rf103_interprfuncs.C

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/// \file
/// \ingroup tutorial_roofit
/// \notebook -js
///  'BASIC FUNCTIONALITY' RooFit tutorial macro #103
///
///  Interpreted functions and p.d.f.s
///
/// \macro_image
/// \macro_output
/// \macro_code
/// \author 07/2008 - Wouter Verkerke


#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooGaussian.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "RooPlot.h"
#include "RooFitResult.h"
#include "RooGenericPdf.h"
#include "RooConstVar.h"

using namespace RooFit ;


void rf103_interprfuncs()
{
   // ----------------------------------------------------
   // G e n e r i c   i n t e r p r e t e d   p . d . f .
   // ====================================================

   // Declare observable x
   RooRealVar x("x","x",-20,20) ;

   // C o n s t r u c t   g e n e r i c   p d f   f r o m   i n t e r p r e t e d   e x p r e s s i o n
   // -------------------------------------------------------------------------------------------------

   // To construct a proper p.d.f, the formula expression is explicitly normalized internally by dividing
   // it by a numeric integral of the expression over x in the range [-20,20]
   //
   RooRealVar alpha("alpha","alpha",5,0.1,10) ;
   RooGenericPdf genpdf("genpdf","genpdf","(1+0.1*abs(x)+sin(sqrt(abs(x*alpha+0.1))))",RooArgSet(x,alpha)) ;


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

   // Generate a toy dataset from the interpreted p.d.f
   RooDataSet* data = genpdf.generate(x,10000) ;

   // Fit the interpreted p.d.f to the generated data
   genpdf.fitTo(*data) ;

   // Make a plot of the data and the p.d.f overlaid
   RooPlot* xframe = x.frame(Title("Interpreted expression pdf")) ;
   data->plotOn(xframe) ;
   genpdf.plotOn(xframe) ;


   // -----------------------------------------------------------------------------------------------------------
   // S t a n d a r d   p . d . f   a d j u s t   w i t h   i n t e r p r e t e d   h e l p e r   f u n c t i o n
   // ==========================================================================================================
   // Make a gauss(x,sqrt(mean2),sigma) from a standard RooGaussian


   // C o n s t r u c t   s t a n d a r d   p d f  w i t h   f o r m u l a   r e p l a c i n g   p a r a m e t e r
   // ------------------------------------------------------------------------------------------------------------

   // Construct parameter mean2 and sigma
   RooRealVar mean2("mean2","mean^2",10,0,200) ;
   RooRealVar sigma("sigma","sigma",3,0.1,10) ;

   // Construct interpreted function mean = sqrt(mean^2)
   RooFormulaVar mean("mean","mean","sqrt(mean2)",mean2) ;

   // Construct a gaussian g2(x,sqrt(mean2),sigma) ;
   RooGaussian g2("g2","h2",x,mean,sigma) ;


   // G e n e r a t e   t o y   d a t a
   // ---------------------------------

   // Construct a separate gaussian g1(x,10,3) to generate a toy Gaussian dataset with mean 10 and width 3
   RooGaussian g1("g1","g1",x,RooConst(10),RooConst(3)) ;
   RooDataSet* data2 = g1.generate(x,1000) ;


   // F i t   a n d   p l o t   t a i l o r e d   s t a n d a r d   p d f
   // -------------------------------------------------------------------

   // Fit g2 to data from g1
   RooFitResult* r = g2.fitTo(*data2,Save()) ;
   r->Print() ;

   // Plot data on frame and overlay projection of g2
   RooPlot* xframe2 = x.frame(Title("Tailored Gaussian pdf")) ;
   data2->plotOn(xframe2) ;
   g2.plotOn(xframe2) ;


   // Draw all frames on a canvas
   TCanvas* c = new TCanvas("rf103_interprfuncs","rf103_interprfuncs",800,400) ;
   c->Divide(2) ;
   c->cd(1) ; gPad->SetLeftMargin(0.15) ; xframe->GetYaxis()->SetTitleOffset(1.4) ; xframe->Draw() ;
   c->cd(2) ; gPad->SetLeftMargin(0.15) ; xframe2->GetYaxis()->SetTitleOffset(1.4) ; xframe2->Draw() ;


}