Logo ROOT   6.08/07
Reference Guide
fitCircle.C File Reference

Detailed Description

View in nbviewer Open in SWAN Generate points distributed with some errors around a circle Fit a circle through the points and draw To run the script, do, eg

root > .x fitCircle.C (10000 points by default)
root > .x fitCircle.C(100); (with only 100 points
root > .x fitCircle.C(100000); with ACLIC
pict1_fitCircle.C.png
Processing /mnt/build/workspace/root-makedoc-v608/rootspi/rdoc/src/v6-08-00-patches/tutorials/fit/fitCircle.C...
****************************************
Minimizer is Minuit / Migrad
MinFCN = 903.174
NDf = 0
Edm = 2.25067e-09
NCalls = 72
x0 = 0.00667777 +/- 0.0141774
y0 = 0.00536467 +/- 0.0141954
R = 3.995 +/- 0.0100048
#include "TCanvas.h"
#include "TRandom3.h"
#include "TGraph.h"
#include "TMath.h"
#include "TArc.h"
#include "Fit/Fitter.h"
//____________________________________________________________________
void fitCircle(Int_t n=10000) {
//generates n points around a circle and fit them
TCanvas *c1 = new TCanvas("c1","c1",600,600);
c1->SetGrid();
gr = new TGraph(n);
if (n> 999) gr->SetMarkerStyle(1);
else gr->SetMarkerStyle(3);
for (Int_t i=0;i<n;i++) {
r.Circle(x,y,r.Gaus(4,0.3));
gr->SetPoint(i,x,y);
}
c1->DrawFrame(-5,-5,5,5);
gr->Draw("p");
auto chi2Function = [&](const Double_t *par) {
//minimisation function computing the sum of squares of residuals
// looping at the graph points
Int_t np = gr->GetN();
Double_t f = 0;
Double_t *x = gr->GetX();
Double_t *y = gr->GetY();
for (Int_t i=0;i<np;i++) {
Double_t u = x[i] - par[0];
Double_t v = y[i] - par[1];
Double_t dr = par[2] - std::sqrt(u*u+v*v);
f += dr*dr;
}
return f;
};
// wrap chi2 funciton in a function object for the fit
// 3 is the number of fit parameters (size of array par)
ROOT::Math::Functor fcn(chi2Function,3);
double pStart[3] = {0,0,1};
fitter.SetFCN(fcn, pStart);
fitter.Config().ParSettings(0).SetName("x0");
fitter.Config().ParSettings(1).SetName("y0");
fitter.Config().ParSettings(2).SetName("R");
// do the fit
bool ok = fitter.FitFCN();
if (!ok) {
Error("line3Dfit","Line3D Fit failed");
}
const ROOT::Fit::FitResult & result = fitter.Result();
result.Print(std::cout);
//Draw the circle on top of the points
TArc *arc = new TArc(result.Parameter(0),result.Parameter(1),result.Parameter(2));
arc->SetLineColor(kRed);
arc->SetLineWidth(4);
arc->Draw();
}
Author
Rene Brun

Definition in file fitCircle.C.