rf313_paramranges.py

## \ingroup tutorial_roofit_main

## \notebook

## Multidimensional models: working with parameterized ranges to define non-rectangular

## regions for fitting and integration

##

## \macro_image

## \macro_code

## \macro_output

##

## \date February 2018

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

import ROOT

# Create 3D pdf

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

# Define observable (x,y,z)

x = ROOT.RooRealVar("x", "x", 0, 10)

y = ROOT.RooRealVar("y", "y", 0, 10)

z = ROOT.RooRealVar("z", "z", 0, 10)

# Define 3 dimensional pdf

z0 = ROOT.RooRealVar("z0", "z0", -0.1, 1)

px = ROOT.RooPolynomial("px", "px", x, [0.0])

py = ROOT.RooPolynomial("py", "py", y, [0.0])

pz = ROOT.RooPolynomial("pz", "pz", z, [z0])

pxyz = ROOT.RooProdPdf("pxyz", "pxyz", [px, py, pz])

# Defined non-rectangular region R in (x, y, z)

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

#

# R = Z[0 - 0.1*Y^2] * Y[0.1*X - 0.9*X] * X[0 - 10]

#

# Construct range parameterized in "R" in y [ 0.1*x, 0.9*x ]

ylo = ROOT.RooFormulaVar("ylo", "0.1*x", [x])

yhi = ROOT.RooFormulaVar("yhi", "0.9*x", [x])

y.setRange("R", ylo, yhi)

# Construct parameterized ranged "R" in z [ 0, 0.1*y^2 ]

zlo = ROOT.RooFormulaVar("zlo", "0.0*y", [y])

zhi = ROOT.RooFormulaVar("zhi", "0.1*y*y", [y])

z.setRange("R", zlo, zhi)

# Calculate integral of normalized pdf in R

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

# Create integral over normalized pdf model over x,y, in "R" region

intPdf = pxyz.createIntegral({x, y, z}, {x, y, z}, "R")

# Plot value of integral as function of pdf parameter z0

frame = z0.frame(Title="Integral of pxyz over x,y, in region R")

intPdf.plotOn(frame)

c = ROOT.TCanvas("rf313_paramranges", "rf313_paramranges", 600, 600)

ROOT.gPad.SetLeftMargin(0.15)

frame.GetYaxis().SetTitleOffset(1.6)

frame.Draw()

c.SaveAs("rf313_paramranges.png")