Rf 3 0 8_Normintegration 2D

Multidimensional models: normalization and integration of p.d.fs, construction of cumulative distribution functions from p.d.f.s in two dimensions

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 Sunday, July 05, 2020 at 08:23 AM.

In [ ]:
from __future__ import print_function
import ROOT

Set up model

Create observables x,y

In [ ]:
x = ROOT.RooRealVar("x", "x", -10, 10)
y = ROOT.RooRealVar("y", "y", -10, 10)

Create p.d.f. gaussx(x,-2,3), gaussy(y,2,2)

In [ ]:
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)

In [ ]:
gxy = ROOT.RooProdPdf("gxy", "gxy", ROOT.RooArgList(gx, gy))

Retrieve raw & normalized values of RooFit p.d.f.s

Return 'raw' unnormalized value of gx

In [ ]:
print("gxy = ", gxy.getVal())

Return value of gxy normalized over x and y in range [-10,10]

In [ ]:
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]

In [ ]:
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)

In [ ]:
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)

In [ ]:
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

In [ ]:
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 p.d.f. gxy_Norm[x,y] which is in the range named "signal"

In [ ]:
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'

In [ ]:
gxy_cdf = gxy.createCdf(ROOT.RooArgSet(x, y))

Plot cdf of gx versus x

In [ ]:
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")

Draw all canvases

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