fitNormSum.py 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

Real time 0:00:00, CP time 0.260
****************************************
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 
Real time 0:00:00, CP time 0.260
Time to generate 1050000 events:  
Time to fit using ROOT TF1Normsum: 

 
import ROOT
 
nsig = 50000
nbkg = 1000000
nEvents = nsig + nbkg
nBins = 1000
 
signal_mean = 3.0
f_cb = ROOT.TF1("MyCrystalBall", "crystalball", -5.0, 5.0)
f_exp = ROOT.TF1("MyExponential", "expo", -5.0, 5.0)
 
# I.:
f_exp.SetParameters(1.0, -0.3)
f_cb.SetParameters(1, signal_mean, 0.3, 2, 1.5)
 
# CONSTRUCTION OF THE TF1NORMSUM OBJECT ........................................
# 1) :
fnorm_exp_cb = ROOT.TF1NormSum(f_cb, f_exp, nsig, nbkg)
# 4) :
 
f_sum = ROOT.TF1("fsum", fnorm_exp_cb, -5.0, 5.0, fnorm_exp_cb.GetNpar())
 
# III.:
parameter_values = fnorm_exp_cb.GetParameters()
f_sum.SetParameters(parameter_values.data())
# Note: in the C++ tutorial, the parameter value sync is done in one line with:
# ```C++
#     f_sum->SetParameters(fnorm_exp_cb->GetParameters().data());
# ```
# However, TF1NormSum::GetParameters() returns an std::vector by value, which
# doesn't survive long enough in Python. That's why we have to explicitly
# assign it to a variable first and can't use a temporary.
 
f_sum.SetParName(1, "NBackground")
f_sum.SetParName(0, "NSignal")
for i in range(2, f_sum.GetNpar()):
    f_sum.SetParName(i, fnorm_exp_cb.GetParName(i))
 
# GENERATE HISTOGRAM TO FIT ..............................................................
w = ROOT.TStopwatch()
w.Start()
h_sum = ROOT.TH1D("h_ExpCB", "Exponential Bkg + CrystalBall function", nBins, -5.0, 5.0)
h_sum.FillRandom("fsum", nEvents)
print("Time to generate {0} events:  ".format(nEvents))
w.Print()
 
# need to scale histogram with width since we are fitting a density
h_sum.Sumw2()
h_sum.Scale(1.0, "width")
 
# fit - use Minuit2 if available
ROOT.Math.MinimizerOptions.SetDefaultMinimizer("Minuit2")
c1 = ROOT.TCanvas("Fit", "Fit", 800, 1000)
# do a least-square fit of the spectrum
result = h_sum.Fit("fsum", "SQ")
result.Print()
h_sum.Draw()
print("Time to fit using ROOT TF1Normsum: ")
w.Print()
 
# test if parameters are fine
for i, pref in enumerate([nsig, nbkg, signal_mean]):
    if not ROOT.TMath.AreEqualAbs(pref, f_sum.GetParameter(i), f_sum.GetParError(i) * 10.0):
        ROOT.Error(
            "testFitNormSum",
            "Difference found in fitted {0} - difference is {1:.2f} sigma".format(
                f_sum.GetParName(i), (f_sum.GetParameter(i) - pref) / f_sum.GetParError(i)
            ),
        )
 
ROOT.gStyle.SetOptStat(0)
# add parameters
t1 = ROOT.TLatex(-2.5, 300000, "NSignal = {0:g} #pm {1:g}".format(f_sum.GetParameter(0), f_sum.GetParError(0)))
t2 = ROOT.TLatex(-2.5, 270000, "Nbackgr = {0:g} #pm {1:g}".format(f_sum.GetParameter(1), f_sum.GetParError(1)))
t1.Draw()
t2.Draw()
 
c1.SaveAs("fitNormSum.png")

Author

Jonas Rembser, Lorenzo Moneta (C++ version)

Definition in file fitNormSum.py.