rf702_efficiencyfit_2D.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 whose 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


flat = ROOT.kFALSE
# Construct efficiency function e(x,y)
# -----------------------------------------------------------------------

# Declare variables x,mean, with associated name, title, value and allowed
# range
x = ROOT.RooRealVar("x", "x", -10, 10)
y = ROOT.RooRealVar("y", "y", -10, 10)

# Efficiency function eff(x;a,b)
ax = ROOT.RooRealVar("ax", "ay", 0.6, 0, 1)
bx = ROOT.RooRealVar("bx", "by", 5)
cx = ROOT.RooRealVar("cx", "cy", -1, -10, 10)

ay = ROOT.RooRealVar("ay", "ay", 0.2, 0, 1)
by = ROOT.RooRealVar("by", "by", 5)
cy = ROOT.RooRealVar("cy", "cy", -1, -10, 10)

effFunc = ROOT.RooFormulaVar(
    "effFunc",
    "((1-ax)+ax*cos((x-cx)/bx))*((1-ay)+ay*cos((y-cy)/by))",
    ROOT.RooArgList(
        ax,
        bx,
        cx,
        x,
        ay,
        by,
        cy,
        y))

# Acceptance state cut (1 or 0)
cut = ROOT.RooCategory("cut", "cutr")
cut.defineType("accept", 1)
cut.defineType("reject", 0)

# Construct conditional efficiency pdf E(cut|x,y)
# ---------------------------------------------------------------------------------------------

# Construct efficiency p.d.f eff(cut|x)
effPdf = ROOT.RooEfficiency("effPdf", "effPdf", effFunc, cut, "accept")

# Generate data(x,y,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)
shapePdfX = ROOT.RooPolynomial(
    "shapePdfX", "shapePdfX", x, ROOT.RooArgList(
        ROOT.RooFit.RooConst(
            0 if flat else -0.095)))
shapePdfY = ROOT.RooPolynomial(
    "shapePdfY", "shapePdfY", y, ROOT.RooArgList(
        ROOT.RooFit.RooConst(
            0 if flat else +0.095)))
shapePdf = ROOT.RooProdPdf(
    "shapePdf",
    "shapePdf",
    ROOT.RooArgList(
        shapePdfX,
        shapePdfY))
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, y, 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, y)))

# Plot fitted, data efficiency
# --------------------------------------------------------

# Make 2D histograms of all data, data and efficiency function
hh_data_all = ROOT.RooAbsData.createHistogram(
    data, "hh_data_all", x, ROOT.RooFit.Binning(8), ROOT.RooFit.YVar(
        y, ROOT.RooFit.Binning(8)))
hh_data_sel = ROOT.RooAbsData.createHistogram(
    data, "hh_data_sel", x, ROOT.RooFit.Binning(8), ROOT.RooFit.YVar(
        y, ROOT.RooFit.Binning(8)), ROOT.RooFit.Cut("cut==cut::accept"))
hh_eff = effFunc.createHistogram(
    "hh_eff", x, ROOT.RooFit.Binning(
        50), ROOT.RooFit.YVar(y, ROOT.RooFit.Binning(50)))

# Some adjustsment for good visualization
hh_data_all.SetMinimum(0)
hh_data_sel.SetMinimum(0)
hh_eff.SetMinimum(0)
hh_eff.SetLineColor(ROOT.kBlue)

# Draw all frames on a canvas
ca = ROOT.TCanvas("rf702_efficiency_2D", "rf702_efficiency_2D", 1200, 400)
ca.Divide(3)
ca.cd(1)
ROOT.gPad.SetLeftMargin(0.15)
hh_data_all.GetZaxis().SetTitleOffset(1.8)
hh_data_all.Draw("lego")
ca.cd(2)
ROOT.gPad.SetLeftMargin(0.15)
hh_data_sel.GetZaxis().SetTitleOffset(1.8)
hh_data_sel.Draw("lego")
ca.cd(3)
ROOT.gPad.SetLeftMargin(0.15)
hh_eff.GetZaxis().SetTitleOffset(1.8)
hh_eff.Draw("surf")

ca.SaveAs("rf702_efficiency_2D.png")