Multidimensional models: normalization and integration of pdfs, construction of cumulative distribution functions from pdfs 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 Tuesday, March 19, 2024 at 07:15 PM.
from __future__ import print_function
import ROOT
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, -2.0, 3.0)
gy = ROOT.RooGaussian("gy", "gy", y, +2.0, 2.0)
gxy = gx(x)*gy(y)
gxy = ROOT.RooProdPdf("gxy", "gxy", [gx, gy])
Return 'raw' unnormalized value of gx
print("gxy = ", gxy.getVal())
gxy = 0.4856717852477124
Return value of gxy normalized over x and y in range [-10,10]
nset_xy = {x, y}
print("gx_Norm[x,y] = ", gxy.getVal(nset_xy))
gx_Norm[x,y] = 0.012933200957206766
Create object representing integral over gx which is used to calculate gx_Norm[x,y] == gx / gx_Int[x,y]
x_and_y = {x, y}
igxy = gxy.createIntegral(x_and_y)
print("gx_Int[x,y] = ", igxy.getVal())
gx_Int[x,y] = 37.552326516436096
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 = {x}
print("gx_Norm[x] = ", gxy.getVal(nset_x))
gx_Norm[x] = 0.1068955044839622
Return value of gxy normalized over y in range [-10,10] (i.e. treating x as parameter)
nset_y = {y}
print("gx_Norm[y] = ", gxy.getVal(nset_y))
gx_Norm[y] = 0.12098919425696865
Define a range named "signal" in x from -5,5
x.setRange("signal", -5, 5)
y.setRange("signal", -3, 3)
[#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'signal' created with bounds [-5,5] [#1] INFO:Eval -- RooRealVar::setRange(y) new range named 'signal' created with bounds [-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, NormSet=x_and_y, Range="signal")
print("gx_Int[x,y|signal]_Norm[x,y] = ", igxy_sig.getVal())
gx_Int[x,y|signal]_Norm[x,y] = 0.5720351351990984
Create the cumulative distribution function of gx i.e. calculate Int[-10,x] gx(x') dx'
gxy_cdf = gxy.createCdf({x, y})
Plot cdf of gx versus x
hh_cdf = gxy_cdf.createHistogram("hh_cdf", x, Binning=40, YVar=dict(var=y, 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")
Info in <TCanvas::Print>: png file rf308_normintegration2d.png has been created
Draw all canvases
from ROOT import gROOT
gROOT.GetListOfCanvases().Draw()