{
"cells": [
{
"cell_type": "markdown",
"id": "4c817fdf",
"metadata": {},
"source": [
"# rf701_efficiencyfit\n",
"Special pdf's: unbinned maximum likelihood fit of an efficiency eff(x) function to a\n",
"dataset D(x,cut), cut is a category encoding a selection, which the efficiency as function\n",
"of x should be described by eff(x)\n",
"\n",
"\n",
"\n",
"\n",
"**Author:** Clemens Lange, Wouter Verkerke (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 08:34 PM."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "a66ed769",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:34:18.766883Z",
"iopub.status.busy": "2026-05-19T20:34:18.766766Z",
"iopub.status.idle": "2026-05-19T20:34:19.722716Z",
"shell.execute_reply": "2026-05-19T20:34:19.722024Z"
}
},
"outputs": [],
"source": [
"import ROOT"
]
},
{
"cell_type": "markdown",
"id": "a4637e75",
"metadata": {},
"source": [
"Construct efficiency function e(x)\n",
"-------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "9141e16a",
"metadata": {},
"source": [
"Declare variables x,mean, with associated name, title, value and allowed\n",
"range"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "80cf79df",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:34:19.724504Z",
"iopub.status.busy": "2026-05-19T20:34:19.724372Z",
"iopub.status.idle": "2026-05-19T20:34:19.881786Z",
"shell.execute_reply": "2026-05-19T20:34:19.881165Z"
}
},
"outputs": [],
"source": [
"x = ROOT.RooRealVar(\"x\", \"x\", -10, 10)"
]
},
{
"cell_type": "markdown",
"id": "80202ad3",
"metadata": {},
"source": [
"Efficiency function eff(x;a,b)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "14c19a3f",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:34:19.883926Z",
"iopub.status.busy": "2026-05-19T20:34:19.883798Z",
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"shell.execute_reply": "2026-05-19T20:34:20.074873Z"
}
},
"outputs": [],
"source": [
"a = ROOT.RooRealVar(\"a\", \"a\", 0.4, 0, 1)\n",
"b = ROOT.RooRealVar(\"b\", \"b\", 5)\n",
"c = ROOT.RooRealVar(\"c\", \"c\", -1, -10, 10)\n",
"effFunc = ROOT.RooFormulaVar(\"effFunc\", \"(1-a)+a*cos((x-c)/b)\", [a, b, c, x])"
]
},
{
"cell_type": "markdown",
"id": "48f078b6",
"metadata": {},
"source": [
"Construct conditional efficiency pdf E(cut|x)\n",
"------------------------------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "b6b29817",
"metadata": {},
"source": [
"Acceptance state cut (1 or 0)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "b8646199",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:34:20.077633Z",
"iopub.status.busy": "2026-05-19T20:34:20.077490Z",
"iopub.status.idle": "2026-05-19T20:34:20.194164Z",
"shell.execute_reply": "2026-05-19T20:34:20.193421Z"
}
},
"outputs": [],
"source": [
"cut = ROOT.RooCategory(\"cut\", \"cutr\", {\"accept\": 1, \"reject\": 0})"
]
},
{
"cell_type": "markdown",
"id": "5db29665",
"metadata": {},
"source": [
"Construct efficiency pdf eff(cut|x)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "e55a247b",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:34:20.196025Z",
"iopub.status.busy": "2026-05-19T20:34:20.195894Z",
"iopub.status.idle": "2026-05-19T20:34:20.312690Z",
"shell.execute_reply": "2026-05-19T20:34:20.311992Z"
}
},
"outputs": [],
"source": [
"effPdf = ROOT.RooEfficiency(\"effPdf\", \"effPdf\", effFunc, cut, \"accept\")"
]
},
{
"cell_type": "markdown",
"id": "f93049cd",
"metadata": {},
"source": [
"Generate data (x, cut) from a toy model\n",
"-----------------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "19e55efd",
"metadata": {},
"source": [
"Construct global shape pdf shape(x) and product model(x,cut) = eff(cut|x)*shape(x)\n",
"(These are _only_ needed to generate some toy MC here to be used later)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "823c7a39",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:34:20.314733Z",
"iopub.status.busy": "2026-05-19T20:34:20.314586Z",
"iopub.status.idle": "2026-05-19T20:34:20.490693Z",
"shell.execute_reply": "2026-05-19T20:34:20.489991Z"
}
},
"outputs": [],
"source": [
"shapePdf = ROOT.RooPolynomial(\"shapePdf\", \"shapePdf\", x, [-0.095])\n",
"model = ROOT.RooProdPdf(\"model\", \"model\", {shapePdf}, Conditional=({effPdf}, {cut}))"
]
},
{
"cell_type": "markdown",
"id": "65461872",
"metadata": {},
"source": [
"Generate some toy data from model"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "75a4a776",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:34:20.492719Z",
"iopub.status.busy": "2026-05-19T20:34:20.492567Z",
"iopub.status.idle": "2026-05-19T20:34:20.643853Z",
"shell.execute_reply": "2026-05-19T20:34:20.643151Z"
}
},
"outputs": [],
"source": [
"data = model.generate({x, cut}, 10000)"
]
},
{
"cell_type": "markdown",
"id": "f293a9cc",
"metadata": {},
"source": [
"Fit conditional efficiency pdf to data\n",
"--------------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "2aa70c12",
"metadata": {},
"source": [
"Fit conditional efficiency pdf to data"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "bff70d28",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:34:20.645861Z",
"iopub.status.busy": "2026-05-19T20:34:20.645731Z",
"iopub.status.idle": "2026-05-19T20:34:20.860783Z",
"shell.execute_reply": "2026-05-19T20:34:20.860076Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:Fitting -- RooAbsPdf::fitTo(effPdf_over_effPdf_Int[cut]) fixing normalization set for coefficient determination to observables in data\n",
"[#1] INFO:Fitting -- using generic CPU library compiled with no vectorizations\n",
"[#1] INFO:Fitting -- Creation of NLL object took 767.433 μs\n",
"[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_effPdf_over_effPdf_Int[cut]_modelData) Summation contains a RooNLLVar, using its error level\n",
"[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n"
]
},
{
"data": {
"text/plain": [
""
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"effPdf.fitTo(data, ConditionalObservables={x}, PrintLevel=-1)"
]
},
{
"cell_type": "markdown",
"id": "fae0c592",
"metadata": {},
"source": [
"Plot fitted, data efficiency\n",
"--------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "9e6f755e",
"metadata": {},
"source": [
"Plot distribution of all events and accepted fraction of events on frame"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "fcf103e4",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:34:20.862428Z",
"iopub.status.busy": "2026-05-19T20:34:20.862294Z",
"iopub.status.idle": "2026-05-19T20:34:21.032028Z",
"shell.execute_reply": "2026-05-19T20:34:21.031584Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:Plotting -- RooTreeData::plotOn: plotting 8176 events out of 10000 total events\n"
]
},
{
"data": {
"text/plain": [
""
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"frame1 = x.frame(Bins=20, Title=\"Data (all, accepted)\")\n",
"data.plotOn(frame1)\n",
"data.plotOn(frame1, Cut=\"cut==cut::accept\", MarkerColor=\"r\", LineColor=\"r\")"
]
},
{
"cell_type": "markdown",
"id": "33235acf",
"metadata": {},
"source": [
"Plot accept/reject efficiency on data overlay fitted efficiency curve"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "5c33b2db",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:34:21.043558Z",
"iopub.status.busy": "2026-05-19T20:34:21.043425Z",
"iopub.status.idle": "2026-05-19T20:34:21.195521Z",
"shell.execute_reply": "2026-05-19T20:34:21.194843Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"frame2 = x.frame(Bins=20, Title=\"Fitted efficiency\")\n",
"data.plotOn(frame2, Efficiency=cut) # needs ROOT version >= 5.21\n",
"effFunc.plotOn(frame2, LineColor=\"r\")"
]
},
{
"cell_type": "markdown",
"id": "f696ac9a",
"metadata": {},
"source": [
"Draw all frames on a canvas"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "5573ba0a",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:34:21.197623Z",
"iopub.status.busy": "2026-05-19T20:34:21.197476Z",
"iopub.status.idle": "2026-05-19T20:34:21.411526Z",
"shell.execute_reply": "2026-05-19T20:34:21.410798Z"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Info in : png file rf701_efficiencyfit.png has been created\n"
]
}
],
"source": [
"ca = ROOT.TCanvas(\"rf701_efficiency\", \"rf701_efficiency\", 800, 400)\n",
"ca.Divide(2)\n",
"ca.cd(1)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"frame1.GetYaxis().SetTitleOffset(1.6)\n",
"frame1.Draw()\n",
"ca.cd(2)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"frame2.GetYaxis().SetTitleOffset(1.4)\n",
"frame2.Draw()\n",
"\n",
"ca.SaveAs(\"rf701_efficiencyfit.png\")"
]
},
{
"cell_type": "markdown",
"id": "e1dffc68",
"metadata": {},
"source": [
"Draw all canvases "
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "735de297",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:34:21.413227Z",
"iopub.status.busy": "2026-05-19T20:34:21.413100Z",
"iopub.status.idle": "2026-05-19T20:34:21.596244Z",
"shell.execute_reply": "2026-05-19T20:34:21.595531Z"
}
},
"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"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.12.12"
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"nbformat": 4,
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