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: Rene Brun
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.
const int np = 49;
float x[np] = {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};
The histogram are filled with bins defined in the array x.
TH1F *h = new TH1F("h", "Example of several fits in subranges", np, 85, 134);
h->SetMaximum(7);
for (int i = 0; i < np; i++) {
h->SetBinContent(i + 1, x[i]);
}
Define the parameter array for the total function.
double par[9];
Three TF1 objects are created, one for each subrange.
TF1 *g1 = new TF1("g1", "gaus", 85, 95);
TF1 *g2 = new TF1("g2", "gaus", 98, 108);
TF1 *g3 = new TF1("g3", "gaus", 110, 121);
The total is the sum of the three, each has three parameters.
TF1 *total = new TF1("total", "gaus(0)+gaus(3)+gaus(6)", 85, 125);
total->SetLineColor(2);
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);
FCN=0.0848003 FROM MIGRAD STATUS=CONVERGED 105 CALLS 106 TOTAL
EDM=1.77382e-07 STRATEGY= 1 ERROR MATRIX ACCURATE
EXT PARAMETER STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 Constant 4.96664e+00 2.83221e+00 4.26889e-04 1.67619e-04
2 Mean 9.54663e+01 1.23905e+01 7.53972e-04 -2.63161e-04
3 Sigma 6.82779e+00 7.49131e+00 5.87496e-05 3.68521e-03
FCN=0.0771026 FROM MIGRAD STATUS=CONVERGED 72 CALLS 73 TOTAL
EDM=2.00364e-07 STRATEGY= 1 ERROR MATRIX ACCURATE
EXT PARAMETER STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 Constant 5.96312e+00 1.14355e+00 4.82019e-04 1.52951e-04
2 Mean 1.00467e+02 1.53372e+00 3.74926e-04 6.69980e-04
3 Sigma 3.54806e+00 1.16899e+00 3.22077e-05 3.86167e-03
FCN=0.0087702 FROM MIGRAD STATUS=CONVERGED 93 CALLS 94 TOTAL
EDM=5.57239e-07 STRATEGY= 1 ERROR MATRIX ACCURATE
EXT PARAMETER STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 Constant 9.12665e-01 4.37176e-01 1.46528e-04 2.91010e-04
2 Mean 1.16309e+02 8.37408e+00 3.57386e-03 -3.17966e-05
3 Sigma 8.38413e+00 1.84577e+01 4.99414e-04 -4.98793e-04
Info in <TCanvas::MakeDefCanvas>: created default TCanvas with name c1
Get the parameters from the fit.
g1->GetParameters(&par[0]);
g2->GetParameters(&par[3]);
g3->GetParameters(&par[6]);
Use the parameters on the sum.
total->SetParameters(par);
h->Fit(total, "R+");
FCN=0.312817 FROM MIGRAD STATUS=CONVERGED 515 CALLS 516 TOTAL
EDM=1.73245e-07 STRATEGY= 1 ERROR MATRIX ACCURATE
EXT PARAMETER STEP FIRST
NO. NAME VALUE ERROR SIZE DERIVATIVE
1 p0 4.91145e+00 1.41387e+00 3.61239e-04 -3.22790e-04
2 p1 9.44525e+01 3.71612e+00 5.60861e-04 -6.78941e-05
3 p2 5.94796e+00 2.41732e+00 4.25396e-04 2.68176e-05
4 p3 3.22134e+00 3.11650e+00 5.86729e-04 -1.82620e-04
5 p4 1.01663e+02 1.67863e+00 5.56527e-04 3.95769e-04
6 p5 2.48454e+00 1.91461e+00 3.85832e-04 7.23818e-05
7 p6 9.11463e-01 3.68235e-01 1.45489e-04 5.77239e-04
8 p7 1.17582e+02 5.06329e+00 2.01798e-03 -8.25382e-05
9 p8 7.58627e+00 8.76000e+00 2.12468e-03 2.02614e-05
Draw all canvases
%jsroot on
gROOT->GetListOfCanvases()->Draw()