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Reference Guide
fitLinearRobust.C File Reference

Detailed Description

View in nbviewer Open in SWAN This tutorial shows how the least trimmed squares regression, included in the TLinearFitter class, can be used for fitting in cases when the data contains outliers.

Here the fitting is done via the TGraph::Fit function with option "rob": If you want to use the linear fitter directly for computing the robust fitting coefficients, just use the TLinearFitter::EvalRobust function instead of TLinearFitter::Eval

Ordinary least squares:
Minimizer is Linear / Migrad
Chi2 = 606758
NDf = 246
p0 = 15.724 +/- 0.0887641
p1 = -0.835912 +/- 0.14096
p2 = -3.40616 +/- 0.0607296
p3 = 4.82569 +/- 0.0602628
Resistant Least trimmed squares fit:
Minimizer is Linear / Robust (h=0.75)
Chi2 = 634792
NDf = 246
p0 = 1.00953
p1 = 1.71148
p2 = 2.97937
p3 = 4.07752
#include "TRandom.h"
#include "TGraphErrors.h"
#include "TF1.h"
#include "TCanvas.h"
#include "TLegend.h"
void fitLinearRobust()
//First generate a dataset, where 20% of points are spoiled by large
Int_t npoints = 250;
Int_t fraction = Int_t(0.8*npoints);
Double_t *x = new Double_t[npoints];
Double_t *y = new Double_t[npoints];
Double_t *e = new Double_t[npoints];
Int_t i;
for (i=0; i<fraction; i++){
//the good part of the sample
x[i]=r.Uniform(-2, 2);
y[i]=1 + 2*x[i] + 3*x[i]*x[i] + 4*x[i]*x[i]*x[i] + e[i]*r.Gaus();
for (i=fraction; i<npoints; i++){
//the bad part of the sample
x[i]=r.Uniform(-1, 1);
y[i] = 1 + 2*x[i] + 3*x[i]*x[i] + 4*x[i]*x[i]*x[i] + r.Landau(10, 5);
TGraphErrors *grr = new TGraphErrors(npoints, x, y, 0, e);
TF1 *ffit1 = new TF1("ffit1", "pol3", -5, 5);
TF1 *ffit2 = new TF1("ffit2", "pol3", -5, 5);
TCanvas *myc = new TCanvas("myc", "Linear and robust linear fitting");
//first, let's try to see the result sof ordinary least-squares fit:
printf("Ordinary least squares:\n");
//the fitted function doesn't really follow the pattern of the data
//and the coefficients are far from the real ones
printf("Resistant Least trimmed squares fit:\n");
//Now let's try the resistant regression
//The option "rob=0.75" means that we want to use robust fitting and
//we know that at least 75% of data is good points (at least 50% of points
//should be good to use this algorithm). If you don't specify any number
//and just use "rob" for the option, default value of (npoints+nparameters+1)/2
//will be taken
grr->Fit(ffit2, "+rob=0.75");
TLegend *leg = new TLegend(0.6, 0.8, 0.89, 0.89);
leg->AddEntry(ffit1, "Ordinary least squares", "l");
leg->AddEntry(ffit2, "LTS regression", "l");
delete [] x;
delete [] y;
delete [] e;
ROOT::R::TRInterface & r
Definition: Object.C:4
#define e(i)
Definition: RSha256.hxx:103
int Int_t
Definition: RtypesCore.h:45
double Double_t
Definition: RtypesCore.h:59
@ kRed
Definition: Rtypes.h:66
@ kBlue
Definition: Rtypes.h:66
virtual void SetLineColor(Color_t lcolor)
Set the line color.
Definition: TAttLine.h:40
The Canvas class.
Definition: TCanvas.h:23
1-Dim function class
Definition: TF1.h:213
A TGraphErrors is a TGraph with error bars.
Definition: TGraphErrors.h:26
virtual void SetMaximum(Double_t maximum=-1111)
Set the maximum of the graph.
Definition: TGraph.cxx:2266
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:1073
virtual void Draw(Option_t *chopt="")
Draw this graph with its current attributes.
Definition: TGraph.cxx:769
virtual void SetMinimum(Double_t minimum=-1111)
Set the minimum of the graph.
Definition: TGraph.cxx:2275
This class displays a legend box (TPaveText) containing several legend entries.
Definition: TLegend.h:23
void SetGrid(Int_t valuex=1, Int_t valuey=1) override
Definition: TPad.h:327
This is the base class for the ROOT Random number generators.
Definition: TRandom.h:27
Double_t y[n]
Definition: legend1.C:17
Double_t x[n]
Definition: legend1.C:17
Definition: legend1.C:34
Anna Kreshuk

Definition in file fitLinearRobust.C.