# rf301_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 Wednesday, November 30, 2022 at 11:22 AM.

In [1]:
import ROOT

Welcome to JupyROOT 6.27/01


## 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)


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, [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({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 0x99a2980>
[#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 0x9b0e120>
[#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, Binning=50, YVar=dict(var=y, 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()