PairAnalysisHelper.cxx

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//                                                                       //
// helper functions wrapped in a namespace.
//
//
// Authors:
//  * Copyright(c) 1998-2009, ALICE Experiment at CERN, All rights reserved. *
//  Julian Book <Julian.Book@cern.ch>
//
//                                                                       //
 
 
#include "PairAnalysisHelper.h"
 
#include "CbmModuleList.h"
 
#include <TDatabasePDG.h>
#include <TError.h>
#include <TF1.h>
#include <TFormula.h>
#include <TGraph.h>
#include <TH1.h>
#include <TH2.h>
#include <THashList.h>
#include <TMCProcess.h>
#include <TMath.h>
#include <TObjArray.h>
#include <TObjString.h>
#include <TPad.h>
#include <TParticlePDG.h>
#include <TProfile.h>
#include <TRandom.h>
#include <TVectorD.h>
 
#include "PairAnalysisStyler.h"
#include "PairAnalysisVarManager.h"
 
//_____________________________________________________________________________
TVectorD* PairAnalysisHelper::MakeLogBinning(Int_t nbinsX, Double_t xmin, Double_t xmax)
{
  //
  // Make logarithmic binning
  // the user has to delete the array afterwards!!!
  //
 
  //check limits
  if (xmin < 1e-20 || xmax < 1e-20) {
    Error("PairAnalysisHelper::MakeLogBinning", "For Log binning xmin and xmax must be > 1e-20. Using linear binning "
                                                "instead!");
    return PairAnalysisHelper::MakeLinBinning(nbinsX, xmin, xmax);
  }
  if (xmax < xmin) {
    Double_t tmp = xmin;
    xmin         = xmax;
    xmax         = tmp;
  }
  TVectorD* binLim = new TVectorD(nbinsX + 1);
  Double_t first   = xmin;
  Double_t last    = xmax;
  Double_t expMax  = TMath::Log(last / first);
  for (Int_t i = 0; i < nbinsX + 1; ++i) {
    (*binLim)[i] = first * TMath::Exp(expMax / nbinsX * (Double_t) i);
  }
  return binLim;
}
 
//_____________________________________________________________________________
TVectorD* PairAnalysisHelper::MakeLinBinning(Int_t nbinsX, Double_t xmin, Double_t xmax)
{
  //
  // Make linear binning
  // the user has to delete the array afterwards!!!
  //
  if (xmax < xmin) {
    Double_t tmp = xmin;
    xmin         = xmax;
    xmax         = tmp;
  }
  TVectorD* binLim  = new TVectorD(nbinsX + 1);
  Double_t first    = xmin;
  Double_t last     = xmax;
  Double_t binWidth = (last - first) / nbinsX;
  for (Int_t i = 0; i < nbinsX + 1; ++i) {
    (*binLim)[i] = first + binWidth * (Double_t) i;
  }
  return binLim;
}
 
//_____________________________________________________________________________
TVectorD* PairAnalysisHelper::MakeArbitraryBinning(const char* bins)
{
  //
  // Make arbitrary binning, bins separated by a ','
  //
  TString limits(bins);
  if (limits.IsNull()) {
    Error("PairAnalysisHelper::MakeArbitraryBinning", "Bin Limit string is empty, cannot add the variable");
    return 0x0;
  }
 
  TObjArray* arr = limits.Tokenize(",");
  Int_t nLimits  = arr->GetEntries();
  if (nLimits < 2) {
    Error("PairAnalysisHelper::MakeArbitraryBinning", "Need at leas 2 bin limits, cannot add the variable");
    delete arr;
    return 0x0;
  }
 
  TVectorD* binLimits = new TVectorD(nLimits);
  for (Int_t iLim = 0; iLim < nLimits; ++iLim) {
    (*binLimits)[iLim] = (static_cast<TObjString*>(arr->At(iLim)))->GetString().Atof();
  }
 
  delete arr;
  return binLimits;
}
 
//_____________________________________________________________________________
TVectorD* PairAnalysisHelper::MakeGausBinning(Int_t nbinsX, Double_t mean, Double_t sigma)
{
  //
  // Make gaussian binning
  // the user has to delete the array afterwards!!!
  //
 
  TVectorD* binLim = new TVectorD(nbinsX + 1);
 
  TF1 g("g", "gaus", mean - 5 * sigma, mean + 5 * sigma);
  g.SetParameters(1, mean, sigma);
  Double_t sum = g.Integral(mean - 5 * sigma, mean + 5 * sigma);
  //printf("full integral gaussian: %f \n",sum);
 
  TF1 g2("g2", "gaus(0)/[3]", mean - 5 * sigma, mean + 5 * sigma);
  g2.SetParameters(1, mean, sigma, sum);  
 
  //  Double_t *params=g2.GetParameters();
 
  Double_t epsilon = sigma / 10000;     // step size
  Double_t xt      = mean - 5 * sigma;  // bin limit
  Double_t pint    = 0.0;               // previous integral
 
  Int_t bin    = 0;        // current entry
  Double_t lim = epsilon;  // requested integral values (start,..., end values)
 
  // calculate intergral until you found all limits
  while ((xt += epsilon) <= mean + 5 * sigma) {
 
    // current integral
    //    Double_t cint = g2.Integral(mean-5*sigma,xt,params,epsilon); //fast, but NOT root 6 (Integral(min,max,epsilon)) compatible
    Double_t cint = g2.Integral(mean - 5 * sigma, xt);  //,params,epsilon);   //slow
    //    printf(" integral to %f:  %f , search limit: %f \n",xt,cint,lim);
 
    if (cint >= lim && pint < lim) {
      //      printf(" %d bin found for %f with requested integral %f, actual integral is %f \n",bin,xt,lim,cint);
      (*binLim)[bin] = xt;
 
      bin++;
      lim = bin * (1. / nbinsX);
      if (bin == nbinsX) lim = 1. - epsilon;
    }
 
    pint = cint;
  }
 
  //  binLim->Print();
  return binLim;
}
 
//_____________________________________________________________________________
TVectorD* PairAnalysisHelper::CombineBinning(TVectorD* low, TVectorD* high)
{
  //
  // Make a new combined binning of "low" and "high"
  // the user has to delete the returned array afterwards!!!
  //
 
  // fill final vector
  Int_t lastEqualsFirst = (Int_t)(TMath::Abs((*low)[low->GetNrows() - 1] - (*high)[0]) < 1.e-15);
  TVectorD* binLim      = new TVectorD(low->GetNrows() + high->GetNrows() - lastEqualsFirst);
  for (Int_t i = 0; i < low->GetNrows(); i++)
    (*binLim)[i] = (*low)[i];
  for (Int_t i = 0; i < high->GetNrows() - lastEqualsFirst; i++)
    (*binLim)[low->GetNrows() + i] = (*high)[i + lastEqualsFirst];
 
  // clean up
  //  delete low;  delete high;
  //  binLim->Print();
  return binLim;
}
 
//_____________________________________________________________________________
TArrayD* PairAnalysisHelper::MakeStatBinLimits(TH1* h, Double_t stat)
{
  //
  // get bin limits for stat. error less than 'stat'
  //
  if (!h || stat > 1.) return 0x0;
 
  Double_t cont = 0.0;
  Double_t err  = 0.0;
  Double_t from = h->GetBinLowEdge(1);
  Double_t to   = 0.0;
 
  TArrayD* vBins = new TArrayD(1 + 1);
  vBins->AddAt(from, 0);
  Int_t vEle = 1;
 
  for (Int_t i = 1; i <= h->GetNbinsX(); i++) {
 
    if (h->GetBinContent(i) == 0.0 && h->GetBinError(i) == 0.) continue;
 
    to = h->GetBinLowEdge(i + 1);
    cont += h->GetBinContent(i);
    err += (h->GetBinError(i) * h->GetBinError(i));
    vBins->AddAt(to, vEle);
 
    // Printf("cont %f/%f=%f err %f(%f) sum of -> rel err %f%% (current: %f%%)",
    //             h->GetBinContent(i),h->Integral(),h->GetBinContent(i)/h->Integral(), h->GetBinError(i), TMath::Sqrt(h->GetBinContent(i)),h->GetBinError(i)/h->GetBinContent(i)*100, TMath::Sqrt(err)/cont*100);
 
    // check for new bin
    if (TMath::Sqrt(err) / cont <= stat
        //      ||   (h->GetBinContent(i)/h->Integral()) < 0.01
        //      || (h->GetBinContent(i)==0.0 && h->GetBinError(i)==0. && vEle==1)
    ) {
      //      Printf("bin from %f to %f with err %f%%",from,to,TMath::Sqrt(err)/cont*100);
      err  = 0.0;
      cont = 0.0;
      vEle++;
      from = to;
      vBins->Set(vEle + 1);
    }
  }
 
  vBins->AddAt(h->GetXaxis()->GetXmax(), vBins->GetSize() - 1);
 
  //  for(Int_t i=0;i<vBins->GetSize();i++)  Printf("%d %f",i,vBins->At(i));
  return vBins;
}
 
//_____________________________________________________________________________
TVectorD* PairAnalysisHelper::MakePdgBinning()
{
  //
  // Make arbitrary binning using defined PDG codes
  //
 
  // array of pdgcodes stored in TDatabasePDG
  TDatabasePDG* pdg = new TDatabasePDG();  //::Instance();
  pdg->ReadPDGTable();
  TIter next(pdg->ParticleList());
  TGraph gr;
  TParticlePDG* p;
  Int_t i = 0;
  while ((p = (TParticlePDG*) next())) {
    if (TMath::Abs(p->PdgCode()) < 1e+6) {
      // printf("%s -> %d \n",p->GetName(),p->PdgCode());
      gr.SetPoint(i++, p->PdgCode(), 1.);
    }
  }
  gr.Sort();
  TVectorD* vec = new TVectorD(gr.GetN(), gr.GetX());
  //  vec->Print();
  delete pdg;
  return vec;
}
 
//_____________________________________________________________________________
Double_t PairAnalysisHelper::EvalFormula(TFormula* form, const Double_t* values)
{
  //
  // evaluate return value for formula with current parameter values
  //
  Double_t params[10] = {0.};
  //put parameter values into array using variables stored as the parameters
  for (Int_t ip = 0; ip < form->GetNpar(); ip++)
    params[ip] = values[(UInt_t) form->GetParameter(ip)];
  return (form->EvalPar(0x0, params));
}
 
//_____________________________________________________________________________
TString PairAnalysisHelper::GetFormulaTitle(TFormula* form)
{
  //
  // evaluate the formula in a readable way (for axis etc)
  //
  // TODO: add units, switch to TMathText, get ride of obsolete parentheses
  TString tform(form->GetExpFormula());
  // TMathText
  //  tform.ReplaceAll("*","\\cdot");   // multiplication sign
  //  tform.ReplaceAll("TMath::","\\"); // get ride of TMath::
  // TLatex
  tform.ReplaceAll("*", "#upoint");  // multiplication sign
  //  tform.ReplaceAll("Sqrt","sqrt"); // sqrt sign
  tform.ReplaceAll("TMath::", "");  // get ride of TMath::
  tform.ReplaceAll("()", "");       // remove function parenthesis
  tform.ToLower();                  // lower cases (e.g. Cos -> cos)
  // replace parameter variables with proper labels
  for (Int_t j = 0; j < form->GetNpar(); j++)
    tform.ReplaceAll(Form("[%d]", j), PairAnalysisVarManager::GetValueLabel((UInt_t) form->GetParameter(j)));
  return (tform);
}
 
//_____________________________________________________________________________
TString PairAnalysisHelper::GetFormulaName(TFormula* form)
{
  //
  // build formula key with parameter names
  //
  TString tform("f(");
  for (Int_t j = 0; j < form->GetNpar(); j++) {
    tform += PairAnalysisVarManager::GetValueName((UInt_t) form->GetParameter(j));
    if (j != form->GetNpar() - 1) tform += ",";
  }
  tform += ")";
  return (tform);
}
 
//_____________________________________________________________________________
TFormula* PairAnalysisHelper::GetFormula(const char* name, const char* formula)
{
  //
  // build a TFormula object
  //
  TString check(formula);
  if (check.IsNull()) return 0x0;
  TFormula* form = new TFormula(name, formula);
  // compile function
  if (form->Compile()) return 0x0;
  //set parameter/variable identifier
  for (Int_t i = 0; i < form->GetNpar(); i++) {
    form->SetParName(i, PairAnalysisVarManager::GetValueName(form->GetParameter(i)));
    //    fUsedVars->SetBitNumber((Int_t)form->GetParameter(i),kTRUE);
  }
  return form;
}
 
//_____________________________________________________________________________
void PairAnalysisHelper::SetPDGBinLabels(TH1* hist, Bool_t clean)
{
  //
  // build formula key with parameter names
  //
 
  TH1* hLbl = PairAnalysisStyler::GetFirstHistogram();
  if (!hLbl) hLbl = hist;
 
  TDatabasePDG* pdg = TDatabasePDG::Instance();
  TAxis* xaxis      = hLbl->GetXaxis();
  for (Int_t i = 1; i < hist->GetNbinsX() + 1; i++) {
    // printf("bin %d: low edge: %.0f --> %s \n",i,xaxis->GetBinLowEdge(i), pdg->GetParticle(xaxis->GetBinLowEdge(i))->GetName());
    if (clean && !hist->GetBinContent(i)) continue;
    Int_t pdgCode   = (Int_t) xaxis->GetBinLowEdge(i);
    TParticlePDG* p = pdg->GetParticle(pdgCode);
    //    xaxis->SetBinLabel(i,(p?p->GetName():""));
    xaxis->SetBinLabel(i, (p ? GetPDGlabel(pdgCode) : ""));
  }
 
  if (hLbl->GetDimension() == 1) return;
 
  TAxis* yaxis = hLbl->GetYaxis();
  TString keyY = yaxis->GetName();
  if (keyY.Contains("pdg", TString::kIgnoreCase)) {
    for (Int_t i = 1; i < hist->GetNbinsY() + 1; i++) {
      // printf("bin %d: low edge: %.0f --> %s \n",i,yaxis->GetBinLowEdge(i), pdg->GetParticle(yaxis->GetBinLowEdge(i))->GetName());
      if (clean && !hist->GetBinContent(i)) continue;
      Int_t pdgCode   = (Int_t) yaxis->GetBinLowEdge(i);
      TParticlePDG* p = pdg->GetParticle(pdgCode);
      //    yaxis->SetBinLabel(i,(p?p->GetName():""));
      yaxis->SetBinLabel(i, (p ? GetPDGlabel(pdgCode) : ""));
    }
  }
}
 
//_____________________________________________________________________________
TString PairAnalysisHelper::GetPDGlabel(Int_t pdg)
{
  //
  // return the label in latex format corresponding to pdg code
  //
 
  TString name = TDatabasePDG::Instance()->GetParticle(pdg)->GetName();
  name.ReplaceAll("dd_1_bar", "primary");
  name.ReplaceAll("proton", "p");
  // correct greek letters
  /*
  if(name.Contains("delta",TString::kIgnoreCase) ||
     name.Contains("gamma",TString::kIgnoreCase) ||
     name.Contains("sigma",TString::kIgnoreCase) ||
     name.Contains("xi",TString::kIgnoreCase) ||
     name.Contains("lambda",TString::kIgnoreCase) ||
     name.Contains("omega",TString::kIgnoreCase) ||
     name.Contains("eta",TString::kIgnoreCase) ||
     name.Contains("tau",TString::kIgnoreCase) ||
     name.Contains("phi",TString::kIgnoreCase) ||
     name.Contains("eta",TString::kIgnoreCase) ||
     name.Contains("upsilon",TString::kIgnoreCase) ||
     name.Contains("nu",TString::kIgnoreCase) ||
     name.Contains("pi",TString::kIgnoreCase) ||
     name.Contains("rho",TString::kIgnoreCase) ) name.Prepend("#");
  */
  name.ReplaceAll("delta", "#delta");
  name.ReplaceAll("gamma", "#gamma");
  name.ReplaceAll("psi", "#psi");
  name.ReplaceAll("sigma", "#sigma");
  name.ReplaceAll("xi", "#xi");
  name.ReplaceAll("lambda", "#lambda");
  name.ReplaceAll("omega", "#omega");
  name.ReplaceAll("eta", "#eta");
  name.ReplaceAll("tau", "#tau");
  name.ReplaceAll("phi", "#phi");
  name.ReplaceAll("upsilon", "#upsilon");
  name.ReplaceAll("nu", "#nu");
  name.ReplaceAll("mu", "#mu");
  name.ReplaceAll("pi", "#pi");
  name.ReplaceAll("rho", "#rho");
 
  // correct anti particles
  if (name.Contains("anti")) {
    name.ReplaceAll("anti", "#bar{");
    name.Append("}");
  }
  else if (name.Contains("_bar")) {
    name.ReplaceAll("_bar", "}");
    name.Prepend("#bar{");
  }
  // correct indices
  name.ReplaceAll("+", "^{+}");
  name.ReplaceAll("-", "^{-}");
  name.ReplaceAll("0", "^{0}");
  name.ReplaceAll("_s", "_{s}");
  name.ReplaceAll("_c", "_{c}");
  name.ReplaceAll("_b", "_{b}");
  name.ReplaceAll("_1", "_{1}");
  // specials
  name.ReplaceAll("/psi", "/#psi");
  //  Printf(" %d = %s",pdg,name.Data());
  return name;
}
 
//_____________________________________________________________________________
void PairAnalysisHelper::SetGEANTBinLabels(TH1* hist)
{
  //
  // build formula key with parameter names
  //
  TAxis* xaxis = hist->GetXaxis();
  for (Int_t i = 1; i < hist->GetNbinsX() + 1; i++) {
    xaxis->SetBinLabel(i, TMCProcessName[i - 1]);
  }
  xaxis->LabelsOption("v");  // vertical labels
  if (gPad) {
    xaxis->SetTitleOffset(3.6);
    gPad->SetTopMargin(0.01);
    gPad->SetBottomMargin(0.4);
  }
}
 
 
//_____________________________________________________________________________
TString PairAnalysisHelper::GetDetName(ECbmModuleId det)
{
  //
  // get detector name
  //
  if (det == static_cast<ECbmModuleId>(9)) return ("");
  TString name = CbmModuleList::GetModuleNameCaps(det);
 
  //  TString name = CbmModuleList::GetModuleName(det);
  return (name);
}
 
//_____________________________________________________________________________
Double_t PairAnalysisHelper::GetContentMinimum(TH1* h, Bool_t inclErr)
{
  //
  // get minimum bin content of histogram (having entries)
  //
  Int_t bin, binx, biny, binz;
  Int_t xfirst     = h->GetXaxis()->GetFirst();
  Int_t xlast      = h->GetXaxis()->GetLast();
  Int_t yfirst     = h->GetYaxis()->GetFirst();
  Int_t ylast      = h->GetYaxis()->GetLast();
  Int_t zfirst     = h->GetZaxis()->GetFirst();
  Int_t zlast      = h->GetZaxis()->GetLast();
  Double_t minimum = FLT_MAX, value = 0., error = 0.;
  for (binz = zfirst; binz <= zlast; binz++) {
    for (biny = yfirst; biny <= ylast; biny++) {
      for (binx = xfirst; binx <= xlast; binx++) {
        bin   = h->GetBin(binx, biny, binz);
        value = h->GetBinContent(bin);
        error = h->GetBinError(bin);
        //      Printf(" \t hist%s bin%d value%f error%f \n",h->GetTitle(),bin,value,error);
        if (gPad->GetLogy() && (value - error) <= 0.) continue;
        if (error > value * 0.9) continue;
        if (inclErr) value -= h->GetBinError(bin);
        if (value < minimum && TMath::Abs(h->GetBinError(bin) - 1.e-15) > 1.e-15) { minimum = value; }
      }
    }
  }
  //  Printf(" RETURN VALUE: hist%s %f \n",h->GetTitle(),minimum);
  return minimum;
}
 
Double_t PairAnalysisHelper::GetContentMaximum(TH1* h, Bool_t inclErr)
{
  //
  // get maximum bin content+error of histogram (having entries)
  //
  Int_t bin, binx, biny, binz;
  Int_t xfirst     = h->GetXaxis()->GetFirst();
  Int_t xlast      = h->GetXaxis()->GetLast();
  Int_t yfirst     = h->GetYaxis()->GetFirst();
  Int_t ylast      = h->GetYaxis()->GetLast();
  Int_t zfirst     = h->GetZaxis()->GetFirst();
  Int_t zlast      = h->GetZaxis()->GetLast();
  Double_t maximum = -1. * FLT_MAX, value = 0., error = 0.;
  for (binz = zfirst; binz <= zlast; binz++) {
    for (biny = yfirst; biny <= ylast; biny++) {
      for (binx = xfirst; binx <= xlast; binx++) {
        bin   = h->GetBin(binx, biny, binz);
        value = h->GetBinContent(bin);
        error = h->GetBinError(bin);
        if (inclErr) value += h->GetBinError(bin);
        if (value > maximum && TMath::Abs(error - 1.e-15) > 1.e-15) { maximum = value; }
      }
    }
  }
  return maximum;
}
 
Double_t PairAnalysisHelper::GetQuantile(TH1* h1, Double_t p /*=0.5*/)
{
  //
  // calculates the quantile of the bin contents, p=0.5 -> Median
  // useful functionallity for plotting 2D distibutions with some extreme outliers
  //
  if (p < 0.0 || p > 1.) return -1.;
  Int_t nbinsX = h1->GetNbinsX();
  Int_t nbinsY = h1->GetNbinsY();
  Int_t nbinsZ = h1->GetNbinsZ();
  Int_t nbins  = (nbinsX * (nbinsY ? nbinsY : 1) * (nbinsZ ? nbinsZ : 1));
  Int_t xbin   = -1;
  Int_t ybin   = -1;
  Int_t zbin   = -1;
  Double_t val[nbins];
  Int_t idx[nbins];
  Int_t nfilled = 0;
  for (Int_t i = 1; i <= nbins; i++) {
    h1->GetBinXYZ(i, xbin, ybin, zbin);
    if (xbin < h1->GetXaxis()->GetFirst() || xbin > h1->GetXaxis()->GetLast()) continue;
    if (ybin < h1->GetYaxis()->GetFirst() || ybin > h1->GetYaxis()->GetLast()) continue;
    Double_t con = h1->GetBinContent(i);
    Double_t err = h1->GetBinError(i);
    if (err != 0.0) {
      //      printf("bin%d %.f+-%.f \n",i,con,err);
      val[nfilled] = con + (h1->GetDimension() < 2 ? err : 0.0);  // w or w/o err?
      nfilled++;
    }
  }
  if (nfilled == 0) return -1.;
  TMath::Sort(nfilled, val, idx, kFALSE);  // kFALSE=increasing numbers
  Int_t pos = (Int_t)((Double_t) nfilled * p);
  //for(int i=0; i<nfilled; i++) cout << i << " " << idx[i] << " " << val[idx[i]] << endl;
  //printf("nfilled %d quantile %f pos %d: %f \n",nfilled,p,pos,val[idx[pos]]);
  return val[idx[pos]];
}
 
void PairAnalysisHelper::NormalizeSlicesY(TH2* h)
{
  //
  // normalize slices along Y in case of a 2D histogram
  //
  TH2* hsum = (TH2*) h->Clone("SliceInts");
  hsum->Reset("CE");
  for (Int_t ix = 0; ix <= hsum->GetNbinsX() + 1; ix++) {
    Double_t ysum = h->Integral(ix, ix, 0, hsum->GetNbinsY() + 1);
    for (Int_t iy = 0; iy <= hsum->GetNbinsY() + 1; iy++) {
      hsum->SetBinContent(ix, iy, ysum);
    }
  }
  h->Divide(hsum);
  delete hsum;
}
 
void PairAnalysisHelper::CumulateSlicesX(TH2* h, Bool_t reverse, Bool_t norm)
{
  //
  // caluclate cumulative sum of bins (normalized to one)
  // for slices along X in case of a 2D histogram
  //
  Int_t xstart = (reverse ? h->GetNbinsX() + 1 : 0 - 1);
  Int_t xend   = (reverse ? 0 : h->GetNbinsX() + 1 + 1);
  Int_t xincr  = (reverse ? -1 : +1);
 
  Double_t integral = 1.;
  for (Int_t iy = 0; iy <= h->GetNbinsY() + 1; iy++) {
    if (norm) integral = h->Integral(0, h->GetNbinsX() + 1, iy, iy);
 
    Double_t cumInt = 0;
    for (Int_t ix = xstart; ix != xend; ix += xincr) {
      cumInt += h->GetBinContent(ix, iy);
      h->SetBinContent(ix, iy, cumInt / integral);
    }
  }
}
 
void PairAnalysisHelper::Cumulate(TH1* h, Bool_t reverse, Bool_t norm)
{
  //
  // caluclate cumulative sum of bins (normalized to one)
  //
  Int_t xstart = (reverse ? h->GetNbinsX() + 1 : 0 - 1);
  Int_t xend   = (reverse ? 0 : h->GetNbinsX() + 1 + 1);
  Int_t xincr  = (reverse ? -1 : +1);
 
  Double_t integral = 1.;
  if (norm) integral = h->Integral(0, h->GetNbinsX() + 1);
 
  Double_t cumInt = 0;
  for (Int_t ix = xstart; ix != xend; ix += xincr) {
    cumInt += h->GetBinContent(ix);
    h->SetBinContent(ix, cumInt / integral);
  }
}
 
 
TObject* PairAnalysisHelper::FindObjectByTitle(TObjArray* arrhist, TString ref)
{
  //
  // shortcut to find a certain pair type object in array
  //
  for (Int_t i = 0; i < arrhist->GetEntriesFast(); i++) {
    if (!ref.CompareTo(arrhist->UncheckedAt(i)->GetTitle())) { return arrhist->UncheckedAt(i); }
  }
  return 0x0;
 
  //  return ( arrhist->FindObject(Form("Pair.%s",PairAnalysis::PairClassName(type))) );
  //  TString ref=Form("Pair.%s",PairAnalysis::PairClassName(type));
}
 
 
//_____________________________________________________________________________
Int_t PairAnalysisHelper::GetPrecision(Double_t value)
{
  //
  // computes the precision of a double
  // usefull for axis ranges etc
 
  Bool_t bfnd     = kFALSE;
  Int_t precision = 0;
  value *= 1e6;
  while (!bfnd) {
    //    Printf(" value %f precision %d bfnd %d",TMath::Abs(value*TMath::Power(10,precision)), precision, bfnd);
    bfnd = ((TMath::Abs(value * TMath::Power(10, precision)) / 1e6
             - TMath::Floor(TMath::Abs(value * TMath::Power(10, precision)) / 1e6))
                != 0.0
              ? kFALSE
              : kTRUE);
    if (!bfnd) precision++;
  }
 
  //  Printf("precision for %f found to be %d", value, precision);
  return precision;
}