rf109_chi2residpull.py

## \ingroup tutorial_roofit_main

## \notebook

## 'BASIC FUNCTIONALITY' RooFit tutorial macro #109

## Calculating chi^2 from histograms and curves in ROOT.RooPlots,

## making histogram of residual and pull distributions

##

## \macro_image

## \macro_code

## \macro_output

##

## \date February 2018

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

import ROOT

# Set up model

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

# Create observables

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

# Create Gaussian

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

mean = ROOT.RooRealVar("mean", "mean", 0, -10, 10)

gauss = ROOT.RooGaussian("gauss", "gauss", x, mean, sigma)

# Generate a sample of 1000 events with sigma=3

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

# Change sigma to 3.15

sigma.setVal(3.15)

# Plot data and slightly distorted model

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

# Overlay projection of gauss with sigma=3.15 on data with sigma=3.0

frame1 = x.frame(Title="Data with distorted Gaussian pdf", Bins=40)

data.plotOn(frame1, DataError="SumW2")

gauss.plotOn(frame1)

# Calculate chi^2

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

# Show the chi^2 of the curve w.r.t. the histogram

# If multiple curves or datasets live in the frame you can specify

# the name of the relevant curve and/or dataset in chiSquare()

print("chi^2 = ", frame1.chiSquare())

# Show residual and pull dists

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

# Construct a histogram with the residuals of the data w.r.t. the curve

hresid = frame1.residHist()

# Construct a histogram with the pulls of the data w.r.t the curve

hpull = frame1.pullHist()

# Create a frame to draw the residual distribution and add the

# distribution to the frame

frame2 = x.frame(Title="Residual Distribution")

frame2.addPlotable(hresid, "P")

# Create a frame to draw the pull distribution and add the distribution to

# the frame

frame3 = x.frame(Title="Pull Distribution")

frame3.addPlotable(hpull, "P")

c = ROOT.TCanvas("rf109_chi2residpull", "rf109_chi2residpull", 900, 300)

c.Divide(3)

c.cd(1)

ROOT.gPad.SetLeftMargin(0.15)

frame1.GetYaxis().SetTitleOffset(1.6)

frame1.Draw()

c.cd(2)

ROOT.gPad.SetLeftMargin(0.15)

frame2.GetYaxis().SetTitleOffset(1.6)

frame2.Draw()

c.cd(3)

ROOT.gPad.SetLeftMargin(0.15)

frame3.GetYaxis().SetTitleOffset(1.6)

frame3.Draw()

c.SaveAs("rf109_chi2residpull.png")