rf702_efficiencyfit_2D.py

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## \file
## \ingroup tutorial_roofit
## \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 whose 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
 
 
flat = False
# 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))", [ax, bx, cx, x, ay, by, cy, y]
)
 
# Acceptance state cut (1 or 0)
cut = ROOT.RooCategory("cut", "cutr", {"accept": 1, "reject": 0})
 
# Construct conditional efficiency pdf E(cut|x,y)
# ---------------------------------------------------------------------------------------------
 
# Construct efficiency pdf eff(cut|x)
effPdf = ROOT.RooEfficiency("effPdf", "effPdf", effFunc, cut, "accept")
 
# Generate data(x,y,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)
shapePdfX = ROOT.RooPolynomial("shapePdfX", "shapePdfX", x, [0 if flat else -0.095])
shapePdfY = ROOT.RooPolynomial("shapePdfY", "shapePdfY", y, [0 if flat else +0.095])
shapePdf = ROOT.RooProdPdf("shapePdf", "shapePdf", [shapePdfX, shapePdfY])
model = ROOT.RooProdPdf("model", "model", {shapePdf}, Conditional=({effPdf}, {cut}))
 
# Generate some toy data from model
data = model.generate({x, y, cut}, 10000)
 
# Fit conditional efficiency pdf to data
# --------------------------------------------------------------------------
 
# Fit conditional efficiency pdf to data
effPdf.fitTo(data, ConditionalObservables={x, y}, PrintLevel=-1)
 
# Plot fitted, data efficiency
# --------------------------------------------------------
 
# Make 2D histograms of all data, data and efficiency function
hh_data_all = data.createHistogram("hh_data_all", x, Binning=8, YVar=dict(var=y, Binning=8))
hh_data_sel = data.createHistogram("hh_data_sel", x, Binning=8, YVar=dict(var=y, Binning=8), Cut="cut==cut::accept")
hh_eff = effFunc.createHistogram("hh_eff", x, Binning=50, YVar=dict(var=y, 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")