 ROOT   Reference Guide rf111_derivatives.C
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1 /// \file
2 /// \ingroup tutorial_roofit
3 /// \notebook -js
4 /// Basic functionality: numerical 1st,2nd and 3rd order derivatives w.r.t. observables and parameters
5 ///
6 /// 
7 /// pdf = gauss(x,m,s)
8 /// 
9 ///
10 /// \macro_image
11 /// \macro_output
12 /// \macro_code
13 ///
14 /// \date July 2008
15 /// \author Wouter Verkerke
16
17 #include "RooRealVar.h"
18 #include "RooDataSet.h"
19 #include "RooGaussian.h"
20 #include "TCanvas.h"
21 #include "TAxis.h"
22 #include "RooPlot.h"
23 using namespace RooFit;
24
25 void rf111_derivatives()
26 {
27  // S e t u p m o d e l
28  // ---------------------
29
30  // Declare variables x,mean,sigma with associated name, title, initial value and allowed range
31  RooRealVar x("x", "x", -10, 10);
32  RooRealVar mean("mean", "mean of gaussian", 1, -10, 10);
33  RooRealVar sigma("sigma", "width of gaussian", 1, 0.1, 10);
34
35  // Build gaussian pdf in terms of x,mean and sigma
36  RooGaussian gauss("gauss", "gaussian PDF", x, mean, sigma);
37
38  // 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
39  // ----------------------------------------------------------------------
40
41  // Derivative of normalized gauss(x) w.r.t. observable x
42  RooAbsReal *dgdx = gauss.derivative(x, 1);
43
44  // Second and third derivative of normalized gauss(x) w.r.t. observable x
45  RooAbsReal *d2gdx2 = gauss.derivative(x, 2);
46  RooAbsReal *d3gdx3 = gauss.derivative(x, 3);
47
48  // Construct plot frame in 'x'
49  RooPlot *xframe = x.frame(Title("d(Gauss)/dx"));
50
51  // Plot gauss in frame (i.e. in x)
52  gauss.plotOn(xframe);
53
54  // Plot derivatives in same frame
55  dgdx->plotOn(xframe, LineColor(kMagenta));
56  d2gdx2->plotOn(xframe, LineColor(kRed));
57  d3gdx3->plotOn(xframe, LineColor(kOrange));
58
59  // 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
60  // ------------------------------------------------------------------------------
61
62  // Derivative of normalized gauss(x) w.r.t. parameter sigma
63  RooAbsReal *dgds = gauss.derivative(sigma, 1);
64
65  // Second and third derivative of normalized gauss(x) w.r.t. parameter sigma
66  RooAbsReal *d2gds2 = gauss.derivative(sigma, 2);
67  RooAbsReal *d3gds3 = gauss.derivative(sigma, 3);
68
69  // Construct plot frame in 'sigma'
70  RooPlot *sframe = sigma.frame(Title("d(Gauss)/d(sigma)"), Range(0., 2.));
71
72  // Plot gauss in frame (i.e. in x)
73  gauss.plotOn(sframe);
74
75  // Plot derivatives in same frame
76  dgds->plotOn(sframe, LineColor(kMagenta));
77  d2gds2->plotOn(sframe, LineColor(kRed));
78  d3gds3->plotOn(sframe, LineColor(kOrange));
79
80  // Draw all frames on a canvas
81  TCanvas *c = new TCanvas("rf111_derivatives", "rf111_derivatives", 800, 400);
82  c->Divide(2);
83  c->cd(1);
85  xframe->GetYaxis()->SetTitleOffset(1.6);
86  xframe->Draw();
87  c->cd(2);
89  sframe->GetYaxis()->SetTitleOffset(1.6);
90  sframe->Draw();
91 }
c
#define c(i)
Definition: RSha256.hxx:101
RooPlot::Draw
virtual void Draw(Option_t *options=0)
Draw this plot and all of the elements it contains.
Definition: RooPlot.cxx:691
RooGaussian.h
kOrange
@ kOrange
Definition: Rtypes.h:67
x
Double_t x[n]
Definition: legend1.C:17
RooGaussian
Plain Gaussian p.d.f.
Definition: RooGaussian.h:24
RooAbsReal
RooAbsReal is the common abstract base class for objects that represent a real value and implements f...
Definition: RooAbsReal.h:61
TCanvas.h
RooDataSet.h
kMagenta
@ kMagenta
Definition: Rtypes.h:66
TGeant4Unit::gauss
static constexpr double gauss
Definition: TGeant4SystemOfUnits.h:263
RooFit
The namespace RooFit contains mostly switches that change the behaviour of functions of PDFs (or othe...
Definition: RooCFunction1Binding.h:29
RooPlot.h
RooPlot::GetYaxis
TAxis * GetYaxis() const
Definition: RooPlot.cxx:1258
RooPlot
A RooPlot is a plot frame and a container for graphics objects within that frame.
Definition: RooPlot.h:44
RooRealVar.h
kRed
@ kRed
Definition: Rtypes.h:66
RooAbsReal::plotOn
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.
Definition: RooAbsReal.cxx:1730
sigma
const Double_t sigma
Definition: h1analysisProxy.h:11
RooFit::LineColor
RooCmdArg LineColor(Color_t color)
Definition: RooGlobalFunc.cxx:57
TCanvas
The Canvas class.
Definition: TCanvas.h:23
TAxis.h
RooFit::Range
RooCmdArg Range(const char *rangeName, Bool_t adjustNorm=kTRUE)
Definition: RooGlobalFunc.cxx:53