{
"cells": [
{
"cell_type": "markdown",
"id": "7e1186f4",
"metadata": {},
"source": [
"# rf302_utilfuncs\n",
"Multidimensional models: utility functions classes available for use in tailoring of\n",
"composite (multidimensional) 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 08:30 PM."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "431ecad8",
"metadata": {
"collapsed": false,
"execution": {
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"shell.execute_reply": "2026-05-19T20:30:33.278170Z"
}
},
"outputs": [],
"source": [
"import ROOT"
]
},
{
"cell_type": "markdown",
"id": "23fd4aa6",
"metadata": {},
"source": [
"Create observables, parameters\n",
"-----------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "91597599",
"metadata": {},
"source": [
"Create observables"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "50085fe4",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:33.280636Z",
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"shell.execute_reply": "2026-05-19T20:30:33.438970Z"
}
},
"outputs": [],
"source": [
"x = ROOT.RooRealVar(\"x\", \"x\", -5, 5)\n",
"y = ROOT.RooRealVar(\"y\", \"y\", -5, 5)"
]
},
{
"cell_type": "markdown",
"id": "925f2ee9",
"metadata": {},
"source": [
"Create parameters"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "e8e11095",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:33.441267Z",
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"shell.execute_reply": "2026-05-19T20:30:33.554084Z"
}
},
"outputs": [],
"source": [
"a0 = ROOT.RooRealVar(\"a0\", \"a0\", -1.5, -5, 5)\n",
"a1 = ROOT.RooRealVar(\"a1\", \"a1\", -0.5, -1, 1)\n",
"sigma = ROOT.RooRealVar(\"sigma\", \"width of gaussian\", 0.5)"
]
},
{
"cell_type": "markdown",
"id": "d385ae1c",
"metadata": {},
"source": [
"Using RooFormulaVar to tailor pdf\n",
"-----------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "0dc40016",
"metadata": {},
"source": [
"Create interpreted function f(y) = a0 - a1*sqrt(10*abs(y))"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "e4227a37",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:33.556358Z",
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"shell.execute_reply": "2026-05-19T20:30:33.740795Z"
}
},
"outputs": [],
"source": [
"fy_1 = ROOT.RooFormulaVar(\"fy_1\", \"a0-a1*sqrt(10*abs(y))\", [y, a0, a1])"
]
},
{
"cell_type": "markdown",
"id": "06cf77d5",
"metadata": {},
"source": [
"Create gauss(x,f(y),s)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "acf85562",
"metadata": {
"collapsed": false,
"execution": {
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"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#0] WARNING:InputArguments -- The parameter 'sigma' with range [-inf, inf] of the RooGaussian 'model_1' exceeds the safe range of (0, inf). Advise to limit its range.\n"
]
}
],
"source": [
"model_1 = ROOT.RooGaussian(\"model_1\", \"Gaussian with shifting mean\", x, fy_1, sigma)"
]
},
{
"cell_type": "markdown",
"id": "482e8587",
"metadata": {},
"source": [
"Using RooPolyVar to tailor pdf\n",
"-----------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "585da505",
"metadata": {},
"source": [
"Create polynomial function f(y) = a0 + a1*y"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "caef230c",
"metadata": {
"collapsed": false,
"execution": {
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"shell.execute_reply": "2026-05-19T20:30:33.977620Z"
}
},
"outputs": [],
"source": [
"fy_2 = ROOT.RooPolyVar(\"fy_2\", \"fy_2\", y, [a0, a1])"
]
},
{
"cell_type": "markdown",
"id": "a9963e1c",
"metadata": {},
"source": [
"Create gauss(x,f(y),s)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "51634fc7",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:33.979981Z",
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"shell.execute_reply": "2026-05-19T20:30:34.083362Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#0] WARNING:InputArguments -- The parameter 'sigma' with range [-inf, inf] of the RooGaussian 'model_2' exceeds the safe range of (0, inf). Advise to limit its range.\n"
]
}
],
"source": [
"model_2 = ROOT.RooGaussian(\"model_2\", \"Gaussian with shifting mean\", x, fy_2, sigma)"
]
},
{
"cell_type": "markdown",
"id": "d3a42dbc",
"metadata": {},
"source": [
"Using RooAddition to tailor pdf\n",
"-----------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "6ff074b3",
"metadata": {},
"source": [
"Create sum function f(y) = a0 + y"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "a4146fe9",
"metadata": {
"collapsed": false,
"execution": {
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"shell.execute_reply": "2026-05-19T20:30:34.194867Z"
}
},
"outputs": [],
"source": [
"fy_3 = ROOT.RooAddition(\"fy_3\", \"a0+y\", [a0, y])"
]
},
{
"cell_type": "markdown",
"id": "a6cbcc5a",
"metadata": {},
"source": [
"Create gauss(x,f(y),s)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "747f09ce",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:34.197066Z",
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"shell.execute_reply": "2026-05-19T20:30:34.300368Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#0] WARNING:InputArguments -- The parameter 'sigma' with range [-inf, inf] of the RooGaussian 'model_3' exceeds the safe range of (0, inf). Advise to limit its range.\n"
]
}
],
"source": [
"model_3 = ROOT.RooGaussian(\"model_3\", \"Gaussian with shifting mean\", x, fy_3, sigma)"
]
},
{
"cell_type": "markdown",
"id": "b4610922",
"metadata": {},
"source": [
"Using RooProduct to tailor pdf\n",
"-----------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "8db1d69b",
"metadata": {},
"source": [
"Create product function f(y) = a1*y"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "34b8249e",
"metadata": {
"collapsed": false,
"execution": {
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"shell.execute_reply": "2026-05-19T20:30:34.411879Z"
}
},
"outputs": [],
"source": [
"fy_4 = ROOT.RooProduct(\"fy_4\", \"a1*y\", [a1, y])"
]
},
{
"cell_type": "markdown",
"id": "fb0dd3d3",
"metadata": {},
"source": [
"Create gauss(x,f(y),s)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "69fc36bb",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:34.414191Z",
"iopub.status.busy": "2026-05-19T20:30:34.414059Z",
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"shell.execute_reply": "2026-05-19T20:30:34.517534Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#0] WARNING:InputArguments -- The parameter 'sigma' with range [-inf, inf] of the RooGaussian 'model_4' exceeds the safe range of (0, inf). Advise to limit its range.\n"
]
}
],
"source": [
"model_4 = ROOT.RooGaussian(\"model_4\", \"Gaussian with shifting mean\", x, fy_4, sigma)"
]
},
{
"cell_type": "markdown",
"id": "17f07ee2",
"metadata": {},
"source": [
"Plot all pdfs\n",
"----------------------------"
]
},
{
"cell_type": "markdown",
"id": "3c4ca5be",
"metadata": {},
"source": [
"Make two-dimensional plots in x vs y"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "4f32e7fc",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:34.519556Z",
"iopub.status.busy": "2026-05-19T20:30:34.519433Z",
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"shell.execute_reply": "2026-05-19T20:30:34.696945Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:NumericIntegration -- RooRealIntegral::init(model_1_Int[x,y]) using numeric integrator RooIntegrator1D to calculate Int(y)\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:NumericIntegration -- RooRealIntegral::init(model_2_Int[x,y]) using numeric integrator RooIntegrator1D to calculate Int(y)\n",
"[#1] INFO:NumericIntegration -- RooRealIntegral::init(model_3_Int[x,y]) using numeric integrator RooIntegrator1D to calculate Int(y)\n",
"[#1] INFO:NumericIntegration -- RooRealIntegral::init(model_4_Int[x,y]) using numeric integrator RooIntegrator1D to calculate Int(y)\n"
]
}
],
"source": [
"hh_model_1 = model_1.createHistogram(\"hh_model_1\", x, Binning=50, YVar=dict(var=y, Binning=50))\n",
"hh_model_2 = model_2.createHistogram(\"hh_model_2\", x, Binning=50, YVar=dict(var=y, Binning=50))\n",
"hh_model_3 = model_3.createHistogram(\"hh_model_3\", x, Binning=50, YVar=dict(var=y, Binning=50))\n",
"hh_model_4 = model_4.createHistogram(\"hh_model_4\", x, Binning=50, YVar=dict(var=y, Binning=50))\n",
"hh_model_1.SetLineColor(\"kBlue\")\n",
"hh_model_2.SetLineColor(\"kBlue\")\n",
"hh_model_3.SetLineColor(\"kBlue\")\n",
"hh_model_4.SetLineColor(\"kBlue\")"
]
},
{
"cell_type": "markdown",
"id": "f928d878",
"metadata": {},
"source": [
"Make canvas and draw ROOT.RooPlots"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "ced0acdd",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:34.699212Z",
"iopub.status.busy": "2026-05-19T20:30:34.699096Z",
"iopub.status.idle": "2026-05-19T20:30:34.942173Z",
"shell.execute_reply": "2026-05-19T20:30:34.941726Z"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Info in : png file rf302_utilfuncs.png has been created\n"
]
}
],
"source": [
"c = ROOT.TCanvas(\"rf302_utilfuncs\", \"rf302_utilfuncs\", 800, 800)\n",
"c.Divide(2, 2)\n",
"c.cd(1)\n",
"ROOT.gPad.SetLeftMargin(0.20)\n",
"hh_model_1.GetZaxis().SetTitleOffset(2.5)\n",
"hh_model_1.Draw(\"surf\")\n",
"c.cd(2)\n",
"ROOT.gPad.SetLeftMargin(0.20)\n",
"hh_model_2.GetZaxis().SetTitleOffset(2.5)\n",
"hh_model_2.Draw(\"surf\")\n",
"c.cd(3)\n",
"ROOT.gPad.SetLeftMargin(0.20)\n",
"hh_model_3.GetZaxis().SetTitleOffset(2.5)\n",
"hh_model_3.Draw(\"surf\")\n",
"c.cd(4)\n",
"ROOT.gPad.SetLeftMargin(0.20)\n",
"hh_model_4.GetZaxis().SetTitleOffset(2.5)\n",
"hh_model_4.Draw(\"surf\")\n",
"\n",
"c.SaveAs(\"rf302_utilfuncs.png\")"
]
},
{
"cell_type": "markdown",
"id": "7accddf1",
"metadata": {},
"source": [
"Draw all canvases "
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "7be2c56b",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:34.950400Z",
"iopub.status.busy": "2026-05-19T20:30:34.950250Z",
"iopub.status.idle": "2026-05-19T20:30:35.148796Z",
"shell.execute_reply": "2026-05-19T20:30:35.148273Z"
}
},
"outputs": [
{
"data": {
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"\n",
"\n"
],
"text/plain": [
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]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from ROOT import gROOT \n",
"gROOT.GetListOfCanvases().Draw()"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
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},
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