rf701_efficiencyfit.py

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## \file
## \ingroup tutorial_roofit
## \notebook
##
## Special p.d.f.'s: unbinned maximum likelihood fit of an efficiency eff(x) function to a dataset D(x,cut), cut is a category encoding a selection, which the efficiency as function of x should be described by eff(x)
##
## \macro_code
##
## \date February 2018
## \author Clemens Lange, Wouter Verkerke (C++ version)
 
import ROOT
 
 
# Construct efficiency function e(x)
# -------------------------------------------------------------------
 
# Declare variables x,mean, with associated name, title, value and allowed
# range
x = ROOT.RooRealVar("x", "x", -10, 10)
 
# Efficiency function eff(x;a,b)
a = ROOT.RooRealVar("a", "a", 0.4, 0, 1)
b = ROOT.RooRealVar("b", "b", 5)
c = ROOT.RooRealVar("c", "c", -1, -10, 10)
effFunc = ROOT.RooFormulaVar(
    "effFunc", "(1-a)+a*cos((x-c)/b)", ROOT.RooArgList(a, b, c, x))
 
# Construct conditional efficiency pdf E(cut|x)
# ------------------------------------------------------------------------------------------
 
# Acceptance state cut (1 or 0)
cut = ROOT.RooCategory("cut", "cutr")
cut.defineType("accept", 1)
cut.defineType("reject", 0)
 
# Construct efficiency p.d.f eff(cut|x)
effPdf = ROOT.RooEfficiency("effPdf", "effPdf", effFunc, cut, "accept")
 
# Generate data (x, cut) from a toy model
# -----------------------------------------------------------------------------
 
# Construct global shape p.d.f shape(x) and product model(x,cut) = eff(cut|x)*shape(x)
# (These are _only_ needed to generate some toy MC here to be used later)
shapePdf = ROOT.RooPolynomial(
    "shapePdf", "shapePdf", x, ROOT.RooArgList(ROOT.RooFit.RooConst(-0.095)))
model = ROOT.RooProdPdf(
    "model",
    "model",
    ROOT.RooArgSet(shapePdf),
    ROOT.RooFit.Conditional(
        ROOT.RooArgSet(effPdf),
        ROOT.RooArgSet(cut)))
 
# Generate some toy data from model
data = model.generate(ROOT.RooArgSet(x, cut), 10000)
 
# Fit conditional efficiency pdf to data
# --------------------------------------------------------------------------
 
# Fit conditional efficiency p.d.f to data
effPdf.fitTo(data, ROOT.RooFit.ConditionalObservables(ROOT.RooArgSet(x)))
 
# Plot fitted, data efficiency
# --------------------------------------------------------
 
# Plot distribution of all events and accepted fraction of events on frame
frame1 = x.frame(ROOT.RooFit.Bins(
    20), ROOT.RooFit.Title("Data (all, accepted)"))
data.plotOn(frame1)
data.plotOn(
    frame1,
    ROOT.RooFit.Cut("cut==cut::accept"),
    ROOT.RooFit.MarkerColor(
        ROOT.kRed),
    ROOT.RooFit.LineColor(
        ROOT.kRed))
 
# Plot accept/reject efficiency on data overlay fitted efficiency curve
frame2 = x.frame(ROOT.RooFit.Bins(
    20), ROOT.RooFit.Title("Fitted efficiency"))
data.plotOn(frame2, ROOT.RooFit.Efficiency(cut))  # needs ROOT version >= 5.21
effFunc.plotOn(frame2, ROOT.RooFit.LineColor(ROOT.kRed))
 
# Draw all frames on a canvas
ca = ROOT.TCanvas("rf701_efficiency", "rf701_efficiency", 800, 400)
ca.Divide(2)
ca.cd(1)
ROOT.gPad.SetLeftMargin(0.15)
frame1.GetYaxis().SetTitleOffset(1.6)
frame1.Draw()
ca.cd(2)
ROOT.gPad.SetLeftMargin(0.15)
frame2.GetYaxis().SetTitleOffset(1.4)
frame2.Draw()
 
ca.SaveAs("rf701_efficiencyfit.png")