/// \file
/// \ingroup tutorial_roofit
/// \notebook -nodraw
///  'ADDITION AND CONVOLUTION' RooFit tutorial macro #204
///
///  Extended maximum likelihood fit with alternate range definition
///  for observed number of events.
///
/// \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 "RooExtendPdf.h"
#include "RooFitResult.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "RooPlot.h"
using namespace RooFit ;

RooAddPdf* getSignal(RooRealVar& x)
{

   // Create two Gaussian PDFs g1(x,mean1,sigma) anf g2(x,mean2,sigma) and their parameters
   RooRealVar* mean = new RooRealVar("mean","mean of gaussians",5) ;
   RooRealVar* sigma1 = new RooRealVar("sigma1","width of gaussians",0.5) ;
   RooRealVar* sigma2 = new RooRealVar("sigma2","width of gaussians",1) ;
   RooRealVar* sigma3 = new RooRealVar("sigma3","width of gaussians",1) ;

   RooGaussian* sig1 = new RooGaussian("sig1","Signal component 1",x,*mean,*sigma1) ;  
   RooGaussian* sig2 = new RooGaussian("sig2","Signal component 2",x,*mean,*sigma2) ;  
   RooGaussian* sig3 = new RooGaussian("sig3","Signal component 3",x,*mean,*sigma3) ; 
	

   // Sum the signal components into a composite signal p.d.f.
   RooRealVar* sig1frac = new RooRealVar("sig1frac","fraction of component 1 in signal",0.8,0.,1.) ;
   RooRealVar* sig2frac = new RooRealVar("sig2frac","fraction of component 2 in signal",0.8,0.,1.) ;
   RooAddPdf* sig = new RooAddPdf("sig","Signal",RooArgList(*sig1,*sig2),RooArgList(*sig1frac, *sig2frac), /*recursive*/true) ;
   
   return sig;
}


void fit_example()
{


   // 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) ; 

   // 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)) ;

   RooAddPdf* sig = getSignal(x);
	
   // 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) ;


   
   RooAddPdf  model("model","(g1+g2)+a",RooArgList(bkg, *sig), RooArgList(nbkg, nsig)) ;


   // 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,Save()) ;
   r->Print() ;
   
   // what's the numer of events from sig3 inside signalRange?
   
   // this doesn't give me the correct result, as sig3 is considered independent from model
   double sig3inRange = 1000*((RooAbsPdf*)model.getComponents()->find("sig3")))->createIntegral(*x, NormSet(*x), Range("signalRange"))->getVal();
   
   // Of course, the correct answer would be sig3inRange*(1-sig2frac)*(1-sig1frac) but they are not in scope
   // Also, this become unwieldy as you add components
   
   

}