fitConvolution.py File Reference

Namespaces
namespace	fitConvolution

Detailed Description

Tutorial for convolution of two functions

 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

 
import ROOT
 
# Construction of histogram to fit.
h_ExpGauss = ROOT.TH1F("h_ExpGauss", "Exponential convoluted by Gaussian", 100, 0.0, 5.0)
for i in range(1000000):
    # Gives a alpha of -0.3 in the exp.
    x = ROOT.gRandom.Exp(1.0 / 0.3)
    x += ROOT.gRandom.Gaus(0.0, 3.0)
    # Probability density function of the addition of two variables is the
    # convolution of two density functions.
    h_ExpGauss.Fill(x)
 
f_conv = ROOT.TF1Convolution("expo", "gaus", -1, 6, True)
f_conv.SetRange(-1.0, 6.0)
f_conv.SetNofPointsFFT(1000)
f = ROOT.TF1("f", f_conv, 0.0, 5.0, f_conv.GetNpar())
f.SetParameters(1.0, -0.3, 0.0, 1.0)
 
# Fit.
c1 = ROOT.TCanvas("c", "c", 800, 1000)
h_ExpGauss.Fit("f")
h_ExpGauss.Draw()
 
c1.SaveAs("fitConvolution.png")

Author

Jonas Rembser, Aurelie Flandi (C++ version)

Definition in file fitConvolution.py.