{
 "cells": [
  {
   "cell_type": "markdown",
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   "metadata": {},
   "source": [
    "# vo005_Combinations\n",
    "In this tutorial we learn how combinations of RVecs can be built.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "**Author:** Stefan Wunsch  \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 08:28 PM.</small></i>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42f3ce32",
   "metadata": {},
   "source": [
    "The starting point are two collections and we want to calculate the result\n",
    "of combinations of the elements."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "7dc7ec34",
   "metadata": {
    "collapsed": false,
    "execution": {
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     "shell.execute_reply": "2026-05-19T20:28:11.129159Z"
    }
   },
   "outputs": [],
   "source": [
    "ROOT::RVecD v1{1., 2., 3.};\n",
    "ROOT::RVecD v2{-4., -5.};"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7e0fa1ba",
   "metadata": {},
   "source": [
    "To get the indices, which result in all combinations, you can call the\n",
    "following helper.\n",
    "Note that you can also pass the size of the vectors directly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "2af2f31a",
   "metadata": {
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    "execution": {
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    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "input_line_53:2:13: error: cannot deduce 'auto' from unknown expression\n",
      " auto idx = Combinations(v1, v2);\n",
      "            ^\n"
     ]
    }
   ],
   "source": [
    "auto idx = Combinations(v1, v2);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1b4ad431",
   "metadata": {},
   "source": [
    "Next, the respective elements can be taken via the computed indices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "388c90ee",
   "metadata": {
    "collapsed": false,
    "execution": {
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     "shell.execute_reply": "2026-05-19T20:28:11.547993Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "input_line_54:2:12: error: cannot deduce 'auto' from unknown expression\n",
      " auto c1 = Take(v1, idx[0]);\n",
      "           ^\n"
     ]
    }
   ],
   "source": [
    "auto c1 = Take(v1, idx[0]);\n",
    "auto c2 = Take(v2, idx[1]);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb9a8fa3",
   "metadata": {},
   "source": [
    "Finally, you can perform any set of operations conveniently."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a8a27f76",
   "metadata": {
    "collapsed": false,
    "execution": {
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     "shell.execute_reply": "2026-05-19T20:28:11.757098Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "input_line_55:2:12: error: cannot deduce 'auto' from unknown expression\n",
      " auto v3 = c1 * c2;\n",
      "           ^\n"
     ]
    }
   ],
   "source": [
    "auto v3 = c1 * c2;\n",
    "\n",
    "std::cout << \"Combinations of \" << v1 << \" and \" << v2 << \":\" << std::endl;\n",
    "for(size_t i=0; i<v3.size(); i++) {\n",
    "    std::cout << c1[i] << \" * \" << c2[i] << \" = \" << v3[i] << std::endl;\n",
    "}\n",
    "std::cout << std::endl;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5886f7ef",
   "metadata": {},
   "source": [
    "However, if you want to compute operations on unique combinations of a\n",
    "single RVec, you can perform this as follows."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "09900907",
   "metadata": {},
   "source": [
    "Get the indices of unique triples for the given vector."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "7f940604",
   "metadata": {
    "collapsed": false,
    "execution": {
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     "shell.execute_reply": "2026-05-19T20:28:11.966124Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "input_line_56:3:13: error: cannot deduce 'auto' from unknown expression\n",
      "auto idx2 = Combinations(v4, 3);\n",
      "            ^\n"
     ]
    }
   ],
   "source": [
    "ROOT::RVecD v4{1., 2., 3., 4.};\n",
    "auto idx2 = Combinations(v4, 3);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "632c287d",
   "metadata": {},
   "source": [
    "Take the elements and compute any operation on the returned collections."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "8a2e5a3e",
   "metadata": {
    "collapsed": false,
    "execution": {
     "iopub.execute_input": "2026-05-19T20:28:11.968302Z",
     "iopub.status.busy": "2026-05-19T20:28:11.968182Z",
     "iopub.status.idle": "2026-05-19T20:28:12.175938Z",
     "shell.execute_reply": "2026-05-19T20:28:12.175246Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "input_line_57:9:19: error: use of undeclared identifier 'v4'\n",
      "for(size_t i=0; i<v4.size(); i++) {\n",
      "                  ^\n",
      "input_line_57:2:12: error: cannot deduce 'auto' from unknown expression\n",
      " auto c3 = Take(v4, idx2[0]);\n",
      "           ^\n"
     ]
    }
   ],
   "source": [
    "auto c3 = Take(v4, idx2[0]);\n",
    "auto c4 = Take(v4, idx2[1]);\n",
    "auto c5 = Take(v4, idx2[2]);\n",
    "\n",
    "auto v5 = c3 * c4 * c5;\n",
    "\n",
    "std::cout << \"Unique triples of \" << v4 << \":\" << std::endl;\n",
    "for(size_t i=0; i<v4.size(); i++) {\n",
    "    std::cout << c3[i] << \" * \" << c4[i] << \" * \" << c5[i] << \" = \" << v5[i] << std::endl;\n",
    "}\n",
    "std::cout << std::endl;"
   ]
  }
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