{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "cc6e95a2",
   "metadata": {},
   "source": [
    "# rf608_fitresultaspdf\n",
    "Likelihood and minimization: representing the parabolic approximation of the fit as a multi-variate Gaussian on the\n",
    "parameters of the fitted 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 08:33 PM.</small></i>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "28064b85",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%%cpp -d\n",
    "#include \"RooRealVar.h\"\n",
    "#include \"RooDataSet.h\"\n",
    "#include \"RooGaussian.h\"\n",
    "#include \"RooAddPdf.h\"\n",
    "#include \"RooChebychev.h\"\n",
    "#include \"RooFitResult.h\"\n",
    "#include \"TCanvas.h\"\n",
    "#include \"TAxis.h\"\n",
    "#include \"RooPlot.h\"\n",
    "#include \"TFile.h\"\n",
    "#include \"TStyle.h\"\n",
    "#include \"TH2.h\"\n",
    "#include \"TH3.h\"\n",
    "\n",
    "using namespace RooFit;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ceb6d93",
   "metadata": {},
   "source": [
    "Create model and dataset\n",
    "-----------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "09217f09",
   "metadata": {},
   "source": [
    "Observable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4eb1f537",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "RooRealVar x(\"x\", \"x\", -20, 20);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5f6a1d9",
   "metadata": {},
   "source": [
    "Model (intentional strong correlations)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5bb6bc40",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "RooRealVar mean(\"mean\", \"mean of g1 and g2\", 0, -1, 1);\n",
    "RooRealVar sigma_g1(\"sigma_g1\", \"width of g1\", 2);\n",
    "RooGaussian g1(\"g1\", \"g1\", x, mean, sigma_g1);\n",
    "\n",
    "RooRealVar sigma_g2(\"sigma_g2\", \"width of g2\", 4, 3.0, 5.0);\n",
    "RooGaussian g2(\"g2\", \"g2\", x, mean, sigma_g2);\n",
    "\n",
    "RooRealVar frac(\"frac\", \"frac\", 0.5, 0.0, 1.0);\n",
    "RooAddPdf model(\"model\", \"model\", RooArgList(g1, g2), frac);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "08807965",
   "metadata": {},
   "source": [
    "Generate 1000 events"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cd02c679",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "std::unique_ptr<RooDataSet> data{model.generate(x, 1000)};"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d23fd5b",
   "metadata": {},
   "source": [
    "Fit model to data\n",
    "----------------------------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d576fd69",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "std::unique_ptr<RooFitResult> r{model.fitTo(*data, Save(), PrintLevel(-1))};"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cbc7edfc",
   "metadata": {},
   "source": [
    "CreateMV Gaussian pdf of fitted  parameters\n",
    "------------------------------------------------------------------------------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fea77329",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "RooAbsPdf *parabPdf = r->createHessePdf(RooArgSet(frac, mean, sigma_g2));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c8e7f535",
   "metadata": {},
   "source": [
    "Some execercises with the parameter pdf\n",
    "-----------------------------------------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dbb2e03f",
   "metadata": {},
   "source": [
    "Generate 100K points in the parameter space, sampled from the MVGaussian pdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c594795c",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "std::unique_ptr<RooDataSet> d{parabPdf->generate({mean, sigma_g2, frac}, 100000)};"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "720f2a45",
   "metadata": {},
   "source": [
    "Sample a 3-D histogram of the pdf to be visualized as an error ellipsoid using the GLISO draw option"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c9846d4c",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "TH3 *hh_3d = (TH3 *)parabPdf->createHistogram(\"mean,sigma_g2,frac\", 25, 25, 25);\n",
    "hh_3d->SetFillColor(kBlue);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4dbef66",
   "metadata": {},
   "source": [
    "Project 3D parameter pdf down to 3 permutations of two-dimensional pdfs\n",
    "The integrations corresponding to these projections are performed analytically\n",
    "by the MV Gaussian pdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "72b07a79",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "RooAbsPdf *pdf_sigmag2_frac = parabPdf->createProjection(mean);\n",
    "RooAbsPdf *pdf_mean_frac = parabPdf->createProjection(sigma_g2);\n",
    "RooAbsPdf *pdf_mean_sigmag2 = parabPdf->createProjection(frac);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a7388e3",
   "metadata": {},
   "source": [
    "Make 2D plots of the 3 two-dimensional pdf projections"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d5074d4d",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "TH2 *hh_sigmag2_frac = (TH2 *)pdf_sigmag2_frac->createHistogram(\"sigma_g2,frac\", 50, 50);\n",
    "TH2 *hh_mean_frac = (TH2 *)pdf_mean_frac->createHistogram(\"mean,frac\", 50, 50);\n",
    "TH2 *hh_mean_sigmag2 = (TH2 *)pdf_mean_sigmag2->createHistogram(\"mean,sigma_g2\", 50, 50);\n",
    "hh_mean_frac->SetLineColor(kBlue);\n",
    "hh_sigmag2_frac->SetLineColor(kBlue);\n",
    "hh_mean_sigmag2->SetLineColor(kBlue);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4193b385",
   "metadata": {},
   "source": [
    "Draw the 'sigar'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "86316251",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "new TCanvas(\"rf608_fitresultaspdf_1\", \"rf608_fitresultaspdf_1\", 600, 600);\n",
    "hh_3d->Draw(\"iso\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c0eb5778",
   "metadata": {},
   "source": [
    "Draw the 2D projections of the 3D pdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "01b26950",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "TCanvas *c2 = new TCanvas(\"rf608_fitresultaspdf_2\", \"rf608_fitresultaspdf_2\", 900, 600);\n",
    "c2->Divide(3, 2);\n",
    "c2->cd(1);\n",
    "gPad->SetLeftMargin(0.15);\n",
    "hh_mean_sigmag2->GetZaxis()->SetTitleOffset(1.4);\n",
    "hh_mean_sigmag2->Draw(\"surf3\");\n",
    "c2->cd(2);\n",
    "gPad->SetLeftMargin(0.15);\n",
    "hh_sigmag2_frac->GetZaxis()->SetTitleOffset(1.4);\n",
    "hh_sigmag2_frac->Draw(\"surf3\");\n",
    "c2->cd(3);\n",
    "gPad->SetLeftMargin(0.15);\n",
    "hh_mean_frac->GetZaxis()->SetTitleOffset(1.4);\n",
    "hh_mean_frac->Draw(\"surf3\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "250933be",
   "metadata": {},
   "source": [
    "Draw the distributions of parameter points sampled from the pdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7a4dbd4e",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "TH1 *tmp1 = d->createHistogram(\"mean,sigma_g2\", Binning(50), Binning(50));\n",
    "TH1 *tmp2 = d->createHistogram(\"sigma_g2,frac\", Binning(50), Binning(50));\n",
    "TH1 *tmp3 = d->createHistogram(\"mean,frac\", Binning(50), Binning(50));\n",
    "\n",
    "c2->cd(4);\n",
    "gPad->SetLeftMargin(0.15);\n",
    "tmp1->GetZaxis()->SetTitleOffset(1.4);\n",
    "tmp1->Draw(\"lego3\");\n",
    "c2->cd(5);\n",
    "gPad->SetLeftMargin(0.15);\n",
    "tmp2->GetZaxis()->SetTitleOffset(1.4);\n",
    "tmp2->Draw(\"lego3\");\n",
    "c2->cd(6);\n",
    "gPad->SetLeftMargin(0.15);\n",
    "tmp3->GetZaxis()->SetTitleOffset(1.4);\n",
    "tmp3->Draw(\"lego3\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b7d72d70",
   "metadata": {},
   "source": [
    "Draw all canvases "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "21bdc6a6",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "gROOT->GetListOfCanvases()->Draw()"
   ]
  }
 ],
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