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rf602_chi2fit.py
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1## \file
2## \ingroup tutorial_roofit
3## \notebook
4##
5## 'LIKELIHOOD AND MINIMIZATION' RooFit tutorial macro #602
6##
7## Setting up a chi^2 fit to a binned dataset
8##
9## \macro_code
10##
11## \date February 2018
12## \author Clemens Lange
13## \author Wouter Verkerke (C version)
14
15from __future__ import print_function
16import ROOT
17
18
19# Set up model
20# ---------------------
21
22# Declare observable x
23x = ROOT.RooRealVar("x", "x", 0, 10)
24
25# Create two Gaussian PDFs g1(x,mean1,sigma) anf g2(x,mean2,sigma) and
26# their parameters
27mean = ROOT.RooRealVar("mean", "mean of gaussians", 5)
28sigma1 = ROOT.RooRealVar("sigma1", "width of gaussians", 0.5)
29sigma2 = ROOT.RooRealVar("sigma2", "width of gaussians", 1)
30
31sig1 = ROOT.RooGaussian("sig1", "Signal component 1", x, mean, sigma1)
32sig2 = ROOT.RooGaussian("sig2", "Signal component 2", x, mean, sigma2)
33
34# Build Chebychev polynomial p.d.f.
35a0 = ROOT.RooRealVar("a0", "a0", 0.5, 0.0, 1.0)
36a1 = ROOT.RooRealVar("a1", "a1", 0.2, 0.0, 1.0)
37bkg = ROOT.RooChebychev("bkg", "Background", x, [a0, a1])
38
39# Sum the signal components into a composite signal p.d.f.
40sig1frac = ROOT.RooRealVar("sig1frac", "fraction of component 1 in signal", 0.8, 0.0, 1.0)
41sig = ROOT.RooAddPdf("sig", "Signal", [sig1, sig2], [sig1frac])
42
43# Sum the composite signal and background
44bkgfrac = ROOT.RooRealVar("bkgfrac", "fraction of background", 0.5, 0.0, 1.0)
45model = ROOT.RooAddPdf("model", "g1+g2+a", [bkg, sig], [bkgfrac])
46
47# Create biuned dataset
48# -----------------------------------------
49
50d = model.generate({x}, 10000)
51dh = d.binnedClone()
52
53# Construct a chi^2 of the data and the model.
54# When a p.d.f. is used in a chi^2 fit, probability density scaled
55# by the number of events in the dataset to obtain the fit function
56# If model is an extended p.d.f, expected number events is used
57# instead of the observed number of events.
58ll = ROOT.RooLinkedList()
59model.chi2FitTo(dh, ll)
60
61# NB: It is also possible to fit a ROOT.RooAbsReal function to a ROOT.RooDataHist
62# using chi2FitTo().
63
64# Note that entries with zero bins are _not_ allowed
65# for a proper chi^2 calculation and will give error
66# messages
67dsmall = d.reduce(ROOT.RooFit.EventRange(1, 100))
68dhsmall = dsmall.binnedClone()
69chi2_lowstat = ROOT.RooChi2Var("chi2_lowstat", "chi2", model, dhsmall)
70print(chi2_lowstat.getVal())