rf110_normintegration.py

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## \file
## \ingroup tutorial_roofit
## \notebook
## Basic functionality: examples on normalization and integration of pdfs, construction
## of cumulative distribution functions from monodimensional pdfs
##
## \macro_image
## \macro_code
## \macro_output
##
## \date February 2018
## \authors Clemens Lange, Wouter Verkerke (C++ version)
 
import ROOT
 
# Set up model
# ---------------------
 
# Create observables x,y
x = ROOT.RooRealVar("x", "x", -10, 10)
 
# Create pdf gaussx(x,-2,3)
gx = ROOT.RooGaussian("gx", "gx", x, -2, 3)
 
# Retrieve raw & normalized values of RooFit pdfs
# --------------------------------------------------------------------------------------------------
 
# Return 'raw' unnormalized value of gx
print("gx = ", gx.getVal())
 
# Return value of gx normalized over x in range [-10,10]
nset = {x}
print("gx_Norm[x] = ", gx.getVal(nset))
 
# Create object representing integral over gx
# which is used to calculate  gx_Norm[x] == gx / gx_Int[x]
igx = gx.createIntegral({x})
print("gx_Int[x] = ", igx.getVal())
 
# Integrate normalized pdf over subrange
# ----------------------------------------------------------------------------
 
# Define a range named "signal" in x from -5,5
x.setRange("signal", -5, 5)
 
# Create an integral of gx_Norm[x] over x in range "signal"
# ROOT.This is the fraction of of pdf gx_Norm[x] which is in the
# range named "signal"
xset = {x}
igx_sig = gx.createIntegral(xset, NormSet=xset, Range="signal")
print("gx_Int[x|signal]_Norm[x] = ", igx_sig.getVal())
 
# Construct cumulative distribution function from pdf
# -----------------------------------------------------------------------------------------------------
 
# Create the cumulative distribution function of gx
# i.e. calculate Int[-10,x] gx(x') dx'
gx_cdf = gx.createCdf({x})
 
# Plot cdf of gx versus x
frame = x.frame(Title="cdf of Gaussian pdf")
gx_cdf.plotOn(frame)
 
# Draw plot on canvas
c = ROOT.TCanvas("rf110_normintegration", "rf110_normintegration", 600, 600)
ROOT.gPad.SetLeftMargin(0.15)
frame.GetYaxis().SetTitleOffset(1.6)
frame.Draw()
 
c.SaveAs("rf110_normintegration.png")