rf304_uncorrprod.py

## \ingroup tutorial_roofit_main

## \notebook

## Multidimensional models: simple uncorrelated multi-dimensional pdfs

##

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

##

## \macro_image

## \macro_code

## \macro_output

##

## \date February 2018

## \authors Clemens Lange, Wouter Verkerke (C++ version)

import ROOT

# Create component pdfs in x and y

# ----------------------------------------------------------------

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

# variables

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

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

data = gaussxy.generate({x, y}, 10000)

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

# gaussxy(x,y)

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)

yframe = y.frame(Title="Y projection of gauss(x)*gauss(y)")

data.plotOn(yframe)

gaussxy.plotOn(yframe)

# Make canvas and draw ROOT.RooPlots

c = ROOT.TCanvas("rf304_uncorrprod", "rf304_uncorrprod", 800, 400)

c.Divide(2)

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.SaveAs("rf304_uncorrprod.png")