vectorizedFit¶
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
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]:
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");
Doing Serial Gaussian Fit **************************************** Minimizer is Minuit2 / Migrad Chi2 = 40217.9 NDf = 39409 Edm = 3.38976e-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 = 8.97826e-10 NCalls = 65 Constant = 120.024 +/- 0.105551 Mean = 0.000138332 +/- 0.000716607 Sigma = 0.99985 +/- 0.000537073 (limited) Real time 0:00:00, CP time 0.550 Doing Vectorized Gaussian Fit
alternatively you can also use the TF1::SetVectorized function f2->SetVectorized(true);
In [2]:
w.Start();
h1->Fit(f2);
h1->Fit(f2,"L+");
w.Print();
**************************************** Minimizer is Minuit2 / Migrad Chi2 = 40217.9 NDf = 39409 Edm = 3.38976e-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 = 8.97826e-10 NCalls = 65 Constant = 120.024 +/- 0.105551 Mean = 0.000138332 +/- 0.000716607 Sigma = 0.99985 +/- 0.000537073 (limited) Real time 0:00:00, CP time 0.420
rebin histograms and scale it back to the function
In [3]:
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
In [4]:
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
In [5]:
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();
Doing Serial Polynomial Fit **************************************** Minimizer is Minuit2 / Migrad Chi2 = 37690 NDf = 38075 Edm = 3.47827e-15 NCalls = 72 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 = 8.16351e-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 0.510 Doing Vectorized Polynomial Fit **************************************** Minimizer is Minuit2 / Migrad Chi2 = 37690 NDf = 38075 Edm = 3.15424e-16 NCalls = 70 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 = 8.16253e-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 0.320
rebin histograms and scale it back to the function
In [6]:
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();
Draw all canvases
In [7]:
gROOT->GetListOfCanvases()->Draw()
