fitNormSum.C File Reference

Detailed Description

Tutorial for normalized sum of two functions Here: a background exponential and a crystalball function Parameters can be set:

1. with the TF1 object before adding the function (for 3) and 4))
2. with the TF1NormSum object (first two are the coefficients, then the non constant parameters)
3. with the TF1 object after adding the function

Sum can be constructed by:

1. by a string containing the names of the functions and/or the coefficient in front
2. by a string containg formulas like expo, gaus...
3. by the list of functions and coefficients (which are 1 by default)
4. by a std::vector for functions and coefficients

Time to generate 1050000 events:  Real time 0:00:00, CP time 0.140
****************************************
Minimizer is Minuit2 / Migrad
Chi2                      =      1018.73
NDf                       =          993
Edm                       =  9.65559e-06
NCalls                    =          233
NSignal                   =        50082   +/-   1231.21     
NBackground               =       998899   +/-   1569.86     
Mean                      =      2.99896   +/-   0.0022426   
Sigma                     =     0.297871   +/-   0.00230279  
Alpha                     =      2.12493   +/-   0.1368      
N                         =       1.1562   +/-   0.468136    
Slope                     =    -0.300341   +/-   0.000644187 
Time to fit using ROOT TF1Normsum: Real time 0:00:00, CP time 0.140

 
#include <Math/MinimizerOptions.h>
#include <TCanvas.h>
#include <TF1.h>
#include <TF1NormSum.h>
#include <TFitResult.h>
#include <TH1.h>
#include <TLatex.h>
#include <TMath.h>
#include <TStopwatch.h>
#include <TStyle.h>
 
void fitNormSum()
{
   const int nsig = 5.E4;
   const int nbkg = 1.e6;
   int nEvents = nsig + nbkg;
   int nBins = 1e3;
 
   double signal_mean = 3;
   TF1 *f_cb = new TF1("MyCrystalBall", "crystalball", -5., 5.);
   TF1 *f_exp = new TF1("MyExponential", "expo", -5., 5.);
 
   // I.:
   f_exp->SetParameters(1., -0.3);
   f_cb->SetParameters(1, signal_mean, 0.3, 2, 1.5);
 
   // CONSTRUCTION OF THE TF1NORMSUM OBJECT ........................................
   // 1) :
   TF1NormSum *fnorm_exp_cb = new TF1NormSum(f_cb, f_exp, nsig, nbkg);
   // 4) :
 
   TF1 *f_sum = new TF1("fsum", *fnorm_exp_cb, -5., 5., fnorm_exp_cb->GetNpar());
 
   // III.:
   f_sum->SetParameters(fnorm_exp_cb->GetParameters().data());
   f_sum->SetParName(1, "NBackground");
   f_sum->SetParName(0, "NSignal");
   for (int i = 2; i < f_sum->GetNpar(); ++i)
      f_sum->SetParName(i, fnorm_exp_cb->GetParName(i));
 
   // GENERATE HISTOGRAM TO FIT ..............................................................
   TStopwatch w;
   w.Start();
   TH1D *h_sum = new TH1D("h_ExpCB", "Exponential Bkg + CrystalBall function", nBins, -5., 5.);
   h_sum->FillRandom("fsum", nEvents);
   printf("Time to generate %d events:  ", nEvents);
   w.Print();
 
   // need to scale histogram with width since we are fitting a density
   h_sum->Sumw2();
   h_sum->Scale(1., "width");
 
   // fit - use Minuit2 if available
   ROOT::Math::MinimizerOptions::SetDefaultMinimizer("Minuit2");
   new TCanvas("Fit", "Fit", 800, 1000);
   // do a least-square fit of the spectrum
   auto result = h_sum->Fit("fsum", "SQ");
   result->Print();
   h_sum->Draw();
   printf("Time to fit using ROOT TF1Normsum: ");
   w.Print();
 
   // test if parameters are fine
   std::vector<double> pref = {nsig, nbkg, signal_mean};
   for (unsigned int i = 0; i < pref.size(); ++i) {
      if (!TMath::AreEqualAbs(pref[i], f_sum->GetParameter(i), f_sum->GetParError(i) * 10.))
         Error("testFitNormSum", "Difference found in fitted %s - difference is %g sigma", f_sum->GetParName(i),
               (f_sum->GetParameter(i) - pref[i]) / f_sum->GetParError(i));
   }
 
   gStyle->SetOptStat(0);
   // add parameters
   auto t1 = new TLatex(
      -2.5, 300000, TString::Format("%s = %8.0f #pm %4.0f", "NSignal", f_sum->GetParameter(0), f_sum->GetParError(0)));
   auto t2 = new TLatex(
      -2.5, 270000, TString::Format("%s = %8.0f #pm %4.0f", "Nbackgr", f_sum->GetParameter(1), f_sum->GetParError(1)));
   t1->Draw();
   t2->Draw();
}

Author

Lorenzo Moneta

Definition in file fitNormSum.C.