{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "0adca4eb",
   "metadata": {},
   "source": [
    "# Minimization\n",
    "Example based on\n",
    "http://stat.ethz.ch/R-manual/R-devel/library/stats/html/optim.html\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "**Author:** Omar Zapata  \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>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "4eb43fae",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:27:49.025822Z",
     "iopub.status.busy": "2026-05-19T20:27:49.025717Z",
     "iopub.status.idle": "2026-05-19T20:27:49.033094Z",
     "shell.execute_reply": "2026-05-19T20:27:49.032713Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "input_line_44:1:9: fatal error: 'TRInterface.h' file not found\n",
      "#include<TRInterface.h>\n",
      "        ^~~~~~~~~~~~~~~\n"
     ]
    }
   ],
   "source": [
    "%%cpp -d\n",
    "#include<TRInterface.h>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "096c892a",
   "metadata": {},
   "source": [
    " in the next function the *double pointer must be changed by a TVectorD,\n",
    "because the pointer has no meaning in R enviroment.\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "3a82e9b4",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:27:49.034524Z",
     "iopub.status.busy": "2026-05-19T20:27:49.034416Z",
     "iopub.status.idle": "2026-05-19T20:27:49.038687Z",
     "shell.execute_reply": "2026-05-19T20:27:49.038214Z"
    }
   },
   "outputs": [],
   "source": [
    "%%cpp -d\n",
    "Double_t RosenBrock(const TVectorD xx )\n",
    "{\n",
    "   const Double_t x = xx[0];\n",
    "   const Double_t y = xx[1];\n",
    "   const Double_t tmp1 = y-x*x;\n",
    "   const Double_t tmp2 = 1-x;\n",
    "   return 100*tmp1*tmp1+tmp2*tmp2;\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "caab2cca",
   "metadata": {},
   "source": [
    " Definition of a helper function: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "59fd2a79",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:27:49.040026Z",
     "iopub.status.busy": "2026-05-19T20:27:49.039917Z",
     "iopub.status.idle": "2026-05-19T20:27:49.048848Z",
     "shell.execute_reply": "2026-05-19T20:27:49.048352Z"
    }
   },
   "outputs": [],
   "source": [
    "%%cpp -d\n",
    "TVectorD RosenBrockGrad(const TVectorD xx )\n",
    "{\n",
    "   const Double_t x = xx[0];\n",
    "   const Double_t y = xx[1];\n",
    "   TVectorD grad(2);\n",
    "   grad[0]=-400 * x * (y - x * x) - 2 * (1 - x);\n",
    "   grad[1]=200 * (y - x * x);\n",
    "   return grad;\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "aaaf6bf7",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:27:49.050277Z",
     "iopub.status.busy": "2026-05-19T20:27:49.050150Z",
     "iopub.status.idle": "2026-05-19T20:27:49.376732Z",
     "shell.execute_reply": "2026-05-19T20:27:49.376029Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "input_line_47:2:8: error: 'R' is not a class, namespace, or enumeration\n",
      " ROOT::R::TRInterface &r=ROOT::R::TRInterface::Instance();\n",
      "       ^\n",
      "input_line_47:2:8: note: 'R' declared here\n",
      "input_line_47:2:32: error: no member named 'R' in namespace 'ROOT'\n",
      " ROOT::R::TRInterface &r=ROOT::R::TRInterface::Instance();\n",
      "                         ~~~~~~^\n"
     ]
    }
   ],
   "source": [
    "ROOT::R::TRInterface &r=ROOT::R::TRInterface::Instance();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cef0dc61",
   "metadata": {},
   "source": [
    "passsing RosenBrock function to R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "0ba30df7",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:27:49.378241Z",
     "iopub.status.busy": "2026-05-19T20:27:49.378126Z",
     "iopub.status.idle": "2026-05-19T20:27:49.583306Z",
     "shell.execute_reply": "2026-05-19T20:27:49.582740Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "input_line_56:2:24: error: 'R' is not a class, namespace, or enumeration\n",
      " r[\"RosenBrock\"]=ROOT::R::TRFunctionExport(RosenBrock);\n",
      "                       ^\n",
      "input_line_56:2:24: note: 'R' declared here\n"
     ]
    }
   ],
   "source": [
    "r[\"RosenBrock\"]=ROOT::R::TRFunctionExport(RosenBrock);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce85f479",
   "metadata": {},
   "source": [
    "passsing RosenBrockGrad function to R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "dc21a42c",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:27:49.585066Z",
     "iopub.status.busy": "2026-05-19T20:27:49.584950Z",
     "iopub.status.idle": "2026-05-19T20:27:49.790446Z",
     "shell.execute_reply": "2026-05-19T20:27:49.789538Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "input_line_57:2:28: error: 'R' is not a class, namespace, or enumeration\n",
      " r[\"RosenBrockGrad\"]=ROOT::R::TRFunctionExport(RosenBrockGrad);\n",
      "                           ^\n",
      "input_line_57:2:28: note: 'R' declared here\n"
     ]
    }
   ],
   "source": [
    "r[\"RosenBrockGrad\"]=ROOT::R::TRFunctionExport(RosenBrockGrad);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5d969480",
   "metadata": {},
   "source": [
    "the option \"method\" could be \"Nelder-Mead\", \"BFGS\", \"CG\", \"L-BFGS-B\", \"SANN\",\"Brent\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22e128c0",
   "metadata": {},
   "source": [
    "the option \"control\" lets you put some constraints like\n",
    "\"maxit\" The maximum number of iterations.\n",
    "\"abstol\" The absolute convergence tolerance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "e8bbbf27",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:27:49.791995Z",
     "iopub.status.busy": "2026-05-19T20:27:49.791870Z",
     "iopub.status.idle": "2026-05-19T20:27:49.994654Z",
     "shell.execute_reply": "2026-05-19T20:27:49.994045Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "input_line_59:2:3: error: use of undeclared identifier 'r'\n",
      " (r.Execute(\"result <- optim( c(0.01,0.01), RosenBrock,method='BFGS',control = list(maxit = 1000000) )\"))\n",
      "  ^\n",
      "Error in <HandleInterpreterException>: Error evaluating expression (r.Execute(\"result <- optim( c(0.01,0.01), RosenBrock,method='BFGS',control = list(maxit = 1000000) )\"))\n",
      "Execution of your code was aborted.\n"
     ]
    }
   ],
   "source": [
    "r.Execute(\"result <- optim( c(0.01,0.01), RosenBrock,method='BFGS',control = list(maxit = 1000000) )\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f2db2d49",
   "metadata": {},
   "source": [
    "\"reltol\" Relative convergence tolerance."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9ca892d",
   "metadata": {},
   "source": [
    "Getting results from R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f5bac971",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:27:49.996262Z",
     "iopub.status.busy": "2026-05-19T20:27:49.996147Z",
     "iopub.status.idle": "2026-05-19T20:27:50.364809Z",
     "shell.execute_reply": "2026-05-19T20:27:50.360408Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "input_line_60:2:2: warning: 'min' shadows a declaration with the same name in the 'std' namespace; use '::min' to reference this declaration\n",
      " TVectorD  min=r.Eval(\"result$par\");\n",
      " ^\n",
      "[runStaticInitializersOnce]: Failed to materialize symbols: { (main, { __orc_init_func.cling-module-292, _ZNK5cling7runtime8internal15LifetimeHandler9getMemoryEv, _ZN12__cling_N52316__cling_Un1Qu323EPv, _ZN12__cling_N52324__dynamic__cling_Un1Qu30E, cling_module_292_.6, cling_module_292_, _ZNSt8ios_base9precisionEl, _GLOBAL__sub_I_cling_module_292, _ZN12__cling_N5233minE, $.cling-module-292.__inits.0 }) }\n",
      "IncrementalExecutor::executeFunction: symbol '_ZN5cling7runtime8internal15LifetimeHandlerC1EPNS1_15DynamicExprInfoEPN5clang11DeclContextEPKcPNS_11InterpreterE' unresolved while linking [cling interface function]!\n",
      "You are probably missing the definition of cling::runtime::internal::LifetimeHandler::LifetimeHandler(cling::runtime::internal::DynamicExprInfo*, clang::DeclContext*, char const*, cling::Interpreter*)\n",
      "Maybe you need to load the corresponding shared library?\n",
      "IncrementalExecutor::executeFunction: symbol '_ZN5cling7runtime8internal15LifetimeHandlerD1Ev' unresolved while linking [cling interface function]!\n",
      "You are probably missing the definition of cling::runtime::internal::LifetimeHandler::~LifetimeHandler()\n",
      "Maybe you need to load the corresponding shared library?\n"
     ]
    }
   ],
   "source": [
    "TVectorD  min=r.Eval(\"result$par\");\n",
    "\n",
    "std::cout.precision(8);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "469abe41",
   "metadata": {},
   "source": [
    "printing results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "de9e1fa6",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:27:50.366425Z",
     "iopub.status.busy": "2026-05-19T20:27:50.366302Z",
     "iopub.status.idle": "2026-05-19T20:27:50.589703Z",
     "shell.execute_reply": "2026-05-19T20:27:50.584394Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "input_line_61:3:26: error: reference to 'min' is ambiguous\n",
      "std::cout<<\"Minimum x=\"<<min[0]<<\" y=\"<<min[1]<<std::endl;\n",
      "                         ^\n",
      "input_line_60:2:12: note: candidate found by name lookup is 'min'\n",
      " TVectorD  min=r.Eval(\"result$par\");\n",
      "           ^\n",
      "/usr/lib/gcc/x86_64-redhat-linux/14/../../../../include/c++/14/bits/stl_algo.h:5696:5: note: candidate found by name lookup is 'std::min'\n",
      "    min(initializer_list<_Tp> __l, _Compare __comp)\n",
      "    ^\n",
      "/usr/lib/gcc/x86_64-redhat-linux/14/../../../../include/c++/14/bits/algorithmfwd.h:416:5: note: candidate found by name lookup is 'std::min'\n",
      "    min(const _Tp&, const _Tp&);\n",
      "    ^\n",
      "/usr/lib/gcc/x86_64-redhat-linux/14/../../../../include/c++/14/bits/algorithmfwd.h:421:5: note: candidate found by name lookup is 'std::min'\n",
      "    min(const _Tp&, const _Tp&, _Compare);\n",
      "    ^\n",
      "/usr/lib/gcc/x86_64-redhat-linux/14/../../../../include/c++/14/bits/stl_algo.h:5686:5: note: candidate found by name lookup is 'std::min'\n",
      "    min(initializer_list<_Tp> __l)\n",
      "    ^\n",
      "input_line_61:3:41: error: reference to 'min' is ambiguous\n",
      "std::cout<<\"Minimum x=\"<<min[0]<<\" y=\"<<min[1]<<std::endl;\n",
      "                                        ^\n",
      "input_line_60:2:12: note: candidate found by name lookup is 'min'\n",
      " TVectorD  min=r.Eval(\"result$par\");\n",
      "           ^\n",
      "/usr/lib/gcc/x86_64-redhat-linux/14/../../../../include/c++/14/bits/stl_algo.h:5696:5: note: candidate found by name lookup is 'std::min'\n",
      "    min(initializer_list<_Tp> __l, _Compare __comp)\n",
      "    ^\n",
      "/usr/lib/gcc/x86_64-redhat-linux/14/../../../../include/c++/14/bits/algorithmfwd.h:416:5: note: candidate found by name lookup is 'std::min'\n",
      "    min(const _Tp&, const _Tp&);\n",
      "    ^\n",
      "/usr/lib/gcc/x86_64-redhat-linux/14/../../../../include/c++/14/bits/algorithmfwd.h:421:5: note: candidate found by name lookup is 'std::min'\n",
      "    min(const _Tp&, const _Tp&, _Compare);\n",
      "    ^\n",
      "/usr/lib/gcc/x86_64-redhat-linux/14/../../../../include/c++/14/bits/stl_algo.h:5686:5: note: candidate found by name lookup is 'std::min'\n",
      "    min(initializer_list<_Tp> __l)\n",
      "    ^\n",
      "input_line_61:4:45: error: reference to 'min' is ambiguous\n",
      "std::cout<<\"Value at minimum =\"<<RosenBrock(min)<<std::endl;\n",
      "                                            ^\n",
      "input_line_60:2:12: note: candidate found by name lookup is 'min'\n",
      " TVectorD  min=r.Eval(\"result$par\");\n",
      "           ^\n",
      "/usr/lib/gcc/x86_64-redhat-linux/14/../../../../include/c++/14/bits/stl_algo.h:5696:5: note: candidate found by name lookup is 'std::min'\n",
      "    min(initializer_list<_Tp> __l, _Compare __comp)\n",
      "    ^\n",
      "/usr/lib/gcc/x86_64-redhat-linux/14/../../../../include/c++/14/bits/algorithmfwd.h:416:5: note: candidate found by name lookup is 'std::min'\n",
      "    min(const _Tp&, const _Tp&);\n",
      "    ^\n",
      "/usr/lib/gcc/x86_64-redhat-linux/14/../../../../include/c++/14/bits/algorithmfwd.h:421:5: note: candidate found by name lookup is 'std::min'\n",
      "    min(const _Tp&, const _Tp&, _Compare);\n",
      "    ^\n",
      "/usr/lib/gcc/x86_64-redhat-linux/14/../../../../include/c++/14/bits/stl_algo.h:5686:5: note: candidate found by name lookup is 'std::min'\n",
      "    min(initializer_list<_Tp> __l)\n",
      "    ^\n"
     ]
    }
   ],
   "source": [
    "std::cout<<\"-----------------------------------------\"<<std::endl;\n",
    "std::cout<<\"Minimum x=\"<<min[0]<<\" y=\"<<min[1]<<std::endl;\n",
    "std::cout<<\"Value at minimum =\"<<RosenBrock(min)<<std::endl;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7048d604",
   "metadata": {},
   "source": [
    "using the gradient"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "fadf29c9",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:27:50.591368Z",
     "iopub.status.busy": "2026-05-19T20:27:50.591246Z",
     "iopub.status.idle": "2026-05-19T20:27:50.796566Z",
     "shell.execute_reply": "2026-05-19T20:27:50.796005Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[runStaticInitializersOnce]: Failed to materialize symbols: { (main, { __orc_init_func.cling-module-292 }) }\n",
      "input_line_63:2:3: error: use of undeclared identifier 'r'\n",
      " (r.Execute(\"optimHess(result$par, RosenBrock, RosenBrockGrad)\"))\n",
      "  ^\n",
      "Error in <HandleInterpreterException>: Error evaluating expression (r.Execute(\"optimHess(result$par, RosenBrock, RosenBrockGrad)\"))\n",
      "Execution of your code was aborted.\n"
     ]
    }
   ],
   "source": [
    "r.Execute(\"optimHess(result$par, RosenBrock, RosenBrockGrad)\");\n",
    "r.Execute(\"hresult <- optim(c(-1.2,1), RosenBrock, NULL, method = 'BFGS', hessian = TRUE)\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0510673f",
   "metadata": {},
   "source": [
    "getting the min calculated with the gradient"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "d4c08c8c",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:27:50.798129Z",
     "iopub.status.busy": "2026-05-19T20:27:50.798012Z",
     "iopub.status.idle": "2026-05-19T20:27:51.003443Z",
     "shell.execute_reply": "2026-05-19T20:27:51.002837Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "cling JIT session error: Failed to materialize symbols: { (main, { _ZNK5cling7runtime8internal15LifetimeHandler9getMemoryEv }) }\n",
      "[runStaticInitializersOnce]: Failed to materialize symbols: { (main, { __orc_init_func.cling-module-295, _ZN12__cling_N52624__dynamic__cling_Un1Qu31E, _GLOBAL__sub_I_cling_module_295, cling_module_295_.6, _ZN12__cling_N52616__cling_Un1Qu327EPv, _ZN12__cling_N5264hminE, $.cling-module-295.__inits.0, cling_module_295_ }) }\n"
     ]
    }
   ],
   "source": [
    "TVectorD  hmin=r.Eval(\"hresult$par\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1bc8944a",
   "metadata": {},
   "source": [
    "printing results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "0776bed4",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:27:51.005295Z",
     "iopub.status.busy": "2026-05-19T20:27:51.005178Z",
     "iopub.status.idle": "2026-05-19T20:27:51.210623Z",
     "shell.execute_reply": "2026-05-19T20:27:51.209946Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[runStaticInitializersOnce]: Failed to materialize symbols: { (main, { __orc_init_func.cling-module-295 }) }\n",
      "cling JIT session error: Failed to materialize symbols: { (main, { _ZN12__cling_N5264hminE }) }\n"
     ]
    }
   ],
   "source": [
    "std::cout<<\"-----------------------------------------\"<<std::endl;\n",
    "std::cout<<\"Minimization with the Gradient\"<<std::endl;\n",
    "std::cout<<\"Minimum x=\"<<hmin[0]<<\" y=\"<<hmin[1]<<std::endl;\n",
    "std::cout<<\"Value at minimum =\"<<RosenBrock(hmin)<<std::endl;"
   ]
  }
 ],
 "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
}