Multidimensional models: normalization and integration of pdfs, construction of cumulative distribution functions from pdfs in two dimensions
Author: Wouter Verkerke
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Wednesday, April 17, 2024 at 11:18 AM.
%%cpp -d
#include "RooRealVar.h"
#include "RooGaussian.h"
#include "RooProdPdf.h"
#include "RooAbsReal.h"
#include "RooPlot.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "TH1.h"
using namespace RooFit;
Create observables x,y
RooRealVar x("x", "x", -10, 10);
RooRealVar y("y", "y", -10, 10);
Create pdf gaussx(x,-2,3), gaussy(y,2,2)
RooGaussian gx("gx", "gx", x, -2.0, 3.0);
RooGaussian gy("gy", "gy", y, +2.0, 2.0);
Create gxy = gx(x)*gy(y)
RooProdPdf gxy("gxy", "gxy", RooArgSet(gx, gy));
Return 'raw' unnormalized value of gx
cout << "gxy = " << gxy.getVal() << endl;
gxy = 0.485672
Return value of gxy normalized over x and y in range [-10,10]
RooArgSet nset_xy(x, y);
cout << "gx_Norm[x,y] = " << gxy.getVal(&nset_xy) << endl;
gx_Norm[x,y] = 0.0129332
Create object representing integral over gx which is used to calculate gx_Norm[x,y] == gx / gx_Int[x,y]
std::unique_ptr<RooAbsReal> igxy{gxy.createIntegral(RooArgSet(x, y))};
cout << "gx_Int[x,y] = " << igxy->getVal() << endl;
gx_Int[x,y] = 37.5523
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)
RooArgSet nset_x(x);
cout << "gx_Norm[x] = " << gxy.getVal(&nset_x) << endl;
gx_Norm[x] = 0.106896
Return value of gxy normalized over y in range [-10,10] (i.e. treating x as parameter)
RooArgSet nset_y(y);
cout << "gx_Norm[y] = " << gxy.getVal(&nset_y) << endl;
gx_Norm[y] = 0.120989
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" This is the fraction of of pdf gxy_Norm[x,y] which is in the range named "signal"
std::unique_ptr<RooAbsReal> igxy_sig{gxy.createIntegral({x, y}, NormSet(RooArgSet(x, y)), Range("signal"))};
cout << "gx_Int[x,y|signal]_Norm[x,y] = " << igxy_sig->getVal() << endl;
gx_Int[x,y|signal]_Norm[x,y] = 0.572035
Create the cumulative distribution function of gx i.e. calculate Int[-10,x] gx(x') dx'
std::unique_ptr<RooAbsReal> gxy_cdf{gxy.createCdf(RooArgSet(x, y))};
Plot cdf of gx versus x
TH1 *hh_cdf = gxy_cdf->createHistogram("hh_cdf", x, Binning(40), YVar(y, Binning(40)));
hh_cdf->SetLineColor(kBlue);
new TCanvas("rf308_normintegration2d", "rf308_normintegration2d", 600, 600);
gPad->SetLeftMargin(0.15);
hh_cdf->GetZaxis()->SetTitleOffset(1.8);
hh_cdf->Draw("surf");
Draw all canvases
gROOT->GetListOfCanvases()->Draw()