rf111_derivatives.C: 'BASIC FUNCTIONALITY' RooFit tutorial macro #111

//////////////////////////////////////////////////////////////////////////
//
// 'BASIC FUNCTIONALITY' RooFit tutorial macro #111
// 
// Numerical 1st,2nd and 3rd order derivatives w.r.t. observables and parameters
//
// pdf = gauss(x,m,s) 
//
//
// 07/2008 - Wouter Verkerke 
// 
/////////////////////////////////////////////////////////////////////////

#ifndef __CINT__
#include "RooGlobalFunc.h"
#endif
#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() ;
  
 
}