Rf 3 0 1_Composition

Multidimensional models: multi-dimensional p.d.f.s through composition, e.g. substituting a p.d.f 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 Sunday, July 05, 2020 at 08:22 AM.

In [ ]:
import ROOT

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

Create observables

In [ ]:
x = ROOT.RooRealVar("x", "x", -5, 5)
y = ROOT.RooRealVar("y", "y", -5, 5)

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

In [ ]:
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 [ ]:
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

In [ ]:
data = model.generate(ROOT.RooArgSet(x, y), 10000)

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

In [ ]:
xframe = x.frame()
data.plotOn(xframe)
model.plotOn(xframe)

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

In [ ]:
yframe = y.frame()
data.plotOn(yframe)
model.plotOn(yframe)

Make two-dimensional plot in x vs y

In [ ]:
hh_model = model.createHistogram("hh_model", x, ROOT.RooFit.Binning(
    50), ROOT.RooFit.YVar(y, ROOT.RooFit.Binning(50)))
hh_model.SetLineColor(ROOT.kBlue)

Make canvas and draw ROOT.RooPlots

In [ ]:
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")

Draw all canvases

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