rf315_projectpdf.py

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## \file
## \ingroup tutorial_roofit
## \notebook
##
## Multidimensional models: marginizalization of multi-dimensional p.d.f.s through integration
##
## \macro_code
##
## \date February 2018
## \author Clemens Lange, Wouter Verkerke (C++ version)

import ROOT


# Create pdf m(x,y) = gx(x|y) * g(y)
# --------------------------------------------------------------

# Increase default precision of numeric integration
# as self exercise has high sensitivity to numeric integration precision
ROOT.RooAbsPdf.defaultIntegratorConfig().setEpsRel(1e-8)
ROOT.RooAbsPdf.defaultIntegratorConfig().setEpsAbs(1e-8)

# Create observables
x = ROOT.RooRealVar("x", "x", -5, 5)
y = ROOT.RooRealVar("y", "y", -2, 2)

# Create function f(y) = a0 + a1*y
a0 = ROOT.RooRealVar("a0", "a0", 0)
a1 = ROOT.RooRealVar("a1", "a1", -1.5, -3, 1)
fy = ROOT.RooPolyVar("fy", "fy", y, ROOT.RooArgList(a0, a1))

# Create gaussx(x,f(y),sx)
sigmax = ROOT.RooRealVar("sigmax", "width of gaussian", 0.5)
gaussx = ROOT.RooGaussian(
    "gaussx", "Gaussian in x with shifting mean in y", x, fy, sigmax)

# Create gaussy(y,0,2)
gaussy = ROOT.RooGaussian(
    "gaussy",
    "Gaussian in y",
    y,
    ROOT.RooFit.RooConst(0),
    ROOT.RooFit.RooConst(2))

# Create gaussx(x,sx|y) * gaussy(y)
model = ROOT.RooProdPdf(
    "model",
    "gaussx(x|y)*gaussy(y)",
    ROOT.RooArgSet(gaussy),
    ROOT.RooFit.Conditional(
        ROOT.RooArgSet(gaussx),
        ROOT.RooArgSet(x)))

# Marginalize m(x,y) to m(x)
# ----------------------------------------------------

# modelx(x) = Int model(x,y) dy
modelx = model.createProjection(ROOT.RooArgSet(y))

# Use marginalized p.d.f. as regular 1D p.d.f.
# -----------------------------------------------

# Sample 1000 events from modelx
data = modelx.generateBinned(ROOT.RooArgSet(x), 1000)

# Fit modelx to toy data
modelx.fitTo(data, ROOT.RooFit.Verbose())

# Plot modelx over data
frame = x.frame(40)
data.plotOn(frame)
modelx.plotOn(frame)

# Make 2D histogram of model(x,y)
hh = model.createHistogram("x,y")
hh.SetLineColor(ROOT.kBlue)

c = ROOT.TCanvas("rf315_projectpdf", "rf315_projectpdf", 800, 400)
c.Divide(2)
c.cd(1)
ROOT.gPad.SetLeftMargin(0.15)
frame.GetYaxis().SetTitleOffset(1.4)
frame.Draw()
c.cd(2)
ROOT.gPad.SetLeftMargin(0.20)
hh.GetZaxis().SetTitleOffset(2.5)
hh.Draw("surf")
c.SaveAs("rf315_projectpdf.png")