[Common] Add code and documentation for glauber fits

Common/Tools/Multiplicity/README.md

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+# Multiplicity/centrality tools in O2/O2Physics
+
+This directory serves to aggregate all files necessary for multiplicity
+and centrality calibration going from pp to Pb-Pb. It offers functionality
+to perform simple slicing in percentiles, such as what is done in
+proton-proton collisions, as well as the Glauber + analytical NBD fitter
+used to perform anchoring and hadronic event distribution estimates in
+nucleus-nucleus collisions.
+
+## Files
+* `README.md` this readme
+* `CMakeLists.txt` definition of source files that need compiling
+* `multCalibrator.cxx/h` a class to do percentile slicing of a given histogram. Used for all systems.
+* `multMCCalibrator.cxx/h` a class to perform data-to-mc matching of average Nch.
+* `multGlauberNBDFitter.cxx/h` a class to do glauber fits.
+* `multModule.h` a class to perform calculations of multiplicity and centrality tables for analysis. Meant to be used inside the main core service wagon 'multcenttable'.
+

Common/Tools/Multiplicity/macros/README.md

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+# Example multiplicity calibration macros
+
+You will find some example macros in this directory that will allow for the calculation of a glauber fit and the corresponding calibration histograms.
+
+A simplified description of the procedure necessary to generate a
+Glauber + NBD fit to a certain histogram is described below.
+
+## Performing a Glauber + NBD fit
+
+### First step: calculation of Glauber MC sample
+
+The Glauber + NBD model assumes that the multiplicity / amplitude
+distribution that one intends to fit can be described as coming
+from a certain number N_{ancestor} of particle-emitting sources called 'ancestors'. Each ancestor is assumed to produce particles
+according to a negative binominal distribution. Further,
+the number of ancestors is assumed to be related to the basic
+glauber quantities N_{part} and N_{coll} via the formula:
+
+N_{ancestor} = f * N_{part}  + (1-f) N_{coll}
+
+Usually, the value f is fixed at 0.8, and thus the range of
+N_{ancestors} is typically 0-700 in Pb-Pb collisions.
+
+In order to allow for Glauber + NBD fitting, the correlation of
+(N_{part}, N_{coll}) needs to be known. For that purpose,
+a tree of Glauber MC needs to be generated using TGlauberMC using the relevant nuclei, which also involves choosing an appropriate nuclear profile.
+
+Once TGlauberMC has been used to produce a tree with N_{part} and
+N_{coll} values, their correlation needs to be saved to a 2D histogram that serves as input to the Glauber + NBD fitter used in
+O2/O2Physics. This is done using the macro called `saveCorrelation.C` contained in this directory, which produces a file named `baseHistos.root`. The file `saveCorrelation.C` serves as
+an example for the Pb-Pb case and minor adaptation may be needed
+in case other nuclei are to be used.
+
+### Second step: execution of Glauber + NBD fitter
+
+The fitting procedure is done via the macro ``. Because
+the numerical fitting utilizes a convolution of a N_{ancestor}
+distribution and NBD distributions, it will not be as fast
+as typical one-dimensional fits: typical times of 10-100 seconds
+are not unusual. The macro will produce an output file
+that contains:
+
+* the original fitted histogram
+* the actual glauber fit distribution, plotted all the way
+to zero multiplicity
+
+This output can then be used to extract percentiles.
+
+### Third step: calculation of percentile boundaries
+
+Once both the data and glauber fit distributions are known,
+the next step is to create a 'stitched' data/glauber distribution in
+which the distribution at low multiplicities follows
+the glauber fit and the distribution at higher multiplicities
+follows the data. The multiplicity value in which the switch from
+glauber to data takes place is called 'anchor point'.
+
+Because of the fact that this 'stitching' procedure may need to be tuned and the actual glauber fit is slow, the stitching is done
+in a separate macro called `runCalibration.C`. It is provided
+in this directory as well and it is the third and last step in calculating percentile boundaries. The macro will printout some
+key boundaries as well as save an output file with the calibration.
+
+*Bonus*: at the stage in which the glauber fit has been done
+and all information is available, a de-convolution process
+can be used to calculate the average N_{part} and N_{coll}
+in centrality slices. This functionality is also provided
+in O2Physics as part of the `multGlauberNBDFitter` and the
+`runCalibration.C` macro can optionally also perform that
+deconvolution. *Warning*: this procedure might take a mooment.

Common/Tools/Multiplicity/macros/runCalibration.C

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+// Copyright 2019-2020 CERN and copyright holders of ALICE O2.
+// See https://alice-o2.web.cern.ch/copyright for details of the copyright holders.
+// All rights not expressly granted are reserved.
+//
+// This software is distributed under the terms of the GNU General Public
+// License v3 (GPL Version 3), copied verbatim in the file "COPYING".
+//
+// In applying this license CERN does not waive the privileges and immunities
+// granted to it by virtue of its status as an Intergovernmental Organization
+// or submit itself to any jurisdiction.
+//
+/// \file saveCorrelation.C
+/// \brief
+/// \author ALICE
+
+#include <iostream>
+
+/// @brief function to calibrate centrality
+/// @param lInputFileName name of input file.
+/// @param anchorPointPercentage anchor point percentage to use
+/// @param matchRange width of region in which data/glauber matching is to be done in rolling anchoring test
+/// @param doNpartNcoll wether or not to attempt calculating Npart, Ncoll in centrality bins
+void runCalibration(TString lInputFileName = "results/AR_544122_glauberNBD_ancestorMode2_hFT0C_BCs.root", double anchorPointPercentage = 90.0, double matchRange = 200.0, bool doNpartNcoll = false)
+{
+  TFile* file = new TFile(lInputFileName.Data(), "READ");
+  file->ls();
+
+  TH1F* hData = (TH1F*)file->Get("hV0MUltraFine");
+  TH1F* hGlauberParameters = (TH1F*)file->Get("hGlauberParameters");
+  TH1F* hGlauberFitRange = (TH1F*)file->Get("hGlauberFitRange");
+  hData->SetName("hData");
+  TH1F* hStitched = (TH1F*)hData->Clone("hStitched");
+  TH1F* hFit = (TH1F*)file->Get("hGlauber");
+
+  TCanvas* c1 = new TCanvas("c1", "", 800, 600);
+  c1->SetLeftMargin(0.17);
+  c1->SetBottomMargin(0.17);
+  c1->SetRightMargin(0.15);
+  c1->SetTopMargin(0.05);
+  c1->SetTicks(1, 1);
+  c1->SetLogz();
+  c1->SetFrameFillStyle(0);
+  c1->SetFillStyle(0);
+
+  cout << "Data bin width: " << hData->GetBinWidth(1) << endl;
+  cout << "Fit bin width: " << hFit->GetBinWidth(1) << endl;
+  cout << "Match range to use: " << matchRange << endl;
+
+  //____________________________________________
+  double anchorPointFraction = anchorPointPercentage / 100.f;
+  double anchorPoint = -1; // the anchor point value in raw
+
+  //____________________________________________
+  // doing partial integration up to certain point for finding anchor point bin
+  for (int ii = 1; ii < hData->GetNbinsX() + 1; ii++) {
+    // renormalize data curve
+    int bin1 = ii + 1;
+    int bin2 = hData->FindBin(hData->GetBinLowEdge(ii + 1) + matchRange + 1e-3);
+    double matchRangeData = hData->Integral(bin1, bin2);
+    double matchRangeFit = hFit->Integral(bin1, bin2);
+
+    // rescale fit to match in the vicinity of the region we're at
+    hFit->Scale(matchRangeData / matchRangeFit);
+
+    double integralFit = hFit->Integral(1, ii);
+    double integralData = hData->Integral(ii + 1, hData->GetNbinsX() + 1);
+    double integralAll = integralFit + integralData;
+
+    cout << "at bin #" << ii << ", integrated up to " << hData->GetBinLowEdge(ii + 1) << " fraction above this value is: " << integralData / integralAll << endl;
+    anchorPoint = hData->GetBinLowEdge(ii + 1);
+
+    if (integralData / integralAll < anchorPointFraction)
+      break;
+  }
+
+  //____________________________________________
+  for (int ii = 1; ii < hData->GetNbinsX() + 1; ii++) {
+    // renormalize data curve
+    if (hData->GetBinCenter(ii) < anchorPoint)
+      hStitched->SetBinContent(ii, hFit->GetBinContent(ii));
+  }
+
+  cout << "Anchor point determined to be: " << anchorPoint << endl;
+  cout << "Preparing stitched histogram ... " << endl;
+
+  hFit->SetLineColor(kRed);
+  hStitched->SetLineColor(kBlue);
+
+  hData->GetYaxis()->SetTitleSize(0.055);
+  hData->GetXaxis()->SetTitleSize(0.055);
+  hData->GetYaxis()->SetLabelSize(0.04);
+  hData->GetXaxis()->SetLabelSize(0.04);
+  hData->SetTitle("");
+  hData->Draw("hist");
+  hFit->Draw("hist same");
+  hStitched->Draw("hist same");
+
+  // All fine, let's try the calibrator
+  multCalibrator* lCalib = new multCalibrator("lCalib");
+  lCalib->SetAnchorPointPercentage(100.0f);
+  lCalib->SetAnchorPointRaw(-1e-6);
+
+  // Set standard Pb-Pb boundaries
+  lCalib->SetStandardOnePercentBoundaries();
+
+  TString calibFileName = lInputFileName.Data();
+  calibFileName.ReplaceAll("glauberNBD", "calibration");
+  TFile* fileCalib = new TFile(calibFileName.Data(), "RECREATE");
+
+  TH1F* hCalib = lCalib->GetCalibrationHistogram(hStitched, "hCalib");
+
+  TCanvas* c2 = new TCanvas("c2", "", 800, 600);
+  c2->SetLeftMargin(0.17);
+  c2->SetBottomMargin(0.17);
+  c2->SetRightMargin(0.15);
+  c2->SetTopMargin(0.05);
+  c2->SetTicks(1, 1);
+  //  c2->SetLogz();
+  c2->SetFrameFillStyle(0);
+  c2->SetFillStyle(0);
+
+  hCalib->GetYaxis()->SetTitleSize(0.055);
+  hCalib->GetXaxis()->SetTitleSize(0.055);
+  hCalib->GetYaxis()->SetLabelSize(0.04);
+  hCalib->GetXaxis()->SetLabelSize(0.04);
+  hCalib->SetTitle("");
+  hCalib->Draw();
+
+  fileCalib->cd();
+
+  hData->Write();
+  hCalib->Write();
+  hStitched->Write();
+  hFit->Write();
+
+  if (doNpartNcoll) {
+    cout << "Will now attempt to calculate % -> Np, Nc map..." << endl;
+
+    TProfile* hProfileNpart = new TProfile("hProfileNpart", "", 100, 0, 100);
+    TProfile* hProfileNcoll = new TProfile("hProfileNcoll", "", 100, 0, 100);
+    TH2F* h2dNpart = new TH2F("h2dNpart", "", 100, 0, 100, 500, -0.5f, 499.5f);
+    TH2F* h2dNcoll = new TH2F("h2dNcoll", "", 100, 0, 100, 3000, -0.5f, 2999.5);
+
+    // Replay
+    multGlauberNBDFitter* g = new multGlauberNBDFitter("lglau");
+    TF1* fitfunc = g->GetGlauberNBD();
+
+    // Step 1: open the (Npart, Ncoll) pair information, provide
+    TFile* fbasefile = new TFile("basehistos.root", "READ");
+    TH2D* hNpNc = (TH2D*)fbasefile->Get("hNpNc");
+    g->SetNpartNcollCorrelation(hNpNc);
+    g->InitializeNpNc();
+
+    fitfunc->SetParameter(0, hGlauberParameters->GetBinContent(1));
+    fitfunc->SetParameter(1, hGlauberParameters->GetBinContent(2));
+    fitfunc->SetParameter(2, hGlauberParameters->GetBinContent(3));
+    fitfunc->SetParameter(3, hGlauberParameters->GetBinContent(4));
+    fitfunc->SetParameter(4, hGlauberParameters->GetBinContent(5));
+
+    Double_t lMax = hData->GetBinLowEdge(hData->GetNbinsX() + 1);
+
+    // uncomment if Np Nc needed -> Warning, slow!
+    g->CalculateAvNpNc(hProfileNpart, hProfileNcoll, h2dNpart, h2dNcoll, hCalib, 0, lMax);
+
+    hProfileNpart->Write();
+    hProfileNcoll->Write();
+    h2dNpart->Write();
+    h2dNcoll->Write();
+  }
+
+  fileCalib->Write();
+}