 ROOT   Reference Guide rf705_linearmorph.C
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1 /// \file
2 /// \ingroup tutorial_roofit
3 /// \notebook
4 /// Special pdf's: linear interpolation between pdf shapes using the 'Alex Read' algorithm
5 ///
6 /// \macro_image
7 /// \macro_output
8 /// \macro_code
9 ///
10 /// \date July 2008
11 /// \author Wouter Verkerke
12
13 #include "RooRealVar.h"
14 #include "RooDataSet.h"
15 #include "RooGaussian.h"
16 #include "RooConstVar.h"
17 #include "RooPolynomial.h"
18 #include "RooIntegralMorph.h"
19 #include "RooNLLVar.h"
20 #include "TCanvas.h"
21 #include "TAxis.h"
22 #include "RooPlot.h"
23 #include "TH1.h"
24 using namespace RooFit;
25
26 void rf705_linearmorph()
27 {
28  // C r e a t e e n d p o i n t p d f s h a p e s
29  // ------------------------------------------------------
30
31  // Observable
32  RooRealVar x("x", "x", -20, 20);
33
34  // Lower end point shape: a Gaussian
35  RooRealVar g1mean("g1mean", "g1mean", -10);
36  RooGaussian g1("g1", "g1", x, g1mean, RooConst(2));
37
38  // Upper end point shape: a Polynomial
39  RooPolynomial g2("g2", "g2", x, RooArgSet(RooConst(-0.03), RooConst(-0.001)));
40
41  // C r e a t e i n t e r p o l a t i n g p d f
42  // -----------------------------------------------
43
44  // Create interpolation variable
45  RooRealVar alpha("alpha", "alpha", 0, 1.0);
46
47  // Specify sampling density on observable and interpolation variable
48  x.setBins(1000, "cache");
49  alpha.setBins(50, "cache");
50
51  // Construct interpolating pdf in (x,a) represent g1(x) at a=a_min
52  // and g2(x) at a=a_max
53  RooIntegralMorph lmorph("lmorph", "lmorph", g1, g2, x, alpha);
54
55  // P l o t i n t e r p o l a t i n g p d f a t v a r i o u s a l p h a
56  // -----------------------------------------------------------------------------
57
58  // Show end points as blue curves
59  RooPlot *frame1 = x.frame();
60  g1.plotOn(frame1);
61  g2.plotOn(frame1);
62
63  // Show interpolated shapes in red
64  alpha.setVal(0.125);
65  lmorph.plotOn(frame1, LineColor(kRed));
66  alpha.setVal(0.25);
67  lmorph.plotOn(frame1, LineColor(kRed));
68  alpha.setVal(0.375);
69  lmorph.plotOn(frame1, LineColor(kRed));
70  alpha.setVal(0.50);
71  lmorph.plotOn(frame1, LineColor(kRed));
72  alpha.setVal(0.625);
73  lmorph.plotOn(frame1, LineColor(kRed));
74  alpha.setVal(0.75);
75  lmorph.plotOn(frame1, LineColor(kRed));
76  alpha.setVal(0.875);
77  lmorph.plotOn(frame1, LineColor(kRed));
78  alpha.setVal(0.95);
79  lmorph.plotOn(frame1, LineColor(kRed));
80
81  // S h o w 2 D d i s t r i b u t i o n o f p d f ( x , a l p h a )
82  // -----------------------------------------------------------------------
83
84  // Create 2D histogram
85  TH1 *hh = lmorph.createHistogram("hh", x, Binning(40), YVar(alpha, Binning(40)));
86  hh->SetLineColor(kBlue);
87
88  // F i t p d f t o d a t a s e t w i t h a l p h a = 0 . 8
89  // -----------------------------------------------------------------
90
91  // Generate a toy dataset at alpha = 0.8
92  alpha = 0.8;
93  RooDataSet *data = lmorph.generate(x, 1000);
94
95  // Fit pdf to toy data
96  lmorph.setCacheAlpha(kTRUE);
97  lmorph.fitTo(*data, Verbose(kTRUE));
98
99  // Plot fitted pdf and data overlaid
100  RooPlot *frame2 = x.frame(Bins(100));
101  data->plotOn(frame2);
102  lmorph.plotOn(frame2);
103
104  // S c a n - l o g ( L ) v s a l p h a
105  // -----------------------------------------
106
107  // Show scan -log(L) of dataset w.r.t alpha
108  RooPlot *frame3 = alpha.frame(Bins(100), Range(0.1, 0.9));
109
110  // Make 2D pdf of histogram
111  RooNLLVar nll("nll", "nll", lmorph, *data);
112  nll.plotOn(frame3, ShiftToZero());
113
114  lmorph.setCacheAlpha(kFALSE);
115
116  TCanvas *c = new TCanvas("rf705_linearmorph", "rf705_linearmorph", 800, 800);
117  c->Divide(2, 2);
118  c->cd(1);
120  frame1->GetYaxis()->SetTitleOffset(1.6);
121  frame1->Draw();
122  c->cd(2);
124  hh->GetZaxis()->SetTitleOffset(2.5);
125  hh->Draw("surf");
126  c->cd(3);
128  frame3->GetYaxis()->SetTitleOffset(1.4);
129  frame3->Draw();
130  c->cd(4);
132  frame2->GetYaxis()->SetTitleOffset(1.4);
133  frame2->Draw();
134
135  return;
136 }
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
kTRUE
const Bool_t kTRUE
Definition: RtypesCore.h:91
RooFit::Bins
RooCmdArg Bins(Int_t nbin)
Definition: RooGlobalFunc.cxx:177
RooIntegralMorph.h
RooGaussian.h
RooFit::ShiftToZero
RooCmdArg ShiftToZero()
Definition: RooGlobalFunc.cxx:51
x
Double_t x[n]
Definition: legend1.C:17
RooGaussian
Plain Gaussian p.d.f.
Definition: RooGaussian.h:24
TAttLine::SetLineColor
virtual void SetLineColor(Color_t lcolor)
Set the line color.
Definition: TAttLine.h:40
TCanvas.h
RooFit::YVar
RooCmdArg YVar(const RooAbsRealLValue &var, const RooCmdArg &arg=RooCmdArg::none())
Definition: RooGlobalFunc.cxx:246
RooFit::Binning
RooCmdArg Binning(const RooAbsBinning &binning)
Definition: RooGlobalFunc.cxx:83
TH1::GetZaxis
TAxis * GetZaxis()
Definition: TH1.h:322
RooDataSet.h
RooNLLVar.h
RooPolynomial.h
RooPlot::frame
static RooPlot * frame(const RooAbsRealLValue &var, Double_t xmin, Double_t xmax, Int_t nBins)
Create a new frame for a given variable in x.
Definition: RooPlot.cxx:249
RooFit
The namespace RooFit contains mostly switches that change the behaviour of functions of PDFs (or othe...
Definition: RooCFunction1Binding.h:29
RooPolynomial
RooPolynomial implements a polynomial p.d.f of the form.
Definition: RooPolynomial.h:28
RooAbsData::plotOn
virtual RooPlot * plotOn(RooPlot *frame, const RooCmdArg &arg1=RooCmdArg::none(), const RooCmdArg &arg2=RooCmdArg::none(), const RooCmdArg &arg3=RooCmdArg::none(), const RooCmdArg &arg4=RooCmdArg::none(), const RooCmdArg &arg5=RooCmdArg::none(), const RooCmdArg &arg6=RooCmdArg::none(), const RooCmdArg &arg7=RooCmdArg::none(), const RooCmdArg &arg8=RooCmdArg::none()) const
Definition: RooAbsData.cxx:547
RooFit::Verbose
RooCmdArg Verbose(Bool_t flag=kTRUE)
Definition: RooGlobalFunc.cxx:189
kFALSE
const Bool_t kFALSE
Definition: RtypesCore.h:92
RooNLLVar
Class RooNLLVar implements a -log(likelihood) calculation from a dataset and a PDF.
Definition: RooNLLVar.h:30
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
RooConstVar.h
RooFit::LineColor
RooCmdArg LineColor(Color_t color)
Definition: RooGlobalFunc.cxx:57
TCanvas
The Canvas class.
Definition: TCanvas.h:23
TAxis.h
TH1
TH1 is the base class of all histogramm classes in ROOT.
Definition: TH1.h:58
RooFit::Range
RooCmdArg Range(const char *rangeName, Bool_t adjustNorm=kTRUE)
Definition: RooGlobalFunc.cxx:53
kBlue
@ kBlue
Definition: Rtypes.h:66
RooDataSet
RooDataSet is a container class to hold unbinned data.
Definition: RooDataSet.h:33
TAttAxis::SetTitleOffset
virtual void SetTitleOffset(Float_t offset=1)
Set distance between the axis and the axis title.
Definition: TAttAxis.cxx:293
RooRealVar
RooRealVar represents a variable that can be changed from the outside.
Definition: RooRealVar.h:37
TH1.h
RooArgSet
RooArgSet is a container object that can hold multiple RooAbsArg objects.
Definition: RooArgSet.h:29
RooIntegralMorph
Class RooIntegralMorph is an implementation of the histogram interpolation technique described by Ale...
Definition: RooIntegralMorph.h:26
TH1::Draw
virtual void Draw(Option_t *option="")
Draw this histogram with options.
Definition: TH1.cxx:3050
RooFit::RooConst
RooConstVar & RooConst(Double_t val)
Definition: RooGlobalFunc.cxx:347