{
"cells": [
{
"cell_type": "markdown",
"id": "64a4a0d2",
"metadata": {},
"source": [
"# rf109_chi2residpull\n",
"'BASIC FUNCTIONALITY' RooFit tutorial macro #109\n",
"Calculating chi^2 from histograms and curves in ROOT.RooPlots,\n",
"making histogram of residual and pull distributions\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": "e2e2d044",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:18.850238Z",
"iopub.status.busy": "2026-05-19T20:29:18.850120Z",
"iopub.status.idle": "2026-05-19T20:29:19.832937Z",
"shell.execute_reply": "2026-05-19T20:29:19.832173Z"
}
},
"outputs": [],
"source": [
"import ROOT"
]
},
{
"cell_type": "markdown",
"id": "38bae8bf",
"metadata": {},
"source": [
"Set up model\n",
"---------------------"
]
},
{
"cell_type": "markdown",
"id": "3f6875ce",
"metadata": {},
"source": [
"Create observables"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "8984c1ac",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:19.841487Z",
"iopub.status.busy": "2026-05-19T20:29:19.841324Z",
"iopub.status.idle": "2026-05-19T20:29:20.001409Z",
"shell.execute_reply": "2026-05-19T20:29:20.000718Z"
}
},
"outputs": [],
"source": [
"x = ROOT.RooRealVar(\"x\", \"x\", -10, 10)"
]
},
{
"cell_type": "markdown",
"id": "0399b256",
"metadata": {},
"source": [
"Create Gaussian"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "356ec63f",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:20.003757Z",
"iopub.status.busy": "2026-05-19T20:29:20.003582Z",
"iopub.status.idle": "2026-05-19T20:29:20.135122Z",
"shell.execute_reply": "2026-05-19T20:29:20.134377Z"
}
},
"outputs": [],
"source": [
"sigma = ROOT.RooRealVar(\"sigma\", \"sigma\", 3, 0.1, 10)\n",
"mean = ROOT.RooRealVar(\"mean\", \"mean\", 0, -10, 10)\n",
"gauss = ROOT.RooGaussian(\"gauss\", \"gauss\", x, mean, sigma)"
]
},
{
"cell_type": "markdown",
"id": "aa838862",
"metadata": {},
"source": [
"Generate a sample of 1000 events with sigma=3"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "cb6540fe",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:20.137004Z",
"iopub.status.busy": "2026-05-19T20:29:20.136821Z",
"iopub.status.idle": "2026-05-19T20:29:20.276522Z",
"shell.execute_reply": "2026-05-19T20:29:20.275915Z"
}
},
"outputs": [],
"source": [
"data = gauss.generate({x}, 10000)"
]
},
{
"cell_type": "markdown",
"id": "6d48d6b3",
"metadata": {},
"source": [
"Change sigma to 3.15"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "b7d46f7d",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:20.278641Z",
"iopub.status.busy": "2026-05-19T20:29:20.278484Z",
"iopub.status.idle": "2026-05-19T20:29:20.386518Z",
"shell.execute_reply": "2026-05-19T20:29:20.385849Z"
}
},
"outputs": [],
"source": [
"sigma.setVal(3.15)"
]
},
{
"cell_type": "markdown",
"id": "775663b1",
"metadata": {},
"source": [
"Plot data and slightly distorted model\n",
"---------------------------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "3b6901f3",
"metadata": {},
"source": [
"Overlay projection of gauss with sigma=3.15 on data with sigma=3.0"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "5d7569ca",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:20.388702Z",
"iopub.status.busy": "2026-05-19T20:29:20.388537Z",
"iopub.status.idle": "2026-05-19T20:29:20.587820Z",
"shell.execute_reply": "2026-05-19T20:29:20.587380Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"frame1 = x.frame(Title=\"Data with distorted Gaussian pdf\", Bins=40)\n",
"data.plotOn(frame1, DataError=\"SumW2\")\n",
"gauss.plotOn(frame1)"
]
},
{
"cell_type": "markdown",
"id": "414616bf",
"metadata": {},
"source": [
"Calculate chi^2\n",
"------------------------------"
]
},
{
"cell_type": "markdown",
"id": "b7d1fefd",
"metadata": {},
"source": [
"Show the chi^2 of the curve w.r.t. the histogram\n",
"If multiple curves or datasets live in the frame you can specify\n",
"the name of the relevant curve and/or dataset in chiSquare()"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "5c35030f",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:20.600491Z",
"iopub.status.busy": "2026-05-19T20:29:20.600342Z",
"iopub.status.idle": "2026-05-19T20:29:20.717039Z",
"shell.execute_reply": "2026-05-19T20:29:20.708525Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"chi^2 = 2.63197794362232\n"
]
}
],
"source": [
"print(\"chi^2 = \", frame1.chiSquare())"
]
},
{
"cell_type": "markdown",
"id": "db952825",
"metadata": {},
"source": [
"Show residual and pull dists\n",
"-------------------------------------------------------"
]
},
{
"cell_type": "markdown",
"id": "38e1c128",
"metadata": {},
"source": [
"Construct a histogram with the residuals of the data w.r.t. the curve"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "af180581",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:20.725451Z",
"iopub.status.busy": "2026-05-19T20:29:20.725304Z",
"iopub.status.idle": "2026-05-19T20:29:20.842952Z",
"shell.execute_reply": "2026-05-19T20:29:20.842309Z"
}
},
"outputs": [],
"source": [
"hresid = frame1.residHist()"
]
},
{
"cell_type": "markdown",
"id": "19c7fc47",
"metadata": {},
"source": [
"Construct a histogram with the pulls of the data w.r.t the curve"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "69bda4d9",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:20.853496Z",
"iopub.status.busy": "2026-05-19T20:29:20.853341Z",
"iopub.status.idle": "2026-05-19T20:29:20.962508Z",
"shell.execute_reply": "2026-05-19T20:29:20.961860Z"
}
},
"outputs": [],
"source": [
"hpull = frame1.pullHist()"
]
},
{
"cell_type": "markdown",
"id": "6f84d312",
"metadata": {},
"source": [
"Create a frame to draw the residual distribution and add the\n",
"distribution to the frame"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "00e90b18",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:20.964288Z",
"iopub.status.busy": "2026-05-19T20:29:20.964157Z",
"iopub.status.idle": "2026-05-19T20:29:21.072670Z",
"shell.execute_reply": "2026-05-19T20:29:21.072022Z"
}
},
"outputs": [],
"source": [
"frame2 = x.frame(Title=\"Residual Distribution\")\n",
"frame2.addPlotable(hresid, \"P\")"
]
},
{
"cell_type": "markdown",
"id": "0e9468fe",
"metadata": {},
"source": [
"Create a frame to draw the pull distribution and add the distribution to\n",
"the frame"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "cf6190b2",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:21.074270Z",
"iopub.status.busy": "2026-05-19T20:29:21.074142Z",
"iopub.status.idle": "2026-05-19T20:29:21.293940Z",
"shell.execute_reply": "2026-05-19T20:29:21.293288Z"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Info in : png file rf109_chi2residpull.png has been created\n"
]
}
],
"source": [
"frame3 = x.frame(Title=\"Pull Distribution\")\n",
"frame3.addPlotable(hpull, \"P\")\n",
"\n",
"c = ROOT.TCanvas(\"rf109_chi2residpull\", \"rf109_chi2residpull\", 900, 300)\n",
"c.Divide(3)\n",
"c.cd(1)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"frame1.GetYaxis().SetTitleOffset(1.6)\n",
"frame1.Draw()\n",
"c.cd(2)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"frame2.GetYaxis().SetTitleOffset(1.6)\n",
"frame2.Draw()\n",
"c.cd(3)\n",
"ROOT.gPad.SetLeftMargin(0.15)\n",
"frame3.GetYaxis().SetTitleOffset(1.6)\n",
"frame3.Draw()\n",
"\n",
"c.SaveAs(\"rf109_chi2residpull.png\")"
]
},
{
"cell_type": "markdown",
"id": "018a7b55",
"metadata": {},
"source": [
"Draw all canvases "
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "6f955aee",
"metadata": {
"collapsed": false,
"execution": {
"iopub.execute_input": "2026-05-19T20:29:21.295656Z",
"iopub.status.busy": "2026-05-19T20:29:21.295497Z",
"iopub.status.idle": "2026-05-19T20:29:21.479528Z",
"shell.execute_reply": "2026-05-19T20:29:21.479007Z"
}
},
"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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"file_extension": ".py",
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