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Reference Guide
fitLinearRobust.C
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1 /// \file
2 /// \ingroup tutorial_fit
3 /// \notebook -js
4 /// This tutorial shows how the least trimmed squares regression,
5 /// included in the TLinearFitter class, can be used for fitting
6 /// in cases when the data contains outliers.
7 /// Here the fitting is done via the TGraph::Fit function with option "rob":
8 /// If you want to use the linear fitter directly for computing
9 /// the robust fitting coefficients, just use the TLinearFitter::EvalRobust
10 /// function instead of TLinearFitter::Eval
11 ///
12 /// \macro_image
13 /// \macro_output
14 /// \macro_code
15 ///
16 /// \author Anna Kreshuk
17 
18 #include "TRandom.h"
19 #include "TGraphErrors.h"
20 #include "TF1.h"
21 #include "TCanvas.h"
22 #include "TLegend.h"
23 
24 void fitLinearRobust()
25 {
26  //First generate a dataset, where 20% of points are spoiled by large
27  //errors
28  Int_t npoints = 250;
29  Int_t fraction = Int_t(0.8*npoints);
30  Double_t *x = new Double_t[npoints];
31  Double_t *y = new Double_t[npoints];
32  Double_t *e = new Double_t[npoints];
33  TRandom r;
34  Int_t i;
35  for (i=0; i<fraction; i++){
36  //the good part of the sample
37  x[i]=r.Uniform(-2, 2);
38  e[i]=1;
39  y[i]=1 + 2*x[i] + 3*x[i]*x[i] + 4*x[i]*x[i]*x[i] + e[i]*r.Gaus();
40  }
41  for (i=fraction; i<npoints; i++){
42  //the bad part of the sample
43  x[i]=r.Uniform(-1, 1);
44  e[i]=1;
45  y[i] = 1 + 2*x[i] + 3*x[i]*x[i] + 4*x[i]*x[i]*x[i] + r.Landau(10, 5);
46  }
47 
48  TGraphErrors *grr = new TGraphErrors(npoints, x, y, 0, e);
49  grr->SetMinimum(-30);
50  grr->SetMaximum(80);
51  TF1 *ffit1 = new TF1("ffit1", "pol3", -5, 5);
52  TF1 *ffit2 = new TF1("ffit2", "pol3", -5, 5);
53  ffit1->SetLineColor(kBlue);
54  ffit2->SetLineColor(kRed);
55  TCanvas *myc = new TCanvas("myc", "Linear and robust linear fitting");
56  myc->SetGrid();
57  grr->Draw("ap");
58  //first, let's try to see the result sof ordinary least-squares fit:
59  printf("Ordinary least squares:\n");
60  grr->Fit(ffit1);
61  //the fitted function doesn't really follow the pattern of the data
62  //and the coefficients are far from the real ones
63 
64  printf("Resistant Least trimmed squares fit:\n");
65  //Now let's try the resistant regression
66  //The option "rob=0.75" means that we want to use robust fitting and
67  //we know that at least 75% of data is good points (at least 50% of points
68  //should be good to use this algorithm). If you don't specify any number
69  //and just use "rob" for the option, default value of (npoints+nparameters+1)/2
70  //will be taken
71  grr->Fit(ffit2, "+rob=0.75");
72  //
73  TLegend *leg = new TLegend(0.6, 0.8, 0.89, 0.89);
74  leg->AddEntry(ffit1, "Ordinary least squares", "l");
75  leg->AddEntry(ffit2, "LTS regression", "l");
76  leg->Draw();
77 
78  delete [] x;
79  delete [] y;
80  delete [] e;
81 
82 }
virtual TFitResultPtr Fit(const char *formula, Option_t *option="", Option_t *goption="", Axis_t xmin=0, Axis_t xmax=0)
Fit this graph with function with name fname.
Definition: TGraph.cxx:1050
This class displays a legend box (TPaveText) containing several legend entries.
Definition: TLegend.h:23
virtual Double_t Gaus(Double_t mean=0, Double_t sigma=1)
Samples a random number from the standard Normal (Gaussian) Distribution with the given mean and sigm...
Definition: TRandom.cxx:256
Definition: Rtypes.h:59
virtual void SetMinimum(Double_t minimum=-1111)
Set the minimum of the graph.
Definition: TGraph.cxx:2175
virtual void Draw(Option_t *option="")
Draw this legend with its current attributes.
Definition: TLegend.cxx:423
int Int_t
Definition: RtypesCore.h:41
virtual void Draw(Option_t *chopt="")
Draw this graph with its current attributes.
Definition: TGraph.cxx:745
Double_t x[n]
Definition: legend1.C:17
This is the base class for the ROOT Random number generators.
Definition: TRandom.h:27
virtual void SetGrid(Int_t valuex=1, Int_t valuey=1)
Definition: TPad.h:327
virtual void SetMaximum(Double_t maximum=-1111)
Set the maximum of the graph.
Definition: TGraph.cxx:2166
virtual void SetLineColor(Color_t lcolor)
Set the line color.
Definition: TAttLine.h:40
ROOT::R::TRInterface & r
Definition: Object.C:4
The Canvas class.
Definition: TCanvas.h:31
double Double_t
Definition: RtypesCore.h:55
TLegendEntry * AddEntry(const TObject *obj, const char *label="", Option_t *option="lpf")
Add a new entry to this legend.
Definition: TLegend.cxx:330
leg
Definition: legend1.C:34
Double_t y[n]
Definition: legend1.C:17
you should not use this method at all Int_t Int_t Double_t Double_t Double_t e
Definition: TRolke.cxx:630
virtual Double_t Uniform(Double_t x1=1)
Returns a uniform deviate on the interval (0, x1).
Definition: TRandom.cxx:627
1-Dim function class
Definition: TF1.h:211
A TGraphErrors is a TGraph with error bars.
Definition: TGraphErrors.h:26
Definition: Rtypes.h:59
virtual Double_t Landau(Double_t mean=0, Double_t sigma=1)
Generate a random number following a Landau distribution with location parameter mu and scale paramet...
Definition: TRandom.cxx:361