rf308_normintegration2d.py

## \ingroup tutorial_roofit_main

## \notebook

## Multidimensional models: normalization and integration of pdfs, construction of

## cumulative distribution functions from pdfs in two dimensions

##

## \macro_image

## \macro_code

## \macro_output

##

## \date February 2018

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

import ROOT

# Set up model

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

# Create observables x,y

x = ROOT.RooRealVar("x", "x", -10, 10)

y = ROOT.RooRealVar("y", "y", -10, 10)

# Create pdf gaussx(x,-2,3), gaussy(y,2,2)

gx = ROOT.RooGaussian("gx", "gx", x, -2.0, 3.0)

gy = ROOT.RooGaussian("gy", "gy", y, +2.0, 2.0)

# gxy = gx(x)*gy(y)

gxy = ROOT.RooProdPdf("gxy", "gxy", [gx, gy])

# Retrieve raw & normalized values of RooFit pdfs

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

# Return 'raw' unnormalized value of gx

print("gxy = ", gxy.getVal())

# Return value of gxy normalized over x _and_ y in range [-10,10]

nset_xy = {x, y}

print("gx_Norm[x,y] = ", gxy.getVal(nset_xy))

# Create object representing integral over gx

# which is used to calculate gx_Norm[x,y] == gx / gx_Int[x,y]

x_and_y = {x, y}

igxy = gxy.createIntegral(x_and_y)

print("gx_Int[x,y] = ", igxy.getVal())

# NB: it is also possible to do the following

# Return value of gxy normalized over x in range [-10,10] (i.e. treating y

# as parameter)

nset_x = {x}

print("gx_Norm[x] = ", gxy.getVal(nset_x))

# Return value of gxy normalized over y in range [-10,10] (i.e. treating x

# as parameter)

nset_y = {y}

print("gx_Norm[y] = ", gxy.getVal(nset_y))

# Integrate normalized pdf over subrange

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

# Define a range named "signal" in x from -5,5

x.setRange("signal", -5, 5)

y.setRange("signal", -3, 3)

# Create an integral of gxy_Norm[x,y] over x and y in range "signal"

# ROOT.This is the fraction of of pdf gxy_Norm[x,y] which is in the

# range named "signal"

igxy_sig = gxy.createIntegral(x_and_y, NormSet=x_and_y, Range="signal")

print("gx_Int[x,y|signal]_Norm[x,y] = ", igxy_sig.getVal())

# Construct cumulative distribution function from pdf

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

# Create the cumulative distribution function of gx

# i.e. calculate Int[-10,x] gx(x') dx'

gxy_cdf = gxy.createCdf({x, y})

# Plot cdf of gx versus x

hh_cdf = gxy_cdf.createHistogram("hh_cdf", x, Binning=40, YVar=dict(var=y, Binning=40))

hh_cdf.SetLineColor("kBlue")

c = ROOT.TCanvas("rf308_normintegration2d", "rf308_normintegration2d", 600, 600)

ROOT.gPad.SetLeftMargin(0.15)

hh_cdf.GetZaxis().SetTitleOffset(1.8)

hh_cdf.Draw("surf")

c.SaveAs("rf308_normintegration2d.png")