TGraphAsymmErrors.cxx

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// @(#)root/hist:$Id$
// Author: Rene Brun   03/03/99
 
/*************************************************************************
 * Copyright (C) 1995-2000, Rene Brun and Fons Rademakers.               *
 * All rights reserved.                                                  *
 *                                                                       *
 * For the licensing terms see $ROOTSYS/LICENSE.                         *
 * For the list of contributors see $ROOTSYS/README/CREDITS.             *
 *************************************************************************/
 
 
#include "TEfficiency.h"
#include "TROOT.h"
#include "TBuffer.h"
#include "TGraphAsymmErrors.h"
#include "TGraphErrors.h"
#include "TStyle.h"
#include "TMath.h"
#include "TVirtualPad.h"
#include "TF1.h"
#include "TH1.h"
#include "TVector.h"
#include "TVectorD.h"
#include "TSystem.h"
#include "Math/QuantFuncMathCore.h"
#include "strtok.h"
 
#include <cstring>
#include <iostream>
#include <fstream>
 
 
ClassImp(TGraphAsymmErrors);
 
/** \class TGraphAsymmErrors
    \ingroup Hist
TGraph with asymmetric error bars.
 
The TGraphAsymmErrors painting is performed thanks to the TGraphPainter
class. All details about the various painting options are given in this class.
 
The picture below gives an example:
 
Begin_Macro(source)
{
   auto c1 = new TCanvas("c1","A Simple Graph with asymmetric error bars",200,10,700,500);
   c1->SetFillColor(42);
   c1->SetGrid();
   c1->GetFrame()->SetFillColor(21);
   c1->GetFrame()->SetBorderSize(12);
   const Int_t n = 10;
   Double_t x[n]   = {-0.22, 0.05, 0.25, 0.35, 0.5, 0.61,0.7,0.85,0.89,0.95};
   Double_t y[n]   = {1,2.9,5.6,7.4,9,9.6,8.7,6.3,4.5,1};
   Double_t exl[n] = {.05,.1,.07,.07,.04,.05,.06,.07,.08,.05};
   Double_t eyl[n] = {.8,.7,.6,.5,.4,.4,.5,.6,.7,.8};
   Double_t exh[n] = {.02,.08,.05,.05,.03,.03,.04,.05,.06,.03};
   Double_t eyh[n] = {.6,.5,.4,.3,.2,.2,.3,.4,.5,.6};
   auto gr = new TGraphAsymmErrors(n,x,y,exl,exh,eyl,eyh);
   gr->SetTitle("TGraphAsymmErrors Example");
   gr->SetMarkerColor(4);
   gr->SetMarkerStyle(21);
   gr->Draw("ALP");
}
End_Macro
*/
 
 
////////////////////////////////////////////////////////////////////////////////
/// TGraphAsymmErrors default constructor.
 
TGraphAsymmErrors::TGraphAsymmErrors(): TGraph()
{
   fEXlow       = 0;
   fEYlow       = 0;
   fEXhigh      = 0;
   fEYhigh      = 0;
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// TGraphAsymmErrors copy constructor
 
TGraphAsymmErrors::TGraphAsymmErrors(const TGraphAsymmErrors &gr)
       : TGraph(gr)
{
   if (!CtorAllocate()) return;
   Int_t n = fNpoints*sizeof(Double_t);
   memcpy(fEXlow, gr.fEXlow, n);
   memcpy(fEYlow, gr.fEYlow, n);
   memcpy(fEXhigh, gr.fEXhigh, n);
   memcpy(fEYhigh, gr.fEYhigh, n);
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// TGraphAsymmErrors assignment operator
 
TGraphAsymmErrors& TGraphAsymmErrors::operator=(const TGraphAsymmErrors &gr)
{
   if(this!=&gr) {
      TGraph::operator=(gr);
      // delete arrays
      if (fEXlow) delete [] fEXlow;
      if (fEYlow) delete [] fEYlow;
      if (fEXhigh) delete [] fEXhigh;
      if (fEYhigh) delete [] fEYhigh;
 
      if (!CtorAllocate()) return *this;
      Int_t n = fNpoints*sizeof(Double_t);
      memcpy(fEXlow, gr.fEXlow, n);
      memcpy(fEYlow, gr.fEYlow, n);
      memcpy(fEXhigh, gr.fEXhigh, n);
      memcpy(fEYhigh, gr.fEYhigh, n);
   }
   return *this;
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// TGraphAsymmErrors normal constructor.
///
/// the arrays are preset to zero
 
TGraphAsymmErrors::TGraphAsymmErrors(Int_t n)
       : TGraph(n)
{
   if (!CtorAllocate()) return;
   FillZero(0, fNpoints);
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// TGraphAsymmErrors normal constructor.
///
/// if exl,h or eyl,h are null, the corresponding arrays are preset to zero
 
TGraphAsymmErrors::TGraphAsymmErrors(Int_t n, const Float_t *x, const Float_t *y, const Float_t *exl, const Float_t *exh, const Float_t *eyl, const Float_t *eyh)
       : TGraph(n,x,y)
{
   if (!CtorAllocate()) return;
 
   for (Int_t i=0;i<n;i++) {
      if (exl) fEXlow[i]  = exl[i];
      else     fEXlow[i]  = 0;
      if (exh) fEXhigh[i] = exh[i];
      else     fEXhigh[i] = 0;
      if (eyl) fEYlow[i]  = eyl[i];
      else     fEYlow[i]  = 0;
      if (eyh) fEYhigh[i] = eyh[i];
      else     fEYhigh[i] = 0;
   }
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// TGraphAsymmErrors normal constructor.
///
/// if exl,h or eyl,h are null, the corresponding arrays are preset to zero
 
TGraphAsymmErrors::TGraphAsymmErrors(Int_t n, const Double_t *x, const Double_t *y, const Double_t *exl, const Double_t *exh, const Double_t *eyl, const Double_t *eyh)
       : TGraph(n,x,y)
{
   if (!CtorAllocate()) return;
 
   n = fNpoints*sizeof(Double_t);
   if(exl) { memcpy(fEXlow, exl, n);
   } else { memset(fEXlow, 0, n); }
   if(exh) { memcpy(fEXhigh, exh, n);
   } else { memset(fEXhigh, 0, n); }
   if(eyl) { memcpy(fEYlow, eyl, n);
   } else { memset(fEYlow, 0, n); }
   if(eyh) { memcpy(fEYhigh, eyh, n);
   } else { memset(fEYhigh, 0, n); }
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// Constructor with six vectors of floats in input
/// A grapherrors is built with the X coordinates taken from vx and Y coord from vy
/// and the errors from vectors vexl/h and veyl/h.
/// The number of points in the graph is the minimum of number of points
/// in vx and vy.
 
TGraphAsymmErrors::TGraphAsymmErrors(const TVectorF  &vx, const TVectorF  &vy, const TVectorF  &vexl, const TVectorF  &vexh, const TVectorF  &veyl, const TVectorF  &veyh)
                  :TGraph()
{
   fNpoints = TMath::Min(vx.GetNrows(), vy.GetNrows());
   if (!TGraph::CtorAllocate()) return;
   if (!CtorAllocate()) return;
   Int_t ivxlow  = vx.GetLwb();
   Int_t ivylow  = vy.GetLwb();
   Int_t ivexllow = vexl.GetLwb();
   Int_t ivexhlow = vexh.GetLwb();
   Int_t iveyllow = veyl.GetLwb();
   Int_t iveyhlow = veyh.GetLwb();
      for (Int_t i=0;i<fNpoints;i++) {
      fX[i]      = vx(i+ivxlow);
      fY[i]      = vy(i+ivylow);
      fEXlow[i]  = vexl(i+ivexllow);
      fEYlow[i]  = veyl(i+iveyllow);
      fEXhigh[i] = vexh(i+ivexhlow);
      fEYhigh[i] = veyh(i+iveyhlow);
   }
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// Constructor with six vectors of doubles in input
/// A grapherrors is built with the X coordinates taken from vx and Y coord from vy
/// and the errors from vectors vexl/h and veyl/h.
/// The number of points in the graph is the minimum of number of points
/// in vx and vy.
 
TGraphAsymmErrors::TGraphAsymmErrors(const TVectorD &vx, const TVectorD &vy, const TVectorD &vexl, const TVectorD &vexh, const TVectorD &veyl, const TVectorD &veyh)
                  :TGraph()
{
   fNpoints = TMath::Min(vx.GetNrows(), vy.GetNrows());
   if (!TGraph::CtorAllocate()) return;
   if (!CtorAllocate()) return;
   Int_t ivxlow  = vx.GetLwb();
   Int_t ivylow  = vy.GetLwb();
   Int_t ivexllow = vexl.GetLwb();
   Int_t ivexhlow = vexh.GetLwb();
   Int_t iveyllow = veyl.GetLwb();
   Int_t iveyhlow = veyh.GetLwb();
      for (Int_t i=0;i<fNpoints;i++) {
      fX[i]      = vx(i+ivxlow);
      fY[i]      = vy(i+ivylow);
      fEXlow[i]  = vexl(i+ivexllow);
      fEYlow[i]  = veyl(i+iveyllow);
      fEXhigh[i] = vexh(i+ivexhlow);
      fEYhigh[i] = veyh(i+iveyhlow);
   }
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// TGraphAsymmErrors constructor importing its parameters from the TH1 object passed as argument
/// the low and high errors are set to the bin error of the histogram.
 
TGraphAsymmErrors::TGraphAsymmErrors(const TH1 *h)
       : TGraph(h)
{
   if (!CtorAllocate()) return;
 
   for (Int_t i=0;i<fNpoints;i++) {
      fEXlow[i]  = h->GetBinWidth(i+1)*gStyle->GetErrorX();
      fEXhigh[i] = fEXlow[i];
      fEYlow[i]  = h->GetBinErrorLow(i+1);
      fEYhigh[i] = h->GetBinErrorUp(i+1);;
   }
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// Creates a TGraphAsymmErrors by dividing two input TH1 histograms:
/// pass/total. (see TGraphAsymmErrors::Divide)
 
TGraphAsymmErrors::TGraphAsymmErrors(const TH1* pass, const TH1* total, Option_t *option)
   : TGraph((pass)?pass->GetNbinsX():0)
{
   if (!pass || !total) {
      Error("TGraphAsymmErrors","Invalid histogram pointers");
      return;
   }
   if (!CtorAllocate()) return;
 
   std::string sname = "divide_" + std::string(pass->GetName()) + "_by_" +
      std::string(total->GetName());
   SetName(sname.c_str());
   SetTitle(pass->GetTitle());
 
   //copy style from pass
   pass->TAttLine::Copy(*this);
   pass->TAttFill::Copy(*this);
   pass->TAttMarker::Copy(*this);
 
   Divide(pass, total, option);
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// TGraphAsymmErrors constructor reading input from filename
/// filename is assumed to contain at least 2 columns of numbers
///
/// convention for format (default=`"%lg %lg %lg %lg %lg %lg"`)
///  - format = `"%lg %lg"`         read only 2 first columns into X, Y
///  - format = `"%lg %lg %lg %lg"`     read only 4 first columns into X, Y,  ELY, EHY
///  - format = `"%lg %lg %lg %lg %lg %lg"` read only 6 first columns into X, Y, EXL, EYH, EYL, EHY
///
/// For files separated by a specific delimiter different from `' '` and `'\t'` (e.g. `';'` in csv files)
/// you can avoid using `%*s` to bypass this delimiter by explicitly specify the `"option" argument,
/// e.g. `option=" \t,;"` for columns of figures separated by any of these characters `(' ', '\t', ',', ';')`
/// used once `(e.g. "1;1")` or in a combined way `(" 1;,;;  1")`.
/// Note in that case, the instantiation is about 2 times slower.
/// In case a delimiter is specified, the format `"%lg %lg %lg"` will read X,Y,EX.
 
TGraphAsymmErrors::TGraphAsymmErrors(const char *filename, const char *format, Option_t *option)
   : TGraph(100)
{
   if (!CtorAllocate()) return;
   Double_t x, y, exl, exh, eyl, eyh;
   TString fname = filename;
   gSystem->ExpandPathName(fname);
   std::ifstream infile(fname.Data());
   if (!infile.good()) {
      MakeZombie();
      Error("TGraphAsymmErrors", "Cannot open file: %s, TGraphAsymmErrors is Zombie", filename);
      fNpoints = 0;
      return;
   }
   std::string line;
   Int_t np = 0;
 
   if (strcmp(option, "") == 0) { // No delimiters specified (standard constructor).
 
      Int_t ncol = TGraphErrors::CalculateScanfFields(format);  //count number of columns in format
      Int_t res;
      while (std::getline(infile, line, '\n')) {
         exl = exh = eyl = eyh = 0;
         if (ncol < 3) {
            res = sscanf(line.c_str(), format, &x, &y);
         } else if (ncol < 5) {
            res = sscanf(line.c_str(), format, &x, &y, &eyl, &eyh);
         } else {
            res = sscanf(line.c_str(), format, &x, &y, &exl, &exh, &eyl, &eyh);
         }
         if (res < 2) {
            continue; //skip empty and ill-formed lines
         }
         SetPoint(np, x, y);
         SetPointError(np, exl, exh, eyl, eyh);
         np++;
      }
      Set(np);
 
   } else { // A delimiter has been specified in "option"
 
      // Checking format and creating its boolean equivalent
      TString format_ = TString(format) ;
      format_.ReplaceAll(" ", "") ;
      format_.ReplaceAll("\t", "") ;
      format_.ReplaceAll("lg", "") ;
      format_.ReplaceAll("s", "") ;
      format_.ReplaceAll("%*", "0") ;
      format_.ReplaceAll("%", "1") ;
      if (!format_.IsDigit()) {
         Error("TGraphAsymmErrors", "Incorrect input format! Allowed format tags are {\"%%lg\",\"%%*lg\" or \"%%*s\"}");
         return ;
      }
      Int_t ntokens = format_.Length() ;
      if (ntokens < 2) {
         Error("TGraphAsymmErrors", "Incorrect input format! Only %d tag(s) in format whereas at least 2 \"%%lg\" tags are expected!", ntokens);
         return ;
      }
      Int_t ntokensToBeSaved = 0 ;
      Bool_t * isTokenToBeSaved = new Bool_t [ntokens] ;
      for (Int_t idx = 0; idx < ntokens; idx++) {
         isTokenToBeSaved[idx] = TString::Format("%c", format_[idx]).Atoi() ; //atoi(&format_[idx]) does not work for some reason...
         if (isTokenToBeSaved[idx] == 1) {
            ntokensToBeSaved++ ;
         }
      }
      if (ntokens >= 2 && (ntokensToBeSaved < 2 || ntokensToBeSaved > 4)) { //first condition not to repeat the previous error message
         Error("TGraphAsymmErrors", "Incorrect input format! There are %d \"%%lg\" tag(s) in format whereas 2,3 or 4 are expected!", ntokensToBeSaved);
         delete [] isTokenToBeSaved ;
         return ;
      }
 
      // Initializing loop variables
      Bool_t isLineToBeSkipped = kFALSE ; //empty and ill-formed lines
      char * token = NULL ;
      TString token_str = "" ;
      Int_t token_idx = 0 ;
      Double_t * value = new Double_t [6] ; //x,y,exl, exh, eyl, eyh buffers
      for (Int_t k = 0; k < 6; k++) {
         value[k] = 0. ;
      }
      Int_t value_idx = 0 ;
 
      // Looping
      char *rest;
      while (std::getline(infile, line, '\n')) {
         if (line != "") {
            if (line[line.size() - 1] == char(13)) {  // removing DOS CR character
               line.erase(line.end() - 1, line.end()) ;
            }
            token = R__STRTOK_R(const_cast<char*>(line.c_str()), option, &rest) ;
            while (token != NULL && value_idx < ntokensToBeSaved) {
               if (isTokenToBeSaved[token_idx]) {
                  token_str = TString(token) ;
                  token_str.ReplaceAll("\t", "") ;
                  if (!token_str.IsFloat()) {
                     isLineToBeSkipped = kTRUE ;
                     break ;
                  } else {
                     value[value_idx] = token_str.Atof() ;
                     value_idx++ ;
                  }
               }
               token = R__STRTOK_R(NULL, option, &rest); // next token
               token_idx++ ;
            }
            if (!isLineToBeSkipped && value_idx > 1) { //i.e. 2,3 or 4
               x = value[0] ;
               y = value[1] ;
               exl = value[2] ;
               exh = value[3] ;
               eyl = value[4] ;
               eyh = value[5] ;
               SetPoint(np, x, y) ;
               SetPointError(np, exl, exh, eyl, eyh);
               np++ ;
            }
         }
         isLineToBeSkipped = kFALSE ;
         token = NULL ;
         token_idx = 0 ;
         value_idx = 0 ;
      }
      Set(np) ;
 
      // Cleaning
      delete [] isTokenToBeSaved ;
      delete [] value ;
      delete token ;
   }
   infile.close();
}
 
////////////////////////////////////////////////////////////////////////////////
/// TGraphAsymmErrors default destructor.
 
TGraphAsymmErrors::~TGraphAsymmErrors()
{
   if(fEXlow) delete [] fEXlow;
   if(fEXhigh) delete [] fEXhigh;
   if(fEYlow) delete [] fEYlow;
   if(fEYhigh) delete [] fEYhigh;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Allocate internal data structures for `size` points.
 
Double_t** TGraphAsymmErrors::Allocate(Int_t size) {
   return AllocateArrays(6, size);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Apply a function to all data points `y = f(x,y)`
///
/// Errors are calculated as `eyh = f(x,y+eyh)-f(x,y)` and
/// `eyl = f(x,y)-f(x,y-eyl)`
///
/// Special treatment has to be applied for the functions where the
/// role of "up" and "down" is reversed.
/// function suggested/implemented by Miroslav Helbich <helbich@mail.desy.de>
 
void TGraphAsymmErrors::Apply(TF1 *f)
{
   Double_t x,y,exl,exh,eyl,eyh,eyl_new,eyh_new,fxy;
 
   if (fHistogram) {
      delete fHistogram;
      fHistogram = 0;
   }
   for (Int_t i=0;i<GetN();i++) {
      GetPoint(i,x,y);
      exl=GetErrorXlow(i);
      exh=GetErrorXhigh(i);
      eyl=GetErrorYlow(i);
      eyh=GetErrorYhigh(i);
 
      fxy = f->Eval(x,y);
      SetPoint(i,x,fxy);
 
      // in the case of the functions like y-> -1*y the roles of the
      // upper and lower error bars is reversed
      if (f->Eval(x,y-eyl)<f->Eval(x,y+eyh)) {
         eyl_new = TMath::Abs(fxy - f->Eval(x,y-eyl));
         eyh_new = TMath::Abs(f->Eval(x,y+eyh) - fxy);
      }
      else {
         eyh_new = TMath::Abs(fxy - f->Eval(x,y-eyl));
         eyl_new = TMath::Abs(f->Eval(x,y+eyh) - fxy);
      }
 
      //error on x doesn't change
      SetPointError(i,exl,exh,eyl_new,eyh_new);
   }
   if (gPad) gPad->Modified();
}
 
////////////////////////////////////////////////////////////////////////////////
///This function is only kept for backward compatibility.
///You should rather use the Divide method.
///It calls `Divide(pass,total,"cl=0.683 b(1,1) mode")` which is equivalent to the
///former BayesDivide method.
 
void TGraphAsymmErrors::BayesDivide(const TH1* pass, const TH1* total, Option_t *)
{
   Divide(pass,total,"cl=0.683 b(1,1) mode");
}
 
////////////////////////////////////////////////////////////////////////////////
/// Fill this TGraphAsymmErrors by dividing two 1-dimensional histograms pass/total
///
/// This method serves two purposes:
///
/// ### 1) calculating efficiencies:
///
/// The assumption is that the entries in "pass" are a subset of those in
/// "total". That is, we create an "efficiency" graph, where each entry is
/// between 0 and 1, inclusive.
///
/// If the histograms are not filled with unit weights, the number of effective
/// entries is used to normalise the bin contents which might lead to wrong results.
/// \f[
/// \text{effective entries} = \frac{(\sum w_{i})^{2}}{\sum w_{i}^{2}}
/// \f]
/// The points are assigned a x value at the center of each histogram bin.
/// The y values are \f$\text{eff} = \frac{\text{pass}}{\text{total}}\f$
/// for all options except for the
/// bayesian methods where the result depends on the chosen option.
///
/// If the denominator becomes 0 or pass > total, the corresponding bin is
/// skipped.
///
/// ### 2) calculating ratios of two Poisson means (option 'pois'):
///
/// The two histograms are interpreted as independent Poisson processes and the ratio
/// \f[
/// \tau = \frac{n_{1}}{n_{2}} = \frac{\varepsilon}{1 - \varepsilon}
/// \f]
/// with \f$\varepsilon = \frac{n_{1}}{n_{1} + n_{2}}\f$.
/// The histogram 'pass' is interpreted as \f$n_{1}\f$ and the total histogram
/// is used for \f$n_{2}\f$.
///
/// The (asymmetric) uncertainties of the Poisson ratio are linked to the uncertainties
/// of efficiency by a parameter transformation:
/// \f[
/// \Delta \tau_{low/up} = \frac{1}{(1 - \varepsilon)^{2}} \Delta \varepsilon_{low/up}
/// \f]
///
/// The x errors span each histogram bin (lowedge ... lowedge+width)
/// The y errors depend on the chosen statistic methode which can be determined
/// by the options given below. For a detailed description of the used statistic
/// calculations please have a look at the corresponding functions!
///
/// Options:
/// - v     : verbose mode: prints information about the number of used bins
///           and calculated efficiencies with their errors
/// - cl=x  : determine the used confidence level (0<x<1) (default is 0.683)
/// - cp    : Clopper-Pearson interval (see TEfficiency::ClopperPearson)
/// - w     : Wilson interval (see TEfficiency::Wilson)
/// - n     : normal approximation propagation (see TEfficiency::Normal)
/// - ac    : Agresti-Coull interval (see TEfficiency::AgrestiCoull)
/// - fc    : Feldman-Cousins interval (see TEfficiency::FeldmanCousinsInterval)
/// - midp  : Lancaster mid-P interval (see TEfficiency::MidPInterval)
/// - b(a,b): bayesian interval using a prior probability ~Beta(a,b); a,b > 0
///           (see TEfficiency::Bayesian)
/// - mode  : use mode of posterior for Bayesian interval (default is mean)
/// - shortest: use shortest interval (done by default if mode is set)
/// - central: use central interval (done by default if mode is NOT set)
/// - pois: interpret histograms as poisson ratio instead of efficiency
/// - e0    : plot efficiency and interval for bins where total=0
///           (default is to skip them)
///
/// Note:
/// Unfortunately there is no straightforward approach for determining a confidence
/// interval for a given confidence level. The actual coverage probability of the
/// confidence interval oscillates significantly according to the total number of
/// events and the true efficiency. In order to decrease the impact of this
/// oscillation on the actual coverage probability a couple of approximations and
/// methodes has been developed. For a detailed discussion, please have a look at
/// this statistical paper:
/// http://www-stat.wharton.upenn.edu/~tcai/paper/Binomial-StatSci.pdf
 
 
void TGraphAsymmErrors::Divide(const TH1* pass, const TH1* total, Option_t *opt)
{
   //check pointers
   if(!pass || !total) {
      Error("Divide","one of the passed pointers is zero");
      return;
   }
 
   //check dimension of histograms; only 1-dimensional ones are accepted
   if((pass->GetDimension() > 1) || (total->GetDimension() > 1)) {
      Error("Divide","passed histograms are not one-dimensional");
      return;
   }
 
   //check whether histograms are filled with weights -> use number of effective
   //entries
   Bool_t bEffective = false;
   //compare sum of weights with sum of squares of weights
   // re-compute here to be sure to get the right values
   Double_t psumw = 0;
   Double_t psumw2 = 0;
   if (pass->GetSumw2()->fN > 0) {
      for (int i = 0; i < pass->GetNcells(); ++i) {
         psumw += pass->GetBinContent(i);
         psumw2 += pass->GetSumw2()->At(i);
      }
   }
   else {
      psumw = pass->GetSumOfWeights();
      psumw2 = psumw;
   }
   if (TMath::Abs(psumw - psumw2) > 1e-6)
      bEffective = true;
 
   Double_t tsumw = 0;
   Double_t tsumw2 = 0;
   if (total->GetSumw2()->fN > 0) {
      for (int i = 0; i < total->GetNcells(); ++i) {
         tsumw += total->GetBinContent(i);
         tsumw2 += total->GetSumw2()->At(i);
      }
   }
   else {
      tsumw = total->GetSumOfWeights();
      tsumw2 = tsumw;
   }
   if (TMath::Abs(tsumw - tsumw2) > 1e-6)
      bEffective = true;
 
 
 
   // we do not want to ignore the weights
   // if (bEffective && (pass->GetSumw2()->fN == 0 || total->GetSumw2()->fN == 0) ) {
   //    Warning("Divide","histogram have been computed with weights but the sum of weight squares are not stored in the histogram. Error calculation is performed ignoring the weights");
   //    bEffective = false;
   // }
 
   //parse option
   TString option = opt;
   option.ToLower();
 
   Bool_t bVerbose = false;
   //pointer to function returning the boundaries of the confidence interval
   //(is only used in the frequentist cases.)
   Double_t (*pBound)(Double_t,Double_t,Double_t,Bool_t) = &TEfficiency::ClopperPearson; // default method
   //confidence level
   Double_t conf = 0.682689492137;
   //values for bayesian statistics
   Bool_t bIsBayesian = false;
   Double_t alpha = 1;
   Double_t beta = 1;
 
   //verbose mode
   if(option.Contains("v")) {
      option.ReplaceAll("v","");
      bVerbose = true;
      if (bEffective)
         Info("Divide","weight will be considered in the Histogram Ratio");
   }
 
 
   //confidence level
   if(option.Contains("cl=")) {
      Double_t level = -1;
      // coverity [secure_coding : FALSE]
      sscanf(strstr(option.Data(),"cl="),"cl=%lf",&level);
      if((level > 0) && (level < 1))
         conf = level;
      else
         Warning("Divide","given confidence level %.3lf is invalid",level);
      option.ReplaceAll("cl=","");
   }
 
   // look for statistic options
   // check first Bayesian case
   // bayesian with prior
   Bool_t usePosteriorMode = false;
   Bool_t useShortestInterval = false;
   if (option.Contains("b(")) {
      Double_t a = 0;
      Double_t b = 0;
      sscanf(strstr(option.Data(), "b("), "b(%lf,%lf)", &a, &b);
      if (a > 0)
         alpha = a;
      else
         Warning("Divide", "given shape parameter for alpha %.2lf is invalid", a);
      if (b > 0)
         beta = b;
      else
         Warning("Divide", "given shape parameter for beta %.2lf is invalid", b);
      option.ReplaceAll("b(", "");
      bIsBayesian = true;
 
      // look for specific bayesian options
 
      // use posterior mode
 
      if (option.Contains("mode")) {
         usePosteriorMode = true;
         option.ReplaceAll("mode", "");
      }
      if (option.Contains("sh") || (usePosteriorMode && !option.Contains("cen"))) {
         useShortestInterval = true;
      }
   }
   // normal approximation
   else if (option.Contains("n")) {
      option.ReplaceAll("n", "");
      pBound = &TEfficiency::Normal;
   }
   // clopper pearson interval
   else if (option.Contains("cp")) {
      option.ReplaceAll("cp", "");
      pBound = &TEfficiency::ClopperPearson;
   }
   // wilson interval
   else if (option.Contains("w")) {
      option.ReplaceAll("w", "");
      pBound = &TEfficiency::Wilson;
   }
   // agresti coull interval
   else if (option.Contains("ac")) {
      option.ReplaceAll("ac", "");
      pBound = &TEfficiency::AgrestiCoull;
   }
   // Feldman-Cousins interval
   else if (option.Contains("fc")) {
      option.ReplaceAll("fc", "");
      pBound = &TEfficiency::FeldmanCousins;
   }
   // mid-P Lancaster interval
   else if (option.Contains("midp")) {
      option.ReplaceAll("midp", "");
      pBound = &TEfficiency::MidPInterval;
   }
 
   // interpret as Poisson ratio
   Bool_t bPoissonRatio = false;
   if (option.Contains("pois")) {
      bPoissonRatio = true;
      option.ReplaceAll("pois", "");
   }
   Bool_t plot0Bins = false;
   if (option.Contains("e0")) {
      plot0Bins = true;
      option.ReplaceAll("e0", "");
   }
 
   // weights works only in case of Normal approximation or Bayesian for binomial interval
   // in case of Poisson ratio we can use weights by rescaling the obtained results using the effective entries
   if ((bEffective && !bPoissonRatio) && !bIsBayesian && pBound != &TEfficiency::Normal) {
      Warning("Divide", "Histograms have weights: only Normal or Bayesian error calculation is supported");
      Info("Divide", "Using now the Normal approximation for weighted histograms");
   }
 
   if (bPoissonRatio) {
      if (pass->GetDimension() != total->GetDimension()) {
         Error("Divide", "passed histograms are not of the same dimension");
         return;
      }
 
      if (!TEfficiency::CheckBinning(*pass, *total)) {
         Error("Divide", "passed histograms are not consistent");
         return;
      }
   } else {
      // check consistency of histograms, allowing weights
      if (!TEfficiency::CheckConsistency(*pass, *total, "w")) {
         Error("Divide", "passed histograms are not consistent");
         return;
      }
   }
 
   // Set the graph to have a number of points equal to the number of histogram
   // bins
   Int_t nbins = pass->GetNbinsX();
   Set(nbins);
 
   // Ok, now set the points for each bin
   // (Note: the TH1 bin content is shifted to the right by one:
   //  bin=0 is underflow, bin=nbins+1 is overflow.)
 
   //efficiency with lower and upper boundary of confidence interval
   double eff, low, upper;
   //this keeps track of the number of points added to the graph
   int npoint=0;
   //number of total and passed events
   Double_t t = 0 , p = 0;
   Double_t tw = 0, tw2 = 0, pw = 0, pw2 = 0, wratio = 1; // for the case of weights
   //loop over all bins and fill the graph
   for (Int_t b=1; b<=nbins; ++b) {
 
      // default value when total =0;
      eff = 0;
      low = 0;
      upper = 0;
 
      // special case in case of weights we have to consider the sum of weights and the sum of weight squares
      if (bEffective) {
         tw = total->GetBinContent(b);
         tw2 = (total->GetSumw2()->fN > 0) ? total->GetSumw2()->At(b) : tw;
         pw = pass->GetBinContent(b);
         pw2 = (pass->GetSumw2()->fN > 0) ? pass->GetSumw2()->At(b) : pw;
 
         if (bPoissonRatio) {
            // tw += pw;
            // tw2 += pw2;
            // compute ratio on the effective entries ( p and t)
            // special case is when (pw=0, pw2=0) in this case we cannot get the bin weight.
            // we use then the overall weight of the full histogram
            if (pw == 0 && pw2 == 0)
               p = 0;
            else
               p = (pw * pw) / pw2;
 
            if (tw == 0 && tw2 == 0)
               t = 0;
            else
               t = (tw * tw) / tw2;
 
            if (pw > 0 && tw > 0)
               // this is the ratio of the two bin weights ( pw/p  / t/tw )
               wratio = (pw * t) / (p * tw);
            else if (pw == 0 && tw > 0)
               // case p histogram has zero  compute the weights from all the histogram
               // weight of histogram - sumw2/sumw
               wratio = (psumw2 * t) / (psumw * tw);
            else if (tw == 0 && pw > 0)
               // case t histogram has zero  compute the weights from all the histogram
               // weight of histogram - sumw2/sumw
               wratio = (pw * tsumw) / (p * tsumw2);
            else if (p > 0)
               wratio = pw / p; // not sure if needed
            else {
               // case both pw and tw are zero - we skip these bins
               if (!plot0Bins) continue; // skip bins with total <= 0
            }
 
            t += p;
            // std::cout << p << "   " << t << "  " << wratio << std::endl;
         } else if (tw <= 0 && !plot0Bins)
            continue; // skip bins with total <= 0
 
         // in the case of weights have the formula only for
         // the normal and  bayesian statistics (see below)
 
      }
 
      // use bin contents
      else {
         t = std::round(total->GetBinContent(b));
         p = std::round(pass->GetBinContent(b));
 
         if (bPoissonRatio)
            t += p;
 
         if (t == 0.0 && !plot0Bins)
            continue; // skip bins with total = 0
      }
 
      //using bayesian statistics
      if(bIsBayesian) {
         double aa,bb;
 
         if ((bEffective && !bPoissonRatio) && tw2 <= 0) {
            // case of bins with zero errors
            eff = pw/tw;
            low = eff; upper = eff;
         }
         else {
 
            if (bEffective && !bPoissonRatio) {
               // tw/tw2 re-normalize the weights
               double norm = tw/tw2;  // case of tw2 = 0 is treated above
               aa =  pw * norm + alpha;
               bb =  (tw - pw) * norm + beta;
            }
            else {
               aa = double(p) + alpha;
               bb = double(t-p) + beta;
            }
            if (usePosteriorMode)
               eff = TEfficiency::BetaMode(aa,bb);
            else
               eff = TEfficiency::BetaMean(aa,bb);
 
            if (useShortestInterval) {
               TEfficiency::BetaShortestInterval(conf,aa,bb,low,upper);
            }
            else {
               low = TEfficiency::BetaCentralInterval(conf,aa,bb,false);
               upper = TEfficiency::BetaCentralInterval(conf,aa,bb,true);
            }
         }
      }
      // case of non-bayesian statistics
      else {
         if (bEffective && !bPoissonRatio) {
 
            if (tw > 0) {
 
               eff = pw/tw;
 
               // use normal error calculation using variance of MLE with weights (F.James 8.5.2)
               // this is the same formula used in ROOT for TH1::Divide("B")
 
               double variance = ( pw2 * (1. - 2 * eff) + tw2 * eff *eff ) / ( tw * tw) ;
               double sigma = sqrt(variance);
 
               double prob = 0.5 * (1.-conf);
               double delta = ROOT::Math::normal_quantile_c(prob, sigma);
               low = eff - delta;
               upper = eff + delta;
               if (low < 0) low = 0;
               if (upper > 1) upper = 1.;
            }
         }
         else {
            // when not using weights (all cases) or in case of  Poisson ratio with weights
            if(t != 0.0)
               eff = ((Double_t)p)/t;
 
            low = pBound(t,p,conf,false);
            upper = pBound(t,p,conf,true);
         }
      }
      // treat as Poisson ratio
      if(bPoissonRatio)
      {
        Double_t ratio = eff/(1 - eff);
        // take the intervals in eff as intervals in the Poisson ratio
        low = low/(1. - low);
        upper = upper/(1.-upper);
        eff = ratio;
        if (bEffective) {
           //scale result by the ratio of the weight
           eff *= wratio;
           low *= wratio;
           upper *= wratio;
        }
      }
      //Set the point center and its errors
      if (TMath::Finite(eff)) {
         SetPoint(npoint,pass->GetBinCenter(b),eff);
         SetPointError(npoint,
         pass->GetBinCenter(b)-pass->GetBinLowEdge(b),
         pass->GetBinLowEdge(b)-pass->GetBinCenter(b)+pass->GetBinWidth(b),
         eff-low,upper-eff);
         npoint++;//we have added a point to the graph
      }
   }
 
   Set(npoint);//tell the graph how many points we've really added
   if (npoint < nbins)
      Warning("Divide","Number of graph points is different than histogram bins - %d points have been skipped",nbins-npoint);
 
 
   if (bVerbose) {
      Info("Divide","made a graph with %d points from %d bins",npoint,nbins);
      Info("Divide","used confidence level: %.2lf\n",conf);
      if(bIsBayesian)
         Info("Divide","used prior probability ~ beta(%.2lf,%.2lf)",alpha,beta);
      Print();
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Compute Range
 
void TGraphAsymmErrors::ComputeRange(Double_t &xmin, Double_t &ymin, Double_t &xmax, Double_t &ymax) const
{
   TGraph::ComputeRange(xmin,ymin,xmax,ymax);
 
   for (Int_t i=0;i<fNpoints;i++) {
      if (fX[i] -fEXlow[i] < xmin) {
         if (gPad && gPad->GetLogx()) {
            if (fEXlow[i] < fX[i]) xmin = fX[i]-fEXlow[i];
            else                   xmin = TMath::Min(xmin,fX[i]/3);
         } else {
            xmin = fX[i]-fEXlow[i];
         }
      }
      if (fX[i] +fEXhigh[i] > xmax) xmax = fX[i]+fEXhigh[i];
      if (fY[i] -fEYlow[i] < ymin) {
         if (gPad && gPad->GetLogy()) {
            if (fEYlow[i] < fY[i]) ymin = fY[i]-fEYlow[i];
            else                   ymin = TMath::Min(ymin,fY[i]/3);
         } else {
            ymin = fY[i]-fEYlow[i];
         }
      }
      if (fY[i] +fEYhigh[i] > ymax) ymax = fY[i]+fEYhigh[i];
   }
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// Copy and release.
 
void TGraphAsymmErrors::CopyAndRelease(Double_t **newarrays,
                                       Int_t ibegin, Int_t iend, Int_t obegin)
{
   CopyPoints(newarrays, ibegin, iend, obegin);
   if (newarrays) {
      delete[] fEXlow;
      fEXlow = newarrays[0];
      delete[] fEXhigh;
      fEXhigh = newarrays[1];
      delete[] fEYlow;
      fEYlow = newarrays[2];
      delete[] fEYhigh;
      fEYhigh = newarrays[3];
      delete[] fX;
      fX = newarrays[4];
      delete[] fY;
      fY = newarrays[5];
      delete[] newarrays;
   }
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// Copy errors from fE*** to arrays[***]
/// or to f*** Copy points.
 
Bool_t TGraphAsymmErrors::CopyPoints(Double_t **arrays,
                                     Int_t ibegin, Int_t iend, Int_t obegin)
{
   if (TGraph::CopyPoints(arrays ? arrays+4 : 0, ibegin, iend, obegin)) {
      Int_t n = (iend - ibegin)*sizeof(Double_t);
      if (arrays) {
         memmove(&arrays[0][obegin], &fEXlow[ibegin], n);
         memmove(&arrays[1][obegin], &fEXhigh[ibegin], n);
         memmove(&arrays[2][obegin], &fEYlow[ibegin], n);
         memmove(&arrays[3][obegin], &fEYhigh[ibegin], n);
      } else {
         memmove(&fEXlow[obegin], &fEXlow[ibegin], n);
         memmove(&fEXhigh[obegin], &fEXhigh[ibegin], n);
         memmove(&fEYlow[obegin], &fEYlow[ibegin], n);
         memmove(&fEYhigh[obegin], &fEYhigh[ibegin], n);
      }
      return kTRUE;
   } else {
      return kFALSE;
   }
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// Should be called from ctors after fNpoints has been set
/// Note: This function should be called only from the constructor
/// since it does not delete previously existing arrays
 
Bool_t TGraphAsymmErrors::CtorAllocate(void)
{
   if (!fNpoints) {
      fEXlow = fEYlow = fEXhigh = fEYhigh = 0;
      return kFALSE;
   }
   fEXlow = new Double_t[fMaxSize];
   fEYlow = new Double_t[fMaxSize];
   fEXhigh = new Double_t[fMaxSize];
   fEYhigh = new Double_t[fMaxSize];
   return kTRUE;
}
 
////////////////////////////////////////////////////////////////////////////////
///  protected function to perform the merge operation of a graph with asymmetric errors
 
Bool_t TGraphAsymmErrors::DoMerge(const TGraph *g)
{
   if (g->GetN() == 0) return kFALSE;
 
   Double_t * exl = g->GetEXlow();
   Double_t * exh = g->GetEXhigh();
   Double_t * eyl = g->GetEYlow();
   Double_t * eyh = g->GetEYhigh();
   if (exl == 0 || exh == 0 || eyl == 0 || eyh == 0) {
      if (g->IsA() != TGraph::Class() )
         Warning("DoMerge","Merging a %s is not compatible with a TGraphAsymmErrors - errors will be ignored",g->IsA()->GetName());
      return TGraph::DoMerge(g);
   }
   for (Int_t i = 0 ; i < g->GetN(); i++) {
      Int_t ipoint = GetN();
      Double_t x = g->GetX()[i];
      Double_t y = g->GetY()[i];
      SetPoint(ipoint, x, y);
      SetPointError(ipoint, exl[i], exh[i], eyl[i], eyh[i] );
   }
 
   return kTRUE;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Set zero values for point arrays in the range [begin, end)
 
void TGraphAsymmErrors::FillZero(Int_t begin, Int_t end,
                                 Bool_t from_ctor)
{
   if (!from_ctor) {
      TGraph::FillZero(begin, end, from_ctor);
   }
   Int_t n = (end - begin)*sizeof(Double_t);
   memset(fEXlow + begin, 0, n);
   memset(fEXhigh + begin, 0, n);
   memset(fEYlow + begin, 0, n);
   memset(fEYhigh + begin, 0, n);
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// This function is called by GraphFitChisquare.
/// It returns the error along X at point i.
 
Double_t TGraphAsymmErrors::GetErrorX(Int_t i) const
{
   if (i < 0 || i >= fNpoints) return -1;
   if (!fEXlow && !fEXhigh) return -1;
   Double_t elow=0, ehigh=0;
   if (fEXlow)  elow  = fEXlow[i];
   if (fEXhigh) ehigh = fEXhigh[i];
   return TMath::Sqrt(0.5*(elow*elow + ehigh*ehigh));
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// This function is called by GraphFitChisquare.
/// It returns the error along Y at point i.
 
Double_t TGraphAsymmErrors::GetErrorY(Int_t i) const
{
   if (i < 0 || i >= fNpoints) return -1;
   if (!fEYlow && !fEYhigh) return -1;
   Double_t elow=0, ehigh=0;
   if (fEYlow)  elow  = fEYlow[i];
   if (fEYhigh) ehigh = fEYhigh[i];
   return TMath::Sqrt(0.5*(elow*elow + ehigh*ehigh));
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// Get high error on X.
 
Double_t TGraphAsymmErrors::GetErrorXhigh(Int_t i) const
{
   if (i<0 || i>fNpoints) return -1;
   if (fEXhigh) return fEXhigh[i];
   return -1;
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// Get low error on X.
 
Double_t TGraphAsymmErrors::GetErrorXlow(Int_t i) const
{
   if (i<0 || i>fNpoints) return -1;
   if (fEXlow) return fEXlow[i];
   return -1;
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// Get high error on Y.
 
Double_t TGraphAsymmErrors::GetErrorYhigh(Int_t i) const
{
   if (i<0 || i>fNpoints) return -1;
   if (fEYhigh) return fEYhigh[i];
   return -1;
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// Get low error on Y.
 
Double_t TGraphAsymmErrors::GetErrorYlow(Int_t i) const
{
   if (i<0 || i>fNpoints) return -1;
   if (fEYlow) return fEYlow[i];
   return -1;
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// Adds all graphs with asymmetric errors from the collection to this graph.
/// Returns the total number of poins in the result or -1 in case of an error.
 
Int_t TGraphAsymmErrors::Merge(TCollection* li)
{
   TIter next(li);
   while (TObject* o = next()) {
      TGraph *g = dynamic_cast<TGraph*>(o);
      if (!g) {
         Error("Merge",
               "Cannot merge - an object which doesn't inherit from TGraph found in the list");
         return -1;
      }
      int n0 = GetN();
      int n1 = n0+g->GetN();
      Set(n1);
      Double_t * x = g->GetX();
      Double_t * y = g->GetY();
      Double_t * exlow  = g->GetEXlow();
      Double_t * exhigh = g->GetEXhigh();
      Double_t * eylow  = g->GetEYlow();
      Double_t * eyhigh = g->GetEYhigh();
      for (Int_t i = 0 ; i < g->GetN(); i++) {
         SetPoint(n0+i, x[i], y[i]);
         if (exlow)  fEXlow[n0+i]  = exlow[i];
         if (exhigh) fEXhigh[n0+i] = exhigh[i];
         if (eylow)  fEYlow[n0+i]  = eylow[i];
         if (eyhigh) fEYhigh[n0+i] = eyhigh[i];
      }
   }
   return GetN();
}
 
////////////////////////////////////////////////////////////////////////////////
/// Print graph and errors values.
 
void TGraphAsymmErrors::Print(Option_t *) const
{
   for (Int_t i=0;i<fNpoints;i++) {
      printf("x[%d]=%g, y[%d]=%g, exl[%d]=%g, exh[%d]=%g, eyl[%d]=%g, eyh[%d]=%g\n"
         ,i,fX[i],i,fY[i],i,fEXlow[i],i,fEXhigh[i],i,fEYlow[i],i,fEYhigh[i]);
   }
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// Save primitive as a C++ statement(s) on output stream out
 
void TGraphAsymmErrors::SavePrimitive(std::ostream &out, Option_t *option /*= ""*/)
{
   char quote = '"';
   out << "   " << std::endl;
   static Int_t frameNumber = 3000;
   frameNumber++;
 
   Int_t i;
   TString fXName   = TString(GetName()) + Form("_fx%d",frameNumber);
   TString fYName   = TString(GetName()) + Form("_fy%d",frameNumber);
   TString fElXName = TString(GetName()) + Form("_felx%d",frameNumber);
   TString fElYName = TString(GetName()) + Form("_fely%d",frameNumber);
   TString fEhXName = TString(GetName()) + Form("_fehx%d",frameNumber);
   TString fEhYName = TString(GetName()) + Form("_fehy%d",frameNumber);
   out << "   Double_t " << fXName << "[" << fNpoints << "] = {" << std::endl;
   for (i = 0; i < fNpoints-1; i++) out << "   " << fX[i] << "," << std::endl;
   out << "   " << fX[fNpoints-1] << "};" << std::endl;
   out << "   Double_t " << fYName << "[" << fNpoints << "] = {" << std::endl;
   for (i = 0; i < fNpoints-1; i++) out << "   " << fY[i] << "," << std::endl;
   out << "   " << fY[fNpoints-1] << "};" << std::endl;
   out << "   Double_t " << fElXName << "[" << fNpoints << "] = {" << std::endl;
   for (i = 0; i < fNpoints-1; i++) out << "   " << fEXlow[i] << "," << std::endl;
   out << "   " << fEXlow[fNpoints-1] << "};" << std::endl;
   out << "   Double_t " << fElYName << "[" << fNpoints << "] = {" << std::endl;
   for (i = 0; i < fNpoints-1; i++) out << "   " << fEYlow[i] << "," << std::endl;
   out << "   " << fEYlow[fNpoints-1] << "};" << std::endl;
   out << "   Double_t " << fEhXName << "[" << fNpoints << "] = {" << std::endl;
   for (i = 0; i < fNpoints-1; i++) out << "   " << fEXhigh[i] << "," << std::endl;
   out << "   " << fEXhigh[fNpoints-1] << "};" << std::endl;
   out << "   Double_t " << fEhYName << "[" << fNpoints << "] = {" << std::endl;
   for (i = 0; i < fNpoints-1; i++) out << "   " << fEYhigh[i] << "," << std::endl;
   out << "   " << fEYhigh[fNpoints-1] << "};" << std::endl;
 
   if (gROOT->ClassSaved(TGraphAsymmErrors::Class())) out<<"   ";
   else out << "   TGraphAsymmErrors *";
   out << "grae = new TGraphAsymmErrors("<< fNpoints << ","
                                    << fXName   << ","  << fYName  << ","
                                    << fElXName  << ","  << fEhXName << ","
                                    << fElYName  << ","  << fEhYName << ");"
                                    << std::endl;
 
   out << "   grae->SetName(" << quote << GetName() << quote << ");" << std::endl;
   out << "   grae->SetTitle(" << quote << GetTitle() << quote << ");" << std::endl;
 
   SaveFillAttributes(out, "grae", 0, 1001);
   SaveLineAttributes(out, "grae", 1, 1, 1);
   SaveMarkerAttributes(out, "grae", 1, 1, 1);
 
   if (fHistogram) {
      TString hname = fHistogram->GetName();
      hname += frameNumber;
      fHistogram->SetName(Form("Graph_%s",hname.Data()));
      fHistogram->SavePrimitive(out,"nodraw");
      out<<"   grae->SetHistogram("<<fHistogram->GetName()<<");"<<std::endl;
      out<<"   "<<std::endl;
   }
 
   // save list of functions
   TIter next(fFunctions);
   TObject *obj;
   while ((obj = next())) {
      obj->SavePrimitive(out, Form("nodraw #%d\n",++frameNumber));
      if (obj->InheritsFrom("TPaveStats")) {
         out << "   grae->GetListOfFunctions()->Add(ptstats);" << std::endl;
         out << "   ptstats->SetParent(grae->GetListOfFunctions());" << std::endl;
      } else {
         TString objname;
         objname.Form("%s%d",obj->GetName(),frameNumber);
         if (obj->InheritsFrom("TF1")) {
            out << "   " << objname << "->SetParent(grae);\n";
         }
         out << "   grae->GetListOfFunctions()->Add("
             << objname << ");" << std::endl;
      }
   }
 
   const char *l = strstr(option,"multigraph");
   if (l) {
      out<<"   multigraph->Add(grae,"<<quote<<l+10<<quote<<");"<<std::endl;
   } else {
      out<<"   grae->Draw("<<quote<<option<<quote<<");"<<std::endl;
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Set ex and ey values for point pointed by the mouse.
 
void TGraphAsymmErrors::SetPointError(Double_t exl, Double_t exh, Double_t eyl, Double_t eyh)
{
   Int_t px = gPad->GetEventX();
   Int_t py = gPad->GetEventY();
 
   //localize point to be deleted
   Int_t ipoint = -2;
   Int_t i;
   // start with a small window (in case the mouse is very close to one point)
   for (i=0;i<fNpoints;i++) {
      Int_t dpx = px - gPad->XtoAbsPixel(gPad->XtoPad(fX[i]));
      Int_t dpy = py - gPad->YtoAbsPixel(gPad->YtoPad(fY[i]));
      if (dpx*dpx+dpy*dpy < 25) {ipoint = i; break;}
   }
   if (ipoint == -2) return;
 
   fEXlow[ipoint]  = exl;
   fEYlow[ipoint]  = eyl;
   fEXhigh[ipoint] = exh;
   fEYhigh[ipoint] = eyh;
   gPad->Modified();
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// Set ex and ey values for point number i.
 
void TGraphAsymmErrors::SetPointError(Int_t i, Double_t exl, Double_t exh, Double_t eyl, Double_t eyh)
{
   if (i < 0) return;
   if (i >= fNpoints) {
   // re-allocate the object
      TGraphAsymmErrors::SetPoint(i,0,0);
   }
   fEXlow[i]  = exl;
   fEYlow[i]  = eyl;
   fEXhigh[i] = exh;
   fEYhigh[i] = eyh;
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// Set EXlow for point i
 
void TGraphAsymmErrors::SetPointEXlow(Int_t i, Double_t exl)
{
   if (i < 0) return;
   if (i >= fNpoints) {
   // re-allocate the object
      TGraphAsymmErrors::SetPoint(i,0,0);
   }
   fEXlow[i]  = exl;
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// Set EXhigh for point i
 
void TGraphAsymmErrors::SetPointEXhigh(Int_t i, Double_t exh)
{
   if (i < 0) return;
   if (i >= fNpoints) {
   // re-allocate the object
      TGraphAsymmErrors::SetPoint(i,0,0);
   }
   fEXhigh[i]  = exh;
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// Set EYlow for point i
 
void TGraphAsymmErrors::SetPointEYlow(Int_t i, Double_t eyl)
{
   if (i < 0) return;
   if (i >= fNpoints) {
   // re-allocate the object
      TGraphAsymmErrors::SetPoint(i,0,0);
   }
   fEYlow[i]  = eyl;
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// Set EYhigh for point i
 
void TGraphAsymmErrors::SetPointEYhigh(Int_t i, Double_t eyh)
{
   if (i < 0) return;
   if (i >= fNpoints) {
   // re-allocate the object
      TGraphAsymmErrors::SetPoint(i,0,0);
   }
   fEYhigh[i]  = eyh;
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// Stream an object of class TGraphAsymmErrors.
 
void TGraphAsymmErrors::Streamer(TBuffer &b)
{
   if (b.IsReading()) {
      UInt_t R__s, R__c;
      Version_t R__v = b.ReadVersion(&R__s, &R__c);
      if (R__v > 2) {
         b.ReadClassBuffer(TGraphAsymmErrors::Class(), this, R__v, R__s, R__c);
         return;
      }
      //====process old versions before automatic schema evolution
      TGraph::Streamer(b);
      fEXlow  = new Double_t[fNpoints];
      fEYlow  = new Double_t[fNpoints];
      fEXhigh = new Double_t[fNpoints];
      fEYhigh = new Double_t[fNpoints];
      if (R__v < 2) {
         Float_t *exlow  = new Float_t[fNpoints];
         Float_t *eylow  = new Float_t[fNpoints];
         Float_t *exhigh = new Float_t[fNpoints];
         Float_t *eyhigh = new Float_t[fNpoints];
         b.ReadFastArray(exlow,fNpoints);
         b.ReadFastArray(eylow,fNpoints);
         b.ReadFastArray(exhigh,fNpoints);
         b.ReadFastArray(eyhigh,fNpoints);
         for (Int_t i=0;i<fNpoints;i++) {
            fEXlow[i]  = exlow[i];
            fEYlow[i]  = eylow[i];
            fEXhigh[i] = exhigh[i];
            fEYhigh[i] = eyhigh[i];
         }
         delete [] eylow;
         delete [] exlow;
         delete [] eyhigh;
         delete [] exhigh;
      } else {
         b.ReadFastArray(fEXlow,fNpoints);
         b.ReadFastArray(fEYlow,fNpoints);
         b.ReadFastArray(fEXhigh,fNpoints);
         b.ReadFastArray(fEYhigh,fNpoints);
      }
      b.CheckByteCount(R__s, R__c, TGraphAsymmErrors::IsA());
      //====end of old versions
 
   } else {
      b.WriteClassBuffer(TGraphAsymmErrors::Class(),this);
   }
}
 
 
////////////////////////////////////////////////////////////////////////////////
/// Swap points.
 
void TGraphAsymmErrors::SwapPoints(Int_t pos1, Int_t pos2)
{
   SwapValues(fEXlow,  pos1, pos2);
   SwapValues(fEXhigh, pos1, pos2);
   SwapValues(fEYlow,  pos1, pos2);
   SwapValues(fEYhigh, pos1, pos2);
   TGraph::SwapPoints(pos1, pos2);
}