rf301_composition.py

## \ingroup tutorial_roofit_main

## \notebook

## Multidimensional models: multi-dimensional pdfs through composition, e.g. substituting

## a pdf parameter with a function that depends on other observables

##

## `pdf = gauss(x,f(y),s)` with `f(y) = a0 + a1*y`

##

## \macro_image

## \macro_code

## \macro_output

##

## \date February 2018

## \authors Clemens Lange, Wouter Verkerke (C++ version)

import ROOT

# Setup composed model gauss(x, m(y), s)

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

# Create observables

x = ROOT.RooRealVar("x", "x", -5, 5)

y = ROOT.RooRealVar("y", "y", -5, 5)

# Create function f(y) = a0 + a1*y

a0 = ROOT.RooRealVar("a0", "a0", -0.5, -5, 5)

a1 = ROOT.RooRealVar("a1", "a1", -0.5, -1, 1)

fy = ROOT.RooPolyVar("fy", "fy", y, [a0, a1])

# Creat gauss(x,f(y),s)

sigma = ROOT.RooRealVar("sigma", "width of gaussian", 0.5)

model = ROOT.RooGaussian("model", "Gaussian with shifting mean", x, fy, sigma)

# Sample data, plot data and pdf on x and y

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

# Generate 10000 events in x and y from model

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

# Plot x distribution of data and projection of model x = Int(dy)

# model(x,y)

xframe = x.frame()

data.plotOn(xframe)

model.plotOn(xframe)

# Plot x distribution of data and projection of model y = Int(dx)

# model(x,y)

yframe = y.frame()

data.plotOn(yframe)

model.plotOn(yframe)

# Make two-dimensional plot in x vs y

hh_model = model.createHistogram("hh_model", x, Binning=50, YVar=dict(var=y, Binning=50))

hh_model.SetLineColor("kBlue")

# Make canvas and draw ROOT.RooPlots

c = ROOT.TCanvas("rf301_composition", "rf301_composition", 1200, 400)

c.Divide(3)

c.cd(1)

ROOT.gPad.SetLeftMargin(0.15)

xframe.GetYaxis().SetTitleOffset(1.4)

xframe.Draw()

c.cd(2)

ROOT.gPad.SetLeftMargin(0.15)

yframe.GetYaxis().SetTitleOffset(1.4)

yframe.Draw()

c.cd(3)

ROOT.gPad.SetLeftMargin(0.20)

hh_model.GetZaxis().SetTitleOffset(2.5)

hh_model.Draw("surf")

c.SaveAs("rf301_composition.png")