{
"cells": [
{
"cell_type": "markdown",
"id": "4a7fac7d",
"metadata": {},
"source": [
"# combinedFit\n",
"Combined (simultaneous) fit of two histogram with separate functions\n",
"and some common parameters\n",
"\n",
"\n",
"\n",
"\n",
"**Author:** Jonas Rembser, Lorenzo Moneta (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 08:24 PM."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "e4ec0fa4",
"metadata": {
"collapsed": false,
"execution": {
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"shell.execute_reply": "2026-05-19T20:24:33.203693Z"
}
},
"outputs": [],
"source": [
"import ROOT\n",
"import numpy as np"
]
},
{
"cell_type": "markdown",
"id": "59ed3565",
"metadata": {},
"source": [
"definition of shared parameter background function"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "eca4f8b5",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:24:33.206412Z",
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"shell.execute_reply": "2026-05-19T20:24:33.318467Z"
}
},
"outputs": [],
"source": [
"iparB = np.array([0, 2], dtype=np.int32) # exp amplitude in B histo and exp common parameter"
]
},
{
"cell_type": "markdown",
"id": "8b4632d6",
"metadata": {},
"source": [
"signal + background function"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "6018de3e",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:24:33.320830Z",
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},
"outputs": [],
"source": [
"iparSB = np.array(\n",
" [\n",
" 1, # exp amplitude in S+B histo\n",
" 2, # exp common parameter\n",
" 3, # Gaussian amplitude\n",
" 4, # Gaussian mean\n",
" 5, # Gaussian sigma\n",
" ],\n",
" dtype=np.int32,\n",
")"
]
},
{
"cell_type": "markdown",
"id": "f72af92f",
"metadata": {},
"source": [
"Create the GlobalCHi2 structure"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "c52a8811",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:24:33.426629Z",
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"shell.execute_reply": "2026-05-19T20:24:33.589372Z"
}
},
"outputs": [],
"source": [
"class GlobalChi2(object):\n",
" def __init__(self, f1, f2):\n",
" self._f1 = f1\n",
" self._f2 = f2\n",
"\n",
" def __call__(self, par):\n",
" # parameter vector is first background (in common 1 and 2) and then is\n",
" # signal (only in 2)\n",
"\n",
" # the zero-copy way to get a numpy array from a double *\n",
" par_arr = np.frombuffer(par, dtype=np.float64, count=6)\n",
"\n",
" p1 = par_arr[iparB]\n",
" p2 = par_arr[iparSB]\n",
"\n",
" return self._f1(p1) + self._f2(p2)\n",
"\n",
"\n",
"hB = ROOT.TH1D(\"hB\", \"histo B\", 100, 0, 100)\n",
"hSB = ROOT.TH1D(\"hSB\", \"histo S+B\", 100, 0, 100)\n",
"\n",
"fB = ROOT.TF1(\"fB\", \"expo\", 0, 100)\n",
"fB.SetParameters(1, -0.05)\n",
"hB.FillRandom(fB)\n",
"\n",
"fS = ROOT.TF1(\"fS\", \"gaus\", 0, 100)\n",
"fS.SetParameters(1, 30, 5)\n",
"\n",
"hSB.FillRandom(fB, 2000)\n",
"hSB.FillRandom(fS, 1000)"
]
},
{
"cell_type": "markdown",
"id": "3556e787",
"metadata": {},
"source": [
"perform now global fit"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "bfe9403b",
"metadata": {
"collapsed": false,
"execution": {
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"shell.execute_reply": "2026-05-19T20:24:33.758134Z"
}
},
"outputs": [],
"source": [
"fSB = ROOT.TF1(\"fSB\", \"expo + gaus(2)\", 0, 100)\n",
"\n",
"wfB = ROOT.Math.WrappedMultiTF1(fB, 1)\n",
"wfSB = ROOT.Math.WrappedMultiTF1(fSB, 1)\n",
"\n",
"opt = ROOT.Fit.DataOptions()\n",
"rangeB = ROOT.Fit.DataRange()"
]
},
{
"cell_type": "markdown",
"id": "b9ac536e",
"metadata": {},
"source": [
"set the data range"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "e9eb4750",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:24:33.766248Z",
"iopub.status.busy": "2026-05-19T20:24:33.766113Z",
"iopub.status.idle": "2026-05-19T20:24:34.099997Z",
"shell.execute_reply": "2026-05-19T20:24:34.099647Z"
}
},
"outputs": [],
"source": [
"rangeB.SetRange(10, 90)\n",
"dataB = ROOT.Fit.BinData(opt, rangeB)\n",
"ROOT.Fit.FillData(dataB, hB)\n",
"\n",
"rangeSB = ROOT.Fit.DataRange()\n",
"rangeSB.SetRange(10, 50)\n",
"dataSB = ROOT.Fit.BinData(opt, rangeSB)\n",
"ROOT.Fit.FillData(dataSB, hSB)\n",
"\n",
"chi2_B = ROOT.Fit.Chi2Function(dataB, wfB)\n",
"chi2_SB = ROOT.Fit.Chi2Function(dataSB, wfSB)\n",
"\n",
"globalChi2 = GlobalChi2(chi2_B, chi2_SB)\n",
"\n",
"fitter = ROOT.Fit.Fitter()\n",
"\n",
"Npar = 6\n",
"par0 = np.array([5, 5, -0.1, 100, 30, 10])"
]
},
{
"cell_type": "markdown",
"id": "abda1499",
"metadata": {},
"source": [
"create before the parameter settings in order to fix or set range on them"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "3abe0234",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:24:34.103413Z",
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"shell.execute_reply": "2026-05-19T20:24:34.214403Z"
}
},
"outputs": [],
"source": [
"fitter.Config().SetParamsSettings(6, par0)"
]
},
{
"cell_type": "markdown",
"id": "579522fd",
"metadata": {},
"source": [
"fix 5-th parameter"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "33acdaa7",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:24:34.217096Z",
"iopub.status.busy": "2026-05-19T20:24:34.216973Z",
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"shell.execute_reply": "2026-05-19T20:24:34.328879Z"
}
},
"outputs": [],
"source": [
"fitter.Config().ParSettings(4).Fix()"
]
},
{
"cell_type": "markdown",
"id": "00032d5f",
"metadata": {},
"source": [
"set limits on the third and 4-th parameter"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "7ceea394",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:24:34.350498Z",
"iopub.status.busy": "2026-05-19T20:24:34.350351Z",
"iopub.status.idle": "2026-05-19T20:24:34.467944Z",
"shell.execute_reply": "2026-05-19T20:24:34.467210Z"
}
},
"outputs": [],
"source": [
"fitter.Config().ParSettings(2).SetLimits(-10, -1.0e-4)\n",
"fitter.Config().ParSettings(3).SetLimits(0, 10000)\n",
"fitter.Config().ParSettings(3).SetStepSize(5)\n",
"\n",
"fitter.Config().MinimizerOptions().SetPrintLevel(0)\n",
"fitter.Config().SetMinimizer(\"Minuit2\", \"Migrad\")"
]
},
{
"cell_type": "markdown",
"id": "44b5aa76",
"metadata": {},
"source": [
"we can't pass the Python object globalChi2 directly to FitFCN.\n",
"It needs to be wrapped in a ROOT::Math::Functor."
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "b1e3ae36",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:24:34.469871Z",
"iopub.status.busy": "2026-05-19T20:24:34.469742Z",
"iopub.status.idle": "2026-05-19T20:24:34.825257Z",
"shell.execute_reply": "2026-05-19T20:24:34.824829Z"
}
},
"outputs": [],
"source": [
"globalChi2Functor = ROOT.Math.Functor(globalChi2, 6)"
]
},
{
"cell_type": "markdown",
"id": "48de82b7",
"metadata": {},
"source": [
"fit FCN function\n",
"(specify optionally data size and flag to indicate that is a chi2 fit)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "7f6d2afd",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:24:34.835472Z",
"iopub.status.busy": "2026-05-19T20:24:34.835336Z",
"iopub.status.idle": "2026-05-19T20:24:35.264702Z",
"shell.execute_reply": "2026-05-19T20:24:35.264012Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"****************************************\n",
"Minimizer is Minuit2 / Migrad\n",
"Chi2 = 131.104\n",
"NDf = 115\n",
"Edm = 2.11602e-08\n",
"NCalls = 225\n",
"Par_0 = 5.5396 +/- 0.0354094 \n",
"Par_1 = 4.66089 +/- 0.050106 \n",
"Par_2 = -0.0514037 +/- 0.00108539 \t (limited)\n",
"Par_3 = 77.2733 +/- 3.93105 \t (limited)\n",
"Par_4 = 30 \t (fixed)\n",
"Par_5 = 4.864 +/- 0.243005 \n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"Info in : png file combinedFit.png has been created\n"
]
},
{
"data": {
"text/html": [
"\n",
"\n",
"\n",
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\n",
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"\n",
"\n"
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},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fitter.FitFCN(globalChi2Functor, 0, dataB.Size() + dataSB.Size(), True)\n",
"result = fitter.Result()\n",
"result.Print(ROOT.std.cout)\n",
"\n",
"c1 = ROOT.TCanvas(\"Simfit\", \"Simultaneous fit of two histograms\", 10, 10, 700, 700)\n",
"c1.Divide(1, 2)\n",
"c1.cd(1)\n",
"ROOT.gStyle.SetOptFit(1111)\n",
"\n",
"fB.SetFitResult(result, iparB)\n",
"fB.SetRange(rangeB().first, rangeB().second)\n",
"fB.SetLineColor(\"kBlue\")\n",
"hB.GetListOfFunctions().Add(fB)\n",
"hB.Draw()\n",
"\n",
"c1.cd(2)\n",
"fSB.SetFitResult(result, iparSB)\n",
"fSB.SetRange(rangeSB().first, rangeSB().second)\n",
"fSB.SetLineColor(\"kRed\")\n",
"hSB.GetListOfFunctions().Add(fSB)\n",
"hSB.Draw()\n",
"\n",
"c1.SaveAs(\"combinedFit.png\")"
]
},
{
"cell_type": "markdown",
"id": "5bb240ca",
"metadata": {},
"source": [
"Draw all canvases "
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "a047eb25",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:24:35.266229Z",
"iopub.status.busy": "2026-05-19T20:24:35.266105Z",
"iopub.status.idle": "2026-05-19T20:24:35.394761Z",
"shell.execute_reply": "2026-05-19T20:24:35.394120Z"
}
},
"outputs": [
{
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"\n",
"\n"
],
"text/plain": [
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]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from ROOT import gROOT \n",
"gROOT.GetListOfCanvases().Draw()"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
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"file_extension": ".py",
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