{
"cells": [
{
"cell_type": "markdown",
"id": "def58f45",
"metadata": {},
"source": [
"# rf105_funcbinding\n",
"'BASIC FUNCTIONALITY' RooFit tutorial macro #105\n",
"Demonstration of binding ROOT Math functions as RooFit functions\n",
"and pdfs\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 08:28 PM."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "9d677215",
"metadata": {
"collapsed": false,
"execution": {
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"shell.execute_reply": "2026-05-19T20:28:53.310672Z"
}
},
"outputs": [],
"source": [
"import ROOT"
]
},
{
"cell_type": "markdown",
"id": "af7d801b",
"metadata": {},
"source": [
"Bind ROOT TMath::Erf C function\n",
"---------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "0725fd7d",
"metadata": {},
"source": [
"Bind one-dimensional ROOT.TMath.Erf function as ROOT.RooAbsReal function"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "8f6889ea",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:28:53.313327Z",
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"shell.execute_reply": "2026-05-19T20:28:53.753739Z"
}
},
"outputs": [],
"source": [
"x = ROOT.RooRealVar(\"x\", \"x\", -3, 3)\n",
"erf = ROOT.RooFit.bindFunction(\"erf\", ROOT.TMath.Erf, x)"
]
},
{
"cell_type": "markdown",
"id": "cc43136a",
"metadata": {},
"source": [
"Print erf definition"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "c3b07a4b",
"metadata": {
"collapsed": false,
"execution": {
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"shell.execute_reply": "2026-05-19T20:28:53.865786Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"RooCFunction1Binding::erf[ function=(0x7ff7b2451000) x=x ] = 0\n"
]
}
],
"source": [
"erf.Print()"
]
},
{
"cell_type": "markdown",
"id": "a7afb780",
"metadata": {},
"source": [
"Plot erf on frame"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "a06155ce",
"metadata": {
"collapsed": false,
"execution": {
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"shell.execute_reply": "2026-05-19T20:28:54.037471Z"
}
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"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"frame1 = x.frame(Title=\"TMath.Erf bound as ROOT.RooFit function\")\n",
"erf.plotOn(frame1)"
]
},
{
"cell_type": "markdown",
"id": "b95d273d",
"metadata": {},
"source": [
"Bind ROOT::Math::beta_pdf C function\n",
"-----------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "8e0c58dc",
"metadata": {},
"source": [
"Bind pdf ROOT.Math.Beta with three variables as ROOT.RooAbsPdf function"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "db32801a",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:28:54.040069Z",
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"shell.execute_reply": "2026-05-19T20:28:54.175099Z"
}
},
"outputs": [],
"source": [
"x2 = ROOT.RooRealVar(\"x2\", \"x2\", 0, 0.999)\n",
"a = ROOT.RooRealVar(\"a\", \"a\", 5, 0, 10)\n",
"b = ROOT.RooRealVar(\"b\", \"b\", 2, 0, 10)\n",
"beta = ROOT.RooFit.bindPdf(\"beta\", ROOT.Math.beta_pdf, x2, a, b)"
]
},
{
"cell_type": "markdown",
"id": "675675b3",
"metadata": {},
"source": [
"Perf beta definition"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "5d7055e9",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:28:54.177823Z",
"iopub.status.busy": "2026-05-19T20:28:54.177692Z",
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"shell.execute_reply": "2026-05-19T20:28:54.281611Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"RooCFunction3PdfBinding::beta[ function=ROOT::Math::beta_pdf x=x2 a=a b=b ] = 0.934689\n"
]
}
],
"source": [
"beta.Print()"
]
},
{
"cell_type": "markdown",
"id": "0aaba49e",
"metadata": {},
"source": [
"Generate some events and fit"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "f08c4dcb",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:28:54.283876Z",
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"shell.execute_reply": "2026-05-19T20:28:54.538240Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:NumericIntegration -- RooRealIntegral::init(beta_Int[x2]) using numeric integrator RooIntegrator1D to calculate Int(x2)\n",
"[#1] INFO:NumericIntegration -- RooRealIntegral::init(beta_Int[x2]) using numeric integrator RooIntegrator1D to calculate Int(x2)\n"
]
},
{
"data": {
"text/plain": [
""
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:Fitting -- RooAbsPdf::fitTo(beta_over_beta_Int[x2]) 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 786.462 μs\n",
"[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_beta_over_beta_Int[x2]_betaData) 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(beta_Int[x2]) using numeric integrator RooIntegrator1D to calculate Int(x2)\n"
]
}
],
"source": [
"data = beta.generate({x2}, 10000)\n",
"beta.fitTo(data, PrintLevel=-1)"
]
},
{
"cell_type": "markdown",
"id": "7dca6f80",
"metadata": {},
"source": [
"Plot data and pdf on frame"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "44729441",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:28:54.540803Z",
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"shell.execute_reply": "2026-05-19T20:28:54.698295Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:NumericIntegration -- RooRealIntegral::init(beta_Int[x2]) using numeric integrator RooIntegrator1D to calculate Int(x2)\n"
]
},
{
"data": {
"text/plain": [
""
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"frame2 = x2.frame(Title=\"ROOT.Math.Beta bound as ROOT.RooFit pdf\")\n",
"data.plotOn(frame2)\n",
"beta.plotOn(frame2)"
]
},
{
"cell_type": "markdown",
"id": "c9695a6a",
"metadata": {},
"source": [
"Bind ROOT TF1 as RooFit function\n",
"---------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "693a5d55",
"metadata": {},
"source": [
"Create a ROOT TF1 function"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "cf9da470",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:28:54.700970Z",
"iopub.status.busy": "2026-05-19T20:28:54.700842Z",
"iopub.status.idle": "2026-05-19T20:28:54.822408Z",
"shell.execute_reply": "2026-05-19T20:28:54.821711Z"
}
},
"outputs": [],
"source": [
"fa1 = ROOT.TF1(\"fa1\", \"sin(x)/x\", 0, 10)"
]
},
{
"cell_type": "markdown",
"id": "e1bed7c1",
"metadata": {},
"source": [
"Create an observable"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "06f7f098",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:28:54.824254Z",
"iopub.status.busy": "2026-05-19T20:28:54.824128Z",
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"shell.execute_reply": "2026-05-19T20:28:54.926867Z"
}
},
"outputs": [],
"source": [
"x3 = ROOT.RooRealVar(\"x3\", \"x3\", 0.01, 20)"
]
},
{
"cell_type": "markdown",
"id": "419e1fdd",
"metadata": {},
"source": [
"Create binding of TF1 object to above observable"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "d18e4780",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:28:54.929518Z",
"iopub.status.busy": "2026-05-19T20:28:54.929388Z",
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"shell.execute_reply": "2026-05-19T20:28:55.037982Z"
}
},
"outputs": [],
"source": [
"rfa1 = ROOT.RooFit.bindFunction(fa1, x3)"
]
},
{
"cell_type": "markdown",
"id": "bea47f16",
"metadata": {},
"source": [
"Print rfa1 definition"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "6280f76e",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:28:55.040909Z",
"iopub.status.busy": "2026-05-19T20:28:55.040786Z",
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"shell.execute_reply": "2026-05-19T20:28:55.143931Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"RooTFnBinding::fa1[ TFn={fa1=sin(x)/x} obs=(x3) params=() ] = -0.0547936\n"
]
}
],
"source": [
"rfa1.Print()"
]
},
{
"cell_type": "markdown",
"id": "1e2b6d3e",
"metadata": {},
"source": [
"Make plot frame in observable, TF1 binding function"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "cb130323",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:28:55.146305Z",
"iopub.status.busy": "2026-05-19T20:28:55.146182Z",
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"shell.execute_reply": "2026-05-19T20:28:55.372945Z"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Info in : png file rf105_funcbinding.png has been created\n"
]
}
],
"source": [
"frame3 = x3.frame(Title=\"TF1 bound as ROOT.RooFit function\")\n",
"rfa1.plotOn(frame3)\n",
"\n",
"c = ROOT.TCanvas(\"rf105_funcbinding\", \"rf105_funcbinding\", 1200, 400)\n",
"c.Divide(3)\n",
"c.cd(1)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"frame1.GetYaxis().SetTitleOffset(1.6)\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(\"rf105_funcbinding.png\")"
]
},
{
"cell_type": "markdown",
"id": "4833846a",
"metadata": {},
"source": [
"Draw all canvases "
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "dff2250e",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:28:55.375620Z",
"iopub.status.busy": "2026-05-19T20:28:55.375478Z",
"iopub.status.idle": "2026-05-19T20:28:55.561305Z",
"shell.execute_reply": "2026-05-19T20:28:55.560575Z"
}
},
"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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