{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "157fb207",
   "metadata": {},
   "source": [
    "# rf312_multirangefit\n",
    "Multidimensional models: performing fits in multiple (disjoint) ranges in one or more dimensions\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 08:31 PM.</small></i>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "32e3e043",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:09.862477Z",
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     "shell.execute_reply": "2026-05-19T20:31:09.876131Z"
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   "outputs": [],
   "source": [
    "%%cpp -d\n",
    "#include \"RooRealVar.h\"\n",
    "#include \"RooDataSet.h\"\n",
    "#include \"RooGaussian.h\"\n",
    "#include \"RooProdPdf.h\"\n",
    "#include \"RooAddPdf.h\"\n",
    "#include \"RooPolynomial.h\"\n",
    "#include \"TCanvas.h\"\n",
    "#include \"TAxis.h\"\n",
    "#include \"RooPlot.h\"\n",
    "#include \"RooFitResult.h\"\n",
    "using namespace RooFit;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "382e20f1",
   "metadata": {},
   "source": [
    "Create 2D pdf and data\n",
    "-------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "468d479a",
   "metadata": {},
   "source": [
    "Define observables x,y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a7abef88",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:09.877897Z",
     "iopub.status.busy": "2026-05-19T20:31:09.877779Z",
     "iopub.status.idle": "2026-05-19T20:31:10.205055Z",
     "shell.execute_reply": "2026-05-19T20:31:10.204462Z"
    }
   },
   "outputs": [],
   "source": [
    "RooRealVar x(\"x\", \"x\", -10, 10);\n",
    "RooRealVar y(\"y\", \"y\", -10, 10);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20a05d1a",
   "metadata": {},
   "source": [
    "Construct the signal pdf gauss(x)*gauss(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "246ae334",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:10.206734Z",
     "iopub.status.busy": "2026-05-19T20:31:10.206590Z",
     "iopub.status.idle": "2026-05-19T20:31:10.415030Z",
     "shell.execute_reply": "2026-05-19T20:31:10.414234Z"
    }
   },
   "outputs": [],
   "source": [
    "RooRealVar mx(\"mx\", \"mx\", 1, -10, 10);\n",
    "RooRealVar my(\"my\", \"my\", 1, -10, 10);\n",
    "\n",
    "RooGaussian gx(\"gx\", \"gx\", x, mx, 1.0);\n",
    "RooGaussian gy(\"gy\", \"gy\", y, my, 1.0);\n",
    "\n",
    "RooProdPdf sig(\"sig\", \"sig\", gx, gy);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf66d0fd",
   "metadata": {},
   "source": [
    "Construct the background pdf (flat in x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "4df936f7",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:10.416749Z",
     "iopub.status.busy": "2026-05-19T20:31:10.416598Z",
     "iopub.status.idle": "2026-05-19T20:31:10.624649Z",
     "shell.execute_reply": "2026-05-19T20:31:10.624094Z"
    }
   },
   "outputs": [],
   "source": [
    "RooPolynomial px(\"px\", \"px\", x);\n",
    "RooPolynomial py(\"py\", \"py\", y);\n",
    "RooProdPdf bkg(\"bkg\", \"bkg\", px, py);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f2319593",
   "metadata": {},
   "source": [
    "Construct the composite model sig+bkg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5d2c3436",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:10.626309Z",
     "iopub.status.busy": "2026-05-19T20:31:10.626185Z",
     "iopub.status.idle": "2026-05-19T20:31:10.834350Z",
     "shell.execute_reply": "2026-05-19T20:31:10.833828Z"
    }
   },
   "outputs": [],
   "source": [
    "RooRealVar f(\"f\", \"f\", 0., 1.);\n",
    "RooAddPdf model(\"model\", \"model\", RooArgList(sig, bkg), f);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ea0d5b3a",
   "metadata": {},
   "source": [
    "Sample 10000 events in (x,y) from the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "2d4c2c6d",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:10.836218Z",
     "iopub.status.busy": "2026-05-19T20:31:10.836091Z",
     "iopub.status.idle": "2026-05-19T20:31:11.077985Z",
     "shell.execute_reply": "2026-05-19T20:31:11.067391Z"
    }
   },
   "outputs": [],
   "source": [
    "std::unique_ptr<RooDataSet> modelData{model.generate({x, y}, 10000)};"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e3336f87",
   "metadata": {},
   "source": [
    "Define signal and sideband regions\n",
    "-------------------------------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9135e028",
   "metadata": {},
   "source": [
    "Construct the SideBand1,SideBand2,Signal regions\n",
    "\n",
    "|\n",
    "+-------------+-----------+\n",
    "|             |           |\n",
    "|    Side     |   Sig     |\n",
    "|    Band1    |   nal     |\n",
    "|             |           |\n",
    "--+-------------+-----------+--\n",
    "|                         |\n",
    "|           Side          |\n",
    "|           Band2         |\n",
    "|                         |\n",
    "+-------------+-----------+\n",
    "|"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f50fb0a3",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:11.097585Z",
     "iopub.status.busy": "2026-05-19T20:31:11.097422Z",
     "iopub.status.idle": "2026-05-19T20:31:11.303427Z",
     "shell.execute_reply": "2026-05-19T20:31:11.303033Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'SB1' created with bounds [-10,10]\n",
      "[#1] INFO:Eval -- RooRealVar::setRange(y) new range named 'SB1' created with bounds [-10,0]\n",
      "[#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'SB2' created with bounds [-10,0]\n",
      "[#1] INFO:Eval -- RooRealVar::setRange(y) new range named 'SB2' created with bounds [0,10]\n",
      "[#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'SIG' created with bounds [0,10]\n",
      "[#1] INFO:Eval -- RooRealVar::setRange(y) new range named 'SIG' created with bounds [0,10]\n",
      "[#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'FULL' created with bounds [-10,10]\n",
      "[#1] INFO:Eval -- RooRealVar::setRange(y) new range named 'FULL' created with bounds [-10,10]\n"
     ]
    }
   ],
   "source": [
    "x.setRange(\"SB1\", -10, +10);\n",
    "y.setRange(\"SB1\", -10, 0);\n",
    "\n",
    "x.setRange(\"SB2\", -10, 0);\n",
    "y.setRange(\"SB2\", 0, +10);\n",
    "\n",
    "x.setRange(\"SIG\", 0, +10);\n",
    "y.setRange(\"SIG\", 0, +10);\n",
    "\n",
    "x.setRange(\"FULL\", -10, +10);\n",
    "y.setRange(\"FULL\", -10, +10);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf2cc83b",
   "metadata": {},
   "source": [
    "Perform fits in individual sideband regions\n",
    "-------------------------------------------------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "add62ead",
   "metadata": {},
   "source": [
    "Perform fit in SideBand1 region (RooAddPdf coefficients will be interpreted in full range)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "bdbc06a5",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:11.305357Z",
     "iopub.status.busy": "2026-05-19T20:31:11.305241Z",
     "iopub.status.idle": "2026-05-19T20:31:11.514856Z",
     "shell.execute_reply": "2026-05-19T20:31:11.514077Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'fit_nll_model_modelData' created with bounds [-10,10]\n",
      "[#1] INFO:Eval -- RooRealVar::setRange(y) new range named 'fit_nll_model_modelData' created with bounds [-10,0]\n",
      "[#1] INFO:Fitting -- RooAbsPdf::fitTo(model) fixing normalization set for coefficient determination to observables in data\n",
      "[#1] INFO:Fitting -- using generic CPU library compiled with no vectorizations\n",
      "[#1] INFO:Fitting -- Creation of NLL object took 1.7411 ms\n",
      "[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_model_modelData) Summation contains a RooNLLVar, using its error level\n",
      "[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n"
     ]
    }
   ],
   "source": [
    "std::unique_ptr<RooFitResult> r_sb1{model.fitTo(*modelData, Range(\"SB1\"), Save(), PrintLevel(-1))};"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e4dbbc1",
   "metadata": {},
   "source": [
    "Perform fit in SideBand2 region (RooAddPdf coefficients will be interpreted in full range)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ce540482",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:11.516379Z",
     "iopub.status.busy": "2026-05-19T20:31:11.516238Z",
     "iopub.status.idle": "2026-05-19T20:31:11.725814Z",
     "shell.execute_reply": "2026-05-19T20:31:11.725168Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[#1] INFO:Fitting -- RooAbsPdf::fitTo(model) fixing normalization set for coefficient determination to observables in data\n",
      "[#1] INFO:Fitting -- Creation of NLL object took 591.543 μs\n",
      "[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_model_modelData) Summation contains a RooNLLVar, using its error level\n",
      "[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n"
     ]
    }
   ],
   "source": [
    "std::unique_ptr<RooFitResult> r_sb2{model.fitTo(*modelData, Range(\"SB2\"), Save(), PrintLevel(-1))};"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7bcd3e27",
   "metadata": {},
   "source": [
    "Perform fits in joint  sideband regions\n",
    "-----------------------------------------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f095adea",
   "metadata": {},
   "source": [
    "Now perform fit to joint 'L-shaped' sideband region 'SB1|SB2'\n",
    "(RooAddPdf coefficients will be interpreted in full range)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "5e271800",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:11.727328Z",
     "iopub.status.busy": "2026-05-19T20:31:11.727202Z",
     "iopub.status.idle": "2026-05-19T20:31:11.936790Z",
     "shell.execute_reply": "2026-05-19T20:31:11.936146Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'fit_nll_model_modelData_SB1' created with bounds [-10,10]\n",
      "[#1] INFO:Eval -- RooRealVar::setRange(y) new range named 'fit_nll_model_modelData_SB1' created with bounds [-10,0]\n",
      "[#1] INFO:Eval -- RooRealVar::setRange(x) new range named 'fit_nll_model_modelData_SB2' created with bounds [-10,0]\n",
      "[#1] INFO:Eval -- RooRealVar::setRange(y) new range named 'fit_nll_model_modelData_SB2' created with bounds [0,10]\n",
      "[#1] INFO:Fitting -- RooAbsPdf::fitTo(model) fixing normalization set for coefficient determination to observables in data\n",
      "[#1] INFO:Fitting -- Creation of NLL object took 850.374 μs\n",
      "[#1] INFO:Fitting -- RooAddition::defaultErrorLevel(nll_model_modelData) Summation contains a RooNLLVar, using its error level\n",
      "[#1] INFO:Minimization -- [fitFCN] No discrete parameters, performing continuous minimization only\n"
     ]
    }
   ],
   "source": [
    "std::unique_ptr<RooFitResult> r_sb12{model.fitTo(*modelData, Range(\"SB1,SB2\"), Save(), PrintLevel(-1))};"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c0524ae9",
   "metadata": {},
   "source": [
    "Print results for comparison"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "4f7f8b6a",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:11.938239Z",
     "iopub.status.busy": "2026-05-19T20:31:11.938112Z",
     "iopub.status.idle": "2026-05-19T20:31:12.148140Z",
     "shell.execute_reply": "2026-05-19T20:31:12.147406Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "  RooFitResult: minimized FCN value: 16261.4, estimated distance to minimum: 5.06415e-07\n",
      "                covariance matrix quality: Full, accurate covariance matrix\n",
      "                Status : MINIMIZE=0 HESSE=0 \n",
      "\n",
      "    Floating Parameter    FinalValue +/-  Error   \n",
      "  --------------------  --------------------------\n",
      "                     f    5.1135e-01 +/-  3.58e-02\n",
      "                    mx    9.8740e-01 +/-  4.03e-02\n",
      "                    my    9.9305e-01 +/-  9.39e-02\n",
      "\n",
      "\n",
      "  RooFitResult: minimized FCN value: 7578.28, estimated distance to minimum: 3.07865e-06\n",
      "                covariance matrix quality: Full, accurate covariance matrix\n",
      "                Status : MINIMIZE=0 HESSE=0 \n",
      "\n",
      "    Floating Parameter    FinalValue +/-  Error   \n",
      "  --------------------  --------------------------\n",
      "                     f    5.4586e-01 +/-  4.46e-02\n",
      "                    mx    1.1276e+00 +/-  1.10e-01\n",
      "                    my    9.6462e-01 +/-  5.60e-02\n",
      "\n",
      "\n",
      "  RooFitResult: minimized FCN value: 27252.6, estimated distance to minimum: 2.25202e-06\n",
      "                covariance matrix quality: Full, accurate covariance matrix\n",
      "                Status : MINIMIZE=0 HESSE=0 \n",
      "\n",
      "    Floating Parameter    FinalValue +/-  Error   \n",
      "  --------------------  --------------------------\n",
      "                     f    5.0082e-01 +/-  1.29e-02\n",
      "                    mx    1.0100e+00 +/-  3.26e-02\n",
      "                    my    9.6348e-01 +/-  3.31e-02\n",
      "\n"
     ]
    }
   ],
   "source": [
    "r_sb1->Print();\n",
    "r_sb2->Print();\n",
    "r_sb12->Print();"
   ]
  }
 ],
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