{
"cells": [
{
"cell_type": "markdown",
"id": "40267c41",
"metadata": {},
"source": [
"# rf313_paramranges\n",
"Multidimensional models: working with parameterized ranges to define non-rectangular\n",
"regions for fitting and integration\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 08:31 PM."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "7ee4c482",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:31:15.527458Z",
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"shell.execute_reply": "2026-05-19T20:31:16.498227Z"
}
},
"outputs": [],
"source": [
"import ROOT"
]
},
{
"cell_type": "markdown",
"id": "449f3266",
"metadata": {},
"source": [
"Create 3D pdf\n",
"-------------------------"
]
},
{
"cell_type": "markdown",
"id": "c4265bc1",
"metadata": {},
"source": [
"Define observable (x,y,z)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "d4004f6a",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:31:16.501052Z",
"iopub.status.busy": "2026-05-19T20:31:16.500909Z",
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"shell.execute_reply": "2026-05-19T20:31:16.663480Z"
}
},
"outputs": [],
"source": [
"x = ROOT.RooRealVar(\"x\", \"x\", 0, 10)\n",
"y = ROOT.RooRealVar(\"y\", \"y\", 0, 10)\n",
"z = ROOT.RooRealVar(\"z\", \"z\", 0, 10)"
]
},
{
"cell_type": "markdown",
"id": "8d00d941",
"metadata": {},
"source": [
"Define 3 dimensional pdf"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "74a9d53a",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:31:16.665819Z",
"iopub.status.busy": "2026-05-19T20:31:16.665690Z",
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"shell.execute_reply": "2026-05-19T20:31:16.875925Z"
}
},
"outputs": [],
"source": [
"z0 = ROOT.RooRealVar(\"z0\", \"z0\", -0.1, 1)\n",
"px = ROOT.RooPolynomial(\"px\", \"px\", x, [0.0])\n",
"py = ROOT.RooPolynomial(\"py\", \"py\", y, [0.0])\n",
"pz = ROOT.RooPolynomial(\"pz\", \"pz\", z, [z0])\n",
"pxyz = ROOT.RooProdPdf(\"pxyz\", \"pxyz\", [px, py, pz])"
]
},
{
"cell_type": "markdown",
"id": "cff263c2",
"metadata": {},
"source": [
"Defined non-rectangular region R in (x, y, z)\n",
"-------------------------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "18f1cb90",
"metadata": {},
"source": [
"R = Z[0 - 0.1*Y^2] * Y[0.1*X - 0.9*X] * X[0 - 10]"
]
},
{
"cell_type": "markdown",
"id": "9ccef188",
"metadata": {},
"source": [
"Construct range parameterized in \"R\" in y [ 0.1*x, 0.9*x ]"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "b91c3810",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:31:16.878284Z",
"iopub.status.busy": "2026-05-19T20:31:16.878145Z",
"iopub.status.idle": "2026-05-19T20:31:17.005550Z",
"shell.execute_reply": "2026-05-19T20:31:17.004984Z"
}
},
"outputs": [],
"source": [
"ylo = ROOT.RooFormulaVar(\"ylo\", \"0.1*x\", [x])\n",
"yhi = ROOT.RooFormulaVar(\"yhi\", \"0.9*x\", [x])\n",
"y.setRange(\"R\", ylo, yhi)"
]
},
{
"cell_type": "markdown",
"id": "3a930be6",
"metadata": {},
"source": [
"Construct parameterized ranged \"R\" in z [ 0, 0.1*y^2 ]"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "8a191d63",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:31:17.007203Z",
"iopub.status.busy": "2026-05-19T20:31:17.007077Z",
"iopub.status.idle": "2026-05-19T20:31:17.126380Z",
"shell.execute_reply": "2026-05-19T20:31:17.125864Z"
}
},
"outputs": [],
"source": [
"zlo = ROOT.RooFormulaVar(\"zlo\", \"0.0*y\", [y])\n",
"zhi = ROOT.RooFormulaVar(\"zhi\", \"0.1*y*y\", [y])\n",
"z.setRange(\"R\", zlo, zhi)"
]
},
{
"cell_type": "markdown",
"id": "c02d4dc5",
"metadata": {},
"source": [
"Calculate integral of normalized pdf in R\n",
"----------------------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "edaa4128",
"metadata": {},
"source": [
"Create integral over normalized pdf model over x,y, in \"R\" region"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "ad26e0c1",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:31:17.127936Z",
"iopub.status.busy": "2026-05-19T20:31:17.127818Z",
"iopub.status.idle": "2026-05-19T20:31:17.261258Z",
"shell.execute_reply": "2026-05-19T20:31:17.260774Z"
}
},
"outputs": [],
"source": [
"intPdf = pxyz.createIntegral({x, y, z}, {x, y, z}, \"R\")"
]
},
{
"cell_type": "markdown",
"id": "c8b1c613",
"metadata": {},
"source": [
"Plot value of integral as function of pdf parameter z0"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "f3c17849",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:31:17.262735Z",
"iopub.status.busy": "2026-05-19T20:31:17.262595Z",
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"shell.execute_reply": "2026-05-19T20:31:17.544545Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:NumericIntegration -- RooRealIntegral::init(pxyz_Int[z|R]_Norm[x,y,z]_Int[y|R]_Int[x|R]) using numeric integrator RooIntegrator1D to calculate Int(x)\n",
"[#1] INFO:NumericIntegration -- RooRealIntegral::init(pxyz_Int[z|R]_Norm[x,y,z]_Int[y|R]) using numeric integrator RooIntegrator1D to calculate Int(y)\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"Info in : png file rf313_paramranges.png has been created\n"
]
}
],
"source": [
"frame = z0.frame(Title=\"Integral of pxyz over x,y, in region R\")\n",
"intPdf.plotOn(frame)\n",
"\n",
"c = ROOT.TCanvas(\"rf313_paramranges\", \"rf313_paramranges\", 600, 600)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"frame.GetYaxis().SetTitleOffset(1.6)\n",
"frame.Draw()\n",
"\n",
"c.SaveAs(\"rf313_paramranges.png\")"
]
},
{
"cell_type": "markdown",
"id": "652a17ee",
"metadata": {},
"source": [
"Draw all canvases "
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "664d6cbe",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:31:17.546492Z",
"iopub.status.busy": "2026-05-19T20:31:17.546374Z",
"iopub.status.idle": "2026-05-19T20:31:17.726133Z",
"shell.execute_reply": "2026-05-19T20:31:17.725703Z"
}
},
"outputs": [
{
"data": {
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],
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]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from ROOT import gROOT \n",
"gROOT.GetListOfCanvases().Draw()"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
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