minuit2FitBench2D.C File Reference

Detailed Description

Minuit2 fit 2D benchmark.

 FCN=7196.63 FROM MIGRAD    STATUS=CONVERGED     169 CALLS         170 TOTAL
                     EDM=3.06507e-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   1.41592e-04
   2  p1           2.00562e+00   9.99521e-03  -6.72962e-05  -5.71942e-03
   3  p2          -1.02279e+00   1.35440e-02   3.22465e-05   2.77029e-03
   4  p3           2.89928e+00   7.94099e-03  -9.38703e-05  -4.55749e-03
   5  p4           3.86656e+00   1.13330e-02   1.06568e-05  -2.11130e-03
Minuit, npass=0  : RT=  0.086 s, Cpu=  0.090 s
****************************************
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=  0.049 s, Cpu=  0.050 s
****************************************
Minimizer is Minuit2 / Migrad
Chi2                      =      7196.63
NDf                       =         7366
Edm                       =  4.35807e-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=  0.080 s, Cpu=  0.080 s
****************************************
Minimizer is Minuit2 / Fumili
Chi2                      =      7196.63
NDf                       =         7366
Edm                       =  2.86819e-07
NCalls                    =            8
p0                        =      52.8669   +/-   0.262931    
p1                        =      2.00562   +/-   0.00992529  
p2                        =      -1.0228   +/-   0.0135821   
p3                        =      2.89928   +/-   0.0078181   
p4                        =      3.86656   +/-   0.0112351   
Fumili2, npass=0  : RT=  0.017 s, Cpu=  0.020 s

 
#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
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
double fitFunction(double *x, double *par) {
  return gaus2D(x,par);
}
 
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.);
  }
}
 
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();
}
 
void minuit2FitBench2D(int n = 100000) {
   TDirectory::TContext ctx{nullptr}; // Don't register histograms to the current directory
   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
   fitFcn = new TF2("fitFcn",fitFunction,-10,10,-10,10,5);
   //fitFcn->SetNpx(200);
   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
   c1->cd(1);
   DoFit("Minuit",gPad,npass);
 
   //with Fumili
   c1->cd(2);
     DoFit("Fumili",gPad,npass);
 
   //with Minuit2
   c1->cd(3);
   DoFit("Minuit2",gPad,npass);
 
   //with Fumili2
   c1->cd(4);
   DoFit("Fumili2",gPad,npass);
}

Author

Lorenzo Moneta

Definition in file minuit2FitBench2D.C.