{
"cells": [
{
"cell_type": "markdown",
"id": "a02ba370",
"metadata": {},
"source": [
"# rf110_normintegration\n",
"Basic functionality: examples on normalization and integration of pdfs, construction\n",
"of cumulative distribution functions from monodimensional pdfs\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 08:29 PM."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "6c5a2efb",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:22.616673Z",
"iopub.status.busy": "2026-05-19T20:29:22.616523Z",
"iopub.status.idle": "2026-05-19T20:29:23.612500Z",
"shell.execute_reply": "2026-05-19T20:29:23.611415Z"
}
},
"outputs": [],
"source": [
"import ROOT"
]
},
{
"cell_type": "markdown",
"id": "d0d395f6",
"metadata": {},
"source": [
"Set up model\n",
"---------------------"
]
},
{
"cell_type": "markdown",
"id": "54330e7d",
"metadata": {},
"source": [
"Create observables x,y"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "eb41b459",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:23.614273Z",
"iopub.status.busy": "2026-05-19T20:29:23.614132Z",
"iopub.status.idle": "2026-05-19T20:29:23.776163Z",
"shell.execute_reply": "2026-05-19T20:29:23.775105Z"
}
},
"outputs": [],
"source": [
"x = ROOT.RooRealVar(\"x\", \"x\", -10, 10)"
]
},
{
"cell_type": "markdown",
"id": "c079da2e",
"metadata": {},
"source": [
"Create pdf gaussx(x,-2,3)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "e7440627",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:23.777900Z",
"iopub.status.busy": "2026-05-19T20:29:23.777766Z",
"iopub.status.idle": "2026-05-19T20:29:23.906055Z",
"shell.execute_reply": "2026-05-19T20:29:23.904993Z"
}
},
"outputs": [],
"source": [
"gx = ROOT.RooGaussian(\"gx\", \"gx\", x, -2, 3)"
]
},
{
"cell_type": "markdown",
"id": "493f373b",
"metadata": {},
"source": [
"Retrieve raw & normalized values of RooFit pdfs\n",
"--------------------------------------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "7fa4788e",
"metadata": {},
"source": [
"Return 'raw' unnormalized value of gx"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "aa505811",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:23.907746Z",
"iopub.status.busy": "2026-05-19T20:29:23.907577Z",
"iopub.status.idle": "2026-05-19T20:29:24.022744Z",
"shell.execute_reply": "2026-05-19T20:29:24.022178Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"gx = 0.8007374029168081\n"
]
}
],
"source": [
"print(\"gx = \", gx.getVal())"
]
},
{
"cell_type": "markdown",
"id": "b0a2154b",
"metadata": {},
"source": [
"Return value of gx normalized over x in range [-10,10]"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "aa76d754",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:24.024617Z",
"iopub.status.busy": "2026-05-19T20:29:24.024476Z",
"iopub.status.idle": "2026-05-19T20:29:24.189670Z",
"shell.execute_reply": "2026-05-19T20:29:24.188596Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"gx_Norm[x] = 0.1068955044839622\n"
]
}
],
"source": [
"nset = ROOT.RooArgSet(x)\n",
"print(\"gx_Norm[x] = \", gx.getVal(nset))"
]
},
{
"cell_type": "markdown",
"id": "60bb89ba",
"metadata": {},
"source": [
"Create object representing integral over gx\n",
"which is used to calculate gx_Norm[x] == gx / gx_Int[x]"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "00bcc4a1",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:24.191352Z",
"iopub.status.busy": "2026-05-19T20:29:24.191221Z",
"iopub.status.idle": "2026-05-19T20:29:24.307874Z",
"shell.execute_reply": "2026-05-19T20:29:24.306965Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"gx_Int[x] = 7.490842639102233\n"
]
}
],
"source": [
"igx = gx.createIntegral({x})\n",
"print(\"gx_Int[x] = \", igx.getVal())"
]
},
{
"cell_type": "markdown",
"id": "e3b151c9",
"metadata": {},
"source": [
"Integrate normalized pdf over subrange\n",
"----------------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "a586079d",
"metadata": {},
"source": [
"Define a range named \"signal\" in x from -5,5"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "a4e6dd60",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:24.309436Z",
"iopub.status.busy": "2026-05-19T20:29:24.309308Z",
"iopub.status.idle": "2026-05-19T20:29:24.419038Z",
"shell.execute_reply": "2026-05-19T20:29:24.418395Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'signal' created with bounds [-5,5]\n"
]
}
],
"source": [
"x.setRange(\"signal\", -5, 5)"
]
},
{
"cell_type": "markdown",
"id": "b981d027",
"metadata": {},
"source": [
"Create an integral of gx_Norm[x] over x in range \"signal\"\n",
"ROOT.This is the fraction of of pdf gx_Norm[x] which is in the\n",
"range named \"signal\""
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "e26b017d",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:24.420722Z",
"iopub.status.busy": "2026-05-19T20:29:24.420561Z",
"iopub.status.idle": "2026-05-19T20:29:24.562242Z",
"shell.execute_reply": "2026-05-19T20:29:24.561594Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"gx_Int[x|signal]_Norm[x] = 0.8347532778470285\n"
]
}
],
"source": [
"xset = {x}\n",
"igx_sig = gx.createIntegral(xset, NormSet=xset, Range=\"signal\")\n",
"print(\"gx_Int[x|signal]_Norm[x] = \", igx_sig.getVal())"
]
},
{
"cell_type": "markdown",
"id": "dfe5ea5c",
"metadata": {},
"source": [
"Construct cumulative distribution function from pdf\n",
"-----------------------------------------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "c974f4d6",
"metadata": {},
"source": [
"Create the cumulative distribution function of gx\n",
"i.e. calculate Int[-10,x] gx(x') dx'"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "4d510b99",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:24.563917Z",
"iopub.status.busy": "2026-05-19T20:29:24.563782Z",
"iopub.status.idle": "2026-05-19T20:29:24.674409Z",
"shell.execute_reply": "2026-05-19T20:29:24.673342Z"
}
},
"outputs": [],
"source": [
"gx_cdf = gx.createCdf({x})"
]
},
{
"cell_type": "markdown",
"id": "96114503",
"metadata": {},
"source": [
"Plot cdf of gx versus x"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "45c9cca3",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:24.676091Z",
"iopub.status.busy": "2026-05-19T20:29:24.675964Z",
"iopub.status.idle": "2026-05-19T20:29:24.835563Z",
"shell.execute_reply": "2026-05-19T20:29:24.834461Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"frame = x.frame(Title=\"cdf of Gaussian pdf\")\n",
"gx_cdf.plotOn(frame)"
]
},
{
"cell_type": "markdown",
"id": "d1fc6be1",
"metadata": {},
"source": [
"Draw plot on canvas"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "4b1e0d56",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:24.837255Z",
"iopub.status.busy": "2026-05-19T20:29:24.837125Z",
"iopub.status.idle": "2026-05-19T20:29:25.040748Z",
"shell.execute_reply": "2026-05-19T20:29:25.040120Z"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Info in : png file rf110_normintegration.png has been created\n"
]
}
],
"source": [
"c = ROOT.TCanvas(\"rf110_normintegration\", \"rf110_normintegration\", 600, 600)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"frame.GetYaxis().SetTitleOffset(1.6)\n",
"frame.Draw()\n",
"\n",
"c.SaveAs(\"rf110_normintegration.png\")"
]
},
{
"cell_type": "markdown",
"id": "f1a3c2f6",
"metadata": {},
"source": [
"Draw all canvases "
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "68cb6610",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:25.042674Z",
"iopub.status.busy": "2026-05-19T20:29:25.042510Z",
"iopub.status.idle": "2026-05-19T20:29:25.226013Z",
"shell.execute_reply": "2026-05-19T20:29:25.225131Z"
}
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"\n",
"
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"\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": {
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"file_extension": ".py",
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