rf201_composite.C

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/// \file
/// \ingroup tutorial_roofit
/// \notebook -js
///  'ADDITION AND CONVOLUTION' RooFit tutorial macro #201
///
///  Composite p.d.f with signal and background component
///
///  pdf = f_bkg * bkg(x,a0,a1) + (1-fbkg) * (f_sig1 * sig1(x,m,s1 + (1-f_sig1) * sig2(x,m,s2)))
///
/// \macro_image
/// \macro_output
/// \macro_code
/// \author 07/2008 - Wouter Verkerke 

#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooGaussian.h"
#include "RooChebychev.h"
#include "RooAddPdf.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "RooPlot.h"
using namespace RooFit ;


void rf201_composite()
{
   // S e t u p   c o m p o n e n t   p d f s 
   // ---------------------------------------

   // Declare observable x
   RooRealVar x("x","x",0,10) ;

   // Create two Gaussian PDFs g1(x,mean1,sigma) anf g2(x,mean2,sigma) and their parameters
   RooRealVar mean("mean","mean of gaussians",5) ;
   RooRealVar sigma1("sigma1","width of gaussians",0.5) ;
   RooRealVar sigma2("sigma2","width of gaussians",1) ;

   RooGaussian sig1("sig1","Signal component 1",x,mean,sigma1) ;  
   RooGaussian sig2("sig2","Signal component 2",x,mean,sigma2) ;  

   // Build Chebychev polynomial p.d.f.  
   RooRealVar a0("a0","a0",0.5,0.,1.) ;
   RooRealVar a1("a1","a1",0.2,0.,1.) ;
   RooChebychev bkg("bkg","Background",x,RooArgSet(a0,a1)) ;


   // ---------------------------------------------
   // M E T H O D   1 - T w o   R o o A d d P d f s
   // =============================================


   // A d d   s i g n a l   c o m p o n e n t s 
   // ------------------------------------------

   // Sum the signal components into a composite signal p.d.f.
   RooRealVar sig1frac("sig1frac","fraction of component 1 in signal",0.8,0.,1.) ;
   RooAddPdf sig("sig","Signal",RooArgList(sig1,sig2),sig1frac) ;


   // A d d  s i g n a l   a n d   b a c k g r o u n d
   // ------------------------------------------------

   // Sum the composite signal and background 
   RooRealVar bkgfrac("bkgfrac","fraction of background",0.5,0.,1.) ;
   RooAddPdf  model("model","g1+g2+a",RooArgList(bkg,sig),bkgfrac) ;


   // S a m p l e ,   f i t   a n d   p l o t   m o d e l
   // ---------------------------------------------------

   // Generate a data sample of 1000 events in x from model
   RooDataSet *data = model.generate(x,1000) ;

   // Fit model to data
   model.fitTo(*data) ;

   // Plot data and PDF overlaid
   RooPlot* xframe = x.frame(Title("Example of composite pdf=(sig1+sig2)+bkg")) ;
   data->plotOn(xframe) ;
   model.plotOn(xframe) ;

   // Overlay the background component of model with a dashed line
   model.plotOn(xframe,Components(bkg),LineStyle(kDashed)) ;

   // Overlay the background+sig2 components of model with a dotted line
   model.plotOn(xframe,Components(RooArgSet(bkg,sig2)),LineStyle(kDotted)) ;

   // Print structure of composite p.d.f.
   model.Print("t") ;


   // ---------------------------------------------------------------------------------------------
   // M E T H O D   2 - O n e   R o o A d d P d f   w i t h   r e c u r s i v e   f r a c t i o n s
   // =============================================================================================

   // Construct sum of models on one go using recursive fraction interpretations
   //
   //   model2 = bkg + (sig1 + sig2)
   //
   RooAddPdf  model2("model","g1+g2+a",RooArgList(bkg,sig1,sig2),RooArgList(bkgfrac,sig1frac),kTRUE) ;    

   // NB: Each coefficient is interpreted as the fraction of the 
   // left-hand component of the i-th recursive sum, i.e.
   //
   //   sum4 = A + ( B + ( C + D)  with fraction fA, fB and fC expands to
   //
   //   sum4 = fA*A + (1-fA)*(fB*B + (1-fB)*(fC*C + (1-fC)*D))


   // P l o t   r e c u r s i v e   a d d i t i o n   m o d e l
   // ---------------------------------------------------------
   model2.plotOn(xframe,LineColor(kRed),LineStyle(kDashed)) ;
   model2.plotOn(xframe,Components(RooArgSet(bkg,sig2)),LineColor(kRed),LineStyle(kDashed)) ;
   model2.Print("t") ;


   // Draw the frame on the canvas
   new TCanvas("rf201_composite","rf201_composite",600,600) ;
   gPad->SetLeftMargin(0.15) ; xframe->GetYaxis()->SetTitleOffset(1.4) ; xframe->Draw() ;


}