fitNormSum¶

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

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

Sum can be constructed by:

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

Author: Lorenzo Moneta
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Monday, March 27, 2023 at 09:47 AM.

In [1]:

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.:

In [2]:

f_exp->SetParameters(1., -0.3);
f_cb->SetParameters(1, signal_mean, 0.3, 2, 1.5);

CONSTRUCTION OF THE TF1NORMSUM OBJECT ........................................

:

In [3]:

TF1NormSum *fnorm_exp_cb = new TF1NormSum(f_cb, f_exp, nsig, nbkg);

:

In [4]:

TF1 *f_sum = new TF1("fsum", *fnorm_exp_cb, -5., 5., fnorm_exp_cb->GetNpar());

III.:

In [5]:

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 ..............................................................

In [6]:

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();

Time to generate 1050000 events:  Real time 0:00:00, CP time 0.300

need to scale histogram with width since we are fitting a density

In [7]:

h_sum->Sumw2();
h_sum->Scale(1., "width");

fit - use Minuit2 if available

In [8]:

ROOT::Math::MinimizerOptions::SetDefaultMinimizer("Minuit2");
new TCanvas("Fit", "Fit", 800, 1000);

do a least-square fit of the spectrum

In [9]:

auto result = h_sum->Fit("fsum", "SQ");
result->Print();
h_sum->Draw();
printf("Time to fit using ROOT TF1Normsum: ");
w.Print();

****************************************
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 0.300

test if parameters are fine

In [10]:

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

In [11]:

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();

Draw all canvases

In [12]:

gROOT->GetListOfCanvases()->Draw()