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rf201_composite.py
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1## \file
2## \ingroup tutorial_roofit
3## \notebook
4## Addition and convolution: composite pdf with signal and background component
5##
6## 
7## pdf = f_bkg * bkg(x,a0,a1) + (1-fbkg) * (f_sig1 * sig1(x,m,s1 + (1-f_sig1) * sig2(x,m,s2)))
8## 
9##
10## \macro_code
11##
12## \date February 2018
13## \authors Clemens Lange, Wouter Verkerke (C++ version)
14
15import ROOT
16
17# Setup component pdfs
18# ---------------------------------------
19
20# Declare observable x
21x = ROOT.RooRealVar("x", "x", 0, 10)
22
23# Create two Gaussian PDFs g1(x,mean1,sigma) anf g2(x,mean2,sigma) and
24# their parameters
25mean = ROOT.RooRealVar("mean", "mean of gaussians", 5)
26sigma1 = ROOT.RooRealVar("sigma1", "width of gaussians", 0.5)
27sigma2 = ROOT.RooRealVar("sigma2", "width of gaussians", 1)
28
29sig1 = ROOT.RooGaussian("sig1", "Signal component 1", x, mean, sigma1)
30sig2 = ROOT.RooGaussian("sig2", "Signal component 2", x, mean, sigma2)
31
32# Build Chebychev polynomial pdf
33a0 = ROOT.RooRealVar("a0", "a0", 0.5, 0., 1.)
34a1 = ROOT.RooRealVar("a1", "a1", -0.2, 0., 1.)
35bkg = ROOT.RooChebychev("bkg", "Background", x, ROOT.RooArgList(a0, a1))
36
37
38# Method 1 - Two RooAddPdfs
39# ------------------------------------------
40# Add signal components
41
42# Sum the signal components into a composite signal pdf
43sig1frac = ROOT.RooRealVar(
44 "sig1frac", "fraction of component 1 in signal", 0.8, 0., 1.)
45sig = ROOT.RooAddPdf("sig", "Signal", ROOT.RooArgList(
46 sig1, sig2), ROOT.RooArgList(sig1frac))
47
48# Add signal and background
49# ------------------------------------------------
50
51# Sum the composite signal and background
52bkgfrac = ROOT.RooRealVar("bkgfrac", "fraction of background", 0.5, 0., 1.)
53model = ROOT.RooAddPdf(
54 "model", "g1+g2+a", ROOT.RooArgList(bkg, sig), ROOT.RooArgList(bkgfrac))
55
56# Sample, fit and plot model
57# ---------------------------------------------------
58
59# Generate a data sample of 1000 events in x from model
60data = model.generate(ROOT.RooArgSet(x), 1000)
61
62# Fit model to data
63model.fitTo(data)
64
65# Plot data and PDF overlaid
66xframe = x.frame(ROOT.RooFit.Title(
67 "Example of composite pdf=(sig1+sig2)+bkg"))
68data.plotOn(xframe)
69model.plotOn(xframe)
70
71# Overlay the background component of model with a dashed line
72ras_bkg = ROOT.RooArgSet(bkg)
73model.plotOn(xframe, ROOT.RooFit.Components(ras_bkg),
74 ROOT.RooFit.LineStyle(ROOT.kDashed))
75
76# Overlay the background+sig2 components of model with a dotted line
77ras_bkg_sig2 = ROOT.RooArgSet(bkg, sig2)
78model.plotOn(xframe, ROOT.RooFit.Components(ras_bkg_sig2),
79 ROOT.RooFit.LineStyle(ROOT.kDotted))
80
81# Print structure of composite pdf
82model.Print("t")
83
84# Method 2 - One RooAddPdf with recursive fractions
85# ---------------------------------------------------
86
87# Construct sum of models on one go using recursive fraction interpretations
88#
89# model2 = bkg + (sig1 + sig2)
90#
91model2 = ROOT.RooAddPdf(
92 "model",
93 "g1+g2+a",
94 ROOT.RooArgList(
95 bkg,
96 sig1,
97 sig2),
98 ROOT.RooArgList(
99 bkgfrac,
100 sig1frac),
101 ROOT.kTRUE)
102
103# NB: Each coefficient is interpreted as the fraction of the
104# left-hand component of the i-th recursive sum, i.e.
105#
106# sum4 = A + ( B + ( C + D) with fraction fA, and fC expands to
107#
108# sum4 = fA*A + (1-fA)*(fB*B + (1-fB)*(fC*C + (1-fC)*D))
109
110# Plot recursive addition model
111# ---------------------------------------------------------
112model2.plotOn(xframe, ROOT.RooFit.LineColor(ROOT.kRed),
113 ROOT.RooFit.LineStyle(ROOT.kDashed))
114model2.plotOn(
115 xframe,
116 ROOT.RooFit.Components(ras_bkg_sig2),
117 ROOT.RooFit.LineColor(
118 ROOT.kRed),
119 ROOT.RooFit.LineStyle(
120 ROOT.kDashed))
121model2.Print("t")
122
123# Draw the frame on the canvas
124c = ROOT.TCanvas("rf201_composite", "rf201_composite", 600, 600)
125ROOT.gPad.SetLeftMargin(0.15)
126xframe.GetYaxis().SetTitleOffset(1.4)
127xframe.Draw()
128
129c.SaveAs("rf201_composite.png")