minuit2FitBench2D¶

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 "TH2D.h"
#include "TF2.h"
#include "TCanvas.h"
#include "TStopwatch.h"
#include "TSystem.h"
#include "TRandom3.h"
#include "TVirtualFitter.h"
#include "TPaveLabel.h"
#include "TStyle.h"


TF2 *fitFcn;
TH2D *histo;

Quadratic background function

In [2]:

%%cpp -d
double gaus2D(double *x, double *par) {
   double t1 =   x[0] - par[1];
   double t2 =   x[1] - par[2];
   return par[0]* exp( - 0.5 * (  t1*t1/( par[3]*par[3]) + t2*t2  /( par[4]*par[4] )  ) ) ;
}

Sum of background and peak function

In [3]:

%%cpp -d
double fitFunction(double *x, double *par) {
  return gaus2D(x,par);
}

Definition of a helper function:

In [4]:

%%cpp -d
void fillHisto(int n =10000) {

  gRandom = new TRandom3();
  for (int i = 0; i < n; ++i) {
     double x = gRandom->Gaus(2,3);
     double y = gRandom->Gaus(-1,4);
     histo->Fill(x,y,1.);
  }
}

Definition of a helper function:

In [5]:

%%cpp -d
void DoFit(const char* fitter, TVirtualPad *pad, int npass) {
   TStopwatch timer;
   TVirtualFitter::SetDefaultFitter(fitter);
   pad->SetGrid();
   fitFcn->SetParameters(100,0,0,2,7);
   fitFcn->Update();

   timer.Start();
   histo->Fit("fitFcn","0");
   timer.Stop();

   histo->Draw();
   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(0.5,0.7,0.85,0.8,Form("%s CPU= %g s",fitter,cputime),"brNDC");
   p->Draw();
   pad->Update();
}

Arguments are defined.

In [6]:

int n = 100000;

In [7]:

TH1::AddDirectory(false);
TCanvas *c1 = new TCanvas("c1","Fitting Demo",10,10,900,900);
c1->Divide(2,2);

create a TF1 with the range from 0 to 3 and 6 parameters

In [8]:

fitFcn = new TF2("fitFcn",fitFunction,-10,10,-10,10,5);

fitFcn->SetNpx(200);

In [9]:

gStyle->SetOptFit();
gStyle->SetStatY(0.6);


histo = new TH2D("h2","2D Gauss",100,-10,10,100,-10,10);
fillHisto(n);

int npass=0;

with Minuit

In [10]:

c1->cd(1);
DoFit("Minuit",gPad,npass);

 FCN=7196.63 FROM MIGRAD    STATUS=CONVERGED     169 CALLS         170 TOTAL
                     EDM=3.06509e-09    STRATEGY= 1  ERROR MATRIX UNCERTAINTY   2.0 per cent
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  p0           5.28670e+01   2.67227e-01   1.71567e-03   1.41590e-04
   2  p1           2.00562e+00   9.99521e-03  -6.72962e-05  -5.71949e-03
   3  p2          -1.02279e+00   1.35440e-02   3.22465e-05   2.77027e-03
   4  p3           2.89928e+00   7.94099e-03  -9.38703e-05  -4.55759e-03
   5  p4           3.86656e+00   1.13330e-02   1.06568e-05  -2.11126e-03
Minuit, npass=0  : RT=  0.207 s, Cpu=  0.200 s

with Fumili

In [11]:

c1->cd(2);
  DoFit("Fumili",gPad,npass);

****************************************
Minimizer is Fumili
Chi2                      =      7196.63
NDf                       =         7366
NCalls                    =           30
p0                        =      52.8672   +/-   0.262932    
p1                        =      2.00562   +/-   0.00992527  
p2                        =     -1.02279   +/-   0.0135821   
p3                        =      2.89927   +/-   0.00781808  
p4                        =      3.86655   +/-   0.011235    
Fumili, npass=0  : RT=  0.067 s, Cpu=  0.070 s

with Minuit2

In [12]:

c1->cd(3);
DoFit("Minuit2",gPad,npass);

****************************************
Minimizer is Minuit2 / Migrad
Chi2                      =      7196.63
NDf                       =         7366
Edm                       =  4.35806e-08
NCalls                    =          176
p0                        =       52.867   +/-   0.264728    
p1                        =      2.00562   +/-   0.00995152  
p2                        =      -1.0228   +/-   0.0137398   
p3                        =      2.89928   +/-   0.00798634  
p4                        =      3.86656   +/-   0.0112306   
Minuit2, npass=0  : RT=  0.124 s, Cpu=  0.130 s

with Fumili2

In [13]:

c1->cd(4);
DoFit("Fumili2",gPad,npass);

****************************************
Minimizer is Minuit2 / Fumili
Chi2                      =      7196.63
NDf                       =         7366
Edm                       =  2.49758e-07
NCalls                    =           99
p0                        =      52.8669   +/-   0.265504    
p1                        =      2.00562   +/-   0.00992463  
p2                        =      -1.0228   +/-   0.0135834   
p3                        =      2.89928   +/-   0.00792724  
p4                        =      3.86656   +/-   0.0113104   
Fumili2, npass=0  : RT=  0.065 s, Cpu=  0.060 s

Draw all canvases

In [14]:

%jsroot on
gROOT->GetListOfCanvases()->Draw()