rf308_normintegration2d.C: 'MULTIDIMENSIONAL MODELS' RooFit tutorial macro #308

/////////////////////////////////////////////////////////////////////////
//
// 'MULTIDIMENSIONAL MODELS' RooFit tutorial macro #308
// 
// Examples on normalization of p.d.f.s,
// integration of p.d.fs, construction
// of cumulative distribution functions from p.d.f.s
// in two dimensions
//
// 07/2008 - Wouter Verkerke 
//
/////////////////////////////////////////////////////////////////////////

#ifndef __CINT__
#include "RooGlobalFunc.h"
#endif
#include "RooRealVar.h"
#include "RooGaussian.h"
#include "RooConstVar.h"
#include "RooProdPdf.h"
#include "RooAbsReal.h"
#include "RooPlot.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "TH1.h"
using namespace RooFit ;


void rf308_normintegration2d()
{
  // S e t u p   m o d e l 
  // ---------------------

  // Create observables x,y
  RooRealVar x("x","x",-10,10) ;
  RooRealVar y("y","y",-10,10) ;

  // Create p.d.f. gaussx(x,-2,3), gaussy(y,2,2) 
  RooGaussian gx("gx","gx",x,RooConst(-2),RooConst(3)) ;
  RooGaussian gy("gy","gy",y,RooConst(+2),RooConst(2)) ;

  // Create gxy = gx(x)*gy(y)
  RooProdPdf gxy("gxy","gxy",RooArgSet(gx,gy)) ;



  // R e t r i e v e   r a w  &   n o r m a l i z e d   v a l u e s   o f   R o o F i t   p . d . f . s
  // --------------------------------------------------------------------------------------------------

  // Return 'raw' unnormalized value of gx
  cout << "gxy = " << gxy.getVal() << endl ;
  
  // 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 ;

  // Create object representing integral over gx
  // which is used to calculate  gx_Norm[x,y] == gx / gx_Int[x,y]
  RooAbsReal* igxy = gxy.createIntegral(RooArgSet(x,y)) ;
  cout << "gx_Int[x,y] = " << igxy->getVal() << endl ;

  // 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 ;

  // 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 ;



  // I n t e g r a t e   n o r m a l i z e d   p d f   o v e r   s u b r a n g e
  // ----------------------------------------------------------------------------

  // 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"
  // This is the fraction of of p.d.f. gxy_Norm[x,y] which is in the
  // range named "signal"
  RooAbsReal* igxy_sig = gxy.createIntegral(RooArgSet(x,y),NormSet(RooArgSet(x,y)),Range("signal")) ;
  cout << "gx_Int[x,y|signal]_Norm[x,y] = " << igxy_sig->getVal() << endl ;




  // C o n s t r u c t   c u m u l a t i v e   d i s t r i b u t i o n   f u n c t i o n   f r o m   p d f
  // -----------------------------------------------------------------------------------------------------

  // Create the cumulative distribution function of gx
  // i.e. calculate Int[-10,x] gx(x') dx'
  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") ;

}