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rf308_normintegration2d.py File Reference

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 rf308_normintegration2d
 

Detailed Description

View in nbviewer Open in SWAN Multidimensional models: normalization and integration of pdfs, construction of cumulative distribution functions from pdfs in two dimensions

from __future__ import print_function
import ROOT
# Set up model
# ---------------------
# Create observables x,y
x = ROOT.RooRealVar("x", "x", -10, 10)
y = ROOT.RooRealVar("y", "y", -10, 10)
# Create pdf gaussx(x,-2,3), gaussy(y,2,2)
gx = ROOT.RooGaussian(
"gx", "gx", x, ROOT.RooFit.RooConst(-2), ROOT.RooFit.RooConst(3))
gy = ROOT.RooGaussian(
"gy", "gy", y, ROOT.RooFit.RooConst(+2), ROOT.RooFit.RooConst(2))
# gxy = gx(x)*gy(y)
gxy = ROOT.RooProdPdf("gxy", "gxy", ROOT.RooArgList(gx, gy))
# Retrieve raw & normalized values of RooFit pdfs
# --------------------------------------------------------------------------------------------------
# Return 'raw' unnormalized value of gx
print("gxy = ", gxy.getVal())
# Return value of gxy normalized over x _and_ y in range [-10,10]
nset_xy = ROOT.RooArgSet(x, y)
print("gx_Norm[x,y] = ", gxy.getVal(nset_xy))
# Create object representing integral over gx
# which is used to calculate gx_Norm[x,y] == gx / gx_Int[x,y]
x_and_y = ROOT.RooArgSet(x, y)
igxy = gxy.createIntegral(x_and_y)
print("gx_Int[x,y] = ", igxy.getVal())
# NB: it is also possible to do the following
# Return value of gxy normalized over x in range [-10,10] (i.e. treating y
# as parameter)
nset_x = ROOT.RooArgSet(x)
print("gx_Norm[x] = ", gxy.getVal(nset_x))
# Return value of gxy normalized over y in range [-10,10] (i.e. treating x
# as parameter)
nset_y = ROOT.RooArgSet(y)
print("gx_Norm[y] = ", gxy.getVal(nset_y))
# Integarte normalizes pdf over subrange
# ----------------------------------------------------------------------------
# Define a range named "signal" in x from -5,5
x.setRange("signal", -5, 5)
y.setRange("signal", -3, 3)
# Create an integral of gxy_Norm[x,y] over x and y in range "signal"
# ROOT.This is the fraction of of pdf gxy_Norm[x,y] which is in the
# range named "signal"
igxy_sig = gxy.createIntegral(x_and_y, ROOT.RooFit.NormSet(
x_and_y), ROOT.RooFit.Range("signal"))
print("gx_Int[x,y|signal]_Norm[x,y] = ", igxy_sig.getVal())
# Construct cumulative distribution function from pdf
# -----------------------------------------------------------------------------------------------------
# Create the cumulative distribution function of gx
# i.e. calculate Int[-10,x] gx(x') dx'
gxy_cdf = gxy.createCdf(ROOT.RooArgSet(x, y))
# Plot cdf of gx versus x
hh_cdf = gxy_cdf.createHistogram("hh_cdf", x, ROOT.RooFit.Binning(
40), ROOT.RooFit.YVar(y, ROOT.RooFit.Binning(40)))
hh_cdf.SetLineColor(ROOT.kBlue)
c = ROOT.TCanvas("rf308_normintegration2d",
"rf308_normintegration2d", 600, 600)
ROOT.gPad.SetLeftMargin(0.15)
hh_cdf.GetZaxis().SetTitleOffset(1.8)
hh_cdf.Draw("surf")
c.SaveAs("rf308_normintegration2d.png")
Date
February 2018
Authors
Clemens Lange, Wouter Verkerke (C++ version)

Definition in file rf308_normintegration2d.py.