Rf 3 0 1_Composition

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

Author: Clemens Lange, Wouter Verkerke (C++ version)
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Saturday, November 28, 2020 at 10:44 AM.

In [1]:
import ROOT
Welcome to JupyROOT 6.23/01

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

Create observables

In [2]:
x = ROOT.RooRealVar("x", "x", -5, 5)
y = ROOT.RooRealVar("y", "y", -5, 5)
RooFit v3.60 -- Developed by Wouter Verkerke and David Kirkby 
                Copyright (C) 2000-2013 NIKHEF, University of California & Stanford University
                All rights reserved, please read http://roofit.sourceforge.net/license.txt

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

In [3]:
a0 = ROOT.RooRealVar("a0", "a0", -0.5, -5, 5)
a1 = ROOT.RooRealVar("a1", "a1", -0.5, -1, 1)
fy = ROOT.RooPolyVar("fy", "fy", y, ROOT.RooArgList(a0, a1))

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

In [4]:
sigma = ROOT.RooRealVar("sigma", "width of gaussian", 0.5)
model = ROOT.RooGaussian(
    "model", "Gaussian with shifting mean", x, fy, sigma)
[#0] WARNING:InputArguments -- The parameter 'sigma' with range [-1e+30, 1e+30] of the RooGaussian 'model' exceeds the safe range of (0, inf). Advise to limit its range.

Sample data, plot data and pdf on x and y

Generate 10000 events in x and y from model

In [5]:
data = model.generate(ROOT.RooArgSet(x, y), 10000)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(model_Int[x,y]) using numeric integrator RooIntegrator1D to calculate Int(y)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(model_Int[x,y]) using numeric integrator RooIntegrator1D to calculate Int(y)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(model_Int[x,y]) using numeric integrator RooIntegrator1D to calculate Int(y)

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

In [6]:
xframe = x.frame()
data.plotOn(xframe)
model.plotOn(xframe)
Out[6]:
<cppyy.gbl.RooPlot object at 0x70c1560>
[#1] INFO:Plotting -- RooAbsReal::plotOn(model) plot on x integrates over variables (y)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(model_Int[x,y]) using numeric integrator RooIntegrator1D to calculate Int(y)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(model_Int[y]_Norm[x,y]) using numeric integrator RooIntegrator1D to calculate Int(y)

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

In [7]:
yframe = y.frame()
data.plotOn(yframe)
model.plotOn(yframe)
Out[7]:
<cppyy.gbl.RooPlot object at 0x719d4f0>
[#1] INFO:Plotting -- RooAbsReal::plotOn(model) plot on y integrates over variables (x)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(model_Int[x,y]) using numeric integrator RooIntegrator1D to calculate Int(y)

Make two-dimensional plot in x vs y

In [8]:
hh_model = model.createHistogram("hh_model", x, ROOT.RooFit.Binning(
    50), ROOT.RooFit.YVar(y, ROOT.RooFit.Binning(50)))
hh_model.SetLineColor(ROOT.kBlue)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(model_Int[x,y]) using numeric integrator RooIntegrator1D to calculate Int(y)

Make canvas and draw ROOT.RooPlots

In [9]:
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")
Info in <TCanvas::Print>: png file rf301_composition.png has been created

Draw all canvases

In [10]:
from ROOT import gROOT 
gROOT.GetListOfCanvases().Draw()