ROOT   Reference Guide
rf111_derivatives.C
Go to the documentation of this file.
1/// \file
2/// \ingroup tutorial_roofit
3/// \notebook -js
4///
5/// Basic functionality: numerical 1st,2nd and 3rd order derivatives w.r.t. observables and parameters
6///
7/// 
8/// pdf = gauss(x,m,s)
9/// 
10///
11/// \macro_image
12/// \macro_output
13/// \macro_code
14///
15/// \date 07/2008
16/// \author Wouter Verkerke
17
18#include "RooRealVar.h"
19#include "RooDataSet.h"
20#include "RooGaussian.h"
21#include "TCanvas.h"
22#include "TAxis.h"
23#include "RooPlot.h"
24using namespace RooFit;
25
27{
28 // S e t u p m o d e l
29 // ---------------------
30
31 // Declare variables x,mean,sigma with associated name, title, initial value and allowed range
32 RooRealVar x("x", "x", -10, 10);
33 RooRealVar mean("mean", "mean of gaussian", 1, -10, 10);
34 RooRealVar sigma("sigma", "width of gaussian", 1, 0.1, 10);
35
36 // Build gaussian p.d.f in terms of x,mean and sigma
37 RooGaussian gauss("gauss", "gaussian PDF", x, mean, sigma);
38
39 // 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
40 // ----------------------------------------------------------------------
41
42 // Derivative of normalized gauss(x) w.r.t. observable x
43 RooAbsReal *dgdx = gauss.derivative(x, 1);
44
45 // Second and third derivative of normalized gauss(x) w.r.t. observable x
46 RooAbsReal *d2gdx2 = gauss.derivative(x, 2);
47 RooAbsReal *d3gdx3 = gauss.derivative(x, 3);
48
49 // Construct plot frame in 'x'
50 RooPlot *xframe = x.frame(Title("d(Gauss)/dx"));
51
52 // Plot gauss in frame (i.e. in x)
53 gauss.plotOn(xframe);
54
55 // Plot derivatives in same frame
56 dgdx->plotOn(xframe, LineColor(kMagenta));
57 d2gdx2->plotOn(xframe, LineColor(kRed));
58 d3gdx3->plotOn(xframe, LineColor(kOrange));
59
60 // 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
61 // ------------------------------------------------------------------------------
62
63 // Derivative of normalized gauss(x) w.r.t. parameter sigma
64 RooAbsReal *dgds = gauss.derivative(sigma, 1);
65
66 // Second and third derivative of normalized gauss(x) w.r.t. parameter sigma
67 RooAbsReal *d2gds2 = gauss.derivative(sigma, 2);
68 RooAbsReal *d3gds3 = gauss.derivative(sigma, 3);
69
70 // Construct plot frame in 'sigma'
71 RooPlot *sframe = sigma.frame(Title("d(Gauss)/d(sigma)"), Range(0., 2.));
72
73 // Plot gauss in frame (i.e. in x)
74 gauss.plotOn(sframe);
75
76 // Plot derivatives in same frame
77 dgds->plotOn(sframe, LineColor(kMagenta));
78 d2gds2->plotOn(sframe, LineColor(kRed));
79 d3gds3->plotOn(sframe, LineColor(kOrange));
80
81 // Draw all frames on a canvas
82 TCanvas *c = new TCanvas("rf111_derivatives", "rf111_derivatives", 800, 400);
83 c->Divide(2);
84 c->cd(1);
86 xframe->GetYaxis()->SetTitleOffset(1.6);
87 xframe->Draw();
88 c->cd(2);
90 sframe->GetYaxis()->SetTitleOffset(1.6);
91 sframe->Draw();
92}
#define c(i)
Definition: RSha256.hxx:101
@ kRed
Definition: Rtypes.h:64
@ kOrange
Definition: Rtypes.h:65
@ kMagenta
Definition: Rtypes.h:64
RooAbsReal is the common abstract base class for objects that represent a real value and implements f...
Definition: RooAbsReal.h:60
virtual RooPlot * plotOn(RooPlot *frame, const RooCmdArg &arg1=RooCmdArg(), const RooCmdArg &arg2=RooCmdArg(), const RooCmdArg &arg3=RooCmdArg(), const RooCmdArg &arg4=RooCmdArg(), const RooCmdArg &arg5=RooCmdArg(), const RooCmdArg &arg6=RooCmdArg(), const RooCmdArg &arg7=RooCmdArg(), const RooCmdArg &arg8=RooCmdArg(), const RooCmdArg &arg9=RooCmdArg(), const RooCmdArg &arg10=RooCmdArg()) const
Plot (project) PDF on specified frame.
Plain Gaussian p.d.f.
Definition: RooGaussian.h:25
A RooPlot is a plot frame and a container for graphics objects within that frame.
Definition: RooPlot.h:44
TAxis * GetYaxis() const
Definition: RooPlot.cxx:1277
virtual void Draw(Option_t *options=0)
Draw this plot and all of the elements it contains.
Definition: RooPlot.cxx:712
RooRealVar represents a variable that can be changed from the outside.
Definition: RooRealVar.h:35
virtual void SetTitleOffset(Float_t offset=1)
Set distance between the axis and the axis title.
Definition: TAttAxis.cxx:294
The Canvas class.
Definition: TCanvas.h:27
RooCmdArg LineColor(Color_t color)
const Double_t sigma
Double_t x[n]
Definition: legend1.C:17
The namespace RooFit contains mostly switches that change the behaviour of functions of PDFs (or othe...
static constexpr double gauss
const char * Title
Definition: TXMLSetup.cxx:67
Ta Range(0, 0, 1, 1)