//////////////////////////////////////////////////////////////////////////
//
// 'ADDITION AND CONVOLUTION' RooFit tutorial macro #204
// 
// Extended maximum likelihood fit with alternate range definition
// for observed number of events.
//
//
//
// 07/2008 - Wouter Verkerke 
// 
/////////////////////////////////////////////////////////////////////////

#ifndef __CINT__
#include "RooGlobalFunc.h"
#endif
#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooGaussian.h"
#include "RooChebychev.h"
#include "RooAddPdf.h"
#include "RooExtendPdf.h"
#include "RooFitResult.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "RooPlot.h"
using namespace RooFit ;


void rf204_extrangefit()
{


  // 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)) ;

  // 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) ;


  // C o n s t r u c t   e x t e n d e d   c o m p s   wi t h   r a n g e   s p e c
  // ------------------------------------------------------------------------------

  // Define signal range in which events counts are to be defined
  x.setRange("signalRange",4,6) ;

  // Associated nsig/nbkg as expected number of events with sig/bkg _in_the_range_ "signalRange"
  RooRealVar nsig("nsig","number of signal events in signalRange",500,0.,10000) ;
  RooRealVar nbkg("nbkg","number of background events in signalRange",500,0,10000) ;
  RooExtendPdf esig("esig","extended signal p.d.f",sig,nsig,"signalRange") ;
  RooExtendPdf ebkg("ebkg","extended background p.d.f",bkg,nbkg,"signalRange") ;


  // S u m   e x t e n d e d   c o m p o n e n t s
  // ---------------------------------------------

  // Construct sum of two extended p.d.f. (no coefficients required)
  RooAddPdf  model("model","(g1+g2)+a",RooArgList(ebkg,esig)) ;

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

  // Generate 1000 events from model so that nsig,nbkg come out to numbers <<500 in fit
  RooDataSet *data = model.generate(x,1000) ;


  // Perform unbinned extended ML fit to data
  RooFitResult* r = model.fitTo(*data,Extended(kTRUE),Save()) ;
  r->Print() ;

}