PWG2/FLOW/AliFlowCommon/AliFlowAnalysisWithMixedHarmonics.cxx

   1 /*************************************************************************\r
   2 * Copyright(c) 1998-2008, ALICE Experiment at CERN, All rights reserved. *\r
   3 *                                                                        *\r
   4 * Author: The ALICE Off-line Project.                                    *\r
   5 * Contributors are mentioned in the code where appropriate.              *\r
   6 *                                                                        *\r
   7 * Permission to use, copy, modify and distribute this software and its   *\r
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   9 * without fee, provided that the above copyright notice appears in all   *\r
  10 * copies and that both the copyright notice and this permission notice   *\r
  11 * appear in the supporting documentation. The authors make no claims     *\r
  12 * about the suitability of this software for any purpose. It is          *\r
  13 * provided "as is" without express or implied warranty.                  * \r
  14 **************************************************************************/
  15
  16 /* $Id$ */\r
  17 \r
  18 /**********************************************************
  19  * In this class azimuthal correlators in mixed harmonics *
  20  * are implemented in terms of Q-vectors. This approach   *
  21  * doesn't require evaluation of nested loops. This class *
  22  * can be used to:                                        *
  23  *                                                        *
  24  *  a) Extract subdominant harmonics (like v1 and v4);    *
  25  *  b) Study strong parity violation.                     *
  26  *                                                        *
  27  * Author: Ante Bilandzic (abilandzic@gmail.com)          *
  28  *********************************************************/ \r
  29 \r
  30 #define AliFlowAnalysisWithMixedHarmonics_cxx\r
  31 \r
  32 #include "Riostream.h"\r
  33 #include "AliFlowCommonConstants.h"\r
  34 #include "AliFlowCommonHist.h"\r
  35 #include "AliFlowCommonHistResults.h"\r
  36 \r
  37 #include "TMath.h"\r
  38 #include "TFile.h"\r
  39 #include "TList.h"\r
  40 #include "TProfile.h"
  41 #include "TProfile2D.h"\r
  42 \r
  43 #include "AliFlowEventSimple.h"\r
  44 #include "AliFlowTrackSimple.h"\r
  45 #include "AliFlowAnalysisWithMixedHarmonics.h"\r
  46 \r
  47 class TH1;\r
  48 class TList;\r\r
  49 ClassImp(AliFlowAnalysisWithMixedHarmonics)\r
  50 \r
  51 //================================================================================================================
  52
  53 AliFlowAnalysisWithMixedHarmonics::AliFlowAnalysisWithMixedHarmonics(): \r
  54 fHistList(NULL),
  55 fHistListName(NULL),\r
  56 fAnalysisLabel(NULL),
  57 fAnalysisSettings(NULL),
  58 fCorrelatorInteger(2),
  59 fNoOfMultipicityBins(10),
  60 fMultipicityBinWidth(2),
  61 fMinMultiplicity(1),
  62 fCorrectForDetectorEffects(kTRUE),\r
  63 fCommonHists(NULL),
  64 fnBinsPhi(0),\r
  65 fPhiMin(0),\r
  66 fPhiMax(0),\r
  67 fPhiBinWidth(0),\r
  68 fnBinsPt(0),\r
  69 fPtMin(0),\r
  70 fPtMax(0),\r
  71 fPtBinWidth(0),\r
  72 fnBinsEta(0),\r
  73 fEtaMin(0),\r
  74 fEtaMax(0),\r
  75 fEtaBinWidth(0),
  76 fWeightsList(NULL),\r
  77 fUsePhiWeights(kFALSE),\r
  78 fUsePtWeights(kFALSE),\r
  79 fUseEtaWeights(kFALSE),\r
  80 fUseParticleWeights(NULL),\r
  81 fPhiWeights(NULL),\r
  82 fPtWeights(NULL),\r
  83 fEtaWeights(NULL),
  84 fReQnk(NULL),\r
  85 fImQnk(NULL),\r
  86 fSpk(NULL),
  87 f3pCorrelatorEBE(NULL),
  88 fNonIsotropicTermsEBE(NULL),
  89 f3pCorrelatorPro(NULL),
  90 fNonIsotropicTermsPro(NULL),
  91 f3pCorrelatorVsMPro(NULL),
  92 fNonIsotropicTermsVsMPro(NULL),
  93 fResultsList(NULL),
  94 f3pCorrelatorHist(NULL),
  95 fDetectorBiasHist(NULL),
  96 fNonIsotropicTermsHist(NULL),
  97 f3pCorrelatorVsMHist(NULL),
  98 fDetectorBiasVsMHist(NULL),
  99 fNonIsotropicTermsVsMHist(NULL)\r
 100 {\r
 101  // Constructor. \r
 102  \r // Base list to hold all output objects:\r
 103  fHistList = new TList();
 104  fHistListName = new TString("cobjMH");\r
 105  fHistList->SetName(fHistListName->Data());\r
 106  fHistList->SetOwner(kTRUE);
 107
 108  // List to hold histograms with phi, pt and eta weights:      \r
 109  fWeightsList = new TList();
 110
 111  // List to hold objects with final results:      \r
 112  fResultsList = new TList();
 113  \r
 114 } // AliFlowAnalysisWithMixedHarmonics::AliFlowAnalysisWithMixedHarmonics()\r
 115  \r
 116 //================================================================================================================  \r
 117 \r
 118 AliFlowAnalysisWithMixedHarmonics::~AliFlowAnalysisWithMixedHarmonics()\r
 119 {\r
 120  // Destructor.\r
 121  \r
 122  delete fHistList;\r
 123 \r
 124 } // end of AliFlowAnalysisWithMixedHarmonics::~AliFlowAnalysisWithMixedHarmonics()\r
 125 \r
 126 //================================================================================================================\r
 127 \r
 128 void AliFlowAnalysisWithMixedHarmonics::Init()\r
 129 {
 130  // Initialize and book all objects.
 131
 132  // a) Cross check if the user settings make sense before starting;
 133  // b) Access all common constants;
 134  // c) Book and nest all lists in the base list fHistList;\r
 135  // d) Book common control histograms;
 136  // e) Book all event-by-event quantities;
 137  // f) Book all all-event quantities;
 138  // g) Book and fill histograms to hold phi, pt and eta weights.
 139
 140  this->CrossCheckSettings();\r
 141  this->AccessConstants();
 142  this->BookAndNestAllLists();
 143  this->BookProfileHoldingSettings();\r
 144  this->BookCommonHistograms();
 145  this->BookAllEventByEventQuantities();
 146  this->BookAllAllEventQuantities();
 147  this->BookAndFillWeightsHistograms();\r
 148 \r
 149 } // end of void AliFlowAnalysisWithMixedHarmonics::Init()\r
 150 \r
 151 //================================================================================================================\r
 152 \r
 153 void AliFlowAnalysisWithMixedHarmonics::Make(AliFlowEventSimple* anEvent)\r
 154 {\r
 155  // Running over data only in this method.\r
 156
 157  // a) Define local variables;
 158  // b) Fill common control histograms;
 159  // c) Loop over data and calculate e-b-e quantities Q_{n,k} and S_{p,k};
 160  // d) Calculate 3-p azimuthal correlator and non-isotropic terms in terms of Q_{n,k} and S_{p,k};
 161  // e) Reset all event-by-event quantities.\r
 162
 163  this->CheckPointersUsedInMake();
 164
 165  // a) Define local variables:
 166  Double_t dPhi = 0.; // azimuthal angle in the laboratory frame\r
 167  Double_t dPt  = 0.; // transverse momentum\r
 168  Double_t dEta = 0.; // pseudorapidity\r
 169  Double_t wPhi = 1.; // phi weight\r
 170  Double_t wPt  = 1.; // pt weight\r
 171  Double_t wEta = 1.; // eta weight
 172  AliFlowTrackSimple *aftsTrack = NULL; // simple track
 173
 174  // b) Fill common control histograms.
 175  fCommonHists->FillControlHistograms(anEvent);
 176
 177  // c) Loop over data and calculate e-b-e quantities:\r
 178  Int_t nPrim = anEvent->NumberOfTracks();  // nPrim = total number of primary tracks, i.e. nPrim = nRP + nPOI + rest, where:\r
 179                                            // nRP   = # of particles used to determine the reaction plane ("Reference Particles");\r
 180                                            // nPOI  = # of particles of interest for a detailed flow analysis ("Particles of Interest");\r
 181                                            // rest  = # of particles which are not niether RPs nor POIs.  \r
 182  // Start loop over data:
 183  for(Int_t i=0;i<nPrim;i++) \r
 184  { \r
 185   aftsTrack=anEvent->GetTrack(i);\r
 186   if(aftsTrack)\r
 187   {\r
 188    if(!(aftsTrack->InRPSelection() || aftsTrack->InPOISelection())) continue; // consider only tracks which are either RPs or POIs\r
 189    Int_t n = fCorrelatorInteger; // integer n in the correlator cos[n(2phi1-phi2-phi3)]\r
 190    if(aftsTrack->InRPSelection()) // checking RP condition:\r
 191    {    \r
 192     dPhi = aftsTrack->Phi();\r
 193     dPt  = aftsTrack->Pt();\r
 194     dEta = aftsTrack->Eta();\r
 195     if(fUsePhiWeights && fPhiWeights && fnBinsPhi) // determine phi-weight for this particle:\r
 196     {\r
 197      wPhi = fPhiWeights->GetBinContent(1+(Int_t)(TMath::Floor(dPhi*fnBinsPhi/TMath::TwoPi())));\r
 198     }\r
 199     if(fUsePtWeights && fPtWeights && fnBinsPt) // determine pt-weight for this particle:\r
 200     {\r
 201      wPt = fPtWeights->GetBinContent(1+(Int_t)(TMath::Floor((dPt-fPtMin)/fPtBinWidth))); \r
 202     }              \r
 203     if(fUseEtaWeights && fEtaWeights && fEtaBinWidth) // determine eta-weight for this particle: \r
 204     {\r
 205      wEta = fEtaWeights->GetBinContent(1+(Int_t)(TMath::Floor((dEta-fEtaMin)/fEtaBinWidth))); \r
 206     } \r
 207     // Calculate Re[Q_{m*n,k}] and Im[Q_{m*n,k}], (m = 1,2 and k = 0,1,2,3) for this event:\r
 208     for(Int_t m=0;m<2;m++)\r
 209     {\r
 210      for(Int_t k=0;k<4;k++) // to be improved (what is maximum k that I need?)\r
 211      {\r
 212       (*fReQnk)(m,k)+=pow(wPhi*wPt*wEta,k)*TMath::Cos((m+1)*n*dPhi); \r
 213       (*fImQnk)(m,k)+=pow(wPhi*wPt*wEta,k)*TMath::Sin((m+1)*n*dPhi); \r
 214      } \r
 215     }\r
 216     // Calculate partially S_{p,k} for this event (final calculation of S_{p,k} follows after the loop over data bellow):\r
 217     for(Int_t p=0;p<4;p++) // to be improved (what is maximum p that I need?)\r
 218     {\r
 219      for(Int_t k=0;k<4;k++) // to be improved (what is maximum k that I need?)\r
 220      {     \r
 221       (*fSpk)(p,k)+=pow(wPhi*wPt*wEta,k);\r
 222      }\r
 223     }    \r
 224    } // end of if(aftsTrack->InRPSelection())  \r
 225   } else // to if(aftsTrack)\r
 226     {\r
 227      cout<<endl;\r
 228      cout<<" WARNING (MH): No particle! (i.e. aftsTrack is a NULL pointer in AFAWMH::Make().)"<<endl;\r
 229      cout<<endl;       \r
 230     }\r
 231  } // end of for(Int_t i=0;i<nPrim;i++) \r
 232 \r
 233  // Calculate the final expressions for S_{p,k}:\r
 234  for(Int_t p=0;p<4;p++) // to be improved (what is maximum p that I need?)\r
 235  {\r
 236   for(Int_t k=0;k<4;k++) // to be improved (what is maximum  that I need?)\r
 237   {\r
 238    (*fSpk)(p,k)=pow((*fSpk)(p,k),p+1);\r
 239   }  \r
 240  }
 241
 242  // d) Calculate 3-p azimuthal correlator in terms of Q_{n,k} and S_{p,k}:
 243  if(anEvent->GetEventNSelTracksRP() >= 3)
 244  {
 245   this->Calculate3pCorrelator();
 246  }
 247  if(anEvent->GetEventNSelTracksRP() >= 0) // to be improved (is this correct if statement?)
 248  {
 249   this->CalculateNonIsotropicTerms();
 250  }
 251
 252  // e) Reset all event-by-event quantities: \r
 253  this->ResetEventByEventQuantities();
 254   \r
 255 } // end of AliFlowAnalysisWithMixedHarmonics::Make(AliFlowEventSimple* anEvent)\r\r
 256 //================================================================================================================\r
 257 \r
 258 void AliFlowAnalysisWithMixedHarmonics::Finish()\r
 259 {\r
 260  // Calculate the final results.
 261
 262  // a) Check all pointers used in this method;
 263  // b) Access settings for analysis with mixed harmonics;
 264  // c) Calculate errors for non-isotropic terms;
 265  // d) Correct for detector effects;
 266  // e) Quantify bias to 3-p correlator coming from detector effects.
 267
 268  this->CheckPointersUsedInFinish();
 269  this->AccessSettings();
 270  this->FinalizeNonIsotropicTerms();
 271  this->CorrectForDetectorEffects();
 272  this->QuantifyBiasFromDetectorEffects();
 273  \r
 274  cout<<endl;\r
 275  cout<<"*************************************"<<endl;\r
 276  cout<<"*************************************"<<endl;\r
 277  cout<<" flow estimates from mixed harmonics "<<endl;
 278  cout<<endl;\r
 279  if(fCorrelatorInteger!=1)
 280  {
 281   cout<< "  cos["<<fCorrelatorInteger<<"(2phi1-phi2-phi3)] = "<<f3pCorrelatorPro->GetBinContent(1)<<endl;
 282  } else
 283    {
 284     cout<< "  cos(2phi1-phi2-phi3) = "<<f3pCorrelatorPro->GetBinContent(1)<<endl;
 285    }
 286
 287  cout<<endl;
 288  cout<<"*************************************"<<endl;\r
 289  cout<<"*************************************"<<endl;\r
 290                                                                                                                                                                                                                                                                                                                \r
 291 } // end of AliFlowAnalysisWithMixedHarmonics::Finish()\r
 292 \r
 293 //================================================================================================================\r
 294 \r
 295 void AliFlowAnalysisWithMixedHarmonics::GetOutputHistograms(TList *outputListHistos)\r
 296 {\r
 297  // Get pointers to all objects saved in the output file.
 298
 299  // a) Get pointers for common control histograms.\r \r
 300  if(outputListHistos)\r
 301  {      \r
 302   this->SetHistList(outputListHistos);
 303   if(!fHistList)
 304   {
 305    cout<<endl;
 306    cout<<" WARNING (MH): fHistList is NULL in AFAWMH::GOH() !!!!"<<endl;
 307    cout<<endl;
 308    exit(0);
 309   }
 310   this->GetPointersForCommonHistograms();
 311   this->GetPointersForResultsHistograms();\r
 312  } else
 313    {
 314     cout<<endl;
 315     cout<<" WARNING (MH): outputListHistos is NULL in AFAWMH::GOH() !!!!"<<endl;
 316     cout<<endl;
 317     exit(0);
 318    }
 319    \r
 320 } // end of void AliFlowAnalysisWithMixedHarmonics::GetOutputHistograms(TList *outputListHistos)\r
 321 \r
 322 //================================================================================================================
 323
 324 void AliFlowAnalysisWithMixedHarmonics::GetPointersForCommonHistograms() \r
 325 {\r
 326  // Get pointers to common control histograms.\r
 327  \r
 328  TString commonHistsName = "AliFlowCommonHistMH";\r
 329  AliFlowCommonHist *commonHist = dynamic_cast<AliFlowCommonHist*>(fHistList->FindObject(commonHistsName.Data()));\r
 330  if(commonHist)
 331  {
 332   this->SetCommonHists(commonHist);
 333  } else
 334    {
 335     cout<<endl;
 336     cout<<" WARNING (MH): commonHist is NULL in AFAWMH::GPFCH() !!!!"<<endl;
 337     cout<<endl;
 338     exit(0);
 339    }
 340
 341 } // end of void AliFlowAnalysisWithMixedHarmonics::GetPointersForCommonHistograms()
 342
 343 //================================================================================================================
 344
 345 void AliFlowAnalysisWithMixedHarmonics::GetPointersForResultsHistograms() \r
 346 {\r
 347  // Get pointers to histograms holding final results.\r
 348  \r
 349  TList *resultsList = NULL;\r
 350  resultsList = dynamic_cast<TList*>(fHistList->FindObject("Results"));\r
 351  if(!resultsList) \r
 352  {\r
 353   cout<<"WARNING: resultsList is NULL in AFAWMH::GPFRH() !!!!"<<endl;\r
 354   exit(0); \r
 355  }
 356
 357  TString s3pCorrelatorHistName = "f3pCorrelatorHist";\r
 358  TH1D *h3pCorrelatorHist = dynamic_cast<TH1D*>(resultsList->FindObject(s3pCorrelatorHistName.Data()));\r
 359  if(h3pCorrelatorHist)\r
 360  {\r
 361   this->Set3pCorrelatorHist(h3pCorrelatorHist);  \r
 362  }
 363  TString detectorBiasHistName = "fDetectorBiasHist";\r
 364  TH1D *detectorBiasHist = dynamic_cast<TH1D*>(resultsList->FindObject(detectorBiasHistName.Data()));\r
 365  if(detectorBiasHist)\r
 366  {\r
 367   this->SetDetectorBiasHist(detectorBiasHist);  \r
 368  }
 369  TString nonIsotropicTermsHistName = "fNonIsotropicTermsHist";\r
 370  TH1D *nonIsotropicTermsHist = dynamic_cast<TH1D*>(resultsList->FindObject(nonIsotropicTermsHistName.Data()));\r
 371  if(nonIsotropicTermsHist)\r
 372  {\r
 373   this->SetNonIsotropicTermsHist(nonIsotropicTermsHist);  \r
 374  }
 375
 376 } // end of void AliFlowAnalysisWithMixedHarmonics::GetPointersForResultsHistograms()
 377 \r
 378 //================================================================================================================
 379
 380 void AliFlowAnalysisWithMixedHarmonics::WriteHistograms(TString outputFileName)\r
 381 {\r
 382  // Store the final results in output .root file.\r
 383  TFile *output = new TFile(outputFileName.Data(),"RECREATE");\r
 384  fHistList->Write(fHistList->GetName(),TObject::kSingleKey);\r
 385  delete output;\r
 386 }\r
 387 \r
 388 //================================================================================================================\r
 389
 390 void AliFlowAnalysisWithMixedHarmonics::WriteHistograms(TDirectoryFile *outputFileName)
 391 {
 392  // Store the final results in output .root file.
 393  fHistList->SetName("cobjMH");
 394  fHistList->SetOwner(kTRUE);
 395  outputFileName->Add(fHistList);
 396  outputFileName->Write(outputFileName->GetName(),TObject::kSingleKey);
 397 }
 398
 399 //================================================================================================================
 400
 401 void AliFlowAnalysisWithMixedHarmonics::BookAndNestAllLists()\r
 402 {
 403  // Book and nest all list in base list fHistList.
 404
 405  // Weights:
 406  fWeightsList->SetName("Weights");\r
 407  fWeightsList->SetOwner(kTRUE);   \r
 408  fHistList->Add(fWeightsList);
 409  // Results:
 410  fResultsList->SetName("Results");\r
 411  fResultsList->SetOwner(kTRUE);   \r
 412  fHistList->Add(fResultsList);
 413
 414 } // end of void AliFlowAnalysisWithMixedHarmonics::BookAndNestAllLists()
 415
 416 //================================================================================================================
 417
 418 void AliFlowAnalysisWithMixedHarmonics::BookProfileHoldingSettings()\r
 419 {
 420  // Book profile to hold all analysis settings.
 421
 422  TString analysisSettingsName = "fAnalysisSettings";\r
 423  fAnalysisSettings = new TProfile(analysisSettingsName.Data(),"Settings for analysis with mixed harmonics",5,0,5);
 424  fAnalysisSettings->GetXaxis()->SetBinLabel(1,"Integer n in cos(n(2#phi_{1}-#phi_{2}-#phi_{3}))");
 425  fAnalysisSettings->Fill(0.5,fCorrelatorInteger);\r
 426  fAnalysisSettings->GetXaxis()->SetBinLabel(2,"Corrected for detector effects?");
 427  fAnalysisSettings->Fill(1.5,(Int_t)fCorrectForDetectorEffects);
 428  fAnalysisSettings->GetXaxis()->SetBinLabel(3,"# of multiplicity bins");
 429  fAnalysisSettings->Fill(2.5,fNoOfMultipicityBins);
 430  fAnalysisSettings->GetXaxis()->SetBinLabel(4,"Width of multiplicity bins");
 431  fAnalysisSettings->Fill(3.5,fMultipicityBinWidth);
 432  fAnalysisSettings->GetXaxis()->SetBinLabel(5,"Minimal multiplicity");
 433  fAnalysisSettings->Fill(4.5,fMinMultiplicity);
 434  fHistList->Add(fAnalysisSettings);
 435
 436 } // end of void AliFlowAnalysisWithMixedHarmonics::BookProfileHoldingSettings()
 437 \r
 438 //================================================================================================================
 439
 440 void AliFlowAnalysisWithMixedHarmonics::BookCommonHistograms()\r
 441 {\r
 442  // Book common control histograms and common histograms for final results.
 443  \r
 444  TString commonHistsName = "AliFlowCommonHistMH";\r
 445  fCommonHists = new AliFlowCommonHist(commonHistsName.Data());\r
 446  fHistList->Add(fCommonHists);  \r
 447  \r
 448 } // end of void AliFlowAnalysisWithMixedHarmonics::BookCommonHistograms()\r
 449
 450 //================================================================================================================
 451
 452 void AliFlowAnalysisWithMixedHarmonics::BookAllEventByEventQuantities()\r
 453 {\r
 454  // Book all event-by-event quantitites.
 455
 456  // Q_{n,k} and S{p,k}:
 457  fReQnk = new TMatrixD(2,4); // to be improved(bound on k)\r
 458  fImQnk = new TMatrixD(2,4); // to be improved(bound on k)\r
 459  fSpk = new TMatrixD(4,4); // to be improved(bound on p and k)
 460  // 3-p correlator <cos[n(2phi1-phi2-phi3)]> for single event:
 461  TString s3pCorrelatorEBEName = "f3pCorrelatorEBE";\r
 462  f3pCorrelatorEBE = new TH1D(s3pCorrelatorEBEName.Data(),"<cos[n(2#phi_{1}-#phi_{2}-#phi_{3})]> for single event",1,0,1);
 463  // Correction terms for non-uniform acceptance to <cos[n(2phi1-phi2-phi3)]> for single event:
 464  TString nonIsotropicTermsEBEName = "fNonIsotropicTermsEBE";\r
 465  fNonIsotropicTermsEBE = new TH1D(nonIsotropicTermsEBEName.Data(),"Non-isotropic terms for single event",10,0,10);
 466
 467 } // end fo void AliFlowAnalysisWithMixedHarmonics::BookAllEventByEventQuantities()\r
 468 //================================================================================================================
 469
 470 void AliFlowAnalysisWithMixedHarmonics::BookAllAllEventQuantities()
 471 {
 472  // Book all all-event quantitites.
 473
 474  // a) Book quantites without multiplicity binning;
 475  // b) Book quantites with multiplicity binning.
 476
 477  // a) Book quantites without multiplicity binning:
 478  // 3-p correlator <<cos[n(2phi1-phi2-phi3)]>> for all events (with wrong error):
 479  TString s3pCorrelatorProName = "f3pCorrelatorPro";\r
 480  f3pCorrelatorPro = new TProfile(s3pCorrelatorProName.Data(),"<<cos[n(2#phi_{1}-#phi_{2}-#phi_{3})]>> for all events (errors are wrong here!)",1,0,1,"s");
 481  fHistList->Add(f3pCorrelatorPro);
 482  // 3-p correlator <<cos[n(2phi1-phi2-phi3)]>> for all events (with correct error):
 483  TString s3pCorrelatorHistName = "f3pCorrelatorHist";\r
 484  f3pCorrelatorHist = new TH1D(s3pCorrelatorHistName.Data(),"<<cos[n(2#phi_{1}-#phi_{2}-#phi_{3})]>> for all events",1,0,1);
 485  fResultsList->Add(f3pCorrelatorHist);
 486  // Correction terms for non-uniform acceptance to <cos[n(2phi1-phi2-phi3)]> for all events (with wrong errors):
 487  TString nonIsotropicTermsProName = "fNonIsotropicTermsPro";\r
 488  fNonIsotropicTermsPro = new TProfile(nonIsotropicTermsProName.Data(),"Non-isotropic terms for all events (errors are wrong here!)",10,0,10,"s");
 489  fNonIsotropicTermsPro->GetXaxis()->SetBinLabel(1,"cos(n(#phi_{1}))");\r
 490  fNonIsotropicTermsPro->GetXaxis()->SetBinLabel(2,"sin(n(#phi_{1}))");
 491  fNonIsotropicTermsPro->GetXaxis()->SetBinLabel(3,"cos(2n(#phi_{1}))");\r
 492  fNonIsotropicTermsPro->GetXaxis()->SetBinLabel(4,"sin(2n(#phi_{1}))");\r
 493  fNonIsotropicTermsPro->GetXaxis()->SetBinLabel(5,"cos(n(#phi_{1}+#phi_{2}))");\r
 494  fNonIsotropicTermsPro->GetXaxis()->SetBinLabel(6,"sin(n(#phi_{1}+#phi_{2}))");
 495  fNonIsotropicTermsPro->GetXaxis()->SetBinLabel(7,"cos(n(2#phi_{1}-#phi_{2}))");\r
 496  fNonIsotropicTermsPro->GetXaxis()->SetBinLabel(8,"sin(n(2#phi_{1}-#phi_{2}))");
 497  fNonIsotropicTermsPro->GetXaxis()->SetBinLabel(9,"cos(n(#phi_{1}-#phi_{2}-#phi_{3}))");\r
 498  fNonIsotropicTermsPro->GetXaxis()->SetBinLabel(10,"sin(n(#phi_{1}-#phi_{2}-#phi_{3})");
 499  fHistList->Add(fNonIsotropicTermsPro);
 500  // Correction terms for non-uniform acceptance to <cos[n(2phi1-phi2-phi3)]> for all events (with correct errors):
 501  TString nonIsotropicTermsHistName = "fNonIsotropicTermsHist";\r
 502  fNonIsotropicTermsHist = new TH1D(nonIsotropicTermsHistName.Data(),"Non-isotropic terms for all events",10,0,10);
 503  fNonIsotropicTermsHist->GetXaxis()->SetBinLabel(1,"cos(n(#phi_{1}))");\r
 504  fNonIsotropicTermsHist->GetXaxis()->SetBinLabel(2,"sin(n(#phi_{1}))");
 505  fNonIsotropicTermsHist->GetXaxis()->SetBinLabel(3,"cos(2n(#phi_{1}))");\r
 506  fNonIsotropicTermsHist->GetXaxis()->SetBinLabel(4,"sin(2n(#phi_{1}))");\r
 507  fNonIsotropicTermsHist->GetXaxis()->SetBinLabel(5,"cos(n(#phi_{1}+#phi_{2}))");\r
 508  fNonIsotropicTermsHist->GetXaxis()->SetBinLabel(6,"sin(n(#phi_{1}+#phi_{2}))");
 509  fNonIsotropicTermsHist->GetXaxis()->SetBinLabel(7,"cos(n(2#phi_{1}-#phi_{2}))");\r
 510  fNonIsotropicTermsHist->GetXaxis()->SetBinLabel(8,"sin(n(2#phi_{1}-#phi_{2}))");
 511  fNonIsotropicTermsHist->GetXaxis()->SetBinLabel(9,"cos(n(#phi_{1}-#phi_{2}-#phi_{3}))");\r
 512  fNonIsotropicTermsHist->GetXaxis()->SetBinLabel(10,"sin(n(#phi_{1}-#phi_{2}-#phi_{3})");
 513  fResultsList->Add(fNonIsotropicTermsHist);
 514  // Quantified bias comming from detector inefficiencies to 3-p correlator <<cos[n(2phi1-phi2-phi3)]>> (in %)
 515  TString detectorBiasHistName = "fDetectorBiasHist";\r
 516  fDetectorBiasHist = new TH1D(detectorBiasHistName.Data(),"Bias coming from detector inefficiences",1,0,1);
 517  fDetectorBiasHist->GetXaxis()->SetBinLabel(1,"#left|1 - #frac{corrected}{not-corrected}#right| (in %)");
 518  fResultsList->Add(fDetectorBiasHist);
 519
 520  // b) Book quantites with multiplicity binning.
 521  // 3-p correlator <<cos[n(2phi1-phi2-phi3)]>> for all events versus multiplicity (with wrong error):
 522  TString s3pCorrelatorVsMProName = "f3pCorrelatorVsMPro";\r
 523  f3pCorrelatorVsMPro = new TProfile(s3pCorrelatorVsMProName.Data(),"<<cos[n(2#phi_{1}-#phi_{2}-#phi_{3})]>> vs M for all events (errors are wrong here!)",fNoOfMultipicityBins+1,0,fNoOfMultipicityBins+1,"s");
 524  for(Int_t b=1;b<=fNoOfMultipicityBins;b++)
 525  {
 526   f3pCorrelatorVsMPro->GetXaxis()->SetBinLabel(b,Form("%d #leq M < %d",(Int_t)(fMinMultiplicity+(b-1)*fMultipicityBinWidth),(Int_t)(fMinMultiplicity+b*fMultipicityBinWidth)));
 527  }
 528  f3pCorrelatorVsMPro->GetXaxis()->SetBinLabel(fNoOfMultipicityBins+1,Form(" M #geq %d",(Int_t)(fMinMultiplicity+fNoOfMultipicityBins*fMultipicityBinWidth)));
 529  fHistList->Add(f3pCorrelatorVsMPro);
 530  // 3-p correlator <<cos[n(2phi1-phi2-phi3)]>> for all events (with correct error):
 531  TString s3pCorrelatorVsMHistName = "f3pCorrelatorVsMHist";\r
 532  f3pCorrelatorVsMHist = new TH1D(s3pCorrelatorVsMHistName.Data(),"<<cos[n(2#phi_{1}-#phi_{2}-#phi_{3})]>> vs M for all events",fNoOfMultipicityBins+1,0,fNoOfMultipicityBins+1);
 533  for(Int_t b=1;b<=fNoOfMultipicityBins;b++)
 534  {
 535   f3pCorrelatorVsMHist->GetXaxis()->SetBinLabel(b,Form("%d #leq M < %d",(Int_t)(fMinMultiplicity+(b-1)*fMultipicityBinWidth),(Int_t)(fMinMultiplicity+b*fMultipicityBinWidth)));
 536  }
 537  f3pCorrelatorVsMHist->GetXaxis()->SetBinLabel(fNoOfMultipicityBins+1,Form(" M #geq %d",(Int_t)(fMinMultiplicity+fNoOfMultipicityBins*fMultipicityBinWidth)));
 538  fResultsList->Add(f3pCorrelatorVsMHist);
 539  // Correction terms for non-uniform acceptance to <cos[n(2phi1-phi2-phi3)]> for all events vs M (with wrong errors):
 540  TString nonIsotropicTermsVsMProName = "fNonIsotropicTermsVsMPro";\r
 541  fNonIsotropicTermsVsMPro = new TProfile2D(nonIsotropicTermsVsMProName.Data(),"Non-isotropic terms for all events vs M (errors are wrong here!)",10,0,10,fNoOfMultipicityBins+1,0,fNoOfMultipicityBins+1,"s");
 542  fNonIsotropicTermsVsMPro->GetXaxis()->SetBinLabel(1,"cos(n(#phi_{1}))");\r
 543  fNonIsotropicTermsVsMPro->GetXaxis()->SetBinLabel(2,"sin(n(#phi_{1}))");
 544  fNonIsotropicTermsVsMPro->GetXaxis()->SetBinLabel(3,"cos(2n(#phi_{1}))");\r
 545  fNonIsotropicTermsVsMPro->GetXaxis()->SetBinLabel(4,"sin(2n(#phi_{1}))");\r
 546  fNonIsotropicTermsVsMPro->GetXaxis()->SetBinLabel(5,"cos(n(#phi_{1}+#phi_{2}))");\r
 547  fNonIsotropicTermsVsMPro->GetXaxis()->SetBinLabel(6,"sin(n(#phi_{1}+#phi_{2}))");
 548  fNonIsotropicTermsVsMPro->GetXaxis()->SetBinLabel(7,"cos(n(2#phi_{1}-#phi_{2}))");\r
 549  fNonIsotropicTermsVsMPro->GetXaxis()->SetBinLabel(8,"sin(n(2#phi_{1}-#phi_{2}))");
 550  fNonIsotropicTermsVsMPro->GetXaxis()->SetBinLabel(9,"cos(n(#phi_{1}-#phi_{2}-#phi_{3}))");\r
 551  fNonIsotropicTermsVsMPro->GetXaxis()->SetBinLabel(10,"sin(n(#phi_{1}-#phi_{2}-#phi_{3})");
 552  for(Int_t b=1;b<=fNoOfMultipicityBins;b++)
 553  {
 554   fNonIsotropicTermsVsMPro->GetYaxis()->SetBinLabel(b,Form("%d #leq M < %d",(Int_t)(fMinMultiplicity+(b-1)*fMultipicityBinWidth),(Int_t)(fMinMultiplicity+b*fMultipicityBinWidth)));
 555  }
 556  fNonIsotropicTermsVsMPro->GetYaxis()->SetBinLabel(fNoOfMultipicityBins+1,Form(" M #geq %d",(Int_t)(fMinMultiplicity+fNoOfMultipicityBins*fMultipicityBinWidth)));
 557  fHistList->Add(fNonIsotropicTermsVsMPro);
 558  // Correction terms for non-uniform acceptance to <cos[n(2phi1-phi2-phi3)]> for all events (with correct errors):
 559  TString nonIsotropicTermsVsMHistName = "fNonIsotropicTermsVsMHist";\r
 560  fNonIsotropicTermsVsMHist = new TH2D(nonIsotropicTermsVsMHistName.Data(),"Non-isotropic terms for all events vs M ",10,0,10,fNoOfMultipicityBins+1,0,fNoOfMultipicityBins+1);
 561  fNonIsotropicTermsVsMHist->GetXaxis()->SetBinLabel(1,"cos(n(#phi_{1}))");\r
 562  fNonIsotropicTermsVsMHist->GetXaxis()->SetBinLabel(2,"sin(n(#phi_{1}))");
 563  fNonIsotropicTermsVsMHist->GetXaxis()->SetBinLabel(3,"cos(2n(#phi_{1}))");\r
 564  fNonIsotropicTermsVsMHist->GetXaxis()->SetBinLabel(4,"sin(2n(#phi_{1}))");\r
 565  fNonIsotropicTermsVsMHist->GetXaxis()->SetBinLabel(5,"cos(n(#phi_{1}+#phi_{2}))");\r
 566  fNonIsotropicTermsVsMHist->GetXaxis()->SetBinLabel(6,"sin(n(#phi_{1}+#phi_{2}))");
 567  fNonIsotropicTermsVsMHist->GetXaxis()->SetBinLabel(7,"cos(n(2#phi_{1}-#phi_{2}))");\r
 568  fNonIsotropicTermsVsMHist->GetXaxis()->SetBinLabel(8,"sin(n(2#phi_{1}-#phi_{2}))");
 569  fNonIsotropicTermsVsMHist->GetXaxis()->SetBinLabel(9,"cos(n(#phi_{1}-#phi_{2}-#phi_{3}))");\r
 570  fNonIsotropicTermsVsMHist->GetXaxis()->SetBinLabel(10,"sin(n(#phi_{1}-#phi_{2}-#phi_{3})");
 571  for(Int_t b=1;b<=fNoOfMultipicityBins;b++)
 572  {
 573   fNonIsotropicTermsVsMHist->GetYaxis()->SetBinLabel(b,Form("%d #leq M < %d",(Int_t)(fMinMultiplicity+(b-1)*fMultipicityBinWidth),(Int_t)(fMinMultiplicity+b*fMultipicityBinWidth)));
 574  }
 575  fNonIsotropicTermsVsMHist->GetYaxis()->SetBinLabel(fNoOfMultipicityBins+1,Form(" M #geq %d",(Int_t)(fMinMultiplicity+fNoOfMultipicityBins*fMultipicityBinWidth)));
 576  fResultsList->Add(fNonIsotropicTermsVsMHist);
 577  // Quantified bias comming from detector inefficiencies to 3-p correlator <<cos[n(2phi1-phi2-phi3)]>> (in %)
 578  TString detectorBiasVsMHistName = "fDetectorBiasVsMHist";\r
 579  fDetectorBiasVsMHist = new TH1D(detectorBiasVsMHistName.Data(),"#left|1 - #frac{corrected}{not-corrected}#right| (in %)",fNoOfMultipicityBins+1,0,fNoOfMultipicityBins+1);
 580  for(Int_t b=1;b<=fNoOfMultipicityBins;b++)
 581  {
 582   fDetectorBiasVsMHist->GetXaxis()->SetBinLabel(b,Form("%d #leq M < %d",(Int_t)(fMinMultiplicity+(b-1)*fMultipicityBinWidth),(Int_t)(fMinMultiplicity+b*fMultipicityBinWidth)));
 583  }
 584  fDetectorBiasVsMHist->GetXaxis()->SetBinLabel(fNoOfMultipicityBins+1,Form(" M #geq %d",(Int_t)(fMinMultiplicity+fNoOfMultipicityBins*fMultipicityBinWidth)));
 585  fResultsList->Add(fDetectorBiasVsMHist);
 586
 587 } // end of void AliFlowAnalysisWithMixedHarmonics::BookAllAllEventQuantities()
 588 \r
 589 //================================================================================================================
 590
 591 void AliFlowAnalysisWithMixedHarmonics::AccessConstants()\r
 592 {\r
 593  // Access needed common constants from AliFlowCommonConstants.\r
 594  \r
 595  fnBinsPhi = AliFlowCommonConstants::GetMaster()->GetNbinsPhi();\r
 596  fPhiMin = AliFlowCommonConstants::GetMaster()->GetPhiMin();         \r
 597  fPhiMax = AliFlowCommonConstants::GetMaster()->GetPhiMax();\r
 598  if(fnBinsPhi) fPhiBinWidth = (fPhiMax-fPhiMin)/fnBinsPhi;  \r
 599  fnBinsPt = AliFlowCommonConstants::GetMaster()->GetNbinsPt();\r
 600  fPtMin = AliFlowCommonConstants::GetMaster()->GetPtMin();           \r
 601  fPtMax = AliFlowCommonConstants::GetMaster()->GetPtMax();\r
 602  if(fnBinsPt) fPtBinWidth = (fPtMax-fPtMin)/fnBinsPt;  \r
 603  fnBinsEta = AliFlowCommonConstants::GetMaster()->GetNbinsEta();\r
 604  fEtaMin = AliFlowCommonConstants::GetMaster()->GetEtaMin();         \r
 605  fEtaMax = AliFlowCommonConstants::GetMaster()->GetEtaMax();\r
 606  if(fnBinsEta) fEtaBinWidth = (fEtaMax-fEtaMin)/fnBinsEta;  \r
 607  \r
 608 } // end of void AliFlowAnalysisWithMixedHarmonics::AccessConstants()
 609
 610 //================================================================================================================\r
 611 \r
 612 void AliFlowAnalysisWithMixedHarmonics::CrossCheckSettings()\r
 613 {\r
 614  // Cross-check if the user settings make sense. \r
 615  \r
 616 } // end of void AliFlowAnalysisWithMixedHarmonics::CrossCheckSettings()\r
 617
 618 //================================================================================================================\r
 619
 620 void AliFlowAnalysisWithMixedHarmonics::BookAndFillWeightsHistograms()\r
 621 {\r
 622  // Book and fill (by accessing file "weights.root") histograms which hold phi, pt and eta weights.\r
 623 \r
 624  if(!fWeightsList)\r
 625  {\r
 626   cout<<"WARNING: fWeightsList is NULL in AFAWMH::BAFWH() !!!!"<<endl;\r
 627   exit(0);  \r
 628  }\r
 629  // Profile to hold flags for weights:   \r
 630  TString fUseParticleWeightsName = "fUseParticleWeightsMH";\r
 631  fUseParticleWeights = new TProfile(fUseParticleWeightsName.Data(),"0 = particle weight not used, 1 = particle weight used ",3,0,3);\r
 632  fUseParticleWeights->SetLabelSize(0.06);\r
 633  (fUseParticleWeights->GetXaxis())->SetBinLabel(1,"w_{#phi}");\r
 634  (fUseParticleWeights->GetXaxis())->SetBinLabel(2,"w_{p_{T}}");\r
 635  (fUseParticleWeights->GetXaxis())->SetBinLabel(3,"w_{#eta}");\r
 636  fUseParticleWeights->Fill(0.5,(Int_t)fUsePhiWeights);\r
 637  fUseParticleWeights->Fill(1.5,(Int_t)fUsePtWeights);\r
 638  fUseParticleWeights->Fill(2.5,(Int_t)fUseEtaWeights);\r
 639  fWeightsList->Add(fUseParticleWeights); \r
 640  // Phi-weights: \r
 641  if(fUsePhiWeights)\r
 642  {\r
 643   if(fWeightsList->FindObject("phi_weights"))\r
 644   {\r
 645    fPhiWeights = dynamic_cast<TH1F*>(fWeightsList->FindObject("phi_weights"));\r
 646    if(TMath::Abs(fPhiWeights->GetBinWidth(1)-fPhiBinWidth)>pow(10.,-6.))\r
 647    {\r
 648     cout<<endl;
 649     cout<<"WARNING (MH): Inconsistent binning in histograms for phi-weights throughout the code."<<endl;\r
 650     cout<<endl;
 651     exit(0);\r
 652    }\r
 653   } else \r
 654     {\r
 655      cout<<"WARNING (MH): fWeightsList->FindObject(\"phi_weights\") is NULL in AFAWMH::BAFWH() !!!!"<<endl;\r
 656      exit(0);\r
 657     }\r
 658  } // end of if(fUsePhiWeights)\r
 659  // Pt-weights:\r
 660  if(fUsePtWeights) \r
 661  {\r
 662   if(fWeightsList->FindObject("pt_weights"))\r
 663   {\r
 664    fPtWeights = dynamic_cast<TH1D*>(fWeightsList->FindObject("pt_weights"));\r
 665    if(TMath::Abs(fPtWeights->GetBinWidth(1)-fPtBinWidth)>pow(10.,-6.))\r
 666    {\r
 667     cout<<endl;
 668     cout<<"WARNING (MH): Inconsistent binning in histograms for pt-weights throughout the code."<<endl;\r
 669     cout<<endl;
 670     exit(0);\r
 671    }\r
 672   } else \r
 673     {\r
 674      cout<<"WARNING (MH): fWeightsList->FindObject(\"pt_weights\") is NULL in AFAWMH::BAFWH() !!!!"<<endl;\r
 675      exit(0);\r
 676     }\r
 677  } // end of if(fUsePtWeights)    \r
 678  // Eta-weights:\r
 679  if(fUseEtaWeights) \r
 680  {\r
 681   if(fWeightsList->FindObject("eta_weights"))\r
 682   {\r
 683    fEtaWeights = dynamic_cast<TH1D*>(fWeightsList->FindObject("eta_weights"));\r
 684    if(TMath::Abs(fEtaWeights->GetBinWidth(1)-fEtaBinWidth)>pow(10.,-6.))\r
 685    {\r
 686     cout<<endl;
 687     cout<<"WARNING (MH): Inconsistent binning in histograms for eta-weights throughout the code."<<endl;\r
 688     cout<<endl;
 689     exit(0);\r
 690    }\r
 691   } else \r
 692     {\r
 693      cout<<"WARNING: fUseEtaWeights && fWeightsList->FindObject(\"eta_weights\") is NULL in AFAWMH::BAFWH() !!!!"<<endl;\r
 694      exit(0);\r
 695     }\r
 696  } // end of if(fUseEtaWeights)\r
 697  \r
 698 } // end of AliFlowAnalysisWithMixedHarmonics::BookAndFillWeightsHistograms()
 699
 700 //================================================================================================================
 701 \r
 702 void AliFlowAnalysisWithMixedHarmonics::CheckPointersUsedInMake()\r
 703 {\r
 704  // Check pointers used in method Make().\r
 705
 706  if(!fReQnk || !fImQnk || !fSpk || !f3pCorrelatorEBE)
 707  {
 708   cout<<endl;
 709   cout<<" WARNING (MH): (!fReQnk || !fImQnk || !fSpk || !f3pCorrelatorEBE) is NULL !!!!"<<endl;
 710   cout<<endl;
 711   exit(0);
 712  }
 713  if(!f3pCorrelatorPro)
 714  {
 715   cout<<endl;
 716   cout<<" WARNING (MH): (!f3pCorrelatorPro) is NULL !!!!"<<endl;
 717   cout<<endl;
 718   exit(0);
 719  }
 720                                                                                                                                                                                                                                                                                                                                    \r
 721 } // end of AliFlowAnalysisWithMixedHarmonics::CheckPointersUsedInMake()
 722
 723 //================================================================================================================
 724 \r
 725 void AliFlowAnalysisWithMixedHarmonics::CheckPointersUsedInFinish()\r
 726 {\r
 727  // Check pointers used in method Finish().
 728                                                                                                                                                                                                                                                                                                                                    \r
 729 } // end of AliFlowAnalysisWithMixedHarmonics::CheckPointersUsedInFinish()\r
 730
 731 //================================================================================================================
 732 \r
 733 void AliFlowAnalysisWithMixedHarmonics::AccessSettings()\r
 734 {\r
 735  // Access the settings for analysis with mixed harmonics.
 736
 737  fCorrelatorInteger = (Int_t)fAnalysisSettings->GetBinContent(1);
 738  fCorrectForDetectorEffects = (Bool_t)fAnalysisSettings->GetBinContent(2);
 739  fNoOfMultipicityBins = (Int_t)fAnalysisSettings->GetBinContent(3);
 740  fMultipicityBinWidth = (Double_t)fAnalysisSettings->GetBinContent(4);
 741  fMinMultiplicity = (Double_t)fAnalysisSettings->GetBinContent(5);
 742                                                                                                                                                                                                                                                                                                                                    \r
 743 } // end of AliFlowAnalysisWithMixedHarmonics::AccessSettings()
 744
 745 //================================================================================================================
 746 \r
 747 void AliFlowAnalysisWithMixedHarmonics::CorrectForDetectorEffects()\r
 748 {\r
 749  // Correct measured 3-p correlator cos[n(2phi1-phi2-phi3)] for detector effects.
 750
 751  Double_t measured3pCorrelator = f3pCorrelatorPro->GetBinContent(1); // biased by detector effects
 752  Double_t corrected3pCorrelator = 0.; // corrected for detector effects
 753  Double_t nonIsotropicTerms[10] = {0.}; // there are 10 distinct non-isotropic terms
 754  for(Int_t nit=0;nit<10;nit++)
 755  {
 756   nonIsotropicTerms[nit] = fNonIsotropicTermsPro->GetBinContent(nit+1);
 757  }
 758  // Calculate corrected 3-p correlator:
 759  corrected3pCorrelator = measured3pCorrelator
 760                        - nonIsotropicTerms[2]*nonIsotropicTerms[4]
 761                        - nonIsotropicTerms[3]*nonIsotropicTerms[5]
 762                        - 2.*nonIsotropicTerms[0]*nonIsotropicTerms[6]
 763                        - 2.*nonIsotropicTerms[1]*nonIsotropicTerms[7]
 764                        + 2.*nonIsotropicTerms[2]*(pow(nonIsotropicTerms[0],2.)-pow(nonIsotropicTerms[1],2.))
 765                        + 4.*nonIsotropicTerms[3]*nonIsotropicTerms[0]*nonIsotropicTerms[1];
 766  // Store corrected 3-p correlator:
 767  f3pCorrelatorHist->SetBinContent(1,corrected3pCorrelator);
 768                                                                                                                                                                                                                                                                                                                                    \r
 769 } // end of AliFlowAnalysisWithMixedHarmonics::CorrectForDetectorEffects()
 770
 771 //================================================================================================================
 772 \r
 773 void AliFlowAnalysisWithMixedHarmonics::FinalizeNonIsotropicTerms()\r
 774 {\r
 775  // Calculate correctly the errors of non-isotropic terms.
 776
 777  // Transfer mean values from profiles to histograms: // to be improved
 778  for(Int_t mv=1;mv<=10;mv++)
 779  {
 780   fNonIsotropicTermsHist->SetBinContent(mv,fNonIsotropicTermsPro->GetBinContent(mv));
 781  }
 782
 783 } // end of void AliFlowAnalysisWithMixedHarmonics::FinalizeNonIsotropicTerms()
 784
 785 //================================================================================================================
 786 \r
 787 void AliFlowAnalysisWithMixedHarmonics::QuantifyBiasFromDetectorEffects()\r
 788 {\r
 789  // Quantify bias from detector inefficiences to 3-p correlator.
 790
 791  // Remark: Bias is quantified as 1 - |corrected/nonCorrected| (in %) and stored in histogram fDetectorBias
 792
 793  Double_t bias = 0.;
 794  if(f3pCorrelatorPro->GetBinContent(1))
 795  {
 796   bias = 100.*TMath::Abs(1.-f3pCorrelatorHist->GetBinContent(1)/f3pCorrelatorPro->GetBinContent(1));
 797  }
 798  fDetectorBiasHist->SetBinContent(1,bias);
 799
 800 } // end of void AliFlowAnalysisWithMixedHarmonics::QuantifyBiasFromDetectorEffects()
 801
 802 //================================================================================================================\r\r
 803 void AliFlowAnalysisWithMixedHarmonics::ResetEventByEventQuantities()\r
 804 {\r
 805  // Reset all event by event quantities.\r
 806  \r
 807  fReQnk->Zero();\r
 808  fImQnk->Zero();\r
 809  fSpk->Zero();
 810
 811  f3pCorrelatorEBE->Reset();\r
 812
 813 } // end of void AliFlowAnalysisWithMixedHarmonics::ResetEventByEventQuantities()
 814
 815 //================================================================================================================
 816
 817 void AliFlowAnalysisWithMixedHarmonics::Calculate3pCorrelator()\r
 818 {\r
 819  // Calculate 3-p azimuthal correlator cos[n(2phi1-phi2-phi3)] in terms of Q_{n,k} and S_{p,k}.\r
 820
 821  // a) Calculate 3-p correlator without using particle weights;
 822  // b) Calculate 3-p correlator with using particle weights.
 823
 824  // a) Calculate 3-p correlator without using particle weights: \r
 825  if(!(fUsePhiWeights || fUsePtWeights || fUseEtaWeights))
 826  {
 827   // Multiplicity (number of RPs):\r
 828   Double_t dMult = (*fSpk)(0,0);\r
 829   // Real and imaginary parts of non-weighted Q-vectors (Q_{n,0}) evaluated in harmonics n and 2n: \r
 830   Double_t dReQ1n = (*fReQnk)(0,0);\r
 831   Double_t dReQ2n = (*fReQnk)(1,0);\r
 832   Double_t dImQ1n = (*fImQnk)(0,0);\r
 833   Double_t dImQ2n = (*fImQnk)(1,0);
 834   // 3-particle azimuthal correlator <cos(n*(2.*phi1-phi2-phi3))>:\r
 835   Double_t three2n1n1n = (pow(dReQ1n,2.)*dReQ2n + 2.*dReQ1n*dImQ1n*dImQ2n - pow(dImQ1n,2.)*dReQ2n
 836                        - 2.*(pow(dReQ1n,2.)+pow(dImQ1n,2.))\r
 837                        - (pow(dReQ2n,2.)+pow(dImQ2n,2.))+2.*dMult)\r
 838                        / (dMult*(dMult-1.)*(dMult-2.));
 839   // Fill event-by-event histogram and all-events profile:
 840   f3pCorrelatorEBE->SetBinContent(1,three2n1n1n);
 841   f3pCorrelatorPro->Fill(0.5,three2n1n1n,dMult*(dMult-1.)*(dMult-2.));
 842
 843   // Correlator vs multiplicity: // to be improved
 844   f3pCorrelatorVsMPro->Fill(0.5+(Int_t)((dMult-fMinMultiplicity)/fMultipicityBinWidth),dMult*(dMult-1.)*(dMult-2.)); // to be improved (cross-checked)
 845  } // end of if(!(fUsePhiWeights || fUsePtWeights || fUseEtaWeights))
 846
 847  // b) Calculate 3-p correlator without using particle weights: \r
 848  if(fUsePhiWeights || fUsePtWeights || fUseEtaWeights)
 849  {
 850
 851  } // end of if(fUsePhiWeights || fUsePtWeights || fUseEtaWeights)
 852
 853 } // end of void AliFlowAnalysisWithMixedHarmonics::Calculate3pCorrelator()
 854
 855 //================================================================================================================
 856
 857 void AliFlowAnalysisWithMixedHarmonics::CalculateNonIsotropicTerms()
 858 {
 859  // Calculate correction terms for non-uniform acceptance to 3-p correlator <cos[n(2phi1-phi2-phi3)]>.
 860
 861  // a) Calculate using particle weights;
 862  // b) Calculate without using particle weights.
 863
 864  // These non-isotropic terms are stored in fNonIsotropicTermsPro. The same results but with
 865  // correct errors are stored in fNonIsotropicTermsHist. Binning of fNonIsotropicTermsPro and
 866  // fNonIsotropicTermsHist is organized as follows:
 867  //  1st bin: <<cos(n*phi1)>>\r
 868  //  2nd bin: <<sin(n*phi1)>>
 869  //  3rd bin: <<cos(2n*phi1)>>\r
 870  //  4th bin: <<sin(2n*phi1)>>
 871  //  5th bin: <<cos(n*(phi1+phi2)>>\r
 872  //  6th bin: <<sin(n*(phi1+phi2)>>
 873  //  7th bin: <<cos(n*(2phi1-phi2)>>\r
 874  //  8th bin: <<sin(n*(2phi1-phi2)>>
 875  //  9th bin: <<cos(n*(phi1-phi2-phi3)>>\r
 876  // 10th bin: <<sin(n*(phi1-phi2-phi3)>>
 877
 878  // a) Calculate using particle weights:
 879  if(!(fUsePhiWeights || fUsePtWeights || fUseEtaWeights))
 880  {
 881   // Multiplicity (number of RPs):\r
 882   Double_t dMult = (*fSpk)(0,0);\r
 883   // Real and imaginary parts of non-weighted Q-vectors (Q_{n,0}) evaluated in harmonics n and 2n: \r
 884   Double_t dReQ1n = (*fReQnk)(0,0);\r
 885   Double_t dReQ2n = (*fReQnk)(1,0);\r
 886   Double_t dImQ1n = (*fImQnk)(0,0);\r
 887   Double_t dImQ2n = (*fImQnk)(1,0);
 888   // 1-particle terms:\r
 889   Double_t cosP1n = 0.; // <cos(n*(phi1))>
 890   Double_t sinP1n = 0.; // <sin(n*(phi1))>
 891   Double_t cosP2n = 0.; // <cos(2n*(phi1))>
 892   Double_t sinP2n = 0.; // <sin(2n*(phi1))>\r
 893   if(dMult>0)\r
 894   { \r
 895    cosP1n = dReQ1n/dMult;
 896    sinP1n = dImQ1n/dMult;
 897    cosP2n = dReQ2n/dMult;
 898    sinP2n = dImQ2n/dMult;
 899    // Single event avarages:\r
 900    fNonIsotropicTermsEBE->SetBinContent(1,cosP1n); // <cos(n*(phi1))>\r
 901    fNonIsotropicTermsEBE->SetBinContent(2,sinP1n); // <sin(n*(phi1))>\r
 902    fNonIsotropicTermsEBE->SetBinContent(3,cosP2n); // <cos(2n*(phi1))>\r
 903    fNonIsotropicTermsEBE->SetBinContent(4,sinP2n); // <sin(2n*(phi1))>
 904    // All-events avarages:\r
 905    fNonIsotropicTermsPro->Fill(0.5,cosP1n,dMult); // <<cos(n*(phi1))>>
 906    fNonIsotropicTermsPro->Fill(1.5,sinP1n,dMult); // <<sin(n*(phi1))>>
 907    fNonIsotropicTermsPro->Fill(2.5,cosP2n,dMult); // <<cos(2n*(phi1))>>
 908    fNonIsotropicTermsPro->Fill(3.5,sinP2n,dMult); // <<sin(2n*(phi1))>>   \r
 909   } \r
 910   // 2-particle terms:\r
 911   Double_t cosP1nP1n = 0.; // <cos(n*(phi1+phi2))>
 912   Double_t sinP1nP1n = 0.; // <sin(n*(phi1+phi2))>
 913   Double_t cosP2nM1n = 0.; // <cos(n*(2phi1-phi2))>
 914   Double_t sinP2nM1n = 0.; // <sin(n*(2phi1-phi2))>\r
 915   if(dMult>1)\r
 916   {\r
 917    cosP1nP1n = (pow(dReQ1n,2)-pow(dImQ1n,2)-dReQ2n)/(dMult*(dMult-1));
 918    sinP1nP1n = (2.*dReQ1n*dImQ1n-dImQ2n)/(dMult*(dMult-1)); \r
 919    cosP2nM1n = (dReQ2n*dReQ1n+dImQ2n*dImQ1n-dReQ1n)/(dMult*(dMult-1));
 920    sinP2nM1n = (dImQ2n*dReQ1n-dReQ2n*dImQ1n-dImQ1n)/(dMult*(dMult-1)); \r
 921    // Single event avarages:\r
 922    fNonIsotropicTermsEBE->SetBinContent(5,cosP1nP1n); // <cos(n*(phi1+phi2))>\r
 923    fNonIsotropicTermsEBE->SetBinContent(6,sinP1nP1n); // <sin(n*(phi1+phi2))>
 924    fNonIsotropicTermsEBE->SetBinContent(7,cosP2nM1n); // <cos(n*(2phi1-phi2))>\r
 925    fNonIsotropicTermsEBE->SetBinContent(8,sinP2nM1n); // <sin(n*(2phi1-phi2))>\r
 926    // All-events avarages:\r
 927    fNonIsotropicTermsPro->Fill(4.5,cosP1nP1n,dMult*(dMult-1.)); // <<cos(n*(phi1+phi2))>>
 928    fNonIsotropicTermsPro->Fill(5.5,sinP1nP1n,dMult*(dMult-1.)); // <<sin(n*(phi1+phi2))>>   \r
 929    fNonIsotropicTermsPro->Fill(6.5,cosP2nM1n,dMult*(dMult-1.)); // <<cos(n*(2phi1-phi2))>>
 930    fNonIsotropicTermsPro->Fill(7.5,sinP2nM1n,dMult*(dMult-1.)); // <<sin(n*(2phi1-phi2))>>   \r
 931   } \r
 932  \r
 933   // 3-particle:\r
 934   Double_t cosP1nM1nM1n = 0.; // <cos(n*(phi1-phi2-phi3))>\r
 935   Double_t sinP1nM1nM1n = 0.; // <sin(n*(phi1-phi2-phi3))>\r
 936   if(dMult>2)\r
 937   {\r
 938    cosP1nM1nM1n = (dReQ1n*(pow(dReQ1n,2)+pow(dImQ1n,2))-dReQ1n*dReQ2n-dImQ1n*dImQ2n-2.*(dMult-1)*dReQ1n)\r
 939                 / (dMult*(dMult-1)*(dMult-2));
 940    sinP1nM1nM1n = (-dImQ1n*(pow(dReQ1n,2)+pow(dImQ1n,2))+dReQ1n*dImQ2n-dImQ1n*dReQ2n+2.*(dMult-1)*dImQ1n)\r
 941                 / (dMult*(dMult-1)*(dMult-2));              \r
 942    // Single event avarages:\r
 943    fNonIsotropicTermsEBE->SetBinContent(9,cosP1nM1nM1n); // <cos(n*(phi1-phi2-phi3))>
 944    fNonIsotropicTermsEBE->SetBinContent(10,sinP1nM1nM1n); // <sin(n*(phi1-phi2-phi3))>\r
 945    // All-events avarages:\r
 946    fNonIsotropicTermsPro->Fill(8.5,cosP1nM1nM1n,dMult*(dMult-1.)*(dMult-2.)); // <<cos(n*(phi1-phi2-phi3))>>
 947    fNonIsotropicTermsPro->Fill(9.5,sinP1nM1nM1n,dMult*(dMult-1.)*(dMult-2.)); // <<sin(n*(phi1-phi2-phi3))>>   \r
 948   }
 949  } // end of if(!(fUsePhiWeights || fUsePtWeights || fUseEtaWeights))
 950
 951  // b) Calculate without using particle weights:\r
 952  if(fUsePhiWeights || fUsePtWeights || fUseEtaWeights)
 953  {
 954
 955  } // end of if(fUsePhiWeights || fUsePtWeights || fUseEtaWeights)
 956
 957 } // end of void AliFlowAnalysisWithMixedHarmonics::CalculateNonIsotropicTerms()
 958