/// \file
/// \ingroup tutorial_roofit
/// \notebook -js
///  'MULTIDIMENSIONAL MODELS' RooFit tutorial macro #303
///
///  Use of tailored p.d.f as conditional p.d.fs.s
///
///  pdf = gauss(x,f(y),sx | y ) with f(y) = a0 + a1*y
///
/// \macro_image
/// \macro_output
/// \macro_code
/// \author 07/2008 - Wouter Verkerke


#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooDataHist.h"
#include "RooGaussian.h"
#include "RooPolyVar.h"
#include "RooProdPdf.h"
#include "RooPlot.h"
#include "TRandom.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "TH1.h"

using namespace RooFit;


RooDataSet* makeFakeDataXY() ;

void rf303_conditional()
{
   // S e t u p   c o m p o s e d   m o d e l   g a u s s ( x , m ( y ) , s )
   // -----------------------------------------------------------------------

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

   // Create function f(y) = a0 + a1*y
   RooRealVar a0("a0","a0",-0.5,-5,5) ;
   RooRealVar a1("a1","a1",-0.5,-1,1) ;
   RooPolyVar fy("fy","fy",y,RooArgSet(a0,a1)) ;

   // Create gauss(x,f(y),s)
   RooRealVar sigma("sigma","width of gaussian",0.5,0.1,2.0) ;
   RooGaussian model("model","Gaussian with shifting mean",x,fy,sigma) ;


   // Obtain fake external experimental dataset with values for x and y
   RooDataSet* expDataXY = makeFakeDataXY() ;



   // G e n e r a t e   d a t a   f r o m   c o n d i t i o n a l   p . d . f   m o d e l ( x | y )
   // ---------------------------------------------------------------------------------------------

   // Make subset of experimental data with only y values
   RooDataSet* expDataY= (RooDataSet*) expDataXY->reduce(y) ;

   // Generate 10000 events in x obtained from _conditional_ model(x|y) with y values taken from experimental data
   RooDataSet *data = model.generate(x,ProtoData(*expDataY)) ;
   data->Print() ;



   // F i t   c o n d i t i o n a l   p . d . f   m o d e l ( x | y )   t o   d a t a
   // ---------------------------------------------------------------------------------------------

   model.fitTo(*expDataXY,ConditionalObservables(y)) ;



   // P r o j e c t   c o n d i t i o n a l   p . d . f   o n   x   a n d   y   d i m e n s i o n s
   // ---------------------------------------------------------------------------------------------

   // Plot x distribution of data and projection of model on x = 1/Ndata sum(data(y_i)) model(x;y_i)
   RooPlot* xframe = x.frame() ;
   expDataXY->plotOn(xframe) ;
   model.plotOn(xframe,ProjWData(*expDataY)) ;


   // Speed up (and approximate) projection by using binned clone of data for projection
   RooAbsData* binnedDataY = expDataY->binnedClone() ;
   model.plotOn(xframe,ProjWData(*binnedDataY),LineColor(kCyan),LineStyle(kDotted)) ;


   // Show effect of projection with too coarse binning
   ((RooRealVar*)expDataY->get()->find("y"))->setBins(5) ;
   RooAbsData* binnedDataY2 = expDataY->binnedClone() ;
   model.plotOn(xframe,ProjWData(*binnedDataY2),LineColor(kRed)) ;


   // Make canvas and draw RooPlots
   new TCanvas("rf303_conditional","rf303_conditional",600, 460);
   gPad->SetLeftMargin(0.15) ; xframe->GetYaxis()->SetTitleOffset(1.2) ; xframe->Draw() ;

}




RooDataSet* makeFakeDataXY()
{
   RooRealVar x("x","x",-10,10) ;
   RooRealVar y("y","y",-10,10) ;
   RooArgSet coord(x,y) ;

   RooDataSet* d = new RooDataSet("d","d",RooArgSet(x,y)) ;

   for (int i=0 ; i<10000 ; i++) {
      Double_t tmpy = gRandom->Gaus(0,10) ;
      Double_t tmpx = gRandom->Gaus(0.5*tmpy,1) ;
      if (fabs(tmpy)<10 && fabs(tmpx)<10) {
      x = tmpx ;
      y = tmpy ;
      d->add(coord) ;
      }

   }

   return d ;
}