minuit2FitBench¶
Demonstrate performance and usage of Minuit2 and Fumili2 for monodimensional fits.
Author: Lorenzo Moneta
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Monday, March 27, 2023 at 09:47 AM.
In [1]:
%%cpp -d
#include "TH1.h"
#include "TF1.h"
#include "TCanvas.h"
#include "TStopwatch.h"
#include "TSystem.h"
#include "TRandom3.h"
#include "Math/MinimizerOptions.h"
#include "TPaveLabel.h"
#include "TStyle.h"
#include "TMath.h"
#include "TROOT.h"
#include "TFrame.h"
/*#include "Fit/FitConfig.h"*/
TF1 *fitFcn;
TH1 *histo;
Quadratic background function
In [2]:
%%cpp -d
double background(double *x, double *par) {
return par[0] + par[1]*x[0] + par[2]*x[0]*x[0];
}
Lorenzian Peak function
In [3]:
%%cpp -d
double lorentzianPeak(double *x, double *par) {
return (0.5*par[0]*par[1]/TMath::Pi()) /
TMath::Max( 1.e-10,(x[0]-par[2])*(x[0]-par[2]) + .25*par[1]*par[1]);
}
Sum of background and peak function
In [4]:
%%cpp -d
double fitFunction(double *x, double *par) {
return background(x,par) + lorentzianPeak(x,&par[3]);
}
Definition of a helper function:
In [5]:
%%cpp -d
bool DoFit(const char* fitter, TVirtualPad *pad, int npass) {
printf("\n*********************************************************************************\n");
printf("\t %s \n",fitter);
printf("*********************************************************************************\n");
gRandom = new TRandom3();
TStopwatch timer;
// timer.Start();
ROOT::Math::MinimizerOptions::SetDefaultMinimizer(fitter);
pad->SetGrid();
pad->SetLogy();
fitFcn->SetParameters(1,1,1,6,.03,1);
fitFcn->Update();
std::string title = std::string(fitter) + " fit bench";
histo = new TH1D(fitter,title.c_str(),200,0,3);
TString fitterType(fitter);
timer.Start();
bool ok = true;
// fill histogram many times
// every time increase its statistics and re-use previous fitted
// parameter values as starting point
for (int pass=0;pass<npass;pass++) {
if (pass%100 == 0) printf("pass : %d\n",pass);
else printf(".");
if (pass == 0)fitFcn->SetParameters(1,1,1,6,.03,1);
for (int i=0;i<5000;i++) {
histo->Fill(fitFcn->GetRandom());
}
int iret = histo->Fit(fitFcn,"Q0");
ok &= (iret == 0);
if (iret!=0) Error("DoFit","Fit pass %d failed !",pass);
}
// do last fit computing Minos Errors (except for Fumili)
if (!fitterType.Contains("Fumili")) // Fumili does not implement Error options (MINOS)
histo->Fit(fitFcn,"E");
else
histo->Fit(fitFcn,"");
timer.Stop();
(histo->GetFunction("fitFcn"))->SetLineColor(kRed+3);
gPad->SetFillColor(kYellow-10);
double cputime = timer.CpuTime();
printf("%s, npass=%d : RT=%7.3f s, Cpu=%7.3f s\n",fitter,npass,timer.RealTime(),cputime);
TPaveLabel *p = new TPaveLabel(0.45,0.7,0.88,0.8,Form("%s CPU= %g s",fitter,cputime),"brNDC");
p->Draw();
p->SetTextColor(kRed+3);
p->SetFillColor(kYellow-8);
pad->Update();
return ok;
}
Arguments are defined.
In [6]:
int npass=20;
In [7]:
TH1::AddDirectory(false);
TCanvas *c1 = new TCanvas("FitBench","Fitting Demo",10,10,900,900);
c1->Divide(2,2);
c1->SetFillColor(kYellow-9);
create a TF1 with the range from 0 to 3 and 6 parameters
In [8]:
fitFcn = new TF1("fitFcn",fitFunction,0,3,6);
fitFcn->SetNpx(200);
gStyle->SetOptFit();
gStyle->SetStatY(0.6);
bool ok = true;
with Minuit
In [9]:
c1->cd(1);
ok &= DoFit("Minuit",gPad,npass);
*********************************************************************************
Minuit
*********************************************************************************
pass : 0
................... FCN=205.276 FROM MINOS STATUS=SUCCESSFUL 44 CALLS 429 TOTAL
EDM=3.83288e-10 STRATEGY= 1 ERROR MATRIX ACCURATE
EXT PARAMETER STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 p0 5.13639e+01 2.01329e+00 -2.79418e-04 -2.05471e-06
2 p1 5.57813e+01 4.80582e+00 3.09127e-03 -9.98919e-07
3 p2 7.42112e+01 1.87041e+00 -1.20311e-03 -1.93173e-07
4 p3 4.27344e+02 2.93232e+00 -1.66243e-02 -7.80957e-07
5 p4 3.58604e-02 3.47005e-04 1.74159e-07 9.80777e-02
6 p5 1.00001e+00 1.64203e-04 1.64203e-04 3.19213e-02
Minuit, npass=20 : RT= 1.042 s, Cpu= 1.040 s
with Fumili
In [10]:
c1->cd(2);
ok &= DoFit("Fumili",gPad,npass);
********************************************************************************* Fumili ********************************************************************************* pass : 0 ...................**************************************** Minimizer is Fumili Chi2 = 206.284 NDf = 194 NCalls = 4 p0 = 51.4325 +/- 2.01397 p1 = 55.5412 +/- 4.81253 p2 = 74.2976 +/- 1.87298 p3 = 427.425 +/- 2.93868 p4 = 0.0358559 +/- 0.000357243 p5 = 1.00001 +/- 0.00016009 Fumili, npass=20 : RT= 0.893 s, Cpu= 0.890 s
with Minuit2
In [11]:
c1->cd(3);
ok &= DoFit("Minuit2",gPad,npass);
********************************************************************************* Minuit2 ********************************************************************************* pass : 0 ...................**************************************** Minimizer is Minuit2 / Migrad Chi2 = 205.34 NDf = 194 Edm = 1.91398e-10 NCalls = 85 p0 = 51.3576 +/- 2.0133 -2.01329 +2.0133 (Minos) p1 = 55.8172 +/- 4.80582 -4.80605 +4.80561 (Minos) p2 = 74.1981 +/- 1.8704 -1.87032 +1.8705 (Minos) p3 = 427.317 +/- 2.93218 -2.93197 +2.93246 (Minos) p4 = 0.0358574 +/- 0.000346961 -0.000345228 +0.000348733 (Minos) p5 = 1.00001 +/- 0.000164204 -0.000164437 +0.000163973 (Minos) Minuit2, npass=20 : RT= 0.890 s, Cpu= 0.870 s
with Fumili2
In [12]:
c1->cd(4);
ok &= DoFit("Fumili2",gPad,npass);
c1->SaveAs("FitBench.root");
return (ok) ? 0 : 1;
********************************************************************************* Fumili2 ********************************************************************************* pass : 0 ...................**************************************** Minimizer is Minuit2 / Fumili Chi2 = 207.495 NDf = 194 Edm = 4.26421e-10 NCalls = 92 p0 = 51.4278 +/- 2.01381 p1 = 55.5389 +/- 4.8062 p2 = 74.3005 +/- 1.8705 p3 = 427.406 +/- 2.93236 p4 = 0.0358584 +/- 0.000346902 p5 = 1.00001 +/- 0.000164198 Fumili2, npass=20 : RT= 0.899 s, Cpu= 0.820 s
Info in <TCanvas::SaveAs>: ROOT file FitBench.root has been created
Draw all canvases
In [13]:
gROOT->GetListOfCanvases()->Draw()
