{
"cells": [
{
"cell_type": "markdown",
"id": "dcd3f4ee",
"metadata": {},
"source": [
"# rf309_ndimplot\n",
"Multidimensional models: making 2/3 dimensional plots of pdfs and datasets\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": "4df87b40",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:31:01.570935Z",
"iopub.status.busy": "2026-05-19T20:31:01.570816Z",
"iopub.status.idle": "2026-05-19T20:31:02.530212Z",
"shell.execute_reply": "2026-05-19T20:31:02.529810Z"
}
},
"outputs": [],
"source": [
"import ROOT"
]
},
{
"cell_type": "markdown",
"id": "d3b0a695",
"metadata": {},
"source": [
"Create 2D model and dataset\n",
"-----------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "2774e989",
"metadata": {},
"source": [
"Create observables"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "3272c90f",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:31:02.544292Z",
"iopub.status.busy": "2026-05-19T20:31:02.544140Z",
"iopub.status.idle": "2026-05-19T20:31:02.709558Z",
"shell.execute_reply": "2026-05-19T20:31:02.708928Z"
}
},
"outputs": [],
"source": [
"x = ROOT.RooRealVar(\"x\", \"x\", -5, 5)\n",
"y = ROOT.RooRealVar(\"y\", \"y\", -5, 5)"
]
},
{
"cell_type": "markdown",
"id": "b6b9cd0c",
"metadata": {},
"source": [
"Create parameters"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "3ed2e83f",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:31:02.711658Z",
"iopub.status.busy": "2026-05-19T20:31:02.711508Z",
"iopub.status.idle": "2026-05-19T20:31:02.825208Z",
"shell.execute_reply": "2026-05-19T20:31:02.824503Z"
}
},
"outputs": [],
"source": [
"a0 = ROOT.RooRealVar(\"a0\", \"a0\", -3.5, -5, 5)\n",
"a1 = ROOT.RooRealVar(\"a1\", \"a1\", -1.5, -1, 1)\n",
"sigma = ROOT.RooRealVar(\"sigma\", \"width of gaussian\", 1.5)"
]
},
{
"cell_type": "markdown",
"id": "9eb7372f",
"metadata": {},
"source": [
"Create interpreted function f(y) = a0 - a1*sqrt(10*abs(y))"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "b9298350",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:31:02.826807Z",
"iopub.status.busy": "2026-05-19T20:31:02.826678Z",
"iopub.status.idle": "2026-05-19T20:31:03.011544Z",
"shell.execute_reply": "2026-05-19T20:31:03.010871Z"
}
},
"outputs": [],
"source": [
"fy = ROOT.RooFormulaVar(\"fy\", \"a0-a1*sqrt(10*abs(y))\", [y, a0, a1])"
]
},
{
"cell_type": "markdown",
"id": "e47cface",
"metadata": {},
"source": [
"Create gauss(x,f(y),s)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "38789f8f",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:31:03.013151Z",
"iopub.status.busy": "2026-05-19T20:31:03.013027Z",
"iopub.status.idle": "2026-05-19T20:31:03.135965Z",
"shell.execute_reply": "2026-05-19T20:31:03.135446Z"
}
},
"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": [
"model = ROOT.RooGaussian(\"model\", \"Gaussian with shifting mean\", x, fy, sigma)"
]
},
{
"cell_type": "markdown",
"id": "d3f2659c",
"metadata": {},
"source": [
"Sample dataset from gauss(x,y)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "2af4d248",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:31:03.138168Z",
"iopub.status.busy": "2026-05-19T20:31:03.138037Z",
"iopub.status.idle": "2026-05-19T20:31:03.292015Z",
"shell.execute_reply": "2026-05-19T20:31:03.291337Z"
}
},
"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": "e7634294",
"metadata": {},
"source": [
"Make 2D plots of data and model\n",
"-------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "efd85ca9",
"metadata": {},
"source": [
"Create and fill ROOT 2D histogram (20x20 bins) with contents of dataset"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "0e537b11",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:31:03.293552Z",
"iopub.status.busy": "2026-05-19T20:31:03.293429Z",
"iopub.status.idle": "2026-05-19T20:31:03.453877Z",
"shell.execute_reply": "2026-05-19T20:31:03.453268Z"
}
},
"outputs": [],
"source": [
"hh_data = data.createHistogram(\"x,y\", x, Binning=20, YVar=dict(var=y, Binning=20))"
]
},
{
"cell_type": "markdown",
"id": "ffb3b7ce",
"metadata": {},
"source": [
"Create and fill ROOT 2D histogram (50x50 bins) with sampling of pdf\n",
"hh_pdf = model.createHistogram(\"hh_model\", x, Binning=50, YVar=dict(var=y, Binning=50))"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "83cb55ec",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:31:03.463271Z",
"iopub.status.busy": "2026-05-19T20:31:03.463138Z",
"iopub.status.idle": "2026-05-19T20:31:03.613385Z",
"shell.execute_reply": "2026-05-19T20:31:03.612783Z"
}
},
"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_pdf = model.createHistogram(\"x,y\", 50, 50)\n",
"hh_pdf.SetLineColor(\"kBlue\")"
]
},
{
"cell_type": "markdown",
"id": "248b13d5",
"metadata": {},
"source": [
"Create 3D model and dataset\n",
"-----------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "b73c7da8",
"metadata": {},
"source": [
"Create observables"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "a3225ec3",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:31:03.614729Z",
"iopub.status.busy": "2026-05-19T20:31:03.614587Z",
"iopub.status.idle": "2026-05-19T20:31:03.751061Z",
"shell.execute_reply": "2026-05-19T20:31:03.750435Z"
}
},
"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": [
"z = ROOT.RooRealVar(\"z\", \"z\", -5, 5)\n",
"\n",
"gz = ROOT.RooGaussian(\"gz\", \"gz\", z, 0.0, 2.0)\n",
"model3 = ROOT.RooProdPdf(\"model3\", \"model3\", [model, gz])\n",
"\n",
"data3 = model3.generate({x, y, z}, 10000)"
]
},
{
"cell_type": "markdown",
"id": "9c415330",
"metadata": {},
"source": [
"Make 3D plots of data and model\n",
"-------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "6bd2e9cf",
"metadata": {},
"source": [
"Create and fill ROOT 2D histogram (8x8x8 bins) with contents of dataset\n",
"hh_data3 = data3.createHistogram(\"hh_data3\", x, Binning=8, YVar=(var=y, Binning=8), ZVar=(var=z, Binning=8))"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "d1ba2590",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:31:03.753004Z",
"iopub.status.busy": "2026-05-19T20:31:03.752881Z",
"iopub.status.idle": "2026-05-19T20:31:03.866543Z",
"shell.execute_reply": "2026-05-19T20:31:03.865967Z"
}
},
"outputs": [],
"source": [
"hh_data3 = data3.createHistogram(\n",
" \"hh_data3\",\n",
" x,\n",
" Binning=8,\n",
" YVar=dict(var=y, Binning=8),\n",
" ZVar=dict(var=z, Binning=8),\n",
")"
]
},
{
"cell_type": "markdown",
"id": "ac8f4759",
"metadata": {},
"source": [
"Create and fill ROOT 2D histogram (20x20x20 bins) with sampling of pdf"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "80011f17",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:31:03.868159Z",
"iopub.status.busy": "2026-05-19T20:31:03.868036Z",
"iopub.status.idle": "2026-05-19T20:31:04.182227Z",
"shell.execute_reply": "2026-05-19T20:31:04.181596Z"
}
},
"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"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"Info in : png file rf309_2dimplot.png has been created\n",
"Info in : png file rf309_3dimplot.png has been created\n"
]
}
],
"source": [
"hh_pdf3 = model3.createHistogram(\n",
" \"hh_model3\",\n",
" x,\n",
" Binning=20,\n",
" YVar=dict(var=y, Binning=20),\n",
" ZVar=dict(var=z, Binning=20),\n",
")\n",
"hh_pdf3.SetFillColor(\"kBlue\")\n",
"\n",
"c1 = ROOT.TCanvas(\"rf309_2dimplot\", \"rf309_2dimplot\", 800, 800)\n",
"c1.Divide(2, 2)\n",
"c1.cd(1)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"hh_data.GetZaxis().SetTitleOffset(1.4)\n",
"hh_data.Draw(\"lego\")\n",
"c1.cd(2)\n",
"ROOT.gPad.SetLeftMargin(0.20)\n",
"hh_pdf.GetZaxis().SetTitleOffset(2.5)\n",
"hh_pdf.Draw(\"surf\")\n",
"c1.cd(3)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"hh_data.GetZaxis().SetTitleOffset(1.4)\n",
"hh_data.Draw(\"box\")\n",
"c1.cd(4)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"hh_pdf.GetZaxis().SetTitleOffset(2.5)\n",
"hh_pdf.Draw(\"cont3\")\n",
"c1.SaveAs(\"rf309_2dimplot.png\")\n",
"\n",
"c2 = ROOT.TCanvas(\"rf309_3dimplot\", \"rf309_3dimplot\", 800, 400)\n",
"c2.Divide(2)\n",
"c2.cd(1)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"hh_data3.GetZaxis().SetTitleOffset(1.4)\n",
"hh_data3.Draw(\"lego\")\n",
"c2.cd(2)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"hh_pdf3.GetZaxis().SetTitleOffset(1.4)\n",
"hh_pdf3.Draw(\"iso\")\n",
"c2.SaveAs(\"rf309_3dimplot.png\")"
]
},
{
"cell_type": "markdown",
"id": "5c672a5b",
"metadata": {},
"source": [
"Draw all canvases "
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "9d24e671",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:31:04.183680Z",
"iopub.status.busy": "2026-05-19T20:31:04.183533Z",
"iopub.status.idle": "2026-05-19T20:31:04.409222Z",
"shell.execute_reply": "2026-05-19T20:31:04.408598Z"
}
},
"outputs": [
{
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}
],
"source": [
"from ROOT import gROOT \n",
"gROOT.GetListOfCanvases().Draw()"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
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