{
"cells": [
{
"cell_type": "markdown",
"id": "0bc6bfe2",
"metadata": {},
"source": [
"# rf303_conditional\n",
"'MULTIDIMENSIONAL MODELS' RooFit tutorial macro #303\n",
"Use of tailored p.d.f as conditional p.d.fs.s\n",
"\n",
"pdf = gauss(x,f(y),sx | y ) 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": "d446b629",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:38.191623Z",
"iopub.status.busy": "2026-05-19T20:30:38.191471Z",
"iopub.status.idle": "2026-05-19T20:30:39.141819Z",
"shell.execute_reply": "2026-05-19T20:30:39.141121Z"
}
},
"outputs": [],
"source": [
"import ROOT\n",
"\n",
"\n",
"def makeFakeDataXY():\n",
"\n",
" trnd = ROOT.TRandom3()\n",
"\n",
" x = ROOT.RooRealVar(\"x\", \"x\", -10, 10)\n",
" y = ROOT.RooRealVar(\"y\", \"y\", -10, 10)\n",
" coord = {x, y}\n",
"\n",
" d = ROOT.RooDataSet(\"d\", \"d\", coord)\n",
"\n",
" for i in range(10000):\n",
" tmpy = trnd.Gaus(0, 10)\n",
" tmpx = trnd.Gaus(0.5 * tmpy, 1)\n",
" if (abs(tmpy) < 10) and (abs(tmpx) < 10):\n",
" x.setVal(tmpx)\n",
" y.setVal(tmpy)\n",
" d.add(coord)\n",
"\n",
" return d"
]
},
{
"cell_type": "markdown",
"id": "2c62adc5",
"metadata": {},
"source": [
"Set up composed model gauss(x, m(y), s)\n",
"-----------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "603a31fb",
"metadata": {},
"source": [
"Create observables"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "bf227697",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:39.143560Z",
"iopub.status.busy": "2026-05-19T20:30:39.143428Z",
"iopub.status.idle": "2026-05-19T20:30:39.302908Z",
"shell.execute_reply": "2026-05-19T20:30:39.302221Z"
}
},
"outputs": [],
"source": [
"x = ROOT.RooRealVar(\"x\", \"x\", -10, 10)\n",
"y = ROOT.RooRealVar(\"y\", \"y\", -10, 10)"
]
},
{
"cell_type": "markdown",
"id": "61c89dcf",
"metadata": {},
"source": [
"Create function f(y) = a0 + a1*y"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "51f8b1ae",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:39.304576Z",
"iopub.status.busy": "2026-05-19T20:30:39.304451Z",
"iopub.status.idle": "2026-05-19T20:30:39.484052Z",
"shell.execute_reply": "2026-05-19T20:30:39.483337Z"
}
},
"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": "9a9e0990",
"metadata": {},
"source": [
"Creat gauss(x,f(y),s)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "c1b993e6",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:39.485714Z",
"iopub.status.busy": "2026-05-19T20:30:39.485573Z",
"iopub.status.idle": "2026-05-19T20:30:39.607180Z",
"shell.execute_reply": "2026-05-19T20:30:39.606645Z"
}
},
"outputs": [],
"source": [
"sigma = ROOT.RooRealVar(\"sigma\", \"width of gaussian\", 0.5, 0.1, 2.0)\n",
"model = ROOT.RooGaussian(\"model\", \"Gaussian with shifting mean\", x, fy, sigma)"
]
},
{
"cell_type": "markdown",
"id": "5c433271",
"metadata": {},
"source": [
"Obtain fake external experimental dataset with values for x and y"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "563cb604",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:39.609088Z",
"iopub.status.busy": "2026-05-19T20:30:39.608962Z",
"iopub.status.idle": "2026-05-19T20:30:39.823509Z",
"shell.execute_reply": "2026-05-19T20:30:39.822991Z"
}
},
"outputs": [],
"source": [
"expDataXY = makeFakeDataXY()"
]
},
{
"cell_type": "markdown",
"id": "777340a1",
"metadata": {},
"source": [
"Generate data from conditional p.d.f. model(x|y)\n",
"---------------------------------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "c8faa342",
"metadata": {},
"source": [
"Make subset of experimental data with only y values"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "c0e86737",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:39.825633Z",
"iopub.status.busy": "2026-05-19T20:30:39.825398Z",
"iopub.status.idle": "2026-05-19T20:30:39.941047Z",
"shell.execute_reply": "2026-05-19T20:30:39.940478Z"
}
},
"outputs": [],
"source": [
"expDataY = expDataXY.reduce({y})"
]
},
{
"cell_type": "markdown",
"id": "ada53239",
"metadata": {},
"source": [
"Generate 10000 events in x obtained from _conditional_ model(x|y) with y\n",
"values taken from experimental data"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "da5f463f",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:39.942978Z",
"iopub.status.busy": "2026-05-19T20:30:39.942852Z",
"iopub.status.idle": "2026-05-19T20:30:40.085680Z",
"shell.execute_reply": "2026-05-19T20:30:40.085125Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"RooDataSet::modelData[x,y] = 6850 entries\n"
]
}
],
"source": [
"data = model.generate({x}, ProtoData=expDataY)\n",
"data.Print()"
]
},
{
"cell_type": "markdown",
"id": "485c6635",
"metadata": {},
"source": [
"Fit conditional p.d.f model(x|y) to data\n",
"---------------------------------------------------------------------------------------------"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "76222c6c",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:40.087166Z",
"iopub.status.busy": "2026-05-19T20:30:40.087040Z",
"iopub.status.idle": "2026-05-19T20:30:40.324993Z",
"shell.execute_reply": "2026-05-19T20:30:40.324415Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:Fitting -- RooAbsPdf::fitTo(model_over_model_Int[x]) 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 683.464 μs\n",
"[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_model_over_model_Int[x]_d) Summation contains a RooNLLVar, using its error level\n",
"[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n"
]
},
{
"data": {
"text/plain": [
""
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"model.fitTo(expDataXY, ConditionalObservables={y}, PrintLevel=-1)"
]
},
{
"cell_type": "markdown",
"id": "9438ee2f",
"metadata": {},
"source": [
"Project conditional p.d.f on x and y dimensions\n",
"---------------------------------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "ed0a1119",
"metadata": {},
"source": [
"Plot x distribution of data and projection of model x = 1/Ndata\n",
"sum(data(y_i)) model(x;y_i)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "ad503248",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:40.326709Z",
"iopub.status.busy": "2026-05-19T20:30:40.326563Z",
"iopub.status.idle": "2026-05-19T20:30:40.509257Z",
"shell.execute_reply": "2026-05-19T20:30:40.508785Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:Plotting -- RooAbsReal::plotOn(model) plot on x averages using data variables (y)\n"
]
},
{
"data": {
"text/plain": [
""
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"xframe = x.frame()\n",
"expDataXY.plotOn(xframe)\n",
"model.plotOn(xframe, ProjWData=expDataY)"
]
},
{
"cell_type": "markdown",
"id": "e838a452",
"metadata": {},
"source": [
"Speed up (and approximate) projection by using binned clone of data for\n",
"projection"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "82ecc252",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:40.511232Z",
"iopub.status.busy": "2026-05-19T20:30:40.511106Z",
"iopub.status.idle": "2026-05-19T20:30:40.635010Z",
"shell.execute_reply": "2026-05-19T20:30:40.634459Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:Plotting -- RooAbsReal::plotOn(model) plot on x averages using data variables (y)\n"
]
}
],
"source": [
"binnedDataY = expDataY.binnedClone()\n",
"model.plotOn(xframe, ProjWData=binnedDataY, LineColor=\"c\", LineStyle=\":\")"
]
},
{
"cell_type": "markdown",
"id": "75e3d258",
"metadata": {},
"source": [
"Show effect of projection with too coarse binning"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "ab0b98fd",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:40.636479Z",
"iopub.status.busy": "2026-05-19T20:30:40.636353Z",
"iopub.status.idle": "2026-05-19T20:30:40.750796Z",
"shell.execute_reply": "2026-05-19T20:30:40.750268Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:Plotting -- RooAbsReal::plotOn(model) plot on x averages using data variables (y)\n"
]
}
],
"source": [
"(expDataY.get().find(\"y\")).setBins(5)\n",
"binnedDataY2 = expDataY.binnedClone()\n",
"model.plotOn(xframe, ProjWData=binnedDataY2, LineColor=\"r\")"
]
},
{
"cell_type": "markdown",
"id": "33408958",
"metadata": {},
"source": [
"Make canvas and draw ROOT.RooPlots"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "f008efc2",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:40.752333Z",
"iopub.status.busy": "2026-05-19T20:30:40.752204Z",
"iopub.status.idle": "2026-05-19T20:30:40.961432Z",
"shell.execute_reply": "2026-05-19T20:30:40.960912Z"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Info in : png file rf303_conditional.png has been created\n"
]
}
],
"source": [
"c = ROOT.TCanvas(\"rf303_conditional\", \"rf303_conditional\", 600, 460)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"xframe.GetYaxis().SetTitleOffset(1.2)\n",
"xframe.Draw()\n",
"\n",
"c.SaveAs(\"rf303_conditional.png\")"
]
},
{
"cell_type": "markdown",
"id": "d0e3cc6a",
"metadata": {},
"source": [
"Draw all canvases "
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "c4478908",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:30:40.963200Z",
"iopub.status.busy": "2026-05-19T20:30:40.963075Z",
"iopub.status.idle": "2026-05-19T20:30:41.145014Z",
"shell.execute_reply": "2026-05-19T20:30:41.144521Z"
}
},
"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
}