rf701_efficiencyfit.py

## \ingroup tutorial_roofit_main

## \notebook

## Special pdf'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_image

## \macro_code

## \macro_output

##

## \date February 2018

## \authors 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)", [a, b, c, x])

# Construct conditional efficiency pdf E(cut|x)

# ------------------------------------------------------------------------------------------

# Acceptance state cut (1 or 0)

cut = ROOT.RooCategory("cut", "cutr", {"accept": 1, "reject": 0})

# Construct efficiency pdf eff(cut|x)

effPdf = ROOT.RooEfficiency("effPdf", "effPdf", effFunc, cut, "accept")

# Generate data (x, cut) from a toy model

# -----------------------------------------------------------------------------

# Construct global shape pdf 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, [-0.095])

model = ROOT.RooProdPdf("model", "model", {shapePdf}, Conditional=({effPdf}, {cut}))

# Generate some toy data from model

data = model.generate({x, cut}, 10000)

# Fit conditional efficiency pdf to data

# --------------------------------------------------------------------------

# Fit conditional efficiency pdf to data

effPdf.fitTo(data, ConditionalObservables={x}, PrintLevel=-1)

# Plot fitted, data efficiency

# --------------------------------------------------------

# Plot distribution of all events and accepted fraction of events on frame

frame1 = x.frame(Bins=20, Title="Data (all, accepted)")

data.plotOn(frame1)

data.plotOn(frame1, Cut="cut==cut::accept", MarkerColor="r", LineColor="r")

# Plot accept/reject efficiency on data overlay fitted efficiency curve

frame2 = x.frame(Bins=20, Title="Fitted efficiency")

data.plotOn(frame2, Efficiency=cut) # needs ROOT version >= 5.21

effFunc.plotOn(frame2, LineColor="r")

# 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")