{
"cells": [
{
"cell_type": "markdown",
"id": "1a40399b",
"metadata": {},
"source": [
"# rf304_uncorrprod\n",
"Multidimensional models: simple uncorrelated multi-dimensional pdfs\n",
"\n",
"`pdf = gauss(x,mx,sx) * gauss(y,my,sy)`\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": "2f8aa854",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:40.763751Z",
"iopub.status.busy": "2026-05-19T20:30:40.763634Z",
"iopub.status.idle": "2026-05-19T20:30:41.744805Z",
"shell.execute_reply": "2026-05-19T20:30:41.723921Z"
}
},
"outputs": [],
"source": [
"import ROOT"
]
},
{
"cell_type": "markdown",
"id": "b0ec6070",
"metadata": {},
"source": [
"Create component pdfs in x and y\n",
"----------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "592e45c3",
"metadata": {},
"source": [
"Create two pdfs gaussx(x,meanx,sigmax) gaussy(y,meany,sigmay) and its\n",
"variables"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "237c2335",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:41.761461Z",
"iopub.status.busy": "2026-05-19T20:30:41.761297Z",
"iopub.status.idle": "2026-05-19T20:30:41.945150Z",
"shell.execute_reply": "2026-05-19T20:30:41.944468Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#0] WARNING:InputArguments -- The parameter 'sigmax' with range [-inf, inf] of the RooGaussian 'gaussx' exceeds the safe range of (0, inf). Advise to limit its range.\n",
"[#0] WARNING:InputArguments -- The parameter 'sigmay' with range [-inf, inf] of the RooGaussian 'gaussy' exceeds the safe range of (0, inf). Advise to limit its range.\n"
]
}
],
"source": [
"x = ROOT.RooRealVar(\"x\", \"x\", -5, 5)\n",
"y = ROOT.RooRealVar(\"y\", \"y\", -5, 5)\n",
"\n",
"meanx = ROOT.RooRealVar(\"mean1\", \"mean of gaussian x\", 2)\n",
"meany = ROOT.RooRealVar(\"mean2\", \"mean of gaussian y\", -2)\n",
"sigmax = ROOT.RooRealVar(\"sigmax\", \"width of gaussian x\", 1)\n",
"sigmay = ROOT.RooRealVar(\"sigmay\", \"width of gaussian y\", 5)\n",
"\n",
"gaussx = ROOT.RooGaussian(\"gaussx\", \"gaussian PDF\", x, meanx, sigmax)\n",
"gaussy = ROOT.RooGaussian(\"gaussy\", \"gaussian PDF\", y, meany, sigmay)"
]
},
{
"cell_type": "markdown",
"id": "8ec464b0",
"metadata": {},
"source": [
"Construct uncorrelated product pdf\n",
"-------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "b7221dd3",
"metadata": {},
"source": [
"Multiply gaussx and gaussy into a two-dimensional pdf gaussxy"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "64ac3a92",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:41.947016Z",
"iopub.status.busy": "2026-05-19T20:30:41.946884Z",
"iopub.status.idle": "2026-05-19T20:30:42.127294Z",
"shell.execute_reply": "2026-05-19T20:30:42.126649Z"
}
},
"outputs": [],
"source": [
"gaussxy = ROOT.RooProdPdf(\"gaussxy\", \"gaussx*gaussy\", [gaussx, gaussy])"
]
},
{
"cell_type": "markdown",
"id": "81c62547",
"metadata": {},
"source": [
"Sample pdf, plot projection on x and y\n",
"---------------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "960b1b2b",
"metadata": {},
"source": [
"Generate 10000 events in x and y from gaussxy"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "7a372139",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:42.129462Z",
"iopub.status.busy": "2026-05-19T20:30:42.129334Z",
"iopub.status.idle": "2026-05-19T20:30:42.263375Z",
"shell.execute_reply": "2026-05-19T20:30:42.262727Z"
}
},
"outputs": [],
"source": [
"data = gaussxy.generate({x, y}, 10000)"
]
},
{
"cell_type": "markdown",
"id": "2d9c818f",
"metadata": {},
"source": [
"Plot x distribution of data and projection of gaussxy x = Int(dy)\n",
"gaussxy(x,y)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "67b43214",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:42.265455Z",
"iopub.status.busy": "2026-05-19T20:30:42.265328Z",
"iopub.status.idle": "2026-05-19T20:30:42.459047Z",
"shell.execute_reply": "2026-05-19T20:30:42.458342Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:Plotting -- RooAbsReal::plotOn(gaussxy) plot on x integrates over variables (y)\n"
]
},
{
"data": {
"text/plain": [
""
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"xframe = x.frame(Title=\"X projection of gauss(x)*gauss(y)\")\n",
"data.plotOn(xframe)\n",
"gaussxy.plotOn(xframe)"
]
},
{
"cell_type": "markdown",
"id": "e20af9b6",
"metadata": {},
"source": [
"Plot x distribution of data and projection of gaussxy y = Int(dx)\n",
"gaussxy(x,y)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "c044832a",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:42.460924Z",
"iopub.status.busy": "2026-05-19T20:30:42.460798Z",
"iopub.status.idle": "2026-05-19T20:30:42.567101Z",
"shell.execute_reply": "2026-05-19T20:30:42.566383Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:Plotting -- RooAbsReal::plotOn(gaussxy) plot on y integrates over variables (x)\n"
]
},
{
"data": {
"text/plain": [
""
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"yframe = y.frame(Title=\"Y projection of gauss(x)*gauss(y)\")\n",
"data.plotOn(yframe)\n",
"gaussxy.plotOn(yframe)"
]
},
{
"cell_type": "markdown",
"id": "7853d9c2",
"metadata": {},
"source": [
"Make canvas and draw ROOT.RooPlots"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "fb5dd602",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:42.569245Z",
"iopub.status.busy": "2026-05-19T20:30:42.569118Z",
"iopub.status.idle": "2026-05-19T20:30:42.800314Z",
"shell.execute_reply": "2026-05-19T20:30:42.799318Z"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Info in : png file rf304_uncorrprod.png has been created\n"
]
}
],
"source": [
"c = ROOT.TCanvas(\"rf304_uncorrprod\", \"rf304_uncorrprod\", 800, 400)\n",
"c.Divide(2)\n",
"c.cd(1)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"xframe.GetYaxis().SetTitleOffset(1.4)\n",
"xframe.Draw()\n",
"c.cd(2)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"yframe.GetYaxis().SetTitleOffset(1.4)\n",
"yframe.Draw()\n",
"\n",
"c.SaveAs(\"rf304_uncorrprod.png\")"
]
},
{
"cell_type": "markdown",
"id": "965b0bbb",
"metadata": {},
"source": [
"Draw all canvases "
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "971fbec3",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:42.801806Z",
"iopub.status.busy": "2026-05-19T20:30:42.801669Z",
"iopub.status.idle": "2026-05-19T20:30:42.985303Z",
"shell.execute_reply": "2026-05-19T20:30:42.984542Z"
}
},
"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
}