Example of fitting with a linear function, using TLinearFitter This example is for a TGraphErrors, but it can also be used when fitting a histogram, a TGraph2D or a TMultiGraph
Author: Anna Kreshuk
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Tuesday, May 13, 2025 at 07:47 AM.
%%cpp -d
#include "TGraphErrors.h"
#include "TF1.h"
#include "TRandom.h"
#include "TCanvas.h"
#include "TLegend.h"
#include "TMath.h"
void makePoints(int n, double *x, double *y, double *e, int p);
Definition of a helper function:
%%cpp -d
void makePoints(int n, double *x, double *y, double *e, int p)
{
int i;
TRandom r;
if (p==2) {
for (i=0; i<n; i++) {
x[i] = r.Uniform(-2, 2);
y[i]=TMath::Sin(x[i]) + TMath::Sin(2*x[i]) + r.Gaus()*0.1;
e[i] = 0.1;
}
}
if (p==3) {
for (i=0; i<n; i++) {
x[i] = r.Uniform(-2, 2);
y[i] = -7 + 2*x[i]*x[i] + x[i]*x[i]*x[i]+ r.Gaus()*0.1;
e[i] = 0.1;
}
}
if (p==4) {
for (i=0; i<n; i++) {
x[i] = r.Uniform(-2, 2);
y[i]=-2 + TMath::Exp(-x[i]) + r.Gaus()*0.1;
e[i] = 0.1;
}
}
}
int n = 40;
double *x = new double[n];
double *y = new double[n];
double *e = new double[n];
TCanvas *myc = new TCanvas("myc",
"Fitting 3 TGraphErrors with linear functions");
myc->SetGrid();
Generate points along a 3rd degree polynomial:
makePoints(n, x, y, e, 3);
TGraphErrors *gre3 = new TGraphErrors(n, x, y, nullptr, e);
gre3->Draw("a*");
Fit the graph with the predefined "pol3" function
gre3->Fit("pol3");
**************************************** Minimizer is Linear / Migrad Chi2 = 36.5406 NDf = 36 p0 = -7.07142 +/- 0.0233493 p1 = -0.0194368 +/- 0.0354128 p2 = 2.03968 +/- 0.0136149 p3 = 1.00594 +/- 0.0139068
Access the fit results
TF1 *f3 = gre3->GetFunction("pol3");
f3->SetLineWidth(1);
Generate points along a sin(x)+sin(2x) function
makePoints(n, x, y, e, 2);
TGraphErrors *gre2=new TGraphErrors(n, x, y, nullptr, e);
gre2->Draw("*same");
gre2->SetMarkerColor(kBlue);
gre2->SetLineColor(kBlue);
The fitting function can be predefined and passed to the Fit function The "++" mean that the linear fitter should be used, and the following formula is equivalent to "[0]sin(x) + [1]sin(2*x)" A function, defined this way, is in no way different from any other TF1, it can be evaluated, drawn, you can get its parameters, etc. The fit result (parameter values, parameter errors, chisquare, etc) are written into the fitting function.
TF1 *f2 = new TF1("f2", "sin(x) ++ sin(2*x)", -2, 2);
gre2->Fit(f2);
f2 = gre2->GetFunction("f2");
f2->SetLineColor(kBlue);
f2->SetLineWidth(1);
**************************************** Minimizer is Linear / Migrad Chi2 = 46.7362 NDf = 38 p0 = 1.0005 +/- 0.0242765 p1 = 0.985942 +/- 0.0279149
Generate points along a -2+exp(-x) function
makePoints(n, x, y, e, 4);
TGraphErrors *gre4=new TGraphErrors(n, x, y, nullptr, e);
gre4->Draw("*same");
gre4->SetMarkerColor(kRed);
gre4->SetLineColor(kRed);
If you don't want to define the function, you can just pass the string with the formula:
gre4->Fit("1 ++ exp(-x)");
**************************************** Minimizer is Linear / Migrad Chi2 = 43.6161 NDf = 38 p0 = -2.04095 +/- 0.0220454 p1 = 1.01171 +/- 0.00904363
Access the fit results:
TF1 *f4 = gre4->GetFunction("1 ++ exp(-x)");
f4->SetName("f4");
f4->SetLineColor(kRed);
f4->SetLineWidth(1);
TLegend *leg = new TLegend(0.3, 0.7, 0.65, 0.9);
leg->AddEntry(gre3, " -7 + 2*x*x + x*x*x", "p");
leg->AddEntry(gre2, "sin(x) + sin(2*x)", "p");
leg->AddEntry(gre4, "-2 + exp(-x)", "p");
leg->Draw();
Draw all canvases
%jsroot on
gROOT->GetListOfCanvases()->Draw()