rf103_interprfuncs.py

## \ingroup tutorial_roofit_main

## \notebook

## Basic functionality: interpreted functions and pdfs

##

## \macro_image

## \macro_code

## \macro_output

##

## \date February 2018

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

import ROOT

# Generic interpreted pdf

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

# Declare observable x

x = ROOT.RooRealVar("x", "x", -20, 20)

# Construct generic pdf from interpreted expression

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

# ROOT.To construct a proper pdf, the formula expression is explicitly normalized internally by dividing

# it by a numeric integral of the expression over x in the range [-20,20]

#

alpha = ROOT.RooRealVar("alpha", "alpha", 5, 0.1, 10)

genpdf = ROOT.RooGenericPdf("genpdf", "genpdf", "(1+0.1*abs(x)+sin(sqrt(abs(x*alpha+0.1))))", [x, alpha])

# Sample, fit and plot generic pdf

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

# Generate a toy dataset from the interpreted pdf

data = genpdf.generate({x}, 10000)

# Fit the interpreted pdf to the generated data

genpdf.fitTo(data, PrintLevel=-1)

# Make a plot of the data and the pdf overlaid

xframe = x.frame(Title="Interpreted expression pdf")

data.plotOn(xframe)

genpdf.plotOn(xframe)

# Standard pdf adjust with interpreted helper function

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

# Make a gauss(x,sqrt(mean2),sigma) from a standard ROOT.RooGaussian #

#

# Construct standard pdf with formula replacing parameter

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

# Construct parameter mean2 and sigma

mean2 = ROOT.RooRealVar("mean2", "mean^2", 10, 0, 200)

sigma = ROOT.RooRealVar("sigma", "sigma", 3, 0.1, 10)

# Construct interpreted function mean = sqrt(mean^2)

mean = ROOT.RooFormulaVar("mean", "mean", "sqrt(mean2)", [mean2])

# Construct a gaussian g2(x,sqrt(mean2),sigma)

g2 = ROOT.RooGaussian("g2", "h2", x, mean, sigma)

# Generate toy data

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

# Construct a separate gaussian g1(x,10,3) to generate a toy Gaussian

# dataset with mean 10 and width 3

g1 = ROOT.RooGaussian("g1", "g1", x, 10, 3)

data2 = g1.generate({x}, 1000)

# Fit and plot tailored standard pdf

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

# Fit g2 to data from g1

r = g2.fitTo(data2, Save=True, PrintLevel=-1) # ROOT.RooFitResult

r.Print()

# Plot data on frame and overlay projection of g2

xframe2 = x.frame(Title="Tailored Gaussian pdf")

data2.plotOn(xframe2)

g2.plotOn(xframe2)

# Draw all frames on a canvas

c = ROOT.TCanvas("rf103_interprfuncs", "rf103_interprfuncs", 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)

xframe2.GetYaxis().SetTitleOffset(1.4)

xframe2.Draw()

c.SaveAs("rf103_interprfuncs.png")