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rf703_effpdfprod.py File Reference

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 rf703_effpdfprod
 

Detailed Description

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Special p.d.f.'s: using a product of an (acceptance) efficiency and a p.d.f as p.d.f.

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)",
ROOT.RooArgList(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(ROOT.RooFit.Title("Efficiency"))
eff.plotOn(frame1, ROOT.RooFit.LineColor(ROOT.kRed))
frame2 = t.frame(ROOT.RooFit.Title("Pdf with and without efficiency"))
model.plotOn(frame2, ROOT.RooFit.LineStyle(ROOT.kDashed))
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(ROOT.RooArgSet(t), 10000)
# Fit pdf. The normalization integral is calculated numerically.
modelEff.fitTo(data)
# Plot generated data and overlay fitted pdf
frame3 = t.frame(ROOT.RooFit.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")
Date
February 2018
Authors
Clemens Lange, Wouter Verkerke (C++ version)

Definition in file rf703_effpdfprod.py.