Rf 3 0 4_Uncorrprod¶

Multidimensional models: simple uncorrelated multi-dimensional pdfs

pdf = gauss(x,mx,sx) * gauss(y,my,sy)

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 Monday, January 17, 2022 at 09:58 AM.

In [ ]:
import ROOT

Create component pdfs in x and y¶

Create two pdfs gaussx(x,meanx,sigmax) gaussy(y,meany,sigmay) and its variables

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

meanx = ROOT.RooRealVar("mean1", "mean of gaussian x", 2)
meany = ROOT.RooRealVar("mean2", "mean of gaussian y", -2)
sigmax = ROOT.RooRealVar("sigmax", "width of gaussian x", 1)
sigmay = ROOT.RooRealVar("sigmay", "width of gaussian y", 5)

gaussx = ROOT.RooGaussian("gaussx", "gaussian PDF", x, meanx, sigmax)
gaussy = ROOT.RooGaussian("gaussy", "gaussian PDF", y, meany, sigmay)

Construct uncorrelated product pdf¶

Multiply gaussx and gaussy into a two-dimensional pdf gaussxy

In [ ]:
gaussxy = ROOT.RooProdPdf("gaussxy", "gaussx*gaussy", [gaussx, gaussy])

Sample pdf, plot projection on x and y¶

Generate 10000 events in x and y from gaussxy

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

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

In [ ]:
xframe = x.frame(Title="X projection of gauss(x)*gauss(y)")
data.plotOn(xframe)
gaussxy.plotOn(xframe)

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

In [ ]:
yframe = y.frame(Title="Y projection of gauss(x)*gauss(y)")
data.plotOn(yframe)
gaussxy.plotOn(yframe)

Make canvas and draw ROOT.RooPlots

In [ ]:
c = ROOT.TCanvas("rf304_uncorrprod", "rf304_uncorrprod", 800, 400)
c.Divide(2)
c.cd(1)
xframe.GetYaxis().SetTitleOffset(1.4)
xframe.Draw()
c.cd(2)