eight = fQCorrelations[pW][eW]->GetBinContent(31); // <<8>>\r
 \r
 // correction terms to QC{2}:\r
 // <<cos(n*phi1)>>^2\r
 Double_t two1stTerm = pow(fQCorrections[pW][eW][1]->GetBinContent(1),2); \r
 // <<sin(n*phi1)>>^2\r
 Double_t two2ndTerm = pow(fQCorrections[pW][eW][0]->GetBinContent(1),2); \r
 // final corrections for non-uniform acceptance to QC{2}:\r
 Double_t correctionQC2 = -1.*two1stTerm-1.*two2ndTerm;\r
 fCorrections[pW][eW]->SetBinContent(1,correctionQC2); \r
 \r
 // correction terms to QC{4}:\r
 // <<cos(n*phi1)>> <<cos(n*(phi1-phi2-phi3))>>\r
 Double_t four1stTerm = fQCorrections[pW][eW][1]->GetBinContent(1)*fQCorrections[pW][eW][1]->GetBinContent(3);  \r
 // <<sin(n*phi1)>> <<sin(n*(phi1-phi2-phi3))>>\r
 Double_t four2ndTerm = fQCorrections[pW][eW][0]->GetBinContent(1)*fQCorrections[pW][eW][0]->GetBinContent(3);  \r
 // <<cos(n*(phi1+phi2))>>^2\r
 Double_t four3rdTerm = pow(fQCorrections[pW][eW][1]->GetBinContent(2),2); \r
 // <<sin(n*(phi1+phi2))>>^2\r
 Double_t four4thTerm = pow(fQCorrections[pW][eW][0]->GetBinContent(2),2); \r
 // <<cos(n*(phi1+phi2))>> (<<cos(n*phi1)>>^2 - <<sin(n*phi1)>>^2)\r
 Double_t four5thTerm = fQCorrections[pW][eW][1]->GetBinContent(2)\r
                      * (pow(fQCorrections[pW][eW][1]->GetBinContent(1),2)-pow(fQCorrections[pW][eW][0]->GetBinContent(1),2));\r
 // <<sin(n*(phi1+phi2))>> <<cos(n*phi1)>> <<sin(n*phi1)>>\r
 Double_t four6thTerm = fQCorrections[pW][eW][0]->GetBinContent(2)\r
                      * fQCorrections[pW][eW][1]->GetBinContent(1)\r
                      * fQCorrections[pW][eW][0]->GetBinContent(1);         \r
 // <<cos(n*(phi1-phi2))>> (<<cos(n*phi1)>>^2 + <<sin(n*phi1)>>^2)\r
 Double_t four7thTerm = two*(pow(fQCorrections[pW][eW][1]->GetBinContent(1),2)+pow(fQCorrections[pW][eW][0]->GetBinContent(1),2));  \r
 // (<<cos(n*phi1)>>^2 + <<sin(n*phi1)>>^2)^2\r
 Double_t four8thTerm = pow(pow(fQCorrections[pW][eW][1]->GetBinContent(1),2)+pow(fQCorrections[pW][eW][0]->GetBinContent(1),2),2);      \r
 // final correction to QC{4}:\r
 Double_t correctionQC4 = -4.*four1stTerm+4.*four2ndTerm-four3rdTerm-four4thTerm\r
                        + 4.*four5thTerm+8.*four6thTerm+8.*four7thTerm-6.*four8thTerm;                            \r
 fCorrections[pW][eW]->SetBinContent(2,correctionQC4);   \r
\r
 // ... to be improved (continued for 6th and 8th order)                                                    \r
\r
\r
} // end of AliFlowAnalysisWithQCumulants::CalculateCorrectionsForNUAForIntQcumulants()\r
*/\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::CalculateQcumulantsCorrectedForNUAIntFlow()\r
{\r
 // Calculate generalized Q-cumulants (cumulants corrected for non-unifom acceptance).\r
 \r
 // measured 2-, 4-, 6- and 8-particle correlations (biased by non-uniform acceptance!):\r
 Double_t two = fIntFlowCorrelationsHist->GetBinContent(1); // <<2>>\r
 Double_t four = fIntFlowCorrelationsHist->GetBinContent(2); // <<4>>\r
 //Double_t six = fIntFlowCorrelationsHist->GetBinContent(3); // <<6>>\r
 //Double_t eight = fIntFlowCorrelationsHist->GetBinContent(4); // <<8>>\r
 \r
 // statistical error of measured 2-, 4-, 6- and 8-particle correlations:\r
 //Double_t twoError = fIntFlowCorrelationsHist->GetBinError(1); // statistical error of <<2>>\r
 //Double_t fourError = fIntFlowCorrelationsHist->GetBinError(2); // statistical error of <<4>>\r
 //Double_t sixError = fIntFlowCorrelationsHist->GetBinError(3); // statistical error of <<6>>\r
 //Double_t eightError = fIntFlowCorrelationsHist->GetBinError(4); // statistical error of <<8>>\r
\r
 // QC{2}:\r
 // <<cos(n*phi1)>>^2\r
 Double_t two1stTerm = pow(fIntFlowCorrectionTermsForNUAHist[1]->GetBinContent(1),2); \r
 //Double_t two1stTermErrorSquared = pow(fIntFlowCorrectionTermsForNUAHist[1]->GetBinError(1),2); \r
 // <<sin(n*phi1)>>^2\r
 Double_t two2ndTerm = pow(fIntFlowCorrectionTermsForNUAHist[0]->GetBinContent(1),2); \r
 //Double_t two2ndTermErrorSquared = pow(fIntFlowCorrectionTermsForNUAHist[0]->GetBinError(1),2); \r
 // generalized QC{2}:\r
 Double_t gQC2 = two - two1stTerm - two2ndTerm; // to be improved (terminology, notation)\r
 fIntFlowQcumulants->SetBinContent(1,gQC2); \r
 //fIntFlowQcumulants->SetBinError(1,0.); // to be improved (propagate error) \r
 \r
 // QC{4}:\r
 // <<cos(n*phi1)>> <<cos(n*(phi1-phi2-phi3))>>\r
 Double_t four1stTerm = fIntFlowCorrectionTermsForNUAHist[1]->GetBinContent(1)\r
                      * fIntFlowCorrectionTermsForNUAHist[1]->GetBinContent(3);  \r
 // <<sin(n*phi1)>> <<sin(n*(phi1-phi2-phi3))>>\r
 Double_t four2ndTerm = fIntFlowCorrectionTermsForNUAHist[0]->GetBinContent(1)\r
                      * fIntFlowCorrectionTermsForNUAHist[0]->GetBinContent(3);  \r
 // <<cos(n*(phi1+phi2))>>^2\r
 Double_t four3rdTerm = pow(fIntFlowCorrectionTermsForNUAHist[1]->GetBinContent(2),2); \r
 // <<sin(n*(phi1+phi2))>>^2\r
 Double_t four4thTerm = pow(fIntFlowCorrectionTermsForNUAHist[0]->GetBinContent(2),2); \r
 // <<cos(n*(phi1+phi2))>> (<<cos(n*phi1)>>^2 - <<sin(n*phi1)>>^2)\r
 Double_t four5thTerm = fIntFlowCorrectionTermsForNUAHist[1]->GetBinContent(2)\r
                      * (pow(fIntFlowCorrectionTermsForNUAHist[1]->GetBinContent(1),2)\r
                      - pow(fIntFlowCorrectionTermsForNUAHist[0]->GetBinContent(1),2));\r
 // <<sin(n*(phi1+phi2))>> <<cos(n*phi1)>> <<sin(n*phi1)>>\r
 Double_t four6thTerm = fIntFlowCorrectionTermsForNUAHist[0]->GetBinContent(2)\r
                      * fIntFlowCorrectionTermsForNUAHist[1]->GetBinContent(1)\r
                      * fIntFlowCorrectionTermsForNUAHist[0]->GetBinContent(1);         \r
 // <<cos(n*(phi1-phi2))>> (<<cos(n*phi1)>>^2 + <<sin(n*phi1)>>^2)\r
 Double_t four7thTerm = two*(pow(fIntFlowCorrectionTermsForNUAHist[1]->GetBinContent(1),2)\r
                      + pow(fIntFlowCorrectionTermsForNUAHist[0]->GetBinContent(1),2));  \r
 // (<<cos(n*phi1)>>^2 + <<sin(n*phi1)>>^2)^2\r
 Double_t four8thTerm = pow(pow(fIntFlowCorrectionTermsForNUAHist[1]->GetBinContent(1),2)\r
                      + pow(fIntFlowCorrectionTermsForNUAHist[0]->GetBinContent(1),2),2);      \r
 // generalized QC{4}:\r
 Double_t gQC4 = four-2.*pow(two,2.)-4.*four1stTerm+4.*four2ndTerm-four3rdTerm\r
               - four4thTerm+4.*four5thTerm+8.*four6thTerm+8.*four7thTerm-6.*four8thTerm;                            \r
 fIntFlowQcumulants->SetBinContent(2,gQC4);   \r
 //fIntFlowQcumulants->SetBinError(2,0.); // to be improved (propagate error) \r
\r
 // ... to be improved (continued for 6th and 8th order)                                                    \r
    \r
} // end of void AliFlowAnalysisWithQCumulants::CalculateQcumulantsCorrectedForNUAIntFlow()\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::CalculateIntFlowCorrectedForNUA()\r
{\r
 // Calculate integrated flow from generalized Q-cumulants (corrected for non-uniform acceptance).\r
 \r
 // to be improved: add protection for NULL pointers, propagate statistical errors from \r
 // measured correlations and correction terms\r
 \r
 // generalized Q-cumulants:\r
 Double_t qc2 = fIntFlowQcumulants->GetBinContent(1); // QC{2}  \r
 Double_t qc4 = fIntFlowQcumulants->GetBinContent(2); // QC{4}  \r
 //Double_t qc6 = fIntFlowQcumulants->GetBinContent(3); // QC{6}  \r
 //Double_t qc8 = fIntFlowQcumulants->GetBinContent(4); // QC{8}\r
 \r
 // integrated flow estimates:\r
 Double_t v2 = 0.; // v{2,QC}  \r
 Double_t v4 = 0.; // v{4,QC}  \r
 //Double_t v6 = 0.; // v{6,QC}  \r
 //Double_t v8 = 0.; // v{8,QC}\r
\r
 // calculate integrated flow estimates from generalized Q-cumulants: \r
 if(qc2>=0.) v2 = pow(qc2,1./2.); \r
 if(qc4<=0.) v4 = pow(-1.*qc4,1./4.); \r
 //if(qc6>=0.) v6 = pow((1./4.)*qc6,1./6.); \r
 //if(qc8<=0.) v8 = pow((-1./33.)*qc8,1./8.); \r
\r
 // store integrated flow estimates from generalized Q-cumulants:\r
 fIntFlow->SetBinContent(1,v2);\r
 fIntFlow->SetBinContent(2,v4);\r
 //fIntFlow->SetBinContent(3,v6);\r
 //fIntFlow->SetBinContent(4,v8);\r
\r
} // end of void AliFlowAnalysisWithQCumulants::CalculateIntFlowCorrectedForNUA()\r
\r
   \r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::FinalizeCorrectionTermsForNUAIntFlow() \r
{\r
 // From profile fIntFlowCorrectionTermsForNUAPro[2] access measured corretion terms\r
 // and their spread, correctly calculate the statistical errors and store the final \r
 // results and statistical errors for correction terms in histogram fIntFlowCorrectionTermsForNUAHist[2].\r
 //\r
 // Remark: Statistical error of correction temrs is calculated as:\r
 //\r
 //          statistical error = termA * spread * termB:\r
 //          termA = sqrt{sum_{i=1}^{N} w^2}/(sum_{i=1}^{N} w)\r
 //          termB = 1/sqrt(1-termA^2)   \r
 \r
 /* // to be improved (implement protection here)\r
 for(Int_t power=0;power<2;power++)\r
 { \r
  if(!(fIntFlowCorrelationsHist && fIntFlowCorrelationsPro && fIntFlowSumOfEventWeights[power])) \r
  {\r
   cout<<"WARNING: fIntFlowCorrelationsHist && fIntFlowCorrelationsPro && fIntFlowSumOfEventWeights[power] is NULL in AFAWQC::FCIF() !!!!"<<endl;\r
   cout<<"power = "<<power<<endl;\r
   exit(0);\r
  }\r
 }\r
 */\r
  \r
 for(Int_t sc=0;sc<2;sc++) // sin or cos correction terms \r
 {\r
  for(Int_t ci=1;ci<=10;ci++) // correction term index\r
  {\r
   Double_t correction = fIntFlowCorrectionTermsForNUAPro[sc]->GetBinContent(ci);\r
   //Double_t spread = fIntFlowCorrectionTermsForNUAPro[sc]->GetBinError(ci);\r
   //Double_t sumOfLinearEventWeights = fIntFlowSumOfEventWeights[0]->GetBinContent(ci);\r
   //Double_t sumOfQuadraticEventWeights = fIntFlowSumOfEventWeights[1]->GetBinContent(ci);\r
   //Double_t termA = 0.;\r
   //Double_t termB = 0.;\r
   //if(sumOfLinearEventWeights)\r
   //{\r
   // termA = pow(sumOfQuadraticEventWeights,0.5)/sumOfLinearEventWeights;\r
   //} else\r
   // {\r
   //  cout<<"WARNING: sumOfLinearEventWeights == 0 in AFAWQC::FCIF() !!!!"<<endl;\r
   //  cout<<"         (for "<<2*ci<<"-particle correlation)"<<endl;\r
   // }\r
   /*\r
   if(1.-pow(termA,2.) > 0.)\r
   {\r
    termB = 1./pow(1-pow(termA,2.),0.5);\r
   } else\r
     {\r
      cout<<"WARNING: 1.-pow(termA,2.) <= 0 in AFAWQC::FCIF() !!!!"<<endl;   \r
      cout<<"         (for "<<2*ci<<"-particle correlation)"<<endl;\r
     }     \r
   Double_t statisticalError = termA * spread * termB;\r
   */\r
   fIntFlowCorrectionTermsForNUAHist[sc]->SetBinContent(ci,correction);\r
   //fIntFlowCorrectionTermsForNUAHist[sc]->SetBinError(ci,statisticalError);\r
  } // end of for(Int_t ci=1;ci<=10;ci++) // correction term index\r
 } // end of for(Int sc=0;sc<2;sc++) // sin or cos correction terms \r
                                                                                                                                                                                               \r
} // end of void AliFlowAnalysisWithQCumulants::FinalizeCorrectionTermsForNUAIntFlow()\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::GetPointersForNestedLoopsHistograms()\r
{\r
 // Get pointers to all objects relevant for calculations with nested loops.\r
   \r
 TList *nestedLoopsList = dynamic_cast<TList*>(fHistList->FindObject("Nested Loops"));\r
 if(nestedLoopsList) \r
 {\r
  this->SetNestedLoopsList(nestedLoopsList);\r
 } else\r
   {\r
    cout<<"WARNING: nestedLoopsList is NULL in AFAWQC::GPFNLH() !!!!"<<endl;\r
    exit(0);\r
   }\r
    \r
  TString sinCosFlag[2] = {"sin","cos"}; // to be improved (should I promote this to data members?)\r
  TString typeFlag[2] = {"RP","POI"}; // to be improved (should I promote this to data members?)\r
  TString ptEtaFlag[2] = {"p_{T}","#eta"}; // to be improved (should I promote this to data members?)\r
  TString reducedCorrelationIndex[4] = {"<2'>","<4'>","<6'>","<8'>"}; // to be improved (should I promote this to data members?)\r
   \r
  TString evaluateNestedLoopsName = "fEvaluateNestedLoops";\r
  evaluateNestedLoopsName += fAnalysisLabel->Data();  \r
  TProfile *evaluateNestedLoops = dynamic_cast<TProfile*>(nestedLoopsList->FindObject(evaluateNestedLoopsName.Data()));\r
  Bool_t bEvaluateIntFlowNestedLoops = kFALSE;\r
  Bool_t bEvaluateDiffFlowNestedLoops = kFALSE;\r
  if(evaluateNestedLoops)\r
  {\r
   this->SetEvaluateNestedLoops(evaluateNestedLoops);\r
   bEvaluateIntFlowNestedLoops = (Int_t)evaluateNestedLoops->GetBinContent(1);\r
   bEvaluateDiffFlowNestedLoops = (Int_t)evaluateNestedLoops->GetBinContent(2);\r
  }\r
  // nested loops relevant for integrated flow:  \r
  if(bEvaluateIntFlowNestedLoops)\r
  {\r
   // correlations:\r
   TString intFlowDirectCorrelationsName = "fIntFlowDirectCorrelations";\r
   intFlowDirectCorrelationsName += fAnalysisLabel->Data();\r
   TProfile *intFlowDirectCorrelations = dynamic_cast<TProfile*>(nestedLoopsList->FindObject(intFlowDirectCorrelationsName.Data()));\r
   if(intFlowDirectCorrelations) \r
   { \r
    this->SetIntFlowDirectCorrelations(intFlowDirectCorrelations);\r
   } else\r
     {\r
      cout<<"WARNING: intFlowDirectCorrelations is NULL in AFAWQC::GPFNLH() !!!!"<<endl;\r
      exit(0);\r
     }\r
   if(fUsePhiWeights||fUsePtWeights||fUseEtaWeights)  \r
   {\r
    TString intFlowExtraDirectCorrelationsName = "fIntFlowExtraDirectCorrelations";\r
    intFlowExtraDirectCorrelationsName += fAnalysisLabel->Data();\r
    TProfile *intFlowExtraDirectCorrelations = dynamic_cast<TProfile*>(nestedLoopsList->FindObject(intFlowExtraDirectCorrelationsName.Data()));\r
    if(intFlowExtraDirectCorrelations) \r
    { \r
     this->SetIntFlowExtraDirectCorrelations(intFlowExtraDirectCorrelations);\r
    } else\r
      {\r
       cout<<"WARNING: intFlowExtraDirectCorrelations is NULL in AFAWQC::GPFNLH() !!!!"<<endl;\r
       exit(0);\r
      }       \r
   } // end of if(fUsePhiWeights||fUsePtWeights||fUseEtaWeights)  \r
   // correction terms for non-uniform acceptance:\r
   TString intFlowDirectCorrectionTermsForNUAName = "fIntFlowDirectCorrectionTermsForNUA";\r
   intFlowDirectCorrectionTermsForNUAName += fAnalysisLabel->Data();\r
   TProfile *intFlowDirectCorrectionTermsForNUA[2] = {NULL};\r
   for(Int_t sc=0;sc<2;sc++) // sin or cos terms\r
   {\r
    intFlowDirectCorrectionTermsForNUA[sc] = dynamic_cast<TProfile*>(nestedLoopsList->FindObject(Form("%s: %s terms",intFlowDirectCorrectionTermsForNUAName.Data(),sinCosFlag[sc].Data())));\r
    if(intFlowDirectCorrectionTermsForNUA[sc]) \r
    { \r
     this->SetIntFlowDirectCorrectionTermsForNUA(intFlowDirectCorrectionTermsForNUA[sc],sc);\r
    } else\r
      {\r
       cout<<"WARNING: intFlowDirectCorrectionTermsForNUA[sc] is NULL in AFAWQC::GPFNLH() !!!!"<<endl;\r
       cout<<"sc = "<<sc<<endl;\r
       exit(0);\r
      }\r
   } // end of for(Int_t sc=0;sc<2;sc++) \r
  } // end of if(bEvaluateIntFlowNestedLoops)\r
    \r
  // nested loops relevant for differential flow:  \r
  if(bEvaluateDiffFlowNestedLoops)\r
  {\r
   // correlations:\r
   TString diffFlowDirectCorrelationsName = "fDiffFlowDirectCorrelations";\r
   diffFlowDirectCorrelationsName += fAnalysisLabel->Data();\r
   TProfile *diffFlowDirectCorrelations[2][2][4] = {{{NULL}}};\r
   for(Int_t t=0;t<2;t++)\r
   {\r
    for(Int_t pe=0;pe<2;pe++)\r
    {\r
     for(Int_t ci=0;ci<4;ci++) // correlation index\r
     {\r
      diffFlowDirectCorrelations[t][pe][ci] = dynamic_cast<TProfile*>(nestedLoopsList->FindObject(Form("%s, %s, %s, %s",diffFlowDirectCorrelationsName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),reducedCorrelationIndex[ci].Data())));\r
      if(diffFlowDirectCorrelations[t][pe][ci])\r
      {\r
       this->SetDiffFlowDirectCorrelations(diffFlowDirectCorrelations[t][pe][ci],t,pe,ci);\r
      } else\r
        {\r
         cout<<"WARNING: diffFlowDirectCorrelations[t][pe][ci] is NULL in AFAWQC::GPFDFH() !!!!"<<endl;\r
         cout<<"t  = "<<t<<endl;\r
         cout<<"pe = "<<pe<<endl;   \r
         cout<<"ci = "<<ci<<endl;\r
        }     \r
     } // end of for(Int_t ci=0;ci<4;ci++) // correlation index  \r
    } // end of for(Int_t pe=0;pe<2;pe++)\r
   } // end of for(Int_t t=0;t<2;t++)   \r
   // correction terms for non-uniform acceptance:\r
   TString diffFlowDirectCorrectionTermsForNUAName = "fDiffFlowDirectCorrectionTermsForNUA";\r
   diffFlowDirectCorrectionTermsForNUAName += fAnalysisLabel->Data();  \r
   TProfile *diffFlowDirectCorrectionTermsForNUA[2][2][2][10] = {{{{NULL}}}};   \r
   for(Int_t t=0;t<2;t++)\r
   {\r
    for(Int_t pe=0;pe<2;pe++)\r
    {\r
     // correction terms for NUA:\r
     for(Int_t sc=0;sc<2;sc++) // sin or cos\r
     {\r
      for(Int_t cti=0;cti<9;cti++) // correction term index\r
      {\r
       diffFlowDirectCorrectionTermsForNUA[t][pe][sc][cti] = dynamic_cast<TProfile*>(nestedLoopsList->FindObject(Form("%s, %s, %s, %s, cti = %d",diffFlowDirectCorrectionTermsForNUAName.Data(),typeFlag[t].Data(),ptEtaFlag[pe].Data(),sinCosFlag[sc].Data(),cti+1)));\r
       if(diffFlowDirectCorrectionTermsForNUA[t][pe][sc][cti])\r
       {\r
        this->SetDiffFlowDirectCorrectionTermsForNUA(diffFlowDirectCorrectionTermsForNUA[t][pe][sc][cti],t,pe,sc,cti);\r
       } else\r
         {\r
          cout<<"WARNING: diffFlowDirectCorrectionTermsForNUA[t][pe][sc][cti] is NULL in AFAWQC::GPFDFH() !!!!"<<endl;\r
          cout<<"t   = "<<t<<endl;\r
          cout<<"pe  = "<<pe<<endl;   \r
          cout<<"sc  = "<<sc<<endl;\r
          cout<<"cti = "<<cti<<endl;\r
         }    \r
      } // end of for(Int_t cti=0;cti<9;cti++) // correction term index\r
     } // end of for(Int_t sc=0;sc<2;sc++) // sin or cos\r
    } // end of for(Int_t pe=0;pe<2;pe++)\r
   } // end of for(Int_t t=0;t<2;t++)
   // number of RPs and POIs in selected pt and eta bins for cross-checkings:
   TString noOfParticlesInBinName = "fNoOfParticlesInBin";
   TH1D *noOfParticlesInBin = NULL;
   noOfParticlesInBin = dynamic_cast<TH1D*>(nestedLoopsList->FindObject(noOfParticlesInBinName.Data()));
   if(noOfParticlesInBin)
   {
    this->SetNoOfParticlesInBin(noOfParticlesInBin);
   } else
     {
      cout<<endl;
      cout<<" WARNING (QC): noOfParticlesInBin is NULL in AFAWQC::GPFDFH() !!!!"<<endl;
      cout<<endl;
     }\r
  } // end of if(bEvaluateDiffFlowNestedLoops)\r
\r
} // end of void AliFlowAnalysisWithQCumulants::GetPointersForNestedLoopsHistograms()\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::StoreHarmonic()\r
{\r
 // Store flow harmonic in common control histograms.\r
\r
 (fCommonHists->GetHarmonic())->Fill(0.5,fHarmonic);\r
 (fCommonHists2nd->GetHarmonic())->Fill(0.5,fHarmonic);\r
 (fCommonHists4th->GetHarmonic())->Fill(0.5,fHarmonic);\r
 (fCommonHists6th->GetHarmonic())->Fill(0.5,fHarmonic);\r
 (fCommonHists8th->GetHarmonic())->Fill(0.5,fHarmonic);\r
\r
} // end of void AliFlowAnalysisWithQCumulants::StoreHarmonic()\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::CalculateDiffFlowCorrelationsUsingParticleWeights(TString type, TString ptOrEta) // type = RP or POI \r
{\r
 // Calculate all correlations needed for differential flow using particle weights.\r
 \r
 Int_t t = -1; // type flag \r
 Int_t pe = -1; // ptEta flag\r
 \r
 if(type == "RP")\r
 {\r
  t = 0;\r
 } else if(type == "POI")\r
   {\r
    t = 1;\r
   }\r
\r
 if(ptOrEta == "Pt")\r
 {\r
  pe = 0;\r
 } else if(ptOrEta == "Eta")\r
   {\r
    pe = 1;\r
   }\r
    \r
 Int_t nBinsPtEta[2] = {fnBinsPt,fnBinsEta};\r
 Double_t minPtEta[2] = {fPtMin,fEtaMin};\r
 //Double_t maxPtEta[2] = {fPtMax,fEtaMax};\r
 Double_t binWidthPtEta[2] = {fPtBinWidth,fEtaBinWidth};\r
\r
 // real and imaginary parts of weighted Q-vectors evaluated in harmonics n, 2n, 3n and 4n: \r
 Double_t dReQ1n1k = (*fReQ)(0,1);\r
 Double_t dReQ2n2k = (*fReQ)(1,2);\r
 Double_t dReQ1n3k = (*fReQ)(0,3);\r
 //Double_t dReQ4n4k = (*fReQ)(3,4);\r
 Double_t dImQ1n1k = (*fImQ)(0,1);\r
 Double_t dImQ2n2k = (*fImQ)(1,2);\r
 Double_t dImQ1n3k = (*fImQ)(0,3);\r
 //Double_t dImQ4n4k = (*fImQ)(3,4);\r
 \r
 // S^M_{p,k} (see .h file for the definition of fSMpk):\r
 Double_t dSM1p1k = (*fSMpk)(0,1);\r
 Double_t dSM1p2k = (*fSMpk)(0,2);\r
 Double_t dSM1p3k = (*fSMpk)(0,3);\r
 Double_t dSM2p1k = (*fSMpk)(1,1);\r
 Double_t dSM3p1k = (*fSMpk)(2,1);\r
 \r
 // looping over all bins and calculating reduced correlations: \r
 for(Int_t b=1;b<=nBinsPtEta[pe];b++)\r
 {\r
  // real and imaginary parts of p_{m*n,0} (non-weighted Q-vector evaluated for POIs in particular (pt,eta) bin):  \r
  Double_t p1n0kRe = 0.;\r
  Double_t p1n0kIm = 0.;\r
\r
  // number of POIs in particular (pt,eta) bin):\r
  Double_t mp = 0.;\r
\r
  // real and imaginary parts of q_{m*n,k}: \r
  // (weighted Q-vector evaluated for particles which are both RPs and POIs in particular (pt,eta) bin)\r
  Double_t q1n2kRe = 0.;\r
  Double_t q1n2kIm = 0.;\r
  Double_t q2n1kRe = 0.;\r
  Double_t q2n1kIm = 0.;\r
\r
  // s_{1,1}, s_{1,2} and s_{1,3} // to be improved (add explanation)  \r
  Double_t s1p1k = 0.; \r
  Double_t s1p2k = 0.; \r
  Double_t s1p3k = 0.; \r
   \r
  // M0111 from Eq. (118) in QC2c (to be improved (notation))\r
  Double_t dM0111 = 0.;\r
 \r
  if(type == "POI")\r
  {\r
   p1n0kRe = fReRPQ1dEBE[1][pe][0][0]->GetBinContent(fReRPQ1dEBE[1][pe][0][0]->GetBin(b))\r
           * fReRPQ1dEBE[1][pe][0][0]->GetBinEntries(fReRPQ1dEBE[1][pe][0][0]->GetBin(b));\r
   p1n0kIm = fImRPQ1dEBE[1][pe][0][0]->GetBinContent(fImRPQ1dEBE[1][pe][0][0]->GetBin(b))  \r
           * fImRPQ1dEBE[1][pe][0][0]->GetBinEntries(fImRPQ1dEBE[1][pe][0][0]->GetBin(b));\r
            \r
   mp = fReRPQ1dEBE[1][pe][0][0]->GetBinEntries(fReRPQ1dEBE[1][pe][0][0]->GetBin(b)); // to be improved (cross-checked by accessing other profiles here)\r
    \r
   t = 1; // typeFlag = RP or POI\r
    \r
   // q_{m*n,k}: (Remark: m=1 is 0, k=0 iz zero (to be improved!)) \r
   q1n2kRe = fReRPQ1dEBE[2][pe][0][2]->GetBinContent(fReRPQ1dEBE[2][pe][0][2]->GetBin(b))\r
           * fReRPQ1dEBE[2][pe][0][2]->GetBinEntries(fReRPQ1dEBE[2][pe][0][2]->GetBin(b));\r
   q1n2kIm = fImRPQ1dEBE[2][pe][0][2]->GetBinContent(fImRPQ1dEBE[2][pe][0][2]->GetBin(b))\r
           * fImRPQ1dEBE[2][pe][0][2]->GetBinEntries(fImRPQ1dEBE[2][pe][0][2]->GetBin(b));\r
   q2n1kRe = fReRPQ1dEBE[2][pe][1][1]->GetBinContent(fReRPQ1dEBE[2][pe][1][1]->GetBin(b))\r
           * fReRPQ1dEBE[2][pe][1][1]->GetBinEntries(fReRPQ1dEBE[2][pe][1][1]->GetBin(b));\r
   q2n1kIm = fImRPQ1dEBE[2][pe][1][1]->GetBinContent(fImRPQ1dEBE[2][pe][1][1]->GetBin(b))\r
           * fImRPQ1dEBE[2][pe][1][1]->GetBinEntries(fImRPQ1dEBE[2][pe][1][1]->GetBin(b));\r
       \r
   // s_{1,1}, s_{1,2} and s_{1,3} // to be improved (add explanation)  \r
   s1p1k = pow(fs1dEBE[2][pe][1]->GetBinContent(b)*fs1dEBE[2][pe][1]->GetBinEntries(b),1.); \r
   s1p2k = pow(fs1dEBE[2][pe][2]->GetBinContent(b)*fs1dEBE[2][pe][2]->GetBinEntries(b),1.); \r
   s1p3k = pow(fs1dEBE[2][pe][3]->GetBinContent(b)*fs1dEBE[2][pe][3]->GetBinEntries(b),1.); \r
     \r
   // M0111 from Eq. (118) in QC2c (to be improved (notation)):\r
   dM0111 = mp*(dSM3p1k-3.*dSM1p1k*dSM1p2k+2.*dSM1p3k)\r
          - 3.*(s1p1k*(dSM2p1k-dSM1p2k)\r
          + 2.*(s1p3k-s1p2k*dSM1p1k));\r
  }\r
   else if(type == "RP")\r
   {\r
    // q_{m*n,k}: (Remark: m=1 is 0, k=0 iz zero (to be improved!)) \r
    q1n2kRe = fReRPQ1dEBE[0][pe][0][2]->GetBinContent(fReRPQ1dEBE[0][pe][0][2]->GetBin(b))\r
            * fReRPQ1dEBE[0][pe][0][2]->GetBinEntries(fReRPQ1dEBE[0][pe][0][2]->GetBin(b));\r
    q1n2kIm = fImRPQ1dEBE[0][pe][0][2]->GetBinContent(fImRPQ1dEBE[0][pe][0][2]->GetBin(b))\r
            * fImRPQ1dEBE[0][pe][0][2]->GetBinEntries(fImRPQ1dEBE[0][pe][0][2]->GetBin(b));\r
    q2n1kRe = fReRPQ1dEBE[0][pe][1][1]->GetBinContent(fReRPQ1dEBE[0][pe][1][1]->GetBin(b))\r
            * fReRPQ1dEBE[0][pe][1][1]->GetBinEntries(fReRPQ1dEBE[0][pe][1][1]->GetBin(b));\r
    q2n1kIm = fImRPQ1dEBE[0][pe][1][1]->GetBinContent(fImRPQ1dEBE[0][pe][1][1]->GetBin(b))\r
            * fImRPQ1dEBE[0][pe][1][1]->GetBinEntries(fImRPQ1dEBE[0][pe][1][1]->GetBin(b));\r
\r
    // s_{1,1}, s_{1,2} and s_{1,3} // to be improved (add explanation)  \r
    s1p1k = pow(fs1dEBE[0][pe][1]->GetBinContent(b)*fs1dEBE[0][pe][1]->GetBinEntries(b),1.); \r
    s1p2k = pow(fs1dEBE[0][pe][2]->GetBinContent(b)*fs1dEBE[0][pe][2]->GetBinEntries(b),1.); \r
    s1p3k = pow(fs1dEBE[0][pe][3]->GetBinContent(b)*fs1dEBE[0][pe][3]->GetBinEntries(b),1.); \r
    \r
    // to be improved (cross-checked):\r
    p1n0kRe = fReRPQ1dEBE[0][pe][0][0]->GetBinContent(fReRPQ1dEBE[0][pe][0][0]->GetBin(b))\r
            * fReRPQ1dEBE[0][pe][0][0]->GetBinEntries(fReRPQ1dEBE[0][pe][0][0]->GetBin(b));\r
    p1n0kIm = fImRPQ1dEBE[0][pe][0][0]->GetBinContent(fImRPQ1dEBE[0][pe][0][0]->GetBin(b))  \r
            * fImRPQ1dEBE[0][pe][0][0]->GetBinEntries(fImRPQ1dEBE[0][pe][0][0]->GetBin(b));\r
            \r
    mp = fReRPQ1dEBE[0][pe][0][0]->GetBinEntries(fReRPQ1dEBE[0][pe][0][0]->GetBin(b)); // to be improved (cross-checked by accessing other profiles here)\r
     \r
    t = 0; // typeFlag = RP or POI\r
    \r
    // M0111 from Eq. (118) in QC2c (to be improved (notation)):\r
    dM0111 = mp*(dSM3p1k-3.*dSM1p1k*dSM1p2k+2.*dSM1p3k)\r
           - 3.*(s1p1k*(dSM2p1k-dSM1p2k)\r
           + 2.*(s1p3k-s1p2k*dSM1p1k));\r
    //...............................................................................................   \r
   }\r
   \r
   // 2'-particle correlation:\r
   Double_t two1n1nW0W1 = 0.;\r
   if(mp*dSM1p1k-s1p1k)\r
   {\r
    two1n1nW0W1 = (p1n0kRe*dReQ1n1k+p1n0kIm*dImQ1n1k-s1p1k)\r
                / (mp*dSM1p1k-s1p1k);\r
   \r
    // fill profile to get <<2'>>     \r
    fDiffFlowCorrelationsPro[t][pe][0]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],two1n1nW0W1,mp*dSM1p1k-s1p1k);\r
    // histogram to store <2'> e-b-e (needed in some other methods):\r
    fDiffFlowCorrelationsEBE[t][pe][0]->SetBinContent(b,two1n1nW0W1);      \r
    fDiffFlowEventWeightsForCorrelationsEBE[t][pe][0]->SetBinContent(b,mp*dSM1p1k-s1p1k);      \r
   } // end of if(mp*dSM1p1k-s1p1k)\r
   \r
   // 4'-particle correlation:\r
   Double_t four1n1n1n1nW0W1W1W1 = 0.;\r
   if(dM0111)\r
   {\r
    four1n1n1n1nW0W1W1W1 = ((pow(dReQ1n1k,2.)+pow(dImQ1n1k,2.))*(p1n0kRe*dReQ1n1k+p1n0kIm*dImQ1n1k)\r
                         - q2n1kRe*(pow(dReQ1n1k,2.)-pow(dImQ1n1k,2.))\r
                         - 2.*q2n1kIm*dReQ1n1k*dImQ1n1k\r
                         - p1n0kRe*(dReQ1n1k*dReQ2n2k+dImQ1n1k*dImQ2n2k)\r
                         + p1n0kIm*(dImQ1n1k*dReQ2n2k-dReQ1n1k*dImQ2n2k)\r
                         - 2.*dSM1p2k*(p1n0kRe*dReQ1n1k+p1n0kIm*dImQ1n1k)\r
                         - 2.*(pow(dReQ1n1k,2.)+pow(dImQ1n1k,2.))*s1p1k                                            \r
                         + 6.*(q1n2kRe*dReQ1n1k+q1n2kIm*dImQ1n1k)                                           \r
                         + 1.*(q2n1kRe*dReQ2n2k+q2n1kIm*dImQ2n2k)                         \r
                         + 2.*(p1n0kRe*dReQ1n3k+p1n0kIm*dImQ1n3k)                      \r
                         + 2.*s1p1k*dSM1p2k                                      \r
                         - 6.*s1p3k)        \r
                         / dM0111; // to be improved (notation of dM0111)\r
   \r
    // fill profile to get <<4'>>     \r
    fDiffFlowCorrelationsPro[t][pe][1]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],four1n1n1n1nW0W1W1W1,dM0111);\r
    // histogram to store <4'> e-b-e (needed in some other methods):\r
    fDiffFlowCorrelationsEBE[t][pe][1]->SetBinContent(b,four1n1n1n1nW0W1W1W1);      \r
    fDiffFlowEventWeightsForCorrelationsEBE[t][pe][1]->SetBinContent(b,dM0111);      \r
   } // end of if(dM0111)\r
 } // end of for(Int_t b=1;b<=nBinsPtEta[pe];b++)\r
\r
} // end of void AliFlowAnalysisWithQCumulants::CalculateDiffFlowCorrelationsUsingParticleWeights(TString type, TString ptOrEta); // type = RP or POI \r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::FillCommonControlHistograms(AliFlowEventSimple *anEvent)\r
{\r
 // Fill common control histograms.\r
 \r
 Int_t nRP = anEvent->GetEventNSelTracksRP(); // number of RPs (i.e. number of particles used to determine the reaction plane)\r
 fCommonHists->FillControlHistograms(anEvent); \r
 if(nRP>1)\r
 {\r
  fCommonHists2nd->FillControlHistograms(anEvent);                                        \r
  if(nRP>3)\r
  {\r
   fCommonHists4th->FillControlHistograms(anEvent);                                        \r
   if(nRP>5)\r
   {\r
    fCommonHists6th->FillControlHistograms(anEvent);                                        \r
    if(nRP>7)\r
    {\r
     fCommonHists8th->FillControlHistograms(anEvent);                                        \r
    } // end of if(nRP>7)  \r
   } // end of if(nRP>5) \r
  } // end of if(nRP>3)                                                                                                                      \r
 } // end of if(nRP>1) \r
 \r
} // end of void AliFlowAnalysisWithQCumulants::FillCommonControlHistograms(AliFlowEventSimple *anEvent)\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::ResetEventByEventQuantities()\r
{\r
 // Reset all event by event quantities.\r
 \r
 // integrated flow:\r
 fReQ->Zero();\r
 fImQ->Zero();\r
 fSMpk->Zero();\r
 fIntFlowCorrelationsEBE->Reset();\r
 fIntFlowEventWeightsForCorrelationsEBE->Reset();\r
 fIntFlowCorrelationsAllEBE->Reset();\r
 \r
 if(fApplyCorrectionForNUA)  \r
 {\r
  for(Int_t sc=0;sc<2;sc++)\r
  {\r
   fIntFlowCorrectionTermsForNUAEBE[sc]->Reset();\r
  } \r
 }\r
    \r
 // differential flow:\r
 // 1D:\r
 for(Int_t t=0;t<3;t++) // type (RP, POI, POI&&RP)\r
 {\r
  for(Int_t pe=0;pe<2;pe++) // 1D in pt or eta\r
  {\r
   for(Int_t m=0;m<4;m++) // multiple of harmonic\r
   {\r
    for(Int_t k=0;k<9;k++) // power of weight\r
    {\r
     if(fReRPQ1dEBE[t][pe][m][k]) fReRPQ1dEBE[t][pe][m][k]->Reset();\r
     if(fImRPQ1dEBE[t][pe][m][k]) fImRPQ1dEBE[t][pe][m][k]->Reset();\r
    }   \r
   }\r
  }\r
 }\r
  \r
 for(Int_t t=0;t<3;t++) // type (0 = RP, 1 = POI, 2 = RP&&POI )\r
 { \r
  for(Int_t pe=0;pe<2;pe++) // 1D in pt or eta\r
  {\r
   for(Int_t k=0;k<9;k++)\r
   {\r
    if(fs1dEBE[t][pe][k]) fs1dEBE[t][pe][k]->Reset();\r
   }\r
  }\r
 }\r
\r
 // e-b-e reduced correlations:\r
 for(Int_t t=0;t<2;t++) // type (0 = RP, 1 = POI)\r
 {  \r
  for(Int_t pe=0;pe<2;pe++) // pt or eta\r
  {\r
   for(Int_t rci=0;rci<4;rci++) // reduced correlation index\r
   {\r
    if(fDiffFlowCorrelationsEBE[t][pe][rci]) fDiffFlowCorrelationsEBE[t][pe][rci]->Reset();\r
    if(fDiffFlowEventWeightsForCorrelationsEBE[t][pe][rci]) fDiffFlowEventWeightsForCorrelationsEBE[t][pe][rci]->Reset();\r
   }\r
  }\r
 }\r
    \r
 // correction terms for NUA:\r
 for(Int_t t=0;t<2;t++) // type (0 = RP, 1 = POI)\r
 {  \r
  for(Int_t pe=0;pe<2;pe++) // pt or eta\r
  {\r
   for(Int_t sc=0;sc<2;sc++) // sin or cos\r
   {\r
    for(Int_t cti=0;cti<9;cti++) // correction term index\r
    {\r
     fDiffFlowCorrectionTermsForNUAEBE[t][pe][sc][cti]->Reset();  \r
    }\r
   }\r
  }      \r
 }\r
    \r
 // 2D (pt,eta)\r
 if(fCalculate2DFlow)\r
 {\r
  for(Int_t t=0;t<3;t++) // type (RP, POI, POI&&RP)\r
  {\r
   for(Int_t m=0;m<4;m++) // multiple of harmonic\r
   {\r
    for(Int_t k=0;k<9;k++) // power of weight\r
    {\r
     if(fReRPQ2dEBE[t][m][k]) fReRPQ2dEBE[t][m][k]->Reset();\r
     if(fImRPQ2dEBE[t][m][k]) fImRPQ2dEBE[t][m][k]->Reset();\r
    }   \r
   }\r
  }\r
  for(Int_t t=0;t<3;t++) // type (0 = RP, 1 = POI, 2 = RP&&POI )\r
  { \r
   for(Int_t k=0;k<9;k++)\r
   {\r
    if(fs2dEBE[t][k]) fs2dEBE[t][k]->Reset();\r
   }\r
  }  \r
 } // end of if(fCalculate2DFlow) \r
\r
} // end of void AliFlowAnalysisWithQCumulants::ResetEventByEventQuantities();\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::CalculateDiffFlowCorrectionsForNUASinTerms(TString type, TString ptOrEta)\r
{\r
 // Calculate correction terms for non-uniform acceptance for differential flow (sin terms).\r
 \r
 // Results are stored in fDiffFlowCorrectionTermsForNUAPro[t][pe][0][cti], where cti runs as follows:\r
 //  0: <<sin n(psi1)>>\r
 //  1: <<sin n(psi1+phi2)>>\r
 //  2: <<sin n(psi1+phi2-phi3)>>\r
 //  3: <<sin n(psi1-phi2-phi3)>>:\r
 //  4:\r
 //  5:\r
 //  6:\r
 \r
 // multiplicity:\r
 Double_t dMult = (*fSMpk)(0,0);\r
 \r
 // real and imaginary parts of non-weighted Q-vectors evaluated in harmonics n, 2n, 3n and 4n: \r
 Double_t dReQ1n = (*fReQ)(0,0);\r
 Double_t dReQ2n = (*fReQ)(1,0);\r
 //Double_t dReQ3n = (*fReQ)(2,0);\r
 //Double_t dReQ4n = (*fReQ)(3,0);\r
 Double_t dImQ1n = (*fImQ)(0,0);\r
 Double_t dImQ2n = (*fImQ)(1,0);\r
 //Double_t dImQ3n = (*fImQ)(2,0);\r
 //Double_t dImQ4n = (*fImQ)(3,0);\r
\r
 Int_t t = -1; // type flag \r
 Int_t pe = -1; // ptEta flag\r
 \r
 if(type == "RP")\r
 {\r
  t = 0;\r
 } else if(type == "POI")\r
   {\r
    t = 1;\r
   }\r
\r
 if(ptOrEta == "Pt")\r
 {\r
  pe = 0;\r
 } else if(ptOrEta == "Eta")\r
   {\r
    pe = 1;\r
   }\r
    \r
 Int_t nBinsPtEta[2] = {fnBinsPt,fnBinsEta};\r
 Double_t minPtEta[2] = {fPtMin,fEtaMin};\r
 //Double_t maxPtEta[2] = {fPtMax,fEtaMax};\r
 Double_t binWidthPtEta[2] = {fPtBinWidth,fEtaBinWidth};\r
\r
 // looping over all bins and calculating correction terms: \r
 for(Int_t b=1;b<=nBinsPtEta[pe];b++)\r
 {\r
  // real and imaginary parts of p_{m*n,0} (non-weighted Q-vector evaluated for POIs in particular pt or eta bin): \r
  Double_t p1n0kRe = 0.;\r
  Double_t p1n0kIm = 0.;\r
\r
  // number of POIs in particular pt or eta bin:\r
  Double_t mp = 0.;\r
\r
  // real and imaginary parts of q_{m*n,0} (non-weighted Q-vector evaluated for particles which are both RPs and POIs in particular pt or eta bin):\r
  Double_t q1n0kRe = 0.;\r
  Double_t q1n0kIm = 0.;\r
  Double_t q2n0kRe = 0.;\r
  Double_t q2n0kIm = 0.;\r
\r
  // number of particles which are both RPs and POIs in particular pt or eta bin:\r
  Double_t mq = 0.;\r
   \r
  if(type == "POI")\r
  {\r
   // q_{m*n,0}:\r
   q1n0kRe = fReRPQ1dEBE[2][pe][0][0]->GetBinContent(fReRPQ1dEBE[2][pe][0][0]->GetBin(b))\r
           * fReRPQ1dEBE[2][pe][0][0]->GetBinEntries(fReRPQ1dEBE[2][pe][0][0]->GetBin(b));\r
   q1n0kIm = fImRPQ1dEBE[2][pe][0][0]->GetBinContent(fImRPQ1dEBE[2][pe][0][0]->GetBin(b))\r
           * fImRPQ1dEBE[2][pe][0][0]->GetBinEntries(fImRPQ1dEBE[2][pe][0][0]->GetBin(b));\r
   q2n0kRe = fReRPQ1dEBE[2][pe][1][0]->GetBinContent(fReRPQ1dEBE[2][pe][1][0]->GetBin(b))\r
           * fReRPQ1dEBE[2][pe][1][0]->GetBinEntries(fReRPQ1dEBE[2][pe][1][0]->GetBin(b));\r
   q2n0kIm = fImRPQ1dEBE[2][pe][1][0]->GetBinContent(fImRPQ1dEBE[2][pe][1][0]->GetBin(b))\r
           * fImRPQ1dEBE[2][pe][1][0]->GetBinEntries(fImRPQ1dEBE[2][pe][1][0]->GetBin(b));         \r
                 \r
   mq = fReRPQ1dEBE[2][pe][0][0]->GetBinEntries(fReRPQ1dEBE[2][pe][0][0]->GetBin(b)); // to be improved (cross-checked by accessing other profiles here)\r
  } \r
  else if(type == "RP")\r
  {\r
   // q_{m*n,0}:\r
   q1n0kRe = fReRPQ1dEBE[0][pe][0][0]->GetBinContent(fReRPQ1dEBE[0][pe][0][0]->GetBin(b))\r
           * fReRPQ1dEBE[0][pe][0][0]->GetBinEntries(fReRPQ1dEBE[0][pe][0][0]->GetBin(b));\r
   q1n0kIm = fImRPQ1dEBE[0][pe][0][0]->GetBinContent(fImRPQ1dEBE[0][pe][0][0]->GetBin(b))\r
           * fImRPQ1dEBE[0][pe][0][0]->GetBinEntries(fImRPQ1dEBE[0][pe][0][0]->GetBin(b));\r
   q2n0kRe = fReRPQ1dEBE[0][pe][1][0]->GetBinContent(fReRPQ1dEBE[0][pe][1][0]->GetBin(b))\r
           * fReRPQ1dEBE[0][pe][1][0]->GetBinEntries(fReRPQ1dEBE[0][pe][1][0]->GetBin(b));\r
   q2n0kIm = fImRPQ1dEBE[0][pe][1][0]->GetBinContent(fImRPQ1dEBE[0][pe][1][0]->GetBin(b))\r
           * fImRPQ1dEBE[0][pe][1][0]->GetBinEntries(fImRPQ1dEBE[0][pe][1][0]->GetBin(b));         \r
                 \r
   mq = fReRPQ1dEBE[0][pe][0][0]->GetBinEntries(fReRPQ1dEBE[0][pe][0][0]->GetBin(b)); // to be improved (cross-checked by accessing other profiles here)  \r
  }    \r
  if(type == "POI")\r
  {\r
   // p_{m*n,0}:\r
   p1n0kRe = fReRPQ1dEBE[1][pe][0][0]->GetBinContent(fReRPQ1dEBE[1][pe][0][0]->GetBin(b))\r
           * fReRPQ1dEBE[1][pe][0][0]->GetBinEntries(fReRPQ1dEBE[1][pe][0][0]->GetBin(b));\r
   p1n0kIm = fImRPQ1dEBE[1][pe][0][0]->GetBinContent(fImRPQ1dEBE[1][pe][0][0]->GetBin(b))  \r
           * fImRPQ1dEBE[1][pe][0][0]->GetBinEntries(fImRPQ1dEBE[1][pe][0][0]->GetBin(b));\r
            \r
   mp = fReRPQ1dEBE[1][pe][0][0]->GetBinEntries(fReRPQ1dEBE[1][pe][0][0]->GetBin(b)); // to be improved (cross-checked by accessing other profiles here)\r
    \r
   t = 1; // typeFlag = RP or POI\r
  }\r
  else if(type == "RP")\r
  {\r
   // p_{m*n,0} = q_{m*n,0}:\r
   p1n0kRe = q1n0kRe; \r
   p1n0kIm = q1n0kIm; \r
           \r
   mp = mq; \r
   \r
   t = 0; // typeFlag = RP or POI\r
  }\r
\r
  // <<sin n(psi1)>>:\r
  Double_t sinP1nPsi = 0.;\r
  if(mp)\r
  {\r
   sinP1nPsi = p1n0kIm/mp;\r
   // fill profile for <<sin n(psi1)>>:\r
   fDiffFlowCorrectionTermsForNUAPro[t][pe][0][0]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],sinP1nPsi,mp);\r
   // histogram to store <sin n(psi1)> e-b-e (needed in some other methods):\r
   fDiffFlowCorrectionTermsForNUAEBE[t][pe][0][0]->SetBinContent(b,sinP1nPsi);\r
  } // end of if(mp)   \r
  \r
  // <<sin n(psi1+phi2)>>:\r
  Double_t sinP1nPsiP1nPhi = 0.;\r
  if(mp*dMult-mq)\r
  {\r
   sinP1nPsiP1nPhi = (p1n0kRe*dImQ1n+p1n0kIm*dReQ1n-q2n0kIm)/(mp*dMult-mq);\r
   // fill profile for <<sin n(psi1+phi2)>>:\r
   fDiffFlowCorrectionTermsForNUAPro[t][pe][0][1]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],sinP1nPsiP1nPhi,mp*dMult-mq);\r
   // histogram to store <sin n(psi1+phi2)> e-b-e (needed in some other methods):\r
   fDiffFlowCorrectionTermsForNUAEBE[t][pe][0][1]->SetBinContent(b,sinP1nPsiP1nPhi);\r
  } // end of if(mp*dMult-mq)   \r
  \r
  // <<sin n(psi1+phi2-phi3)>>:\r
  Double_t sinP1nPsi1P1nPhi2MPhi3 = 0.;\r
  if(mq*(dMult-1.)*(dMult-2.)+(mp-mq)*dMult*(dMult-1.))\r
  {\r
   sinP1nPsi1P1nPhi2MPhi3 = (p1n0kIm*(pow(dImQ1n,2.)+pow(dReQ1n,2.)-dMult)\r
                          - 1.*(q2n0kIm*dReQ1n-q2n0kRe*dImQ1n)  \r
                          - mq*dImQ1n+2.*q1n0kIm)\r
                          / (mq*(dMult-1.)*(dMult-2.)+(mp-mq)*dMult*(dMult-1.));\r
   // fill profile for <<sin n(psi1+phi2)>>:\r
   fDiffFlowCorrectionTermsForNUAPro[t][pe][0][2]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],sinP1nPsi1P1nPhi2MPhi3,mq*(dMult-1.)*(dMult-2.)+(mp-mq)*dMult*(dMult-1.));\r
   // histogram to store <sin n(psi1+phi2)> e-b-e (needed in some other methods):\r
   fDiffFlowCorrectionTermsForNUAEBE[t][pe][0][2]->SetBinContent(b,sinP1nPsi1P1nPhi2MPhi3);\r
  } // end of if(mq*(dMult-1.)*(dMult-2.)+(mp-mq)*dMult*(dMult-1.))   \r
  \r
  // <<sin n(psi1-phi2-phi3)>>:\r
  Double_t sinP1nPsi1M1nPhi2MPhi3 = 0.;\r
  if(mq*(dMult-1.)*(dMult-2.)+(mp-mq)*dMult*(dMult-1.))\r
  {\r
   sinP1nPsi1M1nPhi2MPhi3 = (p1n0kIm*(pow(dReQ1n,2.)-pow(dImQ1n,2.))-2.*p1n0kRe*dReQ1n*dImQ1n\r
                          - 1.*(p1n0kIm*dReQ2n-p1n0kRe*dImQ2n)\r
                          + 2.*mq*dImQ1n-2.*q1n0kIm)\r
                          / (mq*(dMult-1.)*(dMult-2.)+(mp-mq)*dMult*(dMult-1.));\r
   // fill profile for <<sin n(psi1+phi2)>>:\r
   fDiffFlowCorrectionTermsForNUAPro[t][pe][0][3]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],sinP1nPsi1M1nPhi2MPhi3,mq*(dMult-1.)*(dMult-2.)+(mp-mq)*dMult*(dMult-1.));\r
   // histogram to store <sin n(psi1+phi2)> e-b-e (needed in some other methods):\r
   fDiffFlowCorrectionTermsForNUAEBE[t][pe][0][3]->SetBinContent(b,sinP1nPsi1M1nPhi2MPhi3);\r
  } // end of if(mq*(dMult-1.)*(dMult-2.)+(mp-mq)*dMult*(dMult-1.))   \r
 } // end of for(Int_t b=1;b<=nBinsPtEta[pe];b++)\r
 \r
} // end of AliFlowAnalysisWithQCumulants::CalculateDiffFlowCorrectionsForNUASinTerms(TString type, TString ptOrEta)\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::CalculateDiffFlowCorrectionsForNUACosTerms(TString type, TString ptOrEta)\r
{\r
 // Calculate correction terms for non-uniform acceptance for differential flow (cos terms).\r
 \r
 // Results are stored in fDiffFlowCorrectionTermsForNUAPro[t][pe][1][cti], where cti runs as follows:\r
 //  0: <<cos n(psi)>>\r
 //  1: <<cos n(psi1+phi2)>>\r
 //  2: <<cos n(psi1+phi2-phi3)>>\r
 //  3: <<cos n(psi1-phi2-phi3)>>\r
 //  4:\r
 //  5:\r
 //  6:\r
 \r
 // multiplicity:\r
 Double_t dMult = (*fSMpk)(0,0);\r
 \r
 // real and imaginary parts of non-weighted Q-vectors evaluated in harmonics n, 2n, 3n and 4n: \r
 Double_t dReQ1n = (*fReQ)(0,0);\r
 Double_t dReQ2n = (*fReQ)(1,0);\r
 //Double_t dReQ3n = (*fReQ)(2,0);\r
 //Double_t dReQ4n = (*fReQ)(3,0);\r
 Double_t dImQ1n = (*fImQ)(0,0);\r
 Double_t dImQ2n = (*fImQ)(1,0);\r
 //Double_t dImQ3n = (*fImQ)(2,0);\r
 //Double_t dImQ4n = (*fImQ)(3,0);\r
\r
 Int_t t = -1; // type flag \r
 Int_t pe = -1; // ptEta flag\r
 \r
 if(type == "RP")\r
 {\r
  t = 0;\r
 } else if(type == "POI")\r
   {\r
    t = 1;\r
   }\r
\r
 if(ptOrEta == "Pt")\r
 {\r
  pe = 0;\r
 } else if(ptOrEta == "Eta")\r
   {\r
    pe = 1;\r
   }\r
    \r
 Int_t nBinsPtEta[2] = {fnBinsPt,fnBinsEta};\r
 Double_t minPtEta[2] = {fPtMin,fEtaMin};\r
 //Double_t maxPtEta[2] = {fPtMax,fEtaMax};\r
 Double_t binWidthPtEta[2] = {fPtBinWidth,fEtaBinWidth};\r
\r
 // looping over all bins and calculating correction terms: \r
 for(Int_t b=1;b<=nBinsPtEta[pe];b++)\r
 {\r
  // real and imaginary parts of p_{m*n,0} (non-weighted Q-vector evaluated for POIs in particular pt or eta bin): \r
  Double_t p1n0kRe = 0.;\r
  Double_t p1n0kIm = 0.;\r
\r
  // number of POIs in particular pt or eta bin:\r
  Double_t mp = 0.;\r
\r
  // real and imaginary parts of q_{m*n,0} (non-weighted Q-vector evaluated for particles which are both RPs and POIs in particular pt or eta bin):\r
  Double_t q1n0kRe = 0.;\r
  Double_t q1n0kIm = 0.;\r
  Double_t q2n0kRe = 0.;\r
  Double_t q2n0kIm = 0.;\r
\r
  // number of particles which are both RPs and POIs in particular pt or eta bin:\r
  Double_t mq = 0.;\r
   \r
  if(type == "POI")\r
  {\r
   // q_{m*n,0}:\r
   q1n0kRe = fReRPQ1dEBE[2][pe][0][0]->GetBinContent(fReRPQ1dEBE[2][pe][0][0]->GetBin(b))\r
           * fReRPQ1dEBE[2][pe][0][0]->GetBinEntries(fReRPQ1dEBE[2][pe][0][0]->GetBin(b));\r
   q1n0kIm = fImRPQ1dEBE[2][pe][0][0]->GetBinContent(fImRPQ1dEBE[2][pe][0][0]->GetBin(b))\r
           * fImRPQ1dEBE[2][pe][0][0]->GetBinEntries(fImRPQ1dEBE[2][pe][0][0]->GetBin(b));\r
   q2n0kRe = fReRPQ1dEBE[2][pe][1][0]->GetBinContent(fReRPQ1dEBE[2][pe][1][0]->GetBin(b))\r
           * fReRPQ1dEBE[2][pe][1][0]->GetBinEntries(fReRPQ1dEBE[2][pe][1][0]->GetBin(b));\r
   q2n0kIm = fImRPQ1dEBE[2][pe][1][0]->GetBinContent(fImRPQ1dEBE[2][pe][1][0]->GetBin(b))\r
           * fImRPQ1dEBE[2][pe][1][0]->GetBinEntries(fImRPQ1dEBE[2][pe][1][0]->GetBin(b));         \r
                 \r
   mq = fReRPQ1dEBE[2][pe][0][0]->GetBinEntries(fReRPQ1dEBE[2][pe][0][0]->GetBin(b)); // to be improved (cross-checked by accessing other profiles here)\r
  } \r
  else if(type == "RP")\r
  {\r
   // q_{m*n,0}:\r
   q1n0kRe = fReRPQ1dEBE[0][pe][0][0]->GetBinContent(fReRPQ1dEBE[0][pe][0][0]->GetBin(b))\r
           * fReRPQ1dEBE[0][pe][0][0]->GetBinEntries(fReRPQ1dEBE[0][pe][0][0]->GetBin(b));\r
   q1n0kIm = fImRPQ1dEBE[0][pe][0][0]->GetBinContent(fImRPQ1dEBE[0][pe][0][0]->GetBin(b))\r
           * fImRPQ1dEBE[0][pe][0][0]->GetBinEntries(fImRPQ1dEBE[0][pe][0][0]->GetBin(b));\r
   q2n0kRe = fReRPQ1dEBE[0][pe][1][0]->GetBinContent(fReRPQ1dEBE[0][pe][1][0]->GetBin(b))\r
           * fReRPQ1dEBE[0][pe][1][0]->GetBinEntries(fReRPQ1dEBE[0][pe][1][0]->GetBin(b));\r
   q2n0kIm = fImRPQ1dEBE[0][pe][1][0]->GetBinContent(fImRPQ1dEBE[0][pe][1][0]->GetBin(b))\r
           * fImRPQ1dEBE[0][pe][1][0]->GetBinEntries(fImRPQ1dEBE[0][pe][1][0]->GetBin(b));         \r
                 \r
   mq = fReRPQ1dEBE[0][pe][0][0]->GetBinEntries(fReRPQ1dEBE[0][pe][0][0]->GetBin(b)); // to be improved (cross-checked by accessing other profiles here)  \r
  }    \r
  if(type == "POI")\r
  {\r
   // p_{m*n,0}:\r
   p1n0kRe = fReRPQ1dEBE[1][pe][0][0]->GetBinContent(fReRPQ1dEBE[1][pe][0][0]->GetBin(b))\r
           * fReRPQ1dEBE[1][pe][0][0]->GetBinEntries(fReRPQ1dEBE[1][pe][0][0]->GetBin(b));\r
   p1n0kIm = fImRPQ1dEBE[1][pe][0][0]->GetBinContent(fImRPQ1dEBE[1][pe][0][0]->GetBin(b))  \r
           * fImRPQ1dEBE[1][pe][0][0]->GetBinEntries(fImRPQ1dEBE[1][pe][0][0]->GetBin(b));\r
            \r
   mp = fReRPQ1dEBE[1][pe][0][0]->GetBinEntries(fReRPQ1dEBE[1][pe][0][0]->GetBin(b)); // to be improved (cross-checked by accessing other profiles here)\r
    \r
   t = 1; // typeFlag = RP or POI\r
  }\r
  else if(type == "RP")\r
  {\r
   // p_{m*n,0} = q_{m*n,0}:\r
   p1n0kRe = q1n0kRe; \r
   p1n0kIm = q1n0kIm; \r
           \r
   mp = mq; \r
   \r
   t = 0; // typeFlag = RP or POI\r
  }\r
\r
  // <<cos n(psi1)>>:\r
  Double_t cosP1nPsi = 0.;\r
  if(mp)\r
  {\r
   cosP1nPsi = p1n0kRe/mp;\r
   \r
   // fill profile for <<cos n(psi1)>>:\r
   fDiffFlowCorrectionTermsForNUAPro[t][pe][1][0]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],cosP1nPsi,mp);\r
   // histogram to store <cos n(psi1)> e-b-e (needed in some other methods):\r
   fDiffFlowCorrectionTermsForNUAEBE[t][pe][1][0]->SetBinContent(b,cosP1nPsi);\r
  } // end of if(mp)   \r
  \r
  // <<cos n(psi1+phi2)>>:\r
  Double_t cosP1nPsiP1nPhi = 0.;\r
  if(mp*dMult-mq)\r
  {\r
   cosP1nPsiP1nPhi = (p1n0kRe*dReQ1n-p1n0kIm*dImQ1n-q2n0kRe)/(mp*dMult-mq);\r
   // fill profile for <<sin n(psi1+phi2)>>:\r
   fDiffFlowCorrectionTermsForNUAPro[t][pe][1][1]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],cosP1nPsiP1nPhi,mp*dMult-mq);\r
   // histogram to store <sin n(psi1+phi2)> e-b-e (needed in some other methods):\r
   fDiffFlowCorrectionTermsForNUAEBE[t][pe][1][1]->SetBinContent(b,cosP1nPsiP1nPhi);\r
  } // end of if(mp*dMult-mq)   \r
  \r
  // <<cos n(psi1+phi2-phi3)>>:\r
  Double_t cosP1nPsi1P1nPhi2MPhi3 = 0.;\r
  if(mq*(dMult-1.)*(dMult-2.)+(mp-mq)*dMult*(dMult-1.))\r
  {\r
   cosP1nPsi1P1nPhi2MPhi3 = (p1n0kRe*(pow(dImQ1n,2.)+pow(dReQ1n,2.)-dMult)\r
                          - 1.*(q2n0kRe*dReQ1n+q2n0kIm*dImQ1n)  \r
                          - mq*dReQ1n+2.*q1n0kRe)\r
                          / (mq*(dMult-1.)*(dMult-2.)+(mp-mq)*dMult*(dMult-1.));\r
   // fill profile for <<sin n(psi1+phi2)>>:\r
   fDiffFlowCorrectionTermsForNUAPro[t][pe][1][2]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],cosP1nPsi1P1nPhi2MPhi3,mq*(dMult-1.)*(dMult-2.)+(mp-mq)*dMult*(dMult-1.));\r
   // histogram to store <sin n(psi1+phi2)> e-b-e (needed in some other methods):\r
   fDiffFlowCorrectionTermsForNUAEBE[t][pe][1][2]->SetBinContent(b,cosP1nPsi1P1nPhi2MPhi3);\r
  } // end of if(mq*(dMult-1.)*(dMult-2.)+(mp-mq)*dMult*(dMult-1.))   \r
  \r
  // <<cos n(psi1-phi2-phi3)>>:\r
  Double_t cosP1nPsi1M1nPhi2MPhi3 = 0.;\r
  if(mq*(dMult-1.)*(dMult-2.)+(mp-mq)*dMult*(dMult-1.))\r
  {\r
   cosP1nPsi1M1nPhi2MPhi3 = (p1n0kRe*(pow(dReQ1n,2.)-pow(dImQ1n,2.))+2.*p1n0kIm*dReQ1n*dImQ1n\r
                          - 1.*(p1n0kRe*dReQ2n+p1n0kIm*dImQ2n)  \r
                          - 2.*mq*dReQ1n+2.*q1n0kRe)\r
                          / (mq*(dMult-1.)*(dMult-2.)+(mp-mq)*dMult*(dMult-1.));\r
   // fill profile for <<sin n(psi1+phi2)>>:\r
   fDiffFlowCorrectionTermsForNUAPro[t][pe][1][3]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],cosP1nPsi1M1nPhi2MPhi3,mq*(dMult-1.)*(dMult-2.)+(mp-mq)*dMult*(dMult-1.));\r
   // histogram to store <sin n(psi1+phi2)> e-b-e (needed in some other methods):\r
   fDiffFlowCorrectionTermsForNUAEBE[t][pe][1][3]->SetBinContent(b,cosP1nPsi1M1nPhi2MPhi3);\r
  } // end of if(mq*(dMult-1.)*(dMult-2.)+(mp-mq)*dMult*(dMult-1.))   \r
 } // end of for(Int_t b=1;b<=nBinsPtEta[pe];b++)\r
 \r
} // end of AliFlowAnalysisWithQCumulants::CalculateDiffFlowCorrectionsForNUACosTerms(TString type, TString ptOrEta)\r
\r
\r
//==================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::FinalizeCorrectionTermsForNUADiffFlow(TString type, TString ptOrEta)\r
{\r
 // Transfer prolfiles into histogams and correctly propagate the error (to be improved: description)\r
 \r
 // to be improved: debugged - I do not correctly transfer all profiles into histos (bug appears only after merging) \r
  \r
 Int_t t = -1; // type flag \r
 Int_t pe = -1; // ptEta flag\r
 \r
 if(type == "RP")\r
 {\r
  t = 0;\r
 } else if(type == "POI")\r
   {\r
    t = 1;\r
   }\r
\r
 if(ptOrEta == "Pt")\r
 {\r
  pe = 0;\r
 } else if(ptOrEta == "Eta")\r
   {\r
    pe = 1;\r
   }\r
    \r
 Int_t nBinsPtEta[2] = {fnBinsPt,fnBinsEta};\r
 //Double_t minPtEta[2] = {fPtMin,fEtaMin};\r
 //Double_t maxPtEta[2] = {fPtMax,fEtaMax};\r
 //Double_t binWidthPtEta[2] = {fPtBinWidth,fEtaBinWidth};\r
\r
 for(Int_t sc=0;sc<2;sc++) // sin or cos\r
 {\r
  for(Int_t cti=0;cti<9;cti++) // correction term index\r
  {\r
   for(Int_t b=1;b<=nBinsPtEta[pe];b++)\r
   {\r
    Double_t correctionTerm = fDiffFlowCorrectionTermsForNUAPro[t][pe][sc][cti]->GetBinContent(b);\r
    fDiffFlowCorrectionTermsForNUAHist[t][pe][sc][cti]->SetBinContent(b,correctionTerm);\r
    // to be improved (propagate error correctly)\r
    // ...\r
   } // end of for(Int_t b=1;b<=nBinsPtEta[pe];b++)\r
  } // correction term index\r
 } // end of for(Int_t sc=0;sc<2;sc++) // sin or cos\r
\r
}// end of void AliFlowAnalysisWithQCumulants::FinalizeCorrectionTermsForNUADiffFlow(TString type, TString ptOrEta)\r
\r
\r
//==================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::CalculateDiffFlowCumulantsCorrectedForNUA(TString type, TString ptOrEta)\r
{ \r
 // Calculate generalized differential flow Q-cumulants (corrected for non-uniform acceptance)\r
  \r
 Int_t typeFlag = -1;\r
 Int_t ptEtaFlag = -1;\r
\r
 if(type == "RP")\r
 {\r
  typeFlag = 0;\r
 } else if(type == "POI")\r
   {\r
    typeFlag = 1;\r
   } \r
     \r
 if(ptOrEta == "Pt")\r
 {\r
  ptEtaFlag = 0;\r
 } else if(ptOrEta == "Eta")\r
   {\r
    ptEtaFlag = 1;\r
   } \r
  \r
 // shortcuts:\r
 Int_t t = typeFlag;\r
 Int_t pe = ptEtaFlag;\r
     \r
 // common:\r
 Int_t nBinsPtEta[2] = {fnBinsPt,fnBinsEta};\r
 \r
 // 2-particle correlation:\r
 Double_t two = fIntFlowCorrelationsHist->GetBinContent(1); // <<2>>\r
 // sin term coming from integrated flow: \r
 Double_t sinP1nPhi = fIntFlowCorrectionTermsForNUAHist[0]->GetBinContent(1); // <<sin(n*phi1)>>\r
 Double_t sinP1nPhi1P1nPhi2 = fIntFlowCorrectionTermsForNUAHist[0]->GetBinContent(2); // <<sin(n*(phi1+phi2))>>\r
 Double_t sinP1nPhi1M1nPhi2M1nPhi3 = fIntFlowCorrectionTermsForNUAHist[0]->GetBinContent(3); // <<sin(n*(phi1-phi2-phi3))>>\r
 // cos term coming from integrated flow: \r
 Double_t cosP1nPhi = fIntFlowCorrectionTermsForNUAHist[1]->GetBinContent(1); // <<cos(n*phi1)>>\r
 Double_t cosP1nPhi1P1nPhi2 = fIntFlowCorrectionTermsForNUAHist[1]->GetBinContent(2); // <<cos(n*(phi1+phi2))>>\r
 Double_t cosP1nPhi1M1nPhi2M1nPhi3 = fIntFlowCorrectionTermsForNUAHist[1]->GetBinContent(3); // <<cos(n*(phi1-phi2-phi3))>>\r
\r
 for(Int_t b=1;b<=nBinsPtEta[pe];b++)\r
 {\r
  Double_t twoPrime = fDiffFlowCorrelationsHist[t][pe][0]->GetBinContent(b); // <<2'>>\r
  Double_t fourPrime = fDiffFlowCorrelationsHist[t][pe][1]->GetBinContent(b); // <<4'>>\r
  Double_t sinP1nPsi = fDiffFlowCorrectionTermsForNUAHist[t][pe][0][0]->GetBinContent(b); // <<sin n(Psi)>> \r
  Double_t cosP1nPsi = fDiffFlowCorrectionTermsForNUAHist[t][pe][1][0]->GetBinContent(b); // <<cos n(Psi)>> \r
  Double_t sinP1nPsi1P1nPhi2 = fDiffFlowCorrectionTermsForNUAHist[t][pe][0][1]->GetBinContent(b); // <<sin n(psi1+phi2)>> \r
  Double_t cosP1nPsi1P1nPhi2 = fDiffFlowCorrectionTermsForNUAHist[t][pe][1][1]->GetBinContent(b); // <<cos n(psi1+phi2)>> \r
  Double_t sinP1nPsi1P1nPhi2M1nPhi3 = fDiffFlowCorrectionTermsForNUAHist[t][pe][0][2]->GetBinContent(b); // <<sin n(psi1+phi2-phi3)>> \r
  Double_t cosP1nPsi1P1nPhi2M1nPhi3 = fDiffFlowCorrectionTermsForNUAHist[t][pe][1][2]->GetBinContent(b); // <<cos n(psi1+phi2-phi3)>> \r
  Double_t sinP1nPsi1M1nPhi2M1nPhi3 = fDiffFlowCorrectionTermsForNUAHist[t][pe][0][3]->GetBinContent(b); // <<sin n(psi1-phi2-phi3)>> \r
  Double_t cosP1nPsi1M1nPhi2M1nPhi3 = fDiffFlowCorrectionTermsForNUAHist[t][pe][1][3]->GetBinContent(b); // <<cos n(psi1-phi2-phi3)>> \r
  // generalized QC{2'}:\r
  Double_t qc2Prime = twoPrime - sinP1nPsi*sinP1nPhi - cosP1nPsi*cosP1nPhi;\r
  fDiffFlowCumulants[t][pe][0]->SetBinContent(b,qc2Prime);\r
  // generalized QC{4'}:\r
  Double_t qc4Prime = fourPrime-2.*twoPrime*two\r
                    - cosP1nPsi*cosP1nPhi1M1nPhi2M1nPhi3\r
                    + sinP1nPsi*sinP1nPhi1M1nPhi2M1nPhi3\r
                    - cosP1nPhi*cosP1nPsi1M1nPhi2M1nPhi3\r
                    + sinP1nPhi*sinP1nPsi1M1nPhi2M1nPhi3\r
                    - 2.*cosP1nPhi*cosP1nPsi1P1nPhi2M1nPhi3\r
                    - 2.*sinP1nPhi*sinP1nPsi1P1nPhi2M1nPhi3\r
                    - cosP1nPsi1P1nPhi2*cosP1nPhi1P1nPhi2\r
                    - sinP1nPsi1P1nPhi2*sinP1nPhi1P1nPhi2\r
                    + 2.*cosP1nPhi1P1nPhi2*(cosP1nPsi*cosP1nPhi-sinP1nPsi*sinP1nPhi)\r
                    + 2.*sinP1nPhi1P1nPhi2*(cosP1nPsi*sinP1nPhi+sinP1nPsi*cosP1nPhi)\r
                    + 4.*two*(cosP1nPsi*cosP1nPhi+sinP1nPsi*sinP1nPhi)\r
                    + 2.*cosP1nPsi1P1nPhi2*(pow(cosP1nPhi,2.)-pow(sinP1nPhi,2.))\r
                    + 4.*sinP1nPsi1P1nPhi2*cosP1nPhi*sinP1nPhi\r
                    + 4.*twoPrime*(pow(cosP1nPhi,2.)+pow(sinP1nPhi,2.))\r
                    - 6.*(pow(cosP1nPhi,2.)-pow(sinP1nPhi,2.)) \r
                    * (cosP1nPsi*cosP1nPhi-sinP1nPsi*sinP1nPhi)\r
                    - 12.*cosP1nPhi*sinP1nPhi\r
                    * (sinP1nPsi*cosP1nPhi+cosP1nPsi*sinP1nPhi);\r
  fDiffFlowCumulants[t][pe][1]->SetBinContent(b,qc4Prime);   \r
 } // end of for(Int_t p=1;p<=fnBinsPt;p++)\r
 \r
} // end of AliFlowAnalysisWithQCumulants::CalculateDiffFlowCumulantsCorrectedForNUA(TString type, TString ptOrEta)\r
\r
\r
//==================================================================================================================================\r
    \r
\r
void AliFlowAnalysisWithQCumulants::CalculateDiffFlowCorrectedForNUA(TString type, TString ptOrEta)\r
{\r
 // Calculate differential flow corrected for non-uniform acceptance.\r
 \r
 // to be improved (rewritten completely)\r
 \r
 Int_t typeFlag = -1;\r
 Int_t ptEtaFlag = -1;\r
\r
 if(type == "RP")\r
 {\r
  typeFlag = 0;\r
 } else if(type == "POI")\r
   {\r
    typeFlag = 1;\r
   } \r
     \r
 if(ptOrEta == "Pt")\r
 {\r
  ptEtaFlag = 0;\r
 } else if(ptOrEta == "Eta")\r
   {\r
    ptEtaFlag = 1;\r
   } \r
  \r
 // shortcuts:\r
 Int_t t = typeFlag;\r
 Int_t pe = ptEtaFlag;\r
     \r
 // common:\r
 Int_t nBinsPtEta[2] = {fnBinsPt,fnBinsEta};\r
   \r
 // to be improved: access here generalized QC{2} and QC{4} instead: \r
 Double_t dV2 = fIntFlow->GetBinContent(1); \r
 Double_t dV4 = fIntFlow->GetBinContent(2); \r
 \r
 // loop over pt or eta bins:\r
 for(Int_t b=1;b<=nBinsPtEta[pe];b++)\r
 {\r
  // generalized QC{2'}:\r
  Double_t gQC2Prime = fDiffFlowCumulants[t][pe][0]->GetBinContent(b);\r
  // v'{2}:\r
  if(dV2>0)\r
  { \r
   Double_t v2Prime = gQC2Prime/dV2;\r
   fDiffFlow[t][pe][0]->SetBinContent(b,v2Prime); \r
  }  \r
  // generalized QC{4'}:\r
  Double_t gQC4Prime = fDiffFlowCumulants[t][pe][1]->GetBinContent(b);\r
  // v'{4}:\r
  if(dV4>0)\r
  { \r
   Double_t v4Prime = -gQC4Prime/pow(dV4,3.);\r
   fDiffFlow[t][pe][1]->SetBinContent(b,v4Prime); \r
  }  \r
 } // end of for(Int_t b=1;b<=fnBinsPtEta[pe];b++)\r
  \r
} // end of void AliFlowAnalysisWithQCumulants::CalculateDiffFlowCorrectedForNUA(TString type, TString ptOrEta); \r
\r
\r
//==================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::EvaluateIntFlowCorrelationsWithNestedLoops(AliFlowEventSimple* anEvent)\r
{\r
 // Evaluate with nested loops multiparticle correlations for integrated flow (without using the particle weights). \r
\r
 // Remark: Results are stored in profile fIntFlowDirectCorrelations whose binning is organized as follows:\r
 // \r
 //  1st bin: <2>_{1n|1n} = two1n1n = cos(n*(phi1-phi2))>\r
 //  2nd bin: <2>_{2n|2n} = two2n2n = cos(2n*(phi1-phi2))>\r
 //  3rd bin: <2>_{3n|3n} = two3n3n = cos(3n*(phi1-phi2))> \r
 //  4th bin: <2>_{4n|4n} = two4n4n = cos(4n*(phi1-phi2))>\r
 //  5th bin:           ----  EMPTY ----\r
 //  6th bin: <3>_{2n|1n,1n} = three2n1n1n = <cos(n*(2.*phi1-phi2-phi3))>\r
 //  7th bin: <3>_{3n|2n,1n} = three3n2n1n = <cos(n*(3.*phi1-2.*phi2-phi3))>\r
 //  8th bin: <3>_{4n|2n,2n} = three4n2n2n = <cos(n*(4.*phi1-2.*phi2-2.*phi3))>\r
 //  9th bin: <3>_{4n|3n,1n} = three4n3n1n = <cos(n*(4.*phi1-3.*phi2-phi3))>\r
 // 10th bin:           ----  EMPTY ----\r
 // 11th bin: <4>_{1n,1n|1n,1n} = four1n1n1n1n = <cos(n*(phi1+phi2-phi3-phi4))>\r
 // 12th bin: <4>_{2n,1n|2n,1n} = four2n1n2n1n = <cos(2.*n*(phi1+phi2-phi3-phi4))>\r
 // 13th bin: <4>_{2n,2n|2n,2n} = four2n2n2n2n = <cos(n*(2.*phi1+phi2-2.*phi3-phi4))>\r
 // 14th bin: <4>_{3n|1n,1n,1n} = four3n1n1n1n = <cos(n*(3.*phi1-phi2-phi3-phi4))> \r
 // 15th bin: <4>_{3n,1n|3n,1n} = four3n1n3n1n = <cos(n*(4.*phi1-2.*phi2-phi3-phi4))>\r
 // 16th bin: <4>_{3n,1n|2n,2n} = four3n1n2n2n = <cos(n*(3.*phi1+phi2-2.*phi3-2.*phi4))>\r
 // 17th bin: <4>_{4n|2n,1n,1n} = four4n2n1n1n = <cos(n*(3.*phi1+phi2-3.*phi3-phi4))> \r
 // 18th bin:           ----  EMPTY ----\r
 // 19th bin: <5>_{2n|1n,1n,1n,1n} = five2n1n1n1n1n = <cos(n*(2.*phi1+phi2-phi3-phi4-phi5))>\r
 // 20th bin: <5>_{2n,2n|2n,1n,1n} = five2n2n2n1n1n = <cos(n*(2.*phi1+2.*phi2-2.*phi3-phi4-phi5))>\r
 // 21st bin: <5>_{3n,1n|2n,1n,1n} = five3n1n2n1n1n = <cos(n*(3.*phi1+phi2-2.*phi3-phi4-phi5))>\r
 // 22nd bin: <5>_{4n|1n,1n,1n,1n} = five4n1n1n1n1n = <cos(n*(4.*phi1-phi2-phi3-phi4-phi5))>\r
 // 23rd bin:           ----  EMPTY ----\r
 // 24th bin: <6>_{1n,1n,1n|1n,1n,1n} = six1n1n1n1n1n1n = <cos(n*(phi1+phi2+phi3-phi4-phi5-phi6))>\r
 // 25th bin: <6>_{2n,1n,1n|2n,1n,1n} = six2n1n1n2n1n1n = <cos(n*(2.*phi1+2.*phi2-phi3-phi4-phi5-phi6))>\r
 // 26th bin: <6>_{2n,2n|1n,1n,1n,1n} = six2n2n1n1n1n1n = <cos(n*(3.*phi1+phi2-phi3-phi4-phi5-phi6))>\r
 // 27th bin: <6>_{3n,1n|1n,1n,1n,1n} = six3n1n1n1n1n1n = <cos(n*(2.*phi1+phi2+phi3-2.*phi4-phi5-phi6))>\r
 // 28th bin:           ----  EMPTY ----\r
 // 29th bin: <7>_{2n,1n,1n|1n,1n,1n,1n} = seven2n1n1n1n1n1n1n =  <cos(n*(2.*phi1+phi2+phi3-phi4-phi5-phi6-phi7))>\r
 // 30th bin:           ----  EMPTY ----\r
 // 31st bin: <8>_{1n,1n,1n,1n|1n,1n,1n,1n} = eight1n1n1n1n1n1n1n1n = <cos(n*(phi1+phi2+phi3+phi4-phi5-phi6-phi7-phi8))>\r
 \r
 Int_t nPrim = anEvent->NumberOfTracks(); \r
 AliFlowTrackSimple *aftsTrack = NULL; \r
 Double_t phi1=0., phi2=0., phi3=0., phi4=0., phi5=0., phi6=0., phi7=0., phi8=0.; \r
 Int_t n = fHarmonic; \r
 Int_t eventNo = (Int_t)fAvMultiplicity->GetBinEntries(1); // to be improved (is this casting safe in general?)\r
 Double_t dMult = (*fSMpk)(0,0);\r
 cout<<endl;\r
 cout<<"Multiparticle correlations: Event number: "<<eventNo<<", multiplicity is "<<dMult<<endl;\r
 if(dMult<2)\r
 {\r
  cout<<"... skipping this event (multiplicity too low) ..."<<endl;\r
 } else if (dMult>fMaxAllowedMultiplicity)\r
   {\r
    cout<<"... skipping this event (multiplicity too high) ..."<<endl;\r
   } else \r
     { \r
      cout<<"... evaluating nested loops (without using particle weights)..."<<endl;\r
     } \r
 \r
 // 2-particle correlations:       \r
 if(nPrim>=2 && nPrim<=fMaxAllowedMultiplicity)\r
 {\r
  for(Int_t i1=0;i1<nPrim;i1++)\r
  {\r
   aftsTrack=anEvent->GetTrack(i1);\r
   if(!(aftsTrack->InRPSelection())) continue;\r
   phi1=aftsTrack->Phi(); \r
   for(Int_t i2=0;i2<nPrim;i2++)\r
   {\r
    if(i2==i1)continue;\r
    aftsTrack=anEvent->GetTrack(i2);\r
    if(!(aftsTrack->InRPSelection())) continue;\r
    phi2=aftsTrack->Phi();\r
    if(nPrim==2) cout<<i1<<" "<<i2<<"\r"<<flush;\r
    // fill the profile with 2-p correlations: \r
    fIntFlowDirectCorrelations->Fill(0.5,cos(n*(phi1-phi2)),1.);    // <cos(n*(phi1-phi2))>\r
    fIntFlowDirectCorrelations->Fill(1.5,cos(2.*n*(phi1-phi2)),1.); // <cos(2n*(phi1-phi2))>\r
    fIntFlowDirectCorrelations->Fill(2.5,cos(3.*n*(phi1-phi2)),1.); // <cos(3n*(phi1-phi2))>\r
    fIntFlowDirectCorrelations->Fill(3.5,cos(4.*n*(phi1-phi2)),1.); // <cos(4n*(phi1-phi2))>   \r
   } // end of for(Int_t i2=0;i2<nPrim;i2++)\r
  } // end of for(Int_t i1=0;i1<nPrim;i1++)\r
 } // end of if(nPrim>=2)\r
 \r
 // 3-particle correlations:         \r
 if(nPrim>=3 && nPrim<=fMaxAllowedMultiplicity)\r
 {\r
  for(Int_t i1=0;i1<nPrim;i1++)\r
  {\r
   aftsTrack=anEvent->GetTrack(i1);\r
   if(!(aftsTrack->InRPSelection())) continue;\r
   phi1=aftsTrack->Phi();\r
   for(Int_t i2=0;i2<nPrim;i2++)\r
   {\r
    if(i2==i1)continue;\r
    aftsTrack=anEvent->GetTrack(i2);\r
    if(!(aftsTrack->InRPSelection())) continue;\r
    phi2=aftsTrack->Phi();\r
    for(Int_t i3=0;i3<nPrim;i3++)\r
    {\r
     if(i3==i1||i3==i2)continue;\r
     aftsTrack=anEvent->GetTrack(i3);\r
     if(!(aftsTrack->InRPSelection())) continue;\r
     phi3=aftsTrack->Phi();\r
     if(nPrim==3) cout<<i1<<" "<<i2<<" "<<i3<<"\r"<<flush;\r
     // fill the profile with 3-p correlations:   \r
     fIntFlowDirectCorrelations->Fill(5.,cos(2.*n*phi1-n*(phi2+phi3)),1.);       //<3>_{2n|nn,n}\r
     fIntFlowDirectCorrelations->Fill(6.,cos(3.*n*phi1-2.*n*phi2-n*phi3),1.);    //<3>_{3n|2n,n}\r
     fIntFlowDirectCorrelations->Fill(7.,cos(4.*n*phi1-2.*n*phi2-2.*n*phi3),1.); //<3>_{4n|2n,2n}\r
     fIntFlowDirectCorrelations->Fill(8.,cos(4.*n*phi1-3.*n*phi2-n*phi3),1.);    //<3>_{4n|3n,n}\r
    } // end of for(Int_t i3=0;i3<nPrim;i3++)\r
   } // end of for(Int_t i2=0;i2<nPrim;i2++)\r
  } // end of for(Int_t i1=0;i1<nPrim;i1++)\r
 } // end of if(nPrim>=3)\r
\r
 // 4-particle correlations:\r
 if(nPrim>=4 && nPrim<=fMaxAllowedMultiplicity)\r
 {       \r
  for(Int_t i1=0;i1<nPrim;i1++)\r
  { \r
   aftsTrack=anEvent->GetTrack(i1);\r
   if(!(aftsTrack->InRPSelection())) continue;\r
   phi1=aftsTrack->Phi();\r
   for(Int_t i2=0;i2<nPrim;i2++)\r
   {\r
    if(i2==i1)continue;\r
    aftsTrack=anEvent->GetTrack(i2);\r
    if(!(aftsTrack->InRPSelection())) continue;\r
    phi2=aftsTrack->Phi();\r
    for(Int_t i3=0;i3<nPrim;i3++)\r
    {\r
     if(i3==i1||i3==i2)continue;\r
     aftsTrack=anEvent->GetTrack(i3);\r
     if(!(aftsTrack->InRPSelection())) continue;\r
     phi3=aftsTrack->Phi();\r
     for(Int_t i4=0;i4<nPrim;i4++)\r
     {\r
      if(i4==i1||i4==i2||i4==i3)continue;\r
      aftsTrack=anEvent->GetTrack(i4);\r
      if(!(aftsTrack->InRPSelection())) continue;\r
      phi4=aftsTrack->Phi();\r
      if(nPrim==4) cout<<i1<<" "<<i2<<" "<<i3<<" "<<i4<<"\r"<<flush;\r
      // fill the profile with 4-p correlations:   \r
      fIntFlowDirectCorrelations->Fill(10.,cos(n*phi1+n*phi2-n*phi3-n*phi4),1.);            // <4>_{n,n|n,n} \r
      fIntFlowDirectCorrelations->Fill(11.,cos(2.*n*phi1+n*phi2-2.*n*phi3-n*phi4),1.);      // <4>_{2n,n|2n,n}\r
      fIntFlowDirectCorrelations->Fill(12.,cos(2.*n*phi1+2*n*phi2-2.*n*phi3-2.*n*phi4),1.); // <4>_{2n,2n|2n,2n}\r
      fIntFlowDirectCorrelations->Fill(13.,cos(3.*n*phi1-n*phi2-n*phi3-n*phi4),1.);         // <4>_{3n|n,n,n}\r
      fIntFlowDirectCorrelations->Fill(14.,cos(3.*n*phi1+n*phi2-3.*n*phi3-n*phi4),1.);      // <4>_{3n,n|3n,n}   \r
      fIntFlowDirectCorrelations->Fill(15.,cos(3.*n*phi1+n*phi2-2.*n*phi3-2.*n*phi4),1.);   // <4>_{3n,n|2n,2n}\r
      fIntFlowDirectCorrelations->Fill(16.,cos(4.*n*phi1-2.*n*phi2-n*phi3-n*phi4),1.);      // <4>_{4n|2n,n,n}     \r
     } // end of for(Int_t i4=0;i4<nPrim;i4++) \r
    } // end of for(Int_t i3=0;i3<nPrim;i3++)\r
   } // end of for(Int_t i2=0;i2<nPrim;i2++)\r
  } // end of for(Int_t i1=0;i1<nPrim;i1++)\r
 } // end of if(nPrim>=)\r
\r
 // 5-particle correlations:      \r
 if(nPrim>=5 && nPrim<=fMaxAllowedMultiplicity)\r
 {\r
  for(Int_t i1=0;i1<nPrim;i1++)\r
  {\r
   aftsTrack=anEvent->GetTrack(i1);\r
   if(!(aftsTrack->InRPSelection())) continue;  \r
   phi1=aftsTrack->Phi();\r
   for(Int_t i2=0;i2<nPrim;i2++)\r
   {\r
    if(i2==i1)continue;\r
    aftsTrack=anEvent->GetTrack(i2);\r
    if(!(aftsTrack->InRPSelection())) continue;\r
    phi2=aftsTrack->Phi();\r
    for(Int_t i3=0;i3<nPrim;i3++)\r
    {\r
     if(i3==i1||i3==i2)continue;\r
     aftsTrack=anEvent->GetTrack(i3);\r
     if(!(aftsTrack->InRPSelection())) continue;\r
     phi3=aftsTrack->Phi();\r
     for(Int_t i4=0;i4<nPrim;i4++)\r
     {\r
      if(i4==i1||i4==i2||i4==i3)continue;\r
      aftsTrack=anEvent->GetTrack(i4);\r
      if(!(aftsTrack->InRPSelection())) continue;\r
      phi4=aftsTrack->Phi();\r
      for(Int_t i5=0;i5<nPrim;i5++)\r
      {\r
       if(i5==i1||i5==i2||i5==i3||i5==i4)continue;\r
       aftsTrack=anEvent->GetTrack(i5);\r
       if(!(aftsTrack->InRPSelection())) continue;\r
       phi5=aftsTrack->Phi();\r
       if(nPrim==5) cout<<i1<<" "<<i2<<" "<<i3<<" "<<i4<<" "<<i5<<"\r"<<flush;\r
       // fill the profile with 5-p correlations:   \r
       fIntFlowDirectCorrelations->Fill(18.,cos(2.*n*phi1+n*phi2-n*phi3-n*phi4-n*phi5),1.);       //<5>_{2n,n|n,n,n}\r
       fIntFlowDirectCorrelations->Fill(19.,cos(2.*n*phi1+2.*n*phi2-2.*n*phi3-n*phi4-n*phi5),1.); //<5>_{2n,2n|2n,n,n}\r
       fIntFlowDirectCorrelations->Fill(20.,cos(3.*n*phi1+n*phi2-2.*n*phi3-n*phi4-n*phi5),1.);    //<5>_{3n,n|2n,n,n}\r
       fIntFlowDirectCorrelations->Fill(21.,cos(4.*n*phi1-n*phi2-n*phi3-n*phi4-n*phi5),1.);       //<5>_{4n|n,n,n,n}\r
      } // end of for(Int_t i5=0;i5<nPrim;i5++)\r
     } // end of for(Int_t i4=0;i4<nPrim;i4++)  \r
    } // end of for(Int_t i3=0;i3<nPrim;i3++)\r
   } // end of for(Int_t i2=0;i2<nPrim;i2++)\r
  } // end of for(Int_t i1=0;i1<nPrim;i1++)\r
 } // end of if(nPrim>=5)\r
  \r
 // 6-particle correlations:\r
 if(nPrim>=6 && nPrim<=fMaxAllowedMultiplicity)\r
 {\r
  for(Int_t i1=0;i1<nPrim;i1++)\r
  {\r
   aftsTrack=anEvent->GetTrack(i1);\r
   if(!(aftsTrack->InRPSelection())) continue;\r
   phi1=aftsTrack->Phi();\r
   for(Int_t i2=0;i2<nPrim;i2++)\r
   {\r
    if(i2==i1)continue;\r
    aftsTrack=anEvent->GetTrack(i2);\r
    if(!(aftsTrack->InRPSelection())) continue;\r
    phi2=aftsTrack->Phi();\r
    for(Int_t i3=0;i3<nPrim;i3++)\r
    {\r
     if(i3==i1||i3==i2)continue;\r
     aftsTrack=anEvent->GetTrack(i3);\r
     if(!(aftsTrack->InRPSelection())) continue;\r
     phi3=aftsTrack->Phi();\r
     for(Int_t i4=0;i4<nPrim;i4++)\r
     {\r
      if(i4==i1||i4==i2||i4==i3)continue;\r
      aftsTrack=anEvent->GetTrack(i4);\r
      if(!(aftsTrack->InRPSelection())) continue;\r
      phi4=aftsTrack->Phi();\r
      for(Int_t i5=0;i5<nPrim;i5++)\r
      {\r
       if(i5==i1||i5==i2||i5==i3||i5==i4)continue;\r
       aftsTrack=anEvent->GetTrack(i5);\r
       if(!(aftsTrack->InRPSelection())) continue;\r
       phi5=aftsTrack->Phi();\r
       for(Int_t i6=0;i6<nPrim;i6++)\r
       {\r
        if(i6==i1||i6==i2||i6==i3||i6==i4||i6==i5)continue;\r
        aftsTrack=anEvent->GetTrack(i6);\r
        if(!(aftsTrack->InRPSelection())) continue;\r
        phi6=aftsTrack->Phi(); \r
        if(nPrim==6) cout<<i1<<" "<<i2<<" "<<i3<<" "<<i4<<" "<<i5<<" "<<i6<<"\r"<<flush;\r
        // fill the profile with 6-p correlations:   \r
        fIntFlowDirectCorrelations->Fill(23.,cos(n*phi1+n*phi2+n*phi3-n*phi4-n*phi5-n*phi6),1.);       //<6>_{n,n,n|n,n,n}\r
        fIntFlowDirectCorrelations->Fill(24.,cos(2.*n*phi1+n*phi2+n*phi3-2.*n*phi4-n*phi5-n*phi6),1.); //<6>_{2n,n,n|2n,n,n}\r
        fIntFlowDirectCorrelations->Fill(25.,cos(2.*n*phi1+2.*n*phi2-n*phi3-n*phi4-n*phi5-n*phi6),1.); //<6>_{2n,2n|n,n,n,n}\r
        fIntFlowDirectCorrelations->Fill(26.,cos(3.*n*phi1+n*phi2-n*phi3-n*phi4-n*phi5-n*phi6),1.);    //<6>_{3n,n|n,n,n,n}  \r
       } // end of for(Int_t i6=0;i6<nPrim;i6++)\r
      } // end of for(Int_t i5=0;i5<nPrim;i5++)\r
     } // end of for(Int_t i4=0;i4<nPrim;i4++)\r
    } // end of for(Int_t i3=0;i3<nPrim;i3++)\r
   } // end of for(Int_t i2=0;i2<nPrim;i2++)\r
  } // end of for(Int_t i1=0;i1<nPrim;i1++)\r
 } // end of if(nPrim>=6)\r
  \r
 // 7-particle correlations:\r
 if(nPrim>=7 && nPrim<=fMaxAllowedMultiplicity)\r
 {\r
  for(Int_t i1=0;i1<nPrim;i1++)\r
  { \r
   aftsTrack=anEvent->GetTrack(i1);\r
   if(!(aftsTrack->InRPSelection())) continue;\r
   phi1=aftsTrack->Phi();\r
   for(Int_t i2=0;i2<nPrim;i2++)\r
   {\r
    if(i2==i1)continue;\r
    aftsTrack=anEvent->GetTrack(i2);\r
    if(!(aftsTrack->InRPSelection())) continue;\r
    phi2=aftsTrack->Phi();\r
    for(Int_t i3=0;i3<nPrim;i3++)\r
    {\r
     if(i3==i1||i3==i2)continue;\r
     aftsTrack=anEvent->GetTrack(i3);\r
     if(!(aftsTrack->InRPSelection())) continue;\r
     phi3=aftsTrack->Phi();\r
     for(Int_t i4=0;i4<nPrim;i4++)\r
     {\r
      if(i4==i1||i4==i2||i4==i3)continue;\r
      aftsTrack=anEvent->GetTrack(i4);\r
      if(!(aftsTrack->InRPSelection())) continue;\r
      phi4=aftsTrack->Phi();\r
      for(Int_t i5=0;i5<nPrim;i5++)\r
      {\r
       if(i5==i1||i5==i2||i5==i3||i5==i4)continue;\r
       aftsTrack=anEvent->GetTrack(i5);\r
       if(!(aftsTrack->InRPSelection())) continue;\r
       phi5=aftsTrack->Phi();\r
       for(Int_t i6=0;i6<nPrim;i6++)\r
       {\r
        if(i6==i1||i6==i2||i6==i3||i6==i4||i6==i5)continue;\r
        aftsTrack=anEvent->GetTrack(i6);\r
        if(!(aftsTrack->InRPSelection())) continue;\r
        phi6=aftsTrack->Phi(); \r
        for(Int_t i7=0;i7<nPrim;i7++)\r
        {\r
         if(i7==i1||i7==i2||i7==i3||i7==i4||i7==i5||i7==i6)continue;\r
         aftsTrack=anEvent->GetTrack(i7);\r
         if(!(aftsTrack->InRPSelection())) continue;\r
         phi7=aftsTrack->Phi(); \r
         if(nPrim==7) cout<<i1<<" "<<i2<<" "<<i3<<" "<<i4<<" "<<i5<<" "<<i6<<" "<<i7<<"\r"<<flush;\r
         // fill the profile with 7-p correlation:   \r
         fIntFlowDirectCorrelations->Fill(28.,cos(2.*n*phi1+n*phi2+n*phi3-n*phi4-n*phi5-n*phi6-n*phi7),1.); // <7>_{2n,n,n|n,n,n,n}\r
        } // end of for(Int_t i7=0;i7<nPrim;i7++)\r
       } // end of for(Int_t i6=0;i6<nPrim;i6++) \r
      } // end of for(Int_t i5=0;i5<nPrim;i5++)\r
     } // end of for(Int_t i4=0;i4<nPrim;i4++)  \r
    } // end of for(Int_t i3=0;i3<nPrim;i3++)\r
   } // end of for(Int_t i2=0;i2<nPrim;i2++)\r
  } // end of for(Int_t i1=0;i1<nPrim;i1++)\r
 } // end of if(nPrim>=7)\r
 \r
 // 8-particle correlations:\r
 if(nPrim>=8 && nPrim<=fMaxAllowedMultiplicity)\r
 {\r
  for(Int_t i1=0;i1<nPrim;i1++)\r
  {\r
   aftsTrack=anEvent->GetTrack(i1);\r
   if(!(aftsTrack->InRPSelection())) continue;\r
   phi1=aftsTrack->Phi();\r
   for(Int_t i2=0;i2<nPrim;i2++)\r
   {\r
    if(i2==i1)continue;\r
    aftsTrack=anEvent->GetTrack(i2);\r
    if(!(aftsTrack->InRPSelection())) continue;\r
    phi2=aftsTrack->Phi();\r
    for(Int_t i3=0;i3<nPrim;i3++)\r
    {\r
     if(i3==i1||i3==i2)continue;\r
     aftsTrack=anEvent->GetTrack(i3);\r
     if(!(aftsTrack->InRPSelection())) continue;\r
     phi3=aftsTrack->Phi();\r
     for(Int_t i4=0;i4<nPrim;i4++)\r
     {\r
      if(i4==i1||i4==i2||i4==i3)continue;\r
      aftsTrack=anEvent->GetTrack(i4);\r
      if(!(aftsTrack->InRPSelection())) continue;\r
      phi4=aftsTrack->Phi();\r
      for(Int_t i5=0;i5<nPrim;i5++)\r
      {\r
       if(i5==i1||i5==i2||i5==i3||i5==i4)continue;\r
       aftsTrack=anEvent->GetTrack(i5);\r
       if(!(aftsTrack->InRPSelection())) continue;\r
       phi5=aftsTrack->Phi();\r
       for(Int_t i6=0;i6<nPrim;i6++)\r
       {\r
        if(i6==i1||i6==i2||i6==i3||i6==i4||i6==i5)continue;\r
        aftsTrack=anEvent->GetTrack(i6);\r
        if(!(aftsTrack->InRPSelection())) continue;\r
        phi6=aftsTrack->Phi();\r
        for(Int_t i7=0;i7<nPrim;i7++)\r
        {\r
         if(i7==i1||i7==i2||i7==i3||i7==i4||i7==i5||i7==i6)continue;\r
         aftsTrack=anEvent->GetTrack(i7);\r
         if(!(aftsTrack->InRPSelection())) continue;\r
         phi7=aftsTrack->Phi();\r
         for(Int_t i8=0;i8<nPrim;i8++)\r
         {\r
          if(i8==i1||i8==i2||i8==i3||i8==i4||i8==i5||i8==i6||i8==i7)continue;\r
          aftsTrack=anEvent->GetTrack(i8);\r
          if(!(aftsTrack->InRPSelection())) continue;\r
          phi8=aftsTrack->Phi();\r
          cout<<i1<<" "<<i2<<" "<<i3<<" "<<i4<<" "<<i5<<" "<<i6<<" "<<i7<<" "<<i8<<"\r"<<flush;\r
          // fill the profile with 8-p correlation:   \r
          fIntFlowDirectCorrelations->Fill(30.,cos(n*phi1+n*phi2+n*phi3+n*phi4-n*phi5-n*phi6-n*phi7-n*phi8),1.); // <8>_{n,n,n,n|n,n,n,n}\r
         } // end of for(Int_t i8=0;i8<nPrim;i8++)\r
        } // end of for(Int_t i7=0;i7<nPrim;i7++) \r
       } // end of for(Int_t i6=0;i6<nPrim;i6++) \r
      } // end of for(Int_t i5=0;i5<nPrim;i5++)\r
     } // end of for(Int_t i4=0;i4<nPrim;i4++)  \r
    } // end of for(Int_t i3=0;i3<nPrim;i3++)\r
   } // end of for(Int_t i2=0;i2<nPrim;i2++)\r
  } // end of for(Int_t i1=0;i1<nPrim;i1++)\r
 } // end of if(nPrim>=8)\r
 \r
 cout<<endl;\r
\r
} // end of AliFlowAnalysisWithQCumulants::EvaluateIntFlowCorrelationsWithNestedLoops(AliFlowEventSimple* anEvent)\r
\r
\r
//==================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::CrossCheckIntFlowCorrelations()\r
{\r
 // Cross-check results for multiparticle correlations needed for int. flow: results from Q-vectors vs results from nested loops.\r
\r
 cout<<endl;\r
 cout<<endl;\r
 cout<<"   *****************************************"<<endl;\r
 cout<<"   **** cross-checking the correlations ****"<<endl;\r
 cout<<"   ****       for integrated flow       ****"<<endl;\r
 if(!(fUsePhiWeights||fUsePtWeights||fUseEtaWeights))\r
 {\r
  cout<<"   ****   (particle weights not used)   ****"<<endl;\r
 } else\r
   {\r
    cout<<"   ****     (particle weights used)     ****"<<endl;\r
   } \r
 cout<<"   *****************************************"<<endl;\r
 cout<<endl;\r
 cout<<endl;\r
\r
 Int_t ciMax = 32; // to be improved (removed eventually when I calculate 6th and 8th order with particle weights)\r
 \r
 if(fUsePhiWeights||fUsePtWeights||fUseEtaWeights)\r
 {\r
  ciMax = 11;\r
 }\r
\r
 for(Int_t ci=1;ci<=ciMax;ci++)\r
 {\r
  if(strcmp((fIntFlowCorrelationsAllPro->GetXaxis())->GetBinLabel(ci), "") == 0) continue; // to be improved (access finalized histogram here)\r
  cout<<(fIntFlowCorrelationsAllPro->GetXaxis())->GetBinLabel(ci)<<":"<<endl; // to be improved (access finalized histogram here)\r
  cout<<"from Q-vectors    = "<<fIntFlowCorrelationsAllPro->GetBinContent(ci)<<endl; // to be improved (access finalized histogram here)\r
  cout<<"from nested loops = "<<fIntFlowDirectCorrelations->GetBinContent(ci)<<endl;\r
  cout<<endl;\r
 }\r
  \r
} // end of void AliFlowAnalysisWithQCumulants::CrossCheckIntFlowCorrelations()\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::CrossCheckIntFlowCorrectionTermsForNUA()\r
{\r
 // Cross-check results for corrections terms for non-uniform acceptance needed for int. flow: results from Q-vectors vs results from nested loops.\r
\r
 cout<<endl;\r
 cout<<endl;\r
 cout<<"   *********************************************"<<endl;\r
 cout<<"   **** cross-checking the correction terms ****"<<endl;\r
 cout<<"   **** for non-uniform acceptance relevant ****"<<endl;\r
 cout<<"   ****         for integrated flow         ****"<<endl;\r
 if(!(fUsePhiWeights||fUsePtWeights||fUseEtaWeights))\r
 {\r
  cout<<"   ****     (particle weights not used)     ****"<<endl;\r
 } else\r
   {\r
    cout<<"   ****       (particle weights used)       ****"<<endl;\r
   } \r
 cout<<"   *********************************************"<<endl;\r
 cout<<endl;\r
 cout<<endl;\r
\r
 for(Int_t ci=1;ci<=10;ci++) // correction term index\r
 {\r
  for(Int_t sc=0;sc<2;sc++) // sin or cos term\r
  {\r
   if(strcmp((fIntFlowCorrectionTermsForNUAPro[sc]->GetXaxis())->GetBinLabel(ci), "") == 0) continue; // to be improved (access finalized histogram here)\r
   cout<<(fIntFlowCorrectionTermsForNUAPro[sc]->GetXaxis())->GetBinLabel(ci)<<":"<<endl; // to be improved (access finalized histogram here)\r
   cout<<"from Q-vectors    = "<<fIntFlowCorrectionTermsForNUAPro[sc]->GetBinContent(ci)<<endl; // to be improved (access finalized histogram here)
   cout<<"from nested loops = "<<fIntFlowDirectCorrectionTermsForNUA[sc]->GetBinContent(ci)<<endl;\r
   cout<<endl;\r
  } // end of for(Int_t sc=0;sc<2;sc++) // sin or cos term\r
 } // end of for(Int_t ci=1;ci<=10;ci++) // correction term index\r
  \r
} // end of void AliFlowAnalysisWithQCumulants::CrossCheckIntFlowCorrectionTermsForNUA() \r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::EvaluateIntFlowCorrelationsWithNestedLoopsUsingParticleWeights(AliFlowEventSimple* anEvent)\r
{\r
 // Evaluate with nested loops multiparticle correlations for integrated flow (using the particle weights). \r
\r
 // Results are stored in profile fIntFlowDirectCorrelations. \r
 // Remark 1: When particle weights are used the binning of fIntFlowDirectCorrelations is organized as follows:\r
 //\r
 //  1st bin: <2>_{1n|1n} = two1n1nW1W1 = <w1 w2 cos(n*(phi1-phi2))>\r
 //  2nd bin: <2>_{2n|2n} = two2n2nW2W2 = <w1^2 w2^2 cos(2n*(phi1-phi2))>\r
 //  3rd bin: <2>_{3n|3n} = two3n3nW3W3 = <w1^3 w2^3 cos(3n*(phi1-phi2))> \r
 //  4th bin: <2>_{4n|4n} = two4n4nW4W4 = <w1^4 w2^4 cos(4n*(phi1-phi2))>\r
 //  5th bin:           ----  EMPTY ----\r
 //  6th bin: <3>_{2n|1n,1n} = three2n1n1nW2W1W1 = <w1^2 w2 w3 cos(n*(2phi1-phi2-phi3))>\r
 //  7th bin: <3>_{3n|2n,1n} = ...\r
 //  8th bin: <3>_{4n|2n,2n} = ...\r
 //  9th bin: <3>_{4n|3n,1n} = ...\r
 // 10th bin:           ----  EMPTY ----\r
 // 11th bin: <4>_{1n,1n|1n,1n} = four1n1n1n1nW1W1W1W1 = <w1 w2 w3 w4 cos(n*(phi1+phi2-phi3-phi4))>\r
 // 12th bin: <4>_{2n,1n|2n,1n} = ...\r
 // 13th bin: <4>_{2n,2n|2n,2n} = ...\r
 // 14th bin: <4>_{3n|1n,1n,1n} = ... \r
 // 15th bin: <4>_{3n,1n|3n,1n} = ...\r
 // 16th bin: <4>_{3n,1n|2n,2n} = ...\r
 // 17th bin: <4>_{4n|2n,1n,1n} = ... \r
 // 18th bin:           ----  EMPTY ----\r
 // 19th bin: <5>_{2n|1n,1n,1n,1n} = ...\r
 // 20th bin: <5>_{2n,2n|2n,1n,1n} = ...\r
 // 21st bin: <5>_{3n,1n|2n,1n,1n} = ...\r
 // 22nd bin: <5>_{4n|1n,1n,1n,1n} = ...\r
 // 23rd bin:           ----  EMPTY ----\r
 // 24th bin: <6>_{1n,1n,1n|1n,1n,1n} = ...\r
 // 25th bin: <6>_{2n,1n,1n|2n,1n,1n} = ...\r
 // 26th bin: <6>_{2n,2n|1n,1n,1n,1n} = ...\r
 // 27th bin: <6>_{3n,1n|1n,1n,1n,1n} = ...\r
 // 28th bin:           ----  EMPTY ----\r
 // 29th bin: <7>_{2n,1n,1n|1n,1n,1n,1n} = ...\r
 // 30th bin:           ----  EMPTY ----\r
 // 31st bin: <8>_{1n,1n,1n,1n|1n,1n,1n,1n} = ...\r
 \r
 // Remark 2: When particle weights are used there are some extra correlations. They are stored in \r
 // fIntFlowExtraDirectCorrelations binning of which is organized as follows:\r
 \r
 // 1st bin: two1n1nW3W1 = <w1^3 w2 cos(n*(phi1-phi2))>\r
 // 2nd bin: two1n1nW1W1W2 = <w1 w2 w3^2 cos(n*(phi1-phi2))>  \r
 // ...\r
 \r
 Int_t nPrim = anEvent->NumberOfTracks(); \r
 AliFlowTrackSimple *aftsTrack = NULL;\r
 //Double_t phi1=0., phi2=0., phi3=0., phi4=0., phi5=0., phi6=0., phi7=0., phi8=0.;\r
 //Double_t wPhi1=1., wPhi2=1., wPhi3=1., wPhi4=1., wPhi5=1., wPhi6=1., wPhi7=1., wPhi8=1.;\r
 Double_t phi1=0., phi2=0., phi3=0., phi4=0.;\r
 Double_t wPhi1=1., wPhi2=1., wPhi3=1., wPhi4=1.;\r
 Int_t n = fHarmonic; \r
 Int_t eventNo = (Int_t)fAvMultiplicity->GetBinEntries(1); // to be improved (is this casting safe in general?)\r
 Double_t dMult = (*fSMpk)(0,0);\r
 cout<<endl;\r
 cout<<"Multiparticle correlations: Event number: "<<eventNo<<", multiplicity is "<<dMult<<endl;\r
 if(dMult<2)\r
 {\r
  cout<<"... skipping this event (multiplicity too low) ..."<<endl;\r
 } else if (dMult>fMaxAllowedMultiplicity)\r
   {\r
    cout<<"... skipping this event (multiplicity too high) ..."<<endl;\r
   } else \r
     { \r
      cout<<"... evaluating nested loops (using particle weights) ..."<<endl;\r
     } \r
      \r
 // 2-particle correlations:       \r
 if(nPrim>=2 && nPrim<=fMaxAllowedMultiplicity)\r
 {\r
  // 2 nested loops multiparticle correlations using particle weights:       \r
  for(Int_t i1=0;i1<nPrim;i1++)\r
  {\r
   aftsTrack=anEvent->GetTrack(i1);\r
   if(!(aftsTrack->InRPSelection())) continue;\r
   phi1=aftsTrack->Phi();\r
   if(fUsePhiWeights && fPhiWeights) wPhi1 = fPhiWeights->GetBinContent(1+(Int_t)(TMath::Floor(phi1*fnBinsPhi/TMath::TwoPi())));\r
   for(Int_t i2=0;i2<nPrim;i2++)\r
   {\r
    if(i2==i1)continue;\r
    aftsTrack=anEvent->GetTrack(i2);\r
    if(!(aftsTrack->InRPSelection())) continue;\r
    phi2=aftsTrack->Phi();\r
    if(fUsePhiWeights && fPhiWeights) wPhi2 = fPhiWeights->GetBinContent(1+(Int_t)(TMath::Floor(phi2*fnBinsPhi/TMath::TwoPi())));   \r
    if(nPrim==2) cout<<i1<<" "<<i2<<"\r"<<flush;\r
    // 2-p correlations using particle weights:\r
    if(fUsePhiWeights) fIntFlowDirectCorrelations->Fill(0.5,cos(n*(phi1-phi2)),wPhi1*wPhi2);                  // <w1   w2   cos( n*(phi1-phi2))>\r
    if(fUsePhiWeights) fIntFlowDirectCorrelations->Fill(1.5,cos(2.*n*(phi1-phi2)),pow(wPhi1,2)*pow(wPhi2,2)); // <w1^2 w2^2 cos(2n*(phi1-phi2))>\r
    if(fUsePhiWeights) fIntFlowDirectCorrelations->Fill(2.5,cos(3.*n*(phi1-phi2)),pow(wPhi1,3)*pow(wPhi2,3)); // <w1^3 w2^3 cos(3n*(phi1-phi2))>\r
    if(fUsePhiWeights) fIntFlowDirectCorrelations->Fill(3.5,cos(4.*n*(phi1-phi2)),pow(wPhi1,4)*pow(wPhi2,4)); // <w1^4 w2^4 cos(4n*(phi1-phi2))> \r
    // extra correlations: \r
    // 2-p extra correlations (do not appear if particle weights are not used):\r
    if(fUsePhiWeights) fIntFlowExtraDirectCorrelations->Fill(0.5,cos(n*(phi1-phi2)),pow(wPhi1,3)*wPhi2); // <w1^3 w2 cos(n*(phi1-phi2))>\r
    // ...\r
   } // end of for(Int_t i2=0;i2<nPrim;i2++)\r
  } // end of for(Int_t i1=0;i1<nPrim;i1++)\r
 } // end of if(nPrim>=2)\r
\r
 if(nPrim>=3 && nPrim<=fMaxAllowedMultiplicity)\r
 { \r
  // 3 nested loops multiparticle correlations using particle weights:       \r
  for(Int_t i1=0;i1<nPrim;i1++)\r
  {\r
   aftsTrack=anEvent->GetTrack(i1);\r
   if(!(aftsTrack->InRPSelection())) continue;\r
   phi1=aftsTrack->Phi();\r
   if(fUsePhiWeights && fPhiWeights) wPhi1 = fPhiWeights->GetBinContent(1+(Int_t)(TMath::Floor(phi1*fnBinsPhi/TMath::TwoPi())));\r
   for(Int_t i2=0;i2<nPrim;i2++)\r
   {\r
    if(i2==i1)continue;\r
    aftsTrack=anEvent->GetTrack(i2);\r
    if(!(aftsTrack->InRPSelection())) continue;\r
    phi2=aftsTrack->Phi();\r
    if(fUsePhiWeights && fPhiWeights) wPhi2 = fPhiWeights->GetBinContent(1+(Int_t)(TMath::Floor(phi2*fnBinsPhi/TMath::TwoPi())));\r
    for(Int_t i3=0;i3<nPrim;i3++)\r
    {\r
     if(i3==i1||i3==i2)continue;\r
     aftsTrack=anEvent->GetTrack(i3);\r
     if(!(aftsTrack->InRPSelection())) continue;\r
     phi3=aftsTrack->Phi();\r
     if(fUsePhiWeights && fPhiWeights) wPhi3 = fPhiWeights->GetBinContent(1+(Int_t)(TMath::Floor(phi3*fnBinsPhi/TMath::TwoPi())));\r
     if(nPrim==3) cout<<i1<<" "<<i2<<" "<<i3<<"\r"<<flush;\r
     // 3-p correlations using particle weights:\r
     if(fUsePhiWeights) fIntFlowDirectCorrelations->Fill(5.5,cos(2.*n*phi1-n*(phi2+phi3)),pow(wPhi1,2)*wPhi2*wPhi3); // <w1^2 w2 w3 cos(n*(2phi1-phi2-phi3))>\r
     // ...\r
     // extra correlations: \r
     // 2-p extra correlations (do not appear if particle weights are not used):\r
      if(fUsePhiWeights) fIntFlowExtraDirectCorrelations->Fill(1.5,cos(n*(phi1-phi2)),wPhi1*wPhi2*pow(wPhi3,2)); // <w1 w2 w3^2 cos(n*(phi1-phi2))>\r
     // ...\r
     // 3-p extra correlations (do not appear if particle weights are not used):\r
     // ...\r
    } // end of for(Int_t i3=0;i3<nPrim;i3++)\r
   } // end of for(Int_t i2=0;i2<nPrim;i2++)\r
  } // end of for(Int_t i1=0;i1<nPrim;i1++)\r
 } // end of if(nPrim>=3)\r
 \r
 if(nPrim>=4 && nPrim<=fMaxAllowedMultiplicity)\r
 {\r
  // 4 nested loops multiparticle correlations using particle weights:       \r
  for(Int_t i1=0;i1<nPrim;i1++)\r
  {\r
   aftsTrack=anEvent->GetTrack(i1);\r
   if(!(aftsTrack->InRPSelection())) continue;\r
   phi1=aftsTrack->Phi();\r
   if(fUsePhiWeights && fPhiWeights) wPhi1 = fPhiWeights->GetBinContent(1+(Int_t)(TMath::Floor(phi1*fnBinsPhi/TMath::TwoPi())));\r
   for(Int_t i2=0;i2<nPrim;i2++)\r
   {\r
    if(i2==i1)continue;\r
    aftsTrack=anEvent->GetTrack(i2);\r
    if(!(aftsTrack->InRPSelection())) continue;\r
    phi2=aftsTrack->Phi();\r
    if(fUsePhiWeights && fPhiWeights) wPhi2 = fPhiWeights->GetBinContent(1+(Int_t)(TMath::Floor(phi2*fnBinsPhi/TMath::TwoPi())));\r
    for(Int_t i3=0;i3<nPrim;i3++)\r
    {\r
     if(i3==i1||i3==i2)continue;\r
     aftsTrack=anEvent->GetTrack(i3);\r
     if(!(aftsTrack->InRPSelection())) continue;\r
     phi3=aftsTrack->Phi();\r
     if(fUsePhiWeights && fPhiWeights) wPhi3 = fPhiWeights->GetBinContent(1+(Int_t)(TMath::Floor(phi3*fnBinsPhi/TMath::TwoPi())));\r
     for(Int_t i4=0;i4<nPrim;i4++)\r
     {\r
      if(i4==i1||i4==i2||i4==i3)continue;\r
      aftsTrack=anEvent->GetTrack(i4);\r
      if(!(aftsTrack->InRPSelection())) continue;\r
      phi4=aftsTrack->Phi();\r
      if(fUsePhiWeights && fPhiWeights) wPhi4 = fPhiWeights->GetBinContent(1+(Int_t)(TMath::Floor(phi4*fnBinsPhi/TMath::TwoPi())));\r
      if(nPrim>=4) cout<<i1<<" "<<i2<<" "<<i3<<" "<<i4<<"\r"<<flush; // to be improved (replace eventually this if statement with if(nPrim==4))\r
      // 4-p correlations using particle weights:\r
      if(fUsePhiWeights) fIntFlowDirectCorrelations->Fill(10.5,cos(n*phi1+n*phi2-n*phi3-n*phi4),wPhi1*wPhi2*wPhi3*wPhi4); \r
      // extra correlations: \r
      // 2-p extra correlations (do not appear if particle weights are not used):\r
      // ...\r
      // 3-p extra correlations (do not appear if particle weights are not used):\r
      // ...\r
      // 4-p extra correlations (do not appear if particle weights are not used):\r
      // ...\r
     } // end of for(Int_t i4=0;i4<nPrim;i4++) \r
    } // end of for(Int_t i3=0;i3<nPrim;i3++)\r
   } // end of for(Int_t i2=0;i2<nPrim;i2++)\r
  } // end of for(Int_t i1=0;i1<nPrim;i1++)\r
 } // end of if(nPrim>=4)\r
\r
 cout<<endl; \r
\r
} // end of void AliFlowAnalysisWithQCumulants::EvaluateIntFlowCorrelationsWithNestedLoopsUsingParticleWeights(AliFlowEventSimple* anEvent)\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::CrossCheckIntFlowExtraCorrelations()\r
{\r
 // Cross-check results for extra multiparticle correlations needed for int. flow \r
 // which appear only when particle weights are used: results from Q-vectors vs results from nested loops.\r
\r
 cout<<endl;\r
 cout<<endl;\r
 cout<<"   ***********************************************"<<endl;\r
 cout<<"   **** cross-checking the extra correlations ****"<<endl;\r
 cout<<"   ****          for integrated flow          ****"<<endl;\r
 cout<<"   ***********************************************"<<endl;\r
 cout<<endl;\r
 cout<<endl;\r
 \r
 for(Int_t eci=1;eci<=2;eci++) // to be improved (increased eciMax eventually when I calculate 6th and 8th)\r
 {\r
  if(strcmp((fIntFlowExtraCorrelationsPro->GetXaxis())->GetBinLabel(eci), "") == 0) continue;\r
  cout<<(fIntFlowExtraCorrelationsPro->GetXaxis())->GetBinLabel(eci)<<":"<<endl;\r
  cout<<"from Q-vectors    = "<<fIntFlowExtraCorrelationsPro->GetBinContent(eci)<<endl;\r
  cout<<"from nested loops = "<<fIntFlowExtraDirectCorrelations->GetBinContent(eci)<<endl;\r
  cout<<endl;\r
 }\r
\r
} // end of void AliFlowAnalysisWithQCumulants::CrossCheckIntFlowExtraCorrelations()\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::EvaluateIntFlowCorrectionsForNUAWithNestedLoops(AliFlowEventSimple* anEvent)\r
{\r
 // Evaluate with nested loops correction terms for non-uniform acceptance relevant for NONAME integrated flow (to be improved (name)).\r
 //\r
 // Remark: Both sin and cos correction terms are calculated in this method. Sin terms are stored in fIntFlowDirectCorrectionTermsForNUA[0],\r
 // and cos terms in fIntFlowDirectCorrectionTermsForNUA[1]. Binning of fIntFlowDirectCorrectionTermsForNUA[sc] is organized as follows \r
 // (sc stands for either sin or cos):\r
 \r
 //  1st bin: <<sc(n*(phi1))>> \r
 //  2nd bin: <<sc(n*(phi1+phi2))>> \r
 //  3rd bin: <<sc(n*(phi1-phi2-phi3))>>\r
 //  4th bin: <<sc(n*(2phi1-phi2))>>\r
 \r
 Int_t nPrim = anEvent->NumberOfTracks(); \r
 AliFlowTrackSimple *aftsTrack = NULL;\r
 Double_t phi1=0., phi2=0., phi3=0.;\r
 Int_t n = fHarmonic; \r
 Int_t eventNo = (Int_t)fAvMultiplicity->GetBinEntries(1); // to be improved (is this casting safe in general?)\r
 Double_t dMult = (*fSMpk)(0,0);\r
 cout<<endl;\r
 cout<<"Correction terms for non-uniform acceptance: Event number: "<<eventNo<<", multiplicity is "<<dMult<<endl;\r
 if(dMult<1)\r
 {\r
  cout<<"... skipping this event (multiplicity too low) ..."<<endl;\r
 } else if (dMult>fMaxAllowedMultiplicity)\r
   {\r
    cout<<"... skipping this event (multiplicity too high) ..."<<endl;\r
   } else \r
     { \r
      cout<<"... evaluating nested loops (without using particle weights)..."<<endl;\r
     }\r
 \r
 if(nPrim>=1 && nPrim<=fMaxAllowedMultiplicity)\r
 {\r
  // 1-particle correction terms for non-uniform acceptance:       \r
  for(Int_t i1=0;i1<nPrim;i1++)\r
  {\r
   aftsTrack=anEvent->GetTrack(i1);\r
   if(!(aftsTrack->InRPSelection())) continue;\r
   phi1=aftsTrack->Phi();\r
   if(nPrim==1) cout<<i1<<"\r"<<flush;\r
   // sin terms:\r
   fIntFlowDirectCorrectionTermsForNUA[0]->Fill(0.5,sin(n*phi1),1.); // <sin(n*phi1)>  \r
   // cos terms:\r
   fIntFlowDirectCorrectionTermsForNUA[1]->Fill(0.5,cos(n*phi1),1.); // <cos(n*phi1)>\r
  } // end of for(Int_t i1=0;i1<nPrim;i1++)\r
 } // end of if(nPrim>=1) \r
  \r
 if(nPrim>=2 && nPrim<=fMaxAllowedMultiplicity)\r
 {\r
  // 2-particle correction terms for non-uniform acceptance:       \r
  for(Int_t i1=0;i1<nPrim;i1++)\r
  {\r
   aftsTrack=anEvent->GetTrack(i1);\r
   if(!(aftsTrack->InRPSelection())) continue;\r
   phi1=aftsTrack->Phi();  \r
   for(Int_t i2=0;i2<nPrim;i2++)\r
   {\r
    if(i2==i1)continue;\r
    aftsTrack=anEvent->GetTrack(i2);\r
    if(!(aftsTrack->InRPSelection())) continue;\r
    phi2=aftsTrack->Phi();\r
    if(nPrim==2) cout<<i1<<" "<<i2<<"\r"<<flush;\r
    // sin terms:\r
    fIntFlowDirectCorrectionTermsForNUA[0]->Fill(1.5,sin(n*(phi1+phi2)),1.); // <<sin(n*(phi1+phi2))>>
    fIntFlowDirectCorrectionTermsForNUA[0]->Fill(3.5,sin(n*(2*phi1-phi2)),1.); // <<sin(n*(2*phi1-phi2))>>\r
    // cos terms:\r
    fIntFlowDirectCorrectionTermsForNUA[1]->Fill(1.5,cos(n*(phi1+phi2)),1.); // <<cos(n*(phi1+phi2))>>
    fIntFlowDirectCorrectionTermsForNUA[1]->Fill(3.5,cos(n*(2*phi1-phi2)),1.); // <<cos(n*(2*phi1-phi2))>>\r
   } // end of for(Int_t i2=0;i2<nPrim;i2++)\r
  } // end of for(Int_t i1=0;i1<nPrim;i1++)\r
 } // end of if(nPrim>=2)\r
\r
 if(nPrim>=3 && nPrim<=fMaxAllowedMultiplicity)\r
 {\r
  // 3-particle correction terms for non-uniform acceptance:       \r
  for(Int_t i1=0;i1<nPrim;i1++)\r
  {\r
   aftsTrack=anEvent->GetTrack(i1);\r
   if(!(aftsTrack->InRPSelection())) continue;\r
   phi1=aftsTrack->Phi();\r
   for(Int_t i2=0;i2<nPrim;i2++)\r
   {\r
    if(i2==i1)continue;\r
    aftsTrack=anEvent->GetTrack(i2);\r
    if(!(aftsTrack->InRPSelection())) continue;\r
    phi2=aftsTrack->Phi();\r
    for(Int_t i3=0;i3<nPrim;i3++)\r
    {\r
     if(i3==i1||i3==i2)continue;\r
     aftsTrack=anEvent->GetTrack(i3);\r
     if(!(aftsTrack->InRPSelection())) continue;\r
     phi3=aftsTrack->Phi();\r
     if(nPrim>=3) cout<<i1<<" "<<i2<<" "<<i3<<"\r"<<flush; // to be improved (eventually I will change this if statement)\r
     // sin terms:\r
     fIntFlowDirectCorrectionTermsForNUA[0]->Fill(2.5,sin(n*(phi1-phi2-phi3)),1.); // <<sin(n*(phi1-phi2-phi3))>>\r
     // cos terms:\r
     fIntFlowDirectCorrectionTermsForNUA[1]->Fill(2.5,cos(n*(phi1-phi2-phi3)),1.); // <<cos(n*(phi1-phi2-phi3))>>\r
    } // end of for(Int_t i3=0;i3<nPrim;i3++)\r
   } // end of for(Int_t i2=0;i2<nPrim;i2++)\r
  } // end of for(Int_t i1=0;i1<nPrim;i1++)\r
 } // end of if(nPrim>=3)\r
\r
 cout<<endl;\r
}\r
//================================================================================================================================\r
void AliFlowAnalysisWithQCumulants::EvaluateDiffFlowCorrelationsWithNestedLoops(AliFlowEventSimple* anEvent, TString type, TString ptOrEta)\r
{\r
 // Evaluate reduced correlations with nested loops without using the particle weights.\r
 \r
 // Remark 1: Reduced correlations are evaluated in pt bin number fCrossCheckInPtBinNo and eta bin number fCrossCheckInEtaBinNo both for RPs and POIs.\r
 // Remark 2: Results are stored in 1 bin profiles fDiffFlowDirectCorrelations[t][pe][ci], where indices runs as follows:\r
 //           [0=RP,1=POI][0=Pt,1=Eta][0=<2'>,1=<4'>,2=<6'>,3=<8'>] \r
 // Remark 3: <2'> = <cos(n*(psi1-phi2))>\r
 //           <4'> = <cos(n*(psi1+phi2-phi3-phi4))>\r
 // ...\r
 \r
 Int_t typeFlag = -1;\r
 Int_t ptEtaFlag = -1;\r
 if(type == "RP")\r
 {\r
  typeFlag = 0;\r
 } else if(type == "POI")\r
   {\r
    typeFlag = 1;\r
   }      \r
 if(ptOrEta == "Pt")\r
 {\r
  ptEtaFlag = 0;\r
 } else if(ptOrEta == "Eta")\r
   {\r
    ptEtaFlag = 1;\r
   } \r
 // shortcuts:\r
 Int_t t = typeFlag;\r
 Int_t pe = ptEtaFlag;\r
      \r
 Double_t lowerPtEtaEdge[2] = {fPtMin+(fCrossCheckInPtBinNo-1)*fPtBinWidth,fEtaMin+(fCrossCheckInEtaBinNo-1)*fEtaBinWidth};\r
 Double_t upperPtEtaEdge[2] = {fPtMin+fCrossCheckInPtBinNo*fPtBinWidth,fEtaMin+fCrossCheckInEtaBinNo*fEtaBinWidth};\r
 Double_t binWidthPtEta[2] = {fPtBinWidth,fEtaBinWidth};\r
 \r
 Int_t nPrim = anEvent->NumberOfTracks(); \r
 AliFlowTrackSimple *aftsTrack = NULL;\r
 \r
 Double_t psi1=0., phi2=0., phi3=0., phi4=0.;// phi5=0., phi6=0., phi7=0., phi8=0.;\r
 \r
 Int_t n = fHarmonic; 
  \r
 // 2'-particle correlations:\r
 for(Int_t i1=0;i1<nPrim;i1++)\r
 {\r
  aftsTrack=anEvent->GetTrack(i1);\r
  // POI condition (first particle in the correlator must be POI): // to be improved (this can be implemented much better)
  if(typeFlag==1) // this is diff flow of POIs 
  {\r
   if(ptOrEta == "Pt")\r
   { \r
    if(!((aftsTrack->Pt()>=lowerPtEtaEdge[pe] && aftsTrack->Pt()<upperPtEtaEdge[pe]) && (aftsTrack->InPOISelection())))continue;\r
   } else if (ptOrEta == "Eta")\r
     {\r
      if(!((aftsTrack->Eta()>=lowerPtEtaEdge[pe] && aftsTrack->Eta()<upperPtEtaEdge[pe]) && (aftsTrack->InPOISelection())))continue;    \r
     }
  } else // this is diff flow of RPs 
    {
     if(ptOrEta == "Pt")\r
     { \r
      if(!((aftsTrack->Pt()>=lowerPtEtaEdge[pe] && aftsTrack->Pt()<upperPtEtaEdge[pe]) && (aftsTrack->InRPSelection())))continue;\r
     } else if (ptOrEta == "Eta")\r
       {\r
        if(!((aftsTrack->Eta()>=lowerPtEtaEdge[pe] && aftsTrack->Eta()<upperPtEtaEdge[pe]) && (aftsTrack->InRPSelection())))continue;    \r
       }
    }
       \r
  psi1=aftsTrack->Phi(); \r
  for(Int_t i2=0;i2<nPrim;i2++)\r
  {\r
   if(i2==i1)continue;\r
   aftsTrack=anEvent->GetTrack(i2);\r
   // RP condition (!(first) particle in the correlator must be RP):\r
   if(!(aftsTrack->InRPSelection()))continue;\r
   phi2=aftsTrack->Phi();   \r
   // 2'-particle correlations: \r
   fDiffFlowDirectCorrelations[t][pe][0]->Fill(lowerPtEtaEdge[pe]+binWidthPtEta[pe]/2.,cos(1.*n*(psi1-phi2)),1.); // <cos(n*(psi1-phi2))  \r
  }//end of for(Int_t i2=0;i2<nPrim;i2++)\r
 }//end of for(Int_t i1=0;i1<nPrim;i1++)\r
 \r
 /*\r
 \r
 // 3'-particle correlations:\r
 for(Int_t i1=0;i1<nPrim;i1++)\r
 {\r
  aftsTrack=anEvent->GetTrack(i1);\r
  // POI condition (first particle in the correlator must be POI): // to be improved (this can be implemented much better)\r
  if(ptOrEta == "Pt")\r
  { \r
   if(!((aftsTrack->Pt()>=lowerPtEtaEdge[pe] && aftsTrack->Pt()<upperPtEtaEdge[pe]) && (aftsTrack->InPOISelection())))continue;\r
  } else if (ptOrEta == "Eta")\r
    {\r
     if(!((aftsTrack->Eta()>=lowerPtEtaEdge[pe] && aftsTrack->Eta()<upperPtEtaEdge[pe]) && (aftsTrack->InPOISelection())))continue;    \r
    }\r
  psi1=aftsTrack->Phi();\r
  for(Int_t i2=0;i2<nPrim;i2++)\r
  {\r
   if(i2==i1)continue;\r
   aftsTrack=anEvent->GetTrack(i2);\r
   // RP condition (!(first) particle in the correlator must be RP):\r
   if(!(aftsTrack->InRPSelection())) continue;\r
   phi2=aftsTrack->Phi();\r
   for(Int_t i3=0;i3<nPrim;i3++)\r
   {\r
    if(i3==i1||i3==i2)continue;\r
    aftsTrack=anEvent->GetTrack(i3);\r
    // RP condition (!(first) particle in the correlator must be RP):\r
    if(!(aftsTrack->InRPSelection())) continue;\r
    phi3=aftsTrack->Phi();\r
    // to be improved : where to store it? ->Fill(lowerPtEtaEdge[pe]+binWidthPtEta[pe]/2.,cos(n*(2.*phi1-phi2-phi3)),1.); // <w1 w2 w3 cos(n(2psi1-phi2-phi3))> \r
   }//end of for(Int_t i3=0;i3<nPrim;i3++)  \r
  }//end of for(Int_t i2=0;i2<nPrim;i2++)  \r
 }//end of for(Int_t i1=0;i1<nPrim;i1++)\r
 \r
 */\r
 \r
 // 4'-particle correlations:\r
 for(Int_t i1=0;i1<nPrim;i1++)\r
 {\r
  aftsTrack=anEvent->GetTrack(i1);\r
  // POI condition (first particle in the correlator must be POI): // to be improved (this can be implemented much better)
  if(typeFlag==1) // this is diff flow of POIs 
  {\r
   if(ptOrEta == "Pt")\r
   { \r
    if(!((aftsTrack->Pt()>=lowerPtEtaEdge[pe] && aftsTrack->Pt()<upperPtEtaEdge[pe]) && (aftsTrack->InPOISelection())))continue;\r
   } else if (ptOrEta == "Eta")\r
     {\r
      if(!((aftsTrack->Eta()>=lowerPtEtaEdge[pe] && aftsTrack->Eta()<upperPtEtaEdge[pe]) && (aftsTrack->InPOISelection())))continue;    \r
     }
  } else // this is diff flow of RPs 
    {
     if(ptOrEta == "Pt")\r
     { \r
      if(!((aftsTrack->Pt()>=lowerPtEtaEdge[pe] && aftsTrack->Pt()<upperPtEtaEdge[pe]) && (aftsTrack->InRPSelection())))continue;\r
     } else if (ptOrEta == "Eta")\r
       {\r
        if(!((aftsTrack->Eta()>=lowerPtEtaEdge[pe] && aftsTrack->Eta()<upperPtEtaEdge[pe]) && (aftsTrack->InRPSelection())))continue;    \r
       }
    }
    \r
  psi1=aftsTrack->Phi();\r
  for(Int_t i2=0;i2<nPrim;i2++)\r
  {\r
   if(i2==i1) continue;\r
   aftsTrack=anEvent->GetTrack(i2);\r
   // RP condition (!(first) particle in the correlator must be RP): \r
   if(!(aftsTrack->InRPSelection())) continue;\r
   phi2=aftsTrack->Phi();\r
   for(Int_t i3=0;i3<nPrim;i3++)\r
   { \r
    if(i3==i1||i3==i2) continue;\r
    aftsTrack=anEvent->GetTrack(i3);\r
    // RP condition (!(first) particle in the correlator must be RP):\r
    if(!(aftsTrack->InRPSelection())) continue;\r
    phi3=aftsTrack->Phi();\r
    for(Int_t i4=0;i4<nPrim;i4++)\r
    {\r
     if(i4==i1||i4==i2||i4==i3) continue;\r
     aftsTrack=anEvent->GetTrack(i4);\r
     // RP condition (!(first) particle in the correlator must be RP):\r
     if(!(aftsTrack->InRPSelection())) continue;  \r
     phi4=aftsTrack->Phi();\r
     // 4'-particle correlations:\r
     fDiffFlowDirectCorrelations[t][pe][1]->Fill(lowerPtEtaEdge[pe]+binWidthPtEta[pe]/2.,cos(n*(psi1+phi2-phi3-phi4)),1.); // <cos(n(psi1+phi2-phi3-phi4))>     \r
    }//end of for(Int_t i4=0;i4<nPrim;i4++)\r
   }//end of for(Int_t i3=0;i3<nPrim;i3++)\r
  }//end of for(Int_t i2=0;i2<nPrim;i2++) \r
 }//end of for(Int_t i1=0;i1<nPrim;i1++)\r
      \r
 // count # of RPs and POIs in selected pt and eta bins for cross-checkings:\r
 for(Int_t i=0;i<nPrim;i++)
 {
  aftsTrack=anEvent->GetTrack(i); 
  // POI condition (first particle in the correlator must be POI): // to be improved (this can be implemented much better)
  if(typeFlag==1) // this is diff flow of POIs 
  {\r
   if(ptOrEta == "Pt")\r
   { \r
    if(!((aftsTrack->Pt()>=lowerPtEtaEdge[pe] && aftsTrack->Pt()<upperPtEtaEdge[pe]) && (aftsTrack->InPOISelection())))continue;\r
   } else if (ptOrEta == "Eta")\r
     {\r
      if(!((aftsTrack->Eta()>=lowerPtEtaEdge[pe] && aftsTrack->Eta()<upperPtEtaEdge[pe]) && (aftsTrack->InPOISelection())))continue;    \r
     }
  } else // this is diff flow of RPs 
    {
     if(ptOrEta == "Pt")\r
     { \r
      if(!((aftsTrack->Pt()>=lowerPtEtaEdge[pe] && aftsTrack->Pt()<upperPtEtaEdge[pe]) && (aftsTrack->InRPSelection())))continue;\r
     } else if (ptOrEta == "Eta")\r
       {\r
        if(!((aftsTrack->Eta()>=lowerPtEtaEdge[pe] && aftsTrack->Eta()<upperPtEtaEdge[pe]) && (aftsTrack->InRPSelection())))continue;    \r
       }
    }
  if(t==1)t++; 
  fNoOfParticlesInBin->Fill(t+pe+0.5);  
 }\r
\r
} // end of void AliFlowAnalysisWithQCumulants::EvaluateDiffFlowCorrelationsWithNestedLoops(AliFlowEventSimple* anEvent, TString type, TString ptOrEta)\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::CrossCheckDiffFlowCorrelations(TString type, TString ptOrEta)\r
{\r
 // Compare correlations needed for diff. flow calculated with nested loops and those calculated from Q-vectors\r
 \r
 Int_t typeFlag = -1;\r
 Int_t ptEtaFlag = -1;\r
 if(type == "RP")\r
 {\r
  typeFlag = 0;\r
 } else if(type == "POI")\r
   {\r
    typeFlag = 1;\r
   }      \r
 if(ptOrEta == "Pt")\r
 {\r
  ptEtaFlag = 0;\r
 } else if(ptOrEta == "Eta")\r
   {\r
    ptEtaFlag = 1;\r
   } \r
 // shortcuts:\r
 Int_t t = typeFlag;\r
 Int_t pe = ptEtaFlag;\r
      \r
 TString rpORpoiString[2] = {"RP ","POI"}; // to be improved (name in the same way as in the other methods, eventually promote to data member) \r
 TString ptORetaString[2] = {"pt","eta"}; // to be improved (name in the same way as in the other methods, eventually promote to data member) \r
 TString reducedCorrelations[4] = {"<<cos(n(psi1-phi2))>>","<<cos(n(psi1+phi2-phi3-phi4))>>","",""}; // to be improved (access this from pro or hist)\r
 Double_t lowerPtEtaEdge[2] = {fPtMin+(fCrossCheckInPtBinNo-1)*fPtBinWidth,fEtaMin+(fCrossCheckInEtaBinNo-1)*fEtaBinWidth};\r
 Double_t upperPtEtaEdge[2] = {fPtMin+fCrossCheckInPtBinNo*fPtBinWidth,fEtaMin+fCrossCheckInEtaBinNo*fEtaBinWidth};\r
 \r
 Int_t crossCheckInPtEtaBinNo[2] = {fCrossCheckInPtBinNo,fCrossCheckInEtaBinNo};\r
 \r
\r
 cout<<endl;\r
 cout<<"   *****************************************"<<endl;\r
 cout<<"   **** cross-checking the correlations ****"<<endl;\r
 cout<<"   ****   for differential flow ("<<rpORpoiString[t]<<")   ****"<<endl;\r
 if(!(fUsePhiWeights||fUsePtWeights||fUseEtaWeights))\r
 {\r
  cout<<"   ****   (particle weights not used)   ****"<<endl;\r
 } else\r
   {\r
    cout<<"   ****    (particle weights used)      ****"<<endl;\r
   } \r
 cout<<"   *****************************************"<<endl; \r
 cout<<endl;\r
 cout<<"           "<<ptORetaString[pe]<<" bin: "<<lowerPtEtaEdge[pe]<<" <= "<<ptORetaString[pe]<<" < "<<upperPtEtaEdge[pe]<<endl;\r
 cout<<endl;\r
 \r
 for(Int_t rci=0;rci<2;rci++) // to be improved (calculate 6th and 8th order)\r
 {\r
  cout<<"      "<<reducedCorrelations[rci].Data()<<":"<<endl;\r
  cout<<"      from Q-vectors    = "<<fDiffFlowCorrelationsPro[t][pe][rci]->GetBinContent(crossCheckInPtEtaBinNo[pe])<<endl;\r
  cout<<"      from nested loops = "<<fDiffFlowDirectCorrelations[t][pe][rci]->GetBinContent(1)<<endl;\r
  cout<<endl;  \r
 } // end of for(Int_t rci=0;rci<4;rci++)\r
        \r
} // end of void AliFlowAnalysisWithQCumulants::CrossCheckDiffFlowCorrelations(TString type, TString ptOrEta)\r
\r
//================================================================================================================================

void AliFlowAnalysisWithQCumulants::PrintNumberOfParticlesInSelectedBin()\r
{
 // Print on the screen number of RPs and POIs in selected pt and eta bin for cross checkings.
 
 cout<<endl;
 cout<<"Number of RPs in selected pt bin   = "<<fNoOfParticlesInBin->GetBinContent(1)<<endl;
 cout<<"Number of RPs in selected eta bin  = "<<fNoOfParticlesInBin->GetBinContent(2)<<endl;
 cout<<"Number of POIs in selected pt bin  = "<<fNoOfParticlesInBin->GetBinContent(3)<<endl;
 cout<<"Number of POIs in selected eta bin = "<<fNoOfParticlesInBin->GetBinContent(4)<<endl;
 
} // end of void AliFlowAnalysisWithQCumulants::PrintNumberOfParticlesInSelectedBin()\r
\r
//================================================================================================================================

void AliFlowAnalysisWithQCumulants::EvaluateDiffFlowCorrelationsWithNestedLoopsUsingParticleWeights(AliFlowEventSimple* anEvent, TString type, TString ptOrEta)\r
{\r
 // Evaluate reduced correlations with nested loops without using the particle weights.\r
 \r
 // Remark 1: Reduced correlations are evaluated in pt bin number fCrossCheckInPtBinNo and eta bin number fCrossCheckInEtaBinNo both for RPs and POIs.\r
 // Remark 2: Results are stored in 1 bin profiles fDiffFlowDirectCorrelations[t][pe][ci], where indices runs as follows:\r
 //           [0=RP,1=POI][0=Pt,1=Eta][0=<2'>,1=<4'>,2=<6'>,3=<8'>] \r
 // Remark 3: <2'> = <w2 cos(n*(psi1-phi2))>\r
 //           <4'> = <w2 w3 w4 cos(n*(psi1+phi2-phi3-phi4))>\r
 // ...\r
  \r
 Int_t typeFlag = -1;\r
 Int_t ptEtaFlag = -1;\r
 if(type == "RP")\r
 {\r
  typeFlag = 0;\r
 } else if(type == "POI")\r
   {\r
    typeFlag = 1;\r
   }      \r
 if(ptOrEta == "Pt")\r
 {\r
  ptEtaFlag = 0;\r
 } else if(ptOrEta == "Eta")\r
   {\r
    ptEtaFlag = 1;\r
   } \r
 // shortcuts:\r
 Int_t t = typeFlag;\r
 Int_t pe = ptEtaFlag;\r
      \r
 Double_t lowerPtEtaEdge[2] = {fPtMin+(fCrossCheckInPtBinNo-1)*fPtBinWidth,fEtaMin+(fCrossCheckInEtaBinNo-1)*fEtaBinWidth};\r
 Double_t upperPtEtaEdge[2] = {fPtMin+fCrossCheckInPtBinNo*fPtBinWidth,fEtaMin+fCrossCheckInEtaBinNo*fEtaBinWidth};\r
 Double_t binWidthPtEta[2] = {fPtBinWidth,fEtaBinWidth};\r
 \r
 Int_t nPrim = anEvent->NumberOfTracks(); \r
 AliFlowTrackSimple *aftsTrack = NULL;\r
 \r
 Double_t psi1=0., phi2=0., phi3=0., phi4=0.;// phi5=0., phi6=0., phi7=0., phi8=0.;\r
 Double_t wPhi2=1., wPhi3=1., wPhi4=1.;// wPhi5=1., wPhi6=1., wPhi7=1., wPhi8=1.;\r
 \r
 Int_t n = fHarmonic; \r
 \r
 // 2'-particle correlations:\r
 for(Int_t i1=0;i1<nPrim;i1++)\r
 {\r
  aftsTrack=anEvent->GetTrack(i1);\r
  // POI condition (first particle in the correlator must be POI): // to be improved (this can be implemented much better)
  if(typeFlag==1) // this is diff flow of POIs 
  {\r
   if(ptOrEta == "Pt")\r
   { \r
    if(!((aftsTrack->Pt()>=lowerPtEtaEdge[pe] && aftsTrack->Pt()<upperPtEtaEdge[pe]) && (aftsTrack->InPOISelection())))continue;\r
   } else if (ptOrEta == "Eta")\r
     {\r
      if(!((aftsTrack->Eta()>=lowerPtEtaEdge[pe] && aftsTrack->Eta()<upperPtEtaEdge[pe]) && (aftsTrack->InPOISelection())))continue;    \r
     }
  } else // this is diff flow of RPs 
    {
     if(ptOrEta == "Pt")\r
     { \r
      if(!((aftsTrack->Pt()>=lowerPtEtaEdge[pe] && aftsTrack->Pt()<upperPtEtaEdge[pe]) && (aftsTrack->InRPSelection())))continue;\r
     } else if (ptOrEta == "Eta")\r
       {\r
        if(!((aftsTrack->Eta()>=lowerPtEtaEdge[pe] && aftsTrack->Eta()<upperPtEtaEdge[pe]) && (aftsTrack->InRPSelection())))continue;    \r
       }
    }\r
  psi1=aftsTrack->Phi(); \r
  for(Int_t i2=0;i2<nPrim;i2++)\r
  {\r
   if(i2==i1) continue;\r
   aftsTrack=anEvent->GetTrack(i2);\r
   // RP condition (!(first) particle in the correlator must be RP):\r
   if(!(aftsTrack->InRPSelection())) continue;\r
   phi2=aftsTrack->Phi();   \r
   if(fUsePhiWeights && fPhiWeights) wPhi2 = fPhiWeights->GetBinContent(1+(Int_t)(TMath::Floor(phi2*fnBinsPhi/TMath::TwoPi())));\r
   // 2'-particle correlations: \r
   fDiffFlowDirectCorrelations[t][pe][0]->Fill(lowerPtEtaEdge[pe]+binWidthPtEta[pe]/2.,cos(1.*n*(psi1-phi2)),wPhi2); // <w2 cos(n*(psi1-phi2))  \r
  }//end of for(Int_t i2=0;i2<nPrim;i2++)\r
 }//end of for(Int_t i1=0;i1<nPrim;i1++)\r
 \r
 // 4'-particle correlations:\r
 for(Int_t i1=0;i1<nPrim;i1++)\r
 {\r
  aftsTrack=anEvent->GetTrack(i1);\r
  // POI condition (first particle in the correlator must be POI): // to be improved (this can be implemented much better)
  if(typeFlag==1) // this is diff flow of POIs 
  {\r
   if(ptOrEta == "Pt")\r
   { \r
    if(!((aftsTrack->Pt()>=lowerPtEtaEdge[pe] && aftsTrack->Pt()<upperPtEtaEdge[pe]) && (aftsTrack->InPOISelection())))continue;\r
   } else if (ptOrEta == "Eta")\r
     {\r
      if(!((aftsTrack->Eta()>=lowerPtEtaEdge[pe] && aftsTrack->Eta()<upperPtEtaEdge[pe]) && (aftsTrack->InPOISelection())))continue;    \r
     }
  } else // this is diff flow of RPs 
    {
     if(ptOrEta == "Pt")\r
     { \r
      if(!((aftsTrack->Pt()>=lowerPtEtaEdge[pe] && aftsTrack->Pt()<upperPtEtaEdge[pe]) && (aftsTrack->InRPSelection())))continue;\r
     } else if (ptOrEta == "Eta")\r
       {\r
        if(!((aftsTrack->Eta()>=lowerPtEtaEdge[pe] && aftsTrack->Eta()<upperPtEtaEdge[pe]) && (aftsTrack->InRPSelection())))continue;    \r
       }
    }\r
  psi1=aftsTrack->Phi();\r
  for(Int_t i2=0;i2<nPrim;i2++)\r
  {\r
   if(i2==i1) continue;\r
   aftsTrack=anEvent->GetTrack(i2);\r
   // RP condition (!(first) particle in the correlator must be RP): \r
   if(!(aftsTrack->InRPSelection())) continue;\r
   phi2=aftsTrack->Phi();\r
   if(fUsePhiWeights && fPhiWeights) wPhi2 = fPhiWeights->GetBinContent(1+(Int_t)(TMath::Floor(phi2*fnBinsPhi/TMath::TwoPi())));\r
   for(Int_t i3=0;i3<nPrim;i3++)\r
   { \r
    if(i3==i1||i3==i2) continue;\r
    aftsTrack=anEvent->GetTrack(i3);\r
    // RP condition (!(first) particle in the correlator must be RP):\r
    if(!(aftsTrack->InRPSelection())) continue;\r
    phi3=aftsTrack->Phi();\r
    if(fUsePhiWeights && fPhiWeights) wPhi3 = fPhiWeights->GetBinContent(1+(Int_t)(TMath::Floor(phi3*fnBinsPhi/TMath::TwoPi())));\r
    for(Int_t i4=0;i4<nPrim;i4++)\r
    {\r
     if(i4==i1||i4==i2||i4==i3) continue;\r
     aftsTrack=anEvent->GetTrack(i4);\r
     // RP condition (!(first) particle in the correlator must be RP):\r
     if(!(aftsTrack->InRPSelection())) continue;  \r
     phi4=aftsTrack->Phi();\r
     if(fUsePhiWeights && fPhiWeights) wPhi4 = fPhiWeights->GetBinContent(1+(Int_t)(TMath::Floor(phi4*fnBinsPhi/TMath::TwoPi())));\r
     // 4'-particle correlations <w2 w3 w4 cos(n(psi1+phi2-phi3-phi4))>:\r
     fDiffFlowDirectCorrelations[t][pe][1]->Fill(lowerPtEtaEdge[pe]+binWidthPtEta[pe]/2.,cos(n*(psi1+phi2-phi3-phi4)),wPhi2*wPhi3*wPhi4); \r
    }//end of for(Int_t i4=0;i4<nPrim;i4++)\r
   }//end of for(Int_t i3=0;i3<nPrim;i3++)\r
  }//end of for(Int_t i2=0;i2<nPrim;i2++) \r
 }//end of for(Int_t i1=0;i1<nPrim;i1++)      \r
 
 // count # of RPs and POIs in selected pt and eta bins for cross-checkings: (to be improved - moved to dedicated method)\r
 for(Int_t i=0;i<nPrim;i++)
 {
  aftsTrack=anEvent->GetTrack(i); 
  // POI condition (first particle in the correlator must be POI): // to be improved (this can be implemented much better)
  if(typeFlag==1) // this is diff flow of POIs 
  {\r
   if(ptOrEta == "Pt")\r
   { \r
    if(!((aftsTrack->Pt()>=lowerPtEtaEdge[pe] && aftsTrack->Pt()<upperPtEtaEdge[pe]) && (aftsTrack->InPOISelection())))continue;\r
   } else if (ptOrEta == "Eta")\r
     {\r
      if(!((aftsTrack->Eta()>=lowerPtEtaEdge[pe] && aftsTrack->Eta()<upperPtEtaEdge[pe]) && (aftsTrack->InPOISelection())))continue;    \r
     }
  } else // this is diff flow of RPs 
    {
     if(ptOrEta == "Pt")\r
     { \r
      if(!((aftsTrack->Pt()>=lowerPtEtaEdge[pe] && aftsTrack->Pt()<upperPtEtaEdge[pe]) && (aftsTrack->InRPSelection())))continue;\r
     } else if (ptOrEta == "Eta")\r
       {\r
        if(!((aftsTrack->Eta()>=lowerPtEtaEdge[pe] && aftsTrack->Eta()<upperPtEtaEdge[pe]) && (aftsTrack->InRPSelection())))continue;    \r
       }
    }
  if(t==1)t++; 
  fNoOfParticlesInBin->Fill(t+pe+0.5);  
 }
 \r
} // end of void AliFlowAnalysisWithQCumulants::EvaluateDiffFlowCorrelationsWithNestedLoopsUsingParticleWeights(AliFlowEventSimple* anEvent, TString type, TString ptOrEta)\r
\r
\r
//================================================================================================================================\r
\r
   \r
void AliFlowAnalysisWithQCumulants::EvaluateDiffFlowCorrectionTermsForNUAWithNestedLoops(AliFlowEventSimple* anEvent, TString type, TString ptOrEta)\r
{\r
 // Evaluate with nested loops correction terms for non-uniform acceptance (both sin and cos terms) relevant for differential flow.\r
 \r
 // Remark 1: Reduced correction terms for non-uniform acceptance are evaluated in pt bin number fCrossCheckInPtBinNo \r
 //           and eta bin number fCrossCheckInEtaBinNo both for RPs and POIs.\r
 // Remark 2: Results are stored in 1 bin profiles fDiffFlowDirectCorrections[t][pe][sc][cti], where first three indices runs as: \r
 //           [0=RP,1=POI][0=Pt,1=Eta][0=sin terms,1=cos terms], whilst the cti (correction term index) runs as follows: \r
 //  cti: \r
 //    0: <<sc n(psi1)>>\r
 //    1: <<sc n(psi1+phi2)>> \r
 //    2: <<sc n(psi1+phi2-phi3)>>\r
 //    3: <<sc n(psi1-phi2-phi3)>>\r
 //    4:\r
 //    5:\r
 //    6:\r
  \r
 Int_t typeFlag = -1;\r
 Int_t ptEtaFlag = -1;\r
 if(type == "RP")\r
 {\r
  typeFlag = 0;\r
 } else if(type == "POI")\r
   {\r
    typeFlag = 1;\r
   }      \r
 if(ptOrEta == "Pt")\r
 {\r
  ptEtaFlag = 0;\r
 } else if(ptOrEta == "Eta")\r
   {\r
    ptEtaFlag = 1;\r
   } \r
 // shortcuts:\r
 Int_t t = typeFlag;\r
 Int_t pe = ptEtaFlag;\r
      \r
 Double_t lowerPtEtaEdge[2] = {fPtMin+(fCrossCheckInPtBinNo-1)*fPtBinWidth,fEtaMin+(fCrossCheckInEtaBinNo-1)*fEtaBinWidth};\r
 Double_t upperPtEtaEdge[2] = {fPtMin+fCrossCheckInPtBinNo*fPtBinWidth,fEtaMin+fCrossCheckInEtaBinNo*fEtaBinWidth};\r
 Double_t binWidthPtEta[2] = {fPtBinWidth,fEtaBinWidth};\r
 \r
 Int_t nPrim = anEvent->NumberOfTracks(); \r
 AliFlowTrackSimple *aftsTrack = NULL;\r
 \r
 Double_t psi1=0., phi2=0., phi3=0.;// phi4=0.;// phi5=0., phi6=0., phi7=0., phi8=0.;\r
 \r
 Int_t n = fHarmonic; \r
 \r
 // 1-particle correction terms:\r
 for(Int_t i1=0;i1<nPrim;i1++)\r
 {\r
  aftsTrack=anEvent->GetTrack(i1);\r
  // POI condition (first particle in the correlator must be POI): // to be improved (this can be implemented much better)
  if(typeFlag==1) // this is diff flow of POIs 
  {\r
   if(ptOrEta == "Pt")\r
   { \r
    if(!((aftsTrack->Pt()>=lowerPtEtaEdge[pe] && aftsTrack->Pt()<upperPtEtaEdge[pe]) && (aftsTrack->InPOISelection())))continue;\r
   } else if (ptOrEta == "Eta")\r
     {\r
      if(!((aftsTrack->Eta()>=lowerPtEtaEdge[pe] && aftsTrack->Eta()<upperPtEtaEdge[pe]) && (aftsTrack->InPOISelection())))continue;    \r
     }
  } else // this is diff flow of RPs 
    {
     if(ptOrEta == "Pt")\r
     { \r
      if(!((aftsTrack->Pt()>=lowerPtEtaEdge[pe] && aftsTrack->Pt()<upperPtEtaEdge[pe]) && (aftsTrack->InRPSelection())))continue;\r
     } else if (ptOrEta == "Eta")\r
       {\r
        if(!((aftsTrack->Eta()>=lowerPtEtaEdge[pe] && aftsTrack->Eta()<upperPtEtaEdge[pe]) && (aftsTrack->InRPSelection())))continue;    \r
       }
    }\r
  psi1=aftsTrack->Phi(); \r
  // sin terms: \r
  fDiffFlowDirectCorrectionTermsForNUA[t][pe][0][0]->Fill(lowerPtEtaEdge[pe]+binWidthPtEta[pe]/2.,sin(n*psi1),1.); // <<sin(n*(psi1))>>  \r
  // cos terms: \r
  fDiffFlowDirectCorrectionTermsForNUA[t][pe][1][0]->Fill(lowerPtEtaEdge[pe]+binWidthPtEta[pe]/2.,cos(n*psi1),1.); // <<cos(n*(psi1))>>  \r
 }//end of for(Int_t i1=0;i1<nPrim;i1++)\r
   \r
 // 2-particle correction terms:\r
 for(Int_t i1=0;i1<nPrim;i1++)\r
 {\r
  aftsTrack=anEvent->GetTrack(i1);\r
   // POI condition (first particle in the correlator must be POI): // to be improved (this can be implemented much better)
  if(typeFlag==1) // this is diff flow of POIs 
  {\r
   if(ptOrEta == "Pt")\r
   { \r
    if(!((aftsTrack->Pt()>=lowerPtEtaEdge[pe] && aftsTrack->Pt()<upperPtEtaEdge[pe]) && (aftsTrack->InPOISelection())))continue;\r
   } else if (ptOrEta == "Eta")\r
     {\r
      if(!((aftsTrack->Eta()>=lowerPtEtaEdge[pe] && aftsTrack->Eta()<upperPtEtaEdge[pe]) && (aftsTrack->InPOISelection())))continue;    \r
     }
  } else // this is diff flow of RPs 
    {
     if(ptOrEta == "Pt")\r
     { \r
      if(!((aftsTrack->Pt()>=lowerPtEtaEdge[pe] && aftsTrack->Pt()<upperPtEtaEdge[pe]) && (aftsTrack->InRPSelection())))continue;\r
     } else if (ptOrEta == "Eta")\r
       {\r
        if(!((aftsTrack->Eta()>=lowerPtEtaEdge[pe] && aftsTrack->Eta()<upperPtEtaEdge[pe]) && (aftsTrack->InRPSelection())))continue;    \r
       }
    }\r
  psi1=aftsTrack->Phi(); \r
  for(Int_t i2=0;i2<nPrim;i2++)\r
  {\r
   if(i2==i1) continue;\r
   aftsTrack=anEvent->GetTrack(i2);\r
   // RP condition (!(first) particle in the correlator must be RP):\r
   if(!(aftsTrack->InRPSelection())) continue;\r
   phi2=aftsTrack->Phi();   \r
   // sin terms: \r
   fDiffFlowDirectCorrectionTermsForNUA[t][pe][0][1]->Fill(lowerPtEtaEdge[pe]+binWidthPtEta[pe]/2.,sin(n*(psi1+phi2)),1.); // <<sin(n*(psi1+phi2))>>  \r
   // cos terms: \r
   fDiffFlowDirectCorrectionTermsForNUA[t][pe][1][1]->Fill(lowerPtEtaEdge[pe]+binWidthPtEta[pe]/2.,cos(n*(psi1+phi2)),1.); // <<cos(n*(psi1+phi2))>>  \r
  }//end of for(Int_t i2=0;i2<nPrim;i2++)\r
 }//end of for(Int_t i1=0;i1<nPrim;i1++)   \r
 \r
 // 3-particle correction terms:\r
 for(Int_t i1=0;i1<nPrim;i1++)\r
 {\r
  aftsTrack=anEvent->GetTrack(i1);\r
   // POI condition (first particle in the correlator must be POI): // to be improved (this can be implemented much better)
  if(typeFlag==1) // this is diff flow of POIs 
  {\r
   if(ptOrEta == "Pt")\r
   { \r
    if(!((aftsTrack->Pt()>=lowerPtEtaEdge[pe] && aftsTrack->Pt()<upperPtEtaEdge[pe]) && (aftsTrack->InPOISelection())))continue;\r
   } else if (ptOrEta == "Eta")\r
     {\r
      if(!((aftsTrack->Eta()>=lowerPtEtaEdge[pe] && aftsTrack->Eta()<upperPtEtaEdge[pe]) && (aftsTrack->InPOISelection())))continue;    \r
     }
  } else // this is diff flow of RPs 
    {
     if(ptOrEta == "Pt")\r
     { \r
      if(!((aftsTrack->Pt()>=lowerPtEtaEdge[pe] && aftsTrack->Pt()<upperPtEtaEdge[pe]) && (aftsTrack->InRPSelection())))continue;\r
     } else if (ptOrEta == "Eta")\r
       {\r
        if(!((aftsTrack->Eta()>=lowerPtEtaEdge[pe] && aftsTrack->Eta()<upperPtEtaEdge[pe]) && (aftsTrack->InRPSelection())))continue;    \r
       }
    }\r
  psi1=aftsTrack->Phi();\r
  for(Int_t i2=0;i2<nPrim;i2++)\r
  {\r
   if(i2==i1) continue;\r
   aftsTrack=anEvent->GetTrack(i2);\r
   // RP condition (!(first) particle in the correlator must be RP):\r
   if(!(aftsTrack->InRPSelection())) continue;\r
   phi2=aftsTrack->Phi();\r
   for(Int_t i3=0;i3<nPrim;i3++)\r
   {\r
    if(i3==i1||i3==i2) continue;\r
    aftsTrack=anEvent->GetTrack(i3);\r
    // RP condition (!(first) particle in the correlator must be RP):\r
    if(!(aftsTrack->InRPSelection())) continue;\r
    phi3=aftsTrack->Phi();\r
    // sin terms: \r
    fDiffFlowDirectCorrectionTermsForNUA[t][pe][0][2]->Fill(lowerPtEtaEdge[pe]+binWidthPtEta[pe]/2.,sin(n*(psi1+phi2-phi3)),1.); // <<sin(n*(psi1+phi2-phi3))>>  \r
    fDiffFlowDirectCorrectionTermsForNUA[t][pe][0][3]->Fill(lowerPtEtaEdge[pe]+binWidthPtEta[pe]/2.,sin(n*(psi1-phi2-phi3)),1.); // <<sin(n*(psi1-phi2-phi3))>>  \r
    // cos terms: \r
    fDiffFlowDirectCorrectionTermsForNUA[t][pe][1][2]->Fill(lowerPtEtaEdge[pe]+binWidthPtEta[pe]/2.,cos(n*(psi1+phi2-phi3)),1.); // <<cos(n*(psi1+phi2-phi3))>>  \r
    fDiffFlowDirectCorrectionTermsForNUA[t][pe][1][3]->Fill(lowerPtEtaEdge[pe]+binWidthPtEta[pe]/2.,cos(n*(psi1-phi2-phi3)),1.); // <<cos(n*(psi1-phi2-phi3))>>  \r
   }//end of for(Int_t i3=0;i3<nPrim;i3++)  \r
  }//end of for(Int_t i2=0;i2<nPrim;i2++)  \r
 }//end of for(Int_t i1=0;i1<nPrim;i1++)\r
   \r
} // end of void AliFlowAnalysisWithQCumulants::EvaluateDiffFlowCorrectionTermsForNUAWithNestedLoops(AliFlowEventSimple* anEvent, TString type, TString ptOrEta)\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::CrossCheckDiffFlowCorrectionTermsForNUA(TString type, TString ptOrEta)\r
{\r
 // Compare corrections temrs for non-uniform acceptance needed for diff. flow calculated with nested loops and those calculated from Q-vectors\r
 \r
 Int_t typeFlag = -1;\r
 Int_t ptEtaFlag = -1;\r
 if(type == "RP")\r
 {\r
  typeFlag = 0;\r
 } else if(type == "POI")\r
   {\r
    typeFlag = 1;\r
   }      \r
 if(ptOrEta == "Pt")\r
 {\r
  ptEtaFlag = 0;\r
 } else if(ptOrEta == "Eta")\r
   {\r
    ptEtaFlag = 1;\r
   } \r
 // shortcuts:\r
 Int_t t = typeFlag;\r
 Int_t pe = ptEtaFlag;\r
      \r
 TString rpORpoiString[2] = {"RP ","POI"}; // to be improved (name in the same way as in the other methods, eventually promote to data member) \r
 TString ptORetaString[2] = {"pt","eta"}; // to be improved (name in the same way as in the other methods, eventually promote to data member) \r
 //TString sinCosFlag[2] = {"sin","cos"}; // to be improved (eventually promote to data member)\r
 TString reducedCorrectionSinTerms[4] = {"<<sin(n(psi1))>>","<<sin(n(psi1+phi2))>>","<<sin(n*(psi1+phi2-phi3))>>","<<sin(n*(psi1-phi2-phi3))>>"}; // to be improved (access this from pro or hist)\r
 TString reducedCorrectionCosTerms[4] = {"<<cos(n(psi1))>>","<<cos(n(psi1+phi2))>>","<<cos(n*(psi1+phi2-phi3))>>","<<cos(n*(psi1-phi2-phi3))>>"}; // to be improved (access this from pro or hist)\r
 Double_t lowerPtEtaEdge[2] = {fPtMin+(fCrossCheckInPtBinNo-1)*fPtBinWidth,fEtaMin+(fCrossCheckInEtaBinNo-1)*fEtaBinWidth};\r
 Double_t upperPtEtaEdge[2] = {fPtMin+fCrossCheckInPtBinNo*fPtBinWidth,fEtaMin+fCrossCheckInEtaBinNo*fEtaBinWidth};\r
 \r
 Int_t crossCheckInPtEtaBinNo[2] = {fCrossCheckInPtBinNo,fCrossCheckInEtaBinNo};\r
 \r
 cout<<endl;\r
 cout<<"   ******************************************"<<endl;\r
 cout<<"   ****  cross-checking the correction   ****"<<endl;\r
 cout<<"   **** terms for non-uniform acceptance ****"<<endl; 
 cout<<"   ****    for differential flow ("<<rpORpoiString[t]<<")   ****"<<endl;\r
 if(!(fUsePhiWeights||fUsePtWeights||fUseEtaWeights))\r
 {\r
  cout<<"   ****    (particle weights not used)   ****"<<endl;\r
 } else\r
   {\r
    cout<<"   ****     (particle weights used)      ****"<<endl;\r
   } \r
 cout<<"   ******************************************"<<endl; \r
 cout<<endl;\r
 cout<<"           "<<ptORetaString[pe]<<" bin: "<<lowerPtEtaEdge[pe]<<" <= "<<ptORetaString[pe]<<" < "<<upperPtEtaEdge[pe]<<endl;\r
 cout<<endl;\r
 \r
 for(Int_t cti=0;cti<4;cti++) // correction term index\r
 {\r
  for(Int_t sc=0;sc<2;sc++) // sin or cos terms\r
  {\r
   if(sc==0) // to be improved (this can be implemented better)\r
   { \r
    cout<<"      "<<reducedCorrectionSinTerms[cti].Data()<<":"<<endl;\r
   } else\r
     {\r
      cout<<"      "<<reducedCorrectionCosTerms[cti].Data()<<":"<<endl;     \r
     }\r
   cout<<"      from Q-vectors    = "<<fDiffFlowCorrectionTermsForNUAPro[t][pe][sc][cti]->GetBinContent(crossCheckInPtEtaBinNo[pe])<<endl;\r
   cout<<"      from nested loops = "<<fDiffFlowDirectCorrectionTermsForNUA[t][pe][sc][cti]->GetBinContent(1)<<endl;\r
   cout<<endl;  \r
  } \r
 } // end of for(Int_t rci=0;rci<4;rci++)\r
\r
} // end of void AliFlowAnalysisWithQCumulants::CrossCheckDiffFlowCorrectionTermsForNUA(TString type, TString ptOrEta)\r
\r
\r
//================================================================================================================================

\r
void AliFlowAnalysisWithQCumulants::CalculateIntFlowCorrectionsForNUACosTermsUsingParticleWeights()\r
{\r
 // Calculate corrections using particle weights for non-uniform acceptance of the detector for no-name integrated flow (cos terms).\r
 \r
 //                                  **********************************************************************\r
 //                                  **** weighted corrections for non-uniform acceptance (cos terms): ****\r
 //                                  **********************************************************************\r
 
 // Remark 1: When particle weights are used the binning of fIntFlowCorrectionTermsForNUAPro[1] is organized as follows:\r
 //
 // 1st bin: <<w1 cos(n*(phi1))>> = cosP1nW1\r
 // 2nd bin: <<w1 w2 cos(n*(phi1+phi2))>> = cosP1nP1nW1W1\r
 // 3rd bin: <<w1 w2 w3 cos(n*(phi1-phi2-phi3))>> = cosP1nM1nM1nW1W1W1 \r
 // ...\r

 // multiplicity (number of particles used to determine the reaction plane)\r
 Double_t dMult = (*fSMpk)(0,0);\r
 \r
 // real and imaginary parts of weighted Q-vectors evaluated in harmonics n, 2n, 3n and 4n: \r
 Double_t dReQ1n1k = (*fReQ)(0,1);\r
 Double_t dReQ2n2k = (*fReQ)(1,2);\r
 //Double_t dReQ3n3k = (*fReQ)(2,3);\r
 //Double_t dReQ4n4k = (*fReQ)(3,4);\r
 Double_t dReQ1n3k = (*fReQ)(0,3);\r
 Double_t dImQ1n1k = (*fImQ)(0,1);\r
 Double_t dImQ2n2k = (*fImQ)(1,2);\r
 //Double_t dImQ3n3k = (*fImQ)(2,3);\r
 //Double_t dImQ4n4k = (*fImQ)(3,4);\r
 //Double_t dImQ1n3k = (*fImQ)(0,3);\r
\r
 // dMs are variables introduced in order to simplify some Eqs. bellow:\r
 //..............................................................................................\r
 Double_t dM11 = (*fSMpk)(1,1)-(*fSMpk)(0,2); // dM11 = sum_{i,j=1,i!=j}^M w_i w_j\r
 Double_t dM111 = (*fSMpk)(2,1)-3.*(*fSMpk)(0,2)*(*fSMpk)(0,1)
                + 2.*(*fSMpk)(0,3); // dM111 = sum_{i,j,k=1,i!=j!=k}^M w_i w_j w_k\r
 //..............................................................................................\r
        \r // 1-particle:\r
 Double_t cosP1nW1 = 0.; // <<w1 cos(n*(phi1))>>\r
   \r
 if(dMult>0 && (*fSMpk)(0,1) !=0.)\r
 {\r
  cosP1nW1 = dReQ1n1k/(*fSMpk)(0,1); \r
  \r
  // average weighted 1-particle correction (cos terms) for non-uniform acceptance for single event:\r
  fIntFlowCorrectionTermsForNUAEBE[1]->SetBinContent(1,cosP1nW1);\r
  \r
  // final average weighted 1-particle correction (cos terms) for non-uniform acceptance for all events:\r
  fIntFlowCorrectionTermsForNUAPro[1]->Fill(0.5,cosP1nW1,(*fSMpk)(0,1));  \r
 } \r
 \r
 // 2-particle:\r
 Double_t cosP1nP1nW1W1 = 0.; // <<w1 w2 cos(n*(phi1+phi2))>>\r
 \r
 if(dMult>1 && dM11 !=0.)\r
 {\r
  cosP1nP1nW1W1 = (pow(dReQ1n1k,2)-pow(dImQ1n1k,2)-dReQ2n2k)/dM11; \r
  \r
  // average weighted 2-particle correction (cos terms) for non-uniform acceptance for single event:\r
  fIntFlowCorrectionTermsForNUAEBE[1]->SetBinContent(2,cosP1nP1nW1W1);\r
  \r
  // final average weighted 2-particle correction (cos terms) for non-uniform acceptance for all events:\r
  fIntFlowCorrectionTermsForNUAPro[1]->Fill(1.5,cosP1nP1nW1W1,dM11);  \r
 } \r
 \r
 // 3-particle:\r
 Double_t cosP1nM1nM1nW1W1W1 = 0.; // <<w1 w2 w3 cos(n*(phi1-phi2-phi3))>>\r
 \r
 if(dMult>2 && dM111 !=0.)\r
 {\r
  cosP1nM1nM1nW1W1W1 = (dReQ1n1k*(pow(dReQ1n1k,2)+pow(dImQ1n1k,2))
                     - dReQ1n1k*dReQ2n2k-dImQ1n1k*dImQ2n2k
                     - 2.*((*fSMpk)(0,2))*dReQ1n1k
                     + 2.*dReQ1n3k) \r
                     / dM111; \r
  \r
  // average non-weighted 3-particle correction (cos terms) for non-uniform acceptance for single event:\r
  fIntFlowCorrectionTermsForNUAEBE[1]->SetBinContent(3,cosP1nM1nM1nW1W1W1);\r
  \r
  // final average non-weighted 3-particle correction (cos terms) for non-uniform acceptance for all events:\r
  fIntFlowCorrectionTermsForNUAPro[1]->Fill(2.5,cosP1nM1nM1nW1W1W1,dM111);  \r
 } \r
 \r
} // end of AliFlowAnalysisWithQCumulants::CalculateIntFlowCorrectionsForNUACosTermsUsingParticleWeights()\r
\r
\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::CalculateIntFlowCorrectionsForNUASinTermsUsingParticleWeights()\r
{\r
 // calculate corrections using particle weights for non-uniform acceptance of the detector for no-name integrated flow (sin terms)\r
 \r
 //                                  **********************************************************************\r
 //                                  **** weighted corrections for non-uniform acceptance (sin terms): ****\r
 //                                  **********************************************************************\r
 
 // Remark 1: When particle weights are used the binning of fIntFlowCorrectionTermsForNUAPro[0] is organized as follows:\r
 //
 // 1st bin: <<w1 sin(n*(phi1))>> = sinP1nW1\r
 // 2nd bin: <<w1 w2 sin(n*(phi1+phi2))>> = sinP1nP1nW1W1\r
 // 3rd bin: <<w1 w2 w3 sin(n*(phi1-phi2-phi3))>> = sinP1nM1nM1nW1W1W1 \r
 // ...\r

 // multiplicity (number of particles used to determine the reaction plane)\r
 Double_t dMult = (*fSMpk)(0,0);\r
 \r
 // real and imaginary parts of weighted Q-vectors evaluated in harmonics n, 2n, 3n and 4n: \r
 Double_t dReQ1n1k = (*fReQ)(0,1);\r
 Double_t dReQ2n2k = (*fReQ)(1,2);\r
 //Double_t dReQ3n3k = (*fReQ)(2,3);\r
 //Double_t dReQ4n4k = (*fReQ)(3,4);\r
 //Double_t dReQ1n3k = (*fReQ)(0,3);\r
 Double_t dImQ1n1k = (*fImQ)(0,1);\r
 Double_t dImQ2n2k = (*fImQ)(1,2);\r
 //Double_t dImQ3n3k = (*fImQ)(2,3);\r
 //Double_t dImQ4n4k = (*fImQ)(3,4);\r
 Double_t dImQ1n3k = (*fImQ)(0,3);\r
\r
 // dMs are variables introduced in order to simplify some Eqs. bellow:\r
 //..............................................................................................\r
 Double_t dM11 = (*fSMpk)(1,1)-(*fSMpk)(0,2); // dM11 = sum_{i,j=1,i!=j}^M w_i w_j\r
 Double_t dM111 = (*fSMpk)(2,1)-3.*(*fSMpk)(0,2)*(*fSMpk)(0,1)
                + 2.*(*fSMpk)(0,3); // dM111 = sum_{i,j,k=1,i!=j!=k}^M w_i w_j w_k\r
 //..............................................................................................\r
 \r
 // 1-particle:\r
 Double_t sinP1nW1 = 0.; // <<w1 sin(n*(phi1))>>\r
 \r
 if(dMult>0 && (*fSMpk)(0,1) !=0.)\r
 {\r
  sinP1nW1 = dImQ1n1k/((*fSMpk)(0,1)); \r
     \r
  // average weighted 1-particle correction (sin terms) for non-uniform acceptance for single event:\r
  fIntFlowCorrectionTermsForNUAEBE[0]->SetBinContent(1,sinP1nW1);\r
  \r
  // final average weighted 1-particle correction (sin terms) for non-uniform acceptance for all events:   \r
  fIntFlowCorrectionTermsForNUAPro[0]->Fill(0.5,sinP1nW1,(*fSMpk)(0,1));  \r
 } \r
 \r
 // 2-particle:\r
 Double_t sinP1nP1nW1W1 = 0.; // <<w1 w2 sin(n*(phi1+phi2))>>\r
 \r
 if(dMult>1 && dM11 !=0.)\r
 {\r
  sinP1nP1nW1W1 = (2.*dReQ1n1k*dImQ1n1k-dImQ2n2k)/dM11; \r
     \r
  // average weighted 2-particle correction (sin terms) for non-uniform acceptance for single event:\r
  fIntFlowCorrectionTermsForNUAEBE[0]->SetBinContent(2,sinP1nP1nW1W1);\r
  \r
  // final average weighted 1-particle correction (sin terms) for non-uniform acceptance for all events:      \r
  fIntFlowCorrectionTermsForNUAPro[0]->Fill(1.5,sinP1nP1nW1W1,dM11);  \r
 } \r
 \r
 // 3-particle:\r
 Double_t sinP1nM1nM1nW1W1W1 = 0.; // <<w1 w2 w3 sin(n*(phi1-phi2-phi3))>>\r
 \r
 if(dMult>2 && dM111 !=0.)\r
 {\r
  sinP1nM1nM1nW1W1W1 = (-dImQ1n1k*(pow(dReQ1n1k,2)+pow(dImQ1n1k,2))
                     + dReQ1n1k*dImQ2n2k-dImQ1n1k*dReQ2n2k
                     + 2.*((*fSMpk)(0,2))*dImQ1n1k
                     - 2.*dImQ1n3k)\r
                     / dM111; \r
  \r
  // average weighted 3-particle correction (sin terms) for non-uniform acceptance for single event:\r
  fIntFlowCorrectionTermsForNUAEBE[0]->SetBinContent(3,sinP1nM1nM1nW1W1W1);\r
  \r
  // final average weighted 3-particle correction (sin terms) for non-uniform acceptance for all events:  \r
  fIntFlowCorrectionTermsForNUAPro[0]->Fill(2.5,sinP1nM1nM1nW1W1W1,dM111);  \r
 } \r
 \r
} // end of AliFlowAnalysisWithQCumulants::CalculateIntFlowCorrectionsForNUASinTermsUsingParticleWeights()\r
\r
\r
//================================================================================================================================
\r
\r
void AliFlowAnalysisWithQCumulants::EvaluateIntFlowCorrectionsForNUAWithNestedLoopsUsingParticleWeights(AliFlowEventSimple* anEvent)\r
{\r
 // Evaluate with nested loops correction terms for non-uniform acceptance for integrated flow (using the particle weights). \r
\r
 // Results are stored in profiles fIntFlowDirectCorrectionTermsForNUA[0] (sin terms) and
 // fIntFlowDirectCorrectionTermsForNUA[1] (cos terms). 
 \r
 // Remark 1: When particle weights are used the binning of fIntFlowDirectCorrectionTermsForNUA[sc] is 
 // organized as follows (sc stands for either sin or cos):\r
 //\r
 // 1st bin: <<w1 sc(n*(phi1))>> = scP1nW1\r
 // 2nd bin: <<w1 w2 sc(n*(phi1+phi2))>> = scP1nP1nW1W1\r
 // 3rd bin: <<w1 w2 w3 sc(n*(phi1-phi2-phi3))>> = scP1nM1nM1nW1W1W1 \r
 // ...
  \r
 Int_t nPrim = anEvent->NumberOfTracks(); \r
 AliFlowTrackSimple *aftsTrack = NULL;\r
 //Double_t phi1=0., phi2=0., phi3=0., phi4=0., phi5=0., phi6=0., phi7=0., phi8=0.;\r
 //Double_t wPhi1=1., wPhi2=1., wPhi3=1., wPhi4=1., wPhi5=1., wPhi6=1., wPhi7=1., wPhi8=1.;\r
 Double_t phi1=0., phi2=0., phi3=0.;\r
 Double_t wPhi1=1., wPhi2=1., wPhi3=1.;\r
 Int_t n = fHarmonic; \r
 Int_t eventNo = (Int_t)fAvMultiplicity->GetBinEntries(1); // to be improved (is this casting safe in general?)\r
 Double_t dMult = (*fSMpk)(0,0);\r
 cout<<endl;\r
 cout<<"Correction terms for non-uniform acceptance: Event number: "<<eventNo<<", multiplicity is "<<dMult<<endl;\r
 if(dMult<1)\r
 {\r
  cout<<"... skipping this event (multiplicity too low) ..."<<endl;\r
 } else if (dMult>fMaxAllowedMultiplicity)\r
   {\r
    cout<<"... skipping this event (multiplicity too high) ..."<<endl;\r
   } else \r
     { \r
      cout<<"... evaluating nested loops (using particle weights) ..."<<endl;\r
     } \r
      \r
 // 1-particle correction terms using particle weights:       \r
 if(nPrim>=1 && nPrim<=fMaxAllowedMultiplicity)\r
 {\r
  for(Int_t i1=0;i1<nPrim;i1++)\r
  {\r
   aftsTrack=anEvent->GetTrack(i1);\r
   if(!(aftsTrack->InRPSelection())) continue;\r
   phi1=aftsTrack->Phi();\r
   if(fUsePhiWeights && fPhiWeights) wPhi1 = fPhiWeights->GetBinContent(1+(Int_t)(TMath::Floor(phi1*fnBinsPhi/TMath::TwoPi())));\r
   // 1-particle correction terms using particle weights:
   if(fUsePhiWeights) fIntFlowDirectCorrectionTermsForNUA[0]->Fill(0.5,sin(n*phi1),wPhi1); // <w1 sin(n*phi1)>\r
   if(fUsePhiWeights) fIntFlowDirectCorrectionTermsForNUA[1]->Fill(0.5,cos(n*phi1),wPhi1); // <w1 cos(n*phi1)>\r
  } // end of for(Int_t i1=0;i1<nPrim;i1++)
 } // end of if(nPrim>=1 && nPrim<=fMaxAllowedMultiplicity) 
 
 // 2-particle correction terms using particle weights:       \r
 if(nPrim>=2 && nPrim<=fMaxAllowedMultiplicity)\r
 {\r
  for(Int_t i1=0;i1<nPrim;i1++)\r
  {\r
   aftsTrack=anEvent->GetTrack(i1);\r
   if(!(aftsTrack->InRPSelection())) continue;\r
   phi1=aftsTrack->Phi();\r
   if(fUsePhiWeights && fPhiWeights) wPhi1 = fPhiWeights->GetBinContent(1+(Int_t)(TMath::Floor(phi1*fnBinsPhi/TMath::TwoPi())));\r
   for(Int_t i2=0;i2<nPrim;i2++)\r
   {\r
    if(i2==i1)continue;\r
    aftsTrack=anEvent->GetTrack(i2);\r
    if(!(aftsTrack->InRPSelection())) continue;\r
    phi2=aftsTrack->Phi();\r
    if(fUsePhiWeights && fPhiWeights) wPhi2 = fPhiWeights->GetBinContent(1+(Int_t)(TMath::Floor(phi2*fnBinsPhi/TMath::TwoPi())));   \r
    if(nPrim==2) cout<<i1<<" "<<i2<<"\r"<<flush;\r
    // 2-p correction terms using particle weights:    
    if(fUsePhiWeights) fIntFlowDirectCorrectionTermsForNUA[0]->Fill(1.5,sin(n*(phi1+phi2)),wPhi1*wPhi2); // <w1 w2 sin(n*(phi1+phi2))>\r
    if(fUsePhiWeights) fIntFlowDirectCorrectionTermsForNUA[1]->Fill(1.5,cos(n*(phi1+phi2)),wPhi1*wPhi2); // <w1 w2 cos(n*(phi1+phi2))>\r
   } // end of for(Int_t i2=0;i2<nPrim;i2++)\r
  } // end of for(Int_t i1=0;i1<nPrim;i1++)\r
 } // end of if(nPrim>=2)\r
\r
 // 3-particle correction terms using particle weights:       \r
 if(nPrim>=3 && nPrim<=fMaxAllowedMultiplicity)\r
 { \r
  for(Int_t i1=0;i1<nPrim;i1++)\r
  {\r
   aftsTrack=anEvent->GetTrack(i1);\r
   if(!(aftsTrack->InRPSelection())) continue;\r
   phi1=aftsTrack->Phi();\r
   if(fUsePhiWeights && fPhiWeights) wPhi1 = fPhiWeights->GetBinContent(1+(Int_t)(TMath::Floor(phi1*fnBinsPhi/TMath::TwoPi())));\r
   for(Int_t i2=0;i2<nPrim;i2++)\r
   {\r
    if(i2==i1)continue;\r
    aftsTrack=anEvent->GetTrack(i2);\r
    if(!(aftsTrack->InRPSelection())) continue;\r
    phi2=aftsTrack->Phi();\r
    if(fUsePhiWeights && fPhiWeights) wPhi2 = fPhiWeights->GetBinContent(1+(Int_t)(TMath::Floor(phi2*fnBinsPhi/TMath::TwoPi())));\r
    for(Int_t i3=0;i3<nPrim;i3++)\r
    {\r
     if(i3==i1||i3==i2)continue;\r
     aftsTrack=anEvent->GetTrack(i3);\r
     if(!(aftsTrack->InRPSelection())) continue;\r
     phi3=aftsTrack->Phi();\r
     if(fUsePhiWeights && fPhiWeights) wPhi3 = fPhiWeights->GetBinContent(1+(Int_t)(TMath::Floor(phi3*fnBinsPhi/TMath::TwoPi())));\r
     if(nPrim==3) cout<<i1<<" "<<i2<<" "<<i3<<"\r"<<flush;\r
     // 3-p correction terms using particle weights:    
     if(fUsePhiWeights) fIntFlowDirectCorrectionTermsForNUA[0]->Fill(2.5,sin(n*(phi1-phi2-phi3)),wPhi1*wPhi2*wPhi3); // <w1 w2 w3 sin(n*(phi1-phi2-phi3))>\r
     if(fUsePhiWeights) fIntFlowDirectCorrectionTermsForNUA[1]->Fill(2.5,cos(n*(phi1-phi2-phi3)),wPhi1*wPhi2*wPhi3); // <w1 w2 w3 cos(n*(phi1-phi2-phi3))>\r
    } // end of for(Int_t i3=0;i3<nPrim;i3++)\r
   } // end of for(Int_t i2=0;i2<nPrim;i2++)\r
  } // end of for(Int_t i1=0;i1<nPrim;i1++)\r
 } // end of if(nPrim>=3)\r
 \r
 /*
 
 if(nPrim>=4 && nPrim<=fMaxAllowedMultiplicity)\r
 {\r
  // 4 nested loops multiparticle correlations using particle weights:       \r
  for(Int_t i1=0;i1<nPrim;i1++)\r
  {\r
   aftsTrack=anEvent->GetTrack(i1);\r
   if(!(aftsTrack->InRPSelection())) continue;\r
   phi1=aftsTrack->Phi();\r
   if(fUsePhiWeights && fPhiWeights) wPhi1 = fPhiWeights->GetBinContent(1+(Int_t)(TMath::Floor(phi1*fnBinsPhi/TMath::TwoPi())));\r
   for(Int_t i2=0;i2<nPrim;i2++)\r
   {\r
    if(i2==i1)continue;\r
    aftsTrack=anEvent->GetTrack(i2);\r
    if(!(aftsTrack->InRPSelection())) continue;\r
    phi2=aftsTrack->Phi();\r
    if(fUsePhiWeights && fPhiWeights) wPhi2 = fPhiWeights->GetBinContent(1+(Int_t)(TMath::Floor(phi2*fnBinsPhi/TMath::TwoPi())));\r
    for(Int_t i3=0;i3<nPrim;i3++)\r
    {\r
     if(i3==i1||i3==i2)continue;\r
     aftsTrack=anEvent->GetTrack(i3);\r
     if(!(aftsTrack->InRPSelection())) continue;\r
     phi3=aftsTrack->Phi();\r
     if(fUsePhiWeights && fPhiWeights) wPhi3 = fPhiWeights->GetBinContent(1+(Int_t)(TMath::Floor(phi3*fnBinsPhi/TMath::TwoPi())));\r
     for(Int_t i4=0;i4<nPrim;i4++)\r
     {\r
      if(i4==i1||i4==i2||i4==i3)continue;\r
      aftsTrack=anEvent->GetTrack(i4);\r
      if(!(aftsTrack->InRPSelection())) continue;\r
      phi4=aftsTrack->Phi();\r
      if(fUsePhiWeights && fPhiWeights) wPhi4 = fPhiWeights->GetBinContent(1+(Int_t)(TMath::Floor(phi4*fnBinsPhi/TMath::TwoPi())));\r
      if(nPrim>=4) cout<<i1<<" "<<i2<<" "<<i3<<" "<<i4<<"\r"<<flush; // to be improved (replace eventually this if statement with if(nPrim==4))\r
      // 4-p correlations using particle weights:\r
      if(fUsePhiWeights) fIntFlowDirectCorrelations->Fill(10.5,cos(n*phi1+n*phi2-n*phi3-n*phi4),wPhi1*wPhi2*wPhi3*wPhi4); \r
      // extra correlations: \r
      // 2-p extra correlations (do not appear if particle weights are not used):\r
      // ...\r
      // 3-p extra correlations (do not appear if particle weights are not used):\r
      // ...\r
      // 4-p extra correlations (do not appear if particle weights are not used):\r
      // ...\r
     } // end of for(Int_t i4=0;i4<nPrim;i4++) \r
    } // end of for(Int_t i3=0;i3<nPrim;i3++)\r
   } // end of for(Int_t i2=0;i2<nPrim;i2++)\r
  } // end of for(Int_t i1=0;i1<nPrim;i1++)\r
 } // end of if(nPrim>=4)\r

 */\r

 cout<<endl; \r
\r
} // end of void AliFlowAnalysisWithQCumulants::EvaluateIntFlowCorrectionsForNUAWithNestedLoopsUsingParticleWeights(AliFlowEventSimple* anEvent)\r
\r
\r
//================================================================================================================================
\r
\r
void AliFlowAnalysisWithQCumulants::CalculateDiffFlowCorrectionsForNUACosTermsUsingParticleWeights(TString type, TString ptOrEta)\r
{\r
 // Calculate correction terms for non-uniform acceptance for differential flow (cos terms) using particle weights.\r
 
 // Results are stored in fDiffFlowCorrectionTermsForNUAPro[t][pe][1][cti], where cti runs as follows:\r
 //
 //  0: <<cos n(psi)>>\r
 //  1: <<w2 cos n(psi1+phi2)>>\r
 //  2: <<w2 w3 cos n(psi1+phi2-phi3)>>\r
 //  3: <<w2 w3 cos n(psi1-phi2-phi3)>>\r
 //  4:\r
 //  5:\r
 //  6:\r
 \r
 // real and imaginary parts of weighted Q-vectors evaluated in harmonics n, 2n, 3n and 4n: \r
 Double_t dReQ1n1k = (*fReQ)(0,1);\r
 Double_t dReQ2n2k = (*fReQ)(1,2);\r
 //Double_t dReQ1n3k = (*fReQ)(0,3);\r
 //Double_t dReQ4n4k = (*fReQ)(3,4);\r
 Double_t dImQ1n1k = (*fImQ)(0,1);\r
 Double_t dImQ2n2k = (*fImQ)(1,2);\r
 //Double_t dImQ1n3k = (*fImQ)(0,3);\r
 //Double_t dImQ4n4k = (*fImQ)(3,4);\r
 
 // S^M_{p,k} (see .h file for the definition of fSMpk):\r
 Double_t dSM1p1k = (*fSMpk)(0,1);\r
 Double_t dSM1p2k = (*fSMpk)(0,2);\r
 Double_t dSM2p1k = (*fSMpk)(1,1);\r
\r
 Int_t t = -1; // type flag \r
 Int_t pe = -1; // ptEta flag\r
 \r
 if(type == "RP")\r
 {\r
  t = 0;\r
 } else if(type == "POI")\r
   {\r
    t = 1;\r
   }\r
\r
 if(ptOrEta == "Pt")\r
 {\r
  pe = 0;\r
 } else if(ptOrEta == "Eta")\r
   {\r
    pe = 1;\r
   }\r
    \r
 Int_t nBinsPtEta[2] = {fnBinsPt,fnBinsEta};\r
 Double_t minPtEta[2] = {fPtMin,fEtaMin};\r
 //Double_t maxPtEta[2] = {fPtMax,fEtaMax};\r
 Double_t binWidthPtEta[2] = {fPtBinWidth,fEtaBinWidth};\r
 
 // looping over all bins and calculating correction terms: \r
 for(Int_t b=1;b<=nBinsPtEta[pe];b++)\r
 {\r
  // real and imaginary parts of p_{m*n,0} (non-weighted Q-vector evaluated for POIs in particular pt or eta bin): \r
  Double_t p1n0kRe = 0.;\r
  Double_t p1n0kIm = 0.;\r
\r
  // number of POIs in particular pt or eta bin:\r
  Double_t mp = 0.;\r
\r
  // real and imaginary parts of q_{m*n,0} (weighted Q-vector evaluated for particles which are both RPs and POIs in particular pt or eta bin):\r
  Double_t q1n2kRe = 0.;\r
  Double_t q1n2kIm = 0.;\r
  Double_t q2n1kRe = 0.;\r
  Double_t q2n1kIm = 0.;\r
    
  // s_{1,1}, s_{1,2} // to be improved (add explanation)  \r
  Double_t s1p1k = 0.; \r
  Double_t s1p2k = 0.; \r
  
  // number of particles which are both RPs and POIs in particular pt or eta bin:\r
  Double_t mq = 0.;
  \r
  // M0111 from Eq. (118) in QC2c (to be improved (notation))\r
  Double_t dM01 = 0.;\r
  Double_t dM011 = 0.;\r
  
  if(type == "POI")\r
  {           \r
   // q_{m*n,k}:\r
   q1n2kRe = fReRPQ1dEBE[2][pe][0][2]->GetBinContent(fReRPQ1dEBE[2][pe][0][2]->GetBin(b))\r
           * fReRPQ1dEBE[2][pe][0][2]->GetBinEntries(fReRPQ1dEBE[2][pe][0][2]->GetBin(b));\r
   q1n2kIm = fImRPQ1dEBE[2][pe][0][2]->GetBinContent(fImRPQ1dEBE[2][pe][0][2]->GetBin(b))\r
           * fImRPQ1dEBE[2][pe][0][2]->GetBinEntries(fImRPQ1dEBE[2][pe][0][2]->GetBin(b));         \r
   q2n1kRe = fReRPQ1dEBE[2][pe][1][1]->GetBinContent(fReRPQ1dEBE[2][pe][1][1]->GetBin(b))\r
           * fReRPQ1dEBE[2][pe][1][1]->GetBinEntries(fReRPQ1dEBE[2][pe][1][1]->GetBin(b));\r
   q2n1kIm = fImRPQ1dEBE[2][pe][1][1]->GetBinContent(fImRPQ1dEBE[2][pe][1][1]->GetBin(b))\r
           * fImRPQ1dEBE[2][pe][1][1]->GetBinEntries(fImRPQ1dEBE[2][pe][1][1]->GetBin(b));         \r
   mq = fReRPQ1dEBE[2][pe][1][1]->GetBinEntries(fReRPQ1dEBE[2][pe][1][1]->GetBin(b)); // to be improved (cross-checked by accessing other profiles here)\r
   
   s1p1k = pow(fs1dEBE[2][pe][1]->GetBinContent(b)*fs1dEBE[2][pe][1]->GetBinEntries(b),1.); \r
   s1p2k = pow(fs1dEBE[2][pe][2]->GetBinContent(b)*fs1dEBE[2][pe][2]->GetBinEntries(b),1.); \r
  }else if(type == "RP")\r
   {
    // q_{m*n,k}: (Remark: m=1 is 0, k=0 iz zero (to be improved!)) \r
    q1n2kRe = fReRPQ1dEBE[0][pe][0][2]->GetBinContent(fReRPQ1dEBE[0][pe][0][2]->GetBin(b))\r
            * fReRPQ1dEBE[0][pe][0][2]->GetBinEntries(fReRPQ1dEBE[0][pe][0][2]->GetBin(b));\r
    q1n2kIm = fImRPQ1dEBE[0][pe][0][2]->GetBinContent(fImRPQ1dEBE[0][pe][0][2]->GetBin(b))\r
            * fImRPQ1dEBE[0][pe][0][2]->GetBinEntries(fImRPQ1dEBE[0][pe][0][2]->GetBin(b));\r
    q2n1kRe = fReRPQ1dEBE[0][pe][1][1]->GetBinContent(fReRPQ1dEBE[0][pe][1][1]->GetBin(b))\r
            * fReRPQ1dEBE[0][pe][1][1]->GetBinEntries(fReRPQ1dEBE[0][pe][1][1]->GetBin(b));\r
    q2n1kIm = fImRPQ1dEBE[0][pe][1][1]->GetBinContent(fImRPQ1dEBE[0][pe][1][1]->GetBin(b))\r
            * fImRPQ1dEBE[0][pe][1][1]->GetBinEntries(fImRPQ1dEBE[0][pe][1][1]->GetBin(b));\r
    // s_{1,1}, s_{1,2} and s_{1,3} // to be improved (add explanation)  \r
    s1p1k = pow(fs1dEBE[0][pe][1]->GetBinContent(b)*fs1dEBE[0][pe][1]->GetBinEntries(b),1.); \r
    s1p2k = pow(fs1dEBE[0][pe][2]->GetBinContent(b)*fs1dEBE[0][pe][2]->GetBinEntries(b),1.); \r
    //s1p3k = pow(fs1dEBE[0][pe][3]->GetBinContent(b)*fs1dEBE[0][pe][3]->GetBinEntries(b),1.);  
    
    mq = fReRPQ1dEBE[0][pe][1][1]->GetBinEntries(fReRPQ1dEBE[0][pe][1][1]->GetBin(b)); // to be improved (cross-checked by accessing other profiles here) \r
  }    \r
  
  if(type == "POI")\r
  {
   // p_{m*n,k}:   
   p1n0kRe = fReRPQ1dEBE[1][pe][0][0]->GetBinContent(fReRPQ1dEBE[1][pe][0][0]->GetBin(b))\r
           * fReRPQ1dEBE[1][pe][0][0]->GetBinEntries(fReRPQ1dEBE[1][pe][0][0]->GetBin(b));\r
   p1n0kIm = fImRPQ1dEBE[1][pe][0][0]->GetBinContent(fImRPQ1dEBE[1][pe][0][0]->GetBin(b))  \r
           * fImRPQ1dEBE[1][pe][0][0]->GetBinEntries(fImRPQ1dEBE[1][pe][0][0]->GetBin(b));
   mp = fReRPQ1dEBE[1][pe][0][0]->GetBinEntries(fReRPQ1dEBE[1][pe][0][0]->GetBin(b)); // to be improved (cross-checked by accessing other profiles here) 
   // M01 from Eq. (118) in QC2c (to be improved (notation)):\r
   dM01 = mp*dSM1p1k-s1p1k;
   dM011 = mp*(dSM2p1k-dSM1p2k)
         - 2.*(s1p1k*dSM1p1k-s1p2k);
       
   // typeFlag = RP (0) or POI (1):   
   t = 1; 
  } else if(type == "RP")
    {  \r
     // to be improved (cross-checked):\r
     p1n0kRe = fReRPQ1dEBE[0][pe][0][0]->GetBinContent(fReRPQ1dEBE[0][pe][0][0]->GetBin(b))\r
             * fReRPQ1dEBE[0][pe][0][0]->GetBinEntries(fReRPQ1dEBE[0][pe][0][0]->GetBin(b));\r
     p1n0kIm = fImRPQ1dEBE[0][pe][0][0]->GetBinContent(fImRPQ1dEBE[0][pe][0][0]->GetBin(b))  \r
             * fImRPQ1dEBE[0][pe][0][0]->GetBinEntries(fImRPQ1dEBE[0][pe][0][0]->GetBin(b));\r
     mp = fReRPQ1dEBE[0][pe][0][0]->GetBinEntries(fReRPQ1dEBE[0][pe][0][0]->GetBin(b)); // to be improved (cross-checked by accessing other profiles here)\r
     // M01 from Eq. (118) in QC2c (to be improved (notation)):\r
     dM01 = mp*dSM1p1k-s1p1k;
     dM011 = mp*(dSM2p1k-dSM1p2k)
           - 2.*(s1p1k*dSM1p1k-s1p2k); 
     // typeFlag = RP (0) or POI (1): \r
     t = 0;
    }
  \r
  // <<cos n(psi1)>>:\r
  Double_t cosP1nPsi = 0.;\r
  if(mp)\r
  {\r
   cosP1nPsi = p1n0kRe/mp;\r
   \r
   // fill profile for <<cos n(psi1)>>:\r
   fDiffFlowCorrectionTermsForNUAPro[t][pe][1][0]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],cosP1nPsi,mp);\r
   // histogram to store <cos n(psi1)> e-b-e (needed in some other methods):\r
   fDiffFlowCorrectionTermsForNUAEBE[t][pe][1][0]->SetBinContent(b,cosP1nPsi);\r
  } // end of if(mp)   
  
  // <<w2 cos n(psi1+phi2)>>:\r
  Double_t cosP1nPsiP1nPhiW2 = 0.;\r
  if(dM01)\r
  {\r
   cosP1nPsiP1nPhiW2 = (p1n0kRe*dReQ1n1k-p1n0kIm*dImQ1n1k-q2n1kRe)/(dM01);\r
   // fill profile for <<w2 cos n(psi1+phi2)>>:\r
   fDiffFlowCorrectionTermsForNUAPro[t][pe][1][1]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],cosP1nPsiP1nPhiW2,dM01);\r
   // histogram to store <w2 cos n(psi1+phi2)> e-b-e (needed in some other methods):\r
   fDiffFlowCorrectionTermsForNUAEBE[t][pe][1][1]->SetBinContent(b,cosP1nPsiP1nPhiW2);\r
  } // end of if(dM01)   \r
  
  // <<w2 w3 cos n(psi1+phi2-phi3)>>:\r
  Double_t cosP1nPsi1P1nPhi2MPhi3W2W3 = 0.;\r
  if(dM011)\r
  {\r
   cosP1nPsi1P1nPhi2MPhi3W2W3 = (p1n0kRe*(pow(dImQ1n1k,2.)+pow(dReQ1n1k,2.))
                              - p1n0kRe*dSM1p2k
                              - q2n1kRe*dReQ1n1k-q2n1kIm*dImQ1n1k
                              - s1p1k*dReQ1n1k
                              + 2.*q1n2kRe)
                              / dM011;  
   // fill profile for <<w1 w2 w3 cos n(psi1+phi2)>>:\r
   fDiffFlowCorrectionTermsForNUAPro[t][pe][1][2]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],cosP1nPsi1P1nPhi2MPhi3W2W3,dM011);\r
   // histogram to store <w1 w2 w3 cos n(psi1+phi2)> e-b-e (needed in some other methods):\r
   fDiffFlowCorrectionTermsForNUAEBE[t][pe][1][2]->SetBinContent(b,cosP1nPsi1P1nPhi2MPhi3W2W3);\r
  } // end of if(dM011)   \r
  \r
  // <<w2 w3 cos n(psi1-phi2-phi3)>>:\r
  Double_t cosP1nPsi1M1nPhi2MPhi3W2W3 = 0.;\r
  if(dM011)\r
  {\r
   cosP1nPsi1M1nPhi2MPhi3W2W3 = (p1n0kRe*(pow(dReQ1n1k,2.)-pow(dImQ1n1k,2.))+2.*p1n0kIm*dReQ1n1k*dImQ1n1k\r
                              - 1.*(p1n0kRe*dReQ2n2k+p1n0kIm*dImQ2n2k)  \r
                              - 2.*s1p1k*dReQ1n1k
                              + 2.*q1n2kRe)\r
                              / dM011;\r
   // fill profile for <<w1 w2 w3 cos n(psi1+phi2)>>:\r
   fDiffFlowCorrectionTermsForNUAPro[t][pe][1][3]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],cosP1nPsi1M1nPhi2MPhi3W2W3,dM011);\r
   // histogram to store <w1 w2 w3 cos n(psi1+phi2)> e-b-e (needed in some other methods):\r
   fDiffFlowCorrectionTermsForNUAEBE[t][pe][1][3]->SetBinContent(b,cosP1nPsi1M1nPhi2MPhi3W2W3);\r
  } // end of if(dM011)   \r
 
 } // end of for(Int_t b=1;b<=nBinsPtEta[pe];b++)\r
   
} // end of AliFlowAnalysisWithQCumulants::CalculateDiffFlowCorrectionsForNUACosTermsUsingParticleWeights(TString type, TString ptOrEta)

\r
//================================================================================================================================\r
\r
\r
void AliFlowAnalysisWithQCumulants::CalculateDiffFlowCorrectionsForNUASinTermsUsingParticleWeights(TString type, TString ptOrEta)\r
{\r
 // Calculate correction terms for non-uniform acceptance for differential flow (sin terms).\r
  
 // Results are stored in fDiffFlowCorrectionTermsForNUAPro[t][pe][0][cti], where cti runs as follows:\r
 //  0: <<sin n(psi1)>>\r
 //  1: <<w2 sin n(psi1+phi2)>>\r
 //  2: <<w2 w3 sin n(psi1+phi2-phi3)>>\r
 //  3: <<w2 w3 sin n(psi1-phi2-phi3)>>:\r
 //  4:\r
 //  5:\r
 //  6:\r
 \r
 // real and imaginary parts of weighted Q-vectors evaluated in harmonics n, 2n, 3n and 4n: \r
 Double_t dReQ1n1k = (*fReQ)(0,1);\r
 Double_t dReQ2n2k = (*fReQ)(1,2);\r
 //Double_t dReQ1n3k = (*fReQ)(0,3);\r
 //Double_t dReQ4n4k = (*fReQ)(3,4);\r
 Double_t dImQ1n1k = (*fImQ)(0,1);\r
 Double_t dImQ2n2k = (*fImQ)(1,2);\r
 //Double_t dImQ1n3k = (*fImQ)(0,3);\r
 //Double_t dImQ4n4k = (*fImQ)(3,4);\r
 
 // S^M_{p,k} (see .h file for the definition of fSMpk):\r
 Double_t dSM1p1k = (*fSMpk)(0,1);\r
 Double_t dSM1p2k = (*fSMpk)(0,2);\r
 Double_t dSM2p1k = (*fSMpk)(1,1);\r
\r
 Int_t t = -1; // type flag \r
 Int_t pe = -1; // ptEta flag\r
 \r
 if(type == "RP")\r
 {\r
  t = 0;\r
 } else if(type == "POI")\r
   {\r
    t = 1;\r
   }\r
\r
 if(ptOrEta == "Pt")\r
 {\r
  pe = 0;\r
 } else if(ptOrEta == "Eta")\r
   {\r
    pe = 1;\r
   }\r
    \r
 Int_t nBinsPtEta[2] = {fnBinsPt,fnBinsEta};\r
 Double_t minPtEta[2] = {fPtMin,fEtaMin};\r
 //Double_t maxPtEta[2] = {fPtMax,fEtaMax};\r
 Double_t binWidthPtEta[2] = {fPtBinWidth,fEtaBinWidth};\r
\r
 // looping over all bins and calculating correction terms: \r
 for(Int_t b=1;b<=nBinsPtEta[pe];b++)\r
 {\r
  // real and imaginary parts of p_{m*n,0} (non-weighted Q-vector evaluated for POIs in particular pt or eta bin): \r
  Double_t p1n0kRe = 0.;\r
  Double_t p1n0kIm = 0.;\r
\r
  // number of POIs in particular pt or eta bin:\r
  Double_t mp = 0.;\r
\r
  // real and imaginary parts of q_{m*n,0} (weighted Q-vector evaluated for particles which are both RPs and POIs in particular pt or eta bin):\r
  Double_t q1n2kRe = 0.;\r
  Double_t q1n2kIm = 0.;\r
  Double_t q2n1kRe = 0.;\r
  Double_t q2n1kIm = 0.;\r
    
  // s_{1,1}, s_{1,2} and s_{1,3} // to be improved (add explanation)  \r
  Double_t s1p1k = 0.; \r
  Double_t s1p2k = 0.; \r
  
  // number of particles which are both RPs and POIs in particular pt or eta bin:\r
  Double_t mq = 0.;
  \r
  // M0111 from Eq. (118) in QC2c (to be improved (notation))\r
  Double_t dM01 = 0.;\r
  Double_t dM011 = 0.;\r
\r
  if(type == "POI")\r
  {    \r
   // q_{m*n,k}:\r
   q1n2kRe = fReRPQ1dEBE[2][pe][0][2]->GetBinContent(fReRPQ1dEBE[2][pe][0][2]->GetBin(b))\r
           * fReRPQ1dEBE[2][pe][0][2]->GetBinEntries(fReRPQ1dEBE[2][pe][0][2]->GetBin(b));\r
   q1n2kIm = fImRPQ1dEBE[2][pe][0][2]->GetBinContent(fImRPQ1dEBE[2][pe][0][2]->GetBin(b))\r
           * fImRPQ1dEBE[2][pe][0][2]->GetBinEntries(fImRPQ1dEBE[2][pe][0][2]->GetBin(b));         \r
   q2n1kRe = fReRPQ1dEBE[2][pe][1][1]->GetBinContent(fReRPQ1dEBE[2][pe][1][1]->GetBin(b))\r
           * fReRPQ1dEBE[2][pe][1][1]->GetBinEntries(fReRPQ1dEBE[2][pe][1][1]->GetBin(b));\r
   q2n1kIm = fImRPQ1dEBE[2][pe][1][1]->GetBinContent(fImRPQ1dEBE[2][pe][1][1]->GetBin(b))\r
           * fImRPQ1dEBE[2][pe][1][1]->GetBinEntries(fImRPQ1dEBE[2][pe][1][1]->GetBin(b));         \r
   mq = fReRPQ1dEBE[2][pe][0][0]->GetBinEntries(fReRPQ1dEBE[2][pe][0][0]->GetBin(b)); // to be improved (cross-checked by accessing other profiles here)\r
   
   s1p1k = pow(fs1dEBE[2][pe][1]->GetBinContent(b)*fs1dEBE[2][pe][1]->GetBinEntries(b),1.); \r
   s1p2k = pow(fs1dEBE[2][pe][2]->GetBinContent(b)*fs1dEBE[2][pe][2]->GetBinEntries(b),1.); \r
  }else if(type == "RP")\r
   {
    // q_{m*n,k}: (Remark: m=1 is 0, k=0 iz zero (to be improved!)) \r
    q1n2kRe = fReRPQ1dEBE[0][pe][0][2]->GetBinContent(fReRPQ1dEBE[0][pe][0][2]->GetBin(b))\r
            * fReRPQ1dEBE[0][pe][0][2]->GetBinEntries(fReRPQ1dEBE[0][pe][0][2]->GetBin(b));\r
    q1n2kIm = fImRPQ1dEBE[0][pe][0][2]->GetBinContent(fImRPQ1dEBE[0][pe][0][2]->GetBin(b))\r
            * fImRPQ1dEBE[0][pe][0][2]->GetBinEntries(fImRPQ1dEBE[0][pe][0][2]->GetBin(b));\r
    q2n1kRe = fReRPQ1dEBE[0][pe][1][1]->GetBinContent(fReRPQ1dEBE[0][pe][1][1]->GetBin(b))\r
            * fReRPQ1dEBE[0][pe][1][1]->GetBinEntries(fReRPQ1dEBE[0][pe][1][1]->GetBin(b));\r
    q2n1kIm = fImRPQ1dEBE[0][pe][1][1]->GetBinContent(fImRPQ1dEBE[0][pe][1][1]->GetBin(b))\r
            * fImRPQ1dEBE[0][pe][1][1]->GetBinEntries(fImRPQ1dEBE[0][pe][1][1]->GetBin(b));\r
    // s_{1,1}, s_{1,2} and s_{1,3} // to be improved (add explanation)  \r
    s1p1k = pow(fs1dEBE[0][pe][1]->GetBinContent(b)*fs1dEBE[0][pe][1]->GetBinEntries(b),1.); \r
    s1p2k = pow(fs1dEBE[0][pe][2]->GetBinContent(b)*fs1dEBE[0][pe][2]->GetBinEntries(b),1.); \r
    //s1p3k = pow(fs1dEBE[0][pe][3]->GetBinContent(b)*fs1dEBE[0][pe][3]->GetBinEntries(b),1.); \r
  }    
  
  if(type == "POI")
  {
   // p_{m*n,k}:   
   p1n0kRe = fReRPQ1dEBE[1][pe][0][0]->GetBinContent(fReRPQ1dEBE[1][pe][0][0]->GetBin(b))\r
           * fReRPQ1dEBE[1][pe][0][0]->GetBinEntries(fReRPQ1dEBE[1][pe][0][0]->GetBin(b));\r
   p1n0kIm = fImRPQ1dEBE[1][pe][0][0]->GetBinContent(fImRPQ1dEBE[1][pe][0][0]->GetBin(b))  \r
           * fImRPQ1dEBE[1][pe][0][0]->GetBinEntries(fImRPQ1dEBE[1][pe][0][0]->GetBin(b));
   mp = fReRPQ1dEBE[1][pe][0][0]->GetBinEntries(fReRPQ1dEBE[1][pe][0][0]->GetBin(b)); // to be improved (cross-checked by accessing other profiles here) 
   // M01 from Eq. (118) in QC2c (to be improved (notation)):\r
   dM01 = mp*dSM1p1k-s1p1k;
   dM011 = mp*(dSM2p1k-dSM1p2k)
         - 2.*(s1p1k*dSM1p1k-s1p2k);  
   // typeFlag = RP (0) or POI (1):   
   t = 1;           
  } else if(type == "RP")\r
    { 
     // to be improved (cross-checked):\r
     p1n0kRe = fReRPQ1dEBE[0][pe][0][0]->GetBinContent(fReRPQ1dEBE[0][pe][0][0]->GetBin(b))\r
             * fReRPQ1dEBE[0][pe][0][0]->GetBinEntries(fReRPQ1dEBE[0][pe][0][0]->GetBin(b));\r
     p1n0kIm = fImRPQ1dEBE[0][pe][0][0]->GetBinContent(fImRPQ1dEBE[0][pe][0][0]->GetBin(b))  \r
             * fImRPQ1dEBE[0][pe][0][0]->GetBinEntries(fImRPQ1dEBE[0][pe][0][0]->GetBin(b));\r
     mp = fReRPQ1dEBE[0][pe][0][0]->GetBinEntries(fReRPQ1dEBE[0][pe][0][0]->GetBin(b)); // to be improved (cross-checked by accessing other profiles here)    \r
     // M01 from Eq. (118) in QC2c (to be improved (notation)):\r
     dM01 = mp*dSM1p1k-s1p1k;
     dM011 = mp*(dSM2p1k-dSM1p2k)
           - 2.*(s1p1k*dSM1p1k-s1p2k); \r
     // typeFlag = RP (0) or POI (1): \r
     t = 0;
    }
  
  // <<sin n(psi1)>>:\r
  Double_t sinP1nPsi = 0.;\r
  if(mp)\r
  {\r
   sinP1nPsi = p1n0kIm/mp;\r
   \r
   // fill profile for <<sin n(psi1)>>:\r
   fDiffFlowCorrectionTermsForNUAPro[t][pe][0][0]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],sinP1nPsi,mp);\r
   // histogram to store <sin n(psi1)> e-b-e (needed in some other methods):\r
   fDiffFlowCorrectionTermsForNUAEBE[t][pe][0][0]->SetBinContent(b,sinP1nPsi);\r
  } // end of if(mp)   
  
  // <<w2 sin n(psi1+phi2)>>:\r
  Double_t sinP1nPsiP1nPhiW2 = 0.;\r
  if(dM01)\r
  {\r
   sinP1nPsiP1nPhiW2 = (p1n0kRe*dImQ1n1k+p1n0kIm*dReQ1n1k-q2n1kIm)/(dM01);\r
   // fill profile for <<w2 sin n(psi1+phi2)>>:\r
   fDiffFlowCorrectionTermsForNUAPro[t][pe][0][1]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],sinP1nPsiP1nPhiW2,dM01);\r
   // histogram to store <w2 sin n(psi1+phi2)> e-b-e (needed in some other methods):\r
   fDiffFlowCorrectionTermsForNUAEBE[t][pe][0][1]->SetBinContent(b,sinP1nPsiP1nPhiW2);\r
  } // end of if(mp*dMult-mq)   \r
  
  // <<w2 w3 sin n(psi1+phi2-phi3)>>:\r
  Double_t sinP1nPsi1P1nPhi2MPhi3W2W3 = 0.;\r
  if(dM011)\r
  {\r
   sinP1nPsi1P1nPhi2MPhi3W2W3 = (p1n0kIm*(pow(dImQ1n1k,2.)+pow(dReQ1n1k,2.))
                              - p1n0kIm*dSM1p2k
                              + q2n1kRe*dImQ1n1k-q2n1kIm*dReQ1n1k
                              - s1p1k*dImQ1n1k
                              + 2.*q1n2kIm)
                              / dM011;  
   // fill profile for <<w2 w3 sin n(psi1+phi2-phi3)>>:\r
   fDiffFlowCorrectionTermsForNUAPro[t][pe][0][2]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],sinP1nPsi1P1nPhi2MPhi3W2W3,dM011);\r
   // histogram to store <w2 w3 sin n(psi1+phi2-phi3)> e-b-e (needed in some other methods):\r
   fDiffFlowCorrectionTermsForNUAEBE[t][pe][0][2]->SetBinContent(b,sinP1nPsi1P1nPhi2MPhi3W2W3);\r
  } // end of if(dM011)   \r
  
  // <<w2 w3 sin n(psi1-phi2-phi3)>>:\r
  Double_t sinP1nPsi1M1nPhi2MPhi3W2W3 = 0.;\r
  if(dM011)\r
  {\r
   sinP1nPsi1M1nPhi2MPhi3W2W3 = (p1n0kIm*(pow(dReQ1n1k,2.)-pow(dImQ1n1k,2.))-2.*p1n0kRe*dReQ1n1k*dImQ1n1k\r
                              + 1.*(p1n0kRe*dImQ2n2k-p1n0kIm*dReQ2n2k)  \r
                              + 2.*s1p1k*dImQ1n1k
                              - 2.*q1n2kIm)\r
                              / dM011;\r
   // fill profile for <<w2 w3 sin n(psi1-phi2-phi3)>>:\r
   fDiffFlowCorrectionTermsForNUAPro[t][pe][0][3]->Fill(minPtEta[pe]+(b-1)*binWidthPtEta[pe],sinP1nPsi1M1nPhi2MPhi3W2W3,dM011);\r
   // histogram to store <w2 w3 sin n(psi1-phi2-phi3)> e-b-e (needed in some other methods):\r
   fDiffFlowCorrectionTermsForNUAEBE[t][pe][0][3]->SetBinContent(b,sinP1nPsi1M1nPhi2MPhi3W2W3);\r
  } // end of if(dM011)   \r
  
 } // end of for(Int_t b=1;b<=nBinsPtEta[pe];b++)\r

} // end of AliFlowAnalysisWithQCumulants::CalculateDiffFlowCorrectionsForNUASinTermsUsingParticleWeights(TString type, TString ptOrEta)\r
\r
\r
//================================================================================================================================\r
\r
   \r
void AliFlowAnalysisWithQCumulants::EvaluateDiffFlowCorrectionTermsForNUAWithNestedLoopsUsingParticleWeights(AliFlowEventSimple* anEvent, TString type, TString ptOrEta)\r
{\r
 // Evaluate with nested loops correction terms for non-uniform acceptance 
 // with using particle weights (both sin and cos terms) relevant for differential flow.\r
 \r
 // Remark 1: "w1" in expressions bellow is a particle weight used only for particles which were 
 //           flagged both as POI and RP.
 // Remark 2: Reduced correction terms for non-uniform acceptance are evaluated in pt bin number fCrossCheckInPtBinNo \r
 //           and eta bin number fCrossCheckInEtaBinNo both for RPs and POIs.\r
 // Remark 3: Results are stored in 1 bin profiles fDiffFlowDirectCorrections[t][pe][sc][cti], where first three indices runs as: \r
 //           [0=RP,1=POI][0=Pt,1=Eta][0=sin terms,1=cos terms], whilst the cti (correction term index) runs as follows: \r
 //  cti: \r
 //    0: <<sc n(psi1)>>\r
 //    1: <<w2 sc n(psi1+phi2)>> \r
 //    2: <<w2 w3 sc n(psi1+phi2-phi3)>>\r
 //    3: <<w2 w3 sc n(psi1-phi2-phi3)>>\r
 //    4:\r
 //    5:\r
 //    6:\r
     
 Int_t typeFlag = -1;\r
 Int_t ptEtaFlag = -1;\r
 if(type == "RP")\r
 {\r
  typeFlag = 0;\r
 } else if(type == "POI")\r
   {\r
    typeFlag = 1;\r
   }      \r
 if(ptOrEta == "Pt")\r
 {\r
  ptEtaFlag = 0;\r
 } else if(ptOrEta == "Eta")\r
   {\r
    ptEtaFlag = 1;\r
   } \r
 // shortcuts:\r
 Int_t t = typeFlag;\r
 Int_t pe = ptEtaFlag;\r
      \r
 Double_t lowerPtEtaEdge[2] = {fPtMin+(fCrossCheckInPtBinNo-1)*fPtBinWidth,fEtaMin+(fCrossCheckInEtaBinNo-1)*fEtaBinWidth};\r
 Double_t upperPtEtaEdge[2] = {fPtMin+fCrossCheckInPtBinNo*fPtBinWidth,fEtaMin+fCrossCheckInEtaBinNo*fEtaBinWidth};\r
 Double_t binWidthPtEta[2] = {fPtBinWidth,fEtaBinWidth};\r
 \r
 Int_t nPrim = anEvent->NumberOfTracks(); \r
 AliFlowTrackSimple *aftsTrack = NULL;\r
 \r
 Double_t psi1=0., phi2=0., phi3=0.;// phi4=0.;// phi5=0., phi6=0., phi7=0., phi8=0.;\r
 Double_t wPhi2=1., wPhi3=1.;\r
 
 Int_t n = fHarmonic; \r
 \r
 // 1'-particle correction terms:\r
 for(Int_t i1=0;i1<nPrim;i1++)\r
 {\r
  aftsTrack=anEvent->GetTrack(i1);\r
  // POI condition (first particle in the correlator must be POI): // to be improved (this can be implemented much better)
  if(typeFlag==1) // this is diff flow of POIs 
  {\r
   if(ptOrEta == "Pt")\r
   { \r
    if(!((aftsTrack->Pt()>=lowerPtEtaEdge[pe] && aftsTrack->Pt()<upperPtEtaEdge[pe]) && (aftsTrack->InPOISelection())))continue;\r
   } else if (ptOrEta == "Eta")\r
     {\r
      if(!((aftsTrack->Eta()>=lowerPtEtaEdge[pe] && aftsTrack->Eta()<upperPtEtaEdge[pe]) && (aftsTrack->InPOISelection())))continue;    \r
     }
  } else // this is diff flow of RPs 
    {
     if(ptOrEta == "Pt")\r
     { \r
      if(!((aftsTrack->Pt()>=lowerPtEtaEdge[pe] && aftsTrack->Pt()<upperPtEtaEdge[pe]) && (aftsTrack->InRPSelection())))continue;\r
     } else if (ptOrEta == "Eta")\r
       {\r
        if(!((aftsTrack->Eta()>=lowerPtEtaEdge[pe] && aftsTrack->Eta()<upperPtEtaEdge[pe]) && (aftsTrack->InRPSelection())))continue;    \r
       }
    }\r
  psi1=aftsTrack->Phi(); \r
  // sin terms: \r
  fDiffFlowDirectCorrectionTermsForNUA[t][pe][0][0]->Fill(lowerPtEtaEdge[pe]+binWidthPtEta[pe]/2.,sin(n*psi1),1.); // <<sin(n*(psi1))>>  \r
  // cos terms: \r
  fDiffFlowDirectCorrectionTermsForNUA[t][pe][1][0]->Fill(lowerPtEtaEdge[pe]+binWidthPtEta[pe]/2.,cos(n*psi1),1.); // <<cos(n*(psi1))>>  \r
 }//end of for(Int_t i1=0;i1<nPrim;i1++)\r
   \r
 // 2'-particle correction terms:\r
 for(Int_t i1=0;i1<nPrim;i1++)\r
 {\r
  aftsTrack=anEvent->GetTrack(i1);\r
  // POI condition (first particle in the correlator must be POI): // to be improved (this can be implemented much better)
  if(typeFlag==1) // this is diff flow of POIs 
  {\r
   if(ptOrEta == "Pt")\r
   { \r
    if(!((aftsTrack->Pt()>=lowerPtEtaEdge[pe] && aftsTrack->Pt()<upperPtEtaEdge[pe]) && (aftsTrack->InPOISelection())))continue;\r
   } else if (ptOrEta == "Eta")\r
     {\r
      if(!((aftsTrack->Eta()>=lowerPtEtaEdge[pe] && aftsTrack->Eta()<upperPtEtaEdge[pe]) && (aftsTrack->InPOISelection())))continue;    \r
     }
  } else // this is diff flow of RPs 
    {
     if(ptOrEta == "Pt")\r
     { \r
      if(!((aftsTrack->Pt()>=lowerPtEtaEdge[pe] && aftsTrack->Pt()<upperPtEtaEdge[pe]) && (aftsTrack->InRPSelection())))continue;\r
     } else if (ptOrEta == "Eta")\r
       {\r
        if(!((aftsTrack->Eta()>=lowerPtEtaEdge[pe] && aftsTrack->Eta()<upperPtEtaEdge[pe]) && (aftsTrack->InRPSelection())))continue;    \r
       }
    }\r
  psi1=aftsTrack->Phi(); \r
  for(Int_t i2=0;i2<nPrim;i2++)\r
  {\r
   if(i2==i1) continue;\r
   aftsTrack=anEvent->GetTrack(i2);\r
   // RP condition (!(first) particle in the correlator must be RP):\r
   if(!(aftsTrack->InRPSelection())) continue;\r
   phi2=aftsTrack->Phi();
   if(fUsePhiWeights && fPhiWeights) wPhi2 = fPhiWeights->GetBinContent(1+(Int_t)(TMath::Floor(phi2*fnBinsPhi/TMath::TwoPi())));   \r
   // sin terms: \r
   fDiffFlowDirectCorrectionTermsForNUA[t][pe][0][1]->Fill(lowerPtEtaEdge[pe]+binWidthPtEta[pe]/2.,sin(n*(psi1+phi2)),wPhi2); // <<w2 sin(n*(psi1+phi2))>>  \r
   // cos terms: \r
   fDiffFlowDirectCorrectionTermsForNUA[t][pe][1][1]->Fill(lowerPtEtaEdge[pe]+binWidthPtEta[pe]/2.,cos(n*(psi1+phi2)),wPhi2); // <<w2 cos(n*(psi1+phi2))>>  \r
  }//end of for(Int_t i2=0;i2<nPrim;i2++)\r
 }//end of for(Int_t i1=0;i1<nPrim;i1++)   \r
 \r
 // 3'-particle correction terms:\r
 for(Int_t i1=0;i1<nPrim;i1++)\r
 {\r
  aftsTrack=anEvent->GetTrack(i1);\r
  // POI condition (first particle in the correlator must be POI): // to be improved (this can be implemented much better)
  if(typeFlag==1) // this is diff flow of POIs 
  {\r
   if(ptOrEta == "Pt")\r
   { \r
    if(!((aftsTrack->Pt()>=lowerPtEtaEdge[pe] && aftsTrack->Pt()<upperPtEtaEdge[pe]) && (aftsTrack->InPOISelection())))continue;\r
   } else if (ptOrEta == "Eta")\r
     {\r
      if(!((aftsTrack->Eta()>=lowerPtEtaEdge[pe] && aftsTrack->Eta()<upperPtEtaEdge[pe]) && (aftsTrack->InPOISelection())))continue;    \r
     }
  } else // this is diff flow of RPs 
    {
     if(ptOrEta == "Pt")\r
     { \r
      if(!((aftsTrack->Pt()>=lowerPtEtaEdge[pe] && aftsTrack->Pt()<upperPtEtaEdge[pe]) && (aftsTrack->InRPSelection())))continue;\r
     } else if (ptOrEta == "Eta")\r
       {\r
        if(!((aftsTrack->Eta()>=lowerPtEtaEdge[pe] && aftsTrack->Eta()<upperPtEtaEdge[pe]) && (aftsTrack->InRPSelection())))continue;    \r
       }
    }\r
  psi1=aftsTrack->Phi();\r
  for(Int_t i2=0;i2<nPrim;i2++)\r
  {\r
   if(i2==i1) continue;\r
   aftsTrack=anEvent->GetTrack(i2);\r
   // RP condition (!(first) particle in the correlator must be RP):\r
   if(!(aftsTrack->InRPSelection())) continue;\r
   phi2=aftsTrack->Phi();\r
   if(fUsePhiWeights && fPhiWeights) wPhi2 = fPhiWeights->GetBinContent(1+(Int_t)(TMath::Floor(phi2*fnBinsPhi/TMath::TwoPi())));   \r
   for(Int_t i3=0;i3<nPrim;i3++)\r
   {\r
    if(i3==i1||i3==i2) continue;\r
    aftsTrack=anEvent->GetTrack(i3);\r
    // RP condition (!(first) particle in the correlator must be RP):\r
    if(!(aftsTrack->InRPSelection())) continue;\r
    phi3=aftsTrack->Phi();\r
    if(fUsePhiWeights && fPhiWeights) wPhi3 = fPhiWeights->GetBinContent(1+(Int_t)(TMath::Floor(phi3*fnBinsPhi/TMath::TwoPi())));   \r
    // sin terms: \r
    fDiffFlowDirectCorrectionTermsForNUA[t][pe][0][2]->Fill(lowerPtEtaEdge[pe]+binWidthPtEta[pe]/2.,sin(n*(psi1+phi2-phi3)),wPhi2*wPhi3); // <<wPhi2*wPhi3 sin(n*(psi1+phi2-phi3))>>  \r
    fDiffFlowDirectCorrectionTermsForNUA[t][pe][0][3]->Fill(lowerPtEtaEdge[pe]+binWidthPtEta[pe]/2.,sin(n*(psi1-phi2-phi3)),wPhi2*wPhi3); // <<wPhi2*wPhi3 sin(n*(psi1-phi2-phi3))>>  \r
    // cos terms: \r
    fDiffFlowDirectCorrectionTermsForNUA[t][pe][1][2]->Fill(lowerPtEtaEdge[pe]+binWidthPtEta[pe]/2.,cos(n*(psi1+phi2-phi3)),wPhi2*wPhi3); // <<wPhi2*wPhi3 cos(n*(psi1+phi2-phi3))>>  \r
    fDiffFlowDirectCorrectionTermsForNUA[t][pe][1][3]->Fill(lowerPtEtaEdge[pe]+binWidthPtEta[pe]/2.,cos(n*(psi1-phi2-phi3)),wPhi2*wPhi3); // <<wPhi2*wPhi3 cos(n*(psi1-phi2-phi3))>>  \r
   }//end of for(Int_t i3=0;i3<nPrim;i3++)  \r
  }//end of for(Int_t i2=0;i2<nPrim;i2++)  \r
 }//end of for(Int_t i1=0;i1<nPrim;i1++)
               \r
} // end of void AliFlowAnalysisWithQCumulants::EvaluateDiffFlowCorrectionTermsForNUAWithNestedLoopsUsingParticleWeights(AliFlowEventSimple* anEvent, TString type, TString ptOrEta)\r
\r
\r