multifit.py

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## \file
## \ingroup tutorial_fit
## \notebook
##  Fitting multiple functions to different ranges of a 1-D histogram
##      Example showing how to fit in a sub-range of an histogram
##  A histogram is created and filled with the bin contents and errors
##  defined in the table below.
##  Three Gaussians are fitted in sub-ranges of this histogram.
##  A new function (a sum of 3 Gaussians) is fitted on another subrange
##  Note that when fitting simple functions, such as Gaussians, the initial
##  values of parameters are automatically computed by ROOT.
##  In the more complicated case of the sum of 3 Gaussians, the initial values
##  of parameters must be given. In this particular case, the initial values
##  are taken from the result of the individual fits.
##
## \macro_image
## \macro_output
## \macro_code
##
## \authors Jonas Rembser, Rene Brun (C++ version)
 
import ROOT
 
import numpy as np
 
n_x = 49
 
# fmt: off
x = np.array( [ 1.913521, 1.953769, 2.347435, 2.883654, 3.493567, 4.047560,
    4.337210, 4.364347, 4.563004, 5.054247, 5.194183, 5.380521, 5.303213,
    5.384578, 5.563983, 5.728500, 5.685752, 5.080029, 4.251809, 3.372246,
    2.207432, 1.227541, 0.8597788, 0.8220503, 0.8046592, 0.7684097, 0.7469761,
    0.8019787, 0.8362375, 0.8744895, 0.9143721, 0.9462768, 0.9285364,
    0.8954604, 0.8410891, 0.7853871, 0.7100883, 0.6938808, 0.7363682,
    0.7032954, 0.6029015, 0.5600163, 0.7477068, 1.188785, 1.938228, 2.602717,
    3.472962, 4.465014, 5.177035, ], dtype=np.float32,)
# fmt: on
 
# The histogram are filled with bins defined in the array x.
h = ROOT.TH1F("h", "Example of several fits in subranges", n_x, 85, 134)
h.SetMaximum(7)
 
for i, x_i in enumerate(x):
    h.SetBinContent(i + 1, x[i])
 
# Define the parameter array for the total function.
par = np.zeros(9)
 
# Three TF1 objects are created, one for each subrange.
g1 = ROOT.TF1("g1", "gaus", 85, 95)
g2 = ROOT.TF1("g2", "gaus", 98, 108)
g3 = ROOT.TF1("g3", "gaus", 110, 121)
 
# The total is the sum of the three, each has three parameters.
total = ROOT.TF1("total", "gaus(0)+gaus(3)+gaus(6)", 85, 125)
total.SetLineColor(2)
 
# The canvas that the histograms and fit functions are drawn on.
c = ROOT.TCanvas("multifit", "multifit", 800, 400)
 
# Fit each function and add it to the list of functions. By default, TH1::Fit()
# fits the function on the defined histogram range. You can specify the "R"
# option in the second parameter of TH1::Fit() to restrict the fit to the range
# specified in the TF1 constructor. Alternatively, you can also specify the
# range in the call to TH1::Fit(), which we demonstrate here with the 3rd
# Gaussian. The "+" option needs to be added to the later fits to not replace
# existing fitted functions in the histogram.
h.Fit(g1, "R")
h.Fit(g2, "R+")
h.Fit(g3, "+", "", 110, 121);
 
# Get the parameters from the fit.
g1.GetParameters(par[:3])
g2.GetParameters(par[3:6])
g3.GetParameters(par[6:])
 
print(par)
 
# Use the parameters on the sum.
total.SetParameters(par)
 
h.Draw()
h.Fit(total, "R+")
 
# Save the plot for later inspection.
c.SaveAs("multifit.png")