vectorizedFit.C File Reference

Detailed Description

Tutorial for creating a Vectorized TF1 function using a formula expression and use it for fitting an histogram

To create a vectorized function (if ROOT has been compiled with support for vectorization) is very easy. One needs to create the TF1 object with the option "VEC" or call the method TF1::SetVectorized

Doing Serial Gaussian Fit 
****************************************
Minimizer is Minuit2 / Migrad
Chi2                      =      40217.9
NDf                       =        39409
Edm                       =   3.3897e-08
NCalls                    =           75
Constant                  =      120.018   +/-   0.105817    
Mean                      =   0.00114402   +/-   0.000709328 
Sigma                     =     0.979817   +/-   0.000519995    (limited)
****************************************
Minimizer is Minuit2 / Migrad
MinFCN                    =      20355.3
Chi2                      =      40710.5
NDf                       =        39997
Edm                       =  8.97605e-10
NCalls                    =           67
Constant                  =      120.024   +/-   0.105551    
Mean                      =  0.000138332   +/-   0.000716607 
Sigma                     =      0.99985   +/-   0.000537073    (limited)
Real time 0:00:00, CP time 0.460
Doing Vectorized Gaussian Fit 
****************************************
Minimizer is Minuit2 / Migrad
Chi2                      =      40217.9
NDf                       =        39409
Edm                       =   3.3897e-08
NCalls                    =           75
Constant                  =      120.018   +/-   0.105817    
Mean                      =   0.00114402   +/-   0.000709328 
Sigma                     =     0.979817   +/-   0.000519995    (limited)
****************************************
Minimizer is Minuit2 / Migrad
MinFCN                    =      20355.3
Chi2                      =      40710.5
NDf                       =        39997
Edm                       =  8.97605e-10
NCalls                    =           67
Constant                  =      120.024   +/-   0.105551    
Mean                      =  0.000138332   +/-   0.000716607 
Sigma                     =      0.99985   +/-   0.000537073    (limited)
Real time 0:00:00, CP time 0.320
Doing Serial Polynomial Fit 
****************************************
Minimizer is Minuit2 / Migrad
Chi2                      =        37690
NDf                       =        38075
Edm                       =  1.02509e-16
NCalls                    =           68
A                         =     0.202001   +/-   0.00176461  
B                         =     0.268032   +/-   0.0153893   
C                         =      1.05504   +/-   0.0248331   
****************************************
Minimizer is Minuit2 / Migrad
MinFCN                    =      20527.5
Chi2                      =        41055
NDf                       =        39997
Edm                       =  8.16364e-08
NCalls                    =           90
A                         =     0.149763   +/-   0.00165111  
B                         =     0.880262   +/-   0.0135143   
C                         =       0.6066   +/-   0.0181308   
Real time 0:00:00, CP time 0.300
Doing Vectorized Polynomial Fit 
****************************************
Minimizer is Minuit2 / Migrad
Chi2                      =        37690
NDf                       =        38075
Edm                       =  1.32608e-15
NCalls                    =           68
A                         =     0.202001   +/-   0.00176461  
B                         =     0.268032   +/-   0.0153893   
C                         =      1.05504   +/-   0.0248331   
****************************************
Minimizer is Minuit2 / Migrad
MinFCN                    =      20527.5
Chi2                      =        41055
NDf                       =        39997
Edm                       =  8.16326e-08
NCalls                    =           90
A                         =     0.149763   +/-   0.0016511   
B                         =     0.880262   +/-   0.0135143   
C                         =       0.6066   +/-   0.0181308   
Real time 0:00:00, CP time 0.280

 
#include <Math/MinimizerOptions.h>
#include <TCanvas.h>
#include <TF1.h>
#include <TH1D.h>
#include <TStopwatch.h>
#include <TStyle.h>
 
#include <iostream>
 
void vectorizedFit() {
 
   gStyle->SetOptFit(111111);
   
 
   ROOT::Math::MinimizerOptions::SetDefaultMinimizer("Minuit2");
 
   int nbins = 40000;
   auto h1 = new TH1D("h1","h1",nbins,-3,3);
   h1->FillRandom("gaus",nbins*50);
   auto c1 = new TCanvas("Fit","Fit",800,1000);
   c1->Divide(1,2);
   c1->cd(1);
   TStopwatch w;
 
   std::cout << "Doing Serial Gaussian Fit " << std::endl;
   auto f1 = new TF1("f1","gaus");
   f1->SetNpx(nbins*10);
   w.Start();
   h1->Fit(f1);
   h1->Fit(f1,"L+");
   w.Print();
 
   std::cout << "Doing Vectorized Gaussian Fit " << std::endl;
   auto f2 = new TF1("f2","gaus",-3,3,"VEC");
   // alternatively you can also use the TF1::SetVectorized function
   //f2->SetVectorized(true); 
   w.Start();
   h1->Fit(f2);
   h1->Fit(f2,"L+");
   w.Print();
   // rebin histograms and scale it back to the function
   h1->Rebin(nbins/100);
   h1->Scale(100./nbins);
   ((TF1 *)h1->GetListOfFunctions()->At(0))->SetTitle("Chi2 Fit");
   ((TF1 *)h1->GetListOfFunctions()->At(1))->SetTitle("Likelihood Fit");
   ((TF1 *)h1->GetListOfFunctions()->At(1))->SetLineColor(kBlue);
   //c1->cd(1)->BuildLegend();
 
   /// Do a polynomial fit now
   c1->cd(2);
   auto f3 = new TF1("f3","[A]*x^2+[B]*x+[C]",0,10);
   f3->SetParameters(0.5,3,2);
   f3->SetNpx(nbins*10);
   // generate the events
   auto h2 = new TH1D("h2","h2",nbins,0,10);
   h2->FillRandom("f3",10*nbins);
   std::cout << "Doing Serial Polynomial Fit " << std::endl;
   f3->SetParameters(2,2,2);
   w.Start();
   h2->Fit(f3);
   h2->Fit(f3,"L+");
   w.Print();
 
   std::cout << "Doing Vectorized Polynomial Fit " << std::endl;
   auto f4 = new TF1("f4","[A]*x*x+[B]*x+[C]",0,10);
   f4->SetVectorized(true);
   f4->SetParameters(2,2,2);
   w.Start();
   h2->Fit(f4);
   h2->Fit(f4,"L+");
   w.Print();
 
   // rebin histograms and scale it back to the function
   h2->Rebin(nbins/100);
   h2->Scale(100./nbins);
   ((TF1 *)h2->GetListOfFunctions()->At(0))->SetTitle("Chi2 Fit");
   ((TF1 *)h2->GetListOfFunctions()->At(1))->SetTitle("Likelihood Fit");
   ((TF1 *)h2->GetListOfFunctions()->At(1))->SetLineColor(kBlue);
   //c1->cd(2)->BuildLegend();
 
}

Author

Lorenzo Moneta

Definition in file vectorizedFit.C.