Rf 1 0 3_Interprfuncs

Basic functionality: interpreted functions and pdfs

Author: Clemens Lange, Wouter Verkerke (C++ version)
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Monday, January 17, 2022 at 09:49 AM.

In [ ]:
import ROOT

Generic interpreted pdf

Declare observable x

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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 expresssion over x in the range [-20,20]

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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

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

Fit the interpreted pdf to the generated data

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genpdf.fitTo(data)

Make a plot of the data and the pdf overlaid

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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

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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)

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

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

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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

In [ ]:
g1 = ROOT.RooGaussian("g1", "g1", x, ROOT.RooFit.RooConst(10), ROOT.RooFit.RooConst(3))
data2 = g1.generate({x}, 1000)

Fit and plot tailored standard pdf

Fit g2 to data from g1

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r = g2.fitTo(data2, Save=True)  # ROOT.RooFitResult
r.Print()

Plot data on frame and overlay projection of g2

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xframe2 = x.frame(Title="Tailored Gaussian pdf")
data2.plotOn(xframe2)
g2.plotOn(xframe2)

Draw all frames on a canvas

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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")

Draw all canvases

In [ ]:
from ROOT import gROOT 
gROOT.GetListOfCanvases().Draw()