{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "7106673d",
   "metadata": {},
   "source": [
    "# rf109_chi2residpull\n",
    "Basic functionality: Calculating chi^2 from histograms and curves in RooPlots, making\n",
    "histogram of residual and pull distributions\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "**Author:** Wouter Verkerke  \n",
    "<i><small>This notebook tutorial was automatically generated with <a href= \"https://github.com/root-project/root/blob/master/documentation/doxygen/converttonotebook.py\">ROOTBOOK-izer</a> from the macro found in the ROOT repository  on Tuesday, May 19, 2026 at 08:29 PM.</small></i>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "dcf2f787",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%%cpp -d\n",
    "#include \"RooRealVar.h\"\n",
    "#include \"RooDataSet.h\"\n",
    "#include \"RooGaussian.h\"\n",
    "#include \"TCanvas.h\"\n",
    "#include \"TAxis.h\"\n",
    "#include \"RooPlot.h\"\n",
    "#include \"RooHist.h\"\n",
    "using namespace RooFit;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "09f49d20",
   "metadata": {},
   "source": [
    "Setup model\n",
    "---------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7bc340ad",
   "metadata": {},
   "source": [
    "Create observables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "74550fd8",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "RooRealVar x(\"x\", \"x\", -10, 10);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "519b1ccb",
   "metadata": {},
   "source": [
    "Create Gaussian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9e2f285a",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "RooRealVar sigma(\"sigma\", \"sigma\", 3, 0.1, 10);\n",
    "RooRealVar mean(\"mean\", \"mean\", 0, -10, 10);\n",
    "RooGaussian gauss(\"gauss\", \"gauss\", x, 0.0, sigma);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "58bcc19f",
   "metadata": {},
   "source": [
    "Generate a sample of 1000 events with sigma=3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fad5cb7b",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "std::unique_ptr<RooDataSet> data{gauss.generate(x, 10000)};"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a044f1bc",
   "metadata": {},
   "source": [
    "Change sigma to 3.15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0aa081e9",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sigma.setVal(3.15);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf1d5634",
   "metadata": {},
   "source": [
    "Plot data and slightly distorted model\n",
    "---------------------------------------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd4a6054",
   "metadata": {},
   "source": [
    "Overlay projection of gauss with sigma=3.15 on data with sigma=3.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5d99d19f",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "RooPlot *frame1 = x.frame(Title(\"Data with distorted Gaussian pdf\"), Bins(40));\n",
    "data->plotOn(frame1, DataError(RooAbsData::SumW2));\n",
    "gauss.plotOn(frame1);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5152180e",
   "metadata": {},
   "source": [
    "Calculate chi^2\n",
    "------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c464f33",
   "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": null,
   "id": "93a8935d",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "cout << \"chi^2 = \" << frame1->chiSquare() << endl;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1353ec6",
   "metadata": {},
   "source": [
    "Show residual and pull dists\n",
    "-------------------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "15658cb5",
   "metadata": {},
   "source": [
    "Construct a histogram with the residuals of the data w.r.t. the curve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ea9c75d9",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "RooHist *hresid = frame1->residHist();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec543218",
   "metadata": {},
   "source": [
    "Construct a histogram with the pulls of the data w.r.t the curve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d6ca4c2a",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "RooHist *hpull = frame1->pullHist();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b60a1b61",
   "metadata": {},
   "source": [
    "Create a new frame to draw the residual distribution and add the distribution to the frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "98cca9a9",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "RooPlot *frame2 = x.frame(Title(\"Residual Distribution\"));\n",
    "frame2->addPlotable(hresid, \"P\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f3271169",
   "metadata": {},
   "source": [
    "Create a new frame to draw the pull distribution and add the distribution to the frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "35998a3d",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "RooPlot *frame3 = x.frame(Title(\"Pull Distribution\"));\n",
    "frame3->addPlotable(hpull, \"P\");\n",
    "\n",
    "TCanvas *c = new TCanvas(\"rf109_chi2residpull\", \"rf109_chi2residpull\", 900, 300);\n",
    "c->Divide(3);\n",
    "c->cd(1);\n",
    "gPad->SetLeftMargin(0.15);\n",
    "frame1->GetYaxis()->SetTitleOffset(1.6);\n",
    "frame1->Draw();\n",
    "c->cd(2);\n",
    "gPad->SetLeftMargin(0.15);\n",
    "frame2->GetYaxis()->SetTitleOffset(1.6);\n",
    "frame2->Draw();\n",
    "c->cd(3);\n",
    "gPad->SetLeftMargin(0.15);\n",
    "frame3->GetYaxis()->SetTitleOffset(1.6);\n",
    "frame3->Draw();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ab4c393",
   "metadata": {},
   "source": [
    "Draw all canvases "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bdf96ba3",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%jsroot on\n",
    "gROOT->GetListOfCanvases()->Draw()"
   ]
  }
 ],
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