rf211_paramconv.py

## \ingroup tutorial_roofit_main

## \notebook

## 'ADDITION AND CONVOLUTION' RooFit tutorial macro #211

## Working a with a p.d.f. with a convolution operator in terms

## of a parameter

##

## (require ROOT to be compiled with --enable-fftw3)

##

## \macro_image

## \macro_code

## \macro_output

##

## \date February 2018

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

import ROOT

# Set up component pdfs

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

# Gaussian g(x ; mean,sigma)

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

mean = ROOT.RooRealVar("mean", "mean", -3, 3)

sigma = ROOT.RooRealVar("sigma", "sigma", 0.5, 0.1, 10)

modelx = ROOT.RooGaussian("gx", "gx", x, mean, sigma)

# Block function in mean

a = ROOT.RooRealVar("a", "a", 2, 1, 10)

model_mean = ROOT.RooGenericPdf("model_mean", "abs(mean)<a", [mean, a])

# Convolution in mean model = g(x,mean,sigma) (x) block(mean)

x.setBins(1000, "cache")

mean.setBins(50, "cache")

model = ROOT.RooFFTConvPdf("model", "model", mean, modelx, model_mean)

# Configure convolution to construct a 2-D cache in (x,mean)

# rather than a 1-d cache in mean that needs to be recalculated

# for each value of x

model.setCacheObservables({x})

model.setBufferFraction(1.0)

# Integrate model over projModel = Int model dmean

projModel = model.createProjection({mean})

# Generate 1000 toy events

d = projModel.generateBinned({x}, 1000)

# Fit p.d.f. to toy data

projModel.fitTo(d, Verbose=True, PrintLevel=-1)

# Plot data and fitted p.d.f.

frame = x.frame(Bins=25)

d.plotOn(frame)

projModel.plotOn(frame)

# Make 2d histogram of model(x;mean)

hh = model.createHistogram(

"hh",

x,

Binning=50,

YVar=dict(var=mean, Binning=50),

ConditionalObservables={mean},

)

hh.SetTitle("histogram of model(x|mean)")

hh.SetLineColor("kBlue")

# Draw frame on canvas

c = ROOT.TCanvas("rf211_paramconv", "rf211_paramconv", 800, 400)

c.Divide(2)

c.cd(1)

ROOT.gPad.SetLeftMargin(0.15)

frame.GetYaxis().SetTitleOffset(1.4)

frame.Draw()

c.cd(2)

ROOT.gPad.SetLeftMargin(0.20)

hh.GetZaxis().SetTitleOffset(2.5)

hh.Draw("surf")

c.SaveAs("rf211_paramconv.png")