{
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  {
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   "source": [
    "# Integration\n",
    "Numerical integration using R passing the function from ROOT\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "**Author:**   \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 08:27 PM.</small></i>"
   ]
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  {
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   "id": "20737f8a",
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   "source": [
    "%%cpp -d\n",
    "#include<TMath.h>\n",
    "#include<TRInterface.h>\n",
    "#include<Math/Integrator.h>\n",
    "#include<TF1.h>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "179382de",
   "metadata": {},
   "source": [
    " To integrate using R the function must be vectorized\n",
    "The idea is just to receive a vector like an argument,to evaluate\n",
    "every element saving the result in another vector\n",
    "and return the resultant vector.\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "41e4cfe8",
   "metadata": {
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   "outputs": [],
   "source": [
    "%%cpp -d\n",
    "std::vector<Double_t>  BreitWignerVectorized(std::vector<Double_t> xx)\n",
    "{\n",
    "   std::vector<Double_t> result(xx.size());\n",
    "   for(Int_t i=0;i<xx.size();i++)\n",
    "   {\n",
    "      result[i]=TMath::BreitWigner(xx[i]);\n",
    "   }\n",
    "   return result;\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "001c021d",
   "metadata": {},
   "source": [
    " Definition of a helper function: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3789a293",
   "metadata": {
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   },
   "outputs": [],
   "source": [
    "%%cpp -d\n",
    "double BreitWignerWrap( double x){\n",
    "   return TMath::BreitWigner(x);\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "21adc494",
   "metadata": {
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   },
   "outputs": [],
   "source": [
    "ROOT::R::TRInterface &r=ROOT::R::TRInterface::Instance();\n",
    "\n",
    "r[\"BreitWigner\"]=ROOT::R::TRFunctionExport(BreitWignerVectorized);\n",
    "\n",
    "Double_t value=r.Eval(\"integrate(BreitWigner, lower = -2, upper = 2)$value\");\n",
    "\n",
    "std::cout.precision(18);\n",
    "std::cout<<\"Integral of the BreitWigner Function in the interval [-2, 2] R        = \"<<value<<std::endl;\n",
    "\n",
    "\n",
    "ROOT::Math::WrappedFunction<> wf(BreitWignerWrap);\n",
    "ROOT::Math::Integrator i(wf);\n",
    "value=i.Integral(-2,2);\n",
    "std::cout<<\"Integral of the BreitWigner Function in the interval [-2, 2] MathMore = \"<<value<<std::endl;\n",
    "\n",
    "\n",
    "TF1 f1(\"BreitWigner\",\"BreitWignerWrap(x)\");\n",
    "value=f1.Integral(-2,2);\n",
    "std::cout<<\"Integral of the BreitWigner Function in the interval [-2, 2] TF1      = \"<<value<<std::endl;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4965c79",
   "metadata": {},
   "source": [
    "infinite limits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e4eea9ae",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "value=r.Eval(\"integrate(BreitWigner, lower = -Inf, upper = Inf)$value\");\n",
    "std::cout<<\"Integral of BreitWigner Function in the interval [-Inf, Inf] R    = \"<<value<<std::endl;"
   ]
  }
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