rf703_effpdfprod.py

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## \file
## \ingroup tutorial_roofit
## \notebook
## Special pdf's: using a product of an (acceptance) efficiency and a pdf as pdf
##
## \macro_image
## \macro_code
## \macro_output
##
## \date February 2018
## \authors Clemens Lange, Wouter Verkerke (C++ version)
 
import ROOT
 
 
# Define observables and decay pdf
# ---------------------------------------------------------------
 
# Declare observables
t = ROOT.RooRealVar("t", "t", 0, 5)
 
# Make pdf
tau = ROOT.RooRealVar("tau", "tau", -1.54, -4, -0.1)
model = ROOT.RooExponential("model", "model", t, tau)
 
# Define efficiency function
# ---------------------------------------------------
 
# Use error function to simulate turn-on slope
eff = ROOT.RooFormulaVar("eff", "0.5*(TMath::Erf((t-1)/0.5)+1)", [t])
 
# Define decay pdf with efficiency
# ---------------------------------------------------------------
 
# Multiply pdf(t) with efficiency in t
modelEff = ROOT.RooEffProd("modelEff", "model with efficiency", model, eff)
 
# Plot efficiency, pdf
# ----------------------------------------
 
frame1 = t.frame(Title="Efficiency")
eff.plotOn(frame1, LineColor="r")
 
frame2 = t.frame(Title="Pdf with and without efficiency")
 
model.plotOn(frame2, LineStyle="--")
modelEff.plotOn(frame2)
 
# Generate toy data, fit model eff to data
# ------------------------------------------------------------------------------
 
# Generate events. If the input pdf has an internal generator, internal generator
# is used and an accept/reject sampling on the efficiency is applied.
data = modelEff.generate({t}, 10000)
 
# Fit pdf. The normalization integral is calculated numerically.
modelEff.fitTo(data, PrintLevel=-1)
 
# Plot generated data and overlay fitted pdf
frame3 = t.frame(Title="Fitted pdf with efficiency")
data.plotOn(frame3)
modelEff.plotOn(frame3)
 
c = ROOT.TCanvas("rf703_effpdfprod", "rf703_effpdfprod", 1200, 400)
c.Divide(3)
c.cd(1)
ROOT.gPad.SetLeftMargin(0.15)
frame1.GetYaxis().SetTitleOffset(1.4)
frame1.Draw()
c.cd(2)
ROOT.gPad.SetLeftMargin(0.15)
frame2.GetYaxis().SetTitleOffset(1.6)
frame2.Draw()
c.cd(3)
ROOT.gPad.SetLeftMargin(0.15)
frame3.GetYaxis().SetTitleOffset(1.6)
frame3.Draw()
 
c.SaveAs("rf703_effpdfprod.png")