# Rf 2 1 1_Paramconv¶

'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)

Author: Wouter Verkerke (C version)
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Wednesday, January 19, 2022 at 10:16 AM.

In [ ]:
import ROOT


## Set up component pdfs¶

Gaussian g(x ; mean,sigma)

In [ ]:
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

In [ ]:
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)

In [ ]:
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

In [ ]:
model.setCacheObservables({x})
model.setBufferFraction(1.0)


Integrate model over projModel = Int model dmean

In [ ]:
projModel = model.createProjection({mean})


Generate 1000 toy events

In [ ]:
d = projModel.generateBinned({x}, 1000)


Fit p.d.f. to toy data

In [ ]:
projModel.fitTo(d, Verbose=True)


Plot data and fitted p.d.f.

In [ ]:
frame = x.frame(Bins=25)
d.plotOn(frame)
projModel.plotOn(frame)


Make 2d histogram of model(x;mean)

In [ ]:
hh = model.createHistogram(
"hh",
x,
Binning=50,
YVar=dict(var=mean, Binning=50),
ConditionalObservables={mean},
)
hh.SetTitle("histogram of model(x|mean)")
hh.SetLineColor(ROOT.kBlue)


Draw frame on canvas

In [ ]:
c = ROOT.TCanvas("rf211_paramconv", "rf211_paramconv", 800, 400)
c.Divide(2)
c.cd(1)
frame.GetYaxis().SetTitleOffset(1.4)
frame.Draw()
c.cd(2)

from ROOT import gROOT