{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "53a926e1",
   "metadata": {},
   "source": [
    "# rf315_projectpdf\n",
    "Multidimensional models: marginizalization of multi-dimensional pdfs through integration\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": "26dccf02",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:22.367878Z",
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     "iopub.status.idle": "2026-05-19T20:31:22.382030Z",
     "shell.execute_reply": "2026-05-19T20:31:22.381486Z"
    }
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   "outputs": [],
   "source": [
    "%%cpp -d\n",
    "#include \"RooRealVar.h\"\n",
    "#include \"RooDataHist.h\"\n",
    "#include \"RooGaussian.h\"\n",
    "#include \"RooProdPdf.h\"\n",
    "#include \"RooPolyVar.h\"\n",
    "#include \"TH1.h\"\n",
    "#include \"TCanvas.h\"\n",
    "#include \"TAxis.h\"\n",
    "#include \"RooPlot.h\"\n",
    "#include \"RooNumIntConfig.h\"\n",
    "using namespace RooFit;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "84c4e019",
   "metadata": {},
   "source": [
    "Create pdf m(x,y) = gx(x|y)*g(y)\n",
    "--------------------------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bb0bbb12",
   "metadata": {},
   "source": [
    "Increase default precision of numeric integration\n",
    "as this exercise has high sensitivity to numeric integration precision"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a5bcceec",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:22.383796Z",
     "iopub.status.busy": "2026-05-19T20:31:22.383673Z",
     "iopub.status.idle": "2026-05-19T20:31:22.703026Z",
     "shell.execute_reply": "2026-05-19T20:31:22.702299Z"
    }
   },
   "outputs": [],
   "source": [
    "RooAbsPdf::defaultIntegratorConfig()->setEpsRel(1e-8);\n",
    "RooAbsPdf::defaultIntegratorConfig()->setEpsAbs(1e-8);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9eab8606",
   "metadata": {},
   "source": [
    "Create observables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d2f0f476",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:22.704726Z",
     "iopub.status.busy": "2026-05-19T20:31:22.704581Z",
     "iopub.status.idle": "2026-05-19T20:31:22.912599Z",
     "shell.execute_reply": "2026-05-19T20:31:22.911949Z"
    }
   },
   "outputs": [],
   "source": [
    "RooRealVar x(\"x\", \"x\", -5, 5);\n",
    "RooRealVar y(\"y\", \"y\", -2, 2);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4bf0204f",
   "metadata": {},
   "source": [
    "Create function f(y) = a0 + a1*y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d62d88d6",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:22.914515Z",
     "iopub.status.busy": "2026-05-19T20:31:22.914388Z",
     "iopub.status.idle": "2026-05-19T20:31:23.122193Z",
     "shell.execute_reply": "2026-05-19T20:31:23.121775Z"
    }
   },
   "outputs": [],
   "source": [
    "RooRealVar a0(\"a0\", \"a0\", 0);\n",
    "RooRealVar a1(\"a1\", \"a1\", -1.5, -3, 1);\n",
    "RooPolyVar fy(\"fy\", \"fy\", y, RooArgSet(a0, a1));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "19f2b914",
   "metadata": {},
   "source": [
    "Create gaussx(x,f(y),sx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3c0a8c71",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:23.124585Z",
     "iopub.status.busy": "2026-05-19T20:31:23.124467Z",
     "iopub.status.idle": "2026-05-19T20:31:23.332926Z",
     "shell.execute_reply": "2026-05-19T20:31:23.332355Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[#0] WARNING:InputArguments -- The parameter 'sigmax' with range [-inf, inf] of the RooGaussian 'gaussx' exceeds the safe range of (0, inf). Advise to limit its range.\n"
     ]
    }
   ],
   "source": [
    "RooRealVar sigmax(\"sigmax\", \"width of gaussian\", 0.5);\n",
    "RooGaussian gaussx(\"gaussx\", \"Gaussian in x with shifting mean in y\", x, fy, sigmax);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06756a5b",
   "metadata": {},
   "source": [
    "Create gaussy(y,0,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "2429726b",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:23.334717Z",
     "iopub.status.busy": "2026-05-19T20:31:23.334571Z",
     "iopub.status.idle": "2026-05-19T20:31:23.542825Z",
     "shell.execute_reply": "2026-05-19T20:31:23.542120Z"
    }
   },
   "outputs": [],
   "source": [
    "RooGaussian gaussy(\"gaussy\", \"Gaussian in y\", y, 0.0, 2.0);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a17eb105",
   "metadata": {},
   "source": [
    "Create gaussx(x,sx|y) * gaussy(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "1556d015",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:23.544773Z",
     "iopub.status.busy": "2026-05-19T20:31:23.544656Z",
     "iopub.status.idle": "2026-05-19T20:31:23.753115Z",
     "shell.execute_reply": "2026-05-19T20:31:23.752426Z"
    }
   },
   "outputs": [],
   "source": [
    "RooProdPdf model(\"model\", \"gaussx(x|y)*gaussy(y)\", gaussy, Conditional(gaussx, x));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30e829da",
   "metadata": {},
   "source": [
    "Marginalize m(x,y) to m(x)\n",
    "----------------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1adc9a14",
   "metadata": {},
   "source": [
    "modelx(x) = Int model(x,y) dy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "e71439f4",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:23.754996Z",
     "iopub.status.busy": "2026-05-19T20:31:23.754879Z",
     "iopub.status.idle": "2026-05-19T20:31:23.962895Z",
     "shell.execute_reply": "2026-05-19T20:31:23.962211Z"
    }
   },
   "outputs": [],
   "source": [
    "RooAbsPdf *modelx = model.createProjection(y);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b3edb1aa",
   "metadata": {},
   "source": [
    "Use marginalized p.d.f. as regular 1-D p.d.f.\n",
    "------------------------------------------------------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "00b28da3",
   "metadata": {},
   "source": [
    "Sample 1000 events from modelx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "6cfa51e1",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:23.965027Z",
     "iopub.status.busy": "2026-05-19T20:31:23.964908Z",
     "iopub.status.idle": "2026-05-19T20:31:24.172961Z",
     "shell.execute_reply": "2026-05-19T20:31:24.172663Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[#1] INFO:NumericIntegration -- RooRealIntegral::init(SPECINT[gaussy_NORM[y]_X_gaussx_NORM[x]]_Int[y]) using numeric integrator RooIntegrator1D to calculate Int(y)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "input_line_62:2:2: warning: 'data' shadows a declaration with the same name in the 'std' namespace; use '::data' to reference this declaration\n",
      " std::unique_ptr<RooAbsData> data{modelx->generateBinned(x, 1000)};\n",
      " ^\n"
     ]
    }
   ],
   "source": [
    "std::unique_ptr<RooAbsData> data{modelx->generateBinned(x, 1000)};"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5eaac9e9",
   "metadata": {},
   "source": [
    "Fit modelx to toy data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "60314e0c",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:24.174832Z",
     "iopub.status.busy": "2026-05-19T20:31:24.174716Z",
     "iopub.status.idle": "2026-05-19T20:31:24.383529Z",
     "shell.execute_reply": "2026-05-19T20:31:24.382938Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "input_line_63:2:17: error: reference to 'data' is ambiguous\n",
      " modelx->fitTo(*data, Verbose(), PrintLevel(-1));\n",
      "                ^\n",
      "input_line_62:2:30: note: candidate found by name lookup is 'data'\n",
      " std::unique_ptr<RooAbsData> data{modelx->generateBinned(x, 1000)};\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": [
    "modelx->fitTo(*data, Verbose(), PrintLevel(-1));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "063725e5",
   "metadata": {},
   "source": [
    "Plot modelx over data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "869b7e1b",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:31:24.385427Z",
     "iopub.status.busy": "2026-05-19T20:31:24.385311Z",
     "iopub.status.idle": "2026-05-19T20:31:24.593895Z",
     "shell.execute_reply": "2026-05-19T20:31:24.593357Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "input_line_64:3:1: error: reference to 'data' is ambiguous\n",
      "data->plotOn(frame);\n",
      "^\n",
      "input_line_62:2:30: note: candidate found by name lookup is 'data'\n",
      " std::unique_ptr<RooAbsData> data{modelx->generateBinned(x, 1000)};\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(40);\n",
    "data->plotOn(frame);\n",
    "modelx->plotOn(frame);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8e0fa0e0",
   "metadata": {},
   "source": [
    "Make 2D histogram of model(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "766e3366",
   "metadata": {
    "collapsed": false,
    "execution": {
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     "iopub.status.busy": "2026-05-19T20:31:24.595574Z",
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     "shell.execute_reply": "2026-05-19T20:31:24.800632Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "input_line_66:2:3: 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": [
    "TH1 *hh = model.createHistogram(\"x,y\");\n",
    "hh->SetLineColor(kBlue);\n",
    "\n",
    "TCanvas *c = new TCanvas(\"rf315_projectpdf\", \"rf315_projectpdf\", 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(0.20);\n",
    "hh->GetZaxis()->SetTitleOffset(2.5);\n",
    "hh->Draw(\"surf\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77158a7f",
   "metadata": {},
   "source": [
    "Draw all canvases "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "190ddf15",
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     "shell.execute_reply": "2026-05-19T20:31:25.010466Z"
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"Core.unzipJSON(20381,'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').then(json => {\n",
       "   const obj = Core.parse(json);\n",
       "   Core.draw('root_plot_1779222684968', 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_1779222684968();\n",
       "</script>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "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
}