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Reference Guide
rf201_composite.py
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1## \file
2## \ingroup tutorial_roofit
3## \notebook
4## Addition and convolution: composite p.d.f with signal and background component
5##
6## pdf = f_bkg * bkg(x,a0,a1) + (1-fbkg) * (f_sig1 * sig1(x,m,s1 + (1-f_sig1) * sig2(x,m,s2)))
7##
8## \macro_code
9##
10## \date February 2018
11## \author Clemens Lange, Wouter Verkerke (C++ version)
12
13import ROOT
14
15# Setup component pdfs
16# ---------------------------------------
17
18# Declare observable x
19x = ROOT.RooRealVar("x", "x", 0, 10)
20
21# Create two Gaussian PDFs g1(x,mean1,sigma) anf g2(x,mean2,sigma) and
22# their parameters
23mean = ROOT.RooRealVar("mean", "mean of gaussians", 5)
24sigma1 = ROOT.RooRealVar("sigma1", "width of gaussians", 0.5)
25sigma2 = ROOT.RooRealVar("sigma2", "width of gaussians", 1)
26
27sig1 = ROOT.RooGaussian("sig1", "Signal component 1", x, mean, sigma1)
28sig2 = ROOT.RooGaussian("sig2", "Signal component 2", x, mean, sigma2)
29
30# Build Chebychev polynomial p.d.f.
31a0 = ROOT.RooRealVar("a0", "a0", 0.5, 0., 1.)
32a1 = ROOT.RooRealVar("a1", "a1", -0.2, 0., 1.)
33bkg = ROOT.RooChebychev("bkg", "Background", x, ROOT.RooArgList(a0, a1))
34
35
36# Method 1 - Two RooAddPdfs
37# ------------------------------------------
38# Add signal components
39
40# Sum the signal components into a composite signal p.d.f.
41sig1frac = ROOT.RooRealVar(
42 "sig1frac", "fraction of component 1 in signal", 0.8, 0., 1.)
43sig = ROOT.RooAddPdf("sig", "Signal", ROOT.RooArgList(
44 sig1, sig2), ROOT.RooArgList(sig1frac))
45
46# Add signal and background
47# ------------------------------------------------
48
49# Sum the composite signal and background
50bkgfrac = ROOT.RooRealVar("bkgfrac", "fraction of background", 0.5, 0., 1.)
51model = ROOT.RooAddPdf(
52 "model", "g1+g2+a", ROOT.RooArgList(bkg, sig), ROOT.RooArgList(bkgfrac))
53
54# Sample, fit and plot model
55# ---------------------------------------------------
56
57# Generate a data sample of 1000 events in x from model
58data = model.generate(ROOT.RooArgSet(x), 1000)
59
60# Fit model to data
61model.fitTo(data)
62
63# Plot data and PDF overlaid
64xframe = x.frame(ROOT.RooFit.Title(
65 "Example of composite pdf=(sig1+sig2)+bkg"))
66data.plotOn(xframe)
67model.plotOn(xframe)
68
69# Overlay the background component of model with a dashed line
70ras_bkg = ROOT.RooArgSet(bkg)
71model.plotOn(xframe, ROOT.RooFit.Components(ras_bkg),
72 ROOT.RooFit.LineStyle(ROOT.kDashed))
73
74# Overlay the background+sig2 components of model with a dotted line
75ras_bkg_sig2 = ROOT.RooArgSet(bkg, sig2)
76model.plotOn(xframe, ROOT.RooFit.Components(ras_bkg_sig2),
77 ROOT.RooFit.LineStyle(ROOT.kDotted))
78
79# Print structure of composite p.d.f.
80model.Print("t")
81
82# Method 2 - One RooAddPdf with recursive fractions
83# ---------------------------------------------------
84
85# Construct sum of models on one go using recursive fraction interpretations
86#
87# model2 = bkg + (sig1 + sig2)
88#
89model2 = ROOT.RooAddPdf(
90 "model",
91 "g1+g2+a",
92 ROOT.RooArgList(
93 bkg,
94 sig1,
95 sig2),
96 ROOT.RooArgList(
97 bkgfrac,
98 sig1frac),
99 ROOT.kTRUE)
100
101# NB: Each coefficient is interpreted as the fraction of the
102# left-hand component of the i-th recursive sum, i.e.
103#
104# sum4 = A + ( B + ( C + D) with fraction fA, and fC expands to
105#
106# sum4 = fA*A + (1-fA)*(fB*B + (1-fB)*(fC*C + (1-fC)*D))
107
108# Plot recursive addition model
109# ---------------------------------------------------------
110model2.plotOn(xframe, ROOT.RooFit.LineColor(ROOT.kRed),
111 ROOT.RooFit.LineStyle(ROOT.kDashed))
112model2.plotOn(
113 xframe,
114 ROOT.RooFit.Components(ras_bkg_sig2),
115 ROOT.RooFit.LineColor(
116 ROOT.kRed),
117 ROOT.RooFit.LineStyle(
118 ROOT.kDashed))
119model2.Print("t")
120
121# Draw the frame on the canvas
122c = ROOT.TCanvas("rf201_composite", "rf201_composite", 600, 600)
123ROOT.gPad.SetLeftMargin(0.15)
124xframe.GetYaxis().SetTitleOffset(1.4)
125xframe.Draw()
126
127c.SaveAs("rf201_composite.png")