{
"cells": [
{
"cell_type": "markdown",
"id": "ec9293c3",
"metadata": {},
"source": [
"# multifit\n",
" Fitting multiple functions to different ranges of a 1-D histogram\n",
" Example showing how to fit in a sub-range of an histogram\n",
" A histogram is created and filled with the bin contents and errors\n",
" defined in the table below.\n",
" Three Gaussians are fitted in sub-ranges of this histogram.\n",
" A new function (a sum of 3 Gaussians) is fitted on another subrange\n",
" Note that when fitting simple functions, such as Gaussians, the initial\n",
" values of parameters are automatically computed by ROOT.\n",
" In the more complicated case of the sum of 3 Gaussians, the initial values\n",
" of parameters must be given. In this particular case, the initial values\n",
" are taken from the result of the individual fits.\n",
"\n",
"\n",
"\n",
"\n",
"**Author:** Jonas Rembser, Rene Brun (C++ version) \n",
"This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Tuesday, May 19, 2026 at 08:25 PM."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "d363fda9",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:25:13.883983Z",
"iopub.status.busy": "2026-05-19T20:25:13.883863Z",
"iopub.status.idle": "2026-05-19T20:25:14.952117Z",
"shell.execute_reply": "2026-05-19T20:25:14.951488Z"
}
},
"outputs": [],
"source": [
"import ROOT\n",
"\n",
"import numpy as np\n",
"\n",
"n_x = 49"
]
},
{
"cell_type": "markdown",
"id": "7764e091",
"metadata": {},
"source": [
"fmt: off"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "008d347c",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:25:14.954453Z",
"iopub.status.busy": "2026-05-19T20:25:14.954253Z",
"iopub.status.idle": "2026-05-19T20:25:15.070472Z",
"shell.execute_reply": "2026-05-19T20:25:15.068712Z"
}
},
"outputs": [],
"source": [
"x = np.array( [ 1.913521, 1.953769, 2.347435, 2.883654, 3.493567, 4.047560,\n",
" 4.337210, 4.364347, 4.563004, 5.054247, 5.194183, 5.380521, 5.303213,\n",
" 5.384578, 5.563983, 5.728500, 5.685752, 5.080029, 4.251809, 3.372246,\n",
" 2.207432, 1.227541, 0.8597788, 0.8220503, 0.8046592, 0.7684097, 0.7469761,\n",
" 0.8019787, 0.8362375, 0.8744895, 0.9143721, 0.9462768, 0.9285364,\n",
" 0.8954604, 0.8410891, 0.7853871, 0.7100883, 0.6938808, 0.7363682,\n",
" 0.7032954, 0.6029015, 0.5600163, 0.7477068, 1.188785, 1.938228, 2.602717,\n",
" 3.472962, 4.465014, 5.177035, ], dtype=np.float32,)"
]
},
{
"cell_type": "markdown",
"id": "d13ea803",
"metadata": {},
"source": [
"fmt: on"
]
},
{
"cell_type": "markdown",
"id": "33f6e1bd",
"metadata": {},
"source": [
"The histogram are filled with bins defined in the array x."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "521727d2",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:25:15.072674Z",
"iopub.status.busy": "2026-05-19T20:25:15.072519Z",
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"shell.execute_reply": "2026-05-19T20:25:15.202698Z"
}
},
"outputs": [],
"source": [
"h = ROOT.TH1F(\"h\", \"Example of several fits in subranges\", n_x, 85, 134)\n",
"h.SetMaximum(7)\n",
"\n",
"for i, x_i in enumerate(x):\n",
" h.SetBinContent(i + 1, x[i])"
]
},
{
"cell_type": "markdown",
"id": "4d344418",
"metadata": {},
"source": [
"Define the parameter array for the total function."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "dea638bf",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:25:15.205434Z",
"iopub.status.busy": "2026-05-19T20:25:15.205283Z",
"iopub.status.idle": "2026-05-19T20:25:15.308880Z",
"shell.execute_reply": "2026-05-19T20:25:15.308115Z"
}
},
"outputs": [],
"source": [
"par = np.zeros(9)"
]
},
{
"cell_type": "markdown",
"id": "e3ce7fb9",
"metadata": {},
"source": [
"Three TF1 objects are created, one for each subrange."
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "760568f7",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:25:15.311043Z",
"iopub.status.busy": "2026-05-19T20:25:15.310910Z",
"iopub.status.idle": "2026-05-19T20:25:15.438011Z",
"shell.execute_reply": "2026-05-19T20:25:15.437205Z"
}
},
"outputs": [],
"source": [
"g1 = ROOT.TF1(\"g1\", \"gaus\", 85, 95)\n",
"g2 = ROOT.TF1(\"g2\", \"gaus\", 98, 108)\n",
"g3 = ROOT.TF1(\"g3\", \"gaus\", 110, 121)"
]
},
{
"cell_type": "markdown",
"id": "a5d1a539",
"metadata": {},
"source": [
"The total is the sum of the three, each has three parameters."
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "2d432f90",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:25:15.439986Z",
"iopub.status.busy": "2026-05-19T20:25:15.439850Z",
"iopub.status.idle": "2026-05-19T20:25:15.554735Z",
"shell.execute_reply": "2026-05-19T20:25:15.553996Z"
}
},
"outputs": [],
"source": [
"total = ROOT.TF1(\"total\", \"gaus(0)+gaus(3)+gaus(6)\", 85, 125)\n",
"total.SetLineColor(2)"
]
},
{
"cell_type": "markdown",
"id": "bef091f6",
"metadata": {},
"source": [
"The canvas that the histograms and fit functions are drawn on."
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "7770af6b",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:25:15.556863Z",
"iopub.status.busy": "2026-05-19T20:25:15.556723Z",
"iopub.status.idle": "2026-05-19T20:25:15.694727Z",
"shell.execute_reply": "2026-05-19T20:25:15.694009Z"
}
},
"outputs": [],
"source": [
"c = ROOT.TCanvas(\"multifit\", \"multifit\", 800, 400)"
]
},
{
"cell_type": "markdown",
"id": "140c48a1",
"metadata": {},
"source": [
"Fit each function and add it to the list of functions. By default, TH1::Fit()\n",
"fits the function on the defined histogram range. You can specify the \"R\"\n",
"option in the second parameter of TH1::Fit() to restrict the fit to the range\n",
"specified in the TF1 constructor. Alternatively, you can also specify the\n",
"range in the call to TH1::Fit(), which we demonstrate here with the 3rd\n",
"Gaussian. The \"+\" option needs to be added to the later fits to not replace\n",
"existing fitted functions in the histogram."
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "ec0c9c92",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:25:15.696875Z",
"iopub.status.busy": "2026-05-19T20:25:15.696735Z",
"iopub.status.idle": "2026-05-19T20:25:15.841767Z",
"shell.execute_reply": "2026-05-19T20:25:15.841050Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"****************************************\n",
"Minimizer is Minuit2 / Migrad\n",
"Chi2 = 0.0848003\n",
"NDf = 7\n",
"Edm = 8.86911e-08\n",
"NCalls = 106\n",
"Constant = 4.96664 +/- 2.83221 \n",
"Mean = 95.4663 +/- 12.3905 \n",
"Sigma = 6.82779 +/- 7.49131 \t (limited)\n",
"****************************************\n",
"Minimizer is Minuit2 / Migrad\n",
"Chi2 = 0.0771026\n",
"NDf = 7\n",
"Edm = 1.00182e-07\n",
"NCalls = 73\n",
"Constant = 5.96312 +/- 1.14355 \n",
"Mean = 100.467 +/- 1.53372 \n",
"Sigma = 3.54806 +/- 1.16899 \t (limited)\n",
"****************************************\n",
"Minimizer is Minuit2 / Migrad\n",
"Chi2 = 0.00877492\n",
"NDf = 8\n",
"Edm = 4.98832e-06\n",
"NCalls = 87\n",
"Constant = 0.912053 +/- 0.435309 \n",
"Mean = 116.304 +/- 8.32344 \n",
"Sigma = 8.38103 +/- 18.5139 \t (limited)\n"
]
}
],
"source": [
"h.Fit(g1, \"R\")\n",
"h.Fit(g2, \"R+\")\n",
"h.Fit(g3, \"+\", \"\", 110, 121);"
]
},
{
"cell_type": "markdown",
"id": "8c3eaed5",
"metadata": {},
"source": [
"Get the parameters from the fit."
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "0929ed36",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:25:15.844759Z",
"iopub.status.busy": "2026-05-19T20:25:15.844619Z",
"iopub.status.idle": "2026-05-19T20:25:15.953548Z",
"shell.execute_reply": "2026-05-19T20:25:15.952796Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[ 4.96663958 95.46632975 6.8277931 5.9631179 100.46745499\n",
" 3.54806038 0.91205321 116.30403822 8.3810307 ]\n"
]
}
],
"source": [
"g1.GetParameters(par[:3])\n",
"g2.GetParameters(par[3:6])\n",
"g3.GetParameters(par[6:])\n",
"\n",
"print(par)"
]
},
{
"cell_type": "markdown",
"id": "fb4ac6bc",
"metadata": {},
"source": [
"Use the parameters on the sum."
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "5088a0e1",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:25:15.955265Z",
"iopub.status.busy": "2026-05-19T20:25:15.955134Z",
"iopub.status.idle": "2026-05-19T20:25:16.075849Z",
"shell.execute_reply": "2026-05-19T20:25:16.075124Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"****************************************\n",
"Minimizer is Minuit2 / Migrad\n",
"Chi2 = 0.31282\n",
"NDf = 31\n",
"Edm = 3.25007e-06\n",
"NCalls = 495\n",
"p0 = 4.91052 +/- 1.41324 \n",
"p1 = 94.4492 +/- 3.71244 \n",
"p2 = 5.9461 +/- 2.41662 \n",
"p3 = 3.22456 +/- 3.11384 \n",
"p4 = 101.662 +/- 1.67862 \n",
"p5 = 2.48631 +/- 1.91151 \n",
"p6 = 0.911626 +/- 0.368736 \n",
"p7 = 117.581 +/- 5.06092 \n",
"p8 = 7.59194 +/- 8.78217 \n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"Error in : TFitResult is empty - use the fit option S\n",
"Error in : TFitResult is empty - use the fit option S\n",
"Error in : TFitResult is empty - use the fit option S\n",
"Error in : TFitResult is empty - use the fit option S\n",
"Error in : TFitResult is empty - use the fit option S\n",
"Error in : TFitResult is empty - use the fit option S\n",
"Error in : TFitResult is empty - use the fit option S\n",
"Error in : TFitResult is empty - use the fit option S\n",
"Error in : TFitResult is empty - use the fit option S\n",
"Error in : TFitResult is empty - use the fit option S\n",
"Error in : TFitResult is empty - use the fit option S\n",
"Error in : TFitResult is empty - use the fit option S\n",
"Error in : TFitResult is empty - use the fit option S\n",
"Error in : TFitResult is empty - use the fit option S\n",
"Error in : TFitResult is empty - use the fit option S\n",
"Error in : TFitResult is empty - use the fit option S\n",
"Error in : TFitResult is empty - use the fit option S\n",
"Error in : TFitResult is empty - use the fit option S\n",
"Error in : TFitResult is empty - use the fit option S\n",
"Error in : TFitResult is empty - use the fit option S\n",
"Error in : TFitResult is empty - use the fit option S\n",
"Error in : TFitResult is empty - use the fit option S\n"
]
}
],
"source": [
"total.SetParameters(par)\n",
"\n",
"h.Draw()\n",
"h.Fit(total, \"R+\")"
]
},
{
"cell_type": "markdown",
"id": "57ca1f02",
"metadata": {},
"source": [
"Save the plot for later inspection."
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "dc34c729",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:25:16.077625Z",
"iopub.status.busy": "2026-05-19T20:25:16.077478Z",
"iopub.status.idle": "2026-05-19T20:25:16.234944Z",
"shell.execute_reply": "2026-05-19T20:25:16.234188Z"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Info in : png file multifit.png has been created\n"
]
}
],
"source": [
"c.SaveAs(\"multifit.png\")"
]
},
{
"cell_type": "markdown",
"id": "547f9c08",
"metadata": {},
"source": [
"Draw all canvases "
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "e1399fac",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:25:16.236676Z",
"iopub.status.busy": "2026-05-19T20:25:16.236517Z",
"iopub.status.idle": "2026-05-19T20:25:16.456728Z",
"shell.execute_reply": "2026-05-19T20:25:16.456035Z"
}
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"\n",
"
\n",
"\n",
"\n",
"\n"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from ROOT import gROOT \n",
"gROOT.GetListOfCanvases().Draw()"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
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