rf702_efficiencyfit_2D.py File Reference

Detailed Description

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)

 
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("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")

[#0] WARNING:Generation -- RooAcceptReject::ctor(effPdf_Int[]_Norm[cut]) WARNING: performing accept/reject sampling on a p.d.f in 2 dimensions without prior knowledge on maximum value of p.d.f. Determining maximum value by taking 200000 trial samples. If p.d.f contains sharp peaks smaller than average distance between trial sampling points these may be missed and p.d.f. may be sampled incorrectly.
[#0] WARNING:Generation -- RooAcceptReject::ctor(effPdf_Int[]_Norm[cut]): WARNING: 200000 trial samples requested by p.d.f for 2-dimensional accept/reject sampling, this may take some time
[#1] INFO:Fitting -- RooAbsPdf::fitTo(effPdf_over_effPdf_Int[cut]) fixing normalization set for coefficient determination to observables in data
[#1] INFO:Fitting -- using generic CPU library compiled with no vectorizations
[#1] INFO:Fitting -- Creation of NLL object took 1.17089 ms
[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_effPdf_over_effPdf_Int[cut]_modelData) Summation contains a RooNLLVar, using its error level
[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only
[#1] INFO:FastEvaluations -- The class RooEfficiency does not implement the faster batch evaluation interface. Consider requesting or implementing it to benefit from a speed up.
[#1] INFO:FastEvaluations -- The class RooRealIntegral does not implement the faster batch evaluation interface. Consider requesting or implementing it to benefit from a speed up.

Date

February 2018

Authors

Clemens Lange, Wouter Verkerke (C++ version)

Definition in file rf702_efficiencyfit_2D.py.