{
"cells": [
{
"cell_type": "markdown",
"id": "8606bf17",
"metadata": {},
"source": [
"# rf301_composition\n",
"Multidimensional models: multi-dimensional pdfs through composition, e.g. substituting\n",
"a pdf parameter with a function that depends on other observables\n",
"\n",
"`pdf = gauss(x,f(y),s)` 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": "8b9d3877",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:28.384748Z",
"iopub.status.busy": "2026-05-19T20:30:28.384618Z",
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"shell.execute_reply": "2026-05-19T20:30:29.361560Z"
}
},
"outputs": [],
"source": [
"import ROOT"
]
},
{
"cell_type": "markdown",
"id": "c639ceca",
"metadata": {},
"source": [
"Setup composed model gauss(x, m(y), s)\n",
"-----------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "cd4c362f",
"metadata": {},
"source": [
"Create observables"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "f384920f",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:29.364233Z",
"iopub.status.busy": "2026-05-19T20:30:29.364104Z",
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"shell.execute_reply": "2026-05-19T20:30:29.520617Z"
}
},
"outputs": [],
"source": [
"x = ROOT.RooRealVar(\"x\", \"x\", -5, 5)\n",
"y = ROOT.RooRealVar(\"y\", \"y\", -5, 5)"
]
},
{
"cell_type": "markdown",
"id": "16fb2805",
"metadata": {},
"source": [
"Create function f(y) = a0 + a1*y"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "fcf8cee8",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:29.523403Z",
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"shell.execute_reply": "2026-05-19T20:30:29.703630Z"
}
},
"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": "7309fdcb",
"metadata": {},
"source": [
"Creat gauss(x,f(y),s)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "c743b07d",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:29.706185Z",
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"shell.execute_reply": "2026-05-19T20:30:29.831700Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#0] WARNING:InputArguments -- The parameter 'sigma' with range [-inf, inf] of the RooGaussian 'model' exceeds the safe range of (0, inf). Advise to limit its range.\n"
]
}
],
"source": [
"sigma = ROOT.RooRealVar(\"sigma\", \"width of gaussian\", 0.5)\n",
"model = ROOT.RooGaussian(\"model\", \"Gaussian with shifting mean\", x, fy, sigma)"
]
},
{
"cell_type": "markdown",
"id": "af8db8b6",
"metadata": {},
"source": [
"Sample data, plot data and pdf on x and y\n",
"---------------------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "4be02076",
"metadata": {},
"source": [
"Generate 10000 events in x and y from model"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "1edcbe10",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:29.834149Z",
"iopub.status.busy": "2026-05-19T20:30:29.834016Z",
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"shell.execute_reply": "2026-05-19T20:30:29.986926Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:NumericIntegration -- RooRealIntegral::init(model_Int[x,y]) using numeric integrator RooIntegrator1D to calculate Int(y)\n",
"[#1] INFO:NumericIntegration -- RooRealIntegral::init(model_Int[x,y]) using numeric integrator RooIntegrator1D to calculate Int(y)\n",
"[#1] INFO:NumericIntegration -- RooRealIntegral::init(model_Int[x,y]) using numeric integrator RooIntegrator1D to calculate Int(y)\n"
]
}
],
"source": [
"data = model.generate({x, y}, 10000)"
]
},
{
"cell_type": "markdown",
"id": "47b6eee6",
"metadata": {},
"source": [
"Plot x distribution of data and projection of model x = Int(dy)\n",
"model(x,y)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "86e1df5c",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:29.989504Z",
"iopub.status.busy": "2026-05-19T20:30:29.989371Z",
"iopub.status.idle": "2026-05-19T20:30:30.155037Z",
"shell.execute_reply": "2026-05-19T20:30:30.153918Z"
}
},
"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(model_Int[x,y]) using numeric integrator RooIntegrator1D to calculate Int(y)\n",
"[#1] INFO:NumericIntegration -- RooRealIntegral::init(model_Int[y]_Norm[x,y]) using numeric integrator RooIntegrator1D to calculate Int(y)\n"
]
},
{
"data": {
"text/plain": [
""
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"xframe = x.frame()\n",
"data.plotOn(xframe)\n",
"model.plotOn(xframe)"
]
},
{
"cell_type": "markdown",
"id": "2a0e870a",
"metadata": {},
"source": [
"Plot x distribution of data and projection of model y = Int(dx)\n",
"model(x,y)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "67c9e77c",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:30.156690Z",
"iopub.status.busy": "2026-05-19T20:30:30.156541Z",
"iopub.status.idle": "2026-05-19T20:30:30.263259Z",
"shell.execute_reply": "2026-05-19T20:30:30.262139Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:Plotting -- RooAbsReal::plotOn(model) plot on y integrates over variables (x)\n",
"[#1] INFO:NumericIntegration -- RooRealIntegral::init(model_Int[x,y]) using numeric integrator RooIntegrator1D to calculate Int(y)\n"
]
},
{
"data": {
"text/plain": [
""
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"yframe = y.frame()\n",
"data.plotOn(yframe)\n",
"model.plotOn(yframe)"
]
},
{
"cell_type": "markdown",
"id": "07934802",
"metadata": {},
"source": [
"Make two-dimensional plot in x vs y"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "f262b571",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:30.264985Z",
"iopub.status.busy": "2026-05-19T20:30:30.264826Z",
"iopub.status.idle": "2026-05-19T20:30:30.430920Z",
"shell.execute_reply": "2026-05-19T20:30:30.429840Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:NumericIntegration -- RooRealIntegral::init(model_Int[x,y]) using numeric integrator RooIntegrator1D to calculate Int(y)\n"
]
}
],
"source": [
"hh_model = model.createHistogram(\"hh_model\", x, Binning=50, YVar=dict(var=y, Binning=50))\n",
"hh_model.SetLineColor(\"kBlue\")"
]
},
{
"cell_type": "markdown",
"id": "b0777a56",
"metadata": {},
"source": [
"Make canvas and draw ROOT.RooPlots"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "7014e837",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:30.432557Z",
"iopub.status.busy": "2026-05-19T20:30:30.432427Z",
"iopub.status.idle": "2026-05-19T20:30:30.697114Z",
"shell.execute_reply": "2026-05-19T20:30:30.696711Z"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Info in : png file rf301_composition.png has been created\n"
]
}
],
"source": [
"c = ROOT.TCanvas(\"rf301_composition\", \"rf301_composition\", 1200, 400)\n",
"c.Divide(3)\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",
"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(\"rf301_composition.png\")"
]
},
{
"cell_type": "markdown",
"id": "367d2c0c",
"metadata": {},
"source": [
"Draw all canvases "
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "12364b57",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:30.699144Z",
"iopub.status.busy": "2026-05-19T20:30:30.699015Z",
"iopub.status.idle": "2026-05-19T20:30:30.885529Z",
"shell.execute_reply": "2026-05-19T20:30:30.884764Z"
}
},
"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"
},
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