Tutorial for convolution of two functions
Author: Aurelie Flandi
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.
Construction of histogram to fit.
TH1F *h_ExpGauss = new TH1F("h_ExpGauss", "Exponential convoluted by Gaussian", 100, 0., 5.);
for (int i = 0; i < 1e6; i++) {
// Gives a alpha of -0.3 in the exp.
double x = gRandom->Exp(1. / 0.3);
x += gRandom->Gaus(0., 3.);
// Probability density function of the addition of two variables is the
// convolution of two density functions.
h_ExpGauss->Fill(x);
}
TF1Convolution *f_conv = new TF1Convolution("expo", "gaus", -1, 6, true);
f_conv->SetRange(-1., 6.);
f_conv->SetNofPointsFFT(1000);
TF1 *f = new TF1("f", *f_conv, 0., 5., f_conv->GetNpar());
f->SetParameters(1., -0.3, 0., 1.);
Fit.
new TCanvas("c", "c", 800, 1000);
h_ExpGauss->Fit("f");
h_ExpGauss->Draw();
FCN=298.12 FROM MIGRAD STATUS=CONVERGED 457 CALLS 458 TOTAL
EDM=1.08093e-08 STRATEGY= 1 ERROR MATRIX ACCURATE
EXT PARAMETER STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 p0 7.32859e+00 3.70795e-02 1.23437e-05 -3.46193e-02
2 p1 7.33040e-02 2.44083e-03 3.62176e-06 -7.16223e-02
3 p2 -2.26420e+00 4.91803e-02 5.24021e-05 -1.27917e-02
4 p3 1.12811e+00 6.28810e-02 1.94847e-05 -2.72591e-02
Draw all canvases
%jsroot on
gROOT->GetListOfCanvases()->Draw()