{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "963a5fc4",
   "metadata": {},
   "source": [
    "# rf316_llratioplot\n",
    "Multidimensional models: using the likelihood ratio technique to construct a signal\n",
    "enhanced one-dimensional projection of a multi-dimensional pdf\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": "62412658",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:24.853974Z",
     "iopub.status.busy": "2026-05-19T20:31:24.853864Z",
     "iopub.status.idle": "2026-05-19T20:31:24.867764Z",
     "shell.execute_reply": "2026-05-19T20:31:24.867178Z"
    }
   },
   "outputs": [],
   "source": [
    "%%cpp -d\n",
    "#include \"RooRealVar.h\"\n",
    "#include \"RooDataSet.h\"\n",
    "#include \"RooGaussian.h\"\n",
    "#include \"RooPolynomial.h\"\n",
    "#include \"RooAddPdf.h\"\n",
    "#include \"RooProdPdf.h\"\n",
    "#include \"TCanvas.h\"\n",
    "#include \"TAxis.h\"\n",
    "#include \"RooPlot.h\"\n",
    "using namespace RooFit;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d23e656",
   "metadata": {},
   "source": [
    "Create 3D pdf and data\n",
    "-------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "361fdf70",
   "metadata": {},
   "source": [
    "Create observables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a015d99d",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:24.868968Z",
     "iopub.status.busy": "2026-05-19T20:31:24.868856Z",
     "iopub.status.idle": "2026-05-19T20:31:25.181871Z",
     "shell.execute_reply": "2026-05-19T20:31:25.181187Z"
    }
   },
   "outputs": [],
   "source": [
    "RooRealVar x(\"x\", \"x\", -5, 5);\n",
    "RooRealVar y(\"y\", \"y\", -5, 5);\n",
    "RooRealVar z(\"z\", \"z\", -5, 5);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2ca7fe16",
   "metadata": {},
   "source": [
    "Create signal pdf gauss(x)*gauss(y)*gauss(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1ea3db27",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:25.183742Z",
     "iopub.status.busy": "2026-05-19T20:31:25.183616Z",
     "iopub.status.idle": "2026-05-19T20:31:25.391634Z",
     "shell.execute_reply": "2026-05-19T20:31:25.390950Z"
    }
   },
   "outputs": [],
   "source": [
    "RooGaussian gx(\"gx\", \"gx\", x, 0.0, 1.0);\n",
    "RooGaussian gy(\"gy\", \"gy\", y, 0.0, 1.0);\n",
    "RooGaussian gz(\"gz\", \"gz\", z, 0.0, 1.0);\n",
    "RooProdPdf sig(\"sig\", \"sig\", RooArgSet(gx, gy, gz));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e77c8bf8",
   "metadata": {},
   "source": [
    "Create background pdf poly(x)*poly(y)*poly(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d2bc59e0",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:25.402505Z",
     "iopub.status.busy": "2026-05-19T20:31:25.402372Z",
     "iopub.status.idle": "2026-05-19T20:31:25.610344Z",
     "shell.execute_reply": "2026-05-19T20:31:25.609758Z"
    }
   },
   "outputs": [],
   "source": [
    "RooPolynomial px(\"px\", \"px\", x, RooArgSet(-0.1, 0.004));\n",
    "RooPolynomial py(\"py\", \"py\", y, RooArgSet(0.1, -0.004));\n",
    "RooPolynomial pz(\"pz\", \"pz\", z);\n",
    "RooProdPdf bkg(\"bkg\", \"bkg\", RooArgSet(px, py, pz));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24639840",
   "metadata": {},
   "source": [
    "Create composite pdf sig+bkg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "666f44ac",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:25.612237Z",
     "iopub.status.busy": "2026-05-19T20:31:25.612119Z",
     "iopub.status.idle": "2026-05-19T20:31:25.820357Z",
     "shell.execute_reply": "2026-05-19T20:31:25.819789Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "input_line_52:5:1: warning: 'data' shadows a declaration with the same name in the 'std' namespace; use '::data' to reference this declaration\n",
      "std::unique_ptr<RooDataSet> data{model.generate({x, y, z}, 20000)};\n",
      "^\n"
     ]
    }
   ],
   "source": [
    "RooRealVar fsig(\"fsig\", \"signal fraction\", 0.1, 0., 1.);\n",
    "RooAddPdf model(\"model\", \"model\", RooArgList(sig, bkg), fsig);\n",
    "\n",
    "std::unique_ptr<RooDataSet> data{model.generate({x, y, z}, 20000)};"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7127bcf2",
   "metadata": {},
   "source": [
    "Project pdf and data on x\n",
    "-------------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "56978435",
   "metadata": {},
   "source": [
    "Make plain projection of data and pdf on x observable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ce08194f",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:25.821911Z",
     "iopub.status.busy": "2026-05-19T20:31:25.821795Z",
     "iopub.status.idle": "2026-05-19T20:31:26.031349Z",
     "shell.execute_reply": "2026-05-19T20:31:26.030767Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "input_line_53:3:1: error: reference to 'data' is ambiguous\n",
      "data->plotOn(frame);\n",
      "^\n",
      "input_line_52:5:29: note: candidate found by name lookup is 'data'\n",
      "std::unique_ptr<RooDataSet> data{model.generate({x, y, z}, 20000)};\n",
      "                            ^\n",
      "/usr/lib/gcc/x86_64-redhat-linux/14/../../../../include/c++/14/bits/range_access.h:344:5: note: candidate found by name lookup is 'std::data'\n",
      "    data(initializer_list<_Tp> __il) noexcept\n",
      "    ^\n",
      "/usr/lib/gcc/x86_64-redhat-linux/14/../../../../include/c++/14/bits/range_access.h:312:5: note: candidate found by name lookup is 'std::data'\n",
      "    data(_Container& __cont) noexcept(noexcept(__cont.data()))\n",
      "    ^\n",
      "/usr/lib/gcc/x86_64-redhat-linux/14/../../../../include/c++/14/bits/range_access.h:323:5: note: candidate found by name lookup is 'std::data'\n",
      "    data(const _Container& __cont) noexcept(noexcept(__cont.data()))\n",
      "    ^\n",
      "/usr/lib/gcc/x86_64-redhat-linux/14/../../../../include/c++/14/bits/range_access.h:334:5: note: candidate found by name lookup is 'std::data'\n",
      "    data(_Tp (&__array)[_Nm]) noexcept\n",
      "    ^\n"
     ]
    }
   ],
   "source": [
    "RooPlot *frame = x.frame(Title(\"Projection of 3D data and pdf on X\"), Bins(40));\n",
    "data->plotOn(frame);\n",
    "model.plotOn(frame);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c0e1b262",
   "metadata": {},
   "source": [
    "Define projected signal likelihood ratio\n",
    "----------------------------------------------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "25d64ff8",
   "metadata": {},
   "source": [
    "Calculate projection of signal and total likelihood on (y,z) observables\n",
    "i.e. integrate signal and composite model over x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "ffcfc255",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:26.033152Z",
     "iopub.status.busy": "2026-05-19T20:31:26.033040Z",
     "iopub.status.idle": "2026-05-19T20:31:26.240935Z",
     "shell.execute_reply": "2026-05-19T20:31:26.240362Z"
    }
   },
   "outputs": [],
   "source": [
    "RooAbsPdf *sigyz = sig.createProjection(x);\n",
    "RooAbsPdf *totyz = model.createProjection(x);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef68b100",
   "metadata": {},
   "source": [
    "Construct the log of the signal / signal+background probability"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "a7dd21fe",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:26.242800Z",
     "iopub.status.busy": "2026-05-19T20:31:26.242680Z",
     "iopub.status.idle": "2026-05-19T20:31:26.450636Z",
     "shell.execute_reply": "2026-05-19T20:31:26.450102Z"
    }
   },
   "outputs": [],
   "source": [
    "RooFormulaVar llratio_func(\"llratio\", \"log10(@0)-log10(@1)\", RooArgList(*sigyz, *totyz));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d97a9e80",
   "metadata": {},
   "source": [
    "Plot data with a LLratio cut\n",
    "-------------------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88a6796e",
   "metadata": {},
   "source": [
    "Calculate the llratio value for each event in the dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "63c85e57",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:26.452662Z",
     "iopub.status.busy": "2026-05-19T20:31:26.452525Z",
     "iopub.status.idle": "2026-05-19T20:31:26.661381Z",
     "shell.execute_reply": "2026-05-19T20:31:26.660808Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "input_line_62:2:2: error: reference to 'data' is ambiguous\n",
      " data->addColumn(llratio_func);\n",
      " ^\n",
      "input_line_52:5:29: note: candidate found by name lookup is 'data'\n",
      "std::unique_ptr<RooDataSet> data{model.generate({x, y, z}, 20000)};\n",
      "                            ^\n",
      "/usr/lib/gcc/x86_64-redhat-linux/14/../../../../include/c++/14/bits/range_access.h:344:5: note: candidate found by name lookup is 'std::data'\n",
      "    data(initializer_list<_Tp> __il) noexcept\n",
      "    ^\n",
      "/usr/lib/gcc/x86_64-redhat-linux/14/../../../../include/c++/14/bits/range_access.h:312:5: note: candidate found by name lookup is 'std::data'\n",
      "    data(_Container& __cont) noexcept(noexcept(__cont.data()))\n",
      "    ^\n",
      "/usr/lib/gcc/x86_64-redhat-linux/14/../../../../include/c++/14/bits/range_access.h:323:5: note: candidate found by name lookup is 'std::data'\n",
      "    data(const _Container& __cont) noexcept(noexcept(__cont.data()))\n",
      "    ^\n",
      "/usr/lib/gcc/x86_64-redhat-linux/14/../../../../include/c++/14/bits/range_access.h:334:5: note: candidate found by name lookup is 'std::data'\n",
      "    data(_Tp (&__array)[_Nm]) noexcept\n",
      "    ^\n"
     ]
    }
   ],
   "source": [
    "data->addColumn(llratio_func);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2de1bc8",
   "metadata": {},
   "source": [
    "Extract the subset of data with large signal likelihood"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "6c53ce18",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:26.663014Z",
     "iopub.status.busy": "2026-05-19T20:31:26.662902Z",
     "iopub.status.idle": "2026-05-19T20:31:26.869983Z",
     "shell.execute_reply": "2026-05-19T20:31:26.869364Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "input_line_63:2:38: error: reference to 'data' is ambiguous\n",
      " std::unique_ptr<RooAbsData> dataSel{data->reduce(Cut(\"llratio>0.7\"))};\n",
      "                                     ^\n",
      "input_line_52:5:29: note: candidate found by name lookup is 'data'\n",
      "std::unique_ptr<RooDataSet> data{model.generate({x, y, z}, 20000)};\n",
      "                            ^\n",
      "/usr/lib/gcc/x86_64-redhat-linux/14/../../../../include/c++/14/bits/range_access.h:344:5: note: candidate found by name lookup is 'std::data'\n",
      "    data(initializer_list<_Tp> __il) noexcept\n",
      "    ^\n",
      "/usr/lib/gcc/x86_64-redhat-linux/14/../../../../include/c++/14/bits/range_access.h:312:5: note: candidate found by name lookup is 'std::data'\n",
      "    data(_Container& __cont) noexcept(noexcept(__cont.data()))\n",
      "    ^\n",
      "/usr/lib/gcc/x86_64-redhat-linux/14/../../../../include/c++/14/bits/range_access.h:323:5: note: candidate found by name lookup is 'std::data'\n",
      "    data(const _Container& __cont) noexcept(noexcept(__cont.data()))\n",
      "    ^\n",
      "/usr/lib/gcc/x86_64-redhat-linux/14/../../../../include/c++/14/bits/range_access.h:334:5: note: candidate found by name lookup is 'std::data'\n",
      "    data(_Tp (&__array)[_Nm]) noexcept\n",
      "    ^\n"
     ]
    }
   ],
   "source": [
    "std::unique_ptr<RooAbsData> dataSel{data->reduce(Cut(\"llratio>0.7\"))};"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bc0230cd",
   "metadata": {},
   "source": [
    "Make plot frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "08f60b8f",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:26.871665Z",
     "iopub.status.busy": "2026-05-19T20:31:26.871532Z",
     "iopub.status.idle": "2026-05-19T20:31:27.079595Z",
     "shell.execute_reply": "2026-05-19T20:31:27.078889Z"
    }
   },
   "outputs": [],
   "source": [
    "RooPlot *frame2 = x.frame(Title(\"Same projection on X with LLratio(y,z)>0.7\"), Bins(40));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83d2f59a",
   "metadata": {},
   "source": [
    "Plot select data on frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "6050135d",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:27.081404Z",
     "iopub.status.busy": "2026-05-19T20:31:27.081291Z",
     "iopub.status.idle": "2026-05-19T20:31:27.290318Z",
     "shell.execute_reply": "2026-05-19T20:31:27.289673Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "input_line_66:2:3: error: use of undeclared identifier 'dataSel'\n",
      " (dataSel->plotOn(((*(RooPlot **)0x7f5f18032000))))\n",
      "  ^\n",
      "Error in <HandleInterpreterException>: Error evaluating expression (dataSel->plotOn(((*(RooPlot **)0x7f5f18032000))))\n",
      "Execution of your code was aborted.\n"
     ]
    }
   ],
   "source": [
    "dataSel->plotOn(frame2);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a9301f0d",
   "metadata": {},
   "source": [
    "Make MC projection of pdf with same LLratio cut\n",
    "---------------------------------------------------------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "33cb1595",
   "metadata": {},
   "source": [
    "Generate large number of events for MC integration of pdf projection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "d7817c13",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:27.291898Z",
     "iopub.status.busy": "2026-05-19T20:31:27.291784Z",
     "iopub.status.idle": "2026-05-19T20:31:27.499800Z",
     "shell.execute_reply": "2026-05-19T20:31:27.499138Z"
    }
   },
   "outputs": [],
   "source": [
    "std::unique_ptr<RooDataSet> mcprojData{model.generate({x, y, z}, 10000)};"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d4e32271",
   "metadata": {},
   "source": [
    "Calculate LL ratio for each generated event and select MC events with llratio)0.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "0e87e9e9",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:27.501584Z",
     "iopub.status.busy": "2026-05-19T20:31:27.501470Z",
     "iopub.status.idle": "2026-05-19T20:31:27.706827Z",
     "shell.execute_reply": "2026-05-19T20:31:27.706443Z"
    }
   },
   "outputs": [],
   "source": [
    "mcprojData->addColumn(llratio_func);\n",
    "std::unique_ptr<RooAbsData> mcprojDataSel{mcprojData->reduce(Cut(\"llratio>0.7\"))};"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2589e65",
   "metadata": {},
   "source": [
    "Project model on x, integrating projected observables (y,z) with Monte Carlo technique\n",
    "on set of events with the same llratio cut as was applied to data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "ec92ac47",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:27.728037Z",
     "iopub.status.busy": "2026-05-19T20:31:27.727899Z",
     "iopub.status.idle": "2026-05-19T20:31:27.935903Z",
     "shell.execute_reply": "2026-05-19T20:31:27.935614Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "input_line_76:2:3: error: use of undeclared identifier 'frame'\n",
      " (frame->GetYaxis()->SetTitleOffset(1.3999999999999999))\n",
      "  ^\n",
      "Error in <HandleInterpreterException>: Error evaluating expression (frame->GetYaxis()->SetTitleOffset(1.3999999999999999))\n",
      "Execution of your code was aborted.\n"
     ]
    }
   ],
   "source": [
    "model.plotOn(frame2, ProjWData(*mcprojDataSel));\n",
    "\n",
    "TCanvas *c = new TCanvas(\"rf316_llratioplot\", \"rf316_llratioplot\", 800, 400);\n",
    "c->Divide(2);\n",
    "c->cd(1);\n",
    "gPad->SetLeftMargin(0.15);\n",
    "frame->GetYaxis()->SetTitleOffset(1.4);\n",
    "frame->Draw();\n",
    "c->cd(2);\n",
    "gPad->SetLeftMargin(0.15);\n",
    "frame2->GetYaxis()->SetTitleOffset(1.4);\n",
    "frame2->Draw();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "57aa61b3",
   "metadata": {},
   "source": [
    "Draw all canvases "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "42bb096b",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:27.958168Z",
     "iopub.status.busy": "2026-05-19T20:31:27.958037Z",
     "iopub.status.idle": "2026-05-19T20:31:28.202725Z",
     "shell.execute_reply": "2026-05-19T20:31:28.197356Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "\n",
       "<div id=\"root_plot_1779222688127\" style=\"width: 800px; height: 400px; position: relative\">\n",
       "</div>\n",
       "\n",
       "</div>\n",
       "<script>\n",
       "   function process_root_plot_1779222688127() {\n",
       "      function execCode(Core) {\n",
       "         Core.settings.HandleKeys = false;\n",
       "         \n",
       "Core.unzipJSON(20387,'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').then(json => {\n",
       "   const obj = Core.parse(json);\n",
       "   Core.draw('root_plot_1779222688127', obj, '');\n",
       "});\n",
       "\n",
       "      }\n",
       "      const servers = ['/static/', 'https://root.cern/js/7.11.0/', 'https://jsroot.gsi.de/7.11.0/'],\n",
       "            path = 'build/jsroot';\n",
       "      if (typeof JSROOT !== 'undefined')\n",
       "         execCode(JSROOT);\n",
       "      else if (typeof requirejs !== 'undefined') {\n",
       "         servers.forEach((s,i) => { servers[i] = s + path; });\n",
       "         requirejs.config({ paths: { 'jsroot' : servers } })(['jsroot'],  execCode);\n",
       "      } else {\n",
       "         const config = document.getElementById('jupyter-config-data');\n",
       "         if (config)\n",
       "            servers[0] = (JSON.parse(config.innerHTML || '{}')?.baseUrl || '/') + 'static/';\n",
       "         else\n",
       "            servers.shift();\n",
       "         function loadJsroot() {\n",
       "            return !servers.length ? 0 : import(servers.shift() + path + '.js').catch(loadJsroot).then(() => execCode(JSROOT));\n",
       "         }\n",
       "         loadJsroot();\n",
       "      }\n",
       "   }\n",
       "   process_root_plot_1779222688127();\n",
       "</script>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%jsroot on\n",
    "gROOT->GetListOfCanvases()->Draw()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "ROOT C++",
   "language": "c++",
   "name": "root"
  },
  "language_info": {
   "codemirror_mode": "text/x-c++src",
   "file_extension": ".C",
   "mimetype": " text/x-c++src",
   "name": "c++"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}