{
"cells": [
{
"cell_type": "markdown",
"id": "839c5532",
"metadata": {},
"source": [
"# fitNormSum\n",
"Tutorial for normalized sum of two functions\n",
"Here: a background exponential and a crystalball function\n",
"Parameters can be set:\n",
" 1. with the TF1 object before adding the function (for 3) and 4))\n",
" 2. with the TF1NormSum object (first two are the coefficients, then the non constant parameters)\n",
" 3. with the TF1 object after adding the function\n",
"\n",
"Sum can be constructed by:\n",
" 1. by a string containing the names of the functions and/or the coefficient in front\n",
" 2. by a string containg formulas like expo, gaus...\n",
" 3. by the list of functions and coefficients (which are 1 by default)\n",
" 4. by a std::vector for functions and coefficients\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": "ac61f74e",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:25:01.241060Z",
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"shell.execute_reply": "2026-05-19T20:25:02.228021Z"
}
},
"outputs": [],
"source": [
"import ROOT\n",
"\n",
"nsig = 50000\n",
"nbkg = 1000000\n",
"nEvents = nsig + nbkg\n",
"nBins = 1000\n",
"\n",
"signal_mean = 3.0\n",
"f_cb = ROOT.TF1(\"MyCrystalBall\", \"crystalball\", -5.0, 5.0)\n",
"f_exp = ROOT.TF1(\"MyExponential\", \"expo\", -5.0, 5.0)"
]
},
{
"cell_type": "markdown",
"id": "11092104",
"metadata": {},
"source": [
"I.:"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "3abfd5df",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:25:02.230712Z",
"iopub.status.busy": "2026-05-19T20:25:02.230538Z",
"iopub.status.idle": "2026-05-19T20:25:02.351521Z",
"shell.execute_reply": "2026-05-19T20:25:02.350496Z"
}
},
"outputs": [],
"source": [
"f_exp.SetParameters(1.0, -0.3)\n",
"f_cb.SetParameters(1, signal_mean, 0.3, 2, 1.5)"
]
},
{
"cell_type": "markdown",
"id": "c8c74314",
"metadata": {},
"source": [
"CONSTRUCTION OF THE TF1NORMSUM OBJECT ........................................\n",
"1) :"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "08a222ed",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:25:02.353119Z",
"iopub.status.busy": "2026-05-19T20:25:02.352982Z",
"iopub.status.idle": "2026-05-19T20:25:02.466445Z",
"shell.execute_reply": "2026-05-19T20:25:02.465464Z"
}
},
"outputs": [],
"source": [
"fnorm_exp_cb = ROOT.TF1NormSum(f_cb, f_exp, nsig, nbkg)"
]
},
{
"cell_type": "markdown",
"id": "8762566a",
"metadata": {},
"source": [
"4) :"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "827c4592",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:25:02.467947Z",
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"shell.execute_reply": "2026-05-19T20:25:02.843279Z"
}
},
"outputs": [],
"source": [
"f_sum = ROOT.TF1(\"fsum\", fnorm_exp_cb, -5.0, 5.0, fnorm_exp_cb.GetNpar())"
]
},
{
"cell_type": "markdown",
"id": "3b29b278",
"metadata": {},
"source": [
"III.:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "8463cd9e",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:25:02.855473Z",
"iopub.status.busy": "2026-05-19T20:25:02.855335Z",
"iopub.status.idle": "2026-05-19T20:25:02.988120Z",
"shell.execute_reply": "2026-05-19T20:25:02.987501Z"
}
},
"outputs": [],
"source": [
"parameter_values = fnorm_exp_cb.GetParameters()\n",
"f_sum.SetParameters(parameter_values.data())"
]
},
{
"cell_type": "markdown",
"id": "f0231721",
"metadata": {},
"source": [
"Note: in the C++ tutorial, the parameter value sync is done in one line with:\n",
"```C++\n",
" f_sum->SetParameters(fnorm_exp_cb->GetParameters().data());\n",
"```\n",
"However, TF1NormSum::GetParameters() returns an std::vector by value, which\n",
"doesn't survive long enough in Python. That's why we have to explicitly\n",
"assign it to a variable first and can't use a temporary."
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "b9804765",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:25:02.990257Z",
"iopub.status.busy": "2026-05-19T20:25:02.990130Z",
"iopub.status.idle": "2026-05-19T20:25:03.109723Z",
"shell.execute_reply": "2026-05-19T20:25:03.109002Z"
}
},
"outputs": [],
"source": [
"f_sum.SetParName(1, \"NBackground\")\n",
"f_sum.SetParName(0, \"NSignal\")\n",
"for i in range(2, f_sum.GetNpar()):\n",
" f_sum.SetParName(i, fnorm_exp_cb.GetParName(i))"
]
},
{
"cell_type": "markdown",
"id": "6daf89b8",
"metadata": {},
"source": [
"GENERATE HISTOGRAM TO FIT .............................................................."
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "04c29262",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:25:03.111856Z",
"iopub.status.busy": "2026-05-19T20:25:03.111723Z",
"iopub.status.idle": "2026-05-19T20:25:03.360320Z",
"shell.execute_reply": "2026-05-19T20:25:03.359552Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Time to generate 1050000 events: \n",
"Real time 0:00:00, CP time 0.140\n"
]
}
],
"source": [
"w = ROOT.TStopwatch()\n",
"w.Start()\n",
"h_sum = ROOT.TH1D(\"h_ExpCB\", \"Exponential Bkg + CrystalBall function\", nBins, -5.0, 5.0)\n",
"h_sum.FillRandom(f_sum, nEvents)\n",
"print(\"Time to generate {0} events: \".format(nEvents))\n",
"w.Print()"
]
},
{
"cell_type": "markdown",
"id": "4143e84f",
"metadata": {},
"source": [
"need to scale histogram with width since we are fitting a density"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "3373f6ed",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:25:03.362782Z",
"iopub.status.busy": "2026-05-19T20:25:03.362652Z",
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"shell.execute_reply": "2026-05-19T20:25:03.472173Z"
}
},
"outputs": [],
"source": [
"h_sum.Sumw2()\n",
"h_sum.Scale(1.0, \"width\")"
]
},
{
"cell_type": "markdown",
"id": "dd4e6b16",
"metadata": {},
"source": [
"fit - use Minuit2 if available"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "47d9d0b2",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:25:03.494445Z",
"iopub.status.busy": "2026-05-19T20:25:03.494303Z",
"iopub.status.idle": "2026-05-19T20:25:03.636147Z",
"shell.execute_reply": "2026-05-19T20:25:03.635378Z"
}
},
"outputs": [],
"source": [
"ROOT.Math.MinimizerOptions.SetDefaultMinimizer(\"Minuit2\")\n",
"c1 = ROOT.TCanvas(\"Fit\", \"Fit\", 800, 1000)"
]
},
{
"cell_type": "markdown",
"id": "93394a3e",
"metadata": {},
"source": [
"do a least-square fit of the spectrum"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "020ade54",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:25:03.637913Z",
"iopub.status.busy": "2026-05-19T20:25:03.637787Z",
"iopub.status.idle": "2026-05-19T20:25:04.135389Z",
"shell.execute_reply": "2026-05-19T20:25:04.134781Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"****************************************\n",
"Minimizer is Minuit2 / Migrad\n",
"Chi2 = 1018.73\n",
"NDf = 993\n",
"Edm = 9.65559e-06\n",
"NCalls = 233\n",
"NSignal = 50082 +/- 1231.21 \n",
"NBackground = 998899 +/- 1569.86 \n",
"Mean = 2.99896 +/- 0.0022426 \n",
"Sigma = 0.297871 +/- 0.00230279 \n",
"Alpha = 2.12493 +/- 0.1368 \n",
"N = 1.1562 +/- 0.468136 \n",
"Slope = -0.300341 +/- 0.000644187 \n",
"Time to fit using ROOT TF1Normsum: \n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Real time 0:00:00, CP time 0.140\n"
]
}
],
"source": [
"result = h_sum.Fit(f_sum, \"SQ\")\n",
"result.Print()\n",
"h_sum.Draw()\n",
"print(\"Time to fit using ROOT TF1Normsum: \")\n",
"w.Print()"
]
},
{
"cell_type": "markdown",
"id": "736c7052",
"metadata": {},
"source": [
"test if parameters are fine"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "73b0eeb6",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:25:04.137130Z",
"iopub.status.busy": "2026-05-19T20:25:04.137003Z",
"iopub.status.idle": "2026-05-19T20:25:04.374833Z",
"shell.execute_reply": "2026-05-19T20:25:04.374228Z"
}
},
"outputs": [
{
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"\n",
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"metadata": {},
"output_type": "display_data"
}
],
"source": [
"for i, pref in enumerate([nsig, nbkg, signal_mean]):\n",
" if not ROOT.TMath.AreEqualAbs(pref, f_sum.GetParameter(i), f_sum.GetParError(i) * 10.0):\n",
" ROOT.Error(\n",
" \"testFitNormSum\",\n",
" \"Difference found in fitted {0} - difference is {1:.2f} sigma\".format(\n",
" f_sum.GetParName(i), (f_sum.GetParameter(i) - pref) / f_sum.GetParError(i)\n",
" ),\n",
" )\n",
"\n",
"ROOT.gStyle.SetOptStat(0)"
]
},
{
"cell_type": "markdown",
"id": "c217c526",
"metadata": {},
"source": [
"add parameters"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "885d1220",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:25:04.380802Z",
"iopub.status.busy": "2026-05-19T20:25:04.380669Z",
"iopub.status.idle": "2026-05-19T20:25:04.549319Z",
"shell.execute_reply": "2026-05-19T20:25:04.548652Z"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Info in : png file fitNormSum.png has been created\n"
]
}
],
"source": [
"t1 = ROOT.TLatex(-2.5, 300000, \"NSignal = {0:g} #pm {1:g}\".format(f_sum.GetParameter(0), f_sum.GetParError(0)))\n",
"t2 = ROOT.TLatex(-2.5, 270000, \"Nbackgr = {0:g} #pm {1:g}\".format(f_sum.GetParameter(1), f_sum.GetParError(1)))\n",
"t1.Draw()\n",
"t2.Draw()\n",
"\n",
"c1.SaveAs(\"fitNormSum.png\")"
]
},
{
"cell_type": "markdown",
"id": "4f0fe8db",
"metadata": {},
"source": [
"Draw all canvases "
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "b8f3fd42",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:25:04.561271Z",
"iopub.status.busy": "2026-05-19T20:25:04.561127Z",
"iopub.status.idle": "2026-05-19T20:25:04.675596Z",
"shell.execute_reply": "2026-05-19T20:25:04.674937Z"
}
},
"outputs": [
{
"data": {
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"\n",
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"\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"
},
"language_info": {
"codemirror_mode": {
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"file_extension": ".py",
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