# rf305_condcorrprod¶

Multidimensional models: multi-dimensional pdfs with conditional pdfs in product

pdf = gauss(x,f(y),sx | y ) * gauss(y,ms,sx) 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, November 27, 2022 at 11:07 AM.

In [1]:
import ROOT

Welcome to JupyROOT 6.27/01


## Create conditional pdf gx(x|y)¶

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])


Create gaussx(x,f(y),sx)

In [4]:
sigmax = ROOT.RooRealVar("sigma", "width of gaussian", 0.5)
gaussx = ROOT.RooGaussian("gaussx", "Gaussian in x with shifting mean in y", x, fy, sigmax)

[#0] WARNING:InputArguments -- The parameter 'sigma' with range [-1e+30, 1e+30] of the RooGaussian 'gaussx' exceeds the safe range of (0, inf). Advise to limit its range.


## Create pdf gy(y)¶

Create gaussy(y,0,5)

In [5]:
gaussy = ROOT.RooGaussian("gaussy", "Gaussian in y", y, ROOT.RooFit.RooConst(0), ROOT.RooFit.RooConst(3))


## Create product gx(x|y)*gy(y)¶

Create gaussx(x,sx|y) * gaussy(y)

In [6]:
model = ROOT.RooProdPdf("model", "gaussx(x|y)*gaussy(y)", {gaussy}, Conditional=({gaussx}, {x}))


## Sample, fit and plot product pdf¶

Generate 1000 events in x and y from model

In [7]:
data = model.generate({x, y}, 10000)


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

In [8]:
xframe = x.frame()
data.plotOn(xframe)
model.plotOn(xframe)

Out[8]:
<cppyy.gbl.RooPlot object at 0x94251b0>
[#1] INFO:Plotting -- RooAbsReal::plotOn(model) plot on x integrates over variables (y)
[#1] INFO:NumericIntegration -- RooRealIntegral::init([gaussy_NORM[y]_X_gaussx_NORM[x]]_Int[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 [9]:
yframe = y.frame()
data.plotOn(yframe)
model.plotOn(yframe)

Out[9]:
<cppyy.gbl.RooPlot object at 0x95e1420>
[#1] INFO:Plotting -- RooAbsReal::plotOn(model) plot on y integrates over variables (x)


Make two-dimensional plot in x vs y

In [10]:
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 [11]:
c = ROOT.TCanvas("rf305_condcorrprod", "rf05_condcorrprod", 1200, 400)
c.Divide(3)
c.cd(1)
xframe.GetYaxis().SetTitleOffset(1.6)
xframe.Draw()
c.cd(2)
yframe.GetYaxis().SetTitleOffset(1.6)
yframe.Draw()
c.cd(3)
hh_model.GetZaxis().SetTitleOffset(2.5)
hh_model.Draw("surf")

c.SaveAs("rf305_condcorrprod.png")

Info in <TCanvas::Print>: png file rf305_condcorrprod.png has been created


Draw all canvases

In [12]:
from ROOT import gROOT
gROOT.GetListOfCanvases().Draw()