rf111_derivatives.C

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/// \file
/// \ingroup tutorial_roofit
/// \notebook -js
///  'BASIC FUNCTIONALITY' RooFit tutorial macro #111
///
///  Numerical 1st,2nd and 3rd order derivatives w.r.t. observables and parameters
///
///  pdf = gauss(x,m,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"
using namespace RooFit ;


void rf111_derivatives()
{
   // S e t u p   m o d e l 
   // ---------------------

   // Declare variables x,mean,sigma with associated name, title, initial value and allowed range
   RooRealVar x("x","x",-10,10) ;
   RooRealVar mean("mean","mean of gaussian",1,-10,10) ;
   RooRealVar sigma("sigma","width of gaussian",1,0.1,10) ;

   // Build gaussian p.d.f in terms of x,mean and sigma
   RooGaussian gauss("gauss","gaussian PDF",x,mean,sigma) ;  


   // C r e a t e   a n d   p l o t  d e r i v a t i v e s   w . r . t .   x 
   // ----------------------------------------------------------------------

   // Derivative of normalized gauss(x) w.r.t. observable x
   RooAbsReal* dgdx = gauss.derivative(x,1) ;  

   // Second and third derivative of normalized gauss(x) w.r.t. observable x
   RooAbsReal* d2gdx2 = gauss.derivative(x,2) ;  
   RooAbsReal* d3gdx3 = gauss.derivative(x,3) ;  

   // Construct plot frame in 'x'
   RooPlot* xframe = x.frame(Title("d(Gauss)/dx")) ;

   // Plot gauss in frame (i.e. in x) 
   gauss.plotOn(xframe) ;

   // Plot derivatives in same frame
   dgdx->plotOn(xframe,LineColor(kMagenta)) ;
   d2gdx2->plotOn(xframe,LineColor(kRed)) ;
   d3gdx3->plotOn(xframe,LineColor(kOrange)) ;


   // C r e a t e   a n d   p l o t  d e r i v a t i v e s   w . r . t .   s i g m a 
   // ------------------------------------------------------------------------------

   // Derivative of normalized gauss(x) w.r.t. parameter sigma
   RooAbsReal* dgds = gauss.derivative(sigma,1) ;  

   // Second and third derivative of normalized gauss(x) w.r.t. parameter sigma
   RooAbsReal* d2gds2 = gauss.derivative(sigma,2) ;  
   RooAbsReal* d3gds3 = gauss.derivative(sigma,3) ;  

   // Construct plot frame in 'sigma'
   RooPlot* sframe = sigma.frame(Title("d(Gauss)/d(sigma)"),Range(0.,2.)) ;

   // Plot gauss in frame (i.e. in x) 
   gauss.plotOn(sframe) ;

   // Plot derivatives in same frame
   dgds->plotOn(sframe,LineColor(kMagenta)) ;
   d2gds2->plotOn(sframe,LineColor(kRed)) ;
   d3gds3->plotOn(sframe,LineColor(kOrange)) ;



   // Draw all frames on a canvas
   TCanvas* c = new TCanvas("rf111_derivatives","rf111_derivatives",800,400) ;
   c->Divide(2) ;
   c->cd(1) ; gPad->SetLeftMargin(0.15) ; xframe->GetYaxis()->SetTitleOffset(1.6) ; xframe->Draw() ;
   c->cd(2) ; gPad->SetLeftMargin(0.15) ; sframe->GetYaxis()->SetTitleOffset(1.6) ; sframe->Draw() ;

 
}