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.
Author: Jonas Rembser, Rene Brun (C++ version)
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Tuesday, March 19, 2024 at 07:08 PM.
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);
**************************************** Minimizer is Minuit2 / Migrad Chi2 = 0.0848003 NDf = 7 Edm = 8.86911e-08 NCalls = 106 Constant = 4.96664 +/- 2.83221 Mean = 95.4663 +/- 12.3905 Sigma = 6.82779 +/- 7.49131 (limited) **************************************** Minimizer is Minuit2 / Migrad Chi2 = 0.0771026 NDf = 7 Edm = 1.00182e-07 NCalls = 73 Constant = 5.96312 +/- 1.14355 Mean = 100.467 +/- 1.53372 Sigma = 3.54806 +/- 1.16899 (limited) **************************************** Minimizer is Minuit2 / Migrad Chi2 = 0.00877492 NDf = 8 Edm = 4.98832e-06 NCalls = 87 Constant = 0.912053 +/- 0.435309 Mean = 116.304 +/- 8.32344 Sigma = 8.38103 +/- 18.5139 (limited)
Get the parameters from the fit.
g1.GetParameters(par[:3])
g2.GetParameters(par[3:6])
g3.GetParameters(par[6:])
print(par)
[ 4.96663958 95.46632975 6.8277931 5.9631179 100.46745499 3.54806038 0.91205321 116.30403822 8.3810307 ]
Use the parameters on the sum.
total.SetParameters(par)
h.Draw()
h.Fit(total, "R+")
<cppyy.gbl.TFitResultPtr object at 0xad3f4e0>
**************************************** Minimizer is Minuit2 / Migrad Chi2 = 0.31282 NDf = 31 Edm = 3.25006e-06 NCalls = 495 p0 = 4.91052 +/- 1.41324 p1 = 94.4492 +/- 3.71244 p2 = 5.9461 +/- 2.41662 p3 = 3.22456 +/- 3.11384 p4 = 101.662 +/- 1.67862 p5 = 2.48631 +/- 1.91151 p6 = 0.911626 +/- 0.368736 p7 = 117.581 +/- 5.06092 p8 = 7.59194 +/- 8.78217
Error in <TFitResultPtr>: TFitResult is empty - use the fit option S Error in <TFitResultPtr>: TFitResult is empty - use the fit option S Error in <TFitResultPtr>: TFitResult is empty - use the fit option S Error in <TFitResultPtr>: TFitResult is empty - use the fit option S Error in <TFitResultPtr>: TFitResult is empty - use the fit option S Error in <TFitResultPtr>: TFitResult is empty - use the fit option S Error in <TFitResultPtr>: TFitResult is empty - use the fit option S Error in <TFitResultPtr>: TFitResult is empty - use the fit option S Error in <TFitResultPtr>: TFitResult is empty - use the fit option S Error in <TFitResultPtr>: TFitResult is empty - use the fit option S Error in <TFitResultPtr>: TFitResult is empty - use the fit option S Error in <TFitResultPtr>: TFitResult is empty - use the fit option S Error in <TFitResultPtr>: TFitResult is empty - use the fit option S Error in <TFitResultPtr>: TFitResult is empty - use the fit option S Error in <TFitResultPtr>: TFitResult is empty - use the fit option S Error in <TFitResultPtr>: TFitResult is empty - use the fit option S Error in <TFitResultPtr>: TFitResult is empty - use the fit option S Error in <TFitResultPtr>: TFitResult is empty - use the fit option S Error in <TFitResultPtr>: TFitResult is empty - use the fit option S Error in <TFitResultPtr>: TFitResult is empty - use the fit option S Error in <TFitResultPtr>: TFitResult is empty - use the fit option S Error in <TFitResultPtr>: TFitResult is empty - use the fit option S
Save the plot for later inspection.
c.SaveAs("multifit.png")
Info in <TCanvas::Print>: png file multifit.png has been created
Draw all canvases
from ROOT import gROOT
gROOT.GetListOfCanvases().Draw()