{
"cells": [
{
"cell_type": "markdown",
"id": "ea995c21",
"metadata": {},
"source": [
"# rf702_efficiencyfit_2D\n",
"Special pdf's: unbinned maximum likelihood fit of an efficiency eff(x) function\n",
"to a dataset D(x,cut), cut is a category encoding a selection whose 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": "59429992",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:34:26.331276Z",
"iopub.status.busy": "2026-05-19T20:34:26.331162Z",
"iopub.status.idle": "2026-05-19T20:34:27.681040Z",
"shell.execute_reply": "2026-05-19T20:34:27.680641Z"
}
},
"outputs": [],
"source": [
"import ROOT\n",
"\n",
"\n",
"flat = False"
]
},
{
"cell_type": "markdown",
"id": "0d69a793",
"metadata": {},
"source": [
"Construct efficiency function e(x,y)\n",
"-----------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "b7c35e38",
"metadata": {},
"source": [
"Declare variables x,mean, with associated name, title, value and allowed\n",
"range"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "38667811",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:34:27.710998Z",
"iopub.status.busy": "2026-05-19T20:34:27.710848Z",
"iopub.status.idle": "2026-05-19T20:34:27.958172Z",
"shell.execute_reply": "2026-05-19T20:34:27.957797Z"
}
},
"outputs": [],
"source": [
"x = ROOT.RooRealVar(\"x\", \"x\", -10, 10)\n",
"y = ROOT.RooRealVar(\"y\", \"y\", -10, 10)"
]
},
{
"cell_type": "markdown",
"id": "af356eaa",
"metadata": {},
"source": [
"Efficiency function eff(x;a,b)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "0295a022",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:34:27.996006Z",
"iopub.status.busy": "2026-05-19T20:34:27.995854Z",
"iopub.status.idle": "2026-05-19T20:34:28.213542Z",
"shell.execute_reply": "2026-05-19T20:34:28.213010Z"
}
},
"outputs": [],
"source": [
"ax = ROOT.RooRealVar(\"ax\", \"ay\", 0.6, 0, 1)\n",
"bx = ROOT.RooRealVar(\"bx\", \"by\", 5)\n",
"cx = ROOT.RooRealVar(\"cx\", \"cy\", -1, -10, 10)\n",
"\n",
"ay = ROOT.RooRealVar(\"ay\", \"ay\", 0.2, 0, 1)\n",
"by = ROOT.RooRealVar(\"by\", \"by\", 5)\n",
"cy = ROOT.RooRealVar(\"cy\", \"cy\", -1, -10, 10)\n",
"\n",
"effFunc = ROOT.RooFormulaVar(\n",
" \"effFunc\", \"((1-ax)+ax*cos((x-cx)/bx))*((1-ay)+ay*cos((y-cy)/by))\", [ax, bx, cx, x, ay, by, cy, y]\n",
")"
]
},
{
"cell_type": "markdown",
"id": "217b6f1e",
"metadata": {},
"source": [
"Acceptance state cut (1 or 0)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "85de2a5d",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:34:28.215538Z",
"iopub.status.busy": "2026-05-19T20:34:28.215408Z",
"iopub.status.idle": "2026-05-19T20:34:28.333037Z",
"shell.execute_reply": "2026-05-19T20:34:28.332371Z"
}
},
"outputs": [],
"source": [
"cut = ROOT.RooCategory(\"cut\", \"cutr\", {\"accept\": 1, \"reject\": 0})"
]
},
{
"cell_type": "markdown",
"id": "60ec8e7c",
"metadata": {},
"source": [
"Construct conditional efficiency pdf E(cut|x,y)\n",
"---------------------------------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "0019835c",
"metadata": {},
"source": [
"Construct efficiency pdf eff(cut|x)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "46c965d4",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:34:28.334894Z",
"iopub.status.busy": "2026-05-19T20:34:28.334759Z",
"iopub.status.idle": "2026-05-19T20:34:28.451486Z",
"shell.execute_reply": "2026-05-19T20:34:28.450992Z"
}
},
"outputs": [],
"source": [
"effPdf = ROOT.RooEfficiency(\"effPdf\", \"effPdf\", effFunc, cut, \"accept\")"
]
},
{
"cell_type": "markdown",
"id": "e51eb637",
"metadata": {},
"source": [
"Generate data(x,y,cut) from a toy model\n",
"-------------------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "bb3eb352",
"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": "a7c716c1",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:34:28.453216Z",
"iopub.status.busy": "2026-05-19T20:34:28.453096Z",
"iopub.status.idle": "2026-05-19T20:34:28.634238Z",
"shell.execute_reply": "2026-05-19T20:34:28.633628Z"
}
},
"outputs": [],
"source": [
"shapePdfX = ROOT.RooPolynomial(\"shapePdfX\", \"shapePdfX\", x, [0 if flat else -0.095])\n",
"shapePdfY = ROOT.RooPolynomial(\"shapePdfY\", \"shapePdfY\", y, [0 if flat else +0.095])\n",
"shapePdf = ROOT.RooProdPdf(\"shapePdf\", \"shapePdf\", [shapePdfX, shapePdfY])\n",
"model = ROOT.RooProdPdf(\"model\", \"model\", {shapePdf}, Conditional=({effPdf}, {cut}))"
]
},
{
"cell_type": "markdown",
"id": "10e89fae",
"metadata": {},
"source": [
"Generate some toy data from model"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "7ce044e9",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:34:28.635783Z",
"iopub.status.busy": "2026-05-19T20:34:28.635652Z",
"iopub.status.idle": "2026-05-19T20:34:28.912639Z",
"shell.execute_reply": "2026-05-19T20:34:28.890774Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#0] WARNING:Generation -- RooAcceptReject::ctor(effPdf_Int[]_Norm[cut]) WARNING: performing accept/reject sampling on a p.d.f in 2 dimensions without prior knowledge on maximum value of p.d.f. Determining maximum value by taking 200000 trial samples. If p.d.f contains sharp peaks smaller than average distance between trial sampling points these may be missed and p.d.f. may be sampled incorrectly.\n",
"[#0] WARNING:Generation -- RooAcceptReject::ctor(effPdf_Int[]_Norm[cut]): WARNING: 200000 trial samples requested by p.d.f for 2-dimensional accept/reject sampling, this may take some time\n"
]
}
],
"source": [
"data = model.generate({x, y, cut}, 10000)"
]
},
{
"cell_type": "markdown",
"id": "967d3da0",
"metadata": {},
"source": [
"Fit conditional efficiency pdf to data\n",
"--------------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "33cebed3",
"metadata": {},
"source": [
"Fit conditional efficiency pdf to data"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "e4bcea96",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:34:28.947224Z",
"iopub.status.busy": "2026-05-19T20:34:28.947067Z",
"iopub.status.idle": "2026-05-19T20:34:29.229978Z",
"shell.execute_reply": "2026-05-19T20:34:29.229379Z"
}
},
"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 853.164 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, y}, PrintLevel=-1)"
]
},
{
"cell_type": "markdown",
"id": "0ecabcf4",
"metadata": {},
"source": [
"Plot fitted, data efficiency\n",
"--------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "5a3476d3",
"metadata": {},
"source": [
"Make 2D histograms of all data, data and efficiency function"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "90991c82",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:34:29.231530Z",
"iopub.status.busy": "2026-05-19T20:34:29.231408Z",
"iopub.status.idle": "2026-05-19T20:34:29.419932Z",
"shell.execute_reply": "2026-05-19T20:34:29.411637Z"
}
},
"outputs": [],
"source": [
"hh_data_all = data.createHistogram(\"hh_data_all\", x, Binning=8, YVar=dict(var=y, Binning=8))\n",
"hh_data_sel = data.createHistogram(\"hh_data_sel\", x, Binning=8, YVar=dict(var=y, Binning=8), Cut=\"cut==cut::accept\")\n",
"hh_eff = effFunc.createHistogram(\"hh_eff\", x, Binning=50, YVar=dict(var=y, Binning=50))"
]
},
{
"cell_type": "markdown",
"id": "5f5d4459",
"metadata": {},
"source": [
"Some adjustsment for good visualization"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "3fae2de1",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:34:29.436028Z",
"iopub.status.busy": "2026-05-19T20:34:29.435890Z",
"iopub.status.idle": "2026-05-19T20:34:29.553332Z",
"shell.execute_reply": "2026-05-19T20:34:29.552265Z"
}
},
"outputs": [],
"source": [
"hh_data_all.SetMinimum(0)\n",
"hh_data_sel.SetMinimum(0)\n",
"hh_eff.SetMinimum(0)\n",
"hh_eff.SetLineColor(\"kBlue\")"
]
},
{
"cell_type": "markdown",
"id": "7568a268",
"metadata": {},
"source": [
"Draw all frames on a canvas"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "0d071457",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:34:29.554880Z",
"iopub.status.busy": "2026-05-19T20:34:29.554753Z",
"iopub.status.idle": "2026-05-19T20:34:29.795955Z",
"shell.execute_reply": "2026-05-19T20:34:29.793870Z"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Info in : png file rf702_efficiency_2D.png has been created\n"
]
}
],
"source": [
"ca = ROOT.TCanvas(\"rf702_efficiency_2D\", \"rf702_efficiency_2D\", 1200, 400)\n",
"ca.Divide(3)\n",
"ca.cd(1)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"hh_data_all.GetZaxis().SetTitleOffset(1.8)\n",
"hh_data_all.Draw(\"lego\")\n",
"ca.cd(2)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"hh_data_sel.GetZaxis().SetTitleOffset(1.8)\n",
"hh_data_sel.Draw(\"lego\")\n",
"ca.cd(3)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"hh_eff.GetZaxis().SetTitleOffset(1.8)\n",
"hh_eff.Draw(\"surf\")\n",
"\n",
"ca.SaveAs(\"rf702_efficiency_2D.png\")"
]
},
{
"cell_type": "markdown",
"id": "0f346f4d",
"metadata": {},
"source": [
"Draw all canvases "
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "66f18e61",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:34:29.810252Z",
"iopub.status.busy": "2026-05-19T20:34:29.810121Z",
"iopub.status.idle": "2026-05-19T20:34:30.002556Z",
"shell.execute_reply": "2026-05-19T20:34:30.001908Z"
}
},
"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"
}
},
"nbformat": 4,
"nbformat_minor": 5
}