{
"cells": [
{
"cell_type": "markdown",
"id": "8f9d3edf",
"metadata": {},
"source": [
"# rf305_condcorrprod\n",
"Multidimensional models: multi-dimensional pdfs with conditional pdfs in product\n",
"\n",
"`pdf = gauss(x,f(y),sx | y ) * gauss(y,ms,sx)` with `f(y) = a0 + a1*y`\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": "23aa5f86",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:45.001363Z",
"iopub.status.busy": "2026-05-19T20:30:45.001242Z",
"iopub.status.idle": "2026-05-19T20:30:45.973130Z",
"shell.execute_reply": "2026-05-19T20:30:45.972460Z"
}
},
"outputs": [],
"source": [
"import ROOT"
]
},
{
"cell_type": "markdown",
"id": "26101420",
"metadata": {},
"source": [
"Create conditional pdf gx(x|y)\n",
"-----------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "0e36c5ea",
"metadata": {},
"source": [
"Create observables"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "def12f0b",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:45.975223Z",
"iopub.status.busy": "2026-05-19T20:30:45.975097Z",
"iopub.status.idle": "2026-05-19T20:30:46.137310Z",
"shell.execute_reply": "2026-05-19T20:30:46.136913Z"
}
},
"outputs": [],
"source": [
"x = ROOT.RooRealVar(\"x\", \"x\", -5, 5)\n",
"y = ROOT.RooRealVar(\"y\", \"y\", -5, 5)"
]
},
{
"cell_type": "markdown",
"id": "04d62f33",
"metadata": {},
"source": [
"Create function f(y) = a0 + a1*y"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "2c9a143b",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:46.160479Z",
"iopub.status.busy": "2026-05-19T20:30:46.160330Z",
"iopub.status.idle": "2026-05-19T20:30:46.342743Z",
"shell.execute_reply": "2026-05-19T20:30:46.342330Z"
}
},
"outputs": [],
"source": [
"a0 = ROOT.RooRealVar(\"a0\", \"a0\", -0.5, -5, 5)\n",
"a1 = ROOT.RooRealVar(\"a1\", \"a1\", -0.5, -1, 1)\n",
"fy = ROOT.RooPolyVar(\"fy\", \"fy\", y, [a0, a1])"
]
},
{
"cell_type": "markdown",
"id": "0c4adffa",
"metadata": {},
"source": [
"Create gaussx(x,f(y),sx)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "fa9fd067",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:46.353392Z",
"iopub.status.busy": "2026-05-19T20:30:46.353249Z",
"iopub.status.idle": "2026-05-19T20:30:46.507124Z",
"shell.execute_reply": "2026-05-19T20:30:46.494735Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#0] WARNING:InputArguments -- The parameter 'sigma' with range [-inf, inf] of the RooGaussian 'gaussx' exceeds the safe range of (0, inf). Advise to limit its range.\n"
]
}
],
"source": [
"sigmax = ROOT.RooRealVar(\"sigma\", \"width of gaussian\", 0.5)\n",
"gaussx = ROOT.RooGaussian(\"gaussx\", \"Gaussian in x with shifting mean in y\", x, fy, sigmax)"
]
},
{
"cell_type": "markdown",
"id": "441ae9f7",
"metadata": {},
"source": [
"Create pdf gy(y)\n",
"-----------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "8fbdd9d7",
"metadata": {},
"source": [
"Create gaussy(y,0,5)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "db58b31e",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:46.519373Z",
"iopub.status.busy": "2026-05-19T20:30:46.519213Z",
"iopub.status.idle": "2026-05-19T20:30:46.638013Z",
"shell.execute_reply": "2026-05-19T20:30:46.637428Z"
}
},
"outputs": [],
"source": [
"gaussy = ROOT.RooGaussian(\"gaussy\", \"Gaussian in y\", y, 0.0, 3.0)"
]
},
{
"cell_type": "markdown",
"id": "ca64b58a",
"metadata": {},
"source": [
"Create product gx(x|y)*gy(y)\n",
"-------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "b01714c6",
"metadata": {},
"source": [
"Create gaussx(x,sx|y) * gaussy(y)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "8e272762",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:46.640122Z",
"iopub.status.busy": "2026-05-19T20:30:46.639995Z",
"iopub.status.idle": "2026-05-19T20:30:46.791725Z",
"shell.execute_reply": "2026-05-19T20:30:46.791311Z"
}
},
"outputs": [],
"source": [
"model = ROOT.RooProdPdf(\"model\", \"gaussx(x|y)*gaussy(y)\", {gaussy}, Conditional=({gaussx}, {x}))"
]
},
{
"cell_type": "markdown",
"id": "4a468922",
"metadata": {},
"source": [
"Sample, fit and plot product pdf\n",
"---------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "7424c4f6",
"metadata": {},
"source": [
"Generate 1000 events in x and y from model"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "3f236adb",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:46.794830Z",
"iopub.status.busy": "2026-05-19T20:30:46.794689Z",
"iopub.status.idle": "2026-05-19T20:30:46.937498Z",
"shell.execute_reply": "2026-05-19T20:30:46.936966Z"
}
},
"outputs": [],
"source": [
"data = model.generate({x, y}, 10000)"
]
},
{
"cell_type": "markdown",
"id": "91b03c15",
"metadata": {},
"source": [
"Plot x distribution of data and projection of model x = Int(dy)\n",
"model(x,y)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "8e64d79d",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:46.944373Z",
"iopub.status.busy": "2026-05-19T20:30:46.944243Z",
"iopub.status.idle": "2026-05-19T20:30:47.117845Z",
"shell.execute_reply": "2026-05-19T20:30:47.117205Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:Plotting -- RooAbsReal::plotOn(model) plot on x integrates over variables (y)\n",
"[#1] INFO:NumericIntegration -- RooRealIntegral::init(SPECINT[gaussy_NORM[y]_X_gaussx_NORM[x]]_Int[y]) using numeric integrator RooIntegrator1D to calculate Int(y)\n"
]
},
{
"data": {
"text/plain": [
""
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"xframe = x.frame()\n",
"data.plotOn(xframe)\n",
"model.plotOn(xframe)"
]
},
{
"cell_type": "markdown",
"id": "f9c62f3d",
"metadata": {},
"source": [
"Plot x distribution of data and projection of model y = Int(dx)\n",
"model(x,y)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "05da7323",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:47.119816Z",
"iopub.status.busy": "2026-05-19T20:30:47.119689Z",
"iopub.status.idle": "2026-05-19T20:30:47.225578Z",
"shell.execute_reply": "2026-05-19T20:30:47.224915Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:Plotting -- RooAbsReal::plotOn(model) plot on y integrates over variables (x)\n"
]
},
{
"data": {
"text/plain": [
""
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"yframe = y.frame()\n",
"data.plotOn(yframe)\n",
"model.plotOn(yframe)"
]
},
{
"cell_type": "markdown",
"id": "4ae99ad7",
"metadata": {},
"source": [
"Make two-dimensional plot in x vs y"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "c85d74a9",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:47.227819Z",
"iopub.status.busy": "2026-05-19T20:30:47.227697Z",
"iopub.status.idle": "2026-05-19T20:30:47.381408Z",
"shell.execute_reply": "2026-05-19T20:30:47.380774Z"
}
},
"outputs": [],
"source": [
"hh_model = model.createHistogram(\"hh_model\", x, ROOT.RooFit.Binning(50), ROOT.RooFit.YVar(y, ROOT.RooFit.Binning(50)))\n",
"hh_model.SetLineColor(\"kBlue\")"
]
},
{
"cell_type": "markdown",
"id": "997021b1",
"metadata": {},
"source": [
"Make canvas and draw ROOT.RooPlots"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "251c36c5",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:47.383951Z",
"iopub.status.busy": "2026-05-19T20:30:47.383814Z",
"iopub.status.idle": "2026-05-19T20:30:47.643864Z",
"shell.execute_reply": "2026-05-19T20:30:47.643231Z"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Info in : png file rf305_condcorrprod.png has been created\n"
]
}
],
"source": [
"c = ROOT.TCanvas(\"rf305_condcorrprod\", \"rf05_condcorrprod\", 1200, 400)\n",
"c.Divide(3)\n",
"c.cd(1)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"xframe.GetYaxis().SetTitleOffset(1.6)\n",
"xframe.Draw()\n",
"c.cd(2)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"yframe.GetYaxis().SetTitleOffset(1.6)\n",
"yframe.Draw()\n",
"c.cd(3)\n",
"ROOT.gPad.SetLeftMargin(0.20)\n",
"hh_model.GetZaxis().SetTitleOffset(2.5)\n",
"hh_model.Draw(\"surf\")\n",
"\n",
"c.SaveAs(\"rf305_condcorrprod.png\")"
]
},
{
"cell_type": "markdown",
"id": "eea151f2",
"metadata": {},
"source": [
"Draw all canvases "
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "d61a225b",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:47.645954Z",
"iopub.status.busy": "2026-05-19T20:30:47.645831Z",
"iopub.status.idle": "2026-05-19T20:30:47.832957Z",
"shell.execute_reply": "2026-05-19T20:30:47.832623Z"
}
},
"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
}