{
"cells": [
{
"cell_type": "markdown",
"id": "fa13bbfc",
"metadata": {},
"source": [
"# rf703_effpdfprod\n",
"Special pdf's: using a product of an (acceptance) efficiency and a pdf as pdf\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": "315d1c0c",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:34:33.365042Z",
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"shell.execute_reply": "2026-05-19T20:34:34.316500Z"
}
},
"outputs": [],
"source": [
"import ROOT"
]
},
{
"cell_type": "markdown",
"id": "2da85f91",
"metadata": {},
"source": [
"Define observables and decay pdf\n",
"---------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "feaad1a7",
"metadata": {},
"source": [
"Declare observables"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "fec36ad7",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:34:34.319026Z",
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"shell.execute_reply": "2026-05-19T20:34:34.479823Z"
}
},
"outputs": [],
"source": [
"t = ROOT.RooRealVar(\"t\", \"t\", 0, 5)"
]
},
{
"cell_type": "markdown",
"id": "f86deb34",
"metadata": {},
"source": [
"Make pdf"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "d0e1e591",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:34:34.482215Z",
"iopub.status.busy": "2026-05-19T20:34:34.482091Z",
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"shell.execute_reply": "2026-05-19T20:34:34.607577Z"
}
},
"outputs": [],
"source": [
"tau = ROOT.RooRealVar(\"tau\", \"tau\", -1.54, -4, -0.1)\n",
"model = ROOT.RooExponential(\"model\", \"model\", t, tau)"
]
},
{
"cell_type": "markdown",
"id": "32ee4ca4",
"metadata": {},
"source": [
"Define efficiency function\n",
"---------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "3d9d80ac",
"metadata": {},
"source": [
"Use error function to simulate turn-on slope"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "152a8dca",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:34:34.610304Z",
"iopub.status.busy": "2026-05-19T20:34:34.610177Z",
"iopub.status.idle": "2026-05-19T20:34:34.792110Z",
"shell.execute_reply": "2026-05-19T20:34:34.791618Z"
}
},
"outputs": [],
"source": [
"eff = ROOT.RooFormulaVar(\"eff\", \"0.5*(TMath::Erf((t-1)/0.5)+1)\", [t])"
]
},
{
"cell_type": "markdown",
"id": "1bad1b18",
"metadata": {},
"source": [
"Define decay pdf with efficiency\n",
"---------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "278027f5",
"metadata": {},
"source": [
"Multiply pdf(t) with efficiency in t"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "2184cd7c",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:34:34.797753Z",
"iopub.status.busy": "2026-05-19T20:34:34.797597Z",
"iopub.status.idle": "2026-05-19T20:34:34.908134Z",
"shell.execute_reply": "2026-05-19T20:34:34.907365Z"
}
},
"outputs": [],
"source": [
"modelEff = ROOT.RooEffProd(\"modelEff\", \"model with efficiency\", model, eff)"
]
},
{
"cell_type": "markdown",
"id": "6f6cef68",
"metadata": {},
"source": [
"Plot efficiency, pdf\n",
"----------------------------------------"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "7c153e33",
"metadata": {
"collapsed": false,
"execution": {
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"shell.execute_reply": "2026-05-19T20:34:35.122931Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:NumericIntegration -- RooRealIntegral::init(modelEff_Int[t]) using numeric integrator RooIntegrator1D to calculate Int(t)\n"
]
}
],
"source": [
"frame1 = t.frame(Title=\"Efficiency\")\n",
"eff.plotOn(frame1, LineColor=\"r\")\n",
"\n",
"frame2 = t.frame(Title=\"Pdf with and without efficiency\")\n",
"\n",
"model.plotOn(frame2, LineStyle=\"--\")\n",
"modelEff.plotOn(frame2)"
]
},
{
"cell_type": "markdown",
"id": "725254d5",
"metadata": {},
"source": [
"Generate toy data, fit model eff to data\n",
"------------------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "7fabc14b",
"metadata": {},
"source": [
"Generate events. If the input pdf has an internal generator, internal generator\n",
"is used and an accept/reject sampling on the efficiency is applied."
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "c6a1cdee",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:34:35.125502Z",
"iopub.status.busy": "2026-05-19T20:34:35.125366Z",
"iopub.status.idle": "2026-05-19T20:34:35.272790Z",
"shell.execute_reply": "2026-05-19T20:34:35.272060Z"
}
},
"outputs": [],
"source": [
"data = modelEff.generate({t}, 10000)"
]
},
{
"cell_type": "markdown",
"id": "5b102e33",
"metadata": {},
"source": [
"Fit pdf. The normalization integral is calculated numerically."
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "664ec77b",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:34:35.274785Z",
"iopub.status.busy": "2026-05-19T20:34:35.274526Z",
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"shell.execute_reply": "2026-05-19T20:34:35.457010Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:Fitting -- RooAbsPdf::fitTo(modelEff_over_modelEff_Int[t]) 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 807.024 μs\n",
"[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_modelEff_over_modelEff_Int[t]_modelEffData) Summation contains a RooNLLVar, using its error level\n",
"[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n",
"[#1] INFO:NumericIntegration -- RooRealIntegral::init(modelEff_Int[t]) using numeric integrator RooIntegrator1D to calculate Int(t)\n"
]
},
{
"data": {
"text/plain": [
""
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"modelEff.fitTo(data, PrintLevel=-1)"
]
},
{
"cell_type": "markdown",
"id": "86346172",
"metadata": {},
"source": [
"Plot generated data and overlay fitted pdf"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "155c8afe",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:34:35.459818Z",
"iopub.status.busy": "2026-05-19T20:34:35.459679Z",
"iopub.status.idle": "2026-05-19T20:34:35.708066Z",
"shell.execute_reply": "2026-05-19T20:34:35.707635Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:NumericIntegration -- RooRealIntegral::init(modelEff_Int[t]) using numeric integrator RooIntegrator1D to calculate Int(t)\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"Info in : png file rf703_effpdfprod.png has been created\n"
]
}
],
"source": [
"frame3 = t.frame(Title=\"Fitted pdf with efficiency\")\n",
"data.plotOn(frame3)\n",
"modelEff.plotOn(frame3)\n",
"\n",
"c = ROOT.TCanvas(\"rf703_effpdfprod\", \"rf703_effpdfprod\", 1200, 400)\n",
"c.Divide(3)\n",
"c.cd(1)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"frame1.GetYaxis().SetTitleOffset(1.4)\n",
"frame1.Draw()\n",
"c.cd(2)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"frame2.GetYaxis().SetTitleOffset(1.6)\n",
"frame2.Draw()\n",
"c.cd(3)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"frame3.GetYaxis().SetTitleOffset(1.6)\n",
"frame3.Draw()\n",
"\n",
"c.SaveAs(\"rf703_effpdfprod.png\")"
]
},
{
"cell_type": "markdown",
"id": "fb9aeab0",
"metadata": {},
"source": [
"Draw all canvases "
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "f2f6eba5",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:34:35.717517Z",
"iopub.status.busy": "2026-05-19T20:34:35.717377Z",
"iopub.status.idle": "2026-05-19T20:34:35.898872Z",
"shell.execute_reply": "2026-05-19T20:34:35.898475Z"
}
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"\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": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
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