{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "56cce46b",
   "metadata": {},
   "source": [
    "# rf704_amplitudefit\n",
    "Special pdf's: using a pdf defined by a sum of real-valued amplitude components\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 08:34 PM.</small></i>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d7beb98c",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:34:34.666976Z",
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     "shell.execute_reply": "2026-05-19T20:34:34.681794Z"
    }
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   "outputs": [],
   "source": [
    "%%cpp -d\n",
    "#include \"RooRealVar.h\"\n",
    "#include \"RooDataSet.h\"\n",
    "#include \"RooGaussian.h\"\n",
    "#include \"RooFormulaVar.h\"\n",
    "#include \"RooRealSumPdf.h\"\n",
    "#include \"RooPolyVar.h\"\n",
    "#include \"RooProduct.h\"\n",
    "#include \"TH1.h\"\n",
    "#include \"TCanvas.h\"\n",
    "#include \"TAxis.h\"\n",
    "#include \"RooPlot.h\"\n",
    "using namespace RooFit;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06b72811",
   "metadata": {},
   "source": [
    "Setup 2D amplitude functions\n",
    "-------------------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9427d165",
   "metadata": {},
   "source": [
    "Observables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "89f50d23",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:34:34.683991Z",
     "iopub.status.busy": "2026-05-19T20:34:34.683869Z",
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     "shell.execute_reply": "2026-05-19T20:34:35.042821Z"
    }
   },
   "outputs": [],
   "source": [
    "RooRealVar t(\"t\", \"time\", -1., 15.);\n",
    "RooRealVar cosa(\"cosa\", \"cos(alpha)\", -1., 1.);\n",
    "\n",
    "RooRealVar tau(\"tau\", \"#tau\", 1.5);\n",
    "RooRealVar deltaGamma(\"deltaGamma\", \"deltaGamma\", 0.3);\n",
    "RooFormulaVar coshG(\"coshGBasis\", \"exp(-@0/ @1)*cosh(@0*@2/2)\", {t, tau, deltaGamma});\n",
    "RooFormulaVar sinhG(\"sinhGBasis\", \"exp(-@0/ @1)*sinh(@0*@2/2)\", {t, tau, deltaGamma});"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed6f3c39",
   "metadata": {},
   "source": [
    "Construct polynomial amplitudes in cos(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1f12d106",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:34:35.045533Z",
     "iopub.status.busy": "2026-05-19T20:34:35.045384Z",
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     "shell.execute_reply": "2026-05-19T20:34:35.254734Z"
    }
   },
   "outputs": [],
   "source": [
    "RooPolyVar poly1(\"poly1\", \"poly1\", cosa, RooArgList{0.5, 0.2, 0.2}, 0);\n",
    "RooPolyVar poly2(\"poly2\", \"poly2\", cosa, RooArgList{1.0, -0.2, 3.0}, 0);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20a1539b",
   "metadata": {},
   "source": [
    "Construct 2D amplitude as uncorrelated product of amp(t)*amp(cosa)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ac60c856",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:34:35.257572Z",
     "iopub.status.busy": "2026-05-19T20:34:35.257450Z",
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     "shell.execute_reply": "2026-05-19T20:34:35.465644Z"
    }
   },
   "outputs": [],
   "source": [
    "RooProduct ampl1(\"ampl1\", \"amplitude 1\", {poly1, coshG});\n",
    "RooProduct ampl2(\"ampl2\", \"amplitude 2\", {poly2, sinhG});"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "291901b8",
   "metadata": {},
   "source": [
    "Construct amplitude sum pdf\n",
    "-----------------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cee6a81b",
   "metadata": {},
   "source": [
    "Amplitude strengths"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "78490af0",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:34:35.468409Z",
     "iopub.status.busy": "2026-05-19T20:34:35.468289Z",
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     "shell.execute_reply": "2026-05-19T20:34:35.676513Z"
    }
   },
   "outputs": [],
   "source": [
    "RooRealVar f1(\"f1\", \"f1\", 1, 0, 2);\n",
    "RooRealVar f2(\"f2\", \"f2\", 0.5, 0, 2);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "895c02fa",
   "metadata": {},
   "source": [
    "Construct pdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "04864d73",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:34:35.679669Z",
     "iopub.status.busy": "2026-05-19T20:34:35.679537Z",
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     "shell.execute_reply": "2026-05-19T20:34:35.887764Z"
    }
   },
   "outputs": [],
   "source": [
    "RooRealSumPdf pdf(\"pdf\", \"pdf\", RooArgList(ampl1, ampl2), RooArgList(f1, f2));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20da4d3a",
   "metadata": {},
   "source": [
    "Generate some toy data from pdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "7179cb4e",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:34:35.890533Z",
     "iopub.status.busy": "2026-05-19T20:34:35.890412Z",
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     "shell.execute_reply": "2026-05-19T20:34:36.100522Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[#1] INFO:NumericIntegration -- RooRealIntegral::init(coshGBasis_Int[t]) using numeric integrator RooIntegrator1D to calculate Int(t)\n",
      "[#1] INFO:NumericIntegration -- RooRealIntegral::init(sinhGBasis_Int[t]) using numeric integrator RooIntegrator1D to calculate Int(t)\n",
      "[#1] INFO:NumericIntegration -- RooRealIntegral::init(coshGBasis_Int[t]) using numeric integrator RooIntegrator1D to calculate Int(t)\n",
      "[#1] INFO:NumericIntegration -- RooRealIntegral::init(sinhGBasis_Int[t]) using numeric integrator RooIntegrator1D to calculate Int(t)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "input_line_66:2:2: warning: 'data' shadows a declaration with the same name in the 'std' namespace; use '::data' to reference this declaration\n",
      " std::unique_ptr<RooDataSet> data{pdf.generate({t, cosa}, 10000)};\n",
      " ^\n"
     ]
    }
   ],
   "source": [
    "std::unique_ptr<RooDataSet> data{pdf.generate({t, cosa}, 10000)};"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "96ae5239",
   "metadata": {},
   "source": [
    "Fit pdf to toy data with only amplitude strength floating"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "59ba276b",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:34:36.102932Z",
     "iopub.status.busy": "2026-05-19T20:34:36.102812Z",
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     "shell.execute_reply": "2026-05-19T20:34:36.318426Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "input_line_67:2:13: error: reference to 'data' is ambiguous\n",
      " pdf.fitTo(*data, PrintLevel(-1));\n",
      "            ^\n",
      "input_line_66:2:30: note: candidate found by name lookup is 'data'\n",
      " std::unique_ptr<RooDataSet> data{pdf.generate({t, cosa}, 10000)};\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": [
    "pdf.fitTo(*data, PrintLevel(-1));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bc7adf9e",
   "metadata": {},
   "source": [
    "Plot amplitude sum pdf\n",
    "-------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "87109609",
   "metadata": {},
   "source": [
    "Make 2D plots of amplitudes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "f734f1a3",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:34:36.320838Z",
     "iopub.status.busy": "2026-05-19T20:34:36.320719Z",
     "iopub.status.idle": "2026-05-19T20:34:36.529289Z",
     "shell.execute_reply": "2026-05-19T20:34:36.528752Z"
    }
   },
   "outputs": [],
   "source": [
    "TH1 *hh_cos = ampl1.createHistogram(\"hh_cos\", t, Binning(50), YVar(cosa, Binning(50)));\n",
    "TH1 *hh_sin = ampl2.createHistogram(\"hh_sin\", t, Binning(50), YVar(cosa, Binning(50)));\n",
    "hh_cos->SetLineColor(kBlue);\n",
    "hh_sin->SetLineColor(kRed);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "00b4eec8",
   "metadata": {},
   "source": [
    "Make projection on t, plot data, pdf and its components\n",
    "Note component projections may be larger than sum because amplitudes can be negative"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "f4c3fe8a",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:34:36.531432Z",
     "iopub.status.busy": "2026-05-19T20:34:36.531316Z",
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     "shell.execute_reply": "2026-05-19T20:34:36.740203Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "input_line_69:3:1: error: reference to 'data' is ambiguous\n",
      "data->plotOn(frame1);\n",
      "^\n",
      "input_line_66:2:30: note: candidate found by name lookup is 'data'\n",
      " std::unique_ptr<RooDataSet> data{pdf.generate({t, cosa}, 10000)};\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 *frame1 = t.frame();\n",
    "data->plotOn(frame1);\n",
    "pdf.plotOn(frame1);\n",
    "pdf.plotOn(frame1, Components(ampl1), LineStyle(kDashed));\n",
    "pdf.plotOn(frame1, Components(ampl2), LineStyle(kDashed), LineColor(kRed));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ceb1085c",
   "metadata": {},
   "source": [
    "Make projection on cosa, plot data, pdf and its components\n",
    "Note that components projection may be larger than sum because amplitudes can be negative"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "859c5347",
   "metadata": {
    "collapsed": false,
    "execution": {
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     "shell.execute_reply": "2026-05-19T20:34:36.948558Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "input_line_70:3:1: error: reference to 'data' is ambiguous\n",
      "data->plotOn(frame2);\n",
      "^\n",
      "input_line_66:2:30: note: candidate found by name lookup is 'data'\n",
      " std::unique_ptr<RooDataSet> data{pdf.generate({t, cosa}, 10000)};\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",
      "input_line_70:12:1: error: use of undeclared identifier 'frame1'\n",
      "frame1->GetYaxis()->SetTitleOffset(1.4);\n",
      "^\n",
      "input_line_70:13:1: error: use of undeclared identifier 'frame1'\n",
      "frame1->Draw();\n",
      "^\n"
     ]
    }
   ],
   "source": [
    "RooPlot *frame2 = cosa.frame();\n",
    "data->plotOn(frame2);\n",
    "pdf.plotOn(frame2);\n",
    "pdf.plotOn(frame2, Components(ampl1), LineStyle(kDashed));\n",
    "pdf.plotOn(frame2, Components(ampl2), LineStyle(kDashed), LineColor(kRed));\n",
    "\n",
    "TCanvas *c = new TCanvas(\"rf704_amplitudefit\", \"rf704_amplitudefit\", 800, 800);\n",
    "c->Divide(2, 2);\n",
    "c->cd(1);\n",
    "gPad->SetLeftMargin(0.15);\n",
    "frame1->GetYaxis()->SetTitleOffset(1.4);\n",
    "frame1->Draw();\n",
    "c->cd(2);\n",
    "gPad->SetLeftMargin(0.15);\n",
    "frame2->GetYaxis()->SetTitleOffset(1.4);\n",
    "frame2->Draw();\n",
    "c->cd(3);\n",
    "gPad->SetLeftMargin(0.20);\n",
    "hh_cos->GetZaxis()->SetTitleOffset(2.3);\n",
    "hh_cos->Draw(\"surf\");\n",
    "c->cd(4);\n",
    "gPad->SetLeftMargin(0.20);\n",
    "hh_sin->GetZaxis()->SetTitleOffset(2.3);\n",
    "hh_sin->Draw(\"surf\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f31c1d0b",
   "metadata": {},
   "source": [
    "Draw all canvases "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "1793f02e",
   "metadata": {
    "collapsed": false,
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     "shell.execute_reply": "2026-05-19T20:34:37.159079Z"
    }
   },
   "outputs": [],
   "source": [
    "gROOT->GetListOfCanvases()->Draw()"
   ]
  }
 ],
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