rf201_composite.py

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## \file
## \ingroup tutorial_roofit
## \notebook
## Addition and convolution: composite pdf with signal and background component
##
## ```
## pdf = f_bkg * bkg(x,a0,a1) + (1-fbkg) * (f_sig1 * sig1(x,m,s1 + (1-f_sig1) * sig2(x,m,s2)))
## ```
##
## \macro_code
##
## \date February 2018
## \authors Clemens Lange, Wouter Verkerke (C++ version)
 
import ROOT
 
# Setup component pdfs
# ---------------------------------------
 
# Declare observable x
x = ROOT.RooRealVar("x", "x", 0, 10)
 
# Create two Gaussian PDFs g1(x,mean1,sigma) anf g2(x,mean2,sigma) and
# their parameters
mean = ROOT.RooRealVar("mean", "mean of gaussians", 5)
sigma1 = ROOT.RooRealVar("sigma1", "width of gaussians", 0.5)
sigma2 = ROOT.RooRealVar("sigma2", "width of gaussians", 1)
 
sig1 = ROOT.RooGaussian("sig1", "Signal component 1", x, mean, sigma1)
sig2 = ROOT.RooGaussian("sig2", "Signal component 2", x, mean, sigma2)
 
# Build Chebychev polynomial pdf
a0 = ROOT.RooRealVar("a0", "a0", 0.5, 0., 1.)
a1 = ROOT.RooRealVar("a1", "a1", -0.2, 0., 1.)
bkg = ROOT.RooChebychev("bkg", "Background", x, ROOT.RooArgList(a0, a1))
 
 
# Method 1 - Two RooAddPdfs
# ------------------------------------------
# Add signal components
 
# Sum the signal components into a composite signal pdf
sig1frac = ROOT.RooRealVar(
    "sig1frac", "fraction of component 1 in signal", 0.8, 0., 1.)
sig = ROOT.RooAddPdf("sig", "Signal", ROOT.RooArgList(
    sig1, sig2), ROOT.RooArgList(sig1frac))
 
# Add signal and background
# ------------------------------------------------
 
# Sum the composite signal and background
bkgfrac = ROOT.RooRealVar("bkgfrac", "fraction of background", 0.5, 0., 1.)
model = ROOT.RooAddPdf(
    "model", "g1+g2+a", ROOT.RooArgList(bkg, sig), ROOT.RooArgList(bkgfrac))
 
# Sample, fit and plot model
# ---------------------------------------------------
 
# Generate a data sample of 1000 events in x from model
data = model.generate(ROOT.RooArgSet(x), 1000)
 
# Fit model to data
model.fitTo(data)
 
# Plot data and PDF overlaid
xframe = x.frame(ROOT.RooFit.Title(
    "Example of composite pdf=(sig1+sig2)+bkg"))
data.plotOn(xframe)
model.plotOn(xframe)
 
# Overlay the background component of model with a dashed line
ras_bkg = ROOT.RooArgSet(bkg)
model.plotOn(xframe, ROOT.RooFit.Components(ras_bkg),
             ROOT.RooFit.LineStyle(ROOT.kDashed))
 
# Overlay the background+sig2 components of model with a dotted line
ras_bkg_sig2 = ROOT.RooArgSet(bkg, sig2)
model.plotOn(xframe, ROOT.RooFit.Components(ras_bkg_sig2),
             ROOT.RooFit.LineStyle(ROOT.kDotted))
 
# Print structure of composite pdf
model.Print("t")
 
# Method 2 - One RooAddPdf with recursive fractions
# ---------------------------------------------------
 
# Construct sum of models on one go using recursive fraction interpretations
#
#   model2 = bkg + (sig1 + sig2)
#
model2 = ROOT.RooAddPdf(
    "model",
    "g1+g2+a",
    ROOT.RooArgList(
        bkg,
        sig1,
        sig2),
    ROOT.RooArgList(
        bkgfrac,
        sig1frac),
    ROOT.kTRUE)
 
# NB: Each coefficient is interpreted as the fraction of the
# left-hand component of the i-th recursive sum, i.e.
#
#   sum4 = A + ( B + ( C + D)  with fraction fA, and fC expands to
#
#   sum4 = fA*A + (1-fA)*(fB*B + (1-fB)*(fC*C + (1-fC)*D))
 
# Plot recursive addition model
# ---------------------------------------------------------
model2.plotOn(xframe, ROOT.RooFit.LineColor(ROOT.kRed),
              ROOT.RooFit.LineStyle(ROOT.kDashed))
model2.plotOn(
    xframe,
    ROOT.RooFit.Components(ras_bkg_sig2),
    ROOT.RooFit.LineColor(
        ROOT.kRed),
    ROOT.RooFit.LineStyle(
        ROOT.kDashed))
model2.Print("t")
 
# Draw the frame on the canvas
c = ROOT.TCanvas("rf201_composite", "rf201_composite", 600, 600)
ROOT.gPad.SetLeftMargin(0.15)
xframe.GetYaxis().SetTitleOffset(1.4)
xframe.Draw()
 
c.SaveAs("rf201_composite.png")